High Entropy Materials: Processing, Properties, and Applications 9811939187, 9789811939181

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Materials Horizons: From Nature to Nanomaterials

Krishanu Biswas Nilesh Prakash Gurao Tanmoy Maiti Rajiv S. Mishra

High Entropy Materials Processing, Properties, and Applications

Materials Horizons: From Nature to Nanomaterials Series Editor Vijay Kumar Thakur, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, UK

Materials are an indispensable part of human civilization since the inception of life on earth. With the passage of time, innumerable new materials have been explored as well as developed and the search for new innovative materials continues briskly. Keeping in mind the immense perspectives of various classes of materials, this series aims at providing a comprehensive collection of works across the breadth of materials research at cutting-edge interface of materials science with physics, chemistry, biology and engineering. This series covers a galaxy of materials ranging from natural materials to nanomaterials. Some of the topics include but not limited to: biological materials, biomimetic materials, ceramics, composites, coatings, functional materials, glasses, inorganic materials, inorganic-organic hybrids, metals, membranes, magnetic materials, manufacturing of materials, nanomaterials, organic materials and pigments to name a few. The series provides most timely and comprehensive information on advanced synthesis, processing, characterization, manufacturing and applications in a broad range of interdisciplinary fields in science, engineering and technology. This series accepts both authored and edited works, including textbooks, monographs, reference works, and professional books. The books in this series will provide a deep insight into the state-of-art of Materials Horizons and serve students, academic, government and industrial scientists involved in all aspects of materials research. Review Process The proposal for each volume is reviewed by the following: 1. Responsible (in-house) editor 2. One external subject expert 3. One of the editorial board members. The chapters in each volume are individually reviewed single blind by expert reviewers and the volume editor.

Krishanu Biswas · Nilesh Prakash Gurao · Tanmoy Maiti · Rajiv S. Mishra

High Entropy Materials Processing, Properties, and Applications

Krishanu Biswas Department of Materials Science and Engineering Indian Institute of Technology Kanpur Kanpur, Uttar Pradesh, India

Nilesh Prakash Gurao Department of Materials Science and Engineering Indian Institute of Technology Kanpur Kanpur, Uttar Pradesh, India

Tanmoy Maiti Department of Materials Science and Engineering Indian Institute of Technology Kanpur Kanpur, Uttar Pradesh, India

Rajiv S. Mishra Department of Materials Science and Engineering University of North Texas Denton, TX, USA

ISSN 2524-5384 ISSN 2524-5392 (electronic) Materials Horizons: From Nature to Nanomaterials ISBN 978-981-19-3918-1 ISBN 978-981-19-3919-8 (eBook) https://doi.org/10.1007/978-981-19-3919-8 © Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Foreword

All materials are made up of elements from the periodic table. Among them, conventional alloys contain one or two principal elements. With the passage of time, minor alloying elements have been added to improve their properties for their effective applications. This concept of alloy composition has extended from the ancient days of fabricating copper alloys, cast iron, and steel to the current times of fabricating aluminum alloys, alloy steels, satellites, superalloys, refractory alloys, and titanium alloys. Approximately, thirty metallic elements, ranging from the most inexpensive iron to expensive noble elements in the periodic table, have been used as base metals for different alloy systems. Although the traditional concept of composition has been used to produce many alloys for practical applications such as consumer goods and aerospace vehicles, it is widely recognized that many applications of these alloys remain suboptimal, owing to various reasons such as a high cost, poor functionality, toxicity, high weight, shortage of resources, low availability, insufficient lifetime, low efficiency, high energy consumption, and high pollution. Toward the end of the last century, a concept of alloy design termed “high-entropy compositions” was created for alloys and was soon extended to ceramics, polymers, and composites by Professor Jien-Wei Yeh. Going beyond the traditional concept of composition, this concept advocates the idea of using a greater number of major elements. High-entropy alloys are based on five or more major elements, while medium-entropy alloys are based on three or four major elements. The high-entropy effect is the key effect that enables these alloys to form solid-solution phases, which potentially allow these materials to be more ductile or tougher. Without this effect, these alloys would contain a mixture of elements or intermetallic compounds (owing to the sole enthalpy effect from the bonding energies between different elements) and would be brittle, as previously believed. Professor Ranganathan from India and Professor Cantor from England were the two pioneers in this field. Professor Ranganathan has attempted to unravel the complex world of compositions for a long time and finally resonated with Yeh’s research on high-entropy alloys through the Internet. Therefore, he is the first to introduce Yeh’s high-entropy alloy concept and research in the article entitled “Alloyed pleasures: Multimetallic cocktails” in the Nov. 2003 issue of Current Science, before v

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Yeh’s first five publications on high-entropy alloys and Cantor’s publication on “Microstructural development in equiatomic multicomponent alloys” in Materials Science and Engineering A in 2004. This resonance among the three researchers fueled investigations on high-entropy alloys and materials. Since then, the number of yearly publications on high-entropy alloys and related materials has grown exponentially and had exceeded 10,000 by the end of 2021. The number of projects, funds, meetings, special issues, books, and various reports has increased rapidly and has led to a widespread and continued impact on many aspects of academic and social activities. The practical realization and widespread application of high-entropy alloys are the key aims of most researchers and funding agencies in this field. High-entropy alloys and materials are expected to improve the lives of people and sustainability of the society. Because it has been difficult to overcome the shortcomings and bottlenecks of conventional materials using conventional concepts, it is hoped that this new concept will drive advancements in the field, especially considering that many publications have demonstrated promising potential applications for many high-entropy and medium-entropy materials. Therefore, a complete understanding of the abilities of these new materials would allow us to be more efficient in solving the problems faced by conventional materials. India has been a country long devoted to high-entropy alloy and materials research, right since the first publication on this topic in Current Science. Professor Ranganathan and Professor Murty are two notable Indian researchers who have been advocating the use of high-entropy alloys and materials in India and the world. The four authors of the present book, professors K. Biswas, N. P. Gurao, and T. Maiti at the Indian Institute of Technology Kanpur and Professor R. S. Mishra at the University of North Texas, have been engaged in this field in response to the encouragement since the early times. Based on their long-term experience and theoretical understanding, they have collaborated and successfully completed this book on high-entropy materials. The present book on high-entropy materials is a timely publication considering the rapid pace at which this new field is growing. The authors have condensed important findings in the area of high-entropy alloys and materials for people who wish to acquire a complete understanding of this area, clarify previously unclear viewpoints, conduct in-depth research, and achieve more innovations. The book has ten chapters, including an overview, basic concepts, phase and microstructural selection, diffusion, artificial intelligence in design, synthesis of bulk materials, synthesis of coatings and thin films, structural properties, functional properties, and a summary and future direction. This book is well-structured and logical to read and understand. In the last chapter, a survey of patents on high-entropy materials provides the analysis on the many patents granted in this field. This significant growth in the number of patents indicates that research on high-entropy materials has been gradually translated into technological and practical applications. The insights in this book will

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enable investigations on many aspects of high-entropy materials technology, which will contribute to the welfare of the society in the near future. National Tsing Hua University, Taiwan

Jien-Wei Yeh

Preface

The importance of metallic materials can be simply acknowledged from the fact that time periods in human history are referred to as Stone Age, Bronze Age, and Iron Age! The modern Industrial Revolution was made possible by the advent of new engineering materials. One can only look at the numerous conceptualizations of gadgets and machines by Leonardo da Vinci. While da Vinci could draw a flying machine, engineering materials were not available for prototyping such a machine. Over the last two centuries, metallic materials have been the most dominant group of engineering materials. The experience-based approach to alloy development continued till the start of the twentieth century. The scientific understanding started to evolve rapidly by the parallel development of novel processing, microscopy techniques, and dislocation-based theories of metal plasticity. In a similar timeframe as the development of dislocation theories, Prof. W. HumeRothery’s seminal research led to a set of rules governing the formation of a solid solution in metals. These Hume-Rothery rules for a solid solution have been well accepted and guided the development of alloys for more than half a century. A core principle of the alloys was the dissolution of solute atoms in a solvent matrix. In fact, for almost 5000 years, the solvent–solute framework has defined the alloys; there is a matrix, and then there are appropriate alloying elements for that matrix. The periodic table neatly gives the broad range of elements from which to pick the right elements for alloying for a given matrix to obtain a set of target properties. The classic understanding of Hume-Rothery rules and the notion of solvent–solute were challenged by two parallel publications in 2004 by Profs. Yeh and Cantor. High entropy materials (HEMs) have been conceived by them in the last part of the twentieth century and realized at the beginning of the twenty-first century as a breakthrough in material design involving multiple components in equimolar or near equimolar ratios. The efforts of Yeh and Cantor led to a new era of “high entropy alloys” containing multiple principal elements. The very fact that there is no longer a solvent–solute framework demands a framework of new theoretical approaches. Equally important is the opening up of the alloy design possibilities. The scientific curiosity and technical optimism are driving an unprecedented level of interest. These materials are relatively new (17 years old), albeit, this new concept of alloy design ix

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strategy has become the most significant research area among the materials engineering community across the globe. It is no longer confined to the lab scale, and it has made some impact on potential structural and functional applications. Across the globe, widespread research activity is going on to find niche applications in both structural and functional areas, and significant progress has been made in this direction. The figure below captures the number of publications reported in the Scopus database.

The number of publications per year in Scopus database with the keywords “high entropy alloys”

This book is written as a resource for students and researchers engaged in this vibrant field of high entropy materials. The chapters are organized to provide the basics as well as guidance for future possibilities. Chapter 1 gives a historical perspective of high entropy and details the paradigm shift. Chapter 2 presents the basics involved with high entropy alloys including the context for four core effects. The phase and microstructural selection in high entropy materials are presented in Chap. 3. Chapter 4 links back with Chap. 2 with a detailed discussion of diffusion in high entropy alloys. Chapter 5 covers the design of high entropy materials using integrated computational materials engineering (ICME) and materials genome. As the field moves forward, the development of ICME tools is identified as a key area of research. Chapters 6 and 7 cover various aspects of the synthesis and processing of high entropy materials. Ultimately, the engineering applications of new materials are derived from their properties and the advantages a designer can obtain by using the new class of materials. The structural properties are reviewed in Chap. 8 and the

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functional properties in Chap. 9. Finally, Chap. 10 provides the overall context and future directions. Although this book is not the first in this field, it is written to provide both “breadth” and “width” on the evolving subject, providing insights into both the basics and applied aspects of the subject. The authors will feel their efforts worthy provided the students and active researchers find the book useful. Kanpur, India Kanpur, India Kanpur, India Denton, USA

Krishanu Biswas Nilesh Prakash Gurao Tanmoy Maiti Rajiv S. Mishra

Acknowledgments

Composing a book on a contemporary subject is always challenging. It would not have been possible without active help from many. We would like to acknowledge their support, co-operation, and active participation in the book project. First, we would like to acknowledge Prof. J.-W.Yeh for kindly agreeing to provide a foreword for the book. Being a father figure in the area of high entropy materials, the authors are grateful for his willingness to provide the same. It is also equally important to acknowledge the various research groups working on this area across the globe for their publications, patents, and research reports, which have helped us to improve the quality of the book. Krishanu Biswas (KB) acknowledges his research scholars, especially Ph.D. and Masters’ students, for helping in collecting the research papers, references, and figures; among all, thanks to Dr. Fateh Bahadur Singh, Mr. Jitesh Kumar, Mr. Anurag Bajpai, Ms. Saumya Jha, in bringing the chapters in reasonably good shape and readable and to Mr. Buddhvir Singh for typing and compiling chapters. KB also acknowledges the Department of Science and Technology, Government of India, Indian Space Research Organization, Board of Research on Nuclear Sciences, Defence Research and Development Organization for financial support for research and development activity for the last one decade. Nilesh Prakash Gurao (NPG) would like to thank all his students involved in the research of high entropy alloys who have played an important role in developing his understanding of the subject through many interactions over the years. Special thanks to Dr. Reshma Sonkusare, Dr. Fateh Bahadur Singh, Mr. Abheepsit Raturi, Mr. Roopam Jain, and Mr. Vivek Kumar Sahu for their contribution to improving the scientific content of the chapters and Mr. Pradumna Swain for his secretarial help. NPG also acknowledges the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Indian Space Research Organization (ISRO), Tata Consultancy Services Research, and the Indian Institute of Technology Kanpur for their generous support to carry out research in the area of mechanical behavior of high entropy alloys for the last few years.

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Acknowledgments

Tanmoy Maiti (TM) would like to acknowledge his doctoral students Mr. Ritwik Banerjee and Mr. Subhra Sourav Jana for their help in collecting papers, typesetting, and compiling the references and figures. TM is also thankful to an intern in Plasmonics and Perovskites Laboratory, Mr. Sayar Das (B.Tech., NIT Durgapur) for helping in designing some schematics and figures. TM also acknowledges the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Indian Space Research Organization (ISRO), Central Power Research Institute (CPRI), and IIT Kanpur for providing the financial support to carry out research and development activities over the past one decade. Rajiv S. Mishra (RSM) would like to thank his postdoctoral fellows and students working on high entropy alloys, which has resulted in much of his understanding of the fundamentals of high entropy alloys. RSM is grateful to the US National Science Foundation and the US Army Research Laboratory for the financial support of his research group’s effort on high entropy alloys over the last five years. Finally, the authors are grateful to the Springer team, particularly Daniel Joseph Glarance, Ramamoorthy Rajangam, and Swati Meherishi, for their support and guidance in bringing out this book. Kanpur, India Kanpur, India Kanpur, India Denton, USA

Krishanu Biswas Nilesh Prakash Gurao Tanmoy Maiti Rajiv S. Mishra

Contents

1

2

High Entropy Materials (HEMs): An Overview . . . . . . . . . . . . . . . . . . 1.1 Alloys Why So Important for Civilization . . . . . . . . . . . . . . . . . . . . 1.2 Advent of HEMs: Why Multicomponent Equiatomic Alloys Were Not Extensively Investigated Earlier? . . . . . . . . . . . . 1.3 Research on HEMs—How It Started? . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Research Done by Pioneers . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 J.-W. Yeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 S. Rangananthan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Jon-Paul Maria and Jian Luo . . . . . . . . . . . . . . . . . . . . . . . . 1.4 High Entropy Materials—Basic Concepts . . . . . . . . . . . . . . . . . . . . 1.5 Entropy versus Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 HEM Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 HEMs and Beyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9 The Scope of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High Entropy Materials: Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Emergence of Four Core Effects—Framing the Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 The High Entropy Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 The Lattice Distortion Effect . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 The Sluggish Diffusion Effect . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 The “Cocktail” Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 High Entropy Alloys and Ceramics: Definition and Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Constituent Element-Based Classification . . . . . . . . . . . . . 2.3.2 Traditional Crystal Structure-Based Classification . . . . . . 2.3.3 Microstructure-Based Classification . . . . . . . . . . . . . . . . . . 2.3.4 Density-Based Classification . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 4 5 9 10 11 12 14 15 17 19 21 23 27 27 29 30 34 38 40 41 41 42 42 43

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2.3.5 Deformation Mechanism-Based Classification . . . . . . . . . 2.4 Composition Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

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Phase and Microstructural Selection in High Entropy Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Alloy Design Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Predicting Solid Solubility from Hume-Rothery Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Parametric Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 CALPHAD Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Ab Initio Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Pettifor Map Approach to Predict the Formation of HEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Phase Selection Approach to Find Single Phase Versus Multiphase HEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Design Strategies for High Entropy Ceramics (HECs) . . . . . . . . . 3.5 Microstructure of HEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Design Strategies for High Entropy Metallic Glasses . . . . . . . . . . 3.6.1 Trial and Error Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Nearly-Free-Electron Method . . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Valence Electron Concentration Method . . . . . . . . . . . . . . . 3.6.4 Discrete Variational Method . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.5 Machine Learning Methods . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44 44 45 47 47 49 49 51 55 61 67 70 70 73 75 76 76 76 77 78 78

Diffusion in High Entropy Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Diffusion in Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Diffusion in Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . . 4.4 Measured Diffusivities in High Entropy Alloys—Validity of the Core Concept of Sluggish Diffusion . . . . . . . . . . . . . . . . . . . 4.5 Implications for Diffusion-Controlled Processes . . . . . . . . . . . . . . 4.5.1 Creep and Superplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Diffusional Solid State Phase Transformation in HEAs—Phase Separation and Precipitation . . . . . . . . . . 4.5.3 Grain Growth in HEAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83 83 86 87

Application of Artificial Intelligence in the Design of HEMs . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 ICME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 CALPHAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Ab Initio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 DFT/MD Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99 99 101 103 105 107

88 91 92 94 95 97

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5.2.4 MC Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Phase-Field Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6 Machine Learning Approaches . . . . . . . . . . . . . . . . . . . . . . . 5.3 Future Outlook and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109 111 114 118 119

6

Synthesis and Processing of Bulk High Entropy Materials . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Processing of HEAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Melting and Casting Route . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Powder Metallurgical Processing Route . . . . . . . . . . . . . . . 6.3 HEA-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 High Entropy Ceramics: Oxides, Carbides, and Borides . . . . . . . . 6.5 Combinatorial Materials Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 125 125 142 154 157 159 163 170 172

7

Synthesis and Processing of HEA Coating and Thin Films . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 HEA Coatings: Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Mechanical Alloying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Spray Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Laser Cladding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 HEA Thin Films: Preparation and Challenges . . . . . . . . . . . . . . . . 7.3.1 Sputtering Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Ion Beam Sputter Deposition (IBSD) . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

177 177 178 178 178 182 186 186 190 192

8

Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Hot and Cold Working of HEAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Hot Working of HEAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Cold Working of HEAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Severe Plastic Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Mechanical Properties of HEAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Quasistatic Tensile Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3 Transient Plastic Deformation . . . . . . . . . . . . . . . . . . . . . . . 8.3.4 Dynamic Tensile Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.5 Fracture Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.6 Strength Ductility Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.7 Hardness and Wear Resistance . . . . . . . . . . . . . . . . . . . . . . . 8.3.8 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.9 Creep and Superplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Corrosion and Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

195 195 195 196 200 204 209 210 210 227 231 233 236 239 243 245 249

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Contents

8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 9

Functional Applications of High Entropy Alloys . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Thermoelectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Hydrogen Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Catalytic Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7 Sensor Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

259 259 259 271 273 279 281 282 284

10 Summary and Future Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Goals of Property Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Advanced Applications Requiring HEMs . . . . . . . . . . . . . . . . . . . . 10.4 Technology Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Patents on HEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Future Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

289 289 290 292 300 304 305 307

Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

About the Authors

Dr. Krishanu Biswas is currently Ranjit Singh Chair Professor at the Department of Materials Science and Engineering of Indian Institute of Technology Kanpur. The research work performed by him ranges from development of complex concentrated high entropy alloys, understanding the solidification behaviour of alloys, novel processing of ceramic composites, the alloying behaviour at nanoscale, and development of bulk alloy catalysts for hydrogen energy and environment. He has published over 200 papers in international repute peer-reviewed journals and delivered 52 invited talks in different national and international conferences. He is Principal Inventor of three patents. He has international collaboration with Japan and Germany. He teaches extensively at IITK on variety of subjects including phase equilibria, manufacturing processes, phase transformations, process metallurgy, solidification processing, etc. He has taught large number of courses at IIT Kanpur and developed courses on NPTEL platform as well as Massive Open Online Courses for the benefit of students in the materials science community in last 5 years. He has received numerous awards, fellowships and professional reorganization. He has coedited several issues on high entropy materials in various international journals of repute, including Scripta Materials. He is Member of inaugural editorial board of High Entropy Alloys and Materials, by Springer Nature. He is also on the editorial board of Transactions of Indian Institute of Metals. He has served as Key Reader for Metallurgical and Materials Transactions, A (2013–2016). Dr. Nilesh Prakash Gurao is presently working as Associate Professor at the Department of Materials Science and Engineering at the Indian Institute of Technology Kanpur, India. He completed his undergraduate degree in Metallurgical and Materials Engineering from Visvesvaraya National Institute of Technology, Nagpur, India, in 2005 and Ph.D. from the Department of Materials Engineering at the Indian Institute of Science, Bangalore, India, in 2010. He has worked as Postdoctoral Fellow in the Department of Mechanical Engineering at the University of Saskatchewan, Saskatoon, Canada, before joining as Assistant Professor at IIT Kanpur in 2012. He has established the Microstructure-Texture-Stress Laboratory

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About the Authors

at IIT Kanpur and is presently carrying out research in the broad domain of crystallographic texture, mechanical behaviour of materials and materials processing. His current research interests include in situ experiments using electron backscatter diffraction, synchrotron and neutron diffraction, complex concentrated alloys and additive manufacturing. He is Recipient of the Young Metallurgist of the Year award and the INSA medal for young scientist and is working towards establishing high throughput experimentation facilities towards rapid prototyping of materials and processes for structural applications. Dr. Tanmoy Maiti is Associate Professor in the Department of Material Science and Engineering at the Indian Institute of Technology Kanpur, India. Dr. Maiti received his Ph.D. in Materials Science and Engineering from The Pennsylvania State University, University Park, USA, in December 2007. Prior to joining IIT Kanpur, he did his postdoctoral research in Lawrence Berkeley National Laboratory and Pennsylvania State University. He received “PK KelkarYoung Faculty Research Fellowship” from IIT Kanpur for outstanding research. Dr. Maiti is also Recipient of the IEI Young Engineers Award, India. He has been featured in Journal of Materials Research focus issue on “2019 Early Career Scholars in Materials Science”. His research interests span the areas of thermoelectrics, plasmonics, photovoltaics and oxide electronic materials and devices. However, a common thread in his research is to address the global energy problem by developing novel materials for clean energy generation and the design of next generation chip-scale technology based on nanophotonics and nanoelectronics. Dr. Rajiv S. Mishra is currently Distinguished Research Professor at the University of North Texas. Before that he served as Curators’ Professor of Metallurgical Engineering in the Department of Materials Science and Engineering at the Missouri S&T. He is also Director of Advanced Materials and Manufacturing Processes at UNT and Fellow of ASM International. He is Past-Chair of the Structural Materials Division of TMS and served on the TMS Board of Directors (2013–16). He has authored/coauthored >400 papers in peer-reviewed journals and proceedings and is Principal Inventor of four US patents. His current publication-based h-index is 75, and his papers have been cited more than 32,000 times. He has co-authored two books: (1) Friction Stir Welding and Processing and (2) Metallurgy and Design of Alloys with Hierarchical Microstructures. He has edited or co-edited fifteen TMS conference proceedings. He served as Associate Editor of the Journal of Materials Processing Technology (2018–21) and is on the editorial boards of Materials Science and Engineering A, Science and Technology of Welding and Joining, and Materials Research Letters. He is Founding Editor of a short book series on Friction Stir Welding and Processing published by Elsevier and has co-authored seven short books in this series.

Chapter 1

High Entropy Materials (HEMs): An Overview

1.1 Alloys Why So Important for Civilization The design and development of new material is considered the main driver of our civilization. As the usage of materials has major influence on the civilization, we have different era in our history based on the form and type of material used. During prehistoric age, humans have no choice other than using naturally available materials; stone, wood, leather, bone, fur as well as same native metals, which are easily available on surface of the mother earth (Baker et al. 1992). These metals were mainly gold, silver, and probably copper. We learned the ways and means of extraction of metals from naturally available ores much later. Scientific as well as technological development and serendipity caused development of many alloys, which changed the discourse of our civilization, specially use of alloys; brass, bronzes, cast iron, steels become prominent. Figure 1.1a shows the use of materials as a function of time (Ashby and Johnson 2013), spanning from prehistoric (10,000 years BC) to 2020 AD. It is evident that the use of material has dictated human civilization to extent, none has done so. Post Industrial Revolution (1760 and later), the use of alloys was so prominent that the major components of any machining were made up of alloys (Ashby and Johnson 2013). Simultaneously, the scientific understanding of fundamental concept on materials synthesis, properties, and interfacial phenomena were slowly developed in the last century. Figure 1.1b shows a schematic chart illustrating scientific developments as a function of time. Along with metallic alloys, structural and functional ceramics formed the class of engineering materials, which found widespread use in various applications. Industrial Resolution saw all alloys and ceramics being applied to common as well as special applications, including high-speed steels, stainless steels, Al alloys, etc. In the last century, special steels, superalloys, Ti-alloys, intermetallic components, bulk metallic glasses, quasicrystals, toughened zirconia, and composites were discovered. The alloys, old as well as new alloys, were developed based on single or two elements, designed and developed for specific need, and hence, these materials dominated the materials use till 1990s (Westbrook and Fleischer 2000). However, it has increasingly been felt that the © Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8_1

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1 High Entropy Materials (HEMs): An Overview

properties of the exiting metallic alloys, ceramics, and composites have reached an upper limit and can no longer cater to the need of strict technological requirements of new applications, especially supersonic jet engines, hyperloops, ultra-thin electronic gadgets, biomedical applications, etc. In addition, the availability of the strategic materials (Li, Re, rare-earth metals, etc.) has made us over-reliant on some specific sources in few countries, spiraling cost for other countries in the world. Therefore, the need of new alloy design concept, which can satisfy the abovementioned needs, has been felt for sometime. The popular English proverb “Necessity is the mother of all inventions” can probably the reason behind discovery of the multiprinciple multicomponent materials, which are popularly known as high entropy materials (HEMs). Obviously, this brand new strategy of design of materials or alloy design could not be developed overnight, taking several decades of thorough research by numerous scientists. It is evident that “serendipity” overtook the “staggered research” for discovery of HEMs.

1.2 Advent of HEMs: Why Multicomponent Equiatomic Alloys Were Not Extensively Investigated Earlier? The artificial alloys typically based on single or two elements have ruled the materials’ world in the last three centuries. The usage of pure or ultra-pure elements is indeed restricted to only jewelry and same specific optical, electrical applications. This primarily includes, gold, silver, platinum, and copper. Ultra-pure copper is widely used to manufacture electrical appliances. In fact, the alloys, such as steels, aluminum alloys, AlNiCo, Cu–Be alloys, superalloys, and Ti–Al. Ni–Al, alloys have dictated the material use for last 100 years (Suryanarayana and Inoue 2017; ReedHill and Abbaschian 1994). A closer look of the composition of these alloys reveals that many of them are indeed multicomponent alloys. For example, stainless steels consist of Ni, Cr, Ti, Nb, with Fe as primary elements, making them multicomponent alloys; Ni-based superalloys contain 14 different elements to obtain optimum properties needed for jet engine (Suryanarayana and Inoue 2017). A detailed analysis of the composition of different alloys clearly indicates that many of the practical alloys are multicomponent, and some of them contain alloying elements in large concentration. The preparation of superalloys can be compared with making food in a typical Indian kitchen, consisting of mixing different species to obtain specific properties or taste of the food. The fruit cocktails, typically liquid solutions, are homogeneous mixture of different fruit juices. This concept of liquid state solutions has intelligently been extended by metallurgist to synthesize multicomponent alloys having large proportions of different alloying elements (Miracle 2017). Frank Karl-Archard for the first time has demonstrated such multicomponent alloys as early as in 1888 (Achard 1788). However, such research activity has not been pursued subsequently, primarily due to the fact that multicomponent mixture prepared via casting route essentially contains brittle intermetallic phases.

1.2 Advent of HEMs: Why Multicomponent Equiatomic …

3

Fig. 1.1 a Materials usage and b innovation potential as a function of time (from prehistoric to recent times) (Ashby and Johnson 2013). Innovation has significantly changed material usage

Hence, last century saw development of multicomponent alloys, which are mainly one or two major elements based. This led to development of many new alloys containing different alloying elements, for example, Al–Cu–Zn, Al–Cu–Ni–Zn (Suryanarayana and Inoue 2017). Although there are Al-based alloys (Al as principle elements), multicomponent additions are intentionally made to achieve various properties, desired for applications. It is important to note here that the detailed analyses of the hyperdimensional phase diagrams (ternary, quaternary, etc.) reveal the

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1 High Entropy Materials (HEMs): An Overview

presence of intermetallic phases (IMP); indicating choice of alloy composition is important to avoid the formation of brittle IMEs or IMPS. As the alloy compositions shift to central part of the hyperdimension phase diagrams, the chances of formation of IMEs and IMPs are high. Hence, most of the practical multicomponent alloys have composition close to the corners of the ternary phase diagrams (Reed-Hill and Abbaschian 1994). Nevertheless, higher order systems, quaternary, quinary, hexanary, etc., are expected to lead to formation of more number of IMCs and IMAs, and hence, extensive studies have not been carried out on such systems. As a result, it has widely been felt among the scientists and the engineers that it would not be possible to design and develop alloy compositions, which can produce microstructure free from brittle IMCs or IMPs. Hence, material scientists in particular were discouraged to venture into the world of alloys having large number of alloying addition with substantial concentration of each alloying element. Although few trials have been made to probe the possibility of formation of ductile solid solution, an extensive study was considered to be unworthy (Westbrook and Fleischer 2000). Even such endeavors were discouraged, and alloy design was purely restricted to the corners of the higher-dimensional phase diagrams.

1.3 Research on HEMs—How It Started? It has already been mentioned that although conventional alloys’ design strategy has led to discovery of many useful and extraordinary alloys, these are typically based on one or utmost two base elements, and any endeavor to explore alloy compositions in the center of the phase diagrams was not followed up. However, there always exit a few scientists in the world who would ask the question of the efficacy of the conventional design concepts and hence try to experiment with odds trying to prove that it is possible to bring a paradigm shift and look for serendipitous discovery. In fact, the conventional alloy design strategy is restrictive in the sense that it does not allow us to explore the full gamut of alloy compositions. It is akin to placing shackles around our legs to venture into the untraveled territory. Hence, the role of David Livingstone was felt, who could take stride into unknown territory. There are two ways of exploring multicomponent phase space for concentrated solid solutions: (i) extension of conventional strategy by making alloying additions in relatively large quantities or (ii) via equiatomic substitution. In the latter case, one can start with any material composition of interest and then replace each component with multicomponent equimolar or near equimolar mixtures having similar chemical species. That’s how the research on HEMs, in particular, has begun simultaneously in two separate continents, thousands of miles apart. Two independent groups, one led by J.-W. Yeh in Taiwan and other one led by B. Cantor in UK, showed in 2004 that it is possible to stabilize simple substitutional FCC solid solution in an equimolar CoCrFeMnNi alloy via casting route (Yeh et al. 2004; Cantor et al. 2004). Hence, an “out-ofthe-box” novel concept popularly as “high entropy alloy” (HEAs) or multiprinciple multicomponent alloys (MMAs) comes into existence. This new concept involves

1.3 Research on HEMs—How It Started?

5

design of multicomponent equimolar alloys containing at least 5 components with large concentrations (5–35 mol%). Surprisingly, this alloy composition does not lead to formation of IMC or IMP, although the composition lies in the central part of the phase diagram. The solid solution phase is deemed to be stabilized by high configuconf > 1.61R, R = universal gas constraint) (Yeh et al. ration entropy of mixing (ΔSmix 2004). This has been considered to be a paradigm shift in design of multicomponent materials: alloys and ceramics (Yeh et al. 2004; Cantor et al. 2004; Sharma et al. 2018; Miracle and Senkov 2017; George et al. 2019). This concept has led to explosion of research activity in design and development novel alloys, ceramics with detailed investigation on microstructural evolution, stability, and properties of HEMs in last 14 years (Murty et al. 2019). Figure 1.2a shows global publications in this area over last 14 years. In 2018, over 3000 scientific papers have been published in international journals of repute, and 100 patents have been filed internationally as well as in various countries (Murty et al. 2019). Figure 1.2b shows global distribution of publication in last 15 years, Asia–Pacific region contributing the largest % of publication. In addition, a large number of international conferences (listed in Table 1.1) have been conducted and special issues on high entropy materials have been published to take a stock of the research activities over years. These activities demonstrate that the research on HEMs is on the rise and expanding rapidly. Thereafter, the research has increased manifold and expanded from the realm of metallurgists or material scientists to physicists, chemists, other engineering branches. Hence, it is important to take complete stock of the research and development activity and put together in the form of a book. In the following, we shall first discuss the pioneering research carrier out by Yeh, Cantor, and Ranganathan on the development of multicomponent multiprinciple materials at the beginning (Ranganathan 2003). This is intended to provide how each of them contributed to bring about a new, “out-of-the-box” alloy design concept, which is seemed to have far-reaching consequence. The following discussion is not intended to provide historical account of a novel concept, but to provide an avid reader, how scientific curiosity and serendipity play an important role in material development.

1.3.1 Research Done by Pioneers 1.3.1.1

Brian Cantor

The careful analyses of research activities on HEMs indicate that the activity on multicomponent equiatomic materials has been started early on 1981 by Brian Cantor. The journey was long, tedious but scientifically enriching. He has started looking multicomponent alloys with very large number of components (20) via chill casting and rapid solidification routes. His vast experience in the area of rapid solidification was put on use to make these multicomponent alloys and systematically study the microstructural evolution.

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1 High Entropy Materials (HEMs): An Overview

Fig. 1.2 a Publications over years and b pie chart showing publications from different continents (George et al. 2019; Murty et al. 2019)

It started with Alain Vincent, one of his undergraduate students, who started making equiatomic alloy with 20 components (Ag, Al, Bi, Cl, Co, Cr, Cu, Fe, Ge, Mg, Mn, Mo, Nb, Ni, Pb, Sb, Si, Sn, W, Zn) via chill cast. The composition was selected by equiatomic substitution, and alloy compositions were based on complex generic formula, Crx Mnx Fex Cox Nix Nbx Gex Vx Tix . However, Vincent’s work remained unpublished except him thesis submitted to Sussex University, which did not reveal any conclusion (Cantor 2014). However, this work was later continued by another undergraduate student, Peter knight who worked at Oxford University in 2002. Although Peter made some process, work was not complete. Issac Chang, a postdoctoral fellow, later carried out detailed microstructural investigation at Oxford University. This complete work was finally presented at rapidly quenched and metastable materials (RQ 11) held at Oxford University in 2002 and later published in Materials Science and Engineering A in 2004 (Cantor et al. 2004). The paper

64

Planned

JOM

JOM

JOM

Advances in Materials Science and Engineering

Advances in Materials Science and Engineering

Coatings

J. Materials Research

Crystal

High entropy alloys

High entropy alloys

High entropy alloys

High entropy alloys

High entropy alloys

High entropy alloy coatings

Nanocrystalline high entropy materials: processing challenges and properties

Development of high entropy alloys

2016

High entropy alloy: Book fundamentals and applications

2020

2019

2015

2015

2015

2015

2014

2014

–

–

–

67

66

2013

2012

2013

2006

Year

Book

High entropy alloys: First edition

Book

64

JOM

High entropy alloys 65

15

Entropy

High entropy alloys

31

Vol.

Annales de Chimie Science des Materiaux

Journals

Recent advances in high entropy alloys

Special issue

Special issue/books

Table 1.1 Special issues and books published on HEMs

Butterworth-Heinemann Inc

MDPI

Materials Research Society

MDPI

Maney

Hindawi

Springer

Springer

Springer

Springer

MDPI

Lavoisier

Publisher

M. C. Cao, J.-W. Yeh, P. K. Springer International Liaw and Y. Zhang Publishing

B. S. Murty, J.-W. Yeh and S. Ranganathan

Bharat Gwalani

Krishanu Biswas, H. Ryu and C. Pasquale

T. M. Yue

H. K. Bhadeshia

Y. Zhang, J. W. Yeh, I. F. Sun, J. P. Lin, K. F. Yao

M. C. Gao

M. C. Gao

M. C. Gao

M. C. Gao

J. W. Yeh

J. W. Yeh, A. Davison

Editors

(continued)

Switzerland

USA

Switzerland

USA

Switzerland

UK

USA

Germany

Germany

Germany

Germany

Switzerland

France

Country

1.3 Research on HEMs—How It Started? 7

Book

Italics is used to indicate the name of the journal

Journals

Special issue/books

High entropy alloys

Table 1.1 (continued) Vol. 2019

Year B. S. Murty, J.-W. Yeh, S. Ranganathan, P. P. Bhattacharjee

Editors Elsevier

Publisher

The Netherlands

Country

8 1 High Entropy Materials (HEMs): An Overview

1.3 Research on HEMs—How It Started?

9

described a detailed account on the successful synthesis of FCC equimolar CoCrFeMnNi alloy from the first equiatomic alloy consisting of 20 elements. In this process, they also investigated alloys containing 16 elements Ag, Al, Cl, Co, Cr, Cu, Fe, Mg, Mn, Mo, Nb, Ni, Pb, Sn, W, Zn. However, both the alloys have been found to be brittle containing intermetallic compounds. However, two alloy compositions provided [(Co20 Cr20 Fe20 Mn20 Ni20 ) and (Cr16.7 Mn16.7 Fe16.7 Co16.7 Ni16.7 X16.7 with X = Nb, Cu and V)] by Cantor and co-workers showed single phase FCC. However, six-component alloy (Cr16.7 Mn16.7 Fe16.7 Co16.7 Ni16.7 X16.7 ) with X = GE and Ti exhibits two-phase (FCC + BCC) microstructure (Cantor 2014). Similar strategy was adopted by Kim, Zhang, Warren, Eckert, and Cantor to study chill cast TiZrHfNbFeCoNiCuAgAl alloys, typically based on ETM100-x-y LTMx Aly (ETM = Early Transition Metal, LTM = Late Transition Metal), revealing multicomponent amorphous alloys (Huang et al. 1996).

1.3.2 J.-W. Yeh On the other hand, Prof. Jien-Wei Yeh started his journey on multiprinciple alloys in middle of 1990. His journey was full of excitements, hard work, and failure to achieve his intended goal. It is evident that failures have propelled him to change his discourse, leading to discovery of high entropy alloys. He was working on numerous ways to improve mechanical properties (strength, fracture toughness, ductility) of multicomponent alloys by various means, including high pressure, high quenching rate as well as high temperature processing. He designed variety of experimental setups to obtain the abovementioned objectives (Murty et al. 2019). However, he failed to achieve his intended goals. He was separately looking for new exactable ideas to make headway for achieving his targets. One fine day during road trip in the countryside of Taiwan, it struck to his mind to go for multicomponent alloys having equal or near equal properties. He returned quickly and formed a group of researchers and started working on HEAs. In late 1995, his group successfully synthesized equiatomic multicomponent alloy of ~ 100 gm using vacuum arc melting (Yeh et al. 2004). This was followed by successful preparation of large number of equiatomic alloys having 59 components, with measurements of hardness, corrosion resistance, and investigation on microstructure in the cast and annealed conditions. This allowed his team to zero in 20 experimental alloys based on Ti, V, Cr, Fe, Co, Ni, Cu, Mo, Zr, Pd, Al (Murty et al. 2019). However, he categorized these alloys in three broad equiatomic alloys, which were differing in Cu, Al, and Mo. In each case, the alloys were of either 6 or 9 components; Al, Cu, Co, Cr, Mo, Pd, + r with 0–3 atom% TiVFeNiZ. The detailed study on these alloys reveals very high level of hardness (HV ~ 590–890) on these dendritic cast structures. A small addition of boron led to increase in hardness. Interestingly, his work revealed phases, which were unindexed in the X-ray diffraction patterns. After toiling work for about 7 years, the first paper on HEAs from his group on “Multi-principle-element alloys with improved oxidation

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1 High Entropy Materials (HEMs): An Overview

and wear resistance for thermal spray coating” was published in Advanced Engineering Materials (Yeh et al. 2004). Subsequently, team published another paper on Nanostructured high entropy alloys with multiprinciple elements-novel alloy design concepts and outcomes, published in the Advanced Engineering Materials (Lai and Jeh 1998). There two papers virtually set the tone of the research activity in HEAs and other complex concentrated materials, which was then carried forward by other researchers across the globe. National Tsing Hua University became famous as one of major centers of high entropy material research. Prof. Yeh rechristened his laboratory as “High Entropy Material Research Laboratory”. Other groups in different parts of the World have followed similar trend since then. In last couple of years, his group is making concerted efforts to make HEMs useful for industrial applications. He along association with industrial houses in Taiwan has already designed and manufactured several components as machine parts, furnace accessories, kitchen ware, and components for nuclear power plants.

1.3.3 S. Rangananthan In the early years of HEA research, Prof. S. Ranganathan from India made significant contribution. In 2003, he published a classic paper in an Indian journal, Current Science, entitled “Alloying Pleasure—Multimetallic Cocktails” (Ranganathan 2003). This paper played significant role in shaping research on HEMs in which he brought the concept of “cocktail effect” in these multicomponent alloys. In particular, he discussed three important multicomponent alloys: bulk metallic glasses (BMG), gum metals, and multicomponent HEA. In this paper, Ranganathan discussed difficulty in venturing into multicomponent system. This is mainly due to complexity involved in the database for phase diagram in addition to processing variables. Astronomical numbers of possibilities are reported in multicomponent system. The material scientists traditionally resorted to alloys with few components. It is evident this article is based on the work done by Professor Yeh. Prof. Ranganathan visited National Tsing Hua University, Taiwan, being hosted by Prof. Yeh in 2003. It is worth noting that professor Yeh visited India subsequently and wrote a detailed account on HEMs as a proceeding of International Conference held during Annual General Meeting of Indian Institute of Metals (IIM) at Chennai in late 2005. The continued collaboration between Prof. Yeh and Prof. Ranganathan lasted long enough to propagate that high entropy alloys are indeed new class of material. Hence, the efforts of Prof. Cantor, Prof. Yeh and Prof. Ranganathan made significant contribution on the material research and created a paradigm shift in the design of alloys. This was further expanded by Jon-Paul Maria and Jian Luo to include ceramics into the domains of HEMs.

1.3 Research on HEMs—How It Started?

11

1.3.4 Jon-Paul Maria and Jian Luo The ever-increasing hunt for materials with betterment of properties satisfying the stringent and demanding requirements of rapidly growing industrial application has led to rapid expansion of the novel alloy designed concept of Yeh and Cantor to ceramics; especially multicomponent oxides and borides (Hsu et al. 2000; Hung et al. 2001; Chen et al. 2002) compelling us to look beyond metallic materials. The landscape, provided by the pioneering work by Yeh and Cantor, was further explored by successful synthesis of five- or six-component oxides and borides, which are now considered potential candidates for variety of applications. In 2015, J.-P. Maria and his co-workers from Duke University reported successful synthesis of “entropy-stabilized oxides”, i.e., (Co, Cu, Mg, Ni, Zn)O via powder metallurgy route (Fig. 1.3a). Although the information on entropy on non-metallic systems is limited, it is worth mentioning that Navrotsky and Kleppa in 1967 have reported pioneering work stating that entropy of mixing can be used to control the normal-to-inverse spinel transformation (Hsu et al. 2000). It is also important to note that, unlike metallic systems, these oxides have network of oxygen ions, sitting the fixed lattice position of the unit cell (Fig. 1.3c). It is the metallic ions (Co, Cu, Mg, Ni, and Zn) whose arrangement can lead to change in entropy of mixing (Hsu et al. 2000), mix , indicator of “total disorder” in the system, per atom basis is and hence, the ΔScon mix , still the much lower. Although point defects can alter the value of “disorder” ΔScon absolute value per atom basis is never going to reach as high as in case of metallic mix will significantly affect the solid solution phase materials. Nonetheless, the ΔScon and stability of mixed oxides as shown in Fig. 1.3b. Another important question is related to homogeneity of these mixed oxide phase. J.-P. Maria and his co-workers have carried out detailed extended X-ray absorption fine structure (EXAFS) and energy dispersive spectroscopy (EDS) in transmission electron microscopy to probe the chemistry and structure at atomic scale and showed that the different metallic species are indeed atomically mixed, like solid solutions in metallic systems (Hsu et al. 2000). Jian Luo and his co-workers from University of California, San Diego have used powder metallurgy route to synthesize multicomponent diborides; (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)B2, (Hf0.2Zr0.2Ta0.2Mo0.2Ti0.2)B2, (Hf0.2Zr0.2Mo0.2Nb0.2Ti0.2)B2, (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2, (Mo0.2Zr0.2Ta0.2Nb0.2Ti0.2)B2, and (Hf0.2Zr0.2Ta0.2Cr0.2Ti0.2)B2 (Hung et al. 2001). These were prepared by mixing individual borides followed by spark plasma sintering. These borides are deemed to be future generation ultra-high temperature ceramic (UHTC), a potential candidates for re-entry vehicles and supersonic jets. Therefore, the “out-of-the-box” alloy design concept could be extended to multicomponent ceramics, and many more (carbides, nitrides, etc.) are believed to be in store for discovery.

12

1 High Entropy Materials (HEMs): An Overview

Fig. 1.3 Entropy-stabilized oxides: a X-ray diffraction patterns; b entropy as function of concentration of a component (XN ) and number of components (N); c estimation of configurational entropy of mixing for ceramics is distinctly different from metals (Hsu et al. 2000)

1.4 High Entropy Materials—Basic Concepts We have discussed the novel alloy design strategy giving birth to high entropy alloys due to pioneering research by Prof. Yeh and Prof Cantor. It is important now to define HEA and the core effects of the multiprinciple multicomponent alloys. Both are directly linked in such a way the definition will provide core effects. HEAs can be defined from the perspective of composition as well as configurational entropy of mixing. The first definition in found to more subtle and fundamentally correct. HEAs have already been defined as alloys made up of 5 or more principle elements. According to Yeh (2004), the composition of each element can vary from 5 to 35

1.4 High Entropy Materials—Basic Concepts

13

at.%. Obviously for an equiatomic alloy, each element constitutes about 20 atom%. It is always possible to add minor elements (concentration < 5 atom%) to improve properties of the HEAs. HEAs started with two classic publications in 2004 were intended “to investigate the unexplored central regain of multicomponent alloy space” (Murty et al. 2019). As compared to the conventional alloys, the concentrated blend of multiple elements has been used as a new alloy base constituting of specific set of elements. Hence, HEMs are complex concentrated materials (CCMs) as the concentration of each component is more than 5 atom%. It needs to be mentioned the dilute alloys, in general, have solute concentration less than 5 atom%. This novel concept leads to extremely large number of alloys, which can be designed from the available elements in the periodic table. This is typically given by n Cr . Here, n is the total number of elements to be considered and r = 5. Considering 67 metallic elements present in the periodic table, the total number of 5-elemental alloys is about 100 million. This is astronomical number considering the number of useful alloys exists in the world today. Hence, this number is extremely large, when compared to only 67 element alloy base from the pellet of metallic elements available in the periodic table. In addition, the combination of alloys can further be increased by simply changing the concentration of any elements in a five-component alloy, e.g., Aly CoCrFeNi can provide a base FCC alloy for y ≤ 0.4 and BCC alloys for y > 1 and a combination of FCC and BCC in the intermediate value 0.5 ≤ y ≤ 1. Obviously, HEA base alloy consisting of r principle elements can easily be modified by minor additions of minor elements. Hence, altogether these aspects provide HEA/HEMs astronomical numbers of new alloys, which can be designed and thus, provide unique opportunities to design unlimited number of new alloys. From the perspective of entropy of mixing, the HEMs can be classified as materials mix at random state to be at least or larger than 1.6R at room temperature. having ΔScon Here, R is universal gas constant. A detailed discussion on entropy and entropy of mixing will be provided in the following. However, it is important to note that the statistical definition of entropy, given by Boltzmann, can be used to find out the mix ΔScon for a random alloy containing m components in equimolar proportions. mix ΔScon = −R

m 

X i ln X i

i=1

        1 1 1 1 1 1 1 1 ln + ln + ln + ln = R ln(m) = −R m m m m m m m m (1.1) 

mix Therefore, for equimolar HEMs, ΔScon depends on the number of components, mix mix of any system. For m = 5, ΔScon i.e., it provides us a working “handle” to tune ΔScon mix mix ~ 1.6R. Hence, the HEMs can also be defined using values of ΔScon , i.e., ΔScon ≥ 1.6R. Conventional alloys (one or two element based) have significantly lower value mix mix . In fact, most of them has ΔScon < R (low entropy alloys) with a few fall of ΔScon mix with 1.5R < ΔScon < R (medium entropy alloys).

14

1 High Entropy Materials (HEMs): An Overview

1.5 Entropy versus Enthalpy According Yeh et al., single phase HEAs with simple FCC, BCC, or HCP structures are stabilized due to significant contribution of configurational entropy of mixing (Yeh et al. 2004; Murty et al. 2019). Hence, mixing of different components to mix . The classical Boltzmann’s produce solid solutions will be strongly affected by ΔScon equation provides the configurational entropy of any system, which can be arranged in ‘w’ number of ways. S = k ln(w)

(1.2)

Here, k in known as Boltzmann’s constant = NRA , where R is universal gas constant and N A is Avogadro number. Therefore for any p-component (i = p) system, the mix ΔScon is given by mix ΔScon

= −R

p 

X i ln X i

(1.3)

i=1

Here, X i is the mole fraction of each component (i) in the system. As mentioned earlier, for a p-component system having equiatomic or equimolar concentration conf conf = R ln( p). Therefore, it is possible to estimate ΔSmix of each component, ΔSmix for any equiatomic systems by taking logarithmic of number of components multiplied by R. Hence, the formation of HEA has been in general embodied by the conf favors the formation and stabilization of entropy hypothesis implying that ΔSmix HEM phases. In other word, the single phase solid solution is independently favored conf . This essentially leads to make HEMs synonymous with HEAs. However, by ΔSmix conf two important aspects emerge from this discussion. Firstly, the calculation of ΔSmix in based on the underlying assumption that the constituent species are distributed randomly in the lattice of the solid solution phase and hence, can be described by idealized concept of entropy as Boltzmann statistics. Detailed investigation of large number of HEAs clearly indicates that the formation of ideal solid solution is very rare. This is stable for majorly of binary solid solutions follow subsolid solutions conf using Boltzmann model (Miracle and Senkov 2017). Hence, estimation of ΔSmix statistics will probably not work for multicomponent solid solutions. Secondly, the effect of enthalpy ΔHmix cannot be ignored by considering overConf . It is not difficult to understand that the increase in the shadowing effect of ΔSMix number of elements in the alloy will change both enthalpy of mixing and entropy of mixing. Essentially, stability of solid solution phases depends on the relative magniConf . In fact, extensive investigation of thermodynamic tude of both ΔHmix and ΔSMix data indicates ΔHmix significantly increases as the number of constituent element or component is increased, and hence, it is unlikely that the effect of increase of ΔHmix Conf will out compete the gain due to ΔSMix for HEMs. In case of entropy-stabilized Conf ceramics, the effect of ΔSMix will be much less as the metallic species occupying Conf . ΔHmix the voids in the network of anions can lead to much lower increase in ΔSMix

1.6 HEM Family

15

for most of the ceramic solid solution is relatively higher, and hence, the gain in Conf ΔSMix due to large number of components may not lead to substantial change in the Conf and free energy (Miracle and Senkov 2017). Nonetheless, it is evident both ΔSMix ΔHmix would exert important influence and both need to be estimated as accurately as possible. The currently available model considers only binary interactions and extension of this to higher order interactions (ternary, quaternary, quinary, etc.) does not permit accurate estimation of ΔHmix . Better model is therefore, required using widely established thermodynamic concepts. In conclusion, the research on HEMs has made the role of entropy clear and subtle. This has led us to find ways and means of adjusting entropy by controlling component and composition in a material. Hence, it is evident both enthalpy of mixing and configurational entropy of mixing will play stellar role in the phase formation, if the kinetic factors are ignored. However, phase formation in a multi component system is also expected to be dependent on geometrical consideration, i.e., relative atomic size of the elements. W. Hume-Rothery predicted that maximum size difference allowed for a binary substitutional solid solution would be 15% (Mizutani 2012). However, the detailed analyses of available data using parametric approach have indicated that the maximum size difference allowed for a multicomponent multiprinciple material in 6.6%. The lower value is mainly due to the fact that in case the atomic size difference of the component atoms is relatively small, the component can substitute each other easily and likely to have similar probability to accept the lattice sites to form a multicomponent solid solution. Another factor controlling the phase formation is in HEMs is valence electron concentration, as it is well known that the valence electron concentration (VEC or e/a ratio) plays the critical role in controlling phase formation, stability, and properties of HEMs (Guo et al. 2011). Although electron concentration in metallic materials can also be represented by e/a, VEC is widely being used for metallic solid solutions. However, e/a in better suited for structurally complex alloy phases including multicomponent Laves phase, σ phase, or μ-phase (Murty et al. 2019). Recently, the presence of multicomponent Laves phase in TiFeNiVZr system (Mishra et al. 2021) has clearly shown the importance of e/a ratio in stabilizing the Laves phase (Chuang et al. 2011). It is important to note that phase stability is strongly affected by e/a, as was articulated by Hume-Rothery (Mizutani 2012), about 100 years ago, notable example being α, β, brain in Cu–Zn system. Hence, the stabilization of the multicomponent alloyed phase needs to be discussed using ΔHmix Conf and ΔSMix in conjunction VEC or e/a. It is evident that physical, mechanical, and functional properties are connected to DOS at Fermi revel. The stability of some of the alloyed phases also depends on Fermi surface-Brillouin zone interactions, which also significantly depend on VEC or e/a ratio.

1.6 HEM Family The first investigation on HEM was reported on the equiatomic CoCrFeMnNi (Cantor alloy)—all the metals from 3d transition metal (3d-TM) family. During the initial rush

16

1 High Entropy Materials (HEMs): An Overview

of discovery, the emphasis was on discovering single phase FCC multicomponent alloys consisting of 3d transition metals (Miracle and Senkov 2017). There alloys involve four or five elements in equiatomic or near equiatomic proportions from the palette of 9 elements (Co, Cr, Cu, Fe, Mn, Ni, Ti, V along with Al) (Miracle and Senkov 2017), although some minor elements (Si, Sn) were utilized. The design principle was purely based on parametric approach, which is a popular empirical approach to design components and compositions of HEMs (Gorsse et al. 2018). Tazuddin et al. (Gurao and Biswas 2017) have shown that it is possible to utilize CALPHAD approach to unearth fairly large number of single phase FCC and BCC multicomponent equiatomic as well non-equiatomic alloys from a palette of 13 elements, consisting of 3d-TM with Al, Ge, Si, and Sn (Al, Co, Cr, Cu, Fe, Mn, Ni, Ti, V, Sn, Ge, Si). Figure 1.4a, b show the property diagrams for an equiatomic FCC (CoFeMnNiV) and BCC (AlFeMnNbTi) HEM, revealing large temperature range in which both the solid solution phases are stable. It is even possible to design non-equiatomic HEMs using CALPHAD approach as shown in Fig. 1.4c–e for CoCuFeMnNi system. Therefore, CALPHAD was found to be better methodology to find HEM forming systems, which will form single phase microstructure. Therefore, majority of the research has been performed on HEMs based on 3d-TM family (Gorsse et al. 2018). Scientists across the globe gradually looked into other series of metals in the periodic table to find novel HEA forming systems. One such alloy system was discovered in 2010, by Oleg Senkov and his co-workers at Aerospace Research Lab, USA (Senkov et al. 2010). These are known as Refractory HEA (RHEA), primarily consisting of a five refractory metals from the palette of 9 refractory metals (Cr, Hf, Mo, Nb, Re, Ta, V, W, and Zr). Using the palette of these alloying elements, substantial number of equiatomic as well as non-equiatomic HEMs were unearthed. These HEAs have BCC or B2 structure. It is important to note that these HEAs are developed as potential high temperature structural material with maximum usage temperature beyond conventionally available Ni-Based superalloys, i.e. well above 1000 °C (Raturi et al. 2019). This discovery has opened up vistas to utilize other group of metals available in the periodic table, which can be mixed together to form solid solution. Two such groups of elements are (Ag, Au, Cu, Pt, Pd) and (Ir, Os, Re, Rh, Rn). The first group of element forms FCC HEMs, whereas later one forms HCP structure (Urs et al. 2020; Takeuchi et al. 2014). There are called precious metal HEA (PM-HEA). The metallic elements from actinide group have been found to form multicomponent HCP solid solution (Lužnik et al. 2015). Notable examples include equiatomic Y, Gd, Tb, Dy, Lu, Gd, Tb, Dy, Tm, Lu alloys. There multicomponent alloys have been found to exhibit excellent hard magnetic properties (Huo et al. 2019). Therefore, research in last 10 years has led to discovery of at least 6 different types of HEA forming from metallic elements in the periodic table. It is evident that the selection of elements is primarily based on intuitive approach and the experience with different metals dictated the scientific bases of selection of element to HEA phases. The principle elements with high melting temperature form group are used to design RHEAs, low-density elements (Al, Mg, Li, etc.) utilized for low-density HEAs, the elements with HCP structure to form multicomponent HCP solid solution. This approach is based on logic rather than scientific study. As indicated earlier, CALPHAD approach

1.7 HEMs and Beyond

17

which is based on thermodynamic-based calculations provides a robust and useful technique to design HEMs (Zhang et al. 2014a). The components and compositions of various HEMs can effectively be designed using CALPHAD approach. The recent literature suggests the use of CALPHAD approach to design novel HEMs. In case of ceramic solid solutions, design is still based on logic. Multicomponent oxides, diborides, and carbides have been designed and developed by utilizing knowledge from the available phase diagrams (Zhang et al. 2012). Recently, molecular dynamics (MD)-based approach has also been used to design HEMs (Choi et al. 2018). Unlike CALPHAD approach, this approach requires huge and computational power as well as time and hence, it cannot used extensively to design novel HEM compositions. In addition, we need to know the pair potentials for each atomic pair which are not available for many multicomponent systems. Therefore, CALPHAD seems to combine both scientific robustness and optimum computational power to design new HEMs. However, CALPHAD also suffers from some drawbacks. These will be discussed in Chap. 3.

1.7 HEMs and Beyond During the initial period after discovery, the research on HEMs was dominated by research for single phase solid solutions, FCC, BCC, and HCP. Hence, alloying addition was restricted to 5, and equiatomic alloys were primarily investigated. This restriction is form to be unproductive as many alloy systems were excluded. In addition, there were many misconceptions increasing number of elements or compositions would lead to complex microstructure and brittle phase, and hence, research was not followed up. However, some of the misconceptions were overcome by extraordinary research carried by many researches, especially Yeh and his co-workers. However, the stabilization of multicomponent solid solution by high configurational mixing entropy is still debatable and requires more research to reach a conclusion. Recently, it has been concluded that HEM must be too broad to be adequately described by single definition or microstructure. Hence, requirement of new term was felt to remove these barriers. New term, complex concentrate materials (CCMs) or multiprincipal element materials (MPEMs) are found apt. CCMs is found to be better suited as it allows us to keep the focus on concentrated materials, which are predominantly multicomponent and compositionally complex. With no single element base, this avoids many confusions and misconceptions, specially it will have no bearing on importance of configurational entropy of mixing. In fact, CCAs will include all materials, which deem satisfy HEM definition, disused earlier. It will also expand the HEM field by including concentrated ternary and quaternary alloys. At the same time, it allows us to include alloys containing elemental concentration more than 35 atom% even single phase intermetallic alloys (Laves phase) and other intermediate phases. HEMs can also include non-metallic alloys, ceramics, as well as alloys for functional applications. In a nutshell, term CCA can appropriately be utilized as it

18

1 High Entropy Materials (HEMs): An Overview

Fig. 1.4 CALPHAD calculations to design new HEMs: a FCC and BCC equiatomic metallic solid solutions; c–e non-equiatomic CoCuFeMnNi (Gurao and Biswas 2017)

only talks about complexity in composition by incorporating multicomponent in the material. HEMs, although a part of CCMs, can further be expended to include HE glass, HE coatings as well as HE composites. High entropy bulk metallic glass has successfully been synthesized and found to exhibit unique mechanical and magnetic properties (Fang et al. 2018; Ding and Yao 2013). Some of them show excellent soft magnetic properties (Huang et al. 2020; Pavithra et al. 2021). The novel alloy design concept can also be used to design coatings-bond coat, external oxidation resistant coating (Keyvani et al. 2011). Recently, cold spray has been utilized to obtain gold

1.8 Properties

19

quality coating of HEMs on various substrate. Similarly, HEM-based composites containing either soft or hard dispersoids or fibers, exhibiting extraordinary properties, are reported in the literature (Yadav et al. 2019). Thus, the concept of HEMs can be extended to various applications, which make it widely accepted.

1.8 Properties The novel alloy design concept is thought to provide many unique or unusual properties of HEMs. The core effects, high configurational entropy of mixing, lattice distortions, sluggish diffusion, and cocktail effect, are expected to affect the properConf it is expected to ties of HEMs (Pickering and Jones 2016). As pointed out, ΔSMix increase significantly due to the presence of large of number of components in the system with high concentration, affecting both mechanical and functional properties (Zhang et al. 2014b). However, configuration entropy of the solid solution phases, as discussed earlier, will be less than the ideal values. In fact, it is difficult to measure Conf ΔSMix . Computational studies reveal short-range order being present in HEMs. In addition, the presence of multiple phases in the microstructure can further reduce configuration entropy (Li and Raabe 2017; Wu et al. 2021). Therefore, the extent Conf Conf will depend on the amount of increase of ΔSMix in a system. of effect of ΔSMix Lattice distortion is indeed observed in these concentrated multicomponent alloys. The presence of different atomic species of varying size leads to severe distortion of the lattice, which can further be tuned by using specific atomic species and mechanical and physical properties can be tuned (Lee et al. 2018). It is evident, lattice distortion will significantly affect mechanical properties, especially plastic deformation. Although earlier papers proposed that diffusion in HEMs will be sluggish due to the presence of large number of components, the experimental measurements indicate that diffusion is slightly slower in HEMs as compared to the conventional alloys as well as pure metals (Kucza et al. 2018) at identical temperatures. Diffusion co-efficient in HEMs falls within the range of metallic elements if we consider it same/similar homologous temperatures. Nonetheless, diffusion in HEMs is still debatable and complex due to the presence of both cross-terms in the diffusion matrix (Vaidya et al. 2016). Cocktail effect, proposed by Ranganathan, is considered to significantly affect properties of HEMs as minimum five components are used to enhance the properties of HEMs. In fact, each phase in a multicomponent system can be regarded as atomic scale composite and the properties of the composite is considered to be originated not only from the basic properties of individual component but also mutual interactions among all components. As the number of components increases, the interaction among them multiplies. If we consider the cocktail effect in totality, it can range atomical scale multiprincipal element effect to micron scale multiphase effect. Therefore, these four core effects will affect physical, mechanical as well as functional properties of HEMs.

20

1 High Entropy Materials (HEMs): An Overview

A detailed literature review shows that deformation behavior and mechanical properties of HEMs have widely been investigated (Li et al. 2019). This is understandable because any potential structural application mandatorily requires proper understanding of the strengthening and deformation micromechanisms. In this connection, FCC HEMs, especially from 3d-TM series, have extensionally been investigated, both at room temperature as well as high temperature. As FCC HEMs exhibit substantial ductility at RT, these are studied. There studies clearly indicate that planar glide of a/2 ≺110≻ dislocation on plane plays critical role in plasticity in the wide temperature range (77–273 K) (Gludovatz et al. 2014). The dislocation motion on the glide planes will significantly be affected by size difference of the atomic species in HEM. Figure 1.5 indicates the dislocation motion in a multicomponent system (e.g., AlCoCrFeNi) having differently sized atoms in the vicinity expected to be distinctly different from the conventional alloys. The presence of multiple and unequal energy barriers will lead to pinning and jerky motion of the dislocation through the “distorted” lattice. In addition, the presence of stacking faults indicates dissociation of dislocations-revealing the critical role of stacking fault energy (SFE) on the plastic deformation of FCC solid solution. It has been reported that low SFE (~ 18–40 mJ/m2 ) and low activation volume (10–7 b3 ) as well strain rate sensitivity are key feature of these HEMs (Laplanche et al. 2018). At cryogenic temperature, some of the FCC HEMs exhibit extensive twinning, plausibly due to increase of yield stress at low temperature, triggering twinning. Interestingly, extensive twinning leads to extraordinary levels of ductility and fracture toughness (Gludovatz et al. 2014). On the other hand, BCC HEMs have not extensively been investigated, mainly due to the fact that the most of the BCC HEMs exhibit low plasticity at RT (Li et al. 2021). However, few of them show limited ductility, indicating the critical role of a/2 ≺111≻ type screw dislocation dictating the mechanical behavior. However, BCC HEMs exhibit extensive ductility at elevated temperature (1200 °C and above). Unlike FCC HEMs, the deformation in BCC HEMs leads to alternating bands of dislocation populated and dislocation free zones. The deformation micromechanisms of these BCC HEMs need detailed investigation. The deformation of HCP HEMs has not been investigated so far. Although they are relatively new, the main bottleneck in the successful and repeatable synthesis of HCP HEMs consists of metals like Li, Mg, Be, Actinide series of metals. It is also worth mentioning that the strengthening mechanisms of HEMs is important to understand solid solution strengthening, second phase hardening, effect of lattice distortion. Similarly, the mechanical behavior of entropy-stabilized ceramics (oxide, diborides, carbides, etc.) has not been investigated so far. Recent publications indicate the unique functional properties of HEMs, magnetic electrical resistivity thermal conductivity, thermoelectric, hydrogen generation and storage, etc. (Gao et al. 2018). There studies are still in cent stage, requiring detailed investigation. Importantly effort must be directed to design HEMs for specific functional applications by proper and in depth understanding of the functional properties. There are few functional properties which are found attractive to pursue research are then. There include corrosion resistance, soft magnetic behavior, and hydrogen generation as catalyst (Shang et al. 2017).

1.9 The Scope of the Book

21

Fig. 1.5 Schematic showing dislocation motion in a multicomponent FCC (AlCoCrFeNi) HEM with the presence of multiple and unequal energy barriers leading jerky motion (Komarasamy et al. 2016)

1.9 The Scope of the Book Last 15 years, since the discovery in 2004 saw unprecedented growth of the research on HEMs. The conventional materials, i.e., alloys, ceramics, composites, polymers have ruled the material world for last two centuries. The notable examples include steals, Al alloys, zirconia, alumina, C–C composites, etc. However, and everincreasing demand and the stringent requirements of the technology have propelled the scientists to find “out-of-the-box” solution, leading to discovery of novel alloy design concept, “multicomponent multiprinciple” material, popularly known on high entropy alloys (HEAs). HEMs in last 10 years witnessed rapid growth—new HEM forming alloy systems, novel properties, entropy-stabilized ceramics, HE composites, nanostructured HEMs, novel mechanical and functional properties. Opening up new vistas of design and development for multiprincipal multicomponent materials, which has got a big boost with advent of HEA/HEM. With HEM, a new approach of alloy development which seems to close the complexity gap, a will know fact for ages, restricting us to venture into central part of the phase diagram. New design tools and techniques have arrived—ICME, Big Data, IoT, etc. Field inspires new challenges including exploration of hyperdimensional phase diagram, multicomponent diffusion, strength-ductility paradigms, novel ceramics, new functional materials, which inspire the scientific and technological community to pave way for many computation and experimental approaches for accelerated material discovery and innovation. To take a stock of this rapidly advancing field, the present book covers wide range of topic from high entropy alloys to entropy-stabilized ceramic, alloy design to properties, and potential applications to innovation. The first few chapters (2–4) will provide the basic concepts on HEMs, thermodynamics, phase formation rules, physical metallurgy, diffusion in HEMs. There are intended to provide platforms to design HEMs and understand the properties and applications. Chapter 5 will dwell on HE material design using both ICME and genome materials. It will include, HEA ceramics, HE BMG, HE coating, etc. Chapter 6 will discuss synthesis and processing of HEMs in the bulk form; ingot coasting powder metallurgy, additive

22

1 High Entropy Materials (HEMs): An Overview

manufacturing, combinational synthesis, etc. The processing HEM coatings and thinfilm will be discussed in Chap. 7. The novel properties both structural and functional will be discussed in Chaps. 8 and 9, respectively. The potential applications will be dealt with in last two chapters (Chaps. 9 and 10). Chapter 10 will summarize the goals of properly enhancement new application, as well as future directions (Table 1.2). Table 1.2 Conferences, symposiums, and workshops on HEMs Symposium

Meeting

Date

Place

Organizers

BMGs and HEAs

IUMRS-ICA conference

Sep. 25–28, 2010

Qingdao, China

Z. Lu, Y. Li, T. Zhang, X. Hui

BMGs and HEAs

IUMRS-ICA conference

Sep. 19–22, 2011

Taipei, Taiwan J. C. Huang, J. W. Yeh

BMGs and HEAs

IUMRS-ICA conference

Aug. 26–31, 2012

Busan, Korea

E. S. Park, H. Kato, W. H. Wang, J. C. Huang

BMGs and HEAs

IUMRS-ICAM conference

Sep. 22–28, 2013

Qingdao, China

C. T. Liu, Z. Lu, P. K. Liaw

HEAs

MS&T-2012 meeting

Oct. 7–11, 2012 Pittsburgh, USA

M. C. Gao

HEAs (I)

TMS-2013 annual meeting

March 3–7, 2013

San Antonio, USA

P. K. Liaw, G. Y. Wang, M. C. Gao, S. N. Mathaudhu

HEAs (II)

TMS-2014 annual meeting

Feb. 16–20, 2014

San Diego, USA

P. K. Liaw, G. Y. Wang, M. C. Gao, S. N. Mathaudhu

HEAs

Workshop

Dec. 15–16, 2014

Quiyang, China

Z. P. Lu

HEAs (III)

TMS-2015 annual meeting

March 15–19, 2015

Orlando, USA P. K. Liaw, G. Y. Wang, M. C. Gao, S. N. Mathaudhu

1st international workshop on high entropy alloys

Workshop

March 28–29, 2015

Madras, India

B. S. Murty, R. S. Kottada

1st international Conference conference on high entropy materials

November 6–9, 2016

Hsinchu, Taiwan

J.-W. Yeh

2nd international workshop on high entropy alloys

March 11–12, 2017

Hyderabad, India

P. P. Bhattacharya, R. Koteswara Rao

December 9–12, 2018

Jeju, South Korea

H. S. Kim, S. Y. Hong

Workshop

2nd international Conference conference on high entropy materials

(continued)

References

23

Table 1.2 (continued) Symposium

Meeting

Date

Place

Organizers

International conferences on advances in high entropy alloys

Conference

March 14–15, 2019

London, UK

Y. Lu, H. Borkar, M. Pouranvari, B. C. Chukwudi, C. P. Sharma

World congress on Conference high entropy alloys

November 17–20, 2019

Seattle, Washington, USA

Daniel Miracle, John J. Lewandowski

3rd international workshop on high entropy alloys

March 2–3, 2020

Kanpur, India

Krishanu Biswas, Kaustubh Kulkarni

September 27–October 1 2020

Berlin, Germany

Uwe Glatzel

Workshop

3rd international Conference conference on high entropy materials

References F.C. Achard, Recherches sur les propriétés des alliages métalliques (Decker, 1788) M.F. Ashby, K. Johnson, Materials and design: the art and science of material selection in product design (Butterworth-Heinemann, 2013) H. Baker, H. Okamoto, ASM handbook, vol. 3 (Alloy Phase Diagrams, ASM International, Materials Park, Ohio 44073-0002, USA, 1992), p. 501 B. Cantor, Multicomponent and high entropy alloys. Entropy 16(9), 4749–4768 (2014) B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375, 213–218 (2004) K.Y. Chen, T.T. Shun, J.W. Yeh, Development of multi-element high-entropy alloys for spray coating (2002) W.-M. Choi, Y.H. Jo, S.S. Sohn, S. Lee, B.-J. Lee, Understanding the physical metallurgy of the CoCrFeMnNi high-entropy alloy: an atomistic simulation study. NPJ Comput. Mater. 4(1), 1–9 (2018) M.-H. Chuang, M.-H. Tsai, W.-R. Wang, S.-J. Lin, J.-W. Yeh, Microstructure and wear behavior of AlxCo1.5CrFeNi1.5Tiy high-entropy alloys. Acta Materialia 59(16), 6308–6317 (2011) H.Y. Ding, K.F. Yao, High entropy Ti20Zr20Cu20Ni20Be20 bulk metallic glass. J. Non-Cryst. Solids 364, 9–12 (2013) Q. Fang, Y. Chen, J. Li, Y. Liu, Y. Liu, Microstructure and mechanical properties of FeCoCrNiNbX high-entropy alloy coatings. Phys. B 550, 112–116 (2018) M.C. Gao, D.B. Miracle, D. Maurice, X. Yan, Y. Zhang, J.A. Hawk, High-entropy functional materials. J. Mater. Res. 33(19), 3138–3155 (2018) E.P. George, D. Raabe, R.O. Ritchie, High-entropy alloys. Nat. Rev. Mater. 4(8), 515–534 (2019) B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, A fractureresistant high-entropy alloy for cryogenic applications. Science 345(6201), 1153–1158 (2014) S. Gorsse, J.-P. Couzinié, D.B. Miracle, From high-entropy alloys to complex concentrated alloys. C R Phys. 19(8), 721–736 (2018) S. Guo, C. Ng, J. Lu, C.T. Liu, Effect of valence electron concentration on stability of FCC or BCC phase in high entropy alloys. J. Appl. Phys. 109(10), 103505 (2011) N.P. Gurao, K. Biswas, In the quest of single phase multi-component multiprincipal high entropy alloys. J. Alloy. Compd. 697, 434–442 (2017)

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Y.H. Hsu, S.K. Chen, J.W. Yeh, A study on the multicomponent alloy systems with equal-mole FCC or BCC elements (2000) E.W. Huang, G.-Y. Hung, S.Y. Lee, J. Jain, K.-P. Chang, J.J. Chou, W.-C. Yang, P.K. Liaw, Mechanical and magnetic properties of the high-entropy alloys for combinatorial approaches. Curr. Comput.-Aided Drug Des. 10(3), 200 (2020) K.-H. Huang, J.W. Yeh, A study on the multicomponent alloy systems containing equal-mole elements (National Tsing Hua University, Hsinchu, 1996), p. 1 Y.T. Hung, S.K. Chen, J.W. Yeh, A study on the Cu–Ni–Al–Co–Cr–Fe–Si–Ti multicomponent alloy system, master’s thesis of National Tsing Hua University in Taiwan (2001) J. Huo, J.-Q. Wang, W.-H. Wang, Denary high entropy metallic glass with large magnetocaloric effect. J. Alloy. Compd. 776, 202–206 (2019) A. Keyvani, M. Saremi, M.H. Sohi, Oxidation resistance of YSZ-alumina composites compared to normal YSZ TBC coatings at 1100 C. J. Alloy. Compd. 509(33), 8370–8377 (2011) M. Komarasamy, N. Kumar, R.S. Mishra, P.K. Liaw, Anomalies in the deformation mechanism and kinetics of coarse-grained high entropy alloy. Mater. Sci. Eng. A 654, 256–263 (2016) W. Kucza, J. D˛abrowa, G. Cie´slak, K. Berent, T. Kulik, M. Danielewski, Studies of “sluggish diffusion” effect in Co–Cr–Fe–Mn–Ni, Co–Cr–Fe–Ni and Co–Fe–Mn–Ni high entropy alloys; determination of tracer diffusivities by combinatorial approach. J. Alloy. Compd. 731, 920–928 (2018) K.-T. Lai, J.W. Jeh, Microstructure and properties of multicomponent alloy system with equalmole elements, Master’s thesis, National Tsing Hua University (1998) G. Laplanche, J. Bonneville, C. Varvenne, W.A. Curtin, E.P. George, Thermal activation parameters of plastic flow reveal deformation mechanisms in the CrMnFeCoNi high-entropy alloy. Acta Mater. 143, 257–264 (2018) C. Lee, G. Song, M.C. Gao, R. Feng, P. Chen, J. Brechtl, Y. Chen, K. An, W. Guo, J.D. Poplawsky, Lattice distortion in a strong and ductile refractory high-entropy alloy. Acta Mater. 160, 158–172 (2018) Z. Li, D. Raabe, Strong and ductile non-equiatomic high-entropy alloys: design, processing, microstructure, and mechanical properties. JOM 69(11), 2099–2106 (2017) Z. Li, S. Zhao, R.O. Ritchie, M.A. Meyers, Mechanical properties of high-entropy alloys with emphasis on face-centered cubic alloys. Prog. Mater Sci. 102, 296–345 (2019) W. Li, D. Xie, D. Li, Y. Zhang, Y. Gao, P.K. Liaw, Mechanical behavior of high-entropy alloys. Prog. Mater Sci. 118, 100777 (2021) J. Lužnik, P. Koželj, S. Vrtnik, A. Jelen, Z. Jagliˇci´c, A. Meden, M. Feuerbacher, J. Dolinšek, Complex magnetism of Ho–Dy–Y–Gd–Tb hexagonal high-entropy alloy. Phys. Rev. B 92(22), 224201 (2015) D.B. Miracle, High-entropy alloys: a current evaluation of founding ideas and core effects and exploring “nonlinear alloys.” JOM 69(11), 2130–2136 (2017) D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017) S.S. Mishra, A. Bajpai, K. Biswas, TiVCrNiZrFex high entropy alloy: phase evolution, magnetic and mechanical properties. J. Alloy. Compd. 871, 159572 (2021) U. Mizutani, Hume-Rothery rules for structurally complex alloy phases. MRS Bull. 37(2), 169–169 (2012) B.S. Murty, J.-W. Yeh, S. Ranganathan, P.P. Bhattacharjee, High-entropy alloys (Elsevier, 2019) C.L.P. Pavithra, R.K.S.K. Janardhana, K.M. Reddy, C. Murapaka, J. Joardar, B.V. Sarada, R.R. Tamboli, Y. Hu, Y. Zhang, X. Wang, An advancement in the synthesis of unique soft magnetic CoCuFeNiZn high entropy alloy thin films. Sci. Rep. 11(1), 1–8 (2021) E.J. Pickering, N.G. Jones, High-entropy alloys: a critical assessment of their founding principles and future prospects. Int. Mater. Rev. 61(3), 183–202 (2016) S. Ranganathan, Alloyed pleasures: multimetallic cocktails. Curr. Sci. 85(10), 1404–1406 (2003) A. Raturi, N.P. Gurao, K. Biswas, ICME approach to explore equiatomic and non-equiatomic single phase BCC refractory high entropy alloys. J. Alloy. Compd. 806, 587–595 (2019)

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R.E. Reed-Hill, R. Abbaschian, Physical metallurgy principles (PWS Publication, Comp., Boston, 1994), p. 853 O.N. Senkov, G.B. Wilks, D.B. Miracle, C.P. Chuang, P.K. Liaw, Refractory high-entropy alloys. Intermetallics 18(9), 1758–1765 (2010) C. Shang, E. Axinte, W. Ge, Z. Zhang, Y. Wang, High-entropy alloy coatings with excellent mechanical, corrosion resistance and magnetic properties prepared by mechanical alloying and hot pressing sintering. Surfaces Interfaces 9, 36–43 (2017) A.S. Sharma, S. Yadav, K. Biswas, B. Basu, High-entropy alloys and metallic nanocomposites: processing challenges, microstructure development and property enhancement. Mater. Sci. Eng. r. Rep. 131, 1–42 (2018) C. Suryanarayana, A. Inoue, Bulk metallic glasses (CRC Press, 2017) A. Takeuchi, K. Amiya, T. Wada, K. Yubuta, W. Zhang, High-entropy alloys with a hexagonal close-packed structure designed by equi-atomic alloy strategy and binary phase diagrams. JOM 66(10), 1984–1992 (2014) K.M.B. Urs, N.K. Katiyar, R. Kumar, K. Biswas, A.K. Singh, C.S. Tiwary, V. Kamble, Multicomponent (Ag–Au–Cu–Pd–Pt) alloy nanoparticle-decorated p-type 2D-molybdenum disulfide (MoS2) for enhanced hydrogen sensing. Nanoscale 12(22), 11830–11841 (2020) M. Vaidya, S. Trubel, B.S. Murty, G. Wilde, S.V. Divinski, Ni tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys. J. Alloy. Compd. 688, 994–1001 (2016) J.H. Westbrook, R.L. Fleischer, Magnetic, electrical and optical properties and applications of intermetallic compounds (2000) Y. Wu, F. Zhang, X. Yuan, H. Huang, X. Wen, Y. Wang, M. Zhang, H. Wu, X. Liu, H. Wang, Short-range ordering and its effects on mechanical properties of high-entropy alloys. J. Mater. Sci. Technol. 62, 214–220 (2021) S. Yadav, A. Aggrawal, A. Kumar, K. Biswas, Effect of TiB2 addition on wear behavior of (AlCrFeMnV) 90Bi10 high entropy alloy composite. Tribol. Int. 132, 62–74 (2019) J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6(5), 299–303 (2004) C. Zhang, F. Zhang, S. Chen, W. Cao, Computational thermodynamics aided high-entropy alloy design. JOM 64(7), 839–845 (2012) F. Zhang, C. Zhang, S.-L. Chen, J. Zhu, W.-S. Cao, U.R. Kattner, An understanding of high entropy alloys from phase diagram calculations. Calphad 45, 1–10 (2014a) Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructures and properties of high-entropy alloys. Prog. Mater Sci. 61, 1–93 (2014b)

Chapter 2

High Entropy Materials: Basic Concepts

2.1 Introduction As mentioned in the first chapter, the advent of high entropy alloys represents a paradigm shift. The paradigm shift from conventional alloying approach to the transformative alloying of high entropy alloys is illustrated in Fig. 2.1. The conventional approach of addition of alloying elements to a host matrix element limits the possibilities. The new approach of adding multiple principal elements in equiatomic proportion to create simple solid solution alloys is transformative and increases the potential of compositional search space exponentially. For example, addition of Co, Cr, Fe, Mn, and Ni results in a simple face-centered cubic (FCC) solid solution, when all these elements do not have same crystal structure to begin with. This increase in the search space with various combinatorial possibilities is highlighted in reference (Murty et al. 2014). The Hume-Rothery rules for substitutional solid solution alloys mentioned in Chap. 1 have been the guiding principles for selecting alloying elements: • maximum atomic size difference for substitutional solid solution should be lower than 15%, • similar valence electrons, • similar crystal structure, and • similar electronegativity. In this chapter, we will use CoCrFeMnNi (Cantor alloy) and Alx CoCrFeNi alloys as primary examples to discuss various concepts that build the basic understanding. Several aspects discussed in this chapter are built from a review by Sankaran and Mishra (2017). The choice of CoCrFeMnNi alloy is not only driven by the fact that it is very widely researched, but also its embodiment of simplicity and complexity at the same time. Of course, it establishes the first basic principle; there is no single dominant matrix element. Therefore, these alloys are also referred as “multiprincipal element alloys” to capture this fact. It is good to benchmark this alloy against the Hume-Rothery rules and for the ease of access, the values used are from Wikipedia. The atomic radii and crystal structure of each of these constituent elements at room © Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8_2

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2 High Entropy Materials: Basic Concepts

Fig. 2.1 Change in alloy design approach removes the concept of matrix and solute. In high entropy alloys, the overall alloying content exceeds 65% as no single element concentration is above 35%

temperature are Co-125 pm (HCP), Cr-128 pm (BCC), Fe-126 pm (BCC), Mn127 pm (BCC), and Ni-124 pm (FCC). Clearly, while the atomic radii are similar, the crystal structure of all the elements is different. The CoCrFeMnNi alloy forms a FCC solid solution. A series of questions emerge and a few of these are listed below. • What dictates the final crystal structure in a multiprincipal element system or alloy with equiatomic proportions? • In this particular case, the lattice parameter of the final alloy is close to that of Ni. Does the Ni lattice act as the host? • Are all elements truly “principal elements” or one of them has become host because of the final crystal structure selection? Does it depend on the first crystal to solidify? • If Hume-Rothery rules are no longer applicable, what are the new guidelines for selection of elements that will promote full solubility? • How important are criteria of valence electron and electronegativity? These simple questions are not easy to answer and some understanding has developed in the last fifteen years since the first two publications on HEAs appeared in 2004 (Yeh et al. 2004; Cantor et al. 2004). Just from these basic principles of alloying, the concepts can be divided into (a) atomic level considerations and (b) electronic level considerations. We will use this for further discussion. Expansion of High Entropy Alloys to Complex Concentrated Alloys (CCAs): The configurational entropy forms the basis for the name “high entropy materials” (Zhang et al. 2014). The complexity is further enhanced by considering non-equiatomic alloying approach which shifts the nomenclature from HEAs to CCAs. Unlike the equiatomic composition, that occupies a singular central point, the search space shifts from the center and occupies a larger region. It now brings in the concept of major and minor alloying elements (Mishra et al. 2015) (Fig. 2.2). Defining the Novelty of HEAs: An obvious question is “are HEAs novel? The classic framework of Gibbs phase rule has guided alloy design for many decades. For example, if one adds 4–5 elements, a large number of intermetallic phases will form as expected. So, continuation of this approach to HEA compositions can be misleading if the end result is a large number of phases following the Gibbs phase rule. That is the traditional path and mere push to concentrated compositions can be

2.2 Emergence of Four Core Effects—Framing the Basic Concepts

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Fig. 2.2 An illustration of the evolving alloy design shift from the HEA approach to the complex composition search space. Note the initial shift from the traditional corners to equiatomic center; and then movement of compositions away from the center. This expands the search space while maintaining the theme away from the traditional alloying. Adapted from Mishra et al. (2015)

regarded as “not novel”. This is where the central theme of entropy-driven extended solid solution formation becomes a key point. Opinions on what should be considered as HEA differs. A critical review by Miracle and Senkov (Miracle and Senkov 2017) addresses this and readers who want to go deeper on this topic are encouraged to refer to this paper. For the basic discussion here, consideration of CoCrFeMnNi and AlxCoCrFeNi are good to consider the shift from equiatomic composition with single phase F.C.C. matrix to multiphase multiprincipal compositions. In all these compositions, a unique scientific aspect is creation of simple solid solution matrix. The pursuit of complex concentration alloys is to create properties that would be important for engineering applications. So, it is important to keep the scientific discovery space separate from engineering applications of these alloys. Initially, we will focus on the fundamental aspects and then highlight ways to enhance properties to make the alloys attractive for engineering applications.

2.2 Emergence of Four Core Effects—Framing the Basic Concepts We want to cover the initial framework for HEAs set by Yeh (2006) in terms of four core effects in HEAs, (a) the high entropy effect, (b) the lattice distortion effect, (c) sluggish diffusion, and (d) the “cocktail” effect. Right at the outset, we want to emphasize that although not all the effects are proven, these were the basis for treating HEAs differently. With more than 15 years of research from the initial publications, the scientific understanding has evolved and there is quite a bit of experimental data to evaluate some of these basic concepts of core effects. An understanding of the original framing will allow to discuss the emerging pathways. It will provide a basis for separating the discussion of HEAs and CCAs, which finally would be the difference between a scientific exploration and tuning composition-microstructure space for engineering applications. Later in this chapter, as the basic thermodynamics

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and deformation mechanisms are presented, we want to discuss the context of these core effects.

2.2.1 The High Entropy Effect The concept of configurational “entropy” stabilizing the formation of simple solid solution consisting of multiprincipal elements is so fundamental to these alloys that it lends its name to these alloys, i.e., high entropy alloys. This initial argument is setup with a very simple relationship where configurational entropy for the formation of a solid solution from n elements with X i mole fraction is, ΔSconf. , expressed as, ΔSconf. = −R

n 

X i ln X i ,

i=1

where R is the gas constant, 8.314 J/Kmol. This relationship reduced to, ΔSconf. = −R ln n, for equimolar compositions. Using this relationship, if we consider 3–7 elements, the values of ΔSconf. are 1.1R, 1.39R, 1.61R, 1.79R, and 1.95R, respectively. Yeh (2004, 2006) used this to create a definition of what constitutes “high entropy”. Two important groups based on this are (a) medium entropy alloys with ΔSconf. in the range of 1.0R–1.5R and (b) high entropy alloys with ΔSconf. > 1.5R. While it is inadequate in predicting solid solution formation in various combination of elements, the appeal of this definition is its simplicity. It is good to continue this definition as a part of overall approach for HEAs/CCAs. George and co-workers (2013) and Ritchie and co-workers (2016) have discussed ternary alloys as medium entropy alloys (MEAs), while Raabe and co-workers (2015, 2016) are pursuing development of steels and high entropy alloys based on non-equiatomic compositional approach. The entropy of these alloys is in general lower than the equiatomic variant with same number of elements. The importance of expanding the compositional space using a non-equiatomic approach is related to mechanism-based arguments that will be discussed a bit later in this chapter. But it also has an impact on the entropy aspects as well as the lattice distortion aspect that is discussed next. Take an example of a transformative non-equiatomic HEA, Fe40 Mn20 Co20 Cr15 Si5 (Sinha et al. 2019). The configurational entropy of this alloy is 1.44R. Note that Yeh (2004) has defined the compositional range of individual elements in HEA to be between 5 and 35 at.%; so strictly the Fe concentration is higher than this definition, but for this discussion this is a good example for discussion of impact of major and minor elements on configurational entropy. Slight modification of this composition with a minor alloying element Cu (Nene et al.

2.2 Emergence of Four Core Effects—Framing the Basic Concepts

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2019), Fe38.5 Mn20 Co20 Cr15 Si5 Cu1.5 , increases the configurational entropy to 1.51R. Extending this to a hypothetical composition, Fe35 Mn20 Co20 Cr15 Si5 Cu2 X2 Y1 , the value of configurational entropy increases to 1.65R. Note that the five-element equiatomic Cantor alloy has a configurational entropy of 1.61R. So, this core effect can be probed with both equiatomic and non-equiatomic alloying approaches.

2.2.1.1

Connecting the Basic Thermodynamics with Phase Selection

There are two basic aspects that we will present here to complete the discussion on the high entropy core effect. The first is Gibbs phase selection rule, and the second is the total free energy consideration in formation of phases. For HEAs processed by melting of elements together, the key finding is the formation of a single phase solid solution. The Gibbs phase rule states that if a system contains C components and P phases are in equilibrium, then the number of degrees of freedom (F) is given by P + F = C + 2. For most experimental work, the pressure is maintained at atmospheric pressure; therefore, the relationship simplifies to P + F = C + 1. So, for binary alloys with C = 2, the P + F = 3. That means that the values of P can be 1–3, implying that if we fix the temperature and composition of second element, then there will be only one phase. For the eutectic point where 3 phases are in equilibrium, there is no degrees of freedom and therefore the temperature and composition are fixed. Our understanding of equilibrium phases is primarily based on binary and ternary phase diagrams. The simplest of these is the binary phase diagrams. For a limited combination of elements, the binary phase diagrams are isomorphous, i.e., a single solid solution phase exists across the compositional range. For most of the binary phase diagrams, intermetallic phases dominate the compositional space in the middle. Extension of binary phase diagrams to ternary leads to additional phases. Therefore, before the discovery of HEAs, the expectation was that adding more elements together leads to more complex microstructure with many phases. The next consideration is the relative contributions of enthalpy and entropy to the overall stability of a phase. A basic Gibbs free energy relationship is the basis for thermodynamic stability in a number of situations. The Gibbs free energy of a system is given as, G = H + T S,

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where G is the free energy, H the enthalpy, T the absolute temperature, and S the entropy of the system. An obvious question for the high entropy core effect is: What is the role of enthalpy? One way to understand this is again look at the liquid-based processing of HEAs. If the elements are melted, mixed, and cooled to create HEA by solidification, the process starts with nucleation and growth of solid phase. The free energy for this mixture (denoted with suffix “mix”) and the free energy for formation of other phases (denoted with suffix “f ”) can be written as, G mix = Hmix + TSmix , or G f = H f + TS f . Let us take the enthalpy of mixing, Hmix , first. In a binary system if the values of Hmix > 0, it implies that the elements dislike each other—a tendency that will lead to clustering of dissimilar elements. On the other hand, again for a binary system of atoms A and B, if the values of Hmix < 0, it will promote dissimilar A–B bonds which are typical of intermetallic phases. So, for promoting random solid solution as in multielement HEAs, the enthalpy of mixing should be closer to zero Hmix ≈ 0. In that case, the free energy of mixing is directly proportional to the entropy term, TSmix . Based on this, if we consider a temperature close to the melting point, it will lead to the highest value of TSmix . The implication is the solid solution HEAs will have higher stability at higher temperature. Indeed, there are many reports in the last few years that very long-term aging of Cantor alloy at lower temperatures leads to formation of second phase particles. Among multielement alloys, if some atomic pairs have higher negative values of H f , that would also promote formation of intermetallic phases. The intermetallic phase in this case will have higher thermodynamic stability as compared with the solid solution phase. In the Alx CoCrFeNi system, when x > 0.3, second phase formation has been observed.

2.2.1.2

Connecting the Atomic Randomness with Mechanical Properties

When we consider mechanical properties, the distribution of atoms has important implications. All deformation processes are based on two primary mechanisms, (a) formation and movement of vacancies and (b) dislocation-based mechanisms. For atomic processes that depend on formation and movement of vacancies, the binding energy between atom and vacancy is a key thermodynamic consideration. If we consider that the Hmix > 0 for vacancies, then we can ignore vacancy–vacancy interaction. In such conditions, the equilibrium concentration of vacancies, X ve , is given by Porter and Easterling (1995), X ve = exp

−ΔG v , RT

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33

where ΔG v is increase in free energy when vacancy is added to the system. The X ve reaches a value of 10–4 –10–3 at the melting point of solid. In a conventional alloy, we need to consider solute element–vacancy interaction and in many cases this is used to influence a particular aspect of alloy behavior. For example, Ag is added in aluminum alloys to promote higher nucleation density of precipitates through Agvacancy binding. Now, to extend the concept of vacancy-solute binding to HEAs, we face the same question of which solute in a multiprincipal element alloy! Many high temperature processes, like creep and oxidation, also depend on vacancy related processes. The second aspect that we want to consider in this subsection is dislocations. The dislocation line energy per unit length (E/L) is given by Hull and Bacon (2011), ( ) Gb2 R E , = ln Screw dislocation − L 4π ro ) ( Gb2 R E , = ln Edge dislocation − L 4π (1−) ro where G is the shear modulus, b is the Burgers vector, R is the cutoff radius for the strain field, r o is the core radius of the dislocation, and ν is Poisson’s ratio. A critical thing to point here is the shear modulus. The atoms around the dislocation core are displaced from their pristine reference point and have elastic stresses acting on them. Because HEAs are made of up atoms with different individual shear moduli, it is not clear which modulus value is appropriate for these equations. In fact, it can be easily visualized that the shear modulus value along the core will vary depending on the atomic neighbors around the dislocation core. This will lead to fluctuation in the dislocation line energy along the core, which will impact all aspects of dislocation mobility and dislocation–obstacle interactions. A related property is the stacking fault energy (SFE). The stacking fault energy dictates the level of separation between the dislocation partials and dictates the onset of twinning and transformation in fcc metals. Zaddach et al. (2013) have established the SFEs of equiatomic fcc metals from pure Ni to CrMnFeCoNi HEA based on XRD experiments and density functional theory (DFT) simulations (Fig. 2.3). Note that non-equiatomic Cr26 Mn20 Fe20 Co20 Ni14 HEA has the configurational entropy (1.6R) lower than the equiatomic Cantor alloy, the SFE of this non-equiatomic alloy is significantly lower. This has impact on the level of twinning observed in these alloys. This aspect is further discussed with the lattice distortion effect as that also influences the dislocation line energy.

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Fig. 2.3 a Stacking fault energy (SFE) of equimolar fcc metals from pure Ni to CrMnFeCoNi HEA and b SFEs of equiatomic CrMnFeCoNi and non-equiatomic Cr26 Mn20 Fe20 Co20 Ni14 HEAs, as compared with other low SFE alloys (Zaddach et al. 2013)

2.2.2 The Lattice Distortion Effect The lattice distortion effect is based on the fact that atomic radii of constitutive elements of HEA have different sizes. Also, it is important to note that multiple principal elements come together to form a simple crystal structure with a lattice parameter that is quite different from the constituents. For a random solution alloy, each atomic site is occupied probabilistically by one of the constituent elements. Again, if we consider the Cantor alloy CoCrFeMnNi, the atomic radii of the constituent elements in this alloy are similar or have a very low difference. Compared to these elements, Al atom has a much larger diameter. So, the HEAs in Alx CoCrFeNi alloy system have much larger lattice distortions than the Cantor alloy. As shown in Fig. 2.4a, as a consequence of the increase in the compositional complexity, from pure element (Ni) to ternary, quaternary, and to senary HEAs/CCAs, the lattice distortion increases continuously. If the solid solution is truly random, this lattice distortion will be probabilistic in nature. We need to distinguish between the local distortion versus large-scale effect of this. In a dilute solid solution, there are a few sites with larger or smaller atoms. This leads to lattice distortion around the solute atoms. The direct impact of this is on how dislocations interact with lattice strain caused by the solute atom. This is the basis for solid solution strengthening. The magnitude of solid solution strengthening depends on (a) the atomic size mismatch and (b) the modulus mismatch. However, in highly concentrated alloys like HEAs, the classical definition of matrix element and solute element does not apply. Toda-Caraballo and Rivera-Diaz-del-Castillo (2015) have modeled solid solution strengthening in HEAs by considering that the crystal lattice distortion by the solute elements is continuous and the elastic interaction due to atomic size misfit is variable. Their approach included the fact that there is no reference lattice that is modified by the presence of solute atoms, but there is a variation of the interatomic distance in the crystal lattice around its mean unit cell parameter. If we visualize a lattice grid with idealized position of atoms, then because of this lattice distortion, each atom is slightly

2.2 Emergence of Four Core Effects—Framing the Basic Concepts

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displaced from the “ideal lattice position”. Locally, at the atomic level, can this be visualized as lattice strain because the atoms are displaced? One way to think of this issue is elastic strains in crystal. When a crystal is elastically loaded in tension, then the atomic bonds are stretched and this is referred to as elastic strain. So, in a distorted lattice, are all atoms under elastic stress? Although this will cancel out over longer distances and there won’t be any net lattice strain, the interaction of dislocation with these atoms will be different compared to dislocation motion in a relaxed pure element matrix. Some aspects of this lattice distortion can be probed by diffraction techniques. For example, the diffraction peak broadening is expected to be larger for HEAs with high lattice distortion; some work has started emerging in this direction. The impact of lattice distortion on the dislocation line energy variation has been conceptually discussed by Komarasamy et al. (2016) (Fig. 2.4b–e). Additionally, as mentioned earlier, the shear moduli of matrix elements govern the dislocation line energy. All the elements in high entropy alloys have different shear modulus values, and this would lead to the line energy variation along the length of dislocation, as illustrated in Fig. 2.4e. While this aspect has been conceptually discussed, its quantification is needed for development of high performance HEAs/CCAs. What is the impact of lattice distortion on dislocation and twinning? As we look at the fundamentals of each core effect, its linkage(s) with properties is important. For structural properties, understanding of dislocation configuration and mobility is needed. Mishra et al. (2015) proposed that the lattice distortion leads to lattice strain which in turn impacts the energetics and kinetics for dislocations and twins. Figure 2.5a, b show a comparison of the atomic misfit strain and lattice distortion among conventional alloy, Cantor alloy, and Al0.1 CoCrFeNi HEA. The Al0.1 CoCrFeNi HEA has higher lattice distortion because of larger Al atom. Then, what is the energy difference between the lattice without any defect and with a dislocation. Figure 2.5c shows a conceptual illustration of the energy difference (ΔE) because of a dislocation in a conventional pure FCC crystal and a HEA FCC crystal. It hypothesizes that the energy difference is lower for HEAs and therefore it would be easier to nucleate dislocations. Also, similar argument can be extended toward the stacking fault energy. The stacking fault energy of HEAs will be lower because the lattice distortion enhances the ground state energy of the crystal. This has direct impact on twinning and transformation that is discussed next. When the dislocation moves, its sweep because of stress change can be captured as activation volume. Figure 2.5d shows an anomalous behavior in Al0.1 CoCrFeNi HEA, which exhibits a very low activation volume. This means that while dislocation nucleation is easier, its movement is difficult. It is analogous to driving a vehicle on a pebbled road (distorted lattice of HEA) as compared to a smooth road (relaxed lattice of a pure FCC metal). Therefore, addition of Al and Ti as minor/major alloying elements to CrCoFeNi is likely to increase the lattice distortion because of the atomic mismatch. The atomic mismatch, δ, can be calculated based on the relationship (Zhang et al. 2014),

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Fig. 2.4 a Schematic of increase in lattice-distortional with the number of elements as well as selection of elements with the specific atomic size difference (Sankaran and Mishra 2017). Schematic of b atomic arrangement around dislocation core in pure metals and the corresponding dislocation energy with movement in (c), d atomic arrangement around dislocation core in HEA, and e the corresponding energy with displacement (Komarasamy et al. 2016)

┌ | n n  | ( ri )2 δ = √ xi 1 − ,r = x i ri r i=1 i=1 where xi is the atomic fraction, r is the atomic radius of elements, n is the total number of elements in a given HEA/CCA, and r is the average atomic radius. The argument for twinning can be linked with the stacking fault energy of HEAs. Komarasamy et al. (2018) have built on the postulation that lattice distortion will increase the energy state of FCC and along with the increased stability of faulted HCP

2.2 Emergence of Four Core Effects—Framing the Basic Concepts

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Fig. 2.5 Lattice mismatch effect in HEAs: a lattice misfit strain of single phase fcc binary alloys and HEAs and b lattice-distortion effect in Al-(1 at.%)Mg alloy, CrFeCoNi HEA, CrMnFeCoNi HEA and Al2.44Cr24.4Fe24.4Co24.4Ni24.4 HEA. c Schematic drawing showing energy difference for dislocation nucleation in pure element and HEAs, with the influence of lattice strain. E conv is activation energy for dislocation nucleation in conventional alloy, while ΔE HEA is activation energy for dislocation nucleation in HEAs. d Anomalous behavior of the coarse-grained Al0.1 CoCrFeNi HEA with much lower activation volumes, compared to conventional alloys (Mishra et al. 2015)

stacking; a large fraction of the faults (SFs and twins) will be energetically favorable. This framework to reduce the SFE by increasing the lattice distortion of HEAs/CCAs is shown in Fig. 2.6. The conventional discussion on the effect of alloying additions on SFE is also presented (right side). The unique correlation between lattice distortion and the natural tendency to form faults is extremely important in designing HEAs that possess excellent twinnability and work hardenability. This can be further extended to HEAs exhibiting transformation during deformation. Galindo-Nava and RiveraDíaz-del-Castillo (2017) have analyzed the data for austenitic steels to correlate the transition in mechanism with stacking fault energy (Fig. 2.7). When the stacking

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Fig. 2.6 Overall framework for the reduction in SFE via lattice distortion core effect in the case of CCAs (Komarasamy et al. 2018)

fault energy is less than ~ 30 mJ/m2 , then the alloys would exhibit twinning. For alloys that exhibit deformation-induced transformation, the critical stacking fault energy is around 18–19 mJ/m2 . High entropy alloys have lower stacking fault energy as shown in Fig. 2.3 and therefore exhibit twinning readily. Another fundamental which is important to consider is the competition between cross-slip and twinning. If the dislocation can cross-slip easily, then that becomes the dominant mechanism. If cross-slip is difficult, then the alloy twins. Dislocations are dissociated in low stacking fault energy alloys and cross-slip requires constrictions of partials. The stress required for this constriction of course depends on the separation of the partials. So, this aspect also promotes twinning in high entropy alloys.

2.2.3 The Sluggish Diffusion Effect Diffusion is important for many processes and properties at high temperatures. For example, diffusion is key to oxidation, phase transformation, microstructural evolution, thermomechanical processing, creep, and superplasticity. Diffusion involves creation and movement of vacancies. For any material, in the absence any external stress, there is an equilibrium concentration of thermal vacancies. So, the intrinsic enthalpy of formation of vacancies is dependent on the bonding energy of that element. The applied stress influences the thermal equilibrium concentration of

2.2 Emergence of Four Core Effects—Framing the Basic Concepts

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Fig. 2.7 Variation in the volume fraction of α ' , ε, and twinning for different stacking fault energies at ε = 60% (Galindo-Nava and Rivera-Díaz-del-Castillo 2017)

vacancies as well as it creates diffusional flux for stress-driven processes. A very good example of this is diffusional creep of materials. The lattice diffusion primarily involves creation and movement of monovacancies. As mentioned earlier, there is an equilibrium concentration of vacancies at any given temperature. In a conventional FCC lattice, the coordination number is 12. So, a vacancy results in breakage of bonds with 12 neighboring atoms. In the previous section, we discussed the lattice distortion effect’s impact on dislocation core energy variation. Similarly, it can be visualized that some atomic configurations lead to energy wells. The impact of such configurations can be on the activation energy of diffusional processes. The impact can extend to the frequency term as well, which can be lower due to such lower energy points in the lattice; effectively serving as a trap for point defects. The early works of Yeh and co-workers (2004, 2006) have shown slower microstructural coarsening kinetics in HEAs. It was inferred from these observations that the diffusivity in HEAs is lower. Such observations are growing, although Miracle and Senkov (2017) analyzed the data and questioned the claim relating to diffusional activation energy. Both diffusional coefficient and pinning effects impact the overall microstructural stability in a solid solution alloy. This gets more complicated in precipitate containing alloys, where temperature-dependent solubility of elements becomes important. For multiprincipal

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element matrix, this behavior is expected to be more complex than traditional alloys. While the fundamental questions still require careful considerations, the slower grain growth kinetics have been documented in many HEAs. These evidences come for annealing under quasi-static conditions and far-from-equilibrium processing like friction stir processing and additive manufacturing.

2.2.4 The “Cocktail” Effect The cocktail effect is perhaps the most intriguing among the four core concepts. Ranganathan (2003) used the keyword “cocktail” in his thought-provoking paper titled “Alloyed pleasures: Multimetallic cocktails”. The conjecture here is that highly alloyed metallic materials can develop combination of unusual properties because of this effect. A key question can be based on the mechanical behavior combination of strength, toughness, fatigue, and ductility. Can unpredictable combination of properties result in HEAs because of multiple principal element approach? Ranganathan (2003) discussed the unpublished work of Yeh’s group on HEAs and compared with “gum metal” (Saito et al. 2003) and bulk metallic glasses. Let us take a quick example of the gum metal. It was so named because it exhibited high strength, low modulus, little to no work hardening and large ductility. The observation of large elongation with no work hardening led to Saito et al. (2003) claiming superelasticity and superplasticity. They proposed that lack of work hardening was due to dislocation-free plastic deformation. Is this mechanism defendable? Many researchers over the years have been probing this question! In conventional metallic alloys, the work hardening rate is proportional to the uniform elongation and by extension relate to the overall ductility. So, if the gum metal does not exhibit any work hardening, why the failure processes don’t start early? Is this the “cocktail” effect? It is possible to argue that the early results do show trends that establish exceptional properties in singular mode, meaning that one of the strength-toughness-fatigueductility properties is high in a particular alloy. For example, exceptional toughness has been reported in an alloy that has relatively low strength. In a more recent example, Mishra et al. (2020) have shown that the stability of γ (f.c.c. phase) and ε (h.c.p. phase) in a Fe–Mn–Co–Cr–Si high entropy alloy system can be dramatically altered with minor addition of Cu or Al. For example, the Fe40 Mn20 Co20 Cr15 Si5 has ε-phase dominant microstructure at ambient temperature. Just altering the composition to Fe38.5 Mn20 Co20 Cr15 Si5 Cu1.5 by minor addition of Cu stabilizes the γ phase completely which then undergoes deformation-induced transformation (TRIP effect). Would such an observation of profound change in metastability of an alloy through minor chemical variation constitute cocktail effect? Can this effect be used for concurrent enhancement of strength-toughness-fatigue-ductility?

2.3 High Entropy Alloys and Ceramics: Definition and Classification

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2.3 High Entropy Alloys and Ceramics: Definition and Classification Similar to the conventional alloys, several different strategies can be used to classify HEAs and then link them to CCAs. This short section is based on four reviews (Tsai and Yeh 2014; Murty et al. 2014; Zhang et al. 2014; Senkov and Miracle 2016). Figure 2.8 shows a very comprehensive compilation of elements used in all alloys referred as multiprincipal element alloys (MPEAs). Here we have used the terms HEAs and CCAs synonymously with MPEAs. As mentioned at the outset, unlike conventional alloys, the HEAs do not follow the paradigm of host element or solvent– solute framework. So, many researchers prefer the nomenclature of multiprincipal element alloys to imply the lack of a host or dominant element. More recently, a trend is emerging that attaches a prefix of “high entropy” to all the classes of engineered materials. We need to consider if this approach is appropriate. Let us start with metals and alloys which are disordered crystalline materials. Most engineering alloys have f.c.c. or b.c.c. or h.c.p. crystal lattice structure. No specific lattice site is designated for a particular element, i.e., a substitutional solute atom can occupy any lattice site. On the other hand, intermetallics are ordered crystalline materials. For example, in NiAl which has B2 crystal lattice structure, all the corner atoms of a b.c.c. cell can be Ni atoms and the center atom is then Al atom. It is important to note that such an arrangement promotes A–B bonds. Let us now substitute a fraction of Ni with a third element. Then some of Ni–Al bonds will be replaced by X–Al bonds, changing the overall energy of the system. If we keep pushing to enough number of elements where Ni sites are now occupied by a number of different elements and the Al sites are occupied by a number of other set of elements. What is the overall lattice energy of such a “high entropy NiAl” or “high entropy intermetallics”. If we consider the dislocations as the primary means of accomplishing meaningful plasticity, then is the distinction between solid solution intermetallic and binary intermetallic critical for the configuration of dislocations that result from ordered crystal structure? Will such “high entropy intermetallics” exhibit very distinct behavior? Emerging work on f.c.c.-B2 eutectic HEA microstructure provides potential to probe such questions.

2.3.1 Constituent Element-Based Classification In a detailed compilation, Miracle and Senkov (2017) have noted that 3d transition elements have so far dominated the HEA efforts. Based on this, the classification scheme is written as (a) 3d transition element-based HEAs and (b) refractory metal HEAs. The 3d transition element-based systems provide opportunities to explore deformation mechanisms and strength-toughness-fatigue-ductility optimization. The Cantor and Yeh alloys fall under this category. The refractory HEAs (RHEAs) provide high temperature capabilities and are mainly b.c.c. alloys. An example of RHEA is the WNbMoTaV alloy (Senkov et al. 2011).

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Fig. 2.8 Miracle and Senkov (2017) created this infographics to illustrate the choice of elements in multiprincipal element alloys (MPEAs). They considered 408 MPEAs. It shows that the first 15 years of MPEA research was dominated by choice of Al, Co, Cr, Cu, Fe, Mn, Ni, and Ti. Taken from Miracle and Senkov (2017)

2.3.2 Traditional Crystal Structure-Based Classification This approach is rather simple, and the classification scheme is simply written as (a) FCC, (b) BCC, and (c) HCP. A vast majority of the 3d transition element-based HEAs are FCC. Most of the RHEAs are BCC. So far there are only a few reports on HCP HEAs.

2.3.3 Microstructure-Based Classification This approach suits the CCAs best, as it allows to build complex microstructure based on simple structure matrix. Let us consider conventional alloys to deduce a few high level microstructural approaches. Overall, the matrix elements can be simply classified on the basis of allotropic transformation. For example, aluminum is FCC at all temperatures, and magnesium is HCP at all temperatures. So, aluminum

2.3 High Entropy Alloys and Ceramics: Definition and Classification

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Fig. 2.9 Variation of lattice constant and hardness of the Alx CoCrFeNi alloys as functions of Al content. Note the phase change with increasing Al content. Taken from Wang et al. (2012)

and magnesium alloys do not go through any allotropic transformation. Strengthening in these alloys is obtained through solid solution strengthening, grain boundary strengthening, precipitation strengthening, dispersion strengthening, and composite strengthening. The choice of alloying elements and desired second phases are based on these strengthening mechanisms. In contrast, iron and titanium have allotropic forms. For example, Fe is BCC at low temperatures and pressure, and this phase is referred as alpha (ferrite) phase. At higher temperatures, the gamma (austenite) phase with FCC crystal structure is stable. Whereas at high pressures, the epsilon phase with HCP crystal structure is stable. Alloying of iron creates various steels which go through temperature and deformation-based transformations. Such matrix elements are very attractive for designing alloys that can activate various deformation mechanisms and are excellent for designing HEAs/CCAs. The phase transition as a function of Al variation in an Alx CoCrFeNi system is shown in Fig. 2.9. Alloys can, therefore, be simply classified as, (a) single phase solid solution alloys, (b) dual-phase or multiphase solid solution alloys, (c) precipitation strengthened alloys, (d) dispersion strengthened alloys, and (e) composites. Of course, this can be extended or subdivided based on other microstructural features and/or strengthening mechanisms.

2.3.4 Density-Based Classification The density-based classification is also a simple approach that is important for engineering applications. In such cases, instead of absolute values, the specific properties

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(property/density) are considered. The structural efficiency can be increased by maximizing the specific properties. The classification using the density-based approach can be: • Lightweight HEAs—similar to the conventional alloys where titanium, aluminum, and magnesium alloys are considered lightweight alloys, one can use ~ 5 g/cc as a cutoff density value for lightweight HEAs. So far, research in this category is quite limited because the constituent elements that can be used are quite restrictive. Several of these elements are not amenable for casting route, so the efforts so far are based on powder-based processing. • Medium-weight HEAs—conventionally, steels, nickel-based alloys, and cobaltbased alloys belong to this group. So, the upper limit of density for this group can be set around 8.5 g/cc. The CoCrFeMnNi HEA belongs to this group. The transition-element-based HEAs are very amenable for conventional casting-based processing. These HEAs can be thermomechanically processed using traditional infrastructure, which is very important for adaptability and commercialization of HEAs for structural applications. • Heavy-weight HEAs—the refractory element containing HEAs or RHEAs fall in this category.

2.3.5 Deformation Mechanism-Based Classification Recently, Li et al. (2017) have published metastable dual-phase HEAs which are also examples of non-equiatomic compositional approach. Their Fe50 Mn30 Co10 Cr10 alloy had FCC and HCP phases. The metastability of the FCC phase leads to deformationinduced transformation (TRIP). Many of the 3d element HEAs show twinning during deformation (TWIP). As highlighted in Fig. 2.7, manipulation of stacking fault energy through alloying can trigger TWIP and TRIP mechanisms. Based on this, the HEAs can be classified as (a) TWIP HEAs, if they exhibit twinning during deformation, and (b) TRIP HEAs, if they exhibit phase transformation during deformation. Both these mechanisms can be very important for the concurrent enhancement of strengthtoughness-fatigue-ductility. Mishra et al. (2020, 2021) have reviewed the impact of TRIP behavior on the strength, ductility, and fatigue in metastable HEAs.

2.4 Composition Notation The best way to capture the HEA composition is atom% or mole fraction. It is a good practice to simply follow the alphabetical listing of elements in equiatomic compositions, for example, the Cantor alloy CoCrFeMnNi. For non-equiatomic compositions, it is meaningful to list in the order of atom% of the element, for example, Fe35 Mn25 Co20 Cr15 Si5 alloy.

References

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References B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375–377(1–2), 213–218 (2004) A. Gali, E.P. George, Tensile properties of high- and medium-entropy alloys. Intermetallics 39, 74–78 (2013) E.I. Galindo-Nava, P.E.J. Rivera-Díaz-del-Castillo, Understanding martensite and twin formation in austenitic steels: a model describing TRIP and TWIP effects. Acta Mater. 128, 120–134 (2017) B. Gludovatz, A. Hohenwarter, K.V.S. Thurston, H. Bei, Z. Wu, E.P. George, R.O. Ritchie, Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures. Nat. Commun. 7, 1–8 (2016) D. Hull, D.J. Bacon, Introduction to dislocations (Elsevier, 2011) M. Komarasamy, N. Kumar, R.S. Mishra, P.K. Liaw, Anomalies in the deformation mechanism and kinetics of coarse-grained high entropy alloy. Mater. Sci. Eng. A 654, 256–263 (2016) M. Komarasamy, S. Shukla, N. Ley, K. Liu, K. Cho, B. McWilliams, R. Brennan, M.L. Young, R.S. Mishra, A novel method to enhance CSL fraction, tensile properties and work hardening in complex concentrated alloys—lattice distortion effect. Mater. Sci. Eng. A 736, 383–391 (2018) Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off. Nature 534(7606), 227–230 (2016) Z. Li, C.C. Tasan, K.G. Pradeep, D. Raabe, A TRIP-assisted dual-phase high-entropy alloy: grain size and phase fraction effects on deformation behavior. Acta Mater. 131, 323–335 (2017) D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017) R.S. Mishra, N. Kumar, M. Komarasamy, Lattice strain framework for plastic deformation in complex concentrated alloys including high entropy alloys. Mater. Sci. Technol. 31(10), 1259–1263 (2015) R.S. Mishra, S.S. Nene, M. Frank, S. Sinha, K. Liu, S. Shukla, Metastability driven hierarchical microstructural engineering: overview of mechanical properties of metastable complex concentrated alloys. J. Alloys Compd. 842, 155625 (2020) R.S. Mishra, R.S. Haridas, P. Agrawal, High entropy alloys–Tunability of deformation mechanisms through integration of compositional and microstructural domains. Mater. Sci. Eng. A 812, 141085 (2021) B.S. Murty, J.W. Yeh, S. Ranganathan, High entropy alloys (Butterworth Heinemann Publications, London, UK, 2014) S.S. Nene, M. Frank, K. Liu, S. Sinha, R.S. Mishra, B.A. McWilliams, K.C. Cho, Corrosion-resistant high entropy alloy with high strength and ductility. Scr. Mater. 166, 168–172 (2019) D.A. Porter, K.E. Easterling, Phase transformations in metals and alloys (Chapman & Hall, 1992) K.G. Pradeep, C.C. Tasan, M.J. Yao, Y. Deng, H. Springer, D. Raabe, Non-equiatomic high entropy alloys: approach towards rapid alloy screening and property-oriented design. Mater. Sci. Eng. A 648, 183–192 (2015) S. Ranganathan, Alloyed pleasures: multimetallic cocktails. Curr. Sci. 85(10), 1404–1406 (2003) T. Saito, T. Furuta, J.H. Hwang, S. Kuramoto, K. Nishino, N. Suzuki, R. Chen, A. Yamada, K. Ito, Y. Seno, T. Nonaka, H. Ikehata, N. Nagasako, C. Iwamoto, Y. Ikuhara, T. Sakuma, Multifunctional alloys obtained via a dislocation-free plastic deformation mechanism. Science 300(5618), 464– 467 (2003) K. Sankaran, R.S. Mishra, Metallurgy and design of alloys with hierarchical microstructures (2017) O.N. Senkov, D.B. Miracle, A new thermodynamic parameter to predict formation of solid solution or intermetallic phases in high entropy alloys. J. Alloys Compd. 658, 603–607 (2016) O.N. Senkov, J.M. Scott, S.V. Senkova, D.B. Miracle, C.F. Woodward, Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy. J. Alloys Compd. 509(20), 6043– 6048 (2011)

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S. Sinha, S.S. Nene, M. Frank, K. Liu, P. Agrawal, R.S. Mishra, On the evolving nature of c/a ratio in a hexagonal close-packed epsilon martensite phase in transformative high entropy alloys. Sci. Rep. 9(1), 1–14 (2019) I. Toda-Caraballo, P.E.J. Rivera-Díaz-del-Castillo, Modelling solid solution hardening in high entropy alloys. Acta Mater. 85, 14–23 (2015) M.H. Tsai, J.W. Yeh, High-entropy alloys: a critical review. Mater. Res. Lett. 2(3), 107–123 (2014) W.R. Wang, W.L. Wang, S.C. Wang, Y.C. Tsai, C.H. Lai, J.W. Yeh, Effects of Al addition on the microstructure and mechanical property of Al xCoCrFeNi high-entropy alloys. Intermetallics 26, 44–51 (2012) J.-W. Yeh, J.W. Yeh, Recent progress in high-entropy alloys. Ann. Chim. Sci. Mater. 31, 633–648 (2006) J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6(5), 299–303+274 (2004) A.J. Zaddach, C. Niu, C.C. Koch, D.L. Irving, Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. JOM 65(12), 1780–1789 (2013) Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 61, 1–93 (2014)

Chapter 3

Phase and Microstructural Selection in High Entropy Materials

3.1 Introduction It is evident now that HEMs are multicomponent equiatomic or non-equiatomic solid solutions; most of which form a random solid solution with few being partially ordered and equiatomic multicomponent amorphous phases (Guo and Liu 2011; Cantor et al. 2004; Amiri and Shahbazian-Yassar 2021). However, we are interested in the crystalline solid solutions, their formation, and stability here. Hence, it has been proven beyond doubt that the formation of single phase solid solution is the key in these multicomponent systems. Therefore, it is essential to know the rules of formation of a single phase in the HEMs to design and develop novel HEMs. In metallic systems, single phase HEMs with FCC, BCC, and HCP crystal structure have predominantly been reported. However, for the ceramic system, HCP and FCC solid solution phases have been reported (Zhang et al. 2019; Zhang and Akhtar 2019). In this regard, it is important to note that Hume-Rothery rules have been reported to dictate the criteria for the formation of solid solution phases. About 100 years ago, William Hume-Rothery identified four (4) key factors responsible for the formation of substitutional solid solutions; atomic size difference, crystal structure, valency, and electronegativity difference of the constituents of the solid solution phase (HumeRothery and Coles 1969). The atomic size difference must be less than 8% for a complete solid solution. However, for terminal solid solubility, the difference in radius between solute and solvent must be less than 15%. The constituent must have some or similar crystal structure with the same valence. In addition, the constituents should have the same electronegativity for the formation of the solid solution. For the last 100 years, these rules have been used as guiding principles for selecting elements forming solid solution phases. Darken and Garry (2016) have used these rules to represent the charts for the selection of alloying elements. Figure 3.1 shows a map representing electronegativity versus atomic diameter for different elements. The alloying elements forming a solid solution can easily be found by drawing an ellipse with an atomic size difference of 15% (x-axis) and electronegativity difference

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Fig. 3.1 (a) Electronegativity of elements vs. size of atomic species (Darken and Gary 2016); (b) Relationship between δ and ΔH mix for multicomponent alloys; “solid solution” indicates the alloy contains only solid solution, “ordered solid solution” indicates minor ordered solid solution precipitate besides solid solution, and “intermediate phase” indicates intermetallics in HEAs (Zhang et al. 2008)

of 0.4 (y-axis). This allows us to visualize the representation of Hume-Rothery rules and hence, the selection of alloying elements to form a solid solution. Later on, Miedema and his co-workers (1980) used certain Hume-Rothery parameters (electronegativity difference) along with the difference in electron density at the boundary of the Wigner–Seitz cells of pure metals to calculate the heats of formation of binary alloys, )2 ( )2 ( ΔH = −P ∅∗ + Q Δn 1/3 −R ws

(3.1)

Here ∅∗ = electronegativity difference, Δn ws = difference in electron density at Wigner–Seitz cell and P, Q, R are constants. Subsequently, others have utilized these parameters; atomic size, electronegativity difference and electron density to predict solid solution formation and even predict even degree of solid solubility of different elements in a particular host element. Therefore, it is evident that the solid solubility in both metallic alloys and ceramics can be achieved by selecting components satisfying Hume-Rothery rules, which are still found to be sacrosanct for alloys. However, whether these rules can be applied to multiprincipal element multicomponent alloys need to be seen. In this chapter, we shall first discuss the design strategies to find HEM forming compositions and phase selection approaches to obtain single and multiphase metallic HEMs as well as oxides, borides, carbides, etc.

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3.2 Alloy Design Strategies HEMs, being multicomponent and multiprincipal elemental alloys with a simple solid solution, are challenging to design. Fundamentally, the design of HEMs involves the proper selection of components (elements or compounds) and composition of an individual component so that mixing them together will lead to the formation of simple solid solution phases (FCC, BCC, HCP). A simple calculation will reveal an astronomical number of all such combinations possible. If we consider 67 metallic elements present in the periodic table, the number of 5-components equiatomic (all component having equal concentration) alloy systems is 67 C5 = 9,657,648. Hence, in principle, an astronomical number of alloys can be designed. This number can further be increased by simply varying the composition of anyone of the five components, such as Alx CoCrFeNi. It is well known that Al addition to equiatomic CoCrFeNi alloy has a significant effect. For x < 0.2, FCC solutions are stabilized. However for x > 0.5, BCC solutions form and for 0.2 < x < 0.5, a mixture of BCC and FCC solid solutions are observed (Wang et al. 2012). Hence, by varying Al concentrations, a large number of alloys can be designed. If we intend to design non-equiatomic alloys, in which the concentration of each element can be varied from 5 to 35 atom%, the number of permutations can be extremely large. Therefore, it is important to devise strategies to design these alloys in a time bound and effective way. The fundamental question regarding the design of HEMs is what kind of phases and crystal structures are expected to form when we mix so many different elements in different proportions. In other words, answering whether a simple solid solution phase form over intermetallic compounds when we mix 5 or more components. Finally, we would like to design alloy compositions that form simple solid solutions. The design tools predominantly utilized are the parametric approach, which is primarily an empirical methodology; CALPHAD and the ab initio approach. In the following, each of these methodologies will be discussed in detail. However, we shall first deliberate on thermodynamic, geometric, and the electronic factors utilized for design (Gao et al. 2016a; Yifan et al. 2015).

3.2.1 Predicting Solid Solubility from Hume-Rothery Rules Thermodynamic and geometry effect. It is well known that the phase formation in any system, in general, is controlled by Gibbs free energy change, given by ΔG mix = ΔHmix − T ΔHmix

(3.2)

Here, ΔG mix = free energy change, ΔHmix is the enthalpy of mixing, ΔSmix = entropy of mixing and T = temperature. Although − T ΔSmix is positive and has a relatively high value at high temperatures for the commercial alloys, it is

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strongly believed that ΔSmix has a significant effect on the design of multicomponent multiprincipal materials. This is because of the fact that a substantial increase in cont ΔSmix due to the presence of a large number of components can lead to a significantly high value of − T ΔSmix term. However, the magnitude of ΔG mix will also depend on competition between ΔHmix and ΔSmix , which will also be affected by a large number of components in the system. Therefore, one needs to estimate both ΔHmix and ΔSmix properly to obtain ΔG mix . This is a daunting task for multicomponent systems, given that the mutual interactions among different components are not known in the literature. Additionally, the solid solutions may not be perfectively random, and hence, the proper estimation of ΔSmix will be difficult. The other contribution of ΔSmix , especially, magnetic, vibrational, and electronic parts may be significant for some alloy systems, making the estimate difficult. Nonetheless, both ΔHmix and ΔSmix will significantly be altered due to the multicomponent nature of the HEMs, and many of these high order interactions are not adequately known. The other important factors controlling phase formation are atomic size, electronegativity, and valency (Guo and Liu 2011; Guo et al. 2011). The important one is known relative size difference among the atoms, which was brought forward by Hume-Rothery almost a century ago. As HEMs are substitutional solid solutions, relative atomic sizes are expected to play a significant role (Wu et al. 2018). In a binary solid solution, the atomic size difference can easily be estimated by taking the difference in the atomic size. It is defined explicitly as %δ =

(dsolute − dsolvent ) × 100 dsolute

(3.3)

Here d’s stand for atomic diameter. In a multicomponent system, this cannot be defined so simply. Although there exist many different ways to define it, in general, it is defined as (Guo and Liu 2011). ┌ | N ( |Σ ΣN δ = √ xi 1 − di / i=1

j=1

) xjdj

(3.4)

Here x i , x j are compositions of ith and jth elements, d i , d j are the atomic diameters of ith and jth elements. Another important parameter controlling phase formation stability as well as physicochemical properties is the electron concentration. In general, this corresponds to the number of valence electrons per formula unit for a particular alloy composition. There are two ways of defining electron concentration as depicted in the literature (Guo et al. 2011; Poletti and Battezzati 2014); (a) the number of total electrons, including d-electrons in the valence band (VEC) and (b) the average number of iterant electrons per atom (e/a). The significance of (e/a) originates from Hume-Rothery electron concentration rules (Poletti and Battezzati 2014), stating that electron compounds are stable for specific values of e/a. On the other hand, valence electron concentration (VEC) is considered the key parameter, connecting

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51

the density of stales for given energy to the design and development of HEMs. VEC plays a significant role in the stability of the solid solution phases depending on the strong interaction between Brillouin zone and the Fermi surface (Guo et al. 2011). Importantly, the equivalency of the constituent elements in the stabilization of simple solid solution phases, FCC, BCC, or HCP can easily be correlated with the electron concentration effect. VEC, when compared to e/a ratio, is straightforward to estimate and hence is used widely. The other two factors, i.e., valency and electronegativity difference among the constituent elements, must be as small as possible. The large difference between valency and electronegativity is expected to lead to compound formation compared to a solid solution (Hume-Rothery and Coles 1969). Subsequently, various alloy design principles adopted for the design and development of HEMs will be deliberated.

3.2.2 Parametric Approach Parametric approach has widely been utilized by researchers across the globe to design new HEM compositions (Guo and Liu 2011; Hu et al. 2017; Pickering and Jones 2016). This is an empirical approach based on thermodynamic and geometrical factors, i.e., Hume-Rothery rules. It is easy to understand why this approach was extensively used in the early days after the discovery of HEMs in 2004. HumeRothery rules are the earliest guides for the design of solid solutions (Hume-Rothery and Coles 1969). It also considers relative atomic sizes, crystal structures, electronegativity, and valence electron concentration (VEC) as parameters for deciding solid solution formation. Basically, the parametric approach combining Hume-Rothery rules and the thermodynamic factors to design had HEMs-constituents and their compositions. However, equations connecting each of the above parameters are modified for multicomponent systems by using weighted composition terms for both differences in atomic radii as well as electronegativity. The thermodynamic considerations are reflected by using ΔHmix , ΔSmix , melting temperature (Tm S) and Ω. These are described below; Σ ΔHmix = 4 Hi j Ci C j (3.5) i> j

ΔSmix = −R

N Σ

xi Ci xi

(3.6)

i=1

Tm S = Ω=

Σ

Ci Tm

(3.7)

Tm S ΔSmix | ΔHmix |

(3.8)

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3 Phase and Microstructural Selection in High Entropy Materials

Hume-Rothery factors are defined by taking into consideration the multicomponent system, i.e., by considering the weighted average approach. √ δ=

Σ

√

( ri )2 Ci 1 − r

( xi )2 Ci 1 − x Σ VEC = Ci VECi

ΔX =

Σ

(3.9)

(3.10) (3.11)

Here, r i , x i , VECi and T m,i are atomic radius, electronegativity, valence electron concentration and melting temperature of any component i, C i and C j are role fractions of ith and jth component, respectively (Guo and Liu 2011). In fact, ΔHmix is usually estimated using Miedema’s approach, i.e., the enthalpy of mixing of elements i and j at the equimolar concentration in a regular binary solution (Niessen et al. 1983). These parameters (Eqs. 3.4–3.11) are thus estimated using available data of various elements or components and utilized to determine whether a combination of elements is expected to form solid solution phases. However, we need to know the range of values for each of the parameters (3.4–3.11) to conclude the possibility of formation of a solid solution. Hence, it is first essential to obtain an accurate estimate of each of the parameters, followed by finding the range of values required for the formation of the solid solution phases. In fact, this is the reason this technique is known as the parametric approach. This can be done by plotting ΔHmix versus δ for a large number of available alloy compositions. Figure 3.2 shows such a plot for both HEMs and BMGs. Based on the experimental findings (basically X-ray diffraction analysis of the synthesized alloys), different zones in the plot are marked as S = disordered solid solution, B1/B2 = bulk metallic glasses (BMG), S 1 = solution phases with a small number of precipitates. It is evident that solid solutions are expected to form when δ < 6.6% and ΔHmix varies from − 5 to + 5 kJ/mol. As compared to a binary solid solution, a lower value of δ is required as a large number of component atoms can only be accommodated in the solid solution lattice by using a lower value of δ. A significant value of δ is likely to destabilize the solid solution phases. On the other hand, BMGs can accommodate larger δ and more negative ΔHmix as compared to HEMs. Zone C is marked crystalline, meaning the intermetallic phases (IMC) are likely to form. Another important parameter used in this approach is ΔSmix , which can significantly lower the free energy via −T ΔSmix term, and hence, lower the tendency for segregation and ordering during processing. Hence, higher ΔSmix is likely to promote the formation of a solid solution. The effect of ΔSmix in the formation of a solid solution will be significantly felt at relatively high temperature because free energy of mixing is given by; ΔG mix = ΔHmix − T ΔSmix

(3.12)

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Fig. 3.2 Effect of Ω and δ parameters on the phase stability in HEAs (George et al. 2019)

Experimental findings have shown that for some HEMs, the solid solution phases form in preference to IMCs due to the high value of ΔSmix . Figure 3.2 reveals a 3D plot showing the combined effect of ΔSmix , ΔHmix and δ on the formation of different phases; random solid solution, intermetallic phases, bulk metallic glasses (BMGs) as well as ordered solid solution phases. It is evident that random solid solution phases are likely to form for ΔSmix < 16.5 J/mol-K, − 15 < ΔHmix < 5 kJ/mol and δ < 6.6%. On the other hand, BMGs are likely to form for 10 < ΔSmix < 17 J/mol-K, − 5 < ΔHmix < − 30 kJ/mol and 7.5 < δ < 16%. In order to obtain a combined effect of ΔSmix and ΔHmix , a new parameter, Ω can be coined, revealing the stability of the solid solution phases in a better way (Ye et al. 2016). Ω is defined as; Ω=

Tm ΔSmix |Hmix |

(3.12)

Here, T m in the average melting temperature obtained from the combined effect of all the components present in the system, as shown in Eq. 3.6. This new parameter has found its origin in our earlier discussion on ΔG mix , dictating the relative stability of any phase. It is evident from Eq. 3.12 that the ΔG mix strongly depends on the ΔSmix is apt. Figure 3.3 relative values of −T ΔSmix and ΔHmix , hence the ratio T|H mix | shows the variation of Ω as a function of different phases in multicomponent alloys, solid solution, BMGs, and intermetallic phases. It is evident that for HEMs Ω > 1.1 and Ω < 6.6%. BMGs and IMCs require a higher value of δ and lower values of Ω. Another factor controlling phase formation in these complex concentrated alloys is the electron concentration. The type of solid solution formation can be predicted by estimating valence electron concentration (VEC). The HE solid solutions in general

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3 Phase and Microstructural Selection in High Entropy Materials

Fig. 3.3 Relationship between VEC and the fcc, bcc phase stability for HEA systems (Guo et al. 2011)

form in FCC, BCC, and HCP structures or a mixture of them. FCC HEMs are found to exhibit reasonably good ductility and strength. BCC and HCP HEMs show high strength with low plasticity. Guo et al. (2011) have predicted that the formation of FCC, BCC, or HCP solid solutions is possible for different values of VEC. FCC phase can only exist for VEC ≥ 8.0; FCC + BCC phases can co-exist for 6.87 ≤ VEC < 8.0; and BCC phase can only exist for VEC < 6.87; HCP phase can form for VEC ≤ 3.8. In addition to the abovementioned parameters, a few other parameters have also been utilized to obtain the possibility of the formation of different solid solution phases. These are worth mentioning in the broader perspective of the parametric approach, extensively utilized for the design of HEMs. One is mismatch entropy, connected with the atomic size difference among the constituent elements or components. [ ) ΔSmismatch 3 3( 2 ς − 1 y1 + (ς − 1)y2 = k 2 2 ] { } 1 − (ς − 1)(ς − 3) + ln ς (1 − y3 ) and, 2 1 ς= 1−ρ

(3.14)

Here ρ is the packing fraction and y1 , y2 , and y3 are dimensionless parameters are given as follows, y1 =

n 16 Σ (ri + r j )(ri − r j )3 ci c j σ 2 j≥i=1

3.2 Alloy Design Strategies

y2 =

55 n ) 16σ 2 Σ ( ri r j (ri − r j )2 ci c j 3 2 (σ ) j≥i=1

(σ 2 )3 (σ 3 )2 n Σ σk = 2 ci rik y3 =

i=1

Here, r i , and r j are the atomic radii of ith and jth element. Raghavan et al., upon analyzing a large number of HEMs, have shown that the ratio ΔS conf / ΔS fusion can also be used as a screening parameter to decide on the formation of equiatomic and non-equiatomic solid solutions, i.e., ΔS conf / ΔS fusion > 1 for equiatomic and ΔS conf / ΔS fusion < 1.2 for a non-equiatomic solid solution (Raghavan et al. 2012). Hence, the success of the parametric approach depends on the proper and accurate determination of these parameters, as described earlier. This discussion clearly reveals the empirical nature of the parametric approach, indicating the estimation of various parameters to arrive at a conclusion regarding the formation of solid solutions in the HEM forming system. Therefore, this is purely based on the estimation of a large number of parameters, and the success rate of such an approach is low and should be utilized with a caveat (Hu et al. 2017). Nonetheless, this approach is simple and widely utilized to find multicomponent systems forming simple solid solution phases.

3.2.3 CALPHAD Approach Over the years, the phase diagrams in metallurgy and material engineering have been used to design novel alloys like daily routine in our life. Hence, the phase diagrams have always been considered roadmap, guiding us to find pathways to design materials. Essentially, they provide us with information about the different phases present in the form of temperature and concentration of alloying elements. One can also easily obtain the volume fraction, composition, and transformation temperature of phases. As these diagrams provide vital information on the phases, phases diagram of almost all binary (2-component) and many ternary (3–component) systems have experimentally been determined (Senkov et al. 2019; Qi et al. 2019). However, the determination of such diagrams for higher order systems (quaternary, quinary, etc.) is difficult and hence, remains completely unexplored. For high entropy materials, which are complex, concentrated alloys containing more than 4 components, information on phases, composition, the transformation temperature, etc., seem to be essential for the development of these materials. Thus, the design of HEMs is challenging as no phase diagram is available for five or higher component systems, and we need to understand the combined effect of five elements on phase formation

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3 Phase and Microstructural Selection in High Entropy Materials

at a time (Qi et al. 2019). This can be, to the maximum possible extent, achieved by adopting the CALPHAD approach (Gorsse and Senkov 2018). CALculation of PHAse Diagram (CALPHAD) is basically known to be a method for calculation of phase diagrams with the help of advanced computation tools. It is worth mentioning here that this approach has extensively been utilized in various fields of research, including alloy design, corrosion, and environmental science (Qi et al. 2019; Shi et al. 2011). It has been found to be robust because it allows us to estimate the thermodynamic properties of higher order multicomponent systems by method of extrapolation of the available data in the lower order (binary or ternary) systems. CALPHAD calculations, therefore, are carried out in two steps. First, utilize some well-established models for extrapolation of Gibbs free energy of the available lower order systems to obtain those for the higher order systems. This is followed by an estimation of the concerned phase(s) for the lowest energy configuration of the overall systems (Qi et al. 2019). The first step is critical and important as the utilization of a proper extrapolation model is vital for the accuracy of the calculation. The following will provide the details of the scheme of the CALPHAD. The free energy of any phase ψ can be written as (Ye et al. 2016) G = G o + G ideal + G xs

(3.15)

Here Go is the standard Gibbs free energy of the mechanical mixture of the constituent phases, Gideal is free energy for the ideal solution and Gxs in the excess Gibbs free energy. The estimation of Gψ , critically depending on Gxs , can be done using the well-established models, including regular solution models, stoichiometric model, as well as the sublattice model (Sundman et al. 2018). In the case of a regular solution model, the free energy of the binary alloy is given by; ] [ G = x A G oA + x B G oB + [x A la x A + X B ln X B ] + XAXB

n Σ [

G i (x A − x B )i

]

(3.16)

x j=0

The first two terms represent the free energy of the mechanical mixtures (Go ). The third and fourth terms represent free energy of ideal mixing (Gideal ) and excess free energy (Gxs ), respectively. After obtaining the free energy of the individual phases in the binary systems using (3.15), the Gibbs free energy of higher order (quaternary, quinary, etc.) systems can be obtained via extrapolation of the excess energy of the corresponding binary systems. This can be done for any composition of the higher order system. In the literature, various methods are available to carry out this extrapolation. The notable ones are Muggianu’s equation (Choi 1988), Kohler’s method (Choi 1988), and Toop’s method (Choi 1988). In the following, we shall discuss each of these extrapolation methods. It is worth noting that Muggianu’s equation has widely been used to extrapolate the free energy of binary to ternary (Choi 1988; Manasijevic et al. 2005).

3.2 Alloy Design Strategies

57

] [ G δ = x A G oA + x B G oB + xC G Co + RT[ad ln x A + x B ln X B + xc ln xc ] + XAXB

n AB Σ

G i AB(x A − x B )i + x A xC

j=0

+ x B xC

n BC Σ

n AC Σ

G iAc (x A − xi )i

j=0

Cn BC(x A − xi )i

j=0

Similarly, Kohler’s method uses the following approximation to obtain the excess free energy term. { ( )} xA − xB xA xS L oAB + L lAB xA + xB xA + xB xA + xB { ( )} x B − xC x x c B L oBc + L lAB + (x B + xc )2 x B + xC x B + xC x B + xC { ( )} x A − xC x x C A L oAC + L lAC + (x B + xc )2 x A + xC x A + xC x A + xC

G xs = (x A + x B )2

Toop’s equation utilizes a similar form of the equation to derive the excess free energy. { o } 1 G XS x = x A x B L AB + L AB (x A − x B − x C ) { } + x A xC L oAC + L 1AC (x A − xC − x B ) { } + x B xC L oBC + L 1BC (x B − xC − x A ) Here, L stands for interaction terms for the binary couples, which are available for most binary systems. Hence, these extrapolations allow us to estimate the excess free energy of higher order systems by utilizing interaction terms. Figures 3.4a–c reveal the schematic representation of the extrapolation for each of the methods described earlier. It has been shown that for extrapolation of excess free energy for ternary systems from individual binaries, constituting the ternary phase diagram and hence, these methods work fine for ternary systems. However, extrapolation of ternary to higher order systems via these methods would mean oversimplification of these methods for higher order systems. Therefore, this would possibly lead to some error in the estimation of excess free energy for quaternary, quinary, and higher order systems. In the absence of properly available models as well as interaction parameters for quinary, quaternary, and quinary systems, nothing better can be done better than those described. Hence, the CALPHAD approach is considered the most reliable one for interpolating between the binaries with higher order systems. As the existing databases utilize the binary as well as ternary thermodynamic data, extrapolation is mandatorily required, reducing the accuracy of the prediction via CALPHAD. Nonetheless, this provides a good predictive capability. For example, one of the widely investigated

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3 Phase and Microstructural Selection in High Entropy Materials

Fig. 3.4 Distributions of multiprincipal element alloys by categories. Fractions of a SS phases, b IM phases, and c (SS + IM) phases equimolar alloys in 3- to 6-component alloy systems at solidus temperature (T m ) and 600 °C (Senkov et al. 2015)

HEA forming systems is AlCoCrNi, showing various microstructures as a function of Al concentration (Miracle and Senkov 2017). It is worth mentioning that the phase diagram predicted by using extrapolation of binary and ternary databases matches well with the experimental results (Gorsse and Senkov 2018). Hence, different databases can now be constructed using available binary and ternary phase diagrams using extrapolation methodologies. For HEMs, even different versions of databases are now available (2004) to fine-tune the values of the thermodynamic parameters. However, it is also important to check the accuracy and “creditability” of the databases before coming to a conclusion on calculations. Recently, it has also been made possible to find out the “creditability” of any database by adopting the following procedure. Each of the available databases is generated using some binary as well as ternary systems, and hence, each alloy composition is being modeled by available database samples of binary and ternary systems. For example, in a quinary system (S-T-V-U-W), there exist 10 binaries (S-T, S-U, S-V, S-W, T-V, T-U, T-W, U-V, U-W and V-W), 6 ternaries (S-T-U, S-T-V, S-T-W, T-V-W, T-V-U, V-U-W), 3 quaternaries (S-T-V-U, S-T-U-W, T-V-U-W), and 1 quinary (S-T-V-U-W). Let us assume that the available databases for this system are S-T, S-U, S-V, T-U, T-V binaries and S-T-V, as well as S-U-V ternaries and no quaternary. Therefore, for the quaternary system, STUV, available databases are 5 binary and 2 ternaries out of 6 binary and 4 ternaries, respectively. Hence, the fraction of systems with available databases is 5/6 for binaries and 2/4 for ternaries. For the quaternary system, SUVW, in another database, the only database for 2 binaries and no ternary are available, and hence, the fraction of binary is 2/6 and the fraction for ternary is 0. This means that different systems can have different values of fraction for binary and ternary databases available, and therefore, the credibility of any CALPHAD calculation depends on the absolute magnitude of these fractions. Extensive investigations have revealed that a reasonably good agreement is achieved when the value of these fractions reaches as close as 1, whereas nominal agreement can be found if the maximum possible value of the fraction is 0.6 (Lukas et al. 2007). It is also important to describe some other facets of the CALPHAD approach. CALPHAD calculations have extensively been utilized to investigate phase diagrams

3.2 Alloy Design Strategies

59

of about 140,000 different equiatomic alloys having 3–5 elements. These estimations reveal that the chance of formation of solid solution phases rapidly decreases as the number of components N increases. This prediction seems to be valid for any value of fraction at temperatures above 600 °C. Secondly, temperature has been found to have a profound influence on phase formation. This is obvious as ΔG(= ΔH − T ΔS) is strongly dependent on the −T ΔS term. Therefore, single phase alloys may have a solid solution (SS) with less frequent intermediate phases (IP). However, SS phase fields need to be extended, and IP fields are to be restricted. It has also been found that if a multicomponent alloy follows four Hume-Rothery rules, the CALPHAD calculations predict the alloy to be single phase SS. However, vice versa, i.e., all alloys compositions, predicted by CALPHAD to form single phase SS, obeying 4 Hume-Rothery roles is not true. These calculations also reveal that the prominent phases are FCC, BCC with L12 , B2, Laves and M5 Si3 as IP phase for the most creditable database (f AB ~ 1). However, for fraction < 1, HCP, M5 Si3 , B2, FCC phase are observed (Senkov et al. 2015). In case CALPHAD databases are unavailable, it may even be possible to design HEM forming compositions by phase diagram inspection (Perrut 2015). However, such analysis may not always be accurate. It has been observed that the components exhibiting isomorphous solid solutions or relatively large terminal solid solubility in their binary or ternary phase diagrams are likely to form a multicomponent solid solution. The notable examples include Nb–Mo–Ta–W, Hf–Nb–Ta–Ti–Zr, Co–Fe– Ma–Ni. The inspection of binary phase diagrams of the constituents reveals that each of the binary couples forms an isomorphous phase diagram or shows large solid solubility (Gao and Alman 2013). Cotton et al. have recently utilized the terminal solid solubility aspect in binary phase diagram as a key parameter to design lightweight HEMs for aerospace applications. In this regard, it is worth mentioning that three types of the binary phase diagram showing solid solubility need to be considered (i) isomorphous (complete solid solubility) type (Nb–W), (ii) phase diagrams showing extended terminal solid solution (Cr–Ra-showing BCC and HCP solid solution), and (iii) intermediate solid solution phase showing extended solid solubility (Cr–Rh). Hence, it may be possible to find alloys, which are likely to form HEMs by using this approach. In the following, we shall describe, briefly, each of these in order to provide the avid reader how such an approach can be implemented in the absence of thermodynamic database. (i) All binaries showing extended solid solubility. As mentioned earlier, the binary phase diagrams can provide a guiding path to design new HEMs without the need of any other input. The simplest way to design single phase HEM-FCC, BCC, or HCP, is to consider a quinary system in which each of the binaries shows extended or complete solid solubility. Obviously, such systems cannot frequently be found. Let us first consider the FCC solid solution. Phase diagram inspections reveal that each of the edge binaries in CuNiPdPt, CuNiPdPtPh system form FCC solid solution; hence, these quaternary and quinary alloys are likely to form FCC solid solution. As for BCC solid solutions are concerned, one can cite several examples. BaCaErYb, BaErSrYb, BaCaErYb, CaErSrYb

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3 Phase and Microstructural Selection in High Entropy Materials

are likely to form single phase BCC solid solution as each edge binaries form BCC isomorphous system excerpt Eu–Sr and Sr–Yb in which phase diagram information is not available (Gao and Alman 2013). However, wide experience suggests that these two systems may resemble Ca/Ba–Eu and Ca/Ba–Yb binaries. Similarly, Mo–Nb–Ta–Ti–V–W system is likely to form a single phase BCC solid solution because all the edge binaries show an isomorphous phase diagram. In fact, one can design 22 different quaternary, quinary equiatomic (equimolar) alloys using this scenery system. ] [ 4C6 + 5C6 + 6C6 = 15 + 6 + 1 = 22 The experimental studies have shown the formation of some of the quaternary and quinary alloys (Nagase et al. 2018). Another important example is CoOsReRa (Gao and Alman 2013). Phase diagram analysis reveals that all the six binaries [4C2 = 6] exhibit isomorphous HCP solid solution. The most important example following this concept is HEMs based on rare-earth (RE) elements: Dy, Er, Gd, Ho, Lu, Sc, Sm, Tb, Tm, and Y (Gao et al. 2016b). The corresponding quinaries exhibit that the individual binaries exhibit stable HCP solid solution, and hence, one can design a large number of equiatomic multicomponent alloys, i.e., quaternary alloy, [ 4C10 + 5C10 + 6C10 + 7C10 + 8C10 + 9C10 + 10C10 = 78 + 210 + 120 + 45 + 10 + 1 = 974] Moving ahead, some of the elements from the actinide series form a double HCP (DHCP) structure. Notable examples include La, Ca, Pr, Nd, and Pm. Hence, quaternary and quinary equimolar alloys; CeNdPmPr, CeLaPmPr, CeNdPmPr, CeLaNdPm, LaNdPmPr, and CeLaNdPmPr can be designed using this approach. (ii) Combining binary systems showing isomorphous phase diagram with systems exhibiting large terminal solid solubility The phase diagram approach based on the isomorphous type of phase diagrams of end members in a multicomponent system is a well-proven route, but it is limited to only a few systems. In reality, we observe a large number of binary phase diagrams exhibiting large terminal solid solubility instead of continuous or extended solid solubility. Hence, it may be possible to design HEMs by combining isomorphous solid solutions with a phase diagram having large terminal solubility in lower order systems. Let us consider the Cantor alloy; equiatomic CoCrFeMnNi alloy. It is evident that Co–Fe, Co–Ni, Fe–Mn, Fe–Ni, and Mn–Ni show isomorphous type phase diagrams. On the other hand, Co–Cr, Co–Mn, and Co–Ni binaries reveal FCC phase with large solid solubility. It is now believed that FCC solid solution in CoCrFeMnNi systems forms over IM σ-phase (which appears in Co–Cr, Fe–Mn systems). It also provides a new design approach in the following manner. Once a single phase HEM forming systems are identified, which is typically based on an isomorphous solid solution approach; many new alloys can be designed by substituting any one

3.2 Alloy Design Strategies

61

element by a new element which shows extended terminal solid solubility with a majority of the alloys forming system. Such an analogy can be used to explain the formation of BCC solid solution due to the addition of Re to Mo–Nb–Ta–Ti–V–W system. It has been observed that Re exhibits extensive large solid solubility with each of the elements in Mo–Nb–Ta–Ti–V–W system. (iii) Presence of intermediate phase with a sizeable compositional homogeneity range Some binary and ternary phase diagrams exhibit the presence of an intermediate phase with a reasonably large compositional homogeneity range. Figure 3.5 shows the binary equilibrium phase diagram of Cr–Rh system (Okamoto et al. 2016), revealing the presence of an intermediate HCP phase with a large compositional homogeneity range (52–82 at.%. Rh). Similarly, the presence of HCP intermediate phase in the various binary phase diagrams (Mo–Pd, Mo–Rh, Mo–Ru) allows us to design multicomponent HCP solid solution Mo–Pd–Rh–Ru (Gao et al. 2016b). Using chemical similarity between Pd and Pt as well as Rh and Ir, one can design various HEMs, Mo–Pt–Rh–Ru, Mo–Ir–Pt–Rh, Mo–Ir–Pt–Rh–Ru, Mo–Ir–Pd–Pt–Rh–Ru. To conclude, phase diagram information, i.e., careful inspection of available binary and ternary phase diagrams, can effectively be utilized to design multicomponent multiprincipal component (or element) HEMs. In fact, by selective and intelligent addition of elements to the prescribed binary or ternary system, one can design various HEMs. The following aspects must be considered in order of preference. i. isomorphous solid solution for all the end members. ii. isomorphous solid solution in most of the ternary isothermal and isopleth sections. iii. isomorphous solid solution in most of the binary end members as well as reasonably large terminal solid solubility in some end members with the absence of stable compounds and immiscibility. iv. isomorphous solid solution in some of the end members for binaries as well as the absence of compounds and complete immiscibility in the solid state. v. Intermediate solid solution phases with a large range of compositional homogeneity, preferably at the middle of binary and ternary phase diagrams for the majority of the systems. It is thus believed that the phase diagram inspection can be considered an important tool for the design of HEM composition.

3.2.4 Ab Initio Approach It has been mentioned earlier that HEMs, in general, can be obtained by intermixing multiple components (chemical species) on a relatively simple crystal structure, which are thermodynamically stable phase (Tsai and Yeh 2014). Practical experiences show that most of their mixture using random chemical species will not lead

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3 Phase and Microstructural Selection in High Entropy Materials

Fig. 3.5 Example experimental binary phase diagrams that show isomorphous HCP solid solution in Re–Ru, large terminal HCP and BCC solubilities in Cr–Ru, and large homogeneity range of an intermediate HCP phase in Cr–Rh binary (Gao et al. 2016a)

to HEMs. Rather, this leads to the formation of complex intermetallic phases. In lower order systems (binary, ternary), the phase diagrams reveal the thermodynamic stable states as a function of chemical composition and temperature. However, phase diagrams of higher order systems; quaternary, quinary, senary, etc. are not known and prediction of HEM forming compositions seems to be a daunting task. Conceptually basic principle required to predict stable HEM phases is based on the minimization of the Gibbs free energy of the solid solution phases compared to the compound formation (Tsai and Yeh 2014). However, this requires estimation of free energies of all possible phases (experimentally reported and theoretically predicted phases) involved as a function of composition and temperature, which is a challenging task even for simple systems (Ikeda et al. 2019). In this regard, the ab initio approach can effectively be utilized. Ab initio calculations using quantum mechanics allow us to calculate the total energy for even specific crystal structure at OK (zero Kelvin)

3.2 Alloy Design Strategies

63

and extension of this to finite temperature via the application of statistical mechanics (Tian 2017). In fact, the statistical mechanics-based approach allows us to estimate entropy by including various components of entropy along with enthalpy using the quantum mechanical treatment. As compared to CALPHAD approach, which relies on thermodynamic databases, ab-initio-based approaches perform exceedingly well for low-temperature stability where enthalpies of formation are unreliable; finding transition temperature, phase diagram topology etc. is more accurate (Turchi et al. 2007). The majority of these approaches are based on either DFT (Density Functional Theory) calculations or AIMD (Ab Initio Molecular Dynamics) simulation (Paquet and Viktor 2018). DFT calculation is related to the direct means of obtaining the electronic structure of individual atomic species using the Schrödinger equation (Bagayoko 2014). It is worth mentioning that the determination of electronic structure is considered a vital tool for the prediction of the properties of any material. DFT calculations can be utilized to estimate accurate values of ΔH, δ, VEC of the solid solution phases as well as stable intermetallic phases. Following this, accurate data can be used to predict the stability of phases for different alloy compositions. However, the identification of stable compounds or solid solution phases in higher order systems (4 or 5 or higher components) using DFT is computationally extensive and even formidable (Ikeda et al. 2019). The incorporation of the temperature effect can make the computation even more intensive and challenging. In order to circumvent these aspects, the following criterion, proposed by Tropoarevsky et al. (2015), for the formation of equimolar single phase HEMs can be utilized: −RTcritical

N Σ

| | x j ln x j ≥ | Hi j |max

(3.17)

ji=1

Here T critical represents critical temperature, which can be set based on application temperature. For example, T critical can vary from 0.55 to 0.6, T m being the approximate melting temperature of the alloy. |H ij |max is considered the absolute enthalpy value for the most stable intermetallic compounds in a particular system. The application of this criterion for all the six alloys has shown that only CoCrFeMnNi equimolar alloy satisfies the Tropoarevsky criterion. The other five alloys do not satisfy Eq. (3.17), leading to the formation of multiple phases. The simple tool with accurate values of T critical and (H ij )max has also been applied to other HE forming compositions (even with 5–7 components) and found to be satisfied for alloys as listed Table 3.1. Hence, this approach involving DFT, in fact, provides a straightforward way of computer screening as the entropy data of almost all the transition metal binaries are available, and phase stability of compound phases are well documented due to DFT calculation. Therefore, this easy and straight forward approach has been utilized to design HE forming composition. However, there are a few caveats one needs to remember while utilizing this approach. Firstly, it underestimates the total number of possible equiatomic compositions for alloys containing Al and Ti or Al

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3 Phase and Microstructural Selection in High Entropy Materials

and Nb (please refer to Table 3.1), which do not satisfy Eq. (3.17) but are experimentally verified (Nagase et al. 2018; Santodonato et al. 2018). A simple calculation for the Al–Ti system would reveal the fallacy of using this approach. It is known that the most stable Al–Ti binary compound has ΔH f = − 428 meV/atom (Rogal et al. 2017). Hence, we need to design an equimolar alloy with at least 50 components at 1000 °C to compensate ΔH f factor in the Eq. (3.17). A similar discrepancy has also been found in the phase formation in other systems, including MoNbTaWZr, MoNbTaVZr, HfMoNbTaW, HfMoNbTaV, and HfMoNbTaTi, refractory HEA systems in which the predictions do not match with experimental observation. Secondly, the model is silent about the crystal structure of the phases, which would satisfy the Eq. (3.6). One must not forget that it is a challenging and daunting task to predict all the competitive intermetallic phases versus solid solution phase (3.6) for higher order systems. The task becomes extremely challenging if phase diagrams are not available. However, a simple approach by Tropoarevsky can provide us with computer screening but has been found not to be full proof. Hence, there is a need for a better approach to find the HE forming compositions. It is well known that the tendency to form any intermediate phase or intermetallic compounds during solidification processing is connected with interatomic bond strength, i.e., the stronger the bond strength, the higher the possibility of compound formation. Hence, this can provide us with a tool to predict the formation of solid solution phases in multicomponent higher order systems. However, accurate estimation of the bond strength of all possible compounds in a HE forming system is also a daunting task because these strongly depend on the crystal structure. In this regard, AIMD (Ab initio molecular dynamics) simulations can come handy to screen alloy composition (Paquet and Viktor 2018). AIMD simulations in the liquid state can provide important information about the preferred bond in any complex alloy, which may have an impact on the formation of a disordered solid solution. Nonetheless, it is challenging to predict all the competitive intermetallic phases versus solid solution phase for higher order systems. However, AIMD simulations can even provide a signature of the formation of solid solution phases in multicomponent systems. For example, AIMD simulations on the liquid in Al1.25 COCuFeNi alloy reveal that the preferred bond pairs are AlNi, CrFe, and CuCu, and hence, the chance of nucleation of B2, BCC, and FCC phases is relatively high as these precursors will be present in the liquid. Hence, it can be concluded that the disordered solid solutions are likely to form liquid structure, which lacks strong elemental segregation or any short-range order. To confirm, Gao et al. have carried out AIMD simulations on single phase solid solutions, i.e., HfNbTaTiZr (Gao et al. 2015), HfNbTaTiVZr (Gao et al. 2015), GdDyLnTbY (Gao et al. 2016a), CoOsReRn (Gao and Alman 2013), MoPdRhRn (Gao et al. 2016b), as well as multiphase Al1.3 CoCrCuFeNi (Gao and Alman 2013), and even high entropy glasses (Gao and Alman 2013) using Vienna Ab Initio Simulation Package (VASP) in a typical canonical ensemble (constant mole, volume, and temperature with atomicconfiguration relaxation) and temperature controlled by a Nose–Hoover thermostat

0.26

6.6

140

124.6

126.4

127.4

125.2 1.66

1.54

1.91

1.55

1.83

146.5

124.6

126.4

127.4

128.2

ratom

1.91

1.55

1.83

1.88

EN

0.204

9.0

4.44

134.6

124.6

126.4

127.4

125.2

ratom

CoVFeMnNi

1.63 1.48

2.16

1.91

1.55

1.83

1.88

EN

TiCrFeMnNi

0.194

0.184

127.8

126.4

127.4

128.2

125.2

ratom EN

Δ av

1.88

1.90

1.55

1.83

1.66

1.88

EN

CoMoFeMnNi

V

Ti

Mo

0.188

124.6

1.91

Cu

Ni

126.4

1.55

Mn

128.2

127.4

1.66

1.83

Cr

125.2

Fe

1.88

EN

ratom

CoCrFeMnCu

EN

ratom

CoCrFeMnNi

Co

Element

0.194

1.63

1.91

1.55

1.66

1.88

EN

4.6

134.6

124.6

126.4

128.2

125.2

ratom

CoCrVMnNi

Table 3.1 The six alloy systems containing elements (Co, Cr, Cu, Fe, Mo, No, V, Ti) have been investigated using DFT as well as parametric approach (Otto et al. 2013)

3.2 Alloy Design Strategies 65

66

3 Phase and Microstructural Selection in High Entropy Materials

(Evans and Holian 1985). In fact, PAW potentials, as well as revised Perdew–Burke– ErnZerhof-gradient approximation, have been utilized (Toda-Caraballo and RiveraDiaz-del-Castillo 2016). Following this, partial pair distribution functions (PDFs) were generated using nb nb 1 ΣΣ V δ|r y| − 1 g AB (r ) = Z a Z b 4πr i=1 j=1

(3.18)

Here, V stands for volume of the supercell, Z a , Z b are the number of elements type A and B, |r ij | is the distance of different configurations. Accordingly, species-specific PDFs of different HEMs in the liquid are shown in Figs. 3.6 and 3.7. The detailed analyses of the PDFs indicate that the intensity of the first nearest neighbor peak is similar for all except the Cr–Cr pair. This means that Cr would prefer to bond with other elements rather than itself. This seems to be consistent with the atomic structure of CoCrFeNi as well as CoCrFeMnNi solid solution obtained via DFT calculations. Similarly, the partial PDFs of two BCC solid solutions (MoNbTaVW and HfNbTaTiZr) are shown in Fig. 3.6. In particular, Mo–Ta and Ta–W pairs show a slightly higher peak intensity for the first nearest neighbors and the same for all the pairs. One can also look into the PDFs for HCP high entropy alloys, such as DyGdLaTbY, CoOsReRu, MoPdRhRu in the liquid state. Figure 3.7 shows the partial PDFs of these three HEMS forming compositions. It is well known that both DyGdLaTbY and CoOsReRu show extended HCP solid solutions for all the edge binaries and hence are expected to form multicomponent solid solutions. The PDFs for DyGdLaTbY reveal uniform first nearest neighbor peak intensities for all the pairs. However, PDFs of CoOsReRu show that the intensity of the first nearest neighbor peak is uniform for all the pairs except for Co–Co and Re–Re. However, the variation of intensity is low for these two pairs. Therefore, the formation of solid solutions in these two systems can nicely be justified using this concept. For MoPdRhRu, the first nearest neighbor peak of PDFs for all the pairs except Mo-Mo clearly shows the lower intensity of the first nearest neighbor peak, and hence, Mo would like to bond preferably with others especially with Pd, Rh, and Ru. Experimental investigations reveal that HCP intermetallic phases form in the MoPdRhRu system. Interestingly, similar AIMD calculations on multiphase forming HEMs, Al1.25 CoCrCuFeNi also reveal a clear picture of the preferred bond pair in the liquid state. The formation of binary or ternary intermetallic compounds is more likely than a simple multicomponent solid solution, i.e., B2–NiAl, BCC (Cr–Co–Fe) and FCC Cu-rich (Cu–Ni) phases, which is in consonance with experimentally observed microstructure by Tong et al. (2005). Hence, the foregoing discussion has categorically revealed that AIMD simulations perhaps provide us with better predictability for computer-based screening of multicomponent solid solution-based alloys and should be followed for other systems to discover new alloys.

3.2 Alloy Design Strategies

67

Fig. 3.6 AIMD-simulated partial correlation functions of a MoNbTaVW at T = 3100 °C and b HfNbTaTiZr at T = 2500 °C (Gao et al. 2016a)

Fig. 3.7 AIMD-simulated partial correlation functions Al1.25CoCrCuFeNi at T = 1800 °C (Gao et al. 2016a)

of

a

AlCoCrFeNi

and

b

3.2.5 Pettifor Map Approach to Predict the Formation of HEMs The “alloy world” is pretty big and can broadly be categorized into four different categories: crystalline solid solutions, crystalline intermetallic phases, quasicrystalline and amorphous or glassy based on the atomic structure. When we mix multiple elements in different proportions, it is extremely challenging to predict the type of structure of the material will form or that is likely to form, and hence, serious and concerted efforts have been directed to develop predictive capability using models, equations, and computation tools to decipher the structure type which might form. As far as solid solution phases are concerned, the well-known Hume-Rothery rules form the basis for the selection of elements or components, i.e., relative atomic size, electronegativity as well as valency to form solid solution (Hume-Rothery and Coles 1969). This has been discussed earlier in this chapter of the book. However,

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3 Phase and Microstructural Selection in High Entropy Materials

Hume-Rothery rules rarely talk about the structure that can be formed by mixing two or three components. Adding another factor, known as bond orbitals, Pettifor has developed another unique methodology to predict the structure of the binary and ternary intermetallic compounds of different types, AB, AB2 , etc. (Takeuchi et al. 2015). In this approach, Pettifor has generated a number for each element in the periodic table, creating a chemical scale. This number assigned to any element is known as the Mendeleev number (Takeuchi et al. 2015). It needs to be mentioned here that the Mendeleev number is, indeed, a phenomenological concept with no mathematical treatment involved. However, this can be utilized as one dimensional string, passing through the two dimensional periodic tables having a large number of metals. Figure 3.3 shows such a map. The path of the string will vary based on the type of compound formation. For example, for the AB compound, the path of the string will provide the best structural separation and accordingly, the elements which are neighbors in their atomic number happen to have different Mendeleev numbers and vice versa. However, it means that the elements with neighboring Mendeleev numbers are likely to form compounds with a similar structure. Therefore, this phenomenological concept allows us to differentiate among various structures while mixing two or three elements. It is to be noted here that the Pettifor map has already received wide applicability to obtain information about the structure of the binary compounds. This is more subtle for the design of HEMs, which is based on the value of ΔH mix , atomic size difference (δ), electronegativity, and valency. However, such an approach does not include any information about the structure of the phases to be formed. This is because the values of ΔH mix frequently utilized in the design of HEMs are for the binary liquids, which are more likely to be valid for amorphous or glassy alloys. Therefore, it is pertinent to estimate the value of ΔH mix for commonly observed HEMs in metallic systems; BCC, FCC, and HCP, instead of using values for amorphous or liquid states. The resultant ΔH mix , even if estimated, will be extremely complicated and cannot be directly used for the efficient design of HEAs. Hence, in reality, the design of HEAs of the different crystal structures is done based on VEC, which is strongly related to constituent elements or pure metals, as VEC of each element in the periodic table depends on the group and the crystalline structure of each element has been found to change in consonance with the group in the periodic table and VEC. In contrast, binary alloys, when formed, do not exhibit such a trend. For example, the binary alloy with an equiatomic composition (A50 B50 ) has frequently been observed to exhibit different crystal structure from that of the constituent elements, e.g., Mg–Y, Hf–Os, Os–Zr, forms CsCl type of structure, although Mg, Y, Os, Zr have HCP structure. Hence, one needs to develop a distinctly different approach for the multicomponent HEMs depending upon the constituent elements by utilizing the crystal structure. In this regard, Pettifor maps can effectively be utilized to obtain the crystal structure of these compounds. In fact, the Pettifor maps have achieved wide acceptability for information about the structure of the binary compounds formed by over 70 metallic elements in the periodic table, which can be summarized with respect to ΔH mix . As these maps provide the structural information of binary AB-type compound with 1:1 stoichiometry or

3.2 Alloy Design Strategies

69

equiatomic composition, hence, they can be directly related to HEMs because HEMs are primarily based on equiatomicity. Although Pettifor maps for compounds with varying stoichiometry (1:1, 1:2, 1:3, 2:3, 3:4 and 3:5) and opposite ratios are available for computation in advance for usage as a database, they can indeed be utilized for the design of HEMs. Nonetheless, the Pettifor map corresponding to the AB compound (1:1 stoichiometric ratio) is important because of its direct applicability to HEMs, which are predominantly stoichiometric alloys. Takeuchi et al. have carried out detailed work on the utilization of such Pettifor map for the design of by modifying the map by arranging the elements in accordance with the atomic number to coincide with ΔH mix , instead of Mendeleev number (Takeuchi et al. 2015). The authors have categorized the “key” for certain polyhedral structure with increasing coordination numbers for A50 B50 alloy. Here, the upper and lower letters denote the distorted as well as regular polyhedra, respectively. Special attention is to be devoted to rather simple crystal structures— BCC, FCC, and HCP. As Pettifor maps do not deal with disordered BCC, FCC, HCP solid solutions, Takeuchi et al. have worked on chemically ordered phases which are derivatives of BCC, FCC, and HCP – B2, L12 , etc. The easiest way to design new HEMs will involve the addition of elements to these ordered structures, which are frequently observed in intermetallic research. In this regard, the CsCl type of structure is commonly observed for AB compounds with 1:1 stoichiometry (frequently observed in Pettifor map too). This is also popular in lanthanide (Ln)–containing species where the counterparts can be Ag, Au, Cd, Cu, Hg, Mg, Pd, Rh, Tl, Zn, etc. As Rh, Cd, Hg, Tl cannot be practical, Ag, Au Cu, and Mg are the proper candidates. As Au and Mg show relatively low melting temperatures, it is always better to select Ag and Cu; Cu-Ln and Ag-Ln and their mixed systems can be selected. The selected compounds are Gd4 Cu, Gd2 Dy2 Cu, CuDyGdTbY (CuLn4 ) or Cu4 Gd, Cu4 GdTbDyY, Cu4 GdTbDyY and Cu2 Ag2 GdTbDyY (Cu4 Ln). Takeuchi et al. have also studied the HEA compositions obtained by analysis of the Pettifor map via analyzing the Xray diffraction patterns of the cast and homogenized alloys. The XRD patterns of alloys from CuLn4 series, i.e., Gd4 Cu, Gd2 Dy2 Cu, CuDyGDTbY reveal the formation of mixed phases; FCC, HCP, and CsCl-type phases. On the other hand, XRD patterns of alloys with Cu4 Ln (Cu4 Gd, Cu4 GdTbDyY, Cu4 GdTbDyY, Ag4 GdTbDyY, and Cu2 Ag2 GdTbDyY) reveal a single phase structure. Cu2 Ag2 GdTbDyY alloy can form into a single phase with CsCl structure and lattice parameter of 0.357 nm. Similarly, Cu4 GdTbDyY, Ag4 GdTbDyY alloys show BCC structure with different lattice parameters. One can even explain the formation of X4 Ln where X = Cu or Ag via empirical means. Let Σ us consider XGd structure and expand to X4 GdTbDyY using a simple formula: XLn = XLn + XLn1 + XLn2 + XLn3 and hence, X appears 4 times, and one can easily obtain, X4 GdTbDyY. Finally, the further compositional relationship holds true, Cu4 GdTbDyY + Ag4 GdTbDyY → Cu2 Ag2 + GdTbDyY, which conforms to the condition of XLn, indicating equiatomicity of the binary system. Subsequently, Takeuchi et al. (2015) have synthesized the alloys and X-ray diffraction, as well as microstructural investigations of these alloys, reveal single phase microstructure. An interesting system in this regard is Al50 Ni50 . It is important to note that pure Al has an FCC structure. However, Al addition leads

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3 Phase and Microstructural Selection in High Entropy Materials

to stabilization of BCC phases. Once added beyond a certain amount and hence, it is considered a BCC stabilizer. Al50 Ni50 shows ordered B2 or CsCl type structure, although both Al and Ni exhibit FCC structure. Hence, we always face difficulty in the prediction of phases based on the consideration of the crystal structure of the constituent elements. Therefore, the design of multicomponent alloys based on the AlNi system possesses difficulty in predicting phases. In this connection, Pettifor map-based design for 1:1 compounds can provide a better predictive capability of multicomponent alloys. Hence, Pettifor map-based approach is indeed a paradigm shift as it using crystallographic data of different compounds, not those of the constituent elements.

3.3 Phase Selection Approach to Find Single Phase Versus Multiphase HEMs So far, we have discussed the approaches dealing with the prediction of the formation of single phase solid solutions of multicomponent systems. However, experimental research on various systems shows the presence of multiple solid solution phases in the microstructure. It is important to note here that many technological applications demand the use of multiphase materials over single phase ones. This includes duralumin, Ni-based superalloys, steels, etc. Hence, it is practical to discuss phase selection approaches to find multiphase forming HEM compositions. The multiphase solid solutions can be designed using CALPHAD calculations, which would show the presence of multiple solid solution phase forming in the particular alloying system. However, such calculations will also reveal the formation of intermetallic compounds forming in the solid solution matrix, as many conventional materials, including superalloys, alloy steels, aluminum alloys, etc. Hence, there are no generalized rules for the formation of multiphase HEMs. It is rather deciphered from the CALPHAD calculations.

3.4 Design Strategies for High Entropy Ceramics (HECs) High entropy alloys (HEAs), by far, have extensively been investigated, primarily because of early alloy development involving multicomponent systems and partly due to potential applications envisioned (Miracle and Senkov 2017; Tsai and Yeh 2014). However, the concept of HEAs has slowly but steadily percolated to the area of ceramics, leading to the development of high entropy ceramics (HECs). These are considered single phase ceramics with at least 5 cations and/or anions. These include carbides, chalconides, diborides, nitrides, oxides, silicides, etc. As discussed in Chap. 1, the advent of HECs has not only expanded the scope of HEMs but also provided avenues to design novel multicomponent ceramics, which were not even

3.4 Design Strategies for High Entropy Ceramics (HECs)

71

dreamt of some time back. Like metallic alloys, this has led to new phases and hence, the formation and stabilization of these multicomponent HECs are required to be investigated. Unlike multimetallic mixtures, HECs form into solid solutions with a pre-determined network of boron, carbon, nitrogen, oxygen, sulfur, or vice versa. The metallic species can only occupy random sites in these solid solutions. Hence, the formation of these HECs cannot be treated in some way like HEAs. Hence, these two families of materials (HEA and HEC) are fundamentally different, and their applications are also different. HECs are, in general, semiconductors or insulators with some band gap, finding potential applications as functional materials. Some of them (borides, carbides) can find applications as ultra-high temperature ceramics (UHTCs) or hard wear-resistant coatings (nitrides) or even thermoelectric materials. Most importantly, the HECs offer sufficiently large structural variety. The first reported entropy-stabilized oxides, carbides nitrides reveal rock salt structure, whereas there exists hexagonal diborides or nitrides (Zhang and Reece 2019). The design of unknown single phase solid solutions in ceramics is obviously considered as important as HEAs. In fact, certain criteria for formation remain valid. In the following, some of these aspects will be discussed. The stability of any phase in a single or multicomponent system will depend upon the minimization of Gibbs free energy under given pressure temperature and compositions (for multicomponent) and is best described by phase diagrams. These diagrams provide a pictorial representation of the stability of any phase as a function of variables, pressure temperature, and composition. Fundamentally, phase formation and stability of any phase in decided by Gibbs free energy difference described earlier via Eqs. (3.2 and 3.3). ΔG strongly depends on the ΔHmix and ΔSmix at any temperature. ΔHmix , in general, is determined by bonding type and characteristics. The bonding in ceramics is typically covalent type and hence, ΔHmix is highly negative for most of the oxides, diborides, carbides, silicides, chalcogenides, etc. However, the estimation of ΔSmix is distinctly different from the multicomponent system. As compared to HEAs, the profound effect on the estimation of disorder per volume will significantly be lower in HECs (Zhang and Reece 2019). This is because the anion sublattice (O, B, C, N, Si) is more or less ordered, although one cannot ignore the effects of point defects. However, the effect of these point defects will not be significant at room temperature. The chemically uniform cationic sublattice is considered to be a key factor controlling the configuration entropy. Hence, let us discuss the effect of cation on the estimation of ΔSmix in a simple two-component system of the metallic mixture, Co populating a cationic sublattice. There is always an intermediate anion separating neighboring cation sites. Each of the scientific lattice sites can be considered identical as each has the same/similar surroundings. Obviously, if one considers the second nearest neighbors, the difference in the surrounding is apparent. However, each cationic site can be considered identical and energetically singular from the perspective of the entropic disorder. In Chap. 1, we have discussed the effect of this arrangement on the ΔSmix , and this is expected to affect the phase formation and stability. Nonetheless, we shall discuss the design methodologies for the formation of HECs. The approach, commonly utilized in the literature, is based on the Hume-Rothery rules. In this direction, some specific parameters can be coined. One such parameter

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3 Phase and Microstructural Selection in High Entropy Materials

describing atomic solubility in any binary system is given by; =

R 2 ( ΔR ∗ )2 G 2

(3.19)

Here R2 stands for average lattice constant, ΔR ∗ the difference in lattice constant, Z the number of formula units, and G is the average shear modulus. It is evident that the low value of indicates low lattice stain and hence high solid solubility. In this regard, for a multicomponent system can be stained by averaging the value of all the binaries using the entropy of mixing, the value for binary, ternary, quaternary, and quinary solid solution ceramic have been estimated. The values are estimated to be 2.08, 2.92, 3.58, and 4.12 GPa-A−1 for binary, ternary, quaternary, and quinary ceramic solid solutions. This approach has been found to work well for various HECs, especially carbide, sulfides, tellurides. It has also been found that Goldschmidt’s tolerance factor in comparison to the cation size difference affects both the formation and stability (temperature) of cubic perovskite solid solutions. This factor for HECs is found to be close to unity (0.97 − 1.03). However, this factor is insufficient to indicate the formation of a single phase perovskite phase; hence, the requirement of other factors has been felt. Another factor that can be utilized for designing HECs is entropy formation ability (EFA). This is considered to be the inverse of the standard deviation of the energy distribution spectrum of the enthalpies of the possible atomic configurations in a supercell, i.e., ⎛┌ ⎞−1 | Σn | i=1 h i (Hi − Hmix )2 ⎠ EFA = ⎝√ (Σn )−1 i=1 h i

(3.20)

N is known as the number of sampled geometrical configurations, hi ’s are their degeneracies, H i is the entropy of formation at 0 K in a supercell, and H mix is the average of enthalpies H i of all possible configurations. Evidently, large EFA will lead to large entropy for any system. The concept of EFA has widely been utilized to find the compositions for multicomponent carbides, consisting of elements Hf, Mo, Nb, Ta, Ti, V, W, Zr. The components with the highest EFA value are (Mo, Nb, Ta, V, W)C [EFA = 123 atom ev−1 ], where the compound with low EFA value is (Hf, Mo, V, W, Zr)C [EFA = 37 atom ev−1 ]. The experimental investigations reveal that the first composition is indeed single phase, whereas the (HfMoVWZr)C is multiphase. It is also important to discuss the accuracy of each of these descriptors (factors or equations) for the prediction of the formation of HECs. Indeed, there exist many possible descriptors. Nonetheless, the descriptors can be divided based on “grosslevel properties”, “molecular fragment level” as well as “sub-Angstrom level”. EFA can be placed in the first category. On the other hand, the atomic size of the lattice parameter falls under the molecular fragment level. These are the same parameters in the parametric approach described earlier in this chapter. It is evident that there will be more than a dozen such parameters (or descriptors) that have been utilized in

3.5 Microstructure of HEMs

73

the literature. For HEC, the usage of descriptors to predict phase formation is still at a nascent stage. However, it is worth mentioning here that the parameter/descriptorbased approach is not a fool-proof approach because the phase stability cannot be considered not an intrinsic property of any material system and therefore, one needs to consider the kinetics and thermodynamics of all the concerned phases for stability. These parameters may be indirectly related to the free energy, which is considered the fundamental parameter for phased stability. It is again made clear that Gibbs free energy calculations and phase diagrams can indeed provide quantitative information on the phase stability of HEC. Although Gibbs free energy can be estimated using both DFT as well as CALPHAD approaches, the latter provides a robust and reliable tool to predict phase selection and stability. However, there are only a few research works reported on the CALPHAD method for the prediction and stability of HECs, and hence, it is not apt to discuss these aspects of CALPHAD. It utilizes databases containing huge amount of thermodynamic data on binary systems, which can be used to obtain a phase diagram using numerical interpolation or extrapolation schemes. Another thermodynamic approach, known as the cluster expansion method, deals with the creation of mathematical expressions of the concerned physical quantity in the form of series expansions. The major terms of the series will be non-interacting, with some dealing with interactions among particles. As compared to CALPHAD, this method is more robust and systematic, but complicated. Hence, this has not been applied extensively in the design of the HECs.

3.5 Microstructure of HEMs HEAs as well as HECs exhibit a wide range of microstructures; crystalline, nanocrystalline, and amorphous. Crystalline HEMs can have single phase as well as multiphase microstructures. Amorphous HEMs are popularly known as high entropy glasses (HEGs). It is worth discussing the variety of microstructures these materials form, their classification, distribution, and comparison with conventional materials. It is evident that the configurational entropy of the HEMs is expected to stabilize the disordered solid solutions over intermetallic phases or compounds (Miracle and Senkov conf 2017). In general, the multicomponent phases are known to have high ΔSmix . It is evident that the configurational entropy of HEMs is expected to stabilize the disordered solid solution over intermetallic phases (Miracle and Senkov 2017). This may not be true always for some systems. In general, the crystalline multicomponent alloy phases in HEMs are dignified in the following categories (a) whether solid solutions (SS) or intermediate phases or compounds (IM) and (b) if it is SS, then disordered or ordered SS. The solid solution can be either a terminal solid solution in which end element dominates or intermediate solid solutions primarily based on IMs. In the case of HEMs, the SSs are the multicomponent and multiprincipal elemental (MPE) and these are the primarily multicomponent solid solutions and hence, cannot be termed terminal solid solutions. The third aspect of these MPE solid solutions is whether they are random

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3 Phase and Microstructural Selection in High Entropy Materials

or ordered phases. It is well known that many exiting solid solutions can either be disordered or ordered; for example, the B2 phase is an ordered solid solution of BCC (disordered form). The fourth aspect of the solid solution is whether they are simple or complex phases. In general, FCC, BCC, and HCP solid solution is considered simple solid solution. Hence, the solid solutions having crystal structures of L12 (ordered FCC), B2 (ordered BCC), and B4 (ordered HCP) are simple structures. On the other hand, the sigma and Laves phases are examples of complex phases. However, both the sigma and Laves phases can be synthesized as HEMs. Hence, HEMs can be classified as follows. (A) (B) (C) (D)

Solid solution versus intermediate compound phases Disordered versus ordered solid solution phases Terminal solid solutions versus intermediate solid solution phases Simple versus complex phases.

In the following, we shall discuss these phases. It needs to be categorically mentioned that we must not treat IM phases as the only stoichiometric compounds in HEMs. These phases can have compositional variations too. A detailed literature survey reveals HEMs show a variety of microstructures (Miracle and Senkov 2017). So far, there exist about 600 HEAs, 50 HECs from different alloy families—3d TM, RHEA, precious metals, actinide series, oxides, diborides, carbides, and nitrides of different metals. HEAs can be obtained in the cast, heat treated or even in deformed conditions. HECs can be obtained using the powder metallurgy route. This leads to a huge number of microstructures, which is impossible to discuss here. Instead, we shall discuss the unique features of some generalized microstructures. Let us first start with HEAs consisting of 3d-TM. These are considered to be the largest family, primarily consisting of the FCC phase. These alloys can contain a variable amount of Al, Si, Mg, etc. FCC phase is found to be stable up to an Al concentration of 6 atom%. However, some alloys (CoFeMnTix Vy Zrz ) can form even the Laves phase (C14). For the multiphase alloys, the second phase can be σ, Laves, L12 or even BCC phase. The former three secondary phases are ordered. The addition of Al to these alloys leads to the formation of BCC or B2 phases when the concentration of Al is more than 6 atom%. At a high concentration of Al (Al ~ 15 atom%), single BCC phase forms. Some other alloys containing Al show an ordered L12 phase in the microstructure. These FCC single or multiphase alloys can easily be deformed to form nanocrystalline microstructure. Another interesting alloy system is refractory metal alloys. These alloys reveal BCC primary phase. The secondary phases can be B2, Laves, M5 Si3 -type silicides as well as AlxZr3-type phase in case of Al-containing alloys. Some of the Al-containing RHEAs reveal nanometersized precipitates of BCC phase in B2 matrix (Soni et al. 2018) in which the BCC phase is found to be coherent with B2, hence, similar to γ /γ ' microstructure in Nibased superalloys. This type of microstructure provides excellent high temperature properties of RHEAs. The third alloy system is known as precious metal HEAs, which are predominantly FCC multicomponent alloys consisting of five elements from the palette of Ag, Au, Rh, Ru, Pt, Pd, Cu, Ir, and Os. In general, the single phases are observed in these alloys. However, in some cases, intermediate phases of Cu3 Au,

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CuAu, Cu3 Pt, Cu3 Pd are also observed. The metals in the actinide series (La, … Lu) form stable HCP solid solutions. Since the atomic size of these elements does not vary much, solid solution phases are only observed without any intermetallic phases. The configurational entropy of mixing of these multicomponent systems is reported to favor the formation of disordered solid solutions (DSS) phases in the HEAs over ordered phases. This is not always true, as some of the solid solution phases are ordered or even partially ordered. DSS phases usually have a single phase with crystalline lattice with no specific long-range order (LRO). However, they exhibit some short-range order, and these phases usually are an extension of solid solutions. Let us now discuss HECs. HECs are, in general, phase pure compounds containing multiple elements. These are synthesized by various routes: solid-state reaction, wet chemical, and epitaxial growth (Oses et al. 2020). However, the solid-state reaction is used as the predominant route for the synthesis of HECs, and hence, the microstructures of the HECs will also depend on processing conditions. In some cases, the presence of unreacted individual constituents, oxides, diborides, and carbides is found to be present in the microstructure. The grain size depends on the processing route. Wet chemical synthesis and epitaxial growth lead to nanosized grains, whereas solid-state reaction makes micron-sized grains.

3.6 Design Strategies for High Entropy Metallic Glasses Conventionally, metallic glasses (MGs) design has been based on experimental investigations involving casting individual compositions and the evaluation of the glass-forming ability (e.g., critical casting dimensions). The emergence of empirical methods to screen alloy compositions with glass-forming ability was the first step toward the development of computational design strategies to discover novel MG compositions, albeit with their limitations. Inoue (1995) suggested the empirical rules dictating the accomplishment of high glass-forming ability (GFA) in metallic glasses: (a) multicomponent alloys having three or more elements, (b) substantial atomic size difference (≥ 12%) among the primary constituent elements, and (c) negative enthalpies of mixing between the constituents. Considering these rules as foundation principles, various empirical methods (Nagel and Tauc 1975; Wang et al. 2003; Shek et al. 2000; Yan et al. 2001; Chen et al. 2010) have been proposed for the design of novel high entropy metallic glass (HE-MG) compositions. However, these methods have limitations in their universal application. It is challenging for these methods to design the constituents of the HE-MGs accurately and satisfactorily predict their GFAs since they are guided by purely mathematical constraints originating from a limited number of experimental results. A new perspective to design new HE-MG compositions involves understanding the role of thermodynamics, atomic structure, and chemical properties of various constituents in a multicomponent alloy system. In line with this, various design strategies have emerged, showing greater efficiency in designing MGs. They are summarized below:

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3.6.1 Trial and Error Method It is utilized for designing the constituents of the HE-MGs employing available phase diagrams, physical, thermodynamic, and chemical parameters, as well as the knowledge of pre-developed HE-MGs. This is followed by the components being experimented upon one by one for good GFA. However, this method involves a large number of experiments since the constituent range is quite extensive and thus is cumbersome (Zhang et al. 2003; Inoue et al. 1993).

3.6.2 Nearly-Free-Electron Method Nagel and Tauc (1975) proposed that an alloy behaves as a free-electron gas and employed the concepts utilized to describe the system through Ziman’s theory of liquid metals. Glasses are considered to still be in the liquid state for simplicity, which is somewhat an accurate approximation. Various parameters related to GFA, such as energy levels, pseudopotential, fermi momentum, density states, and structure factor using the perturbation theory, are calculated and used to design the compositions of HE-MGs. This method has shown a remarkable ability to predict the compositional space of metallic glasses.

3.6.3 Valence Electron Concentration Method This approach involves the calculation of the chemical bond length, overlapping population, and binding energy through the concepts of quantum chemistry based on the cluster model (Miracle 2004), prediction of GFA, and design of new HEMG compositions. Chen et al. (2007) performed an investigation on the electronic structure of Pd–Y–Si metallic glass and showed that the valence electrons of Y get transported to Si atoms, leading to the formation of polar covalent bonds. These potent covalent bonds between Si and Y atoms assist in the formation of atomic clusters, which impede crystallization. Subsequently, they also showed that the e/a (the number of itinerant electrons per atom) criterion was a more accurate approach to design BMGs since the results showed a better agreement with the experimental values (Wang et al. 2003; Shek et al. 2000). Bajpai et al. (2020) investigated the employability of the PHSS model to design novel HE-BMG systems, considering the impact of the electronic nature of the constituents atoms in an alloy system on glass formation. The study involved the alteration of atomic radii of constituents by considering the electronic factors to understand the role of the local atomic environment in altering the atomic radii of constituents. This was carried out by using two key parameters called electronic shell number (ESN) and VEC to calculate the apparent radius of the constituents in multicomponent alloys. Moreover, the study

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showed that using e/a instead of VEC is a better approach to understand this effect and design new HE-BMG compositions with greater accuracy. These methods, possessing a sound theoretical basis, have been able to produce accurate results in designing new HE-MGs. However, they are restricted to simple cases because of complexity, huge time consumption, and reduced efficiency. Moving forward from these steel-frame design strategies, computer simulation technology has emerged as a viable alternative strategy for the design of complex material systems. High-throughput computational methods to predict glass formation a priori have made a significant impact in accelerating the alloy development cycle, which has been discussed henceforth.

3.6.4 Discrete Variational Method This is a molecular orbital method associated with a numerical self-consistent field method and associated with the density functional theory (DFT). It applies to the solid systems, macroclusters, and macromolecules, chiefly consisting of heavy atoms (Wang and Dong 2002). It involves the selection of a set of discrete sample dots through their determination of the error function, which is based on the approximate solutions of the analogous individual-particle function. This is followed by the modification of the parameters in the trial function of the error function and minimization of the error function, thereby obtaining the secular equations and the expressions of the matrix elements for obtaining an effective single operator. Consequently, the calculation of symmetric orbital base in accordance with the symmetric requirements and the calculation of charge density (q) is done to predict the GFA for multicomponent alloys. The influence of Al on the glass-forming ability of Zrbased alloys was investigated using this method based on the cluster model. The theoretic results showed that the Al atoms could strengthen the atomic interactions between atoms of different alloy atoms in the Zr-based alloys, leading to the stabilization of the atomic clusters. These theoretic results were in close alignment with the experimental findings. Moreover, Song et al. (1999) investigated the role of certain elements on Ti-based alloy through this method. The study showed that elements such as Fe, Mn, Cr, V, Mo, Nb, Zr, W, and Ta show the ability to increase the binding energy of the clusters. Altogether, this is a workable approach to design new HEMG compositions; however, there is a limit on the number of atoms in the cluster model. Moreover, the approach seldom requires long hours of computation for each composition, making it infelicitous, especially for higher-order alloy systems.

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3.6.5 Machine Learning Methods With the advent of the fourth industrial revolution, an innovative computer data processing method called machine learning (ML) has emerged as a pragmatic alternative strategy for material design. It involves gathering data and uncovering complex extrapolative relationships among various variables to evaluate the characteristics and properties of materials. Machine learning has the capability to extricate usable information from a large amount of discrete data and provide solutions for highly complex problems. Machine learning has inherent advantages compared to other modeling methodologies as it can flexibly adapt to the availability of new data and rapidly build relationships between input and target outputs. Several vital aspects relating to materials science that are otherwise difficult to model or convert into a computer code have profited from the implementation of machine learning (Raccuglia et al. 2016; Liu 2018; Butler et al. 2018). In recent times, machine learning has successfully been used for designing new materials and estimating their properties, too (Gubernatis and Lookman 2018; Wen et al. 2019; Ong 2019; Himanen et al. 2019). Pilania et al. (2016) developed an efficient feature-engineering methodology and a robust machine learning algorithm to predict electronic bandgaps in double perovskites accurately. Gong et al. (2019) utilized machine learning to classify superheavy elements and discovered a connection between the classification of elements with their atomic data. Choudhury et al. (2019) used several machine learning algorithms such as logistic regression, decision tree, support vector machine (SVM), K-nearest neighbor (KNN), Naïve-based approach, and neural networks to classify HEAs. Islam et al. (2018) and Zhuang et al. (2019) have attempted to predict the phase formation in HEAs using ML methods with great accuracy. Zhang et al. (2020) used machine learning to reveal the significant role of formation enthalpy and atomic topology in the phase formation in HEAs.

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W.-R. Wang, W.-L. Wang, S.-C. Wang, Y.-C. Tsai, C.-H. Lai, J.-W. Yeh, Effects of Al addition on the microstructure and mechanical property of AlxCoCrFeNi high-entropy alloys. Intermetallics 26, 44–51 (2012). https://doi.org/10.1016/j.intermet.2012.03.005 C. Wen, Y. Zhang, C. Wang, D. Xue, Y. Bai, S. Antonov et al., Machine learning assisted design of high entropy alloys with desired property. Acta Mater. 170, 109–117 (2019). https://doi.org/10. 1016/j.actamat.2019.03.010 C.-S. Wu, P.-H. Tsai, C.-M. Kuo, C.-W. Tsai, Effect of atomic size difference on the microstructure and mechanical properties of high-entropy alloys. Entropy 20(12), 967 (2018) X. Yan, Y. Chang, Y. Yang, F.Y. Xie, S.L. Chen, F. Zhang et al., A thermodynamic approach for predicting the tendency of multicomponent metallic alloys for glass formation. Intermetallics 9, 535–538 (2001). https://doi.org/10.1016/S0966-9795(01)00036-X Y.F. Ye, Q. Wang, J. Lu, C.T. Liu, Y. Yang, High-entropy alloy: challenges and prospects. Mater. Today 19(6), 349–362 (2016). https://doi.org/10.1016/j.mattod.2015.11.026 Y. Yifan, Q. Wang, J. Lu, C.T. Liu, Y. Yang, Design of high entropy alloys: a single-parameter thermodynamic rule. Scripta Materialia 104 (2015). https://doi.org/10.1016/j.scriptamat.2015. 03.023 H. Zhang, F. Akhtar, Processing and characterization of refractory quaternary and quinary highentropy carbide composite. Entropy 21(5), 474 (2019) Y. Zhang, D.Q. Zhao, M.X. Pan, W.H. Wang, Relationship between glass forming ability and thermal parameters of Zr based bulk metallic glasses. Mater. Sci. Technol. 19(7), 973–976 (2003). https:// doi.org/10.1179/026708303225003045 Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-solution phase formation rules for multicomponent alloys. Adv. Eng. Mater. 10(6), 534–538 (2008). https://doi.org/10.1002/adem.200 700240 H. Zhang, D. Hedman, P. Feng, G. Han, F. Akhtar, A high-entropy B4(HfMo2TaTi)C and SiC ceramic composite. Dalton Trans. 48(16), 5161–5167 (2019). https://doi.org/10.1039/C8DT04 555K L. Zhang, H. Chen, X. Tao, H. Cai, J. Liu, Y. Ouyang et al., Machine learning reveals the importance of the formation enthalpy and atom-size difference in forming phases of high entropy alloys. Mater. Des. 193, 108835 (2020). https://doi.org/10.1016/j.matdes.2020.108835 R.-Z. Zhang, M. Reece, Review of high entropy ceramics: design, synthesis, structure and properties. J. Mater. Chem. A. 7 (2019). https://doi.org/10.1039/C9TA05698J

Chapter 4

Diffusion in High Entropy Materials

4.1 Introduction Diffusion is one the very fundamental aspects of a material property. As mentioned in the previous chapters, at any given temperature, we have equilibrium concentration of thermally induced vacancies. Any alloy has two types of alloying atoms: (a) substitutional and (b) interstitial. In this chapter, we are primarily concerned about substitutional atoms or elements, keeping in mind that the high entropy alloys change the paradigm of solvent and solute atoms, and therefore, the use of the term “substitutional” is merely to point to atoms that need to occupy a full lattice site. Similar to Chap. 2, we will focus on FCC alloys. Most of the examples selected in this chapter are based on the Cantor alloy (CoCrFeMnNi) and Alx CoCrNiFe alloys. Diffusion occurs by movement of vacancies, and only mono-vacancies are considered in this chapter. There are many good books on physical metallurgy to get the basics of diffusion in metals and alloys (Abbaschian et al. 2009). For convenience, a relatively recent review by Balogh and Schmitz (2014) is used for capturing the basic aspects very briefly, before turning to the complex aspects involved in the core effect of “sluggish diffusion” in the high entropy alloys. There are basic thermodynamic energy terms that govern the formation and migration of vacancies which is represented by this overall temperature dependence of diffusion coefficient (Balogh and Schmitz 2014), ) ) ( ) ( ( SM + SF λ2 HM + HF ΔH ˜ = D0 exp − exp − , (4.1) D = ┌0 z f exp − 6 kB T kB kB T where D is the diffusivity, λ is the length of the jump vector (usually nearest neighbor distance), ┌˜ 0 is the vacancy jump rate, z is the number of nearest neighbors (coordination number), f is the correlation factor, H M , H F , ΔH are migration, formation, and activation enthalpy, respectively, k B is Boltzmann constant, T is absolute temperature, S M , S F are migration and formation entropy, respectively, and D0 is the pre-exponential factor. © Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8_4

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Note that Eq. (4.1) is relatively quite simple for pure metals. In the early stage of diffusivity discussion and thermally activated processes, such approach worked very well. For example, the activation energy for lattice diffusion-controlled creep deformation matched exactly with the activation energy of lattice diffusion. The foundation of such diffusional process is related to vacancy gradient created by applied stress. It is important to keep this simple concept in mind—diffusion occurs under a concentration gradient. In the case of pure metal, it was thermal vacancy concentration gradient created by applied stress. Application of diffusivity data to high temperature processes also needs to consider the diffusion pathways. In a pure metal, there are four distinct diffusion pathways or types, (a) through lattice, (b) along grain boundaries, (c) along dislocation cores, and (d) at the surface. Note that each of these has implications on kinetics aspects as well as energetics aspects. For example, Eq. (4.1) has factors like vacancy jump rate and lattice coordination number. These are terms that influence the overall kinetics. Biasing any of these factors like coordinated jumps can enhance the overall kinetics. Similarly, the energetics of vacancy formation and migration at grain boundaries and surfaces will be different from inside the crystal lattice. The experimental determination of the diffusivity values in pure metals uses radioactive tracers. A key factor is the availability of suitable radioactive tracer for the element of interest. The half-life of the radioactive tracer must be high enough for conducting the experiments, and this becomes particularly important for grain boundary self-diffusion measurements where the time needed is large due to lower test temperatures. Note that in the self-diffusivity measurements, there is no phase stability issue involved. Figure 4.1 shows the variation of diffusivity in Ni with temperature. It includes lattice diffusion, grain boundary diffusion, and dislocation core diffusion. The example of Ni is particularly good in the context of the high entropy alloys, CoCrFeMnNi (Cantor alloy), and Al0.1 CoCrFeNi alloys, that we covered in Chap. 2. These two alloys are FCC, same as pure Ni, and the lattice parameters of these HEAs are quite close to the lattice parameter of pure Ni. It is good to understand the complexity of sluggish diffusion core effect discussion with a simple baseline. Figure 4.1 helps in establishing a very simple baseline for the discussion of diffusivity in the two HEA systems of our choice, namely CoCrFeMnNi and Al0.1 CoCrFeNi alloys. Another simple correlation that we want to capture before the alloying effect is the relationship between activation enthalpy (ΔQ) (denoted as ΔH in Eq. 4.1) and melting temperature (Tm ) in pure metals known as the van Liempt rule (Balogh and Schmitz 2014), ΔQ = 17RTm ,

(4.2)

where R is the gas constant. When we consider the issue of sluggish diffusivity in HEAs, it is important to consider the basis of comparison. How do we evaluate whether the measured diffusivity or estimated diffusivity is “really” sluggish? Fig. 4.2 shows the plots from Balogh and Schmitz (2014) for FCC, HCP, and BCC metals showing a fit with the van Liempt rule (Eq. 4.2). Note that among the elements we

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Fig. 4.1 An illustration of diffusivity in pure Ni. Note that the slopes on these curves indicate activation energy for self-diffusion. The grain boundary diffusivity has much lower activation energy than the lattice diffusion (Balogh and Schmitz 2014). Simplified illustration adapted from compiled data in Balogh and Schmitz (2014)

are interested in the FCC HEAs, Cr has higher activation enthalpy in BCC lattice. How does that translate into diffusivity in FCC HEA matrix? Additionally, Balogh and Schmitz (2014) have noted that (a) the diffusivities at the melting point tend to be in the range of 10–13 and 10–11 m2 /s depending on the crystal structure, and (b) the pre-exponential factor, D0 , is in the range of 10–6 –10–4 m2 /s. These are good numbers to benchmark the HEAs with.

Fig. 4.2 A strong correlation between the activation enthalpy of pure metals with the melting point. The correlation lines represent the van Liempt rule as expressed by Eq. (4.2) (Balogh and Schmitz 2014)

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4.2 Diffusion in Alloys The next thing to consider is a simple extension of this diffusional mechanism discussion to the simple binary solid solution. If one assumes a random substitutional solid solution, then the diffusivity of the alloying element can still be measured reliably through tracer diffusion. Additionally, diffusion couple experiments are done. Figure 4.3 shows schematics of tracer diffusion measurement. The tracer diffusion experiment relies on measurement of gradient after a specific temperature–time annealing experiment. Typically, these experiments involve low concentrations, and for a polycrystalline materials, it additionally provides information regarding diffusion along grain boundaries. It is important to consider solubility of solute elements as well as possibility of intermetallic phase formation. Similarly, it is assumed that the microstructure is constant during the experiment. These considerations are important to keep in mind as we progress toward the discussion of diffusivity measurements in the high entropy alloys. The next simple experimental procedure is the use of diffusion couples. In this method, two pure elements are put together so that they are under firm contact and annealing time/temperature combination is applied. This is schematically shown in Fig. 4.4 for a few different conditions. When diffusivity of elements is similar and they are mutually soluble, then concentration lines are symmetric and the original interface or weld line does not migrate (Fig. 4.4a). Such situations are rare in practice as it requires fully miscible elements with similar melting points. The next situation to consider is when diffusivity of element B is greater than element A (Fig. 4.4b). In such a case, more B atoms move to the left and the volume of that region increases. This leads to migration of the marker line at the original interface (Smigelskas and Kirkendall 1947). The formation of Kirkendall voids during such experiments is not depicted in Fig. 4.4b. The measurement of concentration profiles allows for calculation of interdiffusion coefficients. The Matano interface (Matano 1933) is depicted in Fig. 4.4c; this lies where the calculated areas X and Y are equal. One of the key findings of such interdiffusion coefficient calculation is that the “interdiffusion coefficient is concentration dependent.” The fundamentals of such discussion can be found in any physical metallurgy book, for example (Abbaschian et al. 2009; Fig. 4.3 A typical impurity tracer experiment and concentration measurement scheme for experimental determination of a solute diffusivity

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Fig. 4.4 Use of diffusion couples to determine interdiffusion coefficient. a An illustration of concentration profiles in a simple diffusion couple where the diffusivities of elements are similar. b An illustration of migration of physical markers like wires placed at the original interface or weld plane when the diffusivity of element B is higher than the element A. c Use of Makano method to define a line where the area X is equal to area Y. This method is used to calculate the interdiffusion coefficient as a function of concentration (Matano 1933)

Smallman and Ngan 2013). The fact that interdiffusion coefficient is concentration dependent is important for the discussion of diffusivity in high entropy alloys.

4.3 Diffusion in Multicomponent Systems Key questions that emerge from the simple techniques of tracer diffusion and diffusion couples discussed in the last section are related to applicability of these alloys to multicomponent systems and further extension to high entropy alloys. Recently, Divinski et al. (2020) have reviewed this critically and we draw much from that review. Particularly, because the full treatment of issues pertaining to diffusion in concentrated alloys is quite complex. In this section, we want to capture a few basics related to concentration multicomponent systems before pivoting to high entropy alloys in the next section.

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Murch and Rothman (1981) examined the dependence of diffusivity of mobile component on concentration. As it will become more apparent in the next section, this paper has a key finding that can be important for evaluating diffusivity if certain experimental measurements can capture the issue of diffusivity in concentrated alloys properly. Since a fundamental discussion needs to evaluate whether the diffusion in high entropy alloys is sluggish, any factor that can reduce the measured value is of interest to us. One such factor that impacts the kinetics of diffusion is the “physical correlation factor” during vacancy diffusion mechanism. Note that in a simple dilute random solid solution, there is no bias in jump frequency in any direction, and in Eq. (4.1), we assumed it to be similar for all atomic sites. In multicomponent system, the randomness of jumps is unlikely. Murch and Rothman (1981) pointed that these conditions can impact the physical correlation factor, (a) interaction between atoms, (b) site inequivalence a priori, and (c) diffusion in presence of obstacles. In a multicomponent system, all these conditions can be present. A key conclusion in their study was the existence of a threshold concentration value for percolation.

4.4 Measured Diffusivities in High Entropy Alloys—Validity of the Core Concept of Sluggish Diffusion Let us start a simple discussion of vacancy diffusion in a dilute solid solution alloy and its extension to concentration binary alloy, as well as the high entropy alloy. Figure 4.5 shows a 50 atomic site 2D depiction with 2 vacancies. Figure 4.5a is for a dilute alloy with 2% solute (one atom out of 50 sites). In a dilute alloy, Balogh and Schmitz (2014) have defined five different jump possibilities. The exchange ‘0’ with a solvent atom does not change the nearest neighbor environment for this vacancy. The exchange ‘1’ creates a rotation around the solute atom. The shift with ‘2’ with the solute atom still keeps 5 solvent atoms as neighbors. Step ‘3’ dissociates the vacancy from the solute, while step ‘4’ associates the vacancy with the solute atom.

Fig. 4.5 Representation of a 50 atomic site 2D layout including 2 vacancies for discussion of vacancy diffusion. a The five different jump possibilities for a vacancy in a dilute alloy (2% solute), adapted from Balogh and Schmitz (2014). Extension of the vacancy jump possibilities to b a binary alloy with 18% solute atoms and c to a high entropy alloy with five elements with concentrations of 18–20%

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Figure 4.5b shows the extension of this to a higher concentration of 18%. Now, for the jump of vacancy to one of the neighboring sites A–F, the conditions are quite different. Switching to site A increases the number of solute-vacancy bonds from 1 to 2. This is true for switching to sites B, C, and E. On the other hand, moving to sites D or F keeps the current first-neighbor configuration of one solute and 5 solvent atoms. Note that the vacancy-atom binding energy is different for each element. Therefore, the movement to different neighbor sites is going to be energetically different. Further extension of this to high entropy alloy is shown in Fig. 4.5c. Now, the vacancy is surrounded by sites A' –F'. Two neighboring atoms are of one type, and four other neighbors are four different elements. As mentioned earlier, the bond energy of vacancy will vary with each of the five elements. Now, unlike the previous discussion of the change in the neighbors with every jump, the nearest neighbor environment change will have much higher variability. The total vacancy bond energy will be different at each site. This is further compounded by different intrinsic diffusivity of each element in the high entropy alloy. So, instead of the frequency of jumps being random, as in binary dilute alloys, the jumps will become more coordinated. These ideas are the basis for the “sluggish diffusion” core effect concept in high entropy alloys. We are interested in both the scientific curiosity and potential engineering applications. Tsai et al. (2013) were the first one to measure diffusivity in high entropy alloys, but the literature is now growing on measurement as well as discussion of the procedure of measurement and interpretation (Beke and Erdélyi 2016; Wilson et al. 2016; Tsai et al. 2017; Esakkiraja and Paul 2018; Kucza et al. 2018; Osetsky et al. 2018; Vaidya et al. 2018; Dash et al. 2020; Divinski et al. 2020; Gaertner et al. 2018; Kottke et al. 2020). The use of diffusion couples (Tsai et al. 2013) and tracer diffusion (Vaidya et al. 2018) needs to be carefully considered, and the review of Divinski et al. (2020) is a good compilation of these aspects. Wilson et al. (2016) have raised questions about the interpretation of diffusion data from diffusion couple. A general article by DeHoff and Kulkarni (2002) on issues involved in diffusion is important to read for broader picture. In this chapter, we are only covering the essential basics to just address the core concept of sluggish diffusion and how it may impact a few diffusion-based processes. Figure 4.6 shows a comparison of various tracer diffusion values from Divinski et al. (2020). This builds from the foundation of self-diffusion in Fig. 4.1. The tracer self-diffusion values for nickel are near the bottom of the band that represents the distribution of values for FCC metals. The activation energy is within the range of values for FCC metals as can be gaged from the slope of the lines. The values of tracer diffusivity and the slope of line for Fe–45.3Ni alloy are very close to pure Ni. In the ternary alloy Fe–15Cr–20Ni, the presence of Cr results in reduction of the tracer diffusivity of Ni in this concentrated alloy. Note that the diffusivity data in Fig. 4.6 is plotted against normalized temperature (T m /T ). This is an important consideration given the van Liempt rule shown in Eq. (4.2). The data for quaternary alloy CoCrFeNi does not influence the diffusivity of Ni tracer beyond the ternary alloy, whereas the tracer diffusivity of Ni in the CoCrFeMnNi alloy reduces further and certainly is below the entire self-diffusion in FCC metals distribution band. The

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decrease of Ni tracer diffusivity in the CoCrFeMnNi alloy as compared to pure Ni matrix is nearly an order of magnitude. The trends from this comparison plot show that (a) there is reduction in diffusivity of Ni tracer atoms, and (b) the magnitude of reduction of diffusivity depends on the specific alloy. This aspect is further discussed with the help of recent tracer measurement values a bit later in this section. The last line in Fig. 4.6 is the diffusivity of tracer Ni in Ni3 Al. Note that in an ordered alloy like Ni3 Al with L12 crystal structure, the diffusion has to be more correlated because of site occupancy. In the Ni3 Al with L12 crystal structure, the Al atoms occupy the corner sites of the FCC lattice and Ni atoms occupy the faces. In ordered alloys, each atom is restricted to its specific lattice site. So, for Ni diffusion, the Ni atoms can only jump to the Ni sites in the vacancy exchange mechanism illustrated in Fig. 4.5. An important inference that can be drawn from Fig. 4.6 is the postulated sluggish diffusion in HEAs can be as high as one or two orders of magnitude depending on the alloying elements and considerations including specific site occupancy and the atom/vacancy binding energy. It is important to always look at the details and context while interpreting these results. Vaidya et al. (2018) have made this point that the sluggish diffusion inference comes across in CoCrFeNi and CoCrFeMnNi alloys only when homologous temperatures are used for comparison. The level of alloying or concentration is equally important in view of the threshold concentration for percolation effect. This is further discussed with some recent results. Kottke et al. (2020) have done a detailed tracer diffusion measurement on Co10 Cr10 Fe10 Mn10 Ni60 and Co2 Cr2 Fe2 Mn2 Ni92 alloys and compared the results with pure Ni and the Co20 Cr20 Fe20 Mn20 Ni20 HEA (Fig. 4.7). It fits into our scheme of using Ni as the benchmark for Cantor alloy type FCC HEAs to understand the impact of alloying on individual tracer diffusivity. There are several points that can

Fig. 4.6 Tracer diffusion of Ni in pure Ni, binary FeNi, and ternary FeCrNi in comparison with that in quaternary CoCrFeNi and quinary CoCrFeMnNi HEAs as function of the inverse homologous temperature T m /T (T m is the melting point of the corresponding compound) (Divinski et al. 2020) [from Divinski et al. 2020]

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be considered from this nice comparison, and it also raises a fundamental question about which alloys are proper for tracer measurements. First, results of Vaidya et al. (2018) clearly have lower tracer element diffusivities in this particular comparison. It should be noted that in their own study, Vaidya et al. (2018) concluded that there may not be a case for sluggish diffusion. From their measurements, they highlighted an interesting correlation between the pre-exponential factor (D0 ) and the activation energy, referred to as the “compensation law” for diffusion in HEAs (Fig. 4.8). The importance of this lies in the fact that the effective diffusivities become similar as the high activation energy is compensated by higher value of D0 . The activation energy values range from 240 to 304 kJ/mol, and the values of D0 vary in the range of 4.6 × 10–7 –4.2 × 10–3 m2 /s. Second, coming back to the comparison presented by Kottke et al. (2020), there is a clear trend related to the overall alloying concentration. All tracer diffusivity values are consistently higher for the Co2 Cr2 Fe2 Mn2 Ni92 Co10 than Cr10 Fe10 Mn10 Ni60 . It is also important to repeat that the Co2 Cr2 Fe2 Mn2 Ni92 Co10 is very dilute. If we go to the conceptual vacancy exchange depiction in Fig. 4.5, we can see that to learn about the concentrated alloys, the measurements need to be in concentrated alloys. Even then, this study is helpful in understanding some of the discrepancies or divergence of thoughts in literature. Divinski et al. (2020) have also extended the tracer diffusion comparison to grain boundary diffusivity as shown in Fig. 4.9. Similar to the earlier discussion, the diffusion of Ni tracer in the alloys is slower than the self-diffusion in pure matrix. The limited measurements for HEAs do show lower rates than the other lines. For comparison, Ni grain boundary diffusion in ordered Ni3 Al for stoichiometric and Ni-rich compositions is shown, too. It is important to keep the phase stability in mind for the HEAs. Over the last several years, a trend is emerging that previously reported single phase alloys may not be thermally stable during long-term exposure at high temperatures. Such microstructural instability or phase formation changes the diffusion measurement and its impact on derivative processes. This is briefly discussed in the next section.

4.5 Implications for Diffusion-Controlled Processes As mentioned earlier, and it is worth repeating, we are interested in diffusion in HEAs not only because it is one of the core effects of “sluggish diffusion” but also because of its implication on many diffusion-controlled and diffusion-assisted processes. In this section, we want to briefly capture the essence of these two aspects, i.e., diffusioncontrolled and diffusion-assisted processes. There is a wide range of these processes, and the selection of discussion here is illustrative of how the fundamentals will apply.

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Fig. 4.7 Compiled results from Kottke et al. (2020) comparing the measured volume diffusion coefficients against the inverse homologous temperature, T m /T, for tracers a 57 Co, b 51 Cr, c 59 Fe, d 54 Mn, and e 63 Ni. The alloys mentioned are Co Cr Fe Mn Ni (60) alloy, Co Cr Fe Mn Ni 10 10 10 10 60 2 2 2 2 92 (92) alloy, pure Ni (100), and the Co20 Cr20 Fe20 Mn20 Ni20 HEA

4.5.1 Creep and Superplasticity Among diffusion-controlled processes, creep and superplasticity are two widely studied phenomena. Both share the fundamental deformation mechanisms, while the applications are opposite! For creep applications, we want the deformation rate

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Fig. 4.8 A correlation between the pre-exponential factor (D0 ) and the activation energy for bulk diffusion of the constituent elements in CoCrFeNi and CoCrFeMnNi HEAs (Osetsky et al. 2018)

Fig. 4.9 Compilation of grain boundary diffusion information by Divinski et al. (2020). A comparison of a grain boundary diffusion of Ni in CoCrFeNi and CoCrFeMnNi HEAs and b the diffusion rates in HEAs with those in pure Ni and binary Fe–Ni alloy on the inverse homologous temperature scale, T m /T

to be as low as possible; i.e., we want to retard the high temperature deformation mechanisms. On the other hand, superplastic forming is used for unitized structures and we want to enhance the kinetics of high temperature deformation. The detailed treatment is out of scope for this book, and readers should refer to any standard mechanical behavior textbook for the background. The key aspect for the current discussion is the role of diffusion in these processes. It is important to understand that the strain during these processes is contributed by the faster micromechanisms, while the rate controlling step is the slowest of the micromechanisms and governs the overall kinetics of the process. Let us again try to understand this by starting with pure metals. In pure metals, rate controlling step for dislocation creep mechanisms is the rate at which dislocations can climb. Dislocation climb process is non-conservative,

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and lattice self-diffusion controls this step. Therefore, the activation energy for dislocation creep is exactly same as the activation energy for lattice self-diffusion. This has been very well correlated for all pure metals. So, in our discussion framework, the activation energy for creep of pure Ni is same as the activation energy for lattice self-diffusion in pure Ni. Experimentally, we can do creep experiments at three temperatures while keeping the microstructure constant and use an Arrhenius plot to determine the activation energy. The creep mechanism in such a case is referred as climb-controlled dislocation creep with activation energy of lattice self-diffusion. When the discussion shifts to creep of binary solid solution alloys, the diffusivity of solvent and solute is compared. Let us take Ni–X binary solid solution alloy. If the element X has lower diffusivity in the Ni matrix, the dislocation motion is impeded by the solute. In such a case, the dislocation glide itself becomes the rate controlling step and the mechanism is referred as solute drag-controlled creep mechanism. The activation energy for this mechanism matches with the activation energy for diffusion of the solute in the matrix. Again, by determining the activation energy for creep deformation, one can conclude if the rate controlling step is related to the solute. Switching to the HEA, now let us consider the CoCrFeMnNi alloy. The classical creep deformation mechanism breaks down because we do not have solvent and solute! Based on the data in Fig. 4.7 from Vaidya et al. (2018), the diffusivity of Co or Ni is slowest depending on the temperature. Consider the schematic in Fig. 4.5c for the vacancy exchange mechanism. When such a mechanism is operative, there is no net disturbance created in the overall distribution of the alloying elements. Now, if the solute drag mechanism is invoked, then the dislocation will drag the solute and there will be a net change in the distribution of alloying element. Such a thought experiment suggests that creep deformation may alter the stability of the alloy. If the microstructure is not constant during the creep mechanism, then the data cannot be analyzed properly for the activation energy determination. Again, carefully conducted experiments are needed to evaluate the impact of “sluggish diffusion” on the solute drag creep mechanism or climb-controlled creep mechanism. Does the creep accelerate phase separation that is observed in many HEAs during extended exposure at high temperatures?

4.5.2 Diffusional Solid State Phase Transformation in HEAs—Phase Separation and Precipitation For this illustrative discussion, we take a comprehensive paper by Gwalani et al. (2018) on Al0.3 CoCrFeNi HEA. Figure 4.10a shows the calculated isopleth of the Alx CoCrFeNi with x from 0 to 1. It should be noted that thermodynamic databases for HEAs are in initial stages and some discrepancy is expected. But the discussion here is not about minor discrepancies in temperature and phase formation, but the ability to modify the transformation pathways through different thermomechanical processing. This becomes a powerful tool to alter the desired outcome microstructurally without

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the need for changing the composition. Usually, phase transformation studies are conducted through isothermal or isochronal annealing. The phase diagram is used to select the temperature range for desired phases. In this particular example, we focus on 620 °C, which according to the Fig. 4.10a should result in three phases, i.e., a FCC matrix, L12, and B2 precipitates. So, the formation of L12 was not consistent with the phase diagram. Note that L12 precipitate is Ni3 Al type and B2 precipitate is NiAl type. The importance of the type of precipitates lies in the fact that the remnant alloying element in the matrix changes which impacts the stacking fault energy and lattice distortion. We will ignore these aspects that impact the dislocation-based mechanical properties as this chapter is focused on the diffusion-based processes. But the same argument does extend to vacancy exchange-based diffusion mechanisms as illustrated in Fig. 4.5. Also, note that much of the previous section discussed early results available on individual elemental tracer diffusion. Ni is a slower diffusing element in these HEAs. So, what happens to effective diffusivities when L12 and B2 precipitate out? That level of detail has not been investigated yet. Coming back to the results of Gwalani et al. (2018) on the Al0.3 CoCrFeNi HEA, it did confirm a three-phase microstructure consisting of the FCC matrix, L12, and B2 precipitates after annealing at 620 °C. When the Al0.3 CoCrFeNi HEA was cold rolled and directly aged at 620 °C, the phases changed to a tri-phase mixture of FCC + B2 + σ phase. Note that the σ phase is rich in Cr and that raises the same question about its impact of net diffusivity in the matrix. In the cold rolled and aged condition, the microstructure is as predicted by the phase diagram. The nucleation barrier is altered by the presence of dislocations from the cold rolling stage. The practical implication of manipulating the transformation pathways is in the stress–strain response of the microstructure.

4.5.3 Grain Growth in HEAs In the final subsection of this chapter, we focus on another phenomenon that depends intrinsically on diffusion, i.e., grain growth. Classic grain growth relationship is expressed as ( n Dgn − D0g = k0 exp

) −Q t, RT

(4.3)

where Dg is the instantaneous grain size, D0g is the initial grain size, n is the grain growth exponent, k 0 is the kinetic constant, Q is the activation energy, R is the gas constant, T is the temperature, and t is the time. The grain growth kinetics depends primarily on the temperature and the grain boundary energy (type of grain boundary). The values of n and Q represent a particular grain growth mechanism, and k 0 represents the overall kinetics of the diffusion process. It is important to note that the value of n = 2 is expected for grain growth in single phase materials and

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Fig. 4.10 a Calculated isopleth of the Alx CoCrFeNi and b schematic showing example of transformation pathways leading to very different microstructures (Gwalani et al. 2018)

References

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this is referred to as a normal grain growth mechanism and usually the value of Q is similar to the activation energy of lattice diffusion. In multiphase materials, the values of n are higher than 2. Liu et al. (2013) reported a value of n = 3 and activation energy of 321.7 kJ mol−1 for the CoCrFeMnNi HEA. They interpreted this combination of n and Q as solute drag-controlled grain growth mechanism. The value of n is 2 during grain growth in pure Ni. It is important to keep in mind that if the single phase solid solution is not stable during the annealing experiments, the value of n will be higher than 2. Wu et al. (2014) made a very comprehensive grain growth study which compared the grain growth in CoCrFeMnNi HEA with quaternary, ternary, and binary alloys derived from this combination of quinary elements. They also concluded that the grain growth exponents of the equiatomic alloys CoCrFeNi, CoFeNi, CoCrNi, FeNi, and CoNi are ~ 4. A key thing to note is that they plotted D versus t on log–log scales to determine the value of n. This is a common mistake because it ignores D0 in Eq. (4.3) and results in higher values of n. Praveen et al. (2016) have extended the analysis to nanocrystalline CoCrFeNi HEA. But as they noted, the synthesis route of ball milling and sintering resulted in multiphase HEA and the grain growth mechanism became controlled by second phase particles. So, in summary, to understand the impact of intrinsic diffusion on diffusion-controlled processes like grain growth, careful design of experiments and proper analysis are needed to draw meaningful conclusions. At this stage, it is difficult to draw conclusions regarding the sluggish diffusion.

References R. Abbaschian, R.E. Reed-Hill, Physical metallurgy principles-SI version (Cengage Learning, 2009) Z. Balogh, G. Schmitz, Diffusion in metals and alloys, in Physical metallurgy (Elsevier, 2014), pp. 387–559 D.L. Beke, G. Erdélyi, On the diffusion in high-entropy alloys. Mater. Lett. 164, 111–113 (2016) A. Dash, N. Esakkiraja, A. Paul, Solving the issues of multicomponent diffusion in an equiatomic NiCoFeCr medium entropy alloy. Acta Mater. 193, 163–171 (2020) R.T. DeHoff, N. Kulkarni, The trouble with diffusion. Mater. Res. 5, 209–229 (2002) S. Divinski, O. Lukianova, G. Wilde, A. Dash, N. Esakkiraja, A. Paul, High-entropy alloys: diffusion, encyclopedia of materials: science and technology (2020) N. Esakkiraja, A. Paul, A novel concept of pseudo ternary diffusion couple for the estimation of diffusion coefficients in multicomponent systems. Scripta Mater. 147, 79–82 (2018) D. Gaertner, J. Kottke, G. Wilde, S.V. Divinski, Y. Chumlyakov, Tracer diffusion in single crystalline CoCrFeNi and CoCrFeMnNi high entropy alloys. J. Mater. Res. 33(19), 3184–3191 (2018) B. Gwalani, S. Gorsse, D. Choudhuri, M. Styles, Y. Zheng, R.S. Mishra, R. Banerjee, Modifying transformation pathways in high entropy alloys or complex concentrated alloys via thermomechanical processing. Acta Mater. 153, 169–185 (2018) E.O. Kirkendall, A.D. Smigelskas, Zinc diffusion in alpha brass. Aime Trans. 171, 130–142 (1947) J. Kottke, D. Utt, M. Laurent-Brocq, A. Fareed, D. Gaertner, L. Perriere, Ł Rogal, A. Stukowski, K. Albe, S.V. Divinski, Experimental and theoretical study of tracer diffusion in a series of (CoCrFeMn) 100−xNix alloys. Acta Mater. 194, 236–248 (2020) W. Kucza, J. D˛abrowa, G. Cie´slak, K. Berent, T. Kulik, M. Danielewski, Studies of “sluggish diffusion” effect in Co–Cr–Fe–Mn–Ni, Co–Cr–Fe–Ni and Co–Fe–Mn–Ni high entropy alloys;

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determination of tracer diffusivities by combinatorial approach. J. Alloy. Compd. 731, 920–928 (2018) W.H. Liu, Y. Wu, J.Y. He, T.G. Nieh, Z.P. Lu, Grain growth and the Hall-Petch relationship in a high-entropy FeCrNiCoMn alloy. Scripta Mater. 68(7), 526–529 (2013) C. Matano, On the relation between the diffusion-coefficients and concentrations of solid metals. Jpn. J. Phys. 8, 109–113 (1933b) G.E. Murch, S.J. Rothman, Diffusion, correlation, and percolation in a random alloy. Philos. Mag. A 43(1), 229–238 (1981) Y.N. Osetsky, L.K. Béland, A.V. Barashev, Y. Zhang, On the existence and origin of sluggish diffusion in chemically disordered concentrated alloys. Curr. Opin. Solid State Mater. Sci. 22(3), 65–74 (2018) S. Praveen, J. Basu, S. Kashyap, R.S. Kottada, Exceptional resistance to grain growth in nanocrystalline CoCrFeNi high entropy alloy at high homologous temperatures. J. Alloy. Compd. 662, 361–367 (2016) R.E. Smallman, Modern physical metallurgy (Elsevier, 2016) K.Y. Tsai, M.H. Tsai, J.W. Yeh, Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys. Acta Mater. 61(13), 4887–4897 (2013) K.-Y. Tsai, M.-H. Tsai, J.-W. Yeh, Reply to comments on “Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys” by KY Tsai, MH Tsai and JW Yeh, Acta Materialia 61 (2013) 4887–4897. Scripta Materialia 135, 158–159 (2017) M. Vaidya, K.G. Pradeep, B.S. Murty, G. Wilde, S.V. Divinski, Bulk tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys. Acta Mater. 146, 211–224 (2018) P. Wilson, R. Field, M. Kaufman, The use of diffusion multiples to examine the compositional dependence of phase stability and hardness of the Co–Cr–Fe–Mn–Ni high entropy alloy system. Intermetallics 75, 15–24 (2016) Z. Wu, H. Bei, F. Otto, G.M. Pharr, E.P. George, Recovery, recrystallization, grain growth and phase stability of a family of FCC-structured multi-component equiatomic solid solution alloys. Intermetallics 46, 131–140 (2014)

Chapter 5

Application of Artificial Intelligence in the Design of HEMs

5.1 Introduction In 1956, much before the advent of modern high-performance computers, John C Slater, a well-known American physicist, was surprised by an experimental approach, predominantly adapted by the metallurgical community on the development of new materials. Although experimental research led to many serendipitous discoveries in the material world, the statement of John C Slater has been found to be important in twenty-first century. His statement was “I don’t understand why you metallurgists are so busy in working out experimentally the constitution (crystal structure and phase diagram) of multinary system. We know the structure of atoms (needing only the atomic number), we have the laws of quantum mechanics, and we have electronic calculation machines which can solve the pertinent equation rather quickly.” He was surprised since the metallurgists did not show much interest in using computational tools to develop new alloys, containing two or more alloying elements. In the middle of twentieth century, it was considered a dream for many to discover new materials using the available computational tools. However, extensive development on various aspects of computational tools (power, processor, memory, visualization, software, etc.) in the last three decades (1990–2020) has made significant changes, and hence, use of computational tool is all pervasive and even cannot be neglected at all in the material development. The design of multicomponent materials using the palette of a large number of constituents in the periodic table indeed requires this “calculating machines,” and hence, usage has become mandatory. However, the development of any material for practical use involves many steps related to the theory as well as experiments, requiring at least 20 years of sustained efforts. On the other hand, the technological requirement of the advanced materials has recently increased many folds. Hence, the development cycle of any new material from design is required to be shortened to satisfy the burgeoning need of the technology. In fact, the new challenges faced by humanity demands accelerated discovery of the advanced materials. These

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challenges are immense, clean energy from the sustainable sources, reduced environmental pollution, reversing the global warming, security, faster transport systems (rail, hyperloop), defense and surveillance, advanced health care for humanity, etc. These grand challenges demand discovery of novel materials with outstanding properties. The standard design and development cycle to transfer the research done at the lab to the industrial applications take about 20–25 years. This timeline is evidently long enough to achieve the target set by challenges. It has been realized for the same time that accelerated discovery of new materials holds the key to take up these challenges and even find the new technologies for future. The discovery of novel materials with targeted properties, in general, requires a large number of trials and tests as shown in Fig. 5.1a. This broadly involves materials concept, synthesis, device manufacturing, and detailed characterization, requiring long time span to make it industrially useful. Hence, these are obviously far from adequate for the multicomponent materials, considering the fact that high entropy materials have astronomically high chemical space (~1060 ). Therefore, efficient and effective investigation of this unexplored space demands none other than computational tools for smart navigation and usage. Recent advances in the proliferation of computing power can provide the enabling factors in solving these challenges. There are several new computational pathways, the promising one being high throughput computer screening (HTS) of a well-defined chemical space for targeted property followed by the experimentations on the most promising candidate materials (Fig. 5.1b). To accelerate discovery and realization of the required advanced materials, the use of Integrated Computational Materials Engineering (ICME), a promising computational approach linked with experiments, can be used. It needs to be mentioned that ICME and ATT (Accelerated Technology Transition), in 2004, led to a boom in the computational material science and engineering. Instead of using “technology by accident,” we need to move to the direction of science-based technology, so that innovation can be done in a think-based manner. The advent of multicomponent high entropy materials (HEMs) (Miracle and Senkov 2017) created the right opportunities to develop new materials using ICME approach. HEMs provide humongously large combinations of alloy compositions and optimization. If alloying and associated properties for various potential applications are considered, the combinations will multiply and may even reach extremely large numbers, which cannot be handled by purely experiment-based approaches. Hence, utilization of the ICME approach for design and development of HEMs is considered effective and rewarding. In Chap. 4, we have extensively discussed the phase formation. In contrast to the alloy design strategy discussed in Chap. 4, ICME provides quantitative means of predicting phase formation, properties, and performance of the newly developed alloys. Hence, ICME is a powerful tool to realize novel HEMs for various applications. In the following, we shall discuss ICME and the various computational tools used for ICME—CALPHAD, ab initio MD and MC simulation, phase-field modeling, and AI, including machine learning and deep learning. The integration of machine learning (ML)-based approaches to the available computational screening, typically known as high throughput virtual screening (HTVS), is found to be more effective to screen significantly large compositional space (106 ). In this chapter, we

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Fig. 5.1 Different material discovery paradigm: a current paradigm and b ATT paradigm utilizing first principle calculations with materials informatics (Miracle and Senkov 2017)

shall discuss each of the approaches in detail to provide insight of the “new tools on the shelf.”

5.2 ICME ICME or Integrated Computational Materials Engineering deals with integrating various available computational tools across different length scales (atomic to component levels) to develop materials for targeted applications (Horstemeyer 2012). It basically involves “integration of the materials information, obtained using computational tools with engineering properties, performance, and manufacturing processes” (Yi Wang et al. 2019). These computational tools may include simple available ones—CALPHAD to even recent and complex deep learning (DL) methods, as part of machine learning (ML). It can even start with atomic level calculation to component level or vice versa depending on the need (Choudhary et al. 2020). However, the phase formation and their stability are crucial for the target properties and applications, and therefore, they form the basic component of ICME. Nonetheless, CALPHAD is used to provide phase information by utilization of the thermodynamic database available (Walle et al. 2018). The existing database can be utilized to determine other thermodynamic parameters—phase stability, phase boundaries, individual components solubility in various phase, phase transition temperature, etc. The information form the basis for the synthesis of various materials for varied applications. Hence, CALPHAD is considered an essential part of ICME. As mentioned earlier, the calculations can even start with atomic levels. This includes various ab initio methodologies—density functional theory (DFT), Monte

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Carlo (MC), or molecular dynamic (MD) followed phase-field simulations (PFM) for microstructural evolution (Choudhary et al. 2020). DFT calculations allow the prediction of the nature, type, and structure of the nucleating phase(s), clusters, and cluster behavior. MD and MC methods can be combined to find out nucleation dynamic of various possible phases, predicted by CALPHAD. PFM allows us to understand the growth behavior of the nucleating phase(s). Therefore, the combination of DFT, MD/MC, and phase-field simulations enables us to predict the microstructural development in new alloy/materials. The new “tool in the shelf” is the machine learning-based approaches, which are mainly data-driven models to predict phases, microstructure, their properties, and manufacturing routes (Ling et al. 2017). The availability of large volume of data with well-developed algorithms and the exponential growth in the computational power led to recent unprecedented surge of research on machine learning and deep learning. In metallurgy and materials science community, data on various aspects on materials synthesis, property, and phase formation have been generated over last 100–150 years, and hence, ML can be utilized effectively and can be considered as a new dimension of ICME. Microstructure forms the key to understand and predict the properties of the materials. Hence, the discovery of new materials can be accelerated by using these methodologies by processing–microstructure–property correlation. Of late, various researchers worldwide have utilized ICME for new HEMs by exploring huge multicomponent compositional space. Let us now discuss each of the computational methods separately. At the end of this chapter, we shall show how these methods can be integrated to find the problem we have started off this chapter (Fig. 5.2).

Fig. 5.2 Schematic diagram showing the roadmap for ICME utilizing ab initio calculations, CAPHAD, and statistical thermodynamics with experiments to match the prediction of the theoretical calculations

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5.2.1 CALPHAD CALPHAD is considered to be the brainchild of two stalwarts—Larry Kauffman and Himo Ansara (Ansara et al. 1978). In the 1970s, they started developing compositional tools to generate or even recalculate binary phase diagrams. They developed this methodology, known as “CALPHAD”—CALculation of PHAse Diagram, which can also be considered as “computer compiling of the phase diagram and thermochemistry” (Kaufman and Cohen 1956). Since then, as the computational power has increased, CALPHAD has become a powerful tool, providing road map for the generation of phase diagrams and quantitatively the microstructural engineering. CALPHAD can be combined with atomistic simulations, including DFT and MD (Wang et al. 2020). DFT (which will be discussed later) is used to calculate the electronic structure associated with single atom/molecule/clusters or even some condensed phases. This instead involves determining material properties of many electron systems via electron density functional by utilizing the Schrodinger equation (Burke 2012). Therefore, CALPHAD combined with DFT has widely been used to determine the various properties of materials, phase evolution, microstructure, etc. (Fig. 5.3). A notable example is the formation of detrimental sigma (σ ) phase in Ni-base superalloys (Antonov et al. 2017). This can be predicted by comparing the electron number with the one estimated from experiments. Bosch and Stanely developed this new method, popularly known as PHACOMP or PHASE Computation in 1964.

Fig. 5.3 Etymology of ICME, data utilization, and application

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This was further improved upon by others by including the concepts of electrons d—orbitals (Morinaga et al. 1985). In this way, the relative phase boundaries of useful γ phase and deleterious σ phase were computed in the Ni-based superalloys. This was considered a significant achievement of the CALPHAD methodology. For the first time, a computational tool was utilized to obtain the answer to a burning problem. However, the solution was not complete because it was essential to predict the formation of the brittle intermetallic phases in the microstructure μ and Laves phase compared to the γ phase. The development in the late 1980s and 1990s provided enough computational prowess to provide phase boundaries of γ with the detrimental phase(s). This was considered the triumph of the computational tool to find a solution to the problem. Let us now discuss the basic formalism of CALPHAD in the design of HEMs. In fact, CALPHAD utilizes the concept of minimization Gibbs free energy of the phase(s) as a function of compositional variables and temperature at a fixed pressure. Hence, the methodology was related to Gibbs free energy as the description of the system to determine the phase or phase mixtures, which are thermodynamically stable. Gibbs free energy of any phase can be described as ideal G φ = G ref + G excess φ + Gφ φ

Here, G ref φ =

n Σ i=1

(5.1)

xi G io is due to the addition of individual contribution of the pure

is known as the contribution of G φ due to ideal component in the system. G ideal φ is the excess part of mixing (obtained from Boltzmann statistics), whereas G excess φ Gibbs free energy. G G excess = φ

ideal

= RT

ΣΣ

n Σ

xi ln xi

(5.2)

i=1

xm xn

Σ

L φmn (xm − xn )γ

(5.3)

m n>m φ

xm and xn denote mole fraction of m and nth components in the system. L mn are known as interaction parameters or Redlich–Kister parameters (B. xxxx), which can be obtained by fitting the experimental data. CALPHAD has widely been utilized in the last three decades to decipher phases, thermodynamically stable under a given condition. Inherently, CALPHAD requires a database—information of the different material systems to be stored and read by optimization software. This information is stored as a database or TDB files to be used for optimization. Most of the modules typically work on personal computer (PC)-based system and are fast enough to derive various interaction in terms of phases, including phase diagrams. It is possible to generate both stables and metastable phase diagrams. Depending on need, various softwares are available—Thermocal (Xiong and Olson 2015), PADAT (Davies et al. 2002), Factstage (Bale et al. 2016), MT DATA (Davies et al. 2002), Matcale, JMatPro

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(Saunders et al. 2003), etc., in the market for direct utilization. We can use these resources extensively in research and development to save time and perform experimental work properly. In the context of HEMs, i.e., multicomponent systems, this approach has many limitations and usage is to be made carefully to analyze, understand, and interpret the results. The thermodynamic descriptions discussed earlier are normally valid for typical binary and almost some ternary systems. Therefore, a linear extrapolation of such descriptors, discussed earlier, is normally valid for typical binaries and ternaries. Hence, such descriptors’ linear extrapolation is not useful and one may need to use strict thermodynamic formalism for extrapolation. This is more serious because experimental validation of such extrapolation is time-consuming and even not possible in some cases. Nonetheless, advent of HEAs has led to extensive usage of thermodynamic calculations to predict phases or phase mixtures using the available databases. In this context, we will discuss a few cases, where CALPHAD calculation works well. Besides, we shall also discuss some cases where CALPHAD calculations are not even close to the experimental findings. CALPHAD calculation has been found to work well in the Cantor alloy or their compositional derivatives (Miracle and Senkov 2017). This includes CoCuFeMnNi (Sonkusare et al. 2018), CoCrFeNi (Li et al. 2016), and AlCoCrFeNi (Niu et al. 2019) systems. In these systems, CALPHAD prediction matches reasonably well with the experimental findings. Similarly, CALPHAD calculation works well with refractory HEAs, including HfMoNbRe (Lederer et al. 2018), etc. Looking at these success stories, some research groups even used CALPHAD calculations to predict alloy systems showing single phase FCC, BCC, and HCP structures from the palette of large numbers of elements (Gao and Alman 2013). In a nutshell, CALPHAD has been successful in predicting phases or phase mixtures in different multicomponent systems. However, CALPHAD calculations are not useful for various other alloy systems, including TiFeNiCoCu (Sathyanarayana Raju et al. 2018) or even Laves phase forming systems TiZrVCrFe. Hence, caution must be exercised to use CALPHAD for all multicomponent systems.

5.2.2 Ab Initio Ab initio calculations have become an important tool in the last quarter century, especially after the advent of powerful computers (from 1990s). These calculations are primarily based on the determination of electronic structure, and in general, they deal with atomic and electronic degrees of freedom (Mardirossian and HeadGordon 2017). This is done by numerical solution of classical Schrodinger equation with some given boundary conditions dictated by the system under investigation and necessary approximations. For a simple problem, the typical wave function can be approximated using Slater determinant for spin orbitals, which are occupied (Goddard 1967) or even the approximation of spatial orbitals as a linear combination of the basic functions (Pipek and Mezey 1989). It is evident that electronic structure of any material plays a critical role in the determination of structural as well as functional properties of the material. It also allows the determination of energies related to the

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formation, magnetization, and even lattice structure of various alloys. However, the primary use of these calculations involves molecular geometries and energies, vibrational frequencies, spectra, ionization energies, electron affinities, dipole moments, and others connected with electron distribution. In a nutshell, it is a powerful tool for the determination of structural as well as functional properties, albeit needing large computational power and time. However, the effective visualization of the calculations forms an important part in interpretation of the results. Ab initio calculation has been tried and tested for multicomponent alloys in the last 10 years to obtain various information. A simple one would be involving the determination of the crystal structure of the phase formed when a group of 5 elements is utilized for HEMs. In this regard, the effect of Al addition to quaternary CoCrFeNi (Pipek and Mezey 1989) and quinary CoCrFeMnNi would be an interesting one, which can be tested with the experimental results available (Kumar et al. 2020). Li and his co-workers use ab initio calculation on Al addition to quaternary CoCrFeNi alloy to find out the evolution of BCC phase and corroborated the experimental findings (Li et al. 2017). The tremendous development in computer software has made these intensive calculations being performed using software. Materials studios and CASTEP are two useful computer software, being utilized extensively to carry out calculations related to HEAs and allied alloys. Another important work to be cited here is carried out on AlCoCrCuFeNi alloys having Al concentrations of 23 and 8 at.%. Although the conventional CALPHAD analysis was found to be successful in the prediction of phase(s) for the alloy with Al concentration of 23 at.%, Ab initio calculation indicates the formation of brittle intermetallic (NiAl) phases in the alloy with an Al concentration of 8 at.% (Sun et al. 2017). Furthermore, the calculations have extensively been used in the prediction of elastic properties of multicomponent phases, deformation behavior (Sun et al. 2020), and factors controlling the formation of single phase solid solution in HEMs. The popular belief is that the formation of single phase HEMs is primarily due to the large entropy of mixing. Ab initio calculation has shown that it needs not be the case. The principle of large “entropy of mixing” for the multicomponent equiatomic alloys is considered to stabilize the solid solution phase by minimization of free energy. If this is the case, then it restricts the freedom of chasing the multicomponent alloys, i.e., restricting alloy design only to equiatomic compositions. However, experimental work reveals that single phase solid solutions form for non-equiatomic compositions and even some of these nonequiatomic alloy compositions have been found to exhibit extraordinary mechanical properties. Ab initio calculations became handy for an explanation of this behavior. Electronic structure calculations indeed show that “entropy maximization” cannot be used as the main factor in deciding the formation of solid solution in the multicomponent alloy. In this direction, atomistic simulation carried by several authors predicted even lower concentration limit as well as temperature limit for which single phase solid solution can be ensured (Zhang et al. 2015). The ab initio studies have further been extended to understand the effect of irradiation on HEAs (El-Atwani et al. 2002), deformation behavior (Ikeda et al. 2019), estimation of the formation enthalpy, and lattice parameter in multicomponent systems.

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Fig. 5.4 Applications of ab initio calculations: pure metals [Al, Ag (Burke 2012), Fe, Mg, Ti *(Wang et al. 2020), *(Binder et al. 1993)], alloys [Co-based (Kaufman and Cohen 1956) and Ni-based alloys, Fe-X alloys, Mg-RE-TM alloys (Antonov et al. 2017), *(Morinaga et al. 1985), refractory high entropy alloys *(Boesch and Slaney 1964; Redlich-Kister 2014), Ti-X alloys *(Wang et al. 2020), *(Binder et al. 1993)], metal melts (vit1 metallic glass (Boesch and Slaney 1964), Al– Cu), oxides (AgO (Burke 2012), Ag2 O (Burke 2012), and Fe3 O), semiconductors (graphene, sulfur, sulfides, and SiC), and structure defects (stacking faults (Wang et al. 2020), antiphase boundaries (Kaufman and Cohen 1956), and grain boundaries). The further experimental validations can be completed by quantitative convergent-beam electron diffraction (QCBED), which is firstly reported by Nakashima et al. (Tian 2017)

The amorphization in HEAs during irradiation as well as atomic displacement has been investigated by some research groups (Sadeghilaridjani et al. 2020) (Fig. 5.4).

5.2.3 DFT/MD Simulation Further, atomistic simulations can be performed using DFT and or MD simulations. Density functional theory (DFT) is based on calculations performed using quantum mechanics (Sholl and Steckel 2011). It provides the ground state energy of any system containing interaction of particles. It has widely been used in physics, chemistry, and materials science to study electronic structure of systems containing many particles, including various condensed physics. This is considered dominant quantum mechanical simulation method of periodic systems. DFT essentially involves estimation of energy of ground state of collection of atoms, by classical time-dependent Schrodinger equation using Born–Oppenheimer approximation. The approximations are utilized mainly due to the fact that it is impossible to solve Schrodinger equation

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for N-body system. The classical Schrodinger equation is given by H (r 1, r 2, r 3 . . . r N ) = E(r 1, r 2, . . . r N )

(5.4)

Here, H is known as the Hamiltonian, which can be given by N N Σ 1 1Σ 2 H= ∇ + Vext + 2 n=1 − rn ] [r m 0.8. Spinodal decomposition occurred at x = 1, and an ordered B2 structure was reported for x > 2.8. Detailed microstructural analysis at different length scale indicated segregation of copper in the interdendritic region followed with formation of nanoprecipitates resulting in nanostructures for low aluminum content (x < 1) while submicroscopic structures were observed after spinodal transformation for high aluminum content alloys which further showed nanoprecipitation to provide complex microstructures of FCC and BCC phase with nanoprecipitates with very high hardness. A schematic of the microstructure evolution in Alx CoCrCuFeNi alloys is shown in Fig. 6.7. Hemphill et al. (2012) also showed that the Al0.5 CoCrCuFeNi alloy prepared according to the procedure developed by Tong et al. (2005) showed microstructural heterogeneity throughout the casting. The investigation by Hemphill et al. (2012) also highlighted that increase in purity of the elements used for the synthesis of HEA can reduce

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133

Fig. 6.6 Energy dispersive spectroscopy elemental maps for equiatomic MoWAlCrTi HEA in ascast condition (Gorr et al. 2015) Table 6.1 Composition analysis (EDS) results of AlCrFeCoNi high entropy alloy (at.%) Region

Al

Cr

Fe

Co

Ni

A

18.31

20.39

22.33

20.73

18.24

B

28.77

11.98

16.15

19.24

23.85

SR

1.57

0.59

0.72

0.93

1.31

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6 Synthesis and Processing of Bulk High Entropy Mateto showrials

Fig. 6.7 Phase transformation sequence during cooling of Alx CoCrCuFeNi HEA for low (x < 1) and high (x > 1) aluminum contents (Tong et al. 2005)

the amount of casting defects like oxide inclusions and interstitial oxygen content to promote twinning that results in better mechanical properties like improved high cycle fatigue life. The evolution of microstructure in cast AlCoCrCuFeNi as a function of different cooling rates was studied in detail by Singh et al. (2011a) using sophisticated characterization tools like X-ray diffraction, TEM, and 3D atom probe tomography. It was observed that the splat-quenched alloy with cooling rate of 106 –107 K s−1 showed only BCC phase while the crucible cast alloy with cooling rate of 10–20 K s−1 showed one BCC and two FCC (FCC1 and FCC2) phases. TEM analysis indicated that the splat-quenched sample contained an imperfectly ordered BCC phase with domain like nanostructures, while the structure of the crucible cast sample was quite complex. The as-cast alloy showed a dendritic microstructure consisting of several BCC phases like plate-like copper-rich precipitate (FCC2), Al-Ni-rich plates and Cr-Fe interpolates with B2 structure, and one rhombohedron-shaped copper-rich precipitate of LI2 structure FCC phase in the dendritic region. The interdendritic region showed another copper-rich phase with L12 structure corresponding to FCC2. The evolution of complex microstructure at different length scales in equilibrium condition was attributed to large difference of enthalpy of mixing between Al–Ni, Fe–Cr, and Cu–Ni that aids in formation of a hierarchical phase-separated microstructure. Representative microstructures from the investigation by Singh et al. (2011a) are shown in Figs. 6.8 and 6.9 while Fig. 6.10 shows the evolution of phases and elemental segregation in AlCoCrCuFeNi HEA. Singh et al. (2011b) synthesized AlCoCrCuFeNi HEA for different conditions, including splat-quenching, as-cast, and aging treatment to study the effect of processing route on the microstructure evolution and soft magnetic properties to show that the as-cast sample shows a better soft magnetic behavior compared to the

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135

Fig. 6.8 a Bright-field TEM micrograph showing polycrystalline microstructure and b dark field TEM micrograph imaged from [001] superlattice reflection showing regions with high contrast at nanometer length scale for splat-quenched AlCoCrCuFeNi HEA (Singh et al. 2011a)

other two samples. The splat-quenched sample is characterized by equiaxed grains with ordered BCC structure while the as-cast sample shows a dendritic microstructure with the presence of plate-like structures and spherical particles. Representative TEM images from the samples clearly show ordering of BCC phase in the spalt quenched sample, and the as-cast sample shows Al-Ni-rich dendrites and Cr–Fe-rich interplates along with spherical and plate-shaped copper precipitates (Fig. 6.11). The superior soft magnetic properties of the as-cast sample are attributed to the decomposition of Fe–Co–Cr at the nanoscale as seen from atom probe tomography investigation (Fig. 6.12 and Table 6.2). Nagase et al. (2018) studied the evolution of microstructure in eutectic high entropy alloy (EHEA) AlCoCrFeNi2.1 during solidification using centrifugal casting equipment using a metal mold of different heights to achieve a range of cooling rate and air cooling (cooling of the melt in the crucible in air atmosphere) process at multiple length scales using a battery of characterization tools like optical microscopy, scanning electron microscopy, electron probe microanalysis, and transmission electron microscopy. It was shown that the cooling rate affects the formation of a typical solidification macrostructure in terms of formation of shrinkage cavity as well as microstructure in terms of phase fraction, interlamellar spacing of eutectic, and size of dendrites o provide a broad range of hardness for the cast EHEA.

6.2.1.4

Synthesis of Single Crystal HEAs

Synthesis of single crystals of metals and alloys in general and HEAs in particular offers a unique challenge in processing but provides an important opportunity and avenue to study fundamental properties like critical resolved shear stress of different slip and twin systems as well as determination of lattice diffusivities and practical applications as in turbine blades. Traditionally, various single crystal growth techniques like the Czochralski, Stepanov, Bridgman, Verneuil, and floating zone techniques to name a few have been used for the growth of single crystals of high quality with minimum impurity (Capper 2017). Mostly single crystals of semi-conductors

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Fig. 6.9 a Bright-field TEM micrograph of dendritic and interdendritic region b plate-like precipitates along direction in the dendritic region of ordered B2 phase c Rhombohedron-shaped precipitates with LI2 structure in the dendritic region and d microstructure of interdendritic region showing LI2 phase for as-cast AlCoCrCuFeNi HEA. The corresponding diffraction patterns with superlattice reflections for zone axis of , , and are shown in (b), (c), and (d), respectively (Singh et al. 2011a)

have received a lot of attention due to the adverse effect of impurity and defects that adversely affect the functional properties of semiconductors in devices that can ruin an entire electronic component like a microprocessor. Single crystal growth techniques such as Czochralski, Stepanov, and Verneuil are mostly used for growth of high melting point ceramics and elements like silicon while the Bridgman and floating zone methods are common for metals and alloys. We shall discuss the Bridgman and floating zone method in detail as most metals and alloys as well as HEA single crystals are synthesized using the two techniques. The Bridgeman technique involves producing of a crystal from the melt by progressive freezing from one end to the other with growth rates in the range of 0.1–30 mm per hour for materials with melting point up to 2643 K. An important

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Fig. 6.10 Schematic showing the phase segregation observed during solidification of AlCoCrCuFeNi HEA by different routes (Singh et al. 2011a)

Fig. 6.11 TEM bright field image with corresponding diffraction pattern from [100] zone axis for a splat-quenched and b as-cast AlCoCrCuFeNi HEA. Characters A, B, and C show copper-rich precipitates in the as-cast alloy and magnified diffraction pattern at the bottom shows satellite around [022] matrix obtained from chromium–iron-rich region (Singh et al. 2011b)

condition for the success of this method is that neither the melt nor the vapor of the material should react with the crucible material. The quality of single crystal is not as good as that of Czochralski technique with dislocation densities greater than 108 m−2 with most single crystals produced by Bridgman technique containing low angle grain boundaries. The technique uses a crucible with tapered tips made of silica, graphite, or even high melting point element like molybdenum to restrict nucleation. A seed crystal is generally used, and the furnace or the crucible is moved horizontally or vertically to achieve the movement of the freezing zone and produce a single crystal. The growth face is generally made concave to avoid spurious nucleation on the walls of the crucible. In order to grow a perfect single crystal with minimum dislocations, it is important to have a high temperature gradient at the growth interface and low temperature gradient along the radial direction to obtain a uniform isotherm. The vertical setup for the Bridgman technique as shown in Fig. 6.13a is

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Fig. 6.12 a Concentration profiles of different elements from APT and b atom clusters containing more than 30 at.% Fe and 20 at.% Co superimposed on 42 at.% Cr iso-surface for as-cast AlCoCrCuFeNi HEA (Singh et al. 2011b)

Table 6.2 The saturation magnetization romance ratio and the coercivity of the splat-quenched, as-cast, and aged HE alloys Materials

Magnetization at 1.5 T and 320 K (emu/g)

Remanence ratio at 320 K (%)

Coercivity at 320 K Oe

Magnetization at 14 T and 300 K (emu/g)

Splat-quenched

41

1.81

11 ± 10

46

As-cast

36

5.14

44 ± 10

44

more common and additional features like the accelerated crucible rotation technique and axial vibrational control can be employed to grow larger crystals of better quality. Stirring of the melt is essential for compositional homogeneity of alloys and this is particularly important for concentrated alloys like HEAs. In the floating zone method, a molten zone is maintained between two sold rods using induction melting RF coil and a seed crystal as shown in Fig. 6.13b. This method is used extensively for the synthesis of semiconductor-grade silicon single crystals and has also been used for the synthesis of HEAs. Due to the use of radio frequency waves, there is significant stirring of the melt that provides better compositional homogeneity and the presence of a steep temperature gradient accompanied with rotation of the seed and feed rods is possible to control the shape of the solid–liquid interface and obtain single crystals of best quality. Feurbacher et al. (2017) claimed to have grown the first cubic centimeter size single crystals of FeCoCrMnAl using Bridgman solidification (BS) technique employing a tapered alumina crucible of 9 cm length and diameter of 9 and 11 mm. The crucible was inserted in a molybdenum tube that aided in radio frequency heating, and a steep temperature gradient was produced using a cold finger mounted on a

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Fig. 6.13 Schematic for single crystal growth using a Bridgman technique and b floating zone method (Capper 2017)

movable rod. The crucible was inserted fully in the susceptor for melting and was gradually moved out to bring the melt out of the hot zone at 5 mm/h in argon atmosphere. Photograph of one such single crystal from different views along with a backscattered electron image is shown in Fig. 6.14. Moon et al. (2018) synthesized 100 and 110 single crystals of CoCrFeMnNi HEA using Bridgman technique to estimate orientation-dependent solid solution strengthening using compression tests. The X-ray diffractograms and pole figures obtained from electron backscatter diffraction for the single crystals prepared in the investigation are shown in Fig. 6.15. Kireeva et al. (2017) prepared 100 single crystal of CoCrFeMnNi HEA using Bridgman method in argon atmosphere using ingot casting in a resistance furnace for studying the onset of deformation twinning in single crystal of Cantor alloy. In another investigation, Ma et al. (2013) placed crushed pieces of homogenized CoCrFeNiAl0.3 and CoCrFeNiAl HEAs in an alumina tube with internal diameter of 3 mm and wall thickness of 1 mm and carried out melting using an induction furnace followed with Bridgman solidification at a velocity of 5 μm/s through a temperature gradient of 45 K/mm into a water-cooled Ga-In-Sn liquid alloy. The authors employed two BS steps that involved rotation by 180° of the cylindrical sample after one BS step. The alloy with lower aluminum content showed a FCC-structured single crystal while the alloy with higher aluminum content showed columnar structure with BCC structure.

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Both the alloys started with dendritic structure followed with equiaxed and columnar grains in the growth direction, and the alloy with lower aluminum content showed a single crystal region after the columnar microstructure that was absent in the alloy with higher aluminum content (Fig. 6.16). The optical micrographs from different regions of CoCrFeNiAl0.3 HEA showing dendritic microstructure, equiaxed grains with twins, columnar grains, and finally single crystal microstructure are shown in Fig. 6.17. In a significant development, Bridgman technique was successfully employed to synthesize single crystal of Co1.5 CrFeNi1.5 Ti0.5 HEA that shows a γ -γ ’ microstructure similar to that of conventional nickel-based superalloys, thus showing the potential of HEAs for actual engineering applications (Yeh et al. 2014). It is clear that a wide variety of HEAs comprising single phase, multiphase comprising two HEA phases or intermetallics including eutectic HEAs can be prepared by melting and casting route. In addition to casting defects common in conventional alloys, HEAs are mostly characterized by compositional heterogeneity at multiple length scales. At the same time, strategies like multiple melting, clean casting practices, and homogenization can provide a compositionally homogeneous and sound casting of different variety including single crystals and different

Fig. 6.14 a Bridgman crystal of FeCoCrMnAl mounted on a goniometer head showing a small grain of different orientation in the top right corner appearing bright, b different views of the crystal with grain boundaries marked, and c backscattered electron image of the same crystal (Feuerbacher et al. 2017)

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Fig. 6.15 a X-ray diffractogram of 100 and 110 single crystals and polycrystalline CoCrFeMnNi HEA. 001 pole figure of b 100 and c 110 single crystal from EBSD with GD representing growth direction (Moon et al. 2018)

Fig. 6.16 A schematic diagram for microstructure evolution by Bridgman solidification technique for a CoCrFeNiAl0.5 and b CoCrFeNiAl HEA (Ma et al. 2013)

morphology of grains like columnar and equiaxed single phase and multiphase HEAs using melting and casting route.

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Fig. 6.17 a–d Optical metallographs of CoCrFeNiAl0.3 alloy synthesized by BST showing microstructural evolution (Ma et al. 2013)

6.2.2 Powder Metallurgical Processing Route Traditionally, the powder metallurgical route for HEAs comprises mechanical alloying using ball milling followed by spark plasma sintering unlike conventional metals and alloys that are processed by conventional sintering techniques using gas atomized powders of metals and alloys. Mechanical alloying (MA) that comprises subjecting elemental powders to large strain deformation at high strain rate by interaction between the powders and the grinding media in a mill is used to produce non-equilibrium alloys as well as nanocrystalline metals and alloys (Suryanarayana 2001). MA is carried out in high energy ball mills (Fig. 6.18) with a variety of grinding vials and balls of tungsten carbide, hardened chrome steel, and zirconia in dry or wet condition using inert atmosphere of argon in the presence of process control agents like toluene or ethanol at room temperature or cryogenic temperature. Different powder to ball ratio, process control agents, milling speed, milling time, type of mill, and milling atmosphere are optimized to obtain the desired product. It is well reported that mechanical alloying is used to synthesize materials in non-equilibrium state by energizing and quenching that achieves a metastable state driven by plastic deformation at high strain rate to high strain that leads to a configurationally frozen state to achieve extraordinary properties like extreme grain refinement to nanometer regime, solubility in immiscible elements, amorphization, and formation of new phases. Mechanical alloying by high energy ball milling technique has been used to produce variety of commercially important and scientifically interesting materials

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like Y-Co intermetallic compound and Ni-Nb system. A variety of investigations have been carried out to synthesize numerous stable and metastable phases like supersaturated solid solutions, crystalline and quasicrystalline intermediate phases, nanocrystalline metals and alloys by top-down approach, amorphous alloys, and oxide-strengthened alloys. However, contamination during MA from the balls and vials is a major drawback of the technique and sufficient process optimization is essential to avoid the same. Nevertheless, mechanical alloying offers a robust tool for synthesis of HEAs in powder form as the stored energy of plastic deformation can help in mixing of different elements into each other due to enhanced diffusion at the nanometer length scale and lead to the formation of solid solutions. The presence of multiple elements in HEAs offers strategies for sequential alloying in which different elements are introduced for ball milling in a sequence to obtain a quinary or higher order HEA from elemental powders instead of conventional alloying in which all the elements are added together (Fig. 6.19). There is no universal advantage of sequential or conventional alloying in terms of reduction in milling time, and optimization is necessary for individual alloy composition.

Fig. 6.18 Inside view of planetary ball mill used for synthesis of HEAs

Fig. 6.19 a Conventional and sequential scheme for alloying followed in the synthesis of AlNiCoFeCr HEA and b BCC phase fraction for different routes (Vaidya et al. 2017)

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Vaidya et al. (2017) carried out a detailed investigation and studied the effect of sequential alloying for the synthesis of AlCoCrFeNi for 12 different sequences based on six different binary systems, namely Al-Co, Al-Ni, Al-Fe (B2 binary); Fe-Cr (BCC binary); and Co-Ni and Fe-Ni (FCC). It was observed that irrespective of the sequence of alloying, the nanocrystalline AlCoCrFeNi HEA showed the combination of FCC and BCC phases; however, the volume fraction of the individual phases was altered depending on the sequence of alloying. This investigation clearly demonstrated that unlike arc melting, mechanical alloying offers an additional handle to control phase fraction in HEAs which can be exploited to achieve optimum properties. The loose powder obtained from MA was compacted in a die cavity for consolidation to obtain a green compact that is subjected to solid-state sintering below the melting point of the alloy in a furnace with inert atmosphere to make bonds between the particles. Consolidation of metastable powders by conventional sintering technique is not desired as all effects of MA would be lost. Therefore, an alternate sintering technique, namely the spark plasma sintering (SPS) in which compaction and sintering take place simultaneously, in a very short time, compared to conventional sintering techniques like hot isostatic pressing (HIP) and hot pressing (HP) was employed. Consolidation by SPS ensured that the nanocrystalline nature of the MA metallic powders and high dislocation density was retained in the sintered product (Yadav et al. 2018a). An investigation on AlCoCrCuFeTi nanocrystalline HEA showed that the crystallite size of 13–20 nm after mechanical alloying increased to 45–50 nm after SPS at 1173 K. Similar observation of retention of nanocrystalline grain or crystallite size after SPS was reported for AlCoCrCuFe and CoCrCuFeNi HEA by Praveen et al. (2012). Figure 6.20 shows a schematic of a SPS unit. MA followed with SPS can provide a net-shaped or near net-shaped object of nanocrystalline metals and alloys, cemented carbides, and oxide-dispersed alloys for various applications. Thus, a combination of mechanical alloying followed with spark plasma sintering (MASPS) can be a viable route for synthesis of bulk HEAs.

6.2.2.1

Synthesis of HEAs by Powder Metallurgical Route

In one of the early investigations on MA of HEAs, Varalakshmi et al. (2008) carried out a systematic investigation on a series of subset alloys based on hexanary AlFeTiCrZnCu HEA comprising Al-Fe, Al-Fe-Ti, Al-Fe-Ti-Cr, Al-Fe-Ti-Cr-Zn, and Al-FeTi-Cr-Zn-Cu alloys to show that a single BCC phase was observed in all the alloys with grain size in the nanometer regime after ball milling elemental powders for 10 h. X-ray diffractograms of different alloys as a function of milling time are shown in Fig. 6.21. Detailed X-ray and transmission electron microscopy analysis confirmed the presence of nanocrystalline grain size, and BCC crystal structure and EDS in TEM indicated the equiatomic nature of the hexanary alloy. The hexanary alloy particles were stable and retained their nanocrystalline nature even after compaction at 1.8 GPa pressure followed with sintering in argon atmosphere at 1073 K for one hour with the sintered sample showing Vickers hardness of 2 GPa. The authors showed that other HEA systems like CuNiCoZnAlTi and NiFeCrCoMnW also show

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Fig. 6.20 Schematic of spark plasma sintering (SPS) setup

single-phase BCC structure after MA, thus paving a way for a deluge of investigations on MA and sintering as a processing route for the synthesis of nanocrystalline HEAs. Zhang et al. (2009) synthesized nanocrystalline CoCrFeNiCuAl HEA solid solution comprising BCC and FCC phase by ball milling elemental powders for 60 h and on further annealing at 1273 K higher fraction of FCC precipitated but the alloy retained its nanocrystalline grain size. Though sintering was not reported in the present investigation, it clearly demonstrates the stable nature of nanocrystalline HEAs produced by ball milling. In a follow-up investigation, Varalakshmi et al. (2010) synthesized nanostructured CuNiCoZnAlTi HEA using MA and vacuum hot pressing at 1073 K with 30 MPa pressure. It was shown that the milled powder showed BCC phase and two minor FCC phases appeared after sintering to yield hardness of 7.55 GPa and compressive strength of 2.36 GPa for the sintered product. Praveen et al. (2012) produced AlCoCrCuFe and NiCoCrCuFe HEAs by mechanical alloying followed with SPS and studied the evolution of phases to address the issue of establishing a thermodynamic framework for predicting solid solution phases. X-ray diffractograms from the two HEA compositions as a function of milling time and after SPS at 1173 K are shown in Fig. 6.22. They showed that copper has a tendency to precipitate out in both the systems and contributes to the formation of the chromium-rich sigma phase and transformation from BCC to B2 structure on sintering that contributes to high hardness. Fu et al. (2013) carried out synthesis of non-equiatomic CoNiFeCrAl0.6 Ti0.4 HEA using MASPS to obtain a microstructure comprising of FCC and BCC phase after mechanical alloying and that of two FCC phases and a new BCC phase (original BCC phase decomposed to new FCC and new BCC phase) after SPS to achieve 98.83

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Fig. 6.21 X-ray diffractograms of mechanically alloyed a AlFe, b AlFeTi, c AlFeTiCr, d AlFeTiCrZn, and e AlFeTiCrZnCu as a function of milling time (Varalakshmi et al. 2008)

relative density and excellent compressive strength and Vickers hardness. This was attributed to the presence of twins in the original FCC phase that might have evolved during MA or SPS. Chen et al. (2013a) showed that synthesis of Al0.6 CoNiFeTi0.4 HEA by MA led to formation of a FCC solid solution that transformed to a mixture of FCC and BCC phase on SPS with nanoscale twins in the FCC phase that impart

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excellent mechanical properties to the alloy at room temperature. Another investigation by Chen et al. (2013b) on FeNiCrCo0.3 Al0.7 showed the presence of two BCC phases rich in Fe-Cr with A2 structure and Ni-Al with B2 structure and a FCC high entropy phase that is characterized by nanoscale twins after SPS which contributed excellent hardness and compressive yield strength. Fang et al. (2014) showed that the FCC + BCC structure of Al0.5 CrFeNiCo0.3 C0 .2 HEA prepared by ball milling decomposed to a new FCC and BCC and ordered BCC phase along with Cr23 C6 carbide on SPS at for. The FCC phase rich in Fe-Ni shows the presence of nanotwins and coupled with Ni-Al-enriched BCC phase and Al-enriched B2 phase contribute to excellent compressive strength and hardness. Representative TEM images showing

Fig. 6.22 X-ray diffractograms of mechanically alloyed powders of a AlCoCrCuFe and b CoCrCuFeNi as a function of milling time and c X-ray diffractogram of SPS processed HEAs (Praveen et al. 2012)

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Fig. 6.22 (continued)

the morphology of twins are shown in Fig. 6.23. Thus, microstructural engineering of the FCC HEA phase to yield nanoscale twins accompanied with ordered BCC phases is an excellent strategy to achieve high strength and hardness in HEA samples prepared by MASPS. Mridha et al. (2013) showed the formation of FCC copper solid solution and BCC chromium solid solution in Cu30 Zn10 Ti20 Fe20 Cr20 HEA after MA as well as MASPS and Youseff et al. (2015) developed a low-density non-equiatomic Al20 Li20 Mg10 Sc20 Ti30 single-phase FCC HEA using MASPS. In another investigation, Ti20 Co20 Cu20 Fe20 Ni20 HEA was successfully prepared via mechanical alloying (MA) followed by consolidation using spark plasma sintering (SPS) at different

Fig. 6.23 TEM microstructure with SAED pattern for FCC1 phase of HEA along a [011] zone axis of matrix and b [0-1-1] zone axis of twin (Fang et al. 2014)

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temperatures (Mohanty et al. 2015). A single phase supersaturated solid solution with FCC (χ ) structure was observed after MA of the elemental powders up to 15 h in argon atmosphere. During the SPS process, the metastable FCC (χ ) phase transformed into a new FCC2 (μ) phase with gray contrast and FCC1 (δ) phase with black contrast in TEM images. After SPS, the TEM micrographs of sintered specimens, especially at higher sintering temperature (1173 K), reveal the presence of both nanosized and coarse grains, with some of the coarse grains showing lamellar microstructure consisting of alternate μ and δ phases and also the nucleation of δ phase precipitates within the μ phase grains as observed in Fig. 6.24. The detailed microscopic studies showed the interconnected morphology of the Co-rich regions indicating that the MA powder undergoes spinodal decomposition during SPS leading to the formation of Cu (μ) and Co (δ)-rich regions in the microstructures. The increase in hardness of the sintered specimen at higher sintering temperature (1173 K) was attributed to the occurrence of spinodal decomposition of the phases during SPS along with the formation of Co-rich precipitates within the Cu-rich grains. Mohanty et al. (2014) utilized the process of MASPS to achieve sinter-ageing in AlCoCuNiZn HEA that shows supersaturated FCC solid solution beta after 15 h of ball milling in argon atmosphere. The FCC beta phase undergoes decomposition into another FCC gamma phase and FCC alpha phase with LI2 structure with a uniform dispersion of the (Co, Ni)Al-rich cuboidal precipitates in the FCC matrix (Figs. 6.25 and 6.26). The formation of ordered FCC α (L12 ) phase during heating or cooling cycle of SPS gives peak hardness, three times that of the solutionized sample. There is an increase in hardness with the increase in temperature followed by decrease at higher temperature for isochronal aging from 873 to 1273 K with the sample sintered at 800 °C showing peak hardness. A similar trend of increase in hardness followed by decrease is obtained for samples subjected to sinter-ageing at 1073 K for different times with the 20-min sinter-aged sample showing maximum hardness. A detailed TEM analysis was carried out to determine the average size of the precipitate, while X-ray diffraction was employed to determine the lattice parameter of the matrix and the precipitate. It was observed that there was a sudden increase in the precipitate size at 1173 K which was accompanied with decrease in hardness due to incoherent nature of the precipitate that can lead to change in mechanism from dislocation cutting the precipitate to dislocation making a loop around the precipitate leading to decrease in hardness. In another investigation by the same authors, the sinteraged Al20 Co20 Cu20 Ni20 Zn20 HEA was solutionized at 1433 K for 96 h followed by ice water quenching to obtain single phase FCC structure (Mohanty et al. 2017a). Isochronal heat treatments of the solutionized specimens at various temperatures for 48 h led to the formation of ordered FCC α (L12 ) phase within the grains of FCC γ phase. This contributed to a significant hardening at temperatures to 773 K before softening sets in for higher annealing temperatures. The hardening behavior at 773 K was attributed to the formation of nanostructured ordered FCC α (L12 ) precipitates embedded in the FCC γ matrix. Thus, the investigations by Mohanty et al. (2014, 2017a) firmly established that conventional precipitation hardening mechanism can be exploited as a possible strengthening mechanism in nanocrystalline HEAs prepared by MASPS route by the proper choice of constituent elements. The

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Fig. 6.24 a TEM images and corresponding diffraction patterns from different regions showing the evolution of microstructure in 3 mm suction cast HEA and higher magnification images for (b–e) phases after annealing at 1223 K (Mohanty et al. 2015)

ability to achieve threefold increase in hardness is similar to that of conventional age-hardening alloys in HEAs though concepts like coherency strain and dislocation precipitate interaction in HEAs is yet to be established and are expected to be complicated compared to that of dilute alloys like Al-4% Cu. Mohanty et al. (2017b) synthesized equiatomic AlCoCrFeNi HEA by mechanical alloying in metastable form to yield supersaturated FCC (τ ) and BCC (κ) phases. Spark plasma sintering of the mechanically alloyed powder led to phase separation yielding Al-Ni-rich L12 (α’) phase and Al-Fe-Ni-Co-rich solid solution (ε), and the presence of nanoprecipitates of Co-Cr-Fe σ phase was observed for the sample

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Fig. 6.25 X-ray diffractograms from milled and SPS processed equiatomic AlCoCuNiZn HEA (Mohanty et al. 2014)

sintered at 1273 K (Figs. 6.27 and 6.28). The presence of eutectoid microstructure, hard σ phase, presence of twin boundaries, and better density imparts high hardness of ~8 GPa to equiatomic AlCoCrFeNi HEA sample sintered at 1273 K. Cheng et al. (2019) studied the evolution of microstructure and mechanical properties of FeCoCrNiMnAlx (x = 0 − 0.5) while Lv et al. (2019) synthesized CrMoNbWTi-C HEA by mechanical alloying followed with high-pressure sintering. Single phase BCC solid solution peaks were observed after MA; however, after sintering at 1723 K, three different phase BCC solid solution phase (volume fraction 57.75%), fine-grained Laves phase (volume fraction 26.68%), and high temperature carbide phase (volume fraction 16.16%) were observed in the microstructure of CrMoNbWTi-C HEA. The refractory CrMoNbWTi-C HEA also exhibited high fracture strength (3094 MPa) and hardness (8.26 GPa) that was attributed to the precipitation strengthening due to the presence of intermetallic Laves phase (Cr2 Nb) and carbide phase ((Ti,Nb)C), and grain boundary strengthening. Colombini et al. (2018) showed that mechanical alloyed powders of showed better densification for SPS compared to microwave sintering resulting in superior mechanical properties for the former. Effect of MASPS and casting route on MEAs like CoCrNi (Moravcik et al. 2017) and AlCrFeNi (Jiang et al. 2019) showed better mechanical properties like modulus and hardness for the MASPS route due to retention of non-equilibrium microstructure as well as smaller grain size. Recent investigation by Colombini et al. (2018) in which the authors employed mechanical activation that comprises short-term milling followed with annealing to synthesize AlCoCrFeNi HEA with a combination of BCC and FCC phase by ball milling elemental powders for 1 h followed with SPS at 1273 K. Attempts were directed to synthesize the same composition using microwave-assisted sintering as it offers a less energy-intensive process. However, partial melting in microwave sintering led to poor densification and contributed to inferior mechanical properties compared to the samples prepared

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Fig. 6.26 TEM micrographs with corresponding selected area electron diffraction pattern for AlCoCuNiZn HEA sintered at a 973 K, b 1073 K, and c 1173 K with higher magnification images in the inset (Mohanty et al. 2014)

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Fig. 6.27 TEM bright field micrographs (a, b) and selected area diffraction pattern (c, d) and higher magnification image with diffraction pattern showing twin from phase in AlCoCrFeNi HEA samples sintered at 1273 K (Mohanty et al. 2017b)

by SPS. Even postmicrowave sintering improvement in densification and microstructure could not offer properties comparable to that of samples prepared by MASPS route. Thus, MASPS route followed with postsintering hipping and/or heat treatment has established itself as the best powder metallurgical route for HEA synthesis.

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Fig. 6.28 High angle annular dark field image of HEA sintered at 1273 K (Mohanty et al. 2017b)

6.3 HEA-Based Composites The concept of HEA composites (HEAc) is based on similar principle as that of metal matrix composites with the metal or alloy matrix being replaced with a HEA matrix and an additive ceramic phase that can offer excellent properties like high modulus, specific strength, and hardness that are not possible to achieve by individual phases. Composite materials evolve from the idea of exploiting the synergy between the properties of the constituent materials with dissimilar properties to achieve properties that are superior to the properties of the individual constituents. Metal matrix composites that essentially contain an alloy with ceramic reinforcements have widely been studied for different materials like aluminum alloys, iron, and titanium alloys as well TiAl intermetallic-based composites. Fan et al. (2014) synthesized the (FeCrNiCo)Alx Cuy high entropy alloy and their composites with titanium carbide using a novel route schematically shown in Fig. 6.29. Elemental

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155

powders of Al, Ti, and C in equimolar proportions were ball milled and compacted to 65–75% relative density to produce a pellet. The pellet was loaded in an arc melting facility, and elemental pieces were kept on top of the pellet with the higher melting point elements in contact with the pellet and lower melting point elements at the top. On striking the arc, the lower melting point elements melted and when the melt pool reached a temperature of 1323 K, a self-propagating reaction between titanium and aluminum started and melted the high melting point elements as well as produced TiC. The melting point of TiC is 3433 K so it does not undergo melting; however, multiple remelting is required to produce a homogeneous composite and placed at the bottom during arc melting with the HEA of arc melting. There was an increase in the volume fraction and particle size of TiC with increasing level of composite preform for different HEA compositions with a homogeneous distribution of the TiC particles throughout the HEA matrix for all the samples (Fig. 6.30). The HEA phase characterized by the presence of a FCC solid solution phase, NiAl intermetallic phase, and spinodal decomposed microstructure showed yield stress of 1637 MPa and ductility of 31.8%, and the composite showed significant improvement in yield strength with little loss in ductility. 3Al(l) + Ti(s) → Al3 Ti(s)

(6.1)

Al3 Ti(s) + C(s) → TiC(s) + Al(l)

(6.2)

Sun et al. (2018a) used a similar approach to synthesize FeCoNiCu HEA reinforced by in situ TiC particles and graphite whiskers using a preform of FeTiC and vacuum induction melting. A schematic showing the details of the process is shown in Fig. 6.31. Powders of Ti, Fe, and C were ball milled and compacted in the cylindrical shape of 20 mm diameter and 2–3 mm height and placed in a graphite

Fig. 6.29 Schematic illustrating the manufacturing of (FeCrNiCo)AlxCuy+z vol.% TiC composite (Fan et al. 2014)

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Fig. 6.30 Secondary electron images for a (FeCrNiCo)Al0.75 Cu0.25 + 2.5 vol.% TiC, b (FeCrNiCo)Al0.75 Cu0.25 + 5 vol.% TiC, c (FeCrNiCo)Al0.75 Cu0.25 + 10 vol.% TiC, d (FeCrNiCo)Al0.7 Cu0.5 + 2.5 vol.% TiC, e (FeCrNiCo)Al0.7 Cu0.5 + 5 vol.% TiC, and f (FeCrNiCo)Al0.7 Cu0.5 + 10 vol.% TiC (Fan et al. 2014)

crucible in an induction furnace along with an elemental feed of FeCoNi, and Cu. Melting was carried out in argon atmosphere at 450 A, and the current was reduced to 300 A to carry out magnetic stirring for achieving homogeneous distribution of TiC in the composite. During the process of melting, iron and titanium reacted to form a FeTi transient phase that decomposed to Fe and Ti phase. Ti then reacted with carbon to form submicron TiC phase, and finally, the eutectoid reaction took place providing graphite. The structure of TiC and graphite was FCC type, and boundaries between the reinforcement and matrix were clean. Contributing to excellent mechanical properties of the 10% (TiC + graphite) composite I addition to in situ composites, many HEAcs were produced by mechanical alloying and SPS or HPS. Sun et al. (2018b) synthesized non-equiatomic Fe18 Ni23 Co25 Cr21 Mo8 WNb3 C2 HEA composite with FCC HEA phase and M6C reinforcement phase that provided high hardness and wear resistance using MA and high-pressure sintering. Sathyamoorthi et al. (2017) carried out heat treatment of CoCrFeNi MEA powders prepared by MA and then performed SPS to obtain a HEAC comprising HEA CoCrFeNi phase along with chromium carbide and chromium oxide at the grain boundaries that contributed to excellent thermal stability at 700 °C for 600 h and retained the ultra-fine grain size due to pinning of grain boundaries by oxide particles at the grain boundaries (Fig. 6.32). Yadav et al. (2018b) prepared composites of (AlCrFeMnV)100-xPbx and (CuCrFeTizn)100-xBix for x = 0, 5, 10 using MASPS route and showed that the composites prepared show excellent wear resistance. They also added TiB2 to the (AlCrFeMnV)90 Bi10 composite to further improve the hardness and wear properties of the composite prepared by MASPS route. Zhang et al. (2017a) used a mixture of argon-atomized CoCrFeNi MEA powder along with nickel-coated MoS2 and graphite powder in 8 and 5 weight percentage and performed SPS at 1423 K

6.4 High Entropy Ceramics: Oxides, Carbides, and Borides

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Fig. 6.31 Illustration for synthesis of HEA composites (Sun et al. 2018a)

higher heating rate of 423 K/min and short holding time of 3 min to avoid decomposition of the lubricants to obtain a composite with uniform distribution of MoS2 and graphite. The composite showed excellent strength, hardness, and wear resistance that was attributed to the HEA phase and the reinforcements while the selflubricating nature due to the presence of reinforcements and formation of oxides provided excellent high temperature wear resistance. Zhang et al. (2017b) used a similar MASPS route to produce self-lubricating HEAcs of HfNbTiVSi0.5 and CoCrFeNi-Ag-BaF2 /CaF2 that showed excellent wear resistance at room temperature as well as sufficiently high temperature. Similarly, Moravick et al. (2017) prepared a composite of CoCrNi/boride composite by MASPS route that has FCC MEA matrix with oxide and carbides with large fraction of Cr5 C3 carbide that provides selflubricating effect while Fu et al. synthesized TiB2 -TiNiFeCrCoAl HEA composite (with 5, 10, and 20 wt.% HEA) using liquid-state SPS to obtain better densification and excellent mechanical properties.

6.4 High Entropy Ceramics: Oxides, Carbides, and Borides The synthesis of high entropy ceramics is generally carried out using processing techniques used for conventional ceramic synthesis comprising of mixing of ceramic powders, calcination, and sintering. Rost et al. (2017) synthesized HEO by mixing MgO, NiO, CuO, CoO, and ZnO powders followed with calcination at 1273 K for 12 h that involved intermittent mixing during the heat treatment. The product was then mixed with isopropyl alcohol to prepare a slurry and was ball milled in yttriastabilized media for 24 h. The mixture was then dried in a fume hood at room temperature and refired at 1273 K for 12 h. The HEO powder was consolidated using

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Fig. 6.32 a Reaction process for Fe-Ti-C alloy and b schematic of the HEA composite microstructure (Sathiyamoorthi et al. 2017)

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Fig. 6.33 Schematic showing the processing route for the fabrication of high entropy ceramics (Tallarita et al. 2019)

SPS or conventional sintering techniques. Similar approach comprising ball milling followed with SPS was employed for the synthesis of carbides and diborides too. In some cases, self-propagating reactions were employed to produce ceramics from elemental powders and consolidation was carried out using SPS. In addition to high entropy oxides, high entropy ceramics like perovskites, carbides, and borides are also prepared using ball milling and spark plasma sintering (Fig. 6.33) (Tallarita et al. 2019). In addition, reaction sintering and flash sintering routes are also used to synthesize high entropy ceramics. Flash sintering of oxides is an upcoming field, and it has been shown that a unique defect structure can be introduced in oxides that can provide additional functionalities to oxides, and this methodology can provide high entropy oxides in particular and high entropy ceramics with excellent properties for futuristic applications.

6.5 Combinatorial Materials Synthesis The concept of multicomponent multiprincipal elements opens up a vast compositional space for the millennial metallurgist to explore. Though thermodynamic modeling using CALPHAD and other computational approaches can help in narrowing the scope of compositions to be explored, experimental verification of the same is of utmost importance for the development of new alloy (Kattner 1997). To this end, combinatorial material synthesis is of tremendous importance as it helps in synthesizing high entropy alloy compositions that have been narrowed by computational techniques. In this sense, combinatorial material synthesis fits in the Integrated Computational Materials Engineering framework and can be coupled with high

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throughput experiments or multifield characterization tools for the design and development of new HEAs. Combinatorial materials synthesis comprises four methods comprising diffusion couple, rapid alloy prototyping, and additive manufacturing for bulk samples, while thin-film deposition can be used for preparing materials in two dimensions for functional applications. Diffusion couple technique has been used to determine the diffusivity of one metal into another since a long time and is very well established. However, with the advent of excellent microscopy techniques and micro and nanomechanical testing techniques, the simple diffusion couple can be used to explore vast compositional spaces and establish a structure–property paradigm for a variety of materials. A diffusion couple between alloys can help us go beyond binary, and deeper insights can be obtained by using alloys to build thermocouples. For instance, Vyasa et al. (2013) studied the shape memory performance of Pd containing NiTi shape memory alloy using a diffusion couple between TiNi and TiPd. The compositional variation from binary TiNi to binary TiPd was mapped using electron microprobe analyzer, and spherical nanoindentation and recovery experiments were performed by heating to determine the recoverable strain as a function of Pd content in TiNi alloy (Fig. 6.34). This was one of the first examples demonstrating the coupling of diffusion couple technique with advanced characterization and mechanical testing tools for development of new ternary alloy with specific properties. Similar analogy has been applied in HEAs, and diffusion couple between a quaternary and single element or a ternary and binary can be prepared to obtain different compositions in the diffusion zone that is the interface. Similarly, instead of preparing dipoles, multipoles between pure metals can be prepared to study microstructures and mechanical properties of high entropy compositions (Fig. 6.35). Once a compositional gradient is obtained, many physical and mechanical properties can be tested using state-of-the-art characterization tools like microfocus Xray diffraction for phase identification, time-resolved thermoreflectance technique for thermal conductivity, nanoindentation for modulus and harness, and micropillar compression and tension for plastic properties. Localized corrosion behavior can be studied using microelectrode technique. Thus, state-of-the-art material testing and characterization techniques operating at smaller length scales can be employed to develop new alloys by combinatorial method using diffusion couple and multiple technique. Rapid alloy prototyping involves multiple casting route to prepare multiple castings with different compositions in one single step (Li et al. 2018). This is followed with batch processing for homogenization, hot working, cold working, and tensile testing and physical property testing to map to establish structure–property–performance paradigm for narrowing the composition range of a HEA for a particular composition from a small number of compositions already screened using thermodynamic modeling. It is to be mentioned here that all characterization tools like X-ray diffraction for phase identification, scanning electron microscopy for microstructure, electron backscatter diffraction for microtexture and testing methods like tensile or compression test at different temperature and strain rate, and fracture toughness which are commonly used for materials development can be integrated with

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Fig. 6.34 Optical micrograph of indents along the diffusion couple of TiNi and TiPd a in the as received condition and b after austenization. The variation of recoverable strain as a function of temperature and Pd content is shown in (c) (Shastry et al. 2013) Fig. 6.35 Combinatorial experiments using different diffusion multiples for quaternary (a and b) and quinary systems in (c) (Li et al. 2018)

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RAP. Another important experimental technique that can be employed is the high throughput experimental technique like correlative indentation (to find hardness and modulus of different phases) and in situ deformation and annealing studies in scanning electron microscope with EBSD or TEM can also be employed to carry out multidimensional analysis of the newly developed alloys by RAP. Nevertheless, a strong theoretical background and modeling results can help in targeted development of alloys. For instance, in a recent investigation (Oh et al. 2019; Li et al. 2017; George et al. 2019; Li and Raabe 2017) predicted the solid solution strengthening potential of CCAs using electronegativity difference between the constituent elements based on first principle calculations. Similarly, prediction of TWIP/TRIP effect by determining SFE of new HEA compositions is also possible. Thus, a RAP method based on sound theoretical background aided with high throughput experimental techniques followed with numerical simulations can aid in combinatorial development of new HEA compositions. A recently developed combinatorial analysis technique is based on additive manufacturing that has become the method of choice in the last few years due to the availability of additive manufacturing facilities. It is expected that the entire manufacturing paradigm will change with AM and democratization of manufacturing process will take place. This is one technique that suits HEAs as it offers an opportunity to explore the vast compositional space available and shall be discussed in a detailed manner in the next section devoted to AM (Fig. 6.36).

Fig. 6.36 High throughput alloy synthesis and characterization for development of new alloys. Important steps are covered from (a–f) that involve casting, rolling, homogenization, cold rolling, machining and tensile testing, and magnetic characterization (Li et al. 2018)

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6.6 Additive Manufacturing Additive manufacturing (AM) is a novel fabrication technique comprising layer-bylayer deposition of the material to build an entire component. It is also known as rapid prototyping or 3D printing and, unlike conventional fabrication techniques that are subtractive in nature, minimizes material wastage and can fabricate complex and intricate geometries. The process of AM comprises building a 3D computer-aided design (CAD) model of the component that is then converted to a layer-by-layer model, which is built by depositing layers of thickness in the range of 20–100 μm. AM processes can use metallic, or alloys in powder, wire, or sheet form, and the process of melting is carried out using a laser of different power or electron beam. AM processes employ an intense power source and cause localized melting to build a component layer by layer. This leads to rapid solidification of the localized melt pool leading to non-equilibrium conditions accompanied with reheating and even melting leading to a completely different microstructure compared to conventional melting and solidification. This contributes to formation of metastable phases, heterogeneous microstructure and chemical composition, and residual stress in AM products compared to conventional manufactured products. Additive manufacture products inherently have porosity as well as poor surface finish that makes secondary heat treatment as well as surface machining or hot isostatic pressing mandatory. Despite the aforementioned limitations of the additive manufacture process, rapid solidification avoids the formation of intermetallics as well as avoids interdendritic segregation which are suitable for high entropy alloy synthesis. The most common AM processes for metals and alloys are (a) laser beam melting (LBM) or selective laser melting (SLM), (b) electron beam melting (EBM), and (c) laser metal deposition (LMD) or direct metal deposition (DMD) or laser-engineered net shaping (LENS) or laser cladding (Li et al. 2019). A schematic of the three important metal additive manufacturing processes is shown in Fig. 6.37. Selective laser melting or laser additive manufacturing is a powder-based technique in which a high power laser beam is scanned over a bed of metal or alloy powder shielded from atmosphere by argon purging the chamber to build a component layer by layer (Zhu et al. 2018). A blade or roller is used to uniformly spread the powder on the bed from a hopper and the height of the bed is reduced and powder is spread over to add another layer. Thus, consecutive cycles of powder spreading followed with laser scanning are used to build a 3D component layer by layer. This technique employs laser with power between 20 and 1 kW and spot size between 50 and 180 μm with layer thickness of 100 μm. The scanning of the laser leads to localized melting followed with rapid solidification that leads to formation of non-equilibrium microstructures. The building of subsequent layers ensures that different layers of the AM part undergo complex heat treatment that leads to heterogeneous microstructure and chemical composition as well as build-up of significant residual stress in the AM part. The surface roughness of the AM part is also poor, and secondary treatment like machining or sand blasting is essential to improve the surface finish of AM components.

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Fig. 6.37 Schematic for different metal additive manufacturing techniques a selective laser melting, b direct energy deposition or laser-enabled near net shaping, and c electron beam welding

Piglione et al. (2018) used pre-alloyed CoCrFeMnNi HEA powder to build a 10 × 10 × 10 mm block during using SLM with a laser of power 200 W, hatch spacing of 125 μm, and spot size of 60 μm on a stainless steel substrate that showed FCC structure with high degree of consolidation and high hardness without microsegregation. It was shown that rapid cooling of the melt caused epitaxial growth, and

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Fig. 6.37 (continued)

repeated heating during deposition led to selective growth while bi-directional scanning pattern led to columnar grains similar to the conventional alloys prepared by regular solidification (Figs. 6.38 and 6.39). In electron beam melting, an electron gun is used as the heating source and metal/alloy powder or wire/sheet can be used as the feeding stock to produce 3D components (Fujieda et al. 2015; Gong et al. 2002; Cui et al. 2019). Unlike SLM that operates in argon atmosphere, EBAM operates in vacuum 10–2 Pa at voltage of up to 60 kV and powders can be replaced with wires for high production rate. Aerospacegrade additive manufacture parts of titanium alloys and Ti6Al4V are prepared using wire-based EBM. The electron beam is focused using electromagnetic lenses while scanning is performed using scanning coils similar to that in a scanning electron microscope. Cui et al. (2018) carried out EAM of AlCoCrFeNi HEA using prealloyed powder to show that the AM part has lower grain size and higher hardness compared to sample prepared by conventional melting and casting route (Fig. 6.40).

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Fig. 6.38 a Secondary electron image and b crystal orientation or inverse pole figure map of one track of SLM Cantor alloy. The cellular structure of the SLM Cantor alloy is shown in higher magnification images (c and d) (Piglione et al. 2018)

Fig. 6.39 Evolution of macrostructure and microstructure on Cantor alloy deposited on stainless steel plate using powder bed fusion. Schematic of deposition (a) with corresponding secondary electron image (b) and EBSD inverse pole figure map (c) from the interface (right bottom) and deposited layer (right top) (Piglione et al. 2018)

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Fig. 6.40 Secondary electron images from SEM of electron beam melted AlCoCrFeNi HEA in (a) as-cast condition (b) SEBM top surface and SEBM bottom surface and corresponding higher magnification images (d–f) (Li 2018)

Laser metal deposition (LMD) or direct metal deposition (DMD) or laser engineered net shaping is the most versatile metal additive manufacturing technique that allows control of the chemistry of the build and is suitable for generating compositionally heterogeneous products (Gwalani et al. 2019; Guan et al. 2019). In this process, metallic or alloy powder is continuously fed through feeders and laser is used to melt the surface and then powder is deposited on that surface/substrate. Multijet or coaxial nozzle is used to feed the powder at rates between 4 and 30 g/min, and Nd:YAG or CO2 laser is used as heat source with spot size and scan speed between 0.3–3 mm and 150 mm/min–1.5 m/min, respectively. This process has a high build rate compared to LBM and EBM, and larger volume object can be fabricated. More importantly, due to the continuous feeding of powder during deposition, it is possible to control the composition by controlling the powder feeding rate from the hoppers. Multiple elemental powders can be premixed in desired composition, or pre-alloyed powders can be used for depositing single alloy composition. Similarly having different powders in different hoppers accompanied with different feeding rate from the hoppers to the nozzle enable one to control the chemistry during deposition and makes chemically heterogeneous component possible. Equiatomic CoCrFeNi MEA was 3D printed using selective laser melting of prealloyed powder by Sun et al. (2019) to achieve a sound build with fine grain size avoiding hot cracking by optimizing process parameters like heat flux and scan speed. In another investigation, Tong et al. (2019) employed postlaser additive manufacturing heat treatment using laser at different powers to obtain microvoid and pore-free build of Cantor alloy. Similarly, postdeposition hot isostatic pressing (HIP) of direct laser fabricated (DLF) Al0.3 CoCrFeNi at room temperature led to improvement in ductility of the HIP sample.

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In a systematic investigation on comparison of microstructure evolution during equilibrium arc melting process and non-equilibrium direct energy deposition process for HEAs, Joseph et al. (2015) carried out a thorough microstructural analysis on Alx CoCrFeNi HEA for different compositions to yield an equilibrium FCC (x = 0.3), FCC, FCC + BCC (x = 0.65), and BCC (x = 0.8) microstructure. It was observed that there was little effect of the processing route for single phase compositions but a distinctly different microstructure of dendritic versus Widmanstätten was observed for the two-phase composition in arc melting and direct energy deposition, respectively (Fig. 6.41). The similarity in the evolution of phases in HEAs for direct energy deposition and arc melting albeit with a refined microstructure for the former was also shown by Choudhuri et al. (2015) for CoCrCuFeNiAlTi HEA. The similarity in phase evolution for arc melting and non-equilibrium process like direct energy deposition opens up a new opportunity to use additive manufacturing and particularly direct energy deposition or laser-enhanced near net shaping as a potent and versatile tool for rapid alloy prototyping. The ability of LENS or DED to synthesize a library of alloy compositions to explore a wide compositional space was demonstrated by Borkar et al. (2016) who combined the versatility of AM with microscopy, micromechanical testing, and magnetic property measurement to establish microstructure–microhardness–magnetic property paradigm as a function of composition in compositionally graded Alx CrCuFeNi2 HEA. The authors employed a double powder feeder arrangement in a commercially available LENS system with5 00 W Nd-YAG laser with near-infrared radiation. Two hoppers with blend of elemental powders with a nominal composition of CrCuFeNi2 and AlCrCuFeNi2

Fig. 6.41 Comparison between a microstructure (normal to cross-section) b stress–strain curves of samples fabricated using direct laser and arc melting (Joseph et al. 2015)

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provided powders to the nozzles, and composition was controlled by controlling the flow rate of powders from the two hoppers. A cylindrical specimen with 10 mm diameter and 25 mm height was built by keeping the feeding rate constant for 2,5 mm deposition height. A choice with 100% feed rate for the hopper containing CrCuFeNi2 for deposition of 2.5 mm was followed with deposition at 90% for the first hopper and 10% for the other hopper. This was followed with deposition at gradually decreasing flow rate from the first hopper and finally 100% feeding rate from the second hopper ensured that the AlCrCuFeNi2 composition was deposited at the top of the cylinder. It was shown that there was an increase in hardness as well as ferromagnetic character of the HEA with increase in aluminum content that contributed to higher volume fraction of the BCC phase (Fig. 6.42). The aforementioned study clearly demonstrates the capability of LENS as a tool for rapid alloy prototyping of HEAs, and similar strategies have been proposed to explore rapid alloy prototyping by combining LENS (Fig. 6.43) with micromechanical testing techniques and microstructural characterization. In one of the recent investigations, Kenel et al. (2019) provide a peek into the future of HEA processing using additive manufacturing in which the authors have employed

Fig. 6.42 Processing of compositional gradient cylinder with composition Alx CrCuFeNi2 (0 < x < 1.5) using LENS accompanied with combinatorial microstructure-hardness-magnetic property assessment as an example of high throughput alloy development (Borkar et al. 2016)

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Fig. 6.43 a Schematic of LENS technique with its capability to build multilayered bulk alloys by using multiple nozzles to feed powders of desired composition. Sketch showing the LMD process and its capability for producing multilayered bulk alloys. b–e Refer to alloys of different compositions (Li et al. 2018)

3D-extruded inkjet printing to synthesize 3D microlattices of ink containing oxides of the elements. This was followed with reduction of the green print to obtain a HEA lattice with controlled porosity characterized by profuse annealing twins that rendered excellent mechanical properties (Figs. 6.44 and 6.45). Thus, additive manufacturing of advanced HEAs with microstructural and topological optimization in AM can provide new materials for structural applications of the future.

6.7 Summary A brief overview of HEM synthesis by conventional techniques like melting and casting routes as well as ball milling coupled with different forms of sintering and novel techniques like additive manufacturing has been provided. It is apparent that existing techniques can be employed to synthesize HEMs by slightly tweaking with the processing parameters. However, issues like elemental segregation, large difference in physical properties of individual elements like melting point, coupling

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Fig. 6.44 Image showing wet-milled ink prepared from elemental oxides of constituent elements of Cantor alloy and plasticizer (top left) followed with extrusion (bottom let) to construct a 3D architecture with struts of 200 μm width forming the green compact. Final CoCrFeNi HEA microlattice after the second step of co-reduction and interdiffusion-assisted sintering (Kenel et al. 2019)

with the applied field, laser absorption, and thermal conductivity play an important role in the processing of HEMs. Processing parameter optimization has been achieved for most metals and alloys, and a concentrated effort is needed for optimizing processing of HEMs of particular interest rather than simply documenting processing of numerous HEM compositions. A large palette to processing techniques enables access to a vast microstructural and thereby property space for a single composition of HEA. Thus, a broad range of processing techniques available for synthesis of metallic and ceramic materials can be employed for the synthesis of high entropy alloys and ceramics to fully explore the hyperdimensional composition–microstructure–property–performance space of HEMs.

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Fig. 6.45 Additive manufacturing of CoCrFeNi MEA by 3D extrusion printing. Top images show cross-section of extruded filament heated to 765 K in hydrogen and quenched in argon depicting a fine structure of Fe, Ni, and Cr with inter-dispersed Cr2 O3 . Filament sintered at 1273 K for 1 h showing CoFeNiCr matrix. The grain structure is seen in figures in the last row (Kenel et al. 2019)

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I.V. Kireeva, Y.I. Chumlyakov, Z.V. Pobedennaya, I.V. Kuksgausen, I. Karaman, Orientation dependence of twinning in single crystalline CoCrFeMnNi high-entropy alloy. Mater. Sci. Eng. A 705, 176–181 (2017) X. Li, Additive manufacturing of advanced multi-component alloys: Bulk metallic glasses and high entropy alloys. Adv. Eng. Mater. 20, 1700874 (2018) Z. Li, D. Raabe, Strong and ductile non-equiatomic high-entropy alloys: Design, processing, microstructure, and mechanical properties. Jom 69, 2099–2106 (2017) Z. Li, F. Körmann, B. Grabowski, J. Neugebauer, D. Raabe, Ab initio assisted design of quinary dual-phase high-entropy alloys with transformation-induced plasticity. Acta Mater. 136, 262–270 (2017) Z. Li, A. Ludwig, A. Savan, H. Springer, D. Raabe, Combinatorial metallurgical synthesis and processing of high-entropy alloys. J. Mater. Res. 33, 3156–3169 (2018) N. Li, S. Huang, G. Zhang, R. Qin, W. Liu, H. Xiong, G. Shi, J. Blackburn, Progress in additive manufacturing on new materials: A review. J. Mater. Sci. Technol. 35, 242–269 (2019) S. Lv, Y. Zu, G. Chen, X. Fu, W. Zhou, An ultra-high strength CrMoNbWTi-C high entropy alloy co-strengthened by dispersed refractory IM and UHTC phases. J. Alloy. Compd. 788, 1256–1264 (2019) S.G. Ma, S.F. Zhang, M.C. Gao, P.K. Liaw, Y. Zhang, A successful synthesis of the CoCrFeNiAl 0.3 single-crystal, high-entropy alloy by Bridgman solidification. Jom 65, 1751–1758 (2013) S. Mohanty, N.P. Gurao, K. Biswas, Sinter ageing of equiatomic Al20Co20Cu20Zn20Ni20 high entropy alloy via mechanical alloying. Mater. Sci. Eng. A 617, 211–218 (2014) S. Mohanty, S. Samal, A. Tazuddin, C.S. Tiwary, N.P. Gurao, K. Biswas, Effect of processing route on phase stability in equiatomic multicomponent Ti20Fe20Ni20Co20Cu20 high entropy alloy. Mater. Sci. Technol. 31, 1214–1222 (2015) S. Mohanty, N.P. Gurao, P. Padaikathan, K. Biswas, Ageing behaviour of equiatomic consolidated Al20Co20Cu20Ni20Zn20 high entropy alloy. Mater. Charact. 129, 127–134 (2017a) S. Mohanty, T.N. Maity, S. Mukhopadhyay, S. Sarkar, N.P. Gurao, S. Bhowmick, K. Biswas, Powder metallurgical processing of equiatomic AlCoCrFeNi high entropy alloy: Microstructure and mechanical properties. Mater. Sci. Eng. A 679, 299–313 (2017b) J. Moon, M.J. Jang, J.W. Bae, D. Yim, J.M. Park, J. Lee, H.S. Kim, Mechanical behavior and solid solution strengthening model for face-centered cubic single crystalline and polycrystalline high-entropy alloys. Intermetallics 98, 89–94 (2018) I. Moravcik, J. Cizek, Z. Kovacova, J. Nejezchlebova, M. Kitzmantel, E. Neubauer, I. Kubena, V. Hornik, I. Dlouhy, Mechanical and microstructural characterization of powder metallurgy CoCrNi medium entropy alloy. Mater. Sci. Eng. A 701, 370–380 (2017) S. Mridha, S. Samal, P.Y. Khan, K. Biswas, Processing and consolidation of nanocrystalline Cu-ZnTi-Fe-Cr high-entropy alloys via mechanical alloying. Metall. Mater. Trans. A 44, 4532–4541 (2013) T. Nagase, M. Takemura, M. Matsumuro, T. Maruyama, Solidification microstructure of AlCoCrFeNi2. 1 eutectic high entropy alloy ingots. Mater. Trans. 59, 255–264 (2018) H.S. Oh, S.J. Kim, K. Odbadrakh, W.H. Ryu, K.N. Yoon, S. Mu, F. Körmann, Y. Ikeda, C.C. Tasan, D. Raabe, Engineering atomic-level complexity in high-entropy and complex concentrated alloys. Nat. Commun. 10, 1–8 (2019) A. Piglione, B. Dovgyy, C. Liu, C.M. Gourlay, P.A. Hooper, M.S. Pham, Printability and microstructure of the CoCrFeMnNi high-entropy alloy fabricated by laser powder bed fusion. Mater. Lett. 224, 22–25 (2018) S. Praveen, B.S. Murty, R.S. Kottada, Alloying behavior in multi-component AlCoCrCuFe and NiCoCrCuFe high entropy alloys. Mater. Sci. Eng. A 534, 83–89 (2012) C.M. Rost, Z. Rak, D.W. Brenner, J.P. Maria, Local structure of the MgxNixCoxCuxZnxO (x = 0.2) entropy-stabilized oxide: An EXAFS study. J. Am. Ceram. Soc. 100, 2732–2738 (2017) P. Sathiyamoorthi, J. Basu, S. Kashyap, K.G. Pradeep, R.S. Kottada, Thermal stability and grain boundary strengthening in ultrafine-grained CoCrFeNi high entropy alloy composite. Mater. Des. 134, 426–433 (2017)

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Chapter 7

Synthesis and Processing of HEA Coating and Thin Films

7.1 Introduction Thin film technology is a natural extension of technology development from bulk materials in materials science and engineering since it offers enormous possibilities for various applications such as energy, space, health care, microelectronics, nuclear industry, and structural and ultra-high temperature applications. Although extensive research works have been carried out in high entropy alloys and ceramics in bulk form, relatively not much work has been done in the development of thin films and coating of high entropy materials. Researchers are yet to realize the full benefit of the application of high entropy alloy (HEA) films and coating. In spite of several processing challenges, thin film technology provides the opportunity to the researchers to obtain desired phases by overcoming thermodynamical energy barrier causing phase transformations in HEA as its processing typically involves rapid thermal annealing or cooling. Nevertheless, it is a huge challenge posed for the thin-film community to obtain high quality single phase solid solution crystalline film in multicomponent HEA system. Especially for functional applications like microelectronics, energy, and optics where the thickness and roughness of the thin film are extremely important factors in the device performance, researchers are struggling to fabricate high quality thin films. Situation is much better for structural and corrosion resistance materials where the demand is to obtain the coating of HEA with desired properties without worrying much about its roughness and nm-scale thickness. Over past five years, lot of progress has been made in the fabrication of protective coating of HEAs by exploiting their good wear resistance, corrosion resistance, oxidation resistance, etc. In this chapter, the challenges for HEA coating and thin films are discussed with respect to various processing technologies. Effect of various processing parameters on the mechanical, thermal, electrical, magnetic, and corrosion resistance properties of HEA is elucidated.

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7.2 HEA Coatings: Challenges Coating of high entropy alloys, diborides, nitride, carbide, and oxides has shown promising results in terms of better hardness, wear resistance, corrosion resistance, oxidation resistance, and thermal resistance. Over the past decades, scientists have used various synthesis techniques for the coating of high entropy materials. Among them, most widely used techniques are mechanical alloying, thermal spray, atmospheric plasma spray, and laser cladding. Typically, thick coating on the order of µm to mm level thickness is fabricated as protective layer in these processes.

7.2.1 Mechanical Alloying Mechanical alloying is one of the most cost-effective and easy synthesis routes to fabricate HEA coatings. It involves the preparation of powders by ball milling or cryomilling followed by consolidation on substrate using hot-press sintering or spark plasma sintering. Because it is similar to solid-state powder processing generally used for bulk HEA synthesis, it is industrially scalable for large volume production. However, the major disadvantage of this technique is the controlling of grain growth resulting in large distribution of grain size and chances of contamination. Shang et al. (2017) used vacuum hot-pressing sintering of the powder made by mechanical alloying to fabricate CoCrFeNi HEA coating on low-cost Q235 steel substrate exhibiting better hardness, wear and corrosion resistance higher hardness. Although they achieved single phase solid solution in CoCrFeNi HEA coating, incorporation of Cu as one more element in this HEA resulted in the segregation of Cu-rich FCC phase. Recently, Chen et al. (2020) reported increased hardness of non-equiatomic AlCuNiFeCr HEA coating on 304 stainless steel substrate synthesized by mechanical alloying. They attributed the better hardness of HEA coating to the work hardening caused by high-impact collisions at the coating–substrate interface during ball milling. Interestingly, they observed the decrease in hardness of HEA coating upon annealing due to the occurrence of (Al,Cr)-rich oxides and secondary BCC phase formation. On the contrary, Ghasemi et al. (2020) observed the improvement of soft magnetic behavior by performing annealing of CoNiMnCrAl HEA thin film in terms of better saturation magnetization and lower coercivity. So additional annealing step in HEA thin-film processing needs to be carefully executed based on the application requirements.

7.2.2 Spray Technique Exploiting HEA’s appealing properties of resistance to wear, corrosion, and oxidation, a protective thermal barrier coating or wear resistant coating of HEA using

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spraying technique gathered tremendous interests in the recent times for the applications in aerospace, petrochemical, mining, and steel industries. Thermal spraying is a mature coating technology widely used for various industrial applications because of its advantage of high deposition rate and versatility in dealing with a wide range of materials and components. Hence, it was natural extension of using thermal spraying technology for the fabrication of HEA coating Huang et al. (2004) immediately after HEA was reported in the bulk form. However, the hardness of the HEA coating was found to be lower than the as-cast HEA due to secondary phase formation. Wang et al. (2011) showed that additional heat treatment step (1100 °C/10 h) after thermal spraying can increase the hardness of Nix Co0.6 Fe0.2 Cry Siz AlTi0.2 HEA coating. Interestingly, they have observed large amount of dislocations obstructed and pinned the matrix of HEA in their TEM study suggesting the formation of semi-coherent interfaces getting energetically more favorable. Nevertheless, earlier studies on HEA coating by thermal spraying did not produce better properties than their as-cast HEA counterpart. Later, researchers started using atmospheric plasma spraying (APS) for the fabrication of HEA coating owing to some benefits of high bonding strength, high-flame temperature, lower dilution of the coating, and high deposition rate. Using APS technique, Tian et al. (2016) showed improvement of wear resistance in AlCoCrFeNiTi HEA coating deposited onto 316 stainless steel substrate. They observed excellent wear resistance of HEA-coated steel at 700 °C with volume wear rate of 0.23 ± 0.029 × 10–4 mm3 /Nm, which is almost one order magnitude lower than that of 316 stainless steel. The subsequent studies on HEA coating made by APS imply that compositional engineering and microstructure modification hold the key to control the phase transformation and secondary phase precipitation in order to improve its wear resistance properties. In plasma spraying, the particle size, shape, and chemical composition of the powder feedstock determine the performance and quality of the coating. Cheng et al. (2019) showed that additional use of a vacuum gas atomization process of raw HEA powder in plasma spraying could provide better control over phase constitution in HEA coating and its physical properties. They have shown that the phase formation in AlCoCrFeNi HEA coating is dictated by the spraying powder size in addition to spraying power and gas flow rate. Recently, Xiao et al. (2020a) reported that the wear behavior of FeCoNiCrMn HEA-coated steel substrate under dry sliding condition can be optimized by controlling H2 flow rates in APS technique. They showed the enhancement of wear resistance by increasing H2 flow rates during coating by APS process due to increase in cohesive strength among splats. However, they obtained fluffy microstructures in SEM imaged on the surfaces of as-sprayed coatings caused by the oxidation of Mn element in FeCoNiCrMn HEA as shown in Fig. 7.1. Further, Xiao et al. (2020a) studied the tribological properties of FeCoNiCrSiAlx HEA synthesized by APS coating, under dry and water sliding conditions against WC-12Co balls. They found much lower wear rates under water sliding than that in dry sliding condition, in which splat spalling is the primary wear mechanism. Interestingly, they have not found any effect of heat treatment in the wear behavior under water sliding condition unlike the decreased wear rate found in heat-treated HEA under dry sliding condition.

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Fig. 7.1 Surface microstructure of as-sprayed FeCoNiCrMn HEA coating deposited at varying H2 flow rates of a, b 3 L/min and c, d 6 L/min (Xiao et al. 2020a)

In spite of all the efforts in process optimization of plasma spraying technique, the major concern of HEA coating is the formation of pores or voids in the film. On the other hand, alternative coating technology like laser cladding has the drawbacks of dilution of substrate especially if the substrate possesses low melting/boiling point and high chemical reactivity. To overcome these challenges in fabrication of HEA coating on low melting point substrate like magnesium, Yue et al. (2013) proposed a combined 2-step approach of using plasma spraying first and then remelting the assynthesized coating by laser. They deposited AlCoCrCuFeNi HEA coating on pure Mg substrate using plasma spraying which reduces the chances of occurring brittle intermetallics due to the excessive melting and boiling of the Mg. In the 2nd step of laser remelting of HEA, they could enhance the coating density which is generally difficult to obtain in plasma spraying alone. The as-sprayed HEA coating was found to contain microporosity with sizes on the order of 50 µm; after laser remelting, no apparent porosity was observed in the resolidified layer. In their microstructural study as shown in Fig. 7.2, they observed microporosity present in flattened lamellae generally found in plasma-sprayed coating. On the other hand, the laser-remelted layer showed the epitaxial growth of columnar dendrites, almost free from porosity. Such kind of surface protective coating can be extremely beneficial for magnesium components under harsh corrosive environment.

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Fig. 7.2 AlCoCrCuFeNi HEA-coated Mg substrate, illustrating the compact porosity-free laserremelted layer on the plasma-sprayed layer having microporosity (Yue et al. 2013)

Although laser remelting technology is a promising step for making the high quality HEA coating, not much work has been done to understand the defect formation mechanism especially since melting process is always associated with solidification cracking. Recently, Wang et al. (2019) investigated the solidification cracking occurred during laser remelting process in CrMnFeCoNi HEA coating using EBSD in conjunction with thermodynamic calculation by CALPHAD. They observed that strain factor arising from the detachment of the columnar dendrites in solidification grain boundaries (SGBs) led to the solidification cracking in the laser-remelted bead as shown in Fig. 7.3. They reported three types of solidification modes in the laserremelted zone of CrMnFeCoNi HEA due to different dilution rate of the stainless steel substrate. They did not observe any solidification cracking in the full-FCC and BCC-FCC solidification mode samples. However, cracking was found for the FCCBCC solidification mode bead under thermal stress due to the weakened dendrite bonding effect. In order to circumvent the issues like phase transformation, element segregation, residual thermal stresses, oxidation, and undesired chemical reactions generally occurred in thermal spraying, cold spraying (CS) technique can be a viable alternative route to prepare HEA coating. CS is a solid-state deposition process, in which the powder feedstock is accelerated by a high-pressure heated gas mixture in order to make impact on the substrate. The schematic of the working principle of CS coating process is shown in Fig. 7.4. Generally, nitrogen or argon is used as the propulsive gas to carry the powder feedstock through a De-Laval type converging–diverging nozzle at high speed above a certain critical value. The advantage of CS compared to the fusion-based coating technology is that the metallurgical bonding of the particles with the substrate is attained by using the kinetic energy of the particle rather than the thermal energy. Since the coating is realized by the severe plastic deformation at the particle–substrate interface and powders are not directly heated in this process, the phase constitution remains intact, which can be extremely beneficial in case of HEA

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Fig. 7.3 Schematic diagram showing the solidification cracking mechanism: a macrostrain and solidification state of the remelted bead, b longitudinal cross-section illustrating grains detaching at solidification grain boundaries (SGBs), and SGB corresponds to the c cracking likely and d cracking unlikely (Wang et al. 2019)

coating. Very few reports (Yin et al. 2019; Anupam et al. 2019) are found in the literature demonstrating the use of CS technique in HEA coating deposition. Yin et al. (2018) first successfully demonstrated 1.5 mm thick dense coating of FeCoNiCrMn HEA without much porosity using the CS technique. Performing EBSD analysis of HEA powder and the cold sprayed HEA, they have shown that significant grain refinement occurred during cold spraying due to severe plastic deformation upon impact as shown in Fig. 7.5. They obtained increased dislocation density and grain boundaries, in the FeCoNiCrMn HEA coating, resulting in better wear resistance than laser cladded HEA coating.

7.2.3 Laser Cladding Among the various processing techniques for depositing HEA of mm-scale thickness as the corrosion resistance and wear resistance coating, laser cladding appears to be the popular choice to the scientists, although it has its pros and cons. Laser cladding is a surface modification technique recently being used in additive manufacturing. In laser cladding process, typically the high energy laser beams are irradiated on the

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Fig. 7.4 Schematic of the working principle of a cold spray system (Yin et al. 2018)

Fig. 7.5 EBSD inverse pole figures maps of a a single HEA particle and b the cold sprayed HEA coating (Yin et al. 2019)

coating materials like powder or wire pre-set on the substrate surface. The concentrated energy of the laser heats up the coating material rapidly causing a melt pool which further solidifies rapidly resulting in a cladded layer on the substrate. The working principle of the laser cladding is shown schematically in Fig. 7.6. The attractive feature of the laser cladding process is its fast cooling rate (103 –108 K/s) leading to the rapid solidification, which can be efficiently utilized in HEA coating. One of the

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Fig. 7.6 Schematic view of laser cladding process (Chen et al. 2020)

major issues of HEA coating is the segregation of brittle intermetallic phases, which adversely affects its strength and corrosion resistance. In laser cladding process, the issue of composition segregation can be avoided. Because the high cooling rate is used in laser cladding technique, one can obtain the metastable solid solution phase of HEA comprising multiple elements, even beyond the solid solubility limit as it promotes the solute trapping. Over the past few years, number of papers in the literature reporting on laser cladded HEA coating has been rapidly increased. Many of them reported improved corrosion resistance of the component after depositing a protective coating of HEA showing tremendous potential for application in turbine blades, hydraulic turbines, marine propellers, oil-drilling pipes, etc. Almost, all the reports on laser cladded HEA coating demonstrated uniform microstructure and a strong metallurgical bonding between HEA coating and the substrate. Zhang et al. (2020a, b) recently studied the effect of various laser irradiation energies in laser cladding technique on the morphology, microstructure, and wear resistance of FeNiCoCrTi0.5 HEA coating. Systematically, they evaluated the laser energy (E s ) using various process parameter such as laser power (P), scanning speed (υ), and laser spot size (D), depicted by the following equation: Es =

P Dυ

Using the cross-sectional topography of FeNiCoCrTi0.5 coatings fabricated by laser cladding at different laser irradiation energies shown in Fig. 7.7, they have illustrated how the quality of solidified coating surface changes with increase in laser

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Fig. 7.7 Cross-sectional topography of FeNiCoCrTi0.5 coatings fabricated by laser cladding at different laser irradiation energies: a 54.17 J mm−2 ; b 55.56 J mm−2 ; c 72.22 J mm−2 ; d 88.89 J mm−2 ; e 108.33 J mm−2 (Zhang et al. 2020a, b)

power from producing teardrop defects to a cladding layer with almost no porosity and cracks. They have observed improved hardness of the 45 steels to almost double by FeNiCoCrTi0.5 coating having equiaxed, dendritic, and columnar crystals in their microstructure. However, the substrate dilution is evident in their study which is expected due to high energy laser used in this process. Substrate dilution is an important issue in laser cladding although it helps in attaining excellent metallurgical bonding with substrate. Partial melting of substrate may lead some of the constituent element of the substrate to infiltrate into the HEA coating which in turns changes the composition, phase, and microstructure of the HEA. Several studies reported the adverse effect on the hardness, corrosion resistance, and wear resistance behavior of the HEA due to substrate dilution, e.g., infiltration of Fe from steel substrate causing decrease in hardness and wear resistance of HEA coating. However, a recent report made by Zhang et al. (2020a, b) suggests otherwise. Interestingly, they observed the improvement in wear resistance of 45 steels coated with Fex Ni2 Co2 CrTiNb by laser cladding with increase in Fe content. Gu et al. (2020) demonstrated that using rare-earth additives like yttrium can improve bonding between substrates and claddings layer in MgMoNbFeTi2 Yx HEA coating. They also showed the enhanced corrosion resistance and microhardness of HEA due to the use of Y additive in the cladding layer. Overall, laser cladding can be used for making thick coating with mm-scale width, but one should be careful for depositing it on substrates with low melting point in order to avoid serious substrate dilution. But for micron or submicron thick coating, it is better to avoid laser cladding as the residual tension and local stress may lead to the cracking in laser cladded HEA coating.

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7.3 HEA Thin Films: Preparation and Challenges Very few reports are available on nm-scale HEA thin films with low roughness required for functional applications as it is extremely challenging to avoid the phase segregation in ultra-thin HEA film. However, lot of progress has been made in the field of HEA thin film with few hundreds of nm to micron level thickness for the applications in thermal barrier coating, corrosion resistance and wear resistance coating, etc. Also, some reports have been made on the magnetic and electrical properties of HEA thin films. Apart from the HEA, thin film of high entropy oxides, nitrides, and carbides has been investigated over the past decade. Sputtering techniques like reactive DC sputtering and magnetron sputtering are most commonly used process in the fabrication of HEA thin film. Also, few reports on HEA thin film synthesis by ion beam sputter deposition (IBSD), pulse layer deposition (PLD), and electrodeposition have been made in the recent times.

7.3.1 Sputtering Technique Ever since Chen et al. (2004) first reported the fabrication of nitride films of HEA by reactive DC sputtering, different types of sputtering deposition techniques have become the most common tool for the fabrication of HEA thin films. Although Chen et al. (2004) could not achieve good crystallinity in Fe-Co-Ni-Cr-Cu-Al-Mn and Fe-Co-Ni-Cr-Cu-Al0.5 HEAs, over the years lot of efforts have been made in order to obtain high quality crystalline thin films by adopting different strategies and optimizing the process parameters. Magnetron sputtering is a physical vapor deposition (PVD) process and a mature thin film fabrication technique widely used in electronics industry over the decades. In magnetron sputtering, basically highly energized partially ionized gas, generally Ar, bombard the target to remove its constituent elements which then travel in a certain direction toward the substrate resulting in the formation of the thin film. Schematic of the working principle of magnetron sputtering system is shown in Fig. 7.8. Two types of magnetron sputtering are used, i.e., direct current (DC) and radiofrequency (RF) magnetron sputtering based on the type of high entropy materials. For depositing insulator-based materials, one needs to use RF magnetron sputtering in order to periodically sweep or clean the accumulated charge on the surface of the insulator target. The most common practice in HEA thin film deposition is making the target of the exact stoichiometric HEA composition by arc melting or powder metallurgy route. However, co-deposition of multiple elements using multiple targets is also used to make HEA thin film, although it is extremely challenging to maintain the stoichiometry. The major advantage of using magnetron sputtering is that one can make conformal coating with minimal roughness on complex structure. Besides, it is easy to synthesize thin films of nitrides, oxides, and carbides of HEA by using

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Fig. 7.8 Schematic of the working principle of magnetron sputtering system (Yan et al. 2018)

magnetron sputtering by incorporating various reactive gases such as N2 , O2 , and C2 H2 .

7.3.1.1

DC Magnetron Sputtering

Over the past decade, a wide range of HEA materials have been synthesized using DC magnetron sputtering. Chen et al. (2019) investigated the high temperature oxidation behavior and electrical conductivity of V19.2 Nb19.4 Mo20.3 Ta19.5 W21.6 HEA thin film deposited on the AISI 304 stainless steel substrates by a DC magnetron sputtering. They observed that this HEA thin film exhibits good oxidation resistance up to 500 °C as they turn into V-Nb-Mo-Ta-W-based oxides at high temperatures resulting in increase in their electrical resistance. They confirmed the formation of oxide layer in their HEA thin film after oxidation at 800 °C for 1 h in air from backscattered electron (BSE) image and X-ray mappings of all the elements such as V, Nb, Mo, Ta, W, O, Fe, Cr, and Ni in HEA as shown in Fig. 7.9. Kirnbauer et al. (2019) synthesized crystalline high entropy oxide thin film of (Al,Cr,Nb,Ta,Ti)O2 by pulsed-DC magnetron sputtering. They obtained single phase solid solution with rutile structure. They have shown that the relative oxygen flowrate ratio during thin film deposition has crucial role on the hardness of high entropy oxides attaining increase in hardness from 22 to 24 GPa by increasing the oxygen flow rate from 30 to 80%. Hahn et al. (2019) investigated the toughness of Si-alloyed (Al,Ta,Ti,V,Zr)N high entropy nitride films grown by DC magnetron sputtering on Si substrate. To measure the hardness and fracture toughness of their high entropy nitride films, they performed nanoindentation of cantilevers milled by dual-beam focused ion beam

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7 Synthesis and Processing of HEA Coating and Thin Films

Fig. 7.9 The cross-sectional backscattered electron (BSE) image and X-ray mappings of all the elements in V19.2 Nb19.4 Mo20.3 Ta19.5 W21.6 HEA thin film after oxidation at 800 °C for 1 h (Chen et al. 2019)

(FIB) as shown in Fig. 7.10. In their micromechanical experiments of Si-alloyed (Al,Ta,Ti,V,Zr)N, they have found significant decrease in the indentation modulus from 433 to 326 GPa implying significant enhancement in damage tolerance due to enhanced elastic deformation. Kim et al. (2019) investigated the electrical and mechanical properties of refractory HEA NbMoTaW grown on Si substrate by DC magnetron sputtering. They have got the nice combination of high hardness (12 GPa) and electrical resistivity (168 µΩ cm) in NbMoTaW thin film due to severe lattice distortion and nanoscale microstructure.

7.3 HEA Thin Films: Preparation and Challenges

189

Fig. 7.10 a SEM image of the FIB milled cantilever before micromechanical testing. The fractured surface of b (Al,Ta,Ti,V,Zr)N and c Si-alloyed (Al,Ta,Ti,V,Zr)N cantilevers, respectively (Hahn et al. 2019)

DC magnetron sputtering can be useful in growing amorphous HEA thin film. Cheng et al. (2016) demonstrated excellent thermal stability and high electrical resistivity (246 µΩ cm) in amorphous BNbTaTiZr HEA thin film grown by DC magnetron sputtering on sapphire substrate. Their XRD, SEM, TEM, and AFM studies showed that BNbTaTiZr HEA thin film can keep up the amorphous structures even after annealing at 800 °C for 1 h. High entropy metallic glass (HEMG) thin film is an emerging concept having huge potential for the applications in micro/nanoelectromechanical systems (MEMS/NEMS) owing to their atomic level smooth surface, high hardness, and large elastic strain limit. Zhao et al. (2017) fabricated thin films of Ti-Zr-Hf-Cu-Ni high entropy metallic glass on glass and Si substrates using DC magnetron sputtering technique. They achieved high strain rate sensitivity of hardness (0.05) in their HEMG thin film along with high hardness (10.4 ± 0.6 GPa) and a high elastic modulus (131 ± 11 GPa) under the strain rate of 0.5 s−1 in nanoindentation tests.

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7.3.1.2

7 Synthesis and Processing of HEA Coating and Thin Films

RF Magnetron Sputtering

Compared to DC magnetron sputtering, RF magnetron sputtering process is relatively costlier. But it offers the opportunity of growing high quality thin films with better interface and smooth like a mirror. Nevertheless, RF sputtering is required for depositing high entropy materials which are dielectric or insulator in nature. Only a handful of papers are available in the literature reporting the use of RF magnetron sputtering for depositing HEA thin films. An et al. (2015) used RF magnetron sputtering to deposit highly crystalline single phase CrCoCuFeNi HEA thin film. Unlike the segregation of Cu element found in the bulk HEA, they obtained uniform distribution of all the constituent elements in their microstructural analysis by SEM and TEM. Although they observed slight Cu enrichment in as-synthesized HEA thin film due to insufficient pre-sputter, Cu has the high sputtering yield. Liao et al. (2017) successfully grew high quality, smooth, homogeneous, nanocrystalline CoCrFeNiAl0.3 HEA thin films on Si substrate using RF magnetron sputtering technique. They achieved very low surface roughness ( dR R

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where R is sqrt (˙ε ∗ ε˙ ) and D is the dissipative function that describes the material behavior. The dissipative power is equal to J, and this leads to the microstructural stability parameter at a constant temperature, ξ, such that: ξ (˙ε) =

(∂ ln(m/(m + 1)) +m >0 (∂ ln ε˙ )

This parameter acts as an indicator for the quality of microstructure with a negative value indicating instability due to adiabatic shear banding, dynamic strain aging, flow localization which by attaining negative strain rate sensitivity that can cause failure. Processing maps are obtained by plotting iso-intensity contours for strain rate sensitivity or efficiency or stability parameter or a superimposition of two parameters as a function of strain rate and temperature. They provide a window or domain for safe processing that constitutes dynamic recrystallization, dynamic recovery, or superplastic flow as well as unsafe processing that constitutes of damage mechanisms like void formation, intergranular cracking, or wedge cracking. Early work on processing maps focused on compression test at true strain rate but with the advent of thermomechanical simulator like Gleeble, different strain path like plane strain compression or torsion is also used to capture the finer details of actual industrial processes like rolling. Though large-scale production of HEAs is yet to materialize, efforts have been directed to optimize the schedule using hot compression tests at different temperature and strain rate using processing maps. Hot compression behavior of Cantor alloy was investigated by Eleti et al. (2018) for a true strain of ~1 in the temperature range of 1073–1273 K and strain rates varying from 10−3 –10 s−1 to show that dynamic recrystallization is the dominant deformation mechanism. The stress–strain curves of the samples show an increase in flow stress with decrease in temperature and increase in strain rate. Samples deformed at the strain rate of 1 s−1 show a peak stress followed with a plateau while flow softening is dominant for the samples deformed at the lowest strain rate for all the temperatures (Fig. 8.2). Samples deformed at strain rate of 1 s−1 showed large fraction of low angle grain boundaries at 1073, 1173, and 1273 K (Fig. 8.3). It was observed that a necklace-type structure comprising of fine equiaxed grains at the boundaries of deformed grains evolved resulting in flow softening in samples deformed at the lowest strain rate. The sample deformed at 1273 K at strain rate of 0.001 s−1 showed a completely recrystallized microstructure while other samples deformed at 0.1 s−1 at 1173 and 1273 K showed a necklace type of microstructure. The activation energy for hot deformation of Cantor alloy was similar to that of nickel which is the slowest diffusing specie in the HEA. Hot deformation behavior of single phase CoCuFeMnNi (Sonkusare et al. 2019a), eutectic CoCuFeNiTi (Samal et al. 2016), and two-phase AlCoCrFeNi2.1 (Rahul et al. 2018) alloy consisting of CoCrFe-rich FCC and NiAl-rich BCC phase HEA has also been studied over a wide range of temperature and strain rate. The complexities of hot deformation in HEAs were demonstrated by an interesting investigation by Sonkusare et al. (2018) who employed CALPHAD simulations and in situ high temperature-ray diffraction to determine a two-phase (comprising of a copper-rich and a copper-lean FCC phases) processing regime for hot working of

8.2 Hot and Cold Working of HEAs

199

Fig. 8.2 True stress–true strain curves for Cantor alloy deformed in compression at different temperature and strain rate from Eleti et al. (2018)

Fig. 8.3 Image quality map with distribution of low (blue) and high (red) angle grain boundaries from EBSD for Cantor alloy subjected to compression at (a–c) temperature of 1073, 1173, 1273 K at strain rate of 1 s−1 , (d–f) temperature of 1073, 1173, 1273 K at strain rate of 0.01 s−1 and (g–i) temperature of 1073, 1173, 1273 K at strain rate of 0.001 s−1 (Eleti et al. 2018)

CoCuFeMnNi HEA. They showed a strong dependence of temperature as well as strain rate on flow stress with characteristic regimes of dynamic recovery and recrystallization. Power dissipation maps as well as the efficiency maps were obtained from the compression tests to determine the optimum processing conditions as shown in Fig. 8.4 (Sonkusare et al. 2019a). Two optimum conditions for thermomechanical processing were found, i.e., T = 1173 K, strain rate = 10–3 s−1 and T

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Fig. 8.4 a Efficiency map of power dissipation and b Processing map for hot compression of CoCu FeMnNi HEA (Sonkusare et al. 2019a)

= 1273 K, strain rate = 10–2 s−1 . Correlating the strain rate sensitivity or efficiency with the evolution of microstructure in two-phase HEA was achieved by carrying out simultaneous energy dispersive spectroscopy with electron backscatter diffraction to reveal the operative mechanisms in copper-rich and copper-lean FCC HEA phase in CoCuFeMnNi HEA (Fig. 8.5). It was shown that deformation was characterized by DRX in copper-rich near grain boundary phase and DRV in copper-lean grain interior phase. Detailed investigation showed that higher efficiency of processing can be obtained by operation of different mechanisms, namely DRX in copper-rich and DRV in copper-lean phase of the CoCuFeMnNi HEA. A comprehensive partitioning of the entire processing space into different operative mechanisms for the copperrich and copper-lean phase was proposed and is represented in Fig. 8.6. The present investigation indicates that posthot working heat treatment like homogenization is warranted for achieving homogeneous microstructure for downstream processing due to the compositional complexities in HEAs.

8.2.2 Cold Working of HEAs Cold rolling of metals and alloys is routinely carried out to produce sheet metal for a variety of applications in automotive and aerospace industries for optimum microstructure control to achieve desired strength ductility, toughness, and formability. Cold rolling leads to the accumulation of dislocations in the material and can contribute to high strength with reduced ductility, toughness, and formability. Therefore, cold rolling is generally followed with annealing treatment that can provide recovered microstructure that retains the strength or recrystallized microstructure that provides sufficient ductility for tertiary processing. The process of cold rolling in terms of evolution of microstructure, texture, and residual stress is studied in great

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Fig. 8.5 Compression direction inverse pole figure map from EBSD for a copper-rich grains and b copper-lean grains of hot compresses CoCuFeMnNi HEA (Sonkusare et al. 2019a)

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Fig. 8.6 a Deformation mechanism map for copper-lean and copper-rich phase and b schematic showing microstructure evolution in CoCuFeMnNi HEA (Sonkusare et al. 2019a)

details for a variety of pure metals and alloys. Complex steels comprising of multiple elements are subjected to cold rolling and subsequent recovery or precipitation hardening or even inter-critical annealing to obtain suitable microstructure and texture for excellent sheet metal forming in automotive and aerospace industries. Cold rolling and subsequent treatment of HEAs are in a nascent state, and few rigorous investigations have been carried out on mostly FCC HEAs. The evolution of microstructure and texture in Cantor alloy was studied by Bhattacharjee et al. (2014) who showed that the HEA showed extreme grain refinement on 90% rolling ⟨ and ⟩ a typical Brass-type texture characterized by a strong Brass component {110} 112 , which is a characteristic of low stacking fault energy FCC material. Figure 8.7 shows the inverse pole figure map of the 90% rolled sample and texture in terms of 111 pole figure from

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203

the work of Bhattacharjee et al. It is clear that the strong Brass texture is attributed to severe shear banding that leads to heterogeneous deformation during cold rolling of Cantor alloy to show a characteristic Brass-type texture in Cantor alloy after cold rolling. Recrystallization experiments on the cold-rolled Cantor alloy samples from 923 to 1273 K showed little grain growth till 1073 K and higher fraction of 3 boundaries above 1073 K while grain growth was dominant at 1273 K. The authors concluded that the cold rolling and annealing behavior of CoCrFeMnNi HEA are similar to that of TWIP steels. Stepanov et al. (2015) studied cryorolling of CoCrFeMnNi HEA till 80% reduction and showed that the rolled samples showed extensive twinning and shear banding to yield a higher strength albeit with lower ductility compared to the room temperature rolled sample. The presence of twinning at cryogenic temperature indicates that the deformation behavior of CoCrFeMnNi HEA is similar to that of medium SFE copper than low SFE TWIP steel as was proposed by Bhattacharjee et al. (2014). Tazuddin et al. (2016) showed that cold rolling of FCC CoCuFeMnNi HEA led to a unique Goss–Brass texture with elongated grains for 90% reduction. A fully recrystallized sample was obtained on annealing at 1273 K for one hour that showed higher ductility but lower strength compared to the rolled sample. They also carried out crystal plasticity simulations using viscoplastic selfconsistent simulations that indicated the evolution of the Goss–Brass type texture to the operation of planar partial slip and octahedral slip (Fig. 8.8). Similar investigations on a variety of FCC HEAs have shown that cold rolling of the cast alloys is characterized by significant improvement in strength and loss of ductility due to increase in dislocation density and decrease in grain size. Senkov and Semiatin (2015) showed a characteristic BCC rolling texture evolution in HfNbZrTaTi BCC HEA with the evolution of cellular grain structure for 65% rolling reduction and on further annealing at 1073 and 1273 K recrystallization and grain growth was observed. Wani et al. (2016) studied warm rolling (773 K till 40% reduction and 923 K beyond 40% till 75% reduction) microstructure and texture of FCC + BCC HEA to show that the harder BCC phase does not deform during initial stages of rolling and undergoes fragmentation at higher reductions while the softer FCC phase shows fine lamellar structure and characteristic Brass texture. Wani and co-authors (2017) also carried out cold rolling and recrystallization of AlCoCrFeNi2.1 eutectic HEA with LI2 and B2 phase till 90% rolling reduction followed with recrystallization to show the evolution of characteristic gamma fiber texture in the B2 phase and Brass-type texture in the LI2 phase that showed disordering with increase in strain. The alloy showed remarkable resistance to grain growth on annealing upto 1573 K due to the formation of homogeneous two-phase deformation structure after deformation, wherein growth of one phase is effectively retarded by the other. Thus, the cold rolling and static annealing of FCC single phase HEAs are similar to that of low SFE FCC metals and alloys. There is a scope to study the forming behavior of different single and multiphase HEAs using the forming limit diagram to realize their potential as structural materials in automotive and aerospace industry.

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Fig. 8.7 Image quality map (a & b) and 111 pole figure (c & d) from EBSD from two different regions of 90% cold-rolled Cantor alloy (Bhattacharjee et al. 2014)

8.2.3 Severe Plastic Deformation In recent years, bulk ultrafine grain-sized materials produced by severe plastic deformation have garnered a lot of attention due to the excellent combination of mechanical properties like high strength with reasonable ductility and fracture toughness with superior fatigue performance and superplastic forming behavior or different class of metals and alloys. Unlike conventional solid-state processing techniques like rolling and forging, severe plastic deformation techniques produce grain size in the submicron to nanometer regime which cannot be achieved by the former. Conventional processing techniques involve change in dimensions of the workpiece with increase in strain and further processing requires drastic modification in the existing equipment to achieve higher deformation. Severe plastic deformation processes are mostly shear-dominated deformation and do not cause significant change in dimensions of the workpiece and it is theoretically possible to deform the sample to infinite strain.

8.2 Hot and Cold Working of HEAs

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Fig. 8.8 a 111 and 200 pole figures and b slip activity and average active lip systems from viscoplastic self-consistent simulations on 90$ cold-rolled CoCuFe MnNi HEA (Tazuddin et al. 2016)

This ensures that a heavily refined microstructure with proper grains separated by high angle grain boundaries can be achieved in the submicron and even nanoregime. Heterogeneity of microstructure and crystallographic texture is a hallmark of all severe plastic deformation techniques and post-SPD heat treatments and combination of conventional solid-state processing techniques like rolling and heat treatments like annealing are employed to obtain desired microstructure in different metals and alloys. SPD methods like high-pressure torsion, equal channel angular extrusion, friction stir processing, multi-axial forging, accumulative roll bonding have been developed over the years to produce metals and alloys in the submicron and nanograin size regime to yield excellent mechanical properties. Most of the SPD techniques provide grain size upto 100 nm and only high-pressure torsion can provide grain size in the nanocrystalline regime. The mechanism of grain refinement and the concept

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8 Structural Properties

of saturation grain size in different SPD techniques and particularly in HPT are well-established. Similarly, new SPD methods that employ continuous processing unlike batch processing have been developed to realize the true potential of ultrafine grain size metals and alloys. Friction stir processing is one such warm SPD technique that has shown its versatility to engineer microstructures in different metals and alloys to provide access to property space provided by materials processed by conventional solid-state processing techniques. A schematic of the three important SPD processes, namely high-pressure torsion, equal channel angular pressing, and friction stir processing, is depicted in Fig. 8.9. The field of production of bulk ultrafine grain size materials by severe plastic deformation techniques is quite mature, and it is no surprise that various SPD processes have been applied to engineer microstructures of HEAs with a hope to provide access to unexplored mechanical property space. Since the field of SPD is quite mature, most investigations on HEAs have focused on HPT to study the evolution of saturation grain size and determine mechanical properties of the processed HEAs and friction stir processing to produce large-scale ultrafine grain size samples for detailed mechanical property characterization. In one of the early investigations, Shahmir et al. (2017a) carried out ECAP of Cantor alloy at 673 K using a die of 110° for four passes by rotating the sample by 90° degree after each pass to achieve an single phase ultrafine grain size of ~100 nm with dislocation density of 1.3 × 1013 m−2 to achieve high hardness of 315 VHN and yield strength of ~980 MPa with ductility of 35%. The increase in hardness, and yield strength is roughly three times of Cantor alloy with microcrystalline alloy while the ductility is almost reduced to half in the ultrafine grain microstructure obtained by ECAP. The authors also carried out postdeformation annealing to show that annealing at 773 K for one hour leads to precipitation of sigma phase that further improves the yield strength above 1 GPa. Schuh et al. (2015) carried out HPT of CoCrFeMnNi HEA at 7.5 GPa pressure for five turns to obtain a grain size of 50 nm without any decomposition with yield strength of 1950 MPa with hardness of 520 HV and moderate ductility in tension. Thermal annealing of the HPT processed sample led to peak hardening to 910 HV after 100 h annealing at 450 °C which was attributed to the formation of nanoscale NiMn, FeCo, and Cr-rich phases. It was proposed that higher fraction of non-equilibrium grain boundaries arising from HPT provide multiple fast diffusion pathways and nucleation sites for precipitation of different phases which are not observed in microcrystalline Cantor alloy. Another investigation by Shahmir et al. (Shahmir et al. 2016) obtained a grain size of 10 nm for 10 turn HPT at 6 GPa pressure for Cantor alloy to yield a hardness of ~4.41 GPa while a 5 turn HPT sample showed UTS of ~1.75 GPa with4% strain to fracture, thus providing extreme strength with limited ductility in a single phase alloy. Similar observation of high grain refinement after HPT was reported for Al0.3 CoCrFeNi HEA that also showed further increase in hardness on annealing at due to decomposition of the single FCC phase to a FCC + BCC microstructure (Tang et al. 2015a). In a detailed investigation on the evolution of microstructure, texture, and mechanical properties of HPT processed CoCuFeMnNi HEA, Sonkusare et al. (2019b, 2020a) showed that there was a decrease in grain size by three orders of magnitude from 50 to 55 nm after 5 turn HPT. The extreme grain size refinement of the 5 turn sample

8.2 Hot and Cold Working of HEAs

207

Fig. 8.9 Schematic showing a equal channel angular processing b high-pressure torsion and c friction stir welding

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at the periphery subjected to a shear strain of ~165 is clearly observed in the grain boundary map obtained from TEM-OIM and conventional bright field imaging from TEM in Fig. 8.10. There was threefold increase in dislocation density and 3.5-fold increase in hardness at the periphery of the 5 turn sample with characteristic shear texture evolution. The high hardness at the periphery of the 5 turn sample could not be explained by the significant reduction in grain size and increase in dislocation density and was attributed to non-equilibrium solid solution strengthening due to partial dissolution of copper-rich nanoclusters in the CoCuFeMnNi HEA. Kumar et al. (2015) carried out friction stir processing of Al0.1 CoCrFeNi HEA to achieve grain refinement from few millimeters in the as-cast condition to 14 ± 10 μm after FSP. The grain refinement contributed to significant improvement in hardness, Fig. 8.10 a Grain boundary map from TEM-OIM and b bright field TEM image of 5 turn HPT processed sample from periphery of CoCuFeMnNI HEA (Sonkusare et al. 2020a)

8.3 Mechanical Properties of HEAs

209

yield strength, and ductility. It was also shown that the Hall–Petch coefficient for the HEA was higher compared to that of conventional metals and alloys. This observation has motivated many investigations to achieve optimum combination of strength and ductility by grain size control using FSP. In single phase as well as dual phase is including TRIP dual phase HEAs like FeMnCoCr and other compositions. Thus, FSP has evolved as a potential processing technique for microstructural engineering of HEAs to achieve excellent combination of strength and ductility as well as superior fatigue performance and superplastic formability.

8.3 Mechanical Properties of HEAs The promise of HEAs likes in exploration of the unexplored compositional space that may also provide access to unchartered property space particularly for structural applications that offer unique mechanical properties not achieved by conventional metals and alloys. One of the biggest challenges in this regard is the vastness of the compositional space and when the mechanical property information is added, it only adds complexity to the desire to unearth the next HEA for application in the next century. Numerous investigations have simply focused on hardness and tensile or compression test for new compositions for HEAs, and only a few investigations have thoroughly probed the mechanical properties in details to address fundamental issues pertaining to mechanical behavior of HEAs. Of particular importance is the evolution of strength, ductility, and ensuing strain hardening mechanisms in single phase HEA. Once the fundamental aspects related to dislocation structure, dislocation–defect interaction, solid solution strengthening, lattice distortion, Hall–Petch strengthening are well understood, secondary issues like fatigue, creep, and fracture properties can be studied and understood in a better way. In this regard, systematic studies on equiatomic CoCrFeMnNi HEA have helped in furthering our understanding of deformation mechanisms of HEAs. This has been followed with Alx CoCrFeMnNi HEAs which offer a systematic transition from FCC to BCC HEA microstructure with increasing aluminum concentration as well as eutectic HEAs that offer excellent strength with sufficient ductility. In addition, there was the development of single phase BCC HEAs from refractory metals that have helped shed light on the deformation mechanisms in BCC HEAs. The development of transformative HEAs that are subsets of quinary Cantor alloy composition has played an important role in exploring the unchartered mechanical property space inaccessible by conventional alloys and also helping in deconvoluting the contribution of different thermodynamic parameters if any on mechanical properties. In the present section, we aim to focus on few representative examples of HEAs that have helped in furthering our understanding of fundamental deformation mechanisms of HEAs rather than providing a laundry list of mechanical properties investigated in a plethora of HEAs. The most widely studied alloy is the equiatomic CoCrFeMnNi Cantors alloy that shows low yield strength but high strain hardening ability at room temperature. This alloy along with the subset quaternary and more importantly ternary alloys

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have been studied over a wide range of temperature, strain rate, strain to develop fundamental understanding of deformation mechanisms of FCC HEAs. Similarly, TiNbZrHfTa BCC HEA that shows sufficient ductility among the BCC HEA has also been studied in great details to develop an understanding of deformation behavior of BCC HEAs and compare them with conventional BCC metals and alloys. Investigations on HCP HEAs are still in a very nascent stage, and only few investigations have been performed on using micropillar compression. Hence, we shall focus on the fundamental aspects of deformation in FCC and BCC HEAs in the subsequent sections.

8.3.1 Elastic Properties Properties like Young’s modulus and shear modulus along with coefficient of thermal expansion are important for estimating the thermally induced stresses in metals and alloys and also have a fundamental bearing on dislocation interactions with each other and other defects. The elastic modulus of the CoCrFeMnNi HEA increases with decrease in temperature from 300 to 77 K similar to that of FCC nickel albeit with a slightly lower temperature dependence while it decreases with increase in temperature above room temperature. The temperature dependence of the Cantor alloy from cryogenic to high temperature has been studied to decouple the role of change in shear modulus in dislocation mechanisms including energy of dislocations, force acting on dislocations, and so on against the operation of distinct deformation mechanisms like twinning and planar slip that contribute to unique mechanical properties of the alloy. A detailed investigation on elastic properties of the Cantor alloy over a wide temperature range 0f 77–1000 K shows a similar temperature dependence to that of conventional FCC nickel with maximum deviation from the behavior of chromium (Fig. 8.11a) (Laplanche et al. 2015). It is to be mentioned here that there is a tendency to apply rule of mixtures to predict Young’s modulus like melting point for HEAs which may certainly not be true for the entire temperature range in the humble opinion of the authors. Similar investigation of TiNbZrHfTa RHEA (Laplanche et al. 2019) showed decrease in Young’s modulus and shear modulus with increase in temperature from 200 to 1000 K (Fig. 8.11b). The RHEA showed a behavior similar to that of Nb while the maximum mismatch was with Ta. The large decrease in shear modulus from 36 to 31 GPa from 200 to 1000 K is expected to play an important role in plastic deformation and is expected to reduce the yield strength with temperature.

8.3.2 Quasistatic Tensile Behavior Otto et al. (2013) carried out a detailed investigation on mechanical behavior of the Cantor alloy by carrying out tensile tests over a temperature range from 77 to 873 K

8.3 Mechanical Properties of HEAs

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Fig. 8.11 Variation of elastic modulus and shear modulus with temperature for a Cantor alloy from Laplanche et al. (2015) and b TiNbZrHfTa HEA (Laplanche et al. 2019)

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and grain size ranging from 4.4 to 155 μm. It was observed that there is a decrease in yield strength as well as ultimate tensile strength with increase in grain size for all the temperatures from 77 to 873 K; however, the dependence of the latter on grain size was not as strong as the former as seen in Fig. 8.12. For a given grain size, there is a strong increase in yield strength and ultimate tensile strength with decrease in temperature. Unlike conventional metals and alloys, the increase in strength did not result in loss of ductility for different grain size samples tested at different temperature. Variation in tensile properties like yield strength, ultimate tensile strength, and ductility shows a strong temperature dependence and for Cantor alloy (Fig. 8.13). The strong dependence of yield strength is similar to that of conventional solid solutions like Al–Mg and distinctly different from that of pure FCC metals. More importantly, the slope of the Hall–Petch curve for samples tested at different temperature is not parallel indicating a strong dependence of grain boundary strengthening on temperature unlike FCC metals and alloys. Detailed TEM investigation revealed the operation of conventional octahedral slip characterized by planar dislocations of Burgers vector ½ < 110 > in {1 1 1} plane at tensile strain of 2% for all the samples tested in the temperature regime of 77–873 K as shown in Fig. 8.14. The deformation / microstructure was also characterized by numerous stacking faults bounded by 1 6[112] partial dislocations on the {11 1} plane. The operation of planar slip was attributed to short-range ordering or clustering as well as the partial dislocation bound stacking faults that made cross-slip difficult. TEM investigation on samples deformed at higher strains showed that there was cell formation indicating a transition from planar to wavy slip at room temperature and above. Low temperature deformation at higher strain of 20% was characterized by operation of deformation twinning that provided additional strain hardening due to dynamic Hall–Petch effect. This effect was more pronounced for coarse-grained sample as the twinning tendency is higher for coarse-grained samples. The change in elastic modulus with temperature cannot explain the variation in yield strength at cryogenic temperature, and the micromechanisms of deformation were addressed in a separate study by Laplanche et al. (2016a) who performed interrupted tensile tests at different temperatures to completely understand the contribution of twinning and slip to overall deformation behavior of Cantor alloy at room temperature and cryogenic temperature. The representative stress–strain curve and strain hardening curves in terms of Kocks–Mecking plot are shown in Fig. 8.15. A thorough transmission electron microscopy examination by Laplanche et al. showed that deformation in Cantor alloy at room temperature was dominated by slip till strain of 20% and deformation twinning was activated close to the fracture strain of around 40%. It was argued that the lower yield strength of the Cantor alloy at room temperature was not sufficient to reach the critical resolved shear stress of twinning and twinning only occurred only after significant strain hardening to achieve high stress level. On the other hand, the sample tested at 77 K showed dislocation plasticity till a strain of 7.4% followed with significant twinning (Fig. 8.16). The twin shear associated with twins is higher in FCC materials so thin twin lamellas are observed throughout the microstructure with lower volume fraction. Thus, the contribution of twinning to the overall tensile strain is relatively small but it significantly contributes

8.3 Mechanical Properties of HEAs

213

Fig. 8.12 a Representative engineering stress–strain curves for 4,4 μm and b 155 μm Cantor alloy samples deformed at different temperatures (Otto et al. 2013)

Fig. 8.13 Variation of a yield strength, b Hall–Petch plots, c ultimate tensile stress, and d strain with temperature for Cantor alloy (Otto et al. 2013)

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Fig. 8.14 TEM micrograph of Cantor alloy deformed at 77 K showing bright field image and dark field image with diffraction pattern (from left to right) at different level of strain (Laplanche et al. 2016a)

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Fig. 8.15 a True stress–true strain curve and b Kocks–Mecking plot for Cantor alloy at room temperature and 77 K (Laplanche et al. 2016a)

to strain hardening by the dynamic Hall–Petch effect by providing a strong barrier to dislocations. There is a decrease in effective grain size due to the formation of twins causing a decrease in effective grain size, and twinning becomes increasingly difficult with increase in strain. Twinning reaches saturation, and the deformation is now dominated by slip again at higher strain. Thus, the deformation behavior of Cantor alloy at 77 K is characterized by slip dominated to slip and twin dominated to finally slip-dominated deformation. Nevertheless, the availability of mobile dislocations at higher strain after twin saturation contributes to higher ductility along with higher strength due to dynamic Hall–Petch effect. The Cantor alloy is able to overcome the strength–ductility anomaly by exploiting strengthening and strain hardening mechanisms like low stacking fault energy FCC materials like TWIP and TRIP steels at room temperature. This behavior of Cantor alloy cannot be simply attributed to the low stacking fault energy as it does not show twinning at room temperature and needs further insight. The shear modulus normalized strain hardening rate of the Cantor alloy samples deformed at room temperature and 77 K coincide till strain of 7.4% after which the strain hardening rate of room temperature sample continues to

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Fig. 8.16 Bright field TEM micrograph for the Cantor alloy samples deformed at 293 K and 77 K (Laplanche et al. 2016a)

decrease while that of 77 K sample shows a plateau due to additional strain hardening from twinning. The distinct behavior of the Cantor alloy which is unlike any FCC alloy cannot be simply attributed to stacking fault energy or increase in shear modulus due to decrease in temperature. Albeit, the optimum value of critical stress required for deformation twinning imparts superior cryogenic mechanical properties to the Cantor alloy which are absent in the existing alloy world. In addition to better yield strength and ultimate tensile strength, higher uniform as well as overall ductility indicates toward high toughness for the Cantor alloy. The unique behavior of Cantor alloy cannot be simply restricted to critical stress for twinning and needs further mechanistic analysis in terms of determining critical resolved shear stress for slip and twinning and their temperature dependence. Efforts were directed in this direction, and few investigations were carried out on single crystals of different orientation of Cantor alloy prepared by Bridgman technique. Abuzaid and Sehitoglu (2017) employed microdigital image correlation technique and coupled it with electron backscatter diffraction to study the deformation of single crystals of different orientations of CoCrFeMnNi HEA in tension. They found that room temperature deformation of single crystals of different orientations shows only slip while twinning was observed in samples deformed at 77 K. Twinning is preceded by some slip activity in the samples deformed at 77 K which is similar to most FCC materials with low stacking fault energy that shows slip activity prior to twinning. It was shown that the CRSS of slip increases from 55 MPa at room temperature to 150 MPa 77 K indicating a strong temperature dependence of CRSS unlike FCC metals but similar to BCC metals and FCC solid solutions as shown in Fig. 8.17. The CRSS of twinning was determined to be 153 MPa at 77 K, and most samples deformed at 77 K show twins but there are exceptions. It is to be mentioned here that twinning was not observed in single crystal samples deformed at room temperature even at higher strain where the resolved shear stress was higher than the critical resolved shear stress for twinning unlike polycrystalline Cantor alloy. This effect can be attributed to the lack of local stress state conducive for twinning in single crystal compared to a

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polycrystal. Earlier investigations have also shown that the increase in CRSS of slip in Cantor alloy cannot be explained due to increase in shear modulus, and hence, lattice distortion and Peierls–Nabarro stress were assumed to contribute to the strong temperature dependence of CRSS. In another investigation “Mechanisms of plastic deformation in [11 1]-oriented single crystals of FeNiMnCrCo high entropy alloy by Kiereva et al. (2016) carried out on single crystals of 001 orientation, the CRSS of twinning in Cantor alloy was found to be 210 ± 10 MPa and the deformation at room temperature was characterized by numerous stacking faults and no twinning. Patriarca et al. (2016) also carried out a detailed experimental and theoretical study of slip nucleation in Cantor alloy by performing uniaxial compression test on [5 9˜ 1] oriented single crystal of Cantor alloy using digital image correlation technique. They showed that the CRSS for slip increased from 70 MPa at room temperature to 175 MPa at 77 K and that the CRSS value experimentally determined at 77 K was very close to that determined theoretically by Peierls–Nabarro formulation. Thus, single crystal deformation behavior of Cantor alloy indicates a strong dependence of CRSS of slip on temperature and higher CRSS or nucleation stress for twinning. The absence of twinning at room temperature accompanied with extensive twinning at cryogenic temperature is a unique feature of Cantor alloy, and this behavior is similar to that of medium SFE copper. Thus, the unique mechanical properties of the Cantor alloy can be attributed to the synergistic effect between planar slip and deformation twinning, and similar observation is made for other equiatomic FCC HEAs like AuCuNiPdPt, CoCuFeMnNi, and AlzCoCrFeMnNi. In comparison with FCC HEAs, BCC HEAs have been studied in less details due to the lower ductility compared to conventional BCC metals and alloys which generally show lower ductility than the FCC counterparts. BCC metals and alloys do not possess a dominant slip family, and deformation occurs by slip along ½ direction in {110}, {112}, and {123} planes. Thus, BCC metals and alloys have 48 available slip systems compared to 12 in FCC materials but show lower ductility. As discussed earlier, the rate controlling mechanism in the deformation of FCC materials is the interaction of dislocations with forest dislocations while for BCC materials, deformation is governed by kink pair annihilation of screw dislocations. The thermal component of stress is dominant in BCC materials compared to FCC materials and dislocation core splitting on multiple planes contributes to lower dislocation mobility at low homologous temperature and contributes to lower ductility. All these aspects are compounded in BCC HEAs, and they are characterized by poor ductility with the exception of refractory HEA TiNbZrHfTa. This is a little counterintuitive as BCC metals like iron exhibit higher ductility than refractory BCC metal like molybdenum or tungsten as the critical cleavage stress on 100 plane is lower than the critical resolved shear stress for slip in the latter. However, BCC HEAs from refractory elements hereafter referred as RHEAs show ductility comparable to transition metal BCC HEAs, and in fact, the BCC RHEA TiNbZrHfTa shows the highest ductility among the BCC HEA family. It was argued that RHEAs offer an avenue to control the critical cleavage and shear stress by controlling the valence electron concentration in HEAs. Senkov and co-workers have carried out a series of investigations on quinary and subset quaternary alloys to show that RHEAs with VEC greater than

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8 Structural Properties

Fig. 8.17 Deformation of 111 single crystal of Cantor allottee deformed at a 293 K and b 77 K. The figure shows stress–strain curve and variation of different in plane strain components in a and surface features showing slip lines and twins in b (Abuzaid and Sehitoglu 2017)

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219

5 show high yield strength and lower ductility while the RHEAs with VEC lower than 4.5 show higher ductility. Stress–strain curves of different RHEAs tested at 300 K provided in Fig. 8.18a clearly show sufficient yield strength with significant strain hardening and ductility in TiNbZrHfTa RHEA compared to other RHEAs like TaNbWMoV and TaNbWMo (Senkov et al. 2011a). On cold rolling, TiNbZrHfTa alloy (Senkov and Semiatin 2015) showed increase in yield strength with reduction in overall ductility and strain hardening similar to any ductile metal and alloy (Fig. 8.18b). On annealing at 1073 K, there was an increase in yield strength and decrease in ductility, which was attributed to decomposition of initial single phase BCC structure into two BCC phases showing partial recrystallization. The loss in ductility can be attributed to residual stresses arising out of decomposition of the single BCC phase to two BCC phases with different lattice structures. However, annealing at 1273 K led to a fully recrystallized single BCC phase microstructure and showed the best combination of yield strength and ductility. Fractography of tensile tested sample showed mixed mode fracture with 8% ductility and YS of 1145 MPa and UTS of 1262 MPa due to the presence of second brittle BCC phase at the grain boundaries. Detailed TEM analysis for defect structure characterization in BCC RHEAs is warranted to develop a complete understanding of deformation processes similar to that in FCC HEAs. Limited TEM analysis on compression tested TiNbZrHfTa RHEA shows lower mobility of screw dislocations compared to that of edge dislocations and the fraction of screw dislocations increase with increase in strain. This observation is completely opposite to that during deformation of FCC metals and alloys including FCC HEAs which show comparable mobilities for edge and screw dislocations and are characterized by increase in fraction of edge dislocations with increase in strain. The higher yield strength of the alloy can be attributed to higher Peierls–Nabarro stress similar to that of BCC metals, and limited strain hardening is attributed to modest forest hardening rate. The effect of temperature on the compression behavior of as-cast and homogenized TiNbZrHfTa HEA showed yield strength in the range of 800–1000 MPa and compressive ductility of maximum 50% over a wide temperature range from room temperature to 1273 K. A systematic investigation by Senkov et al. showed that quaternary NbMoTaW and quinary VNbMoTaW RHEAs outperform conventional superalloys like Inconel 718 and Haynes 230 with little decrease in yield strength at 1273 K compared to room temperature yield strength as shown in Fig. 8.19 (Senkov et al. 2011b). The stress–strain behavior of FC and BCC HEAs is governed by motion of dislocations with characteristic similar to that of conventional FCC and BCC metals and alloys. The evolution of yield strength in single phase FCC Cantor alloy and BCC Senkov alloy can be explained on the basis of different strengthening mechanisms like Hall–Petch strengthening, solid solution strengthening, and forest strengthening while for single phase BCC Senkov alloy an additional Peierls–Nabarro stress term has to be included similar to conventional FCC and BCC metals. σYS = σfr + ΔσSS + ΔσHP + ΔσSH + ΔσTB

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8 Structural Properties

Fig. 8.18 a Engineering stress–strain curve at 296 K for different RHEA (Senkov et al. 2011a) and b true stress–true strain curve for TiNbZrHfTa RHEA after different processing conditions (Senkov and Semiatin 2015)

The P-N stress also known as the friction stress which is assumed to follow rule of mixtures just like elastic modulus is also expected to be negligible for FCC HEAs based on Cantor alloy compositions as most elements have similar atomic radius with the exception of aluminum. Komarswamy et al. (2016) attributed higher yield strength of Al0.1 CoCrFeNi HEA to intrinsic lattice distortion of HEAs compared to that of FCC metals and alloys. It was proposed that the dislocation line energy and Peierls potential in HEAs may have a continuous variation contrary to constant line energy and potential in conventional alloys as depicted in Fig. 8.20. The presence of varying potential barrier offers a unique environment for dislocation movement with the deep wells acting as dislocation pinning points in the lattice. Some researchers also include contribution from lattice distortion as it was considered as one of the core effects of high entropy alloys but this contribution is included in the solid solution

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221

Fig. 8.19 Comparison of variation of yield strength of equiatomic NbMoTaW and VNbMoTaW RHEA with conventional high temperature alloys from Senkov et al. (2011b)

strengthening term. Several studies have shown that the Peierls–Nabarro stress for FCC HEA is not significant while the solid solution strengthening can be more potent compared to dilute alloys. The Hall–Petch coefficient for the Cantor alloy is definitely higher than that of pure metals and even solid solution alloys and is a major contributor to the strength. Additional strengthening mechanisms like precipitation strengthening or dispersion strengthening have also been shown to contribute to the higher strength of HEAs. Most FCC HEAs are characterized by the presence of annealing twins or manifest deformation twinning and hence an additional twin boundary strengthening term similar to that of the Hall–Petch term is included in the strengthening equation. For FCC HEAs like Cantor alloy that show extensive twinning at cryogenic temperature, there is significant twin boundary strengthening due to the dynamic Hall–Petch effect that contributes to additional strengthening and more importantly strain hardening in this alloy contributing to high toughness with higher strength at 77 K. Fig. 8.20 Schematic showing the dislocation core (a & c) and variation in lattice potential (b & d) for pure metal and high entropy alloy (Komarasamy et al. 2016)

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8 Structural Properties

Numerous investigations on single phase Cantor alloy have focused on understanding the role of solid solution strengthening in HEAs which are baseless alloys or 100% solute alloys. Classical solid solution model for dilute solid solution like the Friedel model does not work for HEAs but the Labusch strengthening model for concentrated solutions works well for HEAs with some modification. The former considers the interaction of dislocations with the stress field of solute atoms while the latter considers the interaction of dislocations with solute forests that lead to a stronger concentration dependence in terms of higher exponent of 0.67 compared to 0.5 for the former. Both the models try to capture strengthening due to misfit that is stress field due to difference in size of the solute atom with the solvent atom and the elastic strengthening which is due to difference in elastic modulus of the solute and solvent. The Friedel model is expressed by: 1/2

Δσss = Bi X i 3/2

Bi = 3μ∈i .

η= i

| | | |. ∈i = ||η|+α|δi || i

Z;

dμ 1 da 1 ηi ; δi = ; ηi = 1 + 0.5|ηi | d Xi μ d Xi a

The Labusch model is given by: )2/3 ( . 2/3 2 2 η σss (T = 0) = 3Z μ +α δi ci i

)2/3 ( . 2/3 σss (T ) = 3Z μ η +α 2 δi2 ci e−mkT / Wo i

The model proposed by Toda-Caraballo based on binary interaction between an element and higher-order multicomponent systems considering interatomic spacing between the atoms is provided below. (

))2/3 Σ (. 2 2 σss (T = 0) = 3Z μ ci η +α δi s=

Σ

i

i

si j ci c j and a ave = s ave f p

ij

(

) )2/3 Σ( . η +α 2 δi2 ci σss = σ0 + 3Z μ i

σ0 =

Σ i

i

ci σ0,i

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223

Toda-Caraballo and Rivera-Díaz-del-Castillo (2015) used the Labusch model and proposed a modified version of determining the hardening parameter Bi for capturing the variation in unit cell parameters with composition due to change in interatomic spacing in the presence of atoms of different size in multicomponent alloys. In a separate investigation on CoCuFeMnNi HEA, Agrawal et al. (2018) studied the tensile behavior of subset binary FeMn, ternary FeMnNi, and quaternary FeMnNiCo to understand the evolution of mechanical properties like yield strength and strain hardening as a function of increasing configurational entropy. They showed that the yield strength of the alloys is not related to entropy with the quaternary alloy showing lower strength than the ternary alloy that shows the highest strength (Fig. 8.21a). The authors employed the model developed by Toda-Caraballo to correctly predict the evolution of yield strength in subset alloys of CoCuFeMnNi alloy with strengthening in ternary FeMnNi alloy on addition of nickel and decrease in yield strength with addition of cobalt in FeMnNiCo quaternary followed with increase in yield strength in quinary FeMnNiCoCu with addition of copper due to change in lattice distortion. This investigation clearly demonstrates that the change in lattice spacing contributes directly to solid solution strengthening. It was shown that increase in lattice expansion by addition of Ni to binary FeMn or Cu to ternary FeMnNiCo led to increase in yield strength while addition of Co to ternary FeMnNi led to lattice contraction contributing to decrease in strength (Fig. 8.21b). Toda-Caraballo showed that the model is applicable for most FCC and BCC HEAs and MEAs studied in literature as shown in Fig. 8.22. The success of the model proposed by Toda-Caraballo for FCC as well as BCC HEAs is rather surprising as the fundamental deformation mechanisms in FCC and BCC materials are different. Traditionally solid solution strengthening in BCC alloys is explained using the interaction of solute atoms with screw dislocations as annihilation of kink pairs is the rate controlling mechanism in the deformation of BCC metals and alloys. Also, the BCC HEAs do not show a strong dependence on temperature and strain rate like dilute BCC alloys and there is enough scope for developing a robust theoretical solid solution strengthening model for BCC HEAs. It is to be mentioned here that in 100% solute alloys like HEAs, it is difficult to define a solute and a solvent so each elemental atom is considered as a solute in an average solvent of all constituent elements. In dilute alloys, contribution to strengthening from lattice mismatch and elastic modulus mismatch is routinely determined to accurately estimate the contribution of solid solution strengthening. However, for HEAs, mismatch in lattice volume and local solute environment contribute to solid solution strengthening as it is difficult to differentiate between lattice and modulus mismatch as HEAs are essentially 100% solute alloys. Vevrnene et al. (2016) considered a HEA as a solid solution alloy with a solute embedded in an effective matrix of the surrounding alloy and attributed strengthening to the interaction of dislocation with local random concentration fluctuations around the average composition. They developed ab initio molecular dynamics simulations approach to illustrate their mechanistic theoretical approach using Fe–Ni–Cr alloys. They showed that higher strength can be achieved by choosing elements to maximize the misfit atomic volume in terms of solute misfit parameter and shear modulus and that it is less dependent on the stacking fault

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8 Structural Properties

Fig. 8.21 a Engineering stress–strain curve for equiatomic FeMn, FeMnNi, FeMnNICo, and FeMnNICoCu alloys and b variation of interatomic distance with addition of different elements in subset alloys (Agarwal et al. 2018)

energy of the alloy and independent of number of elements in the alloy. The concept of atomic volume misfit was proposed to capture the strengthening due to addition of a “solute” embedded into an effective “solvent” carrying all the average properties of the alloy. In other words, the model considers the substitutional atoms as local fluctuations in composition with respect to an effective medium reference matrix. The interaction of a dislocation with local fluctuation in effective medium reference matrix or solvent acts as a unique barrier that makes the path of the dislocation line more tortuous, thus increasing the length of the dislocation line at the expense of minimizing the energy to avoid local fluctuations in lattice potential. It is argued that this unique interaction contributes to solid solution strengthening in HEAs and is given by:

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225

Fig. 8.22 Comparison of theoretical critical resolved shear stress predicted from solid solution hardening model for HEAs proposed by with experimental data (Toda-Caraballo and Rivera-Díazdel-Castillo 2015)

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8 Structural Properties

τ y0

] [ ]−1/3 [ [Σ 2 ]2/3 1 + νalloy 4/3 ┌ n cn ΔVn μalloy = 0.01785 2 × b 1−νalloy b6

The change in lattice potential due to a solute atom in a reference solvent is provided by: ] [ ]1/3 [ [Σ 2 ]1/3 1 + νalloy 2/3 ┌ n cn ΔVn ΔE b = 1.5618 2 b3 μalloy × b 1−νalloy b6

(8.2)

And the predicted tensile yield stress is: [ σ y (T , ε) = 3.06 τ y0 1 − τy0 ΔE b ΔV n ┌ μ ν

(

.

ε0 kT ln ΔE b ε˙

)2/3 ] (8.3)

zero-temperature shear yield stress energy barrier (associated with dislocation segment of length ζ c) solute misfit volumes αμb2 edge dislocation line tension shear modulus Possion’s ratio

It was shown that the model proposed by Vervenne was able to predict solid solution strengthening in FCC HEAS as well as MEAs and was used to design new high-strength alloys based on atomic volume distortion. It is important to understand the effect of strain rate and temperature on the different strengthening mechanisms, and hence, the transient behavior of HEAs will be discussed in the next section and the effect of the two most important extrinsic parameters on different strengthening mechanisms will be discussed (Fig. 8.23).

Fig. 8.23 Variation of predicted solid solution hardening with experimental data and relation between predicted and experimental yield strength data (Varvenne et al. 2016)

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8.3.3 Transient Plastic Deformation The macroscopic stress–strain response or flow behavior of materials is associated with microscopic processes that accommodate plastic deformation. This can include interaction of dislocations with each other and other defects in crystalline materials while in amorphous materials shear transformation zones control the macroscopic flow behavior. For crystalline materials, the movement of dislocation through the lattice or past an obstacle like other dislocation/s, solute atom, precipitate, grain boundary, etc., requires overcoming an energy barrier by a combination of mechanical stress and thermal activation. Short-range obstacles like small precipitates, forest dislocations, solutes, jogs in screw dislocations can be overcome by thermal activation while long-range Peierls–Nabarro stress can be overcome by stress only. Thus, plastic deformation of crystalline materials that are dictated by movement of dislocations can be described in terms of the ability of the dislocations to overcome an obstacle in the lattice. This phenomenon is captured in the concept of activation energy or activation volume which describes the probabilistic nature of dislocation overcoming an obstacle. Dislocation motion in crystalline materials is affected by various intrinsic parameters like purity, grain size, dislocation density as well as extrinsic parameters like strain rate, temperature, and pressure. Among all the intrinsic and extrinsic parameters strain rate and temperature are the two most important parameters that play an important role in determining the probability of dislocation overcoming an obstacle for engineering metals and alloys. Traditionally, activation parameters like activation energy, activation volume, and activation area have been mapped as a function of strain rate and temperature to decipher the rate controlling deformation mechanism that controls plastic deformation in crystalline materials. As previously mentioned, shear stress (τ ) required for plastic deformation can be decomposed into internal (athermal) stress (τi ) and effective stress (τ ∗ ) dependent on temperature and strain rate. ( . ) τ = τi (γ ) + τ ∗ T , γ p The athermal component of stress is attributed to long-range stresses impeding dislocation motion and has a temperature dependence due to variation in shear modulus with temperature. On the other hand, the effective stress corresponds to overcoming short-range obstacles and can be related with thermally activated dislocation glide with velocity (v) given by ) ( ΔG(τ ∗ ) v = ϑ × D × exp − kT where ϑ is vibration frequency of the average dislocation segment, D is the magnitude of displacement of the dislocation segment after a successful activation event, ΔG is activation energy necessary to overcome the obstacle, k is Boltzmann constant, and T is temperature. The activation volume expresses the volume, which is physically

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8 Structural Properties

swept by a dislocation from a ground equilibrium state to an activated state after the deformation. Physical activation volume (V ∗ ) is defined as the stress derivative of the activation energy and is expressed as (Caillard and Martin 2003; Lu et al. 2009) V∗ = −

∂ΔG(τ ∗ ) ∂τ ∗

Combining Eqs. (8.2) and (8.3), dislocation velocity (v) can be expressed as ( v = v0 × exp

V ∗ Δτ ∗ kT

)

where v0 is initial dislocation velocity and Δτ ∗ is decrease in effective stress during relaxation for time period t. Thus, physical activation volume captures the stress dependence of dislocation velocity taking into account the variation in mobile dislocation density with deformation. Activation volume can be determined by carrying out strain rate jump tests or stress relaxation test in tension, compression as well as using instrumented micro/nano-indentation. The strain rate sensitivity determined from strain rate jump tests can be related with the activation volume by m=

kT τV∗

(8.3)

Fundamental studies on determining activation volume in conventional metals and alloys and establishing the link between activation volume with micromechanisms of deformation are well-established in the literature. High activation volume in FCC metals and alloys correlate with forest strengthening while low activation volume of 100 b3 in BCC metals and alloys is attributed to high Peierls–Nabarro stress. The former show strong grain size dependence with significant decrease in activation volume with decrease in grain size from micro- to nanoregime but BCC metals and alloys show little change in activation volume with decrease in grain size. The decrease in activation volume of FCC materials is attributed to change in deformation mechanism from forest strengthening to grain boundary-related processes like grin boundary sliding and Coble creep in nanocrystalline FCC materials while the insignificant change in activation volume for BCC materials from micro- to nanograin size regime is attributed to the dominant kink-pair annihilation mechanism operative across the entire grain size regime. Though activation volume studies on Cantor alloy have been few, detailed evolution of activation volume using strain rate jump test as well as repeated stress relaxation tests have been performed. In a rigorous investigation (Laplanche et al. 2018), repeated stress relaxation tests were performed on Cantor alloy for different level of strain at room temperature (Fig. 8.24a) at different temperature to determine the evolution of strain rate sensitivity and activation as a function of temperature (Fig. 8.24b). The activation volume of Cantor alloy has been reported to be 300 b3 at room temperature which is lower than the activation of pure FCC metals (~1000–3000 b3 ) but is comparable to that of most FCC solid

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229

solutions. It is also observed that the activation volume of Cantor alloy decreases with increasing strain indicating that reduction in mean free path for dislocations is the rate controlling mechanism. There is decrease in activation volume with decrease in temperature with the 77 K tested sample showing an activation volume of 25 b3 and enhanced rate sensitivity. This has been attributed to reduced mean free path for mobile dislocations due to profuse twinning. This behavior of Cantor alloy is very similar to that of copper which is a little surprising as stacking fault energy determination by measuring separation between the partials as well as X-ray analysis have established low stacking fault energy for Cantor alloy. We would like to emphasize here that despite the low stacking fault energy of Cantor alloy, it shows behavior similar to that of medium SFE copper and unlike low SFE solid solutions. This unique ability of the Cantor alloy to exploit twinning as an additional deformation mechanism and more importantly to utilize the synergy between conventional octahedral and/or partial slip with twinning demonstrates the unique ability of HEAs to exploit different mechanisms beyond the realm of conventional metals and alloys. Though there have been few studies on BCC TiNbZrHfTa alloy, the lower activation volume shows little change with change in temperature and strain rate of deformations as well as strain. Thus, it is clear that glide of dislocations (mostly edge in character) through an array of randomly distributed obstacles at different length scales like grain boundaries, forest dislocations, and solute atmosphere or short-range ordering governs the plastic deformation of FCC and BCC HEAs. The yield or flow stress of the alloy can be obtained by linear superposition of different strengthening mechanisms and can be clubbed into mechanisms dependent on strain rate and temperature but independent of strain and dependent on strain. Hasen proposed a method to deconvolute the contribution from individual strengthening mechanism by determining the strain rate sensitivity as a function of plastic strain. Differentiating the strength equation with natural logarithm of strain rate yields ( . ) ( . ) σ = σ y ε, T + σdiss ε, T, ε p ∂ ln σ y ∂ ln σdiss ∂σ = σy + σdiss ∂ ln ε˙ ∂ ln ε˙ ∂ ln ε˙ ∂σ = m y σ y + m diss σdiss ∂ ln ε˙ Here my and mdis are the relative rate sensitivities of strengthening mechanisms independent and dependent of plastic strain. The strain rate sensitivity can be correlated with activation volume that carries the fingerprint of deformation mechanism. Thus, plotting of strain rate sensitivity as a function of the difference between flow stress and yield stress, the slope provides strain rate sensitivity due to processes dependent on plastic strain and the y-intercept provides strain rate sensitivity for processes independent of plastic train. This plot prosed by Hassen is generally known as Hassen plot and has been used in traditional alloys to deconvolute the contribution

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8 Structural Properties

Fig. 8.24 a Multiple stress relaxation test on Cantor alloy and b variation in activation volume as a function of strain for different temperature in Cantor alloy from Laplanche et al. (2018)

from different strengthening mechanism as a function of plastic strain. The Haasen plot (George et al. 2020) for FCC CoCrFeMnNi FCC HEA shows linear increase in (MkT/V) with flow stress clearly indicating a decrease in activation volume with increase in plastic strain (Fig. 8.25a). An activation volume of ~300 b3 is significantly lower than that of pure FCC metal like copper that shows an activation volume of the order of 1000–2000 b3 but is comparable to that of FCC solid solutions like CuZn or NiCo alloys. The absolute value of the activation volume in FCC HEAs indicates that forest strengthening is the dominant plastic deformation mechanism in FCC HEAs. Hu et al. studied the evolution of activation volume as a function of temperature for CoCrFeMnNi HEA and many of the subset alloys to show that for FCC HEA and MEAs, there is a significant decrease in activation volume with decrease

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231

in temperature. They showed that long-range bowing of non-straight dislocations by thermal activation is the underlying deformation process for FCC HEAs and MEAs unlike overcoming of short-range barriers that contributes to lower activation volume (Fig. 8.25b) (Wu et al. 2016). The BCC HEA TiNbZrHfTa also shows a linear variation of (MkT/V) with increase in flow stress; however, the change in activation volume with increase in plastic strain or flow stress is not significant (Fig. 8.25a). This observation is similar to that of conventional BCC alloys. Nevertheless, our understanding of deformation processes in BCC HEAs which are characterized by non-monotonic variation in strength and ductility with plastic strain and/or temperature is still in a nascent stage and needs further investigation. ( ) ∂σ = m y σ y + m diss σ − σ y ∂ ln ε˙ MkT ∂σ = ∂ ln ε˙ V

8.3.4 Dynamic Tensile Behavior The dynamic deformation behavior of different FCC HEAs based on the CoCrFeMnNi Cantor alloy shows that the HEAs are characterized by significant strain rate hardening compared to the quasistatic deformed samples. Most investigations on high strain rate are carried out using compression split Hopkinson pressure bar setup by using cylindrical samples to study the dynamic compression behavior while hat-shaped samples provide information about dynamic shear behavior. Generally, the high strain rate or dynamic behavior is observed at strain rate above 1000 s−1 and it was recently shown that the Cantor alloy (Tsai et al. 2019) shows an increase in flow stress in the dynamic strain rate regime along with an increase in the strain rate sensitivity with m > 1 for strain rate above 1000 s−1 in compression (Fig. 8.26). The microstructure of the sample deformed at high strain rate in Fig. 8.27 is also characterized by the presence of deformation twins which is similar to that of high strain rate deformation behavior of FCC metals with medium stacking fault energy. Another important aspect of dynamic deformation is adiabatic heating of the sample due to the short duration of deformation. However, the effect of adiabatic heating on Cantor alloy was found to be negligible. The onset of twinning at high strain rate is similar to that at low temperature as reported in earlier section. The activity of deformation twinning can be explained on the basis of critical stress for twin nucleation in FCC Cantor alloy. The critical resolved shear stress of twinning is expected to be higher than that of octahedral and partial slip in Cantor alloy. At room temperature, the critical resolved shear stress for twinning can be reached at very large strain deformation in Cantor alloy prepared from extremely pure elements but is generally absent. At high strain rate and low temperature, the critical resolved shear stress for

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8 Structural Properties

Fig. 8.25 a Haasen plot for Cantor alloy and TiNbZrHfTa (George et al. 2020), b schematic showing long-range bowing of dislocation for activation volume of 300 b3 , and c schematic showing longrange and short-range obstacles for lower activation volume of 15 b3 (Wu et al. 2016)

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233

octahedral slip is expected to increase substantially while the effect on the critical resolved shear stress of twinning is minimal. Hence, twinning if operative at high strain rate and low temperature wherein the critical resolved shear stress of twinning is comparable to that of slip. It is to be mentioned here that deformation twinning is also known as synchro shear as it involves coordinated movement of partials on parallel 111 plane in FC materials, and hence, some slip is prerequisite for twinning to occur in FCC materials. The critical resolved shear stress for twinning can be given by: τc =

γs f 3Gbs + 3bs L0

It is therefore important to consider the role of SFE in HEAs but it is generally agreed that the FCC HEAs have low SFE as determined from X-ray diffraction or direct measurement of distance between partials in TEM. However, there is a debate whether we can define a SFE for HEA due to local composition fluctuations and significant scatter in the data. However, multiple investigations show that Cantor alloy exhibits behavior similar to that of medium SFE copper despite the low SFE measured from X-ray diffraction and TEM investigations. Li et al. studied the dynamic shear behavior of Cantor alloy and single phase AlCoCrFeMnNi alloy to show that there is significant hardening and profuse twinning and significant resistance to shear band formation in the latter. They also showed that the deformation behavior of the alloy could be fitted using the modified Johnson–Cook constitutive equation which is commonly used to explain the deformation behavior of conventional metals and alloys across temperature and strain rate regimes, thereby underscoring similar deformation of FCC HEAs with that of conventional FCC alloys. Sonkusare et al. (2020b) also showed the occurrence of twinning in CoCuFeMnNi HEA at high strain rate leading to plateau in the strain hardening curve in Fig. 8.28. They also showed that the empirical Johnson–Cook equation could explain the effect of strain rate albeit with higher strain hardening and strain rate-hardening contribution in the HEA compared to the constituent elements. )( )λ ( ) ( T ∈˙ σ = σ0 + B∈ n 1 + Clog ∈˙ Tr

8.3.5 Fracture Toughness The tensile behavior of Cantor alloy and numerous FCC HEAs show that FCC HEAs are characterized by significant ductility with sufficient strength providing a wide range of toughness that can be described as the area under the stress–strain curve for HEAs in general and FCC single phase HEA like the Cantor alloy in

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8 Structural Properties

Fig. 8.26 a True stress–true strain curve and Kocks–Mecking plot for Cantor alloy deformed at different strain rate and b Variation of strain rate sensitivity with strain rate for Cantor alloy (Tsai et al. 2019)

particular across a wide temperature range. Another important design parameter is the fracture toughness which provides information about the resistance of a material to crack propagation and is generally measured in plane strain condition. The mode I plane strain fracture toughness corresponds to the resistance to crack growth in plane strain condition for the tensile crack opening mode in materials and is a design parameter like Young’s modulus and yield strength. K IC is generally used for mostly linear elastic fracture, and JIC is used if there is yielding ahead of the

8.3 Mechanical Properties of HEAs

235

Fig. 8.27 TEM microstructure of 40% compressed Cantor alloy at strain rate of 9 · 103 s−1 a bright field image, b, c centered dark field image and d centered dark field at higher magnification showing two variants of twins (Tsai et al. 2019)

Fig. 8.28 Kocks–Mecking plot with stress–strain curve in inset and evolution of microstructure in CoCuFeMnNi HEA under quasistatic and dynamic loading condition from Ref. (Sonkusare et al. 2020b)

crack tip (elasto-plastic). The resistance to crack propagation can be offered by intrinsic factors like plastic deformation by slip, twinning, phase transformation, or extrinsic factors like crack deflection by the presence of second phase. Cantors alloy is characterized by exceptional fracture toughness across a wide temperature range similar to the high toughness that it manifests in the wide temperature regime. A brief overview of the fracture toughness sample geometry with the evolution of

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the crack and microstructure evolution showing extensive deformation twinning is shown in Fig. 8.29 (Gludovatz et al. 2014). Deformation twinning plays an important role in contributing to higher fracture toughness by reducing the stress field ahead of the crack tip. In addition, formation of multiple twins provides higher fraction of stable grain boundaries which makes the progress of crack difficult. It has also been shown that the occurrence of multiple twins can contribute to crack bridging as shown in Fig. 8.30, thus leading to high fracture toughness (Zhang et al. 2015). It is to be mentioned here that Cantors alloy manifests high tensile strength ranging from 730 to 1280 MPa from room temperature to 77 K and retains a fracture toughness of 200 MPa-m0.5 at cryogenic temperature that make this alloy unique. The high fracture toughness of the alloy was attributed to intrinsic mechanism of profuse deformation twinning and extrinsic crack bridging by deformation twinning that provides excellent resistance to damage evolution, thereby offering sufficient, good ductility with significant toughness as well as outstanding fracture toughness that is not possible in conventional alloys. The Ashby map for different engineering materials for ultimate tensile strength and fracture toughness shows the superior performance of the Cantor alloy (Fig. 8.31) over a wide range of metallic materials (Ashby and Ashby 2011).

8.3.6 Strength Ductility Paradox Transformative HEAs Excellent mechanical properties of the Cantors alloy are attributed to the unique combination of strengthening mechanisms in terms of partial slip, conventional octahedral slip, and deformation twinning motivated researchers to explore nonequiatomic alloys that could exploit different strengthening and strain hardening mechanisms existing in metallic materials. This led to the development of HEAs from mechanistic perspective and researchers involved in HEA research was motivated by extensive research in steel industry on the development of high strength and high toughness steels using strategies like twinning and transformation-induced plasticity. The most noticeable and the first such investigation was by Li et al. (2016) who extended the philosophy of TWIP and RIP in high manganese steels to Cantor alloy subsets. They developed a series of Fe80-x Mnx Co10 Cr10 alloys that showed TWIP behavior at lower manganese content and were characterized by the presence of epsilon martensite for higher fraction of manganese providing dual phase strengthening like the conventional ferrite martensite dual phase steels. The twophase microstructure of FeMnCoCr alloy showed transformation of the austenite phase to HCP epsilon martensite phase with increase in deformation thus enabling additional strain hardening and contributing to TRIP effect (Fig. 8.32). Sinha et al. (2019a) designed alloy that shows higher strength and significant ductility and is characterized by change in c/s ratio of the HCP epsilon martensite phase which deforms extensively by twinning. In this particular alloy, the authors were able to exploit dual

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Fig. 8.29 a Geometry for KIC test b SE image and inverse pole figure map near the notch c electron channeling contrast image near the notch and d image quality + inverse pole figure map from EBSD showing extensive twinning in/cantor alloy sample tested at 77 K from Gludovatz et al. (2014)

phase strengthening, transformation-induced plasticity, and twinning-induced plasticity in the HCP epsilon martensite phase as shown in Fig. 8.33. Investigations on VCoCrFeMnNi equiatomic HEA have also shown transformation from FCC gamma phase to BCC beta phase (Fig. 8.34) which contributes to higher strength due to higher lattice distortion contributing to solid solution hardening by addition of vanadium as well as higher strain hardening rate due to interfacial strengthening between the FCC and BCC phase. Thus, it has been manifested that it is possible to exploit multiple strengthening mechanisms and explore the synergy between them to achieve high strengthening and strain hardening in HEAs. Efforts have also been made to go back from HEAs to steels by designing so-called high entropy steels by adding interstitial carbon and nitrogen in iron-rich non-equiatomic Cantor alloy compositions to obtain

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Fig. 8.30 TEM images showing crack bridging due to nanoscale twins in Cantor alloy (a & b) and corresponding high-resolution TEM images showing nanoscale twins (c & d) (Zhang et al. 2015)

excellent strength, ductility, toughness, and fracture toughness than a known steel developed till date for high entropy steels. Just like steels another class of materials that have motivated HEA researchers are titanium alloys. The BCC beta to orthorhombic martensite transformation in metastable beta titanium alloys has motivated researchers to develop transformationinduced plasticity titanium-based HEAs that show properties comparable to that of existing metastable beta titanium alloys. Thus, it is clearly manifested that HEAs offer a unique palette of mechanical properties thanks to the ability to invoke multiple strengthening and strain hardening mechanisms in the same alloy. Thus, the chemical complexity enables operation of multiple mechanisms in a synergistic manner

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Fig. 8.31 Ashby map for yield strength versus plane strain fracture toughness for different engineering materials including Cantor alloy (Ashby and Ashby 2011)

to offer exceptional properties to HEAs. The ability to design mechanism-based HEAs motivated researchers to develop subset alloys with proper combination of stacking faulty energy or solid solution strengthening to achieve unique properties. This led to the development of equiatomic CoCrNi ternary alloy which shows excellent combination of strength and ductility due to twinning and that of Ni63.2 V36.8 alloy which shows excellent strength and ductility than the quinary BCC HEA. Thus, HEA research has laid the foundation for mechanistic alloy development similar to that in steels and titanium alloys but have offered a multifunctional domain to explore thanks to the multimechanism offering alloy compositions (Fig. 8.35).

8.3.7 Hardness and Wear Resistance High entropy materials also provide a wide range of hardness and wear properties and have been a subject of numerous investigations. Hardness measurements at different length scales ranging from Vickers microhardness to instrumented micro- and nanoindentation have been employed to study the hardness of HEAs. A wide range of

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Fig. 8.32 Initial microstructure of Fe(80-x)MnxCo10Cr10 alloy and evolution of microstructure with increase in strain for Fe50Mn30Co10Cr10 alloy (Li et al. 2016)

hardness ranging from 150 to 1200 HV is obtained for HEAs with HEAs prepared by MASPS route showing higher hardness compared to the HEAS with similar composition produced by melting and casting route. Similarly, BCC HEAs and multiphase HEAs show higher hardness compared to HEAs with FCC phase/s. In one of the most significant contributions in HEA research, Wu et al. (2006) showed that addition of aluminum to CoCrCuFeNi led to increase in hardness in a discontinuous manner. The rate of increase in hardness was low till 6% Al after which showed a steep increase till 26% Al followed with a plateau. This was attributed to the formation of BCC phase gyeong 6% Al that led to the presence of FCC and BCC two-phase microstructure till 26% Al after which only single phase BCC phase was present. Mohanty et al. (2017) carried out a series of investigations using MASPS route to explore different strengthening mechanisms like sinter aging, eutectoid transformation, and spinodal

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Fig. 8.33 Microstructural tunability in Cu containing HEA using friction stir processing and b Property diagram showing different operative mechanisms in transformative HEAs to achieve high tensile strength and strain hardening ability (Sinha et al. 2019b)

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Fig. 8.34 Strain-induced orthorhombic martensite phase in 7% tensile elongated HfNb0.18Ta0.18Ti0.27Zr alloy from EBSD data showing inverse pole figure map for a BCC phase and b orthorhombic martensite phase (Lilensten et al. 2017)

Fig. 8.35 a Understanding solid solution hardening using complexity map of mixing entropy versus electronegativity difference for different alloys including HEAs and MEAs. It is expected that alloys with higher electronegativity difference will show higher solid solution strengthening and NiV system is identified as the potential system for best solid solution strengthening. b Stress– strain curve for different alloys is showing the highest strength for NiV alloy as predicted from electronegativity difference (Oh et al. 2019)

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decomposition to obtain a wide range of hardness in different HEAs. There is an increase in hardness in the presence of two-phase microstructures as the interphase boundaries provide higher resistance to dislocation motion (Ganji et al. 2017). This effect is particularly dominant in nano-eutectic of HEAs with an ordered HEA phase where there is an additional contribution to strengthening from Hall–Petch kind of strengthening and strengthening due to ordering. HEAs with majority FCC HEA phase with intermetallic or Laves phase show high hardness but refractory HEAs with BCC structure or multiphase BCC + B2 phases show extremely high hardness. The higher hardness of HEAs also makes them a candidate material for wear resistance applications. There have been few investigations on wear properties of HEAs, and it has been shown that their behavior is comparable to that of conventional hard coatings and that the mechanisms of wear seem to be similar. However, a mechanistic understanding of wear and tribology of materials is still an open area for conventional materials, and hence, a mechanistic understanding of wear in HEAs can be developed once enough data is collected.

8.3.8 Fatigue In order to truly realize the potential of HEAs as engineering materials, it is paramount to study their deformation behavior in cyclic loading or fatigue. Fatigue is classified as stress-controlled high cycle fatigue and strain-controlled low cycle fatigue with the later showing significant plastic strain per cycle compared to the former. Fatigue failures constitute 90% of engineering failures that can be catastrophic in nature and an understanding of fatigue can shed light on the deformation as well as damage mechanisms operative in HEAs vis-a-vis conventional alloy. Most investigation on HEAs have focused on the high cycle fatigue behavior of single phase and multiphase HEAs, whereas the low cycle fatigue behavior has attracted little attention till date. The stress-controlled high cycle fatigue life of metallic materials is given by the Basquin equation while the strain-controlled low cycle fatigue life is given by the Coffin–Manson equation (Fig. 8.36). Cyclic deformation in metallic materials is characterized by forward and backward motions of slip leading to the formation of intrusions and extrusions, beachmarks and characteristic dislocation substructure comprising of persistent slip bands as well as evolution of surface cracks. During cyclic loading once microcracks are formed, one of the cracks attains the critical size and final failure occurs by cyclic growth of crack with number of cycles ultimately leading to the final failure. In one of the early investigations, Hemphil et al. (2012) studied high cycle fatigue behavior of as-cast and wrought Al0.5 CoCrCuFeNi alloy using four-point bending at room temperature. It was observed that the HEA showed a behavior similar to that of steels and titanium with a clear endurance limit in the range of 540–945 MPa for different conditions which is depicted in Fig. 8.37. In a follow-up investigation by Tang et al. (2015b), the contribution of inclusions (mainly the aluminum oxide inclusions) in reducing the endurance limit of Al0.5 CoCrCuFeNi alloy due to the use of lower purity elements was established. It was also shown that

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the alloy prepared from high-purity elements showed lower inclusion content, higher nanotwinning and was prone to lower microcracking resulting in higher fatigue life and better endurance limit. The better fatigue performance of the alloy with nanotwinning can be attributed to the release of back-stress during cyclic loading as has been reported for other materials like stainless steel and titanium in the literature which provide good high cycle fatigue properties. Other investigations on single phase Cantor alloy and transition metal multiphase HEAs show a behavior comparable to that of steels and titanium alloys in the high cycle fatigue regime. It has been reported that transformative HEA FeMnCoCr that undergoes FCC to HCP transformation shows a better high cycle life performance in terms of higher fatigue strength compared to other single and multiphase HEAs. All the HEAs show typical crack growth behavior comprising of incubation period followed with stage I of decreasing crack growth rate, stage II of stable crack growth rate comprising of the Paris regime and stage III which is the unsteady increasing crack growth rate that constitutes to final failure as seen in Fig. 8.38 (Thurston et al. 2017). Compared to future studies in high cycle regime, low cycle fatigue behavior of HEAs has been studied sparsely. Strain-controlled low cycle fatigue experiments were performed on transformative Fe50 Mn30 Co10 Cr10 alloy by Niendorf et al. (2018) who showed that higher propensity of austenite to martensite transformation during cyclic loading contributed to cyclic hardening leading to better fatigue life. The low cycle fatigue behavior of CoCuFeMnNi HEA comprising of FCC matrix and copper-rich nanoclusters was studied by Bahadur et al. (2020) with a major focus on microstructural investigation. It was observed that interaction of dislocations with copper-rich nanoclusters plays and important role in determining the cyclic hardening and softening response of the alloy leading to final failure by intergranular fracture. Thus, the fatigue behavior of HEAs is similar to that of other engineering alloys and it is anticipated that synergistic combination of mechanisms like twinning, martensitic transformation, and cluster strengthening can be explored to develop new HEAs for mitigating fatigue failure. Fig. 8.36 Typical cyclic behavior of metallic materials in terms of strain amplitude with number of cycles on a logarithmic scale showing the low cycle and high cycle fatigue regime (Suresh 1998)

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Fig. 8.37 High cycle fatigue behavior of as-cast and wrought Al0.5 CoCrCuFeNi alloy using fourpoint bending at room temperature (Hemphill et al. 2012)

Fig. 8.38 Fatigue crack growth rate behavior of Cantor alloy for different load ratio showing a Paris regime from Thurston et al. (2017)

8.3.9 Creep and Superplasticity Deformation behavior at high temperature or more correctly high homologous temperature under constant load or stress constitutes time-dependent plastic deformation or creep. High temperature deformation is described by the following generalized constitutive equation:

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ε=

( ) ADGb b p ( σ )n kT d G

Creep mechanisms like diffusion creep including the Nabarro–Herring lattice diffusion and the Coble grain boundary diffusion mechanism, dislocation creep comprising of dislocation glide and dislocation climb are reported for metallic and ceramic materials in the literature. Another important aspect of high temperature deformation is the phenomenon of superplasticity in which plastic instability is avoided by high strain rate sensitivity achieved by finer grain size at low strain rate and high homologous temperature. Superplasticity is essential for high temperature forming of alloys while a good creep resistance is essential for high temperature applications. Creep data is generally presented in terms of deformation mechanism maps that help delineate the different operating mechanisms as a function of intrinsic parameters like grain size or composition and extrinsic parameters like stress and temperature. There is a tremendous scope to study creep deformation of HEAs as diffusion is central to creep and the understanding of diffusion in complex concentrated alloys is not well-developed. The creep behavior of Cantor alloy by Kang et. al (2018) showed the presence of dislocation glide and climb mechanism in the temperature range of 808–923 K with an activation energy corresponding to diffusion of chromium that has higher atomic size misfit indicating that the diffusion of chromium atom in Cantor alloy restricts glide and climb transition in the deformation of Cantor alloy. Indentation experiments on Alx CoCrFeNi (x = 0 to 1.8 molar ratios) HEAs show that the hardness remains constant for single phase FCC alloys till x = 0.3 in the temperature range of 773– 1173 K while there is a significant drop in hardness for alloys with x > 0.5. In a separate study, stress exponents of 5.6 and 8.8 as well as activation energies of 385 and 334 kJ/mole were reported for alloys with x = 0.15 and x = 0.6 as shown in Fig. 8.39. The stress exponents and activation energy values reported for both the alloys indicate cross-slip as the rate controlling deformation mechanism Cao et al. (2016). Shahmir et al. (2017b) showed superplastic flow for 5 turn HPT processed Cantor alloy sample with grain size of 10 nm with 600% elongation at 973 K. The activation energy for superplastic flow in the temperature regime of 873–1073 K was close to that of grain boundary diffusion indicating activation of grain boundary sliding. This was further corroborated by little change in aspect ratio of grains near the fracture tip despite the large amount of strain. Reddy et al. (2017) performed tests on Cantor alloy sample with grain size of 1.4 micron (Fig. 8.40) and showed superplastic-like flow behavior at temperature of 1023 K for strain rate of 0.001 and 0.0001 s−1 . Considering the existing data in the literature from conventional creep tests and indentation experiments, Chokshi proposed a deformation mechanism map for Cantor alloy which is depicted in Fig. 8.41 (Chokshi 2020). The map is characterized by operation of Coble creep for finer grain size (nanocrystalline to submicron) irrespective of the stress value while superplastic flow is operational for higher grain size in the submicron regime and higher stress value. Dislocation power law creep

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Fig. 8.39 a Variation of steady-state creep rate with stress and b variation of steady-state creep rate for different temperature at constant load for Cantor alloy (Kang et al. 2018)

Fig. 8.40 True stress–elongation curve at 300 and 1023 K for Cantor alloy with grain size of 1.4 μm (Reddy et al. 2017)

is operative for microcrystalline samples at 1073 K at lower value of stress with a power law breakdown regime at high stress.

8.3.9.1

Radiation Damage

Interaction of particles with kinetic energy greater than 1 eV with matter is of tremendous scientific and engineering interest in basic particle physics, nanotechnology, nuclear energy as in nuclear fission and fusion reactors. Development of materials with excellent irradiation resistance at room temperature and elevated temperature is of paramount importance to improve the efficiency and safety of nuclear fission and fusion-based reactors for meeting the energy challenges of the future. The interaction of high energy particles like neutrons, electrons, photons, ions is the generation of point defects due to energy transfer to the atoms. In crystalline materials, this

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Fig. 8.41 Deformation mechanism map for Cantor alloy by Chokshi (2020)

can lead to the formation of vacancies, vacancy loops, dislocations, self-interstitial as well as amorphousization and local increase in temperature. Transfer of kinetic energy from incident particle to an atom in the material gives rise to the primary knockout atom that can cause further displacement of atoms in the material provided it has sufficient energy leading to creation, annihilation and storage of other point defects. Radiation damage in crystalline materials is expressed in terms of displacement per atom which is equal to the average number of displacements per atom in the lattice. Nuclear applications employ a wide range of metallic materials like zirconium alloys with low neutron cross section to handle fuel and materials with high neutron cross section like iron, nickel, and chromium alloys for other structural applications. Stability of microstructure and mechanical properties at high temperature is another important criterion in addition to excellent radiation resistance for nuclear application. High entropy alloys offer an exceptional opportunity in irradiation resistance due to their inherent lattice distortion and high entropy. In addition, traditionally short-range ordering in metallic materials like nickel–chromium alloys can absorb more displacement per atom without swelling causing less damage. Due to the complex composition of HEAs, they too show short-range ordering and are candidate material for nuclear applications. Kumar et al. (2016) showed that HEA showed lower radiation-induced segregation and lower defect cluster size with higher cluster density that indicates toward better radiation resistance of HEAs due to lower defect mobility. Preliminary experimental and theoretical investigations have shown that single phase equiatomic HEAs show better resistance than the constituent elements in terms of generation of defects like vacancies and dislocations. It is proposed that

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due to the chemical disorder and lattice distortion, the HEAs have a tendency of self-healing that leads to a lower swelling rate compared to conventional alloys. Theoretical investigations also indicate the energy transfer mechanism between the primary knockout atom and other atoms in HEA is sluggish in nature due to the different local chemistry as well as short-range ordering.

8.4 Corrosion and Oxidation In order to fully realize the potential of newly developed high entropy alloys with a broad spectrum of mechanical properties, it is essential to study their corrosion resistance as well as oxidation behavior. Efforts to establish a correlation between the structure–processing–corrosion and oxidation behavior linkages for a wide range of single phase and multiple phase HEAs have dominated the literature till date. Similarly, studies focusing on aqueous electrochemical corrosion in various environment as well as high temperature corrosion and oxidation behavior carried out on a wide range of HEAs show a response that is better than, worse and similar to that of conventional alloys. Nevertheless, a mechanistic approach trying to understand the operative micromechanisms of corrosion and oxidation in HEAs are still elusive. A potentiodynamic polarization test which is a standard electrochemical technique is used to study the corrosion behavior of metallic materials. The test provides important parameters like corrosion potential, corrosion current density, pitting or breakdown potential that can be used to judge the corrosion resistance of metallic materials for given environment. A typical polarization curve for 3.5 wt.% NaCl solution is shown in Fig. 8.42a. The pitting potential corresponds to the potential at which the anodic current density continuously increases indicating localized dissolution of alloy due to breakdown of protective oxide or passive film. The lower the value for E pit /Eb , better is the corrosion resistance of the alloy. The icorr provides the current density and is related to the mass loss. Earlier investigation on equiatomic subset alloys of the Cantor alloy, namely the CoFeNi and CoCeFeNi, shows better corrosion properties than ASI 304 stainless steel in NaCl and H2 SO4 environment in terms of lower icorr values and higher Ecorr values; however, the Cantor alloy shows higher dissolution of individual elements compared to 304 stainless steel. In results from a recent investigation depicted in Fig. 8.42b, it was demonstrated that the Cantor alloy shows lower icorr value than 304 SS in 3.5 wt.% aqueous NaCl solution compared to 304 SS but the E b value is lower than Epit value indicating that the Cantor alloy is susceptible to pitting corrosion. The Cantor alloy undergoes extensive corrosion in NaOH environment while it is resistant to acidic H2 SO4 environment due to the formation of passive film in the latter. With the addition of aluminum in Cantor alloy, there is an improvement in corrosion resistance and this can be attributed to the formation of a passive alumina film. It has also been shown that the presence of copper in HEAs reduces the corrosion resistance of the alloy while the presence of elements like Mo improves the corrosion resistance. A brief overview of HEAs and other metallic materials (Shi et al. 2017) in different environments show that

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they offer an excellent alternative to corrosion-resistant stainless steel (Fig. 8.43). Thus, the composition space available for design of corrosion-resistant HEAs is very vast and off late there have been efforts to explore the same using thermodynamic modeling by CALPHAD. Figure 8.44 shows the thermodynamic stability of different corrosion products as a function of different combination of potential and pH for a FCC Ni38 Cr21 Fe20 Ru13 Mo6 W2 HEA developed using CALPHAD modeling with TCHEA2 phase with a composition yielding chromium containing FCC phase that is particularly chosen to have excellent corrosion resistance. A combination of thermodynamic modeling for alloy development combined with thermodynamic modeling of electrochemical reaction as a function of overhead potential and pH can be employed to develop corrosion-resistant HEAs. Fig. 8.42 a Typical potentiodynamic polarization graph for a metallic material showing different regions and b Polarization curve for Cantor alloy and 304 SS exposed to 3.5 at. % NaCl solution (Shi et al. 2017)

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Fig. 8.43 Comparison of corrosion current density and corrosion potential for conventional alloys and HEAs in a 0.5 M NaCl and b 0.5 M H2 SO4 solution at 298 K (Shi et al. 2017)

Similar to corrosion, the oxidation behavior of a wide range of single phase and multiphase HEAs has been investigated. It is agreed that the oxidation behavior of HEAs is characterized by formation of complex oxides of constituent elements and the diffusion of individual elements through their oxides. Weight gain studies on Cantor alloy subjected to oxidation show that manganese oxide formation is controlled by diffusion of manganese in the oxide which accelerates oxidation while chromium provides resistance against oxidation. Formation of chromia layer below the mostly manganese oxide layer and the Cantor alloy at 873 K which leads to depletion of the HEA in manganese and chromium leading to the formation of pores in the base alloy (Fig. 8.45) (Laplanche et al. 2016b). The pores provide shortcircuiting path for vapor transport of manganese contributing to manganese oxide formation. In a systematic investigation on the oxidation behavior of a series of alloys belonging to the Cantor alloy family with and without yttrium addition in ppm levels, the detrimental role of manganese and protective nature of chromium was

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Fig. 8.44 Potential-pH diagram of HEA determined from CALPHAD at 298 K and 1 atmosphere showing regimes of immunity and corrosion. The details of the corrosion products can be found on the right of the diagram, and further details are provided in the reference (Lu et al. 2018)

firmly established. The presence of yttrium upto 1200 ppm level provides excellent oxidation resistance upto 1023 K by reducing the sulfur content of the alloy which leads to the formation of an adherent oxide film. The presence of elements like aluminum and silicon, that form a stable oxide film even in smaller amounts can provide oxidation resistance in FCC HEAs as well as RHEAs that contain elements prone to oxidation like Ti and Zr. Oxidation studies on TiHfZrNbTa RHEA containing aluminum in the temperature range of 973–1473 K show that the stable alumina film provides an excellent resistance to oxidation leading to lower mass gain till 1373 K. However at 1573 K, a porous oxide film forms that provide diffusional channels for oxygen leading to poor oxidation resistance. This is particularly important for RHEAs as good oxidation resistance and thermal stability are mandatory to realize the full potential of RHEAs as high temperature materials for structural applications. We believe that similar to corrosion studies, oxidation behavior of HEAs also demands a mechanistic approach to develop the fundamental understanding of processes during oxidation of HEAs.

8.5 Summary The solid-state processing of HEAs is possible using operations used for thermomechanical processing of metals and alloys and processes like dynamic recovery,

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Fig. 8.45 Backscattered electron micrograph and elemental maps of the oxide scale of Cantor alloy after exposure to atmosphere for 100 h at 1173 K (Laplanche et al. 2016b)

dynamic recrystallization, and static recrystallization can aid in tailoring the microstructure and crystallographic texture as demanded by secondary processing or final application. Apart from conventional processing routes like rolling, forging, and extrusion, microstructural engineering of HEAs can be achieved using severe plastic deformation processes to achieve submicron and nanocrystalline grain size regime to achieve superior mechanical properties. Mechanical properties of single phase FCC Cantor alloy show good strength with sufficient ductility at room temperature, and there is an increase in strength as well as ductility at cryogenic temperature. The alloy is characterized by high fracture toughness at room temperature which is even maintained at cryogenic temperature, thus manifesting the superiority of the Cantor alloy over existing metals and alloys. Conventional strengthening and strain hardening mechanisms are operative in HEAs like the ones operative in conventional alloys. However, there is a synergy between different mechanisms that provided excellent properties to few HEAs. A fundamental understanding of solid solution strengthening and flow kinetics of model HEA like Cantor alloy has paved a way for the

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development of concentrated ternary and even binary counterparts. This has shifted the focus from strictly defined HEA concept to the more accommodating complex concentrated alloy concept. The HEAs show good fatigue, creep, corrosion, and oxidation resistance so that they can be put for actual engineering applications. A fundamental understanding of the deformations mechanisms for different service conditions is still warranted. It is believed that fundamental understanding of deformation and damage mechanisms coupled with good knowledge of thermodynamics and kinetics will help our new generation of complex concentrated alloys for future engineering applications.

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Chapter 9

Functional Applications of High Entropy Alloys

9.1 Introduction As discussed in the previous chapters, many research works have been carried out on high entropy alloys (HEAs), with a primary focus on their synthesis, microstructural analysis, and mechanical behavior. Although the number of investigations on functional applications of HEAs reported in the literature is limited compared to that for structural applications, the future prospect and opportunities for improving functional properties of HEA are certainly limitless because HEA simply offers the exciting possibilities of designing new materials with unusual characteristics. Since the HEA system is associated with an underlying lattice distortion because of chemical and/or physical disorders, at nanoscale to microscale dimensions, it put forward numerous ways to influence wide range of functional properties such as magnetic, electrical, thermal, and optical behavior. Furthermore, the ease of manipulating electronic structure along with microstructure engineering at wide range of length scale from nm to μm level present new opportunities to develop various energy conversion devices such as thermoelectric, magnetoelectric, thermomagnetic, and magneto-caloric. In other words, it becomes a multifarious material being used in multiple applications, and some examples are shown in Fig. 9.2. In this chapter, an overview on the recent developments of HEAs for functional applications has been described in brief. Also, the fundamental requirements for functional applications are emphasized in order to explore the possibilities of developing novel devices based on HEAs (Fig. 9.1).

9.2 Magnetism Most of the magnetic studies on HEA materials have been focused on soft magnetic behavior. Soft magnets are used in wide range of applications such as transformers, generators, motors for electrical power generation, transmission, and distribution to the power grid, as well as for applications in telecommunications, and household © Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8_9

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Fig. 9.1 High entropy materials in different applications (Katiyar et al. 2021a)

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Y. Zhao, D.-H. Lee, J.-A. Lee, W.-J. Kim, H.N. Han, U. Ramamurty, J.-Y. Suh, J.-I. Jang, Hydrogeninduced nanohardness variations in a CoCrFeMnNi high-entropy alloy. Inter. J. Hydrogen Energ. 42(16), 12015–12021 (2017a) Y. Zhao, D.-H. Lee, M.-Y. Seok, J.-A. Lee, M.P. Phaniraj, J.-Y. Suh, H.-Y. Ha, J.-Y. Kim, U. Ramamurty, J.-I. Jang, Resistance of CoCrFeMnNi high-entropy alloy to gaseous hydrogen embrittlement. Scripta Mater. 135, 54–58 (2017b) K.X. Zhou, B.R. Sun, G.Y. Liu, X.W. Li, S.W. Xin, P.K. Liaw, T.D. Shen, FeCoNiAlSi high entropy alloys with exceptional fundamental and application-oriented magnetism. Intermetallics 122, 106801 (2020) T.T. Zuo, R.B. Li, X.J. Ren, Y. Zhang, Effects of Al and Si addition on the structure and properties of CoFeNi equal atomic ratio alloy. J. Magn. Magn. Mater. 371, 60–68 (2014) T. Zuo, M.C. Gao, L. Ouyang, X. Yang, Y. Cheng, R. Feng, S. Chen, P.K. Liaw, J.A. Hawk, Y. Zhang, Tailoring magnetic behavior of CoFeMnNiX (X = Al, Cr, Ga, and Sn) high entropy alloys by metal doping. Acta Mater. 130, 10–18 (2017)

Chapter 10

Summary and Future Direction

10.1 Introduction In the last nine chapters, a detailed account of high entropy materials (HEMs) and the recent scientific as well as technological advancements have been provided. This includes discussions on basics of HEMs—structure, phase formation, diffusion; mechanical and functional properties; and processing and applications. With welldefined design strategies (parametric, CALPHAD, ab initio, ML), new compositions can be designed. Interestingly, with a palette of a large number of elements in the periodic table, almost unlimited combinations can be explored. Hence, machine learningbased approaches become important to effectively design and develop futuristic materials, required to meet the stringent requirements of many demanding applications. In contrast to “high throughput experimentation,” the machine learning approach could be more rewarding. Nonetheless, experimental and theoretical explorations will remain key for serendipitous discovery of novel alloys. The processing route can vary depending on type of materials and application. For HEAs, classical routes; ingot metallurgy, rapid solidification, powder metallurgy, and even modern additive manufacturing can easily be adapted to obtain good quality and reasonably large specimens, needed for testing and applications. In case of HECs, bulk specimens can be synthesized by either powder metallurgy (or solid-state reaction) or wet chemical synthesis and epitaxial growth. These materials exhibit exceptional structural and functional properties, making them potential candidates for various applications. Other advanced processing routes, including semi-solid processing, rapid solidification, high strain rate deformation (equal-channel extrusion, high pressure torsion), superplastic forming, and even joining methods, are still in state of development for this new class of materials. Nonetheless, various combinations and processing routes—fundamental understanding of these processing routes still lacks. Although the motivation of research activity on HEAs was primarily aimed at achieving simple solid solutions containing multiple components, which can easily

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be synthesized and used in practice, it has opened up numerous fundamental questions that need to be addressed—phase formation, thermodynamics, kinetics, diffusion, defects, and properties. These seem to be vital for achieving properties and potential applications. Hence, fundamental understanding of processing routes and basic mechanisms of phase formation, kinetics, diffusion, defects, and properties (as outlined above) is found to be critical for any successful and sustainable applications of HEAs in particular and HEMs in general. The ultimate goal is certainly related to usage of HEMs as substitute for conventional materials in stringent applications by providing superior performance and increased life span. Thus, the new material development is meant to provide improved performance, cost reduction in terms of energy and material saving, reuse, recycle, and even conservation. Hence, scientific curiosity leading to improved fundamental understanding forms an important basis to guide design of alloys for improved performance and potential applications in various high-end applications. HEMs as complex solid solutions, in fact, are most crucial from the basic scientific viewpoint because of the fact that the conceptual advances are indeed necessary to bridge the gap between well-studied and well-understood dilute solid solutions and poorly understood concentrated solid solutions. Research on HEMs has not only satisfied our scientific curiosity, but it has also led to development of new materials with better performance as compared to the conventional materials. The activities on potential applications of HEMs came into limelight in last 5 years. Materials, process, and even products have been developed to cater to the need of the industrial requirements. In this connection, the present chapter is intended to provide some applications of HEMs already attempted, new advanced potential applications, patents, etc., so that the future directions of technology development using this newly developed material are illustrated with the viewpoint of goals of property improvement as compared to the conventional materials. In the last chapter of the book, salient examples from new materials, processes, patents, products, and technology development are described and discussed to show the promise and potentiality of HEMs for a variety of applications. The chapter is structured to provide goals of property improvement first, followed by examples of some applications and future direction. This is intending at providing a summary of the recent advancements in the applications of HEMs for igniting new ideas and activities in this rapidly evolving field of basic research and development.

10.2 Goals of Property Improvement In his classic book, “Selection of Materials for Mechanical Design,” M. Ashby has shown that material selection, in general, involves finding the best match of the required property/properties and cost. The required property/properties is/are dependent on the application. Thus, the basic objective involves meeting stringent property requirements at minimum cost.

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With any new material, the opportunities for innovation are immense. However, any such advance is possible by making rational choice. Component design is always considered as a process of translating a new idea based on a market requirement. This translation will involve decision-making on type of material usage, processing route, cost, etc., at every stage. Hence, properties of the materials play the most critical role in deciding choice of material. The ideal goal of new material development is certainly related to property improvement to reach beyond the available materials. There are many properties of HEMs, which are investigated during research for last 15 years. Let us first list them into two categories: structural and functional. The selection of materials will also depend on type of application and hence property enhancement. Some of the applications require good combination of both structural and functional properties. Structural Applications A. Automobile → Requiring high strength and toughness, high temperature strength, fatigue, creep resistance, corrosion (hot), and oxidation resistance. B. Tool, molds, dies, and hard facing applications → Requiring reasonably good high and room temperature strength, toughness, wear, oxidation, and corrosion resistance, C. Marine → High corrosion resistance with antifouling property D. Chemical (pipes, pump, mixers, reactors, etc.) → Excellent corrosion, oxidation, cavitation, and stress corrosion resistance E. Structural part of next generation nuclear power plants → High temperature strength, toughness, and minimum irradiation damage F. Transportation → Low density, high strength, toughness, stiffness, fatigue resistance, and formability G. Cutting tools → Sintered cemented carbide with HEC tools and hard coating (HEN) for cutting tools H. Soldering → Solders for hard metals with steels Functional Applications A. Hydrogen storage → High H/M ratio, reversible volumetric as well as gravimetric density of hydrogen (storage and retrieval), and cycling at near ambient temperature, B. Magnetic → Soft magnetic → High saturation magnetization, low coercivity, and low density Hard magnetic→ Maximum B-H loop and high magnetic permeability C. Thermoelectric → High electrical conductivity, low thermal conductivity, high Seebeck coefficient, and high figure of merit D. Solid oxide fuel cells → High ionic conductivity, oxidation and creep resistance, and low area-specific resistance E. High frequency communication → High electrical conductivity and magnetic permeability (>3 kHz) F. Superconducting → High critical temperature as well as critical current density

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The conventional alloys and ceramics have widely been used in the last century to meet some of these applications. Indications are clear; this approach can eventually reach a limit and may no longer provide novel materials with properties which can match the stringent requirements to meet technological challenges. These include futuristic applications, supersonic jets, land rovers in space vehicles, hyper-loops, ultra-thin electronic gadgets, etc. It is evident that the Ni-based superalloys have reached maximum temperature limit and search of new material with better temperature capability is being felt. The search for ultra-low-density alloy with good strength and toughness has been on for sufficiently long time. Hence, the need for development of new and novel materials with exceptional properties has been felt for some time. HEMs and their derivatives have been thought to fill the gap and provide huge opportunity for material development. The research and development for last 15 years indicate that HEMs can be designed (composition and processing routes with specific microstructure) to meet the technological requirements for potential applications. In order to showcase the uniqueness of HEMs (HEAs, HECs, HEA cermets, etc.), we shall discuss a few examples of “breakthrough” applications, for which HEMs have been designed and developed.

10.3 Advanced Applications Requiring HEMs We shall first discuss few examples of structural and functional applications. These are considered as potential applications, since none of these have been realized in industrial scale to prepare components for usage. Table 10.1 provides an exhaustive list of potential applications of HEMs. Among these potential applications, some are considered to be “breakthrough” ones. We shall discuss these applications here. (a) Turbine blades for aero-engines Turbine engines form the most important component in aero-engines and selection of materials for the engines are critical for the service and life of the engine. Nibased superalloys are widely used materials for hot sections of the engines. It is well known that efficiency of these engines can substantially be improved by increasing the temperature of the engines. The increased temperature of engine by 40 K can lead to 1% increase in the efficiency, and hence, material development is meant to increase Table 10.1 Properties of HEMs required for applications

Structural

Functional

Strength, toughness Light weight Formability Diffusional resistance High temperature strength

Wear resistance Corrosion resistance Radiation damage resistance Thermal conductivity Thermoelectric properties Magnetic properties Electrical properties

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the service temperature of the engine. Subsequently, we also need to improve the alloy chemistry and processing route (wrought versus cast, directional solidification versus single crystal). It is worth noting that the excellent properties (creep deformation, high temperature strength, ductility, etc.) are mainly due to dispersion of coherent L12 γ' precipitates in the FCC γ matrix. The addition of Ru, Rh, Re, etc., has been done to improve the creep strength further. However, the addition of these heavier materials can increase the density of the superalloys. Nonetheless, the extensive research on various superalloys reveals that application temperature of existing superalloys has reached it upper limit (1100 °C). Due to this aspect, the efforts have been directed to improve the cost performance of the existing superalloys by replacing Re; e.g., CMX-8 has been developed to replace CMSX-4. Most of the available superalloys are medium entropy alloys (MEA), and the effect of configurational entropy is not significant. The widely used Ni-based superalloys are constrained as far as compositional design space, density optimization without compromising on the high temperature properties. In the search for new alloys with better performance and cost, the concept of HEA allows us to design new alloys with better properties and performance. Three important aspects are being considered while designing new HEMs for turbine engine applications: (a) elevation of γ’ solvus temperature of high entropy super alloys (HESA) beyond 1250 °C; (b) processing of cast single crystal blades in which partitioning of elements forms an important tectological challenge, (c) coarsening of precipitates in the matrix, and (d) refractory high entropy alloys as next generation turbine blades. In the last few years, extensive research has been carried out to find out high entropy super alloys, which can withstand higher temperature of operation and consist of alloying elements bearing low density. Novel non-equimolar Alx Co1.5 CrFeNi1.5 Ti(0.5−x) alloys (density < 8 gm/cc) show uniform dispersion of γ' in a FCC matrix (Chang and Yeh 2015). Interestingly, these alloys are called high entropy superalloys (HESA) since the compositions of these alloys have been designed using the concept of HEA and they exhibit the typical γ/γ' microstructure, akin to conventional superalloys. Several alloys having 3d TM elements have been designed showing exceptional mechanical properties with γ' volume varying from 60 to 80 volume %. The basic design philosophy on HEA with addition of relatively cheap elements (Mo, Nb, Ta) can reduce even dependency of Re and Ru and can allow us to go beyond the working temperature much higher than 1100 °C. For example, Co1.5 CrFeNi1.5 Ta0.5 shows better mechanical properties (hardness) from room temperature to 1273 K as compared to IN718. In addition, hardness of this HESA remains almost unchanged from 950 to 1273 K, although IN718 reveals drastic drop in hardness due to the fact of γ' → δ. In fact, partial substitution of Ti by Al has been found to lead to the stabilization of γ' till higher temperature. In a nutshell, the design philosophy of HEA can improve the microstructural stability and mechanical properties substantially. Another set of HEA and RHEA (consisting of refractory metals) have shown lots of promise as high temperature materials for turbine engine applications. The usage of RHEAs as material for turbine blade is considered as another approach to increase temperature capability of HESA beyond the conventional Ni-based or

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Fig. 10.1 a Typical microstructure for Al10 Nb20 Ta16 Ti30 V4 Zr20 RHEA after annealing at 1200 °C for 24 h and furnace cooling at 10 °C/min to RT revealing BCC (discrete) and B2 (continuous) phases; (Soni et al. 2018) b variation of yield strength with temperature of size RHEA along with conventional superalloys, IN718 and CMSX-4 (Yeh and Lin 2018)

Co-based superalloys or even HESA based on 3d transition metals. These are alloys formed by using the elements with high melting temperature, Hf, Mo, Nb, Ta, and Ti (>1700 °C) with typical BCC/B2 microstructure in which B2 phase is embedded in BCC matrix and vice versa. Therefore, single crystals of RHEAs having melting temperature and slow/sluggish diffusion are expected to exhibit better high temperature capability. In fact, this can take a leap of the operation temperature of the turbine blades, leading to substantial increase of the efficiency of aero-engines. Figure 10.1 shows the variation of yield strength of some of the available RHEA along with two commercially available superalloys (Inconel 718 and CMSX-4), indicating that the RHEAs are far stronger than the commercial superalloys above 1000 °C. In fact, equiatomic HfMoNbTaTi shows yield strength of 367 MPa at 1400 °C. However, the creep and oxidation resistance of these alloys need investigation and verification before these alloys can be tested as turbine blade. (b) Sintered carbides for cutting tools High entropy ceramics (HECs) form various useful materials for variety of applications. This includes ultra-high temperature multicomponent ceramics (UHTMCs), multicomponent carbides, coatings, etc. However, sintered carbides containing HEA have been developed for cutting tools as these are in high demand for industry, providing better lifetime and high dry cutting speed. This has been achieved due to higher hardness and fracture toughness (Yeh and Lin 2018). Figure 10.2a shows two curves for conventional cemented carbide bonded by Co. The four data points shown are for carbide bonded by HEA, indicating that HEA bonded cemented outperform the conventional ones. The microstructure of the carbide insert (with HEA) is shown in Fig. 10.2b, indicating distribution of two phases. The comparison of wear of the flanks is shown in Fig. 10.2c, revealing carbides containing HEA exhibiting

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Fig. 10.2 a Fracture toughness versus hardness for conventional sintered carbides with stars showing data points for high entropy carbides; b photographs of sintered carbides bonded with HEA, and c flank wear for conventional sintered carbides along with sintered carbides bonded with HEA (two different compositions) (Yeh and Lin 2018)

lower flank wear. Hence, cutting tool industry can definitely get benefited by the development of such cemented carbide tools. It is worth mentioning that here the life of any cutting tool can further be improved by application of hard coating. In this direction, hard high entropy nitride coatings can find potential application. The required properties for hard coating include high hardness, toughness and significant oxidation resistance. Continuous cutting at high speed leads to substantial temperature rise at the cutting edge, and hence, coating is likely to get oxidized, yielding loose and relative soft oxide layer. This oxide layer can easily be removed from the surface due to friction between the rake face and chip, leading to further oxidation and failure of the cutting tool. Hence, oxidation resistance of hard coating is considered vital for the sustained life of the cutting tool. The concept HEA can thus be utilized for development of such coating. Figure 10.3a shows oxidation resistance of TiN, TiAlN, and (Al0.34 Cr0.33 Nb0.11 Si0.11 Ti0.22 )50 N50 in terms of weight gain during oxidation. TiN and TiAlN have been found to get severely oxidized at 600 °C and above, whereas (Al0.34 Cr0.33 Nb0.11 Si0.11 Ti0.22 )50 N50 remains quite stable till 1300 °C (weight gain of 0.015 mg/cm3 ). SEM investigation on the rake surface of different coating after cutting operation is shown in Fig. 10.3b along with chips (Yeh and Lin 2018). Therefore, high entropy nitride coating will definitely provide much better efficiency and lifetime for cutting tool. (c) Nuclear reactor applications The nuclear reactors, meant to generate electric power, hold key for future energy requirement in the world. However, design and development of materials for 4th generation nuclear reactors, stress on the factors; economic operation, minimum wastage, enhanced safety as well as proliferation. To provide perspectives, let us consider helium gas cooled reactor (considered as 4th generation reactors) with operation temperature of 850 °C. This reactor is deemed to be commercially realized in 2030. However, materials required to sustain such high temperature with nuclear flux have not been available so far. Hence, the need for such materials is indeed felt in order to maintain sustainable energy supply.

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Fig. 10.3 a Typical weight grain as function of temperature for TiN, TiAlN, and HEN (AlCrNbSiTi)N, revealing that HEN performs much better than conventional TiN or TiAlN (Shen et al. 2013); b chips produced during cutting of SS-304 along with insets (top) after the machining operation (Yeh and Lin 2018)

In this connection, it is important to note that few papers published (from Oak Ridge National Lab) reveal that the radiation damage resistance can substantially be improved by increasing the number of component elements to Ni-based FCC alloys (Fig. 10.3), i.e., lower number of defects (surface step, swelling) in HEAs due to irradiation of ions (Zhang et al. 2017). FCC alloy (Fe—28 wt%, Ni—27 wt%, Mn— 18 wt% Cr) shows much reduced radiation damage as compared to conventional austenitic steels (Kumar et al. 2016). This seemed to be due to sluggish diffusion in HEA with limited solute enrichment/depletion at the grain boundaries, leading to no or less number of voids. It is evident that HEAs are suitable for nuclear reactor applications. However, successful applications would require HEAs to have significant high temperature strength, toughness, oxidation resistance, and low neutron absorption cross-section to be qualified for next generation power plants. Surface step height and overall swelling after 3 meV Ni-ion radiation by increasing the number of component elements to Ni-based FCC alloys (Zhang et al. 2017). (d) Dies and Molds HEAs for hot working dies and molds have been envisaged for some time, since they can withstand temperatures as high as 1200 °C. In this regard, few experiments have been carried out in Japan and Taiwan on both standard SKD61 die and die made of Yeh and Lin (2018). SKD61 die made up of HEA was utilized for extrusion of low carbon steels. Figure 10.4a shows the images of the die before and after the extrusion of low carbon steels at 1200 °C. It is evident the holes in the die have completely been worn out after only one run because SKD61 die cannot sustain temperature more than 550 °C. In fact, the materials of SKD61 die soften easily in this temperature range, and hence, these dies can successfully be used for extrusion of Al-alloys, not for steels. On the other hand, Fig. 10.4c shows that some of available HEAs can sustain temperature up to 1000 °C. Hence, HEAs can be used as materials for dies and molds for various high temperature operation, in which conventional materials will not work.

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Fig. 10.4 a, b The images of SKD61 die before and after extrusion of a low carbon steels at 1200 °C and c variation of hot hardness for conventional materials with two HEA (Yeh and Lin 2018)

In this direction, HEA coating can also be used for antisticky mold and even solar cells. It has been observed that the coatings formed from HEAs can easily form amorphous structure, exhibiting low roughness as compared to the crystalline counterpart. Therefore, these coatings can be potential candidates for antisticky applications or even diffusion barrier applications. This has been tested on free sand-blasted surface of SKD61 mold and compared with conventional Cr coatings [Ref]. The results indicate that conventional Cr coating shows roughness much higher than HEA (AlCoCrCuFeNiTi) coating. This will definitely aid easy removal of item by processing. In fact, such antisticky coating has been utilized for electronic packaging as release force required to remove IC component will be low and hence damage inflicted to IC components would be minimum. The same has been observed for molding of bipolar plates of fuel cells at even 200 °C.

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Fig. 10.5 a Typical wear rate (sliding wear test with steel ball) for Al20 Cr20 Fe20 Mn20 V20 containing different amount of soft (Bi) and hard (TiB2 ) dispersoids; (Yadav et al. 2018) b SEM microstructure of the sintered product Al20 Cr20 Fe20 Mn20 V20 −D 10 wt% Bi–15 wt% TiB2 (Yadav et al. 2019)

In addition, HEA coatings have also been used for antisticky molds and diffusion barrier applications. It is evident that HEA coating deposited on a substrate will likely form amorphous structure due to the presence of large number of elements and high cooling rate. Figure 10.5 shows the microstructure of conventional Cr coating as well as HEA (AlCoCrCuFeNiTi) coating deposited on SKD61 mold. The mold was sand blasted prior to deposition. The microstructures reveal that roughness of the HEA coating is lower as compared to Cr coating and the release force needed to take out the items from the mold will be much less for the HEA coating. This can lead to much lower warpage and tearing and damage the component during deformation. It is important to note that these HEA coatings can also be potential candidates for electron packaging (IC components) or fuel cell bipolar plates and solar cells. (e) Bearings Bearing is omnipresent in mechanical components in our daily life. These bearings are integral part of the movable part of machinery, required to transfer various type of bearings available in the industry. The bearings are primarily used to reduce friction, allowing smoother rotation. It is to be noted that friction is omnipresent between the rotating shaft and the part supporting the rotation. Bearings are used between these two components to reduce friction, reducing the energy consumption. Bearing is, in general, externally lubricated. However, usage of external lubrication limits the applicability of the bearings in various applications. In this regard, the self-lubricating bearings are found to be crucial as they do not need supply of external lubrications. Conventionally, Cu-based alloys containing Bi, Sb, Sn, or Pb are extensively utilized as self-lubricating bearings (Yadav et al. 2018). Cu-based alloy matrix provides good thermal conductivity, whereas Bi, Sb, Sn, or Pb act as solid lubricant as soft and fine-scale dispersoids in the matrix. However, the challenge for such bearing is the hardness with some porosity for flow of the lubricants to provide low friction. In

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this connection, HEA-based bearing contains softer dispersoids in the matrix. Since hardness of HEAs can be tailored and adjusted with formation of FCC or BCC solid solution along with good thermal conductivity. HEA-based systems are expected to provide better candidates for self-lubricating bearings. Attempts have been made to fabricate HEA-based self-lubricating bearings via powder metallurgy route, i.e., mechanical alloying followed spark plasma sintering. Figure 10.5 shows performance of bearing made up of multicomponent multiprincipal high entropy alloy (HEA) composite (AlCrFeMnV)90 Bi10 /TiB2 for bearing applications. The alloy composite was synthesized via combination of mechanical alloying and spark plasma sintering routes. The microstructural characterization reveals the homogenous dispersed solid lubricant Bi and TiB2 in the HEA matrix. The abovementioned material exhibited the excellent wear resistance. The observed wear rate was of the order of 10–15 (mm3 /N m), which is much lower than available bearing materials. Thus, by proper combination of soft and hard dispersoid it has been possible to achieve the improved wear resistance. The combination of novel processing routes has been utilized to obtain uniform distribution of dispersoids and finer grain size of the matrix in the material. This involves first ball milling Al20 Cr20 Fe20 Mn20 V20 at room temperature till 25 h to obtain single phase (body-centered cubic) alloy. Size of Bi and TiB2 powder particles have been reduced extensively via cryomilling. Subsequently, nanocrystalline Bi and TiB2 powder obtained has been added to HEA powder and ball milled at room temperature to obtain a homogeneous mixture. This powder was then sintered using spark plasma sintering facility at 900 °C. Figure 10.5b shows microstructure, revealing uniform composition with uniformly distributed solid dispersoids in the HEA matrix. Soft (Bi) and hard (TiB2) dispersoids are meant to provide reasonably high hardness, whereas HEA phase will provide sufficient ductility, fracture toughness, and hence excellent wear resistance (Yadav et al. 2019). Hence, it is evident that HEA-based alloy systems containing relatively soft metals will be potential candidates for self-lubricating bearings in near future. (f) Thin-film resistor These are considered to be useful for small scale devices. The salient properties, which are demanded in these devices, are the high resistance with very low temperature co-efficient of resistance (TCR). Majority of electronic components require this device in order to achieve precision and reliability in measurement of certain property. Recently, the efficacy of HEAs has been probed for such devices. In this direction, Al-Cr-Ni-Si-Ta HEA thin films were deposited on alumina substrate at room temperature, followed by annealing in the temperature range of 250–500 °C (Lin et al. 2015). The detailed investigation reveals that Al16.8 Cr14.6 Ni23.5 Si23.6 Ta21.5 thin film annealed at 300 °C shows the lowers TCR (−10 ppm/°C) with very high resistivity (2200 μΩ.cm). This research reveals that HEA thin film is better than even conventional Ni–Cr-based thin films, indicating that HEAs can potentially be used for such applications.

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10.4 Technology Development The development of matured technologies to fabricate product is considered the key for any successful material. History of material development reveals that it is important to find technological means, process, technique, or even manufacturing route to make useful product to sustain the research and development activity on the new material. In this direction, we shall discuss few case studies to showcase the technological development happened over last 5–7 years and what we can expect. a. Manufacturing of HEA fibers Fibers of extremely high strength are found useful for variety of applications including ropes, composites, etc. It is well known that famous Taylor–Ulitovsky method (TUM) has widely been utilized to prepare wires of amorphous materials. This is basically a glass-coated melt spinning technique, in which any alloy in the form of rod is put inside a glass tube. As soon as the alloy melts due to induction heating, the glass tube gets softened, and hence, a glass capillary is formed at the bottom of the softened glass tube, in which the alloy melt is embedded. Further, the capillary nozzle containing the melt is sprayed so that it is rapidly solidified, leading to formation of glass-coated fiber. Several important conditions need to be met in order to obtain high quality fibers; (a) the melting temperature of the alloy must be close to the glass softening temperature; (b) wetting between glass and alloy melt must be good; (c) alloy melt should be low viscous; and (d) alloy melt must not react with glass capillary. However, this technique leads to formation of amorphous wire for many HEA forming liquid, possibly due to high cooling rate during quenching. In addition, many HEAs cannot fulfill the requirements of TUM method. Hence, alternate routes such as melt-extraction or hot-drawing method have been utilized to prepare HEA fibers. In the melt-extraction method, an alloy rod having cylindrical shape (Fig. 10.6) is placed inside a quartz tube in a sample holder, which is then lifted by BN rod and quartz tube in a sequence. The alloy is subsequently heated by induction to melt the alloy bar. The molten metal is then cut by grooved copper wheel, and metal fiber is pulled. Lastly, the hot-drawing method has also been utilized to obtain fibers. It is a standard technique in which tensile forces are used to stretch bar of HEA using a die. The HEA bar is initially heated, softened, and then stretched to form the fiber. Figure 10.6b shows Al0.3CoCrFeNi fiber having diameter of 1 mm. This fiber exhibits good combination of tensile strength (1.2 GPa) and ductility (7.8%) at room temperature and 1.6 GPa at 77 K (Li et al. 2017). b. Carbon-thermal shock method The development of techniques for successful and repeatable synthesis of high entropy nanoparticles is found to be crucible for various applications, including catalysis, thermoelectric, batteries, etc. Hence, technology development in this regard will be boon to move across different disciplines. Preparation of nanocrystalline powder of these nanocrystalline materials can also be done by using carbon-thermal shock method (Yao et al. 2018). This technique is versatile but it has been developed from

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Fig. 10.6 a Schematic diagram showing the technique of the melt extraction; b hot-drawn Al0.3CoCrFeNi fibers (Li et al. 2017)

a previously known technique called dip-pen lithography in 1999. In this technique, a “dip pen” in the form of tip of atomic force microscope is dipped in a chemical solution for pattern writing on gold substrate. In this process, small quantity of molecular substance on the substrate forms nanocrystalline powder. Subsequently, several types of lithographic technique have been developed. However, scanning probe block co-polymer lithography (SPBCL) involving dissolution of PEO-b-P2VP and HAuCl4 in aqueous solution ink on gold substrate is considered one of the best techniques because finer sized nanoparticles (4–5 nm) can be synthesized in this technique. Chen et al. utilized SPBCL technique to synthesize polyelemental nanoparticles consisting of Au, Ag, Co, Cu, and Ni. However, detailed microstructural characterization shows that these nanoparticles contain elemental segregation and are not homogeneous enough to be called HEA nanoparticles. In order to improve the mixing and homogeneity of the nanoparticles, carbon-thermal shock treatment was conducted on SPBCL nanoparticles to obtain HEA nanoparticles. Figure 10.7 shows schematic of carbon-thermal shock treatment. In this case, the ink is loaded on a carbon fiber, and subsequently, pulsed current is used to heat the fiber rapidly. The extremely high cooling rate due to this process can restrain the compositional partitioning. In fact, this technique has been found to be used to obtain HEA nanoparticles containing up to 8 elements, which exhibit exceedingly good catalytic property (Yao et al. 2018). c. Cryomilling to prepare HEA nanoparticles from cast ingot Cryomilling of cryogrinding, carried out at or below 123K (−150 °C), is considered a clean route to synthesize various nanoparticles from bulk (Kumar et al. 2018). It is evident that the advancement of nanotechnology demands large-scale preparation of nanocrystalline powder of high entropy alloys (HEAs), making those potentials candidates for applications in energy, environment, biomaterials, etc. The need to develop novel synthesis methods to prepare nanocrystalline high-purity HEAs in

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Fig. 10.7 Carbon-thermal shock route for synthesis of HEA nanoparticles (Yao et al. 2018)

large quantity has always been felt to satisfy the burgeoning needs to nanotechnology. Conventional mechanical alloying of the multicomponent metallic powder mixture requires larger milling time, and it is prone to contaminations and phase transformation. Hence, breaking down of cast and homogenized ingots of multicomponent alloys via mechanical milling at cryogenic temperature can effectively be used to prepare high quality nanoparticles. Figure 10.8a shows schematic diagram of a custom built cryomill, being used by Kumar et al. to prepare various nanocrystalline HEAs. Figure 10.8b shows typical TEM micrographs and size distribution of (Fe0.2 Cr0.2 Mn0.2 Ni0.2 Co0 ) HEA nanoparticles.

Fig. 10.8 a schematic diagram showing a custom built cryomill, b–d TEM images (bright and dark field) of Fe0.2 Cr0.2 Mn0.2 Ni0.2 Co0 ) HEA nanoparticles, and c size distribution of the nanoparticles (Kumar et al. 2018)

10.4 Technology Development

303

d. Large castings for component development Bulk processing of HEMs is considered to be critical for application. In this regard, casting of large components and deformation processing are vital. The large sound (defect free) casting with much segregation is needed for any successful cast product. In this regard, an ingot of 18 kg (CoCuFeMnNi) was induction melted and cast in cast iron mold. The compositional inhomogeneity was further removed by annealing treatment at 1000 °C for 24 h. The ingot was tested for feasibility and stable conditions for deformation processing. Such processing was carried out using Gleeble at different temperature and strain rate (Sonkusare et al. 2019). The best conditions were found to be in the range of 900°–1100 °C and strain rate of 10−1 to 10−2 s−1 . Using these conditions, the material has been deformed to obtain sheet of thickness 3 mm. Therefore, it is evident that processing of large components using HEMs is indeed possible using the conventional routes. This will lead to development of large sized components (Fig. 10.9). a. 3D printed objects of high entropy alloys Additive manufacturing to fabricate engineering components using high entropy alloys (HEA) has been investigated in the past five years. Additive manufacturing of high entropy alloys is always considered a step jump to develop components by combining excellent mechanical properties of HEAs with geometrical freedom as well as complexity, opening up new designs with novel components. The initial few studies were carried out using powder bed techniques. In this regard, beam or nonbeam-based approach has been reported to generate shapes using powder mixture of

Fig. 10.9 a Induction melted and cast large sized (18 kg) CoCuFeMnNi casting; b processing map of the alloy; and c undeformed and deformed samples by Gleeble (Sonkusare et al. 2019)

304

10 Summary and Future Direction

Fig. 10.10 a schematic diagram showing laser-based 3D printing; b CoCrFeMnNi powder (Gao and Lu 2019); c 3D printed objects; and d ink-based technique to obtain 3D printed objects (Kenel et al. 2019)

HEMs. From the viewpoint of future applications, it is important to explore methods for producing complex shaped and homogeneous HEAs. Laser 3D printing method to generate complex shapes has been reported for CoCrFeMnNi HEA. Figure 10.10a shows a schematic diagram of co-axial laser power system used to print 3D shapes from pre-alloyed powder. The shapes are also shown in Fig. 10.10a (Gao and Lu 2019). The usage of laser-based 3D printing is difficult for all materials, and hence, a new methodology has been adopted. This involves preparation of ink containing oxide nanopowders (Co3 O4 + Cr2 O3 + Fe2 O3 + NiO), followed by 3D extrusion and co-reduction as well as sintering to obtain full density in hydrogen. Figure 10.10b shows salient features of the technique and the printed products. The preparation of ink using proper glue is found to be critical in this technique, whereas the laser material interaction and availability of HEA powder seem to be critical for the former. It is completely dependent on.

10.5 Patents on HEMs HEMs and related materials (HEAs, CCAs, MPEAs, HECs, etc.) have generated enough scope in last 10 years for design and development of many new materials for future applications. Accordingly, a very large number (>2000) of patents (nationspecific and international) have been filed and even some of them are granted. The very first patent on HEMs was filed in “high entropy multicomponent alloys” dealing with composition of HEA with 5 to 11 elements in 1998 (even before the first publication on HEMs in 2004). The patent was formally granted in 2003 in multiple countries (Taiwan, China, Japan). Since then, a large number of patents on HEMs have been filed/granted across the globe. A reasonable estimate using Google patents (www. google.com→patents) reveals about 1000 patents filed in different countries across the globe. Appendix C lists the patents on HEMs. The patents, in general, can be divided into two groups. The first group consists of HEMs with some specific properties, whereas the second type corresponds to composite materials of HEAs with some reinforcements. The first category will consist of magnetic, catalytic, hard

10.6 Future Direction

305

facing, HEA coating, high temperature, and ultra-high temperature materials based on HEA, HEC, etc. The latter category comprises multiphase materials, cemented carbides with HEAs as binders, HEC composites, and HEAs with other complex concentrated materials. The filing of patents on HEMs has started rising sharply after 2009. In fact, 400 patents have been filed in last 4 years, making HEMs as one of the “hot” research topics in engineering. In addition, more industrial houses are filing patents than universities and institutes, indicating the interest of the companies superseding that of the academic institutes. Some of the patents, leading to development of products, have already been discussed in Sect. 10.4.

10.6 Future Direction Over last 15 years, extensive research has been reported on HEMs and related materials. More than 4000 research papers have been published, 1000 patents have been filed/granted, and several manufacturing technologies have already developed. Interestingly, technology and product development have taken center stage in this area. However, the basic understanding of HEMs is far from complete. Like other areas of metallurgy and materials science, it seems technology is likely to supersede the fundamental research. In fact, the research on MPEAs/MPEMs categorically reveals that we are “sitting on the tip of an iceberg,” lots to learn and discover. Alloys and their development have been crucial for the civilization. The history of alloy development clearly indicates that the “concept of alloying” has evolved from typical “trial-and-error”-based approach to broad knowledge-based innovative one in the last century. The concept of HEMs is considered as a sparkling new idea, indicating a clear departure from the typical “bottom up” approach of alloy design followed, in which secondary elements are added to a primary or base element (matrix) to obtain the property enhancement. Hence, the HEMs are based on design via “top down” approach, in which no clear matrix exists. Rather, HEMs are whole-solute matrix in a defective state. Initial 10 years after the discovery was primarily spent to find ways and means to form HEAs in various alloy systems. Nonetheless, we now have started our journey to understand the basic scientific issues on phase formation, phase transformation, diffusion, property, and performance. This needs to be one in conjunction with development of processes and products to sustain the activity in this area. In this section, we shall deliberate on future trends and prospects on HEMs, concentrating on issues which would require “passionate debate” and way forward. We shall first talk about the basic scientific issues. a. It is now evident that research on HEMs was motivated to find simple multicomponent, multiprincipal element solid solution, which can be synthesized easily and utilized for property enhancement. These “true” solid solutions are rather necessary requirements to understand the fundamental mechanisms on phase

306

10 Summary and Future Direction

formation, defects, phase transformation, and structural and functional properties. According to Yeh et al. (2004); (Tsai and Yeh 2014), the design of these novel materials comes from the concept of “entropic stabilization,” substantial lowering of free energy due to the increase of configurational entropy of the solid solution phases as compared to the intermetallic/intermediate phases. The universality of this aspect on the formation and stabilization of HEMs is still debated. This aspect of entropic stabilization must be discussed in terms of relative effect on both enthalpy and entropy of the multicomponent systems. Enthalpy due to chemical bonding and lattice strain needs to be considered equally as competing factors. In fact, enthalpic contribution can outweigh the entropic one at room and intermediate temperature. At high temperature (near melting temperature), entropic factor can outweigh the enthalpic contribution in a system. As a results, at room temperature, majority of the alloy compositions are expected to yield multiple phases or decomposition of single phase solid solution to more than one possible phases during long annealing treatment. Hence, detailed study on isothermal TTT diagrams can yield the effect of temperature and time on the phase formation. Similarly, the “cocktail effect” needs to be relooked from the perspective that this is not a “core effect,” rather a warning that one cannot generalize the properties of HEMs as a linear superposition of the properties of the individual components. b. The most widely debated core effect is the “sluggish diffusion” in HEMs. With few experimental measurements available so far, the diffusion of the co-efficients of the components in HEAs is not vastly different from the conventional alloys. Therefore, fundamental understanding of diffusion in these concentrated alloys is required. In this regard, another key aspect requiring fundamental understanding is the definition of defects on these systems, which has significant impact on the structure– property relationship of these alloys. This is most important and needed as that “reference state” in HEMs cannot be considered as a perfect matrix. In case of a “whole-solute matrix,” one needs to deal with the fluctuations as well as local deviation. In other words, one needs to deal with defects in “defective reference” state in comparison with the conventional alloys. This will have serious consequence on the movement of the defects, especially dislocations. The dislocations cannot move in a straight manner; both time and length scale with Burgers vector are not well defined. Thus, this “defective reference” state definitely has significant effect on diffusion behavior. In conclusion, this aspect of HEMs needs serious debate and development of experimental and theoretical techniques to understand this aspect. The generation and movement of defects in HECs will be more complicated due to the presence of fixed “anionic lattice,” in which cations are dispersed.

References

307

References Y.-J. Chang, A.-C. Yeh, The evolution of microstructures and high temperature properties of AlxCo1. 5CrFeNi1. 5Tiy high entropy alloys. J. Alloy. Compd. 653, 379–385 (2015) X. Gao, Y. Lu, Laser 3D printing of CoCrFeMnNi high-entropy alloy. Mater. Lett. 236, 77–80 (2019) C. Kenel, N.P.M. Casati, D.C. Dunand, 3D ink-extrusion additive manufacturing of CoCrFeNi high-entropy alloy micro-lattices. Nat. Commun. 10(1), 1–8 (2019) N.A.P.K. Kumar, C. Li, K.J. Leonard, H. Bei, S.J. Zinkle, Microstructural stability and mechanical behavior of FeNiMnCr high entropy alloy under ion irradiation. Acta Mater. 113, 230–244 (2016) N. Kumar, C.S. Tiwary, K. Biswas, Preparation of nanocrystalline high-entropy alloys via cryomilling of cast ingots. J. Mater. Sci. 53(19), 13411–13423 (2018) D. Li, C. Li, T. Feng, Y. Zhang, G. Sha, J.J. Lewandowski, P.K. Liaw, Y. Zhang, High-entropy Al0. 3CoCrFeNi alloy fibers with high tensile strength and ductility at ambient and cryogenic temperatures. Acta Mater. 123, 285–294 (2017) R.-C. Lin, T.-K. Lee, D.-H. Wu, Y.-C. Lee, A study of thin film resistors prepared using Ni-Cr-SiAl-Ta high entropy alloy. Adv. Mater. Sci. Eng. 2015 (2015) W.J. Shen, M.H. Tsai, K.Y. Tsai, C.C. Juan, C.W. Tsai, J.W. Yeh, Y.S. Chang, Superior oxidation resistance of (Al0. 34Cr0. 22Nb0. 11Si0. 11Ti0. 22) 50N50 high-entropy nitride. J. Electrochem. Soc. 160(11), C531 (2013) V. Soni, B. Gwalani, O.N. Senkov, B. Viswanathan, T. Alam, D.B. Miracle, R. Banerjee, Phase stability as a function of temperature in a refractory high-entropy alloy. J. Mater. Res. 33(19), 3235–3246 (2018) R. Sonkusare, A. Swain, M.R. Rahul, S. Samal, N.P. Gurao, K. Biswas, S.S. Singh, N. Nayan, Establishing processing-microstructure-property paradigm in complex concentrated equiatomic CoCuFeMnNi alloy. Mater. Sci. Eng., A 759, 415–429 (2019) M.-H. Tsai, J.-W. Yeh, High-entropy alloys: a critical review. Mater. Res. Lett. 2(3), 107–123 (2014) S. Yadav, A. Kumar, K. Biswas, Wear behavior of high entropy alloys containing soft dispersoids (Pb, Bi). Mater. Chem. Phys. 210, 222–232 (2018) S. Yadav, A. Aggrawal, A. Kumar, K. Biswas, Effect of TiB2 addition on wear behavior of (AlCrFeMnV) 90Bi10 high entropy alloy composite. Tribol. Int. 132, 62–74 (2019) Y. Yao, Z. Huang, P. Xie, S.D. Lacey, R.J. Jacob, H. Xie, F. Chen, A. Nie, T. Pu, M. Rehwoldt, Carbothermal shock synthesis of high-entropy-alloy nanoparticles. Science 359(6383), 1489– 1494 (2018) J.-W. Yeh, S.-J. Lin, Breakthrough applications of high-entropy materials. J. Mater. Res. 33(19), 3129–3137 (2018) J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6(5), 299–303 (2004) Y. Zhang, S. Zhao, W.J. Weber, K. Nordlund, F. Granberg, F. Djurabekova, Atomic-level heterogeneity and defect dynamics in concentrated solid-solution alloys. Curr. Opin. Solid State Mater. Sci. 21(5), 221–237 (2017)

Appendix A

See Table A.1.

Table A.1 HEAs with BCC structure Composition

Processing route

References

MA

Varalakshmi et al. (2008)

Equiatomic alloys AlFeTi CrTiV

MaS

Tsai et al. (2010b)

HfNbZr

Sputtering

Guo et al. (2013c), Nagase et al. (2013)

AlCoFeNi

AM + A

Kulkarni et al. (2018)

AlCrFeTi

MA

Varalakshmi et al. (2008)

AlNbTiV

AM

Stepanov et al. (2015b)

CrFeMoV

AM

Guo et al. (2017b)

CrFeMoV

MA + SPS

Raza et al. (2018)

HfNbTiZr

AM

Wu et al. (2014a)

HfNbTiZr

AM + TMP

Ye et al. (2018)

MoNbTaW

AM

Senkov et al. (2010, 2011b), Widom et al. (2013), Zou et al. (2017)

MoNbTaW

MaS + VA

Feng et al. (2018a)

MoNbTaW

SLM

Zhang et al. (2018a)

MoTaTiV

AM

Qiao et al. (2017)

MoTiVZr

AM

Mu et al. (2017)

NbTaTiV

AM

Yao et al. (2016)

NbTaTiZr

AM + A

Todai et al. (2017)

NbTaVW

AM

Yao et al. (2016)

NbTiVZr

AM

Wu et al. (2015d) (continued)

© Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8

309

310

Appendix A

Table A.1 (continued) Composition

Processing route

References

AlCoCrCuFe

LSA

Zhang et al. (2015a)

AlCoCrFeNi

MA

Ji et al. (2014), Zhang et al. (2018b)

AlCoCrFeNi

SC

Wang et al. (2009b), Qiao et al. (2011)

AlCoCrFeNi

AM

Wang et al. (2008), Zhou et al. (2008b), Jiang et al. (2018d)

AlCoCrFeNi

BS

Zhang et al. (2012b)

AlCoCrFeNi

DLD

Ocelik et al. (2016)

AlCoCrFeNi

ED

Li et al. (2013c)

AlCoCrNiSi

GTAW cladding

Lin and Cho (2008)

AlCoFeNiTi

AM

Wang et al. (2012c)

AlCrCuFeNi

MA

Yurkova et al. (2016)

AlCrFeTiZn

MA

Varalakshmi et al. (2008)

AlCrMoNbTi

AM

Chen et al. (2016a)

AlCuFeNiTi

MA

Yurkova et al. (2016)

CuNiSiTiZr

ED

Wang et al. (2015b)

HfMoNbTiZr

AM

Guo et al. (2015)

HfMoTaTiZr

AM

Juan et al. (2015)

HfNbTaTiZr

AM and HIP

Senkov et al. (2011a, 2012a), Couzinie et al. (2014), Eleti et al. (2018), Schuh et al. (2018), Stepanov et al. (2018a)

HfNbTiVZr

AM

Sobol et al. (2012), Karlsson et al. (2018)

MoNbTaTiW

AM

Han et al. (2017)

MoNbTaVW

AM

Senkov et al. (2010, 2011b)

MoNbTaVW

MA + SPS

Kang et al. (2018)

MoTaTiVZr

AM

Mu et al. (2017)

NbTaTiVW

AM

Yao et al. (2016)

NbTaTiVZr

MS

Gorban et al. (2016)

AlCoCrCuFeNi

MA

Tariq et al. (2013), Zhang et al. (2009b, c)

AlCoCrCuFeNi

SQ

Singh et al. (2011b)

AlCoCrFeNiTi

LC

Chen et al. (2017b)

AlCoCuNiTiZn

MA

Varalakshmi et al. (2010b, c)

AlCrCuFeTiZn

MA

Varalakshmi et al. (2008, 2010a) (continued)

Appendix A

311

Table A.1 (continued) Composition

Processing route

References

AlCrMoNbTiV

AM

Firstov et al. (2014a)

CoCrFeMnNiW

MA

Varalakshmi et al. (2008)

CoCuHfPdTiZr

AM

Takeuchi et al. (2016b)

HfMoNbTaTiZr

AM

Juan et al. (2015)

HfNbTaTiVZr

AM

Gao et al. (2016b)

MoNbTaTiVW

AM

Han et al. (2017)

MoNbTaTiVZr

AM

Mu et al. (2017)

AlCoCrCuFeNiW

MA

Tariq et al. (2013)

CrMoNbReTaVW

AM

Zhang et al. (2017l)

CrMoNbTaTiVZr

AM

Mu et al. (2017)

AlCoCrCuFeNiWZr

MA

Tariq et al. (2013)

CrMoNbTaTiVWZr

AM

Mu et al. (2017)

Non-equiatomic alloys Al0.85 CuFeNi

DLD

Chao et al. (2017)

HfTa0.53 TiZr

AM

Zhang et al. (2017f)

AlCoCrCu0.5 Ni

Sputtering

Yeh et al. (2004b)

AlCoCrCu0.5 Ni

AM

Yeh et al. (2004b)

Alx Coy ~ 20–22 Crz ~ 19–22 (FeMn)100 (x + y + z) (x = ~ 13–27 at %)

MeS

Marshal et al. (2017)

Alx CoCrFeNi (x = 0.9–2)

AM

Wang et al. (2012b)

Al0.7 Co0.3 CrFeNi

MA

Chen et al. (2013b)

Al0.85 CoCrFeNi

DLD

Joseph et al. (2015)

Al18 Co20 Cr21 Fe20 Ni21

AM

Chen et al. (2016b)

Al2 CoCrFeNi

AM

Yusenko et al. (2018)

Al2 CoCrFeNi + 3 at % Sc

AM

Yusenko et al. (2018)

Al0.5 CoFeNiSi0.5

AM and SC

Zhang et al. (2012d)

Alx CoFeNiSi (x > 0.3)

AM

Zhang et al. (2013b)

Al2 CrCuFeNi2

AM

Ma et al. (2013b)

Al2 CrCuFeNi2

SC

Ma et al. (2013b)

Alx CrFe1.5 MnNi0.5 (x = 0.8–1.2)

AM

Tsai et al. (2013c)

Al0.5 CrFe1.5 MnNi0.5

AM

Tang et al. (2010)

Al0.3 CrFe1.5 MnNi

AM

Ren et al. (2014)

Al0.5 CrMoNbTi

AM

Liu et al. (2014b)

AlCr0.5 NbTiV

AM

Stepanov et al. (2015a)

Al0.5 CrNbTi2 V0.5

AM

Stepanov et al. (2017)

AlxMoNbTiV (x = 0.25–1.5)

AM

Chen et al. (2014)

Alx MoTaTiV (x = 0.2, 0.6, and 1)

AM

Qiao et al. (2017) (continued)

312

Appendix A

Table A.1 (continued) Composition

Processing route

References

AlNb1.5 Ta0.5 Ti1.5 Zr0.5

AM

Senkov et al. (2014b)

AlNbTa0.5 TiZr0.5

AM

Senkov et al. (2018)

Al0.25 NbTaTiZr

AM

Senkov et al. (2018)

HfMoNb0.5 TiZr

AM

Guo et al. (2016b)

HfMoNb1.5 TiZr

AM

Guo et al. (2016b)

HfMoNbTix Zr (x = 0.5 and 1.5)

AM

Guo et al. (2016b)

HfMoNbTiZrx (x = 0.5 and 1.5)

AM

Guo et al. (2016b)

Hfx MoNbTiZr (x = 0.5 and 1.5)

AM

Guo et al. (2016b)

Hf0.5 Mo0.5 NbTiZr

AM

Guo et al. (2016b)

HfMo1.5 NbTiZr

AM

Guo et al. (2016b)

HfMo0.5 Nb0.5 TiZr

AM

Chen et al. (2018a)

Hf8 Nb33 Ta34 Ti11 Zr14

AM

Kozelj et al. (2014)

Hf27.5 Nb5 Ta5 Ti35 Zr27.5

IM + TMP

Lilensten et al. (2017)

Hf15 Nb20 Ta10 Ti30 Zr25

AM

Podolskiy et al. (2018)

HfNb0.5 Ta0.5 TiZr

AM

Chen et al. (2018a)

HfNb0.5 TiV0.5 Zr

AM

Chen et al. (2018a)

HfNb2.0 TiVZr2.0

AM

MoNbTaTix W (x = 0, 0.25, 0.5, 0.75, AM and 1.0)

Chen et al. (2018a) Han et al. (2018a)

Mox (NbTaTiZr)100x (x = 0 and 5)

AM

Wang and Xu (2018)

MoNbTiV0.5 Zr

SC

Zhang et al. (2012c)

Mox NbTiVZr (x = 0.3–1.3)

AM

Wu et al. (2015d)

Mox NbTiV0.3 Zr (xx = 0–1.5)

AM

Wu et al. (2015d)

Ag2 Cu2 DyGdTbY

AM

Takeuchi et al. (2015)

AlCoCrCux FeNi

AM

Zhang et al. (2010d)

AlCoCrCu0.5 FeNi

AM

Tung et al. (2007)

AlCoCrCu0.25 FeNi

IC

Zhang et al. (2008b)

Alx CoCrCuy FeNi (x = 1.0 and y = 0–0.5)

AM

Fan et al. (2014b)

Al2 CoCrCuFeNi

LC

Liu et al. (2014c)

Al2 CoCrCuFeNi

MaS

Wu et al. (2014b)

Alx CoCrCuFeNi (x = 20–25 at %)

MaS

Braeckman et al. (2015)

AlCoCrFeMox Ni (x = 0 and

AM

Zhu et al. (2010a)

AM

Zhang et al. (2012c)

AlCoCrFeNiSix (x = 0–0.8)

AM

Zhu et al. (2010b)

Al1.5 CoCrFeNiTi0.5

LC

Zhao et al. (2018a)

AlCoCrFeNiVx (x = 0.0–1.0)

AM

Dong et al. (2014) (continued)

Appendix A

313

Table A.1 (continued) Composition

Processing route

References

Al0.3 CrFe1.5 MnNi0.5 Ti0.2

AM

Ren et al. (2014)

Al0.5 CrMoNbTiV

AM

Liu et al. (2014b)

Al0.4 Hf0.6 NbTaTiZr

AM

Senkov et al. (2014a)

AlMo0.5 NbTa0.5 TiZr

AM

Senkov et al. (2018)

AlMo0.5 NbTa0.5 TiZr0.5

AM

Senkov et al. (2018)

Al0.5 Mo0.5 NbTa0.5 TiZr

AM

Senkov et al. (2018)

Al 0.3NbTa 0.8Ti 1.4V 0.2Zr 1.3

AM

Senkov et al. (2014b)

CoCrFeMn0.5 NiTi0.5

MA

Niu et al. (2016)

Co0.5 Fe0.5 MgNi0.5 TiZr

MA

Zepon et al. (2018)

Crx MoNbTaVW (x = 0.5 and 1)

AM

Zhang et al. (2015c)

HfMox NbTaTiZr (x = 0–1)

AM

Juan et al. (2016)

Alx CoCrCu1x FeNiSi0.2 (x = 0.6)

IC

Ma et al. (2017)

Alx CoCrCu1x FeNiSi0.2

AM, IC

Ma et al. (2017)

(x = 0.8 and 0.9) Alx CoCrCu1x FeNiTi0.5 (x = 0.75)

SC

Wang et al. (2009a)

Al0.5 CoCrCuFeNiV

AM

Chen et al. (2006a)

AlCoCrFe6 NiSiTi

LC

Zhang et al. (2011b, c, d)

AlCrFeMo0.5 NiSiTi

Plasma spray

Huang et al. (2004)

Al2.3 By CoCrCu0.7 FeNiSi0.1 (y = 0.15, 0.3, and 0.6)

LC

He et al. (2017b)

AlCoCrFeMo0.5 NiSiTi

Plasma spray

Huang et al. (2004)

CoCr5 Fe5 MoNbSiTiW

LC

Guo et al. (2016c)

Al2 CoCrCuFeMnNiTiV

AM

Zhang et al. (2008a)

Equiatomic alloys CoCrNi

AM

Adomako et al. (2018)

CoCrNi

IM + Swaging

Laplanche et al. (2018)

CoCuNi

MA

Varalakshmi et al. (2010b)

CoFeNi

IM

Laplanche et al. (2018)

CoFeNi

MA + SPS

Mane and Panigrahi (2018)

CoFeNi

DC

Guo et al. (2014)

CoFeNi

IM

Singh and Subramaniam (2014)

CoFeNi

AM

Wang et al. (2012c)

CoFeNi

MA

Praveen et al. (2012, 2013b)

CoMnNi

IM + Swaging

Laplanche et al. (2018)

FeMnNi

IM + Swaging

Laplanche et al. (2018)

AgAuPdPt

AM

Freudenberger et al. (2017) (continued)

314

Appendix A

Table A.1 (continued) Composition

Processing route

References

AlCuTiNi

IM

Fazakas et al. (2015)

AuCuNiPd

AM

Freudenberger et al. (2017)

AuCuNiPt

AM

Freudenberger et al. (2017)

AuCuPdPt

AM

Freudenberger et al. (2017)

AuNiPdPt

AM

Freudenberger et al. (2017)

CoCrCuNi

MA

Durga et al. (2012)

CoCrFeNi

DC

Guo et al. (2014)

CoCrFeNi

AM

Chen et al. (2018e), Huang et al. (2018), Vaidya et al. (2018)

CoCrFeNi

MA + S

Mane and Panigrahi (2018)

CoCrFeNi

IM

Laplanche et al. (2018), Lin et al. (2018)

CoCrFeNi

GA + HE

Liu et al. (2016d)

CoCrMnNi

AM

Adomako et al. (2018)

CoCuFeNi

MA

Praveen et al. (2012, 2013b)

CoCuNiZn

MA

Varalakshmi et al. (2010b)

CoFeMnNi

MA

Praveen et al. (2013b)

CoFeMnNi

AM

Zuo et al. (2017)

CoFeNiV

AM

Jiang et al. (2015a)

CuNiPdPt

AM

Freudenberger et al. (2017)

AlCoCuNiZn

MA

Varalakshmi et al. (2010b)

AlCoCuNiZn

MA

Mohanty et al. (2014)

AuCuNiPdPt

AM

Freudenberger et al. (2017)

CoCrCuFeNi

MaS

Wu et al. (2014b)

CoCrCuFeNi

LC

Zhang et al. (2014c)

CoCrCuFeNi

AM

Qin et al. (2018b)

CoCrFeMnNi

MeS

Cantor et al. (2004)

CoCrFeMnNi

MA

Zaddach et al. (2013)

CoCrFeMnNi

IM

Kim et al. (2018a), Jang et al. (2018), Ichii et al. (2018)

CoCrFeMnNi

DC + HPT

Heczel et al. (2018)

CoCrFeMnNi

SLM

Li et al. (2018b)

CoCrFeMnNi

IM + HR + A

Jo et al. (2018)

CoCrFeMnNi

IM + CR

Kim and Kim (2018)

CoCrFeMnNi

BS

Kireeva et al. (2018) (continued)

Appendix A

315

Table A.1 (continued) Composition

Processing route

References

CoCrFeMnNi

IM + swaging

Laplanche et al. (2018)

CoCrFeMnNi

SPS + CR + A

Liu et al. (2018a)

CoCrFeMnNi

AM + DC + CR + A

Liu et al. (2018b)

CoCrFeMnNi

IM + HR

Luo et al. (2018)

CoCrFeMnNi

IM + CR + A

Park et al. (2018)

CoCrFeMnNi

IM + HR + SA

Zhao et al. (2018b)

CoCrFeNiTi

AM

Zhang et al. (2009a)

CoCrFeNiTi

MA

Mishra and Shahi (2017)

CoCuFeMnNi

AM

Tazuddin et al. (2017)

CoCrFeMnNi

IM + HF + SA

Zhao et al. (2017)

CoCuFeNiTi

AM

Wang et al. (2012c)

CoCuFeNiV

IC

Zhang et al. (2008b)

CrCuFeMoNi

AM

Li et al. (2009)

CrNbTiVZn

MA

Dwivedi et al. (2016)

CrTiVYZr

MaS

Tsai et al. (2010b)

CuFeMnNiPt

IM + A + WQ

Takeuchi et al. (2017)

AlCoCrCuFeNi

MaS

Dolique et al. (2009, 2010)

AlCoCuFeNiV

AM + MS

Dou et al. (2016)

CoCrFeMnNiCu

MeS

Cantor et al. (2004)

CoCrFeMnNiNb

MeS

Cantor et al. (2004)

CoCrFeMnNiV

MeS

Cantor et al. (2004)

CoCrFeNi + 5 wt % Y2 O3

MA + SPS

Jia et al. (2018)

(Co, Cu, Mg, Ni, Zn)O

MA + A

Dabrowa et al. (2018)

CuIrNiPdPtRh

AM

Sohn et al. (2017)

Non-equiatomic alloys Al0.5 CuFeNi

SQ

Bashev and Kushnerov (2017)

Al0.3 CuFeNi

LD

Chao et al. (2017)

(CoCrFe)100x Nix (x = 20–40)

AM

Zhu et al. (2016)

CoCrFex Ni (x = 0, 0.2, 0.4, and 0.6

LC

Cai et al. (2018a)

Co25.33 Cr25.77 Fe24.53 Ni24.37

AM

Li et al. (2018d)

Co30 Fe30 Mn10 Ni30

MA

Wu et al. (2016)

Co30 Fe30 Mn10 Ni30

MA + SPS

Wu et al. (2016)

(CoFeMn)100x Nix (x = 5–40)

AM

Zhu et al. (2016)

Co30 Fe30 Ni30 Ti10

MA + SPS

Fu et al. (2018)

CoFeNi2 W0.5

AM

Jiang et al. (2016a)

Pb1x SnTeSeLax (x = 0–0.1)

Melting + SPS

Fan et al. (2017) (continued)

316

Appendix A

Table A.1 (continued) Composition

Processing route

References

Al0.5 CoCrFeNi

AM

Lin and Tsai (2011)

Al0.3 CoCrFeNi

AM and BS

Ma et al. (2013a)

Al0.3 CoCrFeNi

AM

Shun et al. (2010a, b)

Al0.5 CoCrFeNi

IC

Zhang et al. (2008b)

Alx CoCrFeNi (x = 0–0.3)

AM

Wang et al. (2014b)

Alx CoCrFeNi (x = 0–0.4)

AM

Wang et al. (2012b)

Alx CoCrFeNi (x = 0–0.45)

AM

Kao et al. (2011)

Alx CoCrFeNi (x = 0–0.65)

AM

Tian et al. (2013a)

Al0.25 CoCrFeNi

AM

Kao et al. (2009)

Alx CoCrFeNi (x = 0–0.375)

AM

Chou et al. (2009)

Al0.3 CoCrFeNi

BS

Ma et al. (2014a)

Al0.3 CoCrFeNi

DLD

Joseph et al. (2015)

Alx CoCrFeNi (x = 0–0.25)

AM

Jasiewicz et al. (2015)

Al0.3 CoCrFeNi1.7

LD

Sistla et al. (2015)

Al13 Co20 Cr23.5 Fe20 Ni23.5

AM

Chen et al. (2016b)

Al0.3 CoCrFeNi

AM + FSP

Zhu et al. (2017b)

Al0.1 CoCrFeNi

AM

Chen and Qiang (2018)

Alx CoCrFeNi (x = 0, 0.25, and 0.5)

AM

Cieslak et al. (2018)

Alx CoCrFeNi (x = 0, 0.2, and 0.3)

AM + LENS

Li et al. (2018c)

Al4.88 Co29.53 Cr18.58 Fe19.62 Ni27.39

AM

Li et al. (2018d)

Al6.64 Co23.82 Cr23.66 Fe23.01 Ni22.87

AM

Li et al. (2018d)

Al0.1 CoCrFeNi

BS

Liu et al. (2018c)

(AlCoCrFeNi)100x Cox (x = 0 and 4)

AM

Qin et al. (2018a)

Al0.3 CoCrFeNi

AM + A + HF

Shi et al. (2018a)

Al0.1 CoCrFeNi

AM + HIP

Xu et al. (2018a)

Al0.3 CoCrFeNi

IM

Yusenko et al. (2018)

(AlCoCrFe)50 Ni50

AM

Zhu et al. (2016)

(AlCu)x CoFeNi (x = 0, 0.2, 0.4, 0.6, 0.7, and 0.8)

AM + SC

Zhang et al. (2017g)

Al7.5 Co25 Cu17.5 Fe25 Ni25

MA, MA + SPS

Fu et al. (2016)

Al0.4 CoCu0.6 NiSix (x = 0 and 0.05)

AM + IC

Chen et al. (2018b)

Al10 Co17 Fe34 Mo5 Ni34

AM

Menou et al. (2018)

Al0.2 CoFeNiSi0.2

BS

Zuo et al. (2015)

Alx CoFeNiSix (x < 0.3)

AM

Zhang et al. (2013b)

Alx CoFeNiSi0.2

AM and SC

Zhang et al. (2012d)

Al0.2 CoFeNiSi0.2

AM and IM

Zuo et al. (2013)

Alx CrCuFeNi2 (× 0.5)

DC

Guo et al. (2013b) (continued)

Appendix A

317

Table A.1 (continued) Composition

Processing route

References

Al0.5 CrCuFeNi2

SC

Ma et al. (2013b)

Al7.5 Cr6 Fe40.4 Mn34.8 Ni11.3

AM

Wang and Baker (2016)

Cx(Co10 Cr10 Fe40 Mn40 )100x (x = 0, 2.2, 3.3, 4.4, 6.6, and 8.9 at %)

AM

Chen et al. (2018c)

Cx (CoCrFeNi)100x (x = 0, 2.5, and 3 at %)

AM + DC

Liu et al. (2018d)

C0.05 CoCrFeNi

SLM

Zhou et al. (2018b)

CoCrCu0.5 FeNi

AM

Hsu et al. (2005)

Co19 Cr19.2 Cu23.5 Fe19.2 Ni19.1

MS

Ma et al. (2014b)

CoCrCu0.5 FeNi

AM

Dahlborg et al. (2015)

CoCrCux FeNi (x = 0, 0.5, 1, and 1.5) LC

Cai et al. (2019)

Cox (CrFeMnNi)100x (x = 0–33.33)

Zhu et al. (2016)

AM

(CoCuFeNi)100x Crx (x = 0–33.33)

AM

Zhu et al. (2016)

(CrCuFeNi)100x Cox (x = 0–33.33)

AM

Zhu et al. (2016)

(CoCrFeMn)100x Nix (x = 15–42.9)

AM

Zhu et al. (2016)

(CoCrFeNi)86 Mn14

AM + DC + CR + A

Liu et al. (2018b)

Co15 Cr20 Fe20 Mn20 Ni25

AM + DC + CR + A

Liu et al. (2018b)

Cox Crx Fex Mnx Ni100,4x (2 < x < 25)

IM

Brocq et al. (2016)

Cox (CrFeMnNi)(100x) (x = 5, 10, and 20)

AM

Zhu et al. (2017a)

Cox (CrFeMnNi)(100x) (x = 10 and 20) AM + A

Zhu et al. (2017a)

CoCrFeMnx Ni (x = 0 and 0.5)

AM

Christofidou et al. (2018)

CoCrFeMo0.3 Ni

AM

Shun et al. (2010a, 2012a)

Co24.1 Cr24.1 Fe24.1 Mo3.6 Ni24.1

MA + SPS

Zhang et al. (2018f)

Co35 Cr15 Fe20 Mo10 Ni20

AM + TMP + HT

Ming et al. (2017)

Co42.5 Cr12.5 Fe20 Mo5 Ni20

AM + TMP + HT

Ming et al. (2017)

CoCrFeNiTa0.1

AM

Huo et al. (2018b)

CoCrFeNiTi0.3

AM

Shun et al. (2012b)

Co1.5 CrFeNi1.5 Ti0.5

MA + SPS

Moravcik et al. (2017)

CoCu0.9 Fe1.05 Mn1.05 Ni

AM

Oh and Hong (2017)

Co5 Cu15 Fe30 Mn25 Ni25

AM

Tazuddin et al. (2017)

Co15 Cu25 Fe15 Mn10 Ni35

AM

Tazuddin et al. (2017)

CoCuFe0.25 Mn1.75 Ni

IM

Bridges et al. (2018)

CoCuFeNiSnx (x = 0–0.05)

AM

Liu et al. (2012)

Co26 Fe27 Mn10 Ni27 Ti10

MA

Wu et al. (2016)

CrCu2 Fe2 MnNi2

AM

Ren et al. (2010, 2012)

Cr2 CuFe2 Mn2 Ni2

AM

Ren et al. (2010, 2012) (continued)

318

Appendix A

Table A.1 (continued) Composition

Processing route

References

CrCuFeMn2 Ni2

AM

Ren et al. (2010, 2012)

Ir0.26 Os0.05 Pt0.31 Rh0.23 Ru0.15

TP

Yusenko et al. (2017)

AgCoCuFeNi Ptx

RF sputtering

Tsai et al. (2009a)

Al7.4 C1.1 Cr5.55 Fe39.93 Mn35.67

AM

Wang et al. (2016a)

Ni10.35 Alx CoCrCu1x FeNi

AM

Zhang et al. (2010d)

Al0.5 CoCrCuFeNi

AM

Yeh et al. (2004b)

Al0.5 CoCrCuFeNi

Sputtering

Chen et al. (2004)

Alx CoCrCuFeNi

RF sputtering

Yeh et al. (2004a)

Alx CoCrCuFeNi

AM

Tong et al. (2005b)

Alx CoCrCuFeNi

AM

Wu et al. (2006)

Al0.5 CoCrCuFeNi

AM

Tung et al. (2007)

Alx CoCrCu1x FeNi

AM

Zhou et al. (2008b)

Alx CoCrCuFeNi

AM

Tang and Yeh (2009)

Al0.5 CoCrCuFeNi

AM

Tsai et al. (2009b)

Al0.5 CoCrCu0.5 FeNi

AM

Li et al. (2013a)

Al0.3 CoCrCu0.5 FeNi

AM

Tsai et al. (2013e)

Al0.5 CoCrCu0.5 FeNi2

IM

Daoud et al. (2013)

Alx CoCrCuy FeNi (x = 0.5 and y = 0.5–1)

AM

Fan et al. (2014b)

Alx CoCrCuFeNi (x = 9–15 at %)

MS

Braeckman et al. (2015)

Al0.5 CoCrCuFeNi

GA

Yang et al. (2017)

Al0.5 CoCrCuFeNi

AM

Sun et al. (2018)

Alx (CoCrFeMnNi)100x (x < 8 at %)

AM

He et al. (2014)

Al0.3 CoCrFeMnx Ni (x = 0.1 and 0.3) IM

Wong et al. (2018)

Al0.5 CoCrFeMnNi

AM

Pauzi et al. (2013)

Al0.5 CoCrFeMox Ni (x = 0 and 0.1)

AM

Zhuang et al. (2018)

Al0.3 CoCrFeMo0.1 Ni

AM

Shun et al. (2010a, b)

Alx CoCrFeMo0.5 Ni (x = 0–0.5)

AM

Hsu et al. (2013a, b)

Al0.3 CoCrFeNiTi0.1

AM

Shun et al. (2010b)

Alx Co1.5 CrFeNiTiy

AM

Chuang et al. (2011)

Alx CoCrFeNiTi0.5 (x = 0 and 0.2)

AM

Dong et al. (2013b)

AlCoCux NiTiZn

MA

Varalakshmi et al. (2010b)

C1.0 CoCrFeMnNi

AM + A

Li et al. (2018e) (continued)

Appendix A

319

Table A.1 (continued) Composition

Processing route

References

CoCrCuFeGex Ni (x = 0–16.2%)

MS

Braeckman et al. (2016)

CoCrCuFeInx Ni (x = 0–4.7%)

MS

Braeckman et al. (2016)

CoCrCux FeMnNi (x = 0 and 0.25)

AM

Xian et al. (2018)

(CoCrCuFeNi)100x Nbx (x = 0 and 4)

AM

Qin et al. (2018b)

CoCrFeMnNiTi0.1

AM + HPT

Shahmir et al. (2018)

CoCrFeMnNix V (x = 2–3)

AM

Karpets et al. (2015a)

Co10 Cr15 Fe35 Mn5 Ni25 V10

IM

Jo et al. (2017)

CoCrFeMnNiV0.25

AM

Stepanov et al. (2015c)

Co20 Cr20 Fe20 Mn5 Ni20 Zn15

MA

Zaddach et al. (2016)

Co1.5 CrFeMox Ni1.5 Ti0.5 (x = 0 and 0.1)

AM

Chou et al. (2010b)

Alx CoCrCu1x FeNiSi0.2 (x = 0.2)

AM

Ma et al. (2017)

Alx CoCrCu1x FeNiSi0.2 (x = 0.4)

IC

Ma et al. (2017)

Alx CoCrCu1x FeNiTi0.5 (x = 0 and 0.25)

SC

Wang et al. (2009a)

Al0.5 CoCrCuFeNiVx (x < 0.4)

AM

Chen et al. (2006a)

AlCoCrCuFeNiV0.2

LSA

Zhang et al. (2015d)

Al0.3 By CoCrFeNiCu0.7 Si0.1 (y = 0.15, 0.3, and 0.6)

LC

He et al. (2017b)

Composition

Processing Major route phase

Minor phase

References

AlCuNi

AM

BCC

FCC

Yeh et al. (2007a)

CoCrNi

MaS

FCC

HCP

Cao et al. (2018)

CoFeMn

AM

BCC

FCC + σ

Zhu et al. (2016)

CrFeNi

IM

FCC

BCC

Singh and Subramaniam (2014)

AlCoCuNi

AM

BCC

FCC

Yeh et al. (2007a)

AlCoCuNi

AM + A

FCC

BCC

Kulkarni et al. (2018)

AlCrCuFe

MA

BCC

FCC

Maulik and Kumar (2015)

AlCrCuFe

MA + SPS

BCC

BCC

Maulik et al. (2016)

AlCrCuNi

AM

FCC + BCC

FCC + B2

Wang et al. (2016f)

CoCrFeNi

MA

FCC

BCC

Praveen et al. (2012)

CoCrFeNi

IM +

BCC

FCC

Laplanche et al. (2018)

CoFeNiTi

AM

HCP

FCC

Tsau (2009)

CoCrFeNi

MA

FCC

BCC

Praveen et al. (2013b)

CoCuFeNi

IM

FCC1

FCC2

Singh and Subramaniam (2014)

Equiatomic alloys

(continued)

320

Appendix A

(continued) Composition

Processing Major route phase

CrFeNiTi

MA

HfScTiZr NbScTiZr

Minor phase

References

FCC1 + FCC2

σ

Mishra and Shahi (2017)

AM

HCP1

HCP2

Rogal et al. (2016a)

AM

BCC

HCP

Rogal et al. (2016b)

AlBFeSiNi

MA + SPS

FCC1

BCC + FCC2 Wang et al. (2016b)

AlCoCrCuFe

LC

FCC

BCC

Qiu et al. (2013)

AlCoCrCuNi

GTAW cladding

FCC

BCC

Lin and Cho (2009)

AlCoCrCuNi

AM

BCC

FCC

Yeh et al. (2007a)

AlCoCrFeNi

MA

BCC

FCC

Ang et al. (2015)

AlCoCrFeNi

PS

FCC

BCC + oxide

Ang et al. (2015)

AlCoCrFeNi

SEBM

BCC_A2 FCC + BCC_B2

Fujieda et al. (2015)

AlCoCrFeNi

SEBM

BCC + B2

FCC

Shiratori et al. (2016)

AlCoCrFeNi

IM

BCC

FCC

Vida et al. (2016)

AlCoCrFeNi

MA + SPS

BCC1

BCC2

Yang et al. (2016a)

AlCoCuFeNi

AM

BCC

FCC

Zhuang et al. (2013)

AlCoCuFeNi

SC

BCC

FCC

Zhuang et al. (2012)

AlCoCuFeNi

AM + A

FCC

BCC

Kulkarni et al. (2018)

AlCoCuFeNi

MA + S

FCC1 + BCC

FCC2

Gandarilla et al. (2018)

AlCrCuFeMg

MA

BCC1

BCC2

Maulik and Kumar (2015)

AlCrCuFeNi

AM

BCC

FCC

Li et al. (2009)

AlCrCuFeNi

MA + HPS

BCC

FCC1 + FCC2

Yurkova et al. (2016)

AlCrFeMoNi

AM

BCC

FCC

Dou et al. (2018)

AlCrMoNiTi

MA + HPS

BCC

FCC

Bo et al. (2014)

AlCrMoTiW

AM

BCC1

BCC2

Gorr et al. (2016b)

AlCuFeNiTi

IM

FCC1

FCC2

Fazakas et al. (2015)

AlCuFeNiTi

MA + S

BCC

FCC1 + FCC2

Yurkova et al. (2016)

AlCuFeNiTi

AM

BCC

FCC1 + FCC2

Zhang et al. (2017a)

AlCuFeNiTi

AM

BCC

FCC

Jiang et al. (2017a)

AlCuHfYZr

AM

HCP1 + HCP2

BCC

Zhang et al. (2016c)

AlCuTiYZr

AM

HCP

BCC

Zhang et al. (2016c)

AlCuFeNiTi

AM

BCC

FCC1 + FCC2

Zhang et al. (2017a) (continued)

Appendix A

321

(continued) Composition

Processing Major route phase

Minor phase

References

AlNbTaTiZr

AM

BCC1

BCC2

Poletti et al. (2015)

CoCrCuFeNi

MA

FCC

BCC

Praveen et al. (2012, 2013b)

CoCrCuFeNi

AM + LM FCC1

FCC2

Wu et al. (2018)

CoCrCuFeNi

AM + CR FCC1

FCC2

Zhang et al. (2018 g)

CoCrCuFeNi

MA

FCC

BCC

Wang et al. (2016e)

CoCrCuFeNi

AM

FCC1

FCC2 + FCC3

Dahlborg et al. (2015)

CoCrFeGaNi

IM

FCC

BCC

Vida et al. (2016)

CoCrFeGeNi

IM

FCC

BCC

Vida et al. (2016)

CoCrFeMnNi

MA

FCC

BCC

Ang et al. (2015)

CoCrFeMnNi

PS

FCC

Oxide

Ang et al. (2015)

CoCrFeMnNi

MA

FCC

BCC

Ji et al. (2015)

CoCrFeMnNi

MA + SPS

FCC1

FCC2

Ji et al. (2015)

CoCrFeMoNi

AM

FCC

BCC

Wu et al. (2015b)

CoCrFeNiPd

AM

FCC1

FCC2

Dahlborg et al. (2015)

CoCrFeNiSn

IM

BCC

FCC

Vida et al. (2016)

CoCrFeNiSn

AM

FCC

Orthorhombic Dahlborg et al. (2015)

CoCrFeNiW

MA

BCC

FCC

Shang et al. (2017)

CoCrFeNiW

MA + VHP

FCC1 + FCC2

δ+σ

Shang et al. (2017)

CoCrNiTiV

VHP

BCC

FCC + TiO + Ni2 V3 + η

Cai et al. (2016a)

CoCuFeMnNi

IM

FCC

FCC

Takeuchi et al. (2017)

CoCuFeMnNi

IM + A + FCC WQ

FCC

Takeuchi et al. (2017)

CoFeGaMnNi

AM

BCC

FCC

Zuo et al. (2017)

CoNbNiTiZr

AM

BCC1

BCC2

Han et al. (2015)

CrCuFeMnNi

AM

FCC

BCC

Li 2009, Ren et al. (2010, 2012)

CrFeMoNiTi

MA

FCC1 + FCC2

σ

Mishra and Shahi (2017)

CrFeMoNiW

IM

BCC

FCC

Vida et al. (2017)

CuFeMnNiPt

IM

FCC

FCC

Takeuchi et al. (2017)

CuDyGdTbY

AM

FCC

HCP + BCC (CsCl)

Takeuchi et al. (2015)

CuHfTiYZr

AM

HCP

BCC

Zhang et al. (2016c)

MoNbTaTiZr

AM + A

BCC1

BCC2

Todai et al. (2017)

MoNbTaTiZr

AM

BCC

HCP

Mathiou et al. (2018)

MoTaVWZr

AM

BCC1 + BCC2

Laves + HCP Anzorena et al. (2016)

NbTaTiVZr

AM

BCC1

BCC2

Poletti et al. (2015)

NbTaTiVZr

AM

BCC1

BCC2

Poletti et al. (2016) (continued)

322

Appendix A

(continued) Composition

Processing Major route phase

AgAlCoCuFeNi

AM

AgAuCuNiPdPt AgCoCuFeGeNi

Minor phase

References

FCC1 + FCC2

BCC

Ji (2015)

AM

FCC1

FCC2

Takeuchi et al. (2016b)

AM

FCC1 + FCC2

BCC

Ji (2015)

AlCoCrCuFeMn

AM

BCC1 + BCC2

FCC

Wang et al. (2015c)

AlCoCrCuFeNi

PS

BCC

FCC

Yue et al. (2013)

AlCoCrCuFeNi

PM

FCC

BCC

Qiu (2013)

AlCoCrCuFeNi

IM

BCC

FCC1 + FCC2

Kuznetsov et al. (2012, 2013), Singh et al. (2011b)

AlCoCrCuFeNi

SC

BCC

FCC

Zhuang et al. (2012)

AlCoCrCuFeNi

LC

BCC

FCC

Yue et al. (2014)

AlCoCrCuFeNi

AM

BCC

FCC

Tung et al. (2007), Yeh et al. (2007a), Wen et al. (2009)

AlCoCrCuFeNi

AM

FCC

BCC

Wu et al. (2006)

AlCoCrCuFeNi

MaS

BCC

FCC

Dolique et al. (2010)

AlCoCrCuFeNi

IM

BCC

FCC

Nayan et al. (2014)

AlCoCrCuFeNi

AM

BCC

FCC1 + FCC2

Karpets et al. (2015b)

AlCoCrCuFeNi

AM

BCC

FCC

Krapivka et al. (2015)

AlCoCrCuFeNi

MA + S

FCC1 + FCC2

BCC

Gandarilla et al. (2018)

AlCoCrCuFeNi

PVD

BCC

FCC1 + FCC2

Nadutov et al. (2016)

AlCoCrFeNbNi

LC

BCC

FCC1 + FCC2 + Fe2 Nb

Lin et al. (2017a)

AlCoCuFeNiTi

AM

BCC

FCC

Wang et al. (2012c)

AlCoCuFeNiTi

SC

BCC

FCC

Zhuang et al. (2012)

AlCoCrFeNiTi

PS

BCC

FCC + B2

Tian et al. (2016)

AlCoCrFeNiZr

AM

BCC1 + FCC1

FCC2

Razuan et al. (2016)

AlCoCuFeNiSi

AM

BCC + B2

FCC

Wang et al. (2016c)

AlCoFeMoNiTi

MA

BCC1

BCC2

Lopez et al. (2015)

AlCoFeMoNiTi

MA + S

FCC

BCC1 + BCC2 + αCoMo + μCoMo + Ti2 o

Lopez et al. (2015)

AlCoFeMoNiTi

MA + AM

BCC1 + BCC2

FCC + Ti2 o

Lopez et al. (2015) (continued)

Appendix A

323

(continued) Composition

Processing Major route phase

AlCrCuFeMnNi

IM

AlCrCuFeMnW AlCrCuFeMnW

Minor phase

References

BCC1 + BCC2

FCC

Soare et al. (2015a)

MA

BCC

FCC

Kumar et al. (2018)

MA + SPS

BCC

B2 + σ + FeMn type phase

Kumar et al. (2018)

AlCrCuFeNiZn

MA

BCC

FCC

Pradeep et al. (2013), Koundinya et al. (2013)

CoCrCuFeMoNi

AM

FCC1 + FCC2

BCC

Wu et al. (2015b)

CoCuHfNiTiZr

AM + SC

BCC1

BCC2

Park et al. (2016)

HfLaScTiYZr

AM

HCP1

HCP2

Takeuchi et al. (2016a)

AlCoCrCuFeMnNi

AM

BCC

FCC

Li et al. (2008a)

AlCoCrCuFeNiTi

AM

BCC1

BCC2, FCC

Li et al. (2008a)

AlCoCrCuFeNiTi

MA + S

FCC1 + BCC

FCC2

Gandarilla et al. (2018)

AlCoCrCuFeNiV

AM

BCC

FCC

Li et al. (2008a)

AlCoCrCuFeNiV

MS

FCC

BCC

Shaginyan et al. (2016)

AlCoCrCuFeNiV

MS

BCC

FCC

Gorban et al. (2016)

AlCoCrCuFeNiSi

AM

BCC

FCC

Yeh et al. (2007a)

AlCoCrCuFeSiTi

AM

FCC

BCC1 + BCC2 + BCC3

Wang et al. (2016c)

AlCrCuFeNbNiTi

AM

FCC1 + FCC2

BCC

Razuan et al. (2013)

HfMoNbTaTiVZr

AM

BCC1

BCC2

Gao et al. (2015)

AlCoCrCuFeNiTiXVMo (X = Zn, Mn)

MA

BCC

FCC

Fazakas et al. (2013)

CoCrNi3

MaS

FCC

HCP

Cao et al. (2018)

Al0.75 CrFeNi

MA

BCC

FCC

Chen et al. (2015e)

Al0.75 CrFeNi

MA + SPS

BCC

FCC

Chen et al. (2015e)

Al0.6 CrFeNi

MA

BCC

FCC

Fu et al. (2015)

Al0.6 CrFeNi

MA + HP + SPS

FCC

BCC

Fu et al. (2015)

AlCrFe2 Ni2

IM

FCC

BCC + B2

Dong et al. (2016a)

Al0.7 CuFeNi

SQ

FCC

BCC

Bashev and Kushnerov (2017)

Co20 Cr20 Fe40 Mn20

IM

HCP

FCC

Li et al. (2017b)

(CoCrFe)100x Nix (x = 0–10)

AM

BCC

FCC + σ

Zhu et al. (2016)

(CoCrFe)85 Ni15

AM

FCC

BCC + σ

Zhu et al. (2016)

CrCuFeNi2

LENS

FCC1 + FCC2

B2 + BCC

Borkar et al. (2016a)

Non-equiatomic alloys

(continued)

324

Appendix A

(continued) Composition

Processing Major route phase

Minor phase

References

Cu(50x) FexMn25 Ni25 (x = 25, 30, 35, and 40)

MWPP

FCC1

FCC2

Veronesi et al. (2016)

CuFeNiSi0.5

SQ

FCC

BCC

Bashev and Kushnerov (2017)

HfTax TiZr (x = 0.6, 0.5, and 0.4)

AM

BCC

HCP

Huang et al. (2017)

NbTiV2 Zr

AM

BCC2

BCC1 + BCC3

Senkov et al. (2013b)

Alx CoCrFeNi

AM

x= BCC 0.5–0.75, FCC

Alx CoCrFeNi (x = 0.5 and 0.75)

x= 0.875–1, BCC

FCC

Chou et al. (2009)

AM

FCC

BCC

Kao et al. (2009)

Alx CoCrFeNi (x = 0.5–0.8)

AM

FCC

BCC

Wang et al. (2012b)

Alx CoCrFeNi (x = 0.45–0.85)

AM

FCC

BCC

Kao et al. (2011)

Al0.1 Co1.5 CrFeNi1.5

AM + HT FCC

β

Chang and Yeh (2015)

Al0.75 CoCrFeNi

MA

BCC

FCC

Chen et al. (2015d)

Al0.75 CoCrFeNi

MA + SPS

FCC

BCC

Chen et al. (2015d)

Al0.6 CoCrFeNi

MA + HP + SPS

FCC

BCC

Fu et al. (2015)

Alx CoCrFeNi (x = 0.5–1.5)

AM

FCC

BCC

Jasiewicz et al. (2015)

Al0.6 CoCrFeNi

MA

BCC

FCC

Fu et al. (2015)

Al0.6 CoCrFeNi

DLD

FCC

BCC

Joseph et al. (2015)

Al0.6 CoCrFeNi

AM + EBW

FCC

BCC

Nahmany et al. (2016)

Al0.8 CoCrFeNi

AM + EBW

FCC

BCC

Nahmany et al. (2016)

Al0.7 CoCrFe2 Ni

AM + SC

BCC + B2

FCC

Wang et al. (2016d)

(AlCoCrFe)100x Nix (x = 27.3–42.9)

AM

BCC

FCC + B2

Zhu et al. (2016)

Al0.6 CoCrFeNi

DLD

FCC

BCC

Chao et al. (2017)

AlCoCrFeNi2.1

GA

FCC

BCC

Ding et al. (2017a)

Al13 CoCrFeNi

BS

FCC

BCC

Abuzaid and Sehitoglu (2018)

Al0.3 CoCrFeNi

PVD

FCC

BCC

Gao et al. (2018)

Al15 Co20 Cr22.5 Fe20 Ni22.5

AM

BCC

FCC + B2

Chen et al. (2016b)

Al10.5 Co20 Cr24.75 Fe20 Ni24.75

AM

BCC

FCC

Chen et al. (2016b)

Alx CoCrFeNi (x = 0.41)

AM + LENS

FCC

BCC

Li et al. (2018c)

Al0.7 CoCrFeNi

BS

BCC

FCC

Liu et al. (2018c)

(AlCoCrFeNi)100x Cox (x = 8)

AM

FCC

BCC

Qin et al. (2018a) (continued)

Appendix A

325

(continued) Composition

Processing Major route phase

Minor phase

References

BCC

FCC

Qin et al. (2018a)

Alx CoCrFeNi (x = 0.5 and 0.7) AM + HT FCC + HF

BCC

Shi et al. (2018b)

(AlCu)x CoFeNi (x = 0.9, 1.0, and 1.2)

AM + SC

BCC

FCC

Zhang et al. (2017g)

Al0.4 CoCu0.6 NiSix (x = 0.2)

AM + IC

FCC

BCC

Chen et al. (2018b)

Al0.75 CoFeMn0.75 Ni

AM

BCC

FCC

Li et al. (2017c)

Al0.5 CoFeMn0.5 Ni

AM

FCC

BCC

Li et al. (2017c)

Al0.3 CoFeNiSi0.3

AM

FCC

BCC

Zhang et al. (2013b)

Al0.3 CoFeNiSi0.3

AM

FCC

BCC

Zhang et al. (2013b)

AlCrCuFeMg0.5

MA

BCC

FCC

Maulik and Kumar (2015)

AlCrCuFeMg1.7

MA

BCC1

BCC2

Maulik and Kumar (2015)

Al1.3 CrCuFeNi2

LENS

B2 + BCC

FCC1 + FCC2

Borkar et al. (2016a)

Al1.5 CrCuFeNi2

LENS

B2 + BCC

FCC

Borkar et al. (2016a)

Al0.5 CrCuFeNi2

DC

FCC1

FCC2

Ng et al. (2014)

AlCrCuFeNi2

SC

FCC

BCC

Ma et al. (2013b)

Al0.3 CrFe1.5 MnNi0.5

AM

FCC

BCC

Tang et al. (2009a)

Al0.3 CrFe1.5 MnNi0.5

AM

FCC

BCC

Chen et al. (2010a)

Al0.3 CrFe1.5 MnNi0.5

AM

BCC

FCC

Tang et al. (2012)

Al0.3 CrFe1.5 MnNi0.5

AM

FCC1

BCC + FCC2 Tsao et al. (2012)

Al0.3 CrFe1.5 MnNi0.5

IM

FCC

BCC

Chuang et al. (2013)

Al2 CrFeMox Ni (x = 0.5–2)

LC

BCC1

BCC2

Wu et al. (2015c)

Al22.5 Cu20 Fe15 Ni20 Ti22.5

IM

FCC1

FCC2

Fazakas et al. (2015)

Al16 Cu16 Fe16 Ni26 Ti26

AM

BCC

FCC1 + FCC2

Zhang et al. (2017g)

Al12 Cu12 Fe12 Ni32 Ti32

AM

BCC

FCC1 + FCC2

Zhang et al. (2017g)

Al16 Cu16 Fe16 Ni26 Ti26

AM

BCC

FCC1 + FCC2

Zhang et al. (2017g)

Al12 Cu12 Fe12 Ni32 Ti32

AM

BCC

FCC1 + FCC2

Zhang et al. (2017g)

Al0.25 CuFeNiSi0.25

SQ

FCC

BCC

Bashev and Kushnerov (2017)

Al0.5 CuFeNiSi0.25

SQ

BCC

FCC

Bashev and Kushnerov (2017)

Al0.3 NbTaTi1.4 Zr1.3

AM

BCC1

BCC2

Senkov et al. (2014b)

Al0.5 Nb0.79 TaTi0.82 Zr0.46

AM

BCC1

BCC2

Poletti et al. (2016)

CoCrCu1.5 FeNi

AM

FCC1

FCC2

Dahlborg et al. (2015)

CoCr0.8 CuFeNi1.2

MA

FCC

BCC

Wang et al. (2016e)

CoCr0.5 CuFeNi1.5

MA

FCC

BCC

Wang et al. (2016e)

CoCr0.2 CuFeNi1.8

MA

FCC

BCC

Wang et al. (2016e)

(AlCoCrFeNi)100× Cox (x = 12 AM and 16)

(continued)

326

Appendix A

(continued) Composition

Processing Major route phase

Minor phase

References

(CoCrCuNi)100_xFex (x = 0–33.33)

AM

FCC2

FCC1

Zhu et al. (2016)

(CoCrCuFe)100_xNix (x = 0–33.33)

AM

FCC2

FCC1

Zhu et al. (2016)

Co20 Cr20 Fe34 Mn20 Ni6

IM

FCC

HCP

Li et al. (2017b)

CoCrFeNb0.25 Ni

AM

FCC

BCT

He et al. (2018)

CoCrFeNiPd0.5

AM

FCC1

FCC2

Dahlborg et al. (2015)

CoCrFeNiPd1.5

AM

FCC1

FCC2

Dahlborg et al. (2015)

Co0.5 CrFeNiTi0.5

MA

BCC

FCC

Fu et al. (2013b)

Co1.5 CrFeNi1.5 Ti0.5

MA

FCC1 + FCC2

BCC

Moravcik et al. (2017)

CoCrMoNbTi0.4

AM

BCC1

BCC2

Zhang et al. (2018c)

Co30 Cu25 Fe35 Mn5 Ni5

AM

FCC1 + BCC

FCC2

Tazuddin et al. (2017)

Co25 Cu35 Fe25 Mn5 Ni10

AM

FCC1

FCC2

Tazuddin et al. (2017)

CoCuyFeNiTix

AM

FCC1 BCC (Cu-rich) (β-Ti–rich) (x + FCC2 = 3/5) (Co-rich) (x = 1/3, 3/7, and 3/5)

Mishra et al. (2012)

CoCuyFeNiTix (x/y = 1/3, 3/7, 3/5, 9/11, 11/9, and 3/2)

SC

FCC1

FCC2

Samal et al. (2014)

CoCuFeNi1.5 V0.5

MA + SPS

FCC1

FCC2

Wang et al. (2017a)

Co26 Fe27 Mn10 Ni27 Ti10

MA + SPS

FCC1

FCC2

Wu et al. (2016)

Cr2 Cu2 FeMn Ni2

AM

FCC

BCC

Ren et al. (2010, 2012)

Cr2 Cu2 Fe Mn2 Ni

AM

FCC

BCC

Ren et al. (2010, 2012)

CrCu2 Fe2 NiMn2

AM

FCC

BCC

Ren et al. (2010, 2012)

Cr2 CuFe2 MnNi

AM

FCC

BCC

Ren et al. (2010, 2012)

Cr0.4 CuFe0.4 MnNi

AM

FCC

FCC

Rao et al. (2017)

CrCuxFeMoyNi (x = 5 and 1) (y = 0.5 and 1)

AM

FCC1 + FCC2

σ

Peng et al. (2017)

CrCuxFeTiZny (x/y = 1/0, 3/1, and 1 and x + y = 40)

MA

FCC

BCC

Mridha et al. (2013)

CrFeMoTixV (x = 0.5–2)

AM

BCC1

BCC2

Guo et al. (2017b)

Cr10 Fe15 Ti35 V35 Zr5

AM

BCC1

BCC2

Xian et al. (2017)

Hf1.1 Mo0.85 Ti0.6 W0.85 Zr1.6

AM

BCC + HCP

BCC

Karantzalis et al. (2017)

Hf8 Nb30.8 Ta30.8 Ti17.7 Zr12.7

ZM

BCC

FCC

Heidelmann et al. (2016)

HfNbTaTiZr

AM + HT BCC

HCP

Stepanov et al. (2018a) (continued)

Appendix A

327

(continued) Composition

Processing Major route phase

Minor phase

References

Mox (TaTiNbZr)100x (x = 10, 15, and 20)

AM

BCC1

BCC2

Wang and Xu (2018)

Mox NbTiVZr (x = 1.5–2.0)

AM

BCC1

BCC2

Wu et al. (2015d)

Al0.8 CoCrCuFeNi

AM

FCC

BCC

Tong et al. (2005b)

AlCo0.5 CrCuFeNi

AM

FCC

BCC

Tung et al. (2007)

AlCoCr0.5 CuFeNi

AM

FCC

BCC

Tung et al. (2007)

AlCoCrCuFe0.5 Ni

AM

FCC

BCC

Tung et al. (2007)

AlCoCrCuFeNi0.5

AM

FCC

BCC

Tung et al. (2007)

Al0.75 CoCrCu0.25 FeNi

AM

BCC

FCC

Zhou et al. (2008b)

Alx CoCrCu1 x FeNi (x = 0.25–0.75)

AM

FCC

BCC

Zhang et al. (2010d)

Al0.8 CoCrCuFeNi

DC

FCC1 + FCC2

BCC

Liu et al. (2011)

Alx CoCrCuFeNi (x = 1–2)

LC

BCC

FCC

Ye et al. (2011)

Alx CoCrCu0.5 FeNi

AM

x = 1, BCC

FCC1

Li et al. (2013a)

Alx CoCrCu0.5 FeNi

AM

x = 1.5, BCC

FCC2

Li et al. (2013a)

Al0.5 CoCrCuFeNi

IM

FCC1

FCC2 (Cu-rich)

Sheng et al. (2013)

Al0.5 Co0.3 CrCu0.2 FeNi

MA

BCC

FCC

Fang et al. (2014)

Alx CoCrCuFeNi (x = 0.45 and 1)

MA

FCC1 + FCC2

BCC

Sriharitha et al. (2013)

Al2 CoCrCuFeNi

LC

BCC

FCC

Qiu et al. (2014)

Alx CoCrCuy FeNi (x = 0.7–0.8 and y = 0.5)

AM

FCC

BCC

Fan et al. (2014b)

Alx CoCrCuy FeNi (x = 0.9 and y = 0.5)

AM

BCC

FCC

Fan et al. (2014b)

Alx CoCrCuFeNi (x = 16–20 at %)

MaS

BCC

FCC

Braeckman et al. (2015)

Alx CoCrCuFeNi (x = 1.5 and 3)

AM

BCC

FCC

Sun et al. (2018)

Al0.5 CoCrCuFeNi

AM

FCC1 ‘

FCC2

Jones et al. (2014)

Al0.5 CoCrCuFeNi

AM

FCC1 + FCC2

BCC

Karpets et al. (2015b)

AlCoCrCu0.5 FeNi

AM

BCC

FCC

Krapivka et al. (2015)

AlCoCrCu2 FeNi

AM

BCC

FCC1 + FCC2

Krapivka et al. (2015)

AlCoCrCu3 FeNi

AM

FCC1 + FCC2

BCC

Krapivka et al. (2015)

Al1.3 CoCrCuFeNi

LC

FCC

FCC + BCC

Liu et al. (2016f)

AlCoCrCuFeSi0.5

LSA

FCC

BCC

Wu et al. (2017b)

AlCoCrCux NiTi (x = 0.5–0.8)

AM

FCC

BCC

Wang et al. (2012a) (continued)

328

Appendix A

(continued) Composition

Processing Major route phase

Minor phase

References

Alx (CoCrFeMnNi)100x (x = 8–16 at %)

AM

FCC

BCC

He et al. (2014)

Al2 CoCrFeMo0.5 Ni

AM

BCC2

BCC1

Hsu et al. (2013a, b)

AlCoCrFeNbx Ni (x = 0.25 and 0.5)

LC

BCC

FCC

Lin et al. (2017a)

AlCoCrFeNb0.75 Ni

LC

BCC

FCC1 + FCC2

Lin et al. (2017)

Al0.5 CoCrFeNiSi0.2

AM

FCC

BCC(A2) + BCC (B2)

Zhang et al. (2015e)

AlCoCrFeNiTix (x = 0.5 and 1) IC

BCC1

BCC2

Zhou et al. (2007b)

Alx CoCrFeNiTi0.5 (x = 0.8–1)

AM

BCC1

BCC2

Dong et al. (2013b)

Al0.6 CoCrFeNiTi0.4

MA

BCC

FCC

Fu et al. (2013a)

AlCoCrFeNiTix (x = 0–2)

AM

BCC1

BCC2

Zhang et al. (2008a)

Alx CoCrFeNiTi (x = 1–2)

AM

BCC

B2

Zhang et al. (2009a)

Al0.4 Co1.5 CrFeNiTi0.3

MA

FCC

BCC

Shaofeng et al. (2014)

Al0.4 Co1.5 CrFeNiTi0.3

MA + S

FCC

BCC1 + BCC2

Shaofeng et al. (2014)

Al0.75 CoCrFeNiTi0.25

MA

BCC

FCC

Chen et al. (2015e)

Al0.75 CoCrFeNiTi0.25

MA + SPS

FCC

BCC

Chen et al. (2015e)

Al0 5 CoCrFex NiTi0.5 (x = 0.5 and 1.5)

AM

BCC + BCC + B2 FCC + σ

Lee and Shun (2016)

Al0 5 CoCrFe1.5 NiTi0.5

AM

BCC + FCC

BCC + B2

Lee and Shun (2016)

Al0 5 CoCrFe2 NiTi0.5

AM

FCC

BCC + B2

Lee and Shun (2016)

Al0.2 CoCrFeNiTi

AM

BCC

FCC + η

Lindner et al. (2017)

Al0.8 CoCrFeNiTi

AM

BCC + B2

FCC + η

Lindner et al. (2017)

Al1.5 CoCrFeNiTi

AM

BCC + B2

FCC

Lindner et al. (2017)

AlCoCrFeNiTix (x = 0.5 and 1.0)

LSA

FCC

BCC

Wu et al. (2017c)

AlCoCr1.5 Fe1.5 NiTi0.5

AM

BCC1

BCC2

Zhang et al. (2017h)

Alx CoCrFeNiTi1x (x = 0.5)

AM

FCC

BCC

Jiang et al. (2018d)

Alx CoCrFeNiTi1x (x = 0.8)

AM

BCC

FCC

Jiang et al. (2018d)

AlCoCrFeNiTi0.5

LC

FCC

BCC

Zhao et al. (2018a)

AlCox CrFeNiTi0.5

SC

x = 1, BCC1

BCC2

Wang and Zhang 2008

AlCox CrFeNiTi0.5

SC

x = 1.5, 2, and 3, BCC

FCC

Wang and Zhang 2008

AlCoCrFeNi2 Wx (x = 0, 0.2, and 0.3)

AM

FCC

BCC

Dong and Lu (2018) (continued)

Appendix A

329

(continued) Composition

Processing Major route phase

AlCoCrFeNiZr0.2

AM

AlCoCrFeNiZr0.4

Minor phase

References

BCC1 + FCC1

BCC2 + FCC2

Razuan et al. (2016)

AM

BCC1 + FCC1

FCC2

Razuan et al. (2016)

AlCoCrFeNiZr0.6

AM

BCC1 + FCC1

FCC2

Razuan et al. (2016)

AlCoCrFeNiZr0.8

AM

BCC1 + FCC1

BCC2 + FCC2

Razuan et al. (2016)

(AlCu)0.8 CoFeGax Ni (x = 0, 0.02, 0.04, 0.06, and 0.08)

AM

BCC

FCC

Li et al. (2018a)

Al19.49 Co19.49 Cu19.49

PC

BCC

FCC1 + FCC2

Cai et al. (2017)

MA

x = 0, BCC

FCC

Varalakshmi et al. (2010b)

Fe19.49 Ni19.49 Si2.55 AlCoCux NiTiZn

x = 8.33, FCC BCC AlCrCuFeMgNi4.75

x = 50, FCC

BCC

MA

BCC

BCC

Al0.1 Cr0.4 CuFe0.4 MnNi

AM

FCC1

FCC2 + BCC Rao et al. (2017)

Khanchandani et al. (2016)

Al0.2 Cr0.4 CuFe0.4 MnNi

AM

FCC1

FCC2 + BCC Rao et al. (2017)

Al0.3 Cr0.4 CuFe0.4 MnNi

AM

FCC1 + BCC1 + B2

FCC2

Rao et al. (2017)

Al0.4 Cr0.4 CuFe0.4 MnNi

AM

FCC + B2

BCC

Rao et al. (2017)

AlCrCuFeNbx Ni

AM

x = 0, FCC1

BCC1

Razuan et al. (2013)

AlCrCuFeNbx Ni

AM

x = 0.5, FCC1 + FCC2

BCC1

Razuan et al. (2013)

AlCrCuFeNbx Ni

AM

x=1 and 1.5, FCC1 + FCC2 + BCC1

BCC2

Razuan et al. (2013)

AlCrCuFeNiTix

AM

x = 0, FCC1

BCC1

Razuan et al. (2013)

AlCrCuFeNiTix

AM

x = 0.5 and 1, BCC1 + FCC1

BCC2

Razuan et al. (2013)

AlCrCuFeNiTix

AM

x = 1.5, BCC1 + BCC2

FCC1

Razuan et al. (2013)

Al0.3 CrFe1.5 MnNi0.5 Ti0.5

AM

BCC

FCC + CrNiFe

Ren et al. (2014) (continued)

330

Appendix A

(continued) Composition

Processing Major route phase

Minor phase

References

Al0.3 CrFe1.5 MnNi0.5 Ti

AM

BCC

FCC + Cr9 Al17

Ren et al. (2014)

AlMo0.5 NbTa0.5 TiZr

AM

BCC1

BCC2

Senkov et al. (2014a)

Al0.5 NbTa0.8 Ti1.5 V0.2 Zr

AM

BCC1

BCC2

Senkov et al. (2014b)

B5 (CoCrCuFeNi)95

PTAC

FCC

BCC

Liu et al. (2015d)

CoCrCuFeGdx Ni (x = 0 and 0.05)

AM

FCC1

FCC2

Zhang et al. (2017i)

CoCrCuFeGdx Ni (x = 0.1, 0.2, and 0.3)

AM

FCC1 + FCC2

HCP

Zhang et al. (2017i)

CoCrCuFeMnNi2

AM

FCC1

FCC2

Karpets et al. (2015c)

CoCrCuFeMnNi2

AM

FCC1

FCC2

Karpets et al. (2015c)

CoCrCux FeMnNi (x = 0.5, 0.75, and 1.0)

AM

FCC1

FCC2

Xian et al. (2018)

CoCrCu0.1 FeMoNi

AM

FCC

BCC

Wu et al. (2015b)

CoCrCu0.3 FeMoNi

AM

BCC

FCC

Wu et al. (2015b)

CoCrCu0.5 FeMoNi

AM

FCC1 + FCC2

BCC

Wu et al. (2015b)

CoCrCu0.8 FeMoNi

AM

FCC1 + FCC2

BCC

Wu et al. (2015b)

CoCr0.25 CuFeNi1.5 V0.25

MA + SPS

FCC1

FCC2

Wang et al. (2017a)

CoCrFeMnNiZrx (x = 0–0.3)

AM

BCC

FCC

Pauzi et al. (2013)

CoCrFeMnNiTax (x = 0.2, 0.4, and 0.6)

AM

BCC

FCC

Pauzi et al. (2016)

CoCrFeMo0.5 NiW0.5

MA

BCC

FCC

Shang et al. (2017)

CoCrFe Mo0.5 NiW0.5

MA + VHP

FCC1 + FCC2

δ+σ

Shang et al. (2017)

Cr2 MoNbTaVW

AM

BCC1

BCC2

Zhang et al. (2015c)

Al1.3 CoCrCuFeMn0.2 Ni

LC

FCC

FCC + BCC

Liu et al. (2016f)

AlCoCrCuFe2 Mo0.2 Ni

MA

BCC

FCC

Yuhu et al. (2013)

Al0.5 CoCrCuFeNiSi0.4

AM

FCC1 + FCC2

BCC

Liu et al. (2015e)

Al0.5 CoCrCuFeNiSi0.8

AM

BCC

FCC

Liu et al. (2015e)

Al0.5 CoCrCu0.5 FeNiSi0.2

AM

FCC

BCC + B2

Li et al. (2016b)

Alx CoCrCu1x FeNiSi0.2 (x = 0.4)

AM

FCC

BCC

Ma et al. (2017)

Alx CoCrCu1 x FeNiSi0.2 (x = 0.5)

AM, IC

FCC

BCC

Ma et al. (2017)

Alx CoCrCu1 x FeNiSi0.2 (x = 0.6)

AM

BCC

FCC

Ma et al. (2017)

Al0.5 CoCrCuFeNiSi1.2

GA

BCC

FCC

Yang et al. (2017)

AlCoCrCux FeNiTi0.5 (x = 0, 0.25, and 0.5)

IC

BCC1

BCC2

Zhou et al. (2008c)

Al0.5 CoCrCu0.5 FeNiTi0.5

SC

FCC

BCC

Wang et al. (2009a) (continued)

Appendix A

331

(continued) Composition

Processing Major route phase

AlCoCrCuFeNiTix

AM

AlCoCrCuFeNiTix

Minor phase

References

x = 0.5, BCC1 + FCC

BCC2

Hongfei et al. (2011)

AM

x = 1, BCC1 + FCC

BCC2

Hongfei et al. (2011)

Al2 CoCrCuFeNix Ti (x = 0–1.0)

LC

FCC

BCC

Qiu and Liu (2013)

AlCoCrx CuFeNiTi (x = 0.5–2.5)

AM

FCC1 + FCC2

BCC

Li et al. (2014)

Al0.5 CoCrCuFeNiVx (x = 0.4–2)

AM

FCC

BCC

Chen et al. (2006a)

AlCoCrCuFeNiVx (x = 0.5–1)

LSA

FCC

BCC

Zhang et al. (2015d)

Al0.5 CoCrFeMnNiZrx (x = 0.1–0.3)

AM

BCC

FCC

Pauzi et al. (2013)

AlCoCrFeNiTi0.5 Vx (x = 0–1)

AM

BCC

FCC + σ

Han et al. (2016)

FCC

BCC

Zhou et al. (2007a)

Al11.1 (CoCrCuFeMnNiTiV)88.9 IM

Composition

Processing route

Phase

References

Er33.33 Ho33.33 Tb33.34

AM + DC

HCP + trigonal

Yuan et al. (2017)

CoFeReRu

AM

HCP

Gao et al. (2016c)

Dy25 Er25 Ho25 Tb25

AM + DC

HCP + trigonal

Yuan et al. (2017)

Er25 Gd25 Ho25 Tb25

AM + DC

HCP + trigonal

Yuan et al. (2017)

Dy20 Er20 Gd20 Ho20 Tb20

AM + DC

HCP

Yuan et al. (2017)

DyGdHoTbY

AM

HCP

Luznik et al. (2015)

DyGdLuTbY

AM

HCP

Takeuchi et al. (2014b)

DyGdLuTbTm

AM

HCP

Takeuchi et al. (2014b)

GdHoLaTbY

AM

HCP

Zhao et al. (2016)

Hf27.5 Nb5 Ta5 Ti35 Zr27.5

AM

Orthorhombic

Lilensten et al. (2014)

Ir0.19 Os0.16 Pt0.22 Rh0.17 Ru0.26

TP

HCP + FCC

Yusenko et al. (2017)

Ir0.23 Os0.10 Pt0.25 Rh0.22 Ru0.19

TP

HCP + FCC

Yusenko et al. (2017)

Ir0.19 Os0.22 Re0.21 Rh0.20 Ru0.19

TP

HCP

Yusenko et al. (2017) (continued)

332

Appendix A

(continued) Composition

Processing route

Phase

References

B2 (Hf, Ta, Ti, V, Zr)

MaS

HCP

Maryhofer et al. (2018)

Ir0.18 Os0.18 Pt0.16 Re0.17 Rh0.16 Ru0.15

TP

HCP + FCC

Yusenko et al. (2017)

A—annealing; AM—arc melting; BS—Bridgman solidification; CR—cold rolling; DC, drop casting; DLD—Direct laser deposition; EBW—electron beam welding; ED—electrospark deposition; GA—gas atomization; HE—hot extrusion; HF—hot forging; HPS—high-pressure sintering; HPT—high-pressure torsion; HR—hot rolling; HT—heat treatment; IM—induction melting; IC— injection casting; SC—suction casting; MeS—melt spinning; LM—levitation melting; LENS— laser engineered net shaping; LC—laser cladding; LD—laser deposition; LSA—laser surface alloying; MA—mechanical alloying; MaS—magnetron sputtering; MWPP—microwave processing of powder particles; PC—plasma cladding; PM—powder metallurgy; PS—plasma spraying; PVD—physical vapor deposition; PTAC—plasma transferred arc cladding; S—sintering; SA— solution annealing; SEBM—selective electron beam melting; SPS—spark plasma sintering; SQ— splat quenching; TP—thermal decomposition of precursors; TMP—thermomechanical processing; VA—vacuum annealing, VHP—vacuum hot pressing; WQ—water quenching; ZM—zone melting

Appendix B

See Tables B.2, B.3 and B.4.

© Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8

333

B2 –

BCC B2 + BCC BCC B2

B2 BCC BCC B2 B2 B2

B2 FCC

LENS AM AM IM AM AM AM AM AM AM AM IM SC BS Electro spark deposition GTAW cladding AM + LENS

AlCrFeNi

Al21.67 Cr21.67 Fe21.67 Ni35

Alx CrFeNi

AlCrFeNi

AlCrTiV

Al13 Fe36 Mn33 Ni18

(CoCrFe)100x Alx

AlCoCrCuNi

AlCoCrCuNi

AlCoCrFeNi

AlCoCrFeNi

AlCoCrFeNi

AlCoCrFeNi

AlCoCrFeNi

AlCoCrFeNi

AlCoCrNiW

Alx CoCrFeNi (x = 0.52, 0.69, and 1.06)

B2

B2

BCC

FCC

B2

BCC + B2

W

–

–

(continued)

Li et al. (2018c)

Lin and Cho (2008)

Li et al. (2013c)

Zhang et al. (2012b)

Qiao et al. (2011)

Manzoni et al. (2013b) –

Wang et al. (2008) σ

Hsu et al. (2013a)

Munitz et al. (2013)

Hsu et al. (2007)

Zhu et al. (2016)

Wang et al. (2016 g)

Qiu et al. (2017)

Singh and Subramaniam (2014)

Chen et al. (2017c)

Zhang et al. (2018e)

Borkar et al. (2017)

Jin et al. (2018)

Borkar et al. (2017)

Kulkarni et al. (2018)

References

–

B2

B2

FCC

B2

B2

–

B2

BCC

L12

AM

Al19 Co20 Fe20 Ni41 B2

LENS

BCC

–

Minor phase

AlCoFeNi

B2

B2

AM + annealed

AlCoNi 1000 °C 48 h

Major phase

Processing route

Composition

Table B.2 B2 phase in HEAs

334 Appendix B

B2 σ

FCC FCC BCC BCC BCC

FCC B2 + BCC FCC B2 FCC

AM + suction casting AM + suction casting AM + suction casting AM + suction casting AM + suction casting AM AM LENS DMD DMD Czochralski process AM AM IM Bridgeman solidification LENS Magnetron sputtering AM AM

Al2 (CoCrFeNi)14

Al2 (Co4 Cr3 Fe3 Ni4 )14

Al2 (CoCrFe2 Ni)14

Al2 (CoCr2 FeNi)14

Al3 (CoCrFeNi)14

Al14 Co4 Cr34 Fe34 Ni14

Alx CoCrFeNi (x = 0.75, 1.0, and 1.75)

AlCoCrFeNi

Al1.7 CoCrFeNi0.3

Al0.7 CoCrFeNi0.3

Al28 Co20 Cr11 Fe15 Ni26

Al10 Co22.5 Cr22.5 Fe22.5 Ni22.5

Al20 Co25 Cr25 Ni25 Si5

AlCoCrFeNi2.1

AlCoCrFeMn

AlCo1x Crx FeNi (x = 0.8, 0.6, and 0.4)

Al0.3 CoCrFeNi

Al0.3 CoCrFeNi

Alx CoCrFeNi (x = 1–3)

B2

FCC

BCC

B2

FCC

BCC (A2)

B2

BCC

BCC

BCC

AM

AlCoCrx FeNi (x = 1.8 and 2.0)

–

B2

(continued)

Li et al. (2010a)

Shun and Du (2009)

Liao et al. (2017)

Borkar et al. (2017) B2

Feuerbacher et al. (2017) BCC + FCC

Lu et al. (2014)

Butler et al. (2015)

Butler et al. (2015)

Feuerbacher (2016)

Sistla et al. (2015)

Sistla et al. (2015)

Kunce et al. (2015)

Cieslak et al. (2018)

Zhou et al. (2018c)

Ma et al. (2018)

Ma et al. (2018)

Ma et al. (2018)

Ma et al. (2018)

Ma et al. (2018)

Lu et al. (2018b)

Li et al. (2018c)

References

B2

B2

BCC

B2

B2

BCC (A2)

B2

B2

B2

B2

B2 + FCC

BCC + B2

BCC + B2

B2

B2

BCC

AM + LENS

Alx CoCrFeNi (x = 1.16)

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

Appendix B 335

B2

BCC B2

AM + MS IM AM AM IC AM AM AM AM TIG overlay AM AM

AlCoCuFeNi

AlCoCuFeNi

AlCoCuFeNi

AlCoFeMnNi

Alx CrCuFeNi2 (x = 0.2–2.5)

AlCrFeNi2 Ti0.5

Al10 Cr18 Fe36 Mn21 Ni15

AlCrFeMox Ni (x = 0.1, 0.25, 0.5, and 0.75)

AlCrFeMox Ni

Al0.3 CrFe1.5 MnNi0.5

AlCrFeNi1.5 Mo0.2

AlCrFeNi1.2 Mo0.2

Xiao et al. (2017)

BCC + B2

B2

BCC

(continued)

Dong et al. (2016b)

Dong et al. (2016b)

Dong et al. (2013a)

BCC + σ

σ

x = 0.8–1.0, B2 + FCC

Hsieh et al. (2009)

B2

x = 0–0.5, BCC

Li et al. (2016c)

Shaysultanov et al. (2017)

Jiang et al. (2015b)

Guo et al. (2013b)

B2

B2

B2

BCC (A2)

FCC

Zuo et al. (2017)

Singh and Subramaniam (2014)

FCC2 + B2

B2

Yu et al. (2016b)

Zhang et al. (2010a)

Lucas et al. (2011), Chen and Kao (2012)

Li et al. (2009)

Kao et al. (2009)

Wang et al. (2014b)

References

FCC

FCC

–

–

BCC

BCC

B2

x0.8, BCC + B2

BCC

FCC

FCC1

B2

Laser cladding

Al3 CoCrFeNi

B2

AM

Al2 CoCrFeNi

B2

B2

B2

x = 0.875–1.25, FCC x = 1.5–2, FCC

–

x = 0.9–1.8, B2 AM

Alx CoCrFeNi AM

B2

x = 0.5–0.7, FCC

AM

Alx CoCrFeNi

Alx CoCrFeNi (x = 1.5–3)

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

336 Appendix B

B2 FCC FCC B2

AM AM AM AM AM + suction casting AM AM AM AM AM

Al2 CuCrFeNi2

Al13 Fe36 Mn33 Ni18 Ti2

Al13 Fe36 Mn33 Ni18 Ti4

Al13 Fe36 Mn33 Ni18 Ti6

AlNbTiVZr

S(CoCrFeAl)100x Nix (x = 0–20)

(CoCrNiAl)100x Fex (x = 0–33.33)

(CoFeNiAl)100x Crx (x = 0–33.33)

(CrFeNiAl)100x Cox (x = 0–33.33)

AlCoCrCuFeNi

AlCoCrCuFeNi

AlCoCrCuFeNi

Tong et al. (2005b)

BCC + FCC FCC + BCC BCC FCC

x > 1, B2 x = 0.5–2.5, B2 x > 2.8, B2 x = 2.5 and 5, B2

B2 B2

AM Sputtering MA AM AM IM AM

Alx CoCrCuFeNi

Alx CoCrCuFeNi

Alx CoCrCuFeNi

Al2 CoCrCuFeNi

Al2 CoCrCuFeNi

Al23 Co15 Cr23 Cu8 Fe15 Ni16

AlCoCrFeNiTi

B2

B2

Welk et al. (2013)

BCC

B2

LENS

Zhang et al. (2009a)

BCC + FCC

(continued)

Manzoni et al. (2016)

Karpets et al. (2015b)

FCC1 + FCC2 BCC

Wu et al. (2006)

–

Sriharitha et al. (2013)

Yeh et al. (2004b)

Shaysultanov et al. (2013)

Cu

B2 + BCC + FCC

IM

Hsu et al. (2007), Zhang et al. (2010b)

Zhu et al. (2016)

Zhu et al. (2016)

Zhu et al. (2016)

Zhu et al. (2016)

Vishwanadh et al. (2016)

Wang et al. (2016g)

Wang et al. (2016g)

Wang et al. (2016g)

Borkar et al. (2016b)

Dong et al. (2016b)

References

FCC

B2

B2

B2

B2

HCP

B2

B2

B2

BCC (A2)

B2

Minor phase

B2

BCC

BCC

BCC

BCC

FCC

BCC

AM

AlCrFeNix Mo0.2 (x = 0.5 and 0.8)

Major phase

Processing route

Composition

Table B.2 (continued)

Appendix B 337

x > 16, B2 B2

B2 B2

AM Laser RSP IM Splat quenching MeS Laser surface alloying AM AM AM Laser cladding AM

Alx (CoCrFeMnNi)100x

Al2 CoCrFeNiSi

AlCoCrFeNiTi0.5

AlCoCrCuFeNi

AlCoCrCuFeNi

AlCoCrNiTiV

Al1.25 CoCrCuFeNi

Al2.5 CoCuFeNiSnx (x = 0 and 0.03)

Al3 CoCrCuFeNi

Alx CoCrFeNiTi0.5 (x = 2 and 2.5)

Al10 Co10 Cr20 Fe25 Mn15 Ni20 AM + HIP + annealing + cooling Casting Casting MeS MeS

AlMo0.5 NbTa0.5 TiZr

CoCrCuFeNiSn0.5

CoCrCuFeNiSn

CoCrCuFeNiSn0.5

CoCrCuFeNiSn

AlCoCuCrFeNi

B2

MA

AlCoCrFeNiTi

FCC

FCC

FCC

FCC

(continued)

Bashev and Kushnerov (2014)

Bashev and Kushnerov (2014) B2

Bashev and Kushnerov B2 + BCC

Bashev and Kushnerov (2014)

Senkov et al. (2018)

Xiao et al. (2017)

Gorban et al. (2014)

Zhao et al. (2018a)

Karpets et al. (2015b)

Liu et al. (2016e)

Munitz et al. (2018)

B2

B2

B2

FCC

BCC + B2

B2

–

B2

B2

B2

BCC

Kourov et al. (2015)

Ivchenko et al. (2014)

Yu et al. (2013)

Zhang et al. (2011a)

He et al. (2014)

Zhang et al. (2010c)

References

(Ni, Co) Ti2 + α-Ti Cai et al. (2016b)

FCC

–

BCC

BCC

–

FCC

Minor phase

FCC

BCC

B2

BCC

FCC

B2

B2

Major phase

Processing route

Composition

Table B.2 (continued)

338 Appendix B

FCC2

L12 L10 B2 + BCC

B2 + FCC1

FCC FCC FCC + L12 L12 + FCC

AM AM DMD AM + copper injection fast solidification MA + SPS AM LENS

AlCoCrFeMo0.5 NiSiTi

AlCoCrFeNi

AlCoCrFeNi

Al0.4 CoCu0.6 NiSix (x = 0.1)

AlCoCuNiZn

Al15 Cr10 Co35 Ni35 Si5

AlCrCuFeNi2

FCC FCC

AM IM IM

Al0.5 CoCrCuFeNi

Al8 Co17 Cr17 Cu8 Fe17 Ni33

Al8 Co17 Cr17 Cu8 Fe17 Ni33

FCC

FCC

MA + SPS

CrFeMnTiV IM + annealing + furnace cooling

FCC

AM + solution treatment 1100 °C 5 h + cold-rolling (80%) + 1100 °C 1 h + 800 °C aging 1 h and 24 h

L12

FCC + B2

L12

L12

L12

L12

L12 + BCC

L12

L12

L12

B2

CoFeCrNiTi0.2

Al0.8 CrCuFeNi2

B2

AM

Alx Si0.2 CrFeCoNiCu1x (x = 0.6, 0.8, and 0.9)

(continued)

Manzoni et al. (2015)

Manzoni et al. (2013a)

Hemphill et al. (2012)

Takeuchi et al. (2017)

Song et al. (2018)

Han et al. (2018b)

Borkar et al. (2016a)

Butler et al. (2015)

Mohanty et al. (2014)

Chen et al. (2018b)

Sistla et al. (2015)

Li et al. (2008b)

Huang et al. (2004)

Li et al. (2016b)

Huang et al. (2004)

FCC1 + FCC2

BCC

AM

AlCrFeMo0.5 NiSiTi B2

Chen et al. (2006b)

BCC

x = 0–0.6, FCC + B2

AM

Al0.5 CoCrCuFeNiTix

References

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

Appendix B 339

Manzoni et al. (2015) Manzoni et al. (2013b)

L12 L12 L12

L12 L12

L12 L12 L12 σ

AM + aging at 900 °C for 50 h FCC FCC

AM + homogenized 1200 °C FCC 4 h + cold-rolling + annealing 1000 °C 4 h + aging 750, 775, 800, and 825 °C 0.5–1022 h FCC

FCC

BCC

AM

IM IM AM + suction casting + annealing

Al10 Co25 Cr8 Fe15 Ni36 Ti6

Al4 (CoCrFeNi)94 Ti2

Al10 Co25 Cr8 Fe15 Ni36 Ti6

(CoCrFeNi)94 Ti2 Al4

Alx Si0.2 CrFeCoNiCu1 x (x = 0.2 and 0.4)

(CoCrFe)40 Ni45 x (AlTi)15 Hfx (x = 0 and 0.2 AM at %) IM + homogenization + water FCC quenching B2

IM + homogenization + cooling in furnace AM + cold-rolling + aging + FCC quenching FCC

AM + aging at 900 °C for 5–50 h

Al0.3 Co1.5 CrFeNi1.5 Ti0.2

Al8 Co17 Cr14 Cu8 Fe17 Ni34.8 Mo0.1 Ti1 W0.1

Al8 Co17 Cr17 Cu8 Fe17 Ni33 W0.1 Mo0.1 Ti1

AlCoCrFeNi

Al2 (CoCr2 FeNi)14 600–800 °C 2 h

FCC

L12

AM + aging at 900 °C for 50 h FCC

Al0.2 Co1.5 CrFeNi1.5 Ti0.3

σ

FCC + L12

L12

AM + aging at 900 °C for 50 h FCC

(continued)

Ma et al. (2018)

Manzoni et al. (2016)

Zhang et al. (2018d)

Li et al. (2016b)

He et al. (2016a)

Manzoni et al. (2016)

Zhao et al. (2018c)

Daoud et al. (2015a)

Chang and Yeh (2015)

Chang and Yeh (2015)

Chang and Yeh (2015)

Manzoni et al. (2016)

Al0.1 Co1.5 CrFeNi1.5 Ti0.4

References

L12

Minor phase

IM + homogenization + water FCC quenching

Al8 Co17 Cr17 Cu8 Fe17 Ni33

Major phase

Processing route

Composition

Table B.2 (continued)

340 Appendix B

L10 σ σ σ

FCC + L12 BCC + FCC x = 0.3 FCC + BCC

AM AM AM

AM

Al15 Cr10 Co35 Ni35 Si5

Al0.3 CrFe1.5 MnNi0.5

Alx CrFe1.5 MnNi0.5

AlCrFeMox Ni

AlCrFeMox Ni (x = 1.0 and 1.25)

CoCrCuFeNi

BCC + B2

FCC2 + σ σ

Cr23 C6 + σ –

σ FCC1 FCC1 FCC1 FCC1 FCC1 + FCC2

FCC FCC σ

MA + SPS MA + SPS MA + SPS MA + SPS IC AM + annealing 850C 12, 24, FCC and 48 FCC

AM

AM MA + sintering 1150 °C MA + VHP AM

CoCr0.8 CuFeNi1.2

CoCr0.5 CuFeNi1.5

CoCr0.2 CuFeNi1.8

CoCrCuFeMn

Cox (CrFeMnNi)(100 x) (x = 5)

(CoCrFeMn)100x Nix (x = 0–12.5)

CoCrFeMnNi

CoCrFeMnNi

CoCrFeMnV

σ

σ

σ

FCC2 + σ

FCC2 + σ

FCC2 + σ

σ

x = 0.8–1.0, B2 + FCC

x = 0.5, BCC

L12

FCC

MA + SPS

AlCoCuNiZn

Lee and Shun (2013)

σ

BCC + B2 + FCC

Al0.5 CoCrNiTi0.5 AM

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

(continued)

Karpets et al. (2015a)

Xie et al. (2018)

Mane and Panigrahi (2018)

Zhu et al. (2016)

Zhu et al. (2017a)

Otto et al. (2013b)

Wang et al. (2016e)

Wang et al. (2016e)

Wang et al. (2016e)

Wang et al. (2016e)

Li et al. (2016c)

Dong et al. (2013a)

Tsai et al. (2013c)

Tsai et al. (2013c, d)

Butler et al. (2015)

Mohanty et al. (2014)

References

Appendix B 341

AM AM AM MA + SPS IC AM AM

CoCrFeNiV

CoCrFeNiV

CrFe1.5 MnNi0.5

CrFeMnx MoV (x = 0.5 and 1.0)

CoFeMnNiV

CrFeNiV0.5 Wx

(x = 0.25–1)

Lee et al. (2008a), Tsai et al. (2013c)

σ

BCC + σ + Mn3 Co7 σ σ σ σ

BCC FCC x = 0–0.5, FCC x = 1–1.5, BCC x = 0.5–1.5, BCC x = 2, BCC + FCC

Laser cladding MA + sintering 1150 °C AM AM

Alx CoCrFeMo0.5 Ni

AlCox CrFeMo0.5 Ni

σ

BCC + σ

AlCoCrFeMnNi

FCC

(continued)

Hsu et al. (2010b)

Hsu et al. (2013a, b)

Mane and Panigrahi (2018)

Zheng et al. (2013)

Jiang et al. (2015c)

Jiang et al. (2015c)

Jiang et al. (2015c)

FCC + BCC

σ σ

Otto et al. (2013b)

σ

FCC FCC

Raza et al. (2018)

σ

FCC

Tsai et al. (2017)

FCC

σ

Salischev et al. (2014)

FCC

σ

Tsai et al. (2017)

FCC

σ

CrFeMoTiW

CrFeNi2 V0.5 Wx (x = 0.75–1.0)

(x = 0.25–0.5) AM

BCC

AM

CoCrFeNiMo

CrFeNi2 V0.5 Wx

σ

x = 0.5, FCC

AM

CoCrFeNiMox

Shun et al. (2012a)

Shun et al. (2013)

σ

FCC

AM

CoCrFeMo0.85 Ni x = 0.85, FCC

References

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

342 Appendix B

σ

x = 0–1.5, BCC + B2

AM AM AM AM AM AM AM

MA + VHP

AlCox CrFeMo0.5 Ni

AlCoCrx FeMo0.5 Ni

AlCoCrFex Mo0.5 Ni

AlCoCrFeMo0.5 Nix

AlCoCrFeMox Ni

Al0.5 CoCrFeMox Ni (x = 0.2, 0.3, 0.4, and 0.5)

AlCoCrFeMoNix

CoCrFeMnNiN0.1

CoCrFeMnNiV

Karpets et al. (2015a) Stepanov et al. (2015c) Stepanov et al. (2015c) Chou et al. (2010b)

FCC FCC σ σ FCC x > 0.1, σ

σ σ FCC FCC σ

AM AM AM AM AM AM

CoCrFeMnNiV

CoCrFeMnNiV

CoCrFeMnNi1.5 V

CoCrFeMnNiV0.5

CoCrFeMnNiV0.75

Co1.5 CrFeNi1.5 Ti0.5 Mox

FCC

Stepanov et al. (2015c)

–

σ

AM

CoCrFeMnNi0.5 V

(continued)

Karpets et al. (2015a)

Karpets et al. (2015a)

Salischev et al. (2014)

FCC

σ

AM

Xie et al. (2018)

Cr2 N + Cr23 C6 + σ

Σ

x = 1.5–2, BCC + B2 + FCC

Hsu et al. (2013a)

Zhuang et al. (2018)

Hsu et al. (2013a)

Juan et al. (2013)

Hsu et al. (2010a), Hsu et al. (2013a)

Hsu et al. (2011), Hsu et al. (2013a)

Hsu et al. (2013a)

References

FCC

σ

σ

x = 0.5–0.9, BCC + B2

x = 0–1, BCC + B2

σ

x = 0, 0.5, and 1, B2 BCC + σ

σ

x = 0.6–2, BCC + B2

FCC

σ

x = 0–2, BCC + B2

x = 2, BCC + B2 + FCC σ

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

Appendix B 343

Zhang et al. (2008a) Feng et al. (2018b)

σ σ Laves + L21

FCC BCC + FCC

AM AM AM

Al1.5 CrFeMnTi

AlCrNbTiV

AM AM

CoCrFeNiNb

CoCrFeNiNbx (x = 0.25 and 0.45)

Laves C36

AM AM

CoCrFeNiHf

CoCrFeNiTa

FCC

BCC

Jiang et al. (2014)

Laves + R + σ FCC

IM

Laves C14

Shun et al. (2012b)

Laves + σ

x = 0.5, FCC

AM

CoCrFeNiTi0.5

(continued)

Tsai et al. (2017)

Tsai et al. (2017)

Huo et al. (2018b)

CoCrFeNiTix

Ai et al. (2018) Laves

Laves

FCC

AM

FCC

Jiang et al. (2017b)

Tsai et al. (2017)

AM

FCC

Laves

FCC

Liu et al. (2015a)

Qin et al. (2018b)

Stepanov et al. (2018b)

Yurchenko et al. (2017)

Stepanov et al. (2015a)

CoCrFeNiTax (x = 0.2, 0.3, 0.395, 0.4, and 0.5)

Laves

FCC

Laves

FCC

Laves

Laves

Laves C14

Laves

Laves

CoCrFeNiTix (0.1, 0.3, 0.43, 0.5, and 0.7)

CoCrFeNiNbx (x = 0.5, 0.75, 1, and 1.2)

FCC

CoCrFeNbx Ni (x = 0.103–0.412) Laves C14

Laves AM

(CoCrCuFeNi)100x Nbx (x = 16 at %)

FCC

B2

AM + HPT AM

BCC

AM

AlCrx NbTiV (x = 0.5, 1, and 1.5)

AlNbTiVZr0.5 (CoCrCuFeNi)100x Nbx (x = 4, 8, and 12 at %)

BCC

AlCr1.5 NbTiV

BCC

BCC

Han et al. (2016)

Chen et al. (2006a)

AM

References

CoCrCuFeMnNiTiV

σ

AlCoCrFeNiTi0.5 Vx (x = 1.5–2)

Minor phase

FCC + BCC

AM

Al0.5 CoCrCuFeNiVx (x = 0.6–1)

Major phase

Processing route

Composition

Table B.2 (continued)

344 Appendix B

AM

CoCrFeNiTax (x = 0.1, 0.2, 0.3, and 0.4)

x > 3/5, Laves

FCC1 (Cu-rich) + FCC2 (Co-rich) + BCC (β-Ti–rich)

AM

AM Laser cladding AM

CoCuy FeNiTix

CoFeNi2 V0.5 Nb0.75

CoFeNi2 V0.5 Nb0.75

CoFeNi2 V0.5 Nb

CoFeNi2 W0.5 Tx (x = 0.2 and 0.4)

Fazakas et al. (2014) Otto et al. (2013b)

Laves σ, Laves HCP (ZrdTi)

BCC BCC FCC BCC + Laves BCC Laves

IM IM IC AM AM AM + suction casting

HfNbTiVZr

CrHfNbTiZr

CrFeMnNiTi

CrNbTaTiZr

CrNbTiVZr

CuNiHfTiZr

–

Laves C15

(continued)

Park et al. (2016)

Yurchenko et al. (2017)

Poletti et al. (2016)

Fazakas et al. (2014)

Poletti et al. (2015)

Laves + HCP

BCC1 + BCC2

AM

CrNbTaTiZr

Laves

x/y = 1, Laves

FCC1 + FCC2

SC

CoCuy FeNiTix

Samal et al. (2014)

FCC

Jiang et al. (2016a)

Jiang et al. (2016c)

Jiang et al. (2016b)

Laves

Laves

Laves

Laves

Mishra et al. (2012)

Zhang et al. (2018c)

Vrtnik et al. (2018)

Tsai et al. (2017)

Jiang et al. (2018b)

References

CoFeNi2 W0.5 T0.6

FCC

FCC

FCC

BCC2 + Laves

BCC

AM + annealing 800, 1000, and 1200 °C

Laves

FCC

AM + drop casting

CoCrMoNbTi0.4

BCC

FCC

CoCrFeNiZrx (x = 0.4, 0.45, and 0.5)

Laves C15

Laves

Minor phase

AM

Laves

FCC

Major phase

CoCrFeNiZr

CoCrFeNiTax (x = 0.5 and 0.75)

Processing route

Composition

Table B.2 (continued)

Appendix B 345

AM SC SC AM AM

AlCoCrFeNbx Ni (x = 0.25–0.75)

AlCoCrFeNbx Ni (x = 0.25–0.75)

AlCoCrFeNiTi0.5

Alx CoCrFeNiTi0.5

AlCoCrFeNiZr0.008

Laves

Laves

BCC Laves

Laves C14 + Laves C15 FCC + BCC + B2

AM AM Plasma transferred arc cladding TIG cladding AM MS LENS

Alx CrNbTiVZr (x = 0.5, 1, and 1.5)

AlCoCuFeNiTi

CoCrCuFeNiNb

CoCrFeMnNbNi

CoFeMnTix Vy Zrz (x = 0.5–2.5, y = 0.4–3, and z = 0.4–3)

CrHfNbTiTaZr

CrFeNiTiVZr

C14 Laves

BCC

Laves C14

FCC

Kunce et al. (2013)

α Ti

(continued)

Gorban et al. (2016)

Kao et al. (2010)

Huo et al. (2015)

Cheng et al. (2014b)

Xiao et al. (2017)

Yurchenko et al. (2017)

Pi et al. (2011)

Chen et al. (2016c)

Dong et al. (2013b)

Qiao et al. (2011)

Ma and Zhang (2012)

Zhang et al. (2012c)

Zhang et al. (2009a)

Zhang et al. (2008a)

Fazakas et al. (2014)

References

Laves

–

Laves

Laves

Laves

BCC1 + BCC2

FCC

BCC

Laves AM

B2 + Laves

AlCrCuFeNiTi

BCC

x = 0.5–0.8, FCC + BCC Laves

BCC

BCC

AlCoCrFeNiZrx (x = 0.3–0.5)

AlCoCrFeNiZr0.05

Laves

x = 0.5, B2 + BCC + FCC

AM

Alx CoCrFeNiTi Laves

x = 3, Laves

BCC1 + BCC2

AM

AlCoCrFeNiTix

BCC

Unknown phase

BCC

IM

HfNbTiVZr

Minor phase

Major phase

Processing route

Composition

Table B.2 (continued)

346 Appendix B

Laves + unknown phase

BCC1 + BCC2

HfMoNbTaTiVWZr AM

Laves

Laves

BCC1 + BCC2 + FCC Laves

AM

AlCoCrCuFeNiTi

Laves

BCC1 + BCC2

BCC + FCC

AM

CrMo0.5 NbTa0.5 TiZr

Minor phase

Major phase

FCC + BCC + B2

AM

CrMo0.5 NbTa0.5 TiZr

Al0.5 CoCrFeMnNiTax (x = 0.2, 0.4, and 0.6) AM

Processing route

Composition

Table B.2 (continued)

Gao et al. (2015)

Pauzi et al. (2016)

Xiao et al. (2017)

Senkov and Woodward (2011)

Senkov et al. (2013c, 2012b)

References

Appendix B 347

AM

Al4 CoNiPdPt

AlCrCuNiZr

IM

AM

MA + SPS

AlCuMgMnZn

(AlCuMnZn)100x Mgx

AlFeCrCuMg0.5

Al-Mn quasicrystal

x = 20, HCP

HCP HCP BCC

AM

AM + annealing

MA + vacuum hot pressing

Al15 Hf25 Sc10 Ti25 Zr25

Al2 NbTi3 V2 Zr

AlFe-type ordered phase + Cu2 Mg

Zr3 Al + Ti2 ZrAl

Do 19

(Zr, Sc)2 Al

BCC

Cu2 Mg

Al-Mn quasicrystal, Mg, Mg7 Zn3

× 6 = 20, HCP

AlFe-type ordered phase + BCC

Quasicrystal

HCP

Al15 Hf25 Sc10 Ti25 Zr25

AlFeCuCrMg1.7

AlFeCuCrMg

Laser cladding

AlCrSiTiV

(continued)

Tan et al. (2016b)

Rogal et al. (2017c)

Rogal et al. (2017c)

Maulik et al. (2016)

Li et al. (2010b)

Li et al. (2011)

Huang et al. (2011)

Lin et al. (2015a)

FCC + L21

BCC

AM

Al5 Cr32 Fe35 Ni22 Ti6

(Ti, V)5 Si3 , Al8 (V, Cr)5

AlCu2 Zr

FCC + BCC

AM BCC

Wang et al. (2016f)

–

CsCl structure

Takeuchi et al. (2016b)

Shon et al. (2015)

Al3 Ni + FeAl3 + Al

Laser cladding

AlCoCrFeNi

BCC1 + BCC2

AM

Al20 Be20 Fe10 Si15 Ti35

Zhang et al. (2017j)

BCC + M3 B

Kokai et al. (2018)

W-rich phase + Cr-rich phase

MA + SPS

W0.25 Ta0.24 V0.25 Cr0.26

Tsau et al. (2009)

Ordered HCP

Si3 Ti5 + unknown structure

FCC

AM

BCoCrFe

Gao et al. (2016c)

References

Fe2 Ti

FCC

AM

CoFeNiTi

Unknown phase

Minor phase

Waseem et al. (2018)

HCP

AM

CoReRuV

V-rich phase

Major phase

Processing route

Composition

Table B.3 Other intermetallic compounds in HEAs

348 Appendix B

FCC

FCC FCC

AM

Heating + quenching + SPS

AM

AM

Laser cladding

AM

AM

AM

BCoCrFeNi

(BiSbTe1.5 Se1.5 )1 x Agx (x = 0–1.2 at %)

CoCrFeHf0.55 Ni2.1

CoCrFeNb0.74 Ni2.1

CoCrFeNiBx (x = 0.5, 0.75, 1, and 1.25)

CoCrFeNiCx (x = 0.05, 0.1, 0.2, 0.3, and 0.5)

CoCrFeNi2.1 Ta0.65

Cox CrFeNiTi0.3 (x = 0.8 and 0.6)

CoCrFeNiTi

Co1.5 CrFeNi1.5 Ti0.5

CoCrFeNiZr0.45

CoCrFeNiZr0.4

CoCrFeNiZr0.35

CoCrFeNiZr0.3

CoCrFeNiZr0.25

CoCrFeNiZr0.2

CoCrFeNiZr0.15

CoCrFeNiZr0.1

FCC + Laves

FCC + Ni7 Zr2 + Laves

–

Ni7 Zr2

(continued)

Sheikh et al. (2017)

Tsai et al. (2017)

AM

CoCrFeNiZr0.05

Tsai et al. (2017)

BCC + YNi

Y(Fe, Co, Ni)3

AM

CoCrFeNiY FCC

FCC

AM + aging at 900° C for 50 h

Chang and Yeh (2015)

Laves C14 + η

χ

AM

Hung et al. (2018)

Lu et al. (2017a)

Huang et al. (2018)

Zhang et al. (2016d)

Lu et al. (2017a)

Lu et al. (2017a)

Fan et al. (2016)

Zhang et al. (2017j)

References

η

σ+η

FCC

M 7C 3

M2 B (M = Fe, Co, Ni, Cr)

(Co, Ni)2 Nb

Ni7 Hf2

–

M3 B

Minor phase

FCC

(Co, Ni)2 Ta

FCC

FCC

Sb2 SeTe2 type solid solution

Major phase

Processing route

Composition

Table B.3 (continued)

Appendix B 349

AM

Co2 Mox Ni2 VWx (x = 0.5)

BCC

(Nb, Zr)Cr2 + ZrV2

AM

Cold crucible levitation melting

AM

MA + SPS

Cr20 Nb20 Ti20 V20 Zr20

HfNbSi0.5 TiV

HfNbNiTaV

Tix(W0.25 Ta0.24 V0.25 Cr0.26 )100x (x = 4 at %) BCC BCC BCC

Tix(W0.25 Ta0.24 V0.25 Cr0.26 )100 x (x = MA + SPS 7 at %)

LENS

Laser cladding + annealing 800, 1000, and 1200 °C

MoNbTiVZr

MoNbTiWZr

W-rich phase

BCC

BCC

TiCo

BCC

AM

CoNbTaTiV

Wang and Liu (2016)

HfNi + Hf2 Ni7

Tix W1 x

NbTi4

(continued)

Zhang et al. (2017d)

Kunce et al. (2014)

W-rich phase + Ti–rich phase Waseem et al. (2018)

Cr-rich phase + Ti–rich phase Waseem et al. (2018)

Zhang et al. (2016b)

Eshed et al. (2018)

Wang and Liu (2016)

(Hb, Nb, Ti)-Si

BCC

FCC + μ

Co2 Mox Ni2 VWx (x = 1, 1.5, and 1.75)

Jiang et al. (2016d)

FCC

μ

μ

Wang and Liu (2016)

HfCo

Co2 Mox Ni2 VWx (x = 0.6 and 0.8)

FCC

BCC

Zuo et al. (2017)

AM

CoHfNbTaV

FCC

BCC

Cai et al. (2018)

AM

CoFeMnNiSn

BCC + Co2 MnSn

Laser cladding

CoCrNiTi0.5 V

Tsai et al. (2017)

(Ni, Co)Ti2 + Ti–rich

AM

CoCrMoNbTix (x = 0, 0.2, 0.4, 0.5, and 1.0)

Zhang et al. (2017k)

μ

AM

CoCrFeNiW

Poletti et al. (2017)

Lu et al. (2017a)

References

Cr2 Nb + Co2 Ti

FCC

FCC BCC

(CodFe)7 W6 type phase

Ni7 Zr2

AM + annealing

FCC

Minor phase

AM

Major phase

CoCrFeNiW0.3

Processing route

CoCrFeNi2.1 Zr0.6

CoCrFeNiZr0.5

Composition

Table B.3 (continued)

350 Appendix B

Wu et al. (2017b) Katakam et al. (2014)

TiC + Laves + unknown phases Fe2 Mo BCC1 + BCC2 + long range periodic structure

BCC FCC + BCC Al-rich matrix FCC

B2 + FCC

BCC BCC

MA + SPS

Laser surface alloying

Laser processing

MA + SPS

Laser surface alloying

Laser surface alloying

Laser surface alloying

Laser surface alloying

AM

AM

MA + SPS

AM

SC

AM

AM

AM

AlCoCrCuFeMo0.5

AlCoCrCuFeNi

Al0.3 Co1.2 CrCuFeNi

AlCoCrCuFeNi1.5

AlCoCrCuFeNix (x = 0.5 and 1)

AlCoCrFeNiTix (x = 2.0)

AlCoCrFeNiTix (x = 1.5)

Alx Co1.5 CrFeNiTiy

AlCoCrCuMnTi

AlCoCrFeNiTi0.5

Al2.5 CoCuFeNiSnx (x = 0.05, 0.07, and 1)

AlCoCuFeNiZr

Al0.3 CrFe1.5 MnNi0.5 Si0.2

Al0.3 CrFe1.5 MnNi0.5 Si0.5

Al0.3 CrFe1.5 MnNi0.5 Si

(Ni, Co)3 Ti (Ni, Co)3 Ti (Ni, Co)3 Ti FCC + AlCu2 Mn

x = 0, y = 1, FCC x = 0.2, y = 1, FCC BCC1 + BCC2

Al2 Fe3 Si4

Al2 Fe3 Si4

Al2 Fe3 Si4

ZrFe3 Al

BCC + FCC BCC

Ni17 Sn3

BCC + B2

σ + TiC

Ti2 Ni

x = 0, y = 0.5, FCC

Ti2 Ni + B2

Ordered FCC

Ordered FCC

TiC

Sn3 Zr5

FCC + BCC

FCC + BCC

FCC + BCC

FCC

BCC

AM

Wx TaTiVCr (x = 32–90 at %)

(continued)

Ren et al. (2014)

Ren et al. (2014)

Ren et al. (2014)

Zhuang et al. (2012)

Liu et al. (2016e)

Moravcik et al. (2016)

Wang et al. (2015c)

Chuang et al. (2011)

Wu et al. (2017c)

Wu et al. (2017c)

Wu et al. (2017a)

Wu et al. (2017a)

Yang et al. (2018b)

Waseem and Ryu (2017)

Poletti et al. (2016)

Wang and Liu (2016)

SnNbTaTiZr

References

TiNi + Ti2 Ni + χ

BCC

AM

NbNiTaTiV

Minor phase

Major phase

Processing route

Composition

Table B.3 (continued)

Appendix B 351

FCC FCC FCC

μ + BCC BCC + μ BCC + μ

AM

AM

AM

AM

AM

AM

AM

CoCr0.5 Cu0.1 Fe0.3 MoNi

CoCr0.5 Cu0.3 Fe0.3 MoNi

CoCr0.5 Cu0.3 Fe0.1 MoNi

CxCoCrFeMnNi (x = 0.1, 0.15, and 0.2)

CoCrFeMnNi + C 1.84 at %

CoCrFeMnNiCx (x = 0.1, 0.175, and 0.25)

CoCrFeMnNiPdx (x = 0.2 and 0.6) FCC FCC FCC

CsCl structure BCC + Laves (Nb, Zr, Ta, Ti)

SEBM

AM

AM

AM

AM + suction casting

AM

IM

CoCrFeMnNiPd1.8

CoCrFeMnNiPd2.0

Co1.5CrFeNi1.5Ti0.5Mo0.1

Co1.5CrFeNi1.5Ti0.5Mo0.1

CoHfNbNiTiZr

CoCuFeTiZrHf

CuHfNbNiTiZr

Cr20Mo10Nb20Ti20Ta10Zr20

HfMo0.5NbTiV0.5Six (x = 0.3, 0.5, and 0.7)

BCC

Cr2 + ZrMo2

BCC

FCC

FCC

CoCrFeMnNiPdx (x = 1.0 and 1.4)

FCC

FCC

FCC

Han et al. (2015)

(continued)

Liu et al. (2017c)

Eshed et al. (2018)

BCC1 + BCC2 (Hf, Nb, Ti)5 Si3

Park et al. (2016)

Unknown phase

Takeuchi et al. (2016b)

Fujieda et al. (2017) FCC + NbNi –

Fujieda et al. (2017) (Cr11 Fe13 Ni4 )Mo + Ni3 Ti

Tan et al. (2018)

Stepanov et al. (2016a)

Ko and Hong (2018)

Chen et al. (2018d)

Liu et al. (2017b)

Liu et al. (2017b)

Liu et al. (2017b)

Liu et al. (2017b)

Zhang et al. (2017j)

References

Ni3Ti

Mn7 Pd9

Mn3 Pd5

Mn7 Pd9

Mn2 Pd3

M7 C3

M23 C6 , M7 C3

M7 C3

μ

BCC + FCC

AM

CoCr0.5 Cu0.1 Fe0.1 MoNi

FCC

M3 B

FCC

AM

BCoCrFeNiY0.1

Minor phase

Major phase

Processing route

Composition

Table B.3 (continued)

352 Appendix B

Yang et al. (2017) Zhang et al. (2017j) Zhang et al. (2017j)

BCC + unknown phase

Cr2 B Fe3 Si BCC + M3 B FCC + M3 B

FCC1 + FCC2 FCC FCC BCC FCC + BCC

BCC FCC BCC

AM

AM

AM

AM + laser cladding

Gas atomization

AM

AM

Atmospheric plasma spraying

HVOF

Atmospheric plasma spraying

MA + VHP

AM

LC

AgAlCoCrCuFeNi

Al0.3BCoCrCu0.7FeNi

AlBCoCrCu0.7FeNi

Al1.8B0.3CoCrCu0.7NiSi0.1

Al0.5CoCrCuFeNiSi2.0

Al1.5BCoCrFeNiCu0.7

Al0.3BCoFeMnNiCu0.7

AlCo0.6CrFe0.2Ni0.2Si0.2Ti0.2

AlCo0.6CrFe0.2Ni0.2Si0.2Ti0.2

AlCo0.6Cr1.5Fe0.2NiSiTi0.2

C0.3CoCrFeMnNiTi0.3

Al0.3BCoCu0.7FeMnNiY0.1

(AlCoCrFeNiTi)BxCx (x = 2 and 4wt %) FCC

BCC

BCC

BCC

FCC

Zhang et al. (2016e)

(Hf, Zr, Nb)-Si + unknown phase

Chen et al. (2017b)

Zhang et al. (2017j) TiC

Cheng et al. (2018) FCC + M3 B

Hsu et al. (2017b)

M23 C6 , M7 C3 , TiC

Hsu et al. (2017a)

Cr3 Si + Al2 O3 + Cr2 O3 + Rutile

Hsu et al. (2017a)

Oxide phase

Oxide phase

Zhang et al. (2017j)

BCC + M3 B

Zhang et al. (2017m)

Zhang et al. (2017j)

M3 B

Ji (2015)

References

Minor phase

BCC1

Cold crucible levitation melting

HfNbSi0.5TiVZr

Major phase

Processing route

Composition

Table B.3 (continued)

Appendix B 353

354

Appendix B

Table B.4 HEAs with HCP strcuture Alloy

Processing Route

Phase

References

Al20 Li20 Mg10 Sc20 Ti30

MA

HCP

Youssef, Zaddach, Niu, Irving, & Koch (2015)

CoFeReRu

AM

HCP

Gao, Zhang, Guo, Qiao, & Hawk (2016)

CoReRuV

AM

HCP

Gao et al. (2016)

HoDyYGdTb

AM

HCP

Feuerbacher, Heidelmann, & Thomas (2015)

GdTbDyTmLu

AM

HCP

Takeuchi, Amiya, Wada, Yubuta, & Zhang (2014)

YGdTbDyLu

AM

HCP

Takeuchi et al. (2014)

GdHoLaTbY

AM

HCP

Takeuchi et al. (2014)

Ir19 Os22 Re21 Rh20 Ru19

TD

HCP

Yusenko et al. (2017)

GdDyErHoTb

AM

HCP

Yuan et al. (2017)

Ir26 Mo20 Rh22.5 Ru20 W11.5

AM

HCP

Takeuchi, Wada, & Kato (2019a)

Ir25.5 Mo20 Rh20 Ru25 W9.5

AM

HCP

Takeuchi et al. (2019a)

Hf25 Ti25 Zr25 Sc10 Al15

AM

HCP

Rogal et al. (2017)

Ir29.0678 Mo15 Rh29.0678 Ru11.8644 W15

AM

HCP

Takeuchi, Wada, & Kato (2019b)

ScYLaTiZrHf

AM

HCP

Takeuchi, Amiya, Wada, & Yubuta (2016)

ErGdHoLaTbY

AM

HCP

Qiao et al. (2018)

DyGdHoLaTbY

AM

HCP

Qiao et al. (2018)

DyErGdHoLuScTbY

AM

HCP

Qiao et al. (2018)

Co20 Cr26 Fe20 Mn20 Ni14

AM + HPT

HCP

Moon et al. (2017)

Appendix B

355

List of Patents

HE nitrides and carbides

Hardness (GPa)

Young’s modulus (GPa)

References

(AlBCrSiTi)N

25

260

Tsai et al. (2012)

(AlCrMoSiTi)N

35

325

Chang et al. (2008b)

(AlCrSiTiV)N

31

300

Lin et al. (2007)

(AlCrTaTiZr)C

40

303

Yeh et al. (2012)

(AlCrTaTiZr)N

36

360

Lai et al. (2006a)

(CrNbSiTiZr)C

33

360

Yeh et al. (2012)

(CrNbSiTiZr)Cx

32.8

358

Jhong et al. (2018)

(x = 36.7 at %) (HfNbTiVZr)N

–

–

Bagdasaryan et al. (2014)

(HfNbTiVZr)N

64

675

Firstov et al. (2014b)

(AlCrNbSiTiV)N

27.59

–

Chang et al. (2018b)

(AlCrNbSiTiV)N

42

350

Huang and Yeh (2009a)

(HfNbTaTiVZr)N

38

–

Pogrebnjak et al. (2016)

(AlMoNbSiTaTiVZr)N

37

350

Tsai et al. (2008b)

Composition

Processing route

References

(TiZrHf)60 (NiCu)40

IC

Ma et al. (2002)

(TiZrHf)50 (NiCu)40 Al10

MA

Zhang et al. (2003)

(TiZrHf)65 (NiCu)27.5 Al7.5

MeS

Kim et al. (2007, 2006c)

(TiZrHf)x (NiCu)90x Al10

MeS

Cantor et al. (2002), Zhang et al. (2003), Kim et al. (2003b), Kim et al. (2003c, 2007)

(TiZrNb)x (CuNi)90x Al10

MA

Zhang et al. (2007)

(TiZrHf)100xy (NiCu)x Aly

MeS

Kim et al. (2003a, 2004)

(TiZrHf)x (NiCuAg)90x Al10

MeS

Cantor et al. (2002), Kim et al. (2003b), Kim (2005)

(TiZrHfNb)90x (NiCu)x Al10

MeS

Kim et al. (2003b, 2006a, b)

(TiZrHfNb)90x (NiCuAg)x Al10

MeS

Kim et al. (2003b)

(CuNiPdPt)80 P20

Flux water quenching

Takeuchi et al. (2011)

(CuNiPd)60 (TiZr)40

MeS

Takeuchi et al. (2013b)

Equiatomic substitution alloys

(continued)

356

Appendix B

(continued) Composition

Processing route

References

(TiZr)40 (CuNi)40 Be20

AM

Ding and Yao (2013)

HfNbZr

Co-sputtering

Nagase et al. (2012)

BeCoMgTi

MA

Chen et al. (2010b)

AlBFeNiSi

MA

Wang et al. (2014a)

AlBFeSiNi

MA

Wang et al. (2016b)

AlCrFeMnNi

Potentiostatic

Soare et al. (2015b)

Equiatomic alloys

Electrodeposition AlCrNiSiTi

MaS

Chen et al. (2005a)

AlCrTaTiZr

MaS

Chang et al. (2011a), Hsueh et al. (2012)

Al20 Co20 Dy20 Er20 RE20 (RE = Gd, Tb and Tm)

AM + suction casting

Li et al. (2018f)

AlCuNiTiZr

MA

Ge et al. (2017)

AlDyErNiTb

IM

Gao et al. (2011)

Be20 Co20 Hf20 Ti20 Zr20

AM + suction casting

Zong et al. (2018)

BeCoMgTiZn

MA

Chen et al. (2010b)

BNbTaTiZr

MS

Cheng and Yeh (2016a)

Be20 Cu20 Hf20 Ti20 Zr20

AM + suction casting

Zong et al. (2018)

Be20 Hf20 Ni20 Ti20 Zr20

AM + suction casting

Zong et al. (2018)

BiCoFeMnNi

Electrodeposition

Yao et al. (2008)

CaMgSrYbZn

IM

Gao et al. (2011), Li et al. (2013b)

FeCrNbNiB

MA

Vaidya et al. (2015)

FeCrNbNiSi

MA

Vaidya et al. (2015)

FeCoCrNiSi

MA

Vaidya et al. (2015)

FeSiBAlNi

MA

Wang et al. (2014a)

NbSiTaTiZr

MaS

Yang et al. (2009), Tsai et al. (2011)

AlBCFeNiSi

MA

Xu et al. (2016a)

AlBCeFeNiSi

MA

Xu et al. (2016b)

AlBFeNbNiSi

MA

Wang et al. (2014a)

AlCrCuFeMnNi

Potentiostatic electrodeposition

Soare et al. (2015b)

AlCrTaTiZrRu

MaS

Chang et al. (2011a)

BCoCrFeNiSi

Laser cladding

Shu et al. (2018)

FeSiBAlNiNb

MA

Wang et al. (2014a)

AlMoNbSiTaTiVZr

MaS

Tsai et al. (2008b)

Non-equiatomic alloys (continued)

Appendix B

357

(continued) Composition

Processing route

References

AlCoCu0.5 Ni

MA

Chen et al. (2009d, e)

AlCoCrCu0.5 Ni

MA

Chen et al. (2009d, e)

Al0.8 CoCrFeNi

MA

Yang et al. (2016c)

Al5 Cu29 Ni19 Ti15 Zr32

Melting + quenching

Fang et al. (2018b)

(FeCoCrNi)100−x Bx (x = 18–24)

MS

Ding et al. (2017b)

Gex NbTaTiZr (x = 0.5 and 1)

MS

Cheng and Yeh (2016b)

(TiZrNbCu)1−x Nix (x = 0.25)

MS

Biljakovic et al. (2017)

Al16.8Cr14.6Ni23.5Si23.6Ta21.5

MS

Lin et al. (2015c)

Al17.6Cr13.8Ni24.5Si23.6Ta20.5

MA

AlCoCrCu0.5 FeNi

MA

Chen et al. (2009d, e)

Bx (Co, Cr, Fe, Mo, Ni)100−x (x = 16, 20, 22, 25, 27, 29, and 31) Melt spinning

Wang et al. (2018b)

CaCu0.5 MgSrYbZn0.5

IM

Gao et al. (2011)

CaSrYb (Li0.55 Mg0.45 )Zn

IM

Gao et al. (2011)

CoCrCuFeGex Ni (x = 16.2–39 at %)

MS

Braeckman et al. (2016)

CoCrCuFeInx Ni (x = 8.6–18.2 at %)

MS

Braeckman et al. (2016)

CoCrCuFeNb1.6 Ni

Magnetron sputtering

Braeckman et al. (2017)

Zr43.5Ti7.6Cu30.4Ni8.5Al10

MA

Idury et al. (2015)

Zr40.3Ti4.6Cu34.1Ni11Al10

MA

AlCoCrCu0.5 FeNiTi

SC

Chen et al. (2005d)

AM MA

Chen et al. (2009d, e)

Al0.5 CuNiTiZrPd

MS

Nagase et al. (2018)

Co25 Fe25 Ni25 (P, C, B)25

MS

Li et al. (2017d)

Fe26.7 Co28.5 Ni28.5 Si4.6 B8.7 P3

IM + MS

Wei et al. (2017)

Co25 Fe25 Ni25 (B0.2 C0.3 Si0.1 P0.4 )25 Co25 Fe25 Ni25 (B0.2 C0.2 Si0.1 P0.4 )25 Co25 Fe25 Ni25 (B0.2 C0.1 Si0.2 P0.5 )25 Co25 Fe25 Ni25 (B0.3 C0.2 Si0.2 P0.3 )25 Co25 Fe25 Ni25 (B0.3 C0.1 Si0.2 P0.4 )25 Co25 Fe25 Ni25 (B0.2 C0.1 Si0.3 P0.4 )25

AM + suction casting

Xu et al. (2018c)

Be20 Hf20 Ti20 Zr20 (Cu50 Ni50 )20

AM + suction casting

Yang et al. (2018c)

AlCoCrFeCu0.5 MoNiTi

MA

Chen et al. (2009d, e)

AM—arc melting; IM—induction melting; IC—injection casting; SC—suction casting; BS— Bridgman solidification; MeS—melt spinning; LENS—laser engineered net shaping; LC—laser cladding; MA—mechanical alloying; MaS—magnetron sputtering

Appendix C

Sr. No.

Year

1 2

Patents no

Patents name

Country

2002 JP-2002173732-A

High entropy multicomponent alloy

Japan

2008 US-7392187-B2

Method and system for the automatic generation of speech features for scoring high entropy speech

US

3

2008 TW-200828938-A

Method for securely extending key stream to encrypt high-entropy data

Taiwan

4

2008 CN-101215663-A

High-entropy alloy-base composite material and preparation method thereof

China

5

2008 CN-101307465-A

Method for preparing high entropy alloy magnetic materials

China

6

2009 CN-100526490-C

Hard alloy sintered by high-entropy alloy binder and compound carbide and preparation method thereof

China

7

2010 CN-101195091-B

Process for producing high entropy metal catalyst

China

8

2011 CN-101386928-B

Method for preparing high-entropy alloy containing immiscible element

China

9

2011 CN-101554685-B

High-entropy alloy solder used for welding copper and aluminum and preparation method thereof

China

10

2011 CN-101590574-B

High-entropy alloy brazing filler metal for welding China TA2 and 0Cr18Ni9Ti and preparation method thereof

11

2011 CN-102220026-A

High-entropy alloy powder conductive polymer composite material and manufacturing method thereof

China

12

2011 CN-101554686-B

High-entropy alloy solder used for welding hard alloy and steel and preparation method thereof

China

13

2012 CN-102672328-A

Method for welding titanium and steel by applying high-entropy effect and welding material

China

14

2012 CN-102676904-A

Material and method used for TA2/0Cr18Ni9Ti welded by high-entropy effect

China

15

2012 CN-102787266-A

Titanium carbonitride based metal ceramic based on high-entropy alloy binder phase and preparation method of metal ceramic

China

(continued)

© Springer Nature Singapore Pte Ltd. 2022 K. Biswas et al., High Entropy Materials, Materials Horizons: From Nature to Nanomaterials, https://doi.org/10.1007/978-981-19-3919-8

359

360

Appendix C

(continued) Sr. No.

Year

Patents no

Patents name

Country

16

2012 CN-102787267-A

Multiple boride metal ceramic based on high-entropy China alloy adhesion agent and preparation method thereof

17

2012 CN-102796933-A

High-entropy alloy binder phase-based nitrogen-containing hard alloy and preparation method thereof

China

China

18

2012 CN-102828139-A

High-entropy alloy powder used for spraying

19

2013 CN-103173716-A

High-entropy alloy coating preparation technology of China tool die

20

2013 CN-103194656-A

Alx CrFeNiCuVTi high-entropy alloy material and preparation method thereof

China

21

2013 CN-103194657-A

AlFeCoNiCrTiVx high-entropy alloy material and preparation method thereof

China

22

2013 CN-103255415-A

TiC-enhanced high-entropy alloy coating and preparation method thereof

China

23

2013 CN-103290404-A

Laser-cladding high-entropy alloy powder and preparation method of high-entropy alloy coating

China

24

2014 CN-103484810-A

Plasma cladding in-situ synthesized TiB2 -TiC-TiN reinforced high-entropy alloy coating material and preparation method thereof

China

25

2014 CN-103556146-A

Method for preparing high-entropy alloy coating

China

26

2014 CN-103567663-A

High-entropy alloy welding wire for welding titanium-steel and preparation method thereof

China

27

2014 CN-103589882-A

Blocky high-entropy metallic glass and preparation method thereof

China

28

2014 CN-103602872-A

TiZrNbVMo[x] high entropy alloy and preparation method thereof

China

29

2014 CN-103602874-A

High-strength low-elasticity modulus TiZrNbHf high-entropy alloy and preparation method thereof

China

30

2014 CN-103757631-A

Preparation method of high-entropy AlCoNiCrFeMo alloy coating

China

31

2014 RO-129460-A2

Carbides of high entropy alloys as thin layers, for coating articular endoprostheses

Romanian

32

2014 CN-103898463-A

Multi-element high-entropy alloy film and preparation method thereof

China

33

2014 CN-103966566-A

Preparing method for double-layer high-entropy alloy diffusion barrier layer

China

34

2014 CN-102776430-B

AlCoCrFeNiTix high-entropy alloy material and method for preparing same

China

35

2014 CN-104120325-A

Low thermal expansion coefficient NaMxAlySiz high China entropy alloy and preparation method thereof

36

2014 CN-104152781-A

A high-entropy alloy of AlCoFeNiSi and a preparation method thereof

China

37

2014 CN-104178680-A

AlCoCrCuFeSiTi high-entropy alloy and preparation method thereof

China (continued)

Appendix C

361

(continued) Sr. No.

Year

38

Patents no

Patents name

Country

2014 CN-102689109-B

Preparation method of high-entropy brazing filler metal for brazing non-oxide ceramics and non-oxide ceramic composite material

China

39

2015 CN-104264116-A

Process for preparing AlTiCrNiTa high-entropy alloy China coating on surface of X80 pipeline steel base material

40

2015 CN-103060797-B

Preparation method of plasma cladding high-entropy alloy coating layer

China

41

2015 CN-103173674-B

Six-element high-entropy alloy with first-order magnetic phase transition and preparation method thereof

China

42

2015 CN-104368814-A

Method for directly molding high-entropy alloy China turbine engine hot end component through laser metal

43

2015 CN-104388764-A

High-entropy alloy reinforced aluminum-based composite material and preparation method thereof

China

44

2015 CN-104451351-A

Method for improving toughness of boracic high-entropy alloy by adding rare earth

China

45

2015 CN-104451338-A

CoCrFeNiAlCuSi high-entropy alloy and preparation China method thereof

46

2015 CN-104480412-A

Amorphous high-entropy alloy solder for braze-welding tantalum and steel and preparation method

China

47

2015 CN-104561878-A

High-entropy alloy powder for spray coating and preparation method thereof, as well as composite material and preparation method thereof

China

48

2015 CN-104646660-A

Powder material for laser high entropy alloying of iron single element base alloy surface

China

49

2015 CN-104651828-A

Powder for high-entropy alloy-based composite material modified layer prepared on ferrous alloy surface

China

50

2015 CN-104694808-A

High-entropy alloy with dispersion nano-sized China precipitate strengthening effect and preparing method thereof

51

2015 CN-103394685-B

Alloy powder for manufacturing high-entropy alloy coatings, and manufacturing method and application for alloy powder

China

52

2015 CN-103252496-B

High-entropy alloy powder containing amorphous nanocrystalline and fabrication method thereof

China

53

2015 CN-104789847-A

High-entropy alloy, high-entropy alloy coating and plating method for high-entropy alloy coating on rolling surface of bearing

China

54

2015 CN-104841930-A

High-entropy alloy powder for 3D (three-dimensional) printing and method for preparing high-entropy alloy coating by using high-entropy alloy powder

China

55

2015 CN-103252495-B

A kind of preparation method containing amorphous nano-crystalline high-entropy alloy coating

China (continued)

362

Appendix C

(continued) Sr. No.

Year

56

Patents no

Patents name

Country

2015 CN-103056352-B

For the high-entropy alloy powder material and preparation method thereof of supersonic spray coating

China

57

2015 CN-104911581-A

Cu-containing high-entropy alloy coating with liquid phase separation tissue and preparation method thereof

China

58

2015 CN-104946912-A

Rear earth high-entropy alloy of close-packed hexagonal structure

China

59

2015 CN-103255414-B

High-entropy alloy coating that a kind of NbC strengthens and preparation method thereof

China

60

2015 CN-103695838-B

A kind of preparation method of high entropy plasticising non-crystaline amorphous metal compound surface

China

61

2015 CN-105088048-A

High-entropy alloy for sewage degradation and preparing method thereof

China

62

2015 CN-105112759-A

High-temperature-resistant high-entropy alloy material and preparation method thereof

China

63

2015 CN-105154702-A

Aluminum-based amorphous/high-entropy alloy composite and preparation method thereof

China

64

2015 US-2015362473-A1

Low-E panels utilizing high-entropy alloys and combinatorial methods and systems for developing the same

US

65

2016 CN-103710607-B

TiZrNbHfO high-entropy alloy of a kind of oxygen strengthening and preparation method thereof

China

66

2016 CN-103276276-B

High-entropy alloy coating that a kind of VC strengthens and preparation method thereof

China

67

2016 CN-103252568-B

A kind of for filling spot welding stainless steel high-entropy alloy powder and the stainless process of a kind of high-entropy alloy powder filling spot welding

China

68

2016 US-2016025386-A1

High Entropy NiMn-based Magnetic Refrigerant Materials

US

69

2016 CN-105296836-A

NxMy high-entropy alloy with shape memory effect and preparing method thereof

China

70

2016 CN-105463289-A

High-strength and wear-resisting high-entropy alloy door and window used for outdoor buildings

China

71

2016 CN-103911578-B

A kind of preparation method of high rigidity BCC high-entropy alloy coating

China

72

2016 CN-103639619-B

A kind of preparation method of the high-entropy China alloy welding wire welded with steel TIG for titanium

73

2016 CN-105525232-A

High-entropy alloy amorphous powder for 3D printing and preparation method thereof

China

74

2016 CN-105543749-A

High-entropy alloy gradient stress modification technology

China (continued)

Appendix C

363

(continued) Sr. No.

Year

75

Patents no

Patents name

Country

2016 CN-105543621-A

Endogenous nano ceramic reinforcement high-entropy alloy composite material and preparing method

China

76

2016 CN-105568335-A

Technology of preparing FeNiCoCuCr high-entropy alloy coating on steel base material surface

China

77

2016 CN-105562680-A

High-entropy alloy powder and method for preparing China high-entropy alloy coating layer through hot-pressed sintering

78

2016 CN-105603287-A

Oxide-based high-entropy alloy ceramic binding agent special for PCBN

China

79

2016 CN-104476010-B

High-entropy alloy welding wire and the application of titanium/stainless steel is welded for TIG

China

80

2016 CN-105624515-A

High-entropy alloy coating material and preparation method thereof

China

81

2016 CN-105648366-A

Temperature-controllable near-isothermal plastic processing technology for high-entropy alloys

China

82

2016 CN-105648297-A

Preparation method for high-entropy alloy composite China material with externally-added nanometer ceramic phase reinforced and toughened

83

2016 CN-104099509-B

A kind of high-entropy alloy and its preparation method

84

2016 CN-105671392-A

Nitrogen-strengthened TiZrHfNb-based high-entropy China alloy and preparation method thereof

85

2016 CN-105671406-A

Nitride-based high-entropy alloy ceramic binder special for PCBN

China

86

2016 CN-105671545-A

High-hardness, single-phase and high-entropy alloy coating and preparation method and application thereof

China

87

2016 CN-104476011-B

High-entropy alloy welding wire and the application of titanium/mild steel is welded for TIG

China

88

2016 CN-105734324-A

Preparing method for powder metallurgy high-entropy alloy based composite material

China

89

2016 CN-105755324-A

High-entropy alloy with high strength and toughness and preparation method thereof

China

90

2016 US-2016201169-A1

High entropy alloys with non-high entropy second phases

US

91

2016 CN-104308153-B

A kind of manufacture method of high-entropy alloy turbogenerator hot-end component based on precinct laser fusion

China

92

2016 CN-105862036-A

High-entropy coating for surface of iron substrate and preparation method of high-entropy coating

China

93

2016 CN-105862035-A

High-entropy alloy coating and preparation method thereof

China

94

2016 CN-105886805-A

High-plasticity five-element refractory high-entropy alloy and preparation method thereof

China

China

(continued)

364

Appendix C

(continued) Sr. No.

Year

95

Patents no

Patents name

Country

2016 CN-105908049-A

High-entropy alloy self-lubricating composite material and preparation method thereof

China

96

2016 CN-105925869-A

Low-density and high-entropy alloy material and preparation method thereof

China

97

2016 CN-104862510-B

A kind of high-entropy alloy particle enhanced aluminum-based composite material and preparation method thereof

China

98

2016 CN-105950943-A

Multi-major-element high-entropy alloy and preparation method thereof

China

99

2016 CN-105950944-A

High-melting-point high-entropy alloy NbMoTaWVTi and preparation method thereof

China

100

2016 CN-105970069-A

Novel multi-element equal-molar-ratio precious metal high-entropy alloy

China

101

2016 CN-106001566-A

High-strength high-entropy alloy NbMoTaWV and preparation method thereof

China

102

2016 CN-104611604-B

A kind of lightweight high-entropy alloy of tetragonal China crystalline structure and preparation method thereof

103

2016 CN-106065450-A

A kind of high-entropy alloy powder and utilize the method that laser prepares cladding layer

China

104

2016 CN-106086712-A

TiZrHf system high entropy amorphous alloy material and preparation method thereof

China

105

2016 CN-106086580-A

Laser melting coating high-entropy alloy powder and China cladding layer preparation method

106

2016 CN-106086486-A

High-entropy alloy that a kind of durability coupling is good and preparation method thereof

China

107

2016 CN-106086713-A

High entropy amorphous composite material and preparation method thereof

China

108

2016 CN-106119835-A

A kind of equiax crystal high-entropy alloy coating and preparation method thereof

China

109

2016 CN-106167870-A

A kind of NbMoTaW high-entropy alloy and preparation method thereof

China

110

2016 CN-106244887-A

A kind of high entropy alloy material and cladding layer preparation method

China

111

2017 CN-104141084-B

Laser melting coating high-entropy alloy powder and China cladding layer preparation method and purposes

112

2017 CN-104141085-B

Hexa-atomic high-entropy alloy powder and laser cladding layer preparation method and application

China

113

2017 CN-104674103-B

A kind of CrFeCoNiNbx high-entropy alloy and preparation method thereof

China

114

2017 CN-104372230-B

High-strength high-toughness ultrafine-grained high-entropy alloy and preparation method thereof

China

115

2017 CN-106350724-A

Multiple boride enhanced high-entropy alloy based composite material and preparation method thereof

China

116

2017 CN-106374116-A

High-entropy alloy composite coating on metal bipolar plate of fuel cell and process

China (continued)

Appendix C

365

(continued) Sr. No.

Year

Patents no

Patents name

Country

117

2017 CN-104878324-B

High entropy block amorphous alloy of a kind of soft China magnetism FeCoNiMB and preparation method thereof

118

2017 KR-101728936-B1

High entropy alloy having excellent strength and ductility

119

2017 CN-106637062-A

Method for preparing surface plasma nitrided layer of China high-entropy alloy

120

2017 CN-106636845-A

HfZrTiTax high-entropy alloy, and preparation method and application thereof

China

121

2017 CN-106756636-A

A kind of anti-corrosion amorphous high-entropy alloy high and preparation method thereof

China

122

2017 CN-106811724-A

A kind of corrosion-resistant high-entropy alloy coating of Mg alloy surface and preparation method thereof

China

123

2017 CN-104550901-B

Nickel single element based alloy surface laser high-entropy alloy powder and preparation technology

China

124

2017 KR-101744102-B1

High entropy alloy having complex microstructure and method for manufacturing the same

South Korea

125

2017 CN-106868379-A

A kind of high-entropy alloy with big magnetostriction coefficient and preparation method thereof

China

126

2017 CN-106894016-A

Enhanced high-entropy alloy base composite coating of Argon arc cladding titanium carbide and preparation method thereof

China

127

2017 CN-104561990-B

A kind of stainless steel surfaces laser of resistance to China cavitation corrosion high-entropy alloy powder and preparation technology

128

2017 KR-101748836-B1

High entropy alloy having twip/trip property and manufacturing method for the same

South Korea

129

2017 CN-106976023-A

A kind of method of sensing heating high-entropy alloy Furnace Brazing of Diamond Grinding Wheel With Ni

China

130

2017 CN-106995898-A

A kind of compacted black high-entropy alloy of high-performance and preparation method thereof

China

131

2017 CN-107012408-A

A kind of high entropy bulk metallic glass materials of rare-earth-based and preparation method thereof

China

132

2017 CN-105624455-B

A kind of porous high-entropy alloy and preparation method thereof

China

133

2017 CN-107034410-A

A kind of many pivot high-entropy alloys and preparation method thereof

China

134

2017 CN-107043884-A

A kind of TiO particles enhancing CoCrCuFeNi high-entropy alloys and preparation method thereof

China

135

2017 US-2017232155-A1

Thermo-mechanical processing of high entropy alloys for biomedical applications

US

South Korea

(continued)

366

Appendix C

(continued) Sr. No.

Year

136

Patents no

Patents name

Country

2017 US-2017233855-A1

High entropy alloy having twip/trip property and manufacturing method for the same

US

137

2017 CN-105478724-B

A kind of high-entropy alloy particle enhanced aluminum-based composite material and its stirring casting preparation technology

China

138

2017 KR-101773298-B1

Body centered cubic high-entropy alloy foam and manufacturing method for the foam

South Korea

139

2017 CN-107130125-A

A kind of preparation method of high-entropy alloy

China

140

2017 RU-2631066-C1

Heat-resistant high-entropy alloy

Russia

141

2017 CN-107186208-A

A kind of high-entropy alloy feeding and its preparation method and application

China

142

2017 WO-2017164601-A1 High-entropy alloy for ultra-low temperature

WIPO (PCT)

143

2017 WO-2017164602-A1 Cr-Fe-Mn-Ni-V-based high-entropy alloy

WIPO (PCT)

144

2017 CN-105401042-B

Application of the high-entropy alloy powder in laser China melting coating

145

2017 KR-101783242-B1

High entropy alloy having interstitial solid solution hardening and method for manufacturing the same

South Korea

146

2017 KR-20170110019-A

High entropy alloy based chromium, iron, manganese, nickel and vanadium

South Korea

147

2017 CN-107243641-A

Brilliant high-entropy alloy powder of a kind of high-activity nano and preparation method thereof

China

148

2017 CN-104607631-B

Powder and preparation technology used in a kind of copper single element based alloy laser high-entropy alloy

China

149

2017 CN-107267845-A

Nano particle TiC strengthens the microwave synthesis method of high-entropy alloy-base composite material

China

150

2017 CN-107267838-A

It is a kind of to prepare the method with high tough fine grain high-entropy alloy using pyromagnetic coupling

China

151

2017 CN-107267842-A

A kind of high-melting-point high-entropy alloy and preparation method thereof

China

152

2017 CN-107267843-A

A kind of high strength and high hardness AlCoCrFeNi high-entropy alloys and preparation method thereof

China

153

2017 CN-107267844-A

A kind of hexa-atomic high-entropy alloy and preparation method thereof

China

154

2017 CN-107267841-A

A kind of CrMoNbTaV high-entropy alloys and preparation method thereof

China

155

2017 CN-107299342-A

A kind of high-entropy alloy coating and its production and use

China

156

2017 US-2017314097-A1

High-strength and ultra heat-resistant high entropy alloy (HEA) matrix composites and method of preparing the same

US

(continued)

Appendix C

367

(continued) Sr. No.

Year

Patents no

Patents name

Country

157

2017 CN-105671404-B

A kind of TiZrHfNb base high-entropy alloys of the China common alloying of nitrogen oxygen and preparation method thereof

158

2017 CN-106319260-B

A kind of high-melting-point high-entropy alloy and its coating production

China

159

2017 KR-20170123968-A

In-situ strengthened high entropy powder, alloy thereof and method of manufacturing the same

South Korea

160

2017 KR-20170124441-A

High- strength and heat-resisting high entropy alloy matrix composites and method of manufacturing the same

South Korea

161

2017 CN-105950946-B

A kind of method that high-entropy alloy composition design is carried out based on segregation situation between constituent element

China

162

2017 CN-107363359-A

A kind of method of compound high-entropy alloy solder ceramic soldering and metal

China

163

2017 CN-106244889-B

A kind of TiCuAlCrMoNi high-entropy alloys and preparation method thereof

China

164

2017 CN-106222517-B

A kind of TiCuAlCrMoNb high-entropy alloys and preparation method thereof

China

165

2017 CN-107419154-A

One kind has hyperelastic TiZrHfNbAl high-entropy alloys and preparation method thereof

China

166

2017 WO-2017209419-A1 High-entropy alloy

WIPO (PCT)

167

2017 CN-106435323-B

A kind of oxide dispersion intensifying ODS high-entropy alloys and preparation method thereof

China

168

2017 CN-106191621-B

It is prepared by cement rotary kiln support roller surface high-entropy alloy powder, preparation and its coating

China

169

2017 CN-107478487-A

FeCoNiCrMn high-entropy alloy electrolytic etching China electrolyte and its display methods of metallographic structure

170

2017 CN-107475596-A

A kind of high entropy intermetallic compound

China

171

2017 CN-107488803-A

Magnesium-yttrium-transition metal high-entropy alloy before a kind of bio-medical

China

172

2017 CN-107488804-A

A kind of superhigh intensity, hardness and corrosion-resistant CrMnFeVTi high-entropy alloys and preparation method thereof

China

173

2017 KR-101811278-B1

Oxide particle dispersed high entropy alloy for heat-resistant materials and method for manufacturing the same

South Korea

174

2017 CN-105734311-B

A kind of magnetic refrigeration HoxTbyMz it is high-entropy alloy and preparation method thereof

China

175

2017 CN-105734312-B

A kind of bio-medical TiZrNbTa systems high-entropy alloy and preparation method thereof

China

176

2017 KR-101813008-B1

Precipitation hardening high entropy alloy and method for manufacturing the same

South Korea (continued)

368

Appendix C

(continued) Sr. No.

Year

177

Patents no

Patents name

Country

2017 CN-107523740-A

CuCrFeNiTi high entropy alloy materials and preparation method thereof

China

178

2017 CN-106048380-B

A kind of high-entropy alloy base composite coating and preparation method thereof

China

179

2018 CN-107537065-A

High-entropy alloy joint prosthesis based on in-situ test couples bionical construction method

China

180

2018 CN-107557644-A

A kind of quick method for preparing NbMoTaW infusibility high entropy alloy materials

China

181

2018 CN-107557641-A

A kind of high-entropy alloy of resistance to strong acid corrosion and preparation method thereof

China

182

2018 CN-107557643-A

A kind of CoFexNiyV0.5 Nbz High-entropy alloy and China preparation method thereof

183

2018 CN-105734390-B

A kind of preparation method for the polycrystalline cubic boron nitride compound material that high-entropy alloy combines

China

184

2018 US-2018022929-A1

Coated article supporting high-entropy nitride and/or oxide thin film inclusive coating, and/or method of making the same

US

185

2018 CN-105506613-B

A kind of preparation method of high-entropy alloy coating

China

186

2018 CN-106756417-B

A kind of method of controllable preparation CoCrCuFeNi high-entropy alloy powders

China

187

2018 CN-107653425-A

The method that Al0.5 CoCrFeNi high-entropy alloy mechanical properties are improved using magnetic field

China

188

2018 CN-107675046-A

A kind of high-strength light magnalium copper high-entropy alloy and preparation method thereof

China

189

2018 CN-107675061-A

A kind of carbon containing FeCoCrNi high-entropy alloys and its preparation technology

China

190

2018 CN-106048374-B

A kind of infusibility high-entropy alloy/carbonization titanium composite material and preparation method thereof

China

191

2018 CN-107699724-A

High-entropy alloy/porous silicon carbide titanium two-phase three-dimensional communication composite material and preparation method thereof

China

192

2018 CN-107740093-A

Laser melting coating high-entropy alloy powder of high temperature seal coating and preparation method thereof

China

193

2018 CN-107739956-A

A kind of Nb microalloyings NiCoFeCrAl high-entropy alloys

China

194

2018 CN-107747019-A

High entropy high temperature alloy of a kind of NiCoCr AlWTaMo systems and preparation method thereof

China

195

2018 CN-107747018-A

A kind of FeMnCoCrAlRu high-entropy alloys and preparation method thereof

China (continued)

Appendix C

369

(continued) Sr. No.

Year

196

Patents no

Patents name

Country

2018 CN-105886812-B

A kind of WNbTaMoV high-entropy alloys and preparation method thereof

China

197

2018 CN-107841673-A

A series of FeCoCrNiAl high-entropy alloys and its Technology for Heating Processing

China

198

2018 CN-105861909-B

A kind of FeSiBAlNiCo blocks high-entropy alloy and preparation method thereof

China

199

2018 CN-107881501-A

A kind of compositions of additives for being used to China prepare the alloy powder of high-entropy alloy coating

200

2018 CN-105714353-B

A kind of method in high-entropy alloy Surface Creation Nano tube of composite oxides array

China

201

2018 CN-107900335-A

A kind of laser 3D printing method of high-entropy alloy

China

202

2018 CN-105950945-B

A kind of high intensity high-entropy alloy NbMoTaWVCr and preparation method thereof

China

203

2018 CN-107946449-A

High entropy thermoelectric material of NbFeSb bases and preparation method thereof and thermo-electric device

China

204

2018 CN-107930637-A

A kind of high entropy solid solution catalyst of China rare-earth-based iron content and preparation method thereof

205

2018 CN-107961794-A

A kind of high entropy solid solution catalyst of rare-earth-based and preparation method thereof

China

206

2018 CN-107971490-A

A kind of increasing material preparation method of surface high-entropy alloy gradient metallurgy layer

China

207

2018 KR-20180044831-A

High entropy alloy having excellent strength

South Korea

208

2018 CN-107999991-A

High entropy flux-cored wire for titanium-steel MIG welding and preparation method thereof

China

209

2018 CN-108004452-A

A kind of CoCrFeNiHfx High entropy alloy material and preparation method thereof

China

210

2018 CN-108015286-A

High-entropy alloy droplet ejection increasing material manufacturing apparatus and method

China

211

2018 CN-108048725-A

High entropy thermoelectric material of ZrNiSn bases and preparation method thereof and thermo-electric device

China

212

2018 CN-108058447-A

A kind of high-entropy alloy honeycomb interlayer harden structure and preparation method thereof

China

213

2018 CN-105965024-B

A kind of method that high-entropy alloy connects CuW and CuCr materials for liquid phase

China

214

2018 CN-108103494-A

A kind of new high-entropy alloy coating and preparation method thereof

China

215

2018 CN-108103381-A

A kind of high-strength FeCoNiCrMn high-entropy alloys and preparation method thereof

China

216

2018 CN-108118337-A

A kind of method of plasma beam surface cladding TiN enhancings high-entropy alloy coating

China (continued)

370

Appendix C

(continued) Sr. No.

Year

217

Patents no

Patents name

Country

2018 CN-108130470-A

A kind of MoNbTaZrHf high-entropy alloys and preparation method thereof

China

218

2018 CN-105970132-B

Regulate and control Alx the method of CoCrFeNi two-phase high-entropy alloy tissues

China

219

2018 CN-108145170-A

A kind of preparation method of infusibility high-entropy alloy spherical powder

China

220

2018 CN-108161277-A

High entropy flux-cored wire for aluminium-steel submerged arc welding and preparation method thereof

China

221

2018 CN-108161278-A

High entropy flux-cored wire for aluminium-steel MIG welding and preparation method thereof

China

222

2018 CN-107034408-B

A kind of high-entropy alloy of the matched China crystallite dimension bimodal distribution of high-strength tenacity and preparation method thereof

223

2018 CN-106756637-B

A kind of high entropy bulk metallic glass matrix composite and preparation method thereof

China

224

2018 CN-106566966-B

The magnesium-based composite material of a kind of high-entropy alloy as enhancing base and preparation method thereof

China

225

2018 KR-101871590-B1

Stress-induced phase transformable dual-phase high South entropy alloy and manufacturing method for the same Korea

226

2018 CN-108220642-A

A kind of preparation method of CoCrCuFeMoNi high-entropy alloys granule reinforced copper base composite material

China

227

2018 CN-108213422-A

A kind of preparation method of carbon containing high-entropy alloy composite material

China

228

2018 CN-108220742-A

A kind of microalloying Ti-Zr-Hf-V-Nb-Ta infusibility high-entropy alloys and preparation method thereof

China

229

2018 CN-108220880-A

A kind of high rigidity high corrosion-resistant high-entropy alloy nitride coatings and preparation method thereof

China

230

2018 CN-106756412-B

It is a kind of to prepare Al0.5 the method of CoCrFeNi high-entropy alloys

China

231

2018 CN-108299006-A

A kind of method of compound high entropy solder coated laser ceramic soldering and metal

China

232

2018 CN-108300926-A

A kind of lightweight infusibility high-entropy alloy and preparation method thereof

China

233

2018 CN-108315630-A

A kind of Fe-Co-Cr-Ni-C high-entropy alloys and its preparation process

China

234

2018 CN-108326427-A

A kind of method of high-entropy alloy twin arc fuse China collaboration increasing material manufacturing

235

2018 CN-108336062-A

A kind of Cu interconnecting integrated circuits high-entropy alloy diffusion impervious layer and preparation method thereof

China

(continued)

Appendix C

371

(continued) Sr. No.

Year

236

Patents no

Patents name

Country

2018 CN-108342666-A

High entropy magnetically soft alloy of a kind of FeCoNi bases with high-ductility and preparation method thereof

China

237

2018 CN-108342635-A

A kind of hexa-atomic high-entropy alloy CoCrFeNiVAl of high intensity infusibility x and preparation method thereof

China

238

2018 KR-101884442-B1

High entropy alloy overcoming strength-ductility trade-off

South Korea

239

2018 CN-108359918-A

High entropy non-crystaline amorphous metal of a kind of iron-based soft magnetic with high-ductility and its preparation method and application

China

240

2018 CN-108359977-A

A kind of laser melting coating FeCoVWNbSc high-entropy alloy powders and application method

China

241

2018 CN-108374113-A

A kind of preparation method of TaTiZrAlSi high-entropy alloys and its powder

China

242

2018 CN-108372294-A

A kind of high-entropy alloy powder and preparation China method thereof

243

2018 CN-105950947-B

Rich iron high-entropy alloy powder body material and preparation method thereof for 3D printing

China

244

2018 CN-108393558-A

A method of using metal wire material increasing material manufacturing high-entropy alloy parts

China

245

2018 CN-108396262-A

A kind of high entropy magnetically soft alloy of amorphous nano-crystalline and preparation method

China

246

2018 KR-101888299-B1

Cryogenic High Entropy Alloy

South Korea

247

2018 CN-108411132-A

A kind of preparation method of magnetic levitation vacuum melting FeMnNiCoCr high-entropy alloys

China

248

2018 CN-108411272-A

A kind of preparation method of bearing AlCrCuFeNi systems high-entropy alloy coating

China

249

2018 CN-107142410-B

CrMoNbTiZr high entropy alloy materials and preparation method thereof

China

250

2018 CN-207758261-U

A kind of high-entropy alloy honeycomb interlayer harden structure

China

251

2018 CN-108439986-A

(HfTaZrTiNb) preparation method of C high entropys China ceramic powder and high entropy ceramic powder and high entropy ceramic block

252

2018 CN-108517452-A

One kind having both high intensity and soft magnet performance AlCoCuFeNi x High-entropy alloy and preparation method thereof

China

253

2018 CN-107151755-B

A method of preparing the high-entropy alloy of close-packed hexagonal structure

China

254

2018 CN-106319513-B

A kind of preparation method of high-entropy alloy powder and high rigidity high-entropy alloy coating

China

255

2018 CA-3055297-A1

High nitrogen, multi-principal element, high entropy corrosion resistant alloy

Canada (continued)

372

Appendix C

(continued) Sr. No.

Year

256

Patents no

Patents name

Country

2018 CN-108531799-A

A kind of low-density high entropy alloy material and preparation method thereof towards high temperature application

China

257

2018 CN-107012347-B

A kind of high-entropy alloy sintered diamond locking nub

China

258

2018 CN-108588704-A

A method of it is quickly cooled down using fixed point input energy and prepares high-entropy alloy/diamond composite film or coating

China

259

2018 CN-108624797-A

A kind of high entropy alloy material and preparation China method thereof making cutter

260

2018 CN-108642449-A

Super hard tough high-entropy alloy nitride nano composite coating hard alloy blade and preparation method thereof

China

261

2018 CN-108642445-A

A kind of AlCrTaTiZr high-entropy alloys nitride film and preparation method thereof

China

262

2018 CN-108660354-A

A kind of high entropy stainless steel of Fe-Mn-Cr-Ni China systems and preparation method thereof

263

2018 CN-108660352-A

A kind of enhanced AlCoCrFeNi2 The preparation method and application of high-entropy alloy-base neutron absorber material

China

264

2018 CN-108672708-A

A kind of preparation method of the high-entropy alloy powder containing Mn

China

265

2018 CN-108677077-A

A kind of infusibility high-entropy alloy of high specific strength high-ductility and preparation method thereof

China

266

2018 CN-108677157-A

A kind of high-entropy alloy method for manufacturing thin film with high hard high resistivity characteristic

China

267

2018 CN-108677129-A

A kind of FeCoNiCrSiAl high-entropy alloys coating China and preparation method thereof

268

2018 CN-108690929-A

The preparation method of interior raw type nano-particle reinforcement high-entropy alloy-base composite material

China

269

2018 KR-101910938-B1

Cr Filament Reinforced CrMnFeNiCu High Entropy Alloy And Method for Manufacturing The Same

South Korea

270

2018 KR-101915906-B1

High Entropy Alloy Based Vanadium, Chromium, Iron and Nickel

South Korea

271

2018 WO-2018203601-A1 Method for improving process ability of high-entropy WIPO alloy to which Al is added (PCT)

272

2018 CN-108823478-A

Ultra-fine high-entropy alloy Binder Phase cermet and preparation method thereof

China

273

2018 CN-108821351-A

A kind of preparation method of the porous high entropy oxide material of spinel-type

China

274

2018 CN-108823481-A

A kind of high-entropy alloy and preparation method China thereof (continued)

Appendix C

373

(continued) Sr. No.

Year

275

Patents no

Patents name

Country

2018 CN-108889954-A

A kind of preparation method of infusibility high-entropy alloy powder

China

276

2018 CN-107739936-B

A kind of high entropy reversible hydrogen storage alloy of Mg base and preparation method thereof

China

277

2018 CN-108907502-A

It is a kind of for being brazed the amorphous state high-entropy alloy solder and preparation method thereof of tantalum Ta1 Yu 1Cr18Ni9 stainless steel

China

278

2018 CN-108913974-A

A kind of sulfur-bearing self-lubricating high-entropy alloy and preparation method thereof

China

279

2018 CN-108914113-A

A kind of method of ultrasonic wave assisted plasma beam cladding high entropy alloy coating

China

280

2018 CN-108911751-A

A kind of high entropy ceramic material of ZrHfTaNbTiC super high temperature and preparation method thereof

China

281

2018 CN-108950286-A

A method of preparing ZnAlCrMnNbB high-entropy alloy

China

282

2018 CN-108941581-A

A kind of in-situ preparation method and product of laser gain material manufacture high-entropy alloy

China

283

2018 CN-108941546-A

A kind of high-entropy alloy combination cubic boron nitride super hard composite material and preparation method

China

284

2018 CN-108950351-A

A kind of high temperature resistant VNbMoTa high-entropy alloy and preparation method thereof

China

285

2018 CN-108977751-A

A kind of method of ultrasonic wave assisted plasma thermal spraying preparation high entropy alloy coating

China

286

2018 KR-101928329-B1

Method for manufacturing nanocrystalline high entropy alloy (HEA) and high entropy alloy (HEA) manufactured there from

South Korea

287

2018 CN-108998715-A

Infusibility high entropy alloy material and preparation method thereof with large plastometric set ability

China

288

2018 CN-107012380-B

A kind of preparation method of Self- propagating Sintering Synthetic founding high-entropy alloy

China

289

2018 CN-108998716-A

A kind of preparation method of electric arc China deposited powder cored filament material and its high entropy alloy coating

290

2018 CN-107245626-B

A kind of method of high entropy effect enhancing (W, Ti, V) C-Co hard alloy mechanical property

China

291

2018 CN-109023015-A

CrCuNiMoV high entropy alloy material and preparation method thereof

China

292

2018 CN-109023004-A

A kind of single-phase infusibility high-entropy alloy China and preparation method thereof towards plasma tungstenic (continued)

374

Appendix C

(continued) Sr. No.

Year

Patents no

Patents name

Country

293

2018 CN-109052491-A

A kind of preparation method of the porous high China entropy oxide material of lithium ion battery negative material spinel-type

294

2019 CN-109112530-A

A kind of laser melting coating high entropy alloy material and cladding layer preparation method

China

295

2019 CN-109136715-A

A kind of Ultra-fine Grained multi-principal high-entropy alloy containing Al and preparation method thereof

China

296

2019 CN-109136601-A

A kind of high hardware heart cubic phase enhances the high-entropy alloy composite material and preparation method of tough modeling face-centred cubic structure

China

297

2019 CN-109161774-A

Haystellite and preparation method thereof by high-entropy alloy as binder

China

298

2019 CN-109161780-A

A method of improving FeCrNiAl base high-entropy alloy processing performance

China

299

2019 CN-109161773-A

A kind of preparation method of high-entropy alloy bonding phase cemented carbide

China

300

2019 CN-109161776-A

A kind of porous high-entropy alloy of pre-alloyed CrMoNbTiZr and preparation method thereof

China

301

2019 CN-109161710-A

A kind of high-entropy alloy composite material and preparation method containing self-lubricating phase

China

302

2019 CN-109182867-A

The stable nano metal material M of high-entropy alloy x Ny It is alloy and preparation method

China

303

2019 CN-109182875-A

A kind of single-phase reversible and anti-oxidant storage hydrogen high-entropy alloy and preparation method thereof

China

304

2019 CN-109180189-A

A kind of high entropy carbide ultra-high temperature China ceramic powder and preparation method thereof

305

2019 CN-109180188-A

A kind of high entropy carbide containing boron ultra-high temperature ceramic powder and preparation method thereof

306

2019 CN-109182876-A

A kind of crystalline state high entropy alloy material China containing beryllium and preparation method thereof

307

2019 CN-109182877-A

(NbMoTaW)100-xMxIt is infusibility high-entropy alloy and preparation method thereof

308

2019 CN-109207829-A

High-entropy alloy and multicomponent carbide China cocrystallizing type composite material and its in-situ preparation method

309

2019 CN-109207985-A

A kind of preparation method of Mg alloy surface high-entropy alloy film layer

China

310

2019 CN-109207830-A

A kind of high-entropy alloy combination cubic boron nitride super hard composite material and preparation method

China

311

2019 CN-109201736-A

A kind of asynchronous rolling method of high-entropy alloy

China

China

China

(continued)

Appendix C

375

(continued) Sr. No.

Year

312

Patents no

Patents name

Country

2019 CN-109234601-A

A kind of solid silk material of high-entropy alloy of electric arc cladding and preparation method thereof

China

313

2019 CN-109234603-A

A kind of high-entropy alloy powder and diamond tool tyre case

China

314

2019 CN-109252082-A

A kind of multi-element alloyed infusibility high-entropy alloy and preparation method thereof

China

315

2019 CN-109252199-A

A kind of high entropy alloy material of surface ceramic deposition and preparation method thereof

China

316

2019 US-2019024198-A1

Precipitation hardening high entropy alloy and method of manufacturing the same

US

317

2019 CN-109266947-A

A kind of high-entropy alloy composite component and preparation method thereof

China

318

2019 US-10190197-B2

Oxidation resistant high-entropy alloys

US

319

2019 CN-109290572-A

A kind of laser melting deposition method of ceramics enhancing high-entropy alloy composite element

China

320

2019 CN-107557645-B

A kind of high-strength high entropy high temperature alloy of BCC base being precipitated with cubic morphology nanoparticle coherence

China

321

2019 CN-109295399-A

A kind of high-damping high entropy alloy material and preparation method thereof

China

322

2019 CN-109295373-A

A kind of application of high-entropy alloy and preparation method thereof

China

323

2019 CN-107326246-B

A kind of high-performance high-entropy alloy and its processing method

China

324

2019 CN-109338308-A

High-entropy alloy thin-film material and preparation China method thereof

325

2019 CN-107130124-B

A kind of method of increases material manufacturing technology forming high-entropy alloy

326

2019 CN-109338199-A

A kind of high-entropy alloy and preparation method China thereof of ceramic particle enhancing

327

2019 CN-109338202-A

A kind of high entropy copper alloy of high toughness wear resistant

China

328

2019 CN-109338172-A

A kind of 2024 aluminum matrix composites and preparation method thereof of high-entropy alloy enhancing

China

329

2019 CN-109355544-A

A kind of addition aluminium, high-entropy alloy of element silicon and preparation method thereof

China

330

2019 KR-101950236-B1

Copper based high entropy alloys, and method for manufacturing the same

South Korea

331

2019 CN-109371307-A

It is a kind of using high-entropy alloy powder as the China preparation method of the WC base cemented carbide of binder

332

2019 CN-109385610-A

The mobile phone plated film made with high entropy liquid alloy target

China

China (continued)

376

Appendix C

(continued) Sr. No.

Year

333

Patents no

Patents name

Country

2019 CN-106011852-B

A kind of preparation method of austenite stainless steel surface high entropy alloy coating

China

334

2019 CN-107083527-B

A method of heat treatment combines plastic deformation to improve single-phase high-entropy alloy intensity

China

335

2019 KR-101955370-B1

CoCrFeMnNi oxynitride high entropy alloy and preparation method for thin film thereof

South Korea

336

2019 CN-109457197-A

A kind of ultrasonic and pressure one auxiliary high-entropy alloy heat treatment technics

China

337

2019 CN-109468678-A

A kind of electrolytic etching solution and its application method for high-melting-point high-entropy alloy

China

338

2019 CN-109487099-A

A kind of CrVTaHfZrTi high-entropy alloy and preparation method thereof

China

339

2019 CN-109518018-A

MnNbTaTiV high entropy alloy material and preparation method thereof that one kind is wear-resisting, anti-corrosion

China

340

2019 KR-101962229-B1

Boron-doped high entropy alloy and manufacturing method of the same

South Korea

341

2019 CN-109518057-A

A kind of tungsten carbide material and its preparation method and application by high-entropy alloy cobalt ferronickel aluminum bronze bonding

China

342

2019 CN-109518066-A

A kind of pre-alloyed high-entropy alloy porous material and preparation method thereof

China

343

2019 CN-109518062-A

A kind of high-strength high abrasion multi-principal China high-entropy alloy cutter and preparation method thereof

344

2019 CN-109550957-A

A method of powder metallurgy, which is prepared, China with 3D printing stretches eutectic high-entropy alloy

345

2019 CN-109554600-A

A kind of preparation method of CoCrFeNiMn high-entropy alloy powder

China

346

2019 CN-106756407-B

A kind of CrMnFeCoNiZr high-entropy alloy and preparation method thereof

China

347

2019 CN-109576609-A

Soft magnetism FeCoNiBCP high entropy amorphous alloy and preparation method thereof

China

348

2019 KR-101966584-B1

In-situ strengthened high entropy powder, alloy thereof and method of manufacturing the same

South Korea

349

2019 CN-109576607-A

A kind of FeCoNi base soft magnetism high-entropy alloy and application

China

350

2019 CN-106222463-B

A kind of lightweight AlSiTi system high-entropy alloy particle enhanced aluminum-based composite material and preparation method thereof

China

351

2019 CN-107096923-B

The preparation method of high-melting-point high-entropy alloy spherical powder based on laser gain material manufacture

China

(continued)

Appendix C

377

(continued) Sr. No.

Year

352

Patents no

Patents name

Country

2019 CN-109608203-A

High entropy disilicide and preparation method thereof

China

353

2019 CN-107699822-B

A kind of high entropy block amorphous alloy and preparation method thereof

China

354

2019 CN-109607615-A

A kind of B high entropy perovskite oxide and preparation method thereof

China

355

2019 CN-106894014-B

A kind of activity Argon arc cladding high entropy alloy coating and preparation method thereof

China

356

2019 CN-106894015-B

Argon arc cladding high entropy alloy coating and preparation method thereof

China

357

2019 CN-109622979-A

A kind of preparation method of pre-alloyed high-entropy alloy porous material

China

358

2019 CN-107893184-B

A kind of nanometer of ultra-fine grained high-entropy alloy and preparation method thereof

China

359

2019 CN-106834878-B

A kind of method that microwave sintering prepares endogenous high-entropy alloy-base composite material

China

360

2019 CN-109628771-A

A kind of high-entropy alloy powder cored filament material electric arc cladding processing technology

China

361

2019 CN-106676365-B

A kind of high-ductility is without constriction high-entropy alloy and preparation method thereof

China

362

2019 WO-2019073023-A1 High entropy alloy

WIPO (PCT)

363

2019 CN-109666911-A

China

364

2019 WO-2019083103-A1 Transformation-induced plasticity high-entropy alloy, WIPO and manufacturing method therefor (PCT)

365

2019 CN-109706362-A

A kind of preparation method of aluminium cobalt ferrochrome nisiloy high-entropy alloy

China

366

2019 CN-109702199-A

A kind of high-entropy alloy-base self-lubricating oily bearing material

China

367

2019 CN-109734451-A

A kind of high entropy ceramics of transition metal diboride and preparation method thereof

China

368

2019 CN-109750209-A

A kind of ultra-fine grained eutectic high-entropy alloy and preparation method thereof

China

369

2019 CN-107699770-B

A kind of high entropy alloy material and preparation China method thereof

370

2019 CN-109762519-A

High-entropy alloy/oxide composite nano wave-absorbing material preparation method

China

371

2019 CN-109763125-A

A kind of high entropy alloy coating and its preparation process, application of high temperature wear resistant

China

372

2019 CN-107619982-B

A kind of hexa-atomic infusibility high-entropy alloy China and its verification method of high-ductility high intensity

The high entropy alloy coating and preparation method thereof of nuclear-used zirconium alloy involucrum surface refractory corrosion

(continued)

378

Appendix C

(continued) Sr. No.

Year

373

Patents no

Patents name

Country

2019 CN-109763057-A

A kind of Fe-Co-Ni-Mn-Cu-B-C high entropy alloy material and preparation method thereof

China

374

2019 CN-109796209-A

One kind (Ti, Zr, Hf, Ta, Nb) B2 high entropy ceramic powder and preparation method thereof

China

375

2019 CN-107779620-B

A method of regulation CoCrFeNiCu high-entropy alloy performance

China

376

2019 CN-109797303-A

A kind of raising Al0.3 the method of CoCrFeNi high-entropy alloy intensity

China

377

2019 CN-106041031-B

A kind of preparation method of cast(ing) surface high entropy alloy coating

China

378

2019 CN-109868405-A

High-entropy alloy CoCrFeMnNi and its powder by atomization method reparation technology

China

379

2019 CN-109881030-A

A kind of double structure high-entropy alloy and preparation method thereof

China

380

2019 CN-109881148-A

A kind of AlCrTiSiN high-entropy alloy nitride coatings of single phase solid solution structure and its preparation method and application

China

381

2019 KR-20190068916-A

High entropy alloy and method for manufacturing the South same Korea

382

2019 WO-2019117519-A1 High entropy alloy, manufacturing method therefor, and rod for bolts, using same

WIPO (PCT)

383

2019 KR-20190070173-A

High entropy alloy powder and method for manufacturing the same

South Korea

384

2019 CN-109913771-A

A kind of VAlTiCrSi high-entropy alloy film and its application under briny environment

China

385

2019 CN-109930052-A

A kind of safe nuclear reactor involucrum high entropy alloy material and preparation method thereof

China

386

2019 CN-109930085-A

A kind of high entropy amorphous soft-magnetic alloy of corrosion-and high-temp-resistant and preparation method thereof

China

387

2019 CN-107663607-B

A kind of high-entropy alloy holds the composite material and preparation method and application of abrasive grain

China

388

2019 CN-108166049-B

A kind of electrolyte and electro-etching processing method for high-entropy alloy

China

389

2019 CN-109955004-A

A kind of high entropy alloy material and application China for welding

390

2019 CN-109970068-A

Utilize the method for high-entropy alloy purifying polycrystalline silicon

China

391

2019 CN-109967733-A

FeCrVTiMn high-entropy alloy and the method for carrying out laser gain material manufacture using it

China

392

2019 CN-109972134-A

A method of FeCoNiCrMn high entropy alloy coating is prepared on potassium steel surface

China

393

2019 CN-109967812-A

A kind of soldering connecting method of CoCrCuFeNi high-entropy alloy

China (continued)

Appendix C

379

(continued) Sr. No.

Year

394

Patents no

Patents name

Country

2019 CN-107760963-B

A kind of nitrogenous FeCoCrNiMn high-entropy alloy and preparation method thereof

China

395

2019 CN-109967852-A

A kind of diffusion welding connection method of CoCrCuFeNi high-entropy alloy

China

396

2019 CN-109967850-A

A kind of connection method of the resistance spot welding of CoCrCuFeNi high-entropy alloy

China

397

2019 CN-108048785-B

A kind of preparation method of thermal spraying nitride enhancing high entropy alloy coating

China

398

2019 CN-110000515-A

A kind of high-entropy alloy CoCrCuFeNi laser re cast layer and preparation method thereof

China

399

2019 CN-110004349-A

A kind of carbon nanotube enhancing high-entropy alloy composite material and preparation method

China

400

2019 CN-110013831-A

A kind of nanoparticle activated carbon and its preparation method and application of load CoCrCuFeNi high-entropy alloy

China

401

2019 CN-108486450-B

A kind of bio-medical high-entropy alloy and preparation method thereof

China

402

2019 CN-110029241-A

High-entropy alloy fining agent refines technical pure China aluminum or aluminum alloy and thinning method

403

2019 CN-110042295-A

A kind of preparation method of nanometer of high-entropy alloy block materials

China

404

2019 KR-20190086931-A

High entropy alloy and manufacturing method of the same

South Korea

405

2019 CN-108034844-B

A kind of semi-solid-state shaping method of the constituent elements high-entropy alloys such as high-melting-point

China

406

2019 CN-110078512-A

High entropy carbide powder of superhigh temperature and preparation method thereof

China

407

2019 CN-110093548-A

A kind of tough high-entropy alloy of Ultra-fine Grained height and preparation method thereof containing rare-earth Gd

China

408

2019 CN-110093547-A

A kind of preparation method of large volume alnico siderochrome high-entropy alloy

China

409

2019 CN-110091035-A

A kind of high-entropy alloy increasing material manufacturing device and increasing material manufacturing method

China

410

2019 CN-110093546-A

A kind of AlFeMoNbZr core involucrum high entropy alloy material and preparation method thereof

China

411

2019 CN-109082582-B

A kind of the magnesium-based high-entropy alloy and preparation method of high-strength tenacity high rigidity

China

412

2019 CN-109023005-B

A kind of soft magnetism high-entropy alloy of novel China resistance to 600 DEG C of high temperature

413

2019 CN-108149117-B

A kind of MoCrFeMnNi high-entropy alloy and preparation method thereof

China (continued)

380

Appendix C

(continued) Sr. No.

Year

414

Patents no

Patents name

Country

2019 CN-107955928-B

A kind of method that high-entropy alloy case-carbonizing is modified

China

415

2019 CN-110104648-A

A kind of high entropy carbide nano powder and preparation method thereof

China

416

2019 CN-110117788-A

A kind of preparation method of CoCrFeMnNi high-entropy alloy cladding layer

China

417

2019 CN-110117789-A

A kind of method for preparing high-entropy alloy and device based on laser clad deposition

China

418

2019 CN-110129522-A

High-entropy alloy magnetic field impulse heat treatment technics

China

419

2019 CN-110125570-A

A kind of tin silver copper silicon high-entropy alloy solder and preparation method thereof

China

420

2019 CN-110129649-A

A kind of preparation method of high entropy alloy coating powder and nanocrystalline high entropy alloy coating

China

421

2019 CN-110129716-A

A kind of preparation method of high entropy alloy coating

China

422

2019 CN-107587158-B

A kind of nanoporous high-entropy alloy electrode and its preparation method and application

China

423

2019 CN-107641751-B

A kind of MoNbCrVTi infusibility high-entropy alloy and preparation method thereof

China

424

2019 CN-110125573-A

A kind of ferro-cobalt Ni-Cr-Mn high-entropy alloy solder and preparation method thereof

China

425

2019 CN-107699769-B

A kind of superplastic Fe-Co-Cr-Ni high-entropy alloy of room temperature compression and its preparation process containing aluminium

China

426

2019 CN-110144476-A

A kind of preparation method of aluminium cobalt ferrochrome nickel high-entropy alloy

China

427

2019 CN-110158008-A

A kind of high entropy alloy coating and preparation method thereof

China

428

2019 CN-110172628-A

A kind of preparation method of the good aluminium China ferro-cobalt nickel chromium triangle high-entropy alloy of corrosion resistance

429

2019 CN-110172629-A

A kind of graphene enhancing high-entropy alloy China elevator traction machine composite worm wheel and preparation method thereof

430

2019 CN-110190259-A

A kind of preparation method and lithium ion battery China negative material of the high entropy oxide of nanometer

431

2019 TW-I670377-B

Precipitation strengthened high-entropy superalloy

Taiwan

432

2019 CN-110194667-A

Superhard single-phase high entropy ceramic material of five constituent elements transition metal carbide of one kind and preparation method thereof

China

433

2019 CN-110202145-A

Preparation method based on laser gain material manufacture high-entropy alloy diamond composite

China (continued)

Appendix C

381

(continued) Sr. No.

Year

434

Patents no

Patents name

Country

2019 CN-109182866-B

High-entropy alloy-diamond composite and preparation method thereof

China

435

2019 CN-110204328-A

A kind of preparation method of high entropy oxide ceramics

China

436

2019 CN-107338385-B

A kind of hydrogen storage high-entropy alloy and preparation method thereof based on body-centered cubic structure

China

437

2019 CN-110241354-A

A kind of carbon containing high entropy alloy coating and preparation method thereof

China

438

2019 CN-110257682-A

A kind of preparation method of high entropy alloy material and its coating

China

439

2019 CN-107686928-B

A kind of high-performance NiCoCrFeMnTi system high-entropy alloy and preparation method thereof

China

440

2019 CN-109234690-B

A kind of high-entropy alloy target and its preparation China process containing aluminium and boron element

441

2019 CN-110257758-A

A kind of high-entropy alloy gradient composites and China preparation method thereof based on reaction in-situ

442

2019 CN-110272278-A

Thermal barrier coating high entropy ceramic powder China and preparation method thereof

443

2019 CN-110273077-A

A kind of preparation method of large scale infusibility high-entropy alloy

China

444

2019 CN-110273153-A

A kind of boracic high entropy alloy coating and preparation method thereof

China

445

2019 JP-2019163535-A

High entropy alloy for exterior component

Japan

446

2019 CN-110280255-A

A kind of nanometer of high-entropy alloy elctro-catalyst and preparation method thereof

China

447

2019 CN-110280921-A

A kind of cable formula welding wire and preparation method thereof for high-entropy alloy built-up welding

China

448

2019 CH-714802-A2

High entropy alloys for dressing components

Switzerland

449

2019 CN-110295347-A

A method of using high-entropy alloy plated film on cutter

China

450

2019 CN-110295363-A

A kind of preparation method of AlCoCrFeMnNi high-entropy alloy powder and its cladding layer

China

451

2019 CN-110306186-A

A kind of siliceous high entropy alloy coating and preparation method thereof

China

452

2019 CN-107858579-B

The method for improving high-entropy alloy magnetic property is heat-treated using constant charge soil

China

453

2019 TW-I674334-B

Manufacturing method of high entropy alloy coating

Taiwan

454

2019 CN-108425060-B

Loaded inversion of phases NbZrTiTaAlx high-entropy alloy and its preparation method and application

China

(continued)

382

Appendix C

(continued) Sr. No.

Year

455

Patents no

Patents name

Country

2019 CN-110317990-A

High entropy high temperature alloy of a kind of Ni-Co-Al-Cr-Fe system monocrystalline and preparation method thereof

China

456

2019 CN-107739958-B

A kind of high-entropy alloy and preparation method China thereof containing eutectic structure

457

2019 CN-110315237-A

A kind of cable formula welding wire and the method China for preparing high-entropy alloy part

458

2019 CN-110331400-A

Al is prepared using axis stream laserx The method and its coating of CoCrNiMnTi high entropy alloy coating

China

459

2019 CN-110330341-A

A kind of single-phase high entropy ceramic powder of high pure and ultra-fine transition metal carbide and preparation method thereof

China

460

2019 CN-110344052-A

A method of superhard Ti10CoCrNiFeNbx high entropy alloy coating is prepared on high purity titanium surface

China

461

2019 CN-110344040-A

A kind of preparation method of the ultralight high-entropy alloy with microarray structure

China

462

2019 CN-110343930-A

A kind of Flouride-resistani acid phesphatase high-entropy alloy, cladding tubes and preparation method thereof

China

463

2019 CN-110343928-A

A kind of FeCrNiAlTi system two-phase high-entropy alloy and preparation method thereof

China

464

2019 CN-110339850-A

A kind of Fe-Co-Ni-P-C system high-entropy alloy elctro-catalyst and preparation method thereof for evolving hydrogen reaction

China

465

2019 CN-110373557-A

A method of improving high-entropy alloy self-passivation ability and anti-homogeneous corrosion ability

China

466

2019 CN-110373595-A

A kind of high entropy high temperature alloy of high-performance and preparation method thereof

China

467

2019 CN-110386595-A

High entropy RE phosphate powder and preparation method thereof

China

468

2019 CN-110407213-A

One kind (Ta, Nb, Ti, V) C high entropy carbide nano China powder and preparation method thereof

469

2019 CN-110408833-A

A kind of preparation method of NbTaTiZr high-entropy alloy and its powder

China

470

2019 CN-108118338-B

A kind of method of high-frequency induction heating cladding TiC enhancing high entropy alloy coating

China

471

2019 CN-109112380-B

A kind of infusibility multi-principal high-entropy alloy and preparation method thereof

China

472

2019 CN-108220741-B

A kind of bio-medical high-entropy alloy and preparation method thereof

China

473

2019 CN-108517451-B

A kind of high-strength tenacity high-entropy alloy and preparation method with gradient grain structure

China (continued)

Appendix C

383

(continued) Sr. No.

Year

474

Patents no

Patents name

Country

2019 CN-110423930-A

A kind of high entropy ceramic–metal composite of Ultra-fine Grained and preparation method thereof

China

475

2019 CN-110423933-A

A kind of bio-medical Ti-Zr-Hf-Nb-Ta system’s high-entropy alloy and preparation method

China

476

2019 CN-109082553-B

The cubic boron nitride superhard composite material China and preparation method that high-entropy alloy combines

477

2019 CN-110438386-A

A kind of preparation method and use of high-entropy alloy solder

478

2019 CN-110453131-A

A kind of high-entropy alloy and preparation method China thereof with good thermal processability energy

479

2019 CN-110467227-A

The high entropy oxide material of novel Ca-Ti ore type and preparation method of the high entropy in five yuan of the position B

480

2019 CN-107829007-B

A kind of method that high-entropy alloy and powder China metallurgic method prepare high-entropy alloy block

481

2019 CN-110484796-A

A kind of high entropy ceramic particle of transition metal carbide and preparation method thereof

China

482

2019 CN-108380892-B

A kind of preparation method of ceramics/high-entropy alloy laminated material

China

483

2019 CN-110499445-A

A kind of eutectic high-entropy alloy and preparation China method thereof

484

2019 CN-110512101-A

A kind of preparation method of the high-entropy alloy of the phase of chrome alum containing hard

China

485

2019 CN-110511035-A

A kind of high entropy ceramics of high-ductility high wear-resistant and its preparation method and application

China

486

2019 CN-110556536-A

Six-element high-entropy oxide material for lithium ion battery and preparation method thereof

China

487

2019 CN-108179343-B

preparation method of ultra-fine grain high-entropy alloy

China

488

2019 CN-108467984-B

Five-membered high-entropy alloy Cu0.5 FeNiVAl x and strength and hardness improving method thereof

China

489

2019 KR-102054735-B1

Transformation induced plasticity high entropy alloy and manufacturing method for the same

South Korea

490

2019 CN-109338300-B

high-hardness material of high-entropy alloy nitride coating and preparation method thereof

China

491

2019 CN-110563462-A

B-site six-element high-entropy novel perovskite type high-entropy oxide material and preparation method thereof

China

492

2019 CN-110576185-A

Nanocrystalline high-entropy alloy powder and preparation method thereof

China

493

2019 CN-110590372-A

Transition metal carbonitride high-entropy ceramic and preparation method and application thereof

China

China

China

(continued)

384

Appendix C

(continued) Sr. No.

Year

494

Patents no

Patents name

Country

2019 CN-109554602-B

High-entropy alloy with high-principal-element single-phase close-packed hexagonal structure and preparation method thereof

China

495

2019 CN-110600724-A

Five-element transition-non-transition high-entropy oxide negative electrode material for lithium ion battery

China

496

2019 CN-110600703-A

Five-element transition metal oxide high-entropy material for lithium ion battery

China

497

2019 CN-110606748-A

Alumina-enhanced high-entropy boride ceramic and preparation method and application thereof

China

498

2019 CN-110615681-A

Porous high-entropy hexaboride ceramic and preparation method thereof

China

499

2019 CN-110629218-A

High-entropy alloy fine grain in-situ additive manufacturing method

China

500

2019 CN-110629059-A

Heterogeneous high-entropy alloy material and preparation method thereof

China

501

2020 CN-110643911-A

Thermal mechanical treatment method of eutectic high-entropy alloy

China

502

2020 CN-108165866-B

Preparation method of multi-element high-entropy alloy

China

503

2020 CN-110666296-A

Wire feeding mechanism for high-entropy alloy surfacing

China

504

2020 CN-110669977-A

Light super-tough high-strength NbTiVAlxZry as-cast high-entropy alloy

China

505

2020 CN-108642399-B

Basal high-entropy alloy and preparation method thereof

China

506

2020 CN-110699587-A

Light high-strength high-toughness NbTiVZrAlx as-cast high-entropy alloy

China

507

2020 CN-110699629-A

High-entropy amorphous powder with high-temperature erosion resistance and plasma spraying function, coating of high-entropy amorphous powder, preparation method of coating and application of coating

China

508

2020 CN-110714154-A

ZrTiHfNbTa high-entropy alloy and preparation method thereof

China

509

2020 CN-109706363-B

Eutectic high-entropy alloy and preparation method thereof

China

510

2020 US-2020030922-A1

Novel high-entropy alloy compositions

US

511

2020 CN-108950299-B

High-entropy alloy-diamond combined superhard composite material and preparation method thereof

China

512

2020 KR-102075751-B1

Preparation method of body-centered cubic high-entropy alloy spherical powder

South Korea

513

2020 CN-110776310-A

Method for preparing perovskite type composite oxide high-entropy ceramic powder by coprecipitation of ion compensation mixture

China

(continued)

Appendix C

385

(continued) Sr. No.

Year

Patents no

Patents name

Country

514

2020 CN-110776311-A

Method for preparing perovskite type composite China oxide high-entropy ceramic by hot-pressing sintering

515

2020 CN-110776323-A

High-purity superfine high-entropy ceramic powder and preparation method thereof

China

516

2020 CN-109266944-B

FeCoCrNiMn high-entropy alloy and preparation method thereof

China

517

2020 CN-110804711-A

High-entropy alloy powder and preparation method and application of laser cladding layer

China

518

2020 CN-110802323-A

High-entropy alloy arc-laser composite additive manufacturing method

China

519

2020 US-2020056272-A1

Twinning/transformation induced plasticity high US entropy steels and method of manufacturing the same

520

2020 CN-110818432-A

Superfine high-entropy boride nano powder and preparation method thereof

China

521

2020 CN-110819839-A

High-entropy alloy reinforced magnesium-based composite material and preparation method thereof

China

522

2020 CN-110835754-A

Preparation method of high-entropy alloy coating on surface of carbon steel

China

523

2020 CN-110079824-B

Method for preparing high-entropy alloy type electro-catalytic oxygen evolution reaction catalyst by high-energy ball milling

China

524

2020 CN-110846618-A

High-entropy alloy composite coating for surface protection of aluminum die-casting mold

China

525

2020 CN-110846547-A

High-entropy alloy combined tungsten carbide hard alloy and preparation method thereof

China

526

2020 KR-102070059-B1

High entropy alloys with intermetallic compound precipitates for strengthening and method for manufacturing the same

South Korea

527

2020 KR-102084121-B1

Quaternary high entropy alloy composition, quaternary high entropy alloy using the same and Manufacturing method thereof

South Korea

528

2020 KR-20200025803-A

High-strength and heat-resistant precipitates/dispersion strengthened high entropy super-alloys and method of manufacturing the same

South Korea

529

2020 CN-109604963-B

Preparation method of heterogeneous high-entropy alloy with variable modulation period and modulation ratio

China

530

2020 CN-109913736-B

Method for improving plasticity of high-entropy alloy China

531

2020 CN-109999830-B

CoCr(Mn/Al)FeNi high-entropy alloy-loaded nanoparticle catalyst and preparation method and application thereof

China

532

2020 CN-110903084-A

High-entropy oxide submicron powder and preparation method thereof

China

533

2020 CN-110899712-A

Aluminum-iron-containing high-entropy alloy suitable for additive manufacturing and modification method thereof

China

(continued)

386

Appendix C

(continued) Sr. No.

Year

534

Patents no

Patents name

Country

2020 CN-110923539-A

High-entropy alloy, preparation method thereof and compression performance testing method

China

535

2020 CN-110923538-A

High-entropy alloy with multidirectional annealing twin crystals and preparation method thereof

China

536

2020 CN-108754277-B

Cobalt-iron-nickel-vanadium-zirconium high-entropy alloy and preparation method thereof

China

537

2020 KR-102096311-B1

Preparation method of body-centered cubic high-entropy alloy powder and the powder thereof

South Korea

538

2020 CN-108330484-B

Preparation method of laser cladding formed refractory element high-entropy alloy coating layer

China

539

2020 CN-110964940-A

High-entropy alloy silver-impregnated composite material and preparation method and application thereof

China

540

2020 CN-109182878-B

Preparation method of pre-alloyed high-entropy alloy China porous material

541

2020 CN-111004959-A

FeNiCrCuCoBx nano high-entropy alloy and preparation method thereof

China

542

2020 CN-111014655-A

Two-phase high-entropy alloy powder and method for surface treatment of iron-based material by using same

China

543

2020 CN-109023002-B

Silicon solid solution reinforced VNbMoTaSi high-entropy alloy and preparation method thereof

China

544

2020 CN-111020339-A

High-entropy alloy for ultrahigh-hardness gear coating and manufacturing method

China

545

2020 KR-20200040970-A

Precipitation strengthenend high entropy steel and method for manufacturing the same

South Korea

546

2020 CN-111058076-A

Zr-based high-entropy alloy material and method for synthesizing porous spherical structure on surface of Zr-based high-entropy alloy

China

547

2020 CN-108060322-B

Preparation method of hard high-entropy alloy composite material

China

548

2020 CN-109277572-B

Pre-alloyed high-entropy alloy porous material and preparation method thereof

China

549

2020 CN-111057960-A

Method for preparing TiC reinforced iron-based high-entropy alloy composite material through electric arc melting

China

550

2020 CN-108504881-B

Method for improving wear resistance of high-entropy alloy

China

551

2020 CN-111056826-A

Gamma-type high-entropy rare earth disilicate with ultrahigh-temperature stability and preparation method thereof

China

552

2020 CN-108359948-B

Cr-Fe-V-Ta-W high-entropy alloy film for high-flux screening and preparation method thereof

China

553

2020 CN-111074199-A

Preparation method of high-entropy alloy layer on surface of tungsten alloy

China (continued)

Appendix C

387

(continued) Sr. No.

Year

Patents no

Patents name

Country

554

2020 CN-111074223-A

Physical vapor deposition preparation method of China high-entropy alloy film with uniform and controllable components

555

2020 CN-108642363-B

High-strength high-plasticity eutectic high-entropy alloy and preparation method thereof

China

556

2020 CN-111085689-A

FeCoCrNi series high-entropy alloy selective laser melting in-situ additive manufacturing method and product

China

557

2020 CN-108085634-B

Composite material containing high-entropy alloy/ceramic continuous gradient composite coating and preparation method and device thereof

China

558

2020 CN-110284042-B

Superplastic high-entropy alloy, sheet and preparation method thereof

China

559

2020 CN-111118378-A

High-entropy alloy for nuclear and preparation method thereof

China

560

2020 CN-111139471-A

Method for preparing superhard Zr on surface of zirconium alloy x Method for CrCoFeNi high-entropy alloy coating

China

561

2020 CN-111155082-A

Preparation method of FeCoNiCrMn high-entropy alloy coating

China

562

2020 US-2020157663-A1

High entropy alloy structure and a method of prepating the same

US

563

2020 CN-108130505-B

Method for preparing high-entropy alloy coating by plasma beam alloying

China

564

2020 CN-111206174-A

Magnetic ultrafine-grain high-strength high-entropy alloy and preparation method thereof

China

565

2020 CN-111206243-A

Biomedical high-entropy alloy coating and preparation method thereof

China

566

2020 CN-111218603-A

Preparation method of high-entropy alloy-based high-temperature solid lubricating composite material

China

567

2020 KR-20200060830-A

High entropy alloy and method for manufacturing the South same Korea

568

2020 CN-111217402-A

Hexahydric spinel type iron-cobalt-chromium-manganese-copper-zinc series high-entropy oxide and powder preparation method thereof

China

569

2020 CN-111218657-A

Amorphous tungsten-based high-entropy alloy thin film material and preparation method thereof

China

570

2020 CN-111233454-A

Preparation method of spinel type iron-cobalt-chromium-manganese-magnesium series high-entropy oxide powder

China

571

2020 CN-109019701-B

Preparation method of rock salt type (MgCoCuNiZn) China O high-entropy oxide powder material (continued)

388

Appendix C

(continued) Sr. No.

Year

572

Patents no

Patents name

Country

2020 CN-111233456-A

Hexahydric spinel type Fe-Co-Cr-Mn-Ni-Zn series high-entropy oxide and powder preparation method thereof

China

573

2020 CN-111254376-A

Preparation method of high-entropy ceramic composite coating

China

574

2020 CN-111254299-A

Method for regulating and controlling performance of CoCrFeNiAl high-entropy alloy

China

575

2020 CN-111254298-A

High-entropy alloy resistant to molten aluminum corrosion and preparation method thereof

China

576

2020 CN-111254339-A

Five-tungsten-series high-entropy alloy and preparation method thereof

China

577

2020 CN-111270094-A

Refractory high-entropy alloy and forming method thereof

China

578

2020 CN-111270207-A

Preparation method of high-entropy alloy thin film material with layered structure

China

579

2020 CN-111270203-A

AlCrNbSiTiCN high-entropy alloy nano composite coating for die-casting die and preparation method thereof

China

580

2020 CN-111286664-A

Superfine tungsten carbide hard alloy with high-entropy alloy as binder phase and preparation method thereof

China

581

2020 EP-3487826-B1

Coated article supporting high-entropy nitride thin film inclusive coating, and method of making the same

European

582

2020 CN-111304479-A

Preparation method of VCrNbMoW refractory high-entropy alloy

China

583

2020 CN-111304512-A

Medium–high entropy alloy material, preparation method and application thereof

China

584

2020 KR-20200071973-A

Design method for high entropy alloys using computer simulation method

South Korea

585

2020 CN-108946787-B

Preparation method of rare earth-based fluorite type high-entropy oxide powder material

China

586

2020 CN-109022989-B

Preparation method of high-entropy alloy binding phase tungsten-based high-specific gravity alloy

China

587

2020 CN-109022990-B

Preparation method of high-entropy alloy binding phase Ti (C, N) -based metal ceramic

China

588

2020 CN-111318805-A

Laser welding method for high-entropy alloy with preset powder

China

589

2020 CN-111318801-A

Intermetallic compound based on high-entropy alloy diffusion welding and preparation method thereof

China

590

2020 CN-111318716-A

High-entropy alloy spherical powder for powder bed melting additive manufacturing and preparation method and application thereof

China

(continued)

Appendix C

389

(continued) Sr. No.

Year

591

Patents no

Patents name

Country

2020 CN-111334698-A

Wear-resistant high-entropy alloy containing modulation and demodulation decomposition structure and capable of generating hard phase and preparation method of wear-resistant high-entropy alloy

China

592

2020 CN-111333124-A

Spinel-type mesoporous high-entropy oxide nanosphere with hollow structure and preparation method and application thereof

China

593

2020 CN-111333414-A

Preparation method of spinel type iron-cobalt-chromium-manganese-zinc series high-entropy oxide powder

China

594

2020 CN-111333415-A

Preparation method of spinel type iron-cobalt-chromium-manganese-nickel high-entropy oxide powder

China

595

2020 CN-111331279-A

High-entropy alloy preform and fusion welding method of titanium and stainless steel

China

596

2020 CN-108950349-B

CoFeNi2VZrx eutectic high-entropy alloy and preparation method thereof

China

597

2020 CN-111349800-A

Preparation method of high-entropy alloy duplex process

China

598

2020 CN-109023013-B

Preparation method of corrosion-resistant high-strength AlCoCrFeNi-Cu high-entropy alloy

China

599

2020 CN-110229991-B

Quinary high-entropy alloy with excellent strong plasticity matching and preparation method thereof

China

600

2020 CN-111362683-A

Hexahydric spinel type China iron-cobalt-chromium-manganese-magnesium-nickel high-entropy oxide and powder preparation method thereof

601

2020 CN-108220740-B

Wear-resistant and corrosion-resistant high-entropy alloy material and preparation method thereof

China

602

2020 CN-109554660-B

Preparation method of high-entropy alloy surface boronizing layer

China

603

2020 CN-111390166-A

High-entropy alloy-based self-lubricating composite China material with imitated lattice structure and containing solid lubricant

604

2020 CN-111394721-A

High-entropy alloy powder mixture, coating and coating preparation method

China

605

2020 CN-108642362-B

High-entropy alloy and preparation method thereof

China

606

2020 CN-109518064-B

Nano porous high-entropy alloy microsphere material and preparation method thereof

China

607

2020 CN-110423904-B

Method for preparing Ni-Cr-Co-Fe-Mn high-entropy alloy by electron beam melting, homogenization and purification

China

608

2020 CN-108747006-B

Laser welding method of CoCrCuFeNi high-entropy alloy

China (continued)

390

Appendix C

(continued) Sr. No.

Year

609

Patents no

Patents name

Country

2020 CN-108359877-B

High-plasticity AlCoCuFeNi 1.5 high-entropy alloy and preparation method thereof

China

610

2020 CN-109252162-B

High-entropy alloy with antifriction and wear-resistant properties

China

611

2020 CN-107824801-B

Preparation method of amorphous CoCrCuFeNi high-entropy alloy powder with different morphologies

China

612

2020 CN-111421261-A

High-entropy alloy solder for electronic packaging assembly brazing and preparation method thereof

China

613

2020 CN-111423236-A

(Hf)0.25 Ti0.25 Zr0.25 W0.25 ) N high-entropy ceramic powder and preparation method thereof

China

614

2020 CN-111441026-A

Preparation method of high-entropy alloy with dual-phase structure

China

615

2020 CN-108179345-B

Wear-resistant and corrosion-resistant CrVNiHfNb high-entropy alloy and preparation method thereof

China

616

2020 CN-108950255-B

Five-element FeCoNiMoSi series high-entropy alloy and preparation method thereof

China

617

2020 CN-111470859-A

Hexahydric spinel type iron-cobalt-chromium-manganese-magnesium-zinc series high-entropy oxide and powder preparation method thereof

China

618

2020 CN-111471909-A

Five-component magnetic high-entropy alloy and preparation method thereof

China

619

2020 CN-109252187-B

High-entropy alloy electrocatalyst, preparation method and application of high-entropy alloy electrocatalyst in water decomposition hydrogen production

China

620

2020 CN-110747383-B

High-entropy alloy based on intermetallic compound and preparation method thereof

China

621

2020 KR-20200093826-A

Refractory high entropy superalloy with bcc dual phase and manufacturing method for the same

South Korea

622

2020 WO-2020155283-A1 High-entropy alloy boride ceramic, and preparation method therefor and application thereof

WIPO (PCT)

623

2020 CN-108728876-B

Preparation method of FeCoNiCuMo high-entropy alloy film

China

624

2020 CN-108842076-B

Ni-Co-Cr-Ti-Ta high-entropy eutectic alloy and preparation method thereof

China

625

2020 CN-111497374-A

Metal and high-entropy alloy laminated composite material and preparation method thereof

China

626

2020 CN-110438385-B

Al-Co-Cr-Ni quaternary high-entropy alloy system and preparation method thereof

China

627

2020 CN-110364717-B

Spinel type high-entropy oxide electrode material and preparation method thereof

China

628

2020 CN-111519078-A

High-nickel eutectic high-entropy alloy powder for additive manufacturing and preparation method thereof

China

(continued)

Appendix C

391

(continued) Sr. No.

Year

629

Patents no

Patents name

Country

2020 CN-111533557-A

Pyrochlore type high-entropy oxide solidified body and preparation method thereof

China

630

2020 CN-109266946-B

Preparation method of Ti-based high-entropy amorphous-dendritic crystal composite material

China

631

2020 CN-111533559-A

Carbon-deficiency type high-entropy transition metal China carbide ceramic material and preparation method thereof

632

2020 CN-111545746-A

Method for improving density and performance of China microwave sintered ferromagnetic high-entropy alloy

633

2020 CN-111560582-A

Method for manufacturing superhard high-entropy alloy nitride coating on alloy cutter

634

2020 CN-108130502-B

Preparation method and device of composite material China containing high-entropy alloy coating

635

2020 CN-108103495-B

High-temperature-resistant high-entropy alloy tool steel coating material and preparation method of coating

China

636

2020 CN-111575574-A

Eutectic high-entropy alloy powder for laser repair and preparation method and application thereof

China

637

2020 EP-3698900-A1

Method for identifying and forming viable high entropy alloys via additive manufacturing

European

638

2020 CN-109468638-B

Preparation method of diamond-enhanced high-entropy alloy composite coating

China

639

2020 CN-111593248-A

High-entropy alloy and preparation thereof, coating comprising alloy and preparation

China

640

2020 CN-110735077-B

AlCrFeNiSiTi high-entropy alloy porous material and preparation method thereof

China

641

2020 CN-111604652-A

Resistance butt welding preparation method of high-entropy alloy coating

China

642

2020 CN-108315686-B

Pseudo-high-entropy alloy coating formula and coating preparation method thereof

China

643

2020 CN-111621660-A

Precipitation strengthening type high-temperature high-entropy alloy capable of precipitating carbide in situ and preparation method thereof

China

644

2020 CN-110919232-B

Gold-based high-entropy brazing filler metal

China

645

2020 CN-110079798-B

Method for laser cladding of titanium-chromium-aluminum-silicon-nickel high-entropy alloy on surface of titanium alloy plate

China

646

2020 CN-111633218-A

High-entropy alloy powder and oxygen-free sintering China preparation method thereof

647

2020 US-2020283874-A1

High-Performance Corrosion-Resistant High-Entropy Alloys

US

648

2020 CN-109722584-B

Method for preparing molybdenum-tungsten-tantalum-titanium-zirconium high-entropy alloy

China

China

(continued)

392

Appendix C

(continued) Sr. No.

Year

649

Patents no

Patents name

Country

2020 CN-111686758-A

RuFeCoNiCu high-entropy alloy nanoparticle catalyst and preparation method and application thereof

China

650

2020 CN-109628777-B

Method for improving corrosion resistance of high-entropy alloy

China

651

2020 CN-109252081-B

High-entropy alloy binding phase superfine tungsten carbide hard alloy and preparation method thereof

China

652

2020 CN-108588627-B

High-entropy alloy coating for thermal insulation protection

China

653

2020 CN-111725380-A

Layered high-entropy MAX-phase ceramic thermoelectric material and preparation method thereof

China

654

2020 US-2020308683-A1

Precipitation Strengthening AlCrFeNiV system high entropy alloy and manufacturing method thereof

US

655

2020 CN-108950343-B

WC-based hard alloy material based on high-entropy China alloy and preparation method thereof

656

2020 CN-111733359-A

AlCu-series high-entropy alloy and preparation method thereof

China

657

2020 CN-109402578-B

Method for preparing high-entropy alloy coating based on reactive magnetron sputtering technology

China

658

2020 CN-110106428-B

High-entropy alloy with banded precipitated phases and preparation method thereof

China

659

2020 CN-110004348-B

Graphene-reinforced high-entropy alloy composite material and preparation method thereof

China

660

2020 CN-108359939-B

Band gap-variable AlCoCrFeNi high-entropy alloy oxide semiconductor film and preparation method thereof

China

661

2020 CN-109108273-B

Preparation method of NbZrTiTa refractory high-entropy alloy powder and NbZrTiTa refractory high-entropy alloy powder

China

662

2020 CN-110777273-B

Method for improving room temperature plasticity of China refractory high-entropy alloy

663

2020 CN-109778050-B

WVTaTiZr refractory high-entropy alloy and preparation method thereof

China

664

2020 CN-111790397-A

Preparation method and application of high-entropy metal oxide catalyst

China

665

2020 CN-111799524-A

Method for preparing five-element high-entropy lithium battery material precursor from retired lithium battery positive plate

China

666

2020 CN-108441706-B

High-entropy alloy reinforced nickel-aluminum composite material and preparation method thereof

China

667

2020 CN-109913673-B

High-entropy alloy resisting molten aluminum corrosion and preparation method thereof

China

668

2020 CN-111809094-A

High-entropy alloy resistant to high-temperature oxidation, thermal barrier coating and preparation method of thermal barrier coating

China

(continued)

Appendix C

393

(continued) Sr. No.

Year

669

Patents no

Patents name

Country

2020 CN-108796444-B

Preparation method of high-hardness quaternary refractory high-entropy alloy film

China

670

2020 CN-111822806-A

NiZr brazing filler metal vacuum brazing Al0.3Method for CoCrFeNi high-entropy alloy

China

671

2020 CN-109261935-B

High-entropy alloy reinforced aluminum-based composite material and extrusion casting method thereof

China

672

2020 CN-111825085-A

CO regulated by ionic liquid2System and method for China preparing graphene by stripping through high-entropy solution induced cavitation field

673

2020 CN-109576519-B

Preparation method of iron-copper-manganese-nickel China high-entropy alloy

674

2020 CN-111850543-A

Laser cladding seven-element high-entropy alloy coating and preparation method thereof

China

675

2020 CN-111850544-A

High-entropy alloy coating and preparation method thereof

China

676

2020 CN-111872388-A

Method for preparing high-entropy alloy based on selective laser melting technology

China

677

2020 CN-110842364-B

Laser cladding welding high-entropy alloy AlCoCrFeNi/27SiMn steel composite layer and preparation method thereof

China

678

2020 CN-108480615-B

High-entropy alloy powder, preparation method thereof and application thereof in 3D printing

China

679

2020 CN-110310793-B

Hard magnetic high-entropy alloy and preparation method thereof

China

680

2020 CN-109457164-B

AlNbMoVTi high-entropy alloy powder and application thereof

China

681

2020 CN-110607473-B

Transition metal carbonitride-based high-entropy metal ceramic and preparation method and application thereof

China

682

2020 CN-111893357-A

Self-supporting three-dimensional nano hierarchical pore high-entropy alloy electrolytic water material and preparation method thereof

China

683

2020 CN-111908922-A

Low-temperature synthesized rare earth hafnate high-entropy ceramic powder and preparation method thereof

China

684

2020 CN-111910114-A

Endogenous nano carbide reinforced multi-scale FCC high-entropy alloy-based composite material and preparation method thereof

China

685

2020 CN-111922468-A

SiC ceramic brazing method based on multi-element high-entropy alloy and brazing material

China

686

2020 CN-111924899-A

Method for preparing nickel-cobalt-iron-aluminum-magnesium five-element high-entropy material, product and application

China

(continued)

394

Appendix C

(continued) Sr. No.

Year

Patents no

687

2020 CN-111926232-A

Patents name

Country

High-entropy alloy material and preparation method thereof

China

688

2020 CN-110106457-B

High-entropy alloy impact heat treatment method

China

689

2020 CN-111926280-A

High-entropy alloy coating of long-life spray gun for Isa smelting and preparation method thereof

China

690

2020 CN-111945099-A

Preparation method of CoCrFeNi high-entropy alloy coating

China

691

2020 CN-111945033-A

High-entropy alloy with neutron poison characteristic China and preparation method thereof

692

2020 KR-102181568-B1

Transformation-induced-plasticity dual-phase high-entropy alloy and manufacturing method of the same

South Korea

693

2020 CN-111961893-A

High-strength high-plasticity high-entropy alloy and preparation method thereof

China

694

2020 CN-110255610-B

A-site high-entropy perovskite oxide and preparation China method and application thereof

695

2020 CN-111979465-A

High-entropy alloy for manufacturing flexible gear and processing method of flexible gear

China

696

2020 CN-111982641-A

FeCoNiCrMnAl high-entropy alloy electrolytic corrosion electrolyte and display method of metallographic structure thereof

China

697

2020 CN-111995400-A

High-entropy ceramic material with excellent tribological property and preparation method thereof

China

698

2020 CN-112011712-A

Component formula and preparation process of novel China light refractory high-entropy alloy

699

2020 CN-109972066-B

Method for improving AlCoCrCuFeNi high-entropy China alloy force magnetic property by using magnetic field

700

2020 CN-112063961-A

Preparation method of high-entropy alloy coating

China

701

2020 CN-212158106-U

Vacuum hot-pressing sintering equipment for high-entropy alloy coating

China

702

2020 CN-112095040-A

Multi-principal-element high-entropy alloy and preparation method thereof

China

703

2020 CN-110157971-B

Induction smelting method of in-situ reinforced high-entropy alloy composite material

China

704

2020 CN-112126803-A

Preparation method of high-entropy alloy nano porous material

China

705

2020 CN-107841672-B

Re-containing high-density ReWTaMoNbx high-entropy alloy material and preparation method thereof

China

706

2021 CN-110284032-B

Preparation method of high-entropy alloy particle reinforced magnesium-based composite material

China

707

2021 CN-112157261-A

Preparation method and application of high-entropy alloy part with laser melting deposition reaction structure

China

(continued)

Appendix C

395

(continued) Sr. No.

Year

Patents no

Patents name

Country

708

2021 CN-108383507-B

Method for preparing high-emissivity complex phase China ceramic and FeCrCoNi high-entropy alloy in one step

709

2021 CN-110541103-B

High-strength high-plasticity quaternary refractory high-entropy alloy and preparation method thereof

China

710

2021 CN-108277418-B

MoNbTaTiHf high-entropy alloy material and preparation method thereof

China

711

2021 CN-110106490-B

High-temperature-resistant high-entropy alloy NbMoTaWV film and preparation method thereof

China

712

2021 CN-112195463-A

AlCoCrFeNi/NbC gradient high-entropy alloy coating material prepared by laser cladding and method

China

713

2021 CN-112225559-A

Zr-doped high-entropy perovskite oxide ceramic China material with high energy storage and high efficiency, and preparation method and application thereof

714

2021 CN-111111693-B

Preparation method of monodisperse platinum-series high-entropy alloy nanoparticle catalyst

China

715

2021 CN-112226766-A

Preparation method of high-entropy alloy powder laser cladding layer

China

716

2021 CN-109898005-B

High-strength WVTaZrHf refractory high-entropy alloy and preparation method thereof

China

717

2021 CN-112222674-A

High-entropy alloy for brazing TiAl and nickel-based China high-temperature alloy and preparation method thereof

718

2021 CN-110818430-B

Uniform high-entropy oxide ceramic submicron spherical powder and preparation method thereof

China

719

2021 CN-110129731-B

Anti-fatigue high-entropy alloy film and preparation method thereof

China

720

2021 CN-112267055-A

ZrTi-based eutectic high-entropy alloy and preparation method thereof

China

721

2021 CN-110983146-B

Preparation method of large-size manganese-containing high-entropy alloy ingot

China

722

2021 CN-112267056-A

High-entropy alloy component and manufacturing method thereof

China

723

2021 CN-109136599-B

Preparation process of high-entropy alloy inoculated hypoeutectic aluminum-silicon alloy

China

724

2021 CN-112276076-A

Preparation method of wide-temperature-range high-entropy alloy-based solid lubricating composite material

China

725

2021 CN-111085685-B

Porous high-entropy alloy material and preparation method and application thereof

China

726

2021 CN-109402590-B

Method for preparing high-entropy alloy coating through magnetron sputtering

China

727

2021 CN-112323058-A

Preparation method of FCC-BCC two-phase high-entropy alloy gradient material

China (continued)

396

Appendix C

(continued) Sr. No.

Year

728

Patents no

Patents name

Country

2021 CN-112331840-A

Nickel-cobalt-rich high-entropy ceramic cathode material for lithium ion battery and preparation method thereof

China

729

2021 CN-110964938-B

High-entropy alloy wear-resistant composite material, preparation method and application

China

730

2021 CN-112340787-A

Single-phase spinel type high-entropy oxide, preparation method and application

China

731

2021 CN-108933248-B

Preparation method of spinel-type spherical high-entropy oxide material as negative electrode material of lithium ion battery

China

732

2021 CN-109097708-B

Method for improving surface performance of single-phase high-entropy alloy

China

733

2021 CN-112376043-A

Method for preparing high-entropy alloy composite coating on surface of low-carbon steel

China

734

2021 CN-110541104-B

Low-density two-phase high-entropy alloy material and preparation method thereof

China

735

2021 CN-108555295-B

Laser three-dimensional forming method of high-entropy alloy component

China

736

2021 CN-109604611-B

Forming method for preparing wear-resistant corrosion-resistant high-entropy alloy gear through powder metallurgy

China

737

2021 KR-102220215-B1

High entropy metallic glasses with high hardness

South Korea

738

2021 EP-3392359-B1

High entropy alloy member, method for producing alloy member, and product using alloy member

European

739

2021 CN-212596086-U

Vertical ball mill for processing high-entropy alloy powder

China

740

2021 CN-110961631-B

Laser rapid preparation method of AlxCoCrFeNi high-entropy alloy

China

741

2021 CN-112408984-A

High-temperature-resistant near-infrared-absorption China high-entropy ceramic and preparation method thereof

742

2021 CN-109987935-B

(ZrHfCeTiZn) O having fluorite structure2Preparation method of-delta high-entropy oxide ceramic powder and block

China

743

2021 CN-112441837-A

High-performance (VNbTaMoW) C high-entropy carbide ceramic and preparation method thereof

China

744

2021 CN-112442668-A

High-entropy alloy-based spectrum selective solar energy absorption coating and preparation method thereof

China

745

2021 CN-111218602-B

High-entropy alloy, preparation method and application thereof, and stirring tool for friction stir welding

China

746

2021 CN-112467119-A

Preparation method and application of layered high-entropy oxide sodium-ion battery positive electrode material

China

(continued)

Appendix C

397

(continued) Sr. No.

Year

747

Patents no

Patents name

Country

2021 CN-112457017-A

High-performance (TiTaHfZrNb) C high-entropy carbide ceramic and preparation method thereof

China

748

2021 US-10941463-B2

High-entropy alloy foam and manufacturing method for the foam

US

749

2021 CN-112458352-A

Corrosion-resistant aluminum-transition metal series biphase high-entropy alloy and preparation method thereof

China

750

2021 CN-112475315-A

Method for universally preparing high-entropy alloy nanoparticles

China

751

2021 CN-111303581-B

High-entropy carbide ceramic precursor containing rare earth, high-entropy ceramic and preparation method

China

752

2021 CN-110195208-B

Variable band gap NbMoTaWV high-entropy alloy oxide film and preparation method thereof

China

753

2021 CN-112522529-A

Method for preparing high-entropy alloy particle reinforced aluminum matrix composite material by electromagnetic stirring casting

China

754

2021 CN-112537804-A

Lithium-doped high-entropy oxide battery negative electrode material and preparation and application methods thereof

China

755

2021 CN-110952041-B

Fe-Mn-Ni-Cr four-component high-entropy alloy

China

756

2021 CN-110904377-B

Refractory high-entropy alloy powder and preparation method thereof

China

757

2021 CN-109402484-B

Preparation method of coupled AlxCoCrFeNi high-entropy alloy by isometric crystal and nano precipitation

China

758

2021 CN-112553517-A

Preparation method and process of wear-resistant CrMoNiTaHfW high-entropy alloy

China

759

2021 CN-112553564-A

Method for further improving wear resistance of high-entropy alloy coating

China

760

2021 CN-111644624-B

High-entropy alloy of refractory metal with porous structure and preparation method thereof

China

761

2021 CN-111471268-B

Carbide high-entropy ceramic precursor, high-entropy ceramic and preparation method

China

762

2021 CN-111004957-B

Non-equal atomic ratio high-entropy alloy and preparation method thereof

China

763

2021 CN-109516811-B

Multi-element high-entropy ceramic and preparation method and application thereof

China

764

2021 CN-110499451-B

High-strength high-plasticity wear-resistant high-entropy alloy and preparation method thereof

China

765

2021 CN-109678523-B

High-entropy ceramic with high-temperature strength China and hardness and preparation method and application thereof

766

2021 CN-110438387-B

Silicide precipitation strengthening refractory high-entropy alloy and preparation method thereof

China (continued)

398

Appendix C

(continued) Sr. No.

Year

767

Patents no

Patents name

Country

2021 CN-112626405-A

High-entropy alloy for hydrogen evolution catalysis and preparation method thereof

China

768

2021 CN-107994228-B

Five-element high-entropy oxide nano film of lithium China ion battery and preparation and application thereof

769

2021 CN-110538945-B

Refractory high-entropy alloy stranded wire material, China application and preparation method thereof

770

2021 CN-110860784-B

Friction stir welding method for preparing bulk high-entropy alloy

China

771

2021 CN-110172630-B

Quaternary hypoeutectic high-entropy alloy with good strong plasticity matching and preparation method thereof

China

772

2021 CN-109252083-B

Multiphase high-entropy alloy and preparation method thereof

China

773

2021 CN-112663049-A

High-temperature-wear-resistant carbide composite high-entropy alloy and laser cladding preparation method thereof

China

774

2021 CN-112662928-A

Amorphous-coated nanocrystalline dual-phase China high-strength high-entropy alloy film and preparation method thereof

775

2021 RU-2746673-C1

Method for producing powder containing single-phase high-entropy carbide of composition Ti-Bb-Zr-Hf-Ta-c with cubic lattice

Russia

776

2021 US-2021114095-A1

Complex concentrated alloy and high entropy alloy additive manufacturing systems and methods

US

777

2021 CN-112692275-A

Low-density biphase high-entropy alloy powder suitable for 3DP printing technology and preparation method thereof

China

778

2021 CN-111172446-B

Strong corrosion-resistant non-equal atomic ratio high-entropy alloy and preparation method thereof

China

779

2021 CN-110405300-B

Method for preparing high-strength AlCoCrFeNi high-entropy alloy joint by adopting Ni-based brazing filler metal

China

780

2021 CN-112708817-A

High-plasticity low-neutron absorption cross-section refractory high-entropy alloy material and preparation method thereof

China

781

2021 CN-112723862-A

Method for preparing high-entropy oxide ceramic material simply and low in consumption

China

782

2021 CN-112719272-A

Method for manufacturing high-entropy alloy gear through additive manufacturing

China

783

2021 CN-110656272-B

Magnesium-based hydrogen storage material based China on high entropy effect and preparation method thereof

784

2021 CN-112725677-A

High-strength high-toughness TiZrHfNbSc refractory China high-entropy alloy and preparation method thereof

785

2021 CN-110257684-B

Preparation process of FeCrCoMnNi high-entropy alloy-based composite material

China (continued)

Appendix C

399

(continued) Sr. No.

Year

Patents no

786

2021 CN-109338200-B

Patents name

Country

High-temperature high-damping high-entropy alloy and preparation method thereof

China

787

2021 US-2021130936-A1

High-entropy alloys with high strength

US

788

2021 CN-109694979-B

High-entropy alloy-based composite material prepared by vacuum induction melting and preparation method thereof

China

789

2021 CN-110714156-B

Light high-strength corrosion-resistant high-entropy alloy and preparation method thereof

China

790

2021 CN-111101043-B

CrMoVNbAl high-entropy alloy manufactured by laser additive manufacturing and forming process thereof

China

791

2021 AU-2021101501-A4

Method for preparing high-entropy alloy layer on surface of medical b type titanium alloy

Australia

792

2021 CN-112792346-A

Preparation method of TiB 2-enhanced high-entropy alloy powder for 3D printing

China

793

2021 CN-111534712-B

Preparation method of graphene-reinforced FCC (fluid catalytic cracking) high-entropy alloy

China

794

2021 CN-111850373-B

Ti (C, N)-based metal ceramic with high-entropy ring-phase structure and preparation method thereof

China

795

2021 CN-110129751-B

Multilayer composite film of high-entropy alloy and metal glass and preparation method

China

796

2021 CN-110423931-B

Method for preparing Ti-Zr-Hf-Nb-Ta refractory high-entropy alloy by electron beam melting homogenization

China

797

2021 CN-109079137-B

In-situ preparation method for gradient powder feeding laser additive manufacturing high-entropy alloy

China

798

2021 CN-112813332-A

High-entropy alloy based on solid solution and precipitation strengthening effect and preparation method thereof

China

799

2021 CN-112813331-A

Co-Cr-Fe-Ni-Mn eutectic high-entropy cast iron, preparation method and application

China

800

2021 US-2021146602-A1

Fused filament fabrication of high entropy alloys

US

801

2021 CN-109175346-B

Soft magnetic high-entropy alloy powder and preparation method thereof

China

802

2021 CN-110373596-B

Soft magnetic high-entropy alloy material with island-shaped magnetic crystal structure and preparation method thereof

China

803

2021 CN-112830785-A

Layered high-entropy diboron carbide ceramic powder and preparation method thereof

China

804

2021 CN-112831711-A

High-performance low-density two-phase high-entropy alloy and preparation method thereof

China

805

2021 CN-112830791-A

High-entropy ceramic and preparation method and application thereof

China

806

2021 CN-112851352-A

Ultrahigh-temperature high-entropy carbide powder and preparation method thereof

China (continued)

400

Appendix C

(continued) Sr. No.

Year

807

Patents no

Patents name

Country

2021 CN-112853347-A

Method for preventing Cr and Al-containing high-entropy alloy coating from being oxidized by adding Si

China

808

2021 RO-134977-A2

High-entropy alloy of the moNbTaTizr system microalloyed with yttrium, for medical applications, and consolidation process

Romania

809

2021 CN-111235455-B

W-Ta-Mo-Nb-Zr high-temperature high-entropy alloy and preparation method thereof

China

810

2021 CN-111349839-B

Whisker toughened FCC (fluid catalytic cracking) high-entropy alloy composite material and preparation method thereof

China

811

2021 CN-110484764-B

Nano porous high-entropy alloy and preparation method thereof

China

812

2021 CN-112876067-A

High-hardness high-young’s modulus oxide high-entropy glass and preparation method and application thereof

China

813

2021 CN-112875703-A

High-entropy two-dimensional material, high-entropy MAX phase material and preparation method thereof

China

814

2021 CN-112872523-A

Brazing method for welding titanium-based high-entropy alloy and silicon nitride ceramic

China

815

2021 WO-2021104108-A1 Marine-microbial-corrosion-resistant high-entropy alloy, preparation method therefor and use thereof

WIPO (PCT)

816

2021 CN-112893852-A

Preparation method of refractory high-entropy alloy powder

China

817

2021 CN-112893468-A

Method for improving strength of Fe-Mn-Cr-Ni high-entropy alloy through corrugated rolling and plain rolling process

China

818

2021 CN-110344047-B

In-situ synthesis low-pressure cold spraying CuNiCoFeCrAl2.8 preparation method of high-entropy alloy coating

China

819

2021 CN-112894076-A

Double-wire electric arc additive manufacturing gradient high-entropy alloy equipment and manufacturing method of high-entropy alloy

China

820

2021 CN-112897989-A

B-site high-entropy perovskite oxide Sr0.9 La0.1 MO3 ceramic and preparation method thereof

China

821

2021 CN-112916870-A

Preparation method of medium–high entropy alloy material

China

822

2021 CN-112921228-A

Preparation method of aluminum-nickel-loaded 3D skeleton high-entropy alloy composite energetic fragment

China

823

2021 CN-112919908-A

Novel perovskite structure high-entropy ceramic and preparation method thereof

China

824

2021 CN-109913732-B

Irradiation-resistant FCC structure high-entropy alloy China

825

2021 CN-108723371-B

Preparation method of high-entropy alloy reinforced aluminum matrix composite

China (continued)

Appendix C

401

(continued) Sr. No.

Year

826

Patents no

Patents name

Country

2021 CN-112935252-A

Method for preparing high-toughness eutectic high-entropy alloy based on selective laser melting technology

China

827

2021 CN-110230056-B

Low-melting-point high-entropy alloy powder for magnesium-lithium alloy laser surface modification and preparation method and application thereof

China

828

2021 CN-112951180-A

Application of amorphous alloy and/or high-entropy alloy in musical instrument

China

829

2021 CN-111235453-B

Hard alloy with high-entropy alloy layer on surface and preparation method thereof

China

830

2021 CN-112960978-A

A-site high-entropy perovskite oxide MeTiO3 Thermoelectric ceramic and preparation method thereof

China

831

2021 CN-111411249-B

Preparation method of VNbMoTaW high-entropy alloy

China

832

2021 CN-112143924-B

Preparation method of multi-scale high-strength China high-entropy alloy material for corrosive environment

833

2021 CN-113030166-A

Measuring device for semi-solid rheological behavior China of high-entropy alloy and using method thereof

834

2021 CN-113024232-A

Light-heavy rare earth mixed high-entropy rare earth silicate compact block and preparation method thereof

China

835

2021 CN-111185188-B

Iron-cobalt–nickel-copper-based high-entropy alloy electrolytic water catalytic material and preparation method thereof

China

836

2021 CN-113025953-A

High-entropy alloy nitride composite coating and preparation method and application thereof

China

837

2021 CN-113046614-A

NbMoHfTiZrAlSi refractory high-entropy alloy and preparation method thereof

China

High-entropy alloy target material preparation device China

838

2021 CN-110965034-B

839

2021 WO-2021128282-A1 Iron-cobalt–nickel-copper-based high-entropy alloy water electrolysis catalytic material and preparation method therefor

WIPO (PCT)

840

2021 CN-113061794-A

Two-phase double-coherent light high-entropy alloy and preparation method thereof

China

841

2021 CN-113061925-A

Preparation method of hierarchical-pore high-entropy China alloy water electrolysis catalyst

842

2021 US-11053567-B2

Method for the fabrication of architected 3D high entropy alloy structures

843

2021 CN-111334697-B

W-Ta-Mo-Nb-C high-temperature high-entropy alloy China and preparation method thereof

844

2021 CN-109987941-B

High-entropy ceramic composite material with oxidation resistance and preparation method and application thereof

US

China

(continued)

402

Appendix C

(continued) Sr. No.

Year

845

Patents no

Patents name

Country

2021 CN-109879669-B

High-entropy ceramic composite material with high strength and preparation method and application thereof

China

846

2021 CN-110452010-B

High-entropy alloy-connected silicon carbide ceramic connecting piece and preparation method and application thereof

China

847

2021 CN-113088746-A

High-entropy alloy particle refinement reinforced aluminum matrix composite and preparation method thereof

China

848

2021 CN-110002879-B

Compact and superhard high-entropy boride ceramic and preparation method and application thereof

China

849

2021 CN-113088785-A

Body-centered cubic high-entropy alloy and preparation method thereof

China

850

2021 CN-113106316-A

High-strength and high-toughness CrMnFeNi dual-phase high-entropy alloy and preparation method thereof

China

851

2021 CN-110219002-B

High-entropy alloy composite coating material for repairing die and die repairing method

China

852

2021 CN-113122764-A

Preparation method of CuCrFeCoNixTi high-entropy China alloy thin strip

853

2021 CN-110093522-B

Improvement of AlCoCrFeNi by magnetic field2.1Method for mechanical property of eutectic high-entropy alloy

854

2021 CN-110777278-B

Ultrahigh-temperature composite material based on China refractory high-entropy alloy and preparation method thereof

China

855

2021 CN-111620681-B

Preparation method of high-entropy oxide material

China

856

2021 CN-113151725-A

Method for enhancing wear resistance of refractory high-entropy alloy

China

857

2021 CN-110358962-B

Large-size regular billet refractory high-entropy alloy China and preparation method thereof

858

2021 CN-113151764-A

Improve Al x Method for high-temperature service performance of CoCrFeNi high-entropy alloy

China

859

2021 CN-111349838-B

Preparation method of high-entropy alloy composite material

China

860

2021 CN-113171779-A

Preparation method and application of B-site five-membered high-entropy perovskite catalyst

China

861

2021 CN-113172108-A

High-entropy alloy thin-walled tube ultralow-temperature extrusion forming device and method

China

862

2021 CN-113185295-A

Method for preparing MAX-phase high-entropy ceramic material

China

863

2021 CN-113182632-A

Method for connecting C/C composite material by adopting high-entropy alloy brazing

China (continued)

Appendix C

403

(continued) Sr. No.

Year

864

Patents no

Patents name

Country

2021 CN-113186443-A

Aluminum-cobalt-chromium-iron-nickel high-entropy alloy containing nano strengthening phase gamma’ phase and preparation method thereof

China

865

2021 CN-111592361-B

Nitride high-entropy ceramic fiber and preparation method and application thereof

China

866

2021 CN-113201678-A

Carbon-containing high-entropy alloy material and preparation method thereof

China

867

2021 CN-111592358-B

Carbide high-entropy ceramic fiber and preparation method thereof

China

868

2021 CN-113215468-A

Two-phase high-entropy high-temperature alloy and additive manufacturing method thereof

China

869

2021 CN-113215563-A

High-temperature-friction-wear-resistant high-entropy alloy coating and preparation method thereof

China

870

2021 CN-113215466-A

AlFeNiCrMo high-entropy alloy, preparation method China and application thereof

871

2021 CN-113210629-A

AlCoCrFeNi2.1 eutectic high-entropy alloy and laser China selective material increase manufacturing method thereof

872

2021 WO-2021158620-A1 Cation-disordered rocksalt type high entropy cathode WIPO with reduced short-range order for li-ion batteries (PCT)

873

2021 CN-111761074-B

Preparation method of carbon-loaded nano high-entropy alloy particle composite material

China

874

2021 CN-113258050-A

Five-element high-entropy alloy oxide negative electrode material and preparation method and application thereof

China

875

2021 CN-111360074-B

Preparation method of heterogeneous lamellar structure medium/high-entropy alloy foil

China

876

2021 CN-111549270-B

Low-density high-strength high-plasticity high-entropy alloy material and preparation method thereof

China

877

2021 CN-113265573-A

High-strength high-toughness high-entropy alloy ceramic and preparation method thereof

China

878

2021 CN-111363964-B

W-Ta-Mo-Nb-Hf-C high-temperature high-entropy alloy and preparation method thereof

China

879

2021 CN-110724949-B

Preparation method of high-entropy alloy layer on surface of medical beta titanium alloy

China

880

2021 CN-111676410-B

High-strength high-toughness CoFeNiTiV high-entropy alloy and preparation method thereof

China

881

2021 CN-110205537-B

High-entropy alloy powder composed of aluminum, magnesium, lithium and titanium and preparation method thereof

China

882

2021 CN-113293370-A

High-entropy alloy coating for laser cladding of aluminum alloy surface and preparation method

China

883

2021 US-11098403-B2

High entropy alloy thin film coating and method for preparing the same

US (continued)

404

Appendix C

(continued) Sr. No.

Year

Patents no

Patents name

Country

884

2021 US-2021260704-A1

Multi component solid solution high-entropy alloys

US

885

2021 CN-113319289-A

Preparation method of FeCoNiCu high-entropy magnetic nano powder for magnetic thermotherapy

China

886

2021 CN-113321533-A

High-entropy ceramic modified coating with controllable components and microstructure and preparation method thereof

China

887

2021 CN-112064024-B

Diffusion-resistant high-entropy alloy coating China material, high-temperature-resistant coating material, and preparation method and application thereof

888

2021 EP-3872197-A1

Composite copper alloy comprising high-entropy alloy, and manufacturing method therefor

889

2021 WO-2021169985-A1 High-entropy alloy containing boron and rare earth and magnetic field treatment method therefor

WIPO (PCT)

890

2021 CN-113351866-A

Powder metallurgy preparation method of oxide-reinforced high-entropy alloy

China

891

2021 CN-113355625-A

NbC-reinforced high-entropy alloy-based composite coating and preparation method thereof

China

892

2021 CN-113372088-A

Method for preparing water-based ceramic functional China coating by using high-entropy oxide as functional pigment

893

2021 CN-111519079-B

CoCrNiCuFeMnAl high-entropy alloy and preparation method thereof

China

894

2021 CN-112795797-B

Method for preparing high-strength and high-toughness aluminum-based high-entropy alloy composite strip

China

895

2021 KR-102302317-B1

Method for forming powder of high entropy ceramic and method for forming thermal spray coatings layer using powder of high entropy ceramic

South Korea

896

2021 WO-2021179654-A1 Carbide-based high-entropy ceramic, rare-earth-containing carbide-based high-entropy ceramic and fibers and precursor thereof, and preparation method therefor

897

2021 CN-108788168-B

High-entropy alloy powder with low nitrogen content China and preparation method and application thereof

898

2021 CN-111961940-B

WC-based hard alloy containing high-entropy ceramic phase and preparation method thereof

China

899

2021 CN-113416072-A

Method for preparing high-entropy rare earth tantalate spherical powder by molten salt growth method

China

900

2021 CN-110526706-B

Eutectic high-entropy oxide powder material and preparation method thereof

China

901

2021 CN-113430445-A

FeCrNiAlMoNb high-entropy alloy and preparation method thereof

China

902

2021 CN-109763056-B

Fe-Co-Ni-Mn-Cu high-entropy alloy material and preparation process thereof

China

European

WIPO (PCT)

(continued)

Appendix C

405

(continued) Sr. No.

Year

Patents no

Patents name

Country

903

2021 CN-111074292-B

Electro-catalytic hydrogen production porous China high-entropy alloy electrode material and preparation method thereof

904

2021 CN-113444960-A

Unequal atomic ratio CoCrFeNiMox high-entropy alloy and preparation method thereof

China

905

2021 CN-111778438-B

High-entropy alloy with integrated structure and function and preparation method thereof

China

906

2021 CN-112030161-B

High-entropy alloy powder for laser cladding and application method thereof

China

907

2021 CN-111996435-B

High-entropy alloy composite powder and method for reinforcing magnesium alloy through ultrahigh-speed laser cladding

China

908

2021 CN-111235454-B

AlCoCrFeMn high-entropy alloy with unequal atomic ratio and preparation method thereof

China

909

2021 CN-113462948-A

ZrTiNbAlV low-neutron absorption cross-section China refractory high-entropy alloy and preparation method thereof

910

2021 CN-111270172-B

Method for improving performance of high-entropy alloy by utilizing graded cryogenic treatment

911

2021 CN-113458418-A

Antibacterial and antiviral CoCrCuFeNi high-entropy China alloy and selective laser melting in-situ alloying method and application thereof

912

2021 CN-110804712-B

Magnesium-containing high-entropy alloy and preparation method thereof

China

913

2021 CN-110359040-B

CoCrFexNiMnMo high-entropy alloy coating considering dilution rate and preparation method thereof

China

914

2021 CN-112222678-B

SiCf high-entropy alloy brazing filler metal of/SiBCN China composite material and preparation process thereof

915

2021 CN-109797391-B

Low-dilution-rate FeCrCoNiMoTi high-entropy alloy China powder for wind power bearing and preparation method of cladding layer of high-dilution-rate FeCrCoNiMoTi high-entropy alloy powder

916

2021 CN-112877579-B

Non-equal atomic ratio high-entropy alloy and method for preparing wire by using same

China

917

2021 EP-3896183-A1

Lightweight high-entropy alloy having high strength and high plasticity and preparation method therefor

European

918

2021 CN-111187964-B

High-strength-plasticity antibacterial high-entropy alloy and preparation method thereof

China

919

2021 CN-112830769-B

High-emissivity high-entropy ceramic powder material and coating preparation method

China

920

2021 CN-111168057-B

Nano-ceramic reinforced high-entropy alloy composite powder for additive manufacturing and preparation method and application thereof

China

921

2021 CN-110204341-B

(Hf, Ta, Nb, Ti) B2 high-entropy ceramic powder and China preparation method thereof

China

(continued)

406

Appendix C

(continued) Sr. No.

Year

922

Patents no

Patents name

Country

2021 CN-111876645-B

Ta-W-Nb-Al-Cr-Ti-Si series high-entropy alloy infiltration coating for high-flux screening and preparation method thereof

China

923

2021 CN-113564577-A

Copper-based surface intermetallic compound reinforced gradient high-entropy alloy coating and preparation method thereof

China

924

2021 CN-113584371-A

Precipitation strengthening type high-entropy alloy with truss structure and preparation method thereof

China

925

2021 CN-113584370-A

Low-density high-strength high-entropy high-temperature alloy and preparation method thereof

China

926

2021 CN-111672906-B

High-entropy alloy particle reinforced metal matrix composite material and preparation method thereof

China

927

2021 CN-110643955-B

High-entropy alloy coating and preparation method thereof

China

928

2021 CN-110358964-B

MoVNbTiCr for nuclear power x high-entropy alloy and preparation method thereof

China

929

2021 CN-110983144-B

Nitride reinforced high-entropy alloy and preparation China method thereof

930

2021 CN-113621958-A

Method for laser cladding of high-entropy alloy coating on copper surface

China

931

2021 CN-110714155-B

Irradiation-resistant impact-resistant FeCoCrNiMn high-entropy alloy and preparation method thereof

China

932

2021 US-2021347699-A1

High-entropy oxides for thermal barrier coating (TBC) top coats

US

933

2021 CN-113652593-A

MoxNbTayTiV high-entropy alloy and preparation method thereof

China

934

2021 CN-113667877-A

TiZrVNb-based high-entropy alloy containing rare earth elements and preparation method thereof

China

935

2021 CN-111663070-B

AlCoCrFeNiSiY high-entropy alloy resistant to high-temperature oxidation and preparation method thereof

China

936

2021 CN-112899531-B

High-entropy alloy particle reinforced aluminum-based composite material and magnetic field auxiliary preparation method

China

937

2021 CN-113695572-A

Preparation method of graphene-based high-entropy alloy material

China

938

2021 CN-112981212-B

Preparation method of non-equiatomic ratio high-entropy alloy semi-solid thixotropic blank

China

939

2021 CN-113718152-A

High-temperature-resistant low-density Ni-Co-Cr-Fe-Al-Ti high-entropy alloy and preparation method thereof

China

940

2021 CN-112614978-B

Cage-shaped eutectic high-entropy oxide lithium ion battery cathode material and preparation method thereof

China

(continued)

Appendix C

407

(continued) Sr. No.

Year

941

Patents no

Patents name

Country

2021 CN-111826573-B

Precipitation strengthening type high-entropy alloy without sigma phase precipitation tendency and preparation method thereof

China

942

2021 CN-113745548-A

High-entropy ceramic material based on spinel structure and preparation method and application thereof

China

943

2021 CN-112614986-B

Rock salt type high-entropy anode material containing sulfur-oxygen dianions and preparation method

China

944

2021 CN-113754432-A

Preparation method of high-entropy oxide ceramic fiber material

China

945

2021 CN-113025865-B

Preparation method of AlCoCrFeNi series two-phase China structure high-entropy alloy

946

2021 CN-111850374-B

High-entropy alloy powder for laser cladding and coating preparation method

China

947

2021 CN-111850372-B

A series of FeCoCrNiW (VC)X preparation of high-entropy alloy and precipitation strengthening process thereof

China

948

2021 CN-113772723-A

CMAS corrosion-resistant multi-component high-entropy pyrochlore structure thermal barrier coating material and preparation method and application thereof

China

949

2021 US-11198197-B2

Fabrication of high-entropy alloy wire and multi-principal element alloy wire

US

950

2021 CN-113789464-A

Ceramic phase reinforced refractory high-entropy alloy composite material and preparation method thereof

China

951

2021 CN-109650876-B

A-site high-entropy perovskite oxide and preparation China method thereof

952

2021 CN-113816747-A

TiC enhanced MAX phase high-entropy ceramic matrix composite material and preparation method thereof

China

953

2021 CN-113444954-B

Ni-Co-Fe-B series eutectic high-entropy alloy and preparation method and application thereof

China

954

2021 CN-112778010-B

High-entropy ceramic with high hardness and high conductivity and preparation method and application thereof

China

955

2021 CN-111809097-B

CoCuTiV series high-entropy alloy and preparation method thereof

China

956

2021 CN-113828880-A

Method for connecting silicon carbide ceramic by adopting refractory high-entropy alloy interlayer discharge plasma diffusion

China

957

2021 CN-113235051-B

Nano biphase high-entropy alloy film and preparation China method thereof

958

2021 CN-113845153-A

Multi-element high-entropy solid solution cathode material and preparation method and application thereof

China

(continued)

408

Appendix C

(continued) Sr. No.

Year

959

Patents no

Patents name

Country

2022 CN-112226758-B

Wear-resistant anti-oxidation high-entropy alloy coating and preparation method thereof

China

960

2022 CN-113881886-A

High-specific-strength Ti-Al-Nb-Zr-Ta refractory high-entropy alloy

China

961

2022 CN-113880580-A

High-entropy carbide ultra-high temperature ceramic China powder and preparation method thereof

962

2022 CN-112626424-B

Fine-grain high-entropy alloy with nanometer precipitated phase and preparation method thereof

China

963

2022 CN-112609118-B

High-temperature-resistant refractory high-entropy alloy and preparation method thereof

China

964

2022 US-2022016705-A1

FeCrCuTiV high-entropy alloy powder for laser melting deposition manufacturing and preparation method thereof

US

965

2022 CN-110202148-B

Method for manufacturing high-entropy alloy-based China multiphase reinforced gradient composite material by laser additive manufacturing

966

2022 CN-109516812-B

Superfine high-entropy solid solution powder and preparation method and application thereof

China

967

2022 CN-113073250-B

Preparation method of high-melting-point high-entropy soft magnetic alloy

China

968

2022 CN-112875764-B

Preparation method of high-entropy oxide of lithium ion battery negative electrode material

China

969

2022 CN-110923750-B

Preparation method of high-entropy alloy

China

970

2022 CN-113073274-B

Novel method for preparing double-phase ultra-fine grain high-entropy alloy

China

971

2022 CN-111733358-B

High-strength high-toughness corrosion-resistant cobalt-free high-entropy alloy and preparation method thereof

China

972

2022 CN-109930053-B

FeCoNiCrMn high-entropy alloy and method for preparing wear-resistant coating by using same

China

973

2022 CN-110331398-B

Composite coating of high-entropy alloy composite large-particle tungsten carbide and preparation method and application thereof

China

974

2022 CN-111254379-B

Preparation method of high-entropy ceramic coating

China

975

2022 CN-111593250-B

L12 precipitation strengthening high-entropy alloy and preparation method thereof

China

976

2022 CN-113718154-B

Ultrahigh-strength-toughness high-density high-entropy alloy and preparation method thereof

China

977

2022 CN-112582629-B

Ultrathin carbon nanosheet loaded nano high-entropy China alloy electrocatalyst and preparation method thereof

978

2022 CN-111020579-B

Preparation of TiB on titanium alloy2Method for particle reinforced high-entropy alloy coating

China

979

2022 CN-111647789-B

Alloying-method-based refined chromium-iron-cobalt–nickel-based high-entropy alloy crystal grain and preparation method thereof

China

(continued)

Appendix C

409

(continued) Sr. No.

Year

980

Patents no

Patents name

Country

2022 CN-114058892-A

Wear-resistant corrosion-resistant high-entropy alloy-based composite material and preparation method thereof

China

981

2022 CN-114058981-A

Refractory high-entropy amorphous alloy material and preparation method and application thereof

China

982

2022 CN-114058922-A

Light hard CoCrAlSiNi high-entropy alloy and preparation method thereof

China

983

2022 CN-112575236-B

High-nitrogen high-entropy alloy and preparation method thereof

China

984

2022 CN-111748721-B

High-entropy alloy/metal glass composite material and preparation method thereof

China

985

2022 CN-112317752-B

TiZrNbTa high-entropy alloy for 3D printing and preparation method and application thereof

China

986

2022 US-2022056567-A1

High entropy alloy structure and a method of preparing the same

US

987

2022 CN-113445041-B

Preparation method of low-cost light high-entropy alloy/aluminum oxide composite coating on surface of magnesium alloy

China

988

2022 CN-114086142-A

High-entropy alloy rotary target and preparation method of cold spraying thereof

China

989

2022 CN-111302781-B

Preparation method of Fe-Ti-Ni-Co-Mn high-entropy China oxide ceramic material

990

2022 CN-112725818-B

Porous high-entropy alloy self-supporting electrode and method for electrolyzing water

China

991

2022 CN-111763087-B

Series of cubic fluorite type high-entropy cerium oxide nano-powder and preparation method thereof

China

992

2022 CN-112582600-B

Preparation method of high-entropy single crystal battery positive electrode material and obtained product

China

993

2022 CN-111139391-B

Precipitation strengthening type high-entropy alloy and preparation process thereof

China

994

2022 CN-112813330-B

Multi-principal-element carbide dispersion type high-entropy alloy material and preparation method thereof

China

995

2022 CN-113337746-B

Preparation method of carbide-reinforced high-entropy alloy composite material

China

996

2022 CN-114180970-A

Nitrogen-containing medium-entropy or high-entropy MAX phase material and preparation method and application thereof

China

997

2022 CN-112725681-B

Iron-cobalt–nickel-manganese-copper high-entropy cast iron and preparation method and application thereof

China

998

2022 CN-113430405-B

High-strength and high-toughness face-centered cubic high-entropy alloy and preparation method thereof

China

(continued)

410

Appendix C

(continued) Sr. No.

Year

Patents no

Patents name

Country

999

2022 CN-114180965-A

High-entropy carbide nano powder material with high sphericity and high activity, and preparation method and application thereof

China

1000 2022 CN-112924510-B

Graphene-based high-entropy alloy nanoparticle and preparation method and application thereof

China

1001 2022 CN-111074224-B

Corrosion-resistant high-entropy alloy nitride coating, and preparation method and application thereof

China

1002 2022 CN-112795800-B

Ultrasonic-assisted preparation method of 2219 aluminum-based high-entropy alloy composite material

China

1003 2022 CN-113149086-B

Two-dimensional high-entropy hydroxide array catalyst and method for synthesizing ammonia by electrocatalysis nitrogen fixation

China

1004 2022 CN-111411319-B

Method for preparing nitride-enhanced high-entropy alloy coating by plasma cladding

China

1005 2022 CN-114196952-A

High-entropy alloy bionic gradient structure composite coating with eutectic interface and preparation method thereof

China

1006 2022 US-11279992-B2

Radiation resistant high-entropy alloy and preparation method thereof

US

1007 2022 CN-111172445-B

High-entropy alloy with double-layer close-packed hexagonal structure

China

1008 2022 CN-111455301-B

Wear-resistant corrosion-resistant high-entropy alloy gradient composite coating of outer cylinder of measurement-while-drilling instrument

China

1009 2022 CN-113073215-B

Preparation method and application of high-entropy alloy for passive heavy bulletproof armor

China

1010 2022 CN-111893364-B

Multi-element doped reinforced toughened high-entropy alloy and preparation method thereof

China

1011 2022 CN-112725679-B

Light high-entropy alloy material with high specific strength and preparation method thereof

China

1012 2022 CN-112570705-B

Binder for refractory high-entropy alloy powder and preparation method thereof

China

1013 2022 EP-3973086-A1

PVD coatings comprising multi-anion high entropy alloy oxy-nitrides

European

1014 2022 CN-111270190-B

Preparation method of high-entropy ceramic-alumina China composite coating

1015 2022 CN-114260468-A

High-entropy alloy bionic additive manufacturing device and method based on shell structure

China

1016 2022 CN-111364040-B

High-hardness high-entropy alloy coating and preparation method and application thereof

China

1017 2022 CN-113293331-B

High-entropy alloy surface carbide/diamond coating and preparation method thereof

China

1018 2022 CN-111848177-B

Ultrahigh-temperature high-entropy boride ceramic powder and preparation method thereof

China (continued)

Appendix C

411

(continued) Patents name

Country

1019 2022 CN-111054378-B

High-entropy oxide type electrocatalytic anode oxygen evolution catalyst material and preparation method thereof

China

1020 2022 CN-110734289-B

Boride high-entropy ceramic and preparation method China thereof

1021 2022 CN-111676408-B

Tungsten-energetic high-entropy alloy composite material and preparation method thereof

China

1022 2022 CN-111039672-B

Sn-doped high-entropy perovskite oxide ceramic material with high power density and preparation method thereof

China

1023 2022 CN-112501485-B

Reversible room-temperature hydrogen storage high-entropy alloy, and preparation and application thereof

China

1024 2022 CN-113307632-B

Preparation method of oxide high-entropy ceramic fiber

China

1025 2022 CN-114318105-A

High-strength high-plasticity CrHfMoNbTi high-entropy alloy and preparation method thereof

China

1026 2022 CN-113430444-B

High-plasticity high-strength high-entropy alloy and preparation method thereof

China

1027 2022 CN-110845237-B

High-entropy ceramic powder, preparation method thereof and high-entropy ceramic block

China

1028 2022 CN-114346256-A

Variant energy density laser material increase method China suitable for high-entropy alloy

1029 2022 CN-111793806-B

Ternary high-entropy foam for high-activity hydrolysis hydrogen production and preparation method thereof

China

1030 2022 CN-112195317-B

Cold rolling composite laser surface annealing process method for high-entropy alloy with heterogeneous structure

China

1031 2022 CN-112222675-B

High-entropy alloy brazing filler metal and preparation method thereof

China

1032 2022 US-2022121122-A1

In-situ synthesis and deposition of high entropy alloy US and multi metal oxide nano/micro particles by femtosecond laser direct writing

1033 2022 CN-113122763-B

Preparation method of high-strength high-toughness high-entropy alloy

China

1034 2022 CN-112024902-B

Preparation method of refractory high-entropy alloy framework-copper spontaneous perspiration composite structure

China

1035 2022 CN-112981208-B

Light refractory high-temperature-resistant eutectic high-entropy alloy and preparation method thereof

China

1036 2022 CN-108504890-B

Basal high-entropy alloy composite material and preparation method thereof

China

1037 2022 CN-113234983-B

NbTaTiZr double-equal atomic ratio high-entropy alloy and preparation method thereof

China

Sr. No.

Year

Patents no

(continued)

412

Appendix C

(continued) Sr. No.

Year

Patents no

Patents name

Country

1038 2022 CN-112680646-B

Preparation method of TiC-based metal ceramic with China high-entropy alloy binder phase

1039 2022 CN-113042759-B

Auxiliary vibration device and laser additive manufacturing method of high-entropy alloy

China

1040 2022 CN-112961016-B

Preparation method of explosive-loaded 3D skeleton high-entropy alloy composite energetic fragment

China

1041 2022 CN-114472922-A

Method for manufacturing copper-based monotectic high-entropy alloy through ultrahigh-speed laser-induction composite cladding and material increase

China

1042 2022 CN-113025966-B

Zr-based high-entropy alloy coating for prolonging China service life of hot forging die and preparation method thereof

1043 2022 CN-112725678-B

Non-equal atomic ratio medium/high entropy alloy containing NiCoCr and preparation method thereof

China

1044 2022 CN-111235565-B

Mo-like high-entropy alloy and application method thereof as cutter coating material

China

1045 2022 CN-111575698-B

High-entropy alloy-based self-lubricating composite material and preparation method thereof

China

1046 2022 CN-112941396-B

High-entropy alloy nano-frame and preparation method thereof

China

1047 2022 CN-113122875-B

High-activity Mn-rich high-entropy alloy electrolytic China water catalytic material and preparation method thereof

1048 2022 CN-113046590-B

High-entropy alloy/aluminum composite foam type wave-absorbing material and preparation method thereof

China

1049 2022 CN-110523997-B

High-entropy alloy particle reinforced subzero treatment aluminum-based composite material and preparation method thereof

China

1050 2022 CN-113000858-B

Graphene-high-entropy alloy composite material and China selective laser melting preparation method thereof

1051 2022 CN-112746213-B

High-entropy alloy nano composite material and preparation method thereof

China

1052 2022 CN-113061763-B

High-entropy alloy and preparation method thereof

China

1053 2022 CN-113549780-B

Powder metallurgy refractory multi-principal-element high-entropy alloy and preparation method thereof

China

1054 2022 CN-111441025-B

Corrosion-resistant high-entropy alloy film, preparation method and application thereof in seawater environment

China

1055 2022 CN-112251659-B

AlCrFe2Ni2C0.24 high-entropy alloy and preparation method thereof

China

1056 2022 CN-113045332-B

Ultrahigh-porosity high-entropy carbide ultrahigh-temperature ceramic and preparation method thereof

China

(continued)

Appendix C

413

(continued) Patents name

Country

1057 2022 CN-112222413-B

Cold rolling composite laser additive manufacturing process method of gradient structure high-entropy alloy

China

1058 2022 CN-111590204-B

Method for inhibiting generation of brittle intermetallic compounds of weld joint by laser high-entropy powder filling welding

China

1059 2022 CN-113321510-B

High-entropy ceramic matrix composite and preparation method thereof

China

1060 2022 CN-113430446-B

High-entropy alloy with super-strong deformability, preparation method and plate prepared from high-entropy alloy

China

1061 2022 CN-112358301-B

Design method of high-entropy ceramic thermal protection material based on electronic structure cooperation

China

1062 2022 CN-112962037-B

Aging ordered hardening method for ultrahigh-strength high-entropy alloy

China

1063 2022 CN-111118496-B

Tough high-entropy alloy forming structure and preparation method thereof

China

1064 2022 CN-111514873-B

High-entropy oxide/TiO2 preparation method of composite photocatalyst

China

1065 2022 CN-112831679-B

Two-phase enhanced high-entropy alloy-based composite material and preparation method thereof

China

1066 2022 CN-113403555-B

Method for improving performance of silicide enhanced refractory high-entropy alloy through thermal deformation process

China

1067 2022 CN-112643040-B

Method for preparing micro-nano medium-entropy and high-entropy material by laser ablation

China

1068 2022 CN-111621808-B

Quaternary high-entropy foam for high-activity electrolyzed water and preparation method thereof

China

1069 2022 CN-111593339-B

Multilayer high-entropy alloy laser cladding layer containing nano tantalum carbide and preparation method thereof

China

1070 2022 CN-113373365-B

Nano silicide reinforced refractory high-entropy alloy and preparation method thereof

China

1071 2022 CN-112408409-B

High-temperature-resistant high-entropy China wave-absorbing ceramic and preparation method and application thereof

1072 2022 CN-113151727-B

Non-equal atomic ratio Fe-Mn-Cr-Ni-Al series high-entropy alloy and preparation method thereof

China

1073 2022 JP-2022531868-A

High entropy rare earth high toughness tantalate ceramics and its manufacturing method

Japan

1074 2022 CN-111636027-B

Eutectic high-entropy alloy with secondary yield, high strength and high plasticity and preparation method thereof

China

1075 2022 CN-113549991-B

Super-hydrophobic nano-structure high-entropy alloy China and preparation method thereof

Sr. No.

Year

Patents no

(continued)

414

Appendix C

(continued) Patents name

Country

1076 2022 CN-113023776-B

Fluorite-structured high-entropy oxide powder for thermal barrier coating and preparation method thereof

China

1077 2022 CN-113621862-B

High-hardness Al-Cr-Ti-V-Cu light high-entropy alloy and preparation method thereof

China

1078 2022 CN-113620712-B

High-entropy carbide ceramic nano powder and preparation method and application thereof

China

1079 2022 CN-112410599-B

Preparation method of high-entropy alloy matrix diamond tool bit

China

1080 2022 CN-112609213-B

High-entropy alloy porous electrode and preparation method thereof

China

1081 2022 CN-112811891-B

Spinel phase high-entropy thermistor material and preparation method thereof

China

1082 2022 CN-111960827-B

Multi-element BCN-series high-entropy ceramic powder and preparation method thereof

China

1083 2022 CN-112935274-B

Method for growing high-entropy alloy nanoparticles China on flexible substrate

1084 2022 CN-112899546-B

Ta regulated CoCrNiTa x eutectic high-entropy alloy and preparation method thereof

China

1085 2022 CN-112899545-B

Nano precipitated phase reinforced body-centered cubic Fe x CrNiAl0.5 Ti0.5 high entropy alloy

China

1086 2022 CN-113089135-B

High-entropy zirconate inorganic fiber and preparation method thereof

China

1087 2022 CN-111250693-B

High-entropy alloy powder for additive remanufacturing and preparation method thereof

China

1088 2022 CN-112542217-B

Design method of high-strength high-toughness high-entropy alloy

China

1089 2022 CN-112899547-B

CoCrNiZr x eutectic high-entropy alloy and preparation method thereof

China

1090 2022 CN-111348910-B

Hexahydric spinel type iron-cobalt-chromium-manganese-nickel-copper series high-entropy oxide and powder preparation method thereof

China

1091 2022 CN-112501569-B

Surface gradient high-entropy alloy layer and preparation method thereof

China

1092 2022 CN-112836344-B

Method for calculating diffusion behavior of interstitial atoms in high-entropy alloy

China

1093 2022 CN-113652566-B

Preparation method of nanocrystalline refractory China high-entropy alloy NbMoTaW-Cu composite material

1094 2022 CN-113621843-B

High-strength and high-toughness corrosion-resistant China FeCoNiCuAl high-entropy alloy wave-absorbing material, preparation method and application

1095 2022 CN-113061937-B

FeCoNiIrRu high-entropy nanoparticle catalytic material applied to acidic oxygen evolution reaction and preparation method thereof

Sr. No.

Year

Patents no

China

(continued)

Appendix C

415

(continued) Patents name

Country

1096 2022 CN-112981321-B

Single-phase structure (CrZrVTiAl) N high-entropy ceramic coating and preparation method thereof

China

1097 2022 CN-113373366-B

Multi-element refractory high-entropy alloy and preparation method thereof

China

1098 2022 CN-113461415-B

Hydrothermal method for preparing high-entropy oxide material (MAlFeCuMg)3 O4 method (2)

China

1099 2022 CN-114315359-B

Method for preparing high-strength and China high-toughness complex-phase high-entropy ceramic by using solid solution coupling method and application

1100 2022 CN-113401939-B

Fluorite-structured high-entropy ceramic aerogel powder with low thermal conductivity and preparation method thereof

Sr. No.

Year

Patents no

China

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