Electrochemical Engineering Across Scales: From Molecules to Processes 9783527333455, 9783527692149, 9783527692125, 9783527692132, 9783527690633, 3527333452

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Advances in Electrochemical Science and Engineering Volume 15 Electrochemical Engineering Across Scales: from Molecules to Processes

Advances in Electrochemical Science and Engineering Advisory Board Philippe Allongue, Ecole Polytechnique, Palaiseau, France A. Robert Hillman, University of Leicester, Leicester, UK Tetsuya Osaka, Waseda University, Tokyo, Japan Laurence Peter, University of Bath, Bath, UK Lubomyr T. Romankiw, IBM Watson Research Center, Yorktown Heights, USA Shi-Gang Sun, Xiamen University, Xiamen, China Esther Takeuchi, SUNY Stony Brook, Stony Brook; and Brookhaven National Laboratory, Brookhaven, USA Mark W. Verbrugge, General Motors Research and Development, Warren, MI, USA

Edited by Richard C. Alkire, Philip N. Bartlett and Jacek Lipkowski

Advances in Electrochemical Science and Engineering Volume 15 Electrochemical Engineering Across Scales: from Molecules to Processes

Editors Richard C. Alkire

Department of Chemical and Biomolecular Engineering University of Illinois Urbana, IL 61801 United States Philip N. Bartlett

Department of Chemistry University of Southampton Southampton SO17 1BJ United Kingdom Jacek Lipkowski

Department of Chemistry University of Guelph N1G 2W1 Guelph, Ontario Canada

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at . © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Print ISBN: 9783527333455 ePDF ISBN: 9783527692149 ePub ISBN: 9783527692125 Mobi ISBN: 9783527692132 oBook ISBN: 9783527690633 Cover Design Schulz Grafik-Design, Fußgönheim, Germany Typesetting Laserwords Private Limited, Chennai, India Printing and Binding Markono Print Media Pte Ltd, Singapore

Printed in the Federal republic of Germany Printed on acid-free paper

V

Contents Series Preface XI Preface XIII List of Contributors XVII 1

The Role of Electrochemical Engineering in Our Energy Future L. Louis Hegedus

References

1

5

2

The Path from Invention to Product for the Magnetic Thin Film Head 7 Lubomyr T. Romankiw and Sol Krongelb

2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 2.4.1 2.4.2 2.4.2.1 2.4.2.2 2.4.3 2.4.3.1 2.4.3.2 2.4.3.3 2.4.4 2.4.4.1

Introduction 7 The State of the Art in the 1960s 8 The Processor 10 Memory 10 Data Storage 11 Electroplating Technology 14 Finding the Right Path to Production 14 First Demonstrations of a Thin Film Head 14 Interdisciplinary Design of a Functional Head 16 Early Tie-in to Manufacturing 18 The Integration of Many Inventions 21 Key Inventions for Thin Film Head Production 22 Device Structures 24 The Plating Process 24 The Paddle Cell 25 The Electroplating Bath, Deposition Parameters, and Controls Patterning 33 Through-mask Plating 33 Frame Plating 37 Ancillary Issues in Pattern Plating 41 Materials 44 Magnetic Materials Studies 44

29

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Contents

2.4.4.2 2.5 2.5.1 2.5.2 2.5.3

Hard-Baked Resist as Insulation 45 Concluding Thoughts 50 Fabrication Technology – the Key to a Manufactured Product 50 Matching Product and Process 51 An Interdisciplinary Combination of Science, Engineering, and Intuition 52 Acknowledgments 55 References 55

3

Electrochemical Surface Processes and Opportunities for Material Synthesis 59 Stanko R. Brankovic and Giovanni Zangari

3.1 3.2 3.3

Introduction 59 Underpotential Deposition (UPD) 60 Metal Deposition via Surface-Limited Redox Replacement of Underpotentially Deposited Metal Layer 63 General Description 63 Stoichiometry of SLRR Reactions and Deposition Process 64 Driving Force for SLRR Reaction and Nucleation Rate of Depositing Metal 66 Reaction Kinetics of Surface-Limited Redox Replacement 69 Future Directions 74 Underpotential Codeposition (UPCD) 76 Energetics: Beyond the Thermodynamic Approximation 78 Ion Adsorption at the Electrode/Electrolyte Interface 78 Potential of Zero Charge (PZC) 79 Surface Defects, Reconstruction, and Segregation 79 Atomistic Description of the Growth Process 80 Kinetics 80 Equilibrium Alloy Structure and Phase Formation 85 Binary Alloys Forming Solid Solutions and Ordered Compounds 86 Intermetallic Compounds 87 Alloys Immiscible in the Bulk 90 Structure and Morphology of UPCD Alloy Films 92 Crystallographic Structure and Microstructure 92 Film Morphology 94 Applications of UPCD Growth Methods 95 Catalysis and Electrocatalysis 96 Photovoltaics 97 Magnetic Recording and Microsystems 99 Acknowledgments 101 References 101

3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.4 3.4.1 3.4.1.1 3.4.1.2 3.4.1.3 3.4.1.4 3.4.2 3.4.3 3.4.3.1 3.4.3.2 3.4.3.3 3.4.4 3.4.4.1 3.4.4.2 3.4.5 3.4.5.1 3.4.5.2 3.4.5.3

Contents

4

Mathematical Modeling of Self-Organized Porous Anodic Oxide Films 107 Kurt R. Hebert

4.1 4.2 4.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.5 4.5.1 4.5.2 4.5.3 4.6

Introduction 107 Phenomenology of Porous Anodic Oxide Formation 108 Mechanisms for Porous Anodic Oxide Formation 118 Elements of Porous Anodic Oxide Models 120 Ionic Migration Fluxes and Field Equations 120 Bulk Motion of Oxide 122 Interfacial Reactions 123 Boundary Conditions 125 Interface Motion 126 Modeling Results 128 Steady-State Porous Layer Growth 128 Linear Stability Analysis 130 Morphology Evolution 133 Summary and Outlook 141 References 141

5

Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes 145 Chong-Yong Lee and Patrik Schmuki

5.1 5.2 5.2.1

Introduction 145 Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores General Aspects of Electrochemical Anodization and Self-Organization 147 Some Critical Factors/Aspects in the Self-Organization Phenomenology 149 Duplex or Double Wall Structure of Al2 O3 and TiO2 152 Tubes versus Pores 153 Geometry Control 154 Improved Ordering via Nanopatterning 161 Al2 O3 162 TiO2 163 Crystallinity and Composition 164 Applications 165 Anodic Al2 O3 as Template Materials 166 Anodic TiO2 for Dye-Sensitized Solar Cells 168 Tube Geometry 170 Crystallinity 173 Approaches to Enhance the Surface Area 174 Doping 175 Single Wall Morphology 177 Prospect for Commercialization 177 Processing Speed 177

5.2.2 5.2.2.1 5.2.2.2 5.2.2.3 5.3 5.3.1 5.3.2 5.4 5.5 5.5.1 5.5.2 5.5.2.1 5.5.2.2 5.5.2.3 5.5.2.4 5.5.2.5 5.5.3 5.5.3.1

147

VII

VIII

Contents

5.5.3.2 5.5.3.3 5.5.3.4 5.5.3.5 5.6

Design: Backside versus Front-Side Illumination 178 Flexible Substrate 180 Scale-Up 180 Long-Term Stability 181 Conclusions 181 References 182

6

Diffusion-Induced Stress within Core–Shell Structures and Implications for Robust Electrode Design and Materials Selection 193 Mark W. Verbrugge, Yue Qi, Daniel R. Baker, and Yang-Tse Cheng

6.1 6.2 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.4 6.4.1 6.4.2 6.4.3 6.5

Introduction 193 Ab initio Simulations: Informing Continuum Models 195 Governing Equations for the Continuum Model 198 Thermodynamics 198 Solute Diffusion 199 Solid Mechanics 200 Analytic Solution for Initial Stress Distribution 205 Results and Discussion 208 Initial Condition 209 Transient Behavior 212 Application to a Host-SEI Core–Shell System 215 Summary and Conclusions 221 References 221

7

Cost-Based Discovery for Engineering Solutions 227 Brian L. Spatocco and Donald R. Sadoway

7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.2.2.1 7.2.2.2 7.2.2.3 7.2.3 7.2.4 7.2.4.1 7.2.4.2 7.2.4.3 7.3 7.3.1 7.3.2

Introduction 227 The Winds of Change: Integrating Intermittent Renewables Cost is the Determining Factor 229 The Path Forward 230 The Liquid Metal Battery as a Grid Storage Solution 230 Principles of Operation 230 Strengths and Weaknesses 231 Scientific Advantages 231 Technology Scale-Up 232 Market Flexibility 233 Review of Competitive Technologies 234 Down-Selection 235 Cost 235 Temperature 237 Scalability 239 Historical Odyssey 241 Molten Salts in Sodium Electrodeposition 241 Molten Salts in Nuclear Reactor Development 245

227

Contents

7.3.2.1 7.3.2.2 7.3.3 7.3.4 7.4 7.5

Aggregated Properties 245 Corrosion Mechanisms 246 Molten Salts in Energy Storage Devices 252 The Window of Opportunity 255 Project Description 256 Conclusion 257 References 257

8

Multiscale Study of Electrochemical Energy Systems 263 Hany El-Sayed, Alois Knoll, and Ulrich Stimming

8.1 8.2 8.2.1 8.2.2 8.2.3

Introduction 263 Architectures of Energy Systems 265 The System and Its Boundary Conditions 266 Architectures of Multiscale Energy Systems 268 Agent-Based Approaches for Run-Time Simulation and Optimization 275 The Big Picture 281 Centralized versus Decentralized Systems 281 Decentralized Energy Systems: a Closer Look 282 Storage Components 285 How to Store Energy 285 Selected Energy Storage Devices 286 Li-Ion Batteries 286 Post Li-Ion Batteries 288 Redox Flow Batteries 290 Application to a City Block 291 Conversion Components, DEFC 292 Introduction to DEFC 292 Ethanol versus Other Fuels 295 Indirect versus Direct Ethanol Fuel Cell 295 Effect of Temperature on DEFC Performance 297 Stack Hardware and Design 297 Materials and Molecular Processes 299 DEFC Components 299 MEA and Electrodes 300 DEFC Processes 301 Ethanol Oxidation Reaction in Acidic Media 301 Anode Catalysts 303 Pt–Sn as DEFC Anode Catalyst 304 Ethanol Oxidation Reaction in Alkaline Media 305 Elevated Temperature Direct Ethanol Fuel Cell Membranes – Pros and Cons 305 Model Catalysts 308 Creating Nanostructured Model Surfaces 309 Acidic Media 310

8.3 8.3.1 8.3.2 8.4 8.4.1 8.4.2 8.4.2.1 8.4.2.2 8.4.2.3 8.4.3 8.5 8.5.1 8.5.2 8.5.3 8.5.3.1 8.5.3.2 8.6 8.6.1 8.6.2 8.6.3 8.6.3.1 8.6.4 8.6.4.1 8.6.4.2 8.6.4.3 8.6.5 8.6.5.1 8.6.5.2

IX

X

Contents

8.6.5.3 8.6.5.4 8.7

Alkaline Media 313 A Few Words about Cathode Catalysts (Conventional and MeOH Tolerant Catalysts) 314 Conclusions – Folding It Back 315 Acknowledgments 316 References 316 Index 323

XI

Series Preface With this volume, we are pleased to welcome Professor Philip N. Bartlett as coeditor. Professor Bartlett matriculated at the University of Oxford and at Imperial College, University of London, and held academic posts at the University of Warwick and University of Bath prior to moving in 1992 to the University of Southampton where he is currently Professor of Electrochemistry. His research interests focus on the templated electrodeposition of nanostructured materials and on bioelectrochemistry. His contributions have been recognized in numerous ways that include selection as Fellow of the Royal Society, and Fellow of the Royal Society of Chemistry, and major awards from the Royal Society of Chemistry, the International Society of Electrochemistry, and The Electrochemical Society, among others. The purpose of the series is to provide high quality advanced reviews of topics of both fundamental and practical importance for the experienced reader.

XIII

Preface Fifty years ago, in a short article in this series on the topic of electrochemical engineering,1) Carl Wagner wrote: … molecular engineering may be important in the future development of industrial electrochemical processes. Today, that time has come. Electrochemical engineering is undergoing a renaissance owing to development of a new generation of methods for bridging between molecular-scale discoveries, concepts, theory, experimental data, and their application to products and processes based on electrochemical operations. This volume describes electrochemical systems for which new experimental and computational approaches are used to facilitate movement between scientific fundamentals and technological applications. These applications range from capturing the future value from “bottom-up” discoveries to quantifying small-scale failure modes for “top-down” investigations, and to making strategic decisions on very large scale electrochemical energy technologies. These new approaches are flexible, and can be used as a template to guide work on additional applications beyond those for which they were originally developed. Taken together, these approaches provide wholly new capabilities for producing well-engineered electrochemical products and processes, while insuring quality at the molecular scale. The continued development and reduction to routine generic use of these modern engineering methods will provide essential tools for the design and control of next-generation electrochemical process technologies. Hegedus describes the intersection of energy technology, economics, and societal issues that point to the increasingly critical role of electrochemical technologies in our energy future. An example of advanced battery technology is presented to highlight the role of electrochemical engineering in addressing critical problems at the nano- and molecular scales, and their relation to the design of well-engineered electric vehicle propulsion systems. Romankiw and Krongelb describe the creation of the magnetic thin film head from initial concept to manufactured product. This iconic application represents 1) Carl Wagner, “The Scope of Electrochemical Engineering,” Advances in Electrochemistry and Electrochemical Engineering, ed. C. W. Tobias, Vol. 2, page 2 (1962).

XIV

Preface

one of the most significant advances of electrodeposition science and engineering in the last half century. They point out that inventions that bring about a major advance in the state of the art invariably require ancillary advances to achieve a viable manufacturing process. The key point is the need to treat the process invention, the materials science, and the design of the device as an integrated interdisciplinary effort from the inception of the concept to its emergence as a product. Brankovic and Zangari describe manipulation of metal surface atoms to achieve controlled, uniform structures by means of underpotential codeposition as well as surface-limited redox replacement of underpotentially deposited metal layers. Quantitative relationships are described for the stoichiometric, energetic, and kinetic phenomena that accompany the nucleation and growth of these unique structures. The chapter provides the fundamental results needed for the development of functional materials, with examples in areas of catalysis, photovoltaics, and magnetic systems. Hebert emphasizes the view that porous anodic oxide formation should be considered as a process involving pattern formation far from equilibrium. As such, the scaling relations and critical parameter ranges associated with anodizing can be understood by using mathematical approaches that have been used with success for pattern formation in other systems in which large-area patterns are formed at high rates. Schmuki and Lee describe the discovery, characterization, and milestone innovations associated with the practical use of self-organized porous Al2 O3 and TiO2 nanotubes formed by electrochemical processes. The principles and mechanisms for formation of both these materials have similarities, even though a wide variety of chemical and physical properties can be obtained. This chapter may be seen as the “applied” side to the chapter by Hebert. Verbrugge, Qi, Baker, and Cheng address the life of lithium-ion batteries and its relation to small-scale phenomena associated with deformation of active materials along with solvent decomposition. Numerical ab initio calculations are described that, even in the absence of detailed structural knowledge, can inform continuum mathematical models in making decisions on robust electrode design and materials selection. Sadoway and Spatocco describe the methodology of “cost-based discovery” to address the challenge of developing new technology for massively large-scale applications through the example of grid-level energy storage for intermittent renewable energy sources. By this methodology, the earliest stages of research include cost as a determining factor in the choice of materials and process chemistry, for example, by using earth-abundant elements and simple manufacturing techniques. By this view, parts of the periodic table are axiomatically off limits on grounds of scalability. El-Sayed, Knoll, and Stimming examine multiscale components in discussing options associated with renewable energy generation and storage options associated with an urban city block. Behavior at multiple scales is incorporated for the electrochemical systems as well as for the materials and molecular processes

Preface

involved. The approach combines scientific “bottom-up” with engineering “top-down” approaches mediated by the capabilities of computer science and engineering. This volume will be of interest to chemical, mechanical, electrical, and computational engineers, as well as chemists, physicists, biochemists, and surface and materials scientists. The opportunities for impact in this field are far greater than what the current researchers trained in electrochemical engineering can accomplish. By providing up-to-date reviews with extensive coverage of background topics, this volume should be of interest to students and professionals entering the field, as well as for experienced researchers seeking to expand their scope and mastery. Richard C. Alkire Urbana, Illinois, USA, July, 2014

XV

XVII

List of Contributors Daniel R. Baker

Hany El-Sayed

General Motors Research and Development Chemical and Materials Systems Laboratory 30500 Mound Road Warren MI 48090-0955 USA

Technical University Munich Department of Physics James-Franck-Street 1 85747 Garching Germany

Stanko R. Brankovic

University of Houston Departments of Electrical and Computer Engineering and Chemical and Biomolecular Engineering N308 Eng. Bldg. 1 Houston TX 77204-4005 USA Yang-Tse Cheng

University of Kentucky Department of Chemical and Materials Engineering 177 FPAT Lexington KY 40506-0046 USA

Alois Knoll

Technical University Munich Institute of Robotics and Embedded Systems Department of Informatics Boltzmannstrasse 3 85748 Garching Germany and TUM CREATE Center for Electromobility 1 CREATE Way CREATE Tower 138602 Singapore Sol Krongelb

Emeritus, IBM T.J. Watson Research Center 9 Greenlawn Road Katonah NY 10536 USA

XVIII

List of Contributors

Kurt R. Hebert

Iowa State University Department of Chemical and Biological Engineering 2114 Sweeney Hall Ames, IA 50011 USA L. Louis Hegedus

RTI International 3040 East Cornwallis Road P.O. Box 12194 Research Triangle Park NC 27709-2194 USA and 1104 Beech Road Bryn Mawr PA 19010 USA Chong-Yong Lee

University of Erlangen-Nuremberg Department of Materials Science Institute for Surface Science and Corrosion (LKO) Martenstrasse 7 91058 Erlangen Germany Yue Qi

General Motors Research and Development Chemical and Materials Systems Laboratory 30500 Mound Road Warren, MI 48090-0955 USA

and Michigan State University Department of Chemical Engineering and Materials Science 428 S. Shaw Lane Room: 3509, East Lansing MI 48824 USA Lubomyr T. Romankiw

IBM T.J. Watson Research Center 1101 Kitchawan Road Yorktown Heights NY 10598 USA Patrik Schmuki

University of Erlangen-Nuremberg Department of Materials Science Institute for Surface Science and Corrosion (LKO) Martenstrasse 7 91058 Erlangen Germany and King Abdulaziz University Department of Chemistry Faculty of Science Jeddah 21569 P.O. Box 80203 Saudi Arabia

List of Contributors

Donald R. Sadoway

Massachusetts Institute of Technology Department of Materials Science and Engineering 77 Massachusetts Avenue Cambridge MA 02139-4307 USA

and Newcastle University School of Chemistry, Faculty of Science, Agriculture and Engineering Bedson Building Newcastle upon Tyne NE1 7RU UK

Brian L. Spatocco

Massachusetts Institute of Technology Department of Materials Science and Engineering 77 Massachusetts Avenue Cambridge MA 02139-4307 USA

Mark W. Verbrugge

General Motors Research and Development Chemical and Materials Systems Laboratory 30500 Mound Road Warren MI 48090-0955 USA

Ulrich Stimming

Technical University Munich Department of Physics James-Franck-Street 1 85747 Garching Germany and TUM CREATE Center for Electromobility 1 CREATE Way CREATE Tower, 138602 Singapore and Technische Universität München Institute for Advanced Study (IAS) Lichtenbergstr. 2a 85748 Garching Germany

Giovanni Zangari

University of Virginia Department of Materials Science and Engineering 395 McCormick Road Charlottesville VA 22904 USA

XIX

1

1 The Role of Electrochemical Engineering in Our Energy Future L. Louis Hegedus

Richard Smalley, Nobel Prize-winning chemist (1996) and co-discoverer of buckminsterfullerene (C60), presented a seminar at Columbia University in New York on 23 September 2003. The title of his talk was “Our Energy Challenge” [1]. He ranked the top 10 challenges facing mankind for the coming 50 years and made a compelling argument for energy being the number one challenge, and that it will also dominate the remaining nine challenges (water, food, environment, poverty, terrorism and war, disease, education, democracy, and population). Eleven years into his 50-year prediction, his analysis is holding strong. The US National Research Council has produced a series of reports about America’s energy future, culminating in the 2009 report America’s Energy Future: Technology and Transformation [2].These reports outline a desirable energy future that is clean, sustainable, and secure, and relies on domestically supplied low-carbon or carbon-free primary energy resources, combined with efficient fuel conversion and end-use technologies. All this may, to a considerable extent, hinge upon technologies to generate, store, distribute, and utilize electricity. Energy technologies, however, represent only the necessary, but not sufficient, conditions for achieving the above. Sufficient conditions include economics (reasonably well recognized and understood) and a whole host of issues in the societal dimensions, including energy policies, politics, public education and public attitudes, energy security, foreign policy, and even defense. These come together with issues of the environment, ecology, and even climate. The resulting “energy conundrum,” the dimensions of which are inseparable and interactive, has only recently started receiving analytical attention [3]. In spite of the complexity of the energy conundrum, the dominant primary energy resources have been evolving in a remarkably orderly pattern as depicted by the logistic analysis of Gruebler and Nakicenovic [4]. In Figure 1.1, F is the estimated fractional saturation level of a given primary energy resource in a given year, and 1 − F represents the remaining potential. Plots of F∕(1 − F) for the United States over the years 1800–2000 revealed logistic substitution waves of the primary energy sources, from wood to coal to oil to natural gas to uranium. Although not yet significant in 2000, it is reasonable to expect that renewable energy, such as wind and solar, will eventually start making the next logistic wave. Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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1 The Role of Electrochemical Engineering in Our Energy Future

102

101 Coal

F 1–F

Wood

10

0

10–1

Oil

10–2 1800

1850

Nuclear

Natural gas

1900 Year

1950

2000

Figure 1.1 Historic logistic wave patterns of the primary energy sources in the United States. (Redrawn from Figure 15 of [2].) F is penetration as a fraction of saturation. Lawrence Livermore National Laboratory

Estimated U.S. Energy Use in 2011: ~97.3 Quads Solar 0.158

Net electricity Imports

0.0175 8.26

Nuclear 8.26 Hydro 3.17 Wind 1.17

7.74 3.15

18.0

0.127

12.6 Electricity generation 39.2

26.6

0.163

0.140

Geothermal 0.226

0.0396

0.430

9.15

Commercial 8.59

6.87

1.14 1.72

4.50

0.0197 3.23 0.0179

0.683 0.0512 0.110

2.27

1.61

4.72

3.33 8.32

Coal 19.7

8.06

Industrial 23.6

Energy services 41.7

18.9

0.444

20.3 0.288

0.735

1.15

0.0260

25.1 Petroleum 35.3

Residential 11.4

Rejected energy 55.6

4.83

Natural Gas 24.9

Biomass 4.41

2.29

4.86

1.17

Transportation 27.0

6.76

Figure 1.2 Estimated US energy use in 2011. About 40% of the primary energy sources were used for the generation of electricity [3].

The current energy infrastructure in the United States is best visualized by the energy flow charts of the Lawrence Livermore National Laboratory [5]. Figure 1.2 shows that in 2011 (the latest year for which data were available) the United States used about 97.3 quads (10E15 British thermal units) of energy from our primary energy resources – solar (0.158), nuclear (8.26), hydro (3.17), wind (1.17), geothermal (0.226), natural gas (24.9), coal (19.7), biomass (4.41), and petroleum (35.3). Altogether, 39.2 quads were used for generating 12.6 quads of electricity. One remarkable feature of our energy infrastructure is that almost none of this electricity was used for transportation (0.26%), and another remarkable feature is

1 The Role of Electrochemical Engineering in Our Energy Future

that almost none of the natural gas was used for transportation either (inspection reveals that the 3% shown in Figure 1.2 corresponds mostly to the amount of natural gas used to power the compressors of the natural gas pipelines, classified as “transportation”). Before the historic 18 June 2010 news release of the Potential Gas Committee [6], announcing a 39% one-step upgrade (largely by reclassifying the economic viability of extracting shale gas via horizontal drilling and hydraulic fracturing), the natural gas resources of the United States were viewed as rather limited. Electricity, generated primarily from coal, natural gas, and nuclear resources, was viewed by some as being limited as well: coal due to its environmental, ecological, and climate-change implications; natural gas due to its perceived limited domestic supply, high price, and large price fluctuations; and nuclear resources due to a combination of public safety concerns and the somewhat related high capital costs. The newly perceived natural gas plenty (about 100 years supply at current rates of consumption), and the expectation of low natural gas prices for decades, prompted many existing and planned power plants to shift to natural gas. It has also prompted a re-evaluation of how natural gas and electricity could be used for powering light-duty vehicles instead of oil. In a 2013 report of the National Research Council [7], projecting technologies suitable for replacing 80% of oil and reducing 80% of CO2 emissions from the lightduty vehicle fleet by 2050, it was concluded that there will likely be enough natural gas to help electrify light-duty vehicle transportation. (Other ways of using natural gas for vehicle propulsion include converting it into liquid synthetic fuels such as gasoline, diesel, and methanol; compressed natural gas, liquefied natural gas, or natural gas-derived hydrogen for fuel cells.) Fuel cell vehicles are approaching volume production standards but are still too expensive, and of course they rely on the development of a hydrogen fueling infrastructure. So what are the leading-edge technical issues within the domain of electrochemical engineering? A recent review of the history, accomplishments, and future potential of the field [8] focuses on electrochemical processes and electrochemical processing. While it does mention fuel cells, it leaves batteries unmentioned. A broader view of the field was represented by a 2007 assessment of US electrochemical engineering research competencies as part of the international benchmarking of US chemical engineering competencies [9]. The study makes observation of the fact that electrochemical engineering has drifted out of the core of the chemical engineering curriculum, with the exception of a handful of leading universities. Among the most notable developments in the field over the previous 10 years were the advances in rechargeable Li ion batteries with liquid, gel, or polymer electrolytes and advances in fuel cells with proton-conducting membranes. For the future, the report projects “increased relevance of the field again, due in part to the world’s repeated energy crises.” Six years after that prediction, we agree. Electrochemical engineering, similarly to many other engineering disciplines, has been advancing from the scales of macro to micro, nano, and molecular. This increasing overlap in scale with the molecular sciences has become a major

3

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1 The Role of Electrochemical Engineering in Our Energy Future

stimulus to both, and the catalyst for much recent progress. Let us examine this thought through the example of advanced battery technology for electric vehicles. The electrification of light-duty vehicles via the electric grid has the appeal of relatively affordable infrastructure additions. However, it requires batteries that are safe and affordable, provide high energy density (weight, volume, vehicle range, and cost are all affected), provide high power density (performance), have a long cycle life, rely on the domestic supply of key raw materials that would preferably be recyclable but in any case environmentally acceptable, and, last but by far not least, can be recharged quickly to alleviate the customer’s range anxiety. Electric vehicles have a number of strong appeals that include the cost of only a few cents of electricity per mile, no tailpipe emissions, greatly simplified vehicle systems (independently controllable electric motors on each wheel, no exhaust system, flexible battery packaging), and startling acceleration due to the fact that an electric motor has its full rated torque at 0 rpm vs. an internal combustion engine that has a narrow revolutions-per-minute band in its torque curve. We are witnessing the rapid penetration of Li ion battery technologies, originally developed for portable electronics, into battery-electric hybrids, plug-in hybrids (such as the Volt) and battery-electric vehicles (such as the Nissan Leaf and the Tesla Model S). Essentially, all the battery price and performance issues listed before have remained active at various levels; thus, intensive research and development work is continuing on Li ion battery technology. In its wake, batteries are being developed with Li metal anodes and solid-state electrolytes (for a combination of high energy density, safety, and high cycle life), with potential game changers on the horizon that might include consumable (rather than rechargeable) Mg or Al anodes with air cathodes (metal–air “fuel cells”), with very large energy density, simple construction, safe aqueous electrolytes, and instant refueling capability; and the rechargeable Li–air battery that has a theoretical volumetric energy density approaching that of gasoline and that appears to be a potentially achievable “holy grail.” The specific energy (weight-specific energy density) of gasoline is about 13 kWh kg−1 , of which about 1.7 kWh is available at the wheels after the thermodynamic and frictional losses have been allowed for. In comparison, the specific energy of today’s rechargeable Li ion batteries is about 150 Wh kg−1 at the cell level, or about 105 Wh kg−1 at the battery pack level. A 200-kg Li ion battery pack yields a driving range of about 70 miles [10]. In a critical review of the Li–air battery [10], it was estimated by cell-level calculations that the Li–air battery could have a practical specific energy of about 1000 Wh kg−1 (6.7 times that of today’s Li ion battery) “if several fundamental challenges can be overcome.” This would increase the range of the electric car to or beyond the range of today’s gasoline-powered vehicles. So what are the fundamental challenges in making the Li–air battery suitable for propelling the electric car, and how can electrochemical engineers contribute to the solutions? As we will see, the problems cover a dynamic range of close to 10E10, from a meter (size of the battery pack) all the way to Angstroms, the molecular scale. We will also see that most (but not all) of the technical challenges appear to reside at the nano- and molecular scales.

References

There are four types of rechargeable Li–air batteries under development, based on their electrolytes: aprotic, aqueous, solid-state, and aprotic–aqueous hybrid. All have Li metal as their preferred anode (negative electrode), and the preferred cathode (positive electrode) is catalyst-impregnated porous carbon. The Li anode requires a protection layer that has to conduct Li ions, is thin, hole-free, chemically stable, flexible to accommodate volume and shape change, and has a high elastic modulus to suppress dendrite formation. The cathode (air electrode) presents particular challenges for aprotic systems: besides being electronically conductive, it has to have a high surface area, which requires small pore diameters; good diffusive properties, which require large pore diameters; and a high pore volume to accommodate the insoluble discharge reaction by-product Li peroxide without pore plugging, which impedes the diffusion of O2 to the electrode’s surfaces. Complex multimodal pore structures have been investigated to find an optimum. Membranes are being developed for aprotic batteries to prevent H2 O from air to enter the cathode of the aprotic battery. The aqueous battery system, in turn, needs membrane technology that selectively transfers OH− ions. Aqueous batteries require a reservoir for the discharge product LiOH⋅H2 O due to its relatively low saturation concentration in the aqueous electrolyte. Catalysts are being developed to help both the reduction of O2 (discharge reaction) levels and the evolution of O2 (charge reaction) in the cathode system. These would enhance the rate of discharge (specific power) and the rate of charge, respectively. Both the aprotic and the aqueous electrolytes need to have high Li ion conductivity, temperature stability, and low viscosity. They also have to be reversible (nonreactive) during the charge–discharge cycles. According to Christensen et al. [10], a sufficiently reversible aprotic electrolyte has yet to be found. As we can see from the above, the technical challenges cover a wide range of scales from battery systems through battery packs, battery cells, battery components, micro- and nanoscale component and materials structures, all the way to chemical compositions and molecular entities. Solving these problems requires working simultaneously along two dimensions: one of these is the collaboration between specialists, and the other one is the engagement of engineers whose interests, training, and experience cover the exceptional dynamic range demanded by modern technologies, as exemplified here by the Li–air battery, leading us to the theme of this volume. References 1. Smalley, R.E. (2003) Our energy

challenge. Slides from a Seminar at Columbia University on September 23, 2003, http://www.americanenergy independence.com/library/pdf/ smalley/OurEnergyChallenge.pdf (accessed 9 September 2014).

2. Committee on America’s Energy Future

and National Research Council (2009) America’s Energy Future: Technology and Transformation, The National Academies Press. 3. Hegedus, L.L. and Temple, D.S. (eds) (2011) Viewing America’s Energy

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4.

5.

6.

7.

Research Council (2013) Transitions Future in Three Dimensions, RTI Press, to Alternate Vehicles and Fuels, The Research Triangle Park, NC. National Academies Press, Washington, Gruebler, A. and Nakicenovic, N. DC. (1991) Long waves, technology diffusion, and substitution. Int. Inst. 8. Stankovic, J. (2012) Electrochemical engineering – its appearance, evolution Appl. Syst. Anal., Laxenburg, Ausand present status. J. Electrochem. Sci. tria, Rev., XIV (2, Spring), 313–342, Eng., 2, ISSN: 1847–9236. www.jesewww.iiasa.ac.at/publication/more_RP-91online.org/Articles/OLF/jESE_0011.pdf 017.php. Lawrence Livermore National 9. Committee on Benchmarking the laboratory. Energy Flow Charts, Research Competencies of the US in http://publicaffairs.llnl.gov/news/energy/ Chemical Engineering and National energy.html (accessed 4 September Research (2007) Council International 2014). Benchmarking of US Chemical Engineering Competencies, The National Potential Gas Committee and Colorado Academies Press. School of Mines Potential Gas (2010) 10. Christensen, J., Albertus, P., Committee Reports Unprecedented Sanchez-Carrera, R.S., Lohmann, T., Increase in Magnitude of US Natural Kozinsky, B., Liedtke, R., Ahmed, J., and Gas Resource Base. News Release, June Kajic, A. (2012) A critical review of li/air 18, 2010. batteries. J. Electrochem. Soc., 159 (2), Committee on Transitions to Alterr1-R30. nate Vehicles and Fuels and National

7

2 The Path from Invention to Product for the Magnetic Thin Film Head Lubomyr T. Romankiw and Sol Krongelb

2.1 Introduction

Innovations in science and technology over the last several decades have changed the way we conduct our business and personal lives. Technological inventions and advances, however, can have such immense impact only if the ideas of visionaries in the laboratory are transformed into useful products on a manufacturing line. The traditional approach to achieving a manufactured product has been to have a development group refine the newly invented idea into a functional device with marketable features. The development engineers subsequently hand over the design to manufacturing engineers to implement a manufacturing-worthy process. This approach may work, more or less, with inventions that can be built with existing process technology. However, an invention that brings about a major advance in the state of the art often requires a number of ancillary inventions to achieve a viable manufacturing process. Process inventions and the supporting process and materials science become so intertwined with the design of the device that all three – process, underlying science, and design – must be treated together in an interdisciplinary effort from the inception of the structure to its emergence as a product. Indeed, the interdisciplinary approach can be advantageous even if no new technology is involved. The importance and practice of such an interdisciplinary program is best understood by following the evolution of a specific invention from initial concept to manufactured product. IBM’s creation of the magnetic thin film head, which brought about a quantum jump in magnetic data storage and simultaneously transformed electrochemical technology from a shop art to a precision manufacturing process, provides an appropriate example. Every invention is, by its very definition, unique, and so it is not possible to define the details of a single path that will lead any invention into production. The authors hope that this chapter will help the reader understand the principles that made the thin film head program so successful in advancing information storage on disk and tape, and to adapt those elements appropriate to his or her work to similarly advance today’s technology to new heights. Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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2 The Path from Invention to Product for the Magnetic Thin Film Head

2.2 The State of the Art in the 1960s

To appreciate how the magnetic thin film head evolved from a concept into a product, one needs a few background details on the state of the art in digital computers and in device fabrication process technology in the 1960s – the period during which the thin film head was conceived and its fabrication process was developed. Maissel and Glang’s [1] Handbook of Thin Film Technology, published in 1970 provides a detailed discussion on the practice and the underlying science of the various thin film fabrication processes used in the electronics industry at that time. The discussion in this section deals only with those aspects of technology relevant to the thin film head. The time line of manufacturing technology evolution in Figure 2.1, simplified to focus on these aspects, will help the reader follow the discussion and appreciate how the interplay among fabrication processes that were developed for seemingly different applications brought the thin film head into mass production. Figure 2.1 highlights the evolution of process technology for fabricating the three major elements of the computer and for electroplating technology:

• The processor, which rapidly carries out the logical and computational operations specified by the programs.

• The working memory, which the processor uses in performing these operations. • The high-density, fast-access data storage that holds the programs and data. (The thin film head is a critical component of disk and tape storage systems.)

• Electroplating technology, in the fourth row, initially had little relevance to computer fabrication. At the end of the 1950s, where this time line starts, plating was seen as a shop art that lacked the precision and control necessary to build any part of the computer other than the circuit boards. In the next decade, however, plating would become the key technology that enabled mass production of the thin film head. Of course, the processor, memory, and storage elements had to be interconnected for the computer to function. As the speed of the computer increased, interconnections became a significant factor in computer performance and took on the form of transmission lines with precisely fabricated structures. While the details of interconnection technology are beyond the scope of this chapter, it may be noted that during the 1990s, electroplating also assumed a key role in the fabrication of critical interconnections [2, 3]. The time axis in Figure 2.1 starts with the left column, which reflects the state of the art in the relevant manufacturing technologies at the end of the 1950s and the objectives for further advances in each of these areas. The next three columns respectively highlight the 1960s, when the major advances that defined the future paths for each of the technologies were made; the 1970s, when the thin film head became a manufacturable product; and the 1980s and beyond, when technology based on the work of the previous two decades continued to evolve into today’s production processes.

2.2

The State of the Art in the 1960s

9

Time line of computer manufacturing technology (abridged to focus on inventions relevant to the thin film head)

State of the art in the late 1950s, needs, and plans to advance the technology

1980 and beyond

1970s

1960s

Processor Discrete transistors replace vacuum tubes Need: Integrated circuits for low cost, high performance. Plan: Invention of the integrated circuit sets stage for LSI (large scale integration) to fabricate si circuit chips.

LSI processes evolve in accord with Moore’s Law to remain the technology for chip fabrication

Memory Magnetic core arrays Need: Fast, high capacity, mass produced for low cost.

Semiconductor memory

Semiconductor memory built by LSI porcesses becomes the dominant memory in computers

Plan: LSI fabrication processes

Magnetic film memory Plan: Films by evaporation, sputtering or electroplating; patterning by etching with photoresist mask.

IBM invents plating processes for film memories

Use of plating to form bubble propagation patterns continues for duration of bubble memory project.

1970 First thin film write head

Data storage Magnetic disks with hand-wound read/write heads Need: Smaller heads for increased areal density; mass produced for lower cost

Plan: Make smaller heads. However, there’s a limit to how small individually wound heads can be made.

While literature shows designs, patents and theoretical analyses for heads beyond the limit for wound coils, there’s no viable fabrication process.

Virtually all disk drive manufacturers turn to LSI in effort to fabricate a thin film head. IBM manufacturing group accepts that heads cannot be built with LSI processes.

Disk drive industry drops LSI to learn and implement IBM’s head fabrication process.

Inventions in plating are integrated with 1979: Thin film head inventions in announced as a patterning and product materials to build the thin film head

Electroplating technology A shop art with minimal underlying science. OK for circuit boards, but not for devices requiring precisely tailored material properties.

IBM’s work on plating for film memories transforms plating from a shop art to a precision, science-based technology.

Legend for fabrication disciplines:

LSI

Plating

Thin film head casts plating in a new light as a precision fabrication process. Patterning

Materials

Figure 2.1 A time line of advances in technologies pertinent to the invention of the thin film head. Note that a combination of inventions from the areas of plating, patterning, and materials science were needed to manufacture the thin film head.

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2 The Path from Invention to Product for the Magnetic Thin Film Head

2.2.1 The Processor

The invention of the integrated circuit in the late 1950s [4, 5] set the stage for an intensive effort to develop LSI (large-scale integration) processes in the 1960s. This technology formed semiconductors on a silicon substrate and interconnected them by thin metal patterns on the flat surface to create functional circuit chips. The essential steps in LSI fabrication included a combination of oxidation processes to form SiO2 on the silicon surface, photolithographic and chemical etching steps to provide openings in the SiO2 , and diffusion or ion implantation to produce appropriately doped n and p regions for the semiconductor devices. The aluminum (and subsequently aluminum–copper) that was evaporated or sputtered over the surface and photolithographically patterned by wet chemical etching formed the metal elements of the semiconductor devices and the interconnections among them. LSI enabled the computer industry to meet the objectives for the nextgeneration processors by mass producing chips with large arrays of interconnected circuits, thus eliminating much of the more expensive manual assembly of individual components. This technology also increased the speed of data processing and transmission within the machines by shrinking the size and increasing the density of the circuits on the chip. A vast majority of people working in advanced electronic fabrication were involved in some aspect of LSI processing, giving rise to rapid advances in this technology. LSI continued to evolve and remains the underlying technology for today’s semiconductor devices. 2.2.2 Memory

The engineers working to advance memory technology were also looking for improved performance and lower cost. State-of-the-art magnetic core memories of the late 1950s were expensive to build because they required several thin wires to be threaded through an array of tiny toroidal cores in specific patterns. Two alternative technologies to replace core memories – magnetic thin film memory and solid-state memory – were pursued concurrently. The solid-state memory approach used large arrays of memory cells, each cell being an integrated transistor circuit that could store one bit of data. By 1968, the advances in semiconductor memories and the fact that these memories could easily be combined with the transistor circuitry on the processor chip led IBM to curtail most magnetic memory work [6]. (Some bubble memory work, in which the plating process described in this chapter was used to build magnetic bubble devices, did continue through the 1970s.) LSI processes were effectively used to fabricate semiconductor memory, and, as the yellow time lines in Figure 2.1 indicate, this technology continues to build both the memory and the processor for today’s computers. Magnetic film memory and an advanced version, the much denser coupled film memory, were serious contenders to semiconductor memory. The magnetic film

2.2

The State of the Art in the 1960s

approach was to deposit films of copper and permalloy (a magnetic alloy of Ni and Fe with appropriate magnetic properties for memory devices) by evaporation, sputtering, or electroplating and to pattern the respective layers by deposition through a mask or by etching with a photoresist mask to produce the various magnetic film memory configurations [7]. Thin magnetic films promised faster switching than ferrites, and building thin film structures was less expensive than assembling core arrays. Using electroplating instead of evaporation would make the thin film structures even less costly to produce, and one of the authors (L.T.R.) was pursuing the electrochemical approach. However, electrodeposition as it was understood and practiced at that time was hard-pressed to reproducibly produce the required magnetic properties. It was the inventions of a new plating tool and of new fabrication processes that enabled IBM to use electroplating in magnetic film memory production (see Sections 2.2.4 and 2.4.2). Magnetic film memory was only used by IBM on two System/360 Model 95 computers that were built under special contract for NASA in 1968. With an access time of 67 ns [6, 8], this memory provided a level of performance that was not achieved by semiconductor memory until several years later. However, the most important impact of IBM’s magnetic memory program on computers came when the electrochemical fabrication processes that had been invented to build film memory structures became a key enabler of a new technology to manufacture the thin film head for data storage. 2.2.3 Data Storage

High performance data storage systems entered a new era in 1956 with the announcement of the RAMAC 305, the first IBM system to offer a disk drive storage system (Figure 2.2). This system used fifty 24 in. diameter magnetic disks, each with sets of moving arms containing inductive read/write heads. Data were recorded on both sides of the 50 disks at a density of 2 kb in.−2 to create a system with a total capacity of 5 MB. Each head consisted of a coil that was hand-wound around a magnetic core and was mounted so that the pole tips were flying in close proximity to the spinning disks. In the write mode, current pulses through the coil encoded data by creating appropriately magnetized spots in concentric, circular tracks in the magnetic coating on the disk’s surface. In the read mode, the system used the voltage induced in the coil as the magnetized spots moved past the pole tips to sense the data. An important measure of performance for a data storage system was the areal density of data on the disk. A higher areal density, in addition to giving the system greater storage capacity on a smaller diameter disk, also meant faster access to data as well as a reduction in the cost per bit of information stored. The size and configuration of the pole tips at the head/disk interface were key factors in determining the size of the magnetized spots and thus, the areal density. By 1965, engineers had decreased the dimensions of the hand-wound heads and made other improvements in technology to achieve an areal data storage

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2 The Path from Invention to Product for the Magnetic Thin Film Head

Figure 2.2 The RAMAC 305, announced in 1957, was IBM’s first system to use magnetic disk storage technology. It used 50 disks, each 24 in. in diameter with a storage

density of 2000 bits/in.2 to provide a total machine capacity of 5 MB. The cabinet visible beyond the operator housed the memory of the RAMAC system with its stack of 50 disks.

density of 300 kb in.−2 . There was, however, a limit to how small mechanically wound heads could be made; at best, the existing fabrication technology might be pushed to gain only one or two more orders of magnitude in areal density. There would still be the need for a mass production process to eliminate the significant cost of winding each head individually. An advanced disk storage device of that era along with a close-up photo of a ferrite head with a wound coil is shown in Figure 2.3 [9]. Various proposals for miniature structures to replace the wire-wound heads had been made over the years since the introduction of the RAMAC system, the most promising of which was the thin film head shown schematically in Figure 2.4. The first patent for a thin film head was filed by Gregg in 1961 and issued in 1967 [10]. Other patents and publications that appeared throughout the 1960s and 1970s presented alternate designs and/or theoretical analyses for thin film heads, but there was no viable process that could manufacture the proposed devices in a structure that met the advanced needs of the next generation disk drive system. As computer manufacturers tried to come up with a suitable manufacturing process, the task fell to their experienced device fabrication engineers. Since the vast majority of people working in advanced electronic fabrication were involved in some aspect of LSI processing, it is not surprising that these engineers sought to adapt the technology of the silicon world to thin film head fabrication. As they envisioned the fabrication of the head, permalloy, an alloy of nickel and iron with appropriate magnetic properties, would be evaporated or sputtered as a blanket film and patterned by photolithographic and etching processes to

2.2

The State of the Art in the 1960s

Coil Head arm

Ferrite core

Feed wire Head gap (look closely) Slider

Figure 2.3 The hand-wound ferrite read/write head remained in use through much of the 1980s until disk drive manufacturers could learn and implement the new thin film head fabrication technology.

(a)

(b)

The figure shows the popular 5.25 in. Seagate ST-251 disk drive of that era along with a greatly enlarged view of the ferrite head mounted at the tip of the actuator arm.

(c)

Figure 2.4 Schematic drawings of thin film head structures discussed in this chapter. (a) A single-turn horizontal head, (b) a single-turn vertical head, and (c) a multi-turn vertical head.

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2 The Path from Invention to Product for the Magnetic Thin Film Head

form the magnetic yokes of the head; the copper windings in the head would be created by similar deposition and etching steps; and sputtered SiO2 would be deposited and patterned by etching to provide insulation. Arrays of heads would be mass produced on a single substrate that would later be diced into individual devices for mounting in the disk drive unit. From the late 1960s through 1979, virtually all computer manufacturers had programs to adapt LSI type processes to the manufacture of a thin film head. 2.2.4 Electroplating Technology

By the 1960s, electroplating had been in use for many decades to deposit a variety of metals for jewelry, decorative coatings, corrosion protection, and wear resistance. However, no attempts to tailor magnetic or most other physical properties in electroplated metallic deposits had been reported. With few exceptions, the processes were carried out by artisans using proprietary solutions and process steps with little understanding of the underlying science. Plating was generally regarded as a shop art and, while being accepted for the fabrication of printed circuit boards, had never been regarded useful in the production of electronic devices with precisely tailored material properties. In particular, those who tried to electroplate magnetic alloys found it difficult to consistently obtain the required magnetic parameters, especially in the configurations required for memory and other devices. Electroplating did have cost advantages and, with the invention of the throughmask plating process described later in this chapter, offered the greatest precision in fabricating microstructures out of plateable materials. As one of the authors (L.T.R.) was attempting to use plating to fabricate magnetic film memories, he encountered the variable results and instability of the magnetic properties of plated permalloy that others had found in doing similar work. He, however, was able to develop sufficient understanding of the plating process and of the plated permalloy, which led to the inventions of a new plating tool, the appropriate plating solutions, and the deposition and annealing parameters that ensured reproducible, stabilized, and precisely controlled magnetic properties in the deposited films [11]. The advances in electroplating that came out of these studies were crucial to the invention of the thin film head and are summarized in Section 2.4.2. 2.3 Finding the Right Path to Production 2.3.1 First Demonstrations of a Thin Film Head

The first demonstration of a batch-fabricated thin film write head came not from a program to advance recording head technology but rather, out of the magnetic

2.3

P3 P1

C2

C1

M2

Finding the Right Path to Production

P1, P2, C1 – Permalloy and conductor of lower line

I2 P3, C2 – Permalloy and conductor of upper line I1, I2 – Insulation required

I1

P1

M1 Figure 2.5 Coupled film memory structure. Although designed for use as a magnetic film memory, the part of the structure comprised of the copper conductor C1 with

Metal ground plane permalloy layers P1 and P2 wrapped around it could just as well function as a one-turn magnetic head if there were a gap in the permalloy surrounding the copper.

film memory work that was described in Section 2.2.2. One of the structures built during this program, the coupled film memory [12], is shown in Figure 2.5. As is pointed out in the caption, the lower line is essentially a copper conductor passing through a closed magnetic yoke. By putting a gap in the yoke, a one-turn magnetic recording head can be obtained. To meet the requirements of a high-density storage system, however, the gap would have to be very narrow – less than 2 μm. One of the fruits of IBM’s film memory program was the invention of throughmask plating, a new fabrication process that did not use the conventional subtractive approach of chemically etching a blanket film of permalloy or copper through a photoresist mask to form the required patterns. Instead, through-mask plating put an inverse mask with openings for the pattern elements on a conductive seed layer, and the required structure was created by the additive process of electroplating through the openings in the resist. Used in combination with the advances in electroplating that also came out of the magnetic film work, through-mask plating had the capability of producing well-defined, thick, 3-D permalloy patterns with precisely controlled magnetic properties. The first batch-fabricated thin film heads, each a single-turn, horizontal structure such as shown in Figure 2.6, were produced using the through-mask-plating approach [13]. The gap was created by including a 2 μm wide band of electron beam resist [14] in the mask for plating the upper layer of permalloy. The structure described in the previous paragraph had not been designed to fly over a spinning disk. However, the static test results reported in the cited reference [13] supported the conclusion of theoretical analyses that “microminiaturized heads fabricated from thin films are expected to give satisfactory performance.” In particular, (i) “the dimensions of the written bits corresponded very closely to the dimensions of the gap” and (ii) no lag in switching was seen with equipment having a time resolution of better than 5 ns.

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2 The Path from Invention to Product for the Magnetic Thin Film Head

g = 2 μm

I

w = 200 μm 2.5 μm I = 2.5 μm y = 250 μm c = 6 μm Figure 2.6 Perspective view showing the dimensions and structure of the first thin film recording head fabricated with a 2 μm gap.

The next step was to build a thin film head that could be flown over a spinning disk to test the read and write performance in a real data storage system. This head was similar to the initial demonstration structures except that the new devices were designed as vertical instead of horizontal heads. (Figure 2.4 shows the head configurations that are relevant to the discussion in this chapter.) The difference was in the location of the gap and in how it was created. In the horizontal head, the top layer of permalloy interfaced with the disk, and the gap was the break in this layer created by the e-beam resist. In the vertical head, the gap was determined by the thickness of a nonmagnetic layer that was introduced between the upper and lower permalloy layers at one end of the structure where these layers were patterned as pole tips. When the wafer was diced into individual heads, the sandwich of the permalloy pole tips and the nonmagnetic copper separator was exposed at the edge of each head. In use, the head was mounted perpendicular to the disk so that the exposed edge interfaced with the disk’s magnetic surface, hence the designation “vertical head.” The vertical head was seen as the preferable configuration for a product because after dicing the substrate became the slider, which could be aerodynamically designed to fly in very close proximity to the disk without ever touching or resting on the disk. Furthermore, since thin film deposition processes were capable of excellent thickness control, the deposition of a nonmagnetic spacer could produce submicron gap widths with tight tolerances and without the need for electron beam lithography. Functional tests found that the head could both read and write data on a magnetic disk, but the read back signal for a single-turn head was too small for a practical storage system. It was clear that a thin film head for a functional data storage product would have to be a multi-turn device as shown schematically in Figure 2.4c. 2.3.2 Interdisciplinary Design of a Functional Head

The fabrication of the first thin film write head by technology invented during the film memory program was triggered by the recognition that part of the coupled film memory structure was basically the same as the structure of a single-turn,

2.3

Finding the Right Path to Production

horizontal inductive head. Furthermore, it was discovered that the plate-throughmask technology could be extended to produce the thick, high aspect ratio structures required for the head. One of the authors of this chapter (L.T.R.), who had invented the through-mask plating technology and had done much of the research that made the electroplating of permalloy a reproducible process, was then using this technology to build the thin film head. As he became familiar with the head structure, it became apparent that LSI processes would be hard pressed to build the thick, 3-D structures required for the thin film head and that through-mask plating was a more appropriate approach for head fabrication. When Dave Thompson, an engineer who had expertise in magnetics, joined IBM in 1969, he joined Romankiw’s program to design functional heads to be built in Yorktown using electroplating processes. Romankiw and Thompson combined their respective expertise in fabrication and in magnetics to design a multi-turn head that would meet the functional requirements of the next-generation data storage system and, although challenging, could be produced with the proposed fabrication paradigm. These challenges and the reasons they had to be resolved to make a viable head included the following:

• Creating a five-turn coil with 2 μm high by 3 μm wide copper conductors spaced

3 μm apart. (The turns of the coil had to be as close to the gap as possible since leakage between the upper and lower legs of the yoke reduced the efficiency of the turns as their distance from the gap increased. For a yoke with 10 𝜇m separation between the legs, this requirement dictated that all the turns had to be within 100 𝜇m from the gap. The through-mask plating process could form the coils, but, as noted in Section 2.4.3.3, removing the seed layer from the narrow spaces between turns required special attention.) • Patterning 2 μm thick, magnetically oriented permalloy with tight composition control and with perfectly smooth edges. (Irregularities at the edges could pin the magnetic domains, increase H c , and create unpredictable domain patterns. Meeting the requirements for permalloy in the head was not possible with through-mask plating and required the invention of the plating frame as discussed in Section 2.4.3.2.) • Providing insulation between the coil and the permalloy that had a near-planar surface for the deposition of the upper permalloy film. (Insulation was necessary in the multi-turn head to prevent current shunting between the turns by the permalloy. The upper yoke had to be deposited on a near-planar surface because any significant surface topography could impede magnetic switching.) • Producing 2–3 μm thick resist patterns with near vertical walls for throughmask plating. (The only commercially available high-resolution resist was designed for semiconductor processing, where only 0.5 𝜇m thick resist was required.) Addressing these and other fabrication issues while building the five-turn vertical head was an essential step in learning how to carry out each of the process steps in the specific context of the thin film head and in integrating these operations into a viable manufacturing process. Several additional inventions that were

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2 The Path from Invention to Product for the Magnetic Thin Film Head

A

A Figure 2.7 Cross section of one of the first five-turn heads that were completed in Yorktown. The first turn of the coil separated the legs at the right end of the head and

defined the thickness of the nonmagnetic gap that will be exposed when the end of the head is lapped back to the plane A–A perpendicular to the photo.

crucial to the successful manufacture of the head were made during this phase of the work and are discussed in Section 2.4. A cross-section photograph of one of the first five-turn heads is shown in Figure 2.7. Details of other prototype heads that were fabricated during this program are shown in Figure 2.8. It is worth noting that the interdisciplinary design approach, wherein the fabricator of the head was actively involved in its design, resulted in a structure that was so well matched to the capabilities of the fabrication process that it took less than 2 months from the start of fabrication to the completion of a working head. Furthermore, the tools and processes that were ultimately used in production were basically the same as those created during the thin film memory program even though the permalloy and copper patterns in the heads were nearly an order of magnitude thicker than in the memory structures. 2.3.3 Early Tie-in to Manufacturing

A crucial factor in bringing the new fabrication approach to the manufacturing floor was the establishment of close ties with IBM’s General Products Division (GPD) laboratory in San Jose, the division that had the responsibility for developing and manufacturing IBM’s next generation of data storage systems. The Watson researchers realized that if their work was to become an IBM

2.3

37 41 9

(a)

25 kV

37 42 5

5V

Photo resist mask on copper seed layer

25 kV

50 V

(b) Electroplated copper coil after resist removal Insulation

Back closure

Finding the Right Path to Production

Permalloy A

Si substrate A Copper (c) winding

(d)

Permalloy

Early version of a thin film head-Yorktown

Figure 2.8 SEM (scanning electron microscope) photos taken during the fabrication of prototype versions of product heads. (a) Photoresist plate-through pattern for a 16 turn coil. (b) Plated coil after removal of resist and seed layer. The turns were of the order of 3 μm wide with 2 μm spaces where the coil passed through the magnetic yoke to minimize the

distance between the gap and the back closure of yoke. Dashed outline shows the area of the yoke. (c) Cross-section drawing of an eight-turn head. Cutting and lapping the structure in the plane A–A perpendicular to the plane of the drawing exposed the gap that interfaced with the disk. (d) SEM photo of a cross section of the eight-turn head.

19

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2 The Path from Invention to Product for the Magnetic Thin Film Head

manufacturing process, it was GPD that would have to accept and implement the technology. Romankiw and Thompson therefore fostered a relationship with their colleagues in San Jose by keeping them informed on a weekly basis of every step in Yorktown’s progress in head fabrication. GPD was aggressively pursuing the LSI approach and, initially, showed little interest in an alternative process. However, in the absence of any completed heads of their own, GPD was willing to evaluate structures such as the single-turn vertical head that had been built in Yorktown. While the five-turn head was being designed and built at the Watson Research Center using plate-through-mask processes, GPD had also designed a multi-turn head and was struggling to overcome a serious obstacle in patterning the 2 μm high coils by LSI’s approach. The coils had to be at least 2 μm tall with a rectangular cross section to carry sufficient write-current in the head. Since subtractive processes and even lift-off do not faithfully replicate the photoresist mask, the best this process could produce was coils with severely reduced cross sections [15]. The Yorktown group had avoided this problem by using the through-mask plating process to create the copper coils. GPD engineers found it hard to believe the results Yorktown was reporting and so, urged by their manager, reluctantly agreed to have one of the authors of this chapter (L.T.R.) come out with all the necessary plating equipment to demonstrate what additive plating-through a mask could do. In less than a week, all the equipment had been set up in San Jose and was producing the coil patterns that could not be achieved by subtractive etching. It took only a single meeting after GPD management saw the extremely well-formed copper coils fabricated in their own laboratory for them to decide that plating was the way to go. The difficulty encountered in forming the coil in the thin film head highlights the importance of matching the fabrication process to the specific structure. Table 2.1 compares the ground rules for designing the most advanced LSI devices around 1970 – the time when head fabrication engineers were looking for a process to mass produce the thin film head – with the actual dimensions of the coil structure in the first manufactured thin film head. The ground rules are based on conversations one of the authors (S.K.) had with Robert Dennard, an IBM Fellow who is widely recognized for his contributions to semiconductor technology throughout his career. The coil dimensions are for the coil structure in the first thin film head product. This comparison makes it clear that chemical etching, even if it had Table 2.1 The most critical patterning requirements in the thin film head compared with the maximum thickness and smallest lateral dimensions allowed in advanced LSI designs around 1970.

Thickness (μm) Line width (μm) Space between lines (μm)

Coil dimensions in thin film head

1970 ground rules for advanced LSI structures

2.5 3.0 2.0

1 T Hc < 1.0 Oe; Hk: 2.0–5.5 Oe Thermal stability to 250 °C Resistant to corrosion High permeability Near zero magnetostriction

Removal of Fe(OH)3 by filter Adjustment of mass balance for pH and Fe based on real time on-line analysis

Ultimate solution:

Used today in many electrochemical applications including BEOL Cu plating

Steady state (“bleed and feed”) enables infinitely long bath operation

Electroplating tool: The paddle cell (1) Plating through mask on thin seed layers (5)

US Patent 4,102,756 US Patent 5,352,350

Frame plating process for permalloy (6)

NiFe electroplating bath (2)

Thin film head I. Inductive head II. MR Head III. Merged Inductive/MR head

High aspect ratio plating and seed layer removal (7) Baked resist as insulation (9)

NiFe bath aging and steady state operation (3) Real time on-line plating bath analysis (4)

Magnetic materials studies (8)

Figure 2.12 The inventions pertinent to any aspect of the plating bath are so interrelated with each other that they are treated together in this section.

2.4

Key Inventions for Thin Film Head Production

B

Weight % Fe in film

30

A

20 Tolerable spread of composition

10

Wolf’s bath 0

10

20

30

40

50

60

70

80

90

100

id (mA cm–2) Figure 2.13 An extensive study of the dependence of composition on bath chemistry and plating parameters provided the information necessary to ensure the deposition of permalloy with consistent magnetic properties on the production line.

was not practical for a manufacturing operation in which control of the composition of the deposit was critical. Figure 2.13 shows the NiFe composition in the deposit as a function of plating current density for plating parameters pertinent to this discussion. The curve at the left shows the extremely strong dependence of composition on current density for permalloy deposited as prescribed by Wolf. It would have been virtually impossible to maintain the required 20% Fe within the specified tolerance from run to run or even within a single wafer using Wolf ’s bath. A systematic study of the properties of permalloy plated in a paddle cell was carried out as a function of bath chemistry, degree of agitation, and current density to establish the optimum conditions for production plating. These studies found that diluting Wolf’s bath by a factor of two or more allowed much tighter control of the plating process. Curves A and B in Figure 2.13 show the dependence of composition on current density for permalloy plated from a diluted bath with moderate agitation. These curves could be translated up or down with an increase or decrease of iron in the bath or with an increase or decrease in agitation rate. (Curve B is an extension of Curve A, but plated with higher iron content in the bath and/or greater agitation to bring it into the composition range of interest.) It can be seen that the diluted bath provided two plateaus, one in the region of 5–20 mA cm−2 , and the other around 100 mA cm−2 . The plateau at the lower current density was chosen as the operating point for production. At this current, the required thickness of permalloy could be deposited in about 20 min, which met the throughput needs of the line and allowed for excellent control of the thickness. Working in the lower current range also avoided the burning (oxidation) that was seen in some deposits at 100 mA cm−2 .

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2 The Path from Invention to Product for the Magnetic Thin Film Head

The studies to determine the optimum operating conditions for plating permalloy played a key role in establishing electroplating as a viable process for producing magnetic films with tailored, tightly controlled properties. It is far beyond the scope of this chapter to present all the details of these studies and to properly reflect their depth and importance. More extensive treatments of this work can be found in the patent issued for the plating process [20] and in chapters by Andricacos and Romankiw [34] and by Romankiw and Thompson [11] in the respectively referenced volumes. Plating Controls The plating process, of course, caused changes in the plating solu-

tion as the permalloy was being deposited. Iron was consumed by being plated out in the deposited permalloy and by the oxidation of Fe++ in solution to Fe+++ , which, because of its low solubility product (ksp = 6 × 10−36 ), was immediately precipitated out as gelatinous Fe(OH)3 and was trapped on the filter. Also, because the deposition was less than 100% efficient, there was some dissociation of water at the cathode with the formation of hydroxyl ions and H2 gas. Continuous adjustment was required to compensate for the losses of iron and for the continuous upward drift in pH of the solution caused by the hydroxyl ions produced at the cathode. Monitoring pH was simple; measurement of Fe++ was complex and could not readily be done in real time. Fortunately, it had been observed that the oxidation of Fe++ to Fe+++ was accelerated by the recirculation of the plating solution between the holding and plating tanks. Since pH drift only occurred during plating and the bulk of the oxidation took place during plating (the only time the recirculation pump was on), the loss of iron could be linked to the change in pH without the direct measurement of Fe++ . Mass balance calculations, confirmed by empirical measurements, determined the correlation, thereby greatly simplifying the bath control issues. The operating temperature also affected the deposition process. As the temperature increased, the anomalous behavior decreased and disappeared completely above 75 ∘ C. For practical reasons, it was chosen to operate the plating solution between 25 and 35 ∘ C. The main reason for this choice was that the oxidation rate of Fe++ to Fe+++ increased with temperature. At temperatures above 35 ∘ C it became difficult to maintain iron in the Fe++ state since most of the added Fe++ was oxidized and trapped on the filter. “Bleed and Feed” Three phases of bath aging were noted in operating the plating

bath: (i) the gradual build-up of Fe+++ and Fe(OH)3 colloid; (ii) continuous stable operation for several months; followed by (iii) excessive anion build-up and deterioration of the bath. The ultimate solution to bath aging was the introduction of steady-state operation, which was named “bleed and feed.” This was an important innovation in the electrodeposition industry, which up to that time had been relying on batch operation, that is, discarding a deteriorated bath and starting the aging process all over again with a fresh bath. Steady-state operation relied on bleeding off a pre-established amount of used plating bath per unit time of

2.4

Key Inventions for Thin Film Head Production

operation and replacing it with an equal amount of fresh plating solution. The “bleed and feed” procedures could be initiated at any chosen point during the second phase of bath aging to freeze the bath chemistry along with the properties of the deposit at that bath age. The NiFe plating bath could then be used for years rather than months without having to dump and replace the entire bath. The bled portion could also be used to initiate operation of a new, pre-aged bath. The “bleed and feed” concept is now used not only for plating magnetic materials, but also in plating solder interconnects and in plating copper in packaging and on silicon chips. While it is good to have a clear understanding of the mechanism of the reaction, this section shows that good engineering practice and common sense achieved reproducibility and control of the complex NiFe plating operation and brought the thin film head into production several years before a satisfactory mechanism of the phenomena had been achieved. 2.4.3 Patterning 2.4.3.1 Through-mask Plating

An important key to building the micron-dimensioned 3-D structures required for the head was the invention of through-mask plating (Figure 2.14). An in-depth study by one of the authors (L.T.R.) of patterns formed by wet chemical etching, sputter etching, ion milling, lift-off, and through-mask plating provided an objective comparison of the capabilities and limitations of each process [15]. The study showed that only through-mask plating could produce the 2–3 μm wide and 2–3 μm tall structures with precisely defined side walls required for the thin film head. The results of this and similar studies are summarized graphically in Figure 2.15. The through-mask plating process is described in Figure 2.16. This process is essentially an atom-by-atom molding of the electrodeposited material in the openings in the resist that precisely replicates both the lateral dimensions and the wall profile of the resist down to atomic dimensions. The smallest possible features were limited only by the capabilities of photolithography and by the ability of the plating solution to penetrate the openings in the resist pattern. Similar considerations determined the height of the structure. Even with the limited capabilities of high resolution resists that were just coming into use in the early 1970s, one of the authors (L.T.R.) was able to demonstrate 12 μm high copper coils with 3 μm wide turns spaced 1 μm apart [35] whereas chemical etching could not produce conductors that were narrower than 5 μm in 0.5 μm thick Al or Cu. Through-mask plating was originally invented to produce conductors with a rectangular cross section in thin film memory structures, but it soon became the only way to produce X-ray masks [36] and magnetic thin film heads and was also an effective way to fabricate magnetic propagation patterns for bubble memories [37]. While the concept of through-mask plating appears to be quite simple, several issues had to be addressed to successfully use this process to build the thin film head. These issues are highlighted in Figure 2.14 and in the dotted links to

33

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2 The Path from Invention to Product for the Magnetic Thin Film Head

1996 Advanced PCs enabled math modeling of primary, secondary and tertiary current

X-ray and litho masks NEMS and MEMS

Adjustment of additives (current suppressors)

1969 Current distribution mapped using conductive paper

C-4 plating

BEOL

Uniform current distribution

Thin film package

Plating through mask on thin seed layers Required uniform current distribution over large area despite pattern density variation Atom-by atom molding of openings in resist precisely replicated wall profile

Precise, high aspect ratio resist patterns

Adherent seed layer with clean surface

Paddle agitation facilitated uniform current distribution

Plating frame A variation of through mask plating Necessary for NiFe Selective removal of seed layer

Electroplating tool: the paddle cell (1) Plating through mask on thin seed layers (5)

Frame plating process for permalloy (6)

US Patent 4,315,985 US Patent 5,352,350

NiFe electroplating bath (2)

Thin film head I. Inductive head II. MR head III. Merged inductive/MR head

High aspect ratio plating and seed layer removal (7) Baked resist as insulation (9)

NiFe bath aging and steady state operataion (3)

Real time on-line plating bath analysis (4)

Magnetic materials studies (8)

Figure 2.14 Through-mask plating was an atom-by-atom molding process that precisely replicated the wall profile of the photoresist mold.

2.4

Key Inventions for Thin Film Head Production

Chemical etching (a)

(b)

Umbrella effect

Sputter etching RIE Ion milling Shrinking umbrella

Lift–off (c)

(d)

Expanding umbrella

Pattern plating Mold replication L.T. Romankiw (2/91)

Figure 2.15 Comparison of pattern replication achievable by the major patterning processes for microelectronic fabrication. Undercut of the mask during chemical etching (a), erosion of the mask during sputter etching or ion milling (b), and expansion of the mask during lift-off deposition (c) all resulted in narrowing of the pattern and distortion of the side wall. These effects

became more pronounced as the pattern thickness increased. Pattern plating through a mask (d) faithfully replicated the resist mold with atomic precision. Removal of the thin seed layer (typically no more than 1000 Å) could be done with minimal effect on the pattern; any adverse effects of seed layer removal became less significant as the pattern thickness increased.

other inventions. A major concern was achieving a uniform plating current density across the substrate. It was known that plating on a patterned surface gave rise to variations in current density that depended on the non-plated spaces between the patterns and the density of the features being plated. In copper plating, this effect causes a variation in thickness of the patterned elements across the substrate. For permalloy, where the composition also depends on the current density, both the thickness and composition can vary across the pattern. The balloons in the upper right area of the figure highlight how the effects of current density variation were understood and minimized. Today, one would start by modeling the operation to better understand the primary, secondary, and tertiary current distribution in the cell and the effects of the

35

36

2 The Path from Invention to Product for the Magnetic Thin Film Head

UV radiation Mask

Metallic adhesion layer and plating base Unexposed resist Dieletric substrate

Plated metal Dieletric substrate

Figure 2.16 Through-mask plating process. A thin conductive layer that served as a plating base was deposited (typically by evaporation or sputtering) and covered with a photoresist mask that was photolithographically patterned to provide openings in the resist for the desired plated pattern. The resist had to be thicker than the final thickness of the plated pattern. The next step was

to electroplate the desired metal through the openings in the resist. The thickness of the deposit from this operation was determined by the plating time and current; the walls of the pattern were precisely defined by the photoresist mold. The final step was to remove the resist mask and to etch away the exposed seed layer, preferably by ion milling.

pattern being plated [38, 39]. In 1969, however, the required mathematics was not available, and even if it were, the modeling would have required a lot of expensive computer time on a main frame system. Therefore, dye injection studies were used to observe the eddy currents created by the agitation, and conductive paper was used to simulate the electric current distribution in the cell. This work led to the invention of paddle agitation discussed in Section 2.4.2.1, which contributed to a more uniform current distribution. The adjustment of current suppression additives in the copper plating solution further improved the uniformity of the copper deposits. In permalloy plating, work on the NiFe bath composition and

2.4

Key Inventions for Thin Film Head Production

operating parameters (Section 2.4.2.2) minimized the dependence of composition on current density. Furthermore, the invention of the plating frame, a variation of through-mask plating discussed in Section 2.4.3.2, reduced the current variation across the pattern to negligible levels. It is important to note that the sophisticated modeling done in 1996, after advanced PCs became available, showed remarkable agreement with the findings of the 1969 dye injection and conductive paper studies [28]. Complex math and calculations are not always necessary if there is a reasonable understanding of the phenomena (in this case, the behavior of the diffusion layer under given agitation or flow conditions) and this understanding is combined with good engineering and intuition. Modeling is a valuable tool in expediting advances in technology, but the importance of good engineering and intuition should not be underestimated. In addition to the electroplating issues, the following also needed to be resolved:

• No high resolution resist was commercially available that could form a platethrough mask thick enough to produce 2–3 μm thick copper and permalloy patterns. • There was no viable process for assuring a residue-free surface for plating after forming the resist pattern. The standard approach to residue removal in LSI fabrication used an oxygen plasma, which would have destroyed the photoresist and oxidized the permalloy seed layer. • The plating base and its adhesion layer had to be removed after plating without adversely affecting the coil or yoke structures. The resolution of the above issues is dealt with in Sections 2.4.3.2 and 2.4.3.3. 2.4.3.2 Frame Plating

The frame plating process, a variation of through-mask plating that was essential for plating permalloy, is outlined in Figure 2.17. Similarly to through-mask plating, the plating frame process started with a conductive seed layer. However, the first mask, instead of providing openings only where the structural elements of the device were to be plated, outlined each element with a narrow (approximately 10 μm wide) frame of resist. Plating was thus done over a pseudo-continuous area with only minor perturbations by the frames. After plating, a second layer of resist was applied and patterned to cover the tops of the structural elements. The combination of the resist frame and the second resist pattern provided essentially complete encapsulation of the plated device features during subsequent seed layer removal. The primary requirements for the permalloy pole tips and yokes were (i) uniform thickness and alloy composition across the magnetic elements, (ii) a properly defined magnetic easy axis, and (iii) side-walls with very smooth edges. The benefits of the frame plating process enumerated in the colored circle of Figure 2.18 show why frame plating was necessary to fabricate the permalloy yokes and pole tips.

37

38

2 The Path from Invention to Product for the Magnetic Thin Film Head

Permalloy seed layer

Photoresist frame

Substrate

Electroplated permalloy

Etch mask

Finished pole tip

Figure 2.17 Steps in the frame plating process. The initial resist pattern on the seed layer outlined the desired structure with a narrow (about 10 μm) band of resist, and a pseudo-continuous film was plated over the entire wafer. A second resist mask was

applied to protect the desired structure, and the surrounding permalloy was removed by chemical etching leaving a structure with side walls precisely as defined by the plating frame.

The left side of the figure focuses on the benefits that come from plating a pseudo-continuous film. As noted in the previous section, through-mask plating resulted in pattern-dependent variations in plating current density across the substrate. For copper, the effect on the deposit was minimized to an acceptable level by additives and by proper agitation in a paddle cell. For permalloy, where the composition of the deposit and hence its magnetic properties were also affected by the current density (see Section 2.4.2.2), depositing a pseudo-continuous layer as produced by the plating frame process provided the same uniformity of current density that occurs while plating a continuous sheet film. This uniformity was confirmed by electron microprobe analysis, which showed no detectable variation in permalloy composition across a 25 μm pole tip plated with a 10 μm wide frame.

2.4

Key Inventions for Thin Film Head Production

39

Frame plating enabled: Psuedo-uniform current distribution Smaller field to define easy axis Easy patterning of laminated films Easy removal of excess plated material Smooth, well-defined NiFe edges

Deposit is a psuedocontinuous layer with minimal pertubation by the frames

Simplified process

Uniform current distribution promoted uniform composition and thickness

Non-critical alignment for etch mask More leeway in etching: Especially important with laminated films

Demagnetizing effects at narrow pole tips were minimized by psuedo-continuous layer allowing small external field to define easy axis

Preserved smooth edges defined by resist frame Prevented “rat bites” encountered in seed removal with through-mask plating process

Electroplating tool: The paddle cell (1) Plating through mask on thin seed layers (5)

Frame plating process for permalloy (6)

NiFe electroplating bath (2)

Thin film head I. Inductive head II. MR head III. Merged inductive/MR head

High aspect ratio plating and seed layer removal (7) Baked resist as Insulation (9)

Device elements protected during etch step

NiFe bath aging and steady state operataion (3)

Real time on-line plating bath analysis (4)

US Patent 3,853,715

Magnetic materials studies (8)

Figure 2.18 The invention of the plating frame resolved a number of issues in fabricating the yoke and pole tip of the thin film head.

40

2 The Path from Invention to Product for the Magnetic Thin Film Head

Easy axis

Figure 2.19 Typical domain configuration in the permalloy pole tip and yoke.

The pseudo-continuous layer also played a critical role in allowing the use of a relatively low, easier to manage 500 Oe field to define the easy axis of the permalloy yoke. (The easy axis is the direction of magnetization in the film in the absence of an external field and is created by iron atom pairing along the direction of an externally applied magnetic field during deposition.) Magnetic considerations dictated that the easy axis for the head in the read mode be oriented across the pole tip as shown in Figure 2.19. The orientation field must be of sufficient magnitude to overcome the demagnetizing field that exists within any magnetized structure. (The reference cited here provides a fuller discussion of the demagnetization factor and other magnetic parameters [40].) The demagnetizing factor is strongly dependent on the geometry. For a continuous, flat film this factor approaches zero, so that an easy axis can be defined with an external field of a few tens of oersteds; in a narrow structure such as the pole tip, the demagnetizing flux can approach the saturation magnetization of the material (about 1 T for permalloy). The much-reduced demagnetizing field in the pseudo-continuous deposition inherent in the plating frame process makes it possible to properly orient the pole tips with a modest external magnetic field. The complete encapsulation of the permalloy by the combination of the plating frame and the second resist mask resolved the issue of maintaining a smooth edge on the permalloy features when removing the seed layer. The etchants used to remove the excess permalloy that formed the pseudo-continuous plating

2.4

Key Inventions for Thin Film Head Production

were quite aggressive. If the basic through-mask plating process described in the preceding section were used, even the relatively short exposure of the unprotected edges to remove a seed layer of less than 1000 Å left would have left undesirable “rat bites.” With the full encapsulation provided by the plating frame process, the smooth, as-plated edge was retained even though the plating frame process called for removing the full 2 μm thickness of the excess permalloy that created the pseudo-continuous layer (Figure 2.20). The complete encapsulation was particularly useful in later work where laminated permalloy (multilayers of permalloy interspersed with layers of nonmagnetic material) was used for the yoke and pole tips [41]. 2.4.3.3 Ancillary Issues in Pattern Plating

The thin film head program faced a few problems that had not previously been addressed in microelectronic fabrication (Figure 2.21). (a). One problem was the lack of a suitable, commercially available high resolution resist. High aspect ratio resist was just coming on the market in the late 1960s, but that resist was aimed at the semiconductor industry, where thin layers of resist were preferred. (b).

(a)

(b) Figure 2.20 (a) SEM micrograph shows the extremely well-defined, smooth edges of a 90∘ corner in a 2 μm thick permalloy pattern plated using a resist frame. (b) SEM shows the same structure produced by

conventional chemical etching using a resist pattern on the top surface. The imperfections on the edges that result from conventional etching serve as nucleation sites for undesirable domain walls.

41

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2 The Path from Invention to Product for the Magnetic Thin Film Head

Good seed layer adherence at elements of head; removable everywhere else

Ancillary issues in pattern plating Resist for thin film head patterning

Resist High resolution High aspect ratio Seed layer Adherent Removable No resist residue

Cr – Widely used as adhesion layer, but difficult to etch

Solution to problem: Ti adhesion layer for Cu – easy to etch with no mask on Cu coils NiFe – Deposit at elevated temperature with no adhesion layer

Required resist: High resolution for 2 μm wide coils High aspect ratio with vertical profile for 2–3 μm high patterns

Available resists in 1960s: Negative working (limited resolution; hard to remove) Positive, high resolution AZ resist introduced in late 1960s for LSI needs: (thickness 0 F [aPp+ ]p

(3.4)

0 0 = EP0 p+ ∕P− EM Here, ΔEEMF (ΔEEMF m+ ∕M ) represents the electromotive force for the 0 repbulk M and P galvanic couple at standard conditions (Figure 3.4). ΔE𝜃→0 resents the equilibrium underpotential of M UPD layer in the 𝜃UPD → 0 limit p+ = 1, aP = 1). The logarithmic term (UPD shift) under standard conditions (am+ M provides the correction due to departure from standard conditions. The relation between the thermodynamic quantities discussed in Eq. 3.4 is graphically depicted in Figure 3.4. Inspection of the above equation implies that the driving force for the redox reaction can be modified by adjusting the activities of Mm+ and Pp+ ions in the reaction solution. If there are no Mm+ ions in the reaction solution, the logarithmic term has a dominant contribution to the value of ΔEredox . This means that under these experimental conditions, an extremely high nucleation overpotential

3.3

Metal Deposition via Surface-Limited Redox

67

aMn+< 1 MUPD/S(h,k,l) stripping peak

M bulk dissolution wave

P bulk dissolution wave aPp+< 1

aMn+< 1

ΔE 0P/Pp+

Current

ΔE 0M/Mn+

Potential

ΔE 0θ→0

ΔEredox

MUPD/S(h,k,l) deposition peak M bulk deposition wave

P bulk deposition wave

ΔE 0EMF

Figure 3.4 Schematics of the thermodynamic quantities determining ΔE redox for an SLRR reaction, and their mutual relation. The gray lines are current–potential dependence for bulk M metal electrode and

UPD of M on substrate S. The dark line is the current–potential dependence for bulk P noble metal electrode. The terms from Eq. (3.4) are identified in the figure.

can be achieved. As a consequence, this leads to a high nucleation rate and small size of stable P metal nuclei on the substrate surface. Examples of the dependence of the thermodynamic driving force and nucleation rate on the ratio between the activities of Pp+ and Mm+ ions in solution are shown in Figure 3.5. This dependence is calculated using parameters valid for Pt deposition on Au(111) via SLRR 1016

a

pt 4

0.8 a

+

pt 4

=

=

1

0.

+

a

pt 4+

0.2 a

pt 4+

=

=0

.01

0.

00 1

a

pt 4+

=1

=0

106

a

104

pt 4

+

102

.00 1

0.0 10−7 10−6 10−5 10−410−3 10−2 10−1 100 101 (a)

108

1

pt 4

m = 1, p = 4, m/p = 0.25

=

a

0.4

a 1012 pt 4+ = 0. 01 1010

4+

JPt (cm−2 s−1)

01

0.6

m = 2, p = 4, m/p = 0.50

1014

m = 1, p = 4, m/p = 0.25

a pt

ΔEredox (V)

+

m = 2, p = 4, m/p = 0.50

aCum+/aptp+

Figure 3.5 (a) Estimate of ΔE redox vs. aCum+ ∕aPt4+ ratio and (b) nucleation rate vs. aCum+ ∕aPt4+ ratio. Estimates are made for Pt deposition via SLRR of Cu UPD layer, black:

100 10−7 (b)

10−6

10−5 aCum+/aptp+

=

1

10−4

2Cu0UPD + {PtCl6 }2− = Pt0 + 2Cu2+ + 6Cl− and red: 4Cu0UPD + {PtCl6 }2− + 2Cl− = 4{CuCl2 }− + Pt0 .

10−3

68

3 Electrochemical Surface Processes and Opportunities for Material Synthesis

of a Cu UPD layer (Figure 3.1a). Two possible scenarios are considered, both having a Pt(IV) salt ({PtCl6 }2− ion) in solution. In the first case, the oxidation state of 0 0 − ΔE𝜃→0 ≈ 0.1 V). Cu is 2+ (H2 SO4 -based reaction solution, m∕p = 0.5, ΔEEMF The second scenario assumes the Cu oxidation state of 1+ (HClO4 -based reaction 0 0 − ΔE𝜃→0 ≈ 0.2 V). It is evident that the driving force solution, m∕p = 0.25, ΔEEMF for SLRR reaction, ΔEredox , is larger in the case of m∕p = 0.5 for aCum+ ∕aPt4+ < 0.1 (Figure 3.5a). Indeed, it is apparent that the stoichiometry coefficient ratio has a large effect on ΔEredox . For example, an almost 0.4 V larger ΔEredox is available for the SLRR reaction when m∕p = 0.5 than in the case of m∕p = 0.25 (aCum+ ∕aPt4+ = 5 × 10−6 and aPt4+ = 0.01). The dilution of Cu ions in the reaction solution and consequent decreasing value of their activity has a strong effect on ΔEredox . This is evident in particular for SLRR reactions with larger m/p ratio (Figure 3.5a). In this case, for ultimately small values of aCum+ ∕aPt4+ mimicking the situation when no UPD metal ions are present in reaction solution (aCum+ ∕aPt4+ < 10−7 ), one can achieve a rather large nucleation overpotential (ΔEredox > 0.5 V). However, the dilution of Pt ions in reaction solution and a lower value of their activity decrease the value of ΔEredox . This trend is stronger for SLRR reactions with smaller m/p ratio. The effect of the driving force for the SLRR reaction is quite important for morphology control of metal deposits. Using classical nucleation theory [55], we can estimate approximately the nucleation rate for Pt on Au(111) achieved during deposition via SLRR of a Cu UPD layer. For the two scenarios discussed previously, the nucleation rate estimates are shown as a function of the aCum+ ∕aPt4+ ratio in Figure 3.5b. The nucleation rate in both cases is very sensitive to the aCum+ ∕aPt4+ ratio. This is particularly important if aCum+ ∕aPt4+ > 10−5 , corresponding to experimental conditions commonly reported in the literature, where this deposition protocol is used for catalyst monolayer synthesis [26]. A 10-fold variation in the aCum+ ∕aPt4+ ratio produces approximately 103 –105 times change in nucleation rate. It is also important to notice that the nucleation rate can quickly drop to values that are practically negligible if the aCum+ ∕aPt4+ ratio falls below about 10−4 . The conditions during the SLRR reaction favoring small nucleation rates will produce a Pt deposit that is not uniformly distributed over the Au (substrate) surface. Instead, the Pt deposit would preferentially nucleate at defect sites. This is an undesirable result if catalyst monolayer synthesis is sought. The calculations in Figure 3.5b should be a general guidance for practitioners who use this protocol for Pt monolayer catalyst design. One can see that an SLRR reaction with m/p ratio of 0.5 yields nucleation rates several orders of magnitude higher at a given Cu and Pt activity ratio. This is quite an important fact that should be appreciated if one is after the control of Pt deposit morphology in terms of Pt cluster size and size distribution. In general, we can assume that SLRR reactions with larger m/p ratio produce stable nuclei of smaller average size and thus a metal deposit consisting of smaller clusters. Depending on the nature of Mm+ and Pp+ ions and on the UPD system adopted for the SLRR reaction, different amounts and coverage of metal deposit can be

3.3

Metal Deposition via Surface-Limited Redox

35 nm 50 nm

(a)

80 nm

(b)

Figure 3.6 (a) Pt submonolayer on Au(111) (𝜃Pt ≈ 0.5) obtained by SLRR of Cu UPD layer, m∕p = 0.5, 0.1 M H2 SO4 -based reaction solution, the mean Pt cluster size is 3 nm [15]. (b) Pt continuous submonolayer on Au(111), (𝜃Pt > 0.6) obtained by SLRR of Pb/Cu UPD bi-layer (S.R. Brankovic et al.,

(c) in preparation), mPb ∕p = 0.5, mCu ∕p = 0.25, 0.1 M HClO4 -based reaction solution. (c) Pt submonolayer on Au(111) (𝜃Pt ≈ 0.42) obtained by SLRR of Cu UPD layer, m∕p = 0.25, the mean Pt cluster size is 4 nm, 0.1 M HClO4 -based reaction solution (S.R. Brankovic et al., in preparation).

achieved. This is illustrated in Figure 3.6 using the example of Pt deposition via SLRR of a Cu UPD layer on Au(111) (Figure 3.6a,c), and Pb UPD layer on a Cu UPD layer covered with Au(111) (Figure 3.6b). The deposit morphology varies from a Pt monolayer continuous film to 2D monoatomically high nanoclusters with very narrow size distribution and varying coverage of the substrate. Particularly interesting in Figure 3.6a,c is the spatially uniform coverage of Pt nanoclusters on Au(111). This suggests that the nucleation process is independent of the availability of thermodynamically favorable nucleation sites such as surface defects. The Pt nanoclusters are uniformly distributed across the surface regardless of the presence of surface steps, where preferential nucleation and growth is typically observed during electrodeposition processes. This represents one of the major advantages of this deposition protocol over the traditionally used ones for application in catalyst synthesis. One should notice that, although the stoichiometry of SLRR produces Pt deposits with larger coverage as in Figure 3.6a than in Figure 3.6c, the Pt nanoclusters are slightly smaller in Figure 3.6a than in Figure 3.6c, (3 nm vs. 4 nm). This observation is in agreement with the previous discussion regarding the effect of SLRR stoichiometry coefficients on nucleation rate, that is, SLRR reactions with higher m/p ratio yield higher nucleation rates and smaller stable nuclei. The example in Figure 3.6 demonstrates that manipulation of the experimental conditions for SLRR reactions gives the opportunity to design and synthesize catalyst monolayers with different morphology, cluster size, and coverage [44, 54, 22]. 3.3.4 Reaction Kinetics of Surface-Limited Redox Replacement

Considerable opportunities and challenges for the deposition protocol based on SLRR of UPD layers have led to its growing popularity in the catalysis

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

community [44–49]. The successful application of this method beyond the realm of academic research and laboratory scale experiments requires that the kinetics of metal deposition via SLRR reactions is well understood. A properly defined functional relation between experimental conditions and the resulting reaction kinetics enables facile scale up of this deposition protocol to the level where the reaction volume and amount of synthesized catalyst material become adequate for industrial application. In order to investigate the kinetics of metal deposition via SLRR reactions a phenomenological model describing the change in coverage of the UPD metal during the course of a deposition experiment should be developed. The phenomenological description of the OCP transients during deposition via SLRR of UPD metal is an indirect way to achieve this. If a representative adsorption isotherm for the UPD metal–substrate system participating in the SLRR reaction is known (E vs. 𝜃UPD , Eq. (3.2)), the analytical model of the potential vs. time dependence during SLRR (E vs. t) is easily obtained by combining the appropriate expression for the rate equation [56] with a representative UPD adsorption isotherm model. Therefore, such E vs. t model can be used to fit OCP transients from deposition experiments, providing a direct method to study the kinetics of metal deposition via SLRR of a UPD layer. In this way, it is possible to quantify the effect of various experimental parameters on the resulting kinetics of the deposition process. In the case of zero-order reaction kinetics (N = 0) in terms of 𝜃UPD (deposition via transport-limited redox replacement (TLRR) of UPD layer), the E vs. t model, which can be used to fit OCP data from deposition experiments, has the following form [24]: ] [ ( ) 1 − k0 t RT 3∕2 E = E𝜃→0 − (3.5) ⋅ ln + f ⋅ (1 − k0 t) + g ⋅ (1 − k0 t) mF k0 t Here, t represents the reaction time and k 0 is the TLRR reaction rate constant. The other terms are defined previously. k 0 is defined as [24] ( ) DPp+ ⋅ C ∞p+ m ⋅ UPD P k0 = (3.6) p Γi ⋅𝛿 Here, DPp+ and 𝛿 represent the diffusion coefficient of Pp+ ions and the thickness of the diffusion layer, respectively. The term CP∞p+ represents the concentration of is the surface concentration of a full and Pp+ ions in the bulk solution and ΓUPD i complete UPD layer. In the case of first-order reaction kinetics in terms of 𝜃UPD , N = 1 (deposition via SLRR of UPD layer), the E vs. t model is defined as [24] RT ⋅ [f ⋅ exp(−k ′ t) + g ⋅ (exp(−k ′ t))3∕2 mF − (k ′ t + ln(1 − exp(−k ′ t)))]

E = E𝜃→0 −

(3.7)

The reaction rate constant, k ′ , has the form [24] k ′ = k(CPis )L ,

(3.8)

3.3

Metal Deposition via Surface-Limited Redox

71

where k represents a fundamental rate constant, CPis is the concentration of Pp+ ions at the electrode/solution interface, and L is the reaction order in terms of Pp+ ion concentration. For an Nth order reaction kinetics in terms of 𝜃UPD (deposition via SLRR of UPD layer, N ≠ 1), the E vs. t model has the most general form [24] [ ( ) (1 + Kt)1∕(1−N) RT ⋅ ln E = E𝜃→0 − mF 1 − (1 + Kt)1∕(1−N) ] (3.9) + f ⋅ (1 + Kt)1∕(1−N) + g ⋅ (1 + Kt)3∕(2−2N) In this case, the reaction rate constant, K, is defined as [24] K = (N − 1) ⋅ k ⋅ (CPis )L ⋅ (ΓUPD )N−1 i

(3.10)

Figure 3.7a shows representative OCP transients of Pt deposition via SLRR of Pb UPD and Cu UPD layers on Au(111) in 0.1 M H2 SO4 -based solutions. Under these conditions, the oxidation state of Pb and Cu is 2+, which results in m = 2 in both experiments. Pt is deposited from a hexachloroplatinate complex ({PtCl6 }2− ), that is, p = 4. From the above stoichiometry coefficients it follows that two UPD adatoms (Pb or Cu) react with one Pt ion. These reactions are elementary ones, and the reaction order in terms of UPD metal adatom concentration/coverage can be obtained from the reaction stoichiometry as N = 2, that is, second order [56]. The second-order reaction kinetics for these UPD systems should be understood to be the result of the cooperative involvement of more than one Cu UPD adatom during the redox process [24]. In the most general case, regardless of the 0.7 0.7 0.6

0.5

E (V vs SCE)

E (V vs SCE)

0.6

SLRR of Cu UPD Model fit SLRR of Pb UPD

0.4 0.3 UPD

K Pb = 9.71 s

0.2

UPD

K Cu = 4.01 s

−1

SLRR of Pb UPD SLRR of Cu UPD Model

0.4 0.3

UPD

K Pb = 0.87 s UPD K Cu

0.2

−1

= 3.61 s

−1 −1

0.1

0.1 0 (a)

0.5

5

10

15 t (s)

20

25

Figure 3.7 (a) Open circuit potential transients for Pt deposition via SLRR of Pb UPD (green) and Cu UPD (red) on Au(111), in 10−3 M {PtCl6 }2− + 0.1 M H2 SO4 reaction solution and 1000 rpm rotation rate. (b) Open circuit potential transients for Pt deposition via SLRR of Pb UPD (green)

0

30 (b)

5

10

15 20 t (s)

25

and Cu UPD (red) layer on Au(111), in 10−3 M {PtCl6 }2− + 0.1 M HClO4 reaction solution and 1000 rpm rotation rate. The solid lines represent the model fit, Eq. (3.9), to experimental data. The values of reaction rate constants obtained from the fits are indicated in the graphs.

30

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

m/p ratio, whenever more than one UPD adatom is necessary for the reduction of the depositing metal ion, the reaction order in terms of the UPD metal coverage should be taken as 2 (N = 2). The fits of the model (Eq. (3.9)) to OCP data are shown as continuous black lines. The extracted values of the rate constants for each reaction suggest that Pt deposition via SLRR of Pb UPD is approximately two times faster than Pt deposition via SLRR of Cu UPD layer. At constant temperature, the faster reaction kinetics suggests lower activation energy for the activated complex [56]. In our case, this means lower activation energy for the activated complex of {PtCl6 }2− –Pb UPD adatom as compared to the activated complex of {PtCl6 }2− –Cu UPD adatom. The activated complex represents the entity with sufficient overall energy, allowing direct electron transfer from the UPD adatom on one side to {PtCl6 }2− ion on the other. The difference in kinetics and activation energies of these two deposition reactions must reflect the difference in bringing the Pb and Cu UPD adatoms to the activated state where the electron transfer to {PtCl6 }2− ion is possible. Since there is no significant difference in stability of Pb and Cu ions in 0.1 M H2 SO4 electrolyte [57], it is physically reasonable to expect that Pb as the UPD metal with lower work function would be more easily activated than the Cu UPD adatom. Whenever the two SLRR reactions of two UPD metals are compared in a supporting electrolyte that does not promote significantly the energetics of the UPD adatom dissolution of either one, the UPD metal with lower work functions should yield the faster reaction kinetics. Figure 3.7b shows the OCP transients from the Pt deposition via SLRR of Pb UPD and Cu UPD on Au(111) in a solution containing 10−3 M {PtCl6 }2− + 0.1 M HClO4 . For an SLRR reaction involving the Pb UPD, m = 2, p = 4. As one can see, the value of the rate constant K is significantly smaller than in a 0.1 M H2 SO4 supporting electrolyte (K = 0.87 (s−1 ) for 0.1 M HClO4 vs. K = 9.7 (s−1 ) for 0.1 H2 SO4 ). This means that Pt deposition via SLRR of a Pb UPD layer depends strongly on the nature of the anion in the supporting electrolyte. This means that the rate of Pt deposition via SLRR of a Pb UPD layer can be altered (increased/decreased) by appropriate choice of the supporting electrolyte. The basic difference between {SO4 }2− and {ClO4 }− anions in supporting electrolytes is that the {SO4 }2− is a relatively strong ligand, while {ClO4 }− has no complexing affinity toward metal ions [57]. For this reason, the metal (Pb) dissolution/oxidation process during the SLRR reaction in {SO4 }2− - based electrolyte is significantly promoted due to a higher stability of the Pb ions in this electrolyte. In the case of Pt deposition via SLRR of Cu UPD in 0.1 M HClO4 reaction solution, the {ClO4 }− does not complex Cu2+ . The ligands in the {PtCl6 }2− complex are Cl− ions and they have a major effect on the final oxidation state of dissolved Cu. In this case, in parallel with the charge transfer process between the depositing metal complex and the Cu UPD adatoms, a simultaneous ligand transfer also occurs [52]. The final oxidation state of Cu is determined by formation of the most stable Cu complex with ligands originating from the depositing metal complex ({PtCl6 }2− ). The presence of the residual chlorides in 0.1 M HClO4 and Cl− ions liberated after reduction of {PtCl6 }2− leads to a thermodynamically favorable

3.3

Metal Deposition via Surface-Limited Redox

path for the dissolution of Cu UPD adatoms into {CuCl2 }− ions with Cu oxidation state of 1+ rendering m = 1. The extracted value of the rate constant for SLRR of Cu UPD in 0.1 M HClO4 is slightly smaller than in the case of 0.1 M H2 SO4 electrolyte (∼10%). This result suggests that switching between sulfate- and perchlorate-based solutions does not have a major impact on the Pt deposition rate or SLRR reaction kinetics. Useful insight into the kinetics of metal deposition via SLRR of UPD layer could be obtained if one compares the rate constants of the SLRR reactions involving Cu UPD and Pb UPD in 0.1 M HClO4 reaction solution. One expects faster kinetics of SLRR with the Pb UPD system based on the previous argument related to the work function difference between Pb and Cu. However, from an analysis of OCP transients, the inverse trend is observed. The reason for this is that the activation energy of the UPD metal–{PtCl6 }2− activated complex is affected significantly by the solution phase, that is, the nature of anions in the supporting electrolyte. The lack of complexing ability of the {ClO4 }− as the dominant anion in the supporting electrolyte toward either Cu or Pb ions leads to the situation where the {CuCl2 }− complex is much more stable than the corresponding Pb ion in perchlorate solution. This results in comparatively lower activation energy for the charge transfer between {PtCl6 }2− and Cu UPD adatoms than between {PtCl6 }2− and Pb UPD adatoms. Therefore, the faster kinetics for Cu UPD layer is not surprising. Obviously, the nature of UPD metal in SLRR reaction and the nature of the complexing anions at the electrode/solution interface both have a significant effect on the kinetics of metal deposition via SLRR of the UPD layer. The rate constant of an SLRR reaction is directly proportional to the surface is concentration of the depositing metal ions, in our case Pt ions, C{PtCl 2- (Eqs. 6} is ∞ (3.8) and (3.10)). The C{PtCl }2- is proportional to C{PtCl }2- [24] and because of 6 6 ∞ that we should expect that, for the same SLRR having different C{PtCl 2- , a faster 6} kinetics is observed when the reaction solution has a higher concentration of the depositing metal ions, ({PtCl6 }2− ). Figure 3.8a shows the OCP transient for Pt deposition via SLRR of Cu UPD in 10−5 M {PtCl6 }2− + 0.1 M HClO4 solution. ∞ The C{PtCl 2- is hundred times smaller than that in Figure 3.7b. The model fit (Eq. 6} (3.9)) to these data yields a value of the rate constant, which is ∼40 times smaller (K(8A) = 0.089 (s−1 ), K(7B) = 3.61(s−1 )). This result indicates the importance of the depositing metal ion concentration in the reaction solution for the control of the reaction kinetics. A higher concentration of depositing ions ({PtCl6 }2− ) always yields faster kinetics of the SLRR reaction and thus a higher metal deposition rate (Pt). The low concentration of {PtCl6 }2− in the bulk solution or large thickness of the diffusion layer (assuming no mixing) inevitably leads to the condition where SLRR becomes controlled by ion transport, that is, to metal deposition via TLRR (Eq. (3.5)). In Figure 3.8b, OCP data are displayed for Pt deposition conducted from the same solution as that in Figure 3.8a, but without electrode rotation. Successful fitting of this data set is achieved using the model for TLRR reaction (Eq. (3.5)). The model provides a very good fit of the data except for the initial

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

0.6

0.4

0.4

E (V vs SCE)

E (V vs SCE)

0.5 K UPD = 0.089 s−1 Cu

0.3 0.2 Experimental data Model

0.1

(a)

50

100 t (s)

150

200

0.2 Experimental data Model

0.1

0.0 0

K0 = 0.002 s−1

0.3

0.0

250 (b)

Figure 3.8 (a) Open circuit potential transients for Pt deposition via SLRR of Cu UPD layer on Au(111) in 10−5 M {PtCl6 }2− + 0.1 M HClO4 reaction solution with 1000 rpm rotation rate. (b) Open circuit potential transients for Pt deposition via TLRR of Cu UPD

0

50

100

150

200

250

t (s) layer on Au(111) in 10−5 M {PtCl6 }2− + 0.1 M HClO4, no rotation. The black solid lines represent the model fits of Eqs. (3.9) and (3.5) to the experimental data. The values of reaction rate constants obtained from the fits are indicated in the graph.

time interval of ∼20 s. The reason is that conditions for transport-limited reaction kinetics are not established immediately upon reaction onset, but after some time, that required for {PtCl6 }2− ions to be depleted at the electrode/solution interface, is that is, to reach C{PtCl 2- = 0 condition. The value of the reaction constant 6} k 0 obtained from the fit is 0.0020 (s−1 ). The value of k 0 can be also calculated from the literature data. For m∕p = 0.25, D{PtCl6 }2- = 7.13 × 10−5 (cm2 s−1 ) [58], 𝛿 = 0.05 (cm) [59], and ΓUPD of the full Cu UPD layer calculated as the i,Cu product of areal surface concentration of Au(111) and packing density of Cu UPD layer, 𝜌UPD × (1.5 × 1015 ∕6.023 × 1023 ), one gets the value of k0 = 0.0019 s−1 Cu 2×2 (Eq. (3.6)). The good agreement between the calculated value of k 0 and the experimentally observed one implies that the model describing the kinetics of TLRR reaction (Eq. (3.5)) is sufficiently comprehensive to allow quantitative prediction of the reaction rate constant if the transport limiting conditions are truly established. 3.3.5 Future Directions

The future prospect of metal deposition via SLRR of a UPD layer for catalysis application is quite exciting. Different flavors of this deposition protocol can be developed in order to better control morphology of the catalyst monolayers and therefore their activity [54]. For example, metal deposition via SLRR of a UPD layer guided by organic templates adsorbed on the surface is one approach that deserves attention [60]. The idea is based on the possibility to spatially control the nucleation probability and nucleation sites using organic phases that show potential for ordering on the electrode surface in the potential range of the OCP transients

3.3

Metal Deposition via Surface-Limited Redox

75

Pt

Au

Au

(a)

(b)

~3.2 nm

(c)

(d)

~3.5 nm

6.0 nm

20 nm

Figure 3.9 The STM images of (a) 4,4′ bipyridine layer adsorbed on Cu UPD on Au(111), E = −0. V vs. SCE in 0.1 M HClO4 , image size: 30 nm × 30 nm. (b) Pt on Au(111) after SLRR of Cu UPD ML by Pt4+ through the 4,4′ -bipyridine adlayer, image size: 100 nm × 100 nm. (c) Same as in b, image size 30 nm × 30 nm. (d) Pt deposit on Au(111)

6.0 nm

20 nm

after SLRR of Cu UPD ML by Pt4+ , no organic template is present during SLRR. In image (a), a model of the 4,4′ -bipyridine molecule is shown in upper left corner. On top, cartoons of the structures corresponding to image (a) (top left) and (b), (c) (top right) are shown.

during SLRR. It is expected that the organic phase influences the surface diffusion of metal adatoms, and consequently the nucleation process and evolution of the shape of the nuclei. It is also possible that large organic molecules at the surface may provide a template for the incoming metal ions and guide them toward positions that would reproduce the symmetry and organization of the absorbed organic layer. The pursuit of this concept is described in Figure 3.9. The 4,4′ bipyridine, adsorbed on a Cu UPD layer on Au(111), serving as a template is shown in Figure 3.9a. As one can see, the 4,4′ -bipyridine forms a rippled layer with a hexagonal lattice on top of the Cu UPD layer structure. The distance to the nearest neighbor of the adsorbed 4,4′ -bipyridine phase is 1.5 nm, while the average width and periodicity of the ripples is 3.5 nm. The Pt deposit formed on Au(111) after redox replacement of the Cu UPD layer by {PtCl6 }2− through the 4,4′ -bipyridine phase is shown in Figure 3.9b,c [61]. The presence of an adsorbed bipyridine phase has a decisive effect on the shape and orientation of the deposited Pt nanoclusters (compare Figure 3.9b,c with Figure 3.9d). The average width of the Pt clusters is approximately the same (∼3.2 nm) as the periodicity of bipyridine ripples shown in Figure 3.9a (∼3.5 nm). The elongated shape of Pt clusters and their propagating direction replicate the arrangement and symmetry of the bipyridine ripples. These preliminary results and observations suggest that the adsorbed organic phase serving as a template has a critical influence on the nucleation and growth of the Pt deposit during an SLRR reaction. This concept undoubtedly will be one of the main research themes in the near future in the context of metal deposition via SLRR of UPD layers.

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

3.4 Underpotential Codeposition (UPCD)

The possibility to electrochemically grow an alloy at a potential more positive than the redox potential of the less noble metal has been known for more than a century, when a sodium amalgam Na(Hg) was observed to form at a potential more positive than that for pure Na reduction [62]. Early technological applications of this process have been reviewed by Stafford and Hussey [63], and Moffat [64] laid the thermodynamic basis for the correlation between the free energy of alloy formation and the alloy deposition potential. This model for UPCD stems from the use of electromotive force measurements in high temperature electrochemical cells [65] and is rooted in classic bulk alloy thermodynamics. In this formalism, the free energy G = G0 + ΔHmix –TΔSmix of a binary alloy is the sum of three contributions: G0 is the free energy of a mechanical mixture of the phase-separated components, ΔH mix represents the bonding interactions in the alloy phase, and −TΔSmix is the contribution from the ideal entropy of mixing. ΔH mix is a function of alloy composition, usually written as a Redlich–Kister expansion [66], which in the following will be simplified to an asymmetric regular solution approximation (Eq. (3.11)). Taking G0 as the reference state, in this approximation the variation in free energy due to alloying ΔGmix is ΔGmix = ΔHmix − TΔSmix = (WGA xA + WGB xB )xA xB + RT(xA ln xA + xB ln xB ) (3.11) In this equation, W GA and W GB are Margules parameters that describe the alloy enthalpy of mixing, xA and xB are the atomic fraction of elements A and B in the alloy, respectively, with xB = 1–xA . In the following, A will be the more noble element in the alloy, while B will be the less noble (more reactive) one; Aw+ and Bz+ will be the corresponding ionic species in solution. Using standard thermodynamic methods [67] the activity coefficient of element B in the alloy electrode can be derived directly from Eq. (3.11) and is written as {[ } ] WGA xA + WGB xB x2 A aB(alloy) = xB exp (3.12) RT (the entropy contribution to the activity is neglected because at typical electrodeposition temperatures the entropy term −TΔSmix is negligible with respect to the enthalpy term). Substituting this expression (Eq. (3.12)) in the generalized Nernst equation for alloy deposition, EB = EB,0 +

a z+ RT ln B zF aB(alloy)

(3.13)

where EB,0 is the standard redox potential for the elemental reduction of B, RT/zF has the usual meaning, and aBz+ is the activity of the Bz+ ion in solution, it is possible to directly relate the redox potential of B at an alloy electrode to the composition of the alloy. The physical meaning of the Margules parameters becomes

3.4

Underpotential Codeposition (UPCD)

77

clearer if we consider first the regular solution approximation, where the enthalpy of mixing has a symmetric dependence on composition: ΔHmix = ΩxA xB . In a quasi-chemical thermodynamic framework [68], the parameter Ω can in fact be associated to the pairwise bond strengths Vij (Eq. (3.14)) and provides a link between the macroscopic bonding energy and atomistic interactions: [ )] 1( (3.14) VAA + VBB Ω = N 0 z VAB − 2 where N 0 is the number of atoms in the solid and z is the number of the nearest neighbors. An asymmetric version of the regular solution approximation is often used because in practice most of the experimental data on enthalpy of mixing in binary alloys are nonsymmetric with respect to composition. Equation (3.13) predicts the electrode potential at which the species Bz+ will be in equilibrium with an alloy electrode of a specified phase (crystal structure) and composition (xA ,xB ); EB represents therefore the most positive potential at which the given alloy phase and composition can be obtained. This implies that, in the absence of any energy barrier, alloy growth may occur at any applied potential Eappl < EB . When the alloy has a negative free energy of mixing, that is, aB(alloy) is Br− > Cl− > SO4 2− > F− (the sulfate anion is added for comparison); the latter is only weakly adsorbed; ΔGads varies between 100 and 200 kJ mol−1 (1–2 eV/atom) [72], of the same order if not larger than the effective interactions in alloys. Specifically adsorbed anions may therefore strongly influence the structure, energetics, and electrochemical reactivity at surfaces, in particular UPD and UPCD processes. Such effects are widely reported in the literature, and relevant examples are briefly discussed here. Chloride adsorbates on Cu(100) surfaces strongly influence the surface morphology, inducing the formation of flat, strongly faceted terraces along the {100} directions [73], and also increasing adatom mobility; the adsorbate structure affects Cu deposition and dissolution, resulting, for example, in a different deposition mechanism [74] and a distinct morphology of electroplated Cu films [75]. Reconstruction of the Au(111) surface depends not only on the applied potential but is also affected by anions in the electrolyte [76]; the resulting interplay between applied potential, reconstruction, and anion coverage significantly affects subsequent UPD and growth processes. The UPD of Cu on Au(111) in particular is significantly affected by anions, altering the energetics of adsorption,

3.4

Underpotential Codeposition (UPCD)

the kinetics of metal deposition, and the structure of the resulting layers [3]. Particularly striking is the possibility to promote or hinder UPD processes via selection of the anion; Ni in fact does not exhibit UPD on Au(111) when using a Watts’ electrolyte [77], but does so on Au(111) when using sulfamate-containing electrolytes [78]. 3.4.1.2 Potential of Zero Charge (PZC)

PZC (potential of zero charge) is the potential at which the electrode has no excess charge; its value depends not only on the chemical composition of the electrode but also on its crystallographic orientation, its defect structure, and the electrolyte composition. Metallic surfaces exhibit PZC values varying roughly from +0.2 VSHE (Pt, Au) to −0.7 VSHE (Ga, In, Ag). At potentials more negative than the PZC, the electrode presents a negative charge, and vice versa. At a given electrode potential the extent of ion adsorption, particularly for non-specifically adsorbed ions, will depend on electrostatic effects, affecting the occurrence and/or the rate of UPD and UPCD processes; these phenomena would be particularly pronounced at polycrystalline or chemically inhomogeneous electrodes, possibly leading to position-dependent adsorption or growth processes [79]. 3.4.1.3 Surface Defects, Reconstruction, and Segregation

Surface defects and surface reconstruction create preferential nucleation sites, characterized by more favorable energetics of nucleation. These surface features accelerate the nucleation kinetics and are discussed in the next section. Surface segregation is conventionally described by a Gibbsian surface thermodynamics approach. According to these models [80, 81] surface segregation is determined by (i) chemical interaction terms that include the difference in the surface energy and the effective pairwise interaction of the two components and (ii) an elastic term that takes into account the difference in the atomic volume of the two species. In the absence of elastic terms, segregation is dictated by a balance of the two chemical terms, with the component having a lower surface energy found preferentially at the surface unless the effective interaction predominates. The elastic energy [80] favors surface segregation of the solute and would reinforce segregation effects when the solute has the lower surface energy; with increasing solute concentration, however, the solute would progressively become the solvent and the effect would be reversed. More sophisticated theories address the structural and energy anisotropy of distinct crystallographic facets, predicting anisotropic segregation phenomena [82]. Pt–Ni alloys exhibit such effects: Pt in fact tends to segregate at the surface at (111) facets, while Ni tends to segregate at the surface at (110) facets [83]. Surface segregation can be precisely estimated based on density functional theory (DFT) or effective medium theory (EMT); these predictions agree closely with those based on Miedema’s rules [84]. Surface segregation energies can be as high as 1 eV/atom in extreme cases (corresponding to surface or grain boundary energies of the order of 1–2 J m−2 ), and therefore may strongly affect and even invalidate bulk thermodynamic predictions.

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

Some binary alloys that are immiscible in the bulk can form solid solutions at free surfaces; the behavior of such systems is dominated by differences in atomic volume, which induce large elastic strain and repulsion in the bulk, but can be more easily accommodated at the surface [85]. Since UPD and UPCD occur at the electrode/electrolyte interface, explicit inclusion of surface alloy thermodynamic effects may result in better predictions than those of bulk thermodynamics. The conditions for the formation of surface alloys have been discussed by Christensen et al. [86]; in particular, DFT calculations have been performed that predict surface segregation energy of various binary systems. Surface alloy phase diagrams can be simply predicted through knowledge of the segregation energy and of the surface mixing energy for a pair of elements; these parameters have been calculated and tabulated [86]. The energies involved in surface alloying are of the order of 0.1–1 eV/atom, sufficient to significantly affect alloy formation by UPCD. 3.4.1.4 Atomistic Description of the Growth Process

In most practical UPCD processes, the deposition of A would occur at overpotential and be dominated by kinetic effects; B however is incorporated at UPD conditions, where the growth process will be partly controlled by atomistic interactions at the surface. UPD of B occurs via a multistep process [87, 43]; at equilibrium the surface configuration is determined by adsorption processes, involving metal–substrate and metal–metal interactions, and by the subsequent formation of an ordered structure, which may require a 2D phase transition, with an attendant nucleation barrier. Various adsorption isotherms are used to model the adsorption process in UPD (see Section 3.2), the most general of which has been introduced by Swathirajan et al. (Eq. (3.1)) [87, 43]. This isotherm takes into account metal–substrate and lateral interactions, as well as surface heterogeneity effects, all of which could be estimated via DFT or EAM methods [88, 89]. In order for these calculations to have predictive power, however, it is essential to include anion adsorption and solvent effects, as shown for the case of UPD of Cu on Au(111), where the coadsorption of sulfate anions stabilizes the Cu monolayer [90]. 3.4.2 Kinetics

The previous thermodynamics-based discussion of UPCD provides a relationship between the composition of the alloy electrode and the redox potential of the less noble metal B; this correlation however is strictly valid only under equilibrium conditions, when growth does not occur. Electrochemical growth requires a deviation from equilibrium in order to overcome any existing energy barrier for film nucleation and to sustain alloy growth at a finite rate. A potentiostatic UPCD process can be described as the steady-state deposition of metal A occurring in parallel with the sustained UPD of B, enabled by the continuing renewal of the surface with A. Achieving thermodynamic compositional control under growth conditions requires negligible deviation from equilibrium; that is, the deposition

3.4

Underpotential Codeposition (UPCD)

kinetics of B should be sufficiently fast to maintain equilibrium conditions at the interface. This condition can be satisfied if the partial current of B is at the most of the order of its exchange current, ensuring minimal deviation from the equilibrium potential; more generally, equilibrium conditions can be approximately fulfilled if the applied potential necessary to maintain the reduction rate of B is very close to the onset potential for the UPCD of B. Equilibrium conditions can be more easily approached when the deposition rate of A is slow; this can be ensured independently of the applied overpotential for A by minimizing the diffusionlimiting current, that is, having a low concentration of Aw+ ions in solution. Equilibrium would be further facilitated by increasing the concentration of the B ion in solution, in order to increase its exchange current and enhance reversibility of the equilibrium Bz+ /B. As a consequence, fundamental UPCD studies are generally performed using electrolytes with a small concentration of A and a high concentration of B. The overall alloy growth rate may be slow, but this is often acceptable in microelectronic fabrication where typical metallic films are only tens of nanometers thick. No detailed analytical theory of UPCD kinetics is yet available; however, the kinetics of UPD metal monolayer formation has been extensively investigated [91], and the relative findings can be used to qualitatively discuss the growth kinetics of UPCD films. Formation of a UPD monolayer typically involves ion transport from the bulk electrolyte, adsorption at the substrate, charge transfer, surface diffusion, and nucleation of the film phase [87]; the actual growth rate will be determined by the slowest among these processes. With regard to the charge transfer process, the exchange current for monolayer growth becomes a function of the electrode coverage, and has been found to be larger than the value of the corresponding bulk growth process [13]. In UPCD, growth kinetics and phase formation will be critically dependent on the relative rate of reduction of the A and B components; the former is often independent of the applied potential, while the latter is determined by UPD kinetics. Since the concentration of the B ions in solution is usually large, diffusion would not limit B reduction kinetics, and the electrode coverage would achieve its equilibrium value unless the time required for growth of an A monolayer 𝜏 ML,A were shorter than the adsorption time of B 𝜏 ads,B . If 𝜏ads,B < 𝜏ML,A the alloy achieves its thermodynamically prescribed composition, but the phase of the growing alloy may not necessarily be the equilibrium one. In order for this to happen the surface diffusion process should be sufficiently fast relative to the rate of monolayer formation by A so as to result in the accommodation of adatoms at equilibrium positions; this condition can be expressed as 𝜏ads,B + 𝜏diff < 𝜏ML,A , where 𝜏 diff is the diffusional time necessary to occupy an equilibrium position. Notice that 𝜏 diff is larger for an ordered phase since the probability of a crystallographic location being the correct one is lower. In addition, the nucleation process should not be a barrier to alloy formation since the component A deposited at overpotential would provide the template for the attachment and incorporation of B in the growing film. Complications may arise however when considering real surfaces; in this case surface coverage is not determined exclusively by the adsorption isotherm; on the contrary, defects such as steps and kinks would provide sites

81

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

with higher bonding energy where the nucleation barrier would be lower than at an ideal surface, leading to an earlier onset of film growth. Growth of UPD films is often monitored by potentiostatic current density transients; these usually consist of an initial double layer charging, followed by a nonmonotonic behavior that describes both adsorption and nucleation. The presence of a current peak is a necessary, but not sufficient, criterion for the occurrence of nucleation, since such a peak may be originated also by charge transfer or bulk diffusion [13]. Kolb has shown that Cu UPD on Au(111) single crystals exhibits nucleation maxima at high quality substrates, but these maxima disappear when the density of defects increases in increasingly miscut crystals [92]. In practical applications of UPCD, the use of polycrystalline substrates with a high density of nucleation sites will result in nucleationless growth, simplifying the interpretation of current transients. An important question in UPCD is whether the quasi-equilibrium conditions discussed above can be achieved in practice. A suitable model system to help answer this question is the Au–Cu binary alloy. This system has been thoroughly studied and its thermodynamic properties are well known [69]; furthermore, both Au and Cu can be reduced at potentials positive to the hydrogen evolution reaction, thus avoiding spurious reactions that may hinder determination of the thermodynamic parameters. Finally, both Au and Cu are characterized by a relatively high exchange current, resulting in reversible reduction processes. The UPCD of Cu with Au has been studied using acidic, slightly complexing solutions consisting of HAuCl4 (0.5–2 mM), CuSO4 (0.05–0.3 M), and H2 SO4 (0.5 M) [93]; onset of Cu codeposition was observed to occur at about −0.22 1.0

150

0.05 M CuSO4 + 0.5 mM HAuCl4 from EDX

0.9

0.3 M CuSO4 + 2 mM HAuCl4 from EDX

100

0.3 M CuSO4 + 1 mM HAuCl4 from EDX

50 0 −50

Ee = −0.421 V. W01 = −34.8 kJ mol−1 W02 = −8.9 kJ mol−1) Ee = −0.400 V. W01 = −40.8 kJ mol−1 W02 = −13.7 kJ mol−1)

0.6

Ee = −0.402 V. W01 = −34.2 kJ mol−1 W02 = −6.3 kJ mol−1)

0.5 0.4 0.3

−100

0.2

−150

0.1

−0.45 −0.40 −0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05

(a)

0.3 M CuSO4 + 1 mM HAuCl4 from EDX

0.7 Cu fraction

dm/dt (ng s−1cm−2)

0.8

Potential (V vs MSE)

0.0

(b)

Figure 3.11 (a) Growth rate of Au–Cu alloys vs. applied potential, as determined by quartz crystal microbalance (EQCM). Deposition rate increases above the diffusion-limiting current for Au at about −0.22 VSSE , showing a positive shift of the onset of Cu reduction. (b) Alloy composition data vs. applied potential is

−0.40

−0.35

−0.30

−0.25

−0.20

plotted for various electrolyte chemistries and fit to Eq. (3.3) to extract the Margules parameters and the redox potential of Cu. The extracted parameters compare very well with those determined experimentally from bulk metallurgical measurements. Reproduced with permission from Ref. [93]. Copyright 2009, The Electrochemical Society.

3.4

Underpotential Codeposition (UPCD)

83

VSSE vs. a Nernst potential value of −0.4 VSSE , suggesting UPCD of Cu in the presence of Au (Figure 3.11a); the resulting alloys formed a continuous series of face-centered cubic (FCC) solid solutions. The observed dependence of alloy composition on potential (Figure 3.11b) was fit to Eq. (3.13), from which values for ECu(Cu) , the redox potential of elemental Cu, WGA , and WGB were extracted. ECu(Cu) closely matched the calculated value for various Cu2+ concentrations, and the Margules parameters yielded enthalpy of mixing curves reasonably similar to literature data for the high temperature solid-solution phase [69]; deviations are discussed in Section 3.4.3 on structure. It should also be noted that the fit to the composition vs. applied potential data reproduces the experimental data down to the most negative potentials, indicating that equilibrium conditions are satisfied even at the highest deposition rates (up to ∼150 ng (s⋅cm2 )−1 , i.e., 0.63 ml s−1 ). Owing to the wide difference in the redox potentials of Au and Cu, Cu is deposited only under diffusion-limiting conditions for Au, and the films grown from the above electrolyte are rough and porous. Selective complexation of Au and Cu was therefore carried out to draw the two redox potentials closer, with the objective of improving film microstructure [94]. To this end, Au was complexed with ethylenediamine and Cu with glycine, resulting in a shift of the redox potential and a decrease in exchange current for both components. The alloy growth rate vs. applied potential from the resulting electrolyte is reported in Figure 3.12a and compared to those of Au and Cu alone. The onset potential of Cu reduction is now much closer to that of Au, and reduction of Cu in the presence of Au is again shifted toward more positive potentials, indicating that UPCD can be achieved even if the metal ions are complexed and the reversibility of the redox process is stifled. In contrast with the acidic electrolyte however, the slower kinetics of Cu deposition results in a deviation of the experimental composition vs. deposition 100 Au Cu Cu–Au

80

300 Cu (at %)

dm/dt (ng s−1 cm−2)

600

0

40 20

−300 −1.0

(a)

60

−0.8 −0.6 −0.4 −0.2 Potential (V vs MSE)

Figure 3.12 (a) Growth rate vs. applied potential for Au, Cu, and Au–cu alloys, as determined by EQCM. The electrolyte consists of 2 mM Au-ethylenediamine, 20 mM CuSO4 , 0.2 M glycine, and 0.2 M Na2 SO4 , pH 8. (b) Alloy composition vs. applied

0

−0.0 (b)

−0.75

−0.70 −0.65 −0.60 Potential (V vs MSE)

potential; notice how the fit of the experimental data using Eq. (3.13) fails at the most negative potentials due to the slow reduction kinetics of Cu. (Reprinted with permission from Ref. [94]. Copyright 2014, American Chemical Society.)

−0.55

3 Electrochemical Surface Processes and Opportunities for Material Synthesis

potential curve from the theoretical prediction (Figure 3.12b). Such deviation occurs only when growing Cu-rich films, suggesting that the reduction kinetics of the Cu–glycine complex is insufficient to achieve equilibrium coverage under these conditions. Despite the deviation, a least squares fit of the experimental data down to −0.725 VSSE to Eq. (3.13) yields Margules parameters that are very similar to those obtained with the acidic electrolyte [94]. These data confirm that UPCD from this complexing electrolyte indeed occurs, leading to similar solid solution phases, but deviations from ideal behavior are observed due to limitations in the Cu reduction kinetics. In contrast with Au–Cu, Ni-based UPCD alloy films present a deviation from the predicted dependence of composition on deposition potential even in the absence of metal complexation. As a late transition metal, Ni reduction is intrinsically irreversible and its reduction kinetics is relatively slow, as shown by the low value of exchange current density (10−5 A/cm2 in an acidic electrolyte containing 0.02–0.05 M Ni2+ [95]). Figure 3.13 shows alloy composition vs. potential data for Ni–Pt deposition from an acidic electrolyte [96]. Note how the regular solution approximation fails to predict the observed composition vs. deposition potential curve at the negative end of the potential range, and how such deviation becomes more pronounced by decreasing the Ni ion concentration. Similar results have been obtained in our laboratories in the context of Au–Ni electrodeposition from an electrolyte containing 0.5 mM HAuCl4 , 5–500 mM NiSO4 , and Na2 SO4 in quantities necessary to maintain the ionic strength constant, at pH 2.5 [97]. The composition vs. deposition potential data (Figure 3.14a) fit the trend predicted by Eq. (3.13) with a negative enthalpy of mixing only at the positive end of the 1.0

0.8 Ni atomic fraction

84

0.6

0.4 0.11 mol l−1 NiCl2 + 3 mM PtCI4

0.2

1.1 mol l−1 Ni2 + 3 mM PtCI4 1.1 mol l−1 Ni2 + 0.3 mM PtCI4

0.0 −0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

Potential (V vs SCE) Figure 3.13 The potential dependence of alloy composition for Ni–Pt films grown from 0.5 M NaCl electrolytes containing different concentrations of metal ions, as shown. Pt was added as PtCl4 ;

Ni as NiCl2 . Dashes represent experimental data, and lines are fit to the subregular solution model. (Reproduced with permission from Ref. [96]. Copyright 2008, The Electrochemical Society.)

3.4

Underpotential Codeposition (UPCD)

85

0.8

10-3

0.6 0.4 0.2

5 mM Ni 50 mM Ni 500 mM Ni

logІjІ

Ni atomic fraction (%)

1.0

10-4

Black spot:

5 mM Ni experimental Red spot: 50 mM Ni experimental Blue spot: 500 mM Ni experimental

0.0 (a)

−1.0

−0.9

−0.8

−0.7

−0.6

−0.5

Potential (V vs SCE)

Figure 3.14 (a) Alloy composition vs. deposition potential obtained by keeping the HAuCl4 concentration at 0.5 mM and varying the NiSO4 concentration (5–500 mM): dots represent experimental data; lines are fits of the first

0 (b)

50

100

150

200

250

Overpotential (-η/mV)

set of data (full circles) to Eq. (3.1) [97]. (b) Compositional data that deviate from the fit in (a) are translated into partial current data and are fit to Tafel expressions. (Reproduced with permission from Ref. [97]. Copyright 2014, Wiley.)

investigated potential range. At more negative potentials the data deviate from the prediction: in order to achieve a predetermined composition an overvoltage must be applied with respect to the predicted value. Such deviation was interpreted in terms of a Tafel overpotential, and the data in Figure 3.10a were fitted for various Ni ion concentrations to estimate kinetic coefficients for Ni reduction. The resulting exchange current was 10−5 –10−6 A cm−2 , close to the experimental values; in contrast, the Tafel slope was 180–210 mV dec−1 , much higher than the measured value [95] (Figure 3.14b). This is not surprising, since there is no reason for the reduction kinetics in UPCD conditions to follow the behavior observed at overpotential. A more appropriate approach to UPCD kinetics would involve an analysis of the adsorption process as outlined above. 3.4.3 Equilibrium Alloy Structure and Phase Formation

The phase diagram – that is, the crystal structure as a function of composition – of electrodeposited alloys is often similar to that observed in the corresponding bulk metallurgical alloys [7]. In some cases, however, the two may differ, mainly as a consequence of the electrodeposition process being conducted out of equilibrium. In particular, the solubility limits of a solute in a matrix are often higher than those observed in bulk alloys, except in cases where the electronegativity difference between the two elements is large [98]. It has also been observed that phases that do not appear in the bulk phase diagram may be produced by electrodeposition; a metastable NiSn phase, for example, has been observed in electroplated films in the compositional range where a mixture of Ni3 Sn2 and Ni3 Sn4 should be stable according to the bulk phase diagram. It is hypothesized

300

86

3 Electrochemical Surface Processes and Opportunities for Material Synthesis

that the NiSn phase could be stabilized due to the increase in free energy in the mixture of the two stable phases, originated by the interfacial energy contribution and enhanced when the grain size is small [99]. In contrast, ordered phases are rarely seen in electrodeposited films due to the low mobility of adatoms during growth at low temperature, which hinders long range order. Exceptions include alloys formed by at least one element with low melting point. UPCD is conducted close to equilibrium; therefore, it is expected that the phase diagram of UPCD alloys should resemble that observed in bulk alloys more closely than in conventional electrodeposited alloys. Excessive deviation from equilibrium conditions, due, for instance, to a large nucleation overpotential, kinetic limitations in the deposition of the less noble element, microstructural effects, or stresses, may however invalidate these predictions, leading to the formation of phases different from those observed in the bulk. Available results for three representative classes of alloys are discussed in the following. 3.4.3.1 Binary Alloys Forming Solid Solutions and Ordered Compounds

A binary alloy that exhibits a continuous series of solid solutions may only form one crystalline phase at or close to equilibrium. If, however, various phases (stable or metastable) coexist at the same composition, the phase with the lowest free energy (i.e., stronger bonding strength) will be selectively formed at the most positive potential, since the activity of the less noble metal B in the alloy would be lowest and the potential shift most pronounced; no other phase could be formed until a potential is reached where the next most stable phase could grow. A common case is that of a binary alloy presenting one or more ordered phase(s) at room temperature together with a disordered solid solution at high temperature. One example is the Au–Cu system, discussed next. Figure 3.15 shows the calculated phase diagram of the Au–Cu system (a) and the enthalpy of mixing (b) for the disordered FCC structure, the tetragonal L10 1400

0 Liquid

−1 −2 Enthalpy (J mol−1)

Temperature (K)

1200 1000 fcc 800 600 L10

L12

−3 −4

320 K

−5 −6 −7



−9

E3

AuCu

−10

200 0 (a)

0.2

0.4 0.6 0.8 Mole fraction Cu

AuCu3

−8

L12

400

720 K

1.0

0 (b)

0.2

0.4 0.6 0.8 Mole fraction Cu

1.0

Figure 3.15 (a) Calculated Au–Cu phase diagram and (b) enthalpy of mixing for both the solid solution and two ordered phases. (Reproduced with permission from Ref. [100]. Copyright 1998, Elsevier.)

3.4

Underpotential Codeposition (UPCD)

CuAu phase, and the cubic L12 AuCu3 phase [100]. The FCC solid solution is stable at intermediate temperatures, but at low temperature the three ordered phases are stable around the compositions xCu = 0.25, 0.5, 0.75. The lower value of the enthalpy of mixing (stronger bonding) of the ordered phases with respect to the solid solution with the same composition results in a smaller activity of Cu in the alloy and therefore a larger positive shift of the redox potential; ideally, the ordered phases could be obtained selectively at a more positive applied potential. Specifically, in the potential range between the onset potential for the growth of the ordered phase and that for the corresponding solid solution, assuming equilibrium, only the ordered phase should be formed. However, formation of a long-range ordered phase requires large adatom mobility and slow growth rate in order for the adatoms to settle at crystallographic locations corresponding to those of the ordered structure; such conditions are rarely achievable even in UPCD conditions. The metastable FCC phase is statistically more accessible and will be formed preferentially since it is a disordered phase that can be achieved via a much larger number of microscopic configurations. Ordered phases may still be obtained by UPCD in alloys with at least one component having a low melting point and thus high surface mobility and/or at very low growth rates so as to limit freezing mobile adatoms in metastable positions. Au–Cu alloys grown by UPCD are observed to form a continuous series of solid solution. The enthalpy of mixing ΔH mix extracted from the experimental composition vs. applied potential dependence is reasonably similar to literature data for the high temperature solid solution FCC phase [93]. A significant difference in the position of the minimum of ΔH mix is however observed, from both the acidic and the complexing solution; possible reasons for such differences include kinetic trapping of adatoms or local ordering. In conclusion, UPCD of Au–Cu occurs close to equilibrium conditions, but the growth process presents some differences with respect to bulk solidification. 3.4.3.2 Intermetallic Compounds

A behavior similar to that discussed in Section 3.4.3.1 is also observed in phase diagrams presenting one or more intermetallic compounds. In this case, the free energy of each intermetallic would have a deep minimum at the stoichiometric composition and increase steeply with any small deviation from such stoichiometry, resulting in the compound being stable only at this composition. The result is that – under the hypothesis of equilibrium – there will be a range of applied potentials where a predetermined intermetallic structure can be selectively grown. Formation of intermetallic compounds, similarly to ordered structures, is however kinetically hindered. An example of this behavior is the investigation of the Pt–Pb binary system by Hwang et al. [101]. Figure 3.16a shows the phase diagram of the Pt–Pb system, which forms three distinct intermetallic compounds and shows no solubility between the various phases. Given the enthalpy of mixing of the various intermetallic phases, it is possible to determine through the use of Eq. (3.13) the potential corresponding to the onset of growth of a given intermetallic α; starting at that potential, under equilibrium conditions only the α phase would

87

0

3 Electrochemical Surface Processes and Opportunities for Material Synthesis

10

20

Weight percent lead 30 40 50 60 70

80

Atomic fraction of Pb, x

L

1400 1200 915 °C ?

795 °C

300 °C PtPb4

(Pt)

400

PtPb

600 Pt3Pb

Temperature (°C)

1600

800

QCM Pb upd coverage taken from Figure 6 of Ref.[35]

0.9

1800 L789.0°C

1000

1.0

1.0

90 100

200

327.502°C 290 °C

0.8 0.7 0.6

0 Pt

10

20

30 40 50 60 70 Atomic percent lead

80

0.6

0.4

PtPb

0.4

0.3 0.2

Pt3Pb

0.2

0.1

94.7 (Pb)

90 100

0.8

0.5

0.0 0.0 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1

0

(a)

Determined from V–1 curve Determined from XRD Determined from EDS Determined from i–t curve Intermetallic compounds

PtPb4

Surface coverage θPb (nPb/nPt)

88

(b)

Figure 3.16 (a) Phase diagram of the Pt–Pb binary system. (b) Alloy composition vs. potential as predicted from the enthalpy of mixing of the various

EPb/Pb2+

Potential (V vs SSE) Onset of Pt deposition

intermetallic compounds (continuous lines) and as observed experimentally (data points). (Reproduced with permission from Ref. [101]. Copyright 2011, The Electrochemical Society.)

be grown until the onset potential for growth of the successive phase β is reached. This ideal behavior is displayed by the continuous lines in Figure 3.16b, where, for instance, formation of Pt3 Pb starts at −0.576 VSSE and is the only phase formed down to −0.634 VSSE . Pt–Pb alloys were grown from slightly acidic electrolytes containing 1 mM K2 PtCl4 , 0.05 M Pb(ClO4 )2 , and 1 mM HClO4 . The range of potentials within which the various intermetallic phases could be obtained is displayed in Figure 3.16b together with experimental data for alloy composition; a plateau in the composition vs. deposition potential curve was observed at 25 at% Pb, suggesting the formation of a Pt3 Pb phase. The observed FCC phase has a lattice parameter similar to that of ordered Pt3 Pb, but no evidence of any superlattice diffraction was observed. In addition, the PtPb intermetallic, predicted below −0.634 VSSE , was observed only below −0.8 VSSE . This indicates that a significant overvoltage is necessary to form the intermetallic, probably due to a large nucleation barrier. Once nuclei are formed, however, intermetallic formation is associated with the development of a dendritic structure in the films, suggesting fast growth probably under diffusion limitations. It is hypothesized that the system starts growing as a supersaturated FCC solid solution, templated by the Pt surface via ongoing UPD of Pb, and once nucleation of the ordered phase occurs, the significant stress associated with the difference in atomic volume between the two components may be released via dendrite formation. Intermetallic compounds often present unique electronic properties and find extensive technological applications. Chalcogenide materials and metal oxides for photovoltaic radiation absorbers are an important example of intermetallic compounds that could be grown to advantage by using UPCD methods. A variety of thermoelectric materials could also be accurately grown by UPCD [102]. The stoichiometric phase of interest can be grown selectively because of the deep minimum in the free energy of this compound, which will result in its preferential

3.4

Underpotential Codeposition (UPCD)

89

formation within a wide potential window. In addition, the stoichiometry would be precisely maintained since any slight deviation would lead to a large increase in free energy and a negative shift in onset potential. In most cases of interest, the difference in the onset potential for compound formation with respect to the less noble element is sufficiently large that a significant overpotential can be applied while maintaining stoichiometry, allowing compound formation at significant growth rates and avoiding the kinetic limitations discussed in Section 3.4.2. Zn and oxygen, for example, show negligible reciprocal solubility, but at the equiatomic composition they form ZnO, a semiconductor compound with the wurtzite structure. ZnO can be grown electrochemically [103]; while Zn 0 is reduced at its standard redox potential EZn 2+ ∕Zn = −0.76 VSHE , ZnO can be obtained at a more positive potential due to its large free energy of formation (ΔHmix = 318 kJ mol−1 ), which leads to a positive shift of the onset potential of 1.65 V, leading to a redox potential for ZnO formation of 1 Zn2+ + O2 + 2e → ZnO E0 = 0.92 VSHE 2 ZnO can be formed exclusively within a wide potential window, enabling deposition at high rate. CdTe is a semiconductor compound with a band gap of 1.45 V, used as a light absorber in solar cells. The phase diagram for the Cd–Te system reproduced in Figure 3.17a shows a line compound at the equiatomic composition, with an enthalpy of formation ΔHmix = −138.3 kJ mol−1 (at 773 K) [105]. Again, formation of the stoichiometric compound occurs selectively since the ΔHmix of the compound will shift the onset potential for Cd deposition in the positive direction, by an amount corresponding to ΔEUPD ∼ ΔHmix ∕2 F = 0.715 V. Figure 3.17b displays the expected deposition behavior by showing the linear sweep voltammetry of Cd and Te alone, and the LSV in the presence of both ionic Cd–Te Date from BINARY (SGTE) alloy databases

Cd

−0.4 V

Current density (a.u.)

1500 1300 T (K)

1100 900

CdTe(s)

700 CdTe(s) + Te(s)

500

0.55 V

+0.1 V

CdTe + Cd

CdTe(s) + Cd(s)

300 0 (a)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mole Te/(Cd+Te)

Te CdTe

1

−1 (b)

0 Potential (V vs NHE)

Figure 3.17 (a) phase diagram of CdTe. (b) UPCD of Cd in presence of Te as shown by linear sweep voltammetry data. (Reproduced with permission from Ref. [104]. Copyright 2005, Elsevier.)

Te

Cd + Te

3 Electrochemical Surface Processes and Opportunities for Material Synthesis

species in solution. The latter implies a depolarization of Cd reduction by about 0.5 V, to 0.1 VSHE . Applied potentials between 0.1 V and the onset potential for pure Cd deposition (−0.4 V) would lead to the selective formation of CdTe. 3.4.3.3 Alloys Immiscible in the Bulk

(a)

1600 1400 1200 1000 800 600 400 200 0

Enthalpy of mixing (J mol−1)

Binary systems with a positive enthalpy of mixing are thermodynamically unstable in solid solution and tend to phase separate into the pure components or in two distinct dilute solid-solution phases [106]. Mechanical alloying, fast solidification of bulk alloys, or film deposition processes conducted very far from equilibrium may force the formation of metastable solid solutions [107, 108], but these conditions would be antitethic to those adopted in UPCD. On the contrary, UPCD of immiscible alloys should ideally lead to formation of a phase-separated mechanical mixture, that is, the macroscopic configuration with the lowest free energy. A model system to study UPCD phase formation in bulk-immiscible systems is Au–Ni. As seen in Figure 3.18a,b, Au–Ni exhibits a miscibility gap in the solid state up to 1089 K, and a positive ΔH mix , despite an attractive chemical

T (°C)

Liquid

Fcc

Fcc + Fcc

0 Au

20

40 60 Mol % Ni

80

100 Ni

8 7 6 5 4

T = 1150 K

3 2 1 E3 0 0

(b)

913 K 1150 K 1383 K

0.2 0.4 0.6 0.8 Mole fraction, Ni

1.0

100 Ni atomic fraction (%)

90

80

Ni ALI

60 40 20 0 −80

(c)

−60 −40 −20 E–Eequi (mV)

0

Figure 3.18 (a) phase diagram of the Au–Ni of metastable solid solutions of Au–Ni alloys. (Fig. (b) is reproduced with permission from binary system; (b) enthalpy of mixing of Au–Ni alloys at 1150 K [26, 109]; and (c) cal- Ref. [109]. Copyright 2005, Elsevier.) culated overpotential E-Eequi for the growth

3.4

Underpotential Codeposition (UPCD)

60% Ni

300 dm/dt (ng s−1cm−2)

250 200 150

0.5 mM HAuCl4 + 0.5 M Na2SO4 0.05 mM NiSO4 + 0.5 M Na2SO4 0.5 mM HAuCl4 + 0.05 M NiSO4 +0.5 M NiSO4

100 50 0 −50

−100 −1.0 (a)

−0.8 −0.6 −0.4 −0.2 Potential (V vs SCE)

Figure 3.19 (a) Growth rate vs. applied potential for Au, Ni, and Au–Ni alloy from a solution containing 0.5 mM HAuCl4 , 0.05 M NiSO4 , 0.5 M Na2 SO4 , at pH 2.5. Notice how Ni reduction is

0.0

0.2 (b)

accelerated by Au deposition. (b) Microstructure of a Au–Ni alloy (60 at% Ni) showing nanoscale Au-rich grains in a Ni-rich matrix. (Reproduced with permission from Ref. [97]. Copyright 2014, Wiley.)

interaction between Au and Ni [109]. The immiscibility is a consequence of the large difference in atomic volume, which introduces significant elastic strain and leads to phase separation. Based on bulk thermodynamics (Eq. (3.13) with positive ΔH mix ), solid solution formation could only be achieved at overpotential (Figure 3.18c), while a phase-separated mixture could be achieved without any shift in onset potential. Experimental data however show that the onset of Ni reduction is depolarized when Ni is codeposited with Au (Figure 3.19a); furthermore, the resulting microstructure is neither a solid solution nor a phase-separated mixture, but instead is heterogeneous and consists of nanoscale Au-rich grains (Au 80–83 at%) separated by Ni-rich (Au 30 at%) grain boundaries (Figure 3.19b) [97]. The observed depolarization of Ni deposition is driven by the attractive pairwise atomic interaction between Au and Ni, which dominates the growth process during atomic adsorption and incorporation at the surface. The difference in atomic volume under these conditions has a limited influence on the growth process since at a surface elastic strains could be easily accommodated, either via a local compositional gradient [110] or by formation of a disordered atomic arrangement [111], whereby atoms of different size could be more easily accommodated. The resulting microstructure could either be the result of a partial spinodal decomposition driven by the miscibility gap and frozen in place by the ongoing deposition flux, or is generated by an alloy growth instability that leads to compositional nonuniformities [110]. Both phenomena are the result of a dynamic growth process and therefore should not be related to alloy energy minimization; this is in partial contrast with the observation that alloy growth occurs under UPCD conditions. The observed depolarization in fact implies that the observed microstructure should have a lower free energy (stronger average bonding strength) than the phase-separated mixture. Extracting the enthalpy of

91

92

3 Electrochemical Surface Processes and Opportunities for Material Synthesis

mixing from experimental compositional vs. deposition potential data in fact shows that the cohesive energy of the binary system is stronger than that of the thermodynamically stable configuration consisting of a physical mixture of the pure elements. We hypothesize that this decrease in free energy is due both to the formation of small grains, which releases part of the strain energy of the supersaturated solid solution at the interface, and to the presence of wide grain boundaries, which further accommodate possible built-in stresses. In summary, UPCD of bulk immiscible alloys leads to a microstructure very far from the expected equilibrium one; this configuration however presents a bonding energy that is estimated to be stronger than the macroscopic equilibrium configuration. 3.4.4 Structure and Morphology of UPCD Alloy Films 3.4.4.1 Crystallographic Structure and Microstructure

As discussed in Section 3.4.3, electroplated alloy films often form supersaturated solid solutions; solute incorporation above the equilibrium solubility is caused by kinetic trapping of adatoms during film growth. A similar behavior is observed in UPCD alloy films; incorporation of B in the alloy is proportional to the surface coverage, and a solid solution having the crystal structure of A is preferentially formed since this requires no nucleation of a new phase. The example of Pt–Pb discussed in Section 3.4.2 exemplifies this behavior: the lattice constant of FCC Pt–Pb alloys is observed to gradually increase up to 40 at% Pb, suggesting solid solution formation; the bulk solubility of Pb in Pt however is negligible [101]. In addition, random solid solutions are often observed even in alloy systems that form ordered structures (such as in equiatomic Fe–Pt [112, 113] or Co–Pt [114]) or intermetallic compounds (again, in Pt–Pb [101]). The metastable solid solution in these instances grows preferentially since the number of atomic configurations resulting in the competing ordered structure is much lower, leading to a statistical preference for the former. The microstructure of electroplated films can be columnar, fibrous, or fine grained, depending on the chemical nature of the elements involved and on the electrolyte chemistry [115]. UPCD alloy films present similar features; in addition, fine grain sizes are often observed despite the slow growth, due to the difficulty in accommodating atoms with different atomic volume in an ordered arrangement. Alloys that include elements with high melting point such as Pt exhibit a particularly fine microstructure, with grain size of the order of 5–10 nm (Figure 3.20). Ordered structures present in the bulk phase diagram may be observed only after annealing at relatively high temperatures and in an inert atmosphere; the annealing temperature required to achieve full crystallization is lower if the initial film is dense and the concentration of impurities (oxygen, carbon, etc.) is low [113]. Figure 3.21 compares the thermal annealing and ordering process of equiatomic Fe–Pt films grown from acidic noncomplexing solutions [116] and from alkaline complexing electrolytes [113]. The former contain up to 30 at% oxygen and were observed to develop an ordered L10

3.4

Underpotential Codeposition (UPCD)

(111) (200) (220) (311) 10nm 10 nm

(a)

30

40 50 2θ (°)

60

(112)

(210)

(200)

600 °C

400 °C 350 °C

As deposited

20

s

500 °C 450 °C

Intensity (a.u.)

700 °C FePt 002 FePt 001

FePt 200

FePt 111

FePt 110

FePt 001

Counts

800 °C

s

s (002)

(110)

700 °C

fcc(111)

900 °C (001)

Fe–Si ?

Cu

Fe–Si ?

Fe–Si–O ?

Figure 3.20 Microstructure and diffraction pattern of an as-deposited equiatomic Fe–Pt film, electroplated from a citrate/glycine alkaline electrolyte. The average grain size of the films is ∼5 nm, and the crystal structure is face-centered cubic.

Si (111)

As-deposited

20

70 (b)

Figure 3.21 (a) XRD patterns of equiatomic Fe–Pt films (as-deposited and after annealing at the specified temperature) grown from electrolytes containing 1 mM H2PtCl6, 0.5 M FeSO4 , 0.1 M Na2 SO4 . (Reproduced with permission from Ref. [116]. Copyright 2004,

30

40 2θ (°)

50

60

American Institute of Physics.) (b) XRD patterns of equiatomic Fe–Pt films grown from a citrate/glycine electrolyte at pH 8. (Reproduced with permission from Ref. [113]. Copyright 2011, The Electrochemical Society.)

tetragonal structure only after annealing in forming gas (5% H2 in Ar) above 600 ∘ C. The latter incorporate a much lower oxygen fraction, and the L10 ordered phase can be obtained starting at temperatures as low as 400 ∘ C (Figure 3.21). Compound semiconductors may present a wide variety of microstructures, strongly dependent on the chemistry of the process. Electrodeposition of Cu2 O

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3 Electrochemical Surface Processes and Opportunities for Material Synthesis

3×104 120000

Kα1 Cu ZnO NRs

2.5×104

30000

72

73

74

{0001} ZnO:Al substrate + NRs

1×104 5000

As-deposited

{0002} ZnO:Al substrate + NRs

0 (a)

40

60 2θ theta scale (°)

Figure 3.22 (a) XRD pattern of ZnO films electrodeposited on ZnO:Al substrates, showing high crystallinity, and good orientation. (Reproduced with permission from Ref. [117]. Copyright 2010, The Institute of Physics.) (b) XRD patterns of electroplated CdTe films

0 20

80 (b)

40

Powder

60

(422)

71

1.5×104

(333)+(511)

0

(331)

60000

Anneated at 403 °C for 5 min

2×104

(400)

Kα Cu ZnO:AI substrate

(220)

Counts (a.u.)

90000

(311)

Kα2 Cu ZnO NRs

(111)

XRD Intensity (a.u.)

2500

80

2θ (°)

in the as-deposited and annealed condition, in comparison with powder diffraction patterns. (Reproduced with permission from Ref. [118]. Copyright 1996, The Electrochemical Society.)

or ZnO results in highly crystalline, and in some cases even single crystal, films, due to the high reversibility of the compound formation process; crystallinity is favored and crystallographic orientations are selected by the use of substrates favoring epitaxial growth [117] (Figure 3.22a). Compounds such as CdS and CdTe in contrast may exhibit poor crystallinity; clear diffraction peaks from the compound phase can only be observed after gentle (∼400 ∘ C) annealing; use of a reactive atmosphere such as CdCl2 assists in controlling p-type doping [118] (Figure 3.22b). 3.4.4.2 Film Morphology

Growth under UPCD conditions occurs at relatively slow rates, roughly from a fraction to ∼10 monoatomic layers per second. On the other hand, as discussed earlier, the concentration of the more noble element A is often kept low, and diffusion-limiting conditions for A are therefore achieved at low overpotentials for A. If the difference in the redox potentials of A and B is large, B could be codeposited only under diffusion-limiting conditions for A, favoring the onset of growth instabilities [119]. This often leads to significant film porosity and sometimes to dendritic growth; in the case of alloys, the oscillatory nucleation process observed in metals [120] may lead to nucleation and growth of elemental phases, even in cases where the solid solution configuration is thermodynamically stable. Figure 3.23a shows the surface morphology of Au–Cu films (20 at% Cu) grown from an acidic non-complexing solution [93]; the film is porous, and a somewhat dendritic growth is observed. Phase separation may ensue by changing deposition conditions; Figure 3.23b shows in fact the presence of hemispherical islands with higher Au fraction on top of the Au–Cu film, as determined by a compositional line scan obtained using energy dispersive spectroscopy EDS.

3.4

LEI

20.0 kV ×30 000

WD 12.4 mm

Underpotential Codeposition (UPCD)

100 nm

(a)

(b)

Figure 3.23 (a) SEM surface morphology of a 20 at% Cu Au–Cu film grown from an acidic solution. (b) Growth instability leads to the localized growth of Au-rich islands, as shown by EDS line scans (D. Liang and G. Zangari, unpublished).

SEI

5.0 kV

×50 000

WD 4.3 mm 100 nm

(a)

SEI

5.0 kV

×50 000

WD 4.5 mm 100 nm

(b)

Figure 3.24 SEM images of the surface morphology of Au–Cu film ((a) Cu 30 at%, (b) Cu 85 at%) grown from a solution of 0.5 mM Au(ethylendiamine)2 , 20 mM CuSO4 , and 0.2 M glycine [97].

Dense and homogeneous films on the contrary are obtained by selective complexation of one or both metal ions in solution: this may draw the redox potentials of the two elements closer and avoid growth under diffusion-limiting conditions for A. Electrodeposition of Au–Cu from a complexing solution, for example, results in dense, smooth, and homogeneous films, as shown in Figure 3.24. Similar effects have been observed in the UPCD of Pt-based alloys: acidic electrolytes where Pt is not complexed form porous films (Figure 3.25a) [96], while complexation of both Pt and Fe leads to dense, smooth, and shiny films, as detected by AFM imaging (Figure 3.25b) [113]. 3.4.5 Applications of UPCD Growth Methods

UPCD alloys target applications that require strict control over compositional homogeneity and crystal structure, in particular on irregular surfaces and across

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NiPt Au

100 nm

10 nm (a)

(b) Figure 3.25 (a) Porous structure of Ni–Pt films grown from a PtCl4 , NiCl2 electrolyte. (Reproduced with permission from Ref. [96]. Copyright 2008, The Electrochemical Society.) AFM images (1 μm2 × 1 μm2 ) of (b) a Fe–Pt film grown from an acidic chloride solution,

(c) and (c) a Fe–Pt film grown from an alkaline solution, showing decreased grain size, and more compact structure in the second electrolyte. (Reproduced with permission from Ref. [113]. Copyright 2011, The Electrochemical Society.)

large areas. Owing to the low growth rate necessary to control composition, such applications may be limited to very thin films, except for metal oxide and semiconductor compounds that can be grown at significant overpotentials while still maintaining the structure and stoichiometry sought for. 3.4.5.1 Catalysis and Electrocatalysis

Metallic monolayers and alloys based on precious metals are extensively used in a variety of heterogeneous (electro)catalysis processes; alloys in particular exhibit quite different properties from those of the parent metals, often providing synergistic effects; in addition, they exhibit tunable properties, achieved by gradually varying the composition [121]. Catalytic properties of alloy surfaces are determined both by electronic effects, whereby heteroatom bonds change the local electronic environment with respect to the pure elements, and by geometric (ensemble) effects, where definite atomic arrangements provide suitable adsorption sites for the reactive species, and, in parallel, strain effects may arise. The two effects are difficult to separate and often interfere with each other; for instance, strain affects the electronic structure [122]. The catalytic properties of a material are overwhelmingly determined by its surface atomic configuration, which is completely controlled in UPD processes but may be different from that of the bulk alloy due to reconstruction effects, segregation, or surface alloy formation. From the thermodynamic standpoint the surface of an alloy should be enriched in the element with lower surface energy, but kinetic limitations may hinder equilibrium between the surface and the bulk over significant time scales. In addition, the external environment may affect the surface composition, due to preferential bonding of gaseous species to one of the alloy components [123]. It has been observed, for example, that Ag–Cu catalysts for ethylene oxide production should present an Ag-enriched surface at equilibrium due to its lower surface energy, but in oxygen-containing environments the surface is enriched

3.4

Underpotential Codeposition (UPCD)

instead with Cu due to the stronger Cu–O bond, stabilizing surface Cu via a chemical interaction [124]. Similarly, in Ag3 Pd surfaces, calculations show that Ag should segregate at the surface, but that in presence of oxygen, adsorption drives Pd to the surface, to an extent depending on the chemical potential of Pd in the alloy, that is, on the composition [125]. The atomic surface configuration of an alloy should be determined precisely since it determines to a large extent its catalytic properties; several examples of direct correlations between surface structure and reactivity are available in the literature. Besenbacher et al. [126], for instance, have shown that substitution of Ni atoms with Au at a Ni surface hinders adsorption of CO and therefore delays carbon formation during reforming of methane. In another example, electrochemical STM with chemical contrast was used to show that Ag–Pd surfaces allow CO adsorption at Pd monomer, while H adsorption from H+ requires the presence of Pd dimers or larger ensembles [127]. Owing to its quasi-equilibrium character, UPCD should lead to surface atomic configurations corresponding to those predicted by surface thermodynamics. Out-of-equilibrium configurations could be achieved by (i) accelerating growth kinetics, which would lead to freezing diffusing adatoms in metastable positions or (ii) depositing under conditions where the kinetics of the less noble metal is slow enough that it cannot follow the thermodynamic predictions. Particularly interesting is the case of bulk immiscible alloys; as discussed earlier, Au–Ni UPCD leads to nanoscale compositional gradients, likely generated by dynamic growth processes; the resulting microstructure, however, exhibits a stronger cohesive energy than the mechanical mixture of the pure elements. Varying the applied potential may lead to widely different microstructures and surface configurations, likely resulting in distinct catalytic properties. UPCD of a series of binary and ternary Pt-based alloys has been used by Moffat in combination with dealloying to prepare nanostructured electrocatalysts [128–130]. Pt–Ni, Pt–Ni–Pd, and Pt–Co were tested for their catalytic activity toward the oxygen reduction reaction; in comparison to Pt, these films exhibit up to 10-fold improvement in activity per unit mass of Pt. Pt–Pb alloys [131] were investigated as electrocatalysts for formic acid oxidation; despite showing significant dealloying under operation, their electrocatalytic activity was found to be significantly enhanced with respect of Pt. 3.4.5.2 Photovoltaics

The solar energy flux on Earth is about 4 × 1020 J h−1 , of the same order of magnitude as the global energy needs per year [132]. Solar power can therefore be considered the only renewable, carbon-free energy source with the potential to significantly displace the use of fossil fuels within the near future. Solar energy can be converted to electricity in thermal solar systems, where a fluid is heated to evaporation and the resulting vapor is made to flow through a turbine, generating electricity. The efficiency of this process however is limited by the maximum temperature achievable, according to the Carnot formula. In contrast, photovoltaic technology utilizes semiconductor materials to directly transform solar light in

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electrical current via light absorption and generation of electron–hole pairs. By fabricating a p–n junction device, an electrical potential gradient is generated within the semiconductor, and the two charge carriers can be separated by the built-in potential and injected in an external circuit, generating current. The efficiency of a single junction device is ideally limited by transmission losses of photons having energy below the band gap, and by the inelastic scattering of charge carriers generated by photons with energy higher than the band gap; the maximum efficiency of such a device would be 31% [133]. Higher efficiencies can be achieved by various methods, including band gap engineering [134], charge carrier multiplication [135], multijunction devices [136], and plasmonic effects [137]. Practical efficiencies are however limited by carrier recombination at defects, in particular grain boundaries; for this reason, the highest efficiencies have been achieved using semiconductor single crystals or epitaxially grown heterojunctions. The first photovoltaic devices utilized single-crystal Si wafers. Si is an indirect band gap material and its large absorption length requires a thickness of about 200 μm to absorb a significant fraction of the solar light. The best single-crystal Si PV cells have achieved an efficiency of 25%. Polycrystalline Si devices can achieve efficiencies around 12–15%, but their cost is close to that of single-crystal Si devices. Thin film solar cells using direct band gap materials could strongly decrease the raw material usage since sufficient absorption could be achieved in films about 1 μm thick. Amorphous Si (A-Si) grown by CVD methods, for instance, has a direct band gap of ∼1.6 eV and exploits hydrogen (∼10%) to passivate dangling bonds; Si–H bonds however are unstable in the presence of visible light, and stabilized efficiencies are limited to 6–7%. Overall, 80% of the PV solar market is dominated by Si, of which 8–10% consists of amorphous Si [138]. Since the early 1960s, thin films of semiconducting compounds grown by CVD or CBD were investigated for PV applications; many Cu-based materials were observed to degrade over time due to Cu diffusion; however, various stable materials have been identified, including II–VI, III–V, and I–III–VI2 compounds. A prototypical II–VI compound is Cd–Te, with a direct band gap of 1.45 eV, high optical absorption (>105 cm−1 ), and p-type conductivity, making it ideal for absorber applications. Cd–Te (2–6 μm thick) is usually integrated in a device with an n-type CdS window layer forming an n–p junction; the highest efficiency achieved is 16.5%. III–V materials are being used as single layers (GaAs has achieved an efficiency of 25%) or to grow epitaxial multijunction cells, by which efficiencies of up to 41% have been achieved; this approach is however very expensive and is mostly used in combination with light concentrators. Among the I–III–VI2 compounds, CuInSe2 has a high absorption coefficient (105 cm−1 ) and a layer of only 0.1–0.3 μm is sufficient for significant absorption [139]. Its band gap can be tuned between 1.04 and 1.68 eV by substituting Ga for In. Films made by co-evaporation have demonstrated efficiency of about 20%. The high efficiency of these devices is due to the highly mobile Cu ions, which contribute to the self-healing of defects being generated during operation, and to the limited recombination at grain boundaries [140]. The best method to produce CIS

3.4

Underpotential Codeposition (UPCD)

films is by selenization of a precursor material, which could be either an alloy containing all the metallic elements or a stack of various layers consisting of single metals, compounds, or alloys. CIGS compounds with the correct stoichiometry can be directly obtained by electrodeposition, resulting in 10% efficiency, or up to 15% (NREL) if followed by evaporation [141]. The strong growth of PV industry over time has led to concerns about the relative scarcity of some of the materials needed in PV devices: Ag for contacts in PV Si devices, In and Ga in CIGS materials, and Te in CdTe. In order to overcome these obstacles, kesterite materials Cu2 ZnSn(S,Se)4 have been recently introduced and studied [142]. CZTS materials have a direct band gap between 1 and 1.5 eV, tunable by progressive substitution of Se with S, and absorption >104 cm−1 . The best devices so far have demonstrated an efficiency of 10.1%; the CZTS films were obtained by a two-step process consisting in deposition of the elements followed by annealing at 500–660 ∘ C under controlled atmosphere, which can include chalcogen addition. The semiconductor compound films discussed above are grown mainly by coevaporation or electrodeposition, the latter being potentially more practical, economical, and scalable. Serious limitations are, however, encountered due to the necessity to use a two-step process where a metallic precursor is first deposited, and then annealed in the presence of the chalcogenide. This process needs to take into account differential evaporation of elements and various compounds, possible compositional gradients through the film and across the surface, and hindrance in achieving the crystal structure of interest. UPCD has been long used for the synthesis of materials such as CdTe and ZnO, and it shows significant promise in the production of the alloy precursor or even for the final composition and structure of CZTS films. The process at present appears complex, but the objective is achievable through sustained effort in understanding UPCD process of ternary and complex alloys and compounds. 3.4.5.3 Magnetic Recording and Microsystems

Magnetic recording is ubiquitous in information storage. Since its inception in 1956 and later with the proliferation of personal computers, hard disk drives have become the principal medium for recording and retrieving information. Continuous technology improvements have led to an exponential increase in recording density and a corresponding decrease in cost per unit memory storage [143]. Since 2005, the market has been dominated by the perpendicular recording technology, whereby the magnetization transitions in the magnetic medium are recorded in the direction perpendicular to the disk. This innovation has helped to bring the record density in commercial products up to 750 Gb in.−2 in 2011; recent laboratory demonstrations in 2012 have increased this record up to 1.5 Tb in.−2 . In magnetic storage systems a recording head flies above a rotating disk coated with a thin magnetic film, consisting of nanometer scale grains separated by nonmagnetic grain boundaries. Magnetizing the head with current results in data being written on the magnetic film in the form of magnetization transitions; such

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transitions are read back by a trailing sensor via a magnetoresistive effect. Recording density has been consistently increased over time by decreasing the bit size; since the signal-to-noise ratio of the readback data is proportional to the number of grains per bit, higher recording density requires the grains in the film to become smaller. In recent years, miniaturization has reached the point where the magnetic energy of the grains becomes of the order of the thermal energy; the imposed magnetization direction cannot be maintained over time and the grain is said to be superparamagnetic [144]. To avoid this physical limitation toward miniaturization, it is necessary to increase the intrinsic magnetic energy of the material by increasing its magnetic anisotropy. The ordered tetragonal L10 phase of equiatomic Co–Pt, Fe–Pt, or Fe–Pd provides promising materials for future high recording density media. Thin film deposition methods however have resulted in the growth of metastable FCC phases, which could be transformed into the L10 phase only after annealing in reducing atmosphere at 500–700 ∘ C. This high annealing temperature leads to unacceptable grain growth, decreasing the potential SNR of the media. UPCD could in principle provide a method to directly grow the ordered L10 phase via thermodynamic selection of the equilibrium phase; recent efforts in this direction have led only to the growth of metastable FCC phases [112, 113], but it may be possible to increase the deposition temperature and adopt pulsed potential schemes in order to increase surface mobility and to overcome the nucleation barrier without sacrificing a slow growth rate, respectively. Electrodeposition has a great potential in the fabrication of magnetic media since an alternative magnetic media design involves the fabrication of an array of magnetic islands of about 10 nm diameter, characterized by strong magnetic coupling within the single islands and by physical separation among the islands. Each island could thus behave as a magnetic unit, the magnetization of which could be switched as a whole at a predetermined applied field, avoiding the SNR intrinsic to continuous media. This patterned media design [145] requires a completely different fabrication method, capable of forming nanometer-scale islands at precise locations over a disk of several inches diameter, at low cost, and in a highthroughput manufacturing process. Electrodeposition is ideal for this purpose, since its selectivity enables growth only at conductive locations, which could be predetermined by a suitable pattern; in addition, the process would be completely additive, avoiding the etching processes necessary when using physical deposition methods, which necessarily damage the magnetic islands and affect their magnetization switching processes. Potential patterning methods that are currently being investigated include electron beam lithography, a slow, serial process, and nanoimprint lithography, which consists in the replication of a quartz mold by a suitable mold, which is then used to imprint a resist spun onto the disk [146]. The integration of high-anisotropy magnetic materials with micro- and nanofabrication methods could be extended to the production of novel magnetic microsystems containing micro-permanent magnets, capable of implementing functions such as magnetic biasing, magnetic field generation, and microactuation. The alloys discussed above could be used in these applications as well;

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films Kurt R. Hebert

4.1 Introduction

Anodic oxide films are formed conveniently on a wide range of metals by simple electrochemical oxidation in a solution that dissolves the oxide. The pores are created by a dissolution process while oxide forms by anodic reaction of the metal with water. Within well-defined windows of process variables such as applied voltage and solution composition, the pores are arranged in hexagonally ordered patterns of parallel columnar cells oriented perpendicular to the metal surface [1, 2]. Each cell contains a cylindrical pore that penetrates entirely through the oxide. Pore diameters are as small as 10 nm while the pore length to diameter ratio can exceed 1000 and their number densities can approach 1010 cm−2 [3]. Numerous devices for (e.g.) energy, optical, catalytic, and biological applications have been constructed from these porous anodic oxide (PAO) films, taking advantage of their high specific surface area and the ability to tune the porous layer geometry by adjusting the anodizing voltage and solution composition [4–7]. Relative to many other nanofabrication methods, anodizing has intrinsic advantages of small processing times, low cost, and suitability to large dimensions. Indeed, anodizing is widely used industrially for corrosion protection on structures such as aluminum architectural panels. The scalability and processing throughput advantages of anodizing are effectively illustrated by the example of dye-sensitized solar cells (DSCs). Vertically aligned nanostructures such as dense nanowire or nanotube arrays are highly favorable for DSCs because of the combination of large interfacial area for light-harvesting and continuous conducting phases for fast transport of charge carriers [8]. PAO-based TiO2 DSCs have been developed by several groups [7]. For comparison, nanostructured ZnO-based DSCs may be prepared by a hydrothermal process yielding dense nanowire films [9–11]. The roughness factor (interfacial area per substrate area) of the nanowire array obtained by this method is about 100, a factor of 10 smaller than values obtainable by anodizing [3], the latter approaching the “ideal” roughness of 1000 cited for DSCs [11]. The Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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typical growth rates of the ZnO nanowire films, ∼0.1−1 μm h−1 , is at least 10 times smaller than that of PAO films [12]. The intrinsically high rates of anodizing procedures derive from large potential driving forces used in anodizing cells, which range from tens to hundreds of volts. As such, self-organized porous oxides are produced by pattern formation far from equilibrium, in contrast with many other nanostructures that are produced by self-assembly close to equilibrium. The typical stages of pattern formation are initial compact growth, followed by instability and finally reordering to a stable morphology [13]. Ordered patterns are produced in well-defined ranges of process conditions, and their geometry obeys scaling relationships with the driving force. Anodizing exhibits these characteristics. For classical systems such as aluminum and titanium, scaling relations have been empirically established between the anodizing voltage and the porous layer geometry. Also, it is found that selforganized films are only produced when the relative rates of metal oxidation and dissolution fall within precise ranges. However, since the reasons for these scaling relations and processing windows are not understood, completely rational design of new types of self-ordered porous anodic layers is not yet possible. This understanding would be practically useful for exploring more complex materials such as multicomponent oxides on alloys or non-oxide anodic films. This chapter focuses on mathematical modeling of the formation of selforganized PAOs. It is argued that application of the theory of pattern formation can directly reveal scaling relations governing the porous layer geometry, and ranges of processing conditions for self-ordered film formation. Indeed, both modeling and experimental work over the last 20 years has produced substantial progress toward these goals. In addition to gaining scientific understanding of the self-ordering phenomenon, modeling can eventually assist efforts to produce defect-free films at high throughput, thereby enhancing the commercial potential of anodizing. The chapter is organized as follows. Section 4.2 establishes the key experimental phenomenology of anodizing by reviewing the experimental literature. More detailed recent reviews of self-ordered porous oxides are available elsewhere [7, 14, 15]. After a discussion of pore formation mechanisms suggested in the literature in Section 4.3, mathematical descriptions of transport and kinetic component processes involved in anodizing are covered in Section 4.4. Finally, Section 4.5 describes the results of modeling investigations, and Section 4.6 summarizes the current state of the art.

4.2 Phenomenology of Porous Anodic Oxide Formation

Two distinct porous oxide morphologies are produced by anodizing – pores and nanotubes, as shown in Figure 4.1 [7, 16]. Anodic films on Al consist of a continuous oxide matrix penetrated by pores [1, 2], while oxide nanotube layers on other metals (TiO2 , ZrO2 , Ta2 O5 , Nb2 O5 , WO3 , and HfO2 ) are composed of arrays of oxide tubes with interstitial voids separating neighboring cells [7, 15]. Tube

4.2

Phenomenology of Porous Anodic Oxide Formation

500 nm

500 nm (a)

1 μm

250 nm

(b) Figure 4.1 Scanning electron microscopy (SEM) images showing typical steady-state geometries of self-organized porous anodic oxides [16]. (a) Porous anodic Al2 O3 formed

at constant applied potential in oxalic acid (top view) and phosphoric acid (cross section). (b) TiO2 nanotube layers.

and pore morphologies share hexagonal pore symmetry and have comparable ranges of typical dimensions such as pore diameters and pore–pore separation distances. As discussed below, the growth of both pore and tube layers seems to be controlled by similar processes, namely, electrical migration, dissolution, and stress-driven transport. Since nanotube layers are typically produced in baths containing fluoride ions to assist oxide dissolution, the separation between cells in such layers may be related to fluoride chemistry. Indeed, it has been proposed that the voids between nanotubes are formed by reaction of incorporated fluoride species with water [17–19]. Other investigators suggest that tubes separate by electrostatic repulsion of cation vacancies generated along the tube walls [20], or through a hydroxide crystallization process [16]. In all these views, common basic mechanisms account for initiation and self-ordering of both pore and tube layers, while tube separation results from a side process. Accordingly, the

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present chapter includes pore formation and self-ordering in both nanotube layers and porous alumina, and the term “porous anodic oxide” will refer to both types of oxide. This chapter does not address porous layers with complex morphologies that may be produced by anodizing [21–23], since fundamental understanding of even the classical pore and tube geometries is not yet fully developed. Microscopic observations suggest that the porous oxide morphology evolves over time after barrier oxide layer growth becomes unstable. Typical electrochemical transients during anodizing are shown in Figure 4.2 for porous anodic alumina [24], and in Figure 4.3 for TiO2 nanotube layers [25]. The initial stage of anodizing both metals produces a compact, conformal barrier oxide layer (a)

(e)

200 nm 50 nm

(b)

(f)

50 nm

(c)

200 nm 50 nm

(g)

Smax

140 120

(d)

S100 100 E (V)

110

Sconst

80 60 S40

40 20

100 nm

S20

0 0

50

100

150

200

250

300

350

400

t (s)

Figure 4.2 Development of porous oxide morphology during anodizing of Al at a constant applied current density of 4.5 mA cm−2 in a 0.4 M H3 PO4 aqueous solution [24]. (a)–(f ) are transmission electron microscopy

(TEM) images of oxide cross-sections after anodizing to the various voltages in the potential transient (g). (a) 20 V, (b) 40 V, (c) 60 V, (d) 100 V, (e) 140 V (Smax), and (f ) 107 V (Sconst).

4.2

(a)

I

II

III

Phenomenology of Porous Anodic Oxide Formation

IV

5V

40 V

20 V

50 V

30 V

I (mA)

10

1

0

60

II–III 50 s (f)

III–IV 160 s

240

300

t (s) (c)

(b)

I–II 7s (d)

180

120

50 nm

100 nm (e)

500 nm

50 nm (g)

100 nm

Figure 4.3 Development of TiO2 nanotube morphology during anodizing of Ti at a constant applied potential in a solution of 0.1 M NH4 F and 1 M H2 O in ethylene glycol [25]. (a) Current density transients at different applied voltages. I–IV are stages of anodizing

500 nm referenced in the text. (b,c) Side and top view scanning electron microscopy (SEM) images after 7 s at 20 V. (d,e) Side and top view SEM after 50 s at 20 V. (f,g) Side and top view SEM after 160 s at 20 V.

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

(Figures 4.2a and 4.3a stage I, (b,c)). This regime is characterized by a linearly increasing potential under constant applied current and a decreasing current density under applied potential. The transient potential or current density variations result from the large electric field approaching 1 V nm−1 needed to drive ionic conduction through the barrier oxide. When the barrier layer grows to a critical thickness, surface roughening at the film–solution interface becomes apparent over the entire electrode surface (Figure 4.2b). This roughening suggests the onset of a morphological instability, as found, for example, in solidification from the melt or electrodeposition [26, 27]. In these processes, spontaneous uniform microscopic roughening occurs at critical values of global variables (temperature gradient or overpotential), and thereafter grows in amplitude, eventually evolving to cellular patterns or dendrites. In a similar manner, the oxide–solution interface roughness increases over time and evolves into a somewhat irregular pore array with a characteristic pore–pore separation distance of tens of nanometers (Figures 4.2d and 4.3a stages II–III and (d,e)) [24, 28, 29]. At the time of the current density minimum in potentiostatic experiments or the potential maximum during galvanostatic anodizing, the disordered pores begin to transform into a more ordered arrangement or more widely spaced pores (Figures 4.2e,f and 4.3a stage IV and (f,g)) [24, 28, 29]. On the basis of SEM (scanning electron microscopy) and TEM (transmission electron microscopy) observations, it has been suggested that this transformation occurs by competition between pores, in which a fraction of the initial pores are enlarged and continue growing, while the growth of others terminates [30, 31]. The transformation to the ordered porous layer is accompanied by a decrease of the barrier oxide thickness at the pore bottoms and the formation of a scalloped pattern at the metal–oxide interface. In constant current and potential experiments, the potential and current density, respectively, relax to their steady-state values. Over time, the arrangement of pores in the second array becomes increasingly ordered. In the case of Al, self-ordering may require extended anodizing periods of several days, while on Ti the process is apparently much more rapid. The geometric parameters of PAOs scale directly with the anodizing potential [7, 32, 33]. For porous aluminum oxide, universal scaling relations are found across the spectrum of various acid solutions used as anodizing baths (Figure 4.4) [2]. A common separation to voltage ratio of 2.5 nm V−1 applies to typical “mild” anodizing processes at current densities of 1–10 mA cm−2 . Self-ordered porous alumina films are characterized by a uniform porosity of 10%, indicating that the pore diameter also scales universally with voltage [34]. While the scaling relations apply across anodizing baths, a given acid can produces self-organized films only at a particular voltage and with corresponding dimensions [35]. Thus, ordered porous films in sulfuric, oxalic, and phosphoric acids with pore separations of 63, 100, and 500 nm are formed respectively at potentials of 25, 40, and 195 V. This dual dependence of geometry on potential and bath composition suggests that the self-ordering mechanism involves an intriguing interplay of physical forces and chemistry. Linear scaling relations with voltage also govern pore diameters

4.2

Phenomenology of Porous Anodic Oxide Formation

500 Sulfuric acid Interpore distance d (nm)

Oxalic acid Phosphoric acid d = −1.7+2.81 Ua 250

0

50

100 Anodic voltage Ua (V)

150

Figure 4.4 Scaling relation between pore–pore separation distance Dint and anodizing voltage for porous aluminum oxide films [2]. The data points represent conditions for growth of self-organized porous oxides in various acidic solutions.

300 d

IR-drop

250 Diameter (nm)

U

200 150 100 50 0

0

20

40

60

80

100

120

Potential (V) Figure 4.5 Dependence of pore diameter on anodizing voltage for TiO2 nanotube films formed in various media: ○ water-based, ▾ glycerol/water 50 : 50, ◽ glycerol, and ◾ ethylene glycol [7].

in TiO2 nanotube films [7] (Figure 4.5). Unlike porous Al2 O3 , different diameterto-voltage ratios are found in anodizing solutions using various organic solvents and water content. However, the effect of anodizing solution ohmic resistance on these ratios has not been resolved, so it is not yet clear whether the scaling relations are universal or else depend on the anodizing solution. One important distinction between alumina and titania is that self-ordered nanotube layers can

113

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

be formed at any applied potential, rather than only at certain discrete values. In broad terms, the different scaling relations on Al and Ti may be related to the different dissolution chemistry. Dissolution during porous alumina formation is due to the acidity of the aqueous anodizing bath [36], while the dissolution reaction involved in nanotube layer growth involves complexation of metal ions by fluoride ions [7]. Indeed, the use of fluoride-containing electrolytes was the key innovation leading to the ability to produce self-organized porous oxides on metals other than aluminum [37, 38]. Metal dissolution in parallel with oxide formation plays an important role in the production of self-organized porous oxide layers. The relative rates of oxidation and dissolution are quantified by the oxide formation efficiency (or anodizing efficiency), which represents the fraction of the anodic charge contributing to oxide growth rather than metal dissolution. As discussed in Section 4.4, the efficiency reflects the kinetics of ion transfer reactions at the oxide–solution interface, namely, the formation of oxygen ions from water and metal ion dissolution. Since metal oxidation is typically the only significant electrochemical reaction during anodizing, efficiencies are measured by comparing the anodic charge with the quantity of metal ions either in the oxide or in solution. Representative measurements during steady-state anodizing of Al [24, 39–41], Ti [29, 42], and Zr [43] are shown in Figure 4.6. These measurements reveal that self-ordered porous films are associated with narrow ranges of anodizing efficiency. Interestingly, the efficiency ranges of each metal are comparable to the oxygen ion transport numbers in these oxides: 0.60 (Al) [45]; 0.61 (Ti) [46, 47]; and 0.88–0.90 (Zr) [46]. It should be noted that during the initial stages of barrier oxide growth and disordered porous layer formation, somewhat different efficiency values are found relative to steady-state values. Efficiencies of 50% and 35% were measured during the initial period of galvanostatic Al anodizing in sulfuric and phosphoric acids 1.0 Efficiency or transport number

114

0.8 0.6 0.4 εo to

0.2 0.0 AI

Ti

Zr

Anodic oxide Figure 4.6 Ranges of anodizing efficiencies 𝜀O measured during formation of porous oxides Al, Ti, and Zr [43, 44]. Also shown are the oxygen transport numbers tO of these oxides [45, 46].

4.2

Phenomenology of Porous Anodic Oxide Formation

[39, 48]. In contrast, the efficiency during the initial stage of potentiostatic anodizing approaches 100%, as a result of the large initial current density [29]. Much research has been stimulated by the discovery of anodizing regimes for self-organized porous oxide formation at high current densities, significantly larger than 100 mA cm−2 [3, 12, 49]. These “hard anodizing” processes can significantly reduce processing times for porous oxides, eventually perhaps leading to commercially viable high-throughput device fabrication. Self-organized film formation during hard anodizing requires pretexturing of the metal surface with a pattern of a similar length scale as the pore separation distance [50]. In addition to physical and chemical processes involved in mild anodizing, hard anodizing is sensitive to heat transfer and solution phase mass transfer [51]. These processes may influence the mechanisms of pore formation and self-ordering. Thus, the self-ordering mechanism during hard anodizing may involve, in addition to processes important in mild anodizing (e.g., ion migration and dissolution), other phenomena such as oxide flow or solution-phase mass and heat transfer. These mechanistic differences may account for the different scaling relations observed to govern porous layer geometry, as the pore separation-to-voltage ratio is 2.0 nm V−1 as found under “hard” anodizing of Al, compared to 2.5 nm V−1 for mild anodizing [3, 52]. The present chapter focuses on mild anodizing, which is more tractable for model development because complications associated with additional transport processes need not be considered. Stress may significantly affect anodizing by modifying rates of interfacial reactions and transport processes. Stress gradients in anodic oxides can arise from reactions that would produce volume changes in the oxide, if the oxide were not constrained by attachment to the metal substrate. Compressive (tensile) stress may be generated at the metal interface when the oxide volume produced by oxidation is greater (less) than the metal volume consumed [2, 53]. It should be noted that this comparison depends significantly on the fraction of ionic current transported by metal or oxygen ions, or the transport number. Thus, without consideration of transport numbers, the densities of anodic oxide and metal phases typically suggest that large compressive stress should be produced, while instead tensile stress may be observed during anodizing of metals such as Al where the metal ions transport appreciable current [54]. Other stress-producing reactions may include hydration/dehydration of the oxide near the solution interface [55, 56] and interfacial reactions that produce or consume point defects (as interstitials and vacancies contribute lattice expansion and contraction, respectively) [57, 58]. Anodic oxides also exhibit electrostriction stress, that is, elastic stress balancing electrical forces on the dielectric oxide material [59]. Significant electrostriction stresses have been detected in anodic oxides with relatively high dielectric constants [60]. Measurements of oxide volume expansion and tracer studies have revealed the important role of bulk oxide motion in the growth of PAOs. The volume expansion is the ratio of the oxide thickness produced to the thickness of consumed metal (Figure 4.7). PAO formation is accompanied by oxide volume expansions significantly larger than unity. Values of 1.3–1.6 are typically found during porous oxide formation on Al [2, 53, 62, 61], and 2.7–3.1 during growth of Ti nanotube

115

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

3

2

1

(a)

4

3

2

1

(b) Figure 4.7 (a and b) Schematic of experiment used to measure oxide volume expansion during Al anodizing [61]. The volume expansion is the ratio of the thickness of

layer 4 (porous anodic oxide) to that of layer 1 (Al metal); layers 2 and 3 are inert oxides. As shown in the drawing, the volume expansion exceeds one.

layers [29]. For barrier oxide layers, volume expansions larger than 1 can result from outward metal ion migration, leading to film formation at the solution interface. However, in porous oxides, no significant electric field exists in the pore walls to support such migration [63]. Therefore, volume expansions greater than 1 imply bulk motion of oxide in the pore walls directed away from the bulk metal, which must be driven by mechanical forces. Gösele and coworkers proposed that these forces arise from elastic compression during oxide formation at the metal–oxide interface, due to the lower density of the oxide compared to the metal [2, 53]. A detailed picture of oxide motion during Al anodizing later emerged from studies in which layers of tungsten tracers originally imbedded in the metal were used to image oxide transport processes (Figure 4.8) [41, 64, 66–68]. These experiments showed the same uniform upward motion of oxide in the pore walls as suggested by the volume expansion measurements, and further indicated that the oxide motion originated from the solution interface at the pore bottoms, as opposed to the metal interface. This motion was characterized as plastic flow, which they suggested may be driven by electrostriction forces arising from the intense electric field in the oxide near the pore bottom. While flow of ceramics near ambient temperature might be considered unusual, a body of evidence in fact exists for room-temperature viscous flow of amorphous thin films during ion beam processing [69–71]. Further evidence for flow during Al anodizing

4.2

(a)

Phenomenology of Porous Anodic Oxide Formation

(b)

100 nm

(c)

100 nm

(d)

100 nm

100 nm

Figure 4.8 Experimental tungsten tracer profiles during aluminum anodizing in phosphoric acid at 195 V [64], along with simulated tracer profiles [65]. Images are crosssectional transmission electron micrographs

with the tungsten layer in dark contrast. Anodizing times are (a) 180 s, (b) 240 s, and (c) 350 s. (d) Simulated profiles at time intervals of 31.2 s.

was obtained by Oh and Thompson through observations of interface deformation during anodizing of confined Al thin films [72]. They also showed evidence that anodic alumina flow may be induced by high electric fields during the transition from the disordered to stable ordered pattern of pores [73]. It is not yet clear whether the self-ordering phenomenon depends on the structural and compositional characteristics of oxides. Most anodic oxides are amorphous [74], including porous aluminum and titanium oxides [75, 76]. The composition of the anodic film tends toward that of the pure oxide in the region near the metal, although nanolayers of fast-migrating fluoride ions adjoin the metal interface of titanium oxide nanotubes [7]. Electrolyte contaminants are incorporated near the film–solution interface at mole fractions of usually less than 10%, including carbon species in TiO2 nanotube layers, and electrolyte anions in porous alumina [7, 77, 78]. The densities of anodic Al2 O3 and TiO2 are both close to 3.0 g cm−3 , 15–25% smaller than those of crystalline oxide counterparts [79–82]. This suggests that the anodic films contain significant quantities of vacancy-type

117

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

defects or voids; in fact, oxygen isotope studies of aluminum anodizing reveal evidence that voids may act as “easy paths” for oxygen ion transport [24, 83, 84].

4.3 Mechanisms for Porous Anodic Oxide Formation

Since the discovery of porous alumina in 1953 [32], a wide range of mechanisms for PAO formation have been proposed. Early papers focused attention on coupled oxide growth and dissolution during steady state anodizing. Several authors tried to explain the constant barrier oxide thickness at pore bottoms, where the oxide–solution and metal–oxide interfaces both seem to recede at the same velocity toward the bulk metal. The recession of the solution interface has been rationalized by locally enhanced oxide dissolution, through the combined effects of elevated acid concentration in the pores and Joule heating [32, 85]. O’Sullivan and Wood also suggested an elevated oxide dissolution rate at pore bottoms, which they attributed to field-assisted dissolution [33]. It was envisioned that electric polarization of the oxide by the high local electric field increases the rate of chemical dissolution. Hoar and Mott realized that since electrochemical current is concentrated at the pore bottom, this surface must be the source of the oxygen accumulating in the pore walls [86]. For this reason, they suggested that oxygen ions are transferred into the film at this interface. It was proposed that the oxide–solution interface does not recede by a dissolution reaction, but through migration of oxygen (as OH− ions in their model) toward the pore walls, coupled with dissolution of Al+3 ions. New oxide was thought to be produced through a separate reaction of water to form O−2 ions. While later papers have cited their work as a precedent for field-assisted dissolution, in fact their mechanism is quite different, instead closely resembling concepts found in recent models by Hebert and coworkers [44, 63, 65, 87]. A variety of mechanisms have been proposed for pore initiation on Al, and the subsequent self-ordering of the pore array. Several investigators viewed pore initiation as localized oxide dissolution at preexisting flaws, rather than as a morphological instability. Thompson and Wood suggested that pores initially develop through current concentration at topographic or compositional inhomogeneities in the native oxide [30]. Similarly, Metzger indicated that pores may initiate by acid-catalyzed field-assisted dissolution at preexisting thin sites in the air-formed oxide [88]. It is well-known that nanoscale concave features formed by imprinting the Al metal can act to initiate individual pores [89]. It was recently shown that pore initiation can be reliably directed to nanoscale sites with locally reduced oxide thickness [52, 90]. Patermarakis considered that pore initiation sites are created during the anodizing process, as a result of large density variations across the oxide [91]. He proposed that low density oxide initially formed at the metal interface later recrystallizes to a higher density phase near the solution interface, with pores initiating at cracks produced by tensile stress in the oxide surrounding the nanocrystals. Self-ordering of pores on Al has been attributed to lateral

4.3

Mechanisms for Porous Anodic Oxide Formation

electrical migration [92], or lateral migration coupled with oxide dissolution [93]. Gösele and coworkers considered that self-ordering is produced by elastic repulsion between oxide cells, as a result of compressive forces produced by the volume increase upon oxide formation [2, 34, 53]. Oh and Thompson suggested that the excess oxide volume produced by the oxidation reaction is transported away from the metal by plastic flow, and that ordering results from the balance of oxide formation and flow rates [72, 73]. Other pore initiation and ordering mechanisms have emerged from research on anodizing of titanium. According to Taveira et al., pores form during competitive oxide growth and dissolution in the initial period of anodizing [31]. They suggested that initiation of pores occurs by localized random attack of the oxide surface by fluoride ions, and that pores are later stabilized by localized acidification as pH gradients that develop along their length. In a subsequent paper, Yasuda et al. described how this process might lead to self-ordering [94]. They argued that pore length dependent acidification would lead to progressive narrowing of the pore length distribution during the early stages of anodizing, and that neighboring pores would establish a separation distance of approximately twice the barrier thickness, to ensure sufficient area for metal oxidation to sustain their growth. This separation-to-barrier thickness ratio was considered to explain the observed scaling ratio of pore separation to anodizing voltage. Devine and coworkers proposed that the region near the oxide–solution interface contains space charge layers and attendant composition variations [95, 96]. They reasoned that by analogy to unstable interfaces during alloy solidification [27], instability would result when the driving force for oxide dissolution increases as a result of localized dissolution through this space charge layer. If porous anodic oxidation is an example of a pattern selection process, modeling approaches traditionally applied to pattern selection can help elucidate its mechanism. Indeed, starting with the seminal work of Parkhutik and Shershulsky [97], a number of mathematical models of PAO growth have been reported. Since these models attempt to calculate interface motion during anodizing, they can provide a basis for rationalizing experimental conditions associated with pore formation and self-ordering. Models may be able to explain some of the key phenomenological observations discussed in Section 4.2, including, for example, scaling relations between anodizing voltage and porous layer geometric parameters; critical ranges of parameters associated with self-ordering, such as efficiency, porosity, and volume expansion factor; and how the acid type influences length scales in porous alumina films. If modeling of self-ordering during mild anodizing of pure metals proves successful, future work can build upon this understanding to analyze more complex porous layers and anodizing processes, such as high-throughput hard anodizing. Therefore, modeling can ultimately be of practical value in supplementing empirical approaches for the development of commercially viable porous oxide devices derived from PAOs. The rest of this chapter describes progress made so far in mathematical modeling of PAO formation. The discussion focuses primarily on continuum modeling approaches used in nearly all the theoretical work to date on this phenomenon.

119

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

These models are highly useful in studies of pattern selection because they can directly reveal stabilizing and destabilizing processes contributing to selfordering. Non-continuum techniques such as first-principle calculations and kinetic Monte Carlo and molecular dynamics simulations have only recently been applied to anodizing [98–100].

4.4 Elements of Porous Anodic Oxide Models

The key components of mathematical models of PAO formation are interface evolution equations, which describe the changing oxide shape during the transition from the barrier to the porous morphology. These equations predict the velocities of the oxide–solution and metal–oxide interfaces on the basis of the spatial distributions of electric potential, stress, and/or composition in the oxide. Porous oxide models also include field or conservation equations and associated boundary conditions, to permit calculation of these distributions. The boundary conditions are based on considerations of interfacial reaction kinetics. When the contribution of bulk oxide motion to interface motion is considered, the oxide velocity distribution must also be determined, using, for example, a plastic flow model. This section discusses in turn these major elements of anodizing models: field equations, interfacial reactions, boundary conditions, bulk oxide motion, and interface evolution equations. 4.4.1 Ionic Migration Fluxes and Field Equations

Differential equations governing the electric potential distribution in the oxide derive from the conservation of ionic current density. Thus, the form of this potential field equation depends on the ionic conduction rate law relating the current density to the electric field. During growth of planar barrier oxides, precise measurements of the anodic oxide layer thickness show that current density depends exponentially on the electric field, according to the high field rate law [101, 102], i = ia0 exp(BE)

(4.1)

Here, the pre-exponential current density ia0 and the field coefficient B are empirical parameters. High-field conduction is usually interpreted in terms of unidirectional hopping of ions over energy barriers between “lattice” sites in the oxide [74]. In this view, the field coefficient is related to the distance a between sites, B = 𝜒a𝛼i F∕RT, where 𝜒 is a transfer coefficient expressing the symmetry of the activation barrier and 𝛼i is the ionic charge. During the transition to the porous oxide morphology, the electric field direction is arbitrary, and so Eq. (4.1) must be expressed in vector form [63, 103]: 𝐢 = −2ia0

𝐄 sinh(B|𝐄|) |𝐄|

(4.2)

4.4

Elements of Porous Anodic Oxide Models

where 𝐢 and 𝐄 are the current density and electric field vectors. The hyberbolic sine function in Eq. (4.2) is convenient for modeling porous oxides, since the current density appropriately vanishes in the pore walls, where the electric field is very small. The potential field equation derived from charge conservation requires that the divergence of the current density is zero: ∇⋅𝐢=0

(4.3)

Because the pre-exponential current density ia0 is several orders of magnitude smaller than the anodizing current density [104], high-field conduction according to Eq. (4.2) introduces severe nonlinearity into anodizing models. Many models have avoided the resulting numerical difficulties by using the low-field approximation of Eq. (4.1), for which the conduction equation becomes equivalent to Ohm’s law 𝐢 = 𝜅𝐄, where 𝜅 is the oxide conductivity. Conservation of charge in the oxide then implies that Laplace’s equation for the electric potential 𝜙, that is, ∇2 𝜙 = 0, governs the electric potential distribution [97, 105–110]. While experiments clearly support high-field conduction in anodic oxides, it is interesting that these models nevertheless can predict some key aspects of porous layer formation (see Section 4.5). Possible errors produced by the assumption of ohmic conduction were discussed in more detail by Houser and Hebert [63]. In addition, Section 4.5.3 describes the possible direct role that nonlinear conduction may play in the morphological instability [44]. Anodizing models have employed differing approaches to calculate stress distributions. Singh et al. determined the stress distribution using the equations of linear elasticity [106, 107]. They approximated the oxide as a crystalline material and calculated misfit strain at the metal–film interface due to different lattice parameters of the metal and the oxide, and then the resulting elastic stress throughout the oxide. This calculation approximated the stress in the oxide resulting from the volume expansion associated with the oxidation reaction. Singh et al. did not include the effect of stress on transport processes, but instead considered that stress modified the activation energies of interfacial reactions. Alternatively, Hebert and coworkers modeled the stress distribution by approximating the oxide as an incompressible material [44, 65, 87]. Indeed, very small elastic strains should be present during anodizing, since elastic moduli of anodic oxides are on the order of 100 GPa, at least 2 orders of magnitude larger than the measured stresses [28, 54]. The incompressibility approximation results in volume conservation constraints on ionic transport processes and reactions [111, 112]. For example, if electrical migration or interfacial reactions would result in a net depletion of volume from a small portion of the oxide, stress gradients then arise to modify transport rates to enforce conservation of volume. Models that explicitly calculate stress generated by reactions and transport processes include individual flux expressions for metal and oxygen ions. The effect of stress on transport is taken into account by considering the stress gradient as a driving force for ionic transport [111, 112]. Hebert and coworkers generalized the driving force for transport as the chemical potential of the ion i, ∇𝜇i , which

121

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

may include contributions from electric potential, stress, and concentration gradients [44, 87]. Thus, ∇𝜇i was given by ∇𝜇i = −𝛼i F∇𝜙 − Ωi ∇𝜎, where Ωi is the ion’s molar volume and 𝜎 is the hydrostatic stress. In terms of the chemical potential gradient, the ionic flux vector 𝐉𝐢 is ( ) 𝜒a ||∇𝜇i || ∇𝜇i sinh (4.4) 𝐉𝐢 = −Ci ui |∇𝜇i | RT where Ci is the ion concentration and ui the ionic mobility [65]. To specify the concentrations and ionic volumes, these models viewed the anodic film as pure oxide consisting of an amorphous packing of oxygen ions, with metal ions occupying interstitial sites [44, 63, 65, 87]. The metal ions were approximated as point charges in a space-filling oxygen packing, a realistic assumption for alumina but perhaps not for oxides such as ZrO2 , in which the size of Zr+4 approaches that of O−2 . The chemical potential gradient of metal ions is determined only by the electric field, ∇𝜇M = −𝛼M F𝐄 where 𝛼M is the metal ion charge. On the other hand, since oxygen ions have nonzero volume, the oxygen chemical potential gradient is ∇𝜇O = 2F𝐄 − ΩO ∇𝜎. In addition to the charge balance (Eq. (4.3)), these models included the volume balance as a field equation: ∇ ⋅ 𝐉𝐎 = 0

(4.5)

Equivalently, the field equations can be taken as species balances for metal and oxygen ions. In their model, Stanton and Golovin also included a species balance on oxygen ions, but did not consider stress as a driving force for transport. Instead, the oxygen ion flux was determined by the electric field and the oxygen concentration gradient in the oxide according to the low-field Nernst–Planck equation [108]. They did not specify the interpretation of the nonuniform oxygen ion concentration in their model, which could imply that the oxide is either a compressible material or contains large concentrations of oxygen vacancy defects. Using the latter interpretation, this model could be useful to depict transport effects associated with the intrinsically low and possibly spatially variable densities of anodic oxide [79–81, 91]. 4.4.2 Bulk Motion of Oxide

As discussed in Section 4.2, observations of volume expansion and tracer motion in anodic oxides clearly indicate that bulk oxide motion accompanies anodizing. Such motion has been interpreted differently as either plastic flow, or rigid body motion due to elastic forces [53, 64, 73]. In mathematical models, oxide motion has been treated as viscous flow [65, 87, 113]. Houser and Hebert tested the interpretation of bulk oxide motion as plastic flow, in a simulation of steady-state growth of porous anodic alumina [65]. Their model included electrical migration of metal and oxygen ions; oxygen migration and Newtonian viscous flow were

4.4

(a)

35

Elements of Porous Anodic Oxide Models

20

(b)

30

10

25

0

20

−10

15

−20

10 25 nm

5

−30 25 nm

−40

0 Figure 4.9 Simulation of Houser and Hebert of steady state aluminum anodizing in oxalic acid at 36 V [65]. (a) Current lines and potential distribution (color scale). (b) Velocity vectors and dimensionless hydrostatic stress (color scale with tensile stress as positive).

coupled through the oxide volume balance. Rather than specifying stressgenerating mechanisms at the film interfaces, they deduced boundary conditions for the velocity from experimentally observed steady-state interface motion, and were able to numerically predict the velocity field in the oxide. Tungsten tracer profiles were simulated based on the calculated velocity distribution, and found to be in agreement with experiment [41, 64, 66–68], thus providing evidence in favor of the Newtonian flow model (Figure 4.8). The calculations also showed that the observed tracer motion is consistent with flow generated by compressive stress at the oxide–solution interface near the bottom of the pore (Figure 4.9). While the stress-producing mechanism is not yet clear, the observed flow pattern was not likely caused by stress associated with metal oxidation [2, 34, 53]. The possible effect of oxidation-induced stress on formation of barrier anodic aluminum oxide was considered in a separate paper by Hebert and Houser [87]. They incorporated stress effects on high-field ion migration fluxes, and included both elastic and viscous strain in the oxide according to a Maxwell viscoelastic model. Their calculations revealed increasingly tensile stress at higher anodizing current density, consistent with some but not all experiments [114]. The morphological instability study by Barkey and McHugh incorporated bulk oxide motion as an essential feature of the instability mechanism driving pattern formation [113]. This model treated oxide motion as Newtonian viscous flow generated by electrostriction stress at the oxide–solution interface. 4.4.3 Interfacial Reactions

Since interfacial reactions control oxide morphological evolution, their specification in anodizing models is centrally important (Figure 4.10). In all models, the

123

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4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

Metal

Oxide

Solution

MOαM/2 (ox) → αM H+ (s) ↔ M+αM (s) +

M → M+αM (ox) + αMe−

αM H2O 2

M+αM (ox) → M+αM (s)

H2O ↔ O−2 (ox) → 2H+ (s) O−2 (ox) M+αM (ox) Figure 4.10 Schematic of interfacial reactions and ion migration process during anodizing.

reaction at the metal–oxide interface has been taken as the oxidation of metal atoms, M → M+𝛼M (ox) + 𝛼M e−

(4.6)

and (ox) denote the oxide phase. At the oxide–solution interface, oxygen ions are produced by reaction of water, H2 O(s) ↔ O−2 (ox) + 2H+ (s)

(4.7)

and metal ions dissolve into solution. Some models include direct metal ion dissolution: M+𝛼M (ox) → M+𝛼M (s)

(4.8)

where (s) represents liquid solution. Alternatively, metal ions have been considered to dissolve as part of stoichiometric oxide dissolution, that is, the field-assisted dissolution reaction discussed in Section 4.3: 𝛼 (4.9) MO𝛼M ∕2 (ox) + 𝛼M H+ (s) ↔ M+𝛼M (s) + M H2 O(s) 2 Since Eqs. (4.6)–(4.8) are charge transfer reactions, their rates increase with the current density. While Eq. (4.9) does not involve charge transfer, its rate is also considered to increase with the electric field, due to electrical polarization effects [33, 73]. It should be noted that anodizing experiments using labeled oxygen atoms call into question the relevance of Eq. (4.9) to anodizing [24, 83, 84]. In these studies, no dissolution of oxygen was detected after sequentially anodizing in 18 O and 16 O isotope-containing solutions. These radioisotope results are instead consistent with the consumption of oxide lattice by migration of oxygen ions into the film accompanied by dissolution of metal ions [86]. While point defect models have been widely applied to describe native (passive) oxide layers on metals and alloys [57, 58], they have not yet been applied to model

4.4

Elements of Porous Anodic Oxide Models

PAOs. In such models, reactions equivalent to Eqs. (4.6)–(4.8) would be written in terms of vacancy or interstitial defects that constitute the mobile ionic species in the film [115]. Since defect formation or removal processes by themselves do not contribute to interface motion, separate reactions, such as Eq. (4.9), would be necessary to describe destruction of the oxide “lattice” at the oxide–solution interface. Alternatively, lattice destruction may be viewed as stoichiometric annihilation of metal and oxygen vacancies, that is, the Schottky reaction [115]. Coupling this reaction with Eqs. (4.7) and (4.8) produces the destruction process 𝛼 MO𝛼M ∕2 (ox) → M+𝛼M (s) + M O−2 (ox) (4.10) 2 implying metal ion dissolution accompanied by oxygen ion migration into the film. 4.4.4 Boundary Conditions

The rates of interface ion transfer reactions in Eqs. (4.6)–(4.8) are determined by the potential differences across the metal–oxide and oxide–solution interfaces [116–119]. The interfacial potential drops can be expressed as overpotentials that contribute to the overall cell potential. Neglecting the cell ohmic drop, the metal potential vs. a hydrogen reference electrode (in equilibrium with the cell solution) is 0 V = EM,MO + 𝜂mo + Δ𝜙 + 𝜂os

(4.11)

is the standard Nernst potential of the oxidation reaction; Δ𝜙 is the Here, potential drop through the oxide; and 𝜂mo and 𝜂os are the overpotentials of Eqs. (4.6) and (4.7). The latter are defined as 𝜂mo = (𝜇M − 𝜇M+𝛼M − 𝛼M 𝜇e− )∕𝛼M F and 𝜂os = (𝜇H2 O − 𝜇O−2 − 2𝜇H+ )∕2F. The oxide potential drop is typically tens of volts, by far the largest term in Eq. (4.11). By comparison, the overpotential terms are on the order of 0.1 V for a number of metals [116–119]. On the basis of the relatively small magnitude of interfacial potential drops, most anodizing models have neglected them entirely and instead applied constant potential boundary conditions at the interfaces. These isopotential boundary conditions imply that ion migration rates in the oxide, and hence the anodizing current density, are not affected by the kinetics of interfacial reactions. Even when the potential drop across the oxide–solution interface is neglected, knowledge of the relative contributions of Eqs. (4.7) and (4.8) to the interface current density is needed to model interface evolution. The relative reaction rates are expressed conveniently as the anodizing efficiency 𝜀O , defined as the fraction of the current density at the interface associated with oxygen transfer (Eq. (4.7)). Since the rates of metal dissolution and oxygen transfer reactions both depend on the oxide–solution interface overpotential, the efficiency can be expressed as a function of the interface current density. For aluminum, the kinetics of these reactions have been measured [117], and on this basis the variation of efficiency with current density has been predicted. These calculations reveal a weak logarithmic dependence, suggesting that 𝜀O may be approximated as 0 EM,MO

125

126

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

constant in many situations [63, 65]. Alternatively, the efficiency is taken directly from the large number of experimental measurements that are available [42, 44]. Several aluminum anodizing models have not assumed isopotential interfaces, instead explicitly incorporating kinetics of metal and oxygen transfer reactions [103, 106–109]. The charge transfer kinetics were represented by typical Butler–Volmer expressions, consistent with the experimental characterization of Våland and Heusler [117]. Singh et al. additionally considered the influences of elastic stress and curvature-dependent oxide surface free energy on the activation energy for the interfacial reactions [106, 107]. As discussed in Section 4.5.3, these effects produced interface stabilization mechanisms of possible relevance to pattern formation during anodizing. Models that include stress or concentration fields require additional boundary conditions. To calculate the oxygen concentration distribution, Sample and Golovin used continuity conditions relating the oxygen flux to the reaction rate at the film interfaces [103]. Hebert and coworkers derived a boundary condition from the oxygen continuity condition (or equivalently volume balance) at the metal–oxide interface: vmo In = vn + ΩO JOn

(4.12)

is the metal–oxide interface velocity, which is determined by the rate Here, vmo In of consumption of metal by the oxidation reaction Eq. (4.6) [44, 65, 87], and vn is the velocity of bulk oxide motion. In this equation and elsewhere, the subscript n indicates the component of a vector normal to the interface in question. Equation (4.12) is equivalent to a volume balance stating that the reacted volume of metal is filled by a combination of oxygen ion migration and flow. In their papers, Hebert and coworkers used different assumptions concerning the partitioning between migration and flow in Eq. (4.12). When oxygen ions are transported to the interface mainly by migration, stress gradients arise when the volume flux carried by electric migration of oxygen does not match the rate of metal volume consumption by oxidation. The proper stress boundary conditions at the oxide–solution interface have not yet been determined. As pointed out in Section 4.4.2, the inward flow implied by tungsten tracer studies suggests compressive stress generation at the oxide–solution interface. However, no model to date has incorporated a mechanism capable of stress generation near the oxide surface. 4.4.5 Interface Motion

The equation governing interface evolution explicitly describes the transition from the barrier to porous oxide morphology. All anodizing models have used Faraday’s law to calculate the motion of the metal–oxide interface based on the rate of metal oxidation: vmo In = −

ΩS i 𝛼M F n

(4.13)

4.4

Elements of Porous Anodic Oxide Models

where in is the local current density and ΩS the molar volume of metal atoms. This equation relates the rate of consumption of metal volume to the current density by Faraday’s law. The addition contribution of metal atom interface diffusion to metal interface motion was considered in a morphological stability model reported by Yang [120]. This model implemented treatments of interface diffusion found in studies of thin film deposition, in which diffusion can play a stabilizing role in pattern formation [121]. Most anodizing models express the oxide–solution interface velocity in terms of the electric field in the oxide near the interface [97, 103, 105–108, 110]. In the seminal paper of Parkhutik and Shershulsky, the interface velocity was determined by oxidation and dissolution terms having different nonlinear field dependences: 0 0 vos In = −𝛾d id exp(kd En ) + 𝛾o io exp(ko En )

(4.14)

vos In

is the velocity of the oxide–solution interface, En is the electric field where in the oxide, i0d and i0o are exchange current densities for oxide dissolution and formation, and 𝛾d and 𝛾o are Faradaic conversion factors [97]. In this expression implies interface motion toward the solution. Parkhutik and hereafter, positive vos In and Shershulsky stated that the kinetic parameters in Eq. (4.14) were obtained from the experimental kinetic study of Våland, but did not provide details of the fitting [117]. Since the field coefficient ko was chosen to be greater than kd , dissolution and oxidation dominated at low and high fields, respectively. As discussed in Section 4.5, the different field dependences of the dissolution and oxidation terms play an important role in pattern formation behavior. Other papers followed the approach of Singh et al. [106, 107] in calculating the oxide–solution interface velocity based on a Butler–Volmer electrochemical kinetic expression [103, 108, 109]. 0 0 vos In = −𝛾d id exp(𝛼𝜙) + 𝛾o io exp(−𝛼𝜙)

(4.15)

Since this expression was closely related to that used for the interface current density (Section 4.4.5), current continuity at the interface produced field-dependent competition effects, similar to those arising from the growth and dissolution terms in Eq. (4.14). Since Hebert and coworkers assumed that only oxygen ions contribute to the film volume, their equations for oxide–solution interface motion followed from the oxygen species balance. This approach avoided some of the empiricism of the field-dependent evolution, Eqs. (4.14) and (4.15). The interface velocity was vos In − vn = ΩO Rox + ΩO JOn

(4.16)

where JOn is the migration flux of O−2 ions and Rox is the rate of the oxygen transfer reaction Eq. (4.7). Equation (4.16) includes contribution to interface motion from the ion transfer reaction, oxygen ion migration, and oxide flow. JOn is negative, so that migration contributes to recession of the oxide surface toward the metal. The oxygen transfer rate can be expressed in terms of the interface current density and the anodizing efficiency, leading to the expression 𝛼M 𝜀 Ω J (4.17) vos In − vn = (1 − 𝜀O )ΩO JOn + 2 O O Mn

127

128

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

where JMn is the migration flux of metal ions. Here, it may be seen that oxygen ion migration always moves the interface toward the metal (since the efficiency is less than one), while metal ion migration moves the interface toward the solution. The separate contributions of the metal and oxygen ion fluxes are important in the self-ordering mechanism predicted by this model [44]. Interesting analogies exist between the oxide–solution interface evolution equations in the different anodizing models. When high-field migration flux expressions are used in the JOn and JMn terms in Eq. (4.17), these terms become mathematically analogous to the dissolution and growth terms in Eqs. (4.14) and (4.15). The ratio of the field coefficients in the metal and oxygen terms in Eq. (4.17) is determined by the ratio of ionic charges, that is, 1.5 in the case of Al2 O3 . Strikingly, in each implementation of Parkhutik and Shershulsky’s model to aluminum anodizing, the ratio ko ∕kd was also chosen as 1.5 [97, 105, 110, 122]. Since self-ordering is strongly influenced by the nonlinear field dependence of interface motion, these correspondences suggest that the analogous interface evolution behavior may be predicted by the different models.

4.5 Modeling Results

The model components discussed in Section 4.4 provide the necessary equations for a complete description of evolution of oxide morphology from barrier oxides to self-organized porous layers. However, since the scale of this problem is quite challenging, several modeling investigations to date have limited their focus to either the steady state of porous oxide growth or the initial stages of the morphological instability leading to pore formation. Successful modeling of the steady-state and instability can inform complete simulations, by revealing the processes contributing to porous layer formation at different stages of topography development. Here, we concentrate mainly on these steady-state and instability models (Sections 4.5.1 and 4.5.3), which have so far produced some encouraging correspondences with experimental behavior. Section 4.5.2 introduces the linear stability analysis method, which has provided useful insight into factors controlling the onset of the instability. 4.5.1 Steady-State Porous Layer Growth

Parkhutik and Shershulsky were first authors to treat porous oxide formation as a morphological instability [97]. The potential distribution in their model was governed by Laplace’s equation with isopotential boundary conditions, and interface motion was determined by Eqs. (4.13) and (4.14). The competing growth and dissolution terms in the equation for the oxide–solution interface velocity (Eq. (4.14)) produce a sharp maximum velocity in the direction of the bulk metal at a critical electric field Eeo . They proposed that Eeo determines the

4.5

Modeling Results

129

field at the pore bottom during the steady state of porous layer growth. This conjecture seems to derive from the “maximum velocity” hypothesis used in modeling dendrite growth during solidification [77]. On this basis, they solved for the conditions guaranteeing invariance of the pore bottom geometry during steady-state anodizing, namely, that the barrier layer thickness and the curvatures of both the metal–oxide and oxide solution interfaces remain constant with time. These conditions were shown to be consistent with direct scaling of the pore–pore separation with anodizing voltage: Dint 1 = V Eeo 𝜓(1 − 𝜓)

(4.18)

where 𝜓 is defined as )] 1 ( [ 2 ko ∕kd − 1 𝛾o 𝛼M F 𝜓 =1− Ωs ko 𝛾o ∕kd 𝛾d + 1

(4.19)

Dint ∕V , therefore, depends on the kinetic parameters of the oxide–solution interface reactions in their model. Other investigators presented refined versions of this calculation, which avoided the assumption of spherical interface contours in the original paper [105, 122]. Results were presented indicating that kinetic parameters for Al anodizing in various acids yielded the same Dint ∕V ratio, similar to the observed scaling of pore separation with voltage (Figure 4.11). However, further details about parameter choices would have strengthened this claim. Nonetheless, the contribution of Parkhutik and Shershulsky showed for the first time that porous anodic films could be viewed as an example of pattern selection far from equilibrium and that considerations of oxide transport processes 60

1.0

50 Cell size (nm)

0.8

Ve / Vem

0.6 0.4 0.2 0.0

30 20 10

Eeo –0.2

0 2.0

(a)

40

2.5

3.0 Ee (V nm–1)

Figure 4.11 Results of porous oxide model of Parkhutik and Shershulsky [97]. (a) Oxide solution interface velocity (Eq. (4.14)) plotted against the electric field in the oxide at the interface, showing maximum velocity at

3.5

0 (b)

50

100 U0 (V)

the field Eeo . (b) Predicted applied voltage scaling of cell radius (one-half the pore separation Dint). Different data symbols represent various acids used in the anodizing bath.

150

130

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

and interfacial reactions govern self-ordering. Subsequent work in this area built upon their results. 4.5.2 Linear Stability Analysis

Linear stability analysis can reveal regimes of experimental parameter space for which pattern formation is possible. When its predictions are tested by experiments or numerical computations, linear stability analysis can be a powerful tool to identify regimes of self-ordering and also directly reveal the underlying mechanisms. Linear stability analysis has been used in a wide range of morphological stability problems, including solidification from melts [77, 123, 124], and epitaxial film deposition [121]. In electrochemistry, it has been applied to porous silicon formation [125–127] and dendrite formation during electrodeposition [128–133]. Schwarzacher reviewed the latter work and provided a discussion on stabilizing and destabilizing influences on deposition [134]. Useful introductions to the mathematical aspects of linear stability analysis are given by Cross and Greenside [135] and Leal [136]. The application of linear stability analysis is illustrated here through the Parkhutik and Shershulsky model, which, as the first work on morphology evolution during anodizing, is simpler than subsequent models. The authors did not include linear stability analysis in their original paper. As discussed in Section 4.4.1, the electric potential distribution in the oxide is governed by Laplace’s equation, with constant potential boundary conditions at both interfaces. Motion of the metal–film interface is governed by the rate of consumption of metal (Eq. (4.13)) and that of the film–solution interface by Eq. (4.14). Linear stability models consider the transient response of the system to perturbations on a “basic state.” The basic state of anodizing is taken as an oxide layer with uniformly flat interfaces growing with applied current density ia . In the Parkhutik and Shershulsky model, the potential distribution in the basic state is one dimensional: ) ( z (4.20) 𝜙 = Eh 1 − h where the z coordinate spans the oxide thickness h, and overbars denote variables in the basic state. Perturbations to the flat interfaces generate distortions of the potential field in the oxide, which in turn cause the perturbations of the interface profiles to either decay with time (stability) or grow with time (instability) (Figure 4.12). The perturbations to the potential and interface profiles in the Parkhutik and Shershulsky model are 𝜙′ (x, y, z, t) = 𝜙 − 𝜙 and zj′ (x, y, t) = zj − zj , where primed variables represent perturbations and j = 1 or 2 for the metal–oxide and oxide–solution interfaces. Linear stability analysis considers only the initial response to the disturbance, when the perturbations to the system variables are still infinitesimally small in amplitude, and therefore a linear approximation to the model is still valid. Linearity implies that the response can be determined by Fourier analysis. Thus, the

4.5

(a)

Modeling Results

Solution Oxide O z

B

Oxide (b)

Solution

A

O

Figure 4.12 Distortion of the electric potential field lines in the oxide (dashed lines) due to a perturbation of the interface contour (thick black line) [77]. (a) Flat interface before perturbation. (b) Perturbed interface.

z

The electric field in the oxide, indicated by the closeness of spacing of the field lines, is increased at the depression at A relative to the peak at B.

response of the model to an arbitrary perturbation is determined by superimposing the responses to individual periodic Fourier modes with different spatial wavelengths. In the Parkhutik and Shershulsky model, the Fourier modes of the poten̂ t) exp(ikx x + iky y), and those of the disturbed interface tial disturbance are 𝜙(z, profiles are ̂zj (t) exp(ikx x + iky y), where kx and ky are spatial wavenumbers in the (lateral) x and y directions, and carets indicate disturbance amplitudes. Laplace’s equation produces a differential equation governing the disturbance amplitude ̂ t): 𝜙(z, ∂2 𝜙̂ − k 2 𝜙̂ = 0 (4.21) ∂z2 √ where k = kx2 + ky2 . The effect of the perturbed interface profiles on the potential is determined through the isopotential boundary conditions [125, 136]. Since 𝜙̂ = 0 is required at the perturbed surfaces z1′ and z2′ , the boundary conditions at the reference planes z = 0 is 𝜙̂ = Êz1 and that at z = h is 𝜙̂ = Êz2 . Note that the fundamental solutions to Eq. (4.21), cosh(kz) and sinh(kz), indicate that the potential disturbance penetrates within the oxide to a depth of order 1∕k; this implies ̂ scales with the wavenumber. that the magnitude of the electric field disturbance E The interface profile disturbances are calculated from the linearized interface velocity equations (Eqs. (4.13) and (4.14)), using the solution for the perturbed

131

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

̂ t). The evolving interface profiles are found to obey potential 𝜙(z, ( ) ( ) ̂z1 ̂z2 ia ΩS d̂z1 =− k − dt 𝛼M Fh tanh (kh) sinh(kh) d̂z2 = −(kO RO − kd Rd ) dt

(

Ek h

) [( sinh (kh) −

(4.22)

) ] ̂z2 cosh(kh) ̂z1 + (4.23) tanh(kh) tanh(kh)

where Ro = 𝛾o i0O exp(ko E) and Rd = 𝛾d i0d exp(kd E) in Eq. (4.14), that is, the rates of oxide growth and dissolution in the basic state. Since these quantities are constants for a given set of anodizing parameters, Eqs. (4.22) and (4.23) are linear ordinary differential equations with solutions in the form ̂zj ̃e𝜔t , where 𝜔(k) is a wavenumber-dependent eigenvalue of Eqs. (4.22) and (4.23), frequently referred to as the “growth rate factor.” The main results of linear stability analysis are embodied in the wavenumber dependence of 𝜔, the “dispersion curve.” The oxide interfaces are stable when the real part of 𝜔 is positive for all k, and otherwise unstable. The implications of a model for instability are explored through dispersion curves. Figure 4.13 displays examples of calculated dispersion curves from Eqs. (4.22) and (4.23), for selected values of Ro and Rd , along with parameters ko and kd cited by Parkhutik and Shershulsky. To specify Ro and Rd , the oxide formation rate was identified as Ro = 𝜀O (1 − tO )ia ΩO ∕2F, where tO is the oxygen ion transport number (𝜀O ia ΩO ∕2F is the overall rate of oxide growth, of which a fraction 1 − tO occurs at the oxide–solution interface). In Figure 4.13, only one of the two eigenvalues is shown, as the other one is always negative and hence does not contribute to instability. The calculations reveal a critical condition for stability determined by the sign of the factor dvos ∕dEn = ko Ro − kd Rd in Eq. In 0.06 Growth rate factor (s−1)

132

0.98

0.04 0.02

0.99 0.00

1.01

−0.02 −0.04 −0.06 0.0

1.02

0.5 1.0 1.5 Dimensionless wavenumber (kh)

Figure 4.13 Dispersion curves obtained by linear stability analysis of the model of Parkhutik and Shershulsky [97], with ratio of field coefficients kO ∕kd = 1.5. Parameters in

2.0

the plot are the ratio kO RO ∕kd Rd in Eq. (4.23). The neutral stability boundary corresponds to kO RO ∕kd Rd = 1.

4.5

Modeling Results

(4.23), the derivative of the oxide–solution interface velocity with respect to the electric field. When the interfaces are perturbed, Laplace’s equation dictates that the local electric field increases at “valleys” on the oxide–solution interface and decreases at “peaks.” If dvos ∕dEn is positive, the interface velocity will then In increase at valleys and decrease at peaks, producing stability. On the other hand, when this factor is negative instability is produced, since valleys deepen over time relative to peaks. Figure 4.13 also demonstrates that the growth rate factor increases linearly with wavenumber due to the direct scaling of the disturbance electric field with k. When linear stability analysis reveals instability, the possibility of pattern formation may be suggested if the dispersion curve contains a maximum at some wavenumber. Fourier modes near the maximum would initially grow faster than any other modes, and if this initial selection is sustained, a pattern would develop with a characteristic wavelength corresponding to the maximum of the dispersion curve. It is clear from Figure 4.13 that the predicted dispersion curves in the Parkhutik and Shershulsky model do not contain maxima for the selected parameter values, and so linear stability analysis does not indicate that patterns would form. Generally, maxima are produced by competition between a process that causes large wavelength disturbances to grow, and another process that stabilizes small wavelength disturbances. Figure 4.13 suggests that at least for the selected parameters, the Parkhutik and Shershulsky model contains a large-wavelength destabilizing factor when dvos ∕dEn is negative, but does not have the necessary In small wavelength stabilization. This lack of a “physically justified short-wave cutoff ” in this model was pointed out by Singh et al. [107]. When interpreting results of linear stability analysis, limitations of this method should be carefully considered. When the interface is unstable, the absence of maxima in dispersion curves does not necessarily preclude the formation of interface patterns. In such cases, morphology evolution is initially disordered, but patterns can sometimes emerge after the amplitude of the surface roughness increases to some critical level. Indeed, Sakaguchi and Zhao showed using numerical calculations that the Parkhutik and Shershulsky model may exhibit such dynamic restabilization [122]. Their simulations demonstrated a transition between an initially small-scale disordered interface morphology into a regular larger-scale pore pattern (Figure 4.14). Since the transition was initiated only after large-amplitude surface roughening, it is outside the scope of linear stability analysis. For similar reasons, predictions of wavelength selection by linear stability analysis should be verified by experiments or additional calculations taking account of model nonlinearities. 4.5.3 Morphology Evolution

Numerical calculations on Al anodizing have been reported embodying the contributions of oxide dissolution and electrical migration to pore formation, as suggested by the Parkhutik and Shershulsky model. The simulation approach

133

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

400 300 200

z

z

134

100 AI 0 100

200 x

300

Figure 4.14 Two-dimensional porous aluminum oxide structure simulated by Sakaguchi and Zhao [122]. The black area represents the porous oxide layer, with the Al metal below and the aqueous solution

400

above. The fine-scale disordered pore morphology at the top of the oxide was produced initially and then evolved to a largerscale ordered pattern of pores at steady state.

can avoid the small-amplitude limitation of linear stability analysis approach, permitting dynamic restabilization processes to be explored. Cheng and Ngan [110] employed the finite element method to simulate anodizing of initially flat barrier oxide layers on aluminum, using a model closely related to that of Parkhutik and Shershulsky. They found that morphology evolution depended significantly on the ratio of prefactors of the oxide dissolution and growth terms in the equation governing the solution interface velocity, that is, 𝛾d i0d ∕𝛾o i0o in Eq. (4.15) (Figure 4.15). Barrier oxide growth without pore formation was found at large values of this ratio, while unstable pore branching occurred at low values. Intermediate ratios produced parallel pores and a scalloped metal–oxide interface, resembling the classical morphology of porous alumina films. The simulations of Cheng and Ngan further demonstrated a tendency toward self-ordering, as the uniformity of the pore spacing increased over time during anodizing. As mentioned in Section 4.5.2, Sakaguchi and Zhao developed a coupled lattice map model for formation of porous alumina films, using a version of the Parkhutik and Shershulsky model including surface tension [122]. The transition between the disordered fine-scale pore structure and the regular steady-state pore array occurred by competition between the initial small pores, leading to enlargement and stable growth of some pores, while the growth of others ceased. This process qualitatively resembles the initiation of stable pores during anodizing, as discussed in Section 4.2. Aarão Reis et al. carried out a kinetic Monte Carlo simulation of pore formation by electric field assisted dissolution [99]. Metal atom oxidation was accompanied by dissolution of oxide “molecules” from the solution interface, according to a stochastic rate equation favoring removal from local minima close to the metal oxidation site. The first application of linear stability analysis to morphological evolution during anodizing was reported by Thamida and Chang [105]. They analyzed an

4.5

nm nm

(a)

0

0

35

−50

50

−100

0

30

−150

−50

25

−200

(b) −100 50

nm

40

50

50

−250

0

−300

−50

−350

−100

−400

−150

−450

−200

−500

20 15 10 5

−550 −250 −100 −50 0 50 100 −100 −50 0 50 100 nm (c) (d) nm

0.14

Modeling Results

Barrier-type alumina

0

Porous-type alumina

Bo (Am−2)

0.12 Nonporous region 0.10 0.08

Stable porous region

0.06

Unstable porous region

0.04

Linear fit of region boundaries Bo = 0.4BAI - 0.024

0.02 (e) 0.00 0.2 0.0

Bo = 0.08BAI 0.4

0.6

0.8 BAI

1.0

1.2

1.4

1.6

(Am−2)

Figure 4.15 Results of two-dimensional porous aluminum oxide simulation by Cheng and Ngan [110]. The parameters BO and BAl in the figure correspond to the pre-exponential current densities io0 and id0 , respectively in the interface evolution equation (Eq. (4.14)). The top panels show porous oxide structures and potential distributions (color maps) for BO = 0.048 A m−2

and different values of BAl : (a) barrier oxide morphology at 0.12 A m−2 ; (b) ordered porous morphology at 0.36 A m−2 ; (c) ordered porous morphology at 0.54 A m−2 ; and (d) disordered porous morphology at 0.78 A m−2 . (e) Morphology map showing that the ratio BO ∕BAl controls the type of morphology produced.

135

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

approximation of the Parkhutik–Shershulsky model valid for long disturbance wavelengths, assuming that the wavelength of the instability is much larger than the barrier oxide thickness. Stable and unstable interfaces were predicted in different ranges of applied voltage and pH. The assumption of long-wavelength disturbances may be criticized, however, since the pore spacing and barrier oxide thickness are on the same magnitude [33, 79, 80]. Sakaguchi and Zhao carried out linear stability analysis on an approximate version of the Parkhutik and Shershulsky model, which additionally included surface tension effects [122]. They presented dispersion curves with maxima that may be attributable to short-wavelength stabilization by surface tension. The morphological stability models of Golovin and coworkers introduced effects due to oxide–solution interface kinetics, enabling the introduction of a variety of stabilization mechanisms not present in the Parkhutik and Shershulsky model [103, 106–108]. Each of their models also incorporated a destabilizing mechanism at long wavelengths, due to the competition between growth and dissolution terms in the oxide–solution interface evolution equation (Eq. (4.15)). Singh et al. showed using linear stability analysis that surface tension effects on interface kinetics caused small wavelength disturbances (with high associated curvature) to be preferentially stabilized (Figure 4.16a) [106, 107]. Weakly nonlinear analysis showed that this capillary effect produced disordered hexagonal surface patterns (Figure 4.16c). In the same papers, Singh et al. also investigated 4

−1

ω (h )

2 0

120

−2 100

−4 −6

0

0.01

0.02

0.03

0.04

0.05 80

−1

(a)

q (nm ) 60 4 40

2 −1

ω (h )

136

0 20 −2 −4 −6

(c)

(b) 0

0.02

0.04 0.06 q (nm−1)

0.08

20

40

60

80

100

120

0.1

Figure 4.16 Morphological stability analysis results of Singh et al. [107]. (a) Typical dispersion curve with broad unstable wavenumber range from model not including elastic stress. (b) Dispersion curves with relatively

narrow unstable range produced by model including elastic stress. (c) Simulated disordered topographic pattern calculated with model that did not include stress.

4.5

Modeling Results

an extension of their model including the additional effect on interface kinetics of elastic stress produced by metal oxidation. Linear stability calculations revealed that elastic stress exerted a stabilizing influence preferentially at long wavelengths (Figure 4.16b). For some parameter values, stress and surface tension produced stability at long and short wavelengths, respectively, while instability due to oxide dissolution was confined to intermediate wavelengths. Weakly nonlinear analysis showed that for these conditions, ordered hexagonal patterns evolved, similar to those seen experimentally. Thus, ordering seemed to be enhanced when instability was confined to a finite range of wavelengths. Morphological stability methods have been used to examine effects of additional transport processes on stability. Sample and Golovin found that inclusion of high-field conduction extended the range of process conditions where instability was found [103]. Stanton and Golovin examined effects of chemical diffusion of oxygen ions on stability. For some parameter ranges, oxygen diffusion produced long-wavelength stability that resulted in ordered patterns. However, the relevance of their results to anodizing might be further clarified by specifying the physical interpretation of the oxygen concentration distribution in their model (see Section 4.1). Smagina and Sheintuch developed long-wavelength approximation of a version of Singh’s model without capillary effects [109]. Yang performed linear stability analysis of a model for metal–oxide interface morphology evolution during Al anodizing, including interface diffusion of metal atoms. It was shown that interface diffusion stabilizes the interface above a critical wavenumber that depends on the interface diffusivity and the electric field [120]. Linear stability analysis has also been used to examine the effect of oxide flow on instability. Barkey and McHugh considered a model of barrier oxide growth in which the rate of oxide–solution interface motion was entirely determined by the flow velocity [113]. Flow was driven by pressure due to the combined effects of electrostriction and capillary forces. Linear stability analysis revealed instability at large wavelengths where electrostriction forces dominated, since flow tended to displace material away from areas where the oxide was relatively thin. The flow direction was reversed at small wavelengths when capillary forces dominated, leading to stabilization. Pattern wavelength selection was produced by competition of these destabilizing and stabilizing mechanisms. It should be noted that the significance of electrostriction and capillary forces has not yet been demonstrated experimentally, so it is not clear that these forces are large enough to drive the observed flow. Barkey and McHugh additionally provided a scaling analysis suggesting that the balance of field-dependent oxide generation and flow determines the pore diameter. Oh and Thompson also presented a scaling analysis in which wavelength selection was determined by the balance of oxide formation and plastic flow [73]. They predicted that pore separation should be proportional to the anodizing current density, qualitatively consistent with the observed scaling of pore separation with anodizing voltage. These papers therefore revealed mechanisms through which flow can contribute to instability. Future work might integrate these concepts in models that additionally include

137

138

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

factors such as dissolution and migration that influence interface motion (see Section 4.4.2). Other papers have used scaling analysis to consider destabilizing mechanisms associated with mechanical and electrical forces on pattern selection. Raja et al. suggested that pattern selection in anodic TiO2 is caused by balancing changes of surface energy and strain energy associated with perturbations. On this basis, they related the pattern wavelength to the surface tension and elastic stress in the oxide [20]. Van Overmeere and Proost disputed their model, since according to their measurements the oxide stress vanishes within the range of practical anodizing current densities [54]. Instead, they proposed that surface energy perturbations are balanced with electrostatic energy changes. This concept led to the scaling relationship of pore separation with the square root of the barrier oxide thickness. Quantitative agreement with the predicted pore–pore distance was demonstrated for anodic TiO2 alumina films in various electrolytes. In the morphological stability model of Hebert et al., coupling of migration fluxes through stress gradients gave rise to new stabilizing and destabilizing mechanisms [44]. This model was able to explain some significant experimental observations, including the existence of critical efficiency ranges for self-ordering (Section 4.2) and scaling of the pattern length scale with anodizing voltage (Figure 4.4). The oxide was assumed to be incompressible, and flow was not considered. Ionic migration was driven by both the electric field and stress gradients according to the high-field migration law (Eq. (4.4)). Interface motion was determined by ionic migration fluxes and interface reaction rates (Eqs. (4.13) and (4.17)). Destabilizing and stabilizing mechanisms in the model of Hebert et al. were governed by the wavenumber dependence of the perturbed electric potential and oxygen chemical potential fields. As in the example of Section 4.5.2, the penê tration depths of √ the disturbances √ 𝜙(z, t) and 𝜇̂O (z, t) decreased with wavenumber, according to BM E∕k and BO E∕k respectively. In the small k limit when the wavelength significantly exceeds the oxide thickness, there was no significant ̂ t) and 𝜇̂O (z, t) through the film thickness. In this limit, the perattenuation of 𝜙(z, turbed ion migration fluxes at the solution interface were constrained by the volume balance at the metal–oxide interface (Eq. (4.12)). This constraint produced an approximate oxide–solution interface evolution equation for small wavenumbers: d̂z2 ≅ ΩÔJO (1 − 𝜀O Φ) (4.24) dt where Φ = 𝛼M ΩO ∕2ΩS is the Pilling–Bedworth ratio, the ratio of oxide volume produced by oxidation to metal volume consumed. Similarly to the example of Section 4.5.2, stability depended on the sign of the factor in parentheses, and thus the interface was respectively stable or unstable when the efficiency is greater or smaller than 𝜀∗O = 1∕Φ. At the opposite extreme of large wavenumber, the penê t) and 𝜇̂O (z, t) were much smaller than tration depths of the field disturbances 𝜙(z, the oxide thickness, and consequently these disturbances decayed to zero within

4.5

Modeling Results

the film. The perturbed migration fluxes were not coupled by the metal–oxide interface volume balance, and the oxide–solution interface profile disturbance obeys √ √ √ d̂z2 = ΩO J O E[(1 − 𝜀O ) BO − 𝜀O (Φ − 1) BM ] (4.25) dt The interface was stable when the factor in brackets is negative, or equivalently when the efficiency exceeded the critical value 𝜀∗∗ O =

1+

√

1 𝛼M (Φ 2

(4.26) − 1)

Note that the minimum efficiencies for stability were different at small and large wavenumbers. Pattern selection in the model of Hebert et al. resulted when the metal charge 𝛼 M exceeded two, which is the case for all known self-ordered anodic oxides (TiO2 , ZrO2 , Ta2 O5 , Nb2 O5 , WO3, and HfO2 ) [44]. In this situation, the critical efficiency at high k is smaller than 𝜀∗O , the critical efficiency at low k. Thus, when the effi𝜀∗∗ O and 𝜀∗O , the anodic film would be ciency was within the “window” between 𝜀∗∗ O unstable at small wavenumbers but stable at large wavenumbers. The resulting dispersion curves had clear maxima suggesting the wavelength of an emergent self-organized pattern (Figure 4.17). A physical explanation can be given with reference to Eq. (4.17), where it was noted that metal ion migration stabilized the interface, while oxygen migration had a net destabilizing effect. When the metal charge exceeds two, the field coefficient of high-field metal ion migration was larger than that of oxygen ion migration, and hence field disturbances selectively enhance metal ion migration. This effect provided differential stabilization at high 2

Growth rate factor

0.54 1

0.57

0 0.58 0.60

−1 −2

0.62

0

2

4 6 Wavenumber (2πh/λ)

Figure 4.17 Dispersion curves calculated by the model of Hebert et al. using parameter values for Al anodizing: metal ion charge 𝛼M = 3, Pilling–Bedworth ratio Φ = 1.65, conduction jump distance a = 0.3 nm, electric field 0.8 V nm−1 . Parameters in plot are

8

10

anodizing efficiencies 𝜀O . When the efficiency lies between the critical values 𝜀∗O = 0.606 and 𝜀∗∗ = 0.557 defined in the text, the disO persion curves have maxima suggesting selfordering behavior.

139

140

4 Mathematical Modeling of Self-Organized Porous Anodic Oxide Films

wavenumbers. However, the effect was limited to a small efficiency range below 𝜀∗O , since smaller efficiencies would destabilize the interface more than the stabilization due to enhanced metal ion transport. The model of Hebert et al. yielded encouraging agreement with significant aspects of self-organizing phenomena. This model was the first to explain the existence of critical ranges of anodizing efficiency in which self-ordered porous oxides are produced. For Al, these ranges agree reasonably with those predicted by the model, but for Ti and Zr the predicted ranges are at smaller efficiencies relative to those found experimentally (the derivation of the limiting efficiencies in the original paper contained an error that led to somewhat better agreement for Ti). The predicted widths of the efficiency ranges are realistic, however. It is interesting to note that the experimental self-ordering efficiency ranges of all three metals lie just below the oxygen ion transport number tO (Figure 4.6). Since this model included an interface volume balance (Eq. (4.13)) but neglected bulk oxide motion, the transport number was related to the Pilling–Bedworth ratio, tO = 1∕Φ. This prediction, while approximately valid for Al, is inaccurate for the other two oxides. Thus, significant bulk motion may accompany anodizing of Ti and Zr, and accounting for this motion may help reconcile the predicted efficiency ranges with experiment. The model of Hebert et al. was also consistent with the scaling of the pattern length scale with voltage. In Figure 4.13, the maxima of the dispersion curves suggest a scaling ratio of Dint ∕V = 2.4 nm V−1 , close to the observed value of 2.5 nm V−1 . The discussion in this chapter has stressed the importance of the oxide–solution interface dynamics in the development of self-ordered porous oxide layers. The physical basis of the interface evolution equations differs between the various models. However, in general, each evolution equation contains two fielddependent exponential terms that respectively cause the interface to “grow” toward the solution or “dissolve” toward the metal. The different field coefficients of the growth and dissolution terms seem to result in critical conditions for interface stability. Strikingly, the Al anodizing model of Hebert et al., and each of the papers based on that of Parkhutik and Shershulsky, all used the same numerical ratio of 1.5 for the field coefficients in the growth and dissolution terms. Since the growth and dissolution terms in the Hebert model represent migration of Al+3 and O−2 ions (Eq. (4.17)), this ratio derived from the ionic charges. Additionally, in both the Hebert and Cheng models, the ratio of the prefactors of the growth and dissolution terms were found to control oxide morphology development. This ratio was controlled by the efficiency in Hebert’s model. In Cheng’s simulations, small values of this ratio produced stable barrier oxide layers, while disordered porous layers were obtained when the ratio was large. Ordered layers at intermediate values of the ratio corresponded to the critical efficiency ranges predicted by Hebert et al. Both of these models then seem to be consistent with the expectation of critical efficiency ranges associated with self-ordered porous oxide formation.

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes Chong-Yong Lee and Patrik Schmuki

5.1 Introduction

Increasingly sophisticated top-down nanofabrication infrastructure enables the design and realization of nanodevices, with ever-increasing precision and miniaturization, to meet ever more demanding specifications, particularly in microelectronics. Despite the common association of high-end technology with high costs, an increasing number of nanomaterial architectures can also be fabricated by low cost and technologically simple, yet efficient self-organized bottom-up methods. One of the commercially most important examples is electrochemical anodization of a metal substrate to achieve coating of the metal with highly ordered self-organized one-dimensional oxide nanostructures (aligned pores, channels, or nanotubes). In addition to classic applications that may range from decorative purposes to corrosion protection in the past decade, exciting new functional uses such as one-dimensional (1D) electron transport media in nanostructured electrodes or solar cells have also attracted a great deal of scientific and technological interest. Scientific efforts in 1D nanostructures, such as nanowires, nanorods, nanofibers, and nanotubes, focus on the unique properties of 1D geometries in comparison to their bulk materials, such as significant alteration of their electronic properties (quantum confinement effects), high specific surface area, and improved mechanical strength [1–4]. All these beneficial effects are well in line with commercialization perspectives that will take advantage of breakthroughs in device performance. Early in the last century, electrochemical anodization of aluminum was intensively investigated with the focus on barrier-type oxide layers, for applications such as protective and decorative films [5–7]. However, a significant landmark was the discovery of porous-type aluminum oxide layers that were first observed by Rummel [8] and Baumann [9] several decades ago. Porosification allowed loading of the alumina with organic dyes or inorganic pigments to provide decorative finishes, which was followed by sealing the films by hydrothermal treatment to block the loaded pores [10]. In view of nanomaterials, in more recent years, self-organized anodization process of aluminum in acidic electrolytes has Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

become one of the most frequently employed methods for the synthesis of highly ordered nanostructures that consist of close-packed cells in a hexagonal arrangement with nanopores at their centers. Today, anodic porous alumina is commercially available, and has served as the most prominent template material for synthesis of nanomaterials ranging from metals, metal oxides, semiconductors, and polymers with nanoscale geometries such as nanodots, nanowires, nanorods, and nanotubes [11–22]. Nevertheless, alumina is an electrically insulating material – this greatly limits its direct use in functional applications. For example, to create electronically active devices such as interdigitated electrodes, core shell structure, and so on, a metal oxide that possesses semiconductive/conductive properties is required. Therefore, the findings of Assefpour-Dezfuly et al. [23] in 1984 and Zwilling et al. [24, 25] in 1999, who demonstrated the feasibility that TiO2 nanopores or nanotubes can be grown by anodization of a Ti metal sheet in a fluoride-containing electrolyte stimulated intense research activity. These early nanotubes were far from an ideal self-organized geometry and had low aspect ratios. However, in the past 10 years remarkable progress was made toward a better control of the nanotube geometry parameters, with respect to the degree of organization, achievable aspect ratios, and properties. Nanoscale TiO2 is one of the most widely used nanoarchitectures in current materials science. Most crucial features are n-type electronic properties, a long electron life-time, and its high photocorrosion stability combined with being of low cost [26–29]. These features make its use in photoelectrochemical devices possible. Widely used in the form of sintered or compacted nanoparticle layers, first efforts were already taken in 1996 to create defined 1D structures. These approaches were based on templating TiO2 precursors in ordered alumina substrates, and led to a successful growth of TiO2 nanotube and nanowire arrays, but required precise template fabrication and critical removal steps. Moreover, the thickness of the layers was limited as thick layers tend to collapse or break into bundles upon template removal [11–13]. Therefore, direct electrochemical formation of highly ordered TiO2 nanotube layers and their modifications attracted wide attention. The structures have been evaluated for potential applications that are based on the semiconducting properties of TiO2 , such as photocatalysis [30] or dye-sensitized solar cells (DSSCs) [31], and also on the excellent biocompatibility of TiO2 in biomedical devices [32–35]. While we recently reviewed some aspects of TiO2 nanotube growth mainly from feasibility and general scientific points of view [30, 35–37], it is the goal of the present work to lay more emphasis on engineering aspects of nanotube and nanopore formation. From the discovery of a phenomenon such as self-organizing anodization to fully exploiting the properties in devices, often decades pass due to reliability, scale-up, and cost–benefit aspects of the process. Nevertheless, these “chemical engineering” aspects are of course key to the valorization of any new finding. Even more, the progress and availability of fundamental understanding meanwhile not only allows a much faster transfer from finding to application

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

but also allows predictions on engineering even more advanced structures and properties. The present chapter illustrates progress in discovery, engineering properties, and applications, focusing on the two most important self-organized electrochemical structures: porous Al2 O3 and TiO2 nanotubes. We discuss the synthesis and growth of Al2 O3 and TiO2 nanotubes/pores, including the conditions that influence the degree of self-organization, tube length, tube diameter, and crystallinity. Note that many principles and mechanisms for formation of self-organized porous Al2 O3 and TiO2 nanotubes are very similar; only the differences in the chemical and physical properties of the anodic oxides lead to different specific applications. With respect to applications, we focus on the use of alumina as a template material. For TiO2 , the main focus will be on the use in DSSCs. In both cases we discuss milestone innovations leading to significant improvements in efficiency and processing speed. This chapter should be seen as the applied side to Chapter 4 where Hebert reviews the development of mathematical models for porous oxide formation and the potential of such models to assist empirical strategies by identifying self-ordering regimes for oxides with a target on material properties.

5.2 Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores 5.2.1 General Aspects of Electrochemical Anodization and Self-Organization

Anodization is an electrochemical process that usually creates a “thick” compact or porous oxide layer on the surface of a metal substrate. It is carried out typically in an electrochemical cell as shown in Figure 5.1a containing a suitable electrolyte, with the metal of interest as a working electrode (anode), and an inert counter electrode (usually platinum or carbon) as a counter-electrode. Upon applying a sufficiently high anodic voltage to the metal M, it is oxidized to Mz+ , which either forms a metal oxide, MOz∕2 (Eq. (5.2a)), or is solvatized and then dissolved in the electrolyte (Eq. (5.2b)). As a counter-reaction, protons are reduced to produce hydrogen gas at the cathode in Eq. (5.3). M → Mz+ + z e−

(5.1)

z M + H2 O → MOz∕2 + z H+ + z e− 2

(5.2a)

Mz+ + solv → Mz+ solv

(5.2b)

zH+ + ze− →

z H 2 2

(5.3)

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

Anode

+

Cathode Electrolyte

Electrolyte TiOOH:C

M

MOz

F− O2−

Ti4+

O2−

Oxidation

(a)

M

(b)

(c)

F−-rich layer

EP PO

j II

Ti4+

Oxidation

M

I

[TiF6]2− Dissolution

III CO

j

Up

U

Porous oxide (PO) Compact oxide (CO)

(d) t Figure 5.1 Schematic drawings of (a) a typical experimental setup for anodization, (b,c) field-aided transport of mobile ions through the oxide layers in the absence and presence of fluoride ions. In (c), rapid fluoride migration leads to accumulation of the fluoride-rich layer at the metal–oxide interface. (d) Typical current–time (j–t) characteristics after a voltage step in the absence (compact oxide) and presence (porous/tubular metal oxide) of fluoride ions

in the electrolyte, with the growth morphological stages I–III. The inset shows typical linear sweep voltammograms (j–U curves) for different fluoride concentrations resulting in either electropolished metal (high fluoride concentration), compact oxide (very low fluoride concentration), or tube formation (intermediate fluoride concentration). (Reproduced with permission from Ref. [36]. Copyright 2011 Wiley-VCH Verlag GmbH & Co.)

Regarding the question of whether Eq. (5.2a) or (5.2b) dominates, factors such as oxidation rate kinetics, and thermodynamic aspects such as solubility products and oxide stability (that can be taken, for example, from Pourbaix diagrams [38]) need to be considered. In an electrolyte where the oxide is insoluble, mainly the reaction in Eq. (5.2a) dominates, that is, a high oxide formation efficiency is obtained. The oxidation process (thickening of the oxide) typically follows a high field law of the form: I = A exp(BE) = A exp(BU∕d), where I is the current and U is the voltage across the oxide layer thickness d defining the electric field E [39, 40]. A and B are experimental constants. This is illustrated in Figure 5.1b, where the transport of M+ ions outward and of O2− ions inward are controlled by the applied field, with E = ΔU∕d. As a result, with increasing film thickness the field (and thus the current, if a constant voltage is applied) drops, and finally

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

the field is decreased so much that it is not able to significantly promote ion transport, and therefore, the film thickness reaches a final value. If, however, a certain degree of solubility of the oxide is provided and equilibrium of film formation and dissolution can be established, a considerable ion and electron flux is maintained in a steady state situation. For example, solvatization of a metal ion such as Ti4+ can be realized by the formation of fluoro-complexes according to Eqs. (5.4) and (5.5). One may consider pure chemical dissolution of the oxide (Eq. (5.4)) and direct complexation of high-field transported cations at the oxide electrolyte interface (Eq. (5.5)): H+

MO2 + 6F− −−−→ [MF6 ]2− + 2H2 O

(5.4)

M4+ + 6F− → [MF6 ]2−

(5.5)

Figure 5.1d schematically illustrates the observed electrochemistry represented in i∕E and i∕t curves of three general categories. Firstly, a continuous metal oxidation and immediate solvatization (Eq. (5.2b)) is commonly described as corrosion or electropolishing (EP) of the metal. Secondly, one may obtain the formation of a stable (insoluble) compact metal oxide according to Eq. (5.2a) and Figure 5.1b. Thirdly, if there is a competition between solvatization and oxide formation, where the former reaction can be promoted by the addition of a suitable agent (such as F− in the TiO2 case, Figure 5.1c), the established equilibrium often leads to the formation of a porous oxide. If formation and dissolution are in an optimum range, highly self-organized oxide pore arrangement or nanotubes can be grown [41]. For aluminum anodization mainly an acidic pH is sufficient to establish solvatization of Al3+ species. For a number of elements, fluoride complexation (that also works for aluminum at neutral pH [42]) has been found as an extremely valuable solvatization agent [36, 43, 44]. Before we turn into more details of self-organization of porous Al2 O3 and TiO2 nanotubes, it is noteworthy that also under certain conditions, for the TiO2 case, an ill-defined and disordered bundle of nanotubes (commonly called as rapid breakdown anodization [45, 46]) or mesoporous structures (also called non-thickness limited anodization [47–49]) can be formed. 5.2.2 Some Critical Factors/Aspects in the Self-Organization Phenomenology

Figure 5.2 shows typical porous oxide structures on aluminum and Figure 5.3 typical self-organized nanotube oxide structures on titanium. Often it is argued that Al2 O3 and TiO2 have distinct physical properties; the former is an insulator while the latter is a semiconductor (see Table 5.1) and thus they should behave differently in anodization. Nevertheless, this argument is weakened by the fact that anodic TiO2 and Al2 O3 grow as amorphous material – which is very far from the properties of their respective crystalline forms. For aluminum, it has been known for decades that ordered porous oxide layers can be grown by anodization

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(a)

(b)

Pore

250 nm

200 nm

(c)

50 nm

(d)

Anions

500 nm 200 nm (e)

(g)

(f)

HA-AAO

Interface

HA-AAO

500 nm

100 nm

Figure 5.2 (a) A typical top view SEM image of a highly ordered nanoporous alumina. The nanoporous layer (so-called an integrated alumina nanotube array) was anodized in sulfuric acid (b) before and (c) after chemical etching in 5 vol% H3 PO4 solution. The inset in (b) shows TEM images of porous alumina array obtained by imprint lithography followed by anodization, and inset in (c) is a tilted fracture cross-sectional image. (Reproduced with permission from Refs [50, 51]. Copyright 2005 Wiley-VCH Verlag GmbH & Co.) (d) SEM cross-sectional image of porous alumina and a schematic

500 nm

diagram (right side) of the distribution of the incorporated anions. (Reproduced with permission from Ref. [50]. Copyright 2003 American Institute of Physics.) (e) Crosssectional SEM micrograph of pulse anodized AAO (jMA) 3.16 mA cm−2 and 𝜏MA 10 s for MA-pulses, (jHA) 200 mA cm−2 and (𝜏HA) 2 s for HA-pulses; (f ) TEM micrograph of a single alumina nanotube, showing a modulated pore structure; and (g) SEM bottom view of HA-AAO, manifesting crack propagation along cell boundaries. (Reproduced with permission from Ref. [52]. Copyright 2008 American Chemical Society.)

typically in aqueous acidic electrolytes (e.g., in sulfuric acid, oxalic acid, phosphoric acid, malonic acid), while anodization in neutral electrolytes typically leads to a compact oxide layer. TiO2 nanotubes occur also in a hexagonal arrangement, essentially with the only difference from porous Al2 O3 being that the cell walls are etched, and this etching results in a tubular appearance as is discussed later.

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

H2O

(a)

(b)

Disordered layer Outer shell

Inner shell

300 nm

Fluoride rich layer (d)

nm 48

25

nm

(c)

250 nm

100 nm

(f)

(e)

500 nm

Figure 5.3 (a) A typical top view SEM image of the TiO2 nanotubes, inset shows the schematic cross section; the diagram illustrates the etching of fluoride layer by water that leads to the nanotubular structure. (b) Schematics of the TiO2 nanotube layer geometry: with fluoride-rich layer, inner shell of the tube containing the electrolyte components and outer shell of the tube. (Reproduced with permission from Ref. [53]. Copyright 2010 Wiley-VCH Verlag

400 nm

GmbH & Co.) TEM images showing (c) the cross-sectional inner tube and (d) the fluoride layer at the bottom of the nanotubes. (Reproduced with permission from Ref. [14]. Copyright 2008 Wiley-VCH Verlag GmbH & Co.) SEM of (e) the bamboo-type tubes grown under alternating voltage conditions, and (f ) their typical bottom view. (Reproduced with permission from Ref. [54]. Copyright 2008 Wiley-VCH Verlag GmbH & Co.)

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Table 5.1 Physical and electronic properties of aluminum oxide and titanium oxide. Materials

Conduction type

Aluminum oxide Titanium oxide

Insulator n-type

Band gap (eV)

7–9.5 3.2–3.8

Initially investigated on metals such as aluminum and titanium, the method to form nanoporous layers has been extended to many other metals. Originally, the approach was thought to be limited to the so-called valve metals such as niobium [55], tantalum [56–60], tungsten [45, 61, 62], vanadium [43], and zirconium [63, 64], but it has been extended to other non-valve metals such as iron [65–68] and cobalt [44], to form nanoporous/tubular metal oxide layers of high aspect ratio. As each metal and its oxide have its specific intrinsic properties, the optimized conditions to achieve self-organization during anodization vary. Please note that the electrochemistry of non-valve metals for the formation of porous oxide can be significantly different from valve metals, mainly because of their lower dielectric breakdown voltage in aqueous environments. For example, different potentials, temperatures, and water contents in the electrolyte are required to establish self-organization for different metals. Nevertheless, virtually all self-organization processes fall into the sequence of Figure 5.1d. In stage I, a compact oxide layer is formed. In stage II, dissolution reactions become noticeable and irregular pores are formed that penetrate the initial compact oxide. This increase in the reactive area causes the raise in the anodic current. In stage III, the current drops again as a regular nanopore or nanotube layer forms. 5.2.2.1 Duplex or Double Wall Structure of Al2 O3 and TiO2

Porous alumina films with parallel nanopores as in Figure 5.2a have a honeycomblike structure with a short-distance ordering (in several tens to hundreds of nanometers) [69]. However, it was not until the work by Masuda and Fukuda [70] that long range very high degree of order for these porous geometries was demonstrated. The anodic alumina structure is typically of a duplex oxide or a double wall layer [10, 71]. This duplex structure emerges from the fact that the inner region of anodized alumina is an oxide layer rich in incorporated anion species from the electrolyte, while the outer part consists of a dense pure alumina. This is illustrated in an example in Figure 5.2b for porous alumina formed in phosphoric acid [50]. While the inner oxide layer consists of pure aluminum oxide, the outer oxide layer consists of incorporated anion species from the electrolyte (see also the schematic illustration in Figure 5.2d). The content of the anion species, and their distribution, depend on anodizing conditions such as electrolyte, potential, and temperature. Incorporation of anions occurs either by adsorption on the growing oxide/electrolyte interface (and overgrowth) or by the field-aided inward migration (competing with O2− ) in Figure 5.1b. The incorporation of anions is reported to alter the properties of the porous alumina

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

films, for example, the modification of their electronic [72], and mechanical properties including flexibility, hardness, and abrasion resistance [10]. Similarly, in the case of typical TiO2 nanotubes as shown in Figure 5.3a, and the schematic representation of Figure 5.3b, a multiwall structure is often obtained [14, 73, 74]. For example, Figure 5.3c shows a high resolution Transmission Electron Miscroscopy (TEM) image of tubes grown in an ethylene glycol (EG) based electrolyte where a very carbon-rich layer at the inner part of the nanotubes is found. This inner layer consists of Ti-oxyhydroxide and carbon species from the EG electrolyte; these are mainly incorporated by EG decomposition, adsorption, and overgrowth; the Ti oxyhydroxide species stems from precipitated Ti-ions ejected from the oxide, but not solvatized as TiF2− . This inner layer is usually more 6 prone to chemical etching by electrolyte fluorides; therefore, often a V-shaped inner tube morphology is obtained (as illustrated in Figure 5.3b), that is, the tops of the tubes usually have significantly thinner walls than their bottoms. A specific feature of fluoride electrolytes is that F− may migrate even faster through an oxide layer than O2− ; thus a fluoride-rich layer is formed at the metal/oxide interface (schematically shown in Figure 5.3b). Except for classical analytical techniques, this fluoride-rich layer can be observed as a haze at the bottom of the tubes such as shown in Figure 5.3d. The type of solvent used to grow nanotubes has a profound impact on the intrinsic chemical composition. This is proposed to be due to the voltage-induced Schottky breakdown mechanism for high-voltage anodization, which leads to a decomposition of the organic electrolyte [75]. In aqueous electrolytes, the inner tube layer is typically more hydroxide-rich than the outer layer, as is the case present in the anodized aluminum in acidic aqueous electrolytes. In some solvents such as organic EG, a significant amount of carbon is incorporated in the inner tube shell. In other organic solvents such as dimethyl sulfoxide (DMSO) or EG/DMSO mixtures, a single tube wall can be achieved, with significantly less carbon species incorporated in the outer anodization layer during the tube-forming process [73, 74, 76]. 5.2.2.2 Tubes versus Pores

In general, the as-anodized alumina formed in acidic solution (or fluoride containing neutral solution [42]) typically shows a nanoporous rather than a nanotubular morphology, while for TiO2 virtually under all self-organizing conditions a tubular shape is formed. It is important to realize that the only significant difference in morphologies is whether the cell boundaries of a porous structure can be etched by the applied electrochemical conditions. As H2 O easily dissolves the fluoriderich layers between TiO2 “cells,” the tubular shape is observed under a wide range of conditions (see inset in Figure 5.3a) [36, 77]. In the case of porous alumina, formed even in fluoride electrolytes, a porous morphology is obtained, as Al fluorides are not easily soluble in H2 O [42]. In this context it is, however, noteworthy that Chu et al. [51] reported, as shown in Figure 5.2c, that cell boundaries in porous alumina can be etched to form a tubular layer. There are only a few examples that produced alumina nanotubes by

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a direct anodization method (Figure 5.2e–g) [52, 78, 79]. One of such approaches was reported by Lee et al. that is based on a pulse anodization process of aluminum [52, 78]. At specific pulse parameters, a continuous tailoring of the pore structure of the resulting nanoporous anodic alumina (i.e., periodic modulation of pore diameters along the pore axis) is achieved as shown for TiO2 in Figure 5.3e–f [80], and this also leads to the weakening of the junction strength between the cells, thereby producing nanotubular structures. In contrast, anodization of titanium as mentioned leads to growth of nanotube layers under most anodization conditions in fluoride-containing electrolytes, either potentiostatically or galvanostatically. Only if the water content is drastically reduced, porous layers are formed [81]. As illustrated in Figure 5.3b, the tubes consist of a V-shape morphology. This means that the bottom of the tubes have an ordered nanoporous appearance, while toward the top, the hexagonal structure is converted continuously into a tubular shape by etching. The inset in Figure 5.3a illustrates dissolution of fluorides at cell boundaries during the growth of the oxide – that is, selective chemical dissolution (in aqueous electrolyte) of the fluoride-rich layer etches out the cell boundaries and thus leads to individual tube shapes. The fact that anodization voltage also affects the pore to tube transition can be ascribed to a field effect on the fluoride ion mobility (faster or slower accumulation) and stress (by electrostriction), which in turn affects viscous oxide effects (and the fluoride layer) [53]. 5.2.2.3 Geometry Control

In this section, we discuss the key parameters that determine the control over the geometry of the pores of Al2 O3 and TiO2 . To date, the fabrication of self-ordered Al2 O3 pore arrays is investigated under two main categories. The first category is conventional “mild anodization” (MA) conditions that suits laboratory-based nanotechnology applications. The MA approach, introduced by Masuda and Fukuda [70], leads to rather slow oxide growth rates (for example, 2–6 μm h−1 ); it therefore has not found use in industrial processes. In this category, it is known that in several electrolytes self-organized growth of ordered nanopores occurs only in a narrow process window, known as “self-ordering regimes.” As shown in Figure 5.4a, for example, (i) in the sulfuric acid electrolyte, anodization at 25 V results in an interpore distance (Dint ) = 63 nm [82, 83], (ii) in oxalic acid at 40 V for Dint = 100 nm [70, 82, 83], and (iii) phosphoric acid at 195 V for Dint = 500 nm [84]. It has been found that anodization potential is a key parameter that controls the interpore distance (Dint ) and the barrier layer thickness (tb ) [51, 86, 87]. As can be seen in Figure 5.4b, the Dint linearly depends on the applied potential, and this is also the case for tb (not shown). The potential dependence of pore diameter (Dp ) is more complex, as it results from the interplay between the current density and the temperature, concentration, and nature of the electrolyte used (solubility of the oxide) [88, 89]. The thickness of the nanopores can be controlled over a wide range by varying the anodization time (see Figure 5.4c). For practical applications, simple and fast fabrication of highly ordered Anodic Alumina Oxide (AAO) with a wide range of pore sizes and Dint would be highly

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

600 DP

500

DInt

MA 2T

Phosphoric acid 160 −195 V, 405−500 nm

Dint (nm)

400 tbarrier

HA

300 Oxalic acid 120−150 V, 220−300 nm

200

Sulfuric acid: 40−70 V, 90−140 nm Oxalic acid: 40 V, 100 nm Sulfuric acid: 19−25 V, 50−60 nm

100 0

50

0

(a)

150 100 Anodization voltage (V)

200

250 4.0

350 Dint

250

3.5 P

200

P (%)

Dint (nm); DP (nm)

300

150 3.0 100 Dp

50 0

(b)

130 Voltage (V)

120

140

150

2.5

140 V

Thickness (μm)

160

HA

120

110 μm

80

MA

40

3.8 μm 40 V

0 0

(c)

1

2 3 Anodization time (h)

Figure 5.4 (a) Summary of self-ordering voltages and corresponding interpore distance (Dint ) in conventional MA in sulfuric (filled and open black squares), oxalic (filled red circle), and phosphoric acid (filled green triangle). The Dint versus anodization voltage observed in oxalic HA is plotted (red open circles) with the corresponding regression line (black solid line). The inset shows the schematic cross section of the porous

4

5

alumina structure with the barrier layer; Dint , Dp = pore diameter, T = thickness of the pore wall, tbarrier = thickness of the barrier layer. (b) The Dint , Dp , and porosity (P) as a function of the HA voltage. (c) Film thickness as a function of time during HA at 140 V (blue line) and an MA process at 40 V (red line). (Reproduced with permission from Ref. [85]. Copyright 2006 Macmillan Publishers Ltd.)

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desirable. To address this challenge, attention has been renewed on the “hard anodization” (HA) process, which was invented in the early 1960s [90–92]. The HA process is characterized by the use of sulfuric acid at relatively low temperatures and high current densities. Under these conditions, a high-speed oxide growth (50–100 μm h−1 ) is achievable, and this method has been widely used for various industrial applications, such as surface finishing of aluminum cookware, automobile engineering, and textile machinery [93–95]. However, due to difficulties in controlling important structural parameters, such as pore size, interpore distance, and the aspect ratio of the nanopores of the resulting alumina membranes, the HA process is not a preferred method to develop highly defined nanostructured materials. An elegant work by Lee et al. demonstrated extension of the self-ordering regimes with the implementation of HA of aluminum under specific conditions [85]. The key strategies are the introduction of a thin protective oxide layer on aluminum prior to performing the HA process, and a careful control of the reaction temperature (heat) during HA. This suppresses burning events and enables growth of self-ordered AAOs using oxalic acid at anodization potentials above 100 V, thereby establishing a new self-ordering regime with Dint of 200–300 nm (Figure 5.4a). The HA process results in a high current density that is typically 1 or 2 orders of magnitude higher than for MA, and a rate of oxide growth that is 25–35 times faster than for MA. Essentially, the method is found suitable also for other electrolyte systems [96, 97]. With this development, advanced alumina geometries were also produced, via fabrication of AAO membranes with periodically modulated diameter of nanopores along the pore axes by combining the MA and HA processes, where each alternating step required the exchange of the electrolyte solution in order to satisfy both MA and HA processing conditions [78]. The fast processing speed of the HA method with an equally high order anodic alumina is considered as an important technological development. The flexibility and achieved tuning of self-ordered nanoporous anodic alumina oxide geometries with various ranges of interpore distances, pore diameters, and thicknesses also demonstrate the versatility that can be reached with electrochemical anodization approaches. As is the case with anodizing alumina, the geometry of the TiO2 nanotubes with respect to their length, diameter, wall smoothness, level of ordering, and top morphology can be tuned and defined by the specific anodization conditions. The set of parameters and variables in anodizing titanium is, however, even larger than in the case of aluminum, especially concerning the interplay of fluoride and water concentrations with anodization voltage. Subtle changes in the anodization conditions can lead to a switch from TiO2 nanotubes to secondary morphologies such as TiO2 nanopores, TiO2 sponges, and rapid breakdown of TiO2 formation. We outline below in more detail the influence of anodization parameters on the resulting oxide morphologies. As outlined before, a key prerequisite is to establish a formation/dissolution equilibrium, while for alumina acidic conditions are sufficient. For titanium,

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

157

addition of fluoride to the electrolyte is essential to establish sufficient solubilcomplexes). In fact, fluoride-containing ity of the oxide (by formation of TiF2− 6 electrolytes, mainly in the interplay with water content in the electrolyte, evolved over the years to achieve today’s smooth, long-range ordered, and high aspect ratio TiO2 nanotubes. Table 5.2 summarizes the progress and shows different types of fluoride-based electrolytes used, and the resulting porous layer morphologies upon anodization. TiO2 nanotube arrays grown just in Hydrofluoric acid (HF) electrolytes or acidic HF mixtures [23–25, 98, 99] showed a limited thickness that would not exceed 500–600 nm. This is largely a consequence of the high chemical dissolution rate of TiO2 in acidic fluoride solutions. Table 5.2 Three categories of the fluoride-based electrolytes used in the formation of TiO2 nanotubes. Generation

Electrolytes

First

• Aqueous • Acidic F− (e.g., HF or mixture with HF)

Representative SEM imagesa)

• Layer thickness up to 500–600 nm • Rippled tube walls • Tubes with not ideal hexagonal geometry

500 nm

200 nm

Second

Features

• Aqueous • Neutral F− (e.g., NaF, NH4 F)

100 nm

150 nm

2.5 μm

• Layer thickness up to 3 μm • Rippled tube walls • Tubes with not ideal hexagonal geometry

100 nm

Third

• Nonaqueous (e.g., glycerol, ethylene glycol) • Neutral F− (e.g., NH4 F)

100 μm

7 μm

100 μm

a)

• Layer thickness up to several 10 μm s • Smooth tube walls • Tubes with almost ideally hexagonal geometry • Anodization potential: 30–150 V

SEM images of the first-generation nanotubes was adapted with permission from Ref. [99] Copyright 2003 The Electrochemical Society, the second generation was adapted with permission from Ref. [100] Copyright 2005 Wiley-VCH Verlag GmbH & Co., and the third generation was adapted with permission from Ref. [101] Copyright 2005 Wiley-VCH Verlag GmbH & Co.

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By replacing HF with buffered neutral electrolytes containing NaF or NH4 F [100, 102–104], a better control over the dissolution rate and localized acidification at the pore bottom could be obtained. Self-organized TiO2 nanotube layers with thicknesses higher than 2 μm could be achieved [100]. The side walls of first and second generations of TiO2 nanotubes show strong irregularities with considerable thickness variations (ripples). The occurrence of side wall corrugation is strongly combined with the water content in the electrolyte, and thus can be prevented by low water contents. The reason is the competition between growth rate of the tube and cell splitting rate [36]. In a low water content organic electrolyte the splitting speed (dissolution of the fluorides between cells) is sufficiently lower [36]. As a result, the third generation nanotubes grown in (almost) waterfree electrolytes show a smooth tube wall, with the side effect that local concentration fluctuations and pH bursts during anodization are also suppressed [101]. In the earliest work, nanotubes formed in glycerol electrolytes were shown to exhibit extremely smooth walls and the tube length was exceeding 7 μm. Today, almost ideally hexagonally ordered TiO2 nanotube arrays of several 100 μm length can be grown under optimized conditions in nonaqueous electrolytes, with tube diameters ranging from 10 to 200 nm [36, 105]. Essentially, the use of aqueous vs. organic solvent-based electrolyte has profound impact, not only on the tube length or other geometrical parameters but also on their intrinsic chemical composition, resulting in double or single wall morphologies as outlined in Section 5.2.2.1. Diameter and length of nanotubes are significantly affected by the types of electrolytes used (Figure 5.5a). Generally for all investigated electrolytes, the diameter of the nanotubes linearly depends on the applied voltage [106–108], but the voltage dependence varies between electrolytes. These differences can be attributed to the conductivity of the electrolytes used, that is, the ohmic drop in nonaqueous electrolytes is large and therefore normally higher voltages have to be applied to reach a desired diameter. As mentioned previously, the tube length is in essence proportional to the anodization time (charge). However, the electrolytes used (e.g., aqueous vs. nonaqueous, water content) determine the rate of chemical dissolution of the tubes, and thus the maximum reachable tube length (Figure 5.5b). In prolonged anodization experiments, etching of the top of the tubes also frequently leads to inhomogeneous needle-like “grassy” surfaces – that is partially perforated tube walls. Regarding the influence of fluoride concentration, one can note two extremes: A very low fluoride concentration leads to almost compact oxide layers while at a very high fluoride concentration, rapid dissolution of titanium metal makes the formation of oxide impossible. Only in an intermediate range fluorides allow to grow nanotubes – for the desired competition between oxide formation and Ti4+ dissolution. Fluoride concentration also affects the fluoride-rich layer of oxide metal and in between cells, and thus the splitting of pores into tubes as explained in the previous section. Figure 5.5c shows, however, that fluoride concentration over a large range is less influential on the geometrical parameters than the water content (Figure 5.6).

5.2

Formation and Growth of TiO2 and Al2 O3 Nanotubes/Pores

300

IR-drop

d 250 Diameter (nm)

U 200 150 100 50

20

60 80 Potential (V)

40

Thickness (μm)

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100

7

80

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3

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Steady

H2O

H2O

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0 0

(a)

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(b)

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180

10 Time (h)

12

14

16

18

Outer diameter

160

D (nm)

140 120 100 80 60 40 1E−3

(c)

0.1 0.01 c(NH4F) (mol L−1)

Figure 5.5 (a) Voltage dependence of the tube diameter for different electrolytes: ○ water-based, ▾ glycerol/H2 O 50 : 50, ◽ glycerol, and ◾ ethylene glycol. (b) TiO2 nanotube-layer thickness with anodization time for different electrolytes (anodization voltage for ethylene glycol electrolyte held at 60 V, and 40 V for other electrolytes): ◾ water-based acidic, ▴ water-based neutral,

1

◽ glycerol, ○ glycerol/H2 O 50 : 50, ∗ ethylene glycol. (Reproduced with permission from Ref. [36]. Copyright 2011 Wiley-VCH Verlag GmbH & Co.) (c) Outer and inner diameter, and wall thickness as a function of the fluoride content. (Reproduced with permission from Ref. [53]. Copyright 2010 Wiley-VCH Verlag GmbH & Co.)

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

Electropolishing

140 120

Breakdown in TiO2 NTs

Voltage (V)

100 80

TiO2 sponge

TiO2 pores

60 40

TiO2 nanotubes

20 0

1 c(H2O) (%)

10

100 10

pH = 6.73−0.0093*c

6.8

8

6.4

6

6.2

4

pH

6.6

6.0

σ (mS cm−1)

0.1

(a)

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5.8

0 20

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40

80

60

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c(H2O) (%)

(b)

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160

220 200 180 160 140 120

Outer diameter Wall thickness Inner diameter

100 80 60 40 20 0

(c)

10

20

30

40

50

60

70

c(H2O) (%)

Figure 5.6 (a) Voltage-H2 O diagrams showing the growth regions of TiO2 nanotubes, pores, and sponge structures as well as the breakdown region. (b) pH and conductivity of an ethylene glycol electrolyte as a function of the water

content. (c) Wall thickness, outer, and inner tube diameter change for the samples anodized at 20 V, 2 h. (Reproduced with permission from Ref. [53]. Copyright 2010 WileyVCH Verlag GmbH & Co.)

5.3

Improved Ordering via Nanopatterning

In Figure 5.6a, for an EG-containing electrolyte at a water content 13 wt%), breakdown leads to the formation of sponge structures, possibly due to repeated breakdown events. The amount of water also influences the diameters of the nanotubes. As shown in Figure 5.6c, the outer and inner diameters change with the water content; this can partially be attributed to the bulk IR drop resulting from higher conductivity of water [53]. For low water contents, at both voltages one can observe a proportional increase in the inner diameter and the wall thickness with the outer diameter, that is, a constant ratio between the outer and inner diameters is established. However, for high water contents, this trend does not hold. With water contents higher than 30 wt%, the outer diameter does not change anymore, that is, the expected behavior that the tube diameter is entirely controlled by the applied voltage is established. These facts illustrate that for low water contents, an additional voltage drop exists either within the tube electrolyte or at the interfaces. Other anodization conditions, such as temperature and pH, also affect tube growth. In organic solvent-based electrolytes, high temperature (e.g., 60 ∘ C) and ultrasonic assistance [109] are found to accelerate the tube growth rate. It is not surprising that in the earlier work based on first generation aqueous electrolytes, because of retardation of chemical dissolution of tubes in highly acidic environment, contrary effect is found where the nanotube length (in total 300 ∘ C alters them to anatase structure, whereas at temperatures >500 ∘ C the rutile phase appears, and at even higher temperatures increasingly rutile formation is observed. In relevance to the double wall structure present in tubes formed in most organic electrolytes, annealing, for example, at 500 ∘ C leads to a separation of the inner and outer shells into two clearly visible layers (Figure 5.8c), and this can also be clearly seen from the TEM image of the layer (Figure 5.8d) [14]. Note that at certain temperatures such as at 450 ∘ C in an example shown in Figure 5.8b, annealing results in undesirable effects such as cracks in the tube walls [31]. Essentially, the annealing temperature determines the crystal phases of either pure or mixed phases of anatase, rutile, and brookite, which has profound influence on the specific electronic and ionic properties of TiO2 [144–146]. For example, anatase phase is the most desired crystal structure for many photoelectrochemical applications (e.g., solar cells or other electron conducting

5.5

(a)

(c)

T

A R

TA A A T

Intensity (a.u.)

T

Applications

T T 550 °C 500 nm

500 °C 300 °C

500 nm

250 °C “As prepared”

20

40

60

80

(d)

2θ (°) (b)

18

Cracks

100 nm

Figure 5.8 (a) X-Ray Diffraction (XRD) data of as-prepared TiO2 nanotube layers and after different annealing temperatures with the formation of anatase “A” and/or rutile “R” phases. (b) SEM of TiO2 nanotubes after annealing at 450 ∘ C showing the crack lines and the grains present in the tube wall. (Reproduced with

nm

30

nm

200 nm

permission from Ref. [31]. Copyright 2010 The Royal Society of Chemistry.) (c) SEM and (d) TEM images of the TiO2 nanotube layer annealed at 500 ∘ C that revealing a doublewall structure. (Reproduced with permission from Ref. [14]. Copyright 2008 Wiley-VCH Verlag GmbH & Co.)

arrangements) since it shows the highest electron mobility [147–150]. Furthermore, it has a larger band gap (3.2 eV vs. 3.0 eV for rutile) and a higher conduction band edge energy Ec that leads to a higher Fermi level and Voc in DSSCs for the same conduction band electron concentration. We discuss more details about this in Section 5.5.2. 5.5 Applications

The development of anodic porous Al2 O3 and TiO2 materials is largely driven by their functional applications. For Al2 O3 , anodization to porous structures has wide technological applications and is established on a per square meter size panel range [10, 151]. For example, HA in sulfuric acid produces a coating with large cells and small diameter pores that is extremely hard and durable, and thus is used for engineering applications such as load-bearing surfaces. On the other hand,

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MA in phosphoric acid as an electrolyte leads typically to a thin coating that, for example, is used as an adhesive bonding primer in aerospace industry. Another well-established application is for architectural decoration purposes as door and window trim and exterior structural panels. In this case, colored coatings can be made by embedding organic acids in the oxide structure that are part of the anodizing bath. These applications of anodic porous alumina are well established [10], and demonstrate the feasibility to scale up anodization processes to an industrial scale. In other words, if upcoming advanced nanotechnology applications require a large-scale anodization process, it will be feasible and economic. Below, we discuss these nanotechnology-based applications of anodic Al2 O3 , mainly in terms of use as a template material in the fabrication of nanotubes, nanowires, nanorods, and nanodots of a functional material. With respect to TiO2 , except for classic applications as a white pigment, anodic layers are mainly used for color coding and for biomedical purposes. Most promising engineering applications are based on the semiconductive properties of anatase and rutile and their use in photocatalysis [26, 27] and solar cells [28, 152, 153]. Self-organized anodic TiO2 nanotubes are expected to take advantage of their one-dimensional nature to further increase the performance of the corresponding photoelectrochemical devices. Among all the applications, the most critical influence of structural and morphological features of anodic TiO2 is shown when employed as a photoanode for DSSCs, and thus we discuss this key application in more detail below. 5.5.1 Anodic Al2 O3 as Template Materials

The low cost fabrication approach and the flexibility in fine tuning the desired geometry of hexagonal patterns of nanopores with an extended long-range perfect order has advocated the use of self-organized Al2 O3 as a template to synthesize nanomaterials. Typically, the use of anodic porous alumina for nanomaterials fabrication can be based either with the anodic Al2 O3 films in the presence of Al substrate, or more commonly using freestanding membranes with through-pore morphology. In the former case where the aluminum substrate remains, the main advantage is the ease of handling of the material, as the mechanical support and direct electronic contact are readily available, for example, for electrodeposition. Nevertheless, in this case the insulating bottom needs to be thinned before electrodeposition can be used to fill the pores from bottom to the top. Easier electrodeposition is achieved with freestanding alumina layers that are gold contacted on one side. In order to produce these layers, Al2 O3 is detached from the aluminum substrate by wet chemical removal methods where the unoxidized aluminum substrate is dissolved in saturated HgCl2 after immersion for a few hours [154, 155] or in mixtures of Br2 and CH3 OH [156], saturated CuCl2 [157], or mixtures of CuCl2 and HCl [158]. Other detachment approaches may be based on electrochemical reverse and pulse voltage techniques [159, 160], or electrochemical etching in 20% HCl with an operating voltage of 1–5 V [136]. Upon

5.5

Applications

(c)

Electrodeposition Electrochemical anodization

Electrodeposition (a)

Metal layer deposition

(b)

Etching

Aluminum

Through-pole template

AAO membrane Semiconductor substrate Metal nanodots

(f)

Selective dry etching or LPCVD

e-Beam evaporation (d)

(e) Reactive ion etching

MBE

(g)

Figure 5.9 Schematic diagram of the fabrication of nanostructured materials with utilization of anodic porous alumina. Step a: metallic nanowire array electrodeposited in AAO; step b: AAO template with metal deposited on its surface; step c: metal nanowire array electrodeposited within the AAO template; step d: metallic nanodot array

deposited on semiconductor substrate; step e: semiconductor substrate with nanopore array; step f: semiconductor freestanding nanopillar array; and step g: heterostructure quantum dot array by molecular beam epitaxy (MBE). (Reproduced with permission from Ref. [161]. Copyright 2002 IEEE.)

removal from the substrate, the subsequent procedure is to open up the pore bottoms to achieve through-hole membranes, commonly by immersion in a H3 PO4 solution [157]. Deposition approaches into the anodic Al2 O3 membrane may be based on electroplating, electroless plating, physical vapor deposition, or chemical vapor deposition. The resulting nanomaterials range from metals, metal oxides, and semiconductors to polymers. Various geometries can be achieved such as nanodots, nanowires, nanorods, and nanotubes. The schematic diagram shown in Figure 5.9 presented by Liang et al. [161] has elegantly summarized the most widely used methods to fabricate nanoarrays based on anodic Al2 O3 . Commonly, metallic nanowires and nanorod arrays can be synthesized by the electrodeposition of materials into the nanochannels of anodic Al2 O3 with the substrate remaining (step a in Figure 5.9) or metallized freestanding anodic Al2 O3 membranes (steps b and c in Figure 5.9). The deposited metals, for example, include Ag [162, 163], Au [164], Co [165], Cu [166], Ni [167], Pb [168], and Pd [169]. With respect to the formation of metallic nanodot arrays, evaporation of metals [170] (step d in Figure 5.9) or chemical deposition [171] into a thin template of anodic Al2 O3 is preferred over electrodeposition because of the ease in controlling nanodot growth. The first step of formation of metal oxide nanodots and nanowires generally can be performed identically to the metals described above, followed by a subsequent thermal oxidation of the metal nanodots or nanowires in the template.

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Owing to the wide range of functional applications, TiO2 and ZnO are the most widely formed materials via this route [172]. For example, ZnO nanowire arrays on GaN can be formed by a catalyzed epitaxial crystal growth where the anodic Al2 O3 is used as a shadow mask to evaporate regular gold dot arrays. The gold nanodots then act as a catalyst, to grow regular straight ZnO nanowires [173]. Other approaches include the use of atomic layer deposition (ALD) to create an array of ordered TiO2 nanotubes inside the channels of anodic Al2 O3 [174]. In line with the prospect of fabricating quantum-well and superlattice nanostructures that could greatly enhance the performance of a variety of electronic and optoelectronic devices, anodic Al2 O3 can serve directly (positive transfer of the nanopore arrangement) as a template for semiconductors by using dry etching methods, such as plasma etching, ion milling, and reactive ion etching (step e in Figure 5.9). In the negative transfer of AAO nanopores, molecular beam epitaxy (MBE) and metal–organic chemical vapor deposition (MOCVD) (steps e and g in Figure 5.9) or vapor–liquid–solid (VLS) growth and low-pressure chemical vapor deposition (LPCVD) (steps d and f in Figure 5.9) methods are commonly employed to produce quantum dots or nanopillars. Based on the template-assisted approach, a variety of quantum dot arrays such as InAs [175], GaN [176], CdTe [177], and SiO2 [178] dots on various semiconductor substrates (Si,GaAs, or GaN) have been fabricated. Ordered porous Al2 O3 membranes also serve as a common template for the fabrication of polymer nanowires and nanotubes [179, 180]. Another prominent area is as a template to grow arrays of multiwalled carbon nanotubes with uniform diameter and periodic arrangement [181, 182]. The improved functionality of nanostructured biomaterials via use of anodic Al2 O3 membranes has also been reported, such as nanopatterning of high-density DNA arrays [183, 184], a high membrane capacity that allows rapid protein binding [185, 186], drug delivery [187, 188], and biosensing [189]. In conclusion, the widespread applicability of anodic Al2 O3 membranes as a template can be attributed to their low cost fabrication approach, the relative maturity in anodization technology to reliably engineer a desired geometry of porous Al2 O3 , and also the relative ease of use in functional applications. 5.5.2 Anodic TiO2 for Dye-Sensitized Solar Cells

Since the pioneering work of O’Regan and Grätzel demonstrated that an efficient photoelectrochemical solar cell could be fabricated using dye-sensitized mesoporous TiO2 films [28], this technology has attracted significant research interest and attention. Owing to low material cost and easy and inexpensive methods of fabrication, as well as the fact that a reasonably high solar conversion efficiency of 8–12% can be reached, DSSCs are being considered to be a possible alternative to other solar cell technologies. This type of solar cells can be made on flexible substrates [190, 191], thus offering the possibility of applications on curved surfaces

5.5

Illumination

−

−

Pt-coated FTO glass

− e−

−

CB −

−

−

− S∗

−

Fermi level

Cell voltage e−

−

3I

hy Dye

(a)

FTO Pt

−

I3−

Electrolyte

S°/S*

VB TiO2

Applications

FTO Pt

Dye-sensitized TiO2 Nanoparticles/tubes Ti metal

Electrolyte

(b)

e−

Figure 5.10 Schematic representation of (a) the principle of a dye-sensitized solar cell and (b) a typical solar cell construction using TiO2 nanoparticles/tubes on a Ti substrate. (Reproduced with Permission from Ref. [31] Copyright 2010 The Royal Society of Chemistry)

such as clothes, bags, or car roofs. Transparency of these cells and their good performance under diffuse light conditions may make DSSCs particularly attractive for applications such as panels on windows, and so on. The basic principle of DSSCs is illustrated in Figure 5.10a. In brief, a DSSC consists of a photoanode from a wide band gap semiconductor (mostly TiO2 ) material with a monolayer of adsorbed dye molecules, an electrolyte (e.g., a triiodide and iodide redox couple), and a conductive substrate coated with a catalyst (e.g., Pt, carbon) as a cathode. The wide band gap semiconductor, in this application, only acts as an electron transport medium – the key for light absorption is the dye that absorbs maximum in the visible range of the solar spectrum, and hence allows for an efficient use of sunlight. Upon illumination, photoexcitation of the dye results in an excited LUMO state that immediately injects the electron into the conduction band of the oxide, leaving the dye in its oxidized state. The key requirement for the dye is that the LUMO of the dye molecule is energetically positioned slightly higher than the conduction band edge of TiO2 . Also, the transfer kinetics of the excited electron to the conduction band has to be faster than the de-excitation of the dye and the regeneration time constant for the dye. The dye is then restored to its original state by electron transfer from the electrolyte, usually an organic solvent or ionic liquid containing the I− ∕I3 − redox system. The regeneration of the sensitizer by iodide prevents the recapture of the conduction band electron by the oxidized dye. The I3 − ions formed by oxidation of I− diffuse a short distance through the electrolyte to the platinum counter electrode, where the regenerative cycle is completed by electron transfer to reduce I3 − to I− . From above, it is clear that four major components to a large extent determine the performance of DSSCs, that is, the properties of the semiconductor (position of conduction band, electron mobility, recombination state density), the dye molecules structure (light absorption spectrum, position of the Highest Occupied Molecular Orbital/Lowest Unoccupied Molecular Orbital (HOMO/LUMO),

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

charge transport property), coupling to the semiconductor (junction characteristics, electron transfer kinetics, red-ox behavior), the nature of the electrolyte (diffusion constants, inertness), and the redox couple in the electrolyte (redox potential, electron recombination kinetics) [152, 192]. Figure 5.10b illustrates a schematic drawing of the sandwich configuration of a DSSC. In the classic arrangement, the cell consists of compacted TiO2 nanoparticle electrode. In the present review we discuss the replacement of this key component by anodically grown nanotubular TiO2 arrays. It should be noted that other components of DSSCs such as the dye, the electrolyte, and the counter-electrode also are intensively investigated for the improvement of DSSCs performance. For these issues, the reader is referred to other recent reviews [152, 193, 194]. The main advantage of nanoparticulate TiO2 is that typically it provides a large surface area for the dye adsorption, which directly corresponds to the amount of light absorbed by the photoanode. Generally, inexpensive methods such as screen printing [195, 196], doctor blading [197, 198], and spray coating [199] are used to distribute the porous TiO2 on substrates such as transparent conducting oxide glass (TCO, Fluoride Tin Oxide (FTO)). In order to obtain electronic contact between the particles and allow electronic conduction through the layer, followup sintering treatment is required. The optimized film thickness usually is about 8–15 μm, with a nanoparticle size of 10–30 nm, yielding a porosity of around 50–60%. However, in this traditional approach, a critical factor regarding charge recombination is the long carrier diffusion paths (by random walk) through the TiO2 network, and the presence of surface trapping states at the grain boundaries. One of the strategies to overcome these issues is the use of one-dimensional nanostructures such as nanotubes or nanowires that provide directionality when the arrays are positioned perpendicular to the surface [200]. This may reduce charge recombination losses occurring by intercrystalline contacts, and the random diffusion. To achieve directionality, self-organization of TiO2 nanotubes produced via electrochemical anodization is considered the most straightforward approach. This approach provides great flexibility by tuning the nanotube geometries as well as a number of properties simply by rational alteration of the anodization parameters. 5.5.2.1 Tube Geometry

The first report of dye-sensitized TiO2 nanotubes was based on first-generation nanotube layers leading to a very low efficiency (0.036%) [201]. Apart from an irregular tube wall structure that is unfavorable for the direct charge transport, the other obvious reason is the limit in the tube layer thickness [202, 203]. The introduction of the organic solvent-based neutral pH fluoride-containing electrolyte (third generation tubes) practically has provided the solution for the two above-mentioned issues. Smooth tube walls allow significantly higher electron mobility [203], enhancing the charge transport and lowering the charge recombination probability. Essentially, a high flexibility in alteration of tube thickness to several hundred micrometers allows a systematic investigation on the critical influence of the tube length and diameter.

IPCE (%)

80 60 40 20

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λ (nm)

(a) 6

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Dn 0 0.3

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Reference(without lactic acid)_D = 180 nm

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Series I: Electrolyte I Series II: Electrolyte II [18] Series II: Electrolyte II [18] (3 h)

So et. al.

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0.6

nEF-EF, redox (eV)

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Efficiency / η (%)

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0.0

0 0

(c)

10−2

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40

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50

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Figure 5.11 (a) Comparison of measured (solid line) and calculated (dotted line) IPCE values for different thicknesses of TiO2 nanotube layers; dashed line – the calculated IPCE spectrum for 20 μm long nanotubes without including the absorption loss due to I3 in the electrolyte. (b) Estimation of electron diffusion length (Ln ) of 20 mm long TiO2 nanotubes from the experimental values of Dn and τn by taking the quasi-Fermi level (QFL) into account. (Reproduced and adapted with permission from Ref. [203] Copyright 2008 American Chemical Society) (c) The plot of nanotube thickness versus efficiency value obtained from literature data (Roy et al. [31], Ghicov et al. [202], and So

(d)

171

200

τn

100

10−6

0

Applications

300

350

400

450

500

550

Annealing temperature (°C)

et al. [206]). Inset shows the schematic trend of solar cell performances of the classical TiO2 nanotube layers with tube length and diameters. (Reproduced with permission from Ref. [31] Copyright 2010 The Royal Society of Chemistry) (d) Compilation of solar cell efficiencies of 16 μm TiO2 nanotube layers at different annealing temperatures (Series I measurements were carried out with 0.1 M lithium iodide + 0.05 M iodine containing 0.6 M tert-butyl pyridine as electrolyte I and Series II measurements were carried out using R50 as electrolyte II and N719 as dye for both cases). (Reproduced with permission from Ref. [31]. Copyright 2010 The Royal Society of Chemistry.)

Consistent with other studies [202, 204, 205], the typical results based on TiO2 nanotubes grown in the conventional fluoride-containing EG electrolyte indicate that optimum solar energy conversion efficiency (∼80% = Incident Photon-toCurrent Conversion Efficiency (IPCE)) is reached with a tube layer thickness of around 20 μm (see Figure 5.11a,b) [203]. When the tube length is too short, the light absorption length is suboptimum. In the case of longer tubes (>30 μm), a higher resistance between the TiO2 nanotubes layer and the Ti substrate may occur [206]. It should be noted that for extended anodization, the properties of

Ln (μm)

20 μm 10 μm 5 μm 1 μm

100

Dn (cm2s−1) and τn (s)

5.5

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

500 nm (a)

500 nm (b)

Figure 5.12 SEM images of TiO2 nanotubes with different tube tops: (a) grassy tubes, (b) open tubes with nucleation layer on the top, and (c) completely open TiO2

500 nm (c)

tubes obtained using a photoresist coating. (Reproduced with permission from Ref. [208]. Copyright 2010 Elsevier B.V.)

the tubes may change due to top surface morphology changes mainly to a grassy top morphology (Figure 5.12a). This bundle-like grassy morphology on the top of the tubes has been reported to be either beneficial or detrimental to the solar cell performance [31, 207, 208]; here, further clarification is needed. It is clear that any remaining part of the initiation layer causes reflection losses (Figure 5.12b) and that in many cases well-defined open tubes provide the best performance (Figure 5.12c) [208]. Also importantly, adherence of TiO2 nanotubes to the substrate generally decreases with increasing nanotube length and may start peeling off from the substrate [206]. Very recent work by So et al. demonstrated that long tubes can be grown rapidly and adhere well if lactic acid (LA) is added to the electrolyte – in this case a maximum solar cell efficiency was observed for a tube length of 40 μm (Figure 5.11c) [206, 209]. The tube diameter is yet another significant parameter affecting the photoconversion efficiency. In a designated area, at the same tube thickness, one would expect tubes with smaller diameter to provide an enhanced surface area. The data in the inset of Figure 5.11c indicates that for tubes with the same length an enhanced solar cell performance is achieved with a decrease in the tube diameter [31, 202]. The recent finding that more robust tubes, such as those grown with addition of LA with larger diameter tubes, perform better in comparison to the smaller diameter tubes grown without the addition of LA (see Figure 5.11c) indicate the essentiality of better electronic contact achieved via stronger adhesion of tubes to the substrate for the former case [206]. A recent report addressed an important point whether tubular morphology provides advantages over other aligned morphologies such as an ordered nanoporous system [210]. At the same thickness, it was found that a nanotubular structure (diameter of 15 nm) not only provides higher surface area for dye loading but also has faster transport time (≈10 times) than a nanoporous structure. The latter effect may be ascribed to the effect on the effective diffusion length of electrons to reach the back contact (i.e., reduction of random walk effects) that is achieved in the tubular morphology. Decreasing tube diameter is a promising path to keep the

5.5

Applications

advantage of tubular geometry (transport), at the same time to enhance the surface area, and as a result could increase the solar cell efficiency. On the other hand, to minimize reflection losses optimum scattering properties may be achieved with larger tube diameters [205]; that is, similar to classic Grätzel cells an optimized light arrangement may be provided by a double layer stack consisting of large tube diameters on top and smaller tubes underneath. 5.5.2.2 Crystallinity

For use in Grätzel solar cells, TiO2 nanotubes are usually annealed to anatase. The crystalline form of TiO2 to a large extent depends on the annealing temperature, but crystallinity and phase distribution are also affected by parameters such as annealing duration and ramping rate [14]. Annealing under appropriate conditions not only improves the crystallinity but also reduces the gap in the grain boundaries [211]. Typically, the short circuit current and open circuit voltage increase with higher annealing temperatures [31, 203]. Generally, a temperature of 400–500 ∘ C is found to be the best range for maximum solar cell performance (Figure 5.11d). Typically, at the optimal annealing temperature to form anatase, a longer annealing duration leads to better crystallization; on the other hand, extended annealing leads to considerable growth of rutile at the metal/tube interface. That is, thicker layers of thermal oxide of rutile phase can be formed underneath the TiO2 nanotubes. Furthermore, it was found that annealing the nanotubes at T > 450 ∘ C resulted in some cracks in the tube walls (mostly in the outer shell of the tube), which was considered to slow down electron transport [31]. Apart from the titania phase, annealing temperature also affected two key parameters that determine the efficiency of the solar cells of nanotubes, which are their specific dye loading and electron transport properties. Since tubes are mainly grown in an EG solvent electrolyte, sufficient temperatures are required to decompose the carbon coverage of the tubes, which otherwise block dye adsorption places on the TiO2 nanotube walls (for example, the dye loading of sample annealed at 350 ∘ C is approximately twice smaller than a 450 ∘ C sample) [202]. Thermal annealing of the TiO2 nanotube layers affects not only the crystalline structure but also the morphology of the individual tubes and the entire nanotube ensembles. The change in the overall morphology depends strongly on the annealing process, particularly on the heating rate [14]. It was found that very fast heating rates result in lower solar cell efficiency because of larger defects present on the tube walls. The average size of the nanocrystallites on the annealed tube walls also depends strongly on the ramp rates of the annealing treatment. For annealing at temperatures higher than 700–800 ∘ C, the structural integrity of the tubes is lost. Recently, unconventional annealing approaches, the so-called “water annealing” or hydrothermal treatment were reported as a way to convert TiO2 nanotubes to crystalline material [140, 212]. However, follow-up work showed clearly that this approach is quite questionable and only partially converts the amorphous phase to anatase and results in much poorer solar cell efficiency than conventional thermal annealing [213].

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

(a)

(b)

100 nm

100 nm

500 nm (c)

500 nm (d)

Outer wall

Inner wall

113 nm

200 nm

139 nm

100 nm

Figure 5.13 SEM top and cross-section view images of TiO2 nanotubes before (a,c) and after TiCl4 (b,d) treatment, showing tube decoration with TiO2 nanoparticles. (Reproduced with permission from Ref. [218]. Copyright 2009 Elsevier B.V.)

5.5.2.3 Approaches to Enhance the Surface Area Particle Decoration via TiCl4 Treatment Typical TiO2 nanotubes with a smooth and robust wall show surface areas in the range of Brunauer–Emmett–Teller (BET) = 30–60 m2 g−1 [80, 202, 203], while classic nanoparticle cells show BET = 80–100 m2 g−1 [214, 215]. As a result, a frequent follow up strategy is to create hierarchical structures on the nanotube walls – in the simplest approach the tube walls are decorated with TiO2 nanoparticles. A typical approach is nanoparticle loading of both outer and inner tube walls via TiCl4 treatment, providing a significant increase in the surface area [215, 216]. The TiCl4 treatment via hydrolysis–precipitation provides a homogenous decoration of TiO2 nanoparticles and is much more reproducible and reliable than direct immersion in an aqueous solution of TiO2 nanoparticles [217]. For TiCl4 treatment of nanotubes, better results are obtained if the treatment is carried out on the annealed crystalline TiO2 , rather than directly on as-grown amorphous nanotube layers (a second annealing is however needed to crystallize the decorated particles). Figure 5.13 shows the top and side Scanning Electron Microscope (SEM) image views for TiO2 nanotubes before and after TiCl4 treatment [218]. Decorated tubes usually show a 0.5–2% increased solar cell efficiency. By using front-side illumination with the transferred freestanding TiO2 nanotubes on FTO glass assisted with titanium isopropoxide as a binder, and follow-up with TiCl4 treatment, solar efficiency of 7.6% was reported [219]. However, in all these cases a comparably high efficiency can be reached but the nanoparticle effect may become dominant;

5.5

Applications

hence, it is difficult to elucidate the influence of tubes (or tube parameters) on the overall observed effect. Advanced Geometries In order to enhance the surface area in a defined way, efforts have been made to alter the tube geometries by changing anodization conditions. As in the case of Al2 O3 , the most common and straigthforward approach for TiO2 is by altering the applied voltage during growth, which can generate morphologies such as nanotube stacks [34, 106, 220] and stratification layers (usually called bamboo) [80, 54] (Figure 5.14a–c). This structure in comparison to conventional smooth TiO2 nanotubes has a larger surface area; in particular, the rings may act as spacers at the exterior of the nanotube walls that allow larger dye loading. Another more spectacular morphology is TiO2 mesosponge (Figure 5.14d–f ) obtained by anodization in a glycerol/K2 HPO4 electrolyte followed by a chemical etching process of the structure [47]. This morphology provides a considerably higher specific surface area than TiO2 nanotubes and consists of a strongly interlinked network of nanosize TiO2 . Other important features are that the layers show a strong adhesion to the titanium substrate and that their thicknesses can be adjusted from some hundred nanometers to several ten micrometers. First experiments under backside illumination showed DSSCs efficiencies of 4.16% (in comparison to 3.3% for the corresponding nanotubes) [47]. The most recent study based on front-side illumination on FTO glass reported a solar energy efficiency of 6.82% for such a mesoporous layer [221]. 5.5.2.4 Doping

To improve the electronic properties of TiO2 , introduction of some doping elements such as zirconium, aluminum, ruthenium, or niobium was found to promote charge transfer and mediate recombination in TiO2 structures [190, 222–226]. A straightforward doping approach is by simple incorporation of the desirable dopant metal into the substrate alloy. In many cases of tube growth, the doping metals were found to be introduced in approximately the same concentration as in the substrate into the oxide. In comparison to other methods, this strategy offers long-term stability [227, 228], and a homogenous incorporation of the dopant in the tube oxide – thus it has been comparably widely investigated for photocatalytic and photoelectrochemical applications [30]. Recently, the alloying approach has been used toward DSSCs applications. In the case of TiO2 nanotubes doped with a small atomic weight percentage (e.g., 0.1 wt%) of Nb, an improved photoconversion efficiency of up to 30% was achieved, which is proposed to be due to improved electron conductivity of the tubes [229]. This beneficial effect was reported to be limited to only 2 μm thick nanotube layers, whereas for a higher length detrimental electronic effects introduced by niobium doping became dominating. Other dopants such as tantalum [230] and ruthenium [231] were found to allow a thicker layer of nanotubes to be grown. For tantalum, the beneficial effect is ascribed to suppression of recombination effects, which at a thickness of 15 μm, at optimal dopant content of 0.1 wt%, leads to an increase in the solar cell efficiency from 4.06 to 5.09%. For

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

TiO2 bambo structure (a)

B-NT2 B-NT1 NT

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Figure 5.14 (a) Bamboo-type tubes B-NT1, grown under AV conditions, with a sequence of 5 min at 120 V and 5 min at 40 V for 4 h anodization; (b) bamboo-type tubes B-NT2, grown under AV conditions, with a sequence of 1 min at 120 V and 5 min at 40 V for 12 h anodization; and (c) I–V curves obtained from solar cells for B-NT1 and B-NT2. (Reproduced with permission from Ref. [80] Copyright 2008 American Chemical Society.) (d,e) SEM images after etching in 30 wt% H2 O2 for 1 h, leading to a highly regular sponge morphology and (f ) I–V curves obtained from solar cells for different stages of sponge

−2

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η (%) 0.29 0.63 1.74 3.45 4.16

formation and for differently etched sponge layers. A: Non-etched and non-annealed, B: etched in H2 O2 and nonannealed, C: nonetched and annealed, D: etched in H2 O2 and annealed, and E: etched in oxalic acid and annealed. (Reproduced with permission from Ref. [47] Copyright 2008 Wiley-VCH Verlag GmbH & Co.) Both tables in (c) and (d) give extracted photovoltaic characteristics and dye loading of the dye-sensitized TiO2 layers. Ldye = dye loading, Jsc = short-circuit current, Voc = open-circuit voltage, FF = fill factor, and 𝜂 = efficiency.

5.5

Applications

the ruthenium case, the effect is attributed to improved conductivity as in the niobium-doped case. 5.5.2.5 Single Wall Morphology

As described in earlier sections, the key step toward obtaining smooth tube walls and highly organized tube arrangement was the use of nonaqueous electrolytes. However, this type of electrolyte leads to a double walled nanotube structure where the inner tube wall consists of a less defined layer of titanium oxy-hydroxide with very high carbon content. This high carbon content originates from the incorporation of electrolyte species into the outer part of the oxide during the anodization process. For optimized properties, it is however desirable to obtain a highly pure single-wall TiO2 since the contamination species have a detrimental effect toward photoelectrochemical and electrical applications. Very recently, it has been demonstrated that introducing a radical capture agent in the electrolyte could suppress the formation of an inner oxide layer, leading to the formation of single-walled tubes [73, 74]. The resulting single-walled tubes are found to provide significantly enhanced physical properties such as conductivity and electron transport times in DSSCs, which leads to enhancement in the DSSCs efficiency from 4.26% (in double wall tube) to 4.80%. 5.5.3 Prospect for Commercialization

The key prospect of commercialization of course requires the anodic TiO2 to be at least on par with the benchmark performance of nanoparticulate-based TiO2 solar cells. We have, in the previous section, described how the performance improved over the years with innovations such as the evolution in the electrolytes used, anodization parameters, better control over the anodic TiO2 geometry, secondary treatments to enhance the anodic TiO2 surface area, doping, and creating single-wall morphology. The obtained experimental results also lead to greater understanding of the fundamental role of geometrical effect of TiO2 , and the beneficial effect of further treatments. In fundamental chemical and physical aspects of engineering TiO2 , further improvement in the performance still can be expected with optimized hierarchical structures and an optimized light management, higher degree of crystallization, and achieving truly size-confined electron transport properties. Several recent innovations, however, are important toward industrial exploitation. We discuss below the significant improvement in the processing speed, the challenges of anodization approach in the upscaling manufacturing process, improving the configuration of DSSCs, and long-term stability of DSSCs. 5.5.3.1 Processing Speed

For industrial applications, efficiency in the product processing speed promotes the overall effectiveness of the cost. This requirement is easily evident considering the formation of porous alumina that is based on the HA approach, that is, that

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5 Engineering of Self-Organizing Electrochemistry: Porous Alumina and Titania Nanotubes

are mainly on a rapid sequential/batch-processing nature. Therefore, it is highly desirable that TiO2 nanotubes with suitable length, geometry, and morphological structure can be grown in a relatively short time. Based on the most common recipe using EG electrolyte containing fluoride and water, typically it takes over 2 h to grow nanotubes with a length of around 15 μm. Several reports investigate the strategies to grow nanotubes at a fast rate such as replacement of water with H2 O2 in a typical electrolyte where the rate is proposed to be promoted by the generation of • OH and HO2 • radicals [232], by the use of perchlorate-containing electrolytes [233], or by simply manipulating the water content and the anodization potential [234]. In those strategies, the fastest time to grow 16 μm nanotubes is 10 min. In a very recent report [209], highly ordered anodic TiO2 nanotube layers with a thickness of 15 μm could be grown in 45 s, as presented in Figure 5.15. This very fast rate is as a result of the addition of LA into the electrolyte used for anodization, which allows nanotube growth at significantly higher anodization voltages (e.g., 120–150 V) than in the LA free case where such voltages cause dielectric breakdown. Importantly, these ultrarapidly grown tube layers show at least comparable performance as the classic reference tubes for application in DSSCs. Also, enhanced adhesion and stability is achieved, which allow higher efficiency DSSCs with long tubes, for example, 40 μm [206]. In this context, it is noteworthy to mention the readily known Rapid Breakdown Anodization (RBA) – typically grown in Cl− or ClO4 electrolytes – an attractive approach not only in view of the very fast grow rate (typically under 60 s) but also because the anodization can be performed in a relatively friendly environment (fluorine free aqueous media) [45, 235, 236]. However, the main disadvantage of these nanotubes is that their morphology is not very defined – they grow in loose patches on the anode surface and are often fused to bundles. Because of this characteristic that does not allow fully directional charge transport, they show poor efficiency (1.5%) when used as such in a backside illumination configuration, but synergetic effects with nanoparticles can result in improvement in efficiency to 3.82% [237]. A recent approach in using the RBA as freestanding membranes on transparent conductive substrates enables the advantage of front-side illumination, resulting in an overall efficiency of about 4.6% [238]. 5.5.3.2 Design: Backside versus Front-Side Illumination

A standard approach in the fabrication of the DSSC photoanode is that mesoporous TiO2 is deposited on transparent FTO glass. This design allows an efficient way of light illumination through the transparent glass (so called front-side illumination) and as light directly hits the dye-absorbed TiO2 surface no additional absorption losses take place. However, the direct application of TiO2 nanotubes grown on Ti-foil requires backside illumination where the light has to pass through the platinum-coated FTO glass and iodine electrolyte. This is a nonoptimal approach for light conversion efficiency, because the Pt coated onto FTO glass partially reflects light, while the iodine electrolyte absorbs photons in the near UV region.

5.5

(a)

Applications

LA NT

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40 s

−2 Current density (mA m )

180

Nanotube length (μm)

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(d)

Figure 5.15 (a) SEM images of TiO2 nanotube layers formed under “classic” conditions in a 0.1 M NH4 F–5 wt% H2 O−EG electrolyte (left) and in the same electrolyte with lactic acid (LA) addition (right). (b) Cross-sectional SEM images of a tube layer grown in the LA electrolyte at 150 V showing the rapid growth in the LA electrolyte. (c) Comparison of nanotube length vs. time

0.0

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2

(mA cm ) 11.50 10.02

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4.73

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4.36

0.4

0.5

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0.7

0.8

Voltage (V)

in LA-containing electrolytes compared with the LA-free case. (d) I–V characteristics for DSSCs fabricated using reference nanotube and LA nanotube samples (both of a tube length of 15 μm) annealed at 450 ∘ C, 3 h. (JSC = short-circuit current, VOC = opencircuit voltage, FF = fill factor, and η = efficiency). (Reproduced with permission from Ref. [209]. Copyright 2012 American Chemical Society)

To resolve this drawback, nanotube arrays were fabricated on transparent FTO glass enabling front-side illumination [239]. The most straightforward approach is the anodization of sputtered or evaporated titanium metal film on FTO glass. A crucial factor for successful fabrication of TiO2 nanotube array devices is the deposition of a high-quality titanium metal layer that is suitable to be fully converted into a nanotube array by anodization [110]. It was found that the quality of a deposited film and its adhesion to the substrate are related to the film thickness and substrate temperature. Another approach to build front-side illuminated

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DSSCs is the transfer of freestanding TiO2 membranes to the FTO glass. The freestanding TiO2 membrane can be achieved via methods such as selective dissolution of a metallic substrate [240], a critical point drying method [241], or by simply immersing the nanotube array in 0.1 M aqueous HCl solution [219]. The obtained TiO2 membrane is then transferred and fixed on FTO with the help of titanium isopropoxide and subsequent annealing [219]. Apart from TiO2 nanotube arrays, front-side illumination is also performed on structures such as anodically grown TiO2 mesosponge [221] and RBA nanotubes [45, 46, 237]. The best efficiency value for TiO2 mesosponge-based DSSCs with a 7 μm thick layer is a solar efficiency conversion of 6.82% [221]. 5.5.3.3 Flexible Substrate

One of the attractive aspects of DSSCs is that this technology can be applied to flexible and curvy surfaces [217, 242]. Flexible solar cells offer great benefits because of the potential for low-cost, roll-to-roll production, and increasing applications due to superior robustness. The advantage of anodization is its feasibility on a wide range of conductive substrates. An example of an anodized layer that adheres well to the substrate, even allowing extensive bending, is the TiO2 mesosponge structures [47]. Another potential anodization approach is to grow TiO2 nanotubes from LA containing electrolytes, as they have superior mechanical adherence to the substrate [206]. Generally, anodization can be performed on flexible substrates such as a plastic substrate coated with a thin layer of Ti metal, the use of a thin Ti foil, or even transferring the TiO2 nanotubes array membranes. For the former, an optimal front-side illumination cell configuration can be employed with a transparent conductive plastic. 5.5.3.4 Scale-Up

To date, the prototype of the DSSCs that are on the verge of commercialization are based on the usage of TiO2 nanoparticles in photoanodes. Owing to the large size of cells required for practical applications, the scale-up of the manufacturing process could compromise the reliability and performance of a large DSSC module, which is far more complex than a laboratory test cell. With a sandwichbased design, the difficulty when scaling-up lies in the interconnected cells in a DSSCs module that may interact in a non-desired way. There are several different designs for up-scaling the DSSCs cell based on TiO2 nanoparticles that have been addressed in a recent review by Hagfeldt et al. [152]. In view of anodic TiO2 , the first key challenge for engineering is to produce a homogeneous large-scale anodization product. In principle, large-scale anodization of Al2 O3 has been successfully and widely employed in the coating and coloring industries. Hence, the current state-of-the-art large-scale anodization manufacturing infrastructures of Al2 O3 may also be extended to the TiO2 case. In comparison to anodization of Al2 O3 that is typically performed in aqueous-based electrolytes, for highly ordered and defined tubes, nonaqueous electrolytes are

5.6

Conclusions

needed; this implies challenges due to higher solution resistance. In view of current distribution and local heating effects, if iR drop becomes significant, uniformity may vary significantly over a very large metal substrate. This results in variation of the effective anodization potential on a specific location, and therefore affects the overall homogeneity of the geometry of the formed anodic TiO2 , and as a result the performance of the DSSCs. Therefore optimized new anodization parameters may be required where heat and mass transfer as well as current distribution are adjusted to the larger scale and different anodization geometry. 5.5.3.5 Long-Term Stability

An important consideration for commercialization of DSSCs is in the durability and long-term stability. For the nanoparticulate DSSCs system, this has been addressed in many reports, especially concerning the development of suitable new dye complexes and redox couples [243–245]. At the commercial level, the durability issue has been addressed by several companies such as Samsung and Sony [246], and seems partially solved for nanoparticle DSSCs. However, for anodic TiO2 in DSSCs, this factor has not been considered in detail even in laboratory-scale testing.

5.6 Conclusions

Advances and accumulated knowledge gained over the years in self-organizing electrochemical anodization of a large range of metal substrates has rapidly helped the evolution of the field to reach a more mature level in terms of greater precision in controlling and engineering porous anodic oxides. Today, many functional devices have been devised that exploit the high surface area of these films, the ability to tune pore dimensions through anodizing process parameters, and the material properties of oxides on particular metals. We reviewed in this chapter two most prominent self-organized oxide materials, which are on the one hand already commercially available anodic porous alumina, and on the other hand anodic TiO2 nanotubes that have received a great deal of scientific interest in recent years (in expectation of future commercialization). We compare and show that fundamentally both anodic alumina and TiO2 are very similar in view of achieving optimized self-organization, duplex oxide structure, and many mechanistic growth aspects. For both materials, an extensive range of pore or tube dimensions can be achieved and tuned for a targeted application. In particular, evolution of the type of electrolytes used has had a profound impact on the geometrical and functional properties of anodic TiO2 nanotubes. We discuss two most examined nanotechnology applications of anodic porous alumina and TiO2 nanotubes. This is for the direct use of Al2 O3 as a nanotemplate material. On the other hand, DSSCs based on TiO2 nanotube films illustrate that the progress and evolution of TiO2 nanotubes over the last 10 years

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has greatly improved their efficiencies in DSSCs. Nevertheless, a similar contribution of progress comes from surface engineering approaches such as strategies to enhance their surface area (in parallel with enhancement of dye absorption) via nanoparticles decoration and advanced geometries, the introduction of a suitable doping element to improve tube electronic properties, and the recent finding on a formation of highly pure single-wall TiO2 nanotube morphology. The achieved progress is also in line with a greater fundamental understanding of the charge transport properties, especially related to tube annealing conditions. We addressed several areas of significance relevant to anodic TiO2 for prospective commercialization of DSSCs. Essentially, the key prospect for commercialization lies in the need to further improve the performance of the DSSCs, to be at least on par, if not above the performance of the widely investigated nanoparticulate system, in order to realize the full potential of anodic TiO2 nanotube arrays. Furthermore, DSSCs represent a very complex functional system that is not only determined by TiO2 and its modifications, but essentially also improvement of other components such as the discovery of new dyes, electrolytes, and redox couples may be decisive for the future prospects of commercialization of anodic TiO2 . References 1. Lieber, C.M. (1998) One-dimensional

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6 Diffusion-Induced Stress within Core–Shell Structures and Implications for Robust Electrode Design and Materials Selection Mark W. Verbrugge, Yue Qi, Daniel R. Baker, and Yang-Tse Cheng

6.1 Introduction

The life of lithium-ion batteries utilizing insertion or alloy electrode materials is related to the mechanical expansion and contraction of the active materials and solvent decomposition at the active material surfaces [1–22]. It is well known that lithium-ion batteries would not work if a protective layer did not form over the active material surfaces during initial cycling. At the negative electrode, commonly a graphitic material, the protective layer is often termed the solid electrolyte interphase [23, 24], or SEI. Solvent reduction, prior to passivation of graphitic electrodes, which leads to a stable SEI, takes place at about 0.7 V vs. a Li∕Li+ reference (cf. Figure 5 of Ref. [25]; the high surface area graphitic material shows a strong peak on the first cyclic voltammogram for solvent decomposition). Tapping mode AFM (atomic force microscopy) has been used to estimate an SEI thickness of about 20 nm, although interpretation of AFM results is difficult [26, 27]. Furthermore, the necessity of using very smooth surfaces for the AFM analyses motivates the use of HOPG (highly oriented pyrolytic graphite), which does not replicate the active edge planes of graphite in a lithium-ion cell. The attempt by Yan et al. [28] to model the complex nature of the SEI over graphite highlights many unresolved questions [29, 30]. As Verma et al. [31] note in their recent review of the SEI formed on carbonaceous electrodes, “the composition of the SEI is a highly debated subject.” Similar observations are reported by Xu and von Cresce [32] in their recent review of SEIs in lithium-ion batteries. Protective layers that have also been termed SEIs exist over positive electrode materials. As with the negative electrode, these protective layers form, for the most part, during the initial cycles and involve solvent and salt decomposition. Propylene carbonate, for example, oxidizes at a platinum electrode at about 2.1 V vs. a Li∕Li+ reference [33]. Aurbach [34] has reviewed the in situ formation of protective layers over lithiated carbon negative electrodes and lithiated transition metal oxide positive electrodes.

Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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6 Diffusion-Induced Stress within Core–Shell Structures and Implications

In addition to particle/SEI systems, there are many electrode material systems for lithium-ion batteries that are based on a core–shell structure wherein both the core and the shell materials are electrochemically active. References [35–46] discuss such structures for both negative and positive electrode systems. In the review by Ogumi and Wang [47] on carbon materials for lithium-ion batteries, they discuss surface-modified graphites (which they point out are core–shell systems) wherein the graphite core is covered by a less ordered carbon. The use of thermal vapor decomposition to form carbon shells over low-cost natural graphite [48–50] is an example of current application. For higher capacity negative electrodes, alloys of lithium have been coated by a similar protective carbon shell. A recent example of this geometry (including relevant images of the tin and carbon constituents) is that of a tin core with a substantially graphitic carbon shell [51]. In this case, the carbon shell mitigates solvent reduction over the otherwise exposed tin surface, and stable cycling at 800 mAh g−1 is obtained. In this work, we refer to these systems as conventional core–shell structures. While significant progress has been made on describing diffusion-induced stress (DIS) within electrode materials [52–84], far less attention has been devoted to characterizing DIS within core–shell or multilayer structures [85–88]. In this work, we formulate a set of equations to simulate solute (lithium) diffusion and the associated stress distribution within the core–shell structure. A schematic of the spherical core–shell system being examined is depicted in Figure 6.1. The system is treated as isotropic, and the solid mechanics approach is based on small, elastic displacements [89–91]. Numerical results are presented for conventional core–shell systems that provide an understanding of how stress evolves within insertion and alloy materials. We note that it may be possible to extend prior semi-analytic methods for diffusion in core–shell structures [92–94] to subsequently obtain the stress distribution in a manner similar to that employed by Chu and Lee [95] to analyze thermally induced stress in a core–shell system.

α phase (core)

ri a β phase (shell)

θ r

Figure 6.1 Problem schematic. The core is of radius ri and the total particle radius is a. Shown also are the spherical coordinates r and 𝜃.

6.2

Ab initio Simulations: Informing Continuum Models

Frequently, host materials in lithium-ion batteries expand upon solute addition, and the outer shell plays a protective role and does not expand as much. Under such circumstances, the stress jump at the core–shell interface is maximum when the particle is fully saturated with the solute (fully lithiated), as the core is fully expanded and the shell is stretched over the core. Analytic solutions for this maximum stress condition provide insight for the rational design and materials selection of robust core–shell structures. Hence, our overall approach is to employ numerical calculations for a conventional core–shell system, and we utilize the analytic solutions for the maximum stress condition for an infinitely thin SEI stretched over a lithiated graphite core and over a lithiated Si core. Last, we note that there is lack of knowledge of key material properties that are needed for quantitative mathematical modeling of many core–shell systems, particularly for SEI materials; therefore, we employed predictive modeling methods based on density functional theory (DFT). The next section reviews the role of DFT and related methods in the analysis of core–shell structures. Following the brief review, continuum equations are presented for the stress analysis of core–shell electrode materials, which are then analyzed and discussed in the rest of the text.

6.2 Ab initio Simulations: Informing Continuum Models

True ab initio simulations, requiring only atomic information as inputs (elements and positions), can provide basic material properties by solving Schrödinger’s equation for the electronic structure. Because of the need to treat the multibody problem, the Schrödinger equation can only be solved accurately for a small number of electrons. DFT, however, provides numerical and approximate solutions for systems involving many interacting electrons. The crucial DFT Ansatz is based on theorems of Hohenberg and Kohn [96] and Kohn and Sham [97]. Hohenberg and Kohn demonstrated that the total ground state energy E of a system of interacting particles is completely determined by the electron density 𝜌e and proved that the correct ground-state electron density minimizes the energy functional E[𝜌e ]. Kohn and Sham transformed the multibody problem of interacting electrons in a static external potential field into a tractable problem of non-interacting electrons subject to an effective potential. The Kohn–Sham effective potential includes the external potential and the exchange and correlation interactions of electrons. Although the exact functional of the exchange and correlation interaction is unknown, many approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, and hybrids (see the review in [98]) have proved useful. Despite difficulties remaining in properly describing van der Waals forces (dispersion), charge-transfer reactions, and some systems with strongly correlated electrons, DFT has been highly successful (cf. [99]) in calculating various properties that can be derived from the electronic ground state, such as equilibrium crystal structures and lattice parameters, elastic constants, surface energies, phonon dispersion, and so on [100]. More recently,

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Ceder [101] has summarized both the opportunities and challenges to design new cathode materials for lithium batteries starting from DFT calculations. The calculation of DIS with a core–shell model requires material properties for each phase, including solute diffusivity and partial molar volume as well as elastic moduli. Many in situ and ex situ characterization tools (e.g., X-ray analysis and scanning and transmission electron microscopy) have already provided structural information on electrode materials. By computing the equilibrium lattice parameters for these structures at different Li concentrations via DFT, the volume expansion coefficient can be determined [102]. Lithium diffusion mechanisms and diffusion barriers can be computed by using the nudge-elastic-band method to find the transition state along the designed diffusion pathways. Diffusion coefficients can then be derived analytically or with Monte Carlo simulations based on the DFT results [103]. For many layered intercalation compounds, Li diffusion is considered in a nondilute system, and the diffusion coefficients have been determined as a function of Li concentration [104]. The diffusivity of Li in crystalline graphite as a function of Li concentration has been computed by Persson et al. [105]. Based on the crystal structures (at different Li concentration), the stiffness tensor, Cij , can also be determined by computing the energies or the stresses of deformed unit cells and fitting either the energy and strain (e.g., to a quadratic function) or the stress and strain (e.g., to a linear function) [106]. The applied strains should be crystallographic symmetry-unique in order to obtain all the independent elastic constants. Since micron-sized electrode particles are typically a polycrystal, but are often modeled as an isotropic elastic material (for example, in this work), two independent elastic properties (typically Young’s modulus and Poisson’s ratio) can be obtained by taking the average of Cij based on Reuss’s lower bound or Hill’s higher bound averaging schemes. If the structure itself is amorphous and already isotropic (such as a lithiated Si electrode over a broad potential range), one can first compute the bulk modulus and the modulus C 11 , and then use the relations between different elastic constants [107] to deduce Young’s modulus and Poisson’s ratio. The modulus for lithiated graphite is higher than that of either pure Li metal or graphite, mainly due to the strong interaction formed between positively charged Li-ions and negatively charged graphene planes of graphite. As a result, the modulus of fully lithiated graphite (LiC6 ) is 3 times that of pure graphite [102]. In transition metal oxides, such as LiTi2 O4 [108] and LiFePO4 [109], the overall modulus change upon lithiation is much less dramatic (less than 10%). For alloy-forming electrode materials, such as Si [107] and Sn [110], DFT calculations have shown that the moduli of lithiated compounds follow the linear rule of mixtures. This computed lithiation-induced softening effect also has been confirmed by nano-indentation of lithiated Si [111]. Concentrationdependent elastic properties have been used in continuum DIS models [72, 73, 83]; the favorable comparison of calculated strains with experimentally obtained (in situ) strain maps of lithiated graphite lends strong support for the approach [112].

6.2

Ab initio Simulations: Informing Continuum Models

The challenge in computing any basic material properties of the SEI lies in its complex and still debatable structure (as we mentioned earlier). Ab initio calculations have contributed to the understanding of SEI formation, along with various chemical analysis and structural characterization experiments. Early modeling work focused on revealing the reduction reaction pathways of one or a few organic solvent molecules inside a bulk liquid (including the solvation effect), with one additional electron injected onto the molecule (without explicitly considering a charge-transfer step or the electrode-surface effect) [113]. Recently, DFT-based molecular dynamics has been applied to much larger systems to simulate organic solvent decomposition reactions at the solid–liquid interfaces [114]. Such calculations can be used to simulate the reaction kinetics. In the absence of experimental information on the structure–property relationships of SEI films, taking known components in the SEI and directly computing their properties can provide valuable information. As an initial step toward predicting the properties of the SEI, Leung and Qi put (computationally) a few atomic layers of Al2 O3 and LiAlO2 , typical artificial SEI films made by atomic layer deposition (ALD) [43], on a Li metal surface, and then simulated the charge-transfer step from the Li metal to organic solvents after passivation [115]. They found that on bare Li metal surfaces, ethylene carbonate (EC) accepts electrons and decomposes within picoseconds. In contrast, with the oxide coating, the molecular reorganization energy of EC plays a key role in slowing down the electron transfer. Shi et al. started from Li2 CO3 , one of the most chemically stable SEI components reported to appear in SEI films formed on both positive and negative electrode surfaces [31, 116, 117]. They first identified the dominant Li diffusion carriers in Li2 CO3 as a function Li chemical potential (or the open circuit voltage of the electrode it covers) by comparing the formation energy and concentrations of all seven Li-associated point defects using DFT [118, 119]. The main diffusion carriers in Li2 CO3 on negative electrodes were found to be excess Li ion interstitials, while on positive electrodes, the main carriers were Li ion vacancies. Li diffusion coefficients and ionic conductivities were computed from simulated diffusion pathways and energy barriers. The mechanical properties of Li2 CO3 have also been computed with DFT, and phonon dispersion calculations were used to show that Li2 CO3 is mechanically stable [120]. Although the SEI structure is complex, it is well recognized that it typically contains a dense inorganic layer near the electrode surface and a porous organic layer near the electrolyte. Recent AFM measurements confirmed the existence of the two-layer structure in the SEI (on MnO anode) and illustrated that the two layers have different mechanical properties [121]. Isotope exchange experiments along with DFT simulations have led to a two layer–two diffusion mechanism model to describe Li diffusion mechanism in the SEI [119]. In the future, as the relevant material properties become known either through predictive modeling or experimental measurement, the value of modeling these systems will be greatly enhanced.

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6.3 Governing Equations for the Continuum Model 6.3.1 Thermodynamics

For a conventional core–shell system [35–50] wherein both the core and the shell material are electrochemically active, we consider a core material 𝛼 covered by a shell layer 𝛽. Initially (time t = 0), both phases are equilibrated, and we equate the solute (lithium) chemical potential of the 𝛼 and 𝛽 phases: 𝜇𝛼 = 𝜇𝛽 𝜇𝛼0 + RT ln 𝛾𝛼 Θ𝛼 = 𝜇𝛽0 + RT ln 𝛾𝛽 Θ𝛽 or Θ𝛼 = KΘ𝛽

(6.1)

where K=

𝛾𝛽 𝛾𝛼

exp

𝜇𝛽0 − 𝜇𝛼0 RT

(6.2)

The solute fractional occupancy of available sites (or mole fraction of available sites) is given by Θ, and activity coefficients are represented by 𝛾. We consider a system at constant temperature and pressure, and the reference state activities 𝜇 0 are constants. We do not account for the impact of the hydrostatic stress on the chemical potential [57, 58, 60, 61]. We shall assume the solute is dilute in both the 𝛼 and 𝛽 phases, and we ignore variations in activity coefficients. Hence, K is taken to be constant in this work. For a core–shell system wherein the shell is an electrolyte phase (e.g., an SEI or a porous polymer layer that is often associated with an SEI) under diffusion control (i.e., solute Li diffusion through the core and shell materials dominates the resistances in the system), the interface can be taken as equilibrated. For the reaction 0 −−−−−−−−−−−− → Li+𝛽 + e−𝛼 − ← − Li𝛼

the voltage E of the core (𝛼-phase) relative to a lithium reference that is in contact with the shell (𝛽-phase) electrolyte is given by E = U0 + In this case, KSEI =

RT 𝛾𝛽 Θ𝛽 ln F 𝛾𝛼 Θ𝛼

[ )] F ( exp − E − U0 𝛾𝛼 RT 𝛾𝛽

(6.3)

and Θ𝛼 = KSEI Θ𝛽

(6.4)

6.3

Governing Equations for the Continuum Model

Hence, the value of K SEI is dependent on the potential V. For potentiostatic experiments, E is constant. As noted above, for this dilute solution analysis we shall ignore activity coefficient variations, yielding a constant value for K once E is set. As would be expected, a more detailed analysis of the host–SEI interface yields more complex relations [10]. 6.3.2 Solute Diffusion

Consistent with the dilute solution approach to the system thermodynamics, we investigate Fickian diffusion of a solute within the two phases 𝛼 and 𝛽 for a conventional core–shell system (cf. Eqs. (6.1) and (6.2)). While the model equations are general, we are interested in systems in which the core expands upon solute addition, and the shell either moderately expands or does not expand at all upon solute addition. For such systems, throughout electrode operation, the stress jump at the core–shell interface is largest when (i) the particle is initially saturated with solute (e.g., Li) and fully expanded and (ii) the concentration at the surface of the particle is set to zero (diffusion-controlled discharge of solute from the particle), reflecting the maximum possible rate of discharge for an active material. This is the situation we shall ultimately model, as it is useful in terms of materials selection and particle design. The solute concentration within the spherical particle is symmetric, and only variations in the radial direction are relevant. Within the 𝛼-phase core, 0 < r < ri , ) ( 2 ∂ Θ𝛼 2 ∂Θ𝛼 ∂Θ𝛼 + = D𝛼 ∂t r ∂r ∂r2 Within the 𝛽-phase shell, ri < r < a, ( 2 ) ∂Θ𝛽 ∂ Θ𝛽 2 ∂Θ𝛽 = D𝛽 + ∂t r ∂r ∂r2 At the interface r = ri between the shell and the core, we assume equilibrium prevails (Θ𝛼 = KΘ𝛽 ) and the solute flux is conserved: D𝛼

∂Θ𝛽 ∂Θ𝛼 = D𝛽 ∂r ∂r

At the particle surface r = a, the concentration is set (for calculations, the concentration Θa will be set to zero; cf. Table 6.2.) Θ𝛽 (t, r = a) = Θa The solution is well behaved at the center of the particle r = 0 ∂Θ𝛼 =0 ∂r

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6 Diffusion-Induced Stress within Core–Shell Structures and Implications

Initially, the particle is taken to be at equilibrium, with the active material concentration corresponding to the initial state of charge Θ0𝛼 : Θ𝛼 (0, 0 < r < ri ) = Θ0𝛼 and KΘ𝛽 (0, ri < r < a) = Θ0𝛼 The following definitions facilitate scaling and nondimensionalization of the equation system. 𝜏=

D𝛽 Θ𝛽 tD𝛼 Θ r , x= , 𝜉= , Θ𝛼 = 𝛼0 , and Θ𝛽 = K 0 2 a D𝛼 a Θ𝛼 Θ𝛼

The field equations can now be restated as ∂Θ𝛼 ∂2 Θ𝛼 2 ∂Θ𝛼 = for 0 < x < xi + ∂𝜏 x ∂x ∂x2 ( 2 ) ∂ Θ𝛽 2 ∂Θ𝛽 ∂Θ𝛽 =𝜉 + for xi < x < 1 ∂𝜏 x ∂x ∂x2 Initially, Θ𝛼 (0, 0 < x < xi ) = 1 Θ𝛽 (0, xi < x < 1) = 1 At the center of the particle ∂Θ𝛼 || | =0 ∂x ||𝜏,0 Equilibrium and flux continuity prevail at the 𝛼 –𝛽 interface Θ𝛼 = Θ𝛽

| ∂Θ𝛼 || 𝜉 ∂Θ𝛽 || | = ∂x ||𝜏,x K ∂x || i |𝜏,xi

Last, the concentration is set at the particle surface, Θ𝛽 (𝜏, 1) = Θa We mention that the definition of the concentrations yielding Θ𝛼 = Θ𝛽 at the interface allows one to treat the concentration problem as a single variable from a numerical perspective, simplifying numerical evaluation. 6.3.3 Solid Mechanics

We employ directly the stress–stain (𝜎 –𝜀) relations described by Timoshenko and Goodier [90] for infinitesimal deformation of a perfectly elastic, isotropic sphere.

6.3

Governing Equations for the Continuum Model

The concentration profile is symmetric with respect to the center of the sphere, and mechanical equilibrium in both the core and shell phases necessitates that ∂𝜎r 2 + (𝜎r − 𝜎𝜃 ) = 0 ∂r r

(6.5)

In direct analogy with analyses of thermally induced stress, the stress–strain relations in both phases are expressed as 𝜀r =

1 1 1 1 (𝜎 − 2𝜈𝜎𝜃 ) + ΩcT Θ and 𝜀𝜃 = [(1 − 𝜈)𝜎𝜃 − 𝜈𝜎r ] + ΩcT Θ (6.6) E r 3 E 3

where cT is the total concentration of sites available for solute occupancy, E is Young’s modulus, 𝜈 is Poisson’s ratio, Ω is the partial molar volume of the solute, and the radial and tangential strains of the spherically symmetric particle are related to the radial displacement u: 𝜀r =

du u and 𝜀𝜃 = dr r

(6.7)

The reference state for Eqs. (6.6) and (6.7) is that of the host material, devoid of solute. For lithium-ion batteries, materials tend to expand upon addition of Li solute, and the partial molar volume is positive. Conversely, it would be negative if the material contracted upon lithiation. By combining Eqs. (6.5)–(6.7), one can generate the differential equation governing displacement that is applicable in both the core and shell phases. Hence, within the 𝛼-phase core, ) ( ∂Θ𝛼 d2 u𝛼 2 du𝛼 2u𝛼 1 + 𝜈𝛼 Ω𝛼 − c + = r dr 1 − 𝜈𝛼 3 T,𝛼 ∂r dr2 r2 and within the 𝛽-phase shell, d 2 u𝛽 dr2

+

2 du𝛽 2u𝛽 − 2 = r dr r

(

1 + 𝜈𝛽 1 − 𝜈𝛽

)

Ω𝛽 3

cT,𝛽

∂Θ𝛽 ∂r

The center of the symmetric sphere remains stationary: u(0) = 0 For the remaining boundary conditions, it is helpful to cast the radial stress in terms of displacement through the use of the stress–strain (Eq. (6.6)) and strain–displacement (Eq. (6.7)) relations: ] [ du E u 1 + 2𝜈 − (1 + 𝜈) ΩcT Θ 𝜎r = (1 − 𝜈) (1 + 𝜈)(1 − 2𝜈) dr r 3 In a similar manner, we can express the tangential stress as [ ] du E u 1 +𝜈 − (1 + 𝜈) ΩcT Θ 𝜎𝜃 = (1 + 𝜈)(1 − 2𝜈) r dr 3 At the core–shell interface, r = ri , the displacement is continuous, u𝛼 (ri− ) = u𝛽 (ri+ ), and the radial stress emanating from the core is equal to that of the shell

201

202

6 Diffusion-Induced Stress within Core–Shell Structures and Implications

reduced by the surface energy Γ𝛼𝛽 (e.g., surface tension) that is associated with the interface [122]. ]| [ ) du𝛼 ( u𝛼 E𝛼 1 | + 2𝜈𝛼 − (1 + 𝜈𝛼 ) Ω𝛼 cT,𝛼 Θ𝛼 | = 1 − 𝜈𝛼 ( ) | − dr r 3 1 + 𝜈𝛼 (1 − 2𝜈𝛼 ) |r=ri ]| [ u𝛽 E𝛽 ) du𝛽 ( 1 2 | + 2𝜈𝛽 − (1 + 𝜈𝛽 ) Ω𝛽 cT,𝛽 Θ𝛽 | − Γ𝛼𝛽 1 − 𝜈𝛽 ( ) | dr r 3 1 + 𝜈𝛽 (1 − 2𝜈𝛽 ) | + ri r=ri

At the surface of the shell, r = a, and the radial stress is expressed as [62, 63] 2 𝜎r (a) = − Γ𝛽 a or ]| [ u𝛽 E𝛽 ( ) du𝛽 1 | 1 − 𝜈𝛽 + 2𝜈𝛽 − (1 + 𝜈𝛽 ) Ω𝛽 cT,𝛽 Θ𝛽 | ( ) | dr r 3 1 + 𝜈𝛽 (1 − 2𝜈𝛽 ) |r=a− 2 = − Γ𝛽 a where Γ𝛽 is the surface energy of the shell material in the presence of the electrolyte phase. For both the interface and the surface, we have neglected any changes in the modulus of the materials in the immediate vicinity of the boundary. For very large particles with a very thin shell, Γ𝛼𝛽 /ri and Γ𝛽 /a tend to zero, and the surface energies can be neglected. However, for nanostructures such as nanoparticles of carbon or Si coated by a protective layer, we would expect surface energies to play a significant role. Nondimensionalization of the problem is helpful in determining the relative influence of these factors. The following additional definitions are employed: E𝛽 (1 + 𝜈𝛼 )(1 − 2𝜈𝛼 ) Ω𝛽 cT,𝛽 1 u , , Ω= u= Ω , 𝛼 E𝛼 (1 + 𝜈𝛽 )(1 − 2𝜈𝛽 ) Ω𝛼 cT,𝛼 K a 3 cT,𝛼 Θ0𝛼 ) ( 6(1 + 𝜈𝛽 )(1 − 2𝜈𝛽 ) 6 1 + 𝜈𝛼 (1 − 2𝜈𝛼 ) = Γ𝛼𝛽 , Γ𝛽 = Γ𝛽 0 aE𝛼 Ω𝛼 cT,𝛼 Θ𝛼 aE𝛽 Ω𝛼 cT,𝛼 Θ0𝛼 E=

Γ𝛼𝛽

The field equations can now be restated as d2 u𝛼 2 du𝛼 2u𝛼 − 2 = + x dx dx2 x

(

1 + 𝜈𝛼 1 − 𝜈𝛼

)

∂Θ𝛼 for 0 < x < xi ∂x

and d 2 u𝛽 dx2

+

2 du𝛽 2u𝛽 − 2 = x dx x

At the center of the particle, u𝛼 (0) = 0

(

1 + 𝜈𝛽 1 − 𝜈𝛽

) Ω

∂Θ𝛽 ∂x

for xi < x < 1

6.3

Governing Equations for the Continuum Model

At the 𝛼 –𝛽 interface [ ]| ( ) du𝛼 u | 1 − 𝜈𝛼 + 2𝜈𝛼 𝛼 − (1 + 𝜈𝛼 )Θ𝛼 | | − dx x |x=xi [ ]| u𝛽 Γ𝛼𝛽 ( ) du𝛽 | + 2𝜈𝛽 − (1 + 𝜈𝛽 )Ω Θ𝛽 || = E 1 − 𝜈𝛽 − dx x xi | + |x=xi Last, at the particle surface, [ ]| 6(1 + 𝜈𝛽 )(1 − 2𝜈𝛽 ) ( ) du𝛽 | 1 − 𝜈𝛽 + 2𝜈𝛽 u𝛽 − (1 + 𝜈𝛽 )Ω Θ𝛽 || = −Γ𝛽 = −Γ𝛽 dx aE𝛽 Ω𝛼 cT,𝛼 Θ0𝛼 | − |x=1 Table 6.1 provides a recapitulation of the equations to be solved for the problem. The equation system was solved numerically using a finite difference routine [123]. Typically, 451 mesh points were used for both the core and the shell regions. Upon solving these equations, we can calculate various stresses within the particle and clarify the impact of the governing parameters (including material properties as well as the particle size and protective coating thickness) on the potential for mechanical degradation, such as fracture of the outer protective layer or interfacial delamination at the core–shell phase boundary. The stress components are nondimensionalized as 𝜎=

3(1 + 𝜈𝛼 )(1 − 2𝜈𝛼 ) Ω𝛼 cT,𝛼 Θ0𝛼 E𝛼

𝜎

The dimensionless radial and tangential stresses can be represented as } ) du ( u 𝜎 x,𝛼 = 1 − 𝜈𝛼 dx𝛼 + 2𝜈𝛼 x𝛼 − (1 + 𝜈𝛼 )Θ𝛼 for x < xi du u 𝜎 𝜃,𝛼 = x𝛼 + 𝜈𝛼 dx𝛼 − (1 + 𝜈𝛼 )Θ𝛼 and

] [( ) du u 1 − 𝜈𝛽 dx𝛽 + 2𝜈𝛽 x𝛽 − (1 + 𝜈𝛽 )Ω Θ𝛽 [u ] ) ( du = E x𝛽 + 𝜈𝛽 dx𝛽 − 1 + 𝜈𝛽 Ω Θ𝛽

𝜎 x,𝛽 = E 𝜎 𝜃,𝛽

⎫ ⎪ ⎬ for x > xi ⎪ ⎭

(6.8)

(6.9)

At the center of the particle, the above equations are ill posed for direct use due to the 1/x terms. However, we recognize that the stress at the center is purely hydraulic, 𝜎 x,𝛼 = 𝜎 𝜃,𝛼 , and ) ( du𝛼 for x = 0 (6.10) 𝜎 x,𝛼 = 𝜎 𝜃,𝛼 = (1 + 𝜈𝛼 ) − Θ𝛼 dx To determine the onset of plastic deformation, the principal shear stress is relevant. Both the tangential and principal shear stresses take on their largest values at the start of discharge for a particle that (i) is initially filled with solute, (ii) contracts upon discharge of the solute, and (iii) is subjected to the diffusion-limited

203

1+𝜈𝛼 1−𝜈𝛼

2 2𝛼 = (x )

1 − 𝜈𝛼

)

Γ𝛼𝛽

| | | + |x=xi

dx

du𝛽

+ 2𝜈𝛼

u𝛼 x

]| − (1 + 𝜈𝛼 )Θ𝛼 || = |x=x−i ] | u + 2𝜈𝛽 x𝛽 − (1 + 𝜈𝛽 )Ω Θ𝛽 || − |x=x+i

𝜉 ∂Θ𝛽 K ∂x

du𝛼 dx

[( ) E 1 − 𝜈𝛽

[(

| | | − = |x=xi =

1−𝜈𝛽

1+𝜈𝛽

2 𝛽 = (x2 )

u

∇2x u𝛽 −

𝜉∇2x Θ𝛽

∂𝜏

∂Θ𝛽

Ω

Θ𝛽 (0, x) = 1

Θ𝛼 (0, x− ) = 1, Θ𝛽 (0, x+ )=1 i i ∂Θ𝛼 ∂x

xi < x < 1

Shell (𝜷)

x = xi

Core–shell interface

∂x

∂Θ𝛽

−Γ𝛽

[( ) 1 − 𝜈𝛽

Θ𝛽 = Θa

dx

du𝛽

Θ𝛽 (0, x) = 1

x=1

Particle surface

]| + 2𝜈𝛽 u𝛽 − (1 + 𝜈𝛽 )ΩΘ𝛽 || = |x=1−

(K, xi , Θa , and 𝜉), and six additional dimensionless parameters impact the solid mechanics analysis (E, Γ𝛼𝛽 , Γ𝛽 , Ω, along with ν𝛼 and ν𝛽 ), yielding a total of 11 dimensionless groups.

First row: position within the sphere. Second row: initial conditions. Third row: field equations and boundary conditions for the concentration problem. Fourth row: ∂2 + 2x ∂x∂ . Four dimensionless parameters govern the diffusion analysis equations governing the displacement of the particle. In these equations, ∇2x = ∂x 2

u𝛼 = 0

∂Θ𝛼 ∂x

∂Θ𝛼 = ∂𝜏 ∇2x Θ𝛼

∂Θ𝛼 ∂x

u

Θ𝛼 (0, x) = 1

Θ𝛼 (0, x) = 1

∇2x u𝛼 −

0 < x < xi

x=0

=0

Core (𝜶)

Origin

Table 6.1 Equations to be solved for the concentration and displacement problem.

204 6 Diffusion-Induced Stress within Core–Shell Structures and Implications

6.3

Governing Equations for the Continuum Model

rate [Θ𝛽 (t, a) = Θa = 0 for t = 0+ ]. The principal shear stresses (𝜎r − 𝜎𝜃 )∕2 can be expressed in dimensionless form as [ ] 𝜎 r,𝛼 − 𝜎 𝜃,𝛼 (1 − 2𝜈𝛼 ) du𝛼 u𝛼 = − 2 2 dx x [ ] 𝜎 r,𝛽 − 𝜎 𝜃,𝛽 (1 − 2𝜈𝛽 ) du𝛽 u𝛽 = − 2 2 dx x Last, the jump in tangential stress at the core–shell interface, Δ𝜎𝜃 = 𝜎𝜃 (x+i ) − 𝜎𝜃 (x−i ), can be expressed in dimensionless form as [ ] u𝛽 du𝛽 ( ) + 𝜈𝛽 − 1 + 𝜈𝛽 Ω Θ𝛽 𝜎 𝜃,𝛽 |x=x+ − 𝜎 𝜃,𝛼 |x=x− = Δ𝜎 𝜃 = E i i x dx x=x+i ] [ ) ( u du − 𝛼 + 𝜈𝛼 𝛼 − 1 + 𝜈𝛼 Θ𝛼 (6.11) x dx x=x− i

6.3.4 Analytic Solution for Initial Stress Distribution

The results we present in this section pertain to both conventional core–shell systems and to systems with an active core and an SEI shell. This generality stems from the fact that transport need not be considered when the system is initially equilibrated, Θ𝛼 = Θ𝛽 = 1, and we shall provide an analytic solution to the solid mechanics equations. For systems of interest with respect to lithium-ion batteries, the core material (e.g., graphite and other negative electrode materials [124]) expands upon solute (Li) addition, and the shell (e.g., SEI) has either moderate expansion upon lithiation or does not measurably expand (Ω𝛽 = 0). For such systems, the stresses within the particle are largest at time zero, when the particle is fully charged with solute. Thus, analytic solutions for this condition are particularly useful for materials selection and particle design. At time zero, the displacement equations can be rendered as d2 u𝛼 2 du𝛼 2u𝛼 − 2 = 0 for 0 < x < xi + x dx dx2 x 2 d u𝛽 2 du𝛽 2u𝛽 − 2 = 0 for xi < x < 1 + x dx dx2 x The most general solutions to these equations are of the form u𝛼 (x) = C1,𝛼 x + u𝛽 (x) = C1,𝛽 x +

(6.12)

C2,𝛼 x2 C2,𝛽

(6.13) x2 The constants Ci,j must be determined from the boundary conditions. Since u𝛼 (0) = 0, it follows that C2,𝛼 = 0, and u𝛼 (x) = C1,𝛼 x

(6.14)

205

206

6 Diffusion-Induced Stress within Core–Shell Structures and Implications

At the 𝛼 –𝛽 interface, u𝛼 (xi ) = u𝛽 (xi ); hence, C1,𝛼 xi = C1,𝛽 xi +

C2,𝛽

(6.15)

xi 2

The other two boundary conditions are formulated in terms of the stress functions. At the 𝛼 –𝛽 interface, [ (

]| ) du𝛼 u𝛼 | 1 − 𝜈𝛼 + 2𝜈𝛼 − (1 + 𝜈𝛼 ) | | − dx x |x=xi [ ]| u𝛽 Γ𝛼𝛽 ) du𝛽 ( | + 2𝜈𝛽 − (1 + 𝜈𝛽 )Ω || = E 1 − 𝜈𝛽 − dx x xi | + |x=xi

which can be expressed as (1 + 𝜈𝛼 )(C1,𝛼 − 1) − E

[ (

)

1 + 𝜈𝛽 (C1,𝛽 − Ω) − 2(1 − 2𝜈𝛽 )

C2,𝛽 xi 3

] =−

Γ𝛼𝛽 xi

(6.16)

At the particle surface [ (

u𝛽 ) du𝛽 + 2𝜈𝛽 − (1 + 𝜈𝛽 )Ω Θ𝛽 1 − 𝜈𝛽 dx x

]| | | = −Γ𝛽 | | − |x=1

or (C1,𝛽 − Ω)(1 + 𝜈𝛽 ) − 2C2,𝛽 (1 − 2𝜈𝛽 ) = −Γ𝛽

(6.17)

Equations (6.15)–(6.17) can be solved to yield the required constants: ]) ( [ ( ) E 2Ω 1 + 𝜈𝛽 (1 − 2𝜈𝛽 )(1 − x3i ) − 3Γ𝛽 (1 − 𝜈𝛽 ) C1,𝛼 =

+[1 + 𝜈𝛼 − (Γ𝛼𝛽 ∕xi )][1 + 𝜈𝛽 + 2x3i (1 − 2𝜈𝛽 )] 2E(1 + 𝜈𝛽 )(−1 + 2𝜈𝛽 )(−1 + x3i ) + (1 + 𝜈𝛼 )[1 + 𝜈𝛽 + 2x3i (1 − 2𝜈𝛽 )] [ ( ) )] ( −Γ𝛽 1 + 𝜈𝛼 + 2E 1 − 2𝜈𝛽 − 2(1 − 2𝜈𝛽 )x2i [Γ𝛼𝛽 − xi (1 + 𝜈𝛼 )]

C1,𝛽 =

C2,𝛽 = −

+Ω(1 + 𝜈𝛽 )[1 + 𝜈𝛼 − 2E(1 − 2𝜈𝛽 )(−1 + x3i )] 2E(1 + 𝜈𝛽 )(−1 + 2𝜈𝛽 )(−1 + x3i ) + (1 + 𝜈𝛼 )[1 + 𝜈𝛽 + 2x3i (1 − 2𝜈𝛽 )]

x2i Γ𝛼𝛽 (1 + 𝜈𝛽 ) + x3i {(−1 + Ω)(1 + 𝜈𝛼 )(1 + 𝜈𝛽 ) − Γ𝛽 [1 + 𝜈𝛼 − E(1 + 𝜈𝛽 )]} 2E(1 + 𝜈𝛽 )(−1 + 2𝜈𝛽 )(−1 + x3i ) + (1 + 𝜈𝛼 )[1 + 𝜈𝛽 + 2x3i (1 − 2𝜈𝛽 )] (6.18)

6.3

Governing Equations for the Continuum Model

For the stress components, we can substitute Eq. (6.18) into the stress Eqs. (6.8), (6.9), and (6.11) to obtain 𝜎 x,𝛼 |x≤xi ,𝜏=0 = (1 + 𝜈𝛼 )(C1,𝛼 − 1) 𝜎 𝜃,𝛼 |x 0). When both the core and shell expand with solute addition, larger

0.8

0.9

1

displacements result, but the stress jump at the core–shell interface is reduced, as are the magnitudes of all other stresses.

6.4

Results and Discussion

0.6 E = 0.5 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3 xi = 0.7

Dimensionless displacement or stress

0.5 0.4 0.3 0.2

Displacement u

Tangential stress σθ

0.1 Interfacial stress jump Δσθ

0 −0.1

Radial

−0.2

stress σx

−0.3 −0.4 −0.5

τ=0 0

0.1

0.3

(a)

E=1 Ω=0 Γαβ = 0 Γβ = 0.15 να = 0.3 νβ = 0.3 xi = 0.7

0.5 Dimensionless displacement or stress

0.4

0.5

0.6

0.7

0.8

0.9

1

Position x = r/a 0.6

0.4 0.3 0.2

Core α

Shell β

τ =0

Displacement u

0.1

Tangential stress σθ

0 Interfacial

−0.1

stress jump Δσθ

−0.2 −0.3 −0.4 −0.5

(b)

Shell β

Core α

0.2

Radial stress σx

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position x = r/a

Figure 6.3 Effect of modulus ratio (a) and surface energy (b). The upper plot illustrates that when the shell modulus is reduced (reduced shell stiffness) relative to the base case (Figure 6.2a), larger displacements result, and the stress jump at the core–shell interface is reduced, as are the magnitudes

of all other stresses. The lower plot shows that a positive surface energy (analogous to surface tension) leads to more compressive stresses and reduced displacements, but has no influence on the interfacial stress jump when the core and shell materials have similar mechanical properties (E = 1, 𝜈𝛼 = 𝜈𝛽 ).

211

212

6 Diffusion-Induced Stress within Core–Shell Structures and Implications

the upper plot of Figure 6.3. While the stress is reduced, the displacement magnitudes through the shell and core are increased relative to the base case, as the more flexible shell provides less resistance to particle expansion. The lower plot of Figure 6.3 shows that a positive surface energy (analogous to surface tension) leads to more compressive stresses and reduced displacements, but has no influence on the interfacial stress jump. Thus, while smaller particles lead to a compressive stress when surface energies are positive, which has been viewed as an explanation for why small particles can be more stable [62, 63], the tendency of the interface to fail by shear forces represented by the stress jump may not be reduced by going to smaller particle sizes if the modulus and Poisson ratio of the core and shell materials are similar and the shell does not expand upon solute addition. The initial behavior of the dimensionless displacement and the stresses at the core–shell interface as a function of the shell thickness is depicted in Figures 6.4 and 6.5. As xi approaches 1, the particle tends to be of core material only; as xi approaches 0, the particle tends to be shell material only. The base-case condition (cf. Table 6.2) is provided in the upper plot of Figure 6.4, and the lower plot treats a shell material that expands upon solute addition (Ω = 0.5), similar to the analysis of the lower plot of Figure 6.2. Thus, the upper plot shows that the interface has a larger displacement than that of the surface for all values of xi . In contrast, because the shell expands upon solute addition for the results associated with the lower plot (Ω = 0.5), the surface displacement is always larger than that of the interface, and all stresses are decreased in magnitude. The influence of a more flexible shell material is depicted in the upper plot of Figure 6.5 (cf. upper plot of Figure 6.3), and the lower plot can be used to examine the role of surface energy (cf. Figure 6.3b). Because the modulus of the shell differs from that of the core, the interfacial stress jump does vary with changes in the interface position xi (Figure 6.3a). The mechanical properties E and ν of the core and shell are identical for the lower plot, and the stress jump is not altered by the value of the surface energy. 6.4.2 Transient Behavior

As noted in the base case described in Table 6.2, we examine a conventional core–shell particle with similar properties that impact the diffusion problem: 𝜉 = 1, reflecting equal solute diffusion coefficient in the core and shell phase, and K = 1, which gives rise to a smooth concentration profile across the interface. Shown in Figure 6.6 are the transient concentration profiles for solute extraction from an initial condition wherein all sites that can store the solute are filled (full charge). Figures 6.7 and 6.8 provide the corresponding profiles in tangential stress, displacement, and radial stress. The initial stress and displacement profiles provide a check on the numerical routine with the analytic solution. The transient behavior of the stress distributions indicates that the general form of the profiles are qualitatively similar to those of the initial condition; as time progresses, the solute concentration tends to zero throughout the system, concentration

6.4

Results and Discussion

1 Interfacial stress jump

Dimensionless displacement or stress

0.8

Interfacial displacement

0.6 Shell tangential stress at interface

0.4 0.2

Surface displacement

0 −0.2 −0.4 −0.6

E=1 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3

Core radial and tangential stresses

−0.8 −1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

τ=0

0.8

0.9

1

Interface position xi = ri/a

(a) 1

Dimensionless displacement or stress

0.8 Surface displacement

0.6 0.4 0.2 0

−0.4

Core radial and tangential stresses

E=1 Ω = 0.5 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3

−0.6

−1

Shell tangenitial stress at interface

Interfacial displacement

−0.2

−0.8

(b)

Interfacial stress jump

0

0.1

τ=0 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Interface position xi = ri/a

Figure 6.4 Behavior of displacement and stresses at the core–shell interface for varying shell thicknesses. As xi approaches 1, the particle tends to be of core material only; as xi approaches 0, the particle tends

to be of shell material only. (a) Base case (cf. Table 6.2). (b) Ω = 0.5, denoting a shell material that expands upon solute addition (cf. Figure 6.2b).

213

6 Diffusion-Induced Stress within Core–Shell Structures and Implications

1 Interfacial displacement

Dimensionless displacement or stress

0.8 Interfacial stress jump

0.6 0.4 0.2

Shell tangential stress at interface

0

Surface displacement

−0.2 −0.4 −0.6

−1

Core radial and tangential stresses

E = 0.5 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3

−0.8 0

0.1

τ=0 0.2

(a)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Interface position xi = ri /a 1 0.8

Dimensionless displacement or stress

214

Interfacial stress jump

0.6 0.4

0.2 Interfacial displacement 0

Shell tangential stress at interface

−0.2 −0.4

Surface displacement

−0.6 Core radial and tangential stresses

−0.8 −1 (b)

E=1 Ω=0 Γαβ = 0 Γβ = 0.5 να = 0.3 νβ = 0.3

τ=0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Interface position xi = ri /a

Figure 6.5 Behavior of displacement and stresses at the core–shell interface for varying shell thicknesses. (a) Influence of a more flexible shell (cf. Figure 6.3a). (b) Influence of surface energy over the shell (cf. Figure 6.3b).

6.4

Dimensionless solute concentration Θ

1

τ = 0+

Results and Discussion

Shell β

Core α

0.9 0.8

xi = 0.7 ξ=1 K= 1

0.05

0.7 0.6

0.1

0.5 0.4 0.3

0.2

0.2 0.1 0.5

0

0

0.1

0.2

0.3

0.4 0.5 0.6 Position xi = r/a

0.7

0.8

0.9

1

Figure 6.6 Dimensionless solute concentration versus position for various times during solute extraction. The shell and core are taken to have equal solution diffusion coefficients (𝜉 = 1) and interfacial equilibrium concentrations (K = 1).

gradients continuously decline, and the stresses decline as well. The tangential and radial stress at the origin (cf. Eq. (6.10)) do reach a maximum (compressive in this case) at an intermediate time as the solute begins to reach the origin of the particle in much the same manner as has been described for single phase particles [62–64]. Plots of the displacements and stress components at the core–shell interface are of practical interest for the determination of when maximum interfacial stresses occur. Results for the base case (Figure 6.8a), for an expanding shell (Ω = 0.5, Figure 6.8b), and for a flexible shell (E = 0.5, Figure 6.9) all indicate that the jump stress that can cause delamination at the core–shell interface is largest at time zero. Raising the partial molar volume of the solute in the shell allows the shell to expand upon solute addition, leading to reduced stresses and increased displacements (as was found in the analyses associated with the lower plots of Figures 6.2 and 6.4). Likewise, lowering the modulus of the shell, implying a more flexible shell material, reduces the stress components and increases the displacements (as was found in the analyses associated with Figures 6.3a and 6.5a). 6.4.3 Application to a Host-SEI Core–Shell System

As mentioned in Section 6.1, the analytic solution provided for time zero is valid for both conventional core–shell systems. For specific calculations, we shall start with parameters and properties reflecting a graphite core covered by a Li2 CO3 shell. (We shall investigate a dominantly polymer shell layer briefly as well.) The

215

6 Diffusion-Induced Stress within Core–Shell Structures and Implications

0.6 E=1 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3 xi = 0.7 ξ= 1 K= 1

Dimensionless tangential stress σθ

0.5 0.4 0.3 0.2 0.1 0

0 0.05 0.1 0.2 0.5

0.5

−0.1

0.2

0.1

−0.2

0.05

−0.3

τ=0

−0.4 −0.5

Shell β

Core α

0

0.1

0.2

(a)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Interface position x = r/a 0.6

Dimensionless displacement or radial stress

216

E=1 0.5 Ω = 0 Γαβ = 0 0.4 Γβ = 0 να = 0.3 0.3 νβ = 0.3 xi = 0.7 0.2 ξ = 1 0.1 K = 1

0.05 0.1

0.2 0.5

0

0.5

−0.1

0.2

−0.2

0.1

−0.3

0.05

Radial stress σx

0

−0.4 −0.5

(b)

τ=0

Displacement u

Shell β

Core α

0

0.1

0.2

0.3

0.4 0.5 0.6 Position x = r/a

Figure 6.7 Base case (cf. Table 6.2) dimensionless tangential stress (a) and displacement and radial stress (b) versus position for various times during solute extraction, with the solute profiles provided in Figure 6.6.

0.7

0.8

0.9

1

The 𝜏 = 0 curves correspond to the analytic (and numerical) solution for the initial condition. For a specified time, the stress jump corresponds to the differing tangential stress values across the interface x∕a = 0.7.

6.4

Results and Discussion

1 Concentration Θ

0.9

Interfacial displacement or stress

0.8

E=1 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3 xi = 0.7 ξ= 1 K= 1

Stress jump Δσθ

0.7

Displacement u

0.6 0.5 0.4

Tangential stress σθ,α

0.3 0.2 Tangential stress σθ,β

0.1 0 −0.1

Radial stress σx

−0.2 −0.3 −0.4 −0.5 0

0.05

0.01

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time τ = tD/a2

(a) 1 Concentration Θ

0.9

Interfacial displacement or stress

0.8

Stress jump Δσθ

0.7 0.6

Displacement u

0.5 0.4

Tangential stress σθ,α

0.3 0.2 0.1 0 −0.1

Radial

−0.2

Tangential stress σθ,β

−0.3 −0.4 −0.5

(b)

E=1 Ω = 0.5 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3 xi = 0.7 ξ= 1 K= 1

0

0.05

0.01

0.15

stress σx

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time τ = tD/a2

Figure 6.8 (a) The base case (cf. Table 6.2) interfacial values for stresses and displacement. (b) The influence of a shell material that expands upon solute addition (Ω = 0.5).

Li2 CO3 shell is intended to reflect the protective SEI. Accounting for property variations with concentration as well as the complex structure and architecture of an actual SEI is beyond the scope of this work; the extension of this work to better represent actual systems is an important future endeavor that will likely be paced

217

6 Diffusion-Induced Stress within Core–Shell Structures and Implications

1 Concentration Θ

0.9 0.8 Interfacial displacement or stress

218

E = 0.5 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.3 xi = 0.7 ξ= 1 K= 1

Stress jump Δσθ

0.7 0.6

Displacement u

0.5 0.4

Tangential stress σθ,α

0.3 0.2 0.1 0 −0.1 −0.2

Tangential stress σθ,β

−0.3

Radial stress σx

−0.4 −0.5

0

0.05

0.1

0.15

0.2 0.25 0.3 0.35 Time τ = tD/a2

0.4

0.45

0.5

Figure 6.9 Influence of a flexible shell material E = 0.5 similar to the analyses of the upper plots in Figures 6.3 and 6.5. As seen in Figure 6.8, the stress jump is largest at 𝜏 = 0.

Table 6.3 Parameters employed for the graphite-SEI core–shell analysis. Parameter or property

Value

Comments

a

5 μm

cT ,𝛼 cT , 𝛽

0.031 mol cm−3 8.7 × 10−10 mol cm−3

Characteristic of substantially graphitic particles used in lithium-ion batteries (design variable, but includes the Li2 CO3 thickness) See text associated with Eq. (6.22) [119]

D𝛼 E𝛼 E𝛽 a − ri 𝜈𝛼 𝜈𝛽 Θ0𝛼

10−10 m2 s−1 70 GPa 66 GPa 10 nm 0.3 0.25 1

Ω𝛼 Ω𝛽

3.2 cm3 mol−1 0

References [130, 131] [102] [120] Li2 CO3 thickness [26, 116] [102] [120] Initially charged lithiated graphite, Θ0𝛼 = 1 (process variable) See text associated with Eq. (6.22) No significant expansion upon putting dilute Li (see cT,𝛽 above) into Li2 CO3 [120]

For the purposes of this analysis, Li2 CO3 is chosen as the SEI material.

6.4

Results and Discussion

219

by available data. We describe how the parameters and property values listed in Table 6.3 were estimated, and then provide a discussion of the system behavior. We first address the estimation of parameters used for lithiated graphite. In going from graphite (Θ = 0, corresponding to the reference volume with no expansion) to LiC6 (Θ = 1), the fractional expansion is approximately 10% [102, 126]. Thus, per Eq. (6.22), ΩcT ≈ 0.1. For a graphite density of 2.2 g/cm3 and a molecular weight 72.06 mol/g for six carbons, we find cT for a graphite host to be 0.031 mol m−3 and Ω = 0.1∕0.031 = 3.2 cm3 mol−1 [132]. Last, we note that often a linear expansion coefficient 𝛼 is used for isotropic materials, in direct analogy to thermal elasticity of homogeneous materials [89–91]. With that formulation, the stress–strain relations are cast as 𝜀r =

1 1 (𝜎 − 2𝜈𝜎𝜃 ) + 𝛼T Θ and 𝜀𝜃 = [(1 − 𝜈)𝜎𝜃 − 𝜈𝜎r ] + 𝛼T Θ E r E

and 𝛼T = ΩcT ∕3 = 0.033. The property data listed in Table 6.3 are taken from experimental results or from plane wave DFT calculations. Single crystal rhombohedral LiC6 and monoclinic Li2 CO3 were used to represent ideal, fully lithiated graphite and the passivating SEI layer in DFT calculations. Although these structures are highly anisotropic, Reuss’s average for isotropic polycrystals was used to estimate the Young’s modulus and Poisson’s ratio. For the values provided in Table 6.3 for the LiC6 core and Li2 CO3 shell, from Eq. (6.20), lima→∞,x →1,Ω=0 Δ𝜎 𝜃 |x=xi ,𝜏=0+ = 0.653, which is very close to the value shown in i the Figure 6.10 for the stress jump. Further, using Eq. (6.21), we calculate the corresponding dimensioned stress jump for a large spherical particle of LiC6 surrounded by a Li2 CO3 shell to be lima→∞,x →1,Ω=0 Δ𝜎𝜃 |x=xi ,𝜏=0+ = 2.9 GPa. i The Li2 CO3 (SEI) shell can be contrasted with that of a purely organic layer for the protective coating. Using the properties of polypropylene as representative of a polymer shell (𝜈𝛽 = 0.45 and E𝛽 = 1.1 GPa) [133, 134], we obtain the results plotted in Figure 6.11. Relative to the Li2 CO3 (SEI) shell, the protective polymer

0.7 0.6

(a)

Core α (LiC6)

0.5 0.4 Interfacial stress jump Δσθ

Displacement u

0.3 0.2 0.1

Radial stress σx

0 0

0.1

0.2

0.3

0.4

0.5

Tangential stress σθ

0.6

0.7

Position x= r/a

0.8

0.9

1

0.9 0.8

τ=0

Shell β (Li2CO3)

0.99768 0.99736

0.7

0.99704

0.6

Tangential stress σθ

0.5 0.4 Displacement u

0.3 0.2 0.1 0

0.99641 0.99609 0.99577 0.99545 0.99514

Radial stress σx

−0.1 0.998

(b)

0.99672 E = 0.784 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.25 xi = 0.998

0.99482 0.9985

0.999 0.9995 Position x= r/a

Figure 6.10 The LiC6 /SEI (solid electrolyte interface) system. For these results, the properties of Li2 CO3 are chosen for the SEI.

1

0.99450

Dimensionless displacement

0.8

−0.1

0.99800

1 τ=0

E = 0.784 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3 νβ = 0.25 xi = 0.998

Dimensionless displacement or stress

Dimensionless displacement or stress

1 0.9

6 Diffusion-Induced Stress within Core–Shell Structures and Implications 1

1

0.8 0.7

Core α (LiC6)

νβ = 0.45 xi = 0.998

0.6

0.4 Displacement u

0.2 0.1

Radial stress σx

(a)

0.5

0.3

0.1

0 −0.1

0.6

0.2

Interfacial stress jump Δσθ

Tangential stress σθ

0.7

0.4

E = 0.563 Ω=0 Γαβ = 0

0.1

0.2

0.3

0.4

0.5

0.6

Position x= r/a

0.7

0.8

0.9

(b)

Figure 6.11 The LiC6 /polymer-coating system. For these results, the properties of polypropylene are chosen for the shell layer (see text); all other parameters and properties are the same as those employed in the construction of Figure 6.10, allowing for a direct comparison between an inorganic SEI

0.99704 0.99672 0.99641 0.99609

Displacement u 0.99577

να = 0.3 β = 0.45 xi = 0.998

0.99545 Tangential stressσθ

0.99514 0.99482

−0.1 0.998

1

0.99736

Γβ = 0

0 0

0.99768

Shell β (polymer, polypropylene properties)

0.8

0.5

0.3

0.99800

τ=0

0.9

Dimensionless stress

Dimensionless displacement or stress

τ=0

E = 0.0563 Ω=0 Γαβ = 0 Γβ = 0 να = 0.3

0.9

Dimensionless displacement

220

Radial stress σx 0.99450

0.9985

0.999

0.9995

1

Position x= r/a

layer and that of a protective polymer. The low modulus of the polymer layer, relative to that of Li2 CO3 , (i) substantially reduces the interfacial stress jump and (ii) yields greater displacements in the shell (cf. Figures 6.3, 6.5, and 6.9).

layer reduces the interfacial jump stress from 2.9 GPa to 66 MPa, which can be compared to the tensile yield stress of conventional polypropylene of 37 MPa. To get a sense of whether these SEI interfaces would be stable, it is helpful to view plots that incorporate material strengths at failure for various materials (e.g., Figure 4.6 of Ashby [135]). For the 2.9 GPa we find for the maximum tensile stress of a spherical particle of LiC6 surrounded by a Li2 CO3 shell, 𝜎ISS (Eq. (6.24)) would need to be at least as large as the strength values associated with engineered ceramics. Conversely, the 37 MPa value for a protective polymer layer over graphite is within the range of failure strengths of many engineered polymers. The common observation that the initial SEI is inorganic in character [2, 28, 34] and the subsequent protective film growth in an organic polymer is consistent with the notion that a Li2 CO3 (SEI) shell is challenged in terms of being stable, but subsequent formation of polymer films over the inorganic shell would yield a more stable system. This line of reasoning is also consistent with the well-known fact that additives that yield protective polymer layers over the electrodes in lithiumion cells (such as vinylene carbonate) lead to improved cell life [134]. Lithium-ion traction batteries commonly last about 1000 deep charge– discharge cycles [17, 19, 20, 22]. After the initial cycles have been executed on a lithium-ion battery, we can approximate the remaining number of cycles to failure by the following relation:1) ) ( Qfinal 1∕N 𝜂I = (6.25) Qinitial 1) For a constant current efficiency 𝜂 I , the capacity Q is initially Qinitial . After the first complete charge–discharge cycle, the capacity is 𝜂 I Qinitial ; after the second such cycle, the capacity is (𝜂 I )2 Qinitial ; after the Nth cycle, the capacity is (𝜂 I )N Qinitial .

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7 Cost-Based Discovery for Engineering Solutions Brian L. Spatocco and Donald R. Sadoway

7.1 Introduction

When cost is an impediment to the adoption of new technology, further research must embed cost as a key performance criterion. A prime example is grid-level storage. The mix of uncommonly high power, long service lifetime, and low price point make technical innovation in this space exceptionally challenging. The conventional approach to research, namely, a cost-agnostic pursuit of the most advanced chemistry with the hope that one can move down the cost curve in the manufacturing of product has proved to be inadequate. For example, after over two decades of production of lithium-ion batteries their cost has not fallen low enough for them to enter the stationary storage market, not to mention mainstream electric vehicles. The remedy, in our judgment, is cost-based discovery–a process in which, even at the earliest stages of research, one must include cost as a determining factor in the choice of chemistry. In other words, the invention of a storage device capable of serving the electricity market rests on the discovery of a chemistry that derives from earth-abundant elements and a design that can be built using simple manufacturing techniques. Inventing to the price point of the electricity market means that parts of the periodic table are axiomatically off limits on grounds of scalability. In this chapter, we set forth a methodology of cost-based discovery through the example of grid-level storage. 7.1.1 The Winds of Change: Integrating Intermittent Renewables

On the morning of 31 January 2012, the residents of the west coast seaport of Esbjerg, Denmark, woke to the sound of high winds and ripping tree branches. The gusts in the early hours of the morning had been record-setting, with peak recordings at 4:00 a.m. of 54 mph that maintained strength until noon. With an average annual wind speed of 13.1 mph, Esbjerg is one of the windiest cities in Denmark and would rank in the top five windiest cities were it located in the continental United States [1]. In spite of that morning’s anomaly, the city of Esbjerg is not only Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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familiar with such energetic weather but has come to depend on it. Since 2010, Esbjerg can lay claim to hosting the largest offshore wind farm in Denmark and the third largest in the world with the complementary Horns Rev 1 and 2 rated together at approximately 369 MW generation capacity. Denmark is no stranger to wind farms or renewable energy – it is currently the largest producer of wind turbine technology and demonstrates a clear lead in turbine penetration in its own energy sector with nearly 30% of electricity capacity coming from renewable wind resources [2]. For this reason, Denmark is a common planning case study for countries hoping to augment their renewable energy portfolio with intermittent sources such as wind and solar and reliably integrate them into the existing network. A common topic of investigation is in the area of balancing grid inflows and outflows – a challenge resulting from the fact that most power grids maintain very little storage, and grid operators must therefore maintain in situ control in order to ensure dispatchable generation can meet demand. Without such minute-to-minute control, oversupply of energy from unexpected generation or undersupply driven by underpredicted demand would equate to economic loss and inefficiency. As a result, integration of intermittent resources such as wind power brings with it legitimate concerns regarding increased variability and asynchronicity between production and demand that could render a poorly planned wind farm a resource sink rather than a source. Although unusual for Danish installations, large perturbations such as the one experienced in the early hours of 31st do result in substantial impacts upon the market. In fact, Esbjerg was not alone in its overproduction, as the entire Danish western grid soon became loaded with greater than 2600 MWh h−1 production rates for 14 straight hours, 2.6 standard deviations above the hourly wind production mean for this area [3]. Shortly after the initial generation spikes from the local wind turbines, Nordpool’s Elspot energy price for the western Denmark power grid dropped to below €0 for over 4 h, indicating the need to distribute excess energy so rapidly that the western Danish grid operators were literally paying to have their excess energy exported to neighboring countries. Events such as these, though uncommon, have led some researchers to believe that Denmark’s renewable energy business model creates a perverse outcome that disproportionately exports tax-supported renewable energy at depressed spot prices to neighbors [4]. On the other side, there are just as many researchers that have shown that intermittent exports do not appear to abnormally correlate with periods of peak wind production and that wind-generated electricity goes disproportionately to satisfying domestic demand while higher merit order sources are exported or recouped [5]. In either case, there is agreement that the ability to store excess energy, regardless of its source, provides not only significant economic gain but also improved efficiency and reliability. The case study of Denmark teaches that moving towards a fully renewable future is fundamentally predicated on our ability to intelligently deploy grid-scale storage options to smooth fluctuations implicit with variable demand and intermittent supply.

7.1

Introduction

7.1.2 Cost is the Determining Factor

Although perhaps the most poignant and popular example, wind installations are just one of many integration points where storage could offer benefits in economy, efficiency, and reliability. Numerous reports [6, 7] have identified more than a dozen unique, though not mutually exclusive, functional areas in which tandem storage could improve our ability to supply electricity sustainably in excess of ∼4000 TWh [8] to US consumers. Though the United States has made great strides in the research and development of renewable energy technologies, it still lags behind several European peers with approximately 13% penetration into the electricity market in 2013. Of this 522 TWh renewable generation, ∼177 TWh, comes from intermittent sources such as wind and solar [9]. In spite of the fact that the United States electricity grid is not only significantly more physically expansive but also complicated by multiple layers of federal, regional, and local regulations that do not exist in many smaller European counterparts, a majority of states around the country have continued to set competitive targets via renewable portfolio standards (RPSs). Though variable across the nation, some geographic areas are aggregately targeting greater than 20% renewable penetration by as early as 2020. One such region, under the purview of the Western Electricity Coordinating Council (WECC), has received attention in a recent study by Pacific Northwest National Lab [10] that investigates the balancing requirements implicit in its RPS target as well as cost-effective technology options. The study found that the anticipated renewable expansion via intermittent wind would require a total of 6.32 GW of balancing power with between 0.07 and 0.22 units of new storage capacity per unit of additional wind power. Such an amount is 27% of the total existing storage in the United States [11] and would represent a significant departure from the current storage growth rate. A more detailed analysis [12] has noted that by taking into account the lifetimes of each technology as well as the full cradle-to-gate energy inputs, most modern electrical energy storage (EES) technologies fall short of being viable candidates for deployment as load-balancing solutions at the global scale. In fact, in spite of the torrent of research into high-technology solutions, the most stringent criteria for comprehensive deployment are likely the severe system cost and material availability metrics. Programs such as ARPA-E have set aggressive goals for both cost of energy and power delivery for their grid storage portfolio with 10 000) 70 (3000) Lead acid 75–90 (4500) 50–75 (1000) 75 (20000) LMB (Li|Pb–Sb) 65–70 (5 000–10 000)

Power cost ($ kW−1 )

Energy cost ($ kWh −1 )

1800–4 100 900–1 700 — 600 — 3200–4 000 445–555 — 350 — 3000–3 310 750–830 — 600 1670–2015 340–1 350 400 2000–4600 625–1 150 — 330 84b) 283b)

Maturity

Embodied ESOIa) energy (MJ kg −1 )a)

Demo

454

10

Commercial

488

6

Demo

694

3

Demo

504

3

Demo

321

2

R&D

500–700

5–14

a) Embodied energy and energy stored on investment (ESOI) data from Barnhart work [12]. b) Indicates calculation with only active component costs. Blue data from 2010 EPRI Report [6], red data from 2010 Yang Report [14], green data from various literature compiled in 2011 Sandia Report [19], orange data from 2010 Argonne Report [20], black bolded data from GroupSadoway experiments and calculations.

7.2.4 Down-Selection

Although there is a wide variety of potential LMB chemistries, determining optimal electrolyte chemistries for every couple is far beyond the scope of a purely experimental research program. Herein, we offer a systematic downselection methodology to assist in identifying the most promising chemistries for LMB development. Candidates are screened on the basis of cell couple costs, operating temperature, and scalability to assist in narrowing the scope of the laboratory work. 7.2.4.1 Cost

Because LMBs are relatively simple devices, their cell materials input costs are fairly well understood prior to scale-up and can therefore be optimized during the research stages. Typically, the active materials cost comprises between 30% and 40% of the cost of the entire unit. As a result, it is possible to de-risk the process of scale-up by first targeting cost savings through intelligent selection of

235

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7 Cost-Based Discovery for Engineering Solutions

Table 7.2 Theoretical prices (dollars per kilowatt hour) for various battery chemistries.

B (T MP , ∘ C)

A (T MP , ∘ C) $ mol−1

Li (181) $0.444

Na (98) $0.064

K (64) $5.080

Mg (650) $0.069

Ca (842) $0.140

Ba (727) $0.822

Al (660) Si (1414) Zn (419) Ga (30) Ge (938) Cd (321) In (157) Sn (232) Sb (631) Hg (−39) Pb (327) Bi (271) Te (450)

$0.056 $0.067 $0.127 $30.875 $101.372 $0.269 $66.390 $2.496 $1.648 $0.422 $0.420 $4.974 $27.886

$62 $32 $103 $2 014 $6 606 $57 $4 749 $172 $84 N/A $58 $248 $611

N/A N/A N/A $10 994 N/A $103 $13 774 $285 $86 $45 $53 $310 $653

N/A N/A N/A N/A N/A N/A $20 512 N/A $323 $519 $621 $555 $689

$24 $17 $22 $5 766 $11 128 $73 $14 162 $343 $139 N/A $96 $575 $2 193

$10 $11 $23 N/A N/A N/A $4 959 $147 $64 $38 $30 $222 $2 195

$51 N/A N/A N/A N/A N/A N/A $117 $60 N/A $36 $176 $2 222

electrode materials. Table 7.2 is a chart demonstrating the cost of various couples based on tonnage materials costs from 2012 world market exchanges [21], voltages of the various couples as distilled from previous thermodynamic literature [17], and approximate compositional utilization for each of the couples based on intermetallic presence in their phase diagram data [22]. Each estimated couple price, C est , is calculated via the following relationship: ∑ C est =

̂i xi P

i

̂cell xA,d zF E

̂i is the average where xi is the mole or mass fraction of component i in the cell, P monthly bulk metal market price per mole of component i, xA,d represents the estimated positive electrode full-discharge composition, z is the valence change ̂cell is the linearized of the ion in the redox reaction, F is Faraday’s constant, and E average equilibrium cell voltage over the discharge range. From these data, one is quickly able to eliminate various couple chemistries on the basis of cost per mole. Provided that the active materials cost makes up approximately a third to half of the total cell cost one can project that couples with active costs much over $300 would likely result in a final cell design that places behind many of the aforementioned competitive technologies as well as moving out of range of being able to address grid storage’s stringent price points. For this reason, one can eliminate couple chemistries based on K, Ga, Ge, In, and Te. These couples are highlighted in light red (Table 7.3) to signify they have been removed from consideration due to cost.

7.2

The Liquid Metal Battery as a Grid Storage Solution

Table 7.3 Symbolic representation of Table 7.2 in which red indicates couples ruled out due to price, orange due to temperature, and gray due to lack of thermodynamic data or phase separation.

(TMP/°C) Al (660) Si (1414) Zn (419) Ga (30) Ge (938) Cd (321) In (157) Sn (232) Sb (631) Hg (−39) Pb (327) Bi (271) Te (450)

Li (181)

Na (98)

K (64)

Mg (650)

Ca (842)

Ba (727)

7.2.4.2 Temperature

As noted earlier, the electrolyte tends to set the operational temperature of the device due to the higher melting temperatures of molten salts in comparison to the electrodes. In addition to having relatively high intrinsic costs due to the need for higher purity materials, the electrolyte also plays a substantive role in impacting the final cost of the device through a number of indirect, temperature-related cost contributions. For two of these cost reductions, sealing and corrosion, one is able to preliminarily estimate the savings accrued from lower temperatures. Sealing Sealing of high-temperature electrochemical devices such as LMBs

requires not only hermetic protection from the environment for keeping atmospheric contaminants such as O2 and H2 O out but also electrical isolation of the positive and negative leads. In selecting a seal for LMBs, there are two general categories to choose from: compressive and adhesive seals. Compressive seals are commonly found between metal parts in the form of metal fittings or compressed elastomeric gaskets and O-rings. Unfortunately, the need for electrical insulation rules out the use of metal-based seals. Similarly, the high temperatures of operation of modern LMBs render elastomeric materials unsuitable. As a result, most high temperature electrochemical devices, such as the NaS and ZEBRA battery, use adhesive-type seals such as glass seals or ceramic-metal diffusion bonding. A major challenge with both of these adhesive seal options is their cost and energy intensiveness. A study [23] on the cost breakdowns of 100 Ah NaS batteries used by the British Rail found that diffusion bond seals are the second most expensive part and compose approximately 17% of the total manufacturing cost of the device. In this case, the cost of sealing came out optimistically at $21.60 kWh−1 . For a similar 100 Ah LMB cell with a 6′′ diameter, the ability to seal with a simpler

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7 Cost-Based Discovery for Engineering Solutions

Teflon O-ring would cost $14.34 before bulk savings. This would represent at least a 33% savings in sealing though closer to 50% could be expected from scale-up. Such savings are only possible if the device’s operating temperature were dropped to below 300 ∘ C to enable the use of polymeric seals. Corrosion Corrosion of metals by molten salts is a well-studied and reviewed

phenomenon [24] that occurs via both dissolution and metal oxidation reactions. Both reactions are dependent on temperature, oftentimes exhibiting Arrheniustype behavior. These corrosive reactions result in self-discharge currents, parasitic capacity losses, or degradation of the cell container. Reducing the temperature can drastically suppress the aforementioned corrosion pathways and increase service lifetime. Although every salt–metal combination is different, one can look to similar systems to get a sense of the orders of magnitude decrease in corrosivity resulting from temperature decrease. For halide degradation of steel, Colom and Bodalo [25] found that for a KCl–LiCl eutectic, a decrease from 500 to 400 ∘ C resulted in a 73% decline in corrosion (0.3–0.08 mg cm−2 h−1 ). For nitrate systems [26] (KNO3 –NaNO3 ) a decrease from 630 to 600 ∘ C depresses corrosion from 0.1 to 0.01 mm year−1 . Finally, for a molten sodium hydroxide system [26] corrosion can be reduced by up to two orders of magnitude with a 300 ∘ C decrease (Figure 7.3). Thus, a depression in operation temperature can multiply the service lifetime of the device by 2–10×. This increased lifetime feeds directly back into the dollars per kilowatt hour metric by growing the amortizing period and linearly dropping the cost of energy.

Corrosion of metals in molten NaOH 1 Corrosion Rate (mm year–1)

238

Ni-201 Ni-400 Ni-600 301SS

0.1

0.01 400

450

500

550

600

650

700

Temperature (°C) Figure 7.3 Examples of corrosion rate versus temperature for common structural materials.

7.2

The Liquid Metal Battery as a Grid Storage Solution

Thermal Management LMBs require ancillary heating units to raise them to temperature from the solid state. In addition, temperature management systems are required to protect against temperature fluctuations and failure. Lowering the temperature of the device may not only bring it in range to harvest waste heat from other commercial equipment such as boilers/heaters but also reduce the capacity demands on active cooling and heating units.

Although there have been no rigorous quantitative modeling approaches to understanding the functional impact of temperature on cost in LMBs or any other high-temperature storage device (e.g., Na–S) the impact of temperature on the total cost (dollars per kilowatt hour) of the cell would be directed principally to the remaining 60–70% cost contribution of cell packing materials, assembly, ancillary systems, as well as the amortizable life. While intelligent selection of active materials directly linearly impacts the dollars per kilowatt hour metric through raw material input prices, decreasing temperature has the potential to simultaneously suppress costs from a number of downstream reductions. Based on this criterion, all negative electrode materials with temperatures far above 300 ∘ C are discounted. Though there are several positive electrode materials with temperatures exceeding 300 ∘ C, there is a pathway for alloying such metals to form low-temperature eutectics with minimal penalty to the voltage of the system. Hence, removing elements from the positive electrode column would be premature. The negative electrode materials, on the other hand, are significantly more complicated to suppress in melting temperature through alloying as doing so both decreases itinerant species activity and introduces another electropositive species that may co-oxidize and deposit during cycling. Couples ruled out due to negative electrode temperature are shown below in Table 7.3 as light orange. 7.2.4.3 Scalability

Owing to the sheer scale of the grid-storage problem space, candidate solutions may potentially infringe upon both the annual production and natural abundance of resources and constraints stemming from the need to spend large sums of energy up front in order to manufacture a large volume of batteries. Although one cannot yet use the latter energy stored on investment analysis (ESOI) to discriminate on a metal-by-metal basis, Wadia’s work [15] on the impact of resource constraints does provide an initial screening tool for determining which couple chemistries stand to create the greatest impact for grid storage. By using the 2012 annual production of raw negative electrode materials [27], an efficiency of 95%, and a voltage value averaged over all known candidate positive electrode materials [17], one is able to develop rough estimates for how much total energy storage could be built each year if the entire production were diverted toward making LMB batteries. This upper boundary defines the absolute maximum amount of storage available for a given negative electrode chemistry deployed in an LMB battery (Figure 7.4 and Table 7.4). Figure 7.2 finds that even in the impossible scenario that all global metal production is dedicated to LMB production, not all metals meet the short-term goal

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7 Cost-Based Discovery for Engineering Solutions

Li 0.00709

Element

Na

38.1 4.39

K 1.01

Mg Ca

112

10

1

1 0.

01

2.22

0.

–3

Ba

1E

240

Max annual production (TWh year−1) Figure 7.4 Energy storage production estimates shown versus 1% of the daily US electricity consumption. Table 7.4 Energy storage production estimates based on annual production of elements. Element

Ore source

Li Na K Mg

LiCO3 NaCl Potash Brine, hydroxide, carbonate Lime Barite

Ca Ba

Element mass (g)

Theoretical capacity (Ah g−1 )

Annual production (g yr−1 )

Couple voltage (vs Sb)

Energy storage potential (TWh)

6.941 22.99 39.09 24.30

0.208 0.185 0.167 0.367

3.70 × 10+10 2.80 × 10+14 3.40 × 10+13 6.10 × 10+12

0.92 0.74 0.78 0.45

0.0071 38.11 4.39 1.01

40.06 137.327

0.331 0.207

3.40 × 10+14 8.40 × 10+12

0.99 1.28

111.50 2.2

of 1% of the United States’ 2009 daily electricity usage (109 MWh). This amount serves as an annual production rate target that should simultaneously allow the United States to pursue its RPS goals in the short term (10–15 years) without incurring significant penalties from concurrent penetration of intermittency [15]. Using this metric, one is able to identify a clear difference between sodium- and lithium-based chemistries. There is also an opportunity to drastically expand magnesium production via seawater desalination though such ramp-up would likely need to occur during the same time period as renewable ramp-up is expected to take place. Following this down-selection methodology, one arrives at the conclusion that the most promising negative electrode chemistries to pursue, and therefore the

7.3

Historical Odyssey

best systems for investigating candidate electrolyte systems, are sodium based. This result is somewhat unsurprising given sodium’s low cost ($.06 mol−1 ), low melting temperature (97.8 ∘ C), lithospheric abundance (1150 × more abundant than lithium), and strongly electropositive properties.

7.3 Historical Odyssey

In addition to the more generalized molten salt investigations of the early twentieth century, historical work specifically targeting sodium-based nonaqueous electrolytes can be grouped into three rough categories: sodium metal electrodeposition, nuclear energy heat transfer media development, and electrochemical regenerative battery research. Each of these applications coveted different characteristics of sodium-based fused salts. It is interesting to understand why research in each of the three aforementioned areas came to a close and why activity was confined to a limited suite of sodium-based molten salt systems. 7.3.1 Molten Salts in Sodium Electrodeposition

Since its discovery in 1807 by Sir Humphrey Davy [28], sodium has grown in importance and usefulness as chemists and engineers have found its unique physical, thermal, and electrochemical properties of utility. Though initially a curiosity, following the discovery (1825) by Hans-Christian Oersted that sodium metal could be used to reduce aluminum chloride to pure aluminum, interest in the metal rapidly grew. Initial production methods utilized a thermochemical deposition similar to the initial technique deployed by Davy. Such approaches most commonly involved the reaction of a fused sodium salt with a variety of heated reducing agents including materials such as carbon [29–32], calcium carbide [31–34], iron carbide [35], iron [36], and magnesium [32]. The sodium salts most commonly reduced were sodium carbonate [32], sodium hydroxide [37], and sodium chloride [38]. Although bulk thermochemical reductive processes such as the Deville process [39] (1854) rapidly increased the supply of sodium to support early aluminum production and dropped the latter’s price from $1200 kg−1 in 1852 to $40 kg−1 in 1859, the process’s inefficiencies and impurities drove Charles Martin Hall and Paul Héroult to simultaneously develop an electrochemical method for production of aluminum. This leap in aluminum production coupled with the yield inefficiencies and product impurities implicit in thermochemical pathways reduced demand for metallic sodium and motivated researchers to devise a similarly efficient and cheap electrochemical manner of producing sodium. In 1888, the Castner process [40] was born. The electrochemical Castner process involves the electrolysis of sodium hydroxide (NaOH) to form pure sodium on the cathode while oxygen and water are

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generated on the anode. The primary reactions are shown below: Cathode∶ Na+ + e− → Na(l) Anode∶ 4OH− → 2H2 O + O2(g) + 4e− Owing to the hygroscopicity of NaOH and the solubility of metallic sodium at high temperatures, the Castner process also experiences a number of detrimental side reactions that act to reduce the efficiency of the process and lower the yield. Two such parasitic reactions are shown below: Water at cathode∶ 2Na + 2H2 O → 2NaOH + H2 Sodium at anode∶ 4Na + O2 → 2Na2 O In the first reaction, sodium metal produced at the cathode is lost back to its ionic state through a reaction with dissolved water. In the second reaction, sodium metal that has dissolved in the melt reacts with oxygen to form a relatively insoluble sodium oxide product. These two inefficiencies resulted in an electrochemical processing route that rarely attained greater than 50% current efficiency or 18% energy efficiency. Although seemingly unique to the NaOH system, these two loss mechanisms, the solubility of sodium in its molten salt electrolytes and the challenges imposed by contaminant water, are in fact principal challenges of modern sodium-based molten salts. From 1891 until around 1920, Castner’s process was responsible for a vast majority of the sodium metal produced in the United States and Europe [41]. It operated at around 4.5–5.0 V, a current density of 1.5–2 A cm−2 , and resulted in ∼15 000 tons year−1 (∼10 kg day−1 per cell) for nearly 30 years. In addition to the noted inefficiencies, sodium hydroxide was still a relatively energy-intensive component to produce as chloralkali Hooker diaphragm cells had not yet been invented [42]. As a result, the Castner process fell out of favor (Figure 7.5) [41] when compared to a newer process that utilized plentiful NaCl as cell feedstock. This new device, the Downs cell [43], is still in use today with only minor modifications and remains the industry standard for sodium production. It would be incorrect to say that the Downs cell was the first to use NaCl as a feed electrolyte. Rather, various configurations, including the Acker cell [44], the Ashcroft cell [45], the McNitt cell [46], the Seward cell [47], and the Ciba cell [48] were developed based on adaptations or permutations from earlier Castner concepts. Compared to this prior art, the Downs cell leveraged two distinct advantages in its design as well as its chemistry. First, it deploys a cylindrically symmetric carbon anode and steel cathode separated by an iron screen to prevent cross-contamination of electrolysis products (Figure 7.6) [49]. Secondly, it obviates the traditional challenge of high NaCl melting temperatures (MP = 801 ∘ C) by using a second CaCl2 (58% by weight) component to lower the overall operating temperature of the melt. Such a reduction in temperature not only reduces chlorine-based corrosion but also retards metallic sodium vaporization as well as sodium solubility in the electrolyte. In addition to producing higher purity sodium (>98%) the Downs cell also provides an additional benefit of

7.3

100

0

Downs cells installed at Niagara Falls

200

300 Evolution of sodium manufacturing processes Castner cell plant built at Niagara Falls, New York

Castner thermal reduction plant, Oldbury, england (300,000 lbs/yr)

Millions of pounds of sodium per year

300

1890

200

100 Electrolysis of NaCI

Deville thermal reduction process –since 1655 (12 000–13 000 lbs/yr)

1880

Historical Odyssey

Electrolysis of NaOH

1900

1910

1920

1930

1940

1950

0 1960

Figure 7.5 Historical trends in sodium manufacturing.

NaCI(s), CaCI2(s) in

CI2(g) out

CI2(g) Na(I) out

Molten NaCI/ CaCI2 Molten Na Iron screen

Cathode (−): steel cylinder Cathode: Na+ + e−

Na(I)

Anode (+): graphite Anode: CI−

1 2

CI2(g) + e−

Figure 7.6 Schematic representation of a Down’s cell for producing sodium metal and chlorine gas.

243

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7 Cost-Based Discovery for Engineering Solutions

generating pure chlorine gas on the anode. With these enhancements, the device operates between 590 and 610 ∘ C, at ∼7 V, with current densities ranging between 0.6 and 0.9 A cm−2 [50]. The overall current efficiency of the cell is around 80–90% with the losses coming mostly from solubility of sodium metal in the melt and its passage through the iron screen to recombine with anodic Cl2 product [50]. Although the NaCl–CaCl2 baths were used to great effect in the first half of the twentieth century, as applications requiring sodium metal became more advanced, their tolerances for calcium contamination in the product as well as purchasing cost became more stringent and drove researchers to investigate new sodium-based electrolyte chemistries. In 1958, Cathcart [51] investigated and patented the replacement of calcium-based chlorides with strontium and barium chlorides to reduce sodium metal impurities from 1% to 25 ppm. He also experimented with further additives such as sodium fluoride to increase the conductivity of the melt and improve the energy efficiency. Four years later, Loftus [52], also working for DuPont, patented work on a process utilizing barium-heavy salts that operated at 610 ∘ C with an efficiency of 89%. In addition to the development of the Down’s process, electrometallurgists occasionally resurrected older technologies with new approaches in hopes of finding a pathway toward cheaper and lower temperature sodium production. A 1939 patent by Gilbert [53] that improved the one-pot sodium hydroxide Castner cell by decoupling the reaction into two vessels in order to enable the usage of aqueous electrolytes rather than molten salts set the stage for two major patented works by Yoshizawa [54] in 1966 and Heredy [55] in 1969. Yoshizawa conducted electrolysis with several novel ternary systems employing NaCN, NaBr, and NaI. Such electrolytes (Figure 7.7 [54]), previously unattainable in the dehydrated state, expanded the number of sodium salt permutations available for electrolytes to work with. Similarly, Heredy’s work introduced NaNH2 as a polyanionic chemistry with the ability to substantially reduce molten salt melting points. NaOH 90 %NaOH

221

50 250 270

40 30 20

90

10 20

80 70 60

NaOH

270 250 240 230

270

250

%NaOH

30

270

230

%NaBr

50

221 50 230 240

40

60

30

70

20

80 90

10 NaI

20

70

60 240

40

220

F

T

10

80

90 80 70 60 50 40 30 20 10 %NaI

NaBr

220 230 95

200

210 240

240 30 230 230 40 240

50

%NaCN

60 70 80 90

10 NaI

90 80 70 60 50 40 30 20 10

NaCN

Figure 7.7 Experimental phase diagrams of NaI–NaOH–NaBr and NaI–NaOH–NaCN ternary phase diagrams.

7.3

Historical Odyssey

The development of cheaper and lower temperature sodium production resulted in significant growth over the next several decades. The two principal research paths that benefitted from the ample supply of sodium and advanced our understanding of sodium-based salts were the post-war nuclear power industry beginning in the 1950s and the early molten-salt-based energy storage devices that were developed in the 1960s to harvest waste heat from the rapidly growing portfolio of nuclear power plants. These two research paths produced vast physical, thermal, chemical, and electrochemical knowledge that aid our understanding today. 7.3.2 Molten Salts in Nuclear Reactor Development 7.3.2.1 Aggregated Properties

Although it had long been recognized that sodium had many suitable properties to serve as a heat transfer medium, it was not until the growth and subsequent demand of the nuclear age with its molten salt and molten metal breeder reactors (Figure 7.8, [56]) that production and research into sodium and sodium salts achieved international preeminence and support. While much of the earlier sodium electrolysis research was conducted by private companies such as DuPont and patented to secure intellectual property rights, the results of molten salt and sodium research of the 1950s and 1960s can be found more prominently in the peer-reviewed literature. Various government agencies and laboratories, including the Atomic Energy Commission, National Bureau of Standards, Argonne National Laboratory, and Oak Ridge National Laboratory, 120

Number of plants

100 80 60 40

Number of operating Nuclear power plants

20 0 1950

1960

1970

1980

1990

2000

2010

2020

Year Figure 7.8 Number of operable nuclear power plants in the United States since 1950.

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7 Cost-Based Discovery for Engineering Solutions

collaborated closely with private companies such as General Electric, Atomics International, and North American Rockwell to produce a sizable body of literature covering thermophysical properties, kinetic models, and corrosion measurements. Simultaneously, and driven by cold war competition, Soviet scientists developed a sizable tome of molten salt research. A thorough treatment of this period’s molten salt work is beyond the scope of this review and the reader is directed to a number of excellent works on general molten salt properties [50, 57], the structure and modeling of molten salts [58, 59], corrosion in molten salt systems [24, 60], and transport properties [61]. Of interest here are those works that present either physical property data for sodiumbased systems or address solubility/corrosion phenomena with sodium salts. Fortunately, beginning in 1968 the US National Bureau of Standards, under the Secretary of Commerce, contracted an aggregation of all known molten salt work up to that point (Table 7.5). Much of what is presented below (Table 7.6, Figure 7.9) has been aggregated by Janz et al. [62] in their comprehensive publications with only minor supplements from work scattered throughout the subsequent years. Considering the 10 basic sodium salts (excluding Na2 MoO4 and Na2 WO4 due to rarity), there are 45 possible binary combinations and 120 possible ternary combinations. Although with each combination there is a continuous range in compositional variation, there will generally be one, or a continuous range centered closely on one, composition that corresponds to the eutectic, which offers optimal performance for a battery electrolyte. In addition to sodium salts, sodium itinerant batteries may also be able to incorporate lithium-based salts as lithium is sufficiently electropositive relative to sodium to avoid unintended co-deposition during charge and discharge cycles.1) With this addition of 10 simple salts we are left with 190 binary combinations and 1140 ternary combinations. Although sodium binary systems have been moderately studied, the ternary systems have been nearly untouched. This is in contrast to lithium binary and ternary systems that have been exhaustively researched [81] due to their potential application in metal sulfide “thermal” batteries [82] to be discussed later. 7.3.2.2 Corrosion Mechanisms

The use of molten salts at elevated temperatures as a heat transfer medium instigated further work in sodium and sodium-salt based corrosion processes [83]. In the context of liquid metal batteries, the following processes are worth considering when mitigating the effects of corrosion: (I) corrosion of the metal container by the liquid molten salt via chemical reaction (II) corrosion of the metal container by the liquid metal anode or cathode via solubility (III) corrosion of the positive or negative electrode by the liquid molten salt via chemical reaction 1) Calcium has been shown repeatedly to co-deposit with sodium as in the Down’s cell.

T MP (K)

1253 1073

1023 935

1127 558 583 1157 960 971 583 591

Salt (references)

NaF [63, 64]

NaCl [65, 66]

NaBr [67, 68]

NaI [68, 69]

Na2 CO3 [70, 71]

NaNO2 [72, 73]

NaNO3 [72, 74, 75]

Na2 SO4 [76, 77] Na2 MoO4 [78]

Na2 WO4 [78] NaSCN [79]

NaOH [80]

2.22 − 0.74 × 10−3 T 2.32 − 0.71 × 10−3 T

13.2e−2600∕RT −1.57 + 4.38 × 10−3 T 11.89e−3819.9∕RT −3.17 + 5.24 × 10−3 T 7.45e−3931∕RT 43e−4740∕RT −3.23 + 9 × 10−3

3.8 × 10−5 e26260∕RT 187.11 − 0.87T + 1.41 × 10−3 T 2 10.41 × 10−2 e3886∕RT — —

2.47 − 0.44 × 10−3 T

−2.89 + 7.58 × 10−3 T − 2.23 × 10−3 T 2 13.75e−1327∕RT

4.62 − 0.79 × 10−3 T 526.39 − 2.49T + 3.96 × 10−3 T 2.06 − 0.47 × 10−3 T

2.62 − 4.83 × 10−3 T 3.40 − 0.62 × 10−3 T

164.77 − 0.61T + 7.80 × 10−4 T 2

— —

64.32 − 0.15T + 1.23 × 10−4 T 2 7.17 × 10−2 e5673∕RT

3.17 − 0.81 × 10−3 T 3.62 − 0.94 × 10−3 T

81.90 − 0.18T + 1.42 × 10−3 T 2

—

2.65 − 0.54 × 10−3 T

1.46 + 2.73 × 10−3 T −2.49 + (8.04 × 10−3 T − 2.22 × 10−6 T 2 ) 9.09e−2324∕RT 2.13 − 0.54 × 10−3 T

Viscosity

Density

Conductivity, k

Table 7.5 Melting temperatures, conductivities, and viscosities of common sodium-based salts.

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7 Cost-Based Discovery for Engineering Solutions

7 Electrical conductivity, κ (S cm−1)

248

NaF NaCI NaBr NaI Na2CO3

6 5

NaNO2

4

NaNO3 Na2SO4

3

Na2MoO4

2

Na2WO4

1

NaSCN NaOH

0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 50 60 70 80 90 100 110 120 130 140 150 160 170 180 Temperature (K) Figure 7.9 Plot of conductivity versus temperature for various pure molten salts. Table 7.6 Listing of all US Bureau of Standards Molten Salt Studies conducted by Janz et al. [61]. Volume (part)

Year

Description

1 2 3 4 (1) 4 (2) 4 (3) 4 (4) 5 (1)

1968 1969 1972 1974 1976 1977 1979 1980

5 (2)

1983

Single salts – conductivity, viscosity, density Single salts – surface tension Binary mixtures – nitrates and nitrites Binary mixtures – fluorides Binary mixtures – Chlorides Binary mixtures – bromides and iodides Binary mixtures – mixed halides Binary mixtures – mixed anions other than nitrates, nitrites, and halides Additional systems

(IV) corrosion of the positive or negative electrode by the liquid molten salt via solubility. Processes I and II have been variously explored in the literature as they most closely mirror those issues faced by nuclear breeder reactors and thus were the topic of inquiry for many years [84]. Process I is generally categorized by the anionic component and purity of the molten salt as this most often drives the chemical oxidation of the metal species. Process II is typically driven by solubility of one metal in another and can be understood via the location of the solidus line in a phase diagram. Though the selection of appropriate container materials for

7.3

−150

Historical Odyssey

10Na + 2NaNO3 6Na2O + N2

ΔGrxn (kJ mol−1 sodium)

4Na + 2NaNO3 3Na2O2 + N2

−152

−154

−156 0

100

200

300

400

500

600

Temperature (°C) Figure 7.10 Theoretical thermodynamic free energies of reaction for two potential nitrate reaction pathways versus temperature.

a given system is by no means a trivial task, the exploration and identification of such materials should be considered following an initial investigation into sodiumbased chemistries. In addition, several common candidate container materials such as aluminum and stainless steel have shown preliminary signs of compatibility with liquid sodium [85, 86] and molten sodium salts [87]. In contrast to corrosion of the structural components in processes I and II, processes III and IV are less studied and have more to do with the selection of active components in the battery. Process III can be subdivided into corrosion of the positive and negative electrodes, with the negative (sodium) electrode frequently being trivial as the simplest molten salts provide no potential chemical pathways for corrosion outside of those afforded by impurities such as water. Some of the salts with larger anionic species do have the tendency to react with pure or highactivity alkali metals such as the sodium nitrate in contact with sodium metal (Figure 7.10 [88]). As a result, developing a molten salt that is chemically stable with sodium metal requires purification and drying processes for simpler salts and thermodynamic calculations coupled with experimental data for more complex salts. On the other side of the battery, the reaction of sodium-based molten salts with the positive electrode is, with a few notable exceptions including NaCl, NaNO3 , and NaOH, underexplored. The development of suitable sodium molten salts therefore impacts the range of possible cathode materials (or vice versa). Corrosion process IV, the solubility of molten metallic species into molten salts, is of principal concern, particularly for sodium-based chemistries. Though it is uncommon for a metal to dissolve in its metallic state into a melt of differing

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cationic species, it has been numerously documented that sodium is highly soluble in sodium-based melts, particularly at higher temperatures in halide solutions. Bredig first observed and measured [89] this phenomenon through careful mixing, separation, and titration of sodium–sodium halide melts and found that the halide salt and metal species were mutually soluble in each other and demonstrated increased solubility at higher temperatures. Bredig and his associates later went on to use a thermal analysis technique [90], similar to modern differential scanning calorimetry (DSC), to detect minor inflections in heat absorption/emission resulting from phase separation at the edge of the miscibility gap. This technique was able to make measurements at higher temperatures with greater accuracy and was applied [91] to sodium-based melts to determine a compositionally complete phase diagram (Figure 7.11 [91]) for sodium and its various halide salts. Far from being a scientific curiosity, metal solubilization in its molten salt results in a variety of drawbacks for electrochemical processes. Early electrochemical winning of sodium using NaCl was principally held back by the efficiency losses resulting from the sodium “fogs” that indicated product loss and parasitic back-reactions. Similarly, in LMB setups, the dissolution of sodium metal not only causes capacity fade due to loss of the negative electrode but also results in reduced round-trip efficiency as the solubilized sodium can transport to the anode and oxidize. In addition, sodium solubility also worsens fade rate as the solubilized sodium increases the electronic component of conductivity [92] and promotes discharge at non-faradaic voltages. Although most work on sodium solubility in molten salts has been conducted on halide systems, literature investigating the deposition of sodium metal from non-halide melts often shows signs of sodium solubility. In a 2003 work investigating hydroxide melts as electrolytes [93], sodium deposition peaks are repeatedly shown without corresponding stripping peaks in a voltammetric scan (Figure 7.12 [93]). Nevertheless, explicit studies of sodium solubility in non-halide sodium salts or binary halide melts have not yet been conducted. New investigations of alternative sodium itinerant electrolytes must not only be aware of this detrimental tendency but will also need to quantify the solubility of sodium metal via techniques similar to Bredig’s and electronic conductivity contributions via polarization methods as developed by Wagner [94] and employed by Haarberg et al. [95, 96]. Current miscibility mitigation strategies [97] include (i) the use of mixtures of molten salts to decrease solubility, (ii) the operation of the device at lower temperatures, and (iii) further separation of the anode and cathode compartments to reduce the rate of back reaction. Determining the effect of polyanionic salt components as well as the suppression of temperatures below 300 ∘ C on solubility would be a novel contribution to the literature.

7.3

1200

Mole fraction MX. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1180°

Mole fraction MX. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

1200

Cooling curves, this work Equilibration, MAB, JWJ,WTS Equilibration, MAB, MAD

a 1100

Historical Odyssey

b

1080°

1100

NaF–Na 990°

1000

1000 Two liquids °C

°C 900

NaCI–Na

904°

900

KF–K 795° 800

800 Solid salt + Liquid metal 700

700 CsF–Cs

600

600

c 1100

One liquid 1026°

d One liquid

1100

1033°

1000

1000

°C

°C Two liquids

Two liquids

900

900 NaBr–Na NaI–Na 800

800 740° 700

Solid salt + Liquid metal

700 656° Solid salt + Liquid metal

600

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mole fraction of metal

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

600

Mole fraction of metal

Figure 7.11 Sodium metal solubility in a) NaF b) NaCl c) NaBr and d) NaI, as demonstrated with liquid coexistence curves.

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7 Cost-Based Discovery for Engineering Solutions

40 No stripping peak on voltage reversal

20 0 I (mA)

252

−20 −40 −60 −80 −100 −120 −2.6

−2.2

−1.8

−1.4

−1.0 E (V)

−0.6

−0.2

0.2

0.6

Figure 7.12 Voltammetric study at 100 mV s−1 with a platinum electrode in molten LiOH–NaOH at 270 ∘ C.

7.3.3 Molten Salts in Energy Storage Devices

Following the rapid growth of nuclear power and concurrent advances in the synthesis and characterization of molten salts, researchers began to turn their acquired skills toward a new problem – namely, power plants and reactors generated significant quantities of waste heat and there existed an opportunity to harvest this thermal energy for useful purposes. In 1958 Yeager [98] proposed the concept of a “thermally regenerative closed cycle battery” that would convert waste heat into chemically stored energy by selectively separating a binary alloy, AB, into its two constituent metals by exploiting large differentials in vapor pressure between liquid A and B. Through this process it would preferentially vaporize metal A to recharge a three-layer galvanic cell (Figure 7.13 [99]). Anode metal vapor Condenser A (g) A (I)

A (g) Anode metal Vapor Cathode alloy T2 Heat source Regenerator AB (I)

Electrolyte Heat exchanger

Cathode alloy T1 Galvanic cell A (I) + B (I)

A (g) + B (I)

Figure 7.13 Diagram of a thermally regenerative battery.

AB (I)

− Electrical power +

7.3

Historical Odyssey

253

Table 7.7 Experimental results from various thermal battery studies during the 1960s and 1970s for thermally regenerative as well as secondary bimetallic devices.

Units

Temperature Electrolyte Open circuit voltage Current density Duration

∘C V A cm−2 h

Na–Sn [103]

Thermally regenerative K–Hg [103] Na–Hg [104–106]

Na–Pb [107]

625–650 NaCl–NaI 0.33–0.43 N/A 0.3

325 KOH–KBr–KI 0.70–0.84 N/A 430

575 NaF–NaCl–NaI 0.30–0.50 0.11 45

490 Na halides 0.30–0.80 N/A 1 200

Secondary bimetallic

Temperature Electrolyte Open circuit voltage Current density Duration

Units C V A cm−2 h

Na–Sn [103] 700 NaCl–NaI 0.33–0.43 N/A 744

K–Hg [103] 325 KOH–KBr–KI 0.70–0.84 0.087 N/A

Na–Bi [107] 580 NaF–NaCl–NaI 0.55–0.75 0.667 12 240

Li–Te [107, 108] 480 LiF–LiCl–LiI 1.7–1.8 2 >300

Although this device acts similarly to the LMB upon discharge, it is important to note that it is ultimately limited by the Carnot efficiency and that its temperature is set by the harvesting of waste heat from reactors at predetermined operating temperatures. Despite these constraints, research into thermal-type batteries exploded in the 1960s and 1970s and branched into a number of different directions. In 1960, Agruss filed for the first patent on thermally regenerative cells [100] and shortly thereafter began publishing work [99] on Na–Sn systems that operated around 700 ∘ C with NaCl–NaI electrolytes. Work on similar systems (Table 7.7 [17]) grew under Atomics International, General Motors, and Argonne National Laboratory until such a point as systems that were fully electrically rechargeable were developed. These secondary bimetallic cells operated similarly to modern LMBs though with several design differences. At the time, emphasis was placed on the voltage and current density in order to maximize performance of the cells for vehicular applications. Over the next decade, secondary bimetallic battery work split into two major thrusts. The Li–Te [101], and later Li-Se [102], cell marked a shift in the research direction of secondary bimetallic cells toward high voltage and rate capability liquid metal cells for vehicular applications. After difficulty was encountered with selenium’s solubility and conductivity, work continued up the chalcogenide family until research landed on Li–S systems [109]. These systems eventually evolved into the Li–Al|Fex S systems that eventually found commercial production. On the other end of the development spectrum, although the longevity of the Na–Bi secondary bimetallic cells was impressive, liquid cells were ill-suited for

130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

7 Cost-Based Discovery for Engineering Solutions

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

254

Figure 7.14 Research papers published that focused on application of β′′ -alumina electrolytes for energy uses.

vehicular applications. This need inspired further work and development of new solid electrolytes, nearly simultaneously at Ford Motor Company (β′′ -Al2 O3 ) and at Dow Chemical Company (glass electrolyte). Both of these advancements removed the challenge of working with molten salts though necessitated that the devices operate above 300 ∘ C. By the 1980s, β′′ -Al2 O3 work came to dominate the field of Na-based batteries (Figure 7.14 [110]). Both of the above research thrusts did produce some relevant molten salt work. Prior to the widespread focus on β′′ -Al2 O3 , researchers working on the Na–Hg and Na–Bi systems patented a couple of promising lowtemperature binary/ternary chemistries including NaF–NaI–NaCN [111] and NaI–NaOH–NaNH2 [112]. Only relatively recently has work refocused on the use of molten salts as electrolytes. This is due to the recognition that the closed-one-end tube format of β′′ -Al2 O3 solid electrolytes has proved difficult to scale economically [113, 114]. As a result, Na|S and ZEBRA researchers have begun exploring “intermediate-temperature” electrolytes by using ionic liquids [115] and low-temperature molten salts mixed with aluminum chlorides [116] to achieve safety improvements without performance compromise. Large companies have also moved toward lower temperature research following NGK’s NaS battery explosion in 2011 [117]. Sumitomo, in partnership with Kyoto

7.3

Historical Odyssey

University, has announced the development of a proprietary sodium-itinerant molten salt with a melting temperature of 57 ∘ C. In spite of these recent advances, these devices all retain the β′′ -Al2 O3 separator, which imposes severe limitations on scalability and manufacturability. On the Li-based chalcogenide side, work has remained focused on molten-salt based systems. A variety of review papers [81, 82] and recent investigations into iodide-based Li salts [118, 119] can be found in the literature. Companies have also been active in developing or claiming a variety of chemistries and mixtures of molten salts. One recent patent by Fujiawa on behalf of Panasonic Corporation [120] targets Li-based molten salts with melting points between 350 and 430 ∘ C with conductivities of 2.2 S cm−1 and provides 155 quaternary mixtures as claims. Although more strategic than inventive, the approach and state of Li-based molten salt research can be used to guide work in the relatively untapped sphere of sodium multi-component molten salts. 7.3.4 The Window of Opportunity

Before embarking on a research program targeting low-temperature sodiumbased liquid metal batteries, it is important to address two important questions whose answers could indicate a null solution set to the search. 1) If low-temperature sodium-based salts exist and were researched by sodium producers, why have they not been deployed over the higher temperature NaCl–CaCl2 salts? 2) If LMB-like batteries have been known since the 1960s and sodium has been investigated as a negative electrode material, why has there not already been an exhaustive search of sodium-based electrolytes? Regarding the first question, the reaction at the anode is of great interest to sodium producers. Aside from producing valuable chlorine by-product it is also the place where undesirable reactions with larger anionic compounds could take place. Since the lowest melting temperature salts often use more than a halide-based solution, this oxidation reaction not only produces undesirable by-product but may also be highly corrosive to the device. The second line of reasoning, and likely more influential answer to the question, has to do with cost. Although the energy storage market is highly constrained by cost, the costs of the components of an electrochemical battery can be amortized over many cycles and thus the sum of each input only needs to be less than the value of energy saved over the lifetime of the device. In sodium production, the feedstock is the reactant and as a result is consumed on a one-to-one basis with the product, sodium. In this scenario, the cost of the electrolyte must come in below that of product on a per unit basis. Because of this, salts more complex than NaOH and NaCl, although researched in the patent literature, are likely not economically realistic solutions for sodium production.

255

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On the second question, during the period of molten salt battery development in the 1960s the main down-selection criteria for materials selection were vapor pressure differentials, voltage performance, and stability at high temperatures. In all of these categories, sodium is outdone by lithium due to the latter’s lower vapor pressure, lower electronegativity, and lower solubility in its salts. It was not until solid electrolytes such as sodium itinerant glass and β′′ -Al2 O3 were developed to support research into vehicular battery technologies that sodium reemerged as a potential battery component. Following these innovations, sodium-based battery research has been nearly entirely devoted to Na–S and ZEBRA cells that utilize solid electrolytes and/or membranes and as a result have not devoted much attention to fully molten electrolytes. The window of opportunity that now exists is driven by the fact that the explorations of sodium electrolytes have occurred in the context of sodium production and are limited by cost and anionic species while studies of molten salt batteries have not investigated sodium molten salts due to the historic desire to produce vehicular batteries and the subsequent attractiveness of beta-alumina based systems. Future work would harness the knowledge accumulated but not put into practice from sodium production with the increasing demands for cheap gridscale energy storage by identifying exciting candidates and systematically characterizing them for use in LMB-type batteries.

7.4 Project Description

Based on the previous analysis a credible research program would comprise identification and characterization of promising low-temperature sodium-based molten salt electrolytes for LMB applications. Historic Down’s cell studies and analogous research paths in Li-based molten salt electrolytes would supply early candidates to be initially screened through a process of thermodynamic calculations, basic phase diagram modeling, and electrochemical characterization, for example, voltammetry and impedance spectroscopy. These tests would identify candidates on the basis of their thermodynamic stability with sodium, predicted melting temperatures, and liquidity range, and electrochemical stability window. Following down-selection, a number of physical and electrochemical tests would be performed on the selected salt(s) to characterize their phase transitions, densities, conductivities, and sodium solubilities as a function of composition and temperature. These data will not only allow for the construction of experimentally confirmed binary/ternary phase diagrams but also insight into the conduction mechanisms and stability of the electrolyte(s) in question. With this baseline, electrolyte modifications such as insoluble additives and binders can be attempted.

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7.5 Conclusion

It has been systematically shown that growing demand upon energy resources coupled with the renewable targets set by nations drives one to conclude that an important enabler for a sustainable energy future is the ability to store vast quantities of energy for grid back-up and intermittent enabling. Because of the low price of natural gas and coal and the high cost of most battery technologies, current electrochemical energy storage solutions have only made very modest entry into the grid-storage market. For this reason, the development of truly low-cost grid-scaled battery systems would fundamentally evolve our grid from a wasteful generation-on-predicted-demand system to one that responds more accurately to actual usage. Liquid metal batteries, due to their simple construction, are both of low cost and predictably scalable at the sizes required to solve storage needs on the grid. Temperature has been identified as a variable that can be adjusted to provide “cascading” reductions on final assembly cost and to bring the device below the threshold for ubiquitous deployment. A number of lower-temperature sodium electrolytes has been shown to exist, yet very little work has been done on molten sodium electrolyte systems due to the restrictions posed by Down’s cell cost restrictions and Na–S/ZEBRA’s attention to β′′ -Al2 O3 solid electrolytes. The methodology set forth herein offers a path forward to bridge the gap in knowledge that exists between sodium-based electrolyte chemistries and Li-based systems such as Li–Al∕Fe2 S by scanning a handful of candidate systems and conducting a rigorous electrolyte study on those flagged most promising. By adopting a cost-based discovery model we believe that successful completion of the work would make a difference in the marketplace. References 1. Diebel, J. and Norda, J. Weath-

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8 Multiscale Study of Electrochemical Energy Systems Hany El-Sayed, Alois Knoll, and Ulrich Stimming

8.1 Introduction

The development of science has led to a huge diversification of approaches, methods and conclusions in investigating complex problems. While it is necessary to keep increasing the detail of the subjects being researched on, it becomes more difficult to fold the results back in an a priori, complex reality. It is not only the high degree of detail being covered that lets us forget where we originally started from but also the development of the different branches of science away from each other that makes it more difficult to combine results in a meaningful and scientifically correct way. Examples are the development between natural science on the one hand and, for example, engineering and medicine, on the other hand. The problems we are facing, for example, in the environmental and energy areas are so pressing that science solely as an intellectual playground cannot serve us for our future. Thus, recombining of what we have learned in the various disciplines is a necessity also for science to prove that it is useful for our future. Encouraging are approaches by theoreticians, for example, in natural science and engineering science, to attempt the so-called multiscale modeling that can bridge length scales from angstroms to meters. These attempts, however, show how difficult it is but understanding the necessity of such an approach is a crucial first step. Electrochemistry started out mainly as an empirical and macroscopic branch of science until in the 1920s and 1930s when microscopic physical models were introduced due to Heisenberg’s quantum theory. Today, electrochemical research is broadly positioned from theoretical and physical over analytical and biological electrochemistry to engineering and application. In this volume, two further aspects are covered: The history of electrochemical deposition processes in the electronics industry and, relevant also for the discussion in this chapter, the role of electrochemical engineering in battery research. In the broad spectrum of possibilities regarding the kind of approach to be taken, the question of identifying the important questions to be solved is rather controversial. A common perception is that the natural scientist solves molecular-based problems, then the Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

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electrochemical engineer takes over the study of large-scale processes, and finally the mechanical engineer designs a device and brings it to functionality. Such a process would be characterized as bottom up. This serial process is tedious and time consuming and this may be part of the reason that even breakthrough discoveries at the level of natural science may take decades before they can be converted into technology and products are available on the market. Another approach would try to use application and functionality as a starting point. Then, the various elements, for example, of a device, are described regarding their respective properties and functionalities. Improvements will be performed down to the molecular level. The efficiency of such an approach may be considerably higher since the functionality and performance are in focus from the very beginning. Typical design processes, such as the

• construction of fossil fuel power plants, wind and hydro power plants, solar thermal, photovoltaics,

• development of storage facilities, such as pressurized air, accumulator batteries, hydrogen, and solar fuels,

• construction of power grids, gas pipelines, hydrogen tanks, are performed individually, and the resulting components optimized separately. Such a process would be characterized as top down. In comparing both approaches, the latter is more direct and is often quite successful. The former, however, may go through various sidelines; it is curiosity driven. This may be more of a zigzag course in terms of a specific application but bears the potential of being highly innovative in the end. The conclusion is quite obvious; it is not good to have these two approaches as alternatives but rather in a combination. We need both qualities, and the question is how to organize this in a research environment. In the following is a schematic that tries to illustrate this (Figure 8.1). In the three elements systems, components, and fundamentals top-down and bottom-up approaches should be pursued; in the systems section and the fundamentals section top-down and bottom-up, respectively, may be more important. In the end, the mixture of both is the decisive approach. “We need to develop a curiosity for what happens with my results, so I better understand what others do with my results.” This helps to bridge the different sections. In order to foster this kind of understanding, the purpose of this chapter is to attempt to draw a line in the example of an energy system that includes electrochemical processes from a system description and evaluation and the methods to analyze those to components, to materials and down to molecular functionality. This chapter is far from being comprehensive or even complete; it is rather sketchy but with the intention to show a continuous red line combining all levels of abstraction in such a complex system. So it should not be understood as the place where one can obtain the best description of the latest research results, but it has a conceptual character trying to point out how things belong together.

8.2

Architectures of Energy Systems

Electrochemical energy systems

Up

Top Systems

Components

Fundamentals

Down

Bottom

Figure 8.1 Structure of an energy system with different components.

If this can be achieved, a better understanding of a complex research process is possible. On the basis of the discussion above, the chapter is structured in a way that first the system and its boundary conditions are described and discussed. In this discussion also the question of organization and hierarchy is addressed from the point of computer science. Then, a very simple example is described as to how a building block in an urban city (example: Munich, Germany) is powered by renewables. It shows that more than three quarters of the annual electricity demand can be covered by renewables provided you have an appropriate energy storage and management. Further on, the case of an autonomous electricity supply is assumed based on renewables. A fuel cell system is conceived that is based on bioethanol obtained from biowaste. In this direct ethanol fuel cell (DEFC), the operational concept and the materials are discussed. In the end, the important aspect of electrocatalysis and its criteria for the DEFC are analyzed. In the conclusions section, the results of the various sections are being put in perspective to each other. Especially, the aspect of top down versus bottom up is discussed again and compared to the principal ideas put up before. It is shown that the processes are not linear but rather circular in nature.

8.2 Architectures of Energy Systems

As outlined above, energy technology is still strongly influenced by hardware developments, and it is essentially about the principles of energy conversion, energy storage, and energy transport. Until now, the meaningfully coupled design of these entities, as well as the organization of the practical operation of the resulting systems, has been dealt with only on a secondary level. One example is the ongoing discussion about “smart grids”: it is now generally understood that

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computer science and communications engineering concepts will have to play a central role in both the planning and run-time phase of all layers of energy systems. This will become necessary, not only because the renewable energy supply typically fluctuates but also because there will be many more producers in close proximity to the electricity consumers, and with the advent and deployment of electric cars, storage capacity may not only be distributed, but may even be physically movable across large geographic regions. 8.2.1 The System and Its Boundary Conditions

Energy systems such as smart grids and their constituents (components and processes) are systems of systems [1]. The upcoming need for the holistic design, optimization, and operation of such systems at their various levels (from the molecule to the city) will give rise to a new interdisciplinary research field: Computational Energy Science. There are two discernible phases in the lifetime of a smart multiscale and multisystem energy system: 1) Design time: based on a specification of system requirements, available components are considered to be candidate entities, and then and only then, can the subsystems be compiled. On the basis of simulations, the borders of the subsystems are defined and redefined in an iterative cycle such that the optimal functional units and cells emerge. These units will have to be implemented and connected via hardware; therefore, the result of this phase will be a static scheme. This will have to be done increasingly on computers with massive power, so that different scenarios can be investigated in detail, that is, “exploratory simulation.” 2) Run time: when the system (composed of its subsystems) is in operation, the input, output, and dynamic requirements will change continuously depending on the timescale. To operate the system according to a set of optimality criteria, some kind of predictive simulation will be necessary. This simulation will make it possible to permanently adjust the internal system parameters to follow an optimal trajectory. Both phases are based on suitable models of systems and component behavior. From an informatics perspective, a microgrid in a car will not be much different from a smart grid section formed by a small village because of the abstraction into computational models. A typical future scenario is shown in Figure 8.2. The overarching smart grid can be logically divided into smaller cells (microgrids) that have a large autarky1) 1) There is frequently some confusion about the semantics of autonomy versus autarky. We understand autarky as the property of being self-sufficient and independent of external supply (e.g., a self-sufficient national economy that need not import raw materials from outside the country). By autonomy we mean that an entity (creature, state, system) has the quality of being self-governed, that is, the rules according to which it functions can be changed on its own will.

8.2

Architectures of Energy Systems

Physical micro-grid Networked control, virtual power station Virtual energy connections Physical energy connections Virtual control network

Figure 8.2 Future scenario for smart grid and (physical) microgrids with virtual power stations. (Image adapted from Ref. [2]. Acatech, March 2012.)

of their own. The logical limits of the virtual microgrid do not necessarily correspond to spatial constraints (such as city limits or terrain topology) or to classical grid layers, such as voltage distribution levels. Nevertheless, by defining a border, both a real and virtual microgrid define a region; such regions are autarkic if there is no energy or material stream between them. Typically, they are autonomous if they can control the internal flows (energy and materials) inside their borders based on their own rules (and there is no entity outside their borders that has control over them). This virtualization of the energy network has two consequences: (i) electricity production and consumption can be dynamically coupled and load production peaks can be compensated for very quickly, provided that the data exchange facilities between all of the entities of the network are powerful enough. (ii) For each component to be integrated into the management system, a corresponding data model is needed that can represent its (static) properties and (dynamic) behavior. The general goal is to reduce energy exchange between regions to a minimum so as to avoid transport losses and network fees. This data-driven energy distribution management approach suggests that efficient management systems be developed first, from which the criteria for the design of concrete hardware and software systems can be derived. If the behavior model(s) of a complete grid at nano, micro, meso, and macro levels are defined

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to the necessary degree of detail, realistic simulations of the energy flow can obviously be performed for an optimized planning of the grid (network topology, placement of storage elements, etc.). However, if these models can also be computed at run time, a multivariate, multilevel, online optimization can be performed, in which all those parameters that cannot be measured (or are too costly to measure) can at least be estimated. The scientific question is then how the computational resources should be spread across the entire network and how they can use the communication pathways in the most efficient way, because a fine-grained simulation will have to cope with huge amounts of data (which should ideally be kept as local as possible, in full compatibility with the principles of local use and autarky). Finally, it is important to realize that in the future, the flow in the network will not only become more fluctuant because more and more electricity from renewable sources will be fed into it – but also that the consumption will become more dynamic because electric transportation will play an increasingly more important role. Therefore, online planning based on real-time data is mandatory, and it may also prove to be very useful for integrating predictive simulations about other important aspects, such as the immediate future of the weather in a microgrid or short-term development of traffic and the resulting need for recharging electric vehicles. Consequently, energy science must deal with these questions, including the following:

• Development of new architectural structures, which interweave energy generation and consumer needs with distributed hierarchical layered “autonomy for autarky” concepts, • Development of behavior models of components and models for these models (meta-models), as well as methods for creating these models in a straightforward manner, • Definition and development of (Internet-based) communication methods for relaying status, planning, and scheduling information in real-time, with high accuracy and of the highest reliability and security to enable accurate monitoring and control of the network, • Development of mechanisms for decentralized, fault-tolerant control with possible local and (semi-)automated balancing of production, storage, and consumption, including links to temporarily available energy buffers to maintain self-sufficiency. 8.2.2 Architectures of Multiscale Energy Systems

Energy systems are networks with a certain topology in which extraction, refinement, conversion, transportation, distribution, and utilization of different forms of energy take place to provide a set of services. An energy system involves multiple interconnected “energy chains” that provide a certain energy service. Inside one system, these energy chains may, to some extent, compete with each other as

8.2

Architectures of Energy Systems

there may be multiple possible chains that lead to the provision of the same energy service (e.g., having a constant flow of electricity in one’s home – regardless of its origin, such as nuclear, fossil, solar). Clearly, today’s energy systems are of an extremely high complexity, especially on a large scale with a huge amount of interconnected energy chains. Each of these individual chains contains a large number of components (technical subsystems), into which and out of which there are flows of material and energy (commodities). They are interconnected through transportation processes. In order to make the properties of an energy system accessible to computer simulations and computer-assisted design, its overall structure (network topology and network components) and the relations between the components (commodity exchange processes) must be expressible in a machine-interpretable form. The development of a formally describable model for such energy systems has happened over a long time, beginning in 1972 [3]. Based on this pioneering work, a Reference Energy System (RES) has been developed over the years [4]. The basic layout of an energy system is shown in Figure 8.3. In [5], a new graphical representation and additional elements, which were not originally proposed by Hoffman [3], were introduced into the RES concept. They extend and enhance the original model by several concepts, which became necessary because of technology developments over time. In [6] and [7], these concepts were refined even further to become the extended RES (eRES) as available today. This is described in Figure 8.4. Using this formal (and yet human-understandable) representation, we can attach clearly defined semantics to every energy system structure. In our context of multiscale energy systems, it is particularly important that energy systems are structured into containers (typically spatial regions), which can be part of a surrounding container. In other words, due to the concept of a recursively defined container, an arbitrary level of detail can be clearly specified in terms of “is part of” or “contains” relationships. There are just a few more terms that need to be defined here to provide a basic understanding:

• A container is the basic entity for constructing hierarchical structures among the elements of an eRES. Containers can be aggregated by “grouping” elements and, conversely, they can also be disaggregated. Depending on the (variable) definition of their semantics, containers can be seen as regions for a geographical separation, or as a specific technology, for example, containing all elements consuming fossil fuel, and so on. • A process is a representation of an arbitrary physical device, which transforms commodities into other commodities. For practical usage, they have to be further specialized into internal or exchange processes. • A commodity is defined as a material stream or a set of streams that are quantitatively ascertainable and that are produced and consumed by other processes. They are typically even further categorized as internal, input, and output commodities. Storage as such is also introduced as a commodity that can be exchanged for another commodity (e.g., a fuel) for different periods of time, while the act of storing is seen a process.

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Refinement and conversion

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Figure 8.3 Example of an energy system in formal graphical notation showing the relationships between all of the defining elements of an RES using the original graphical RES representation. (Adapted from Ref. [4].)

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Architectures of Energy Systems

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Figure 8.4 Abstract energy system showing the relationships between all of the defining elements of an eRES using the graphical eRES representation.

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Notably, the concept of containers makes it possible to create top-down as well as bottom-up models in the eRES notation. In a bottom-up procedure, the elements are aggregated complex energy systems. In the top-down “design mode,” containers can be introduced that can later be gradually refined. Hence, the eRES notation is very ergonomic and user friendly, because the combined bottom-up and top-down approaches allow for hybrid modeling and extensions at any later point in time. As part of our ongoing work, the conceptual definition of eRES has been transformed into a formal alternative language, the Universal Scheme for modeling Energy Systems (USES). The advantage of USES over eRES lies in its clearly defined concepts and their relationships with each other. USES is minimal in terms of its concepts, which means that no unnecessary exceptions are introduced. This represents a significant simplification compared to eRES while offering the same expressive power – and the same power for graphical representation as depicted above. A complete formal description of the syntax of USES that takes advantage of both graph theory and the unified modeling language (UML) class diagram language can be found in [8]. To illustrate the power of the approach, we can examine the network in Figure 8.2 in more detail. Figure 8.5 shows the same network, but with labeled entities: power stations; virtual power stations; PMG, physical microgrid; VPS,virtual power station; C, consumer; PP, power station; T, transformer. This network transforms into the graphical representation shown in Figure 8.6, employing the USES graphical language. This picture corresponds 1 : 1 to a formal textual description that can be read and processed by a computer. This picture shows only the physical and virtual microgrids, whereas Figures 8.7 and 8.8 break down the physical microgrids PMG4 and PMG5 with their interconnected entities of real entities, such as power stations of various types, transformers, and individual consumers (houses, e-cars-charging stations). While the formal representations of the imaginary smart grid in Figure 8.2 can be used to model a rather small grid with few components, the USES formalism is powerful and scalable enough to be utilized for the complete description and modeling of very large grids. As an example, we can briefly review the electric power system of Singapore. Singapore can serve as an ideal example because (i) it is a small island with no connections to the outside world, (ii) the number of components is tractable even on small computers, (iii) the modeling of the entire network including its components can be completed in a short time frame, and (iv) the simulation can be performed in real-time to a great level of detail. Figure 8.9 shows the top-level topology of Singapore’s electric energy system. There are a number of power stations that are connected to each other, there are smaller substations, and there are a number of components (switches, transformer stations, etc.) that need to be controlled in an adequate manner for the smooth general operation of the grid.

8.2

Architectures of Energy Systems

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Figure 8.5 Smart grid from Figure 8.2 with annotated entities. PMG, physical microgrid; VPS, virtual power station; C, consumer; PP, power station; T, transformer. (Image adapted from Ref. [2]. Acatech, March 2012.)

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Figure 8.6 Representation of labeled smart grid from Figure 8.2 with annotated entities.

In order to present a basic impression of what this system would look like in graphical USES notation, we transformed the topology (together with some additional knowledge of the stations and the grid) into a logical description of the grid (see Figure 8.10).

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Figure 8.7 Disaggregated PMG4. This physical microgrid breaks down into a number of power stations, transformers, and consumers. ... (VPS9)

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Figure 8.9 Outline of the power conversion and transmission system of Singapore. There are five power station compounds PSC1–PSC5, each consisting of a number

of power stations. There are also switches Sw1–Sw8 and transformer stations T1–T16; not all of them are shown in this picture.

8.2

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Figure 8.10 Model of the power system in Singapore in USES graphical notation, with power lines shown as commodities. The boxes represent each entity of the grid; each

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box can be broken down into a more finegrained, lower level description. This model can be used directly for all modeling purposes (at design time and at run time).

Figure 8.10 shows the five power station compounds (PSC1 to PSC5) as aggregated source processes (where each one contains a number of power stations on a lower hierarchical level, which is not shown in the picture). PSC1 to PSC5 are connected to transformers (T1 to T13) that distribute the energy via power lines (commodities L40 to L70), isolated transformers (T13, T16), and switches (Sw1 to Sw8) to the consumers. All of the modeled entities combined constitute the power transmission system of Singapore. As mentioned before, this is only a very rough overview of the power of the USES approach. It is important to keep in mind, however, that it is the first approach to modeling complete systems in a consistent and uniform way – from the top level power stations down to the smallest consumer – so that these systems become computationally tractable – both at design time and later at run time (with the potential to transform the necessary models automatically between these two phases). In particular, the run-time models of component behavior are an essential element for the run-time optimization approach outlined in the following subsection. 8.2.3 Agent-Based Approaches for Run-Time Simulation and Optimization

Until now, we have only considered the energy flow in the heterarchy (or hierarchy) of systems. We tacitly assumed that the control of this flow would follow some basic rules; typically, in real systems the control is static (i.e., determined

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at design-time) or moderately dynamic, in that it follows some time and demand profiles over a day, a week, or a year. In future virtual autonomous networks, however, each component of the systems is connected to the overlaying data network – resulting in complete communication “reachability” between all devices. This means that all the network components can control their behavior according to knowledge about the state of the complete system, that is, they are permanently informed about the needs (of consumers), the supply situation (of power stations), the overall strategy to be followed (as determined by the network operator) as well as additional systemrelated information, such as failure or overload of components. This gives rise to the question of how such a network can be efficiently organized according to a super-ordinated general goal (expressed by a target function). This goal could be the overall minimization of transport losses, the optimal scheduling of device operation, the management of supply in certain places, or any combination of these. The control strategy must be scalable (the number of devices in the network will increase over time), it must be robust (there will always be communication and/or component failures), and it must be adaptive (the operational requirements will change at various timescales). Furthermore, the strategy must be implementable on the most diverse computer platforms and embedded systems, it must be straightforward to realize, and it must enable the components to phase into and out of the complete network at any time (“plug-and-play”). Such a system would be characterized by the following key properties:

• Simplicity: the interfaces between the power system components (hardware and software) should be easy to implement and the components’ operation should be transparent, that is, easy to monitor. • Fault tolerance: If an individual component is detected as being temporarily or permanently defective, it should be automatically phased out of the normal system operation and, if possible, replaced with one or more alternative components. The system’s performance should always degrade gracefully; it should never come to a complete stop. • Self-organization: the distributed power system must be able to form “teams” of cooperating components (agents) in (virtual) cells. At run time, team formation must be completely automatic, that is, only dependent on the tasks to be performed (and on the state of the environment). • Heterogeneity and integration: the system should allow for the transparent combination of components of different principles of operation and of different performance levels. It must be possible to establish online control loops on demand, which makes it necessary to provide communication modes that guarantee realtime interaction between all individual components. As outlined in [8] for sensor networks, our approach to solving this multifaceted problem space is the contract network protocol [9, 10]. The extension to power systems (which are, in essence, sensor-actuator-networks) is straightforward. Before doing so, let us briefly look at organization theory [11], which forms the basis for our study.

8.2

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Figure 8.11 (a–d) Different forms of hierarchical organizations.

The “nucleus” – the smallest functional unit – of our overall model of power system organization is an agent, that is, a network component with some functionality (conversion, distribution, storage), together with an automatic controller and some communication abilities. The agent is connected to the network. It can control its own behavior over an infinite period of time, but it can also correspond with any other agent in the network to synchronize its behavior with other agents. Synchronized agents are called teams, and teams can form over time – in a transient or a permanent manner. The team structure is specified by the relations between team members. These depend on the capabilities of the team members, which are defined by assigning competences and responsibilities to them. An obvious choice for a structure is the simple hierarchy in Figure 8.11a, where the agents A1 … Ak at the lower level all specialize in unique classes of tasks (for which they are individually competent and take responsibility). In an example from human organizations, the mandator M would be an executive officer who wants a report to be printed and bound and who controls every step in this process by successively having it typed (A1 ), copied (A2 ), and so on. In the context of our smart grid, this implies that certain agents may specialize in particular tasks, such as power conversion; others work on different problems (e.g., bi-directional switching, up-down transformation, establishing communication paths, or coordinating subordinated agents). There need not be a temporal relation between agent operations (i.e., a certain operation is done before the other), but clearly a relationship between them in that they may all be sensibly coordinated by one superior mandator. A different form of hierarchy is shown in Figure 8.11b, where a team of nonspecialized agents works on and returns complete solutions to the upper-level agent (e.g., a pool of typists are given tasks by the upper-level agent according to their current workload). This would correspond to several instantiations of the same agent type (with equal competences and duties) that can handle tasks depending on their current load – for example, an array of solar generators that can be individually controlled. In an extended hierarchy there may be more than one level of coordinating agents. Agents at the lower level may communicate with each other (e.g., for computation load compensation), but they are still individually identifiable by the upper-level agents; see Figure 8.11c. However, if there are nonspecialized agents on the same level, then there is a potential for these agents to coordinate themselves by exchanging information directly without any arbitration by a superior agent, Figure 8.11d. This is the

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(a)

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concept of lateral structures. Both hierarchical and lateral structures may coexist in one network; subtrees are structured laterally and organize their cooperation within their layer of the subtree autonomously after receiving a certain task from their superior agent (or the external mandator M). In such organizations, there is no coordinating authority, and agents may be members of different transient teams. In more detail, Figure 8.12a shows the situation for a completely flat organization: every agent can be a member of any team; teams are formed in a transient manner upon demand. The organization is completely determined by the task injected into the system and the current load, as well as system parameters. The shaded areas show different teams that may coexist (and may never appear in this

8.2

Architectures of Energy Systems

exact configuration again). Agents may be members of different teams at the same time (and have an internal queue for scheduling the activities they have to perform for the different teams). In an extended hierarchy (Figure 8.12b), there are flat structures at different layers. Layers on top of another layer can exert a certain level of control, that is, they manage the agent sets on the lower level and are managed by their upper level. While this concentration of decision power introduces single points of failure (there is only one top level agent), it also reduces the need for synchronization work, that is, bandwidth and time needed for forming a team. As depicted below, usually no recommendation for structuring the network can be given a priori. Typically, only extensive simulations can answer this question. Clearly, however, given the power of today’s networks, even this structuring can be dynamic – depending, for example, on the prevalent task at a certain time of the day. Let us construct an example and assume that mandator M wants a certain task to be worked on, for example, the overnight recharging of a small number of electric cars in a neighborhood in the PMG. It injects this task into the network by negotiating with a number of candidate agents, and the first agent (called 1 in Figure 8.13a), which has the competence to communicate with the energy exchange broker, starts working on the task. It determines what the current price would be for importing electricity for recharging the car fleet – either simultaneously (all cars together) or sequentially (car by car over a longer period of time). It then hands over to agent 2 (again, after a negotiation phase with similar agents such as 2), which gathers local information from other agents about the state of the components (storage levels, current energy supply from power stations, expected consumption for the next few hours, etc.). Based on the information gathered, it constructs a plan for this specific situation. The execution of this plan is negotiated with other agents, which offer their services to agent 3 and have the ability to dispatch the recharging process (because they are part of the recharging infrastructure). In cooperation with agent 4, agent 3 then executes the charging; after its completion, billing and termination activities can be handled by yet other agents, 5 and 6. Figure 8.13b depicts a situation in which agent 4 terminates its work because of a hardware failure and another agent with the same competences takes over. Finally, M

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Figure 8.13c shows a configuration in which there are a number of parallel tasks injected by several mandators (which is the normal case), and permanent negotiations take place between all agents in the network for performing the subtasks. Agents used sequentially in processing more than one task are shaded in gray. In this example, agents 1, 2, and 3 are responsible for information processing in the PMG. They could be replaced easily by other information processing agents in the network that can perform the same tasks, depending on their workload. Clearly, one could even think of a completely centralized solution, where all of the information collection and data management is done in a remote data center outside the PMG. This would, however, violate the principle of autarky, would cause much more traffic, would be less resilient in high load situations, and would be much more vulnerable to network component failures, and so on. Nevertheless, a limited hierarchy could be a viable alternative, where one centralized top-level agent per PMG is the single entry point for all tasks, and a number of equally competent agents for one (sub)task class would be below this agent (this would be the situation according to Figure 8.13b). To compare these two situations from an information processing perspective, we have conducted extensive simulations with a large number of parameters. These parameters included (among others) the network size K, a required fixed deadline for a given task, the completion probability V (the percentage of tasks successfully completed before a given deadline), the probability b of an agent accepting an offered task, the failure probability f (of an agent being unable to complete the task), and the repair delay r (time after an agent failed to resume its work). We conclude by looking at one result: the performance of the network when reconfiguration is necessary because of the failure of individual nodes. Figure 8.14 illustrates the effect of increasing the network size K and varying the failure probability f , which was 0.01 and 0.05, in Figure 8.14a,b, respectively. In addition, the performance of flat (fl) and hierarchical (hi) organizations are V 90 80 70 60 50 40 30 20 10

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V

90 80 70 60 50 40 30 20 10

f = 0.05 b = 0.5 f1 f1

b = 0.3 b = 0.5

hi b = 0.3 hi

10

20

30

40

50

K

completion probability. (a) Low failure probability f = 0.01 and long repair delay r. (b) Same parameters but high failure probability f = 0.05 and long repair delay r. The repair delay in these cases is 10 times longer than the required completion deadline.

8.3

The Big Picture

shown for different degrees of task acceptance probabilities b (the reciprocal of task complexity). In the case of low failure probability f (Figure 8.14b) fl is superior to hi: even with small network sizes, fl provides a higher percentage V of tasks completed successfully than hi. This advantage increases with growing network size K because the set of potential agents that a mandator may select from becomes larger in the case of fl. This is also true in the case of high failure probability. Here, too, a larger network size will increase the likelihood of finding a working agent, reducing the average amount of time needed for repeated futile negotiation phases. Moreover, in a larger network an increase in complexity (b getting smaller) results in less degraded performance for fl when compared to hi. Nevertheless, we note that with small network sizes, hi shows a better performance than fl. Still, as K increases, a break-even point is reached, at which fl’s performance exceeds that of hi. A more detailed analysis is beyond the scope of this chapter, but the modeling tool and the simulation with a very rich parameter set make it possible to design autonomous energy systems with very high precision with respect to a desired target by looking at various scenarios. However, even the presented analyses show that there are many ways of organizing a complex network of interdependent communication and energy flows – and that there is no “one-architecture-fits-it-all” approach to setting up these systems. Nevertheless, if there is a certain degree of redundancy in the hardware structures and the communication pathways are sufficiently developed to handle protocols such as the contract net protocol, the control software can provide an unprecedented degree of flexibility!

8.3 The Big Picture 8.3.1 Centralized versus Decentralized Systems

A critical endeavor for researchers in the field of energy systems is to transform our energy landscape toward a sustainable and green future. Based on the existing energy storage technologies, we believe that we need not only a restructuring and decentralization of the electricity production, but also a whole new architecture of the energy system in order to tap the full potential of smart production, transportation, and storage of electricity. As will be shown later, the establishment of quasi-autonomous energy clusters can be a solution to reduce the need for grid extension considerably. Given the rapid development of renewable energy we are currently facing, there are two design approaches one could pursue in the structuring of our energy system: The top-down approach (i) is to construct large-scale wind parks and photovoltaic (PV) sites, and to heavily invest in grid extension for the transport of electricity to the consumer and the increase of the storage capacity of the grid. This approach will most probably lead to the fulfillment or even over-fulfillment

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(a)

(b)

(c) Figure 8.15 Scalability of energy clusters by choice of technology from single homes (a), to blocks (b), to districts (c). (Reprinted from Ref. [12].)

of the obligations for electricity production on the way to a completely renewable energy supply by 2050. However, in this scenario effective energy management is restricted to a limited number of large-scale storage technologies, such as pumped-storage power plants and compressed air storage sites. In addition, grid extension to that extend can be quite costly. In contrast, the bottom-up approach (ii) favors self-sustaining and largely autonomous energy clusters together with a need-based, local production of electricity. By this, one could minimize the need for energy storage and greatly reduce supplementation from the grid. With the right choice of technology for energy conversion and storage, those energy clusters could range from single-family homes to city blocks or even whole districts, production sites, and small remote villages (see Figure 8.15). All of this demands the development of an efficient management structure, hereafter referred to as computational energy science, under which those energy clusters can act as quasi-autonomous microgrids. A novel architecture of the energy system based on energy clusters could focus on the combination of multiple small-scale technologies to design generation, storage, and consumption in a smart way. Figure 8.16 depicts what an energy cluster within the smart grid could look like. In Chapter 2 some governing principles were described; see also Figure 8.5. 8.3.2 Decentralized Energy Systems: a Closer Look

In a decentralized energy system the energy production facilities are located closer to the sites of energy consumption. The key point of a decentralized energy system is that it allows for more optimal use of renewable energy as well as combined

Energy cluster Self-sustaining, largely autonomous micro grid

Smart grid Implementation of information nad communication technology to the power grid

8.3

Volatile generation Wind and PV produce electricity depending on weather and time of day

PV site

Controllable generation In times of no wind and sunshine controllable plants take over

The Big Picture

283

Biomass power station

Electricity is fed into grid Natural gas power station

Wind park

Large-scale consumer Control center with variable load profile Assessment of grid data and Some large-scale Consumers management of production and demand consumers adapt their extract electricity electricity demand to from grid Photovoltaics production Need-based generation of electricity for domestic appliance Smart meter Digital electricity meter regulates demestic appliance with repect to pries and user input

Pumpedstorage plant

Energy storage Excess electricity is stored and fed into grid on demand Redox flow battery Medium-scale storage technology provides electricity during load peaks

Heat pump Heat pump operates in times of small load (e.g., at night) and during high wind production

Figure 8.16 Smart grid architecture featuring autonomous energy cluster. (Rearranged from Ref. [13].)

e-Mobility Li-ion battery is loading when renewable production is high or remaining load is small

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8 Multiscale Study of Electrochemical Energy Systems

heat and power, simultaneously reducing fossil fuel use and increasing overall ecoefficiency. The use of decentralized energy systems is a relatively new methodology in the power industry in most countries. Traditionally, the power industry focuses on developing large, central power stations where the power is generated and then transmitted across long distribution lines to sites of consumption. On the other hand, decentralized energy systems seek to put power sources closer to the end user. Sourcing energy generation in a similar decentralized manner as that of the end users can reduce the transmission and distribution inefficiencies, and the related economic and environmental costs. A decentralized system relies mainly on distributed generation and energy storage. The primary element of a decentralized energy system is distributed generation, also known as on-site generation. Although both heat and electricity can be generated in a decentralized system, only electricity can be transported over larger distances while heat needs to be consumed within some 10 km. Switching to decentralized power generation allows for heat and power generation coordination in combined heat and power plants, for example, by using fuel cells. This in turn results in increasing the system’s efficiency because heat is a by-product of many electricity-generating techniques. The use of more than one generation of sources in a decentralized system may lead to new difficulties in controlling supply to best match demand. However, storage techniques such as batteries, compressed air, and pumped hydro storage can help in storing energy when supply exceeds demand and feeding it back into the

Wind power partially used for electrolysis

Main generation by wind in north

Combined heat and power by fuel cells Transport and storage

Energy storage by redox flow batteries

Smart demand side management Some generation by PV in south (a)

Generation by PV on site (b)

Figure 8.17 Possible scenarios for layouts of centralized (a) and decentralized energy systems (b) in Germany.

8.4

Storage Components

grid during peak hours. Storage is particularly useful for intermittent renewable energy plants, which often produce electricity at their highest capacities during nonpeak hours. In the next section, we give a brief overview of the main storage devices that can be integrated into a decentralized energy system. Figure 8.17 shows a comparison between a centralized energy system (Figure 8.17a) and a decentralized energy system (Figure 8.17b) in Germany, where the latter offers a combination of multiple small-scale technologies to design generation, storage, and consumption in a smart way. The decentralized energy system is characterized by the generation of electricity where it is needed, and a minimum need for energy storage and minimal supplement from the grid.

8.4 Storage Components 8.4.1 How to Store Energy

The technical performance of energy storage devices is mainly described by four key parameters. The energy density (i) is the amount of energy stored in a system of given mass (gravimetric) or a region of space (volumetric), while the power of an energy storage device per mass or volume is referred to as the power density (ii). The time of energy storage characteristic for a specific device design is called storage time (iii), and internal reactions, which reduce the stored charge in a device without any load connected in the external circuit is the so-called self-discharge (iv). The above-described criteria apply to different technical realizations of energy storage systems. One generally distinguishes between thermodynamic energy storage devices that store energy as latent heat and electrical energy storage devices that allow multiple ways of energy conversion. A representative of the first category is building material featuring micro-encapsulated phase change materials (PCMs) that absorb heat when they change from solid to liquid and release heat and vice versa [14]. The second category is represented by (super-) capacitors (energy stored in electric fields), batteries (energy stored in the charge state of single molecules within an encased system), or flywheels and pumpedstorage power plants (energy stored mechanically). Furthermore, chemicals (such as hydrogen) can be used for long-term energy storage in combination with converters (e.g., fuel cells). Figure 8.18 puts several battery-related technologies into context with electrical and mechanical energy storage devices. In general, electrochemical energy storage possesses a number of desirable features, including pollution-free operation, high round-trip efficiency, long cycle life, low maintenance, as well as flexible power and energy characteristics to meet different grid functions (like load leveling and power quality management) [15]. Therefore, the next section focuses on some of the most relevant electrochemical energy storage systems.

285

Long duration flywheels

Metal–air batteries

minutes

Discharge time at rated power

hours

8 Multiscale Study of Electrochemical Energy Systems

ZnBr

Redox flow batteries VRB PSB

Pumpedstorage plant Compressed air

Na-S batteries

High energy supercaps

En

erg

yM

an

ag

Lead-acid batteries

em

en

t

Ni-Cd batteries Li-ion batteries Br

idg

Other advanced batteries un

int

High power flywheels seconds

286

ing

po

we

Po

r

we

rq err up and ualit ted y po we rs up p

ly

SMES*

High power Supercaps 1 kW

10 kW

100 kW

1 MW

10 MW

Systems power rating

100 MW

1 GW

Superconducting magnetic energy storage

Figure 8.18 Comparison of power rating and discharge time for various energy storage systems.

8.4.2 Selected Energy Storage Devices

Electrochemical energy storage devices can be classified in terms of their diverse operating principles. Regardless of their specific internal chemistry, batteries store energy through charge transfer reactions within their electrode structure. Redox flow batteries (RFBs), in contrast, possess storage tanks containing redox species that are continuously circulated through the cell under change of their charge state. In supercaps, an electrical double-layer arises at the electrode/electrolyte interface, that is, energy is stored in the electric field between spatially separated charges. Consequently, supercaps could be categorized as both electrochemical and pure electrical energy storage devices. Finally, fuel cells represent yet a different, non-rechargeable kind of electrochemical storage system, since the energy is stored in the reactants (hydrogen, ethanol, etc.) that are externally fed to the device. 8.4.2.1 Li-Ion Batteries

Figure 8.19 compares a state-of-the-art Li-ion battery pack used in battery electric vehicles (BEVs) with a standard lead–acid car battery. The mature scientific approach of Li-ion technology to intercalate Li+ ions into host structures outperforms conventional batteries in terms of energy and power density, no matter what battery chemistry it is compared to (see Table 8.1). The reaction mechanism is summarized in Eq. (8.1).

8.4

Storage Components

Positive plate set Pack of 18 modules

single module Plate module Negative plate set Single negative plate

Stack of 12 battery cells

(a)

(b)

Negative mesh Positive plate PbO2 Positive shield Positive mesh

Figure 8.19 (a) Li-ion battery pack comprised of 216 single cells in 18 modules [16] and (b) standard lead–acid car battery. Table 8.1 Key parameters of state-of-the-art batteries with different chemistries [17]. Battery type

Pb

Ni–Cd

Ni–MeH

Na–S/Na–NiCl2

Energy density volume (Wh l−1 ) Energy density gravimetry (Wh kg−1 ) Power density volume (W l−1 ) Power density gravimetry (W kg−1 ) Self-discharge Fast charging

90 35 910 430 + −

150 50 2000 700 + ++

200 70 3000 1200 + +

345/190 170/120 270 180 − −

Li+ + e− + 2Li0.5 CoO2 ↔ 2LiCoO2 LiC6 ↔ Li+ + e− + 6C

(cathode) (anode)

LiC6 + 2Li0.5 CoO2 ↔ 2LiCoO2 + 6C;

ΔU0 ≈ 4.1 V

Li-ion

300–400 200–300 4200–5500 3000–3800 ++ +

(8.1)

In state-of-the-art rechargeable Li-ion batteries transition metal oxides serve as reversible cathode materials [18]. Lithiation of the transition metal oxides results in LiMO2 compounds (in most commercial systems M = Co) that serve as the source of lithium in the cell. As an anode host structure that allows Li intercalation, most Li-ion battery types rely on graphite, whereas the standard electrolyte solutions are alkyl carbonate solvents. Beyond the above-described graphite–LiCoO2 system that powers most of today’s portable electronic devices, such as laptops and cell phones, there is a new generation of Li-ion batteries that features novel anode and cathode materials. A compendious presentation of these advanced Li-ion battery concepts is far beyond the scope of this chapter and there are excellent reviews that provide a comprehensive overview of the recent developments [19]. However, one particular system shall be highlighted here, which renders Li-ion technology suitable for stationary applications, such as load leveling.

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8 Multiscale Study of Electrochemical Energy Systems

By introducing lithium titanate Li4 Ti5 O12 (LTO) as a new anode intercalation material and combining it with highly stable LiMPO4 cathodes, the resulting battery system exhibits very prolonged cycle lifetime, impressive stability, and excellent safety features [20, 21]. LTO electrodes are inferior to graphite in terms of their capacity, which leaves LTO-based batteries with rather low energy density. However, in terms of load leveling applications for which energy density is not important, LTO electrodes seem highly suitable, because they are very fast and excel in low temperature performance [22]. At the redox potential of this electrode there are no major reduction processes of standard electrolyte solutions. Because of this fact, LTO electrodes exhibit very prolonged cycle life. As a family of cathode materials LiMPO4 and especially its representative LiFePO4 feature a practical capacity that almost reaches the theoretical one (165 out of 170 mAh g−1 ). It furthermore possesses an excellent rate capability even at low temperatures and very good safety features. As another decisive advantage, it is much less thermally active with standard electrolytes than lithiated transition metal oxides. Prototype cells employing the upper combination of novel anode and cathode materials represent impressive demonstrations of how Li-ion technology can contribute to the storage of renewable energy. 8.4.2.2 Post Li-Ion Batteries

Apart from the long-commercialized Li-ion battery concept, significant research effort is put into Li–S and Li–air systems, the so-called post Li-ion batteries. For use in BEVs the theoretical energy density of Li-ion batteries (387 Wh kg−1 ) is too low to approach the desired driving range of ∼500 km between charging [23]. The move from Li-ion to Li–S and Li–air would represent a great leap forward in terms of energy density. The reaction products on the cathode side, namely Li2 S and Li2 O2 , store more lithium and hence more charge per unit mass, than LiCoO2 . On the anode side lithium metal stores more charge per unit mass than Li-intercalated graphite electrodes. Figure 8.20 depicts a schematic representation of Li–S and Li–air batteries, while Eqs. (8.2) and (8.3) provide the main reaction mechanisms. S + 2Li+ + 2e− ↔ (Li2 S)solid 2Li ↔ 2Li+ + 2e− 2Li + S ↔ (Li2 S)solid O2 + 2Li+ + 2e− ↔ (Li2 O2 )solid 2Li ↔ 2Li+ + 2e− 2Li + O2 ↔ (Li2 O2 )solid

(cathode) (anode)

(8.2)

ΔU0 ≈ 2.0 V (cathode) (anode)

(8.3)

ΔU0 ≈ 4.1 V

In Li–S batteries, the Li–metal anode is oxidized upon discharge, releasing Li+ into the electrolyte (vice versa upon charge). At the cathode, elemental sulfur is reduced upon discharge to form various polysulfides. These compounds then combine with Li+ to form the final discharge product Li2 S (on charging it is decomposed again to S + 2Li+ + 2e− ).

8.4

+ e− Li2S2 and Li2S

e−

e− Li2S2/Li2S

S8 Li+

Li2S8

Li+

Li2S6

Li+

Li2S4

Li+

Poly-sulfide redox-shuttle

Li2S4

Current-collector

Separator Li

e−

+

−

Current-collector

e−

Storage Components

Sulfur-electrode (e.g., porous carbon)

Li-electrode

Separator

e−

e− c

c

c

c

Li2O2/Li2O Li+

Li

O2 (air)

LixO2

(H2O, CO2)

Li2CO3 LiOH Li-electrode

c

c

[LiO2]solv.

c e− Porous air-electrode

+

−

Current-collector

(a)

(b) Figure 8.20 Prinicple of Li–S (a) and Li–air battery (b) [24].

Li–S batteries represent a promising concept due to (i) the natural abundance and low cost of sulfur and (ii) the high theoretical energy density of 2567 Wh kg−1 [25, 26]. However, major drawbacks that hampered the commercialization of Li–S technology are (i) the poor electrode rechargeability owing to the solid reaction product Li2 S (“cathode clogging”) and (ii) the diffusion of polysulfide intermediates Li2 Sn (3 ≤ n ≤ 6) to the anode (“capacity fading”). In Li–air batteries, molecular oxygen O2 from air enters the cathode’s porous carbon structure. It dissolves in the electrolyte found inside the pores and is reduced to O2 2− upon discharge. In combination with Li+ , produced at the anode as in Li–S batteries, the final discharge product lithium peroxide Li2 O2 is formed (on charging, it is decomposed again to O2 + 2Li+ + 2e− ). Li–air batteries offer an even higher theoretical energy density than Li–S of 3505 Wh kg−1 . Among others, the most apparent problem of Li–air batteries, which they also share with polymer electrolyte membrane fuel cells (PEMFCs), is the oxygen reduction reaction (ORR). Until now, no research group has succeeded in the synthesis of a suitable ORR catalyst to replace high-cost noble metal catalysts such as Pt, Au, or Pd. The designing and preparation of highly

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active non-noble metal cathode catalysts for Li–air batteries and PEMFCs is one of the most eagerly pursued targets of modern electrochemistry. A common R&D challenge of both Li–S and Li–air technology is the poorly controlled Li/electrolyte interface at the anode side. An improved Li–metal anode design or an alternative material is a prerequisite for both systems to advance to maturity. 8.4.2.3 Redox Flow Batteries

For energy storage in the medium scale (10 kW to 10 MW), RFBs offer a multitude of advantages over other technologies, such as flexibility (energy and power scale independently), depth of discharge, rapid response, instantaneous refueling, high cycle lifetime, and good safety features (nonhazardous materials). This renders RFBs a suitable device when it comes to applications such as load leveling or power quality control. In typical RFBs, two external reservoirs contain soluble electroactive species. These are continuously circulated through the cell and undergo a reduction/oxidation process at the interface with the respective electrode. To maintain electroneutrality, an ion-selective membrane separating the positive and the negative redox species within the two flow compartments allows the transport of non-reaction ions, for example, H+ [27]. Successful prototypes mostly rely on the all-vanadium chemistry with a V2+ /V3+ redox couple in the negative compartment and the corresponding V4+ /V5+ redox couple in the positive compartment [28]. Table 8.2 lists several other RFB chemistries and the corresponding cell voltage, efficiency, as well as energy and power density. Here, special focus shall be placed on a new concept featuring the so-called mega ions that contain multiple transition metal redox centers. Since the energy in RFBs is stored in the form of reduced and oxidized electroactive species in the electrolyte, the use of mega ions offers a great potential. Multiple redox states and the high number of electrons per unit volume could lead to considerably higher energy and power density than in conventional RFBs. Under electrochemical analysis, mega ions have been proved to exhibit fast Table 8.2 Main parameters for the characterization of different redox flow battery chemistries. Redox couple

Iron–chromium All-vanadium Vanadium-bromide Mega-ions

𝚫Ucell (V)

Overall efficiency (%)

Energy density (Wh l−1 )

Power densitya) (W m−2 )

1.2 1.6 1.4 1.5

95 83 74 96b)

13–15 25–35 35–70 250c)

200–300 600–700 220–320 2000

a) Estimated as measured current density times cell voltage. b) Coulomb efficiency of half-cell. c) Estimated value based on solubility of 1 mol l−1 and six electrons per redox molecule [29].

8.4

Storage Components

and reversible multielectron redox activity [29]. Besides, their application in RFBs and also in supercaps could possibly benefit from the advantageous properties of mega ions. However, RFBs and supercaps relying on mega ions have not reached a state beyond laboratory status. 8.4.3 Application to a City Block

In an exemplary simple calculation, we want to outline the capabilities of such energy clusters in terms of need-based production and autonomy. The energy cluster we consider in the following is a 100 × 100 m2 five-story city block in Munich, Germany, with a net floor space of 9000 m2 (see Figure 8.21). The first floor is assumed to accommodate shops and service industry with an average electricity consumption of 100 kWh (m2 a)−1 [30]. From the second to the fifth floor two-person apartments will be established. Assuming a standard size of 80 m2 per apartment, the contemplated four stories provide space for 450 apartments. Under consideration of an average electricity consumption of 2500 kWh a−1 for a two-person household the total electricity demand of the energy cluster amounts to 2 025 000 kWh a−1 [30]. On the generation side, a multitude of renewable energy converters comes into play; all estimates are based on the typical climate situations of Munich, Germany. The roof area of 9000 m2 can be equipped with panels of advanced

30 m

100 m

30 m

100 m

Legend PV module Redox flow battery

Organic PV

Wind turbine

Pumped-storage plant

Figure 8.21 Largely autonomous city block as example for energy cluster.

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8 Multiscale Study of Electrochemical Energy Systems

monocrystalline solar cells that nowadays possess an efficiency of more than 20% [31]. Presuming an irradiance of 1000 kWh (m2 a)−1 , an air mass of 1.5, and a flat roof with an orientation of the panels toward the south, and taking into account 25% of losses (due to shadowing, snow coverage, reflection, etc.) a PV generation of 1 350 000 kWh a−1 is feasible [32]. Furthermore, organic PV covering the inner yard of the building can produce 75 000 kWh a−1 , implying the same parameters as before and an efficiency of 10% [31]. An additional installation of eight house wind turbines with a power of 10 kW per turbine and 2000 full load hours per year could contribute 160 000 kWh a−1 . In total, the on-site generation of the energy cluster sums up to 1 585 000 kWh a−1 . In consequence, only a difference of 440 000 kWh a−1 cannot be produced by the cluster itself and has to be supplemented from the power grid or by other kind of decentralized power production (e.g., by fuel cells). This is equal to 22% of the total consumption. Besides energy demand and generation, the third pillar that the energy cluster is based on is energy storage. An ambitious goal would be to store 30% of the daily consumption, in order to account for the volatility of renewables. Upon the installation of four small-scale pumped-storage units with a volume of 106 l each, the height of 15 m from the top floor to the basement of the building results in a storage capacity of 220 kWh. An advanced RFB featuring an energy density of 0.25 kWh l−1 (this is based on the possibly achievable energy density using mega ions) would be a suitable energy storage device to store the remaining 1440 kWh. For this scale of application, the electrolyte storage tanks would need to contain 5760 l of electrolyte, which is a reasonable size for stationary devices. All in all, the results of this assessment render energy clusters a self-sustaining and largely autonomous element of novel energy architectures. In case of a completely autonomous cluster where a supply of the residual electricity through the grids is not feasible or not desirable, additional systems with a high availability need to be set up. One such system that uses a fuel that has very low carbon footprints is the DEFC. Ethanol can be produced from organic waste, which is plentiful and does not interfere with the food chain. In the next section, we discuss DEFCs as an energy conversion supplement and how it fits in the big picture of decentralized energy systems.

8.5 Conversion Components, DEFC 8.5.1 Introduction to DEFC

Fuel cell technology promises to sustainably change electrical energy production by being significantly more efficient and environmentally friendly than the traditional combustion of fossil fuels. Fuel cells are electrochemical devices that

8.5

Conversion Components, DEFC

convert chemical energy to electrical energy through electrochemical reactions and so they are not limited by the Carnot efficiency. The basic operation of a hydrogen fuel cell is fairly simple, being the reverse of water electrolysis [33]. PEMFCs are generally considered to be among the most advanced fuel cell technologies. In a PEMFC, hydrogen is oxidized (reaction (8.4)) by a platinum (Pt) electrocatalyst at the anode, generating electrons and protons. The protons migrate through a proton-conducting membrane toward the cathode, which is also composed of Pt or Pt-based alloy, while the electrons move to the cathode through an external circuit, generating usable electricity. Reacting with protons and electrons at the cathode, oxygen is reduced (reaction (8.5)), thereby forming clean water. PEMFCs are well suited for portable and microdevices, as well as for automotive applications. 2H2 → 4H+ + 4e−

(8.4)

O2 + 4e− + 4H+ → 2H2 O

(8.5)

Most research in fuel cells for use as portable power has employed PEMFCs. For low-temperature (∼90 ∘ C) PEMFCs running on hydrogen, the hydrogen can be generated from electricity via electrolysis of water, but this process suffers from the low system efficiency (60–73%) of commercial electrolyzers [34]. On the other hand, hydrogen could be reformed from hydrocarbons and alcohols (e.g., methanol or ethanol) on board. While hydrogen production is common place in the chemical industry and some interesting biotechnological advances were made [35, 36], it is more demanding for mobile applications because of issues such as weight, size, transient operation, and consumer safety [37]. Moreover, low-temperature PEMFCs require a supply of almost pure H2 . Especially, the CO content in the fuel has to be low (1 s) second pulse leads to steady growth of metal particles without further nucleation [153]. It has been recently shown that using the double-pulse technique the size of platinum particles on a boron-doped diamond (1 0 0) surface can be tuned between 1 and 15 nm in height and 5 and 50 nm in apparent radius, while keeping the particle density constant [154]. Once a suitable nanostructured model system has been created to experimentally identify parameters that influence reactivity, the second and third steps are to measure the reactivity of the created nanostructures and to combine these findings, often assisted by theoretical calculations and models, to a valid theory. In the following section, we discuss the status of model catalyst research performed for the ethanol oxidation reaction, both in acidic and alkaline media. Specifically, we elaborate on the influence of coordination, composition, substrate, particle size, and dispersion on the electrocatalytic activity. As it is of significance for the ethanol oxidation reaction (EOR), we treat the degree of alloying of bimetallic catalysts as an additional parameter. In addition, we discuss experiments dealing with temperature dependence of some catalysts for the EOR. 8.6.5.2 Acidic Media

To study the kinetics of ethanol oxidation on various Pt single crystal surfaces (i.e., Pt of various coordination numbers), the adsorption of CO and evolution of CO2 on Pt(111), Pt(110), and Pt(100) electrode surfaces were monitored with FTIR while applying potential steps in 0.1 or 1 M EtOH solution in a flow cell [155]. The correlation of the FTIR spectra with CV data of the three Pt basal planes (CV data not shown here) revealed the potential dependence of COads coverage and capability of the planes to cleave the C–C bond. Pt(111) was not only found to have the lowest intensity of CO adsorption but it also exhibits the lowest activity toward C–C bond splitting. Both the Pt(100) and the Pt(110) basal planes are more active for C–C bond cleavage than Pt(111). Also, when the C–C splitting rate on Pt(111) was compared with polycrystalline and stepped (Pt(355)) platinum, the Pt(111) basal plane showed a lower activity, as indicated by CO2 production [156]. Colmati et al. [157] found that ethanol oxidation on Pt(111) produces mostly acetaldehyde as it showed little or no COads coverage. The group was also able to detect a difference in activity between Pt(100) and Pt(110), and assigned the higher C–C splitting activity to the Pt(110) electrode, which was attributed to the high activity of the Pt(110) steps toward C–C splitting. The COads oxidation requires adsorbed OH species [68, 72, 84], which is not readily supplied when the entire surface is covered with COads . Therefore, an intermediate C–C cleavage rate, as obtained for the Pt(554) surface, which is simply a combination of Pt(111) and Pt(110) properties, is found to produce optimal catalytic conditions. Figure 8.30 shows the maximum current density and the peak potential versus

8.6

3500

H2SO4

3000

HCIO4

j (μA cm−2)

2500

(554)

2000

(553)

1500 1000

Materials and Molecular Processes

(110) (15 15 14) (111)

500

Peak potential vs RHE (V)

(a)

0 0.80

H2SO4

0.75

(110)

HCIO4

0.70 0.65 0.60

(15 15 14) (111)

(553) (554)

0.55

0.0 (b)

0.1 0.2 Step density

Figure 8.30 (a) Maximum current density and (b) peak potential versus RHE of bulk ethanol oxidation over step density in 0.5 M H2 SO4 and 0.1 M HClO4 on different Pt

0.7

0.8

model electrodes. (Reprinted with permission from Ref. [158], Copyright (2008), Royal Society of Chemistry.)

reference hydrogen electrode (RHE) of bulk ethanol oxidation on Pt(111), Pt(15 15 14), Pt(554), Pt(553), and Pt(110) electrodes in H2 SO4 and HClO4 . The highest current densities were achieved on Pt(554) in HClO4 and on Pt(553) in H2 SO4 . The influence of the supporting electrolyte on the electrocatalytic activity can be explained by the preferential adsorption of bi(sulfate) on Pt on terraces rather than on steps [158, 159]. In addition to the coordination of Pt, there is another approach that can be used in order to enhance the electrocatalytic activity, which is changing the composition of the catalyst by combining the Pt with a second metal to obtain a binary catalyst. This can result in a noticeable change in the electronic properties, for example, changes in the adsorption energy, and thus changing the catalytic activity of the Pt (electronic effect). On the other hand, this composition change may allow for a bifunctional mechanism [160]. Some of the metals that are added to Pt in order to enhance its long-term catalytic activity include Ru, Ni, Mo, or Sn [161]. The reasoning behind the bifunctional mechanism is similar to that of the superiority of Pt(554) over Pt(110), although the latter is more active toward C–C

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bond cleavage [158, 162]. Pure Pt exhibits the highest activity for the C–C bond cleavage; however, the high coverage of COads on platinum results in blocking the Pt sites that are available for OHads , and thus impedes the oxidation of CO to CO2 [62]. The required surface oxygenated species can be supplied by the adjacent cocatalyst atom, allowing for higher catalytic activity [97]. The effect of the addition of a second metal (Ru, Pd, W, and Sn) to Pt was investigated in terms of the platinum lattice parameter [97]. It was found that the addition of Ru or Pd results in decreasing the Pt lattice parameter, while it is increased by alloying Pt with Sn or W. The activity of these binary catalysts for the ethanol oxidation reaction was found to increase in the following order PtPd < PtW < PtRu < PtSn. When various compositions of PtSn catalyst, ranging from Pt1 Sn1 to Pt4 Sn1 , were examined for their activities, an almost volcano plot was obtained when the peak power of a DEFC with the respective catalysts over atomic percentage of Sn was plotted. The apex of the volcano forms due to the interplay between the enhanced activity due to lattice expansion and the decreased conductivity as a result of the higher amounts of semiconducting tin oxide [163]. For temperatures from 60 to 90 ∘ C, the optimal Sn content was found to be 30–40% [97], while a slightly higher value of 50% was found to be the optimum for ethanol oxidation at room temperature [164]. So it was concluded that the operating temperature has an influence on the optimal composition [160]. Increasing the lattice parameter results in changing the Pt electronic properties, and thus the catalytic activity, by shifting the d-band of the Pt down, as reported for Pt3 Sn [165, 166]. It has been reported that the oxidation state of Sn in the bimetallic catalyst, whether it is in the alloy form, such as in Pt–Sn, or in the oxide form, such as in Pt–SnOx , has a pronounced effect on the reaction mechanism [167–169]. Godoi et al. investigated the activity of Pt–SnOx catalysts with different amounts of alloyed and oxidized forms of Sn, while keeping the same overall composition (Pt ∶ Sn = 7 ∶ 3, particle size ≈ 3 nm) [168]. The obtained catalytic activities toward ethanol oxidation were higher for catalysts that were treated in hydrogen atmosphere and therefore showed a higher degree of alloying than for catalysts with a higher amount of oxidized Sn. This enhancement in catalytic activity was attributed to an electronic effect that is caused by increased filling of the Pt 5d band when the degree of alloy increases. Besides the catalyst itself, the support may play a crucial role in the catalytic activity [134, 170]. Multiwalled carbon nanotubes (MWCNTs) were compared to commercial Vulcan carbon as a support for Pt–Sn catalyst [171]. CO stripping voltammetry and electrochemical impedance spectroscopy results indicate higher exchange currents on the MWCNT support. These higher currents were attributed to the oxygenated surface functional groups on the support that act as nuclei to anchor the Pt–Sn particles, the improved electronic conductivity of the MWCNTs, and the improved metal–support interaction. In a similar manner, Pt and Pt–Ru nanoparticles were investigated on graphene support and compared to graphite and Vulcan substrate [172]. Although well-defined supports, such as HOPG, were employed for studies on the deposition of DEFC-relevant catalysts such as Pt–Sn [173], there are only a

8.6

Materials and Molecular Processes

few reports on the influence of model supports on the ethanol oxidation reaction. In a study performed by El-Shafei and Eiswirth [174], Sn sub-monolayers were deposited on Pt(100), Pt(110), and Pt(111) single crystal electrodes and the effect of Sn coverage rate of ethanol oxidation was investigated. For all the three investigated basal planes, the addition of Sn was found to enhance the activity, and the highest increase was reported for Pt(110) on which it led to a more than 10fold increase in oxidation current. The optimum coverage was found to depend on the basal plane, where 0.2, 0.25, and 0.52 of a monolayer of Sn for Pt(100), Pt(111), and Pt(110), respectively, were reported. Zheng et al. [175] performed similar work and it was concluded that Sn adsorbs preferably on the hollow sites of the low-index basal planes Pt(111) and Pt(100); however, it does not show significant adsorption on Pt(110) single crystals. The influence of particle size was also investigated by comparing the activity of catalysts (Pt/C, Pt–Ru/C, and Pt3 Sn/C ) synthesized via the polyol route with commercial ones [176]; however, no size-induced effects could be observed as a lower degree of alloy formation for the synthesized particles led to a decrease in activity that overlaid other effects (compare [168]). Another study investigated the particle size effects using Pt particles on carbon support in a half-cell. This study revealed a maximum specific activity for a particle size of 2.5 nm. This was attributed to a compromise between structural effects and oxophilicity of the Pt surface [177]. 8.6.5.3 Alkaline Media

Although the activity of organic molecule oxidation is higher in alkaline media than in acidic media [178], the ethanol oxidation reaction was much less studied in alkaline media due to some challenges including the carbonation, which leads to membrane deactivation. Lai and Koper [158] investigated the ethanol oxidation reaction in alkaline media on Pt single crystal electrodes. The results indicate that the catalytic activity of ethanol oxidation on all the investigated Pt single crystals in NaOH is significantly higher than in HClO4 . The initial current for the ethanol oxidation is higher in alkaline media than in acidic media; however, deactivation of the electrodes is more prominent in the alkaline solution. The deactivation is even stronger for surfaces with wide terraces (Pt(111) and Pt(15 15 14)). This deactivation is due to the formation of adsorbed CHx species, which cannot be stripped as easily as in acid media [158]. These species were detected in higher amounts on Pt(111) than on Pt(554) surfaces. It was suggested that CHx,ads species are stable only on terrace sites, while they quickly oxidize to COads on (110) sites. Also, the onset potential for oxidation currents was found to be as low as 0.35 V versus RHE for Pt(110) in alkaline media [178]. Tian et al. [179] used electrodeposited Pd nuclei in order to grow tetra-hexahedral Pd nanocrystals. These nanocrystals predominantly feature [180] facets that are composed of two (210) steps followed by one (310) step. These crystals showed four- to sixfold increase in ethanol oxidation reaction current when compared to commercial Pd-black in 0.1 M EtOH and 0.1 M NaOH. This behavior was attributed to the high concentration of surface atomic steps on these crystals.

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For the effect of the catalyst composition on the catalytic activity of ethanol oxidation in alkaline media, it was found that the activity of Pd is slightly higher than that of Pt [92, 181]. However, as for Pt in acidic media, the C–C bond cleavage is rather difficult and acetate ions are the main product [88]. As in acidic media, the addition of Sn to the catalyst was investigated for the ethanol oxidation reaction in alkaline environment [182–184]. Templated Pt–Sn (80 : 20) catalysts showed a slight improvement over templated Pt catalysts [184]. As the observed current densities at lower potentials are higher for the Pt–Sn catalyst, it was hypothesized that the presence of tin oxides facilitates the oxidation of adsorbed intermediates. Antolini and Gonzalez gave an overview about studies investigating the different catalyst systems that were investigated for the ethanol oxidation reaction in alkaline media [118]. In addition to bimetallic PtMx and PdMx , they list additions of various oxides to Pt/C and Pd/C and also catalyst systems such as Ru–Ni without any Pd or Pt content. Zhu et al. [185] reported the observation of a substrate and composition effect when growing Pd on carbon-supported gold nanoparticles. While the absolute ethanol oxidation current is highest for pure Pd on Vulcan carbon, the current per microgram of Pd is highest when measured for a Pd:Au ratio of 1 : 4. This was attributed to a shift in the Pd3 d binding energy, induced by the Au, which weakens the bonding interaction between the adsorbed species and Pd and therefore enhances the anti-poison capabilities of the catalyst [186]. Studies on the influence of the size or dispersion of catalyst nanoparticles on their activity toward ethanol oxidation reaction in alkaline media are rare. One recent publication investigated the activity of spherical Pd nanopoarticles with varying sizes on Ni-foil [187]. To correct for the size-dependent catalyst loading, the measured currents were converted to currents per millimole of Pd and found that nanoparticles with a diameter of 12.0 nm showed a 359 times higher loading-normalized current during CV measurements than catalyst particles with a diameter of 28.8 nm. Particles with intermediate diameters (14.0 and 18.9 nm) followed the same trend. The authors stated that enhancement of intrinsic catalytic activity of the electrodes with smaller particles is due to an increase in “true” surface area and the availability of more energized surface Pd atoms [187]. 8.6.5.4 A Few Words about Cathode Catalysts (Conventional and MeOH Tolerant Catalysts)

The ideal material for a DEFC cathode should have a high activity for the ORR and a high tolerance for ethanol oxidation. Pt alloyed with some of the first-row transition metals was found to give a higher activity for ORR than pure platinum in low temperature fuel cells [188–191]. The improvement in the ORR activity obtained when Pt–M alloy electrocatalysts are used was attributed to both geometric (decrease of the Pt–Pt bond distance) [192] and electronic factors (increase of Pt d-electron vacancy) [188]. Ethanol adsorption and oxygen adsorption are competing with each other for the surface sites. Similar to the case of methanol oxidation on Pt surface, the dissociative chemisorption of ethanol requires the existence of ensembles of several adjacent Pt atoms [48, 193], and the presence of foreign atoms around Pt-active sites within these ensembles

8.7

Conclusions – Folding It Back

could block ethanol adsorption on Pt sites due to the dilution effect. On the other hand, oxygen adsorption requires only two adjacent sites and so it is not affected significantly by the presence of the second metal. In addition to a high ORR activity, Pt–Ni and Pt–Co alloys also presented a good tolerance for methanol oxidation [194–197]. On this basis, many binary alloy electrocatalysts were investigated as an ethanol-tolerant cathode material including Pt–Co and Pt–Pd, both supported on carbon. When a commercially available carbon supported Pt–Co (3 : 1) electrocatalyst was tested in a single DEFC, it was found that in the cathode region of the potential (0.7–0.9 V vs RHE) Pt/C and Pt–Co/C have the same activity for ethanol oxidation [198]. On the other hand, by measurements of oxygen reduction in H2 SO4 in the presence and in the absence of ethanol, promising results were obtained using a Pt–Pd (9 : 1) catalyst [199]. The Pt–Pd/C catalyst possesses about the same ORR activity, but a higher ethanol tolerance than Pt and Pt–Co.

8.7 Conclusions – Folding It Back

In the preceding chapters, a description was given of an autonomous energy system where electrochemical devices play an important role. The problem of energy management is a striking one when various devices for energy conversion and energy storage need to be used. Since technical characteristics of the devices are quite different, a thorough analysis of the primary energy supply is necessarily contrasted by the anticipated electricity demand structure. Here, the importance of a sophisticated procedure as represented by the computer science approach is needed for analysis, control, and optimization of the overall system. Taking this a step further, one can think of implementing computing capabilities into the devices themselves in order to make them “smart,” that is, providing intelligence in their operation depending on external factors. So, devices themselves know how their efficiency, time response, expected life time, and so on are under the given parameters such as operating conditions and actual state of health. In the overall context of operation, the devices decide themselves which one takes over a required task in order to fulfill the operational demand. In such a kind of bottom-up process hardware components with usually limited technical capabilities but which are continuously operating and being monitored can eventually be improved considerably through software in their functionality in an energy system. Another aspect, which is almost opposite, is how to improve the hardware itself of components. Achieving a better understanding of the functionality of single components in the complete system allows for a better feedback for a possible hardware optimization of single components. This would be done in a typical topdown approach. Having fully understood the main operational parameters of a certain device its improvement can be done in much more focused way.

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Combining the various views described in the previous chapters one can see how further developments and improvements in energy systems can be accomplished. In some areas it is a top-down approach and in others it is bottom up. Understanding the functioning of these different ways in a rather complex system avoids a biased view toward certain ways of solving problems (influenced by the philosophy of a given discipline), be it a scientific or an engineering one. The combination of both, maybe mediated by a discipline such as computer science, can considerably enhance our capabilities to deal with complex systems.

Acknowledgments

This work was supported in part by TUM CREATE, Singapore. Editing work by Sundar Pethaiah and Jochen Friedl and contributions by David Ciechanowicz are appreciated. References 1. Jamshidi, M. (2008) Systems of Systems

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321

323

Index

a aluminum anodizing models 126 anodic oxide films 107 anodic porous alumina – applications 165, 166 – crystallinity 164 – duplex structure 152 – electrochemical anodization 145–147, 149 – geometry control – – hard anodization 156 – – mild anodization 154 – improved ordering 162, 163 – morphology 153, 154 – nanomaterials fabrication – – electrodeposition 166 – – metal oxides 168 – – metals 167 – – polymers 168 – – semiconductors 168 – self-organization 149, 152 – template materials 146 aprotic Li–air batteries 5 aqueous Li–air batteries 5 ARPA-E program 229 AZ-1350 resist 43, 47, 49

b batch-fabricated thin-film heads 15 “bleed and feed” procedures 33 bottom-up process 264, 282, 315 Bruckenstein–Swathirajan (BS) isotherm Butler–Volmer electrochemical kinetic expression 127

c catalysis, UPCD – atomic surface configuration 96, 97 – binary and ternary Pt-based alloys 97

63

– electronic and geometric effects 96 centralized energy system 284 chemical etching 21 combined MR read/inductive write head 24 computational energy science – design-time energy system 266 – extended Reference Energy System – – containers 272 – – graphical representation 271 – – process and commodity 272 – – USES, see Universal Scheme for modeling Energy Systems (USES) – Reference Energy System 269, 270 – run-time energy system 266 – smart grid, virtual power stations 266–268 – virtual autonomous networks, hierarchy – – extended hierarchical organization 278, 280, 281 – – flat organization 278–281 – – goal and control strategy 276 – – structure 277 conventional core–shell structures – continuum DIS models – – boundary conditions 205 – – concentration induced deformation 207 – – displacement equations 205 – – jump stress 208 – – solute diffusion 199, 200 – – stress–strain relations 201–203, 205 – – thermodynamics 198 – displacement and stress – – initial behavior of 209–214 – – transient behavior of 212, 215–218 – schematic diagram 194 core–shell structures – ab initio simulations 195, 197 – conventional, see conventional core–shell structures

Electrochemical Engineering Across Scales: From Molecules to Processes, First Edition. Edited by Richard C. Alkire, Phil N. Bartlett, and Jacek Lipkowski. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

324

Index

core–shell structures (contd.) – density functional theory – – Hohenberg and Kohn theorem 195 – – Kohn–Sham effective potential 195 – diffusion-induced stress calculation 196 – Li diffusion mechanism 197 – lithiated graphite, see graphite-SEI core–shell structures – lithiated Si, see Si-SEI core–shell structures – SEI 193 coupled film memory structure 15

– – – – –

crystallinity 173 doping 175, 177 single wall morphology 177 surface area enhancement 174–175 tube geometry 170, 172, 173, 175

e

electric vehicles 4 electrical energy storage devices 285 electrochemical anodization 145 electrochemical atomic layer deposition (EC-ALD) 60 electrochemical energy systems d – architectures, see computational energy decentralized energy system 282, 284, 285 science DEFC, see direct ethanol fuel cell (DEFC) – bottom-up approach 264, 282, 315 design-time energy system 266 – centralized energy system 284 direct ethanol fuel cell (DEFC) – decentralized energy system 282, 284, 285 – anode catalyst – DEFC, see direct ethanol fuel cell (DEFC) – – Pt–Ru catalysts 303, 304, 306 – PEMFCs – – Pt–Sn/C catalysts 304–306 – – ethanol 294 – cathode catalysts – – methanol 294 – – methanol oxidation tolerance 315 – – oxygen reduction reaction (ORR) activity – – reforming process 293, 294 – storage devices 314 – – lead–acid car battery 287 – cell performances 297, 298 – – Li–air batteries 289 – electrocatalyst layer 300 – – Li-ion batteries 287, 288 – electrodes 300 – – Li–S batteries 288, 289 – elevated temperatures 299, 305, 307, 308 – – Munich city block, Germany 291, 292 – energy density 295 – – parameters 285 – ethanol oxidation reaction – – power rating and discharge time 286 – – acidic media 301, 302, 310, 312, 313 – – RFBs 290 – – alkaline media 305, 313, 314 – – thermodynamic and electrical storage – gas diffusion layer 300 devices 285 – vs. indirect ethanol fuel cells 296 – structure 265 – MEA 301 – top-down approach 264, 281, 315 – membranes 299 – nanostructured model catalyst system 309, electroplating 8, 14 extended Reference Energy System (eRES) 310 – containers 272 – reforming process 296 – graphical representation 271 – stack hardware and design 297 – process and commodity 272 – system layout 297 – USES, see universal Scheme for modeling dye sensitized solar cells (DSSCs) 107 Energy Systems (USES) – basic principle 169 – sandwich configuration 170 f – TiO2 nanotubes, see dye-sensitized TiO2 field-assisted dissolution 118 nanotubes five-turn vertical thin film head 17–18 dye-sensitized TiO2 nanotubes frame plating 37, 38 – commercialization fuel cell-vehicles 3 – – backside vs. front-side illumination 178–180 g – – flexible substrates 180 graphite-SEI core–shell structures – – long term stability 181 – analytic parameters 218 – – processing speed 177, 178 – DFT calculations 196, 219 – – scale-up 180, 181

Index

inductive read/write head 24 intermittent renewables 227, 228

– – scalability 239 – – sealing vs. temperature 237, 238 – – thermal management 239 lithiated graphite core–shell structures, see graphite-SEI core–shell structures lithiated Si core–shell structures, see Si-SEI core–shell structures lithium-ion batteries – core–shell structures, 193 see core–shell structures – electrochemical energy systems 287, 288 locally enhanced oxide dissolution 118 low-temperature sodium-based liquid metal batteries 255

l

m

large scale integration (LSI) fabrication 10, 12, 17, 20, 21, 43, 51, 53 Lawrence Livermore National Laboratory energy flow charts 2 lead–acid car battery 287 levelized energy costs (LECs) 229 Li–air battery 4, 289 Li ion battery technologies 4 Li–S batteries 289 LiC6 /polymer-coating system 219–221 light-duty vehicles, electrification of – electric grid 4 – natural gas 3 linear stability analysis – dispersion curves 132 – limitations 133 – morphological stability problems 130 – morphology evolution, 130 see also morphological stability model – Parkhutik and Shershulsky model 130, 133 – wavelength destabilizing factor 133 liquid metal battery (LMB) – charge transfer overpotential 232 – vs. competitive technologies 234, 235 – disadvantages 232 – market considerations 233 – mass transport overpotential 232 – molten salts, see molten salt-based batteries – ohmic overpotential 232 – overpotential losses 232 – principles of operation 230, 231 – scale-up 233 – strengths 232 – systematic down-selection methodology – – cell couple costs 235, 236 – – corrosion rate vs. temperature 238 – – energy storage production estimates 240

magnetic film memory 10, 51 magnetic microsystems 100 magnetic recording, UPCD – patterned media design 100 – perpendicular recording technology 99 – recording density 100 – thin film deposition methods 100 magnetic thin film head, see thin film head magnetoresistive (MR) read head 24 Margules parameters 76 membrane electrode assembly (MEA) 301 mild anodizing 115 molten salt-based batteries – nuclear reactor development – – corrosion effects 246, 249–252 – – molten salt properties 247, 248 – – number of operable nuclear power plants 245 – sodium electrodeposition – – Castner process 241–243 – – Davy process 241 – – Deville process 241 – – Downs cell 242–244 – thermally-regenerative battery – – β′′ -Al2 O3 254 – – diagram 252 – – Li-based molten salt research 255 – – vs. secondary bimetallic devices 253 morphological stability model – Cheng and Ngan simulations 134 – coupled lattice map model 134 – ionic migration fluxes 138, 139 – kinetic Monte Carlo simulation 134 – long-wavelength disturbances 136 – mechanical and electrical forces 138 – oxide flow effects 137 – oxide-solution interface kinetics 136 – surface tension effects 136

grid-level storage, see liquid metal battery (LMB)

h hand-wound ferrite read/write head 12, 13 hard anodizing 115 hard-baked photoresist 48–50 highly oriented pyrolytic graphite (HOPG) 193 high performance data storage systems 11

i

325

326

Index

morphological stability model (contd.) – transport processes 137 – weakly nonlinear analysis 137 multi-turn, vertical thin film head 16

n natural gas 3 Nernst equation

76

p Parkhutik and Shershulsky’s model – linear stability analysis 130, 133 – oxide-solution interface motion 127, 128 PEMFCs, see polymer electrolyte membrane fuel cells (PEMFCs) permalloy plating process – electroplate NiFe alloys 29 – NiFe bath aging and steady state operation 32 – paddle cells 25 – plating parameters 31 – real-time, on-line plating bath control 32 photovoltaics, UPCD – Cd–Te films 98 – CuInSe2 films 98 – CZTS films 99 – single crystal Si wafers 98 – vs. solar systems 97 plate-through-mask technology, 17 see also through-mask plating plating frame process, see frame plating point defect models 124 polymer electrolyte membrane fuel cells (PEMFCs) – ethanol 294 – methanol 294 – reforming process 293, 294 porous anodic oxides – electrochemical transients 110 – hard anodizing 115 – mathematical models – – boundary conditions 125, 126 – – bulk oxide motion 122, 123 – – interface evolution equation 120, 126–128 – – interfacial reactions 123, 125 – – ionic flux 121, 122 – – linear stability analysis 130–133 – – morphology evolution, 110, 133 see also morphological stability model – – potential field equations 120, 121 – – steady state porous layer growth 128, 130 – – stress distributions 121

– – – – – – – – –

mechanisms – field-assisted dissolution 118 – locally enhanced oxide dissolution 118 – pattern selection 119 – pore initiation 118, 119 – self-ordering 119 metal dissolution 114 nanotubes 109, 110 oxide volume expansion and tracer studies 115, 116 – pores 109, 110 – porous alumina, see anodic porous alumina – stress 115 – TiO2 nanotubes, see TiO2 nanotubes – universal scaling relations 112 – vacancy-type defects 117 post Li-ion batteries 288 potential of zero charge (PZC) 79 primary energy sources, US 1, 2 PZC, see potential of zero charge (PZC)

r RAMAC 305 11, 12 rechargeable Li–air batteries 5 rechargeable Li ion batteries 3 Redlich–Kister expansion 76 redox flow batteries (RFBs) 290 renewable portfolio standards (RPS) 229 run-time energy system 266

s Schrödinger’s equation 195 SEI, see solid electrolyte interface (SEI) selective electrodesorption based atomic layer deposition (SEBALD) 59 self-organized porous anodic oxides, see porous anodic oxide formation semiconductor memory 51 Si-SEI core–shell structures 196, 221 Singapore’s electric energy system 272, 274, 275 single-turn, horizontal thin film head 15 single-turn, vertical thin film head 16 SLRR, see surface-limited redox replacement (SLRR) solid electrolyte interface (SEI) 193 solid state memory 10 surface-limited redox replacement (SLRR) 59 – deposition protocol 63, 64 – deposit morphology 69 – electrochemical driving force 66–68 – nucleation rate 67, 68 – organic templates 74, 75 – Pt monolayer catalyst design 68, 69

Index

– – long term stability 181 – – processing speed 177, 178 – – scale-up 180, 181 – crucial features 146 – crystallinity 164 – DSSCs – – crystallinity 173 – – doping 175 – – single wall morphology 177 t – – surface area enhancement 174, 175 thermodynamic energy storage devices 285 – – tube geometry 170, 172, 173 thin film head – duplex structure 153 – batch-fabricated thin film write head 14 – electrochemical anodization 147, 149 – device structures 22 – geometry control – – combined MR read/inductive write head – – diameter 158 24 – – fluoride based electrolytes 157, 158 – – inductive head 24 – – fluoride concentration 158 – – magnetoresistive (MR) read head 24 – – temperature and pH 161 – electroplating 8, 14 – – tube length 158 – high performance data storage systems 8, – – water content 161 11 – improved ordering 163 – IBM’s General Products Division (GPD) 18 – morphology 153, 154 – interdisciplinary design approach 16, 52 – self-organization 149, 152 – manufacturing technology evolution, time top-down process 264, 281, 315 line of 8, 9 – materials 23 u – – hard-baked photoresist 45 U.S. Bureau of Standards Molten Salt Studies – – magnetic materials studies 44 248 – memory 8, 10 underpotential co-deposition (UPCD) 59 – patents 12 – bulk alloy thermodynamic model – patterning 22 – – activity coefficient 76 – – ancillary issues 41 – – assumption 78 – – plating frame process 37 – – enthalpy of mixing 77 – – through-mask plating 33 – – free energy of mixing 76 – permalloy plating process 22 – – Nernst equation 76 – – electroplate NiFe alloys 29 – catalysis – – NiFe bath aging and steady state operation – – atomic surface configuration 96, 97 32 – – binary and ternary Pt-based alloys 97 – – paddle cells 25 – – electronic and geometric effects 96 – – plating parameters 31 – crystal structure, Pt–Pb alloys 92 – – real-time, on-line plating bath control 32 – energetics – processor 8, 10 – – atomistic interactions 80 – schematic drawings 12, 13 – – ion adsorption 78, 79 – 3-D structures 17, 33, 47, 51 – – PZC 79 through-mask plating 15, 21, 22, 33, 34, 36, – – surface defects and reconstruction 79 52 – – surface segregation 79, 80 – clean interface 44 – growth kinetics – resist for 43 – – Au–Cu binary alloy 82–84 TiO2 nanotubes – – Au–Ni alloys 84, 85 – – Ni–Pt films 84 – applications 166 – immiscible alloys 90–92 – commercialization – intermetallic compounds 87–90 – – backside vs. front-side illumination – magnetic microsystems 100 178–180 – magnetic recording – – flexible substrates 180

– – – –

reaction kinetics 70 – first order 70 – Nth order 71 – open circuit potential (OCP) transients 71–73 – – second order 71 – – zero order 70 – reaction stoichiometry 65, 66

327

328

Index

underpotential co-deposition (UPCD) (contd.) – – hard disk drives 99 – – patterned media design 100 – – perpendicular recording technology 99 – – recording density 100 – – thin film deposition methods 100 – microstructure – – CdTe films 94 – – Fe–Pt films 92, 93 – – ZnO films 94 – phase diagram – – Au–Cu alloys 86, 87 – – Au–Ni binary system 90–92 – – Cd–Te system 89 – – electrodeposited alloys vs. bulk metallurgical alloys 85, 86 – – Pt–Pb binary system 87, 88 – photovoltaics – – Cd–Te films 98 – – CuInSe2 films 98 – – CZTS films 99 – – single crystal Si wafers 98 – – vs. solar systems 97 – solid solution 86, 87 – surface morphology – – Au–Cu films 94–96 – – Fe–Pt films 96 underpotential deposition (UPD) – adsorption isotherms 62

– Bruckenstein–Swathirajan (BS) isotherm 63 – cyclic voltammetry features 61, 62 – fuel cell catalyst synthesis 61 – investigation studies 60 – SLRR, see surface-limited redox replacement (SLRR) – surface decoration 61 universal Scheme for modeling Energy Systems (USES) – disaggregated physical micro grids 274 – vs. eRES 272 – graphical representation 273 – Singapore’s electric energy system 272, 274, 275 UPCD, see underpotential co-deposition (UPCD) UPD, see underpotential deposition (UPD) USES, see Universal Scheme for modeling Energy Systems (USES)

v vanadium redox batteries (VRB) 233

w Western Electricity Coordinating Council (WECC) 229

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