NATO ASI Series Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities.
The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation B Physics London and New York
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Solid State Batteries
edited by
C.A.C. Sequeira Instituto Superior Tecnico Technical University of Lisbon 1 096 Lisboa Codex, Portugal
A. Hooper Materials Development Division AERE Harwell Oxfordshire OX11 ORA, UK
1985 Martinus Nijhoff Publishers Dordrecht / Boston / Lancaster
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on Solid State Batteries, Alcabideche, Portugal, September 2-14, 1984
Library of Congress Cataloging in Publication Data
ISBN-13:978-94-010-8786-5 e-ISBN-13:978-94-009-5167-9 001:10.1007/978-94-009-5167-9
Distributors for the United States and Canada: Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, USA
Distributors for the UK and Ireland: Kluwer Academic Publishers, MTP Press Ltd, Falcon House, Queen Square, Lancaster LA1 1RN, UK
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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publishers, Martinus Nijhoff Publishers, P.O. Box 163, 3300 AD Dordrecht, The Netherlands
Copyright © 1985 by Martinus Nijhoff Publishers, Dordrecht Softcover reprint of the hardcover 1 st edition 1985
PREFACE
The holding of an Advanced Study Institute on the topic of "Solid­ State Batteries" at this time represented a logical progression in a series of NATO-sponsored events. Summer Schools at Belgerati,
v
Italy in 1972 and Ajaccio, Corsica in 1975 on the topic of "Solid­ -State IOllics" dealt with fundamental aspects of solid-state electro­ chemistry and materials science. The application of specific solid ionic conductors played a significant role in the Science Committee Institute on "Materials for Advanced Batteries" held at Aussois, France in 1979. Interest in these and related fields has grown substantially over this period, and is sustained today. Research and development programmes exist within universities, governmental research laboratories and industry, worldwide and a series of international conferences and collaborations have been set up.
Advanced batteries, both secondary and primary, have a potentially important role ~o play in the development of many areas of tech­ nology in the late 20th century and beyond. Applications include stationary storage, vehicle traction and remote power sources, as well as industrial and domestic cordless products and consumer and military electronics. The concept of an all-so lid-state battery is not new but, until recently, their performance has precluded their use in other than specialist low power, primary, applications. Recent materials' developments, however, make the solid-state battery a real possibility in all of the application sectors mentioned above. Further, such cells offer many attractive features over alternative present-day and advanced systems.
The aims of this Institute were to forge stronger links between those already involved in the various aspects of this technology and also to educate those who may either be able to contribute to, or benefit from, its future development. The lecturing team, many members of which also formed a scientific committee, included forerunners in the field of solid-state ionics and representatives from the battery industry. The choice of Portugal as the meeting site reflected the enthusiasm of the Director and the related emergence of solid-state electrochemistry in that country.
VI
The general approach was to review the fundamental materials and experimental aspects of solid-state electrochemistry (Week 1) and then to focus on battery technology, (Week 2). This included both an introduction to, and a review of, batteries, in general, as well as details of solid-state systems and relevant technologies. The aim, here, was to provide comparative information for an assessment of the potential strengths and weaknesses of the solid-state approach. Also included in the second week were a number of general, but related, lectures. These again helped to provide a perspective to the battery work.
To give both structure and continuity to the programme, the lectures were divided, on a roughly daily basis, into groups, each with a particular theme:
- Basic Concepts - Solid Electrolytes - Electrode Processes - Electrode Materials - Experimental Techniques - Introduction tv Batteries - Solid-State Batteries, and - New Technology
Involvement of the participants was encouraged by the provision both of short discussion periods after each lecture and also eight Formal Discussion Groups. The topics of these groups reflected the lecture themes with an emphasis on future developments. Summaries of all the discussion periods are included in the text thanks to the efforts of the Session and Discussion Group Chairmen and their assistants. Also included are abstracts of a number of short presentations by participants of the Institute.
In addition to the lecturing staff, approximately 80 people from 23 countries participated in the Institute. These included repre­ sentatives from industrial and military sectors together with university staff and students. Provision for a number of student grants and various local facilities was made possible by the augmentation of the NATO funding through the sponsorship of:
- US Department of Energy (Lawrence Berkeley Laboratory) - US Army Research, Development and Standardization Group - Sociedade Portuguesa do Acumulador Tudor - Funda~ao Calouste Gulbenkian - Instituto Nacional de Investiga~ao Cientifica - Banco Fonsecas and Burnay - Cockburn Smithes and Cia, Lda. - Direc~ao de Arma, de Transmissoes
and this is gratefully acknowledged.
VII
Finally it is necessary to thank all of those people involved in the local organization of the Institute. In particular, a great deal of the administrative load was ably carried by the Director's wife Maria Elisa and the assistance of Mrs. Alexandra Galante with slide presentation was much appreciated. The overall success of the meeting was due in part to the splendid surroundings and welcoming atmosphere which Portugal provided for us but also to the contributions of everyone involved, at whatever level.
We can look forward to the future of solid-state batteries with considerable optimism and excitement.
Cesar de Sequeira
Director: Prof. C.A.C. Sequeira
Co-Director: Dr. A. Hooper
Advisory Committee
Dr. R.M. Dell, ABRE Harwell, England Prof. G.C. Farrington, University of Pennsylvania, USA Dr. J. Jensen, Energy Research Laboratory, Odense, Denmark Prof. B. Scrosati, University of Rome, Italy Prof. B.C.H. Steele, Imperial College, London, England Prof. J.B. Wagner, Jr., Arizona St. University, USA
Lecturers
Dr. K.M. Abraham, EIC Laboratories, Norwood, USA Dr. M.B. Armand, ENSEEG, Saint Martin d' Heres, France Dr. S. Atlung, Technical University of Denmark, Lyngby, Denmark Dr. R.M. Dell, AERE Harwell, Oxfordshire, England Prof. G.C. Farrington, University of Pennsylvania, USA Dr. A. Hooper, AERE Harwell, Oxfordshire, England Prof. R.A. Huggins, Stanford University, USA Dr. D.W. Murphy, AT&T Bell Laboratories, Murray Hill, USA Dr. J.R. Owen, University of Salford, Manchester, UK Dr. B.B. Owens, Medtronic Energy Technology, Minneapolis, USA Prof. R.A. Pethrick, University of Strathclyde, Glasgow, UK Prof. B. Scrosati, University of Rome, ,Italy Prof. C.A.C. Sequeira, Instituto Superior Tecnico, Lisbon, Portugal Prof. B.C.H. Steele, Imperial College, London, England Dr. B.C. Tofield, AERE Harwell, Oxfordshire, England Dr. S. Yde-Andersen, Energy Research Laboratory, Odense, Denmark Prof. J.B. Wagner, Jr., Arizona State University, USA
Chairmen of the Study Groups
Prof. J.B. Wagner, Jr. Dr. S. Atlung Dr. C.A.C. Sequeira Dr. B.B. Owens Dr. R.M. Dell Dr. D.W. Murphy
IX
CONTENTS
Theme 1: Basic Concepts
Phenomenology of ionic transport in solid-state battery mater ia1s • Robert A. Huggins
Structural aspects of ionic transport in solid-state . battery materials. Gregory C. Farrington
Theme 2: Solid Electrolytes
Ionica11y conducting glasses John R. Owen
Ionica11y conductive polymers M.B. Armand
Composite materials as solid electrolytes J.B. Wagner, Jr.
Theme 3: Electrode Processes
Xl
3
5
19
27
29
35
49
63
77
91
93
XII
Electrode processes in solid state cells. I: The metal electrode. B. Scrosati
109
Electrode processes in solid state cells. 119 II: The intercalation electrode. F. Bonino and B. Scrosati
Porous and composite electrodes for solid 129 state batteries. S. Atlung
Solid state electrodes: A materials introduction 163 B.C.H. Steele
Theme 4: Electrode materials 179
Insertion compounds: Relationship of structure to 181 electrochemistry. D.W. Murphy
Conductivity in polymeric materials. 197 Richard A. Pethrick
Theme 5: Experimental techniques 217
D.C. methods of cell characterization. 219 Part I: Evaluation of materials and components. C.A. C. Sequeira
D.C. methods of cell characterization. 241 Part II: Definition of full cell/battery parameters. C.A.C. Sequeira
A.C. measurement and analysis techniques. 261 A. Hooper
Non-electrical techniques of cell characterization. 283 K.M. Abraham
Theme 6: Introduction to batteries 297
Battery performance parameters 299 J. Jensen, S. Yde-Andersen, J.S. Lundsgaard and S. Atlung
Canpetitive systems':Primary batteries 311 B.B. Owens
Competitive systems: Ambient temperature rechargeable batteries. R.M. Dell
Lithium organic liquid electrolyte batteries K.M. Abraham
Competitive systems: High temperature batteries R.M. Dell
Utilization of conductive polymers in rechargeable batteries. M.B, Armand
Energy storage Johs. Jensen
Theme 7: Solid-state batteries
Solid-;-state rechargeable batteries. Alan Hooper
Theme 8: New Technology
Micro-batteries John R. Owen
II. SHORT PRESENTATIONS
ProtonI~nd lithium ion conductors based upon the AM2 (P04) 3 type structlUre. A. Clearfield, M.A. Subramanian, B.D. Roberts and R. Subramanian
Conductivity of modified lithium iodide samples G. Eichinger
XIII
319
337
351
363
377
387
389
399
411
413
423
445
449
XIV
Activation energies of the electrical conductivity of doped beta" alumina samples. W. Jakubowski, J. Garbarczyk and M. Wasincionek
Phase transition and ionic conductivity of the spinel system Li2-2XMgl+xCl4' R. Kanno, O. Yamamoto, C. Cros: and J.L. Soubeyroux
Lithium insertion compounds of the high and low temperature polymorphs of LiFeSn04' M. Greenblatt, E. Wang, H. Eckert, N. Kimura, R.H. Herber
Transport properties of lithium intercalated InSe. E. Hatzikraniotis, C. Julien, M. Balkanski
Oxide electrodes at high temperatures. G.P. Wirtz and H.S. Isaacs
Structure, electrical and electrochemical properties of Ag~bS2' H.J.M. Bouwmeester, G.A. Wiegers and B.A. Boukamp
Photoelectrochemical intercalation reactions and their possible applications. G. Betz
Investigation of ternary lithium intermetallic systems as solid state cathode materials. W. Sitte and W. Weppner
Fractal geometry and kinetics. A. Le Mehaute
Solid state electrochemical applications of EXAFS. R.G. Linford
Measurement of chemical diffusion coefficients by the point electrode technique. H. -D. Wiemh&fer
Thin film cathode material in Li-I2 primary battery. R. Bannehr and J.P. Wiaux
Models for impedance plots of metal/RbAg4I5/ metal cells. J.I. Franco, C.M. Garcia, J.C. Lopez Tonazzi and N.E. Wals8e de Reca
455
461
465
479
483
489
493
499
503
509
515
519
523
Ambient temperature polymer solid state batteries. A. Le Mehau te
III. FORMAL DISCUSSION GROUP REPORTS
Solid electrolytes
The future of batteries
Robert A. Huggins
Department of Materials Science and Engineering Stanford University Stanford, CA 94305
INTRODUCTION
The purpose of this paper is to give a general overview of some of the principles and macroscopic phenomena that are rele­ vant to batteries, particularly those in which there is an appreciable amount of ionic transport within solid components, either the electrolyte or electrodes.
In this context, a battery is composed of one or more electrochemical devices (cells) which act as transducers to convert internally stored chemical energy into externally useful electrical energy. Although other types are possible, most such devices are galvanic cells in which chemically different electrodes are separated by an electrolyte.
THERMODYNAMIC CONSIDERATIONS
Under open circuit conditions there is a voltage between the electrodes related to the tendency for a chemical reaction to take place between the two electrode materials. However, for this reaction to occur there must be transport of some chemical species (neutral atoms) from one of the electrodes to the other.
Ideally, the electrolyte acts as a selective filter, allow­ ing the passage of only ions, not neutral atoms. Thus in order for neutral chemical species to move across the cell so that the chemical reaction can take place, there must be another path available for the electrons. This path is through the external
5
6
circuit connected to the electrodes. It is these electrons that are available to do work, and thus to take electrical energy out of this chemically-driven device.
Under ideal open circuit conditions, no ions cross the electrolyte and no chemical reaction takes place. This will occur when the chemical driving force tending to cause the transport of ions through the electrolyte is just balanced by the electrical force upon them due to the voltage between the electrodes acting upon their electrical charge. This force balance thus serves to couple the virtual chemical .reaction of the cell· to its externally measurable, and useful, electrical voltage.
There are two different ways in which one can describe the chemical force across such a galvanic cell. One of these is to write the virtual cell reaction - the overall net chemical reaction that would take place upon the transfer of the neutral species from one electrode to the other. Examples might be of the type:
A + B .. AB
A+BM=AM+B
In such cases, the voltage across the cell is given by
v = - llG/nF
where IlG is the Gibbs free energy change that occurs by the transfer of one mole of A across the cell, n is the number of elementary charges carried by each A ion, and F is Faraday I s constant.
Alternately, one can express the chemical force across the cell in terms of the change in chemical potential of the neutral form of the species. that is transported through the electro­ lyte. In this case, we can write
While this may appear to be a trivial difference, this latter representation will be seen to be more useful in cases in which the electrode reaction involves the change in the composi­ tion of a solid solution, rather than a phase transformation. In such cases, the equilibrium cell voltage changes continually
as a function of the amount of charge that has passed through it.
In this case, it is best to write the cell reaction in forms such as:
xA + B
xA + BX
A B x
A BX x
where the value of x indicates the mole fraction of species A that has been transported across the cell. The ideal cell voltage may change with the value of x.
The amount of chemical energy that is stored in a galvanic cell, and thus could be extracted under ideal conditions, can be written as:
Energy = JVdq
where V is the value of the cell voltage at any state of charge, and q is the amount of charge that is passed across the cell. This latter quantity represents the cell capacity.
If one divides this value by only the weight of the chemi­ cal reactants, neglecting all other components of a practical system, including the electrolyte, container, connections, etc., one gets the maximum theoretical specific energy of such a cell. If one divides it by the volume of the reactants (only), one obtains the maximum theoretical energy density. While these values cannot, of course, be obtained by any real device, they are often useful in comparing one potential electrochemical system with another.
The power delivered by any such cell is the product of the voltage and the current. Since there is no simple theoretical limit for the current, there is no comparable maximum theoreti­ cal power value for a cell composed of specific chemical consti­ tuents. One can say, however, that the available power will be decreased by any internal power consumpt ion mechanisms related to internal impedances. Thus
Actual output power = Ideal output power - (I)2Z. l.nt
where Z. is the sum of all internal (and connector) impedanclC~ This includes the electrolyte resistance and the reaction impedances at each of the electrodes.
7
8
Types of Electrode Reactions
In addition to the simple stripping and deposition upon elemental single phase electrodes, such as pure lithium, there are two general types of electrode reactions. We shall classify these as either displacement reactions or insertion reactions. Displacement reactions involve a change in the amounts of one or more phases present in the electrode microstructure, but not in their compositions. Insertion reactions, on the other hand, involve changes in the composition of one or more phases by the introduction or deletion of atomic species into or out of their crystal structures.
There are important differences between these two types of reactions that deserve mention. These are related to both their thermodynamic and kinetic properties.
The Gibbs phase rule tells us that under constant pressure and temperature conditions the intensive (composition-indepen­ dent) properties of a chemical system in equilibrium are completely determined (there are no available degrees of freedom) if two phases are present in a two-component system, or three phases are present in a three-component system.
While this may seem a bit esoteric, it has important prac­ tical consequences for galvanic ce11s, for it determines the kind of voltage - composition relation that wi11 be present in any electrode reaction.
Under ideal (open circuit or very low current) conditions, if there are no available degrees of freedom, the electrode potential will be independent of the electrode composition. This means that it wi 11 not change during the course of the electrode reaction, so that cells containing such electrodes will exhibit a constant-voltage plateau during discharge or recharge.
On the other hand, electrodes whose reactions involve insertion or deletion of atomic species from within their crystal structures will have potentials that vary with the concentration of inserted species. Cells with such insertion reaction electrodes will therefore necessarily have sloped voltage - capacity curves during discharge and recharge, even under ideal conditions.
The difference between these two types of electrode reactions is illustrated schematically in Figure 1.
v v
q q
reaction. and right: insertion reaction electrodes.
KINETIC CONSIDERATIONS
Contributions to Overall Cell Kinetics
The overall kinetic behavior of any cell is going to be determined by both the thermodynamic driving force and a series combination of the impedances due to the electrode reactions and transport across the electrolyte, in addition to the obvious connector resistances. The sum of these impedances thus consti­ tutes the internal impedance of the cell, and acts to reduce its output voltage as current is drawn from it.
Ionic transport in electrolytes is due primarily to the presence of an internal field, and thus the electrolyte impedance is resistive and, except at high currents when concen­ tration gradients may build up, will be independent of current density. It will then act to reduce the output voltage, and thus the power, in proportion to the current. Obviously, the greater the conductivity, the smaller this effect. Thus there is great interest in developing electrolytes with as high values of conductivity as possible.
9
10
On the other hand, the electrode impedances are more complicated. They may include a significant component due to the electrolyte/electrode interfacial reaction, although this factor is often inconsequential in solid state systems, as other processes are generally more dominant.
In the case of insertion reaction electrodes, the rate at which the electroactive species are incorporated into the electrode's host crystal structure is determined by solid state diffusion kinetics. Since the mass flux density at the !urface decreases with time (often being proportional to (t)-l 2) the effective electrode reaction impedance increases with time at any constant current. The rate of this increase depends upon the current density and the appropriate boundary conditions. Therefore, this contribution to the overall cell behavior can cause significant drops in the output voltage and power that depend upon the time or the total amount of charge passed.
The impedance of displacement reaction electrodes can be more complicated, since it can involve several possible pheno­ mena. These include solid state diffusion through growing reaction product layers, transport in a permeating electrolyte phase, etc. In addition, the microstructural geometry can change appreciably during the reaction. While these matters will not be discussed in detail here, one generally finds that the rates of such reactions decrease with time and total charge passed. Therefore, the impedance· contribution due to them becomes more important at higher currents, longer times, and greater values of total charge transferred.
Ionic Transference Number
One of the important properties of any electrolyte is its electronic, as distinct from ionic, conductivity. Because of its nominal selective filter characteristics, the transport of electronic species, either electrons or holes, allows the equivalent amount of ionic transport across the electrolyte. This constitutes internal leakage, and results in a decrease in the amount of stored energy, a process generally called self discharge. In addition, the external voltage of the cell is decreased by this internal short circuit.
Actual open circuit voltage = (Ideal open circuit voltage) x ti
where ti is the ionic transference number, the fraction of the total charge transport through the electrolyte carried by ionic species. With no electronic leakage, ti is unity.
Transport of Ionic Species in Solids
The operation of a galvanic cell involves the transport of chemical species into and out of the electrodes, and through the electrolyte. Here we shall discuss the general phenomenological features of such mass transport.
One can express the force Fi acting on any species i within a solid as
where Ui is the total potential energy of species i at a given location.
The requirement for equilibrium, and thus no current flow, is that the total potential gradient be zero for all species. This does not mean that the individual components of the poten­ tial gradient must be equal to zero, but only that their sum equals zero.
For a situation in which gradients in only the chemical potential and the electrostatic potential are important
Ui = n i = 11 i + z i qcp
where ni is the electrochemical potential and l1i the chemical potential per particle of species i, the latter related to the partial molar free energy per particle at fixed temperature and pressure. zi is the charge number, the number of positive elementary charges carried by a particle of species i, and q is the absolute magnitude of an elementary charge. cp is the local value of the inner electric potential.
The chemical potential is related to the concentration of species i by
where l1i· is the chemical potential of the proper standard state, and ai is an effective concentration, called the actlvlty. The activity and concentration are related by ai = y[i] and y is the so-called activity coefficient.
For simple one-dimensional transport the particle flux density of species i is
J. = til v. I I
11
12
where [i] is the concentration (particles per cm3) and vi is the average (drift) velocity (em/sec). The general mobility bi is a measure of the response of the i particles to an applied force, and is defined by
b. = [v./F.] 1. 1. 1.
Note that this is a different quantity from the electrical mobility ui' which is defined as the velocity per unit electrostatic field, or
These two different mobilities have different dimensions, and they are related by
If a chemical gradient and an electrostatic gradient are both present,
F. = - dn./dx = - [d~./dx + z.q d~/dx] 1. 1. 1. 1.
and thus the particle flux density of species i is
J. = - [i]b. [d~./dx + z.q d~/dx] 1. 1. 1. 1.
Transport Due Only to a Concentration Gradient
Let us now look at the special case in which there is no gradient in the inner electrostatic potential (no internal field). This is the case for metals, very heavily doped semiconductors, and "supported electrolytes", in which there is a very large concentration of mobile charged species. It is thus the situation in many electrode materials.
The particle flux density then can be written as
J i = - [i] bi d~i/dx
If we translate from a gradient in chemical potential to a gradient in concentration we can write the particle flux density as
This equation is directly analogous to the empirically observed diffusion relation commonly called Fick's First Law, which is generally written as
where the proportionality constant diffusion coefficient for species i.
D·* 1
D. = b.kT (d~na./d~n[i]) 1 1 1
is the chemical
The factor in front of the parentheses also has the dimensions of a diffusion coefficient. It is a measure of the random thermal motion of species i in the solid in the absence of a concentration gradient, and is called the self-diffusion coefficient. Thus
D. = b. k T 1 1
This is often called the Einstein relation.
The quotient in the parentheses in the prior equation is an enhancement factor, which relates the chemical and self diffu­ sion coefficients
D.* = D. (d~na./d~n[i]) 111
In some cases it can be extremely large. It was experimentally found to be as large as 7 x 10'+ in the intermetallic phase Li3Sb.
Transport Due Only to an Internal Field
Let us now look at the case in which there is no concentra­ tion gradient, and the only force causing particle flux is due to an internal field. This is generally true for electrolytes.
With this assumption, we have
J i = - [i]biziq dq,/dx
Since each particle carries a charge ziq, the electrical charge flux density, or partial current density Ii' carried by species i is
From Ohm's Law we can relate the partial conductivity <1i due to the drift of species i to the partial current density and the internal field by
13
14
The partial conductivity due to species i is related to the total conductivity a by
a. = a t. ~ ~
These relationships may now be substituted to give
J i = - [at/ziq] [dcjl/dx]
bi = [ati]/([i] (ziq)2]
By use of the Einstein relation, we can now find an expression for the relation between the self diffusion coefficient and the partial conductivity
D. = [a.kT/[i](z.q)2] ~ ~ ~
This is known as the Nernst-Einstein equation. It is useful when one wishes to compare conductivity data obtained from experiments in which only an electrostatic gradient is present, as is true for most electrolytes, to the results of self diffu­ sion experiments.
THE ELECTROLYTE STABILITY WINDOW
While the potential utility of a solid electrolyte is greatly dependent upon the magnitude and selectivity of its ionic conductivity, as well as the absence of appreciable electronic conduction, its practical utilization in galvanic cells also requires that it meet certain stability require­ ments. In addition to not being subject to thermal decomposi­ tion, it must be both chemically and electrochemically stable with respect to both the atmosphere and the electrodes with which it is in contact.
This is a particularly important matter, as a number of potential high performance battery systems being considered involve the use of very aggressive, and therefore very demand­ ing, electrode materials.
It is not enough to know the voltage at which a phase decomposes, which establishes its electrolytic limit. In addi­ tion, the actual values of the limiting potentials must be known in order to evaluate its electrochemical stability with regard to its possible use in conjunct ion with specific electrodes, each of which establishes the value of the potential at its electrolyte/electrode interface.
In the case of binary phases the stability range can be readily computed if the Gibbs free energies of formation are known for the adjacent phases. In the case of terminal phases, the value of the negative end of the window is the potential of the cationic component.
The situation is more complicated for ternary electrolyte phases. In such cases one needs to know the phases present in the ternary system, and the identity of the stable tie lines in the ternary phase diagram. This then allows the identification of the polyphase reactions that determine the bounds of the stability window of the phase in question. If one has the values of the Gibbs free energies of formation of the pertinent phases, the potentials at which these reactions will occur under equilibrium conditions can be determined.
Data on the stability windows of a number of cation­ conducting electrolytes are included in Table I. It is seen that some electrolytes have quite wide windows, but they do not extend to potentials as negative as the alkali metal itself. This does not mean that they cannot be used, but ins tead that they will only be in equilibrium with alloy or compound electrodes that have more positive potentials. A number of such materials are now known.
Another possibility that is actually employed in some battery systems is to use an electrolyte/electrode combination that is not inherently stable, but which produces a protective solid electrolyte as a reaction product on the electrode sur­ face. This layer acts as a second electrolyte in series with the primary electrolyte, and effectively extends the stability window of the cell.
15
16
Li-Rich Li-Poor Material E vs. Li E vs. Li Temp.
Lil 0 2.79 2S·C Li3N 0 0.44 2S·C LiCl 0 3.98 2S·C LiAlC14 1.68 4.36 2S·C LiAICl4 1. 70 4.20 13S·C Li9NzCl3 0 2.S 100·C LillN3ClZ 0 1.8 322·C Li6NBr3 0 1.3 176·C Li13N4Br(LT) 0 1.3 146·C Li 13N4Br(HT) 0 0.6S 300·C LiSN1Z (LT) 0 1.9 98·C LisN1z(HT) 0 1.6 287·C Li6· 67Nl .S9 I 0 0.9 313·C Li9 ·UNz .7 1 0 0.9 316·C LizO 0 2.84 1S0·C LiN03 2.S 4.2 IS0·C Li4Si04 0.14 3.06 41S·C LizSi03 0.86 3.3S 41S"C LiZSiZOS 1.31 3.31 41S·C Lis Zr06 0 > 2.6S 32S"C Li4Zr04 0 > 2.70 32S·C LizZr03 < 0.3S 3.06 32S·C
Dr. Phil Bennett asked for clarification of the details of the e.m.f. versus composition curve in the LiyKO.Z7VZOS system. Professor Huggins explained that it exhibLted both insertion and two-phase reaction behaviour.
17
Dr. Don Murphy introduced the topic of the role of film formation on the lithium electrode in thionyl chloride primary cells and nitrate melt secondaries. He suggested that failure to recharge in the former case was not a function of conductivity of the film (LiCI) but attributable to the nature of the cathode reaction. Professor Huggins felt that both the conductivity and structure of the anode films did playa role in the possible cycling behaviour of such cells.
Dr. Sven Atlung pointed out that, although "supported" layer structures were not expected to exhibit expansion during interca­ lation, they did experimentally show volume increases.
There followed a number of comments regarding thermodynamic and kinetic considerations. In reply to a question from Dr. G. Wirtz, Professor Huggins suggested that the so-called "kinetic stability" of lithium beta-alumina to lithium was in fact attributable to the formation of a protective interfacial film. Dr. Ron Dell made the general comment that thermodynamics only predicts what should happen during chemical reactions. These predictions are more likely to be correct at higher temperatures. On the question of phase diagrams, it was agreed that their usefulness should be brought more to the attention of battery technologists.
STRUCTURAL ASPECTS OF IONIC TRANSPORT IN SOLID STATE BATTERY MATERIALS
Gregory C. Farrington
Department of Materials Science University of Pennsylvania 3231 Walnut St. Philadelphia, PA 19104 USA
1. INTRODUCTION
High conductivity solid electrolytes have been known since the 1830's. At that time, Faraday, reported that PbF2 at red heat conducts electricity about as well as pt. We now know that the high conductivity of PbF2 is the result of the rapid ~!ffusion of F- ions through a relatively immobile Pb sublattice. PbF was the first reported example of a solid electrol~te with high ionic conductivity.
19
Around the turn of the century, Frenkel and Schottky proposed their classic mechanisms that explain how electricity can be conducted through ionic solids by the flow of ions. Frenkel disorder, in which ions move from normal lattice sites to interstitial sites, and Schottky disorder, by which the volume of a crystal expands and vacancies are introduced in normal lattice positions, established a clear structural basis for the occurrence of ionic conductivity in a crystalline solid.
These first models for ionic defects stimulated interest in ionic conductivity in crystalline solids. But most solids were found to have very low conductivities at normal temperatures, and the study of ionic conductivity in crystalline solids was primarily directed toward understanding the rich defect chemistry
20
and physics that occurs in these materials.
The first detailed study of the structural basis for high ionic conductivity in a crystalline solid was carried out by Ketellar and co-workers in the 1930's. Ketelaar investigated the properties of Ag 2Hgl 4 , which undergoes a tra~sition at 49-50°C to a form a phase in which the Ag ions are disordered among a much larger population of tetrahedral sites in the structure. The !~nic condu£iivity of this phase is in the range of 10 (ohm-cm) • Ketelaar and colleagues carried out a coordinated study of the thermochemistry of this phase transition, and the changes in conductivity and structure that accompany it. Their work is a prototype for later studies of other high conductivity solid electrolytes.
Recent interest in high conductivity solid electrolytes was stimulated by the report from Yao and Kummer in 1965 [1] that sodium beta alumina has a sodium ion conductivity at room temperature comparable to that of an aqueous sodium chloride solution. The simultaneous invention of the sodium/beta alumina/sulfur battery by the same research group at the Ford Motor Company intensified interest in the commercial applications of solid electrolytes.
Now we know of a variety of solids that have high ionic conductivities. These include crystalline compounds, glasses, polymers, and heterogeneous dispersions. We also know that high ionic conductivity in solids is not restricted to the motion of monovalent ions. Beta" alumina, for example, is a good2fondu'2~or of a ~~riet~+of d~~alent cations, including Pb , Ca" , Ba , Zn , Sn [2], as well as various trivalent cations [3].
The diversity of high conductivity solid electrolytes might suggest that the only characteristic that unites them is their high conductivity. This is partly true, but all high conductivity solid electrolytes share another characteristic. They all owe their conductivities to highly disordered regions in their structures. These regions may encompass an entire crystal (Agl), be restricted to specific internal interfaces (A1 2 0 1 dispersed in Lil), occur as highly disordered regl0fls in a crystal (beta aluminas), or involve liquid-like disorder of an amorphous material (glasses and polymers). For all of the diversity of the hosts, the challenges in understanding the structures of
21
2. WHAT IS A HIGH CONDUCTIVITY SOLID ELECTROLYTE?
The definition of what constitutes a high conductivity solid electrolyte depends somewhat on the interests of the person doing the defining. Most generally, any solid that develops a high ionic conductivity before it melts is a high conductivity solid electrolyte. The materials that have received the most investigation are those that are potentially useful or have unusually high conductivities at relatively low tempera tures.
Some compounds that have been intensively investigated have very poor conductivities at moderate (2S-100°C) temperatures, and only become good conductors at SOO-IOOO°C. For example, the stabilized zirconias, e.g. CaO.ZrO , have unexceptional conductivities at moder~te temperatures. However, their melting points are high, and they develop truly high ionic conductivities well before they melt. They are important technologically as electrolytes for commercial oxygen sensors and prototype high temperature fuel cells, and therefore have been investigated extensively.
The truly exceptional solid electrolytes are those that have conductivities comparable to liquid electrolytes at moderate temperatures. The conductivities of these materials, which are also known as fast ion conductor~4and super!£nic conductors, are typically at least 10 (ohm-cm) at 2S-100°C. Examples of materials of this type include crystalline compounds" such as RbAg I , be ta alumina, and LilN; ionically-conductfv~ polymer complexes [4], and composite electrolytes, for example, those formed by dispersing Al203 in LiI.
In all of these materials, a key challenge is to understand the relationship between structure, composition, and ionic conductivity. The meaning of the words composition and conductivity are well-defined, but structure is a more elusive concept that is used in many different ways. In its strictest sense, it means an arrangement of species on the points of an ideal Bravais lattice. The result is a unit cell that can be replicated by translation in three dimensions to form a crystal. But, structure is also used to describe the local arrangement of atoms in a material that is
22
otherwise amorphous on the macroscopic scale. It can also be used to describe the arrangement of species in the interfacial region between two materials.
Our ability to probe structure varies considerably. The structure of the conductive region in a heterogeneous composite electrolyte is most difficult to study. These materials have high ionic conductivities that are believed to be the result of specific interactions and disorder at the interface between a matrix (i.e. LiI) and a dispersed particle (i.e. Al 0 ). As with conventional electrochemical in~eifaces, the interfacial region in which the conduction occurs is as thin as IO-IOOA. Good techniques for determining the local arrangement of species in an interfacial region of this scale are simply not available.
Ionically-conductive glasses and polymer complexes are somewhat more amenable to structural study. They are homogeneous compositions whose properties resemble those of high-viscosity liquids. Understanding structure in these materials means examining how intertwined polymer chains or interconnected covalent-ionic networks support ionic conductivity in what are essentially amorphous compositions. In these materials, the study of structure is an attempt to understand the makeup of the amorphous network in which ions are mobile and how changes in composition alter the network and the magnitude of the observed ionic conductivity.
Structure is most easily probed in crystalline electrolytes. Materials of this sort can be examined with classical diffraction techniques. They offer the most fertile territory for understanding the ion/ion and ion/lattice interactions that give rise to fast ion transport in solids.
3. GENERAL CONDITIONS FOR HIGH IONIC CONDUCTIVITY IN SOLIDS
Several conditions must be met for a solid to be a good ionic conductor at moderate temperatures. First, the potentially-mobile species must be present as ions and not be trapped in strong covalent bonds. Second, a population of alternate ~ites that the ions can potentially occupy and that are not their principal crystallographic positions must also exist. Third, the energy to disorder the ions among the larger population
23
of alternate sites and the energy to move the ions among those sites must be low.
In most crystals, the energy to move an ion from a normal crystallographic position to an alternate site, that is, the energy to create a defect, is quite high, typically 1-2 eV (23-46 kcal/mole). consequently, the population of defects, examples of which are interstitial ions and vacancies, is quite small. Since ionic conductivity requires the motion of ions from normal to alternate sites, the ionic conductivities of nO~~61 crys!ils are qui!i low, generally in the range of 10 to 10 (ohm-cm) at 29°C.
The population of defects and their mobility vary according to an Arrhenius expression of the type shown in the equation below. The expression predicts
cr T A exp[-E/kT]
that, at some sufficiently-high temperature, the defect concentration and ionic condutivity should be quite high, most normal solids melt before this occurs.
What makes high conductivity solid electrolytes remarkable is that their populations of defects is very high at moderate temperatures, because their defect formation energies are very low. The defect formation energy may be low for one of several reasons. Some compounds, such as AgI, Ag HgI , and RbAg IS' undergo specific order/dis8rde~ transitioAs that involve a latent heat similar to the latent heat of melting of a solid. This latent heat represents the enthalpy required to disorder ions among the alternate sites in the crystal and therefore to create a large population of defects. At temperatures above the transition, the defect creation enthalpy is essentially zero. Other compounds, such as the beta aluminas, owe their high conductivities to ionic defects and disorder that are the result of specific compositional non-stoichiometry introduced during their formation.
Crystalline high conductivity solid electrolytes are not simple solids perturbed by occasional, non-interacting point defects. High conductivity solid electrolytes have high defect concentrations that may be confined to specific regions of the solid. The overall crystalline framework may resemble a classical crystalline solid, but the highly disordered regions are more closely related to liquids. These materials are far
24
more complex structurally than more traditional crystals that have small concentrations of defects.
Understanding high ionic conductivity in such solids involves studying disorder and defects that often occur in restricted dimensions on the scale of 5-10A. The situation is similar to the disorder found in ionically-conductive polymers, glasses, and composites. In this way, these very different hosts are quite similar.
4. SUMMARY
The principal goal of examining the structures of high conductivity solid electrolytes is to define the special conditions that produce a high concentration of mobile ion defects in a material and to use that information to predict other solids that should be good ionic conductors. What structure means and our ability to define it precisely depend on an electrolyte's degree of crystallinity and its heterogeneity.
In all materials of this type, the study of structure is particularly challenging because of the high defect population. In some materials, the defect population is distributed homogeneously throughout an otherwise crystalline (e.g. AgI) or amorphous (glasses, polymers) network. In others, the defect population is confined to specific regions of disorder that occur regularly in a classical, crystalline framework (e.g. the beta aluminas).
For these special reasons, the diffraction techniques developed for determining the structures of more well-behaved materials are frequently inadequate for these highly disordered electrolytes. Their structures combine characteristics normally seen separa tely in solids and liquids. The study of high conductivity solid electrolytes has, therefore, pushed traditional techniques for studying structure to their limits and forced the development of more-powerful approaches for understanding large-scale disorder in the solid state.
5. ACKNOWLEDGEMENTS
Support for the research from which this article was derived was generously provided by the National Science
Foundation, MRL Program, Grant No. DMR-7923647, and by the Office of Naval Research.
25
1. Yao, Y-F.Y. and J.T. Kummer. J. Inorg. Nucl. Chern. 29 (1967) 2453
2. Farrington, G.C. and B. Dunn. Solid State Ionics. 7 (1982) 267
3. Farrington, G.C., Dunn, B., and J.O. Thomas. Appl. Phys. A. 32 (1983) 159
4. Blonsky, P.M., D.F. Shriver, P. Austin, and H.R. Allcock. J. Am. Chern. Soc. 106 (1984) 6854
26
DISCUSSION ==============
The lively discussion period after this lecture focussed on B and B" alumina. Professor Farrington emphasised that these two non-stoichiometric substances are sufficiently different in their structural and transport properties as to merit distinctive names. In response to a question on the preparation of these phases in single cyrstal form, suitable for structural studies, he emphasised the difficulty of growing these crystals; flux melt techniques are employed at 1700oC. The non-availability of certain compositions in single crystal form, for instance Li-doped B", has seriously impeded structural work.
Dr. H. Duncan drew attention to the fact that the earliest reports of the B" ~hase related to the pure (undoped) compound, sug~esting that Na ions'may enter the spinel blocks in place of Al3 to provide charge compensation for excess Na+ in the conduction plane. A stoichiometric relationship holds between the atom % of MgO or Li20 needed to substitute in the spinel block to compensate for excess Na20, viz: one Mg2+ substituted for A13+ compensates for one additional Na+, while one Li+ compensates for two added Na+. The possibility of anion substitution (e.g. N3- for 0=) as a means of charge compensation was raised by Dr. M. Armand; little has been done on this topic as yet.
Dr. D. Whitmore enquired about the reason for Pb2+-doped B" Al203 being a better conductor than Ca2+ or Ba2+ doped material. This is not yet clear, but ordering studies, using neutron techniques, are in progress at Uppsala.
Dr. A Clearfield finally drew attention to the 3 dimensional cavity structure of NASICON and how, by judicious substitutions, the cavity size can be changed with dramatic effects upon the conductivity. It was generally agreed that for both 2 and 3 dimensional conductors there exists enormous scope for improving our understanding of the effects of substitutions on structure and ionic conductivity. Although such fundamental studies are not immediately relevant to battery developments, there is a general feeling that it is necessary to understand the fundamental principles governing the relationship between composition, structure and ionic conductivity in order to be able to predict the most promising battery materials.
THEME 2
Gregory C. Farrington
Department of Materials Science University of Pennsylvania 3231 Walnut st. Philadelphia, PA 19104 USA
1. INTRODUCTION
High conductivity solid electrolytes include many different materials with diverse physical characteristics. All share a high4ionic cong~ctivity that is generally greater than 10 (ohm-cm) at some technolo­ gically-useful temperature. This discussion briefly reviews their general physical characteristics, mechanical and chemical properties, as well as their ease of study and application in real devices.
2. GENERAL PHYSICAL CHARACTERISTICS
Solid electrolytes can be generally separated into crystalline, amorphous and heterogeneous conductors. Crystalline electrolytes include compounds such as Li 3N, Na-beta alumina, NASICON, the stabilized zirconias, AgI, RbAg4I S' and many others. In each, ionic conductivity occurs within a well-defined crystalline host whose structure and composition must be maintained for high ionic conductivity to be observed. The mechanisms by which ions diffuse rapidly in these materials are related to those that lead to ionic conductivity in classic ionic solids, such as NaCl, BaC12 , and LiI.
Amorphous solid electrolytes, in contrast, more
30
closely resemble liquid electrolytes than crystalline solids. They include ionically-conductive glasses and polymer complexes. Many different examples of conductive glasses are known. Examples of conductive polymer electrolytes are the complexes formed by polyethylene oxide (PEO) and various ionic salts.
A third group of solid electrolytes includes the heterogeneous conductors, typified by the dispersions of A120~ in LiI tha~ have been shown to be good condoctors of Li • In these materials, ionic conductivity is believed to occur in the thin interfacial region surrounding the dispersed particles.
3. PREPARATION
Some solid electrolytes are easy to prepare, others are much more difficult. Crystalline solid electrolytes require the greatest control of composition and preparation conditions. Single crystals of these materials generally have the highest ionic. conductivities. Most can be grown in this form. The study of the relationship between structure, composition, and ion transport in single crystals of high conductivity solid electrolytes has been a central research topic in solid state ionics.
Unfortunately, crystalline solid electrolytes may be fine for study, but they can be difficult to use. Single crystals are far too expensive for most applications, so real devices use polycrystalline ceramic electrolytes. Soft electrolytes that flow under pressure, such as AgI, can be easily pressed into useful forms. However, preparing polycrystalline ceramics of hard, refractory electrolytes, examples of which include the stabilized zirconias, NASICON, and the beta aluminas, is quite difficult.
A polycrystalline solid electrolyte membrane that is a relatively poor ionic conductor may be useful in sensor applications for which high conductivity and high strength are not essential. However, for batteries and fuel cells an electrolyte must have high conductivity, high strength, and long-term electrochemical stability. Taking a single solid electrolyte that has the right characteristics as a single crystal and translating it into a ceramic that retains those desirable properties at an acceptable cost for a technological application can be a quite challenging and formidable task. It may require several years of ceramic development to prepare an appropriate electrolyte for a single application.
31
One such program has been the development of tubes of polycrystalline sodium beta and beta" alumina for the sodium/sulfur battery. Research and development to prepare beta/beta" alumina tubes that can hold molten sodium in contact with molten sulfur at 300-350°C and withstand extended electrochemical cycling have been underway for more than 15 years. Excellent electrolytes are now available, but the required cost/performance requirements are still not completely satisfied. Even if they ultimately are, the electrolytes produced will not necessarily be useful in other applications. The development of beta/~ta" alumina ceramics wi th optimum characteristics as Na conductors for another application at another temperature, such as IOO-200°C, would require considerably more work.
The complexity of working with crystalline solid electrolytes has stimulated interest in electrolytes that are much easier to form into useful shapes. The various conductive polymer complexes formed from PEO and alkali ion salts are the archetypes of these materials. They can be easily formed in thin films by solution casting. These thin film electrolytes may ultimately be useful in rechargeable lithium batteries, although many problems must be solved to make these devices a commercial reality.
4. MECHANICAL AND CHEMICAL PROPERTIES
From the mechanical standpoint, the crystalline ceramic solid electrolytes are the most appropriate for applications that require physical strength, such as membranes to separate molten liquid electrodes. Polymer electrolytes, in contrast, are physically weak and principally useful as separators in thin film, solid state systems.
The chemical stability of solid electrolytes varies greatly. Many crystalline and glassy compositions are stable in the presence of molten sodium. Among them are various beta alumina and NASICON materials. However, very few are stable with molten lithium. Li N is one electrolyte that is thermodynamically ~table in the presence of molten lithium, but unfortunately is thermodynamically unstable in the presence of most oxidants. The polymer complexe electrolytes are particularly delicate. They dissolve in many organic solvents, decompose at moderate temperatures, and react with molten alkali metals and strong oxidants. However,
32
they appear to be kinetically stable in contact with solid lithium electrodes and various solid cathodes.
5. IONIC DIFFUSION AND CONDUCTIVITY MEASUREMENTS
The first challenge in studying a potential solid electrolyte is assessing its conductivity. There is no more convincing demonstration that ionic transport occurs in a solid than a dc transport measurement or tracer diffusion experiment carried out with a high quality single crystal or well-characterized sample of an amorphous electrolyte. However, practical considerations complicate studies of this sort. Single crystals are not always available, and electrolytes are not always stable under the chemical conditions required for dc conductivity and tracer diffusion experiments.
The ac techniques that use blocking electrodes for conductivity measurements, discussed elsewhere in this volume, were developed specifically to circumvent many of these difficulties. When applied properly, they are arguably the most powerful techniques for measuring the ionic conductivities of various electrolytes over a wide range of chemical and physical conditions. But, they have been frequently misused. Anyone beginning studies of this sort is urged to learn as much as possible from established programs and to begin his work by studying selected standard materials that have well-characterized properties.
The quality and usefulness of the information produced by conductivity measurements are strongly related to the characteristics of the samples being studied. The most vexing challenge is that of evaluating the conductivity of an electrolyte that is only available as a powder. Normal conductivity measurements and tracer diffusion studies are of little or limited usefulness with powder samples. Other techniques that indicate the occurrence of ionic motion in a solid, such as nuclear magnetic resonance and ac dielectric loss measurements, have been applied to the problem with limited success. It is reasonable to say that a definitive demonstration of ionic conductivity in a solid requires measurements on a dense sample of the material with reasonable dimensions, typically the range of 1-2 mm.
In the particular case of crystalline electrolytes, it is essential to study single crystal specimens to obtain truly intrinsic conductivity and ion transport data. The conductivity of a polycrystalline specimen is generally dominated by grain boundaries that have lower
33
conductivities than the grains they separate. Grain boundary conductivity is an extrinsic characteristic that is influenced by the conditions under which a specific sample has been prepared. For example, the conducti~~ty of a single_1rystal of sodium beta alumina is about 10 (ohm-cm) at 25°C, but the conductivities of polycrystalline samples of sodium beta alumina at the same temperature vary frQ~ slightly_less than the single crystal value to 10 (ohm-cm) and lower, depending on the conditions under which the samples are prepared.
Measurements on a single crystal determine the maximum conductivity than can be expected for a particular electrolyte composition and structure. Measurements on polycrystalline samples demonstrate how close real materials approach the single crystal limit. Each type of measurement is important for different reasons. But, it should be no surprise when a polycrystalline sample of an electrolyte has a lower conductivity than has been measured or reported for a single crystal of the same material.
6. INTERFACIAL CONTACT
Achieving good interfacial contact across a solid electrolyte interface can be quite difficult. For applications that do not require extensive ionic charge transport across the interface, such as in solid state potentiometric sensors, the problem can generally be solved. Battery applications in which the interface must withstand extended charge flow and cycling are not so difficult if the interface is between a liquid electrode or electrolyte and a solid electrolyte. The most challenging situation arises in an all-solid-state battery in which considerable ionic charge must flow from one solid electrode, through a solid electrolyte, and into another solid electrode.
The most successful solid state batteries are those that have been made using crystalline electrolytes that deform under stress, such as those based on the AgI and RbAg I salts, and those that use polymer complex elec!r61ytes, which have a similar ability to flow. The deformability of these electrolytes produces interfaces with solid electrodes that are self-healing. The interfaces can accommodate the significant changes of lattice parameter and volume that accompany mass flow from one electrode to the other.
34
High conductivity solid electrolytes vary greatly in their physical characteristics, mechanical strength, chemical stability, and the ease with which they can be used in real devices.
Hard, crystalline electrolytes generally require precise control of composition and structure. They include the strongest and most stable materials, but, in real applications, must be used as polycrystalline ceramics. These ceramics are not simple to develop and their optimization can require many years of effort. The hard, crystalline electrolytes have been most useful as separators in high temperature batteries using liquid electrodes (Na/S battery), in high temperature fuel cells (the stabilized zirconias), and in potentiometric sensors.
Crystalline electrolytes that deform easily also require careful control of composition and structure, but are much easier to form into technologically useful shapes. They are not as strong as the ceramic electrolytes and not as stable in harsh chemical environments. They are being applied mostly as separators in low power, high energy solid state batteries.
Amorphous, soft electrolytes based on various polymer complexes are the easiest to form into useful shapes and into thin films. However, they are physically weak and not stable at high temperatures. Their principal applications are in all-solid-state batteries operating at moderate temperatures.
8. ACKNOWLEDGEMENTS
Support for the research from which this article was derived was generously provided by the National Science Foundation, MRL Program, Grant No. DMR-7923647, and by the Office of Naval Research.
IONICALLY CONDUCTING INORGANIC CRYSTALLINE MATERIALS
Robert A. Huggins
Department of Materials Science and Engineering Stanford University Stanford, CA 94305
HISTORICAL COMMENTS
While we may think of this area of interest as new, due to the rapidly increasing current interest and the hopes for inter­ esting applications to battery systems, this is not really the case. Actually, electrical conduction as the result of the motion of ions in solids has been recognized and attracted scientific attention for a long time.
During the period 1833-39 Michael Faraday observed electri­ cal conduction in nonmetallic solids (Ag2S and PbF2) at high temperatures. These two materials are still of great interest as examples of fast ionic conduction. Warburg and his associ­ ates published reports on these phenomena in 1884 and 1888 (1,2). During the two decades 1910-30 Tubandt and his group (3) demonstrated high ionic conductivity in a number of simple salts, and demonstrated that Faraday's law is obeyed, proving that electrical charge is carried by the ions in these mater­ ials. One of the more interesting papers was that by Tubandt and Lorenz (4), who showed the very high conductivity in AgI, AgBr and Agel, and used marker experiment s to demons t rate that the charge was carried by the silver ions. Their measurements showed that the ionic conductivity in AgI is actually more than 20 % higher in the solid state near the melting point than it is after melting.
35
36
Contrary to the common perception that this early work involved only silver and copper conductors, in addition to the report of ionic conduction (due to fluorine ions) in PbF2 by Faraday, mentioned above, the high ionic conductivity of the lithium conductor Li2 S04 at elevated temperatures was demon­ strated by Benrath and Drekopf in 1921 (5).
Haber, Treadwell, Katayama and others used solid electro­ lytes in galvanic cells for thermodynamic measurements during the period 1904-20 (6).
In 1926 Frenkel introduced the concept of the thermodynamic equilibrium of vacancies and interstitials'in solids, analagous to the dissociation of diatomic molecules in .gases, and showed that one can apply the law of mass action to such processes (7). Furthermore, he presented the first realistic and quanti­ tative physical mechanisms for the rapid transport of ionic species in solids, the motion of ions by jumps between intersti­ tial sites, and also the interstitialcy mechanism, which involves the coordinated displacement of ions on normal lattice sites by adjacent interstitials to form new interstitial species at a different location.
A general treatment of the equilibria of crystalline defects, vacancies, interstitials and anti-structure defects, in terms of statistical mechanics was published by Wagner and Schottky in 1931 (8).
In 1933 Wagner showed that the mechanism of solid state reactions such as oxidation and tarnishing must involve the transport of two charged species, typically one ionic and the other electronic (9). He also introduced the concept of (elec­ tronicj holes in semiconductors and other nonmetals. Short ly thereafter he showed that doping of semiconductors with other aliovalent atomic species can be used to change the concentra­ tions of electrons and holes.
This area has received greatly renewed emphasis in recent years. Recognit ion of the potential utility of solid ionic conductors for a wide range of purposes arose from a group of important papers by Wagner and his co-workers (10-13). This interest was accelerated by the discovery of two important families of materials with unusually high values of ionic conductivity at surprisingly low temperatures. These were the silver-conducting ternary silver iodides, which were simulta­ neously discovered in England and the United States (14-17), and the alkali metal-conducting beta alumina family, whose high conductivity was discovered by workers at the Ford Scientific
Laboratory (18,19). The latter was of special importance because it lead to the recognition that a wide variety of ions can exhibi't rapid transport in solids. The Ford group also showed (20) that solid electrolytes such as sodium beta alumina could be employed in a radical new design of a high performance secondary battery, a Na/S cell having liquid electrodes and a solid electrolyte.
Solids with Schot tky disorder, in which ionic transport occurs by the motion of vacancies, such as the alkali halides, generally have relatively low ionic conductivities and high activation enthalpies. One the other hand, materials with Frenkel disorder, such as some silver and copper halides, typically transport electrical charge primarily by the motion of interstitial species, and have considerably greater conductivi­ ties and lower activation enthalpies. A third group of materials, called "fast ionic conductors", or even "superionic conductors" in some circles, have more extreme behavior, with very high ionic conductivity and unusually low values of activa­ tion enthalpy. There are also many intermediate cases, as well as situations in which a given material shifts from one type of behavior to another.
It is now apparent that materials which exhibit fast ionic conduction do so because of special characteristics related to their crystal structures. We shall now discuss this crystal structure dependence of fast ionic conduction and the reasons for this crystallographic influence on ionic transport kinetics. in solids.
MINIMUM ENERGY PATH MODEL OF IONIC TRANSPORT
A relatively simple structure-dependent model for the transport of ions through specific crystal structures was presented some time ago (21-24) which gives useful insight into the important crystallographic features of this process. It involves the determination of the potential profiles relative to the mobile species within specific arrangements of the other ions, with the basic assumption that the other constituents in the lattice are fixed in position on the time scale of the mot ion of the mobile species.
This type of calculation follows the general method initiated by Born and Mayer (25), in which the total energy is assumed to be the sum of two-body interaction energies between the mobile ion i and the surrounding lattice ions, j. It is the sum of three types of terms, the electrostatic coulombic interaction, dipolar polarization (van der Waals) interactions, and overlap repulsion between the closed shell ions. That is:
37
38
where
Ep = -(.~~-) L aj qi/r4 2 •
J
ER = b L exp [(ri + rj - rij)/a] j
and qi and qj are the charges, aj the polarizability, ri and r' repulsLon radii, b and a constants and rij the dis­ tance ~etween the mobile cation and the jth static lattice ion.
With the use of a computer, the total interact ion energy between a single mobile ion arbitrarily placed at any position within the crystal structure and the other atoms in the lattice can be calculated, with the simplifying assumption that all of the others remain fixed in position, rather than relaxing to accomodate the position assumed for the mobile ion. It was also assumed that there is no interaction between nearby mobile species, but that all of the energy resides in the mobile ion­ static lattice interaction.
By this method the variat ion of the total energy with the assumed position of the mobile ion within the available space in the structure can be found for a series of different crystal structures, lattice parameters and host ions, as well as different values of the cation repulsion radius. In addition to a series of points along the centerline between normal lattice sites, a three-dimensional array of off-center positions was also investigated.
One of the important results from this rather simple theoretical model was the conclusion that the potential profile is such that the minimum energy path between sites often does not follow the centerline. Instead, its location is strongly influenced by the value of the cation radius and the details of the host lattice. In the case of small mobile cations there is often a symmetrical pair or group of preferred paths which deviate toward the nearby anions along the inter-site path due to the relatively large influence of the attractive polarization energy term compared to the replusive term. In the case of the larger cations the opposite is true, and equivalent mLnLmum energy paths are sometimes found which deviate from the center-
line in the opposite sense, away from the nearby anions, as a result of the predominance of the repulsion term. The posi­ tional variation of both these short-range interactions is greater than that due to the coulombic term in many structures.
As a cation progresses between sites it moves through an array of anions which may be described as forming a series of apertures. In a bcc structure, for example, alternating north­ south and east-west dumbbell pairs of static ions define a series of very flexible apertures through which the mobile ions move. This type of aperture permits a variety of paths to accommodate the relative magnitudes of the short range attrac­ tive and repulsive forces as the mobile ion progresses through the structure.
After determining the potential profile, and thus the mini­ mum energy path, the variation of the (minimum) energy with position along the path can be found for ions of any radius. The competing effects of the polarization and repulsive terms, which are out of phase in some structures, can result in a flat­ ter potential profile for ions of particular sizes in favorable cases. If one assumes that the peak-to-valley distance can be treated as the activation enthalpy for motion, the variation of that quantity with ionic size and structural variables can be obtained. It has been found that ions of intermediate size should be more mobile in some structures than either smaller or larger ones.
Although the initial example involved cubic structures, calculations have also been made on interstitial motion in materials with the tetragonal rutile structure using the minimum energy path model (23). However, in this case the anions are not in positions of cubic symmetry and thus have a permanent dipole moment. This requires the introduction of an additional monopole-permanent dipole interaction energy EM' where
EM = p .• p. ·n?· J 1.J 1.J
.... and II j is the permanent dipole moment of the polarizable ion in the structure and i'ij is the unit vector from the ith to the jth ion. The value of t j must be calculated from the polarizability of the ion and the geometry of the structure.
This structure is also different from simple binary materials such as a-Agi as it also contains highly charged static cations, which provide an important additional coulombic repulsive force upon the mobile ions. It was found that the
39
40
minimum energy path does not deviate from the inter-site center­ line of the tunnel in this crystal structure.
These calculations have been made for interstitial motion in both oxides and fluorides. A lower activation enthalpy was found in the fluoride structure due to a decrease in the overlap repulsion term caused by the dependence of the preexponent ial factor upon the charges and polarizabilities of the ions present.
INTERSTITIAL MOTION IN BODY-CENTERED CUBIC STRUCTURES
One of the materials first recognized to have unusually high values of ionic conductivity was the high temperature alpha phase of AgI (4), which is stable above 146·C. Its crystal structure has a body-centered cubic arrangement of iodine ions, within which the silver ions move interstitially (26,27). This material is often considered to be a prototype of the simple fast ionic conductors, and illustrates several principles involved in such materials. It has been the subject of a large number of investigations (28).
The high temperature phase of Ag2S has a structure which is similar to that of Ag!. In this case, however, Ag ions move interstitially through tunnels in a body-centered cubic array of sulfur ions. This phase has been known for some time (10,29) to be a mixed conductor in which the Ag ions are very mobile, although the charge transport is dominated by electronic conduc­ tion. The chemical diffusion coefficient (30) has extremely high values (0.47 cm2/sec at 200·C). This is due in part to a large enhancement factor, which makes the chemical diffusion coefficient much greater than the self diffusion coefficient, and causes accelerated ionic transport when a concentration gradient is present.
It is also interesting that hydrogen diffusion in body­ centered cubic metals has a number of characteristics which are similar to those found in materials with the a-AgI structure that exhibit fast ionic conduction (6,31,32).
MATERIALS WITH UNIDIRECTIONAL TUNNELS
There are a number of materials containing unidirectional crystallographic tunnels within which ionic species can be quite mobile. While some of these are primarily ionic conductors, others show mixed ionic-electronic conduction. Among those which have received the greatest attention to date are several with the rutile structure, the alkali metal vanadium oxide
bronzes the quaternary lithium oxide aluminosilicate Il-eucryptite, and the phase ramsdellite).
hollandites, the alkali lithium titanium oxide
MATERIALS WITH THE FLUORITE AND ANTI-FLUORITE STRUCTURES
A number of materials with the fluorite (CaFz) structure have long been recognized as having high values of anionic conductivity at elevated temperatures. The most common is the ZrOZ family, in which oxide ions are mobile.
The properties of these fluorite structure oxides and many of their applications have been reviewed elsewhere (33-36) and will not be repeated here.
There are also a number of fluorides and chlorides with this same structure which show large values of anionic conduc­ tivity at elevated temperatures. Of special interest because of its very large conductivity (for fluoride ions) is PbFz which has been the subject of a number of investigations (37-50).
Experiments have also been reported on several materials with the anti-fluorite structure which have been found to be interesting cationic. conductors, especially for lithium ions. It has been found possible to produce structures, e.g., LisA104 , LiSGa04 and Li6Zn04, which have large concentrations of built-in vacancies (51,52), and high values of lithium ionic conductivity at moderate temperatures.
It has also been found (53-56) that rapid ionic diffusion is present in the electronically conducting phases Li 3Sb and Li3Bi, which have cubic structures similar to the anti-fluor­ ites. In these cases, however, both the tetrahedral and octa­ hedral interstices in the face-centered cubic Sb (or Bi) lattice are occupied by Li ions at the ideal stoichiometric composi­ tion. Ionic transport occurs by the motion of Li ions, and it was found that the interaction of ionic and electronic fluxes produces large values (up to 70,000 at 360·C in Li 3Sb) of the enhancement factor, and thus high chemical diffusion coeffi­ cients in the presence of compositional gradients.
Because it exhibits rather high values of both anionic (in the fluorite structure) and cationic (in the anti-fluorite structure) transport, it is worth giving consideration to the special features of this type of crystal structure.
Calculat ions have been made on simple minimum energy path model (23).
this structure using the The mobile ions normally
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reside in tetrahedrally coordinated sites within the face­ centered cubic sublattice of the other (static) species. While it has often been assumed in the literature that the mobile ions jump directly from tetrahedral to tetrahedral sites, an alter­ nate path is possible, involving motion in the direction of an intermediate normally empty octahedral site.
It was found that the minimum energy path from one tetra­ hedral site to the next follows a path that passes close to, but not through the center of, the intermediate octahedral site. This "is the jump path recent ly determined experimentally by use of sophisticated diffraction experiments (88). These experi­ ments have also shown that the thermal vibration of the mobile ion is highly anisotropic as well as anharmonic.
The calculated energy profile along a direct tetrahedral­ tetrahedral path was found to require a considerably greater activation enthalpy than for the tetrahedral-octahedral-tetra­ hedral path in all cases studied.
MATERIALS WITH LAYER STRUCTURES
The beta alumina family comprises the presently most important and visible group of ionically conducting materials with layer-type crystal structures.
Since a number of detailed reviews are available elsewhere a discussion of these materials will not be included here. Some of the earlier work can be found in (6,57-59).
Another structure that has been found to exhibit rapid transport, but of anions, is the tysonite (LaF3) type. Doped LaF3 is used commercially in fluoride ion-selective electrodes (60), and there have been several investigations of fluoride ion transport in LaF3-based materials (61-67). Materials with this structure, based on CeF3, have also been investigated and found to also have high values of fluoride ionic conductivity (68).
The mobile anions reside in three different types of sites in this structure, and according to NMR studies (69) transport of ions in and among these sites involves different values of activation enthalpy, which become important in the overall transport process in different temperature ranges.
The lithium nitride structure is also of the layer type. However, it is a cationic conductor, and there are two types of sites for the lithium ions, one in the hexagonal Li2N layers, and the other in the relatively open intermediate layers, where
they form N-Li-N bridges (70,71). Ionic conductivity results on polycrystalline (72,73) and single crystalline (74) samples have indicated that lithium ion transport is quite fast in this structure, and it is apparently very anisotropic. Evidently, transport is mainly by vacancies that are introduced into the lithium sublattice of the Li2N layers by the presence of hydro­ gen.
Rapid motion of inserted ions can also be found in a number of mixed-conducting materials with layer structures, such as those with the CdI2 structure, in which the layers of the binary host composition are bound together primarily by van der Waals forces, rather than being ionica11y bridged, as in the beta aluminas. Examples of such materials are the transition metal disulphides, such as TiS2.
There has been a considerable amount of work recently on other layered ionica11y conducting materials, such as group IV acid salts. A number of these materials have been known for some time to possess interesting ion exchange properties. Members of this family which appear to be most interesting are the zirconium hydrogen phosphates (75).
MATERIALS WITH 3-DlMENSIONAL ARRAYS OF TUNNELS
Of special interest are materials with crystal structures containing atomic-sized tunnels that are oriented in all three directions, so as to produce relatively isotropic ionic trans­ port.
The structures of the ternary silver iodides of the RbAg415 family (76,77) are of this type, and have very high Ag+ con­ ductivity values at ambient temperatures.
Several other groups of materials have subsequently been found which have skeleton or network structures composed of various arrays of corner-shared and edge-shared tetrahedra and octahedra, which are permeated by tunnels which are dilutely populated by mobile monovalent ions (78,79). There are many variants, including materials with the high pressure KSb03, defect pyrochlore, and boracite structures. One of the most prominent members of this group is the family of sodium zirconium phosphosilicates that has been given the general name Nasicon.
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STRUCTURES WITH ISOLATED TETRAHEDRA
Several relatively good lithium conductors have been found whose structures are characterized by isolated tetrahedral an­ ionic groups, between which the cations move.
One example of this group of materials is Li4Si04, and it has been shown (80-82) that Li ions are quite mobile in this type of structure. Moreover it has been found (72,83-85) that the conductivity can be considerably enhanced in Li4Si04-Li3P04 and related vanadate, antimonate and aluminate solid solutions.
Several alkali metal chloroaluminates also have structures in which alkali metal ions percolate between isolated tetrahed­ ral AlC14 groups. Conductivity measurements on LiAlC14, NaAlC14 and KAlC14 (86,87) have shown relatively rapid alkali metal ion motion in these materials as well.
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