Layeredness in Materials: Characteristics, Strategies and Applications (Engineering Materials) 9819962986, 9789819962983

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Engineering Materials

Abdul Majid Alia Jabeen

Layeredness in Materials Characteristics, Strategies and Applications

Engineering Materials

This series provides topical information on innovative, structural and functional materials and composites with applications in optical, electrical, mechanical, civil, aeronautical, medical, bio- and nano-engineering. The individual volumes are complete, comprehensive monographs covering the structure, properties, manufacturing process and applications of these materials. This multidisciplinary series is devoted to professionals, students and all those interested in the latest developments in the Materials Science field, that look for a carefully selected collection of high quality review articles on their respective field of expertise. Indexed at Compendex (2021) and Scopus (2022)

Abdul Majid · Alia Jabeen

Layeredness in Materials Characteristics, Strategies and Applications

Abdul Majid Department of Physics University of Gujrat Gujrat, Pakistan

Alia Jabeen Department of Physics University of Gujrat Gujrat, Pakistan

ISSN 1612-1317 ISSN 1868-1212 (electronic) Engineering Materials ISBN 978-981-99-6298-3 ISBN 978-981-99-6299-0 (eBook) https://doi.org/10.1007/978-981-99-6299-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed 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 Paper in this product is recyclable.

Contents

1 Characteristics, Strategies and Applications of Layered Materials: An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 van Der Waals Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Layeredness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Layered Versus Non-layered Materials . . . . . . . . . . . . . . . . . . . . . . . 1.5 Scheme to Study the Layered Materials . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 3 6 12 14

2 Synthesis and Properties of Layered Materials . . . . . . . . . . . . . . . . . . . . 2.1 Natural Conditions-Graphite to Diamond Transformation . . . . . . . 2.2 Rigid and Soft-Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Exfoliation of Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Surfactant-Aided Exfoliation . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Electrochemically Aided Exfoliation . . . . . . . . . . . . . . . . . . 2.3.3 Cathodic Intercalation of the Positive Ions . . . . . . . . . . . . . 2.3.4 Anodic Intercalation of Negative Ions . . . . . . . . . . . . . . . . . 2.3.5 Bipolar Electrochemical Exfoliation . . . . . . . . . . . . . . . . . . 2.3.6 Liquid Phase Exfoliation (LPE) . . . . . . . . . . . . . . . . . . . . . . 2.4 Synthesis of the Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Top-Down Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Bottom up Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Tailoring the Properties of Layered Materials . . . . . . . . . . . . . . . . . . 2.5.1 Effect of Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Pressure-Dependent Properties . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Effect of Lattice Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4 Effect of Intercalation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 18 20 21 21 23 24 24 25 26 27 27 30 32 33 33 34 34 40

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3 Theoretical Modeling and Approaches to Study the Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Theories Related to Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Exfoliation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Potential Energy Surface (PES) . . . . . . . . . . . . . . . . . . . . . . 3.2 Theoretical Parameters Related to Layered Materials . . . . . . . . . . . 3.2.1 Dispersion Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Importance of Computational Studies . . . . . . . . . . . . . . . . . 3.2.3 Exchange Correlation Functional . . . . . . . . . . . . . . . . . . . . . 3.2.4 Strategy to Study the Layered Materials . . . . . . . . . . . . . . . 3.2.5 The Structure of the Materials . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Use of Appropriate Functional . . . . . . . . . . . . . . . . . . . . . . . 3.2.7 K-Point Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8 Potential Energy Surface (PES) . . . . . . . . . . . . . . . . . . . . . . 3.2.9 Exfoliation Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Why Layered Materials? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Anisotropic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Anisotropic Thermal Conductivity . . . . . . . . . . . . . . . . . . . 3.3.3 Anisotropic Electrical Conductivity . . . . . . . . . . . . . . . . . . . 3.3.4 Thickness-Dependent In-Plane Conductivity . . . . . . . . . . . 3.3.5 Applications of Layered Materials . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Elemental Layered Solids: Group IV and V Materials . . . . . . . . . 4.1 Parameters of the Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 In-Plane and Out-of-Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Bond Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Layered Versus Non-layered . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 2D Carbon (Graphene) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Boron Nitride (BN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Layered Versus Non-layered BN . . . . . . . . . . . . . . . . . . . . . 4.3.2 Synthesis and Uniqueness of h-BN Sheets . . . . . . . . . . . . . 4.3.3 Problems with h-BN and the Solutions . . . . . . . . . . . . . . . . 4.4 Phosphorous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Allotropic Forms of Phosphorous . . . . . . . . . . . . . . . . . . . . 4.4.2 Crystal and Electronic Structure of Black Phosphorous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Structure of Monolayer Phosphorous-Phosphorene . . . . . 4.4.4 Synthesis and Uniqueness of Layered 2D Phosphorene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Arsenic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Allotropic Forms and Structural Arrangements in Arsenic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Layered Versus Non-layered Arsenic . . . . . . . . . . . . . . . . .

45 46 46 47 48 48 49 49 54 55 55 56 57 57 59 59 60 61 61 62 65 69 70 70 71 71 72 73 74 75 77 77 78 78 79 80 81 81 82 83

Contents

4.6

Antimony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Allotropes of Antimony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Prospects of 2D Antimony . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Properties of Monolayer Antimony-Antimonene . . . . . . . . 4.7 Bismuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.1 Synthesis Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2 2D Bismuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Layeredness in Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Silicene—A Single Layer of Silicon . . . . . . . . . . . . . . . . . . 4.8.2 Layered Versus Non-layered Silicon . . . . . . . . . . . . . . . . . . 4.9 Stannous (Tin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.1 2D Stannous-Stanene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.2 Layered Versus Non-layered Stannous . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Transition Metal Dichalcogenides—An Important Class of Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Why Chalcogenides? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Importance of Transition Metals Dichalcogenides (TMDs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Synthesis of TMDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Hot-Plate Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Hydro- or Solvothermal Method . . . . . . . . . . . . . . . . . . . . . 5.2.3 One-Pot Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Electrospinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 MoS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 2D MoS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Layered Versus Non-layered MoS2 . . . . . . . . . . . . . . . . . . . 5.4 WS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Synthesis of WS2 Monolayer . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 2D-WS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Layered Versus Non-layered WS2 . . . . . . . . . . . . . . . . . . . . 5.5 MoSe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 2D-MoSe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Layered Versus Non-layered MoSe2 . . . . . . . . . . . . . . . . . . 5.6 WSe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 2D-WSe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Layered Versus Non-layered WSe2 . . . . . . . . . . . . . . . . . . . 5.7 MoTe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.1 2D-MoTe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.2 Layered Versus Non-layered MoTe2 . . . . . . . . . . . . . . . . . . 5.8 WTe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 General Trends of TMDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Applications of TMDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10.1 Alkali-Ion Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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84 84 84 85 86 86 87 88 89 90 91 91 92 93 103 103 104 105 106 106 106 108 109 111 111 112 114 114 115 116 116 117 118 119 119 120 120 121 122 123 123 123

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5.10.2 Photocatalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6 Conclusive Remarks and Recommendations: Way Forward on Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Appearance of Layered Materials in Specific Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Appearance of Chalcogenides Materials as Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Dissimilar Behavior of Oxygen Among Chalcogen Atoms in Layered Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Origin of the VdW Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Do VdW Interactions Essentially Leads to Layered Materials? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141 142 143 143 144 144 145

Abbreviations

2D 3D ADF-BAND AMIBs As b-As Bi Bi2 O3 Bi2 Se3 Bi2 WO6 BiOCl BiPO4 BMPTF 2 N BN BP CB c-BN CDWs CMS CO2 Co3 O4 CVD DFT DOS DSSC GaS g-As GaTe GGA GICs h-BN

Two-dimensional Three-dimensional/bulk Amsterdam density functional Alkali metal ion batteries Arsenic Black arsenic Bismuth Bismuth oxide Bismuth selenides Bismuth tungstate Bismuth oxyhalide Bismuth phosphate Methyl-pyrrolidinium bis(triflouromethylsulfonyl)-imide Boron nitride Black phosphorous Conduction band Cubic boron nitride Collective macroscopic modulation Chiral magnetic soliton Carbon dioxide Cobalt oxide Chemical vapor deposition Density functional theory Density of states Dye-sensitized solar cells Gallium sulfide Gray arsenic Gallium telluride Generalized gradient approximations Graphite intercalation compounds Hexagonal boron nitride ix

x

HF InSe LDA LDHs LIB Li-ions LPE MnO2 MoO3 MoS2 MoSe2 MoTe2 N2 pEDA-NOCV PES Po Pt PV r-BN S Sb SDBS Se Si SiC SiO2 Sn SnOx SOC Ta2 O5 TBG Te TiO2 TMDs V2 O5 VASP VB VdW VHSs VOCs w-BN WS2

Abbreviations

Hartree–Fock Indium selenide Local density approximations Layered double hydroxide Lithium ion battery Lithium ions Liquid phase exfoliation Manganese dioxide Molybdenum oxides Molybdenum disulfide Molybdenum diselenide Molybdenum ditelluride Nitrogen gas Periodic energy decomposition analysis-Natural orbitals for chemical valency Potential energy surfaces Polonium Platinum Polyvinyl alcohol Rhombohedral boron nitride Sulfur Antimony Sodium dodecyl benzene sulfonate Selenium Silicon Silicon carbide Silicon oxides Stannous Tin oxides Spin-orbit coupling Tantalum pentoxide Twisted bilayer graphene Tellurium Titanium dioxide Transition metal dichalcogenides Vanadium pentoxide Vienna ab-initio simulation package Valence bands Van der Waals Van Hove singularities Volatile organic compound Wurtzite boron nitride Tungsten disulfide

Abbreviations

WSe2 WTe2 y-As ZnO

xi

Tungsten diselenide Tungsten ditelluride Yellow arsenic Zinc oxide

Chapter 1

Characteristics, Strategies and Applications of Layered Materials: An Introduction

Abstract The structure - property relationship provides liberty of tuning the properties of the materials by changing the crystal structures. The materials can be categorized in several classes, yet on the basis of the crystal structure, the materials may be classified in two major types i.e. layered and non-layered materials. The nonlayered materials are materials with isotropic bonding throughout while the layered materials are materials with anisotropic bonding i.e. the strong in-plane and weak van der Waals interactions in out-of-plane directions. In this introductory chapter, The synopsis that layeredness, the ability of materials to exist in the form of atomic layers, is an intrinsic property of the materials which has been elaborated in this chapter. The two dimensionality is merely a repetition of unit-cell structure in twodimensions and each material can be peeled off to make their 2D counter parts whereas the layeredness is an intrinsic material property. The misconception that all 2D materials or monolayers are not essentially layered and vice versa has also been addressed. Further, the methodology to study the layered materials through first principles techniques is also discussed in details.

1.1 Introduction The crystal structure of the materials is very important due to structure–property relationship. The changes in the crystal structure are known to modify the properties which leads to variation in the applications of the materials. The inorganic materials may be classified in various classes; however, on the basis of atomic bonding, these may be categorized into layered and non-layered. The layered materials, also known as van der Waals (VdW) materials, have strong in-plane covalent or ionic bonding and weak VdW out-of-plane interactions. Thus, due to anisotropy in the atomic bonding, these materials are found in the form of atomically thick sheets connected through the VdW interactions. On the other hand, the bonding in non-layered materials appears uniform throughout the crystal structures within a crystallite or even in a single crystal. The situation can be suitably explained by analyzing the structure of carbon which exists in various allotropes out of which diamond and graphite are well known for their stable phases. Graphite appears in the form of the layered structure, while © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Majid and A. Jabeen, Layeredness in Materials, Engineering Materials, https://doi.org/10.1007/978-981-99-6299-0_1

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1 Characteristics, Strategies and Applications of Layered Materials …

diamond possesses the non-layered structure. Owing to this crystal structure, as well as electrical and thermal properties, graphite is vastly used as electrode in electrical devices including batteries and solar panels. The layered materials exhibit some exciting phenomenon which offer additional applications such as intercalation of other elements through the layers. The possibility of the intercalation opens door to additional applications like electrodes in rechargeable ion batteries, optoelectronic devices, ion transport, catalysis, energy production as well as storage devices etc. However, diamond due to strong and isotropic bonding, as well as electrical, thermal and mechanical properties, is of least importance for electrical devices but widely used in jewelry, engraving, cutting and industrial applications. The lower-dimensional materials used in nanotechnology have brought a revolution in twenty-first century. Hence, miniaturization of the materials is key to prepare nanomaterials which offer novel properties when compared with the bulk counterparts. The layered materials are apposite in this regard as their trimming leads to production of monolayers similar to the structural downscaling of three-dimensional (3D) graphite to two-dimensional (2D) graphene, firstly carried out by in 2004 that later consequent on award of noble prize. The utilization of the majority of known layered materials in nanotechnology, upon miniaturization of bulk counterparts to lower dimensions, is still underrated and underdocumented. Despite the significant report work on the layered materials, the integrated knowledge on the relevant phenomenon is scarce and several issues need to be addressed, especially when new materials are being explored. The growth of surfaces and monolayers has recently earned exceptional research interests due to their widespread applications. The frequent usage of terms “layered” and “monolayer” in plethora of research articles on the 2D materials has blurred the difference in their meanings. The monolayers are also being termed as layered despite the fact that several non-layered materials can be downscaled to monolayers. The misconception rises that only layered materials can be transformed into the monolayers or the surface materials. Indeed, the 2D monolayers or surfaces can be prepared from any materials: either layered or non-layered. The fact of the matter is that two-dimensionality is the repetition of unit cell in two dimensions, whereas the layeredness is an intrinsic property in which a material exhibits anisotropy in bonding irrespective of its dimensionality. The properties of the layered materials are dependent on number of layers, which is less focused issue, along with other parameters. The majority of reported efforts are found dedicated to study of monolayers when prepared for catalysis or relevant applications. The layer-dependent studies of VdW materials are difficult due to challenges related to experimental characterizations and expensive calculations in computational investigations. The consolidation of the relevant literature and description of recently developed first-principles strategies in this regard need to be narrated. The recent research activities are mainly focusing monolayers which has undervalued the layered materials. The survey of the literature on the known VdW materials will be helpful to utilize potential of the materials in order to meet the future requirements in devices.

1.3 Layeredness

3

1.2 van Der Waals Solids The technological development strongly owes to devices whose functioning depends on the materials involved. A major component of scientific research is currently dedicated to produce miniature, cost effective, human friendly, and portable devices operating under required conditions for future applications. There has been extensive efforts to explore new materials, offering required structural, electronic, transport, thermal, optical properties, etc. as potential candidates for the devices. The humanity is indebted to the services of material scientists they have discovered and synthesized plenty of new materials for the applications in the best interest of mankind. The material science has already played a key role in the progress of emerging technologies, especially nanotechnology which is believed to significantly contribute in future technologies. The scientists and researchers are currently more eager to develop new materials which are nanoscaled analogue of the existing bulk counterparts. The van der Waals (VdW) solids comprise neutral layers having atomic thickness [1]. These layers are connected with one another with the help of weak VdW interactions, while the intra-layer atomic interactions are of strong covalent or ionic nature. One of the best examples of VdW solids is the graphite which comprises of atomically thick layers—each one is called graphene. These layers are made up of sp2 hybridized carbon atoms configured in a honeycomb lattice. The nanomaterials are scaled-down version of the bulk materials due to which they offer diverse properties. In general, the nanomaterials show quantum confinement effects and their surface-to-volume ratio is enhanced which opens up the new applications of the same materials. The materials are classified into four classes on the basis of their dimensionality i.e. 3D, 2D, 1D and OD. Graphene and other members of flat-land family are known as two-dimensional (2D) materials which occur either naturally or may be synthesized. The 2D materials include transition metals dichalcogenides (TMDs), metal nitrides and carbides, monoatomic arsenic, antimony, bismuthene, black phosphorous and hexagonal boron nitride etc. as shown in Fig. 1.1. In majority of the cases, unparalleled characteristics emerged when thickness of the bulk multilayered solids is lessened up to one or few layers. The monolayers have offered unique electronic, optical, transport, magnetic as well as the catalytic properties which opened up endless opportunities for researchers, technologists and industrialists. There has been incredible achievements to synthesis high-quality monolayers in recent past by following top-down as well as bottom-up approaches.

1.3 Layeredness The bulk materials in general and 2D materials in particular, on the basis of their structure, are further classified into two categories, i.e. layered materials and non-layered materials [3]. The layeredness is not commonly understood property of the materials which may be characterized on the basis of atomic bonding. The non-layered

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1 Characteristics, Strategies and Applications of Layered Materials …

Fig. 1.1 Representative layered materials. Reprinted with permission from Dong et al. [2]. Copyright (2019)

3D materials are those in which there is only one type of bonding throughout the structure and consequently offer greater surface energy and higher activity due to the dangling bonds at the surface. The majority of 3D materials are non-layered indeed, but there is likelihood to grow them in the form of 2D slabs or even as atomically thick single layer known as monolayer. These 2D materials have recently been found as potential candidate for novel applications due to their diverse catalytic, electrical, magnetic and optoelectronic characteristics. In addition to their trademark physical and chemical characters, these materials exhibit additional surface properties which has given birth to unique scientific phenomenon during past decade.

1.3 Layeredness

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Only a small fraction of entire known bulk materials exhibits layeredness. The structure of such VdW-layered solids can be distinguished from rest of the solids on the basis of their atomic structures. The structures of both graphite and diamond comprise carbon atoms, but the former appears in layered form due to its sp2 hybridization, whereas the later adopts sp3 hybridization. The same applies to the other elements/compounds, such as black phosphorous, h-BN etc. Like those of non-layered slabs, there has been a scientific interest to fabricate 2D layered materials in the form of ultrathin nanofilms having nanoscale thickness [4]. The layered 2D material is such a material which has anisotropic bonding; a strong intra-layer covalent bond with bond energy in range of eV/atoms and weak inter-layer bond through VdW interaction in vertical direction with strength of bonds in range of meV [5]. For example, the VdW material graphite (single component) has the strong covalent bond of about 7.3 eV/atom in plane. At the same time, the VdW interactions along the c-axis are about 30–60 meV/atom. The layers of the layered materials can be peeled off from the bulk due to weak VdW interactions due to which several strategies have been developed to obtain them. The 2D layered slabs, depending on number of layers, are known to offer tunable and exciting characteristics like valley polarization, band structure and optical properties etc. The boron nitride (BN), black phosphorous, x-enenes (germanene, silicene, etc.), metallic oxides (like MO3 , where M = Mo, W, Ta), dichalcogenides (like MoS2 , MoSe2 , MoTe2 ) are few known examples of such materials. For instance, the electronic band gap of various band gap is visualized in Fig. 1.2.

Fig. 1.2 The electrical aspects for various two-dimensional crystals. Reprinted with permission from Tanjil et al. [6]. Copyright (2019)

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1.4 Layered Versus Non-layered Materials It has been computationally predicted that more than 1800 materials are potentially capable to exfoliate down to atomically thin layers. It has been recently found that layeredness in a material gives birth to novel scientific phenomenon due to which layered materials offer such exceptional properties which are absent in their nonlayered counterparts. Boron nitride (BN) exists in four different crystalline forms, i.e. hexagonal BN (h-BN), cubic BN (c-BN), rhombohedral BN (r-BN) and wurtzite BN (w-BN) [7, 8]. The most stable polymorph h-BN is analogous to the graphite while the cubic structure is analogous to the diamond. The former exists as the layered materials such as the layers arranged along c-axis having the B exactly above the N in the alternating layers possessing the ABCABC stacking sequence. While in the zinc blend or cubic structure, the atoms are arranged in closely packed in cubic structure having sp3 bonding. The c-BN as well as w-BN are dense, hard phases of BN in which atoms are bonded by strong sp3 hybridization with the formation of sigma bonds as shown in Fig. 1.3a, b. These polymorphs comprised of tetrahedral coordinated nitrogen and boron atoms with (111) planes of cubic BN ordered in a three layer stacking sequence (ABCABC….), while for w-BN the (0002) planes ordered in two layers (ABAB…) [9]. Hexagonal and rhombohedral BN, analogous to the graphite, exists as the layered structure, which are order in either three layers with ABCABC…. Staking sequence or ABAB… stacking sequence in two layers. In h-BN, the hexagonal rings are placed directly above each other and can be seen in Fig. 1.3c. Moreover, such layers are rotated by 180° from layer to the layer. However, the in-plane atoms are bonded by the localized sp2 hybridization, while the out of plane is bonded by the delocalized π bonds, that are considered as reason for the connection in between two adjacent layers.

Fig. 1.3 Schematic representation of crystal structure of a C-BN, b w-BN and c h-BN. Reprinted with permission from Janotti et al. [10]. Copyrights (2001), American Physical Society

1.4 Layered Versus Non-layered Materials

7

The h-BN is used as dielectrics in next-generation nano-electronic devices, vertical tunneling device, protective coatings, gas sensing, as filler for binder-free anode for lithium-ion batteries, and hyperbolicity in h-BN. While the c-BN are mostly used as abrasives and in cutting tool applications, the second highest thermal conductivity, low dielectric constant. The pnictogens, elements in group 15, are considered as appropriate for the fabrication of single elemental 2D materials [11] that are potential candidate for the several applications in the field of electronic as well as optoelectronic devices, plasmonics and sensors. Phosphorous, one of the superabundant elements kept in earth, exists in various allotropic forms, some of which are white phosphorous, red phosphorous, blue phosphorus and black phosphorous. Among these, the blue phosphorous and black phosphorous exist as the layered materials while others exist as non-layered materials. Phosphorous, in general, is non-metal and a very poor conductor of heat as well as electricity. White and red phosphorous are broadly utilized in safety matches and other explosives. In industries, the phosphorous is widely utilized as chemicals in cleaning compounds, fertilizers and food additives. It is also used in the production of steel and also in the fabrication of the phosphor bronze. The blue phosphorous exists as the layered materials in which the in-plane hexagonal configuration and the stacking of the layers in the bulk structure resembles to the graphite [12]. Within the layers of the blue phosphorous, the atoms are covalently bonded at the distance of the 2.27 Å, while the interlayer distance is 5.63 Å that specifies the easy exfoliation of the layers. The main advantage of blue phosphorous is that the weak van der Waals interactions in between the layers leads to the easy exfoliation of the layers to produce the quasi-2D configuration/structure and a broad fundamental band gap of 2 eV would make it a potential candidate for various electronic applications. Black phosphorous, a very rare allotropic form of phosphorous, was first fabricated from the red phosphorous at high pressure and temperature in 1914 [14]. At ambient conditions, the black phosphorous is a well-known layered material whose structure is analogous to the graphite. The layered configuration of the black phosphorous owes the orthorhombic structure [15], in which the each adjacent layers are connected by the weak VdW interactions. The unit cell consists of eight atoms that offers the computed density of the 2.69 g/cm3 . With unit cell consisting of two layers, in which every phosphorous atom is bonded with that of the three other neighboring atoms 2.18 Å. Two of the three atoms are arranged in-plane of the layer at 99° from each other. While the third one lies in between the layers at an angle of 103° that make the average angle of 102°. Analogous to the graphite, the adjacent layers of black phosphorous are stacked together by the weak VdW interactions, where every single layer is formed through the sp3 hybridization of phosphorous atoms by covalent bonds as shown in Fig. 1.4. Because of this sp3 hybridizations, every single phosphorous atom owns the covalent bonds to the three neighboring phosphorous atoms along with a lone pair that would lead to a quadrangular pyramid structure that resembles to the puckered honeycomb configuration as shown in Fig. 1.5a. The crystal structure of the said material, i.e. black phosphorous, could be significantly distinguished under

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1 Characteristics, Strategies and Applications of Layered Materials …

very high pressure. It is also expected that the VdW interactions along z-direction could be compressed appreciable. Contrary to other allotropic forms, i.e. white or red phosphorous, the BP is stable thermodynamically, which is obtained at high temperature and pressure from that of red or white phosphorous, due to the phase transition. At atmospheric pressure, it owes the orthorhombic structure with a very narrow band gap. The band gap of BP is about 0.2–0.3 eV, but could be extended from 1.0–2.0 eV that is based on the number of layers. The few-layer configuration of BP is of great fascination because of their higher mobility along with an appropriate band gap [18]. The BP is greatly used in various electronic applications such as in super-capacitors, carrier mobility at normal condition as well as carrier mobility at variable pressure. It is recently utilized in several devices such as field effect transistors (FETs) [19] optoelectronic devices, anisotropic transportation, photocatalyst specifically for solar water splitting, humidity and gas sensors, ultrafast photonics and several biomedical applications. It is also widely utilized as an effective substrate of the replication of DNA [20]. The isoelectronic systems like phosphorous are regarded as the potential candidates due to the their higher mobility along with vigorous intrinsic band gap that could be varied by virtue of several factors such as applying strain, transverse electric field and number of layers, etc. [21]. Arsenic, an element of 5th group, is a well-known n-type dopant within the semiconductors that are widely utilized in electronic devices. The compounds of Arsenic are used in the generation of insecticides, pesticide and herbicides that are going to

Fig. 1.4 Layered configuration of black phosphorous (BP). Reprinted with permission from Saleem et al. [13]

1.4 Layered Versus Non-layered Materials

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Fig. 1.5 Monolayer patterns of a black phosphorous and b blue phosphorous. Reprinted with permission from Zhu and Tománek [16]. Copyright (2014), American Physical Society, while c and d showed the layered configurations. Reprinted with permission from Antonatos et al. [17]. Copyright (2020), The Royal Society of Chemistry

decrease due to the toxicity of said materials. In humans, even a smaller quantity of arsenic is responsible for the production of cancer causing agents [22]. The three most common allotropic forms of arsenic are black, gray and yellow, out of which the most stable form is gray arsenic [23]. The gray arsenic acquires a buckled structure analogous to the blue phosphorous and is metallic in nature. This gray arsenic acquires the double-layered configuration that contains several interlocked refined six-membered rings. However, the distance between two layers of arsenic is smaller as compared to the black phosphorous. The arsenic is brittle as well as owes the low Mohs hardness of 3.5 due to the presence of the weak VdW interactions. Also, there is a greater possibility of synthesis of single layer by utilizing the micromechanical cleavage methodology just like graphene because of the presence of weak VdW interactions. The gray arsenic exhibits the semimetallic nature in its bulk configuration, while exhibits an appropriate band gap of about

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1.2–1.4 eV in its few-layered structure. This band gap is sensitive to the interlayer distance, stacking of layers as well as the in-layer strain [18]. The single layer of gray arsenic shows a low-buckled 2D hexagonal structure [23]. The electronic properties computed by theoretical means revealed an indirect band gap of 1.5 eV from GGAPBE and 2.2 eV from hybrid functional for single layer. The single layer of arsenic could be utilized in various application such as in optoelectronic devices. The insulating waxy yellow arsenic owes the structure analogous to the white phosphorous along with the tetrahedral symmetry [24]. Contrary to this, the black arsenic possess the puckered layered configuration and is analogous to the black phosphorous. The black arsenic possesses the anisotropy in armchair and zigzag direction. In this puckered layer, every single arsenic atom forms covalent bond to the three nearest neighbors by two different bond lengths, the shorter out-of-plane bond length of about 2.49 Å, while the in-plane larger bond length of about 2.51 Å. The distance between two layers are 5.46 Å leads to the mechanical exfoliation in order to fabricate the flakes having several number of layers. The anisotropy along armchair and zigzag direction leads to the higher carrier mobility, conductance as well as thermal conductivity. The ratio of mobility along armchair and zigzag is greatest of all the known 2D materials. These properties lead to the utilization in thermoelectric and nanoelectronic devices and applications. The arsenic in general could act as a new catalyst for several catalytic procedures as well as for organic reactions [15]. In addition, it could be utilized in several electrical, optical devices and several sensors etc. Antimony, a rare element, usually occurs in four allotropic forms that includes gray, black, yellow and an explosive white form [25]. Out of which the gray is the most stable and the only semimetal, while others are non-metals as well as unstable. In elemental form, antimony is widely utilized as an anode material within the Li-ion batteries due to the higher computed theoretical capacity, when it is lithiated to the Li3 Sb. Contrary to this, the non-metal antimony is doped (as a trivalent impurity) due to the greater interest in the semiconductors in several applications such as transistors within the integrated circuits. Doped ZnO acts as a p-type semiconductor, while the doping within the Si results as an n-type material due to increase in the hole-conducting characteristics (Fig. 1.6). The structure of gray allotrope of antimony is analogous to the graphite, where the layer of antimony contains the six-membered fused rings [27] as can be seen in Fig. 1.6. The closest and next closest antimony atoms make an irregular octahedral complex having 3 atoms in every double layer that are a bit nearer to the next 3 atoms. This closely packed arrangement of atoms in gray antimony leads a higher density of about 6.7 gcm−3 . Also, the presence of weak bonding in between the layers leads to be the synthesize of nanosheets of antimony through the top-down technique. Few-layered antimony sheets as exfoliated by bulk antimony, also known as antimonene, exhibit the excellent electrochemical activity as compared to its bulk counterparts specifically in super-capacitors, electrolytic evolution of H2 as well as the reduction of CO2 etc. [28]. Such magnificent electrochemical activity exploit from the plane structure in two-dimensional configuration as well as the edge impacts provoke their utilization in the field of rechargeable batteries.

1.4 Layered Versus Non-layered Materials

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Fig. 1.6 Schematic presentation of atomic crystal structures and electronic band diagram of single layer of a β-antimony and b α-antimony. Reprinted with permission from Wang et al. [26]. Copyright (2018), Author(s)

The transition from the bulk toward the monolayers is associated with a sudden change within the electronic characteristics from the semimetal to the semiconductors [29, 30]. The monolayer of antimony exhibits an indirect band gap of about 2.28 eV that fill up the vacancy of the band gap of recently known two-dimensional materials. Moreover, by the application of small biaxial strain, the said material could be transformed into direct band gap semiconductor that suggests the utilization of this material as a mechanical sensor in addition to their novel electronic and optoelectronic properties. Present-day research reveals that the antimonene owes several fascinating characteristics such as spintronic properties, higher mobility, excellent thermal conductivity and marvelous optical properties such as higher refractive index, direction dependent optical transparency as well as the broad range absorption.

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The two-dimensional inorganic compounds incorporate a variety of compounds, which involve hexagonal boron nitride, black phosphorous, transition metal dichalcogenides, monochalcogenides and oxides [20, 31]. The transition metal dichalcogenides are broadly studied after graphene due to their fascinating applications in batteries, spintronic, valleytronics, lubricants, catalysis, microelectronics and thermoelectric devices, nano-electronics, optical filters, photodetector, optical communication and quantum devices etc. Specifically, the tungsten and molybdenum dichalcogenides are considered as inorganic fullerenes due to the fact that they present transition from indirect to direct band gap that is based on their thickness. This would refer an amazing 104 fold enhancement in photoluminescence. Moreover, the layered MoS2 , due to their ion transport properties, are important for neuromorphic computing. Similarly, SnS2 nanosheets have also been utilized as saturable absorbers in conjunction along with Er-doped fiber lasers in order to attain the 11th ordered soliton molecule, revealing their applications within the fiber lasers as well as optical-fiber communications. The group 14-based monochalcogenides like GeS and SnS exhibit the anisotropic crystal structure. The theoretical investigations anticipated several fascinating characteristics such as higher carrier mobility, ferroelectricity at room temperature and larger exciton binding energies etc. Such materials are considered as potential candidate for several applications such as field effect transistors as well as energy conversion at severe surrounding. Layered transition metal oxides have slightly less studied. This may be due to their broad band gap that makes them electrically insulator. Nevertheless, the recent study reveals the n-type conduction could be produced within α − MoO3 , either the doping of fluorine or by the interclation of H+ that would generate the vacancy of oxygen. The crystal structure of MoO3 is given in Fig. 1.7. Moreover, these vacancies of oxygen could play an important role for the improvement of the gas sensing abilities in the devices based on the α −MoO3 . Also, the the addition of the H+ within the nanoflakes of two-dimensional α − MoO3 could fabricate the substiometric semiconductors having improved plasmonic behavior. Similarly, two-dimensional-layered V2 O5 has presented a wide band photodetection as well as memrisitive behavior.

1.5 Scheme to Study the Layered Materials The utilization and study of the layered materials using either the theoretical framework or experimental setup require robust strategy in comparison to the non-layered ones due to structural and electronic differences [33–35]. First of all, the presence of weak VdW forces between adjacent layers to keep them together while strong in-plane covalent interactions which tightly packs the atoms together. Secondly, the atomic scale and uniform thickness of the layers which enables utilization of the materials in transparent and ultraflexible optoelectronics as well as transport of charge carriers. Thirdly, the layered materials can be exfoliated like “peeling off of onion” as compared to “potato-type slicing” in non-layered solids. The layered

1.5 Scheme to Study the Layered Materials

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Fig. 1.7 Crystal structure of layered MoO3 where a unit cell and b corner connected. Reprinted with permission from Huang et al. [32]. Copyright (2014)

materials comprise layers which are packed perpendicular to c-axis and possess high symmetry [36, 37]. On the other hand, the compounds which do not meet the symmetry benchmark can be investigated on the basis of the packing ratios (ratio of covalent volume to the total volume). While considering the layered materials using the theoretical framework, the bonding analysis can be performed by various means. Besides other techniques, the covalent radii are taken into account and compared with the optimized crystal structure. The compounds having the gap greater than 2.4 Å in between the layers across the direction of their stacking have been taken into account. The covalent bond as well as the gap between the layers have investigated to discover either there exists covalent bond that lies across the gap within the crystal structure. For this purpose, the distance among the two adjacent atoms near to the aggregate of their covalent radii have been calculated. If there exist no bonds in the stacking direction across the gap then the material can be regarded/considered/identified as the layered material having weak bonding across the layers and further investigated on the extraction and of the single layer their utilization in various applications [38]. The graph between the interlayer separations as a function of binding energy has also been plotted in literature for most of the layered materials [39, 40]. The interlayer distance at minimum energy are taken into accounts. For most of the layered material, the interlayer distance is about 3–4 Å. The exfoliation energy, the energy to peel off a layer, of most of the layered compounds have been found to be below 150 meV/atom that is very close to successfully synthesized SnSe. Most of the layered structure owes the exfoliation energy in between the 60 and 100 meV/atom that proves it to be an effective benchmark to distinguish the VdW-bonded-layered materials from the non-layered materials. Moreover, to evaluate/examine the feasibility of the exfoliation, the phonon frequencies have been taken into account. Almost 80% of experimentally exfoliated 2D materials showed positive phonon dispersion.

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The major part of recent literature reports 2D materials and several new journals, forums, research institutes, funding opportunities appeared in this regard. However, due to frequent study of monolayers, the distinction between layered and non-layered materials has been blurred which raised serious misconceptions. It has been mistakenly perceived that all the 2D materials are layered materials and vice versa. The monolayer can be exfoliated from any of the layered material but every atomically thick 2D material is not in-essence a layered material. Such materials can be considered as 2D materials, slabs or surfaces, but these are not essentially layered materials. Among a large number of recently studied 2D materials, only a fraction fulfills the criteria of layered material, i.e., exist in the forms of layers and anisotropy in bonding that is strong in-plane covalent bonding and weak VdW interactions in between the layers. Though carefully published literature has considered the above-mentioned flaws but no book dedicated solely to the layered materials is available. The comprehensive explanation on the layeredness in materials, mechanism involved, synthesis and characterization strategies and applications is given in the coming sections. This book will be a complete document not only in the scope of text book knowledge but also give an overview of the published literature so far. This book is aimed at documenting the above-mentioned issues, describing the phenomenon involved, comparative analysis of experimental and theoretical analysis, shedding light on the literature and bridging the gap between the VdW material’s studies and utilization in applications. The write-up is organized in different chapters out of which introduction of the layered materials, and their several prospects are described in this chapter. Chapter 2 highlights the experimental setup for the growth of layered materials and relevant issues, whereas Chap. 3 provides the theoretical backgrounds with focus on relevant theories and their implementation to explore the layered materials. Furthermore, in this chapter, in light of recently developed ab-initio methodologies, the strategy is devised to study the layered materials. Besides these, in Chaps. 4 and 5, the computed results on layeredness on some famous layered materials will be described. For this purpose, the various crystalline forms of the known layered materials are discussed. The analysis of graphite and diamond crystal structure was considered to investigate the prospects of the layeredness. Finally, in last chapter, the conclusions are given and some questions are discussed with the recommendations and open research questions in this regard. This book would be helpful for the researchers, scientists, industrialists and students working in variety of fields especially solid state physics, chemistry, material science and engineering.

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4. Zhan, H., Guo, D., Xie, G.X.: Two-dimensional layered materials: from mechanical and coupling properties towards applications in electronics. Nanoscale 11(28), 13181–13212 (2019). https://doi.org/10.1039/c9nr03611c 5. Duong, D.L., Yun, S.J., Lee, Y.H.: Van der Waals layered materials: opportunities and challenges. ACS Nano 11(12), 11803–11830 (2017). https://doi.org/10.1021/acsnano.7b07436 6. Tanjil, M.R.-E., et al.: Ångström-scale, atomically thin 2D materials for corrosion mitigation and passivation. Coatings 9(2), 133 (2019) 7. Challenge, N.: Next Challenge プログラム会議, pp. 5–6 (2019) 8. Bhimanapati, G.R., Glavin, N.R., Robinson, J.A.: 2D boron nitride: synthesis and applications. Semicond. Semimetals 95, 101–147 (2016). https://doi.org/10.1016/bs.semsem.2016.04.004 9. Vel, L., Demazeau, G., Etourneau, J.: Cubic boron nitride: synthesis, physicochemical properties and applications. Mater. Sci. Eng. B 10(2), 149–164 (1991). https://doi.org/10.1016/09215107(91)90121-B 10. Janotti, A., Wei, S.-H., Singh, D.: First-principles study of the stability of BN and C. Phys. Rev. B 64(17), 174107 (2001) 11. Wolff, S., Gillen, R., Assebban, M., Abellán, G., Maultzsch, J.: Two-dimensional antimony oxide. Phys. Rev. Lett. 124(12), 1–6 (2020). https://doi.org/10.1103/PhysRevLett.124.126101 12. Zhu, Z., Tománek, D.: Semiconducting layered blue phosphorus: a computational study. Phys. Rev. Lett. 112(17), 1–5 (2014). https://doi.org/10.1103/PhysRevLett.112.176802 13. Saleem, Z., et al.: Two-dimensional materials and composites as potential water splitting photocatalysts: a review. Catalysts 10(4), 464 (2020) 14. Liu, H., Du, Y., Deng, Y., Ye, P.D.: Chem Soc Rev (2014). https://doi.org/10.1039/C4CS00 257A 15. Sturala, J., Sofer, Z., Pumera, M.: Chemistry of layered Pnictogens: phosphorus, arsenic, antimony, and bismuth. Angew. Chemie—Int. Ed. 58(23), 7551–7557 (2019). https://doi.org/10. 1002/anie.201900811 16. Zhu, Z., Tománek, D.: Semiconducting layered blue phosphorus: a computational study. Phys. Rev. Lett. 112(17), 176802 (2014) 17. Antonatos, N., et al.: Acetonitrile-assisted exfoliation of layered grey and black arsenic: contrasting properties. Nanoscale Adv. 2(3), 1282–1289 (2020) 18. Zhu, Z., Guan, J., Tomanek, D.: Unusual electronic structure of few-layer grey arsenic: a computational study (2014). [Online]. Available: http://arxiv.org/abs/1410.6371 19. Quhe, R., et al.: Black phosphorus transistors with van der Waals-type electrical contacts. Nanoscale 9(37), 14047–14057 (2017). https://doi.org/10.1039/c7nr03941g 20. Gutiérrez, H.R.: Two-dimensional layered materials offering expanded applications in flatland. ACS Appl. Nano Mater. 3(7), 6134–6139 (2020). https://doi.org/10.1021/acsanm.0c01763 21. Mardanya, S., Thakur, V.K., Bhowmick, S., Agarwal, A.: Four allotropes of semiconducting layered arsenic that switch into a topological insulator via an electric field: computational study. Phys. Rev. B 94(3), 1–8 (2016). https://doi.org/10.1103/PhysRevB.94.035423 22. Mandal, B.K., Suzuki, K.T.: Arsenic round the world: a review. Talanta 58(1), 201–235 (2002). https://doi.org/10.1016/S0039-9140(02)00268-0 23. Kou, L., Ma, Y., Tan, X., Frauenheim, T., Du, A., Smith, S.: Structural and electronic properties of layered arsenic and antimony arsenide. J. Phys. Chem. C 119(12), 6918–6922 (2015). https:// doi.org/10.1021/acs.jpcc.5b02096 24. Chen, Y., et al.: Black arsenic: a layered semiconductor with extreme in-plane anisotropy. Adv. Mater. 30(30), 1–6 (2018). https://doi.org/10.1002/adma.201800754 25. Hansell, C.: All manner of antimony. Nat. Chem. 7(1), 88 (2015). https://doi.org/10.1038/ nchem.2134 26. Wang, J., et al.: Enhanced doping effect on tuning structural phases of monolayer antimony. Appl. Phys. Lett. 112(21) (2018) 27. Gu, J., Du, Z., Zhang, C., Ma, J., Li, B., Yang, S.: Liquid-phase exfoliated metallic antimony nanosheets toward high volumetric sodium storage. Adv. Energy Mater. 7(17), 1–8 (2017). https://doi.org/10.1002/aenm.201700447

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28. Gao, Y., et al.: Tailoring natural layered β-phase antimony into few layer antimonene for Li storage with high rate capabilities. J. Mater. Chem. A 7(7), 3238–3243 (2019). https://doi.org/ 10.1039/c8ta11218e 29. Yan, Z., Song, X.F., Zhang, S., Xie, Z.: Erratum: few-layer antimonene: large yield synthesis, exact atomical structure, and outstanding optical limiting. J. Am. Chem. Soc. 139(9), 3568 (2017). https://doi.org/10.1021/jacs.6b08698 30. Zhang, S., Yan, Z., Li, Y., Chen, Z., Zeng, H.: Atomically thin arsenene and antimonene: semimetal-semiconductor and indirect-direct band-gap transitions. Angew. Chemie 127(10), 3155–3158 (2015). https://doi.org/10.1002/ange.201411246 31. Ramasamy, K., Sims, H., Butler, W.H., Gupta, A.: Mono-, Few-, and multiple layers of copper antimony sulfide (CuSbS2 ): a ternary layered sulfide (2014) 32. Huang, P.-R., et al.: Impact of lattice distortion and electron doping on α-MoO3 electronic structure. Sci. Rep. 4(1), 7131 (2014) 33. Akhtar, M., et al.: Recent advances in synthesis, properties, and applications of phosphorene. ANPJ 2D Mater. Appl. 1(1), 1–12 (2017). https://doi.org/10.1038/s41699-017-0007-5 34. Cao, W., et al.: 2-D layered materials for next-generation electronics: opportunities and challenges. IEEE Trans. Electron Devices 65(10), 4109–4121 (2018). https://doi.org/10.1109/TED. 2018.2867441 35. Ganatra, R., Zhang, Q.: Ganatra2014.Pdf. ACS Nano 8, 4074–4099 (2014) 36. Björkman, T., Gulans, A., Krasheninnikov, A.V., Nieminen, R.M.: Van der Waals bonding in layered compounds from advanced density-functional first-principles calculations. Phys. Rev. Lett. 108(23), 1–5 (2012). https://doi.org/10.1103/PhysRevLett.108.235502 37. Zhang, X., Chen, A., Zhou, Z.: High-throughput computational screening of layered and twodimensional materials. Wiley Interdiscip. Rev. Comput. Mol. Sci. 9(1), 4–6 (2019). https://doi. org/10.1002/wcms.1385 38. Opoku, F., Govender, K.K., Van Sittert, C.G.C.E., Govender, P.P.: Role of MoS2 and WS2 monolayers on photocatalytic hydrogen production and the pollutant degradation of monoclinic BiVO4 : a first-principles study. New J. Chem. 41(20), 11701–11713 (2017). https://doi.org/10. 1039/c7nj02340e 39. Li, S., Sun, M., Chou, J.P., Wei, J., Xing, H., Hu, A.: First-principles calculations of the electronic properties of SiC-based bilayer and trilayer heterostructures. Phys. Chem. Chem. Phys. 20(38), 24726–24734 (2018). https://doi.org/10.1039/c8cp03508c 40. Idrees, M., Nguyen, C.V., Bui, H.D., Amin, B.: Electronic and optoelectronic properties of van der Waals heterostructure based on graphene-like GaN, blue phosphorene, SiC, and ZnO: a first principles study. J. Appl. Phys. 127(24), 9 (2020). https://doi.org/10.1063/5.0011303

Chapter 2

Synthesis and Properties of Layered Materials

Abstract The property of materials to exist in the form of layers is known as layeredness. It is an important structural aspect of a class of materials which exhibits primarily in-plane strong covalent bonds and out-of-plane weak van der Waals (VdW) interactions. The anisotropic atomic bonding leads to formation of layers in such materials, which are known as layered materials or VdW solids. This chapter deals with some important concepts, for instance, the natural conditions that allow the materials to exist either in onion like layered structures or potato like non-layered configurations. In order to elaborate the relevant issues, example of carbon is suitable which exists in the form of layered graphite as well as non-layered diamond. Further, the study of transition from graphite to diamond helps to shed light on conditions to grow the layered materials. This chapter includes the description of synthesis conditions on growth of layered materials by revealing the role of top-down and bottom-up techniques. The suitability of wet chemical method, topochemical transformation, microwave-aided transformation, and chemical vapor deposition are elaborated in this regards. Besides these, the roles of several exfoliation techniques such as liquid phase exfoliation, mechanical exfoliation, ultrasonic exfoliation along with the several intercalation mechanisms are also discussed.

The layeredness is a unique structural property of VdW-layered materials. The distinction between layered and non-layered material can be understood on the basis of the structural properties. The relevant definitions and phenomenon related to the layered materials are described in details in the upcoming sections. The conditions that become the reason for materials to exist as either in layered or non-layered materials are also narrated.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Majid and A. Jabeen, Layeredness in Materials, Engineering Materials, https://doi.org/10.1007/978-981-99-6299-0_2

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2.1 Natural Conditions-Graphite to Diamond Transformation Carbon, a well-known material, has been a great fascination for the researchers when chemistry and physics of the materials is taken into consideration for different applications. The diverse allotropes of carbon is one of the reasons behind this assertion. There have been several fields including the organic chemistry rely on utilization of carbon. Graphite is the renowned layered material which comprises of carbon atoms distributed in layers connected via VdW interactions, while diamond is a non-layered material that is also a carbon materials. Both of these are based on carbon atoms and the difference only arises in their crystal structure that are considered to be based on their growing conditions. There is a famous saying “No pressure-No diamond” which is implemented in material science with the outcome that graphite under pressure transforms into the diamond. Carbon, in nature, exists in several allotropic forms, out of which the graphite and diamond are the most stable forms. The former exist in the layered material while the latter is found in the non-layered form as discussed earlier. The main reason behind this is different C–C bonding of these materials in such a way that sp 2 and sp 3 bonding exists in the structure of graphite and diamond respectively. The ample dissimilarity in the carbon-based structures stems from the fundamental electronic configurations 1s 2 , 2s 2 , 2 p 2 which faces alteration by the orbital hybridization in the materials. By sp 2 hybridization, three of the electronic density lobes arising from the similar planes are apart by the angle of 120° which in turn enables the covalent bonding (i.e. sigma ( σ ) bond) into the flat structures of graphene sheets that resembles to the honeycomb structure. These graphene sheets could be stacked into three-dimensional (3D) structure to establish the graphite or similar structures. The 4th electron lobe (i.e. π bond) is along the perpendicular direction that tends to the form the perpendicular plane. Moreover, the sp 3 hybridization leads to the formation of the four electronic lobes in tetragonal geometry within the 3D structure having the 180° inter-lobe angle. It results into the formation of face-centered cubic diamond that exists in the lowest energy configuration having the tetragonal symmetry. The most stable phase of carbon appears in form of hexagonal (i.e. Bernal) graphite configuration, which comprises the sp 2 hybridized hexagonal layers having covalent bonds stacked in ABAB arrangement as shown in Fig. 2.1. The successive layers are shifted in such a way that about the half of the atoms from one of the layer (also known as bridging atoms) lie vertically over the successive layers, whereas the remaining are located above the hexagon centers. Besides this, the graphite might also occur in rhombohedral configuration having the ABC stacking of the layers despite the atypical nature of the phase as shown in Fig. 2.1d. The intra-layer covalent bonds of two above discussed allotropes are very strong having intra-layer C–C bond length of 1.415 Å (in graphite) and 1.54 Å (in diamond), whereas the significantly larger inter-layer distance of ~3.35 Å is found in case of graphite. Hence, the weaker interlayer interactions make an easy exfoliation of the graphene layers. The larger

2.1 Natural Conditions-Graphite to Diamond Transformation

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AA stacking

a

d C-C

AB stacking

a

d C-C

Side view

Top view

Fig. 2.1 Crystal structure of graphite in different stacking sequences. Reprinted with permission from Ziambaras et al. [1]. Copyright (2007) by the American Physical Society (would like to name the different structures as a, b, c and d)

natural single crystals are therefore scarce and majority of the crystals perforate along with the stacking faults in graphite. Diamond, on the other hand, generally exists in face centered cubic lattice having a foundation of two atoms laying at point 0 0 0 and ¼ ¼ ¼ along with the covalent bonds between the closest neighbor. Besides this, the hexagonal configuration, also declared as lonsdaleite, has also been thoroughly investigated. The graphite as well as diamond lattice might be formed in hexagonal rings of carbon atoms which are flat in graphite but folded into boat shaped configuration in hexagonal diamond and chair like conformation in cubic diamond. It must be taken into consideration that lonsdaleite is not an allotropic form rather it is the cubic diamond having a higher concentration of the stacking faults as well as structural defects [2]. The material can exist in several polymorphic forms which may either be layered or non-layered. The environmental or synthesis conditions may provide the circumstances which arrange the atoms in the form of a specific structure. The provision

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of high temperature and pressure to the graphite would turn it to be the non-layered material and vice versa to cause the phase transition.

2.2 Rigid and Soft-Layered Materials The typical layered materials could be classified into the rigid and soft materials based on the interactions present between the layers [3, 4]. The commonly known inorganic-layered materials such as graphite, transition metal dichalcogenides and black phosphorous etc. contains van der Waals (VdW) interactions between the layers while some other layered materials such as the clays, transition metal oxides, layered double hydroxide contains the electrostatic interaction between the layers. In general, the interlayer interactions are supposed to be the stronger for the layered materials having electrostatic interaction, whereas the VdW interaction are taken as weaker. The materials having stronger electrostatic interlayer interactions between the inter-layer ions and the charged ions are termed as the rigid layered materials while the materials having weak VdW interactions are known as soft layered materials. The rigid layered materials could be exfoliated into nanosheets by manipulating the electrostatic inter-layer interactions. Mostly, the rigid layered materials demand ionic exfoliation agents like the bulky ions as well as surfactants in spite of the fact that some of the clays could be exfoliated by means of the dispersion within the aqueous as well as polar organic media. For instance, a general strategy adopted by the Sasaki and fellows [5, 6] comprises widely spreaded exfoliation method for the layered transition metal oxides. The intercalation of the massive ions starts the exfoliation by the process of osmotic swelling of the layered materials. By following this exfoliation technique, a number of single layers/monolayers could be attained. The nanosheets obtained via the exfoliation of the soft layered materials mainly contain the weak VdW interactions had grasped a lot of attention just after the discovery of the graphene. The soft layered materials including black phosphorous (BP), transition metal dichalcogenides (TMDs) and the graphite have been peeled-off into the nanosheets within the organic medium via implementation into the foreign stimuli like the sonication. Currently, the broad range of the latest as well as novel layered materials are being peeled-off in the form of the nanosheets that includes the covalent organic frameworks, metal–organic frame work and the typical organic layered materials. The soft layered materials could be elucidated as the layered architects showing the molecular motion. Their flexibility plays a vital role in the emergence of the dynamic characteristics as well as the function depending upon the molecular motion. Besides these, the two-dimensional anisotropy enables to give the particular morphology as well as the homogeneous coating over a substrate. Their molecular designs as well as the intercalation are important techniques to control over the structure along with the function of the soft layered materials.

2.3 Exfoliation of Layered Materials

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2.3 Exfoliation of Layered Materials Besides the graphene, there are various other 2D materials which exist naturally or could be synthesized, for example, elemental layered materials including phosphorene, antimonene and bismuthene, etc. Hexagonal boron nitrides (h-BN), transition metal dichalcogenides (TMDs) have general formula M2 X3 and MX2 (where M is metal atom and X is the chalcogen atom) such as transition metal oxides, metal nitrides as well as carbides. The exfoliation refers to peeling-off the bulk layered material into a single layer. The remarkable material’s characteristics are emerged when thickness of the bulk layered solid is reduced to the one or the few layers that could be exploited in multiple ways for the utilization of the materials in optical, electronic and catalytic applications. The exfoliability of the layered materials has earned great research interest which gave birth to the variety of methods for the synthesis of the 2D monolayers or fewer layers. The methods involve both the top-down and bottom-up techniques which will be elaborated in the coming sections. The exfoliation process of the solid crystal could be achieved within the liquid phase where the electrolytes as well as solvents intercalated in between the layers by the assistance of the three viable driving systems that could be utilized within the combination to attain the inflate efficiencies. These methods include electrochemistry, ultrasonication and mechanical exfoliation. Besides these, the intercalation provides a strategy in the form of top-down technique in order to exfoliate the layered structure via different intercalants like the transition metal halides as well as the alkali metals [7].

2.3.1 Surfactant-Aided Exfoliation The surfactant-aided exfoliation is of great interest because of its advantages [7]. Firstly, the solvent utilized is water which makes it environment friendly. Secondly, the execution of the surfactant supply for the purpose of the exfoliation requires the increased surface to volume ratio which helps formation of large interface. As within the aggregate, the hydrophobic end of the surfactant directs to the core and the polar head group leads to the formation of the outer shell. In a similar way, the surfactant might be gathered at the non-polar organic solvent at which the structure of the materials had been mentioned as the reverse aggregate. Considering the exceptional, green and effective replacement over the typical organic solvents, the supercritical carbon dioxide (CO2 ) owes an exciting characteristic that will aid the solutions of the surfactant-water in order to assemble the reverse aggregation emulsions in the microenvironment. The schematic representation of the surfactant-aided exfoliation using CO2 and H2 O medium is shown in Fig. 2.2. Besides these, the behavior of phase of emulsions microenvironment could be exploited via the tailoring of the physical characteristics of the solutions. In particular, like the “switch” for the molecular

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Fig. 2.2 Schematic diagram representing the surfactant-aided exfoliation. Reprinted with permission from Wanf et al. [8]. Copyright (2015), The Author(s)

micelle of that of the surfactant, the tailoring of the micelle behaviors of that of surfactant via CO2 is reversible in nature that could be perceived through the process of depressurization and pressurization. The fabrication through the exfoliation of the layered materials provides 2D materials for variety of applications [7]. The exfoliation of graphite via above described exfoliation technique provides good-quality graphene exhibiting excellent electrical characteristics. In this context, the exfoliated BN nanosheets appears suitable for augmentation of the polymeric films. An environment friendly as well as stable dispersion permits the BN nanosheets to act as the effective fillers for the preparation of the higher performance composites of the polyvinyl alcohol (PV). In addition to these, the light transmission characteristics of the polymeric films do not alter considerably by embedding the BN sheets. Moreover, the BN nanosheets did not absorb light in visible range of solar spectrum because of the wide band gap and consequently had comparatively weak optical transmission of the polymeric matrix in contrast to the carbon fillers.

2.3 Exfoliation of Layered Materials

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2.3.2 Electrochemically Aided Exfoliation The electrochemically aided exfoliation holds the promising potential for the largescale production of the 2D layered sheets [9]. The procedure involves the implementation of the fixed current or potential, which could establish the ionic species within the solution in order to intercalate suitable atoms between the layers, hence reducing the inter-layer forces to increase the inter-layer separation and set the layers free within the solution [10]. The procedure could be executed within the aqueous solution along with the organic solvents and utilizing of the cathodic reduction or anodic oxidation to introduce (intercalate) the positive or negative species respectively. The step-by-step mechanism is given in Fig. 2.3. The sort of the electrolyte and solvent plays an important role in quality of the exfoliated materials along with having a considerable impact on effectiveness and efficiency of the process [11].

Fig. 2.3 Schematic representation of electrochemically aided exfoliation. Reprinted with permission from Parvez et al. [12]. Copyright (2013), American Chemical Society

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2.3.3 Cathodic Intercalation of the Positive Ions The application of the negative potential to the layered material could lead to attain the intercalation of positive ions present in the solution and most often occur with co-intercalation of the solvent molecule. Further, it facilitates the expansion of the materials ensuring the intercalation. The lithium ions (Li ions) are potential intercalants because of the popular Li-intercalated compounds as broadly used in batteries since 1970 [13]. As motivated by the procedure involved in batteries, Wang et al. suggested the utilization of the LiClO4 within the propylene carbonate (Li+ /PC) in order to exfoliate the graphene sheets from the graphite via application of negative voltage of − 15 ± 5 V [14]. A post-exfoliation reaction in H2 O along with ultrasonication appeared facilitating the exfoliation. The controlled intercalation of the Li ions helps exfoliation of different layered compounds like h-BN, TMDs, graphite etc. [15]. The process of the Li-ions insertion can be tracked during galvanic discharge which provides control to complete the process of intercalation. In this method, Limetal has been utilized as an cathode while the layered materials are used as an anode of battery cell. After the complete insertion of the Li ions, the cell is dismantled and the material is sonicated in H2 O during which the emergence of the Li(OH) along with H2 gas takes place that helps the separation of 2D nanosheets. Some other cationic materials also been suggested for the exfoliation and intercalation of graphite like N-butyl, methyl-pyrrolidinium bis(triflouromethylsulfonyl)-imide (BMPTF 2 N) as well as tetra-alkyl ammonium ions Na+ as utilized in aqueous, ionic as well as organic liquids respectively [16].

2.3.4 Anodic Intercalation of Negative Ions The anodic exfoliation could be obtained via application of positive voltage to the layered materials by insertion of the negative ions present in the solution [9, 17]. Furthermore, the procedure could be performed within the organic as well as aqueous solvents having different anionic species. The electrochemical exfoliation technique involving anodic conditions is useful for obtaining the graphene from the bulk graphite. The choice of a suitable electrolyte in the aqueous solution is important for mass-scale production of 2D materials. The rods of graphite have been used as electrodes under the application of suitable bias voltage in the presence of the poly (sodium-4-styrenesulfonate) that serves as the intercalants along with the surfactant sheet stabilizer [18]. The surfactant like sodium dodecyl benzene sulfonate (SDBS) has also been utilized for the exfoliation of graphite [19]. Undoubtedly, the sulfate appeared to be promising negative ion intercalants. In the context of fabrication of the graphite intercalation compounds, prior efforts for the electrochemical exfoliation of graphite have been carried out in the presence of dilute H2 SO4 that caused faster anodic exfoliation.

2.3 Exfoliation of Layered Materials

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The anodic exfoliation within an aqueous solution can be elaborated via a common procedure irrespective of the involvement of the layered materials. In the first step, the execution of the positive bias produces the .O and .OH radicals by the oxidation process of the water. The radicals attack the grain boundaries as well as the edge sites to generate oxygen functional group specifically with the graphene that tend to enhance the interlayer separation. The radicals combined with the anions penetrate between the layers to increase the interlayer separation. The anodic oxidation of the radicals as well as the anions present within the material generates the gaseous species CO2 , O2 , SO2, etc., which separates the layers to cause the exfoliation.

2.3.5 Bipolar Electrochemical Exfoliation The bipolar electrochemistry utilizes the application of voltage between the operating electrodes dipped within the conductive solution of electrolyte along with the conductive materials [9]. The uniform electric field through the solution between the electrodes causes asymmetric polarization along the ultimate ends of the bipolar electrodes in contact-less mode. This would lead to the generation of the potential difference in the material within the solution that are based on the bipolar electrode size (I elec ) along with the distance between the operating electrode (designated as I channel ) as well as the total applied electric field (E tot ) as per Eq. (2.1).  E tot = E tot

Ielec Ichannel

 (2.1)

The idea of the bipolar chemistry could be utilized to attain the asymmetric reactions within the solution at the poles of the material like the phenomenon of water splitting. It produces oxygen at the anode and hydrogen at the cathodic pole within the aqueous solution by the application of the appropriate operating potential [20]. The setup for the bipolar electrochemistry can be utilized in order to suppress the size of the suspended layered material’s particles to attain the nanoparticles having the thickness of the few-layers. The setup comprising of platinum (Pt) electrodes within the aqueous solution of Na2 SO4 at suitable distance from Pt electrode is suitable for exfoliation. The employed operating voltage of ~10 V between the Pt electrodes generate the remarkable reduction in size of the sheets of WS2 that were present within the solution as well as suspended through the magnetic stirring. The generated nanoparticles of the WS2 can be utilized for the electrochemical signaling labels for different application with higher reproducibility, selectivity as well as the sensitivity for the sensing applications and devices. This technique has been found useful to synthesize nanomaterials including black phosphorous and MoSe2 .

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2.3.6 Liquid Phase Exfoliation (LPE) The liquid phase exfoliation (LPE) has become a promising procedure for the generation of the mass scale production of 2D sheets [21]. This process includes the synthesis and fabrication of several layered sheets through the application of the ultrasound or high shear within the layered crystals in the stabilizing liquids (that includes the suitable surfactant, solvents as well as the polymer solutions) [22] as shown in Figs. 2.4, 2.6a and 2.7. In every manifestation, the interactions at the nanosheets and the liquid interface suppress the overall exfoliation energy and as a results stabilize the nanosheets over the aggregation [23]. The consequent dispersions are preferably stable and could be generated at concentration above 1 gL−1 . This technique has been used for the fabrication of variety of the 2D materials that includes the graphene, TMDs, transition metal oxides (TMOs), MXenes, h-BN, Ni(OH)2 , phosphorene and gallium sulfide (GaS), etc. This procedure, in addition of being simpler and inexpensive, fabricate the few layered nanosheets (generally the 1–10 monolayers stacked) while restoring the yield of the single layers that are comparatively lower in other methods. Besides these, the distribution of the lateral size of these nanosheets as synthesized via LPE could be wide, e.g. for the MoS2 its value is 40–400 nm [25]. This distribution of size differs from material to material, in which the nanosheets based

Fig. 2.4 Schematic representation of liquid phase exfoliation. Reprinted with permission from Shen et al. [24]. Copyright (2015), American Chemical Society

2.4 Synthesis of the Layered Materials

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on MoS2 and WS2 that are significantly smaller as compared to the black phosphorous and graphene. Nevertheless, the scope of the technique had been elaborated by the selection of the nanosheets in the context of the size as well as the enhanced the single-layer population. The consequent dispersion could be simply converted into the nanostructured materials through a variety of techniques like freeze drying, spray deposition and inkjet printing. Such structure had been utilized in a variety of applications including photodetectors, barrier composites and battery electrode etc. The LPE could be attained through a kitchen blender along with the ordinary soap [21]. As a result, the liquid exfoliation seems to be the simpler as well as inexpensive. Nevertheless, several parameters should be controlled with great precision to enable the reproducibility a challenging task (making reproducibility a challenging task). In most of the cases, the quality and the yield are based on the delicacy of the procedure. The synthesis strategies will be discussed in detail in the coming section.

2.4 Synthesis of the Layered Materials Considering their anisotropic structure, the synthesis of the layered materials somehow differs from those of non-layered materials [26]. Thus, several schemes have been adopted for the fabrication of the layered materials and their exfoliation to determine high-quality ultrathin sheets. These schemes include the micromechanical exfoliation, chemical vapor deposition (CVD), ultrasonic exfoliation, topochemical transformation, hydrothermal methodology and various others. In the context of the fabrication of 2D materials, both top-down and bottom-up approaches may be utilized. The first approach comprises slicing the bulk structures into nanosheets through controlled withdrawal of the materials. On the other hand, the bottom-up technique utilizes molecular or the atomic precursors which react under specific growth conditions to produce the layered materials or the monolayers.

2.4.1 Top-Down Approach The synthesis of ultrathin nanosheets is carried out via chemical or physical based process in the top-down fashion. The methods involving ultrasonic waves or mechanical force are used to exfoliate the naturally existing layered solids into 2D materials in the form of single or few layers. However, the chemical top-down technique is essentially based on the chemical reaction-assisted via heat treatment, ion exchange etc.

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Fig. 2.5 Schematic representation of mechanical and chemical exfoliation where a represents the procedure of mechanical exfoliation b exhibits the procedure of electrochemical lithiation as well as intercalation for 2D sheets c shows the thermolysis procedure and d is the framework for the synthesis by the gaseous reaction of S and MoO3 . Reprinted with permission from Li et al. [28]. Copyright (2015), The Authors. Published by Elsevier Ltd

2.4.1.1

Mechanical Exfoliation

The mechanical exfoliation is a simple technique to attain monolayer or nanosheets comprising of fewer layered structures from the bulk VdW solids. The micromechanical exfoliation was utilized initially by Novoselov and Geim for the exfoliation of graphite to produce graphene monolayer. This technique is quite famous for the synthesis of the 2D materials and highly convenient for the basic research because of its comparatively lower cost and versatility. It is useful for exfoliation of VdW material to produce the quality ultrathin nanosheets. However, this technique is limited to the laboratory research and appears unfeasible to scale up for mass production in the industries. The nanosheets of the non-layered as well as ionic layered materials could not be attained via this approach. The relevant factors including stacking orders and the stoichiometry play the major role to obtain the single layer of MX2 nanostructures via mechanical exfoliation as shown in Figs. 2.5a and 2.7. The synthesis of graphene through this method has been well documented in literature [26, 27].

2.4.1.2

Ultrasonic Exfoliation

The ultrasonic exfoliation is an effective approach to trim the VdW solids in order to obtain high-quality 2D materials. It is considered to be more efficient when yield is taken into account in comparison to the mechanical exfoliation. The implementation of this strategy involves the appropriate solvents having the suitable surface energies as well as the sonication time as shown in Fig. 2.6c. The exfoliated nanosheets are comparatively stable against the re-aggregation by utilizing the good solvents. In other cases, when the bad solvents are used, the sedimentation along with the reaggregation would take place. The organic solvents can also be utilized for slicing

2.4 Synthesis of the Layered Materials

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Fig. 2.6 Schematic diagrams for the representation of a liquid phase exfoliation, b ion exchange method, c sonication methods. Reprinted with permission from Huo et al. [34]. Copyright (2021), Science China Press. Published by Elsevier B.V

Fig. 2.7 Various approaches to synthesize the 2D layered materials. Reprinted with permission from Shanmugam et al. [35]. Copyright (2022), The Authors. Published by Wiley–VCH GmbH

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the VdW solids as a dispersing media. Besides the advantages and advancement in this method, there is great difficulty to attain the high-purity 2D monolayer materials for several electronic applications. The synthesis of the BP by using this method has been well documented in literature [26, 29].

2.4.1.3

Lithium Intercalation and Exfoliation

The inability of the ultrasonic approach to exfoliate the bulk VdW structures encouraged the community to use lithium (Li) intercalation method for obtaining the monolayers as shown in Fig. 2.5b. During the Li-intercalation process to synthesize 2D MoS2 the generation of the intermediate compound Lix XS2 has been observed [30, 31]. The product monolayer of transition metal dichalcogenides obtained through this process are found in excellent structural quality, yet some problems need to be solved. First of all, the experiment needs higher temperature sustained for long interval of time. Secondly, the lithium intercalation needs to be controlled with great care to attain the monolayer sheets, while prohibiting the formation of the metallic nanoparticles as well as the Li2 S precipitations. The detail synthesis scheme and description of relevant issues are well reported [26].

2.4.1.4

Ion Exchange Exfoliation

Besides the advantages of above described schemes to slice the VdW solids into the ultrathin nanostructures, the exfoliation of layered ionic solids like layered double hydroxide (LDHs), e.g. LiCoO2 is challenging. This is due to the fact that the ionic solids contain ionic bonds between the layers. The ion exchange method is used to obtain monolayers from ionic layered material and hence synthesis of 2D materials based on LiCoO2 could be effectively carried out [32, 33] and schematic diagrams are presented in Fig. 2.6b.

2.4.2 Bottom up Technique The top-down technique is useful to prepare high-quality and large area ultrathin nanosheets. The yield of the 2D materials using top-down methods is generally low which restrict the applications of these methods for industrial purposes. In bottom-up technique, the nanomaterials are fabricated from the molecular or the atomic precursors. The reactions lead to growth of self-assembled and complex configurations of 2D materials. These methods, which provide liberty to obtain large scale 2D materials for industrial applications, are described in the following sections. The generalized strategies for various approaches can be visualized in Fig. 2.7.

2.4 Synthesis of the Layered Materials

2.4.2.1

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Wet Chemical Method

The wet chemical method is favorable for the synthesis of majority of 2D materials because of its cost-effectiveness and higher yield. It offers a broad category of the synthesis methods that involve the template fabrication via solvothermal/ hydrothermal strategies. The commonly used wet chemical methods are briefly discussed in the following. The solvo/hydrothermal method is quite familiar method utilized for the preparation of the inorganic materials. The crystal growth at low temperature (normally at the temperature domain of ~100–240 °C) and provision of adjustable reaction conditions make this method a promising technique of synthesis of 2D materials. The optimization of temperature, reactants ratio, reaction time and relevant parameters helps synthesis of high-quality thin nanostructures. This technique has been utilized to synthesize several 2D materials including zinc oxide (ZnO), MoS2 , manganese dioxide (MnO2 ), titanium dioxide (TiO2 ) and cobalt oxide (Co3 O4 ) [36–39]. The conventional method involving the template approach helps growing the crystals followed by elimination of the template by adjusting the pH or hightemperature treatment. Almost all kinds of the nanostructure such as 2D (nanosheets), 1D (nanowires) and 0D (quantum dots or clusters) could be synthesized using this technique. Several non-layered configuration of 2D materials could also be prepared by using the templates like Au, CuInS2 , Fe2 O3 [40–42].

2.4.2.2

Microwave-Assisted Technique

The microwave-assisted chemical approach is useful for the synthesis of the nanostructures. The comparatively higher efficiency and relatively short reaction time (normally within a few minutes) makes this method a promising technique. This method has been utilized to prepare variety of 2D materials including CuSe, SnO2 , K0.17 MnO2 and α–Ni(OH)2 [43–47].

2.4.2.3

The Topochemical Transformation

The topological transformation method is an approach which preserves the product’s structure from the subsequent precursor via growth as well as nucleation within the precursor. The favorable outcome of this approach lies under the degrees of match between the precursor and the product. On the account of the anisotropic nature of the layered materials, this is favorable method to obtain the 2D hydroxides instead of the oxide materials. This method is a suitable for the synthesis of the non-layered oxides such as the δ–FEOOH and CeO2 [48–50]. The description of the methodology to prepare Ni and Co3 O4 can be found in literature [26].

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2 Synthesis and Properties of Layered Materials

Chemical Vapor Deposition

The chemical vapor deposition (CVD) is a versatile approach to produce the highquality layers of transition metal dichalcogenides (TMDs) with control on size as well as thickness. This is high-temperature chemical synthesis method in which the material of our choice can be deposited on to the substrate. It has been broadly employed for the preparation of the thin films of variety of materials that includes the insulators, metals and semiconductors. The CVD approach is known to offer fabrication of high-quality 2D materials having the controlled characteristics like defects, morphology and crystallinity via adjustment of growth conditions. The variety of 2D materials like h-BN, graphene and MoS2 , WS2 , WSe2 , MoSe2 have been synthesized via this method [51–55] as shown in Fig. 2.7. The precursors, choice of substrate, temperature and control on chamber environment are key requirements to grow 2D materials using CVD [56–66].

2.5 Tailoring the Properties of Layered Materials The layered materials contain the strong intra-layer covalent bonds but VdW interactions that permits the segregation of the monolayers through the chemical or the mechanical exfoliation method are comparatively much weaker as discussed previously in chapter 1. Though the adjacent layers are caught via weaker VdW interactions, their physical characteristics depends on the VdW separation and interlayer coupling [67]. For an instance, though some exception exists, e.g. in case of ReS2 [68], various TMDs face changes in electronic properties when an indirect band gap is observed for the bulk which transforms to direct band gap for a single layer [69, 70]. Nonetheless, some other layered semiconductors such as indium selenide (InSe) showed the opposite behavior and exhibits the transition to the indirect band gap from the direct band gap as bulk is downscaled to the single layer [71]. This normalization of the band diagram via the inter-layer coupling highlights a traverse from the 2D structure in the form of a single layer to 3D structure of bulk. Consequently, the two dimensionality can be characterized through the strength of the inter-layer coupling. By tailoring the interlayer coupling (either decreasing or increasing the coupling), the electronic dimensionality could be attuned that will shed light on physics of lower dimensions. It has been realized through experimentation by the application of hydrostatic pressure or via chemical intercalation approach. For example, by the application of relatively high hydrostatic pressure of ~10–20 GPa, a transformation from the insulator toward metal having a quick drop of the resistivity had been observed in the MoS2 [72–74]. The advancement of the electronic industry is heavily based on processing of semiconductor and tuning their properties for using in a particular application. The relevant example may be the strained semiconductor technology which considers the growth of Si thin films over a substrate, normally termed as the SiGe. The generation of the strain is due to lattice mismatch that consequently enhance the mobility

2.5 Tailoring the Properties of Layered Materials

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of holes as well as electrons within the materials which may increase efficiency and performance of the MOSFETs. The band gap engineering in the pervoskites to enhance the efficiency of the solar cells is another example. The band gap can be tuned through several methods that includes the application of electric filed, magnetic field, pressure and manipulating the interlayer spacing.

2.5.1 Effect of Electric Field Gallium telluride (GaTe) is a layered materials whose layers could be exfoliated from bulk via scotch-tape approach [75]. The 2D material could also be synthesized via the chemical vapor deposition onto the mica substrate. This semiconducting material has grasped a lot of attention due to its direct band gap of about 1.7 eV. It leads to the higher absorption co-efficient as well as the effective electron–hole pair generation under the photoexcitation with high responsivity and small response time in the photodetector. Besides these, GaTe is considered as the potential candidate for the thermoelectric devices, solar cells and radiation detector. Moreover, particularly for the radiation detector, the tightly packed crystal structure of GaTe points to dense electrosphere of the materials that points to enhanced capture of high energy photons. The theoretical study has been conducted on GaTe and other group III-Te materials to investigate the effect of applied electric field. The results revealed that the band gap of the III-Te in form of single layer or multilayers could be tuned from the metals to ~1.46 eV. This can be considered as the promising method to tune the band gap of the materials for the specific applications. The application of the electric field, in general, leads to the generation of the topological phases within the 2D materials. For the case of GaTe, the band inversion has been observed on occupied levels, though parity remained conserved.

2.5.2 Pressure-Dependent Properties The tuning of properties is possible when a VdW material transforms from 2D to 3D by application of the hydrostatic pressure [76]. The application of the pressure chiefly suppresses the weakly bonded inter-planar separation to initiate transition to three dimensionalities. Furthermore, the implementation of the hydrostatic pressure could be utilized to control the VdW inter-planar separation and to tune up the crystal structure to provide the electron exchange passage to the 3D character [77]. The tunability of the properties by application of the pressure is a non-chemical and controlled approach in comparison to the other methods such as uniaxial strains or chemical reactions. FePS3 is an ising antiferromagnetic material having the Neel temperature (T N ) of about 118 K [76]. At the ambient-pressure, the magnetic structure is arranged so as the zigzag ferromagnetic chains are formed along a-axis. These moments are

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parallel to c-axis perpendicular to the plane of the crystal and such chains are coupled antiferromagnetically in plane along the planner axis. The investigation of magnetic ordering of Mott-insulators based on 2D honeycomb antiferromagnetic FePS3 at high pressure and low temperature has been carried out [78]. The application of pressure induces the shift of magnetic order from antiferromagnetic at ambient pressure to the ferromagnetic case. In general, the antiferromagnetic ordering is conserved, yet the propagation vector is transformed from k = (0, 1, 1/2) to k = (0, 1, 0) by reducing the size of the unit-cell. Thus change in magnetic ordering and insulator to metal transformation is caused within this compound upon application of pressure.

2.5.3 Effect of Lattice Vibrations Although a lot of work deals with the normalization of the electronic structures against the artificially tailored inter-layer coupling [67]. However, the lattice vibrations corresponding to the inter-layer coupling are less studied. Within the bulk (3D) or the multiple layered system, the Raman-active modes have been found to strengthen by the increase in the applied pressure [72–74]. Nonetheless, the homogeneous layered material comprised of the stacking of the similar layers, hence, it is usually difficult to differentiate the vibrational modes arising from the single layers in layered materials. The study of Raman modes in WS2 /MoS2 heterostructure bilayers and the individual WS2 as well as MoS2 single layers has been made after application of hydrostatic pressure [67]. The high pressure is applied to the single layer of MoS2 as stacked on the single layer of WS2 to study the lattice vibrations perceived in the electronic band diagram. The renormalization of the lattice vibrations had been considered. The study revealed that the vibrational spectra of the single layers are modified by the artificial modulation of the interaction between the layers of WS2 /MoS2 via application of the pressure up to 39 GPa. By increasing the pressure, a strong effect on the out-of-plane Raman modes has been observed. The layers are found repelling each other which in turn showed the coherent vibrations over the VdW separation with acoustic like and optical like vibrational modes. These results shed light on the variation in lattice vibrations when inter-layer coupling is taken into account in 2D to 3D layered materials.

2.5.4 Effect of Intercalation The intercalation is an important phenomenon in processing and applications of layered materials. The intercalation in the layered materials is a produced when atoms, molecules or ions are introduced between the weakly bonded VdW layers

2.5 Tailoring the Properties of Layered Materials

35

Fig. 2.8 Visualization of importance of intercalation in fabrication, properties and applications. Reprinted with permission from Rajapakse et al. [81]. Copyright (2021), The Author (s)

[79]. In recent years, the extensive research interests in the intercalation within the layered materials has been observed especially on graphite intercalation compounds (GICs) [80]. The intercalation process in the form of exfoliation technique has been utilized for the production of large-scale 2D materials for different applications. The usage of the intercalation mechanism for the synthesis methods of 2D materials includes the electrochemical intercalation, vapor phase intercalation and liquid phase intercalation as shown in Fig. 2.8.

2.5.4.1

Batteries and Layered Materials

The alkali-ion batteries based on Li, Na and K ions are basically composed of the cathode, anode and electrolytes. For materials to act as cathode in lithium ion battery (LIB), Li should be a present in the electrode, whereas organic materials in the form of electrolyte are employed. The anode does not require the presence of Li, but it should have properties of temporarily hosting the Li ions coming from or to the cathode during charging and discharging process of the battery. Therefore, the appropriate intercalation and de-intercalation or adsorption and desorption are required for functioning of such batteries. Hence, considering the intercalation as the basic phenomenon of the Li-ion batteries, the importance of the layered materials for LIB is obvious [79] as presented in Fig. 2.9. As an example, the commercialized Li-ion batteries uses the graphite as an anode material where inter-layer separation turn out to be the host for the reversible insertion and deinsertion of the Li ions in charge and discharge cycles. The reversible

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Fig. 2.9 Intercalation mechanism in lithium ion batteries. Reprinted with permission from Rajapakse et al. [81]. Copyright (2021), The Author(s)

cycle of the intercalation of the Li-atoms happens in accordance with the reaction as given xLi+ + xe− + C6 ↔ Lix C6 reaction, where 0 ≤ x ≤ 1 [82]. Through the course of reaction, Li ions move to and from the anode material via electrolyte, whereas electrons flow through the external electrical circuit. Since the transport of the ions in the battery is influenced by the interlayer separation of the layered materials, the process of the intercalation faces complications related to the standard electrochemical reactions that involve the volumetric expansion and strain produced through the process [83] for example as shown in (Fig. 2.10). By the advancement in the lithium ion batteries, various battery configurations have been utilized in which either one or both of the electrodes may consists of the layered materials. The type of the LIB batteries in which only the cathode material is formed with the layered host for the Li ions is known as the half-intercalation cells. The recent batteries are those in which both cathode and anode are made up of the layered materials and hence stores the Li ions at distinct potentials that could generate a potential difference. In contrast to the former type, this configuration includes not only the Li cations, yet some anions also undergo the process of intercalation/ de-intercalation between the two layered materials. In order to customize the process of intercalation in the layered materials, the strategies including strain engineering, dimensional sizing, stacking orders tailoring and the application of external fields may be utilized [79]. Throughout the process of intercalation, the donor-type intercalants, upon insertion between the layers of 2D host causes withdrawal of electrons from that of the adjacent host layers. This would result in the shifting of the Fermi level that modifies the material’s properties. The examples of the acceptor- and donor-type intercalants within the graphite are the photonic acids and alkali metals respectively. In general, the process allows the extensive tailoring of the carrier concentration that provides control over characteristics of the host materials. This results in the improvement in several application including

2.5 Tailoring the Properties of Layered Materials

37

Fig. 2.10 Impact of the intercalants on inter-layer distance. Reprinted with permission from Liu et al. [84]

gas sensing, optically as well as electronic active structures, catalysts etc. However, in some cases, the intercalation could lead to the phase transition like metallic to insulator transformation and emergence of superconductivity and magnetism etc. Furthermore, the intercalants (the guest materials) have a strong impact over the inter-layer distance as discussed in details in [84]. The 2D semiconducting materials are potential candidate for the optoelectronic devices and other applications due to their distinctive electronic and optical characteristics exploited in photoconversion, light emission and tunable light matter interactions [85]. The intercalation could be used to improve the polarization and conductivity of such materials to enhance their extent of utilization for optoelectronic applications. For further insights to the effects of intercalation on 2D materials, let’s have a look on a situation described below. The tailoring of optical properties of α–MoO3 via intercalation and deintercalation process has been studied [86]. The zero-valent metals like the Co and Sn have been intercalated into the α–MoO3 , whereas the reverse process has been done through the oxidative de-intercalation by utilizing the hydrogen peroxide or the iodine along with temperature-induced phase transitions. The intercalation

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process leads to the tailoring of the color of precursor from transparent white to deep blue indigo. Meanwhile, the thermally or chemically guided process leads to the native transparent white color. The intercalated metals hold the positions onto the layers, which are disordered as compared to the precursor. Contrary to this, the de-intercalation process helps in re-ordering of such sites within the phase transition. The optical tailoring of α–MoO3 exhibits the likelihood for the applications of the temperature-dependent color changing in sensors and chemochromic applications. The distortion of the host structure leads to the modification in the initial electronic structures. The intercalants give rise to appearance of inter-band states which may reduce the band gap of the material. The ab-initio investigations on the n-type doping (in comparison to the zero-valent metallic intercalation) have been carried out to investigate this issue [87]. The intercalation of the H+ -ions within the nanosheets of α–MoO3 leads to the tailoring of the band diagram of the wide band gap materials. Furthermore, the consequence of intercalation of the H+ -ions are the production of unstable H2 O groups that might be free up as molecular H2 O by the inclusion of oxygen vacancies to the system. In result, the Hx MoO3 configuration transforms to MoO3 , which contain a defect state in he band gap and could be utilized as the photo-active material for photocatalysis and optoelectronic applications [88, 89].

2.5.4.2

Magnetic Properties

The magnetic properties of the 2D materials could be tuned via intercalation process [79]. The addition of external agents (having unfilled d and f sub-shells i.e. transition metals) at the varied concentration into the layers of 2D host materials in order to tailor the lattice parameters[90], spin–orbit effects [91, 92] and orbital moments [93–95] leads to the introduction of the magnetic ordering or change in the magnetic properties. The introduction of Mn atoms into the octahedral holes in between the trigonal prismatic layers of the NbS2 crystallized in the form of MnNb3 S6 has been studied [96]. The added Mn ions give rise to temperature-dependent magnetization in the otherwise non-magnetic host. Moreover, the observed magnetization was significant in along c-plane of the crystal as compared to the in-plane directions which is due to the chiral magnetic soliton (CMS) magnetic states that may be adjusted via external fields. The CMSs are basically intermediary superlattice configurations that includes the helical spin textures. Because of having topological nature, they are vigorous in case of the material defects. Hence, the atoms that are intercalated couple to c-axis along with the a–b plane. Chromium, upon intercalation on NbS2 shows the effect similar to previous example and crystallized as Cr1/3 NbS2 having the monoaxial chiral magnet and hence exhibits stronger magnetic anisotropy by the application of external field that was perpendicular to the c-axis [97].

2.5 Tailoring the Properties of Layered Materials

2.5.4.3

39

Superconductivity

By introducing the donor intercalants in graphite, the generation of the donor-type GIC has been observed and the material attains more of the metallic nature [79]. It is due the fact that the enhanced density of states (DOS) appears at the Fermi-level and the Fermi level goes upward. It results in the emergence of strongly correlated phenomenon like superconductivity that has been studied for various GICs such as BaC6 [98, 99] and YbC6 [100]. The same effect and the emergence of the superconducting states by the intercalation induced by doping has been perceived in several 2D layered materials. The intercalation of several metals has been recorded to generate the superconductivity within the BP [101]. The superconductivity in BP is observed at pressure greater than 10 GPa at which its phase transition occurs. Nevertheless, no superconductivity had been recorded at their standard orthorhombic phase, while the insertion of alkali and alkaline earth (Li, Rb, K, Ca and Cs) metallic-intercalated phosphorous manifested the superconductivity at temperature 3.8 ± 0.1 K that is not dependent of the intercalants. The superconductivity appeared by the substantial doping of the 2D phosphorous (i.e. phosphorene layer) and as a result the intercalants worked like the reservoirs of the charges. The emergence of the superconductive phase as induced by doping has also been illustrated in superatomic (i.e. atomic clusters having the properties of the elemental atoms) VdW 2D layered material, i.e. Re6 Se8 Cl2 from the several phase class of the material [102]. However, a sudden increase within the carrier concentration has been observed which in turn leads to the formation of superconductive phase. It was attained through a procedure equivalent to the deintercalation at the point the current annealing that has been implemented for the doping of electrons by the dissociation as well as losing the inter-planar Cl atoms. The prospects quantum phases of a robustly correlated systems reveals that the superconductivity is normally associated with the further quantum phases. Specifically, the interaction between collective macroscopic modulation (i.e. CDW states) and the superconductivity of the electronic charge density as emerged from the electron–phonon as well as electron–electron inter-play had been studied for several strongly correlated systems, e.g. heavily doped 2D materials [103]. Moreover, the CDWs could be generated as well as controlled via tailoring of carrier concentrations while considering other system’s specifications such as electric field, temperature, pressure and strain. The 2D TMDs like TaSe2 , MoS2 , TaS2 and TiSe2 provided a platform to investigate the relation between the superconductivity as well as CDWs. The intercalation approach is considered to suppress the inter-layer coupling of the bulk WTe2 and MoTe2 and as a result, a topology transition in the band structure to a weak topological insulation from the type-II semimetals [79, 104]. The intercalation approach is a novel approach to provide control over dimensionality of TMDs having the unique electronic states resulting the emergence of complex band topology as well as superconductivity. The procedure of intensified superconductivity could be ascribed to the increased DOS close to the Fermi level because of the split of balance in between the compensated holes as well as electron packets. The appearance of the extra phonon modes followed from the intercalants along with the amplified

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screening of the Coulombic interaction between the electrons within the layers of TMDs might also play a major role in increasing the Curie temperature (T c ).

2.5.4.4

Thermal Properties

The intercalation process within the layers of layered material such as BP, graphite, MoS2 , TiS2 has been considered as an efficient method to control the thermal characteristics that includes the remarkable reduction of the thermal conductance [79]. The addition of the guest species within the VdW gaps could results in the change in structure of layered materials. Such changes as induced by the intercalation process could be used to tailor the propagation of phonon and hence change the thermal characteristic of the materials.

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93. Kumar, P., Skomski, R., Pushpa, R.: Magnetically ordered transition-metal-intercalated WSe2 . ACS Omega 2(11), 7985–7990 (2017) 94. Skomski, R., Kashyap, A., Enders, A.: Is the magnetic anisotropy proportional to the orbital moment? J. Appl. Phys. 109(7), 07E143 (2011) 95. Bruno, P.: Tight-binding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transition-metal monolayers. Phys. Rev. B 39(1), 865 (1989) 96. Dai, Y., et al.: Critical phenomenon and phase diagram of Mn-intercalated layered MnNb3 S6 . J. Phys.: Condens. Matter 31(19), 195803 (2019) 97. Han, H., et al.: Tricritical point and phase diagram based on critical scaling in the monoaxial chiral helimagnet Cr1/3 NbS2 . Phys. Rev. B 96(9), 094439 (2017) 98. Heguri, S., et al.: Superconductivity in the graphite intercalation compound BaC6 . Phys. Rev. Lett. 114(24), 247201 (2015) 99. Yang, S.-L., et al.: Superconducting graphene sheets in CaC6 enabled by phonon-mediated interband interactions. Nat. Commun. 5(1), 1–5 (2014) 100. Mazin, I.: Intercalant-driven superconductivity in YbC 6 and CaC 6. Phys. Rev. Lett. 95(22), 227001 (2005) 101. Kawamura, H., Shirotani, I., Tachikawa, K.: Anomalous superconductivity and pressure induced phase transitions in black phosphorus. Solid State Commun. 54(9), 775–778 (1985) 102. Telford, E.J., et al.: Doping-induced superconductivity in the van der Waals superatomic crystal Re6 Se8 Cl2 . Nano Lett. 20(3), 1718–1724 (2020) 103. Wagner, K., et al.: Tuning the charge density wave and superconductivity in CuxTaS2 . Phys. Rev. B 78(10), 104520 (2008) 104. Zhang, H., et al.: Enhancement of superconductivity in organic-inorganic hybrid topological materials. Sci. Bull. 65(3), 188–193 (2020)

Chapter 3

Theoretical Modeling and Approaches to Study the Layered Materials

Abstract The materials having dissimilar atomic bonding along planer and perpendicular directions appear in form of weakly connected layers. These materials, commonly known as layered or van der Waals (VdW) solids, have several specific applications in modern devices. The experimental characterization of such materials is challenging; however, the theoretical approaches are often found resourceful in this regard due to recent improvement in hardware and computational programs. The first-principles methods based on density functional theory (DFT) have been found effective to provide the direct insight to the structures of the layered materials at atomic level. This chapter deals with the theoretical backgrounds, different theories and strategies in order to investigate the layered materials. The role of theories in exfoliation of the layered materials based on potential energy surface is also described. To deal with the out-of-plane VdW interactions, the character of the dispersion functional to correctly describe the structural and electronic properties of the layered materials is elaborated. A theoretical strategy to study the layered materials and to distinguish the layered and non-layered materials is also provided.

The theoretical study using computational programs has become an efficient tool to investigate the structures and properties of materials. Owing to anisotropy in structure of the layered materials, the conventional experimental characterization techniques may not provide the requisite information. However, their first-principles investigation has been found worthwhile to predict the material properties provided that reasonable theory is employed. In Chaps. 1 and 2, a detailed understanding of layered materials have been developed and a clear distinction between layered and non-layered materials is also provided. This chapter is dedicated to shedding light on theoretical framework and relevant theories in order to study the materials.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Majid and A. Jabeen, Layeredness in Materials, Engineering Materials, https://doi.org/10.1007/978-981-99-6299-0_3

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3 Theoretical Modeling and Approaches to Study the Layered Materials

3.1 Theories Related to Layered Materials In this section, we are going to give the brief description of the theories that are necessary for the understanding and the study in theoretical framework for the layered materials.

3.1.1 Exfoliation Besides all other potential materials for the future electronic devices and their applications, the two-dimensional (2D) layered materials are important category of the materials. Such materials are consisting of the layers with the thickness in atomic units and could be realized by removing the monolayer from its bulk counterparts. This removal or “peeling off” the layers from the bulk is known as exfoliation. The mechanical exfoliation is a simplest method to synthesize the thin films from layered materials that has came into practice after discovery of the graphene [1, 2]. The experimental background and relevant strategies on exfoliation have been thoroughly elaborated in Chap. 2. The exfoliation energy is an important parameter in order to characterize the layered materials. The energy required to remove or peel off a layer from the surface of material’s bulk counterpart is called the exfoliation energy [3]. The value of exfoliation energy is associated with the binding energy between the layers [4]. Indeed, the value of the exfoliation energy is nearly twice of the surface energy that is E exf = 2× E Surf , where E Surf is the surface energy of the material under study [5]. It has been demonstrated that the exfoliation energy corresponds to the difference in energy in between the bulk as well as the isolated monolayer [3, 6]. In former approach, the exfoliation energy can be computed using the difference between the total energy for the thick slab containing multiple layers and that of the isolated atomic layers plus the remaining other N − 1 layers within the slab. The boundary conditions for the isolated slab as well as the remaining layers of slab have been put down in a similar supercell (containing the large amount of vacuum within the region that is present between them). Such approach abandoned a probable variation within the lattice parameters of the exfoliated layers. Moreover, to attain the converging results by simulating the slabs/surfaces from their bulk counterparts, a really large number of layers, i.e. N had been needed that, in turn, results in the immense computational load. This is often termed as the “slab method”. To suppress the computational expense, the inter-layer binding energy is somehow conceptual idea and may not be measured through the experiment directly. The procedure related to the inter-layer binding energies might be understood by dissolution of the layered materials in a liquid which considers the involvement of the undesired interaction between the layered materials and solvent molecules. Such investigations presume that the inter-layer interactions might be served in pairwise manner,

3.1 Theories Related to Layered Materials

47

in such a way that the relaxation within the in-plane lattice variables of the exfoliated layers is almost negligible. In addition to these, the layers close to the surfaces contain the similar atomic configurations present within the bulk and hence surface reconstruction or the relaxation could be abandoned. The inter-layer binding energy must be related to exfoliation energy. The value of the exfoliation energy should lie between the inter-layer binding energies of their bulk counterpart along with the binding energies of the 2D atomic layers [7]. This is because an energy is needed to split the atomic layers linked with each other. For instance, in order to obtain the phosphorene, the energy values of the individual isolated system as well as the remainder has been reported [8]. The values for the remainder have been attained by separating the layers by comparing the energies of the two as well as three layers as attained by the calculations of coupled clusters. In case of n number of layers, when initial and final surfaces are similar, the value of exfoliation energy per unit area is given in the following [3], E exf (n) =

E iso (n) − E bulk n/m A

(3.1)

Here the E iso (n) is the isolated n-layer slab’s energy within the vacuum, E bulk is the bulk energy and A represents the area of the unit-cell bulk.

3.1.2 Potential Energy Surface (PES) The potential energy surface (PES) is a resourceful tool in material science and engineering to study a material comprising of more than one components [9–11]. The PES exhibits the connection in between the energy of the chemical system and their respective geometry coordinate (e.g. bond length and bond angles). This could provide the relevent information regarding the characteristics as well as the reactivity of the chemical system. When only one geometric coordinate (e.g. bond lengths) is taken into consideration then one-dimensional potential energy curve is helpful. However, higher-dimensional PES is drawn when two or more geometric coordinates (e.g. bond lengths, bond angles) are taken into account. Generally, the PES is used to describe the equivalent crystal structure to study the bond length or bond angle (or any specific geometric parameter) related to the specific crystal structure. In layered materials, the PES is an important parameter to shed light on their structural properties. The inter-layer distance term is not related to the non-layered materials so the PES can be used to distinguish the characters of the non-layered and layered materials. A representative 1D and 3D PES drawn for layered tantalum pentoxide (Ta2 O5 ), layered heterostructure of MoS2 /WS2 and bilayer graphene is given in Fig. 3.3 [12] and Fig. 3.1 respectively.. The procedure to draw potential energy surface for WTe2 has been reported [13].

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3 Theoretical Modeling and Approaches to Study the Layered Materials

Fig. 3.1 PES drawn for layered MoS2 /WS2 heterostructure and bilayer graphite while considering the inter-layer distance. Reprinted with permission from Kumar et al. [14]. Copyright (2016), The Author(s)

3.2 Theoretical Parameters Related to Layered Materials In theoretical modeling, the parameters used to simulate specific impacts are of great importance. By changing the parameters and hence level of theory, the results of the computations can vary drastically. Hence, it is advised to carefully choose to level of theory to define the parameters some of which are discussed in the following.

3.2.1 Dispersion Interactions The out-of-plane interactions are of VdW type which are also termed as London dispersion attractive forces between layers in a layered material. The dispersion forces are related to the correlative interactions between the fluctuating as well as instantaneous electric dipole moments that mostly exist within the crystalline as well as the molecular systems [15, 16]. The dispersion forces are basically weak forces arising from the coupling between the fluctuations of charges within the quantum– mechanical systems. The dispersion interactions are based on the product of the electron polarizabilities of the interacting atoms and decay as R−6 , where R is the separation between the interacting systems. The contribution of dispersion relations toward the vibrational and geometrical parameters has been found to put a minor contribution. The forces or interactions involving covalent bonding are comparatively short-ranged and have a strong impact of structural of electronic materials. The dispersion forces would have a great impact, dominant and necessary to be taken into account while describing the bonding attributes of the following systems (i) when the non-covalent bonding/interactions are dominant, (ii) large systems and (iii) flexible systems. The layered materials are important category of the materials, where the dispersion interactions are usually dominant while describing the structure of the materials.

3.2 Theoretical Parameters Related to Layered Materials

49

Such materials have the dominant short-range covalent forces in a specified in-plane direction of that structure, while the inter-molecular interactions are involved in staking of the layers. In the absence of any foreign element within the layers, e.g. Li atom between the layers of graphene, the dispersion interactions play a key role to decide the finalized structure as well as ability of swelling, so these dispersion forces should be taken into account very carefully.

3.2.2 Importance of Computational Studies Besides the success of the experimental technique in synthesis and applications of layered materials, the importance of the theoretical studies is vital in this regard. The theoretical strategies have been resourceful in describing the structure, predicting properties and explaining the mechanisms involved in utilizing them for applications. Theoretical modeling of materials provides insights into electronic structure of the materials by employing first-principles-based strategies [17, 18]. There exist several electronic structure methods based on the quantum chemistry and physics. These methods are classified into ab-initio methods, empirical methods and semiempirical methods. The ab-initio-based methods are divided into the wave function-based methods and density-based methods in which one typical example of wave functionbased method is Hartree–Fock (HF) theory, while the density-based method is density functional theory (DFT). The layered materials comprise of in-plane strong covalent bonding and out-ofplane weak VdW interactions due to which the computational details, to study these materials, need to be chosen carefully. The choice of “exchange correlation functional” is very important to study the layered materials using DFT approach. Besides these, the accuracy of the computed results depends on convergence of different parameters. These issues, in order to make DFT-based calculations meaningful, are elaborated in the following.

3.2.3 Exchange Correlation Functional The importance of functional in DFT-based calculations is of prime importance. The choice of functional is material dependent due to which calculations on the layered materials require the availability of VdW dispersion interactions. The significance of the VdW interactions goes beyond the cohesive and the binding energies to describe the structural, electronic, mechanical, kinetic as well as the spectroscopic properties of the materials. The contribution of VdW interactions in energy calculations is small, but its application is crucial for ensuring the accuracy of findings [19]. In the light of the above discussion, the application of VdW interaction by suitable choice of level of theory has become vital. Nevertheless, the concern to exact modeling of such interactions via first-principles methods are strongly restricted due to the

50

3 Theoretical Modeling and Approaches to Study the Layered Materials

high computational cost of the high-level wave function approaches in the quantum chemistry. Besides these, the shortfall of the effective and exact approximations to the many-body electronic correlation problem for the larger systems is a major concern in the field of theoretical studies. The sophistication of the approximate methods to correctly present the VdW interactions has been improving in DFT-based electronic structure methods. The VdW interactions could have significant impact over the electronic properties along with the structure of the material. Thus, such interaction could have noticeable impact over the electronic charge distribution as well as the other characteristics as attained through the charge density (e.g. electron affinities, multipole moments, polarizability and work-function) in addition to have influence over structure as well as dynamics of such systems. This is in agreement with the theoretical understanding of the VdW interactions as prompted by the Feynman. These facts revealed the importance of the including VdW interactions in the first-principles methods out of which it is important to include the full self-consistent treatment of VdW interactions which explicitly based on the orbitals or the charge densities. In the case of the layered materials, we are not going to describe the details of the functional [20]. Rather we are going to describe the suitability of the functional for DFT calculations on the layered materials. The frequently utilized quantum–mechanical investigation provides the theoretical basis for two fragments, i.e. A and B (that may include infinitesimally regions of the electronic density, atoms or the localized orbitals) set apart through a distance RAB . This distance settle them outward of the orbital overlap whereby the secondorder perturbation theory estimates the VdW interaction energies occur to be the −6 (toward the major order) [19]. Besides the other approaches, proportional to the RAB DFT is most frequently utilized approach in solid-state and quantum-chemical molecular calculations [21]. Nevertheless, the DFT-based methods experience some drawbacks, out of which, the foremost important is the sparse treatment of the weak VdW interactions. In the field of solid-state physics and chemistry, the local density approximations (LDA), generalized gradient approximations (GGA) and meta-GGA functional are famous for dealing the materials. However, the conventional local as well as semilocal functional DFT approaches are gone wrong to narrate the dispersion impacts which are basically non-local in nature. As a result, the typical DFT methods are erroneous for computing the cases in which the dispersion plays a central role in describing the structure as well as the energies, e.g. molecular crystals, layered materials and the surface adsorption. The VdW-inclusive DFT approaches could be distributed in two groups, the first one are the methods established on the basis of semiempirical corrections normally accompanied through the dispersion corrections to KS energy (i.e. Kohn–Sham Energy), and second one is the non-local correlation density functional that makes modification into the Kohn–Sham Hamiltonian [21, 22]. The former groups are entitled as DFT-D as well as DFT-D2 that utilities the constant values for C6 -coefficients for each of the chemical species [23, 24]. In this approximation, the hybridization or the several oxidation state of single material had not been taken into consideration.

3.2 Theoretical Parameters Related to Layered Materials

51

Fig. 3.2 Consideration of energies dispersion along with the two threefold coordinated carbon atoms considering and comparing various functionals. Reprinted with permission from Grimme et al. [27]. Copyright (2010)

To include these impacts, the further amendments to the above described approaches had been included that includes the environment-based C6 coefficients. The DFT-D3 technique as introduced by the Grimme et al. incorporated the system’s environment dependence over the C6 coefficients by considering the each atom’s neighbor [25]. On the other hand, a scheme as suggested by Tkatchenko and Scheffler [26] that again scaled the “C6 ” coefficients by taken into account C6 coefficients of the reference atoms, atomic polarizability as well as the effectual volume atoms that is attained by dividing the total electronic density of system between the individual atoms by utilizing the Hirshfeld splitting method as can be seen in Fig. 3.2. For the case of the molecular systems, the damped empirical corrections, entitled as DFT-D were put forward by the Grimme et al. [23–25]. There are three basis corrections termed as DFT-D, DFT-D2 and DFT-D3. The fundamental difference in the above described approaches is the procedure by which the empirical dispersion (C6 ) coefficient is calculated. It should be considered that C6 coefficient is directly related to the VdW interaction energy term as described above. The DFT-D2 correction as well as the original parameterization utilizes the empirically driven interpolation formulas, whereas the DFT-D3 correction is the unconventional technique that is liable on the ab-initio computation of the C6 (and C8 in addition) coefficients. In past few years, Backe-Johnson approach in DFT-D3 (i.e. DFT-D3-BJ) have been developed that vary from the DFT-D3 specifically in the weighting function only. Considering all the cases, the dispersion energy is being computed in isolation from the DFT-energy along with the fact that it does not rely on the wave function. By taking account this fact, the polarization term is not considered and hence this is merely a function of type and position of atom. The supremacy of the Dn correction approaches arises in the fastidious parameterization as well as the computational efficiency as shown in Fig. 3.2. In a system containing the molecules or molecular

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3 Theoretical Modeling and Approaches to Study the Layered Materials

system gives the results that are very near to the coupled clusters singles having the values of the perturbation triples (CCSD(T)) at the expense of the GGA-DFT computation. Furthermore, since the DFT-D3 approach is limited to the molecular standard sets so this not clear whether it can be applied to the periodic materials or not. This arises because of the C6 -coefficients dependence over the hybridization, which are contingent over the coordination number (CN). The summary of various functionals and consideration of various parameters is shown in Table 3.1. One main extremity regarding the computational cost, in the additional dispersion correction approach, is due to consideration of the chemical surrounding [28]. This happens to be the reasonable step to establish the atomic polarizabilities on the basis of the electronic densities that decline the speed of calculation by instigating the computationally challenging steps. To get over the problem, that is eminent in the DFT-D3 approach, where the atomic polarizabilities had been interpolated in between the atomic reference dependent on the fractional CNs. This prohibits the demands of the electronic density, whereas the chemical surrounding is completely described by the CNs. In a current addition to the approximations, the DFT-D4 surpass by making the charge-dependent atomic polarizabilities [29]. Furthermore, to keep the computational efficiency, the information of the charge is not derived from the electronic density yet work under the classical as well as the effective electronegativity equilibration (EEQ) model computation. Although this approach of DFT-D4 is new and a lot of advancement is required, but for several energy standards, this performs better as compared to the DFT-D3, specifically the system containing metals that introduces the dependence of charges and hence make amendments in thermochemical characteristics [30]. For the past few years, the DFT-D2 and D3 corrections had been widely utilized for the periodic systems, Now, here a brief discussion on the comparison of different DFT-D functional as implemented over the different materials is going to describe. Table 3.1 Summary of various DFT methods to consider the London dispersion interactions (ignoring the Grimme Functional) Property

DFT-D

vdW-DF

DCACP

DF

Correct R−6

Yes

Yes

No

No

Good thermochemistry

Yes

?

?

Yes

Numerical complexity

Low

High

Low

Medium

Simple forces

Yes

No

Yes

Yes Yes

System dependency

No yes

Yes

Noc

Electronic effect

No

Yes

Yes

Yes

Empiricism

Medium low

No

High

Medium

Analysis/insight

Good

?

?

No

Reprinted with permission from Grimme et al. [27]. Copyright (2010)

3.2 Theoretical Parameters Related to Layered Materials

53

In a study, some of the layered materials, e.g. graphite, vanadium pentoxide ( V2 O5 ) and molybdenum disulphide ( MoS2 ) has been considered [31]. These materials offer the weak VdW interactions that is prominent through the dispersion. In these cases, the typical GGA-PBE functional does not give the true predictions. The inter-layer separation as calculated by the lattice parameter c is overestimated by ~11% for V2 O5 and nearly 30% for the cases of graphite and MoS2 . This variation could be justified by considering the fact that MoS2 as well as graphite layers are connected with each other only via the dispersion interactions that are present in between the S and C atoms, respectively. However, in the former case, the presence of the dipole–dipole interactions also come into light and have significance impact over it. According to this study, the remaining lattice constant has almost the similar values as that of the reported experimental values. The PBE-D2 as well as PBE-D3 functional shows the significant improvement within the several inter-layer parameters such as the inter-layer separation etc. In this study, the inter-layer binding, that is attractive in nature, of MoS2 as well as graphite is defined with great accuracy while the deviation of V2 O5 had been decreased by an amount of about 2.4% in case of PBE-D2 and 0.8% for PBE-D3. Nevertheless, these corrections do not accurately estimate and had problems with the graphite. The D2 and D3 approaches misjudge i.e. underestimate and overestimates the “c” lattice parameter by ~4% and ~3% respectively. In addition to these, the cohesive energies are critically affected and overestimated through the DFT-D methods. This all happens because of the absurd over-binding of PBE approach that is ~290 kJ/ mole, 50 kJ/mole and − 35 kJ/mole for V2 O5 , graphite and MoS2 respectively that shows that only for the last case, i.e. MoS2 , the cohesive energy is negative and not feasible formation in the experimental framework. The result concluded during this study was that the overall D2 and D3 approach provides comparatively precise results quantitatively as well as qualitatively for the “c” parameter for the layered materials such as MoS2 , graphite as well as V2 O5 . Considering the layered materials and all other cases including the dispersion effects, the comparison of PBE-D2 and PBE-D3 evident that PBE-D3 showed better results as compared to the PBE-D2 and it has been suggested to utilize the PBE-D3 functional for the periodic systems in future. The investigation on structural and electronic properties of Ta2 O5 has been performed, in which the layeredness of said material is also taken into consideration [12] as shown in Fig. 3.3. The structural and electronic properties of the said material have been investigated on GGA-PBE, GGA-PBE-D3, GGA-PBE-D3-BJ, GGABP86-D3 and GGA-BP86-D3-BJ level of theory as can be visualized in Fig. 3.3c. The minimum energy was obtained at GGA-BP86-D3-BJ showing the achieving the most stable structure at this level of theory. Similarly, in another study, the 20 sets of the layered materials had been investigated for the electrochemical energy storage devices and the effect of functional have been investigated [21]. In this study, the several functional such as vdW-DF2, dDsC, BEEF, D3, optPBE-vdW, D3-BJ, optB88, optB86b-vdW had been utilized for the set of electroactive layered materials to be used in the lithium ion (Li-ion) batteries. However, for the system calculating/study the energy storage and generation because of their inadequacy of suitably reproducing the cell parameters of the

54

3 Theoretical Modeling and Approaches to Study the Layered Materials

Fig. 3.3 Visualization of layered materials Ta2 O5 where a represents the bilayer b represents the monolayer and c exhibits the PES by ignoring the dispersion functional (GGA-PBE) and then considering the dispersion functional (GGA-PBE-D3). Reprinted with permission from Majid et al. [12]. Copyright (2021). Elsevier B.V

bulk Li, the C 6 coefficient is not recommended [32, 33]. This situation arises due to the overestimation of the VdW interactions within the metallic systems [34]. The results obtained revealed that for the correct predictions of the atomic structures at equilibrium as well as the redox potential, it is necessary to accurately include the VdW interactions. Furthermore, the addition of the appropriate VdW treatment is of specifically great importance in order to describe the delithiated compound. Moreover, on the edge of utilization of specific functional, the results obtained from the PBE are much better as compared to the VdW and BEEF. Besides these, the dDsC as well as optB6b-vdW presents the better results of all consideration in order to predict the geometries at equilibrium. Also, the effect of the VdW interactions is less pronounced over the average redox potential as the PBE provides the values that are comparatively very close to the values obtained from the experimental work. Considering all these facts, it should be remembered that the choice of the functional or the level of theory is totally based on the materials and the specific application under study. So before running any calculation or starting a new project, perform the convergence test to select appropriate functional and relevant computational parameters. Moreover, the help from the literature may be sought. For example, if you are taking the reported value of lattice constant, it should be appropriate to optimize in your systems prior to calculating the properties.

3.2.4 Strategy to Study the Layered Materials One of the main questions here is the choice of theoretical strategy to study the layered materials. In this section, the strategy to study the layered materials is going to be discussed in details.

3.2 Theoretical Parameters Related to Layered Materials

55

Fig. 3.4 Optimized structure of a layered hexagonal BN along x-axis (side view) b non-layered cubic BN along x-axis (side view)

3.2.5 The Structure of the Materials The distinction between the layered and non-layered material is based on their atomic crystal structures. By optimizing the unit cell of layered materials, each layer is separated and by adding further atoms in each independent layer, the anisotropy appears in structure along z-axis as shown in case of h-BN in Fig. 3.4. Yet we have to consider that each layer should contain a complete formula unit, e.g. in case of Ta2 O5 the layers contain the complete Ta2 O5 structure as shown in Fig. 3.3a, b. On the other hand, the non-layered materials form the single slab/surface and hence when the atoms are being added to this (for supercell approach), the slab thickness increases and consequently leads to the formation of the network-type materials. The non-layered materials present the isotropic bonding throughout the structure. In simple words, the non-layered materials would be a “single-piece or single-crystalline material” in contrast to the layered materials. An example from daily life may be of “onion” like layered configuration while those having the “potato” like structure are considered as non-layered materials. For further explanation, the layered and non-layered materials are shown in pictorial form in Fig. 3.4a and b respectively.

3.2.6 Use of Appropriate Functional The uniqueness of the layered materials is due to presence of layers in the material which are connected via weak VdW interactions. In theoretical modeling, the most important step is the optimization of any structure which is based on the level of theory, i.e. use of specific functional. The details of the functional are elaborated in the previous section. Here we are going to give a short glimpse by utilizing the several functional on some famous layered materials to highlight their importance (Table 3.2). Here we have optimized the structure of some famous layered materials at different functional at DFT-based code Vienna ab-initio simulation package (VASP) and calculated their formation energy per atom (eV/atom). The results are given in Table 3.2

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3 Theoretical Modeling and Approaches to Study the Layered Materials

Table 3.2 Convergence of functional/the analysis of formation energy as compared to the functional/impact of functional over formation energy Functional

Formation energy per atom (eV/atom) Graphite

h-BN

MoS2

MoSe2

WS2

WSe

GGA-PBE

− 9.2138

-4.8222

− 0.8338

− 0.3680

− 0.5040

0.358

GGA-PBE-D2

− 9.2138

− 4.8226

− 0.8338

− 0.3680

− 0.5040

0.358

GGA-PBE-D3

− 9.2777

− 4.881

− 1.0415

− 0.610

− 0.711

− 0.234

GGA-PBE-D3-BJ

− 9.3309

− 4.923

− 1.1888

− 0.7584

− 0.8676

− 0.357

GGA-PBE-D4

− 9.2183

− 0.8338

− 0.3680

− 0.5040

0.358

-4.8222

Table 3.3 K-points convergence for graphene and h-BN K-points

Formation energy/atom (eV/atom) Graphene

h-BN

5×5×1

− 9.3309

− 4.9233

7×7×1

− 9.3493

− 4.9268

9×9×1

− 9.3358

− 4.9269

11 × 11 × 1

− 9.3433

− 4.92698

13 × 13 × 1

− 9.3440

− 4.926985

15 × 15 × 1

− 9.3416

− 4.92699

17 × 17 × 1

–---

− 4.92698

which revealed the fact that the minimum energy is attained by utilizing the GGAPBE-D3-BJ functional. Nevertheless, the GGA-PBE, GGA-PBE-D2, GGA-D4 gives the same value of formation energy, and hence, it is right to say that the DFT-D4 and D2 are as worst as GGA-PBE. It might be due to the fact that D4 functional is newly implemented theory and a lot of work is needed to be done on it. Furthermore, it is important to note that these are the convergence tests for the given materials which should not be taken as reference for all other materials. Hence, performing the convergence tests is a crucial requirement prior to making DFT calculations on new materials.

3.2.7 K-Point Convergence K-points play an important role in theoretical modeling of materials. Here we have given the convergence of K-points for graphene and h-BN (at AA stacking because this is considered to be the structure with minimum energy and hence most stable stacking configuration) at VASP code by utilizing the GGA-PBE-D3-BJ functional and 600 eV cutoff energy values and the results are given in Table 3.3. Since we have optimized values for 2D materials so we have taken 1 along z-axis. Here, as we can

3.2 Theoretical Parameters Related to Layered Materials

57

see that minimum energy per atom was attained at 7 × 7 × 1 and 9 × 9 × 1 for graphene and h-BN respectively. So these are the optimized values and the converged K-points are 7 × 7 × 1 and 9 × 9 × 1 for graphene and h-BN respectively. The choice of K-points along z-axis should be carefully made in order to describe the anisotropy in the structure of the layered materials. Hence, the convergence of the K-points along z-axis (over optimized values of K-points) has also been done and results in graphical form is given in Fig. 3.5. Here, we come to know that minimum energy attained for graphene and h-BN are 7 × 7 × 2 and 9 × 9 × 5. Hence it can be concluded that the choice of K-points along z-axis is very important to study the layered materials. In general, according to the experts, the infinte K-points should be taken into account along z-axis/c-axis for true optimization of a layered structure.

3.2.8 Potential Energy Surface (PES) The potential energy curve for layered material can be drawn by varying the interlayer separation along z-axis without any movement of the layers along x-axis or y-axis as can be seen in Fig. 3.3c. The PES is drawn by using the single-point calculation on the optimized structure of the bilayered material. Periodic Energy Decomposition Analysis The periodic energy decomposition analysis (pEDA-NOCV) is a useful tool to investigate the interactions in terms of decomposition densities and energies. It is basically calculated in the form of fragments for which the interaction studies are required. For instance, to study the layered materials, each layer is considered as an independent fragment and after that the interaction between them is studied in depth. For instance, the pEDA for h-BN as performed on Amsterdam density functional (ADF-BAND) is given in Fig. 3.6. Here as it can be seen that the major density within the layer instead of region between the layers which shows the presence of primary bonding (strong ionic or covalent) along the planes and weak VdW interactions between the layers. In addition to this, the energy analysis shows that the attraction and repulsion terms are balanced by each other and at the end the attraction terms dominate. The readers are referred to literature for further explanation of this process [12].

3.2.9 Exfoliation Energy Higher the exfoliation energy, more easily will the layers be exfoliated. The methods to computed the exfoliation energy for the layered materials are given in previous sections. The exfoliation energy is of great importance and can be computed only for the layered materials. The exfoliation energies of majority of the layered materials lie in the range of 30–60 meV.

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3 Theoretical Modeling and Approaches to Study the Layered Materials -9.3490

(a)

K-point Convergence

Graphene

Energy (eV)

-9.3495

-9.3500

-9.3505

-9.3510

-9.3515 7x7x1 7x7x2 7x7x3 7x7x4 7x7x5 7x7x6 7x7x7 7x7x8 7x7x9

K-Points -4.926976

(b)

K-point convergence

Energy (eV)

-4.926978

-4.926980

-4.926982

9x9x1 9x9x2 9x9x3 9x9x4 9x9x5 9x9x6 9x9x7 9x9x8 9x9x9 9x9x10 9x9x11 9x9x12 9x9x13 9x9x14 9x9x15

K-points Fig. 3.5 Plots for convergence of K-points in a graphene b h-BN

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59

Fig. 3.6 Plots for deformation density a side view b top view

3.3 Why Layered Materials? The uniqueness of the layered materials lies in their anisotropic bonding behaviour and hence the anisotropic properties which provides basis for their applications. In this section, the anisotropic behavior and impact of applied foreign agency such as electric field, magnetic field, pressure, stress, etc. are going to describe that will lead to tune the properties of the layered materials.

3.3.1 Anisotropic Properties As discussed above, the layered materials contain the two type of bonding, i.e. inplane strong primary bonding (mostly covalent bonding) and out-of-plane weak VdW interactions. This difference in bonding is known as anisotropic bonding behaviour of the materials, due to which the layered materials exhibit direction-dependent behavior of the applied field. The anisotropic mechanics of the layered solids provides a way to exfoliate the individual layer of layered materials and expected to reveal interesting chemistry and physics of the materials [35]. Several properties of the layered materials such as elasticity, fracture strength and bonding are dependent on the orientation. This will provide the trust on the devices based on the 2D materials along with providing the broad prospects for the synthesis of the materials at atomic thickness having the tunable properties. A brief description of the mentioned anisotropy of some physical properties is elaborated in the following.

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3.3.2 Anisotropic Thermal Conductivity Because of the anisotropy in the structure of layered materials, the anisotropy in the thermal conduction, i.e. the difference in the thermal conductivity along in-plane and out-of-plane direction, should be taken into consideration. Considering the fundamental monolayered material, the most of the thermal characteristics of the graphene are attained from the graphite and have lasting impacts of the highly anisotropic essence of the crystal. The in-plane covalent bonding (having sp2 hybridization) between the successive carbon atoms are one of the strongest bond lying in the nature having the bonding energy of ~5.9 eV. Contrary to this, the adjacent layers of the graphene in a graphite crystals are associated with each other by means of the weak VdW interactions having energy ~50 meV. The spacing between the two adjacent layers is ~3.35 Å. The anisotropic behavior of thermal conductivity in graphene along in-plane and out-of-plane directions can be visualized from Fig. 3.7 In graphene, heat is transmitted only along the direction parallel to the plane and there is no transmission perpendicular to the plane [37]. The underlying reason is the thermal transfer carriers, i.e. phonon of the graphene is moved by the bonds presents between the atoms. Such particular phonons are not helpful in transferring from one layer of graphene to the other layers of graphene as there is the absence of the inter-atomic bond between the layers [38]. The theoretical results along with the verification of the experimental results showed the c-axis (out-of plane) thermal conductivity is of the order of ~0.7 W/ m K that is nearly four orders of the magnitude smaller than in-plane conductivity [39, 40]. The greater in-plane thermal conductivity is attributed towards the strong covalent bonding having sp2 hybridization while having weak VdW interactions in out-of-plane directions restricts the flow of heat [36]. An astonishing strong in the characteristics of the functionalized multilayered graphite has been spotted [41]. Higher thermal conductivity (~112 W/m K) as well

Fig. 3.7 Anisotropic behavior of graphite in in-plane (X–Y plane) and out-of-plane (Z-axis). Reprinted with permission Zeng et al. [36]. Copyright (2019)

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as the electrical conductivity (~386 S/cm) along with the extremely low coefficient of thermal expansion (~ − 0.71 ppm/K) within the in-plane direction of the functionalized multilayer graphene are attained considering no suppression process.

3.3.3 Anisotropic Electrical Conductivity The layered material’s structure is shown in Fig. 3.4, from where it is obvious that the values of in-plane and out-of-plane electrical conductivity are different because of the movement of charge carriers i.e. free electrons. Moreover, it is reported that the because of the unusual diamagnetism in perpendicular direction to basal plane (out-of-plane), it has been supposed that much larger electrical conductivity within the in-plane as compared to the out-of-plane direction [42]. Experimentally it has been proven that the electrical conductivity of graphite along in-plane direction is nearly 10,000 times greater than that of out-of-plane directions, while the specific resistance along the in-plane direction is of the order of 10−4 cm. whereas the specific resistance along out-of-plane direction is 2–3 cm. Similar anisotropy has been observed in the other layered materials such as In2 Se3 [43]. This may be attributed towards the strong in-plane bonding that would aid the easy movement of electrons within the structure whereas this is restricted in out-of-plane direction because of the weak forces that would hinder the flow of charges/electrons in the vicinity of the out-of-plane. Although much less work has been reported on the anisotropic electrical conduction as compared to the thermal conductivity that may be due to the flow and path of the electrons which are responsible for the electrical conduction, since the potential can be applied only along one direction and hence it is difficult to explain the electric conduction along in-plane and out-of-plane direction.

3.3.4 Thickness-Dependent In-Plane Conductivity Besides the fact that several physical properties are direction specific, the thicknessdependent properties of materials are important attributes of the layered materials. The thickness-dependent thermal conductivity is of prime importance in order to do thermal management in various ultrathin devices [37, 44–46]. Several studies have been put forward in this regards. For instance, the work carried out by means of ab-initio methods revealed the fact that the in-plane thermal conductivity of fewlayered graphene reduces by the enhancement in the number of layers. The highest in-plane thermal conductivity of ~2250 W/m K come out in case of the single layer of graphene. Moreover, the value of thermal conductivity reaches close to that of the bulk graphite as the number of layers approaches to 5. This high value of thermal conductivity in single layer of graphene is ascribed toward the fact that there is no scattering of in-pane phonon modes [47]. Furthermore, the similar impact has also

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been noticed within the natural MoS2 . By the enhancement in number of layers to 3 from 1, the reduction in the thermal conductivity of 98 W/m K, i.e. close to the value for the bulk MoS2 from 138 W/m K (for single layer) has been observed [48, 49]. This reduction in the thermal conductivity is associated with the increase in anharmonicity that points toward the robust phonon scattering for the degenerated acoustic branches. Hence, it may be said that graphene as well as the MoS2 presents the similar situation that is the in-plane thermal conductivity suppresses by the increase in the thickness. However, contrary to the above described layered MoS2 and graphene, the layered black phosphorous shows a sharp increment in the in-plane thermal conductivity by the enhancement in the thickness from 9.6 to 15 nm [50]. By the opinion of the authors, in the experiment, the boundary scattering was the reason behind this increment as the boundary scattering reduces by the increment in the thickness that consequently showed the increment in the thermal conductivity. Similarly, the thicknessdependent thermal conductivity of another layered material, i.e. tungsten di-telluride (WTe2 ) has also been studied through DFT computations [46]. By the enhancement in the number of layer from 1 to infinity, the thermal conductivity exhibits the trend from decrease to increase. The fundamental phenomenon is associated with the transition in the phonon dispersion relations. By the enhancement in the number of layers, the optical phonon branches move downward, that yield more channels for the Umklapp scattering and as a results leads to the reduction in the thermal conductivity. Moreover, the increment in the number of layers assemble lower frequency optical phonon branches with the higher group velocity and tends to the increment in the lattice thermal conductivity.

3.3.5 Applications of Layered Materials 3.3.5.1

Lithium Ion Batteries

Lithium ion batteries (LIB) are a well-known and one of most widely used energy storage devices. The research efforts had been put forward to investigate the new and up-to-date electrodes for the lithium ion (Li-ion) batteries during the current years because of having the great influence over the energy storage techniques for the portable electronics as well as the electrical vehicles (EVs). Because of their lower expenditures and the higher energy densities, the LIB batteries had been of prime importance, so far, for the EVs as well as the portable electronics. At the same time, this energy storage devices suffer some constraints. These batteries more often contain a major segment of the volume along with the mass of the portable electronic devices and nevertheless restrain the available amount of energy and hence require the “frequent” charging. In the present days, the EVs as powered by the batteries either provide the small-scale driving scopes or they are high-cost because of the elevated charges of LIBs. By enhancement within the battery’s energy density, specifically the volumetric energy density could substantially enhance as well as enlarge the probabilities toward the portable electronic devices. If the same products

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are produced in the less expenditures per unit energy and hence the per unit cell at the similar time, large range and sustainable EVs could be manufactured. To deal with the requirement of cost-effectiveness as well as the enhance the energy density, several researchers have set their eyes to boost the volumetric density of the anodes as well as cathodes. The LIB consists of several parts out of which anode, cathode and electrolyte are the main components. The standard thickness of an electrode layer spans as 60–100 µm at every verge of the foils. Within the battery, the electrodes are parted though the electrically insulated porous membrane having a conventional thickness of ~15 to 25 µm. By utilizing the active materials with large capacity, designing materials which suppresses the requirement of the separator membrane, current collectors, binders and thus the energy density could be improved. There are several materials used as an electrode material, i.e. cathode and anode. The materials used as an anode are Si, graphite, silicon oxides (SiO2 ), bismuthene, antimonene, phosphorene, tin and tin oxides (SnOx ) etc. Traditionally, the intercalation type of electrodes is the most commercialized and successful electrodes; one of them is graphite anode along with the metallic oxide cathodes. The intercalation electrodes have ability to provide the fast transport of Li-ions through the conductive Li in 2D planes or 1D paths in comparatively higher individual particles (most of cases > 1 µm within the diameter of cathode particles as well as > 5 µm in diameter anode particles). The edge of having the small volume expansion over the process of lithiation as well as delithiation (generally < 7%) as a consequence provide the better electrochemical as well as the mechanical stability of those intercalated electrodes. The smaller volume changes within the graphite-based anodes are of prime importance as they require to maintain the smaller strain inside the solid electrolyte inter-phase. This might be responsible for the formation of the electrolyte, continual growth by the reduction mechanism along with the solvent permeable defects at some comparatively lower anode potentials. Considering all the facts and advantages of the layered materials, each material with the VdW interactions are of prime importance to the researchers for investigating as anode materials for metal (Li, Na and K) ion batteries. Besides the researchers, the industrialists are fascinated by layered materials, as one of the most used anode material is graphite that despite of the lower theoretical capacity, are one of the most often used anode material. The reason is its structural stability of the materials during the process of intercalation.

3.3.5.2

Twistronics

Twistronics is a recently emerged research area in the material sciences which specifically deals with the layered materials. The layered materials offer the unique properties that the layers of the materials could be twisted and as a result offer the modulation or modification in the several properties such as the stacking of the materials and the electronic properties. The electronic characteristics of the layered materials

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could be modulated markedly through the Moiré superlattice potential that is highly dependent on the twist angle amid compounds [51]. The stacking of layers in the 2D layered materials is of prime importance that has great impact over the properties and as results the applications are based upon them. The technique to integrate the monolayer into multilayered structure has emerged marvelous control on the respective orientation, i.e. twist of the adjacent layers [52– 55]. This may be of the order of 0.1° and consequently the structure exhibits a novel category of the materials having properties extending across the wide range which contain the superconductors, insulators, metals and the semiconductors [56]. The distinct ordering of the layers of 2D materials offers an interesting and exciting platform in order to investigate the new physics as well as the promising applications on the basis of the thermal, electronic, magnetic and optical properties. The respective orientation of the adjacent layers is frequently characterized through the twist angle between the ideal in-plane lattices that exhibits the extra knob to regulate the properties of system under investigation. The twist at comparatively low angle for various layered materials is shown in Fig. 3.8. Besides this, the chemical or mechanical exfoliation and the stacking of one layer over the other permits for the respective twist in between the successive layers that could demolish the alignment and as a result break the translation symmetry within the integrated system [53, 54, 57]. The structure obtained as a result might have a “commensurate” stacking for specific orientations, yet most of them may have a “incommensurate” structures, which permits a fascinating behavior of the materials. The investigations over the bilayer graphene provided important insights in this regards, i.e. the twist-dependent characteristics and properties in conductivity as well as the electronic properties (e.g. density of states & band diagram) [58–60]. Graphene is the foremost studied layered material that is considered as typical layered material. Besides the conventional applications, the bilayer and multilayered graphene is of great importance for twistronics. The bilayer graphene is regarded as a potential candidate that has gained a lot of attention in this regards. The theoretical computations as well as the experimental work disclose the reality that the VdW interactions presents between the layers (inter-layer) along with the band diagram of the bilayer graphene could be modified drastically through the twist in between the two adjacent layers of graphene [62]. By the larger twist angles of ~ ϑ > 5.5°, the

Fig. 3.8 Twisted bilayers of graphene, WSe2 , WS2 and MoS2 at 19° rotation. Reprinted with permission from Polanco-Gonzalez et al. [61]. Copyright (2017)

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two layers of graphene are, in general, electronically separated. Consequently, each layer acts as the monolayer graphene excluding the smaller sets if angles that result in the corresponding configurations. By reducing the twist angles, the smaller energy van Hove singularities (VHSs) of the twisted bilayer graphene (TBG) slowly move nearer to them. This would go along with the reduction of the Fermi velocity because of the presence of the stronger inter-layer coupling. As the twist angle reaches to the magic angle (i.e. ~1.1° for graphene), the Fermi velocity nearly disappears that results in the two highly dispersive flat Moiré bands nearly bound to the charge neutrality point. Besides these, as the Fermi level exists in the flat bands of the TBG close to the magic angles, it is expected that the coulomb forces surpass to the kinetic energy of the electrons that could propel the environment toward the several strongly correlated phases. Furthermore, this strongly correlated states of the flat bands can also be observed in various other layered materials having the inter-layer twist. By the past few years, the TBG close to the magic angles has unlock a captivating novel chapter in perspective of the strongly correlated quantum matter. The exceptionally broad range of the correlates state’s physics, like topology, Mott insulator, ferromagnetism and superconductivity are those properties and applications that are perceived experimentally in the TBG close to the magic angle. Similar impacts might be observed in other layered materials such as h-BN and TMDs. By the discussion present above, it is clear that for the observance of the twistronics, the inter-layer twist is compulsory and such a twist can be observed only by the layered materials. The inter-layer twist happened to be a sole property of the layered materials and could not be observed in the non-layered materials.

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12. Majid, A., et al.: On the prospects of layeredness in tantalum pentoxide. Mater. Sci. Eng., B 272, 115349 (2021) 13. Liu, X., et al.: Vertical ferroelectric switching by in-plane sliding of two-dimensional bilayer WTe2 . Nanoscale 11(40), 18575–18581 (2019) 14. Kumar, H., Dong, L., Shenoy, V.B.: Limits of coherency and strain transfer in flexible 2D van der Waals heterostructures: formation of strain solitons and interlayer debonding. Sci. Rep. 6(1), 21516 (2016) 15. Ugliengo, P., et al.: Role of dispersive interactions in layered materials: a periodic B3LYP and B3LYP-D* study of Mg(OH)2 , Ca(OH)2 and kaolinite. J. Mater. Chem. 19(17), 2564–2572 (2009) 16. Tawfik, S.A., et al.: Evaluation of van der Waals density functionals for layered materials. Phys. Rev. Mater. 2(3), 034005 (2018) 17. Sholl, D.S., Steckel, J.A.: Density functional theory: a practical introduction. John Wiley & Sons (2011) 18. Röthlisberger, U.: Introduction to electronic structure methods. EPFL, Lausanne (2015) 19. Hermann, J., DiStasio, R.A., Jr., Tkatchenko, A.: First-principles models for van der Waals interactions in molecules and materials: concepts, theory, and applications. Chem. Rev. 117(6), 4714–4758 (2017) 20. Hyldgaard, P., Jiao, Y., Shukla, V.: Screening nature of the van der Waals density functional method: a review and analysis of the many-body physics foundation. J. Phys.: Condens. Matter 32(39), 393001 (2020) 21. Lozano, A., et al.: Assessment of van der Waals inclusive density functional theory methods for layered electroactive materials. Phys. Chem. Chem. Phys. 19(15), 10133–10139 (2017) 22. Klimeš, J., Michaelides, A.: Perspective: advances and challenges in treating van der Waals dispersion forces in density functional theory. J. Chem. Phys. 137(12), 120901 (2012) 23. Grimme, S.: Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem. 25(12), 1463–1473 (2004) 24. Grimme, S.: Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27(15), 1787–1799 (2006) 25. Grimme, S., et al.: A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132(15), 154104 (2010) 26. Tkatchenko, A., Scheffler, M.: Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 102(7), 073005 (2009) 27. Grimme, S., et al.: A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132(15) (2010) 28. Caldeweyher, E., et al.: Extension and evaluation of the D4 London-dispersion model for periodic systems. Phys. Chem. Chem. Phys. 22(16), 8499–8512 (2020) 29. Caldeweyher, E., Bannwarth, C., Grimme, S.: Extension of the D3 dispersion coefficient model. J. Chem. Phys. 147(3), 034112 (2017) 30. Caldeweyher, E., et al.: A generally applicable atomic-charge dependent London dispersion correction. J. Chem. Phys. 150(15), 154122 (2019) 31. Reckien, W., et al.: Implementation of empirical dispersion corrections to density functional theory for periodic systems. J. Comput. Chem. 33(25), 2023–2031 (2012) 32. Tkatchenko, A., et al.: Accurate and efficient method for many-body van der Waals interactions. Phys. Rev. Lett. 108(23), 236402 (2012) 33. Buˇcko, T., et al.: Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning. J. Chem. Phys. 141(3), 034114 (2014) 34. Aykol, M., Kim, S., Wolverton, C.: Van der Waals interactions in layered lithium cobalt oxides. J. Phys. Chem. C 119(33), 19053–19058 (2015) 35. Gao, Z.-D., et al.: Anisotropic mechanics of 2D materials. Adv. Eng. Mater. 24(11), 2200519 (2022) 36. Pop, E., Varshney, V., Roy, A.K.: Thermal properties of graphene: fundamentals and applications. MRS Bull. 37(12), 1273–1281 (2012)

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Chapter 4

The Elemental Layered Solids: Group IV and V Materials

Abstract Layeredness is an important structural aspect of a class of inorganic materials which leads to formation of atomic layers that are connected via weak van der Waals (VdW) interactions. This chapter sheds light on appearance of elemental materials and their various possible crystal structures as monolayers and layered structures. The studied materials include carbon, boron nitride, phosphorous, arsenic, antimony, bismuth, stannous and silicon. The allotropic forms, crystal structures, properties and applications of the materials with emphasis on layeredness of the materials are described on the basis of theoretical computations performed by the authors using density functional theory (DFT) implemented Vienna ab-initio simulation packages (VASP) and Amsterdam density functional (ADF-BAND) codes. The results revealed that carbon and BN are layered in hexagonal crystal structure, while the black phosphorous, black arsenic are layered in orthorhombic crystal structures. Contrary to this, carbon and BN are non-layered in cubic crystal structures. The findings points to the fact that materials appeared in layered structures in specific crystal structure and the layeredness have roots in p–p hybridization.

Theme of Chapter Material science fundamentally deals with the properties and hence applications of the materials which are basically structure dependent. The synthesis of the highquality materials in bulk and lower dimensions for utilization in applications has been a prime focus of the relevant community. The two-dimensional (2D) materials have recently earned extensive research and industrial interest; however, there is a common misconception that the 2D materials are layered materials or any material structurally downscaled to monolayer is a layered material. Despite the fact that the term “monolayer” correctly conveys the meaning as “single layer”, but its description as “layered” is conceptually incorrect which should be avoided in scientific literature. It is necessary to point out that the materials having strong covalent or ionic in-plane bonding and out-of-plane VdW interactions in their structure are layered materials or VdW solids. The monolayer of any material can be obtained by trimming of any three dimensional (3D) bulk material either layered or non-layered. Moreover, the layeredness, the ability of any material to exist in the form of independent layers, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Majid and A. Jabeen, Layeredness in Materials, Engineering Materials, https://doi.org/10.1007/978-981-99-6299-0_4

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is an intrinsic property of the materials (having onion like structure), which has been discussed in detail in Chap. 3. It should be noted that, the layered material exists in the form of layers in both 3D and 2D. However, this aspect is prominent in the 2D materials having thickness of nanometers (nm) as the individuality of the layers becomes prominent. In this chapter, the layeredness and relevant properties of elemental layered materials will be described in detail. In order to elaborate some important situations, some first-principles calculations were carried out which will be discussed in the coming sections. The majority of the calculations were carried out using density functional theory (DFT) approach implemented in Vienna ab-initio simulation package (VASP) and Amsterdam density functional (ADF) codes. The structural properties of the studied materials were characterized via analysis of the structural parameters such as lattice parameters, bond lengths and bond angles etc.

4.1 Parameters of the Layered Materials Due to diverse nature of the layered materials, the parameters related to these materials are somehow specific which will be described in the following sections.

4.1.1 In-Plane and Out-of-Plane The phrases in-plane and out-of-plane will be commonly used in case of layered materials due to their anisotropic structure. The term in-plane refers to a property within a specific plane or within a single layer in which atoms are strongly bonded via covalent or ionic bonding, as shown in Fig. 4.1. For elemental solids like carbon, phosphorous, etc., the atoms in the single layers are covalently bonded, whereas in case of compounds the ionic character is also involved. On the other hand, in out-ofplane case, there is not covalent or ionic bonding, but the layers are connected via weak VdW interactions to keep these layers in contact as shown in Fig. 4.1. Fig. 4.1 Crystal structure of a representative layered material, i.e. graphite for the understanding of the in-plane and out-of-plane terms

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4.1.2 Bond Lengths The layered materials can be distinguished from the non-layered materials via atomic bonding which can be analyzed through bond lengths and dihedral angles. Sometimes, during the calculations on the materials, the bonds in the relaxed crystal structures do not appear which may not be taken as absence of the bonds between neighboring atoms. In order to analyze such situations, the interatomic distances or the bond lengths are recorded on the basis of which the formation of bond and strength of bond is estimated. The in-plane bonding is strong and shorter bond length will be present, but the out-of-plane bonding is found in the form of weak VdW interactions because of the presence of comparatively longer bond length. The primary bonding can be either covalent or ionic, which can be characterized by the ionic and covalent radii of the elements involved. If the sum of covalent radii, in case of layered compounds, is larger as compared to calculated bond length or the sum of ionic radii is greater as compared to the calculated bond lengths, then strong in-plane bonding is present [1]. The general criteria regarding the presence of weak VdW interactions are that the bond length (i.e. inter-planar distance) should be more than 2.4 Å, more the distance, weaker the interactions and vice versa. If the distance is the less than 2.4 Å, then there is greater probability of presence of primary bonding.

4.2 Carbon Carbon is one of the most fascinating materials due to diverse structures and promising properties for daily life usage and applications. It is naturally found in several allotropic forms out of which graphite, diamond, fullerene and Buckminster fullerene are famous due to their applications. Considering the basic classification of solids into layered and non-layered, graphite and diamond are considered as the representative structures. Diamond exists in cubic structure having sp3 hybridization in which atoms are connected to each other by strong bonding in the form of networking materials. The crystal structure of diamond is shown in Fig. 4.2, from which it is obvious that each carbon atom is bonded with other carbon atoms by the strong covalent bonding. The diamond, because of its crystal structure, offers large values of modulus of elasticity, hardness as well as wear resistance and lower friction coefficients. Besides these, diamonds possess the lower value of thermal expansion and higher thermal conductivity [2]. These are also considered as the bad conductor of electricity due to strong covalent bonding and deficiency of free electrons. Out of two allotropic forms, i.e. diamond and graphite, graphite is more stable [2].

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Fig. 4.2 Crystal structure of diamond and graphite. Reprinted with permission from Popov et al. [3]. Copyright (2019), The Owner Societies

4.2.1 Layered Versus Non-layered There is an obvious question: graphite is layered while the diamond is not, why? Diamond and graphite, both are formed by the carbon, but the former is present in cubic crystal structure, while the latter is present in the hexagonal crystal structure. The crystal structures of these allotropes of carbon are shown in Fig. 4.2. There is strong covalent bonding in the cubic diamond structure in such a way that each carbon is attached with neighboring carbon atoms by sp3 hybridization throughout the structure which points to isotropic bonding therein. On the other hand, in case of graphite, each carbon is attached with neighboring carbon atoms in-plane by sp2 hybridization but connected to the out-of-plane carbon atoms via VdW interactions which points to anisotropic bonding. In order to shed light on the layered materials, theoretical investigations were performed on the graphite crystal structure. The work was carried out using the density functional theory (DFT) implemented on Vienna ab-initio simulation package (VASP) code. The optimized crystal structure as drawn by Amsterdam density functional (ADF-BAND) is given in Fig. 4.3 where figures (a) and (c) are shown along x-axis or side wise, while (b) revealed top view along z-axis. The relaxed crystal structure clearly points out that the material exists in the form of layers in such a way that inter-layer atoms are attached via non-covalent/non-ionic bonds that may be the VdW interactions. Due to the presence of this weak interaction, the layers can be exfoliated to collect a monolayers that has variety of applications which include lithium ion batteries, sensors, electronics, photocatalysts and biomedical applications [3–6]. The crystal structure was optimized at different level of theory and the calculated values of the formation energy are given in Table 3.2 in Chap. 3. The results indicated that the minimum energy is obtained when dispersion corrections via functionals DFT-D3 and DFT-D3-BJ are included which indicate the presence of weak interactions between the layers. Furthermore, the solid line in Fig. 4.3 represents the bond order 1 exhibiting the covalent bonding, while the dotted line represents the bond order 1.5 which shows the resonance in bonding that may be due to the unhybridized p-orbitals.

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Fig. 4.3 Optimized structure of the graphite a unit cell along x-axis b unit cell along z-axis/top view c supercell

4.2.2 2D Carbon (Graphene) In the post-silicon era, graphene is the mostly investigated material. It is a single layer (i.e. atomic plane) of graphite that is isolated enough from its surrounding that it exists in the form of a freestanding material [4–7]. The graphene is also termed as monolayer graphite. The atomic planes are comprised of the crystals analogous to that of bulk, yet the thickness is in atomic scale.

4.2.2.1

Synthesis of Graphene

The synthesis of 2D materials is technologically challenging. The lack in stability of 2D materials is a point of concern as it causes either breaking of atomic bonds to crack the flat structures or transition of sp2 to sp3 hybridization to mold the planner crystals into bulk counterparts. There may be two paths to grow 2D crystals; first is the mechanical splitting of the layers which is also known as exfoliation. This method, commonly referred as scotch-tape method, had been used for the isolation of the graphene from bulk graphite for the first time in 2004. Besides this, contrary to the manual cleaving of the graphite, there are several parallel exfoliation methods such as ultrasonic cleavage. This escorts the stable suspensions of the sub-micrometer graphene crystallites that could be utilized for the formation of the polycrystalline films as well as the composites materials. The ultrasonic technique is considered as more effective as the atomic planes are partially separated through the intercalation. The sonication permits the industrial-scale production of the graphene [8, 9]. The other method comprises growth of graphene structure over substrates. The growth in such a way is known as the three-dimensional growth in which the epitaxial

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layers are constrained to nucleate over the surface of a suitable substrate. The structural fluctuations leading to the breaking of the bonds may be suppressed by proper choice of synthesis conditions and the substrate. As the epitaxial structure is cooled down, the substrate could be detached through the chemical etching method. This method has been adopted to grow variety of 2D structures like SiN membrane, whose synthesis in lower dimensions is experimentally intriguing [10–12]. The isolation of the epitaxial monolayer on substrates and their isolation has often been carried out these days [13].

4.2.2.2

Uniqueness of Graphene

Graphene offers unique properties in comparison with the contemporary 2D materials [14, 15]. This is electrically conductive, optically transparent as well as flexible that derive it a perfect for the production of the flexible electronic and display devices. The theoretically computed electron mobility is ~200,000 cm2 /V s at nearly 5 K which is because of the conjugated π-electrons and this is much higher than the silicon having value of ~1500 cm2 /V s [16]. The electrons present in the graphene sheet are represented as the massless particles that are moving without being scattered and are referred as the ballistic transport which is considered to be the reason for the comparatively higher carrier mobility [17]. The sheets of graphene appeared to have tensile strength of ~130 GPa which is much larger than that of steel with value 0.4 GPa and hence is considered as the strongest material known today [18]. The interesting property of graphene is its larger surface area of ~2000 m2 /g and lightweight. Moreover, graphene exhibits the elastic characteristics having the large value of the Young’s modulus of ~500 GPa, whereas the rubber shows the Young’s modulus in the range of ~0.01–0.1 GPa. The lightweight, higher strength, elastic properties and large electrical conductivity of the graphene are special characters of the graphene that make it favorable for several applications including flexible electronics [19].

4.3 Boron Nitride (BN) Boron nitride (BN) is a well-known refractory material which consists of covalent bond between boron (B) and nitrogen (N) atoms [14]. The main reason of considering this material just after the graphene is that, in most of the cases, structure of BN is comparable to that of carbon. Similar to carbon, BN is also present in six allotropic forms which are similar to carbon in structural and electronic arrangement. The allotropic forms are cubic BN (c-BN also known as the diamond or zinc blend structure), rhombohedral (r-BN), hexagonal (h-BN similar to graphite), wurtzite (wBN), single as well as multiwalled nanotubes of BN and fullerene alike BN [20, 21] as shown in Fig. 4.4. The cubic BN (c-BN) has diamond-like crystal structure, while the hexagonal BN (h-BN) has the structure similar to the graphite crystal structure

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Fig. 4.4 Various allotropic forms of boron nitride (BN). Reprinted with permission from Sharma et al. [25]. Copyright (2019), Elsevier Ltd.

[14, 22]. The crystal structure of h-BN is similar to the graphite [23], where B and N atoms are substituted at the vertices of the planar hexagons which leads to sp2 hybridization and VdW forces appear as reason of connecting the layers together [24]. Because of this anisotropy in bonding, i.e. different in-plane and out-of-plane bonding, the h-BN exists as layered material. Moreover, these 2D sheets/layers are considered as the most stable as well as the soft among its different crystal structures, i.e. different polymorphs. In addition to this, the in-plane bonding is alike to that present in the aromatic compound, yet the covalent character suppresses and the ionic character increases and this is due to the electronegativity difference of B (2.04) and N (3.04) [26]. It makes the material as best candidate for the proton conductors and at the same time, it is an electrically insulator which helps its utilization as fuel cells [27]. The thermal conductivity is the greatest over all the electrical insulators as per detailed reported studied [25]. The h-BN, due to the higher thermal conductivity and lower electrical conductivity, is broadly utilized in industrial as well as scientific applications [21, 28]. Because of the higher mechanical and thermal stability as well as the unsurpassed thermal shock resistance, the BN ceramics are utilized as a portion of the higher temperature equipment. Besides the other properties, the BN allotropes show some properties specific to that allotrope like they are non-toxic, offer higher Young’s modulus (c-BN, BN-NTs), hardness (c-BN) and transparent to the microwaves (h-BN) [29].

4.3.1 Layered Versus Non-layered BN As per discussion in the previous section, the h-BN is layered, while the rest polymorphs are non-layered, which puts a question mark and needs explanation. For

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Fig. 4.5 Crystal structure of h-BN a side view b top view c top view of c-BN, where blue color represents the N atoms and other represents the B atoms

this purpose, we considered c-BN and h-BN as representative structures and investigated using DFT methodology implemented VASP. The structures were optimized at GGA-PBE-D3-BJ level of theory with 600 eV as cutoff by using 9 × 9 × 1 mesh. The relaxed crystal structure of the h-BN, as shown in Fig. 4.5a, b appears in the form of layers studied either via unit cell or supercell approach. The two formula units of BN prefer to be in the form of two layers rather than in the single layers to produce layered structure. Contrary to this, the relaxed c-BN exists in single-crystal structure or single-piece structure as shown in Fig. 4.5c. This would lead to the anisotropic behavior in the structure in h-BN crystal structure, whereas the c-BN shows isotropic behavior. This is also expected from the inter-layer and intra-layer bond length, i.e. in case of h-BN, the inter-layer distance is 3.5 Å, which is enough for the evidence of the presence of secondary type of bonding. The primary bonding can be present in in-plane direction since the intra-layer B–N bond length is 1.44 Å that is in great agreement with literature [23, 30]. Whereas in case of c-BN, the bond length between the B and N atoms is 1.75 Å, that is same in complete structure, and hence, no anisotropy is expected in case of c-BN. Furthermore, in case of the compound layered materials, the stacking arrangement is also important [23]. In the present case, the h-BN sheets are present in AB stacking, but for the c-BN, the stacking is irrelevant. Moreover, the periodic energy decomposition analysis performed for h-BN, given in previous chapter as shown in Fig. 3.6, was evident to the interaction between these layers and the density of electrons was localized only to the layers, i.e. where the atoms are present and also reveal the presence of weak forces between these layers [23]. Because of the presence of the layers, the h-BN can be exfoliated and single layer with atomic thickness can be achieved, but this is not possible in case of the c-BN. The above-described facts showed that due to anisotropy in bonding, the existence of h-BN is in the form of layers with a certain exfoliation energy, while c-BN structure appeared as non-layered material.

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4.3.2 Synthesis and Uniqueness of h-BN Sheets The h-BN, also known as “white graphene”, is one of the most famous 2D materials because of its attractive characteristics and distinctive physical phenomenon involved. The h-BN is used as the ideal substrate to fabricate the large-scale graphene films due to the lower-lattice mismatch with the graphene of ~1.7%. The h-BN sheets with atomic thickness could be fabricated through the chemical vapor deposition (CVD) using precursor ammonia borate. The exfoliation of the bulk h-BN under the appropriate conditions can also be used to extract the monolayers for broad applications within the cosmetic as well as the coatings. The h-BN sheets have also been synthesized through the controlled energetic electron irradiation by the procedure of the layer-by-layer sputtering [31]. The monolayers of the h-BN show the exceptional thermal stability, higher optical transparency as well as the chemical inertness in comparison with the graphene. Contrary to the electronically conducting graphene, the layers of h-BN are electronically insulators with the wide band gap of ~5.96–6 eV. This is due to the suppressed electronic delocalization [24, 32, 33] as well as the unavailability of the π-electrons which makes it a potential candidate as the fire-retardant agent [34].

4.3.3 Problems with h-BN and the Solutions Besides the above-described prospects and properties of the h-BN, the wide band gap is the major shortfall of this material that hinders this material for the utilization in the several applications. As the utilization of the material in semiconducting devices needs a moderately small band gap for controlling the conductivity in between the on and off states. The theoretically estimated band gap of the 2D h-BN is 4.71 eV due to the well-known underestimation of the band gap by the DFT methods and the level of theories utilized for the calculations. In order to modify the band gap specifically decreasing the band gap, several physical as well as chemical methods have been adopted [31]. For instance, it has been concluded that the specific line defects could be the reason to tailor the band edges on the sheets of the h-BN that could considerably decrease the band gap of the sheets [35]. Furthermore, it has been proposed that the embedded acetylenic chains could give more flexibility in order to control the electronic properties of the h-BN [36]. Nevertheless, the fully hydrogenated h-BN layers have been proposed as a semiconductor having a band gap of ~3.3 eV [37]. Furthermore, the results suggested that by the substitution of the carbon atoms within the h-BN layers could give rise to a suppression in the electronic band gap [38]. Another method suggested by the researchers has been the stabilization of several other allotropes of the boron nitride. In this respect, a detailed study has been reported on the pentagonal penta-Bx Ny sheets [39]. The investigations on the electronic properties, stability as well as the mechanical characteristics showed that the penta-BN2

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is an eye-capturing material for the researchers. Furthermore, the detailed investigations has been carried out in the electronic and structural characteristics of the six different single-layered allotropes of the BN similar to the graphene that are constituted on the alternate B–N bonds and incorporate the atoms of distinct types of hybridization, i.e. sp2 , sp2 + sp3 and sp2 + sp1 [40]. This study has been carried out by utilizing the density functional tight binding (DFTB) approach and the results revealed that such allotropes are least stable as compared to the h-BN, although their integrity was conserved during simulation of molecular dynamics. Nevertheless, a new BN allotrope (named as P-BN), inspired with the P-carbon structure, that is superhard, stable and transparent has been investigated and the results showed that at pressure greater than 4 GPa, it becomes energetically favorable on the h-BN [41].

4.4 Phosphorous Phosphorous is an ample element from the group V (commonly known as pnictogen group) of the periodic table [42]. As phosphorous loses its valence electrons with a great ease, it has higher reactivity and hence, its natural occurring as a free element on the earth is not reported yet. By and large, it occurs in an oxidized state in the rocks of phosphates; one such element is Ca3 (PO4 )2 .

4.4.1 Allotropic Forms of Phosphorous Phosphorous exists in four allotropic forms named as black, white, red and violet depending on their physical appearance. The white and red phosphorous are two major allotropic forms, where the former comprised of tetrahedral P4 molecule that could be easily attained through the sintering of the phosphate rocks within the presence of the silica and coke. This form is volatile, reactive as well as ignites within the air at ~34 °C and thus, it needs the sealing of water for the storage purposes, whereas the latter exists as the derivative of the P4 , in which the P–P bond detaches and makes the new bonds with the adjacent tetrahedron P4, which, in due course, results a chain structure analogous to the polymer. The amorphous red phosphorous could be produced through heating the white phosphorous either in the presence of the nitrogen gas (N2 ) at ~300 °C or exposed to the sunlight. The additional heating results in obtaining the crystalline red phosphorous. The violet phosphorous could be attained through the annealing of long time of red phosphorous at ~550 °C having the aid of molten lead [43]. The black phosphorous (BP), a thermodynamically stable allotropic form, resembles in appearance with the graphite, i.e. a good conductor of electricity and a shiny black material. It could be synthesized from the white phosphorous while heating at immensely high pressure (i.e. 200 °C at 1.2 GPa) [44]. The crystals of bulk BP comprised of the stacking of layers, named as phosphorene [45, 46]. These layers are

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stacked together with the VdW interactions that could be detached/broke in order to attain the single layer of phosphorous [47, 48]. The black phosphorous, analogous to the graphite, belongs to that limited elements that are layered crystals comprised of monoatomic species [49, 50]. Although this is the most stable allotropic form, its high-density phase has been prepared after the long period of time since the first discovery of elemental phosphorous. Besides these, the dimer of phosphorous, termed as diphosphorous, i.e. P2 , occurs naturally in gaseous state and could be attained through the thermal decomposition of the white phosphorous at ~800 °C. Additional cracking of the material (i.e. P2 ) at ~2000 °C results in the formation of atomic monomer within the vapor phase [51, 52]. The elemental phosphorous could be attained by phosphoric acid, phosphane (PH3 ) [53, 54], adenosine triphosphate [55] and monopotassium phosphate (KH2 PO4 ) [56].

4.4.2 Crystal and Electronic Structure of Black Phosphorous The black phosphorous (BP), that is, comparatively rarely observed allotrope of the phosphorous element firstly exhibited in 1914 by the Bridgman [44, 57]. The BP possesses an orthorhombic crystal structure and the P atoms are placed into the hexagonal puckered layered tie up through the weak VdW forces [58]. The bulklayered BP, that is, analogous to the graphite to a great extent, exhibits the wrinkle configuration. Unusually, the structural arrangement is nearly similar to the graphene. Simultaneously, the blue phosphorous possesses the similar appearance as the BP that could be considered as the wrinkled graphene. There exist 8 atoms within the unit cell of BP and offer density of 2.69 g/cm3 . The lattice configuration of BP has been observed through the X-ray diffraction which revealed that every cell consists of 2 layers of atoms. Moreover, each P atom is linked with the nearby neighboring atoms (in-plane) by the bond length of ~2.18 Å and the bond angles of ~99° and 103° with an average value of 102°. Besides the anisotropy in crystal structure, because of its unique crystal structure as shown in Fig. 4.6, the material offers the anisotropy in the single layer of phosphorous. In order to deal with this anisotropy, the x-axis and y-axis are termed as armchair and zigzag directions respectively. Moreover, the phosphorene shows the superb mechanical characteristics, higher mobility of holes, i.e. ~1000 cm2 V−1 s−1 , anisotropic optical, thermal and electrical properties as well as tunable band diagrams. These properties lead their utilization in several applications such as device fabrication. The sp3 hybridization established through the three sigma bonds as well as one lone pair bonds brings about the non-planar puckered crystal structure of the phosphorene (single layer of phosphorous) [60]. The geometric distortion within the pure phosphorene is stabilized by the non-bonding lone pair bond [61]. Due to the out-ofplane orbitals, the lone pair of the electrons gives rise to the inter-layer interactions and often termed as VdW interactions [47, 62] and oxidizing gases like NO2 and O2 mostly occupy the lone pair. Besides this, the decoration with the metallic particles gives rise to the orbital hybridization having the lone pair [63–65]. Furthermore, the

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Fig. 4.6 Crystal structure of black phosphorous where blue-colored balls represent the phosphorous atoms, n and az represent number of layers and out-of-plane lattice constant. Reprinted with permission from Low et al. [59]. Copyright (2014), American Physical Society

lone pairs lead to the rearrangement of the structure under the high pressure of nearly 5 GPa that consequently causes the transformation of phases into the rhombohedral crystal [60, 66]. Hence, the lone pair electrons could be regarded as the basic cause for the phase transformation as well as chemical reactivity.

4.4.3 Structure of Monolayer Phosphorous-Phosphorene Phosphorene, a single layer of phosphorous, owns a puckered configuration, when noticed from a side view that is perpendicular to the armchair direction. The multilayered phosphorene, as built by the stacking of single layers of phosphorous. The threedimensional lattice constants for the phosphorous are a1 = 0.34 nm; a2 = 0.45 nm; and a3 = 1.12 nm [67–69], while the inter-layer separation observed between two layers is 0.53 nm (which is less than that of graphene, i.e. 0.33 nm) [70, 71]. The comparatively greater spacing is because of its puckered structure and the AB Bernal stacking of the layers within a single unit cell. These layers are held together by weak VdW interactions (~20 meV/atom) that can be detached easily and an independent layer of the phosphorene can be achieved easily [46, 71, 72]. Furthermore, the top view exhibits that the single layer of phosphorous possesses the honeycomb configuration, similar to the graphene, yet an anisotropy in the basic structure because of the non-planar structural edges. The 2D perpendicular lattice constants for the single layer of phosphorous are a1 = 0.34 nm; a2 = 0.46 nm [73–75]. Because of the anisotropic structural, electronic and optical properties of the material, its behavior

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is highly anisotropic contrary to the graphene. This shows that the monolayer phosphorous is a promising material for the infrared thin-film electronics [76–79].

4.4.4 Synthesis and Uniqueness of Layered 2D Phosphorene The layered allotrope of phosphorous similar to the graphene sheets has been observed in 2014 through the micromechanical exfoliation procedure of the black phosphorous [14, 80]. Contrary to graphene, phosphorene possesses a band gap of nearly 2 eV that is considered as ideal candidate for the semiconducting applications. The procedure of the liquid-phase exfoliation has also been adopted for the synthesis that assures its industrial and commercial applications [81]. As the phosphorene is greatly reactive to the oxygen atoms, the deoxygenation of the solvents as well as the stabilizing agent or appropriate solvent is required. While omitting the oxygen, the material is stable within water. Nevertheless considering the sensitivity of the air, phosphorene exhibits the potential for its utilization in catalysis, transistors and sensors [49]. The black phosphorous (BP), because of its attractive properties and applications, has grasped a lot of attention among contemporary 2D materials [82]. In addition to the suitable band gap, the material involves some exceptional properties like inplane anisotropy, enormous on–off ratio, larger light absorption as well as the higher carrier mobility (~6500 cm2 V−1 s−1 ) along with the greater biological compatibility. Moreover, the lateral or vertical heterostructures with atomically sharp interfaces might be generated providing the appropriate basis for investigating the atomicscale layer-to-layer interactions and apparatus having the unusual properties. These properties lead their utilization in broad range of applications such as ultrafast lasers [83], photodetector [57, 79, 84], modulators, sensors [85], optical switches [86] and biomedicines [85, 87]. The readers are referred to the literature which points to comprehensive studies on BP as a layered material shedding light on layeredness, its bonding, PES, VdWs forces and electronic properties [47, 48].

4.5 Arsenic The element “arsenic (As)”, in the pnictogen group, has been broadly regarded as an extremely toxic materials, yet it is crucial for the human life as it is required up to 25 μg/day [58, 88]. Moreover, As is mostly used in car industry in order to strengthen the lead component of car batteries. Furthermore, it is a famous n-type dopant widely used in semiconducting materials. Arsenic in its bulk form exists in various allotropic forms that exhibit the distinctive crystal configurations as well as the electrical characteristics [89]. As the thickness of the material decreases to realize its 2D limit, the unusual characteristics appeared when compared to its bulk counterpart. The theoretical studies have

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suggested that As would show peculiar charge transport properties as the thickness of the material is brought down to the single-layer limit. It causes transformation from indirect to direct band gap and semimetallic to semiconductor transition. Furthermore, the 2D As material having dissimilar crystal structure exhibits the significant disagreement in their response at the ambient air conditions.

4.5.1 Allotropic Forms and Structural Arrangements in Arsenic Arsenic exists in several allotropic forms such as black arsenic (b-As), gray arsenic (gAs) and yellow arsenic (y-As). The crystal structure for black, gray and yellow arsenic is orthorhombic, rhombohedral and tetrahedral molecular configurations respectively [90, 91]. Initially, the b-As was considered as the vitreous or amorphous arsenic, but with the further considerations of b-As, because of the orthorhombic crystal structure and resemblance with the BP, it was named as b-As. The g-As is another stable allotropic form and the crystal configuration is analogous to the graphite that possesses the layered honeycomb configuration. Each layer of the g-As comprised of the buckled hexagonal rings devised through the arsenic atoms [92, 93]. The monolayers of g-As stacks are piled up to form a bulk crystal structure in the ABC stacking fashion. The g-As, also termed as β-phase, exists in rhombohedral structure having a space group of R3m. The conventional gAs exhibits the semimetallic nature. The g-As is termed as the layered material that is some how different from the normal layered material due to the cross-layer orbitals that are responsible for the stronger inter-layer binding energy as shown in Fig. 4.7a. Consequently, this leads to the semimetallic nature as well as the greater conductivity [91]. Moreover, because of the comparatively weaker inter-layer interaction than inplane bonding, the g-As is generally brittle and hence arranged into a multilayered 2D material through the mechanical exfoliation and sonication methods. The b-As, a metastable phase Bmab, is analogous to the BP. It possesses the orthorhombic configuration with layered architect comprised of the puckered atomic layers put out together with VdW interactions as shown in Fig. 4.7b. The b-As exhibits the semiconducting characteristics with a direct band gap of nearly 0.3 eV [95, 96]. Moreover, the b-As exhibits the supreme anisotropy in the thermal as well as the electronic properties [95]. The b-As is the most frequent naturally existing material with mineral arsenolamprite [97]. However, the artificial fabrication of the b-As is not common. The artificial fabrication of the orthorhombic arsenic can be carried out in the presence of the impurities, whereas the pristine orthorhombic As is metastable. To overcome this, the fabrication of the kinetically controlled method is required [98]. Furthermore, it was estimated that b-As can be transformed into the g-As at a critical pressure of ~3.48 GPa and the structure reverts back into its original form (i.e. b-As) by the release of ~1–3 GPa pressure [95]. The b-As and g-As, both are reported

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Fig. 4.7 Crystal structure of a gray arsenic and b respective nanosheets, i.e. arsenene in top as well as side views. Reprinted with permission from Liu et al. [94]. Copyright (2016), Scientific Reports (Sci Rep)

layered materials and hence, the 2D sheets could be produced through the epitaxial growth or exfoliation. The yellow arsenic (y-As) occurs in the tetrahedral structure with unit cell consisting of 4 As atoms [99]. The y-As, reported as isomorphic structure having white phosphorous, is extremely unstable and slowly transfers into the g-As under normal conditions as shown in Fig. 4.7c. Contrary to the g-As or b-As, the y-As is an insulator and shows the waxy attributes. The y-As is highly reactive between the various allotropes and because of this, it is highly utilized in the chemical reaction associated with the arsenic source. Besides these, another form of As, known as amorphous arsenic exists and occur exist in several densities in the range of 4.3–5.2 cm−3 and could be generated that narrate the fact that this configuration/structure is more tunable as well as open as compared to the other crystalline allotropic forms [100]. Furthermore, more than one metastable forms of arsenic might occur based on the synthesis conditions [101].

4.5.2 Layered Versus Non-layered Arsenic The crystal structure of black arsenic was optimized using the DFT-based VASP module. The calculations were carried out using GGA-PBE-D3-BJ level of theory and the k-mesh of 5 × 5 × 5 was used with cutoff energy of 600 eV. The optimized crystal structure of the b-As is given in Fig. 4.8, where the bond lengths are also given in Å units. The in-plane As–As bond length is 2.5 Å, whereas the out-of-plane As–As bond length is 3.8 Å which points to anisotropy in structure that leads to layeredness of the material. Furthermore, the out-of-plane bond length gives an insight to the presence of weak interactions. Besides this, in order to do the bonding analysis, the pEDA-NOCV calculations were performed as given in Fig. 4.8b. The results revealed that the density is highly

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Fig. 4.8 a crystal structure of the b-As, where the metallic gray balls represent the arsenic atoms, b electron density clouds as computed by pEDA

localized to the layers and not delocalized within the planes, which means that the material exists in the form of layers. Therefore, the b-As is a layered material.

4.6 Antimony Antimony (Sb), another element of pnictogen group, appeared poisonous when ingested or inhalated which makes it a carcinogenic material [102]. Recently, the utilization of antimony trioxide has been reported as fire retardant within the plastics [103]. Moreover, the alloying of antimony with the other metals has been utilized as a strategy to enhance the tensile strength as well as the hardness.

4.6.1 Allotropes of Antimony The antimony exists in several allotropic forms just similar to the other group V elements and these allotropes are similar to the group V elements. Analogous to the arsenic and phosphorous, antimony also exists in orthorhombic (α-form) and rhombohedral (i.e. β-form) arsenic etc.

4.6.2 Prospects of 2D Antimony Among the allotropes, the rhombohedral phases are generally found in ABC stacking of antimony that offers better stability [104]. Furthermore, a transition from the

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semimetal to semiconductor takes place when the material is structurally downscaled from bulk to 2D. The theoretical investigations of 2D antimonene revealed high thermal conductivity [105], superior carrier mobility [106] and fascinating spintronic characteristics [107]. The 2D antimonene has grasped a lot of research attention because of the theoretically estimated broad band gap and high stability that is responsible for its fascinating applications in high-performance electronic devices [105, 108–113]. Because of the indirect band gap, the 2D antimonene would suffer from poor efficiency in light emission for applications in photovoltaic and optoelectronic devices [105, 108– 110]. Furthermore, it has been utilized in energy storage device, electrocatalysis and biological applications [114]. The 2D antimony oxide has been a promising semiconducting material with capability of tuning the direct band gap in addition to the higher carrier mobility [113]. To date, the few-layered antimony allotropes have been synthesized by using different approaches including vapor deposition, electrochemical exfoliation and plasma-aided procedures [115–118].

4.6.3 Properties of Monolayer Antimony-Antimonene The single layer of antimony, commonly known as antimonene, is found in two phases α and β which are semiconductors and found appropriate for applications in electronics [110]. The β antimonene exhibits isotropic mechanical characteristics [105]. The anisotropy in structure of a single layer has been investigated and reported in literature, whereas our study on the same will be briefly discussed here [105, 119]. The monolayers of antimony in α-Sb, β-Sb, γ -Sb and δ-Sb phases have been reported in literature [105, 120] out of which some important features are described here as shown in Fig. 4.9. The single layers of α-Sb and β-Sb own the non-planar configuration [121]. The optimized lattice constants for α-Sb are a = 4.74 Å and b = 4.36 Å, whereas the Sb–Sb bond length is 2.95 Å. Similarly, the lattice parameters for β-Sb are a = b = 4.07 Å, and bond length is 2.84 Å. Moreover, every Sb atom is analogous to the threefold bond in both cases, but because of the atomic arrangements within a α-Sb, there exist three different angles as shown in Fig. 4.9. Contrary to this, the β-Sb exists in hexagonal arrangements, because of which a similar dihedral angle of 91.47° is found. The α-Sb and β-Sb show the semiconducting nature with the respective values of band gap of 0.25 eV and 1.99 eV as calculated using the HSE06 level of theory. Furthermore, the α-Sb offers the direct band gap, while the βSb owns the indirect band gap nature. Analogous to this, the other allotropic forms, i.e. γ -Sb and δ-Sb in monolayer have been studied in detail, but these forms are comparatively unusable and hence not considered here [105]. In few-layer stacking, the inter-layer distances decrease that eventually transforms the structure into the 3D pseudolayered bulk crystals [110]. The armchair as well as zigzag nanoribbons of both structures/phases own the respective band gaps as extracted from the re-constructed edges and show the variety of electronic and magnetic properties based on the geometry of the edge as well as their gap.

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Fig. 4.9 Allotropic forms of antimony, where a α-Sb, b β-Sb, c γ -Sb and d δ-Sb [105]. Copyright (2015), American Chemical Society

4.7 Bismuth Bismuth (Bi), another element from group V, is an outstanding environment-friendly material, which is considered as a promising candidate for a large number of applications [122–125]. This material owes such attractive traits which make it fascinating materials for energy-related applications. Analogous to other elements from the similar group, bismuth exists in several allotropic forms, out of which the orthorhombic and rhombohedral crystal structures are famous [91, 126, 127]. Furthermore, similar to other pnictogen elements, Bi crystallizes as rhombohedral-layered structure that is the most stable allotropic form of the material. The atomic positions are moved in order to generate the hexagonal layers at varied distances, whereas, in the perfect rhombohedral structure, only one kind of the interstitial site is present same as present in simple cubic crystal structure [128]. Moreover, the shattered sequel of the layers give rise to the emergence of two kinds of the interstitial sites that are related with the crystallographic group, i.e. D3d . The dissimilarity among the rhombohedral BP, β-Sb, β-As and β-Bi arises from the interaction of the atomic orbitals among the independent double layers. The dissimilarity in the interatomic distance of out-of-plane and in-plane is large enough to enunciate the layered material owing the anisotropy in its physical characteristics [127].

4.7.1 Synthesis Techniques Because of the fact that bismuth is a metal in the bulk form, one may think that it may not exist as a layered material, yet there exists some evidence which proves that bismuth is a layered material. Similar to the other group V elements [129, 130], Bi due to the rhombohedral configuration possesses a highly brittle nature and could be pulverized with a great ease. Consequently, this could be exfoliated through the

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top-down methods, i.e. ultrasonication method or any other mechanical exfoliation method [127]. The shear exfoliation of the layered materials in the presence of liquid could be attained by utilizing the rotating blades mixers [131–133], i.e. the simple household kitchen blenders could be utilized, whenever the exfoliation is carried out in the presence of the aqueous surfactants [127]. The quality of the material fabricated concerning the exfoliation degrees is reported analogous to the sonication within the large-scale production of defect-free graphene [134]. The described method could be applied in several layered materials including the BN, molybdenum disulphide (MoS2 ) [135] and BP [136]. Besides these, the shear exfoliation of the materials has been utilized to attain the pnictogen elements, i.e. nanosheets of Sb, Bi and As [127]. By morphological and chemical characterizations, it has been revealed that the exfoliated materials illustrated the reduction within the thickness as well as the partial oxidation because of the greater surface area.

4.7.2 2D Bismuth Bismuth (Bi), the rearmost element within the pnictogen group, represents the bulk gap of ~800 meV [137, 138]. This arises due to the large atomic number (i.e. 83) of elemental Bi and hence intensifies the spin–orbit coupling (SOC) that permits the said material to be the potential candidate for the cryogenic-free quantum spin Hall material [139–141]. Furthermore, the 2D-Bi, also known as "bismuthene" presents the greater mobilities of charge carriers as well as the theoretically estimated electronic band gap of nearly 0.99 eV, enabling it to be the promising material for the utilization in the electronic applications [142–144]. Nevertheless, the multilayered 2D-Bi, as fabricated through the ice-bath sonication and liquid exfoliation, has been utilized in sodium-ion storage because of intercalation as well as alloying [145, 146]. Besides these, the large surface along with the enhanced electrochemical activity permits the 2D bismuth to occur as an effective electrocatalyst for the N2 fixation as well as for the reduction of CO2 that could empower a continual energy industry possessing the huge economic influence [147–150]. Besides the above-described primacy of the 2D bismuth sheets associated with energy applications, the better air stability as well as the ignorable toxicity is supreme properties for their usage in the practical applications [151]. In addition to this, Bi owes the properties regarding the response on the visible light and suitable band gap that leads the materials to be a photocatalyst [152, 153]. Moreover, the Bi-based photocatalyst represents the exceptional photocatalytic activity that is fundamentally associated with the polarizable Bi 6s2 lone pairs of electrons as well as the better migration and separation of charge carriers due to the well-dispersed bismuth material [154]. Furthermore, the Bi-based photocatalysts offer the band gap ranging between 0.3 and 3.6 eV [122] that leads to be the light absorption in ultraviolet and visible range. Because of the reasonable photocatalytic performance within the visible range, the Bi-based materials have been engineered into several kinds in order to stabilize the

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Bi3+ ions. One method is unitary structure, which provides rhombohedral Bi having the layered configuration with larger inter-layer spacing of ~3.10 Å that permits the insertion/intercalation of the cations. The other methods allow the formation of some other materials that include the bismuth oxide (Bi2 O3 ), bismuth selenides (Bi2 Se3 ), bismuth oxyhalide (e.g. BiOCl) [154], bismuth phosphate (BiPO4 ) and bismuth tungstate (Bi2 WO6 ) etc. The 2D bismuth could be synthesized using the top-down and bottom-up techniques, in which the former approach comprise of several techniques such as liquid exfoliation, aqueous shear exfoliation and hot-pressing method, whereas the latter approach includes the physical vapor deposition method, pulsed laser deposition method and wet chemical methods [137]. The orthorhombic and rhombohedral [155] structural phases, also known as αphase and β-phase, have equal binding energy values [137]. The orthorhombic crystal structure represents the puckered structure that is often known as pseudocubic 012 or A17 phase [156], while the rhomobohedral or β-phase shows the buckled structure, also known as distorted A7 structure [157]. For 2D-Bi, the Bi (110) and Bi (111) have shown the appropriate planes to study regarding the layered material for α-phase and β-phase, respectively [137]. Besides the above-described materials, there exists some materials that are known layered material, but these are indeed not layered materials. One such example is a silicon that is often referred as a layered material. The issue of layeredness in silicon is elaborated in the following section.

4.8 Layeredness in Silicon Silicon (Si), a group IV element, occurring as second most abundant element present in the earth crust, has rich oxygen content [158]. The pure silicon shows semiconducting properties due to which it is a crucial material in modern technology and hence broadly utilized in electronic devices. Silicon is brittle and hard crystalline solid owing the blue-gray metal luster and is tetravalent semiconductor as well as metalloid. The melting and boiling points of Si are 3265 °C and 1414 °C, respectively [159]. In general, silicon exists in amorphous and crystalline forms out of which crystalline Si is important for majority of applications. The most common crystal structure of Si is the cubic diamond structure with lattice parameter ~5.43 Å [160, 161] that is thermodynamically stable at room temperature and atmospheric pressure [158]. The tetrahedral bonding among the Si atoms leads to complicated energy landscape having quite a few hypothetical allotropes having minute difference in the energy from the ground state [162–164]. Several allotropic forms have been brought to light and reported under the conditions of high pressure that includes the two metastable phases, which can be restored at ambient conditions. Besides these, a vast variety of the crystal structures as well as bonding arrangements are entertained within the tetrahedral coordinated cubic (diamond)-like structure to the close packing of

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atoms at comparatively higher pressure [165]. More than ten allotropic forms owing the distinct crystal configurations are familiar and studied. The common electronic configuration of the silicon including the s and p-orbitals made it fascinating for the phase stability as well as the lattice dynamic characteristics. By an enhancement in pressure, the cubic Si changes to the tetragonal structure at ~12 GPa [166] that is converted to the primitive hexagonal structure at nearly 16 GPa. The theoretical studies revealed the occurrence of the average orthorhombic structure among 13– 16 GPa [167]. Furthermore, the hexagonal close packed structure [168, 169] has been seen at nearly 42 GPa that changes to the face centered cubic crystal structure at 78 GPa [170]. The above-described higher pressure structure is estimated to be the superconductive as well as metals [171, 172]. The silicon era comprised vast usage of silicon in diodes, transistors and other electronic devices that led the basics of the modern technology. Silicon is the cornerstone of the semiconductor technology as it owns the excellent properties such as comparatively economical, abundant, capability for doping of other elements as well as natural oxide passivation layers. The indirect band gap of ~1.7 eV is much smaller than majority of compound semiconductors which indicate that phonons assist in making the electronic transitions in the material. This restricts the utilization in modern high-efficiency applications like greater performance transistors [173], thinfilm photovoltaic and light emitting devices [174, 175]. Generally, the perfect photovoltaic applications need a direct band gap of nearly 1.3 eV that cannot be attained in the cubic phase; for this purpose, the orthorhombic Si24 has been synthesized which offers band gap of 1.3 eV. It offers fascinating properties such as carrier mobility as well as the promising light emission that make it suitable for the thin-film solar cells and optoelectronic applications [158].

4.8.1 Silicene—A Single Layer of Silicon The single layer of the silicon (Si) as well as germanium (Ge), analogous to the graphene, has been predicted by means of first-principles computations in 1994 by Shiraishi and Takeda [176, 177]. The single layer or 2D structure of Si was initially introduced as “silicene” in 2007 by the Guzman-Verri and Lew Yan Voon [178, 179]. Contrary to the graphene, wherever the sub-lattices A and B exist in the similar plane while in case of the silicene, the two sub-lattices are moved within the perpendicular direction to that atomic plane leading to the buckled geometry [176, 179] rather than a flat sheet. The lattice constant of the optimized crystal structure has been reported as 3.82 Å and in case of the bulk silicon, the out-of-plane atoms of Si contain the distance of 0.78 Å from (111) plane. The 2D honeycomb lattice of Si has been synthesized on the substrate of Ag (111) [180]. Silicon is an indirect semiconductor at room temperature with band gap of ~1.1 eV. Furthermore, the valleys observed are attributed to the quadratic dispersion [178]. However, for silicene in the absence of spin–orbit coupling, the band diagram showed the material to be the zero gap material at the Fermi energy. Moreover, the conduction

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band (CB) as well as the valence bands (VB) crosses the Fermi level, while owing the linear dispersions and hence is termed as Dirac cones, which exists at the K and K' points within the hexagonal Brillouin zone. These Dirac cones give rise to the formation of valleys within the Brillouin zone, and hence, the two degenerate bands at a given point initiated by those sub-lattices A and B from the structure of silicene. The inclusion of spin–orbit coupling introduces the small band gap of ~1.55 meV [181]. Contrary to graphene, the strong impact of spin–orbit coupling within silicene leads the noticeable spin Hall effect and other fascinating properties [181, 182]. Furthermore, the harmony of the silicene with the silicon-based technology derives this material attractive specifically for the device applications [180]. Silicene, being analogous to graphene, is a topological insulator in 2D that is contrary to the silicon that owns the band insulator characteristics [178, 183]. The topological insulator owns the band gap in bulk, yet it has gapless edge states, which permits the correlated charge as well as transport of spin. They could be differentiated from the band insulators as the charge transport is secured from the disorder because of the correlation with the spin and could be indicated through the distinct quantum number or the topological order [178]. Furthermore, the difference in structure in silicene from the graphene, in that buckled configuration, permits the arise of more topological phases. For instance, the electric field applied in vertical direction opens a band gap within the graphene, yet this is not analogous to graphene and could introduce the transition in the topological phase.

4.8.2 Layered Versus Non-layered Silicon The single layer of the silicon, that has been synthesized and theoretically predicted, is often reported as layered material. However, on the basis of our calculations using first principles, it is revealed that silicon is not a layered or VdW material. In order to perform the calculations, the hexagonal and cubic crystal structures of silicon were optimized as per computational parameters similar to the previously mentioned cases. The optimized structures are given in Fig. 4.10. The value of formation energy calculated for cubic and hexagonal structure was − 5.73 eV/atom and − 5.70 eV/atom respectively, which shows that cubic phase is more stable as compared to the hexagonal phase as in good agreement with literature [184, 185]. Furthermore, this formation energy gives the feasibility of existence in experimental technique, and there is very minute difference in energy in both phases, which means that the probability of variation in existence is very minute [178, 180]. The bond length observed was ~2.35 Å for the cubic crystal structure that indicates the presence of single-crystal material. However, for hexagonal crystal structure, the bond length computed was ~2.35–2.37 Å (along plane and bucking length). Moreover, the well-known fact is the presence of sp3 hybridization in both cases. Furthermore, because of the existence of silicon in single-crystal materials, there is no probability of formation of layers. Moreover, the density is expected to be localized to the atoms

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Fig. 4.10 Crystal structure (in bulk) of a cubic Si b, c hexagonal Si in top and side views, respectively

of silicon and the density plots are not given in this case. The study revealed that neither cubic nor hexagonal crystal structure of silicon is a layered or VdW material.

4.9 Stannous (Tin) Stannous (Sn) is another important element from group IV which is a promising material for variety of uses. Sn occurs mostly in two stable allotropic forms known as gray tin and white tin. The gray tin, also termed as α-Sn, possesses less-dense diamond cubic crystal structure, while the white tin or β-Sn owns the malleable tetragonal crystal structure at room temperature [186]. The α-Sn offers the topological Dirac semimetal nature and can be transfigured into the topological insulator phase or common semiconductor through the application of epitaxial strain [187, 188]. This illustrates the compression or tension, as a result of the substrate, might impact the electronic structure of that epitaxial films. Hence, to look for an appropriate substrate that could conserve the topological characteristics and a wide band gap freestanding sheet is of great importance for tin to be used in the recent semiconducting applications. For this purpose, several substrates have been utilized such as antimony telluride (Sb2 Te3 ) and bismuth telluride (Bi2 Te3 ) [187].

4.9.1 2D Stannous-Stanene The single atomic layer of stannous, also termed as stanene, owes the configuration similar to the graphene having the hexagonal lattice. The theoretical prediction revealed that stanene is comprised of the buckled hexagonal lattice owing the lattice constant of ~4.67 Å [189]. The comparatively large size of stannous atoms within the

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stanene sheets introduces the strong inner-core repulsion contrary to those graphene atoms because of smaller-sized carbon atoms. Therefore, the stanene offers the wavealike configuration, whereas the adjacent atoms would favor to have an out-of-plane direction having a mixture of sp3 as well as sp2 hybrid states. Furthermore, the bond length between Sn–Sn atoms in the material under study is ~2.69–2.83 Å [190, 191]. This longer bond lengths weakens the π–π overlap and hence forbids the formation of ideal honeycomb flat and planar structure rather leads to the formation of the buckled structure. This buckled structure would form the bonds of smaller energy through the movement of the neighboring atoms/sub-lattices within the out-of-plane orientation. Furthermore, the stanene owes a zero band gap in the absence of spin–orbit coupling (SOC), whereas the band gap of ~0.1 eV is introduced by the inclusion of SOC [191–193]. This zero band gap characteristic restricts the utilization of the stanene within the higher performance semiconducting-based devices like field-effect transistors. The stannous, having an atomic number of 50, offers the non-negligible SOC that makes this material the promising topological insulator [190], similar to the quantum spin Hall (QSH) state presented by Kane and Mele [183, 194]. The band gap as introduced by the inclusion of SOC at K as well as K' that is fundamental reason of the emergence of QSH states, which is much greater and expected to excel the thermal energy even considering the ambient conditions, i.e. room temperature. The resistance toward the deformation within the geometric crystal structure of comparatively heavy Sn atomic sheets by the application of the physical strain, stress, defects and adsorptions is of great importance [186]. The mechanical properties are analyzed by Young’s modulus, Poisson ratio and ultimate tensile strength (UTS). Because of the buckled structure, the anisotropic mechanical properties have been observed. The values of Young’s modulus as computed by quantum chemistry calculations of stanene are 26.684 Nm−1 , whereas the computed UTS as generated from the response of stress–strain is 3.635 and 4.903 Nm−1 along armchair and zigzag directions respectively. The above-described properties and prospects make this material a promising candidate for several applications specifically the topological insulators, several electronic and spintronic devices and utilization as Li- and Na-ion batteries [193, 195]. Furthermore, as discussed above, the low band gap restricts this material to be utilized in several applications specially those having the requirement of being semiconductor. For this purpose, the band gap can be tuned by various methods such as passivation of sheets, doping, adsorption that make it potential material for gas sensing [196–199].

4.9.2 Layered Versus Non-layered Stannous Just like the previous cases, the investigations regarding the layeredness of stannous (tin) were carried out. For this case, the cubic and tetragonal [200] phases were considered due to natural existence of material in the given crystal phases and the optimized structure is given below in Fig. 4.11. The computed values of formation

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Fig. 4.11 Optimized structure of a cubic and b tetragonal stannous in bulk periodicities

energy were − 4.12 eV/atom and − 4.18 eV/atom which means that tetragonal phase of the Sn is more stable as compared to the cubic phase. Furthermore, the structural parameters reveal that the material is a single crystalline in bulk periodicities but as the extended bond lengths can be observed in the structure as shown in Fig. 4.11. Hence, the calculations were performed for the 2D analogous of materials and the results revealed the non-layered structure of the material. This transition of sp2 into sp3 as well as of the increased bond lengths occurs during the fabrication and simulation of nanosheets (or 2D) of stannous [186]. Consequently, the π–π overlapping reduces by the increment of the bond length and as a result reduces the strength of bonding.

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Chapter 5

Transition Metal Dichalcogenides—An Important Class of Layered Materials

Abstract The layered solids exhibit dissimilar in-plane and out-of-plane atomic bonds which lead the to the formation of layers stacked through weak van der Waals (VdW) interactions. The structural arrangements in chalcogenides appear in the form of the layers in which metal atoms are sandwiched between chalcogen atoms in the form of closely packed configurations. This chapter deals with the importance of transition metal dichalcogenides (TMDs), synthesis routes, prospects of layeredness and applications. The layeredness in TMDs is investigated by the authors using density function theory (DFT) implemented Vienna ab-initio simulation package (VASP) and Amsterdam density functional (ADF-BAND) code. The well-known materials molybdenum disulfide (MoS2 ), molybdenum diselenide (MoSe2 ), molybdenum ditelluride (MoTe2 ), tungsten disulfide (WS2 ), tungsten diselenide (WSe2 ) and tungsten ditelluride (WTe2 ) are taken into account. The calculations were carried out in two phases for each material and results revealed that all the materials are layered materials with anisotropy in out-of-plane and in-plane bonding. The findings revealed that the TMDs have greater tendency to be layered materials and the VdW forces arise due to the p–d hybridization in the materials. Hence, in order to utilize the TMDs for a specific application, the layeredness of the materials should be taken into account.

The elemental layered materials were comprehensively discussed in the previous chapter by shedding light on the prospects of layeredness and their properties. This chapter is dedicated to significant family of layered materials i.e. transition metal dichalcogenides (TMDs), which are natural prototypes of layered or van der Waals (VdW) solids.

5.1 Why Chalcogenides? The elements sulfur (S), tellurium (Te), selenium (Se) and polonium (Po) are termed as chalcogen and the compounds comprising of these elements are known as chalcogenides [1]. The first element sulfur is non-metal, while tellurium and selenium are © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Majid and A. Jabeen, Layeredness in Materials, Engineering Materials, https://doi.org/10.1007/978-981-99-6299-0_5

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considered as the metalloid semiconductors. The chalcogenide group of compounds was firstly introduced by Wilhelm Blitz along with Werner Fische in 1932 [2]. The chalcogenides, a famous class of materials, have grabbed incredible attention because of their fascinating structural, magnetic, electronic as well as catalytic prospects. These materials, in general, go through the structural transformation from octahedral to rhombohedral upon switching [1]. The chalcogenides are usually synthesized in thin films and are used in photovoltaics for solar energy harvesting [3]. The chalcogenides have been grown by utilizing several synthesis techniques such as solvothermal or low-temperature hydrothermal approaches [4].

5.1.1 Importance of Transition Metals Dichalcogenides (TMDs) The TMDs are sulfides, selenides and tellurides, which can be termed as M-sulfides, M-selenides and M-tellurides respectively, where M being transition metal [2]. TMDs grabbed substantial attention within the recent years because of their utilization in catalytic activities, ion batteries, energy storage and production devices. The layered chalcogenides are regarded as the norm of the 2D inorganic materials, whose fundamental properties have been widely investigated. The layered chalcogenides own a crystal structure of MX2 and M2 X2 where X and M represent the atoms from chalcogen and transition metal elements respectively [5]. The structural arrangements in chalcogenides are the layers where metals are sandwiched among chalcogen atoms, i.e. X–M–X or X–M–M–X, while these atomic layers make the closely packed configurations. Moreover, these sandwiched units are separated from each other through the well-known VdW gap along the z-direction (crystallographic c-axis). The chemical saturation as well as the close packing of chalcogenides atoms establish the inner surfaces. Analogous to the elemental layered materials, the bonding within a section of sandwiched material is strong and is of covalent nature having the electrostatic contribution based on the ionic nature of the M–X bonds. The metals, within the structure, are arranged within the trigonal prismatic coordination for most covalent chalcogenides to deal with the covalent overlap, while the ionic compound presents the octahedral coordination upon minimizing the electrostatic repulsion [6]. The electronic forces present along the either VdW gap or hetero-interface having the VdW surfaces are because of the electronic states that are pointed normal to the layers, also called z-states [5, 7]. Besides the z-states, along with the pure x as well as y electronic states, the yz and xz are also significant in this regards for the various combinations of px and py states. A particular case in this regards includes the chalcogenides of Ga and In having the stoichiometry MX (i.e. M2 X2 ) that constitutes the single bond of metals–metals from group III elements [5]. The bonding analysis reveals that these sandwiched components are separated from each other by weak interactions referred as VdW interaction along c-axis. Besides this, the significant electronic interactions have been realized along the VdW gap as the band dispersion

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Fig. 5.1 General synthesis strategies, structure and applications for TMDs. Reprinted with permission from Wu et al. [8]. Copyright (2020), The Authors. InfoMat published by UESTC and John Wiley & Sons Australia, Ltd.

computed across the c-axis toward the VdW plane. The generalized trends can be visualized in Fig. 5.1.

5.2 Synthesis of TMDs The various approaches can be adopted for the preparation and fabrication of TMDs and their related composites that involve the electrospinning method, hot-plate method, solvothermal or hydrothermal method, one-pot heat up approaches along with various other strategies that can be shown in Fig. 5.1. A brief introduction to these approaches is given in the following.

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5.2.1 Hot-Plate Method An easy procedure, whereas a metal plate is heated at a specific temperature that undergoes oxidation reaction which leads to the growth of the metal oxides over the surfaces of hot plate [2]. In this method, the metal behaves as substrate as well as source for the material. The mechanism followed by the TMDs is the temperature of the growth points, which is kept at lower edge. In addition to this, the formation of vapors does not correspond to the particular count [9]. In order to obtain the layered TMDs nanostructures, the parameters such as temperature, time, molar ratios and capping agents having the appropriate choice of metallic precursor are important [10]. The hot-plate approach is said to be the most promising chemically preparation method while considering the size and shape of monocrystalline nanostructure of TMDs.

5.2.2 Hydro- or Solvothermal Method The hydrothermal method is a widespread approach utilized for the synthesis of the nanoparticles [2, 11]. The procedure takes place within a chemically isolated autoclave that refers toward the growth of the crystals under elevated temperature as well as pressure. The crystalline nanomaterials could be generated at comparatively lower temperature through this process. The parameters such as organic materials, pH, time, pressure, concentration, temperature as well as reducing agent have a great impact on synthesis [12]. The solvothermal procedure is another approach, which takes place at temperature greater than boiling point, on the condition that pressure must be greater than 1 bar [2]. The solvent medium utilized could be either water or any organic or inorganic solvent or any alcohol solvent. The current research also involves change to hydrothermalbased fabrication in place of solvothermal method [13]. The schematic representation is given in Fig. 5.2 b. The fabrication of the TMDs nanoparticles carried out through the hydrothermal method, for instance, cobalt–nickel selenide dispersed on the nanofilms of graphene has been obtained within a nanohybrid in order to utilize as a counter electrode for the dye sensitized solar cells (DSSC) [14]. The further details of the procedure have been well elaborated in the literature [15, 16].

5.2.3 One-Pot Method This approach is favorable for controllable fabrication and is greatly utilized for large-scale production [2]. This approach assists the chemical reactions as well as the progression of nanosheets, whereas the molecular precursors are placed within

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Fig. 5.2 Typical fabrication methods for the fabrication of MoS2 , a represents the electrochemical exfoliation by lithiation procedure, b shows the nanoparticle synthesis through solvothermal method, and c illustrates the fabrication of MoS2 thin layers through the sulfurization of MoO3 . Reprinted with permission from Wu et al. [8]. Copyright (2018), Institution of Chemical Engineers. Published by Elsevier B.V.

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a single reactor at relatively low temperature, i.e. < 120 °C. Furthermore, the onepot technique described for the elemental chalcogenide precursor as well as metal chloride, for instance, WS2 along with ReS2 heterojunction fabrication. It has been employed with hydrogen activator that behaves as a switching procedure for the growth of the WS2 while decreasing the ReS2 growth. The process involves the usage of rhenium as well as tungsten as precursors put together in a crucible. The heterojunction WS2 -ReS2 has been grown at ~850 °C placed on substrate, whereas the successive inception of Ar as well as Ar-H2 gas has been made possible for the growth of the suitable heterojunction. The results revealed the marvelous crystalline property, no defects, atomic sharpness of the heterophase as well as extreme clean characteristics. Moreover, the other chalcogenides can be produced using this technique such as Cu4 SnS4 [17, 18].

5.2.4 Electrospinning The electrospinning is considered as the versatile fabrication technique, which could be implemented for synthesis of the TMDs or their heterostructures. By using this method, the desired voltage (mostly high) is applied to flow the current toward the syringe tip which has been already filled with the desired viscous precursors [2, 19]. Besides the above-described synthesis techniques, the microwave-aided approaches or template-aided approach permits to control the several factors such as size as well as shape exhibiting the fabrication and inscribing the nucleation comparative to the tradition approaches for preparation and hence decreasing time [2, 20]. Furthermore, the chemical vapor deposition (CVD) approach and the exfoliation techniques are widely used for the synthesis and fabrication of nanoparticles of the TMDs [11] as shown in Fig. 5.1. Because of the several combinations of transition metals (TM) and chalcogen atoms, beyond 40 different TMDs owing the layered architecture has been studied [21, 22]. These TMDs showed different chemical and physical characteristics. The electronic characteristics of the bulk TMDs could vary from insulator-semiconductorsemimetals-superconductor on the basis of behavior of d-electrons of transition metals. The weak VdW interaction among the inter-layers makes possibility to the exfoliation or cleavage of bulk TMDs into multilayer or single layer. The details of some representative TMDs are described in the following. Now, considering the name of TMDs, one may think that all of the transition metals atoms may contribute in the formation of TMDs. But according to literature, not all the TMs are involved in formation of TMDs. To give insight over the phenomenon involved in the emergence of TMDs based on different TMs, the periodic table is given in Fig. 5.3, where the highlighted TM and chalcogen atoms represent the possibility of the formation of TMDs, out of which some are going to discuss briefly similar to the elemental materials discussed in previous chapter.

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Fig. 5.3 a Represents the periodic table representing the possible combinations for the formation of TMDs, where b represents the stable 2H and 1T phases of representative TMDs, whereas blue- and yellow-colored balls exhibit the TM and chalcogen elements respectively. Reprinted with permission from Wu et al. [8]. Copyright (2021), The Authors. InfoMat published by UESTC and John Wiley & Sons Australia, Ltd.

5.3 MoS2 Molybdenum disulfide (MoS2 ), one of the widely investigated TMDs, is the most promising candidate for a number of application such as in optoelectronic [23, 24], photocatalysis [24] and hydrogen generation [25]. The formula unit of MoS2 contains two atoms of sulfur and one atom of molybdenum [26, 27]. The crystal structure of the bulk MoS2 comprised the vertical arrangement of the layers of MoS2 attached with each other by weak VdW forces. The physical, electronic and chemical characteristics of the material are of great interest and found potential candidate in order to replace the several already-utilized semiconductor and graphene-based devices [26]. Based on the coordination nature as well as the stacking orders of MoS6 polyhedra either octahedral or trigonal prisms, bulk MoS2 owns the distinctive crystal phases [21]. The phases involve polytypes 3R, 1T as well as 2H, where the letters R, T and H exhibit the structural symmetry presenting the rhombohedral, trigonal and hexagonal phases respectively [10]. The Mo–S coordination within the 1T phase is octahedral, whereas the coordination is trigonal prismatic within

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the 3R and 2H. These phases be a part of distinctive point group, i.e. D6d , D6h and C3v for the 1T, 2H and 3R respectively as shown in Fig. 5.4. Furthermore, the naturally abundant and thermodynamically stable phase among above-described phases is 2H-MoS2 , for example, molybdenite. Moreover, the 3R and 1T phases are metastable phases that exist in synthetic MoS2. The bulk 1T phase has been initially proposed in 1991 [28], where the octahedral coordination within 1T having the distorted layered configuration demonstrating the√connection among the unit cells of 2H and 1T-MoS2 , i.e. c1T = 0.5 c2H and a1T = 3a2H . Besides these, the 1T phase has lattice parameters a = b = 3.190 Å and c = 5.945 Å having a space group P3m1. The independent S–Mo–S components are comprised of MoS6 octahedra sharing edges, avoiding the clustering of Mo–Mo. Moreover, the 2H and 3R are comprised of the p63 /mmc and R3m space group respectively, whereas the trigonal prismatic Mo–S coordination symmetry appears for both 2H and 3R. The fabricated MoS2 represents a 3R configuration owing the rhombohedral symmetry having the three layers/unit cell and is tremendously unstable [29]. The structure could reorganize their orientation into 2H-polytypes upon heating treatment. Whereas in the 3R and 2H-MoS2 structures, the molybdenum hexagonal arrays are sandwiched among the sulfur layers [30]. The 1T crystal configuration possesses the stacking order of ABC and is created due to the disorientation of the sulfur layers within the MoS2 [31]. Furthermore, 1T metallic phase refers the symmetrical

Fig. 5.4 Crystal structure of IT, 2H and 3R phases of MoS2 . Reprinted with permission from Samy et al. [26]. Copyrights (2021)

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Mo–Mo bonds and offers the trigonal symmetry. The electrical conductivity of these materials is based on the specific phase i.e. specific crystal structure. The 1T phase offers more exposed active sites and hence increases the electrical conductivity [32].

5.3.1 2D MoS2 The 2D MoS2 could be synthesized by several approaches like mechanical as well as chemical exfoliation technique, CVD approach, atomic layer deposition and pulsed laser deposition. The indirect band gap of ~1.2–1.3 eV for bulk MoS2 , while the direct band gap of ~1.8–1.9 eV has been reported for single layer of MoS2 [29, 33, 34]. The absorption spectra of 2D MoS2 lie in the visible range of the electromagnetic spectra that unlocks the doors for a variety of applications. The materials based on the MoS2 have been considered as promising candidate for several applications such as disinfection [35], energy storage [36], contamination degradation [37] and hydrogen generation [38]. Currently, MoS2 has been considered as photocatalysts for several classes of applications. The direct band gap of ~1.8 eV of the thin films of MoS2 is of much attention contrary to the zero band gap graphene, when application is taken into account. Furthermore, the thin films of MoS2 do not possess the dangling bonds and offer greater carrier mobility. This material is considered as the perfect candidate for the thin-film transistors and its synthesis is not complicated that leads to the large scale and economical production [39, 40]. Nonetheless, the electronegativity difference between Mo (2.16) and S (2.58) is 0.42 which refers to the presence of the covalent bonds in between Mo–S (in-plane direction) and weak VdW bonding in between the layers that make it favorable for the gas sensing.

5.3.2 Layered Versus Non-layered MoS2 The feasibility of the material to whether exist in the form of layered materials or non-layered structure will be discussed on the basis of theoretical calculations in this section. The computation was carried out using density functional theory (DFT) implanted in Vienna ab-initio simulation package (VASP), while the reported figures are drawn using graphical user interface (GUI) based Amsterdam density functional (ADF-BAND) (2023.104) module. The computation was done using the GGA-PBED3-BJ along with plane wave basis sets with 720 eV cutoff energy and the K-mesh of 15 × 15 × 9. Here, for the case of MoS2 , two phases are considered, i.e. 2H and 1T with respective crystal structures of hexagonal and trigonal and the optimized structures are visualized in Fig. 5.5. The results revealed that the 2H and 1T phases are energetically favorable with the calculated values of formation energy which are − 1.217 eV/atoms and − 0.96 for 2H and 1T phase respectively. Hence, the 2H phase is more energetically feasible

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Fig. 5.5 Optimized structure of MoS2 where a, b represent the side and top views of 2H-MoS2 , while c, d represent the side and top views of 1T-MoS2

as described in literature. Moreover, as we can see from side view, that the both phases exist in the form of atomic layers that are arranged in a suitable distance. The computed values of intra-layer bond length are 2.41 Å and 2.43 Å for 2H and 1T phases, respectively, while the inter-layer distance is 4.01 Å and 3.61 Å. The findings indicate the strong in-plane bonding in addition to the presence of weak VdW forces in out-of-plane directions. Moreover, the inter-layer distance showed that the forces in the 1T phase are somehow stronger as compared to the 2H phases which would have impact on the exfoliation of the layers. Furthermore, this discrimination in the bond lengths shows the anisotropy in bonding and hence showing the primary features of layered materials. Furthermore, the charge will be localized to the inplane directions, which restricts the presence of primary bonding in the out-of-plane vicinity. The results point to existence of MoS2 as layered materials in form of the phases 2H-MoS2 as well as 1T-MoS2 .

5.4 WS2 The tungsten disulfide WS2 , another member from TMDs class, owns the sandwichlike configuration, whereas every sandwich is made up of three atomic layers, the tungsten atomic layer is sandwiched in between the two layers of sulfur atoms as S– W–S [41] as given in Fig. 5.6a. The thickness of every layer is nearly 0.6–0.7 nm. The atoms present within every slab or film or sheet of the structure are associated with each other by the ionic bonds owing major contribution of covalent bonding [42]. This is due to the electronegativity difference of 0.22 between W (2.36) and S (2.58) which refers to mixed ionic and covalent character. Furthermore, these sandwiched

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layers are held together through weak VdW interactions. This separation of 0.65 nm is sufficient enough within the 2D materials that gives greater room for the insertion as well as extraction of guest elements [43]. On the basis of crystal structure, the materials may either have space group of P63 / mmc owing the lattice constants of a = 0.31 nm and c = 1.23 nm or the space group of R3m having the lattice constants of a = 0.31 nm and c = 1.84 nm. Moreover, depending on the stacking sequence, the WS2 material might show the 3D crystal structure. The 3R-WS2 has the stacking of three atomic layers within the rhombohedral lattice structure, the 2H-WS2 owes the two layers stacked within the hexagonal crystal structure and 1T-WS2 has the only one layer stacked within the trigonal lattice configuration [10, 44, 45] as shown in Fig. 5.6b. The 3R-WS2 be a part of R3m space group while 2H-WS2 be a part of P63 /mmc space group. Furthermore, one comparatively thermally unstable phase 1T' with monoclinic crystal structure exists. The 1T' -WS2 offers the C2/m space group having lattice constants a = 12.848 Å, b = 3.2178 Å and c = 5.693 Å [46]. One atom of tungsten is centered within the unit cell having the six atoms of sulfur engaging the edges within the crystal structure of 1T-WS2 . The crystal exhibits the metallic phases of WS2 owing the conductivity of ~105 times greater as compared to the conductivity of 2H phase of same material, which makes the former better possibility for the utilization in the electrochemical applications. Furthermore, the 2H-WS2 shows the semiconducting phase of WS2 owing a hexagonal polytype crystal structure, whereas the tungsten atoms are present at center, while the sulfur atoms share the trigonal prism. Within this crystal structure, the 2nd layer is revolved around the z-axis through the angle of 60° w.r.t the 1st layer. The crystal configuration represents the natural stability with the semiconductor prospects and properties. The 3rd phase, i.e. 3R-WS2 , there exists the trigonal prism within the adjacent layers that lie in the parallel arrangement with each other, whereas every 4th layer observes the 1st layer. Hence, all the layers within this structure owe the similar direction, yet a bit moved w.r.t one another. This particular structure owes the semiconducting activity

Fig. 5.6 Crystal structure of WS2 where a represents the layeredness and b exhibits the different phases, i.e. 2H, 3R and 1T crystal structure of WS2 crystal structure. Reprinted with permission from Thiehmed et al. [41]. Copyright (2021)

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having a lack of inversion symmetry that makes it appropriate choice for various fields such as optoelectronic devices and in the field of spin valley physics [47, 48].

5.4.1 Synthesis of WS2 Monolayer In general, the synthesis of the single layers of TMDs could be obtained via exfoliation, substrate growth as well as the colloidal fabrication [49]. The exfoliation technique could be either purely physical or chemically aided. It could be purely chemical when intercalation method is utilized [50, 51]. The exfoliation methods permit the fabrications of the huge quantities of the single layers, specifically from the chemical exfoliation method yet normally gives rise to the poly-dispersed distribution of flakes without controlling the shape, nature or size of their edges. However, the substrate growth approach generates the large single layers having the greater crystallinity and a great control on their edges as well as shapes [52]. This approach is restricted as the amount of the single layers produced is limited. Lastly, the colloidal chemical fabrication approach could be capable of the generation of huge batches of TMDs single layers owing the better crystallinity, single dispersion as well as the control on the edges. Nonetheless, this approach is a bit underdeveloped in comparison with the two other synthesis approaches and only few examples are known [53–55].

5.4.2 2D-WS2 WS2 is of great interest because of its electronic band gap, which transits from indirect band gap of ~1.4 eV to direct band gap of ~2 eV, as the downscaling from bulk to single layer occurs [49, 56]. The single layer of WS2 finds its implementation in several fields like field-effect transistors (FETs) [57], photocatalysis, fluorescent emitters [58] and photovoltaics [59].

5.4.2.1

Electrical Conductivity in Bulk and 2D WS2

In the WS2 , being promising material in several energy conversion fields, much efforts have been put forward in order to realize and increase the electrical properties like conductivity (ρ), concentration of charge carriers (p), electrical mobility (μ) etc. By theoretical investigations [60], WS2 owes the greatest mobility among the TMDs class, because of its decreased effective masses. The early investigation disclosed that WS2 in its bulk periodicities shows the electrical parameter as μ = 30 cm2 V−1 s−1 , ρ = 3.37 cm and p = 7 × 1016 cm−3 [61]. The current studies revealed that by decreasing the number of layers of said materials up to monolayers or bilayers could enhance the electronic mobility [57]. The experimental work carried on monolayer

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as well as bilayer of WS2 -based FET showed the electrical mobility of up to 50 cm2 / VS at room temperature. Similarly, the carrier concentration of nanotubes of WS2 exhibited the greater values than the bulk as well as sheets of ~3.0 × 1017 to 1.6 × 1018 cm−3 respectively [62].

5.4.3 Layered Versus Non-layered WS2 Here, the existence of crystal structures of WS2 in two phases, i.e. 2H and 1T having the crystal structures of hexagonal and trigonal, is computed using the DFT implemented VASP code, while the diagrams are drawn using the ADF-BAND module. The computational details are similar as that described previously for the MoS2 and used for upcoming all the cases. The optimized structure in side and top views is shown in Fig. 5.7, where the 2H phase exists in the AB stacking, while the 1T phase occurs in perfect AA stacking. Both phases are energetically favorable as the formation energy computed is − 0.896 eV/atom and − 0.895 eV/atoms for hexagonal and trigonal phases, respectively. Furthermore, both phases occur in the form of atomic layers that are separated with each other by a gap known as VdW gap or inter-layer distance. The bonding analysis showed that anisotropy in bonding exists as the inplane bond length observed was 2.41 Å for both cases, while the out-of-plane bond length (inter-layer distance) is 4.92 Å and 3.82 Å for 2H and 1T, respectively. Here, again the inter-layer distance is less for the 1T phase than 2H phase which shows that the VdW forces are stronger in the 1T phase in comparison with 2H, which has direct influence over the experimental exfoliation. Besides these, the charge is localized to the atomic planes, hence the absence of stronger bonding in the vicinity of out-of-plane directions. Hence, it is concluded that WS2 is a layered material in the both phases 2H-WS2 and 1T-WS2 .

Fig. 5.7 Optimized structure of WS2 where a, c represent the side view of 2H- and 1T-WS2 , while b, d represent the top view of 2H and 1T-WS2 , respectively

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5.5 MoSe2 Molybdenum diselenide (MoSe2 ), an interesting TMDs, has grasped a lot of attention for applications in optoelectronic, electrochemical and photocatalytic fields [63]. Similar to other TMDs, the MoSe2 also occurs in three crystal structures named as 2H, 3R and 1T crystal phases as illustrated in detail earlier. MoSe2 exists in earth’s crust as a deficient mineral drysdallite [64]. The 2H-MoSe2 having the space group of hP6 owns the cell parameters of a = 3.28 Å and c = 12.91 Å. The electronic mobility of 2D MoSe2 is greater as compared to 2D MoS2 . Furthermore, the bond lengths of Mo–Se and Se–Se atoms are 2.52 Å and 3.29 Å which have been observed that make it potential candidate for several applications. Furthermore, the MoSe2 is an excellent material that offers more electrical conductivity as compared to the MoS2 .

5.5.1 2D-MoSe2 The single layers based on the MoSe2 are thicker as compared to MoS2 that is attributed towards the large atomic radius of Se atoms [65]. The bilayer of MoSe2 shows the direct band gap that transits to the indirect band gap by the increment in the number of layers [10]. Moreover, the said material has been observed as non-photothermal agent as placed in the near-infrared (NIR) laser light [66]. After implementing the photothermal experiments, the obtained single layers of said material are utilized as biosensor, in order to indicate and sense the volatile organic compound (VOCs) within the lung cancer, specifically whenever the aluminium (Al) is inserted in MoSe2 (i.e. doping of Al within the MoSe2 ) as illustrated in the literature [67]. Furthermore, the MoSe2 materials could be utilized within the switchable transistor and photodetector. Moreover, the said material is considered as an exotic material as it could absorb the gaseous molecules over its surfaces that aid during the charge transfer procedure. Because of these properties, the MoSe2 surfaces are considered as the novel gas sensors for the NO2 detection at room temperature [68], similar to the monolayer MoSe2 on the basis of NH3 which is utilized as the gas sensors [69]. Currently, the N-doped carbon at the basic MoSe2 nano-architects showed excellent storage of lithium [70]. The existence of covalent bonds in between the layers generates the conventional MoSe2 structure having the single layer of Mo atomic layer sandwiched in between the two atomic layers of selenium atoms [71]. The modification in the crystal structure of MoSe2 is possible by changing either the inter-layer spacing or stacking sequence. On the basis of the crystal structure, distinct polymorphs could be generated that are previously described in this chapter. However, these may not be stable and stability of these materials should be considered, before utilizing in a specific application. The fascinating electronic properties of TMDs make it excellent candidate for the catalytic properties. The MoS2 had been broadly studied as an effectual hydrogen evaluation reaction (HER) catalyst. Nevertheless, the experimental investigations

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reveal the MoSe2 to be more recommended for said application because of having metallic nature, lower band gap as well as smaller Gibbs free energy [72–75]. The catalytic performance of the MoSe2 is strongly based on the edge sites as well as the morphology. Besides these, the lower band gap as well as the capability to behave as the electronic exporter within the bi-catalytic systems makes it a favorable cocatalyst for the water photocatalysis [74, 76]. However, the said material suffers some downsides such as poor conductive comparable to the noble metal catalysis along with the aggregation of MoSe2 through synthesis is driving the scientists to instigate the novel strategies for improvement within the HER activity of the MoSe2 [77]. Besides these, the said material i.e. MoSe2 showed greater electrical conductivity as compared to the MoS2 because of the more metallic nature of selenium atoms of ~1 × 10–3 S/m as compared to the sulfur atoms with ~5 × 10–28 S/m [78]. Furthermore, the 2H phase showed smaller electrical conductivity in comparison with the 1T phase, yet the 2H phase is considered as stable, while the 1T structure is comparatively thermodynamically unstable in addition to the fact that it could be transformed to the 2H crystal structure [79, 80].

5.5.2 Layered Versus Non-layered MoSe2 MoSe2 existence as a layered or non-layered material is investigated using theoretical framework via DFT implemented VASP, whereas the reported diagrams were visualized using the ADF-BAND code. The computational details are in correspondence with the previous sections, i.e. in case of MoS2 or WS2 . For the MoSe2 , the two cases are considered, i.e. 2H and 1T phases having the hexagonal as well as trigonal crystal structure, respectively. The K-mesh used was 19 × 19 × 5 for both of the cases. The optimized structures of 2H along with 1T phase are given in Fig. 5.8. By seeing the side-wise view, it is understood that both of the phases exist as layered materials with the presence of strong in-plane bonding while absence of strong bonding in outof-plane direction. This is validated by the bond distance analysis where the in-plane bond length (2.54 Å for both cases) is much smaller than out-of-plane bond distance (5.62 Å and 4.01 Å for 2H and 1T, respectively). Hence, anisotropy in bonding exists. Further, just as previous cases, the inter-layer distance of trigonal structure is smaller than the 2H phase; hence, the layers from 1T crystal configuration are more strongly bonded with each other. Moreover, the charge is localized to the atomic planes and hence confirms the absence of strong forces in between the layers. The energy analysis provides the insights to the stability of the layered materials. Out of two considered phases of MoSe2 phases, the 2H crystal structure is energetically comparable to 1T phase as the formation energy is − 0.79 eV/atoms and − 0.79 eV/atoms for 2H and 1T phases respectively.

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Fig. 5.8 Optimized crystal structures of MoSe2 where a, b represent the side as well as top views of 2H-MoSe2 , while c, d exhibits the side and top views of 1T-MoSe2

5.6 WSe2 Tungsten diselenides (WSe2 ) has grasped considerable attention because of its applications in FETs as well as photodetectors etc. [81–85]. The crystal lattice structure owns the representative TMDs having the W atoms confined within the trigonal prismatic coordination sphere surrounded with selenium (Se) atoms. Similar to other TMDs, the WSe2 exists in several polymorphs such as 2H, 1T and 1T' phases exhibiting the hexagonal, trigonal and monoclinic crystal structures respectively [86]. The 2H-WSe2 phase is similar to 2H-MoS2 having the space group of P63 / mmc, where the tungsten atoms are organized within the 2(c): ± (1/3, 2/3, ¼), while the chalcogen elements in 4(f): ± (1/3, 2/3, z; 1/3, 2/3, ½-z) [87]. Contrary to the thermodynamically stable 2H-TMDs that represents the semiconducting characteristics, the most of the 1T' as well as 1T phases of TMDs are mostly semimetallic and thus exhibit outstanding performance in superconductivity, optoelectronic, energy storage as well as catalysis [46]. Although, the 1T' phase of WSe2 exists, but similar to other TMDs, this phase is thermally unstable as compared to other phases of same materials. The key attributes of WSe2 arise because of the electronic structures [85]. The first remarkable aspect of WSe2 is the spin–orbit coupling (SOC) that is more intensified in the material than other TMDs [88, 89]. For example, the splitting of valence band maxima (VBM) is 0.15 eV for MoS2 that is much smaller as compared to 0.46 eV for WSe2 [89]. Because of this fact, the WSe2 is a potential candidate for the spintronic applications. Furthermore, the doping of element from group 3, i.e. p-type doping in this material induces interesting properties due to high positions of conduction band minima (CBM) as well as VBM [90] than the typical TMDs like MoS2 , where n-type doping is preferential [91]. However, this is a common estimate of the tendency of

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materials, since the doping of the MoS2 with elements of group V would give rise to the p-type doping [92]. Similarly, the n-type WSe2 could also be realized [93].

5.6.1 2D-WSe2 The intriguing feature of the WSe2 arises in its 2D counterpart which exhibits important applications [85]. The single layer of the WSe2 is deposited over the surfaces of gold (Au) through controlling the growth temperature as well as partial pressure of the hydrogen amid the fabrication by the process of CVD [94]. The former-described parameter controls the growth rate, whereas the latter one would control the quantity of tungsten that is supplied through WO3 reductions. The Au surface supports the growth of uniform thickness films of the material. Further, as the structure of the WSe2 is held through the weak forces in c-axis, each layer could be exfoliated [85]. This is the key feature of the implementation of WSe2 , where the reaction does not occur in the solid state in the bulk counterpart. The simplest approach for the exfoliation of the layers of said material is scotchtape approach [95–97], yet this method cannot be used commercially for the growth of layers. The most common exfoliation technique used is liquid-phase exfoliation, the details of which are described in Chap. 2. WSe2 finds its promising applications in several fields like anode in the Li-ion batteries, supercapacitors, sensors and biosensors, electrocatalysis and photocatalysis [85].

5.6.2 Layered Versus Non-layered WSe2 This section describes the calculations carried out on WSe2 structure in 2H and 1T phases as computed using DFT implemented VASP, whereas the relaxed structures were visualized by GUI-based ADF-BAND program. The computational parameters were similar as per used in previous sections and the optimized structures were given in Fig. 5.9, where a and c parts showed the side views and b and d parts represent the top views. Both the phases are layered materials with the presence of anisotropy in bonding. The inter-layer distance is 5.19 Å and 3.59 Å for 2H as well as 1T phases respectively, showing that the 2H phase is weakly bonded as compared to the 1T phases. Further, the energy analysis shows that the hexagonal phase is slightly more energetically stable than trigonal phase as the formation energy is − 0.39 eV/atom and − 0.35 eV/atom, respectively.

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Fig. 5.9 Optimized crystal phases of WSe2 where a, c represent the side view of 2H- and 1T-WSe2 , while b, d represent the top view of 2H- and 1T-WSe2 , respectively

5.7 MoTe2 Molybdenum ditelluride (MoTe2 ), an important material from the class of TMDs, crystallizes in two phases 2H and 1T' crystal, which appears in the form of hexagonal and monoclinic structures respectively [64, 98], as can be visualized in Fig. 5.10. The 2H phase be a part of space group of Hp6 , p63 /mmc having the unit cell parameters of a = 3.51 Å and c = 13.94 Å [99]. Furthermore, the 1T phase be a part of mP12, p22 /m space group having the unit cell parameters of a = 6.33 Å, b = 3.46 Å and c = 13.86 Å. The unit cell size transforms by temperature because of the thermal expansion since the energy gap in between such crystal structures is very minute, i.e. ~40 meV [99, 100]. Moreover, it has been observed that the 2H crystal structure is relatively less stable, i.e. up to temperature 815 °C (1088 K) after which the material transforms to the comparatively more stable phases of 1T' that is stable at temperature higher than 900 °C (1194 K) [101]. Due to the weak bonding between the atoms of Mo and Te, the growth of material under study in a pure phase is quite challenging that restricts its further investigations.

5.7.1 2D-MoTe2 Similar to the other TMDs, the bulk 2H-MoTe2 owns an indirect band gap of ~0.93 eV, while the monolayer of similar material offers the direct band gap of ~1.1 eV [64, 100]. The value obtained for the single layer is much close to that of Si and therefore finds several applications. Since the band gap of said material occurs in the infrared region, it could be utilized in an infrared detector. Furthermore, it has been claimed that the MoTe2 could show the greater phonon mobility as compared to the MoS2 at ambient temperature [102].

5.7 MoTe2

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Fig. 5.10 Crystal structures of different phases of MoTe2 , where a, b represent the monoclinic (1T' phase) and hexagonal (2H phase) crystal structures respectively. Reprinted with permission from Phalswal et al. [64]. Copyright (2022), The Royal Society of Chemistry

5.7.2 Layered Versus Non-layered MoTe2 Contrary to the previous cases, here the 2H and 1T' phases of MoTe2 with the crystal structures in respective hexagonal and monoclinic phases are considered. The 1T' phase is somehow distorted in comparison with 2H phase as per literature described in Sect. 5.7.1. The computational details for the calculations are similar to those of given in the previous sections (Fig. 5.11). The formation energy analysis revealed the fact that the 2H phase is less stable than 1T' phase as the formation energy computed is − 1.22 eV/atom and − 2.00 eV/ atom respectively. The bonding analysis and the results revealed the anisotropy in structures of both 2H an 1T' phases and hence, 2H and 1T' phases of MoTe2 are layered.

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Fig. 5.11 Optimized structure of MoTe2 where a, b represent the side and top views of 2H-MoTe2 , while c, d represent the side and top views of 1T' -MoTe2

5.8 WTe2 Tungsten ditelluride (WTe2 ) is a compound of the heaviest elements among the TMDs class which has typical features like the other TMDs [85, 103, 104]. The WTe2 exhibits some peculiarities due to the structural distortions which is due to the heavy tungsten atoms from the zigzag chains along the crystallographic axis generating the quasi-one-dimensional arrangement. Further, the metallic behavior of typical TMDs is pronounced within the WTe2 that could be accounted as the semimetal having the suppressed density of states at the Fermi level. This is because of the overlap in between the CB and VB, and hence, no band gap is left. Indeed, this is atypical characteristics of the WTe2 within the family of the 2D TMDs, since the metallic phase has appeared as more stable than the semiconducting phase [105, 106]. Magnetoresistance (MR) refers to the change in the electrical resistance of a material by the application of magnetic field that is a fruitful phenomenon which has been exploited in spintronic. The fundamental materials used in the past were the TM of the 1st row, but recently TMDs are considered as a promising materials, out of which WTe2 is a fascinating material. This material exhibits greater uniaxial positive magnetoresistance that did not saturate within the magnetic field until 60 T [107, 108]. This shows the suitable compensation of the holes as well as electrons. Moreover, the studies revealed that electrons are not strictly 2D, and hence, to balance the electronic as well as hole states, at least three Te–W–Te layers are required [109]. Besides these, WTe2 are used in various applications such as energy conversion as well as storage although this is not economical for large-scale development [85]. The electrocatalytic activity of the bulk WTe2 is considerably better as compared to its MoTe2 counterpart, yet the exfoliation reserves the supremacy [110]. The exfoliation approaches the results that work well with MoTe2 do not go well with the WTe2 .

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5.9 General Trends of TMDs The band gap of TMDs (MoX2 , where X = S, Se, Te) reduces gradually from 1.8 to 1.1 eV by the increment in the atomic radii of the chalcogen element [64]. Consequently, it provides the chance to tailor the band gap by utilizing the distinct concentrations of the chalcogen atoms [111, 112]. Furthermore, in MoX2 , the Mo exists in + 4 oxidation state with the valence electronic configuration of 4d 2 . Moreover, within the trigonal prismatic configuration, the electrons are filled within the dz 2 orbitals and transformation in d xy and dx 2 −y 2 from the above-described dz 2 makes it semiconductor, whereas in the octahedral coordination, the electrons are filled within the t2g orbital (such as unfilled in d yz and d xy ) that leads to the VB within the electronic structure of the 1T phase. This partially filled VB within the 1T phase is the reason of material to exist within the semimetallic nature [111]. Since dz 2 has a relatively smaller energy as compared to the t2g orbital, the general energy of electrons is smaller in case of 2H phase that makes it more stable thermodynamically as compared to the 1T configuration. Besides these, the lone pairs of the chalcogen atoms put an end to the edges of the layers that makes it more stable against reaction with the environmental species [113].

5.10 Applications of TMDs TMDs because of their specific crystal structure as well as the specific electronic properties are of great interest. Contrary to the typical monolayer such as graphene, which is gapless material, the 2D TMDs offer the several unusual characteristics like the strong spin–orbit coupling (SOC) (because of having higher atomic number leading to generate the SOC), outstanding optical as well as electronic properties such as direct band gap that in turn leads toward the quantum confinement [33, 114]. This fact prompts the researchers to investigate the fundamental understanding of the TMDs as well as their utilization within the state-of-the-art applications like energy production, optoelectronics, spintronic and electronic applications [115–117].

5.10.1 Alkali-Ion Batteries The TMDs have been broadly investigated recently as potential “anode” materials for various alkali metal-ion batteries (AMIBs) [118]. This is because of the fact that these materials have showed greater diffusion of Na+ , Li+ and K+ ions that owe to the layered structures of these materials. Moreover, these materials offer the greater theoretical capacity on the basis of the four electronic transfer reaction under the small value of cutoff voltages. In order to enhance the performance of the AMIBs, countless attempts have been put forward including the testing several

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materials for anode materials along with the charge storage mechanism that have been widely studied. Furthermore, the inherent structure of the TMDs involving the expansion in the inter-layer separation, alloying, surface defects, phase control as well as the doping of heteroatoms has exhibited a great impact over the charge storage mechanisms as well as the electrochemical activity of the AMIBs. Owing to the particular crystal structure of TMDs having the MX2 where (M = Mo, Ti, W, Nb and V and X = Se, S and Te) and isolated atomic layers have grabbed a lot of attention in the area of energy storage as well as conversion and several optoelectronic devices due to the peculiar chemical, electronic as well as physical properties. More specifically, the layered TMDs materials having the weak VdW interaction in out-of-plane (i.e. inter-layer) direction are favorable for the Na+ , Li+ as well as the K+ intercalation [10, 119–123]. For instance, the Li ions (Li+ ) could be reversibly intercalated in the inter-layer space of TiS2 having the higher diffusion speed at a higher cutoff voltage of ~1.5 V [118–120]. The 2D MoS2 has been considered to be an effective host for the intercalation of the Mg ions, i.e. Mg2+ [124]. Besides this, the TMDs offer the higher theoretical capacity on the basis of the conversion reaction in between the one atom of MX2 along with the four atoms of the alkali metals. Therefore, the TMDs have been widely studied as the promising anode materials for several AMIBs [125–129]. Nevertheless, the performance of the TMDs anodes of the AMIBs is still limited because of the spontaneous aggregation as well as the unstable electrochemistry in the conversion reaction. Because of this, the TMDs exhibit the poor cyclic ability as well as stability for the anode materials of AMIBS. To deal with the issue described above, several attempts have been put forward, for example, the synthesis and production of the numerous architectures of TMDs for usage as electrode to enhance the performance of the AMIBs. For instance, the relation between the modified configurations, electrodes as well as the electrochemical performance of TM-disulfides-based nanocomposites for the Na-ion and Li-ion batteries has been investigated [129]. The evaluation/development of the hierarchical nanostructure is considered as the efficient approach as such structure aids the ion transport as well as increases the structural integrity during the process of the cycling [126, 130, 131]. The similar effect can be observed by the coupling of the TMDs nanostructures with carbon, particularly graphene in order to build the graphene/TMDs nanostructures that result in an increased structural stability along with the electrical conductivity [132, 133]. The described approach could be useful for efficiently increasing the electrochemical performance of TMDs and this has been thoroughly studied and reported [129, 130, 133, 134]. The structure optimization of materials to be used as electrodes is important due to its role in the electrochemical characteristics of TMDs, which includes the structural stability, electrical conductivity as well as ionic diffusion kinetics [135–140]. Currently, much efforts have been considered to the engineering of the inherent structures of TMDs to attain the improved performance of said alkai metal-ion batteries. The material engineering includes doping of the heteroatoms, surface defects, alloying, expansion of inter-layer space as well as the phase control [111, 141–145]. Some important aspects of the AMIBS are described in the following.

5.10 Applications of TMDs

5.10.1.1

125

Diffusion Kinetics of TMDs in AMIBs

The electrical properties are discussed on the basis of several factors that are briefly described earlier. The electrical conductivity of the TMDs is a key factor for the activities of the electrochemical reactions involved in the AMIBs [118]. The 2H crystal structure having the trigonal prismatic coordination and 1T phase owing the octahedral coordination represent the three and two degenerate states within the dorbitals of transition metals. The occupation of the d-orbitals plays central role while describing the electrical aspects of TMDs. The partial and complete filling would give rise to the metallic and semiconductor conductivity respectively. It has been reported that TMDs are comprised of groups 4, 6 and 7 having d 0 , d 2 and d 3 metallic centers respectively, which showed the semiconducting conductivity, whereas TMDs are comprised of group 5 owing the d 1 metallic centers exhibit the metallic conductivity [10, 56, 122, 146–148]. Furthermore, the electrical conductivity of the semiconducting TMDs could be tailored through the adjustment of the intrinsic structures, for instance, the engineering of the phase control [118, 141]. The phases 2H-MoS2 and 1T-MoS2 represent the semiconducting and metallic conductivity respectively [31]. Besides these, some other approaches could be helpful in this regards, for instance, the electrical conductivity could be highly modified by H-doping within the TiS2 [149]. The inter-layer intercalation rate, also known as the inter-layer alkali metal ion diffusion kinetics, offers a central role in the performance of the electrochemical reaction of the TMDs. The weak VdW interaction present in between the layers (i.e. inter-layer) owes a great impact over the diffusion kinetics [150]. The smaller VdW forces in the TMDs can generate the smaller resistance toward the ionic diffusion. The VdW interactions are decided through the intrinsic structure along with the composition of the TMDs. For instance, the theoretical work using the density function theory approach revealed that 1T' -ReS2 exhibited the weaker VdW forces of ~18 meV/unit cell that is much less as compared to the ~460 meV/unit cell for 2HMoS2 [151, 152]. Consequently, the diffusion kinetics associated with Li+ for ReS2 is comparatively greater in comparison with MoS2 [153]. The VdW forces of TMDs could be modified through the engineering of their inherent structure. Currently, the inter-layer spacing expansion approach had been broadly utilized in order to decrease the VdW interactions as well as the resistance offered in the ionic diffusion for MoS2 and other related TMDs [138, 144]. Some other raising approaches like alloying or surface defects etc. for the modification in inherent structures could be widely utilized for the modification in ionic diffusion kinetics in the TMDs.

5.10.1.2

The Storage Mechanism of Na/Li/K in TMDs

The storage procedure of Na/Li/K within the TMDs had been broadly investigated using theoretical and experimental frameworks. In general, the alkali metals, i.e. Na, Li and K exhibited the same behavior toward the charge storage because of the similar

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physical characteristics [154–156]. Nevertheless, the enhanced ionic radii from Li+ ;K+ could provoke the diffusion resistance along with the volume transition within TMDs [157–159]. Furthermore, the studies revealed that the storage procedures are strongly influenced through the cutoff voltages as well as the characteristics of the TMDs. The TMDs particularly MX2 (e.g. MoS2 ) showed the reversible intercalation as well as extraction reaction at higher cutoff voltage of nearly 1 V [124], whereas some other TMDs such as M"X2 (where M" = Ti, Nb) could show the reversible intercalation as well as the extraction reactions even at comparatively smaller cutoff voltages of nearly 0.1 V because of the stronger metal-chalcogenides interactions. However, there exist some TMDs such as M' X2 (where M' = Re, V, W and Mo), which suffer some difficulties from the conversion reactions. In conversion storage mechanism, the M' as well as A2 X (where A = Na, Li and K) products are found as the 1st discharge process is completed. The oxidation products are influenced through the dynamical characteristics of the M' X2 [160]. The irreversible formation of M' along with X just after initial charge process is caused by the poor dynamical characteristics. This results in the formation of X rather than M' X2 within the succeeding cycles. Also, the superb dynamical prospects result in the full reversible oxidation reaction. Moreover, the M' X2 is again generated after the first charge procedure and behaves as the active material within the sequential cycles.

5.10.1.3

Intercalation Mechanism

The procedure of intercalation of Na/Li/K storage within the MX2 has been found reversible, which is similar to the graphite anode [118]. The reversible extraction/ intercalation procedure in MX2 and its dependence over several factors such as intercalation depth, atomic structure and migration dynamics have been discussed through theoretical computation as well as experimental techniques as shown in Fig. 5.12. Fig. 5.12 Storage mechanism of Li for the application of Li-ion batteries using TMDs. Reprinted with permission from Zhao et al. [161]. Copyright (2019), American Chemical Society

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The intercalation of Li ions in the TMDs specifically for the MoS2 has been broadly investigated as shown in Fig. 5.13. The transition in the crystal phases for commercial MoS2 has been investigated and reported [163]. The results revealed that the material exhibits the reversible reaction as the cutoff voltage is ~0.8 V. Furthermore, the transition in composition for MoS2 has been observed within the voltage range of ~3.0–0.8 V [164]. Moreover, the phase transformation from 2H to distorted 1T has been observed during the process of intercalation. Furthermore, the structure modification at atomic level through the in-situ high-resolution transmission electron spectroscopy has also been investigated [165]. The results validate that the material, i.e. MoS2 could keep its layered configuration during the processes of the reversible intercalation as well as extraction reactions. It is noteworthy that the transition from the 2H to 1T phases has been observed that is indicated by the superstructure along with the 1T symmetry appearance after the intercalation of Li atoms at the inter-layer S–S tetrahedron [166]. Besides these, the same technique was utilized to study the atomic configurations as well as migration dynamics and the results exhibited that the phase transformations take place at the interface of MoS2 /Lix MoS2 upon the intercalation of Li ions. Similarly, the dynamics of the Li intercalation within the nanofilms are comprised of MoS2 through the in-situ optical observations. The results revealed that the Li ions intercalate in the nanofilms of MoS2 through the edges and hence slowly diffuses to the center. Furthermore, it has been concluded that phase transformation from the 2H-1T takes place at nearly 1.1 eV versus Li/Li+ [167]. MoS2 exhibits the preferable structural stability along with the longer life span cycling performance within the smaller voltage window of ~3.0–1.0 V [118]. Nevertheless, the material offers the lower theoretical capacity of ~167 mAh/g. Even so, it requires the expansion of the Li depth within the MoS2 , in order to increase the storage sites within the commence of maintaining its inherent layered configuration

Fig. 5.13 Intercalation mechanism in TMDs. Reprinted with permissions from Fan et al. [162]. Copyright (2017), American Chemical Society

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during charging–discharging process. The smallest discharge voltages have been investigated by reducing the cutoff voltages and hence considering the related transformation in the MoS2 . The layered configuration of the MoS2 could be maintained during the discharging up to 0.6 V, while the structural degradation takes place as the discharge is carried out to 0.5 V. The expansion in the inter-layer distance has been observed while reducing the cutoff voltages from 1.0 to 0.6 V, indicating the deeper intercalation of the Li atoms. By comparing, the nanofilms set off the disorderliness in the large voltage window of 3.0–0.5 V, which is attributed toward the conversion reaction at ~0.6–0.5 V. Consequently, the highest voltage window is ~3.0–0.6 V at which the material could conserve the parent layered structure. Hence, the deeper lithiation results the reversible configuration which indicates that MoS2 offers greater capacity along with the longer life span cycling. Besides the Li, the intercalation of the other alkali metal ions such as Na ions and K ions have grabbed a lot of interest for usage in rechargeable batteries. However, the diffusivity of the Na ion is much smaller as compared to the Li ions as per reported literature [118, 160].

5.10.2 Photocatalysis Catalyst is a material that does not take part in chemical reaction but supports the happening of a chemical reaction under the process known as catalysis. The catalysts can be of several types and each has its own merits and demerits. The photocatalyst and the process of photocatalysis by taking into account the layered materials specifically TMDs are elaborated in the following.

5.10.2.1

Photocatalysis Supremacy

The process of photocatalysis harvests solar energy to produce renewable, natural and ample source of energy [168–171]. Contrary to the typical thermal catalysis for which the general requisite is the higher pressure as well as temperature operating environment. The photocatalysis, in most of the cases, is operated at the ambient environment [170, 172, 173]. Furthermore, the thermal catalysis suffers some difficulties such as the catalyst deactivation as well as over-oxidation, yet these could be ignored in case of photocatalysis [168, 170].

5.10.2.2

TMDs for Photocatalysis

The fundamental procedure is based on three steps: first is the absorption of sunlight through the light-absorbing material present in the photocatalyst [174–177], the second step involves the separation and the migration of the photo-generated charge

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Fig. 5.14 Fundamental mechanism of photocatalysis. Reprinted with permission from Zhang et al. [178]. Copyright (2012)

carriers and third step comprises the redox reactions over the surface of the semiconducting material. It is noteworthy that the carrier migration procedure goes along with the carrier recombination process involving the bulk recombination as well as the surface recombination that forbids the conduction toward the photocatalysis and it should be tried to be kept away to the fullest extent. The fundamental mechanism of photocatalysis is shown in Fig. 5.14.

5.10.2.3

Thermodynamic Requisites

The phenomenon of the photocatalytic reactions requires the fulfillment of some thermodynamic requisites [179, 180]. Firstly, the energy of the incident photons must be equal or greater than the optical band gap of the semiconductor; secondly, the VBM of the semiconductor under study should be more positive as compared to the oxidation potential of the donor. Thirdly, the CBM should be the more negative than the reduction potential of the acceptor.

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5.10.2.4

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Kinetic Challenges

Besides the above-described thermodynamic conditions, there are several kinetic challenges involved in the process of photocatalysis [181, 182]. First, the three fundamental steps span a large timescale ranging from 10−15 s to 10−1 s (where the 10−15 − 10−9 s for light absorption, < 10−15 s of the charge separation as well as transport, along with this, 10−3 –10−1 s is required for reactions occurring at surface) that causes the huge challenge in order to maximize the alliance in between the three-step reactions. Second, a good photocatalyst requires the simultaneous grip over the wide light absorption, requiring the small band gap, within the solar spectrum as well as the strong redox capability requiring the broad band gap, yet this realization is intrinsically contrast. Third, the semiconducting material-based photosensitizers are usually deficient in active sites and hence, co-catalysts are generally needed to be filled on the surface of semiconductor to enhance the charge separation as well as their transfer along with the reduction in activation energy [183].

5.10.2.5

Configuration of Photocatalytic Systems

The rational formation of the photocatalytic system is crucial for the process of the photocatalysis. Normally, there exist two classes of the configuration systems within photocatalysis named as “fixed” system and “suspension” system [171, 184]. The first case, as name indicate, leads toward the photocatalyst that is fixed over a substrate for the photocatalytic reactions. Whereas in latter case, the particulate photocatalyst is suspended directly within the reaction solution. For further study, the readers referred to the literature [184].

5.10.2.6

Activity Evaluation Parameters

The eventual goal of the photocatalysis involves the effective usage of the solar energy. Hence, it is important to know how to estimate the efficiency of the system under investigation? Some chief parameters include the solar-to-chemical conversion efficiency (for instance, solar-to-hydrogen conversion efficiency, also abbreviated as STH), turnover frequency (TOF) and apparent quantum yield (AQY). The brief description of the terms is given in Eqs. 5.1–5.3. Besides these, the stability is also of prime importance for the practical implementation of photocatalytic system. The direct estimation method for the stability is to manage the long-term photocatalytic reaction test. For further study in this regards, the readers are referred to the relevant literature [185]. STH (%) =

Output energy as H2 × 100% Energy of incident solar light

(5.1)

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131

No. of reacted electrons × 100% No. of incident photons

(5.2)

No. of reacted electrons per second No. of active sites in a photocatalysts

(5.3)

AQY (%) = TOF =

5.10.2.7

Supremacy of TMDs for Photocatalysis

The photocatalytic activity requires suitable semiconductors; hence, TMDs with semiconducting phases, for example, the 2H-MoS2 , are found promising candidates for photocatalysis [186, 187]. The relevant properties are described in the following. (i) Narrow band gap TMDs offer the narrow band gaps which are generally less than 2.4 eV; for example, the monolayer of MoS2 shows the band gap of 2.16 eV [188] that exhibits wider spectral absorption and more effectiveness toward the usage of solar spectrum [189]. It has been found that nearly 50% of solar spectrum can be utilized by using multilayers of MoS2 [190] as compared to the typical semiconductor (for instance, TiO2 with 3.2 eV uses 4% of solar spectrum, similarly, the WO3 with the band gap of 2.8 eV uses 10% of solar spectrum, while the CdS with band gap of 2.4 eV uses 20% of solar spectrum). In addition to this, the smaller band gap leads toward the stronger lightmatter interactions and validates the stronger electron–hole pair generation [191, 192]. (b) Favorable energy levels The energy levels associated with the TMDs fulfill the thermodynamic needs of several photocatalytic reactions [168], for example, reduction of carbon dioxide (CO2 ) [193], the evaluation of H2 [194–196], nitrogen fixation [197], organic synthesis [186], sterilization [190, 198] as well as pollution degradation [187]. (iii) Atomically thin sheets Besides these, the atomic thickness of sheets permits the excellent characteristics as the light harvesting materials within the photocatalysis, involving the smaller transmission distance for the carriers, quantum confinement, greater surface to volume ratio and many others. The quantum confinement impact enables them having the tailored band diagram as verified through the experimental work [199] as well as theoretical computations [200]. This leads toward the broad range of optical characteristics to fulfill the range of the photocatalytic reactions [168]. Similarly, the smaller transmission distance of carriers from the inner toward the surface is superior in order to the effectual reduction of bulk recombination of the carrier, consequently extending the life time of the quanta and hence enhancing the quantum efficiency. Likewise, the larger surface-to-volume ratio is favorable for light capturing also makes large impact over the rich point contact in between the reactants as well as

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catalytic sites and gives the better platform for the emergence of doping, mild defects as well as heterojunction, that are in great favor for the additional improvement of the photocatalytic performance. The above-mentioned considerations reveals that the 2D TMDs semiconductors provide a perfect platform for photocatalysis [168]. These materials could be utilized to illustrate the directional as well as the time-dependent transfer of carriers after the excitation of light at the heterostructure interface [192]. The 2D TMDs-based VdW heterostructures, for instance, developed heterostructure using the single layers of MoS2 and WS2 , which exhibit speedy transfer of the carriers at such interface. The migration of the photo-induced holes is observed from the layers of MoS2 to WS2 within the very short time (nearly 50 fs) after the excitation of light as per femto-second pump-probe spectroscopy and photoluminescence mapping.

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Chapter 6

Conclusive Remarks and Recommendations: Way Forward on Layered Materials

Abstract Layeredness - an important aspect of a specific class of materials is focal theme of this book. Because of the exciting crystal structure, the layered materials offer the excellent applications that are specified to the layered materials. For instance, intercalation of ions or twisting of atomic layers generate exciting properties of the layered materials. This chapter is dedicated to highlighting the conclusive remarks on the descriptions given in the previous chapters. The likelihood of hexagonal crystal structure to exist as layered materials is addressed. The origin of the van der Waals (VdW) interactions and rational behind existence of specific crystal structures in the form of layered materials are discussed. Furthermore, considering the fact that transition metal dichalcogenides (TMDs), in most of the cases, appear as layered materials provide guidelines to explore the parameters involved in the layeredness. Moreover, the future directions and recommendation regarding the layered materials are provided.

Material science and engineering deal with the synthesis of useful materials for studying their properties and applications in daily life or in devices. The structure– property relationship has become a universal truth according to which the characteristics of materials changes when structural modifications are made. Hence, doping, alloying, phase modification, structural engineering, non-layered to layered change cause alterations in material properties. The recent emergence of device opportunities which require layered materials opened a gateway to search new layered materials or to prepare layered counterparts of the existing non-layered materials. Keeping this into account, several efforts are being observed where the materials initially synthesized in the form of monolayers are attempted to be grown as layered structures. In the same vigor, the layeredness of commonly used materials is being investigated since previously majority of the materials have been used without any emphasis on this property. This book deals with an important structural aspect of materials which is layeredness, i.e. property of materials to exist in the form of layers. The layered materials extrinsically appear in the form of layers having inter-layer separation as an additional structure feature besides the bond type and strength, bond lengths, bond angles, lattice constants, etc. In the layered materials, an anisotropy in bonding (i.e. difference © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Majid and A. Jabeen, Layeredness in Materials, Engineering Materials, https://doi.org/10.1007/978-981-99-6299-0_6

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in in-plane and out-of-plane or along c-axis) is found. The in-plane atomic bonds are strong having covalent and/or ionic nature, whereas the out-of-plane bonds are of weak van der Waals (VdW) nature. The layered materials are hence also known as VdW materials. Considering the mentioned structural anisotropy, these materials are essentially different from the corresponding non-layered materials. The example of graphite and diamond allotropes of carbon as respective layered and non-layered forms is appropriate in this regard. Hence, in case of the layered materials, the experimental synthesis/theoretical modeling as well as characterization needs different strategies and extra precautions. The specific synthesis techniques involve liquid phase and mechanical exfoliation, sputtering techniques and chemical vapor deposition etc. However, the commercial scale growth of layered materials having good crystal quality demands more feasible methods which are still under development. Chapter 2 of the book deals with experimental synthesis, theoretical simulations, properties and potential applications of the layered materials. In Chap. 3 theoretical modeling, the layered materials have been discussed thereby shedding light on the strategies to distinguish the non-layered and layered materials. After developing the enough theoretical background and elaborating several elemental layered materials, the relevant stuff on the transition metal dichalcogenides (TMDs) have been described in Chaps. 4 and 5. In order to validate the discussions, these chapters include the theoretical calculations performed by the authors to reveal, whether these materials are layered or non-layered. The well-known materials were investigated using density functional theory (DFT) implemented in Vienna ab-initio simulation packages (VASP) and Amsterdam density functional (ADF-BAND) codes. The presence of layers in VdW solids is an intrinsic property of the layered materials. The layeredness in materials brings several questions in mind, out of which one may be the asking for reasons behind layeredness in transition metal dichalcogenides. The discussions lead to the information that the presence of the sulfur, telluride and selenide helps formation of the layers in such materials. The inability of oxygen to make the layered material in TMDs may be the nature occurrence of oxygen in gaseous state while the rest of the elements in the group exist as solids. The reasons behind layeredness in VdW solids should be known if real potential of these materials and their possible applications needs to be exploited in its full vigor. A lot of research work needs to be done in this regard.

6.1 Appearance of Layered Materials in Specific Crystal Structures The survey of the known layered materials points to a conclusion that majority of the materials having hexagonal and orthorhombic crystal structures exist in the form of layers. One probable reason is the structure of such crystals in which lattice constants appear in the form that the length along c-axis is much greater as compared to the other axis (i.e. a = b = c) that may lead to anisotropy and hence occurrence of

6.3 Dissimilar Behavior of Oxygen Among Chalcogen Atoms in Layered …

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layers connected via weak VdW interactions in such materials. The weak interactions provide the opportunity of peeling-off the layers from free standing layered materials. However, on the other hand, this effect is difficult to be realized in other crystal structures such as cubic which have equal lattice constants (i.e. a = b = c) due to the close and isotropic packing in all directions.

6.2 Appearance of Chalcogenides Materials as Layered Materials The chalcogen elements, i.e. sulfur, selenide and telluride, when combined with transition metal give rise to the formation of layered materials. This may be due to p-d hybridization arising from chalcogen-TM elements, which are responsible for the VdW interactions. This question may be the talk of the town and deserves a detail work. For the time being, it can be said that the reason may be the specific electronic structure of the chalcogen atoms that tends to introduce layeredness in the layered materials. On the same account, there are several open questions which need to be addressed to shed light on the origin of VdW interaction in the layered materials.

6.3 Dissimilar Behavior of Oxygen Among Chalcogen Atoms in Layered Materials There exists a large drop in electronegativity values for O, S, Se and Te, i.e. 3.44, 2.58, 2.55 and 2.10 (Pauling scale) respectively. When value of electronegativity is high, the pull on electron is strong, the electrons are attracted with greater force and hence there would be a chance to make the strong covalent bond as compared to the weak VdW bonding. It would lead to sp3 -hybridization rather than sp2 -hybridization in such materials which avoids formation of layers, and thus, non-layered materials are obtained. Hence, the presence of highly electronegative oxygen in TMDs provides electrons with greater pulling tendency to cause formation of the covalent bonding throughout the crystal structure leading to an isotropic crystal structure. Yet some transition metal oxides like molybdenum oxides (MoO3 ), vanadium pentoxide (V2 O5 ) and tantalum pentoxide (Ta2 O5 ) exist as layered materials due to the presence of the large electronegativity difference which consequent upon appearance of major iconic character as compared to covalent character. It is consequent upon formation of weaker bonds in certain crystalline direction which leads to the layered materials. Furthermore, the electrical conductivity of MoSe2 is more as compared to MoS2 . This may also be attributed toward the electronegativity difference and Columbic preferences to generate free electrons which are responsible to electrical conductivity in the materials.

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6.4 Origin of the VdW Materials The VdW interactions are basically the electromagnetic interactions that are weak interactions but have a great impact on the layered materials. These interactions provide basic phenomenon in appearance of such solids in the form of layered materials. However, the origin of VdW interactions in the layered materials is a less studied phenomenon to the best of our knowledge. In case of graphite, it is the known fact that there exists a sp2 hybridization, due to which carbon makes three bonds with neighboring carbon atoms, while a single p-orbital specifically pz -orbital is free and is delocalized from every carbon atom. These pz -orbitals are basically said to be the responsible for VdW interactions. Furthermore, the majority of the VdW materials are such materials which have p-orbitals in most of the cases, e.g. TMDs, TMOs or even elemental materials. These materials contain p-orbitals in their structure that give rise to either p–p interactions or p–d interactions which is basically a reason behind the layeredness in such materials. Nevertheless, the three-dimensional VdW interactions occur in inorganic molecular crystals like Sb2 O3 or P4 Se3 which is basically due to p–p hybridization.

6.5 Do VdW Interactions Essentially Leads to Layered Materials? In this book, the layered materials are defined as the materials with anisotropy in bonding such as in-plane covalent bonding and out-of-plane VdW interactions. The layers are separated and hence connected via VdW interactions, but all materials having anisotropy in bonding as well as VdW interactions cannot be termed as the layered materials. One such example is the inorganic molecular crystals that include some of the rare materials such as Sb2 O3 in which the material/crystal is formed by the periodic repetition as the inert cages of Sb4 O6 (Fig. 6.1) which are inter-connected via weak VdW interactions. Besides these, such materials offer the anisotropy along all three dimensions, i.e. 3D anisotropy exists, but these materials cannot be termed as typical layered materials. Typical layered materials possess the VdW interactions in out-of-plane direction and the material can be exfoliated in the form of monolayer, similar to that of graphene. Thus, each material with weak VdW interactions cannot be termed as the layered material and only the materials having out-of-plane VdW interactions are established as layered materials.

6.6 Recommendations

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Fig. 6.1 Crystal structure of Sb2 O3 , an example of inorganic molecular crystals with 3D anisotropy

6.6 Recommendations Although, a lot of work has been performed on layered materials considering the various aspects and prospects of the materials for different applications, but still a lot needs to be performed in order to utilize the full potential of the available layered materials and explore new materials. In this book, the origin of VdW forces in layered materials has been elaborated in detail, but the description can be guaranteed as exhaustive. The theoretical study of the layered materials to explore the origin of VdW interactions and predict material properties using available level of theory is still underestimated or overestimated due to inaccurate modeling of the dispersion effects. Furthermore, as discussed in Chap. 4, there exist some materials in which the transition from sp2 to sp3 is observed which means that there exists layeredness to some extent that in turn shows that presence of layers in 2D, e.g.

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silicon carbide (SiC) appears in the form of layers up to 5 or 6 layers, after which the material transformed into isotropic 3D structure. This issue has not been investigated in case of majority of known functional layered materials which may restrict their utilization in applications. Therefore, a complete study to explore the relevant mechanism and onset of possible sp2 to sp3 transition should be carried out. The manipulation of inter-layer interactions based on foreign agents including external pressure, applied electric fields, applied magnetic fields, environmental and thermal effects is a least studied area in the layered materials. The inter-play of electronic, structural, mechanical, magnetic, piezoelectric, catalytic and transport properties in the layered materials should be explored in order to utilize the layered materials for future applications. The recently emerged applications of the layered materials, i.e. intercalation for rechargeable batteries and twistronics, point to the fact that still a lot of research work is due in order to fill the research gap on the issues mentioned in this book. Besides these, in chapter-2, the environmental conditions for materials to exists either as layered or non-layered materials are discussed in details. The only well-known and broadly investigated material in this regards is carbon whose study guided to the findings that extreme pressure and temperature leads to the formation of non-layered diamond. On the other hand, at ambient condition carbon would appear in the form of be layered graphite. Although, work on some other layered materials such as h-BN has been reported but a detailed study to check validity of the mentioned finding, like that of carbon, should be planned. The application of extreme pressure and temperature may shed light on phase transition between the layered and non-layered structures of the known materials. In general, the application of the extreme pressure leads to suppress the inter-layer distance in the layered materials and hence strengthening the inter-layer bonding which may lead to the structural transition in non-layered materials. The chemists, physicists, material scientists, engineers and especially future researchers and technologists should work in collaborative arrangements to explore the full potential of the layered materials for future applications.