Handbook of Solid State Batteries [2 ed.] 9789814651899, 9814651893

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HANDBOOK OF SOLID STATE BATTERIES

Second Edition

19/6/15 9:56 am

World Scientific Series in Materials and Energy* ISSN: 2335-6596

Series Editor: Leonard C. Feldman (Rutgers University)

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Published Vol. 2 Handbook of Instrumentation and Techniques for Semiconductor Nanostructure Characterization edited by Richard Haight (IBM TJ Watson Research Center, USA), Frances M. Ross (IBM TJ Watson Research Center, USA), James B. Hannon (IBM TJ Watson Research Center, USA) and Leonard C. Feldman (Rutgers University, USA) Vol. 3

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Vol. 6

Handbook of Solid State Batteries (2nd Edition) edited by Nancy J. Dudney (Oak Ridge National Laboratory, USA), William C. West (Nagoya University, Japan) and Jagjit Nanda (Oak Ridge National Laboratory, USA)

Forthcoming Batteries edited by Jack Vaughey (Argonne National Lab., USA) and David Schroeder Northern Illinois, USA) Encyclopedia of Practical Semiconductors (In 4 Volumes) edited by Eugene A. Fitzgerald (Massachusetts Institute of Technology, USA) Graphene edited by Michael G. Spencer (Cornell University, USA) Handbook of Silicon Surfaces and Formation of Interfaces: Basic Science in the Industrial World (2nd Edition) Jarek Dabrowski and Hans-Joachim Mussig (Institute for Semiconductor Research, Germany) *The complete list of titles in the series can be found at http://www.worldscientific.com/series/mae

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M AT E R I A L S A N D E N E R G Y – Vo l. 6

HANDBOOK OF SOLID STATE BATTERIES Second Edition

Nancy J Dudney

Oak Ridge National Laboratory, USA

William C West Nagoya University, Japan

Jagjit Nanda Oak Ridge National Laboratory, USA

World Scientific NEW JERSEY

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LONDON

9487_9789814651899_tp.indd 2

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SINGAPORE

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BEIJING

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SHANGHAI

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19/6/15 9:56 am

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

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UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

World Scientific Series in Materials and Energy — Vol. 6 HANDBOOK  OF  SOLID  STATE  BATTERIES 2nd Edition Copyright © 2016 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 978-981-4651-89-9 In-house Editor: Rhaimie Wahap Typeset by Stallion Press Email: [email protected] Printed in Singapore

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Preface

Solid-state batteries hold the promise of providing energy storage with high specific energy and high power density, yet with far less safety and temperature stability issues relative to those associated with conventional liquid or gel-based lithium-ion batteries. Solidstate batteries are envisioned to be useful for a vast range of energy storage applications, from powering automobiles, stationary storage and load-leveling of renewably generated energy, and powering the wide range of electronics that have become so pervasive in our lives. Tantalizing evidence of the promise of solid-state battery technology can be found in solid-state thin film batteries which are now commercially produced for specialized low energy applications. These solid-state batteries are capable of tens of thousands of deep discharge cycles at useful charge and discharge rates. The components are highly stable, with no appreciable electrolyte side reactions or electrode dissolution. These cells often incorporate very high specific energy lithium metal anodes resulting in high activemass basis specific energy. Since the last edition of this book, significant strides in the field of solid-state batteries have been achieved. In this second edition of this book, we have bought together many subject-matter experts

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Preface

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in the field of solid-state batteries, covering a wide range of topics. Herein, the authors summarize advancements in: ◦ Very high ionic conductivity sulfide- and oxide-based solid electrolytes with ionic conductivity nearly on-par with liquid lithiumion electrolytes ◦ New solid electrolytes for thin film batteries prepared by a number of different techniques ◦ Adaptation of powerful characterization tools including synchrotron based in-operando methods for studies of solid-state batteries ◦ In-depth characterization and modeling of the nature of the critical solid electrolyte-electrode interface ◦ Development of advanced in-situ and in-operando electron microscopy methods ◦ Incorporation of solid-state batteries into multi-functional and structural components ◦ Advanced ab initio modeling capabilities to predict structure and performance of solid electrolytes and solid-state batteries ◦ New cell designs incorporating three-dimensional structures ◦ New solid electrolytes for conduction of lithium, fluoride, and silver ions ◦ Advanced polymer electrolytes with a wide range of compositions, structural motifs, and additives for improved ionic conductivity and mechanical stability Yet many scientific and technological challenges remain. Many research activities focus on the ionic transport and electrochemical reactions of a single material, yet the challenge for devices hinge on the stability and unimpeded motion of ions across interfaces between the electrode-electrolyte and in some cases between multiple electrolytes. Cell designs utilizing thick, energy dense electrodes with a relatively small electrolyte contact area will be particularly challenging due to the high current density. The community also needs to investigate and provide avenues for practical industrial processing and mass production.

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While a commercially viable solid-state battery competitive with conventional lithium-ion batteries has yet to be fully realized, we anticipate further advancements that will soon bring this exciting new technology to fruition.

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Nancy J Dudney Oak Ridge National Laboratory William C West Nagoya University Jagjit Nanda Oak Ridge National Laboratory 14 June 2015

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May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory

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Contents

Preface Part 1.

v Enabling Techniques and Fundamentals of Solid State Systems

Chapter 1.

Fundamental Aspects of Ion Transport In Solid Electrolytes

1 3

S. R. Narayanan, Aswin K. Manohar and B. V. Ratnakumar Chapter 2.

In-situ Neutron Techniques for Lithium Ion and Solid-State Rechargeable Batteries

51

Yuping He and Howard Wang Chapter 3.

Synchrotron X-ray Based Operando Studies of Atomic and Electronic Structure in Batteries

79

Faisal M. Alamgir and Samson Y. Lai Chapter 4.

Analytical Electron Microscopy — Study of All Solid-State Batteries Ziying Wang and Ying Shirley Meng

ix

109

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Contents

Chapter 5.

Li-ion Dynamics in Solids as Seen Via Relaxation NMR

133

Viktor Epp and Martin Wilkening

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Chapter 6.

Crystalline Inorganic Solid Electrolytes: Computer Simulations and Comparisons with Experiment

191

M. D. Johannes and N. A. W. Holzwarth Part 2.

Novel Solid Electrolyte Systems and Interfaces

Chapter 7.

Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport and Mechanical Strength

233

235

Wyatt E. Tenhaeff and Sergiy Kalnaus Chapter 8.

Fluoride-Ion Conductors

277

Munnangi Anji Reddy and Maximilian Fichtner Chapter 9.

Thin Film Lithium Electrolytes

307

Jea Cho, Jane Chang, Amy Prieto and Nancy Dudney Chapter 10.

Solid Electrode–Inorganic Solid Electrolyte Interface for Advanced All-Solid-State Rechargeable Lithium Batteries

337

Yasutoshi Iriyama and Zempachi Ogumi Chapter 11.

Crystalline Sulfide Electrolytes for Li-S Batteries

365

Gayatri Sahu and Chengdu Liang Chapter 12.

Super-ionic Conducting Oxide Electrolytes Jeff Sakamoto

391

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Contents

Chapter 13.

Interface of 4 V Cathodes with Sulfide Electrolytes

page xi

xi

415

Kazunori Takada Chapter 14.

Glass and Glass-Ceramic Sulfide and Oxy-Sulfide Solid Electrolytes

433

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Steve W. Martin Chapter 15.

Crystalline Polymer Electrolytes

503

Yuri G. Andreev, Chuhong Zhang and Peter G. Bruce Chapter 16.

Polymer Electrolytes

523

Sabina Abbrent, Steve Greenbaum, Diana Golodnitsky and Emanuel Peled

Part 3.

Devices and 3D Architectures

591

Chapter 17. All Solid-State Thin Film Batteries

593

Jie Song and William West Chapter 18. Advancing Conversion Electrode Reversibility with Bulk Solid-State Batteries

627

Thomas A. Yersak and Se-Hee Lee Chapter 19.

Structural Batteries, Capacitors and Supercapacitors

657

J. F. Snyder, D. J. O’Brien and E. D. Wetzel Chapter 20.

Three-dimensional Batteries Nicolas Cirigliano and Bruce Dunn

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Chapter 21.

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Contents

Electrochemical Simulations of 3D-Battery Architectures

731

Vahur Zadin and Daniel Brandell

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Chapter 22.

Silver Ion Conducting Electrolytes and Silver Solid-State Batteries

779

Kevin Kirshenbaum, Roberta A. DiLeo, Kenneth J. Takeuchi, Amy C. Marschilok and Esther S. Takeuchi Index

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Chapter 1

Fundamental Aspects of Ion Transport In Solid Electrolytes S. R. Narayanan and Aswin K. Manohar Loker Hydrocarbon Research Institute University of Southern California Los Angeles, CA 90089, USA

B. V. Ratnakumar

Electrochemical Technologies Group Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109, USA

1. Introduction Solid electrolytes (also termed as superionic solids or fast ion conductors) are characterized by high ionic conductivity, sometimes comparable to concentrated liquid electrolytes or even molten salt electrolytes, made possible by rapid transport of ions in the solid lattice. The electronic conductivity is small with an electron transference number (te ) of less than 10−4 . A semi-empirical rule formulated by Heyne1 stipulates the allowable values for the electronic bandgap in good solid electrolytes to be higher than T/300 eV, i.e. a low electronic conductivity of 10−6 S/cm at any temperature — a necessary but not sufficient condition. Such superionic solids 3

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paved the way for the development of solid-state electrochemistry or solid-state ionics and also furthered progress in related technologies such as galvanic cells (batteries), fuel cells, capacitors, electrochromic devices and sensors. The conductivity of superionic solids (e.g. RbAg4 I5 — 0.27 S/cm at room temperature) is typically many orders of magnitude higher than that of commonly known ionic solids, (e.g. NaCl, KCl — 10−16 S/cm). Many ionic solids exhibit such high electrical conductivity above a certain temperature, often associated with distinct structural change (e.g. AgI). Furthermore, structures that permit rapid ion transport are generally disordered, channeled, or layered.2 Microscopically, the ionic conductivity in solids is caused by the existence of defects or disorder. A perfect crystal of an ionic compound would be an insulator.3 Based on the types of defects or disorder, the superionic solids can be classified as follows: Point defect (zero dimensional) type: Here, the concentration of the point defects is in the order of 1020 cm−3 . Molten-sub-lattice type: a case of liquid-like sub-lattice, in which the number of ions of a particular type is less than the number of sites available for them. The number of mobile ionic charge carriers is 1022 cm−3 . These materials are often marked by a channeled or layered structure or amorphous liquid-like regions as in polymeric materials.

Despite the fact that cations as well as anions can move in the solid lattice, mobility of cations is generally favored due to their small ionic size. Many of the known superionic solids are cationic conductors and especially of small size, e.g. Li+ , Na+ , K+ . Also many of the solid electrolytes involve a monovalent ion, owing to the relatively strong coulombic interactions between divalent or trivalent ions within the lattice. A rigorous correlation between the ionic conduction and the structural aspects of the solid electrolytes has been reported.2, 4–6 Anion conduction is represented largely by oxide ion conductors as in defect oxides with the perovskite structure7 and fluoride ion conduction occurs in doped-lanthanum fluoride.8–11 Ion conduction is encountered in solid polymeric electrolytes in the

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Fundamental Aspects of Ion Transport In Solid Electrolytes

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5

absence of free liquid phase. Lithium-ion and anion conduction are observed when ionic lithium salts are dispersed in polyethylene oxide or polyethers.12–14 Similarly, proton conduction is observed in certain anhydrous salts, solid acid compounds and polymeric materials.15–20 In these polymeric materials, ionic motion in salt– polymer complexes is not due to charges hopping from site to site. Rather it is a continuous motion occurring in the amorphous region of the polymeric material. 2. Defects and Disorders 2.1. Types of Defects The lattice defects present in an ionic solid are conventionally represented using the Kroger–Vink notation, which specifies the nature, location and effective charge of a defect relative to the neutral unperturbed lattice. The various kinds of point imperfections possible (Fig. 1) in an ionic crystal (MX, M and X are monovalent) taking into account the requirement of charge neutrality are as follows. (i) Vacancies: a missing M+ ion in a pure binary compound missing from its normal site depicted as V
M . Likewise a vacant anion site is represented by V·x (V stands for a vacancy, the subscript for the missing species and the superscript for the charge, prime for effective negative charge and dot for effective positive charge). (ii) Interstitials: An ion M+ or X− occurs in an interstitial site denoted as M·i or X
i . The term vacancy (or interstitial) defect may be understood to occur if in a volume element of the lattice, a particle is missing (or contains an excess particle) with respect to the ideal lattice, independent of whether at the point or in its immediate vicinity, particles deviate from their normal position or not. In other words, any such defect is believed to cause a certain distortion of the lattice in the immediate neighborhood. (iii) Antisite defects: An atom M occupying a normal X site or vice versa, MX , or XM . (iv) Schottky defects: A cation vacancy together with an anion vacancy (V
M , V·X ) predominantly present in alkali halides. In

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Fig. 1. Schematic illustrations of simple point defects that occur in a pure crystal compound MX and with impurity atoms (L, metal. S. non-metal).

this vacancy mechanism of conduction, positive and negative ions leave their normal sites to jump into vacancies. (v) Frenkel defect: A cation vacancy together with an interstitial cation (V
M , M·i ) as in silver halides. Anti-Frenkel defects (V
x , X
i ) occur in ThO2 and CaF2 . If the migration of atoms takes place by jumps of interstitials from interstice to interstice, it is termed an interstitial mechanism. When an interstitial jumps to a normal site pushing the atom at it to another interstice, it is termed an interstitialcy mechanism. (vi) Impurities: Aliovalent impurities substituting for a normal or interstitial site. Impurity cations of higher (than host cation)

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valence generate impurity cation + interstitial anion (LM , X) or impurity cation + cation vacancy (LM , VM ) defects. With a lower valence impurity, it is possible to get an impurity cation + anion vacancy or impurity cation + cation interstitial defect. A summary of the types of defects established in different ionic crystals is given in Table 1. In general, defect types based on interstitial anions (types ii, iii and vi) are less likely than their cation counterparts, due to a relatively closer packing of anions in most ionic solids.

Table 1.

Summary of defects in ionic crystals.

Type of substance and examples

Structure

Defect structure and transport mechanisms

Alkali halides LiF, NaCl, KI, etc.

NaCl (face centered cubic)

Schottky defects. Cation vacancies more mobile

Cesium halides CsI, CsCl, etc.

CsCl (simple cubic)

Schottky defects. Anion vacancies more mobile

Silver halides AgCI, AgBr, etc.

NaCl (face centered cubic)

Cation Frenkel defects. Cation motion by both vacancy and interstitialcy

Alkaline earth halides CaF2 , SrCl2 , etc.

Fluorite & others

Anion Frenkel defects. Anion vacancy and interstitial both mobile

Other halides PbBr2 , LaCl3 , etc.

Various

Schottky defects

Simple salts with complex anions NaNO3 , Ag2 SO4

Low symmetry

Cation Frenkel defects

Alkaline earth oxides

Wurtzite and NaCl

Schottky defects. Cation concentration controlled by impurities

Fluorite structure UO2 , ZrO2 :CaO

Fluorite

Anion Frenkel defects

Transition metal oxides FeO, Cr2 O3

Various

Cation diffusion by vacancies. Oxygen diffusion by dislocations

Divalent chalcogenides ZnS, PbTe

NaCl and others

Neutral Frenkel defects, both cation and anion

Small cations and large anions AgI, RbAg4 I5 , Li2 SO4 , etc.

Mostly cubic

Cation disorder

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2.2. Expressions for Defect Concentration

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The ionic conductivity as well as the diffusion coefficient are governed by the concentration of defects. The concentrations of the defects of both the Schottky and Frenkel type, under various conditions can be expressed in terms of the thermodynamic parameters corresponding to the defect formation as shown below22 : (i) Pure crystal Consider the case of Schottky defects. Let the mole fractions of positive and negative ion vacancies be x1 , and x2 and their numbers be n+ and n− respectively. n+ = n− = N exp ( − Gs /kT) x 1 x2 =

x02

(1)

= exp ( − Gs /kT)

= exp (Ss /K) exp ( − Hs /kT)

(2)

where Gs , Ss and Hs are the Gibbs energy, entropy and enthalpy, respectively, of the formation of a Schottky pair. N is the number of cation or anion sites. For a pure crystal, the charge neutrality condition is written as x1 = x2 = x0 , The Frenkel defects can likewise be expressed as nF = (NN
)1/2 exp ( − GF /2kT)

(3)

where N
is the number of interstitial sites and GF is the Gibbs energy for formation of Frenkel defects. (ii) Doped Crystal If an ionic crystal is doped by an aliovalent impurity (e.g. Ca++ in NaCl), additional cation vacancies are produced to compensate for the charge difference. The charge neutrality equation would then be x1 = x2 + c1 , where c1 is the mole fraction of the divalent impurity.

(4)

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9

From Eqs. (1), (2) and (4), we get x1 = 1/2c1 {[1 + (2x0 /c1 )2 ]1/2 + 1}, 2 1/2

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x2 = 1/2c1 {[1 + (2x0 /c1 ) ]

− 1}.

(5a) (5b)

For a large dopant concentration, i.e. c  x0 , the above equations reduce to x1 = c1 and x2 = x02 /c1 . For small concentrations, on the other hand, the concentrations reduce to the pure crystal values as expected, i.e. x1 = x2 = x0 . For a divalent anion impurity with a concentration c2 , the charge neutrality condition becomes x1 + c2 = x2

(6)

and the values of x1 and x2 would be x1 = 1/2c2 {[1 + (2x0 /c2 )2 ]1/2 − 1}, 2 1/2

x2 = 1/2c2 {[1 + (2x0 /c2 ) ]

+ 1}.

(7a) (7b)

The extra charge on the divalent cation impurity may also induce an association of the oppositely charged cation vacancies. Since these complexes will not contribute to the conductivity, it is essential to know and correct for the number of this associated impurity — vacancy pairs. 2.3. Lattice Disorder and Association of Defects The lattice disorder could be isotropic as in AgI, doped-ZrO2 and ThO2 , or in one direction as in crystals with a tunnel-type structure22 (e.g. tungsten bronze) or in two directions as in the crystals with a plane containing a loose, random packing of atoms sandwiched between close packed planes (e.g. β-alumina type23 ). The defects resulting from aliovalent impurities are in general randomly distributed over the appropriate sub-lattice sites and often carry a net charge. Electrostatic attraction between such charged defects may promote the formation of defect pairs or large clusters that may be electrically neutral or carry a net charge. Due to such association of defects, the concentration of free or quasi-free defects does not increase linearly with increasing defect concentration and

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may decrease with decreasing temperature. It follows from Lidiards analysis3 that at a given temperature, the conductivity varies with the impurity addition at first linearly (up to about 1% defect concentration) and then at a decreasing rate until it becomes nearly asymptotic. Beyond about 3–4% of defect concentration, however, the above analysis appears to break down, since the conductivity decreases with increasing defect concentration. At these high defect contents, clustering or ordering of defects starts. Calculations based on near-neighbor interactions24 show that the effective charge carrier concentration goes through a maximum at a certain dopant level in massively defective solids. When very large defect contents are involved, new compounds can occur. 3. Structural Features The potential utility of the solid electrolyte materials for a wide range of technological applications was brought out by Wagner and coworkers.25, 26 Further impetus to this field was provided by three families of materials exhibiting unusually high ionic conductivities at surprisingly low temperatures. These were: (a) Silver-conducting ternary silver iodides: Bradley and Greene27, 28 and Owens and Argue29 had described solid electrolyte of the form MAg4 I5 with conductances at ambient temperature in excess of 10−3 S/cm, the same value of conductance of a 10 M KCl aqueous solution. (b) Alkali metal-conducting β-aluminas: Yao and Kummer30, 31 showed that a single crystal of β-alumina exhibited rapid diffusion (diffusion coefficient of sodium ions: 1 × 10−5 cm2 /s at 300◦ C — a value comparable to that of molten NaNO3 ) of univalent cations in a plane perpendicular to the c-axis. (c) Inorganic lithium-ion conductors: Crystalline Li-ion conductors include perovskite-type lithium lanthanum titanates, NASICON-type, LiSICON- and Thio-LiSICON as well as garnettype conducting oxides with a conductivity of 3 × 10−3 S/cm close to room temperature. Amorphous Li-ion conductors include oxide and sulfide-based glasses as well as LIPON and

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related systems where conductivity values in the range of 10−6 to 1 × 10−3 S/cm have been observed. The β-alumina type materials were of particular importance due to a wide variety of fast ionic solid materials that emerged therefrom and to the formulation of a new battery system, sodium-sulfur32 of high specific energy and power with the solid electrolyte acting as a separator between the liquid reactants. The β-alumina type electrolyte is also employed in sodium-metal chloride (ZEBRA) batteries to transport sodium ions between a metallic sodium anode and a solid cathode composed of transition metal chlorides in chloroaluminate melts.33–36 In general, solid electrolytes with Schottky disorder, such as alkali halides, in which ionic transport occurs by the motion of vacancies have high activation enthalpies and low ionic conductivities. On the other hand, the materials with Frenkel disorder, such as some silver and copper halides, in which ionic transport occurs by the motion of interstitial species have low activation enthalpies and high ionic conductivities. The third group of materials called fast ionic or superionic conductors exhibit very high ionic conductivities and unusually low values of activation enthalpy. Many of the solid electrolytes may fall in between these three categories or even shift from one type of behavior to another. A number of structural features have been found to characterize the solids which have rapid ion transport and to distinguish them from the more usual ionic crystals. Typically, their structures are not close-packed but contain networks of ion-sized passageways consisting of interconnected polyhedra of the fixed ions, through which selected mobile ions may move. In general, the number of sites available for the mobile ions is much larger than the number of mobile ions themselves; hence the solid has a highly disordered structure. The high conductivity is brought about by a combination of mobile particles and a low enthalpy of activation for ion motion from site to site. It is now clear that the materials that exhibit fast ion conduction have special characteristics related to their crystal structures. Several reviews have appeared37–53 dealing with such fast ion conductors.

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These materials are broadly classified below based on their characteristic features related to the crystal structure.

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3.1. Interstitial Motion in Body Centered Cubic (BCC) Structure One of the first materials in this class54 was AgI above 146◦ C containing BCC arrangement of I− ions with which Ag+ ion moves interstitially.55 The high temperature phase of Ag2 S has a similar structure that permits Ag ions to move interstitially through the tunnels in the body-centered cubic array of sulfur ions.25 3.2. Interstitial Motion in Rutile Structure The rutile (TiO2 ) structure has a tetragonal symmetry in which the cations are octahedrally coordinated by anions and these octahedras are joined into a 3D framework by sharing corners such that each anion is adjacent to these cations. This arrangement produces a relatively open tunnel in the ‘c’ direction made up of a string of distorted edge-sharing tetrahedral sites that are empty in the ideal structure. Motion of ions residing in these sites would involve passing through a two-coordinate aperture (the shared edge) similar to that in the α-AgI structure. In such structures, lithium-ions56, 57 are quite mobile and the ionic transport is highly directional. 3.3. Other Materials with Unidirectional Tunnels Several other materials containing unidirectional crystallographic tunnels within which ionic species can be quite mobile, exist either primarily as ionic or as mixed conductors. Some examples are alkali metal vanadium oxide bronzes,60 the quarternary titanium oxide hollandites,61–63 the alkali aluminosilicate β-eucryptite,64–67 and the ramsdellite phase of lithium titanium oxide. 3.4. Materials with Fluorite and Antifluorite Structures The most common of the fast ion conductors with fluorite CaF2 structure is the ZrO2 family in which the mobile species are the oxide ions. Doped-ZrO2 has been used in a number of applications such as

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oxygen sensors.40, 68–70 Another material of special interest because of its large anionic (fluoride ion) conductivity is PbF2 .71–83 Among the materials having the antifluorite structures, Li5AlO4 , Li5 GaO4 and Li6 ZnO4 exhibit high lithium-ion conductivity at moderate temperatures.84 It is thus possible to find high values of both anionic (in the fluorite structure) and cationic (in the antifluorite) transport in these unique crystal structures. 3.5. Materials with Layered Structures The β-alumina family is the most important of the group of materials with layer-type crystal structures. Comprehensive reviews of these materials are presented by Kummer,23 Kennedy85 and Collongues et al.86 The crystal structure of hexagonal β-alumina consists of four cubic close-packed layers of oxygen with three Al3+ ions occupying some of the resulting octahedral and tetrahedral positions between each pair of oxygen layers — an arrangement similar to the spinel, MgAl2 O4 . These spinel blocks are separated by basal planes containing a loose packing of Na and O ions, the spaces between the mirror planes being 1.12 nm. Another structure that has been found to exhibit rapid anionic transport is the tysonite (LaF3 ) which is used in fluoride ion selective electrodes.87 Materials with this structure based on CeF3 were found to have higher fluoride ion conductivity.88 Lithium nitride also has a layered type structure but with a cationic conductivity. The conductivity for lithium-ions is fairly high and anisotropic.67, 89 There exists two types of sites for Li ions, one in the hexagonal Li2 N layers and the other in the relatively open intermediate layers, where they form N–Li–N bridges.90 Several mixed conducting materials that are layered in structure similar to Cdl2 e.g., transition metal chalcogenides are also available. Here, the cation is bonded to the lattice by Van der Waals forces, rather than by ionic bonding as in β-alumina. These materials are used as cathode materials in rechargeable lithium cells. 3.6. Materials with 3D Arrays of Tunnels One of the pioneering class of compounds in this category of solid electrolytes containing atomic-sized tunnels oriented in three

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directions and providing isotropic ionic transport is ternary silver iodides of the Rb4AgI5 family.27, 28, 91 Several such groups of materials having skeleton or network structures composed of arrays of corner and edge shared tetrahedra and octahedra are being developed at various laboratories. 3.7. Structures with Isolated Tetrahedra Examples in this category of compounds with characteristic isolated tetrahedral anionic groups between which cations move include Li4 SiO4 ,92 Li4 GeO4 93, 94 and several alkali metal chloroaluminates having structures with alkali metals in between isolated AlCl4 groups. It is clear from the above discussion that the fast ionic conduction in solids is rather sensitive to the crystallographic features. Though the presence of unusually large concentration of mobile species was originally viewed as the dominant factor, the static part of the crystal structure plays a significant role in determining the nature and ease of ionic transport. 4. Mechanisms of Ion Transport In solid electrolytes, ions are in perpetual random movement in all possible directions (Brownian motion) from a lattice point to a vacancy or interstitial site, or from one interstitial site to another, even in the absence of an electric field. By this random movement, the concentration of ions and defects are rendered uniform throughout the solid, and this process is referred to as diffusion. When an electric field is impressed on the solid, the ions still move about randomly, but migrate as a whole along the direction of the electric field manifesting as ionic conduction. Thus diffusion and migration of ions via defects constitute the basic processes of ionic conduction in crystalline ionic solids. In amorphous polymeric materials ionic diffusion is possible by local motion of polymer chains. Hence, a liquid-like character attainable above the glass transition temperature of the polymer becomes necessary for ionic diffusion.

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4.1. Microscopic Aspects of Diffusion — The Jump Mechanism During diffusion and ionic conduction, ions must move through the lattice by some jumping process. A direct cation–anion exchange is ruled out and the ion transport is mediated through defects. The ion transport is thus governed by the jump probability of an ion into a defect. This in turn is proportional to94 : (a) the probability for the ion to jump into the defect in a given direction in unit time, which is the jump frequency and (b) the probability that a given site has a defect on a nearest neighbor site, i.e. the product of the number of nearest neighbor sites and the mole fraction of the defects. The jump frequency ω depends upon the potential barrier experienced by the ion (Fig. 2). Assuming the Einstein model to be applicable, i.e. that the ions are vibrating harmonically around their equilibrium positions with a vibrational frequency, ν0 , the expression for the jump frequency of a point defect is of the form95 ω = νo exp ( − G/kT),

Fig. 2.

(8)

Energy along jump direction in the absence of applied electric field gradient.

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where G is the free energy of migration. ‘ω’ can be expressed in terms of H (enthalpy of migration) and S (entropy of migration) as

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ω = νo exp (S/k) exp ( − H/kT).

(9)

This is an expression for the thermodynamic equilibrium, allowing an equal number of jumps in both left and right directions. However, such is not the case if a gradient is generated due to differences in either applied electrochemical potential or concentration (chemical potential). In the case of an imposed electric field, the potential energy experienced by the interstitial ion jumping from one interstitial position to another is asymmetric as shown in Fig. 3. Due to the electric field, E, an additional term, — (a/2)qE is added to the potential energy term, where q is the charge on the interstitial ion and “a” is the interionic distance. The subsequent saddle point energy decreases by an amount (a/2)qE. A jump in the direction of the field would therefore take place with increased probability:  
   1
ω = νo exp − G − qaE /kT (10) 2

Fig. 3. Energy along jump direction in the presence of an applied electric field gradient.

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and a jump against the field occurs with reduced probability,  
   1

ω = νo exp − G + qaE /kT . 2

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(11)

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The net number of ions moving per unit volume in the direction of the field, n
= n(ω
− ω

) ≈ nωqaE/kT assuming qaE  kT. Here, n is the number of interstitial ions per unit volume. The current density, j (which is the amount of charge passing per unit area per unit time) is given by j = na2 q2 ωE/kT.

(12)

The expression for the ionic conductivity, σ, is expressed in terms of the jump frequency as σ = j/E = na2 q2 ω/kT = nqµ,

(13)

where µ is the mobility, given by µ = a2 qω/kT.

(14)

Finally, an additional numerical factor is added to the above equation to account for the fact that the charge carrier can jump to multiple forward positions (e.g. 4 for NaCI) in the lattice. Similar expression holds good for the vacancy or interstitial mechanism. The net ion transport induced by a concentration gradient is termed as diffusion and is dealt in detail in Sec. 4.3. 4.2. Models of Ionic Motion Development of models of ionic motion may be considered to have taken place in three stages: (i) Of the early transport mechanisms suggested, apart from the free ion model of Rice and Roth96 most tried to extend the above simple hopping model from its successful application to the defect conductivity mechanism to systems where the mobile ion concentration was high. (ii) In the second group

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of theories, recognition was given to cooperative motion, where the influence of mobile ions on one another was taken into consideration. (iii) Finally, for systems in which the flight time between sites was shown by spectroscopic methods to be of the same order as the dwell time, motion was characterized in terms of quasi-liquid sub-lattice behavior. The modeling of transport mechanisms in polymeric electrolytes is an active field reviewed in another chapter of the handbook. One of the well-developed microscopic models for describing the transport mechanism in polymer electrolytes, is the dynamic bond percolation model.97–99 This theory is based on the principle that local segmental mobility of the polymer host controls the ionic conductivity and diffusion processes. Occasional independent hopping of ions is assumed to occur in addition, however, only rarely. In a fixed configuration of the polymer host with ions all in low energy equilibrium positions, the probability of an ion hopping at a characteristic rate can be visualized as a percolation process governed by the availability of accessible empty ion sites. However, in the case of a polymer host above its glass transition temperature, the chains are constantly in motion altering and readjusting the probability values. Thus, availability of empty sites gets renewed in a time scale determined by the polymer motion. For observations greater than this time scale, a diffusive behavior would be observed. For shorter time scales the motion would be equivalent to hopping. Static percolation would be observed if the polymer motion is extremely slow. When polymer motion rates increase, the diffusion coefficients and conductivity increase monotonically until the ion-transport changes to ion-hopping type independent of the chain motion. Such a condition is called renewal saturation. The full implementation of this model awaits understanding of ion– ion interactions in ion hopping, experimental input on relaxation processes (such as NMR data), and extension of the lattice formalism to describe amorphous systems.15 4.3. Phenomenological Description of Diffusion Despite the fact that the processes of diffusion and migration are microscopic phenomena governed by fundamental interactions

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between the lattice and defect sites, a phenomenological description based on concentration of diffusing species, electric field gradient, and experimentally accessible quantities such as diffusion coefficients and ionic mobility is of immense practical value.

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4.3.1. Fick’s Laws and Diffusion Equations When a concentration gradient exists in a solid, diffusion results in a net ionic flux in the direction which tends to make the concentrations uniform. In 1855, Fick stated that the diffusion flux J (defined as material flow per unit time) is proportional to the concentration gradient. Thus, for a concentration gradient in one dimension we have Fick’s first law as, Jx = −D(dC/dx),

(15)

where D is called the diffusion coefficient. The negative sign in Eq. (15) is due to a positive diffusion flux resulting from a negative concentration gradient. When the concentration gradient varies with x, there is difference in the fluxes at x and x + x, given by (Jx − Jx+x ). In a time t, there occurs an accumulation of material given by (Jx − Jx+x ) ∗ t. This material accumulation manifests itself as a change in concentration with time, C (= Ct+t − Ct ), or total material accumulation of C ∗ x. Thus, (Jx − Jx+x ) · t = C · x or in the differential form, dC/dt = −dJx /dx.

(16)

Combining this with the first law (Eq. (15)) we have, dC/dt = d{D(dC/dx)}/dx.

(17)

If D is a constant, Eq. (17) may be written as, dC/dt = Dd2 C/dx2

(18)

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and may be generalized into 3D isotropic diffusion equation.

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dC/dt = D(d2 C/dx2 + d2 C/dy2 + d2 C/dz2 ).

(19)

Solutions for Eq. (18) yield concentration distribution with time for a given set of boundary and initial conditions. For example, let us consider diffusion in either direction (∞ > x > −∞) from a plane source containing at t = 0 an amount, M of a substance. The concentration distribution changes with time and is given by:     x2 M C(x,t) = exp − . (20) 1 4Dt 2(πDt) 2 Diffusion under these conditions proceeds symmetrically from the origin (x = 0) and the simple average position of the diffused substance is always the origin. However, the mean square x2 of the distance at any time t can be derived to be equal to 2Dt. The mean square increases proportionally with time and the proportionality constant is 2D. Therefore, D is a measure of the spreading velocity of the substance. Another typical example of diffusion in ionic solids is characterized by the following conditions: Semi-infinite (i.e. 0 < x < ∞) and linear (one-dimension) diffusion from a surface maintained always at a constant concentration C0 . At t = 0 and x > 0, C = 0. Under these conditions the concentration distribution is given by: √ (21) C = C0 (1 − erf{x/2 Dt}) for all t > 0 where erf denotes the error function. Analytical solutions for various sets of boundary and initial conditions are given by Crank,94 and the mathematically equivalent problems in heat transfer by Carlsaw and Jaeger.95 The diffusion process in which the concentration changes with time is called non-stationary diffusion, while that which is not time dependent is called stationary diffusion. For stationary diffusion, thus dC/dt = 0 and thus from Eq. (16), dJ/dx = 0 and therefore, J is a constant.

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4.3.2. Modified Fick’s First law and the Nernst–Einstein Equation In a more generalized interpretation of diffusion, Einstein96 and Hartley97 believed that the true driving force for diffusion was the chemical potential gradient, instead of the concentration gradient claimed in Fick’s first law. Such an interpretation accommodates the thermodynamic non-ideal character of real systems. Chemical potential of a system is defined as the partial molal Gibbs free energy and has the units J mole−1 . This generalized description of diffusion is embodied in Wagner’s theory98 for ion transport in crystals. The flux Ji of a particular species i is then given by Ji = −Ci Bi (1/N)dµi /dx,

(22)

where Ci is the concentration (mole cm−3 ), Bi is the absolute mobility (cm2 J−1 S−1 ) and N is Avogadro’s number. The absolute mobility (or mechanical mobility as it is sometimes called) is thus the migration velocity of the species per unit energy gradient. The chemical potential is related with activity ai of species i and the activity coefficient γi as µi = µo + RT ln ai = µo + RT ln γi + RT ln Ci . The gradient of the chemical potential is then given by dµ/dx = RT{1 + (d ln γi /d ln Ci )}(1/Ci ) · dCi /dx.

(23)

Substituting the above relation for dµ/dx in Eq. (22) and comparing with Fick’s first law (Eq. (15)), we find Di = Bi kT{1 + (d ln γi /d ln Ci )}.

(24)

This relationship between diffusion coefficient, absolute mobility and the concentration of the diffusing species describes ideal and non-ideal systems and is called the Nernst–Einstein equation. The diffusion coefficient defined by Eq. (24) is referred to as the component

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diffusion coefficient. When γi = 1 as in an ideal solution, Di = Bi kT

(25)

and then Di is equal to that defined by Fick’s first law.

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4.4. Diffusion Coefficients 4.4.1. Self and Isotope Diffusion Coefficient The measure of random (Brownian) motion of ions or atoms is usually called the self-diffusion coefficient. However, for practical reasons sometimes the diffusion of the isotope of the ion or atom (called tracer) is studied. The diffusion coefficient thus obtained is termed as the isotope or tracer diffusion coefficient. The selfdiffusion coefficient is related to the isotope diffusion coefficient by a correlation factor which is usually less than unity. 4.4.2. Defect Diffusion Coefficient In the example of vacancy diffusion, if the concentration ratio of vacancies to ions on the lattice site is 100:1, an ion jumps on average once for every hundred jumps of a vacancy. This leads up to a relation between the diffusion coefficient of the vacancy, Dv and the selfdiffusion coefficient, D as Dv Cv = DC, Cv is the concentration of the vacancies and C the concentration of the lattice sites. 4.4.3. Chemical Diffusion Coefficient When ions are involved in chemical reactions, such as insertion into a lattice to form a new phase or in exchange processes where one type of ion replaces another or changes in the stoichiometry, the diffusion of the ions is accompanied by a solid-state chemical change. The rate of these chemical processes is often controlled by the diffusion of the ions. Such diffusion processes could involve the participation of more than one chemical or ionic species and is termed chemical diffusion. The chemical diffusion coefficient can thus be related to the

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self-diffusion coefficient by a factor proportional to the interactions in chemical diffusion.105 4.4.4. Haven Ratio

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Over a wide range of temperatures, experimentally measured diffusion coefficients often obey the relation D = D0 exp ( − E/kT), where D0 is a constant, pre-exponential factor and E is the activation energy for diffusion. The diffusion coefficient D and the electrical conductivity are related, as will be shown later in Sec. 5.1, by the Nernst–Einstein relation σ/D = nq2 /kT,

(26)

where q is the charge of the moving species and n is their number per unit volume. The diffusion coefficient, D(calc) calculated from the measured value of the conductivity as D(calc) = (kT/nq2 )σ

(27)

is generally different from the directly measured value, D, e.g. by tracer diffusion coefficient. The disagreement between the two is attributed to the fact that in the electrical conductivity measurements under applied field, the successive jump directions of defects are uncorrelated with one another, while such is not the case in the absence of an electric field. The correlation between both the diffusion coefficients is given by the relation: Hr = D/D(calc)

(28)

and is called the ‘Haven Ratio’. This is almost the same as the theoretical correlation factor ‘f ’ introduced in the equation relating the diffusion coefficient with the jump frequency and jump length. 4.5. Measurement of Diffusion Coefficients A wide variety of methods have been used for solving Fick’s equations.106–108 There are two main approaches to the theory: (a) the atomisitic approach where the atomic nature of the diffusing

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species is specially considered, and (b) the continuum approach where the atomic nature is ignored. The former relates the diffusion coefficient to quantities like atom jump frequency, relaxation time etc. and the latter relates to the initial and final state (concentration) of the system. The experimental methods used for the measurement of diffusion coefficient are related to the above methods of treating the diffusion phenomenon and can be described as follows. Direct method: The mass flow or concentration is measured as a function of either distance or time Indirect method: The jump frequency or relaxation time is measured to evaluate the diffusion coefficient D = 1/6f λ2 ω,

(29)

where λ is the jump length, ω is the jump frequency and f is the correlation factor. The value of the jump frequency can be determined by relaxation measurements like light scattering, NMR, diffuse neutron and X-ray scattering. The direct methods evaluate the diffusion coefficient by measuring the concentration of the diffusing species as a function of depth of penetration. Such methods are often more reliable and include a wide variety of physico-chemical methods like mass spectrometry, radio-active tracer technique, spectrophotometry etc. The electrochemical methods also fall into this category and are based on measuring the concentration profile through a variation of either electrode potential (chronopotentiometry), reaction current (chronoamperometry) or coulombic charge (chronocoulometry). Among the various direct methods, tracer diffusion technique is generally adopted wherever possible, as irreproducibility may exist in other direct methods. 4.5.1. Tracer Method This method is applicable to a polycrystalline or single-crystal slab of the specimen. The tracer diffusion coefficient of an ion M+ in a matrix MX is measured by applying a very small amount of a radio-isotope of M on a plane perpendicular to the direction in

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which the diffusion coefficient is to be measured. The sample is now annealed for a desired time. The distribution of isotopes can be followed by sectioning the samples and estimating the amount of the isotope in each section by radio-counting or by secondary ion mass-spectrometry. Analytical expressions for spatial concentration distribution with semi-infinite boundary conditions can be used to evaluate the diffusion coefficient. Kilner et al. have employed secondary ion mass spectrometry (SIMS) to determine the self-diffusion coefficient of oxygen in nickel doped ferrites and yttrium iron garnet materials using an 18 O tracer.109 The authors have determined the diffusion coefficients for insulating and polycrystalline samples and have found that highly reliable data can be obtained using the SIMS method. The tracer diffusion coefficient of oxygen in LaCoO3 perovskite materials has been reported by Ishigaki et al.110 In this study, the authors have determined the diffusivity of oxygen ions at various temperatures and oxygen pressure using SIMS and gas phase analysis. The diffusion coefficient of oxide ions was found to decrease with increase in oxygen pressure and the authors propose that oxide ion diffusion occurs through a vacancy mechanism. Good agreement in the diffusion coefficients was observed between SIMS and gas phase analysis measurements in this study. 4.5.2. NMR Method A nucleus with a non-zero nuclear spin quantum number I, when placed in a uniform magnetic field H0 suffers an energy level splitting into 2I + 1 discrete levels with equal energy differences of E = γhHo /2π, where γ is the gyromagnetic ratio. The gyromagnetic ratio characterizes the nucleus and its environment. The energy absorbed by the nucleus is in the radio frequency range and the phenomenon is called nuclear magnetic resonance (NMR). For an isolated nucleus a sharp line is observed. However, splitting or broadening of lines occurs due to the interaction of the nucleus with its surroundings. So information of the local structure of molecules or atomic groups are hidden in this broad band. As the temperature is raised, the thermal motion of atoms results in an average magnetic dipole interaction

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causing narrowing of the resonance band, and this phenomenon is called motional narrowing. Motional narrowing of resonance lines can be used to determine the nature of the diffusing species. To determine the diffusion coefficient, the relaxation of the excited state as it recovers by releasing its energy to its surroundings (spin-lattice relaxation), must be observed. The spin-lattice relaxation time when plotted as a function of 1/T passes through a minimum value τc for a constant applied frequency. Then τc can be used to estimate a value of diffusion coefficient which agrees well with the self-diffusion coefficient. Further details on the NMR method are provided by Bannet.111 The NMR method has been widely used in studying the diffusion of anions and cations in gel and polymer electrolytes.112–115 For example, in a recent study, Gobet et al. report the use of pulsed-field gradient NMR to measure the lithium-ion self-diffusion coefficient in a β-Li3 PS4 ceramic electrolyte.112 Every et al. have also employed pulsed field gradient NMR measurements to determine the diffusion coefficients of methanol in different polymer electrolytes. In this study, the authors have compared the diffusion of methanol in Nafion 117 and BPSH 40 type membranes. An increase in the diffusion coefficient of methanol with increasing concentration was observed due to the increased solvent uptake by the Nafion membrane.113 4.5.3. Electrochemical Methods Diffusion coefficients can be determined from galvanic cells employing the solid electrolyte by combining current generation and potential measurements. In this method, a perturbation of the concentration gradients of the mobile ionic or electronic species is accomplished by a controlled transient electrical current or potential signal. The attainment of a steady-state concentration gradient following such a perturbation is measured. These methods are described in the following: 4.5.3.1. Chronoamperometry In this method, the uniform distribution of the mobile species is suddenly altered at the electrode/electrolyte interface by a potential

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step. A time-dependent current flow immediately results in response to the concentration gradient until a new and homogeneous composition is reached. The time dependence of the concentration profiles is determined by the diffusion coefficient and the direction of diffusion and geometry of the boundaries. Commonly, experiments are arranged to approximate to linear diffusion to a plane or cylinder. For linear diffusion to a plane of unit area for time t  L2 /D, where L is the thickness over which diffusion occurs, and for a potential step E, the current density I is given by √ I = zqNA t−1/2 D/(VM π1/2 ),

(30)

where z is the charge on the mobile species, q is the elementary charge, and VM is the molar volume. Thus, the slope of the plot of I versus t−1/2 at short times will be a straight line from which the diffusion coefficient D may be evaluated. Lindstrom et al. have used the chronoamperometry method to study the insertion of lithium-ions in titanium oxide films. The diffusion coefficients of lithium-ion insertion and extraction from nano-porous and CVD TiO2 films have been measured.116 The diffusion of lithium-ions was found to be directly proportional to the inner electrode area of the nano-porous electrodes. 4.5.3.2. Galvanostatic (or current step) Method In this method, the current is stepped from zero to a constant value I0 . The concentration changes and diffusion of mobile species results in a time-dependent potential which is measured. For short times, the linear diffusion to a plane under a current step I0 results in a time dependent potential, E expressed as: E = {2VM I0 t1/2 }/zqNA π1/2 D1/2 .

(31)

Thus, the slope of E versus t1/2 can be used to evaluate D. Experimentally, an important advantage of this method is that any fixed impedance does not change the shape of the voltage–time curve. Thus, compensation of the internal resistance drop and exact knowledge of the position of the reference electrode are not crucial

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to this method. Since the current is the controlled variable, the extent of concentration change caused by the method can be calculated for the chosen current. With the potential step method large currents can flow momentarily causing uncontrolled concentration changes. On the other hand, the galvanostatic method does not allow determination of the diffusion coefficient from long-time experiments. Variations of the galvanostatic method employing short pulses is reviewed by Weppner and Huggins.117 The galvanostatic intermittent titration technique (GITT) is being extensively used to study the transport properties of ion insertion electrodes.117, 118 The GITT consists of applying several short current pulses and monitoring the potential response. Ding et al. have determined the diffusion coefficient of lithium-ions in nano silicon using the GITT method.118 They observe that the diffusion coefficient determined from GITT is slightly higher compared to the results from impedance measurements due to the non-equilibrium nature of the measurement. In addition to the DC techniques discussed above, electrochemical impedance spectroscopy (EIS) is also frequently used to estimate the diffusion coefficients and the conductivities of mobile species in solid electrolytes.119–122 In a recent report, Hassoun et al. have employed EIS to measure the diffusion coefficient of lithium-ions in a Li10 GeP2 S12 electrolyte.119 The fundamental aspects of EIS have been discussed in Sec. 5.3.2. 5. Ionic Conduction 5.1. Phenomenological Description of Ionic Conduction Charged particles can migrate even without a concentration gradient if there is an electric field. The flux is called conduction. When an electric field dφ/dx is applied on a charge of magnitude Ze the energy gradient Ze (dφ/dx) is generated and the flow equation is then given by j = −C B Z e (dφ/dx).

(32)

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The current I (= ZFj, coulombs cm−2 s−1 where F is the Faraday constant) is given by I = C B Z2 F e(dφ/dx).

(33)

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Then we may express CBZ2 Fe as σ, the conductivity. Combining the above relationship with that of Eq. (25) we have B = D/kT = σ/C Z2 Fe,

(34)

thus allowing a calculation of D from σ or vice-versa when one of the values are known. 5.2. Electrochemical Potential Gradient and a Generalized Formalism for Diffusion and Conduction In the general situation where charges move by diffusion and conduction, the fluxes can be combined and expressed as J = −(CB/N)d(µ + ZFφ)/dx

(35)

where F/N is e. As a consequence, it would be possible to define a combined driving force due to chemical and electrical gradients dη/dx where η is called the electrochemical potential and is equal to (µ + ZFφ) and a generalized flow equation may be expressed as J = −BZe(dη/dx).

(36)

The generalized description of flux (Eq. (36)) based on the electrochemical potential can thus be written for cations, anions and electrons in a crystal as follows: J+ = −C B Z1 e(dη+ /dx),

(37)

J− = −C B Z2 e(dη− /dx),

(38)

Je = −C B e(dηe /dx).

(39)

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5.3. Measurement of Total Ionic and Electronic Conductivity

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5.3.1. Direct Current Measurements When direct current is passed through an electrolyte or mixed conductor, electrochemical reactions occur that cause compositional changes. However, if the compositional changes caused by passage of current are exactly reverse of each other at either electrodes (such a system is referred to as a system of reversible electrodes), then there is no net change in the chemical potential of the system. Irreversible effects of compositional change are also referred to as electrochemical polarization. Thus, reversibility is achieved when the electron transfer reactions at the two electrodes are the exact reverse of each other and only one ionic species conducts exclusively. Under these circumstances the flux of anions, cations and electrons is given by: J = J + + J − + Je = (σ+ + σ− + σe )/F dηe /dx = (σ+ + σ− + σe ).E.

(40)

E is the electric field gradient. Thus, the total conductivity is obtained as J/E. Therefore, measurement of conductivity by direct current methods requires the use of reversible electrodes. Also, in direct current measurements, since the potential distribution near the electrode contacts are non-uniform, the potential difference is measured between two points away from each of the current carrying electrodes and thus the method is also called the four-probe method. Experimental details for the measurements of electrical conductivity and transport properties of solid electrolytes has been reviewed by Rapp and Shores123 and Kvist70 and more recently by Blumenthal and Seitz.124 5.3.2. Alternating Current Measurements Alternating currents (ac) of small amplitude, in principle do not cause changes in the composition of the solid electrolyte and thus

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the ac method can be used with non-reversible electrodes (blocking electrodes). Usually, the smaller the amplitude of alternating current, the higher the degree of reversibility. For this reason the ac method is widely used.

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5.3.2.1. Electrical Equivalent Circuits for the Electrode/Electrolyte Interface If a sample is a pure ionic conductor (i.e. σe = 0), and the electrodes are inert to any conducting species (i.e. a blocking electrode) the electrode/solid electrolyte interface behaves as a capacitor. In such an interfacial capacitor, electronic charge stored on the metal electrode is compensated by ionic charges in the solid electrolyte. These two layers of charge are referred to as an “electrical double layer” and the capacitance is termed as a “double layer” capacitance. Under these circumstances, an equivalent electrical circuit for the electrode and the solid electrolyte is given in Fig. 4(a), where Rs and Cdl represent the electrolyte resistance (1/(σ+ + σ− )) and the double layer capacitance respectively.

Fig. 4.

Equivalent circuits for the electrode/electrolyte interface.

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In actual cases, however, charge transfer (which is an electrochemical reaction) always occurs at the electrode/electrolyte interface and is represented by Rt as in Fig. 4(b). The charge transfer resistance Rt is the linear equivalent of resistive (or polarizing) characteristic of the interface when it sustains an electrochemical charge transfer. When a steady-state current i results in a steadystate potential drop of E across the interface, the dE/di is termed the faradaic polarization resistance which is the sum of charge transfer resistance Rt and mass transfer resistance Rm . A linear relation between E and i is usually found when the perturbations are less than 5 mV. Unlike charge transfer, the process of mass transfer is per se a time-dependent process and thus exhibits transient properties as determined by the diffusion coefficient and concentration of the diffusing species. Transient mass transfer polarization has thus been understood to arise from an impedance (with the equivalent of ladder-type network of capacitors and resistors) and in a commonly encountered case of semi-infinite boundary conditions, termed as Warburg impedance.125 Thus, a generalized equivalent circuit of Fig. 4(c) with the electrochemical effects at the interface includes the double layer capacitance, charge-transfer resistance and Warburg impedance. When the distance of separation between the electrodes is small, the geometric capacitance between the electrodes becomes significant and the equivalent circuit should include a geometric capacitance Cg as shown in Fig. 4(d). Thus, the ac method can be used not only to obtain the conductivity of solid electrolytes but also investigate the properties of the electrode/electrolyte interface. 5.3.2.2. Analysis of Impedance Data In the alternating current method, a sinusoidal varying potential Em sin ωt (ω equals 2πf where f is the sinusoidal frequency in Hz) of small amplitude (usually, 5 mV) is applied to the cell consisting of the electrolyte sandwiched between two electrodes. The sinusoidal current that results is shifted in phase by φ and is given by Im sin (ωt + φ). The two terminal impedance, Z (is given by Em /Im ), and phase angle difference (between the applied sinusoidal voltage and

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33

observed sinusoidal cell current), φ are measured as a function of frequency of the applied sinusoidal voltage, ω. In order to represent the variation of Z as well as φ together, a plot of Z cos φ (also called Z
or Zreal or in phase component) versus Z sin φ (also called Z

or Zimaginary or out-of-phase component) at various frequencies is commonly presented as impedance data and is referred to as the complex-plane plot. Thus, in a plot of Z
versus Z

by definition, √

(41) Z = (Z
2 + Z 2 ) and φ = tan−1 (Z

/Z
)

(42)

Because the nature of the algebra used in such analysis being similar to that employed in the study of complex numbers, such a representation is also called complex-plane impedance analysis. For the electrical equivalent circuit of Fig. 4(a) the impedance Z is given by √ Z = (Rs2 + (1/ωCdl )2 ) (43) Thus in a complex-plane plot for Fig. 4(a), Z
is equal to Rs and Z

is equal to 1/ωCdl at any frequency and thus the value of Rs and Cdl can be evaluated. For the circuit in Fig. 4(b), a parallel combination of the charge transfer resistance Rt and double layer capacitance Cdl in series with the ionic resistance Rs , Z can be derived from ac theory as √ 2 2 2 2 Z = [{Rs + Rt /(1 + ω2 Rt2 Cdl )} + {ωCdl Rt2 /(1 + ω2 Rt2 Cdl )} ] (44) Under these conditions, the complex-plane plot takes the shape of a semicircle and the ionic resistance Rs is determined from the value of Z
extrapolated to ω = ∞. At ω → 0, Z
= Rs +Rt . When tan−1 (Z

/Z
) is maximum, the value of ω = 1/Rt Cdl . Thus, the value of the circuit elements can be calculated. With measurements from solid electrolyte–electrode systems, it is usual to compare the results with that of a theoretical model to determine the equivalent circuit and the significance of its different components. MacDonald126 has developed theoretical models to

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describe the impedance of a system in a number of different situations applicable to solid electrolytes. Experimental and analytical details of the alternating current method are discussed by MacDonald,126 Bauerle128 and Armstrong.127 Despite the successes with the impedance methods, these measurements provide little information concerning the inter-crystalline effects. Such bulk phenomenon would normally occur in a highly conducting solid in the range of 109 –1012 Hz, well outside the range of normal ac equipment. Hodge et al.129 have therefore pointed out the advantages of low temperature effects to bring the conductivities below 10−6 S/cm and the conductance dispersion in a more accessible frequency range. Cole and Cole130 introduced the dielectric relaxation function 1/(1 + jω o )1−α and showed that this represents a depressed circular arc in the complex impedance plane. The parameter, α is a measure of the departure from simple Debye behavior, i.e. a measure of the depression of the center of the circle below the real axis. NonDebye nature is attributed to inter-ionic forces in a disordered interface region or to the existence of surface roughness. Intracrystalline response is reportedly governed mainly by concentration of mobile ions.130 Thus, materials having relatively ordered structures and small concentration of mobile defects such as β–PbF2 and AgCl approximate to the ideal impedance behavior with perfect semicircles. On the other hand, the pronounced dispersion with a single crystal β-alumina is attributed to strong interaction among the mobile Na+ ions or to a wide distribution of ion jump frequencies reflecting disorder in the conduction plane. An automated four-probe DC resistance measurement has been reported by Badwal et al. for the measurement of the conductivities and transport numbers in various oxide conducting electrolytes.131 Sone et al. have employed EIS to determine the proton conductivity of Nafion 117 membrane at various conditions of humidity and temperature. The results of the measurements demonstrated the decrease in conductivity of Nafion with increasing temperature and heat treatment. The authors attributed the decrease in conductivity to loss of water and changes in membrane structure.120

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5.4. Separation of Ionic and Electronic Conductivity In the measurement methods described above, both ionic and electronic species are mobile and their total conductivity is measured. For mixed conductors, the electronic conductivity can be separated from the ionic conductivity by the use of a combination of ionblocking and reversible electrodes. The objective is to block the ionic flow and sustain only electronic conduction. For example, a metal electrode such as silver functions as a reversible electrode in contact with silver bromide. A graphite or carbon electrode in contact with silver bromide does not sustain any electrochemical reaction readily with the ions of the electrolyte when polarized positively and thus functions as an ion-blocking electrode. When a direct current is passed through such a mixed conductor as silver bromide and the voltage between the two electrode terminals (carbon as the positive electrode and silver the negative electrode) is less than the decomposition voltage of silver bromide (bromine evolution from bromide does not occur under these conditions), ionic migration cannot be sustained. However, a steady-state current is observed due to the electronic conductivity. Change of polarity that is reverse of that suggested would result in silver deposition at the carbon electrode converting it into a reversible electrode. In effect, the reversible electrode serves as a potential invariant electrode (electrochemists refer to such an electrode as a reference electrode) and all potential changes at the blocking electrode can be measured with respect to this reference. Since ion transfer is forbidden at the blocking electrode, the ionic current in the electrolyte is zero. The steady-state electronic current, ie at various potentials E can be measured and the electronic conductivity for a solid electrolyte of thickness x and cross-sectional area A calculated from Ohm’s Law is described as: σe = −{x/A}die /dE.

(45)

This method is known as the Hebb–Wagner technique.132, 134 5.5. Methods of Determining the Transference Number For an electrolyte dissociating to give simple cationic and anionic species, the transport number, e.g. of cation t+ is defined as the

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number of Faradays of charge carried by the cation across a reference plane (fixed relative to the solvent), when a total of one Faraday of charge passes across the plane.135 In a conventional electrolyte, experimental techniques such as the moving boundary methods are sufficiently well developed to allow routine determination of transference numbers with great accuracy. For polymer electrolytes, however, these methods are inapplicable and a number of alternate methods have been developed.136–142 The Tubandt method139 is the technique most commonly applied to conventional solid electrolytes. It is directly based on Faraday’s laws and requires weight variations in the electrolyte regions near the two cell electrodes caused by the passage of a known amount of charge, to be measured. It is difficult to apply this method to polymer systems because of the requirement to maintain the electrolyte as a series of nonadherent sections. Leveque et al.136 were able to carry out such an experiment for highly cross-linked networks where the electrolyte could readily be separated into its component sections after the passage of the current. Bouridah et al.140 developed a technique based on the measurement of emf 26 of a concentration cell formed by contacting two previously thermally activated half cells. This method is experimentally difficult and has the disadvantage of requiring prior knowledge of the variation of salt activity with the concentration. The most popular technique for transference number measurements in polymer electrolytes is that developed by Sorensen and Jacobsen138 using an analysis of the impedance response of a cell with two electrodes, each non-blocking with respect to the cation. Here, the current flowing through the cell is affected at low frequencies by concentration gradients near the electrodes, which give rise to a characteristic diffusional impedance in the complex impedance plane. The method is, however, often difficult to interpret143 and applicable only at high temperatures, since at normal temperatures the frequencies required to show the diffusional part of the impedances are too low to be of practical value. The steady-state current method of Blonsky et al.141 is prone to errors due the electrode effects which might significantly affect the potential distributions and the current flowing through the

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cell. A combination of dc and ac polarizations has been proposed by Bruce and Vincent144 to alleviate the above problem and thus to determine the transference number even when the diffusion coefficients are low and even in the presence of passivating layers on the electrode and slow electrode kinetics. This method has been recently applied to transport number measurements in anhydrous proton conductors.145 6. Thermodynamic and Kinetic Measurements on Solid Electrolyte Cells 6.1. Thermodynamic Measurements from Electrochemical Cells A significant amount of data on the thermodynamic properties pertinent to solid electrolytes, especially oxide systems has been generated from electrochemical cells utilizing solid electrolytes. From the reversible potential of such cells, it is possible to obtain values for the Gibbs free energy change G, for the corresponding chemical reaction in the cell.146 The use of solid electrolyte-based galvanic cells for determination of the thermodynamic parameters, e.g. free energy of formation of oxides and halides, was pioneered by Kiukkola and Wagner26 and Peters et al.147, 148 Wagner149 derived an expression for the steadystate open-circuit potential across a compact mixed-conductor oxide. Consider an electrochemical cell comprising a solid electrolyte MO, wherein oxygen ions (O2− ), excess electrons e’ and electron

2− holes h· are the charge carriers. Let µ
2− be the chemical o and µo potentials at the electrode/electrolyte interfaces as shown below:



2− Pt, µ
2− o /MO/µo , Pt

x=0

x = L.

The partial current density, Ii of the species i at any location within the electrolyte may be written as Ii = (−σi /zi F)dηi /dx,

(46)

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where σi is the partial conductivity of species i, zi is the valency, F is the Faraday constant, x is the distance coordinate and ηi is the electrochemical potential of species ‘i’. The electrochemical potential is defined as:

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ηi = µi + zi Fφ, where µi is the chemical potential of i and φ is the local electrostatic potential. The sum of the partial current densities of the oxygen ions, excess electrons and electron holes in MO may be written as IO2− + Ih· + Ie
= −(dφ/dx)(σo2− + σh· + σe
) + σ02− /2F(dµO2− /dx) + σe
/F(dµe
/dx) − σh· /F(dµh· /dx).

(47)

The open circuit potential is defined as the limiting case when the sum of partial currents, IO2− + Ih· + Ie
tends to zero. Thus at open circuit, from the above equation, dφ = (tO2− /2F)dµO2− + te
/Fdµe
− th· /Fdµh· ,

(48)

where tO2− , th· , te
are the transference numbers of oxygen ions, electron holes and excess electrons, respectively, and are given by the ratios of the respective partial conductivities to the total conductivity. In the solid electrolyte MO, the equation may be assumed as 1/2 O2 + 2e
= O2− , ·




h + e = null

(49) (50)

From above equations, dµO2− − 2dµe = 1/2 dµ002 , dµh = −dµe
. The above two equations, combined with the conditions that tO2− + th· + te
= 1 yield ∂ϕ =

dµe
tO2− dµO2− + 4F F

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and integration from x = 0 to L  µ
1 1 O2− 2−


ϕ −ϕ = tO − dµO2− + (µe

− µe
). 4F µO2− F

page 39

39

(51)

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Since ϕ

− ϕ
equals the open-circuit voltage (Eoc ) and µ
e = µ
e

Pt = µ

e ,

we get Eoc

1 = 4F



µ

2− O

µ

2− O

tO2− dµO2− .

The more general form of the above equation is  µ

1 O2− tion dµO2− . Eoc = 4F µ

2−

(52)

(53)

O

This equation forms the basis for the thermodynamic measurements using solid electrolytes. In most such measurements, tion ≥ 0.99. 6.1.1. Stability of the electrolyte While the potential utility of the solid electrolyte is greatly dependent upon the magnitude and selectivity of the ionic conductivity, its practical utilization in galvanic cells also requires that it meets the requirements of stability at the electrode potentials. This is a particularly important factor since many of the advanced galvanic cells utilize highly reducible cathodes and oxidizable anodes. It is not enough to know the voltage at which a phase decomposes, which establishes its electrolyte limit. In addition, the actual values of the limiting potentials in the galvanic cell environment need to be known in order to assess its stability in conjunction with the specific electrode materials, each of which establish characteristic reduction /oxidation potentials at the electrode/electrolyte interface. In the case of binary phases, the stability range can be computed from the Gibbs free energies of formation of adjacent phases. The situation is rather complicated for the ternary electrolyte. From an electrochemical stand point, the stability of the solid electrolyte in a given

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galvanic cell is estimated using cyclic voltammetry, wherein the solid electrolyte is polarized to extreme positive and negative potentials in a cell comprising inert but electrocatalytic metals such as noble metals or carbon as the current collector. 6.2. Determination of Thermodynamic Parameters by Conventional Methods The important parameters necessary for a reasonable thermodynamic description of any system are (a) specific heat as a function of temperature and pressure; (ii) enthalpy and entropy of formation; and (iii) phase diagrams in the case of solid solutions. The rest of the properties may be evaluated by using various thermodynamic relations. Some of the methods for evaluating the above parameters are outlined below. 6.2.1. Specific heat or heat capacity The heat capacity of a body is defined as the amount of heat required to raise its temperature by one degree, i.e. specific capacity   Q c∗ = lim . (54) T→0 T The specific capacity is similarly defined as c = c ∗ /m, where m is the mass of the body. The molar specific heat C is given by C = c × M, where ‘M’ is the molecular weight of the body. From the first law of thermodynamics, it is clear that the specific heat of a body at constant volume is the temperature derivative of its internal energy U, i.e. Cv = (dU/dT)v .

(55)

A knowledge of Cv would thus tell us the manner in which the internal energy is distributed among the different modes of thermal excitation. Such a knowledge as a function of temperature would provide information about superionic solids, which have

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high degree of disorders and mostly undergo disorder–order type transformations. The experimental determination of CV presents problems for solids in terms of maintaining constancy of volume. On the other hand, maintaining a constant pressure would be easy. Hence, the specific heat at constant pressure is often measured and is related to Cv by Cp − Cv = Vm a2 T/b,

(56)

where Vm is the molar volume, ‘a’ is the thermal volume expansion coefficient and b is the compressibility. In the absence of a precise value of b at all temperatures, the Nernst–Lindemann empirical relation, Cp − Cv = ACP2 T = Vm a2 T/b

(57)

can be used. Here, A is a constant evaluated from Vm , a and b at any temperature. A large number of experimental methods have been described in the literature.150, 151 Such measurements fall broadly into two categories. Drop methods: A heated sample is dropped into a calorimeter which measures the heat released (−Q). The heat released by the sample is measured as a sum of heat gained by the calorimeter and radiation losses. In a variation of this method, the equilibrium time is reduced by using a calorimeter whose temperature remains constant at the phase transformation of one of its components (e.g. Bunsen ice calorimeter). Electrical heating methods: A known amount of heat is supplied to the sample by an electrically heated resistance wire and the resulting change in temperature is measured. Either an isothermal or adiabatic calorimeter could be used. The latter is more widely used and contains no temperature gradient across the reaction chamber and the jacket. A comprehensive account of the various solid electrolytes, the conduction mechanism, an assessment of the errors involved in

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the emf measurements and their applications has been given by Schlmazried.146

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6.3. Comparison of Solid Electrolyte Method with Other Methods for Thermodynamic Measurements Characterization of oxide systems can be done by a measurement of the enthalpies of formation by calorimetric method and a determination of free energies of formation either by the equilibration of the system with a gas mixture of known oxygen partial pressure or by the emf method. The former method involves errors related to the phase changes during cooling (quenching) for a chemical/physical analysis of the equilibrated phases. The latter method, on the other hand, permits direct measurement of thermodynamic parameters at the temperature of the experiment with no quenching. Also, the emf method is quicker and more accurate within 1 mV (or 92 cal) as compared to 100–200 cal in the high temperature measurements. Obvious choice from the oxide thermodynamic measurements would be zirconia-based electrolyte for moderate oxygen partial pressures and thoria-based electrolytes for low oxygen partial pressures.152 6.4. Kinetic Measurements In kinetic studies, the current through the electrochemical cell is non-zero. The oxide ion current density is given by IO2− =

σO2− dηO2− . 2F dx

Since dµ2− O − 2dµe = 1/2dµO2− . and ηi = µi + zi Fφ. We get IO2−

σ 2− = O 2F



 dµO2− 2dµe dφ + + 2F . dx dx dx

(58)

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43

The above current density of oxygen ions is related to the ionic current iion in the external measuring circuit through

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IO2− = −

iion , A

where ‘A’ is the cross sectional area of the electrolyte. Combining the above two equations and integrating from x = 0 to x = L, we obtain 

1 µO2− Ecell = dµO2− + iion ion , (59) 4f µ

2− O

where ion =

1 A



x=L

x=0

1 σO2−

dx

is the ionic resistance of the electrolyte and Ecell = φ

− φ
. This equation forms the basis for kinetic measurements using solid electrolyte cells. 6.5. Factors Limiting the Applicability of Solid Electrolyte Cells for Thermodynamic/Kinetic Measurements (a) At ionic transport number tion < 0.99, the electronic conduction in the electrolyte is significant to cause problems in maintaining the desired chemical potentials at the electrode/electrolyte interface. In solid oxide electrolytes, however, there is a useful range of oxygen pressure and temperature where tion > 0.99. (b) Even at low short circuit currents, the emf though stable, contains an overvoltage due to a shift in the oxygen potential at the interface as a result of oxygen transfer. (c) Reactions between the electrode and electrolyte are often complicated by the formation of a layer of reaction product. (d) Studies at low oxygen pressures are to be preferably carried out in inert atmosphere (He or Ar), instead of vacuum, after ensuring that the flow rate of the inert gas has no effect on the measured emf.

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(e) Slow equilibration of the electrode constituents limited by the sluggish diffusional processes. (f) Polarization effects at the electrode/electrolyte interfaces are to be adequately accounted for. (g) Electrode porosity/homogeneity: A definite study on the effect of density on the partial conductivities of the sintered compacts has not been made. However, sintered compacts with 95% theoretical density seem to be acceptable for most thermodynamic and kinetic applications. Low density electrolytes might permeate gases leading to unsteady emfs. Inhomogeneities in the electrolyte can lead to localized regions of enhanced electronic transference number (10−2 ). Finally, the solid electrolyte tends to exhibit a high degree of susceptibility to cracking under temperature gradients and thermal cycling. (h) Experimental uncertainties: The accuracy of the measured Gibbs free energy is high due to a high accuracy possible in the measurements of cell emfs. The changes in the enthalpy and entropy measured from the variation of cell emf with temperature are relatively inaccurate due to the differential quotient dE/dT. Nevertheless, these values are superior to the calorimetric data. It is, however, possible that the measurements on the solid electrolyte cells are often complicated by instrument-related problems such as polarization of the cell due to low input impedance of the voltmeter and electrical pick up due to improper shielding of the lead wires and/or grounding of the instruments. References 1. L. Heyne, Fast Ion Transport in Solids, ed. W. van Gool, (North Holland, Amsterdam, 1973). 2. H. Wiedersich and S. Geller, The Chemistry of Extended Defects in Non-metallic Solids, eds. L. Eyring and M. O’Keefe, (North Holland, Amsterdam, 1971). 3. A. B. Lidiard, Handbuch der Physik, ed. S. Flugge, Vol. 20, (SpringerVerlag, Berlin, 1957), p. 246. 4. J. C. Phillips, J. Electrochem. Soc. 123 (1976) 924. 5. D. O. Raleigh, Electrode Processes in Solid State Ionics, eds. M. Kleitz and J. Dupuy, (D. Reidel Pub. Co., Holland, 1976).

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6. M. S. Whittingham and B. G. Silbernagel, Solid Electrolyte, eds. P. Hagenmuller and W. van Gool, (Academic Press, New York, 1978). 7. T. Ishihara, M. Matruda and Y. Takita, J. Am. Chem. Soc. 116 (1994) 3801. 8. J. Schoonman, G. Oversluizen and K. E. D. Wapenaar, Solid State Ionics 1 (1980) 211. 9. Y. Saito and J. Maier, J. Electrochem. Soc. 142 (1995) 3078. 10. W. Bollmann, Phys. Status Solidi A 18 (1973) 313. 11. C. Rongeat, M. A. Reddy, R. Witter and M. Fichtner, ACS Appl. Mater. Inter. 6 (2014) 2103. 12. P. V. Wright, British Polymer Journal 7 (1975) 319. 13. C. Berthier, W. Gorecki, M. Minier, M. B. Armand, J. M. Chabagno and P. Rigaud, Solid State Ionics 11 (1983) 91. 14. M. Minier, C. Berthier and W. Gorecki, Journal de Physique 45 (1984) 7390. 15. S. R. Narayanan, S. P. Yen, L. Liu and S. G. Greenbaum. J. Phys. Chem. B. 110 (2006) 3942. 16. T. Takahashi, S. Tanase, O. Yamamoto and S. J. Yamauchi, Solid State Chem. 17 (1976) 353361. 17. J. C. Lassegues, Protonic Conductors, ed. P. Colomban, (Cambridge University Press, Cambridge, 1992), p. 311. 18. O. Trinquet, PhD Thesis, University of Bordeaux (1990). 19. C. R. I. Chisholm, R. B. Merle, D. A. Boysen and S. M. Haile, Chem. Mater. 14 (2002) 3889. 20. S. M. Haile, P. M. Calkins and D. A. Boysen, Solid State Ionics 97 (1997) 145. 21. S. Chandra, Superionic Solids: Principles and Applications, (NorthHolland, Amsterdam, 1981). 22. A. D. Wadsley, Non-Stoichiometric Compounds, ed. L. Mandelcorn, (Academic Press, New York, 1964), Ch. 3. 23. J. T. Kummer, Progress in Solid State Chemistry, Vol. 7, eds. H. Reiss and J. O. McCaldin, (Pergamon Press, New York, 1972), p. 141. 24. B. C. H. Steele and C. B. Alcock, Trans. Metall. Soc. AIME 233 (1965) 1359. 25. C. Wagner, J. Chem. Phys. 21 (1953) 1819. 26. K. Kiukkola and C. Wagner, J. Electrochem. Soc. 104 (1957) 308. 27. J. N. Bradley and P. D. Greene, Trans. Faraday Soc. 62 (1966) 2069. 28. J. N. Bradley and P. D. Greene, Trans. Faraday Soc. 63 (1967) 2516. 29. B. B. Owens and G. R. Argue, Science 157 (1967) 308. 30. Y. F. Yao and J. T. Kummer, J. Inorg. Nucl. Chem. 29 (1967) 2453. 31. R. H. Radzilowski, Y. F. Yao and J. T. Kummer, J. Appl. Phys. 40 (1969) 4716.

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32. N. Weber and J. T. Kummer, Proc. Ann. Power Sources Conf. 21 (1967) 37. 33. J. Coetzer, J. Power Sources 18 (1986) 377. 34. R. J. Bones, J. Coetzer, R. C. Galloway and D. A. Teagle, J. Electrochem. Soc. 134 (1987) 2379. 35. R. Bones, D. A. Teagle, S. D. Brooker and F. L. Cullen, J. Electrochem. Soc. 136 (1989) 1361. 36. J. L. Sudworth, J. Power Sources 100 (2001) 149. 37. D. O. Raleigh, Solid State Electrochemistry, Progr. Solid State Chem. 3 (1967) 83. 38. L. Heyne, Electrochim. Acta 15 (1970) 1251. 39. B. B. Owens, Adv. Electrochem. Electrochem. Engg. 8 (1971) 1. 40. B. C. H. Steele, Solid State Chemistry, ed. L. E. J. Roberts, (Butterworths, Washington DC, 1973). 41. M. S. Whittingham and R. A. Huggins, Solid State Chemistry, eds. R. S. Roth and S. J. Schneider, (Nat. Bur. Std. Spec. Publ. 364, Washington, 1972). 42. J. Hladik (ed.), Physics of Electrolytes, Vols. 1 and 2, (Academic Press, New York, 1972). 43. W. van Gool, Fast Ion Conductions in Solids, ed. W. van Gool, (NorthHolland Publishing Amsterdam, 1973). 44. W. van Gool, Phase Transitions, 1973, eds. H. K. Henisch, R. Roy and L. E. Cross, (Permagon, Oxford, 1974). 45. W. van Gool, Ann. Rev. Mater. Sci. 4 (1974) 311. 46. R. A. Huggins, Diffusion in Solids: Recent Developments, eds. A. S. Nowick and J. J. Burton, (Academic Press, New York, 1975). 47. R. A. Huggins, Adv. Electrochem. Electrochem. Engg. 10 (1977) 323. 48. B. C. H. Steele and G. J. Dudley, Solid State Chemistry, ed. L. E. J. Roberts, (Butterworths, Washington DC, 1975). 49. G. Holzapfel and H. Rickert, Festkorperprobleme, ed. H. J. Queisser, Vol. 15, (Permagon, Oxford, 1975). 50. C. D. Mahan and W. L. Roth (eds.), Superionic Conductors ed., (Plenum Press, New York, 1976). 51. S. Hull, Rep. Prog. Phys 67 (2004) 1233. 52. L. Malavasi, C. A. J. Fisher and M. Saiful Islam, Chem. Soc. Rev. 39 (2010) 4370. 53. P. Knauth, Solid State Ionics 180 (2009) 911. 54. C. Tubandt and E. Lorenz, Z. Phys. Chem. 87 (1914) 513. 55. K. Funke, Progr. Solid State Chem. 11 (1976) 345. 56. J. P. Hardy and J. W. Flocken, CRC Crit. Rev. Solid State Sci. 1 (1970) 605. 57. O. W. Johnson, Phys. Rev. 136 (1964) A284.

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58. O. W. Johnson, S. H. Pack and J. W. DeFord, J. Appl. Phys. 46 (1975) 1026. 59. O. W. Johnson, J. W. DeFord and S. H. Pack, Mass Transport in Ceramics, eds. A. R. Cooper and A. H. Heuer, (Plenum Press, New York, 1975). 60. T. K. Halstead, W. U. Benesh, R. D. H. Gullivar and R. A. Huggins, J. Chem. Phys. 58 (1973) 3530. 61. J. S. Dryden and A. D. Wadley, Trans. Faraday Soc. 54 (1958) 1574. 62. J. Singer, H. E. Kautz, W. L. Fielder and J. S. Fordyce, Fast Ion Transport in Solids: Solid State Batteries and Devices, ed. W. van Gool, (NorthHolland Publishing, Amsterdam, 1973). 63. H. U. Beyeler, T. Hibma and C. Schuler, Electrochimica. Acta (1977). 64. R. T. Johnson, B. Morosin, M. L. Knotek and R. M. Biefeld, Bull. Am. Phys. Soc. 20 (1975) 330. 65. R. T. Johnson, R. M. Biefeld, M. L. Knotek and B. Morosin, J. Electrochem. Soc. 123 (1976) 680. 66. I. D. Raistrick, C. Ho and R. A. Huggins, J. Electrochem. Soc. 123 (1976) 1469. 67. U. von Alpen, A. Rabenau and G. H. Talat, Appl. Phys. Lett. 30 (1977) 621. 68. R. E. Carter and W. L. Roth, Electromotive Force Measurements in High Temperature Systems, ed. C. B. Alcock, (Institute of Mining and Metallurgy, London, 1968). 69. T. H. Etsell and S. N. Flengas, Chem. Rev. 70 (1970) 339. 70. A. Kvist, Physics of Electrolytes, Vol. 1, ed. J. Hladik, (Academic Press, New York, 1972). 71. J. Schoonman, G. J. Dirksen and G. Blasse, J. Solid State Chem. 7 (1973) 245. 72. C. E. Derrington and M. O’Keefe, Nature Phys. Sci. 246 (1973) 44. 73. J. H. Kennedy and R. Miles, J. Electrochem. Soc. 123 (1976) 47. 74. R. Benz, Z. Phys. Chem. 95 (1975) 25. 75. C. C. Liang and A. V. Joshi., J. Electrochem. Soc. 122 (1975) 467. 76. J. M. Reau et al., C. R. Acad. Sci. Paris (C) 280 (1975) 225. 77. J. H. Kennedy, R. Miles and J. Hunter, J. Electrochem. Soc. 120 (1973) 1441. 78. A. F. Halff, J. Schoonman and A. J. H. Rykelenkamp, J. Phys. Chem. 34 (1973) C9. 79. T. Y. Hwang, M. Engelsberg and I. J. Lowe, Chem. Phys. Lett. 30 (1975) 303. 80. M. Mahajan and B. D. N. Rao, Chem. Phys. Lett. 10 (1971) 29. 81. A. V. Joshi and C. C. Liang, J. Phys. Chem. Solids 36 (1975) 927. 82. R. W. Bonne and J. Schoonman, J. Electrochem. Soc. 124 (1977) 28.

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83. I. D. Raistrick, C. Ho. Y. W. Hu and R. A. Huggins, J. Electroanal. Chem. 77 (1977) 319. 84. R. A. Huggins, Electrochim. Acta 22 (1977) 733. 85. J. H. Kennedy, Solid Electrolytes, ed. S. Geller, (Springer Verlag, Berlin, 1977). 86. R. Collongues, J. Thery and J. P. Boilot, Solid Electrolytes, eds. P. Hagenmuller and W. van Gool, (Academic Press, New York, 1978). 87. C. O. Tiller, A. C. Lilly and B. C. LaRoy, Phys. Rev. B. 8 (1973) 4787. 88. T. Takahashi, H. Iwahara and T. Ishikawa, J. Electrochem. Soc. 124 (1977) 280. 89. B. A. Boukamp and R. A. Huggins, Phys. Lett. 58A (1976) 231. 90. A. Rabenau and H. Shultz, J. Less Common Metals 50 (1976) 155. 91. S. Geller, Science 157 (1967) 310. 92. A. R. West, J. Appl. Electrochem. 3 (1973) 327. 93. B. E. Liebert and R. A. Huggins, Mater. Res. Bull. 11 (1976) 533. 94. F. Beniere, Physics of Electrolytes, ed. J. Hladik, (Academic Press, New York, 1972). 95. H. R. Glyde, Rev. Mod. Phys. 39 (1967) 373. 96. M. J. Rice and W. L. Roth, J. Solid State Chem. 4 (1972) 294. 97. S. D. Druger, M. A. Ratner and A. Nitzan, Solid State Lonics 9/10 (1983) 1115. 98. S. D. Druger, M. A. Ratner and A. Nitzan, J. Chem. Phys. 79 (1983) 3133. 99. S. D. Druger, M. A. Ratner and A. Nitzan, Phys. Rev. B. 31 (1985) 3939. 100. J. Crank, The Mathematics of Diffusion, (Oxford University Press, London, 1956). 101. H. S. Carslaw and J. C. Jaegeer, Conduction of Heat in Solids, (Oxford University Press, London, 1959). 102. A. Einstein, Annalen der Physik (4) 17 (1905) 549. 103. G. S. Hartley, Trans. Faraday Soc. 27 (1931) 10. 104. C. Wagner, Proc. Intern. Comm. Electrochem. Thermodyn. Kinet. 7 (1957) 361. 105. C. Wagner, Atom Movements, Am. Society Metals, (Cleveland, 1951). 106. W. Jost, Diffusion in Solids, Liquids and Gases, (Academic Press, New York, 1952). 107. J. R. Manning, Diffusion kinetics for Atoms in Crystals, (D. Van Nostrand Co Inc., New York, 1968). 108. A. S. Nowick and J. J. Burton (eds.) Diffusion in Solids, (Academic Press, New York, 1975). 109. J. A. Kilner, B. C. H. Steele and L. Ilkov, Solid State Ionics 12 (1984) 89. 110. T. Ishigaki, S. Yamauchi, J. Mizusaki and K. Fueki, J. Solid State Chem. 54 (1984) 100.

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111. M. H. Bannet, Nuclear and Electron Resonance Spectroscopy Applied to Materials Science, eds. E. N. Kaufman and G. K. Shenoy, (Elsevier, 1981). 112. M. Gobet, S. Greenbaum, G. Sahu and C. Liang, Chem. Mater. 26 (2014) 3558. 113. H. A. Every, M. A. Hickner, J. E. McGrath and T. A. Zawodzinski, J. Mem. Sci. 250 (2005) 183. 114. S. Arumugam, J. Shi, D. P. Tunstall and C. A. Vincent, J. Phys. Condens. Mat. 5 (1993) 153. 115. C. P. Grey and S. G. Greenbaum, MRS Bull. (2002) 613. 116. H. Lindstrom, S. Sodergren, A. Solbrand, H. Rensmo, J. Hjelm, A. Hagfeldt and S.-E. Lindquist, J. Phys. Chem. B. 101 (1997) 7710. 117. W. Weppner and R. A. Huggins, Ann. Rev. Mater. Sci. 8 (1978) 269. 118. N. Ding, J. Xu, Y. X. Yao, G. Wegner, X. Fang, C. H. Chen and I. Lieberwirth, Solid State Ionics 180 (2002) 222. 119. J. Hassoun, R. Varrelli, P. Reale, S. Panero, G. Mariotto, S. Greenbaum and B. Scrosati, J. Power Sources 229 (2013) 117. 120. Y. Sone, P. Ekdunge and D. Simonsson, J. Electrochem. Soc. 143 (1996) 1254. 121. V. S. Borovkov and A. K. Ivanov-Shitz, Electrochim. Acta 22 (1977) 713. 122. W. Wieczorek, Mat. Sci. Eng. B15 (1992) 108. 123. R. A. Rapp and D. A. Shores, Techniques of Metals Research, Vol. 4, part 2, eds. R. A. Rapp, (Interscience, New York, 1970). 124. R. N. Blumenthal and M. A. Seitz, Electrical Conductivity in Ceramics and Glass, ed. N. M. Tallan, (Marcel Dekker, New York, 1974). 125. D. C. Grahame, J. Electrochem. Soc. 99 (1952) 350C. 126. J. R. Macdonald, Electrode Processes in Solid State Ionics, eds. M. Kleitz and J. Dupuy, (Reidel Publishing Co., Dordrecht-Holland, 1976). 127. W. I. Archer and R. D. Armstrong, Electrochemistry, Specialist Periodical Report, Vol. 7, (The Chemical Society, London, 1976). 128. J. E. Bauerle, J. Phys. Chem. Solids 30 (1969) 2657. 129. M. I. Hodge, M. D. Ingram and A. R. West, J. Electroanal Chem. 74 (1976) 125. 130. K. S. Cole and R. H. Cole, J. Phys. Chem. 9 (1941) 341. 131. S. P. S. Badwal, F. T. Ciacchi and D. V. Ho, J. Appl. Electrochemistry 21 (1991) 721. 132. C. Wagner, Z. Elektrochem. 60 (1956) 47. 133. M. H. Hebb, J. Chem. Phys. 20 (1952) 185. 134. G. M. Choi, J. H. Kim and Y. M. Park, Mat. Res. Soc. Symp, Proc. 699 R9.6.1. 135. M. Spiro, Techniques of Chemistry, Vol. 1, Part II, eds. A. Weissberger and B. W. Rosseter, (Wiley, New York, 1970).

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136. M. Leveque, J. F. Le Nest, A. Gandini and H. Charadame, Makromol. Chem. Rapid Commun. 4 (1983) 497. 137. M. Leveque, J. F. Le Nest, A. Gandini and H. Charadame, J. Power Sources 14 (1985) 27. 138. P. R. Sorensen and T. Jacobsen, Electrochim. Acta 27 (1982) 1671. 139. C. Tubandt, Handbuch der Experimentalphysik, Vol. XII. Part I, eds. W. Wein and F. Harms, (Akademie Verlag, Leipzig, 1932). 140. A. Bouridah, F. Dalard, D. Deroo and M. B. Armand, Solid State Ionics 18/19 (1986) 287. 141. P. M. Blonsky, D. F. Shriver, P. Austin and H. R. Allcock, Solid State Ionics 18/19 (1986) 258. 142. M. Watanabe, K. Sanui, N. Ogata, T. Kobayashi and Z. Ohtaki, Z. Appl. Phys. 57 (1985) 123. 143. D. Fauteux, Solid State Ionics 17 (1985) 133. 144. P. G. Bruce and C. A. Vincent, J. Electroanalytical Chem. 225 (1987) 1. 145. B. Yang, A. Manohar, G. K. Surya Prakash, W. Chen and S. R. Narayanan, J. Phys. Chem. B. 115 (2011) 14462. 146. H. Schmalzried, Proc. Symp. of Natl. Phys. Labs., (1972) 39. 147. H. Peters and H. Mobius, Z. Phys. Chem. 209 (1958) 298. 148. H. Peters and G. Mann, Z. Electrochem. 63 (1959) 244. 149. C. Wagner, Z. Phys. Chem. B 21 (1933) 25. 150. P. H. Keesom and N. Pearlman, Methods of Experimental Physics, Vol. VI, Solid State Physics, eds. K. Lark Horovitz and V. A. Johnson, (Academic Press, New York, 1959). 151. E. M. Sherwood, High Temperature Materials and Technology, eds. I. E. Campbell and E. M. Sherwood, (John Wiley, New York, 1967). 152. B. C. H. Steele, Emf Measurements at High Temperature, ed. C. B. Alcock, (Institution of Mining and Metallurgy, London, 1968).

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Chapter 2

In-situ Neutron Techniques for Lithium Ion and Solid-State Rechargeable Batteries Yuping He and Howard Wang∗

Institute for Material Research and Department of Mechanical Engineering State University of New York, Binghamton, NY 13902, USA Material Measurement Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899, USA ∗[email protected]

In this chapter, we review in-situ neutron techniques for studying lithium ion and solid-state rechargeable batteries. Three neutron measurement techniques, neutron powder diffraction (NPD), neutron reflectivity (NR), and neutron depth profiling (NDP) are discussed using specific examples. They are used to quantify the structure and the real-time distribution of Li in active battery components during battery operations, and gain new insights in the function and failure of battery systems. New opportunities of applying in-situ neutron diagnoses for studying the performance and lifetime of secondary batteries are also discussed.

1. Introduction Today’s society demands increasingly for electric energy storage with high energy and power density, long use life, low cost, and enhanced safety.1–3 Rechargeable Li-ion batteries (LIBs) are a promising technology to meet most application demands. Since the initial proposal by Whittingham in the 1970s,4 LIBs have evolved over decades and become commonly used in portable electronics

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such as laptop computers and mobile phones. However, for largescale energy storage needs such as plug-in hybrid electric vehicles, renewable energy management, and electric grid regulation applications, batteries need to have significantly increased energy and power capacities as well as safety and lifetime.5–7 Because of the transient and non-equilibrium nature of electrochemical processes in a working LIB, much of the critical structural information is not easily accessible, impeding advances of battery technologies. Precise, in-situ diagnostic techniques will play a critical role in every aspect of effort in developing next generation LIBs, including materials and processes innovation, system optimization, safety analysis, failure diagnosis and lifetime prediction. Researchers have applied in-situ microscopy, spectroscopy, X-ray scattering techniques, and others towards understanding the structure and performance of LIB systems. The typical examples are the innovative use of in-situ transmission electron microscopy,8, 9 scanning probe microscopy,10, 11 nuclear magnetic resonance spectroscopy,12, 13 and synchrotron XRD.14–16 Applications of neutron techniques for in-situ diagnosis of LIBs are relatively new; however, they can be very powerful because of neutron’s high penetration power and its relatively high sensitivity to Li isotopes. Among many neutron measurement methods, neutron powder diffraction (NPD) has been successfully used to reveal changes in the chemical compositions and crystal structures of electrode materials during battery operation.17–36 Two other neutron techniques, neutron reflectivity (NR)37–41 and neutron depth profiling (NDP)42 have recently also been applied to in-situ battery studies. In-situ NR is able to precisely probe the variation of thin films and interfacial structures in thin film battery stacks, while in-situ NDP can directly visualize the distribution and flow of Li in a working battery. In this chapter, those in-situ neutron techniques are discussed with specific examples. Together, they offer structural information of active materials over wide length scales from atomic lattices to layered battery cells, and yield valuable new insights in the performance and failure of battery systems.

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2. Neutron Powder Diffraction Batteries work in charge and discharge cycles as Li-ions move back and forth between two electrodes. The insertion and removal of Li-ions cause electrodes materials to undergo structural changes from crystal lattice expansions and retractions to phase transitions. In certain cases, changes of crystalline structures in electrodes are metastable and subject to relaxation towards equilibrium upon the removal of applied electric fields. Better knowledge of structural processes helps reveal mechanisms of battery operation. It is therefore desirable to investigate real-time structural changes in electrodes during charge/discharge using in-situ diffraction techniques. In-situ X-ray diffraction (XRD) has been extensively used in studying LIBs,15, 43–45 whereas much fewer in-situ NPD studies have been carried out, as summarized in Table 1. Neutrons interact with atomic nuclei of materials, in contrast to X-rays interacting with electrons surrounding nuclei. Hence, NPD complements XRD in determining crystalline structures. Compared to XRD, NPD has the following advantages: (1) higher sensitivity to light elements such as Li, the working ion in LIBs, usually in the presence of heavy species, thus capable of determining their locations and site occupancy; (2) larger contrast between transition metal elements such as Fe, V, Ni, Cr, Co and Mn, which are often present simultaneously in novel battery electrodes; (3) capability of differentiating isotopes such as 6 Li and 7 Li due to their large difference in neutron absorption crosssections, 940 versus 0.0454 barn (at λ = 1.798 Å),46 and 1 H and 2 H (D) with incoherent scattering cross-sections of 80.27 versus 2.05 barn;46 (4) less dependence of diffracted peak intensity on the wavelength λ and scattering angle θ;33 (5) larger penetration depth of neutrons allowing for probing all components of LIBs packed in metal cases. One downside is that NPD measurements are susceptible to the large incoherent scattering of hydrogen and coherent scattering of carbon in common LIBs, which add a significant background to diffraction patterns, reducing the signal-to-noise ratio. To take advantage of in-situ NPD for studying LIBs, a suitable electrochemical cell needs to be developed. Efforts during the

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In-situ NPD study of LIBs.

Electrode studied

Reference

LiMn2 O4 cathode

Bergstrom et al., 199817

Lix Mn2 O4 cathode LiFePO4 cathode

Berg et al., 200118 Roberts et al., 201333

Li1.1 (Ni1/3 Mn1/3 Co1/3 )0.9 O2 cathode Li4 Ti5 O12 anode

Rosciano et al., 200820 Colin et al., 201021

Roll-over cell

MoS2 anode Br doped Li4 Ti5 O12 anode Li(Co0.16 Mn1.84 )O4 cathode LiFePO4 cathode LiCoO2 , LiMn2 O4 , LiFePO4 , graphite, YFe(CN)6 , FeFe(CN)6

Sharma et al., 201124 Du et al., 201123 Sharma et al., 201125 Sharma et al., 201228 Sharma and Peterson, 201229

Commercial cell

LiCoO2 cathode, graphite anode LiCoO2 cathode, graphite anode Lix Niy Mnz Co(1−y−z) O2 cathode, graphite anode LiCoO2 cathode, graphite anode LiCoO2 cathode, graphite anode Graphite anode revisited Lix Mn2 O4 cathode, graphite anode Lix CoO2 cathode, Lix C6 anode

Rodriguez et al., 200419 Sharma et al., 201022 Wang et al., 201230

Li1+y Mn2 O4 cathode Cathode Li[Ni1/3 Mn1/3 Co1/3 ]O2 versus Li[Li0.2 Ni0.18 Mn0.53 Co0.1 ]O2

Sharma et al., 201336 Liu et al., 201332

Cylindrical cell

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Cell type

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Coin cell

Lab-made, similar to commercial cell

Dolotko et al., 201226 Senyshyn et al., 201227 Senyshyn et al., 201334 Cai et al., 201331 Sharma and Peterson, 201335

past 15 years have resulted in four types of in-situ NPD cells: cylindrical,17, 18 coin,20 roll-over,24 and new cylindrical cells with roll-over concept involved.33 The first in-situ NPD cell as developed in 1998 by Bergstrom et al. is shown in the left panel of Fig. 1(a).17 The cell comprises of a Pyrex tube with gold-plated inner surfaces

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Fig. 1. Custom-built in-situ NPD cells: (a) the first cylindrical cell17 (left) and its modified version18 (right); (b) redesigned cylindrical cell;33 (c) coin cell;20 (d) rollover cell.29

as the cathode current collector, a Li rod anode at the cylindrical axis, and a solid-polymer electrolyte and separator between two electrodes. A modified version by the same group (the right panel of Fig. 1(a))18 reversed the two electrodes with a Li foil lining against the cell tube and cathode materials loaded to fill the tube and a stainless-steel rod inserted along the tube axis as its current collector. This cylindrical cell has been used to monitor structural changes occurring in the LiMn2 O4 cathode after being partially charged to Li0.84 Mn2 O4 ,17 and reveal the phase transition from the spinel Lix Mn2 O4 to cubic λ-MnO2 with the extraction of Li-ions.18 More recently, they have redesigned a cylindrical cell (Fig. 1(b)),33 which followed the concept of the roll-over cell. The electrode, separator (pre-soaked in electrolyte), Li foil, and another piece of separator

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are placed on top of one another to form a stack, which is rolled into a coil (top view in Fig. 1(b)). The rolled coil is inserted in a quartz or Al tube with both ends sealed by Swagelok joints (side view in Fig. 1(b)). Using this new design, the phase change reaction occurring in LiFePO4 cathodes has been monitored in-situ.33 The Novák group has designed a coin-type electrochemical cell for in-situ NPD study of Li1.1 (Ni1/3 Mn1/3 Co1/3 )0.9 O2 cathode20 and Li4 Ti5 O12 anode,21 as shown in Fig. 1(c). This design only exposes the cathode to the neutron beam, resulting in cleaner diffraction patterns. The variation of crystalline structures of the Li1.1 (Ni1/3 Mn1/3 Co1/3 )0.9 O2 cathode has been studied from the shift of its characteristic (003) diffraction peak upon charging.20 In addition, in-situ NPD data on the Li4 Ti5 O12 anode using the same setup have revealed the evolution of the unit cell parameters, oxygen position and quantitative ratio between Li4 Ti5 O12 and lithiated Li7 Ti5 O12 .21 However, both the cylindrical17, 18 and coin-type20 cells have suffered from the low rate limitation of large amount of cathode mass (5 g and 2.2 g) in a single thick cathode layer (ca. 10 mm and 5 mm, respectively), resulting in tens to hundreds of hours per charge or discharge half cycle. Such measurements are advantageous for investigating equilibrium or quasi-equilibrium states in one cell17, 18, 20, 33 or multiple cells simultaneously to minimize the loss of neutron beam;21 however, kinetic information is not attainable from those measurements. Sharma et al.24 have developed a roll-over cell (Fig. 1(d)) that mimics the commercial 18650-type batteries while maximizing the signal-to-noise ratio of the diffraction from the electrodes of interest by reducing the hydrogen content in the battery assembly through limiting the use of liquid electrolytes as well as isotope replacement to deuterated species.20, 24 In preparing the cell, layers of active materials and insulator films are stacked and rolled to fit in a vanadium can, followed by adding electrolyte and sealing with wax. This rollover cell design can circumvent the thickness/mass limitation in the aforementioned cylindrical and coin cells, resulting in better size and geometry for in-situ NPD measurements. In addition, the unique

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neutron beam line, Wombat, with the combination of relatively intense neutron beam and area detector covering 120◦ in 2θ simultaneously instead of point-by-point 2θ scan optimizes in-situ realtime NPD measurements using this type of cells. NPD spectra were collected continuously and recorded every a few minutes over many hours of electrochemical cycling. Combining this novel cell design and the unique NPD facility, they have successfully investigated the crystallographic evolution of multiple electrodes including MoS2 ,24 Br doped Li4 Ti5 O12 ,23 Li(Co0.16 Mn1.84 )O4 ,25 LiCoO2 ,29 LiMn2 O4 ,29 LiFePO4 ,28, 29 graphite,29 YFe(CN)6 ,29 and FeFe(CN)6 .29 In the following, the structural evolution of LiFePO4 cathode28 is taken as an example. Lithium iron phosphate has become an intercalation cathode material of great interest since it was first proposed by Padhi et al. in 1997,47 because it is stable, safe, cheap and environmental benign, particularly, it can be modified for high power and long cycle life applications. To further improve its battery performance, better understanding the mechanism of charge/discharge associated with the transformation between FePO4 and LiFePO4 phases is needed. Extensive efforts in the past decade have resulted in significant progresses, while the mechanism of phase transformation underlying battery operations remains the subject of dispute. A variety of models have been proposed: isotropic two-phase growth such as shrinking-core47 and mosaic,48 anisotropic two-phase growth such as new core-shell49 and domino-cascade,50, 51 spinodal decomposition type,52 dynamic amorphization,53–55 and most recently nonequilibrium solid-solution single-phase transformation.56 On the other hand, the solid-solution phase transformation mechanism has been predicted theoretically56 but not confirmed experimentally. Using the real-time in-situ NPD technique, Sharma et al.28 have observed the coexistence of the solid-solution and two-phase reactions in LiFePO4 of a roll-over cell during charge and discharge. To build this roll-over cell (Fig. 1(d)), Celgard films were used as both insulator and separator, deuterated ethylene carbonate (EC) and deuterated dimethyl carbonate (DMC) were used as electrolyte solvent.

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Fig. 2. In-situ NPD data and the parameters of the cathode derived from Rietveld refinements: (a) selected 2θ region of in-situ NPD data; (b) applied current; (c) measured voltage; (d) phase fractions of LiFePO4 (green crosses) and FePO4 (black crosses); (e) lattice parameters of LiFePO4 (solid symbols) and FePO4 (open symbols).28

The in-situ NPD data show time-dependent crystal structure changes of the LiFePO4 cathode (Fig. 2(a)) during the electrochemical cycling between 0.75 and 4.2 V (Fig. 2c). With Gaussian fits to the characteristic reflections, LiFePO4 (221) and FePO4 (221), their peak position and intensity as a function of charge/discharge time are

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obtained and plotted in Fig. 3. From the shaded region in Fig. 3(a), the position of the LiFePO4 (221) peak shifts visibly toward larger angles, corresponding to the decrease of its unit cell volume; however, none of the FePO4 peaks can be detected. The observations imply the delithiation of LiFePO4 via a solid-solution reaction between 3.42 and 3.52 V. On the other hand, Fig. 3(b) shows that the FePO4 (221) peak appears, and its intensity increases with charging while LiFePO4 (221) peak intensity decreases, indicating LiFePO4 to FePO4 phase transition. Meanwhile, the LiFePO4 (221) peak increases at a rate of 3(6) × 10−5 (◦ )/min, indicating the existence of solid-solution reaction. Therefore, in the potential range of 3.49 V and 3.52 V, both the solid-solution and two-phase reactions occur concurrently. Through Rietveld refinements of in-situ NPD data, the timedependent evolution of the phase fractions (Fig. 2(d)) and lattice parameters (Fig. 2(e)) of LiFePO4 and FePO4 can be derived. The onset of solid-solution reaction is indicated by the vertical black lines in Fig. 2, and the vertical purple lines indicate the midpoint of the two-phase reaction where the second phase is growing beyond the first phase in amount. The variation in the LiFePO4 /FePO4 phase fractions evidences the two-phase reaction and the change in the Li1−y FePO4 (and Lix FePO4 ) lattice parameters evidences the solidsolution reaction, both of which occur simultaneously in the shaded region in Fig. 2. The electrochemical reaction mechanisms of the LiFePO4 in the in-situ NPD roll-over cell are summarized in Fig. 4: (1) no long-range crystallographic changes between 0.75 V and 3.42 V, (2) a Li1−y FePO4 solid-solution reaction between 3.42 and 3.52 V, (3) a combination of Li1−y FePO4 −Lix FePO4 two-phase and Li1−y FePO4 solid solution reactions between 3.49 V and 3.52 V, (4) a Li1−y FePO4 to Lix FePO4 two-phase reaction between 3.49 V and 3.67 V, (5) a Lix FePO4 solidsolution reaction at higher voltages (not plotted) producing FePO4 . As viewed from Fig. 2, the sequence of these reaction mechanisms is reproducible in the subsequent cycles at higher currents (see Fig. 2(b)). Although custom-built cells are more flexible for in-situ NPD study of electrodes with signal-to-noise ratio enhanced by simply

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Fig. 3. (Color online) Results of Gaussian fits to the LiFePO4 and FePO4 (221) reflections in the in-situ NPD data: Changes in the peak position and intensity of LiFePO4 (red) and FePO4 (black) in the full cycling time region (a) and in the region where solid-solution (Li1−y FePO4 ) and two-phase (Li1−y FePO4 to Lix FePO4 ) reactions occur concurrently.28

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Fig. 4. Electrochemical reaction mechanisms of LiFePO4 derived from in-situ NPD data analysis.28

tuning the content of hydrogen-containing and liquid components, there is increasing interest in applying in-situ NPD technique to various commercial cells including prismatic cell,22 18650-type,26, 27, 34, 35 pouch cell,30, 31 and else.19 Due to the large penetration depth of neutrons, both the cathode and anode materials of interest can be monitored simultaneously. For example, the time-resolved lattice responses of the Lix CoO2 cathode and Lix C6 anode in a commercial 18650-type cell were found to vary proportionally with the magnitude of the current applied; higher currents result in faster structural change and lower battery capacity.35 The fatigue process of commercial 18650-type cells was analyzed to build the direct correlation between the capacity fade and the structural changes in both LiCoO2 cathode and graphite anode, where the loss of active Li-ions in electrodes was considered to the primary reason for LIB fatigue.26, 27 Asymmetric lithiation and delithiation pathways — LiC24 phase not formed during charge at 1C but formed during discharge — were probed in a commercial pouch cell under realistic cycling conditions.30 In addition, inhomogeneous degradation was

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detected in a large format pouch cell after a loss of 40% capacity,31 as demonstrated below. The degraded pouch cell was obtained by continuously cycling a fresh 15 Ah commercial battery, consisting of graphite anode and spinel Lix Mn2 O4 -based cathode, at currents of ±40 A (or 2.67 C) in a 40◦ C chamber until ca. 9 Ah capacity retained. For the degraded cell, NPD measurements were conducted on the VULCAN instrument, an engineering diffractometer at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL).31 The measured spot volume was confined as 10 × 5 × 5 mm3 using the incident beam slit and collimators. During charging/discharging at ±2 A, neutron diffraction data were recorded continuously and sliced to 15 min intervals for each spectrum. As shown in Fig. 5, in the center area (Point 5, Fig. 5(a)), the d-spacing of the cathode (222) peak decreases during charge, as Li-ions intercalate into the graphite layer to form LiC12 and then LiC6 . During discharge, the (222) d-spacing follows the reverse path to its uncharged state. At the same time, LiC6 transits to LiC12 and then to graphite. In Fig. 5(b), at the edge (Point 1), unlithiated graphite remains the major phase throughout the full cycle, indicating that few Li-ions intercalate into the anode. As for the spinel cathode, the (222) peak splits into two peaks at an early stage of charging. The d-spacing of the less intense peak evolves normally — active cathode, but the more intense peak exhibits only small changes, showing a limited Liions insertion/removal process — non-active cathode byproducts. Therefore, both the graphite anode and Lix Mn2 O4 cathode lost a significant amount of capacity near the edges while both electrodes functioned properly near the central area. Additionally, in the degraded area, the loss of local capacity of the anode and cathode is coupled. The degradation coupling was further investigated by NPD mapping at a fully charged state. The mapping was carried out along the lines shown by the arrows in the cell photo (inset of Fig. 6). The collection time at each location was ca. 90 minutes. NPD data were analyzed quantitatively by calculating the uncharged graphite phase fraction in the anode and the normalized intensity of (222)

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Fig. 5. The contour plots of neutron diffraction patterns together with the timedependent voltage (on the left) and current (on the right) curves during cycling at (a) Point 5 and (b) Point 1, as illustrated in the inserted photo of the commercial cell.31

peak of the active cathode material with respect to the Cu (111) peak from the Cu current collector. As shown in Fig. 6(a), along both horizontal lines, the uncharged graphite phase fraction is close to 80% near the left edge at 10 mm. It decreases to less than 20% between 100 mm and 160 mm and then increases to 40% at ca. 180 mm along the upper horizontal line. Meanwhile, the amount of active cathode material is minimal close to 10 mm in both horizontal lines, and it increases toward 100 mm. After ca. 160 mm, the amount of active

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Fig. 6. The graphite phase fraction and the normalized intensity of cathode (222): (a) along the blue line (the Cu tab) and the purple line (the Al tab); (b) along the vertical red line.31

cathode material decreases again along the upper line. The same finding also occurs along the vertical line (Fig. 6(b)). Accordingly, the degradation at the anode and cathode occurs in the same locations and is thus coupled together. The findings imply the viability of in-situ NPD for diagnosing the degradation behaviors and mechanisms of LIBs, which opens the door for designing remediation recipes accordingly, thus enabling the development of better electrode and packaging designs for LIBs. 3. Neutron Reflectivity Lithiation and delithiation of intercalation compounds cause lattice parameter changes or phase transitions that can be measured using diffraction techniques, which, however, do not readily quantify amorphous materials. In addition, the composition and structure

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across interfaces between different components in batteries are of critical importance to the transport of Li-ions and electrons. Precise measurements are needed to quantify these variations at sub-nanometer levels particularly near interfaces for understanding interfacial phenomena. NR is a high resolution technique for probing structure, composition, and magnetism in thin films with sub-angstrom accuracy for films as thin as 1.5 nm.57, 58 NR measures the scattering length density (SLD) as a function of depth, which is readily interpreted as a compositional profile of constituent materials. As NR has been used for studying a wide range of thin films, its applications to addressing battery issues remain at the infancy.59 There are a few recent reports37–41 on in-situ NR studies of batteries. Wagemaker et al.37 have measured the intercalation of Li into anatase TiO2 thin film, and interpreted the intercalation scheme in terms of phase boundary movement. During Li insertion, the Li-rich titanate phase progressively moves inside the anatase TiO2 electrode as a front parallel to the interface; while during Li extraction, the phase front moves back exactly reversing the Li insertion process. Hirayama et al.38 have characterized the electrode surface structure change of an epitaxial LiFePO4 film in a LIB using in-situ reflectivity techniques. NR data have revealed the formation of an interfacial layer between LiFePO4 and electrolyte and the reversible variation of its SLD during Li (de)intercalation processes, which were not possibly captured by X-ray reflectivity (XR) measurements. Owejan et al.39 have carried out a detailed in-situ NR investigation on SEI formation as a function of potentiostatic voltage in a working half cell of Li/Cu/Ti/Si using deuterated electrolyte. Note that, the formation and evolution of SEI has also been observed by another in-situ neutron technique, small angle neutron scattering (SANS), in an ordered mesoporous hard carbon electrode during electrochemical cycling.60 Besides the electrochemically driven SEI formation, Veith et al.61 observed that SEI can form spontaneously via chemical reaction between an amorphous silicon (a-Si) electrode surface and a liquid electrolyte (1.2 M LiPF6 in 3:7 wt% ethylene carbonate:dimethyl carbonate) using ex-situ NR measurement. More

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recently, Jerliu et al.40, 41 have used in-situ NR to study the lithiation of a-Si electrodes, which is discussed below as an example. Silicon is a promising anode material for LIBs for its high theoretical specific capacity of ca. 4200 mAh/g (Li4.4 Si), which is more than 10 times that of commercial graphite anodes (ca. 372 mAh/g, LiC6 ).62–64 However, upon Li-ion insertion and extraction, Si exhibits large volume change up to 400%,62, 64 which induces substantial stress that gives rise to mechanical issues and eventual fade of capacity.2, 3, 62 Despite extensive studies on electrochemical lithiation/delithiation cycling and ex-situ morphological observations, much is uncertain about the reliability and failure of Si electrodes. New insights have been obtained from in-situ NR analysis of Si anode by Jerliu et al.40 Their battery assembly for in-situ NR measurements is schematically illustrated in Fig. 7(a) and photographed in Fig. 7(b). A half cell consisting of sputtered 40 nm a-Si on a Pd-coated quartz block as the working electrode, 1.5-mm thick metal Li as the counter and reference electrodes, and 1 M LiClO4 in propylene carbonate as the electrolyte has been used in the study. The cell was sealed against high density polyethylene housing

Fig. 7. (a) Schematic sketch of in-situ NR cell used: (1) 5 mm thick Al ground plate; (2) 10 mm thick Pd coated quartz substrate with a-Si electrode on it (circle); (3) Kalrez
gaskets; (4) 20 mm thick high density polyethylene base; (5) Li counter electrode; (6) Li reference electrode; and (7) copper base. (b) Image of the cell: (1) Al ground plate; (2) quartz substrate and electrode; (3) polyethylene housing; and (4) contacts to potentiostat. The shaded area depicts the position of the neutron beam incidence.40

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using Kalrez
gaskets and filled with the electrolyte through two ports bored into the polyethylene. NR data were collected on the V6 reflectometer located at the Helmholtz–Zentrum, Berlin, Germany, with neutrons directed through the side of the quartz block (see Fig. 7(b)), reflected from the SiO2 /Pd/Si/electrolyte interfaces, and detected from the opposite side of quartz block. Data analysis was performed using the Parratt32 software package.65 The first NR pattern was taken after the initial assembly (noted as the virgin state), followed by stepwise galvanostatic lithiation and delithiation steps (Fig. 8(a)). After each step, current was interrupted to allow the system to establish equilibrium for a NR measurement. Characteristic potential versus time curves for (de)lithiation at currents of 100 µA are shown in Fig. 8(b). During the first lithiation step at 20 µA for 1 hour, the potential decreased from ca. 2.92 V

Fig. 8. (a) Flow chart of the current applied to the electrode for different intercalation steps. During the interruption of intercalation as indicated at the abscissa, the system was allowed to relax for ca. 1 h, followed by ca. 5 h NR data collection. (b) Galvanostatic charge–discharge curves cycled at a constant current of 100 µA for various time steps. (c) NR data at different stages (open circles) with the fitting results by Parratt32 (lines). (d) SLD profiles corresponding to the fits of the NR data in (c).40

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to 0.75 V, which is still above the redox potential of Li in a-Si electrode, ca. 0.6 V. During relaxation, the potential restored to its initial value. The corresponding NR spectrum after equilibrium was found identical to that of the virgin state (Fig. 8(c)-0). In a second step, a higher current of 100 µA was applied for 1 hour. The corresponding potential decreased to 0.3 V (Fig. 8(b)), but increased during equilibration to a value of 0.68 V, indicating that Li insertion took place. This is also reflected in the NR pattern of Fig. 8(c)-2 with visible changes compared to that of the virgin state (Fig. 8(c)-0). The lithiation process was completed by an additional step of 100 µA for 2 hours, followed by two delithiation steps with a reversed current at 100 µA for 2 hours and 9 minutes, respectively. NR data show that after a complete cycle, the virgin pattern is not restored, indicating irreversible lithation/delithiation processes. A box-model has been used to fit the NR data and yield SLD depth profiles, as shown in Fig. 8(d) with selected fitting parameters listed in Table 2. From Fig. 8(d) and Table 2, the thickness of a-Si layer increases while its SLD decreases, as caused by increasing incorporation of Li in the a-Si film. In addition, a better fitting of NR spectra at the delithiated states implies the possible existence of an SEI layer between Lix Si and electrolyte. Table 2. The parameters of the a-Si electrode obtained from the best fits for the electrode system at various lithiation states.40 Amorphous silicon Thickness (Å)

SLD (×10−6 Å−2 )

Roughness (Å)

425 ± 25 425 ± 25 544 ± 17 769 ± 10

1.95 ± 0.05 1.95 ± 0.05 1.67 ± 0.08 1.00 ± 0.17

14 ± 3 14 ± 3 4±4 10 ± 5

424 ± 9 414 ± 14

1.68 ± 0.12 1.61 ± 0.18

5±5 20 ± 6

Intercalation step 0 1 2 3

Virgin 20 µA for 1 h +100 µA for 1 h +100 µA for 2 h

De-intercalation step 4 5

+100 µA for 1 h +100 µA for 9 min

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As demonstrated in this example, NR offers the unique capability of sub-nanometer resolution measurements of interfaces and films, which are much needed for advancing fundamental understanding of LIB materials and systems. Critical LIB issues to be addressed using NR include the mechanism of lithiation/delithiation of active materials, SEI formation, lithiation-induced volume change, degradation of electrodes, and the interfacial structure of electrolytes/electrodes. 4. Neutron Depth Profiling Lithium ions move back and forth between electrodes during battery uses, so it is desirable to directly visualize the distribution of Li in working LIBs. Simultaneous space- and time-resolved Li measurements allow for direct comparison of ionic motion in battery electrodes with the electric current in the external circuit, yielding new insights in the transport mechanisms and normalcy of battery performance. Based on the neutron activation and energy loss spectrum of energetic ions in matter, NDP has been applied to resolve nano- to micro-scale Li distributions in working battery systems during charge/discharge cycles. NDP was developed in the early 1970s and used to quantitatively measure the abundance and depth distribution of several important elements (Li, B, N, He, Na, etc).66, 67 NDP is now a mature technique and increasingly used to measure Li distributions in modern battery technologies.68–70 However, reports on in-situ NDP of solid state battery are rather limited.42 Typical NDP setup and principles of measurement have been described in details in the previous reports.59, 66 Briefly, a nuclear reaction, 6 Li + n → α + 3 H, is used for NDP measurement of Li distribution in specimen, in which the energy spectra of charged particles are recorded with surface barrier detectors. The energy of the detected particles is used to determine the initial location of the activation reaction, while the normalized counts are used to measure the abundance of elements at the corresponding depth. The full depth range of the profile varies from a few micrometers

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Fig. 9. Time-resolved in-situ NDP plots on a thin film battery during (a) charging and (b) discharging. The assignments of the electrode and electrolyte layers in the spectra are labeled. Arrows indicate the flow of Li in each electrode.59

to tens of micrometers, depending on the atomic composition of the specimen as well as the particle of detection, α or 3 H. Likewise, the depth resolution varies from a few nanometers to a few hundred nanometers. The selective nature of nuclear activation ensures that Li spectra are clean, being free of interference from other elements. These differences represent a significant advantage of NDP for continuous in-situ measurement of Li transport during prolonged battery operation. One example of in-situ NDP real-time assessment on battery operation is shown in Fig. 9. The battery was fabricated by sputter deposition of thin films, with a layered structure of mica/Pt (200 nm)/LiCoO2 (5 µm)/LiPON (2 µm)/Li (4 µm)/Pt (200 nm)/ mica. The 7.5% natural abundance of 6 Li in the electrode and electrolyte layers allows for convenient NDP measurements without special alteration in battery preparation. The NDP spectra recorded during charge/discharge are shown in Figs. 9(a) and 9(b), respectively. The Li metal layer is shown as a prominent peak around 1200 keV, while the LiCoO2 layer is shown as a plateau ranging from 1700 keV to 2100 keV. During charging, lithium is pumped out from the LiCoO2 cathode layer and deposited in the anode, while during discharging, lithium flows back from the anode to cathode. Figure 10(a) shows the potential profiles of the battery during several cycles of charge and discharge. Using the SRIM software to

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Fig. 10. Time-resolved (a) potential profile, and (b) electric versus ionic charge displacement. The potential anomaly at the beginning of the second discharge coincides with the mismatched charge at the same time.59

calculate the stopping power of 3 H+ in different battery layers,71 NDP data are quantitatively analyzed to yield Li depth profiles, allowing for direct comparison of the Li transport inside the battery and the electric current flow in the external circuit. Figure 10(b) compares the Li ion density in the cathode measured by NDP (symbols) and displaced electric charge recorded by the potentiostat (lines). A good match is maintained till the instability occurs as indicated by the erratic responses of current and potential during the second discharge, which may be related to a soft short circuit in the battery. The sudden discrepancy between the ionic transport in the cathode and the electric transport in the external circuit marks the onset of severe battery degradation, resulting in a shortened cycle life. Oudenhoven et al.42 have employed in-situ NDP to probe Li mobility in a thin film micro-battery sputtered with enriched 6 LiCoO and LiPON. The battery stack structure is sketched in the 2 inset of Fig. 11(a). The Li metal anode was formed during the first charge cycle by in-situ Li plating. The total thickness of the battery layers was 2.35 µm, which allows for detecting α particles with higher depth resolution. The NDP setup42 at the Reactor Institute Delft is very similar to that at NIST,59 while they use thermal neutrons with energy of ca. 25 meV and NIST uses cold neutron of

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Fig. 11. The NDP plots of a thin film battery sputtered with enriched 6 LiCoO2 and standard LiPON during several stages of the charging process (a) and during equilibration in the charged state after 0, 1 and 2 hours (b).42

4 meV or lower. The NDP profiles of the battery during several stages of the charging process are plotted in Fig. 11(a). Prior to cycling, 6 Li remains mostly in the cathode and no significant Li exchange occurs between cathode and electrolyte in the time between battery production and NDP analysis (ca. one week). Upon charging at 0.5 C, 6 Li depleted inhomogeneously from the cathode mostly prominently near the LiPON interface, while 6 Li in the electrolyte increased mostly near cathode and moved towards the anode. One observation in the study was that the decrease of Li signal in a part of the cathode layer went beyond the average delithiation level of the entire electrode, which was interpreted as the dynamic exchange of Li isotopes between cathode and LiPON. This interpretation, however, assumes the identical electrochemical activity of the entire cathode layer, which remains to be verified. Furthermore, upon the cessation of charging, Li isotopes equilibrated in the LiPON electrolyte to yield a homogenous composition after 2 hours, as shown in Fig. 11(b), whereas the profile in the Lix CoO2 electrode remained largely unchanged. The observation was attributed to the high mobility of Li-ions in LiPON in the absence of the external field, while their motion in LiCoO2 required a driving force. The in-situ NDP technique has been demonstrated to be a valuable tool to reveal the processes occurring in thin film solid-state

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batteries during electrochemical cycling. It can reveal the distribution and mobility of Li inside the battery stack, and is therefore a useful technique for the optimization of thin film all-solid-state batteries. With higher neutron flux and better detection capability, NDP could be further improved to become a powerful tool to probe the reliability and lifetime of Li-containing batteries under real operation circumstances. Fast NDP measurement will be particularly useful for understanding battery performance at high charge/discharge rates, which is critical for applications in electrical vehicles and power devices. 5. Conclusions and Outlook The applications of three in-situ neutron measurement techniques for studying lithium ion and solid state batteries, NPD, NR, and NDP have been reviewed in this chapter. NPD has been successfully utilized to analyze the chemical composition and crystal structure evolution occurring in electrodes of working batteries. NR is capable of precisely probing the interfacial structure evolution induced by Li insertion and extraction such as SEI formation, phase boundary movement, degradation of electrodes, and volume change in thin film batteries with sub-nanometer resolution. NDP offers direct visualization of the distribution and flow of Li based on neutron activation of isotope 6 Li. The potential applications of three neutron techniques for in-situ studying battery systems are illustrated with specific examples. As those techniques together provide multi-scale measurements of the Li distribution and transport in active electrodes to yield valuable new insights in the performance and failure of battery systems, further development of neutron techniques is needed to meet the increasing demands in spatial, temporal, and composition resolutions in lithium ion and solid state rechargeable battery research. Acknowledgments HW and YPH would like to thank the financial support from General Motors Company, University of Maryland through the

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NIST-ARRA program, and North East Center for Chemical Energy Storage (NECCES) through the EFRC program of US Department of Energy.

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References 1. D. Larcher, S. Beattie, M. Morcrette, K. Edstroem, J. C. Jumas and J. M. Tarascon, J. Mater. Chem. 17 (2007) 3759. 2. W. J. Zhang, J. Power Sources 196 (2011) 13. 3. J. R. Szczech and S. Jin, Energ. Environ. Sci. 4 (2011) 56. 4. M. S. Whittingham, Science 192 (1976) 1126. 5. M. S. Whittingham, MRS Bull. 33 (2008) 411. 6. M. Armand and J. M. Tarascon, Nature 451 (2008) 652. 7. J. B. Goodenough and Y. Kim, Chem. Mater. 22 (2010) 587. 8. J. Y. Huang, L. Zhong, C. M. Wang, J. P. Sullivan, W. Xu, L. Q. Zhang, S. X. Mao, N. S. Hudak, X. H. Liu, A. Subramanian, H. Fan, L. Qi, A. Kushima and J. Li, Science 330 (2010) 1515. 9. X. H. Liu, L. Q. Zhang, L. Zhong, Y. Liu, H. Zheng, J. W. Wang, J.-H. Cho, S. A. Dayeh, S. T. Picraux, J. P. Sullivan, S. X. Mao, Z. Z. Ye and J. Y. Huang, Nano Lett. 11 (2011) 2251. 10. N. Balke, S. Jesse, A. N. Morozovska, E. Eliseev, D. W. Chung, Y. Kim, L. Adamczyk, R. E. Garcia, N. Dudney and S. V. Kalinin, Nat. Nanotechnol. 5 (2010) 749. 11. S. V. Kalinin, S. Jesse, A. Tselev, A. P. Baddorf and N. Balke, ACS Nano 5 (2011) 5683. 12. R. Bhattacharyya, B. Key, H. Chen, A. S. Best, A. F. Hollenkamp and C. P. Grey, Nat. Mater. 9 (2010) 504. 13. B. Key, M. Morcrette, J.-M. Tarascon and C. P. Grey, J. Am. Chem. Soc. 133 (2011) 503. 14. J. Yoon, S. Muhammad, D. Jang, N. Sivakumar, J. Kim, W.-H. Jang, Y.-S. Lee, Y.-U. Park, K. Kang and W.-S. Yoon, J. Alloy Comp. 569 (2013) 76. 15. Y. Orikasa, T. Maeda, Y. Koyama, H. Murayama, K. Fukuda, H. Tanida, H. Arai, E. Matsubara, Y. Uchimoto and Z. Ogumi, J. Am. Chem. Soc. 135 (2013) 5497. 16. D. Mikhailova, A. Thomas, S. Oswald, W. Gruner, N. N. Bramnik, A. A. Tsirlin, D. M. Trots, A. Senyshyn, J. Eckert and H. Ehrenberg, J. Electrochem. Soc. 160 (2013) A3082. 17. O. Bergstrom, A. M. Andersson, K. Edstrom and T. Gustafsson, J. Appl. Crystallogr. 31 (1998) 823.

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18. H. Berg, H. Rundlov and J. O. Thomas, Solid State Ionics 144 (2001) 65. 19. M. A. Rodriguez, D. Ingersoll, S. C. Vogel and D. J. Williams, Electrochem. Solid St. 7 (2004) A8. 20. F. Rosciano, M. Holzapfel, W. Scheifele and P. Novak, J. Appl. Crystallogr. 41 (2008) 690. 21. J.-F. Colin, V. Godbole and P. Novak, Electrochem. Commun. 12 (2010) 804. 22. N. Sharma, V. K. Peterson, M. M. Elcombe, M. Avdeev, A. J. Studer, N. Blagojevic, R. Yusoff and N. Kamarulzaman, J. Power Sources 195 (2010) 8258. 23. G. D. Du, N. Sharma, V. K. Peterson, J. A. Kimpton, D. Z. Jia and Z. P. Guo, Adv. Funct. Mater. 21 (2011) 3990. 24. N. Sharma, G. Du, A. J. Studer, Z. Guo and V. K. Peterson, Solid State Ionics 199 (2011) 37. 25. N. Sharma, M. V. Reddy, G. Du, S. Adams, B. V. R. Chowdari, Z. Guo and V. K. Peterson, J. Phys. Chem. C 115 (2011) 21473. 26. O. Dolotko, A. Senyshyn, M. J. Muehlbauer, K. Nikolowski, F. Scheiba and H. Ehrenberg, J. Electrochem. Soc. 159 (2012) A2082. 27. A. Senyshyn, M. J. Muehlbauer, K. Nikolowski, T. Pirling and H. Ehrenberg, J. Power Sources 203 (2012) 126. 28. N. Sharma, X. Guo, G. Du, Z. Guo, J. Wang, Z. Wang and V. K. Peterson, J. Am. Chem. Soc. 134 (2012) 7867. 29. N. Sharma and V. K. Peterson, J. Solid State Electr. 16 (2012) 1849. 30. X.-L. Wang, K. An, L. Cai, Z. Feng, S. E. Nagler, C. Daniel, K. J. Rhodes, A. D. Stoica, H. D. Skorpenske, C. Liang, W. Zhang, J. Kim, Y. Qi and S. J. Harris, Scientific Reports 2 (2012) 747. 31. L. Cai, K. An, Z. Feng, C. Liang and S. J. Harris, J. Power Sources 236 (2013) 163. 32. H. D. Liu, C. R. Fell, K. An, L. Cai and Y. S. Meng, J. Power Sources 240 (2013) 772. 33. M. Roberts, J. J. Biendicho, S. Hull, P. Beran, T. Gustafsson, G. Svensson and K. Edstrom, J. Power Sources 226 (2013) 249. 34. A. Senyshyn, O. Dolotko, M. J. Muehlbauer, K. Nikolowski, H. Fuess and H. Ehrenberg, J. Electrochem. Soc. 160 (2013) A3198. 35. N. Sharma and V. K. Peterson, Electrochim. Acta 101 (2013) 79. 36. N. Sharma, D. Yu, Y. Zhu, Y. Wu and V. K. Peterson, Chem. Mater. 25 (2013) 754. 37. M. Wagemaker, R. van de Krol and A. A. van Well, Physica B — Condensed Matter 336 (2003) 124. 38. M. Hirayama, M. Yonemura, K. Suzuki, N. Torikai, H. Smith, E. Watkinsand, J. Majewski and R. Kanno, Electrochemistry 78 (2010) 413.

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39. J. E. Owejan, J. P. Owejan, S. C. DeCaluwe and J. A. Dura, Chem. Mater. 24 (2012) 2133. 40. B. Jerliu, L. Doerrer, E. Hueger, G. Borchardt, R. Steitz, U. Geckle, V. Oberst, M. Bruns, O. Schneider and H. Schmidt, Physical Chemistry Chem. Physics 15 (2013) 7777. 41. B. Jerliu, E. Hueger, L. Doerrer, B. K. Seidlhofer, R. Steitz, V. Oberst, U. Geckle, M. Bruns and H. Schmidt, J. Phys. Chem. C 118 (2014) 9395. 42. J. F. M. Oudenhoven, F. Labohm, M. Mulder, R. A. H. Niessen, F. M. Mulder and P. H. L. Notten, Adv. Mater. 23 (2011) 4103. 43. J. N. Reimers and J. R. Dahn, J. Electrochem. Soc. 139 (1992) 2091. 44. S. T. Myung, S. Komaba, N. Hirosaki, N. Kumagai, K. Arai, R. Kodama and I. Nakai, J. Electrochem. Soc. 150 (2003) A1560. 45. K. Nikolowski, C. Baehtz, N. N. Bramnik and H. Ehrenberg, J. Appl. Crystallogr. 38 (2005) 851. 46. V. F. Sears, Neutron News 3 (1992) 29. 47. A. K. Padhi, K. S. Nanjundaswamy and J. B. Goodenough, J. Electrochem. Soc. 144 (1997) 1188. 48. A. S. Andersson and J. O. Thomas, J. Power Sources 97–98 (2001) 498. 49. L. Laffont, C. Delacourt, P. Gibot, M. Y. Wu, P. Kooyman, C. Masquelier and J. M. Tarascon, Chem. Mater. 18 (2006) 5520. 50. C. Delmas, M. Maccario, L. Croguennec, F. Le Cras and F. Weill, Nat. Mater. 7 (2008) 665. 51. G. Brunetti, D. Robert, P. Bayle-Guillemaud, J. L. Rouviere, E. F. Rauch, J. F. Martin, J. F. Colin, F. Bertin and C. Cayron, Chem. Mater. 23 (2011) 4515. 52. C. V. Ramana, A. Mauger, F. Gendron, C. M. Julien and K. Zaghib, J. Power Sources 187 (2009) 555. 53. N. Meethong, Y.-H. Kao, M. Tang, H.-Y. Huang, W. C. Carter and Y.-M. Chiang, Chem. Mater. 20 (2008) 6189. 54. M. Tang, H. Y. Huang, N. Meethong, Y. H. Kao, W. C. Carter and Y. M. Chiang, Chem. Mater. 21 (2009) 1557. 55. Y. H. Kao, M. Tang, N. Meethong, J. M. Bai, W. C. Carter and Y. M. Chiang, Chem. Mater. 22 (2010) 5845. 56. R. Malik, F. Zhou and G. Ceder, Nature Materials 10 (2011) 587. 57. M. P. Seah, S. J. Spencer, F. Bensebaa, I. Vickridge, H. Danzebrink, M. Krumrey, T. Gross, W. Oesterle, E. Wendler, B. Rheinlander, Y. Azuma, I. Kojima, N. Suzuki, M. Suzuki, S. Tanuma, D. W. Moon, H. J. Lee, H. M. Cho, H. Y. Chen, A. T. S. Wee, T. Osipowicz, J. S. Pan, W. A. Jordaan, R. Hauert, U. Klotz, C. van der Marel, M. Verheijen, Y. Tarnminga, C. Jeynes, P. Bailey, S. Biswas, U. Falke, N. V. Nguyen, D. Chandler-Horowitz, J. R. Ehrstein, D. Muller and J. A. Dura, Surf. Interface Anal. 36 (2004) 1269.

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58. M. P. Seah, W. E. S. Unger, H. Wang, W. Jordaan, T. Gross, J. A. Dura, D. W. Moon, P. Totarong, M. Krumrey, R. Hauert and Z. Q. Mo, Surf. Interface Anal. 41 (2009) 430. 59. H. Wang, R. G. Downing, J. A. Dura and D. S. Hussey, in Polymers for Energy Storage and Delivery: Polyelectrolytes for Batteries and Fuel Cells, eds. K. A. Page, C. L. Soles and J. Runt, Am. Chem. Soc. 1096 (2012) 91. 60. C. A. Bridges, X.-G. Sun, J. Zhao, M. P. Paranthaman and S. Dai, J. Phys. Chem. C 116 (2012) 7701. 61. G. M. Veith, L. Baggetto, R. L. Sacci, R. R. Unocic, W. E. Tenhaeff and J. F. Browning, Chem. Commun. 50 (2014) 3081. 62. R. Teki, M. K. Datta, R. Krishnan, T. C. Parker, T. M. Lu, P. N. Kumta and N. Koratkar, Small 5 (2009) 2236. 63. L. B. Chen, J. Y. Xie, H. C. Yu and T. H. Wang, J. Appl. Electrochem. 39 (2009) 1157. 64. C. K. Chan, H. L. Peng, G. Liu, K. McIlwrath, X. F. Zhang, R. A. Huggins and Y. Cui, Nature Nanotechnol. 3 (2008) 31. 65. C. Braun, in Parratt32 or The Reflectivity Tool, Version 1.6.0 (1997–2002). 66. R. G. Downing, G. P. Lamaze, J. K. Langland and S. T. Hwang, J. Res. Nat. Inst. Stan. 98 (1993) 109. 67. J. P. Biersack and D. Fink, Nucl. Instr. Meth. 108 (1973) 397. 68. G. P. Lamaze, H. H. Chen-Mayer, D. A. Becker, F. Vereda, R. B. Goldner, T. Haas and P. Zerigian, J. Power Sources 119 (2003) 680. 69. S. Whitney, S. R. Biegalski, Y. H. Huang and J. B. Goodenough, J. Electrochem. Soc. 156 (2009) A886. 70. S. M. Whitney, S. R. F. Biegalski and G. Downing, J. Radioanal. Nucl. Chem. 282 (2009) 173. 71. J. F. Ziegler, M. D. Ziegler and J. P. Biersack, Nucl. Instrum. Methods Phys. Res. Sect. B — Beam Interact. Mater. Atoms 268 (2010) 1818.

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Chapter 3

Synchrotron X-ray Based Operando Studies of Atomic and Electronic Structure in Batteries Faisal M. Alamgir and Samson Y. Lai

School of Materials Science and Engineering Georgia Institute of Technology Atlanta GA 30332-0245, USA

In this chapter, we will discuss the principal advantages of using synchrotron methods for the real-time species-specific structural measurements of the active materials in batteries and related electrochemical devices. Specifically, we will look at the inherent versatility of and the remaining challenges with real-time measurement of X-ray absorption, a core-hole spectroscopy method that probes the local structure. The rich content of structural information using X-ray absorption will be discussed in the context of battery chemistry.

1. Introduction The long-term endurance of batteries and other electrochemical devices used in highly discriminating applications, such as in automotive power, is intimately related to the ability of the cathode and anode materials to accommodate and release mobile ions with pre-designed predictability and fidelity. A crosscutting challenge in developing the understanding of energy storage and energy transfer processes in Li batteries rests in the direct measurement of the atomistic processes involved during battery operation. The characterization tool required needs to provide element-specific information and should do so with high resolution spatially, temporally and 79

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in information-space. With such information we would have an element-specific electrochemical roadmap that would allow us to have a much more knowledge-driven approach to the design of the next generation of Li-ion batteries. To map the mechanistic causality between the local atomic/ electronic structure of functional components of batteries and their electrochemical performance, time resolved measurements under operating conditions are critical. In this chapter we will examine the various reasons for why synchrotron based X-ray methods provide inherent advantages and the largest flexibility in obtaining detailed mechanistic information with structural studies under operating conditions, so-called operando studies. Further details on some of the issues discussed in this chapter are also reviewed in an earlier review paper on Li and Li air batteries.1 2. Operando Measurements Measurement of real-time changes in electronic and local atomic/ ionic structure of electrodes during the operation of a battery (i.e. operando) provides critical mechanistic information from active materials that is missed even with in-situ measurements (where just some, but not all, of the real-life operating conditions are replicated). This subtle difference between operando and in-situ methods was shown clearly in an example from another electrochemical system, a solid oxide fuel cell at high temperature and in the presence of CO22 (Fig. 1), where the presence of a cathodic bias (operando) amplifies the oxidation observed compared to when the bias is absent (in situ). 3. Why Synchrotron Sources? The reasons for devoting this chapter to synchrotron-based methods are manifold. First, properly designed experiments can take advantage of the penetrative power of X-rays in order to design operando photon in–photon out experiments. Consider, for example, that the attenuation length for X-rays through a typical cathode material, LiCoO2 is on the order of 10–50 µm in the 3–10 keV Xray energy range (a typical hard X-ray range for interrogating 3d

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Fig. 1. The X-ray absorption spectrum edge energy shifts for both Fe and Co in La0.6 Sr0.4 Fe0.8 Co0.2 O3−δ caused by exposure to CO2 were greater under operando conditions than they were under in-situ conditions (without external bias) at both 400 and 700◦ C. The presence of CO2 has an oxidizing effect and cathodic bias amplifies the degree of oxidation.2

transition metals that are present in a large number of cathode materials). This coincides very well with the usual active cathode layer thickness in batteries. Since the other functional components of batteries are usually less absorptive of the X-rays than the cathode (except, in some cases, for the packaging material), Xrays in this and higher energy range can reach the active material and, as importantly, can escape from the battery (as signal) with feasible levels of transmission to allow structural interrogation during battery operation. A second advantage of synchrotron X-rays is its energy tunability. In order to get true mechanistic information, the characterization tools need to provide element-specific information and should do so with high resolution in information-space. Information local to each atomic species can come from atom-specific electronic transitions. The broad energy range of a synchrotron allows us to tune to a specific energy range which is resonant with characteristic atomic transitions.

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Fig. 2. Three closely related core-hole spectroscopies resulting from irradiation by incident X-rays, namely, XAS, XPS and XES.

Element specific methods that rely on excitation of bound electrons fall under the general description of core-hole spectroscopies. In this class of spectroscopic methods, the element-specific signal is generated by an initial event whereby a core electron absorbs the energy of incident X-rays and gets excited beyond the Fermi level, leaving behind a core hole (Fig. 2). A finer point about the usefulness of synchrotron sources is that by selecting energy to the right electron transitions, the bound and unoccupied states that are most relevant to a specific battery chemistry can be probed. As an example, one may be interested in whether the charge compensation reaction in a LiMO2 cathode involves the O2p states or not or whether it only involves the 3d states of the transition metal M. This question that is important in determining whether oxygen is oxidized during battery charging — which could lead ultimately to oxygen evolution reactions and, therefore, battery safety. In this case, one can probe the L edge of the metal together with the K edge of oxygen (where transitions to 3d and 2p states of the metal and oxygen are probed, respectively) rather than the K-edge of the metal (which would probe its less interesting 4p states. These factors together with some general properties of the synchrotron beam, such as high brightness, short photon pulse trains (down to sub-picoseconds), polarization of the synchrotron beam and future high spatial resolution (currently in the 100 nm scale in

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best cases, but projected to be ∼few nm range at some beam lines in the next generation facilities such as the National Synchrotron Light Source II (NSLS II)) make synchrotron-based techniques for fundamental characterization of battery materials.

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4. Synchrotron Based Core-Hole Spectroscopic Methods X-ray absorption spectroscopy (XAS) is unique among the core-hole techniques because it simultaneously provides the local electronic structure (e.g. chemical state) and the local atomic structure (e.g. bond distance and coordination). Furthermore, XAS can be carried out with the specificity of nearly every element of the periodic table (with H and He typically too low in energy for the X-ray optics of beam lines) depending on the low and high cut-off energies. At a wide energy range synchrotron, such as the NSLS-II that is optimized for both soft X-rays and hard X-rays, XAS of nearly every element is possible. Two other core hole techniques that are highly complementary to XAS are X-ray emission spectroscopy (XES) and X-ray photoelectron spectroscopy (XPS), which provide bound state electronic structure. XES probes the occupied density of states — information complementary to that of the near-edge of XAS that measures the density of unoccupied states. In this case, when an electron is excited to an unoccupied state, it leaves behind a core hole. This core hole may be filled by an electron which is within its excitedstate lifetime from an earlier excitation event, or it may be filled by an electron from an occupied state. The decay of electrons from the valence band to fill the core hole may involve fluorescence. In XES, a spectrometer is used to select only those fluorescence photons of energies corresponding to decays from occupied valence states. Careful measurement of XES will, therefore, probe the nearFermi valence electron states (Fig. 3). Combined with the near-edge XAS measurements (which, in well-designed experiments, can be at the same synchrotron beamline), one can measure the near-Fermi conduction band states as well. XES and XAS, used in this combined way, is the only way to measure the element-specific band gap,

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Fig. 3. Band energy diagram of the effect of a doping on the valence and conduction band states as observed by XES and XAS, respectively.

as well as the relative shifts of the valence and conduction bands with respect to each other. The signal photons in XES has nearly the full energy of the source photons, and so their attenuation through the active and passive components of an operando cell should be similar to those of the source. Sophisticated operando experiments that combine XAS and XES have the potential to reveal the realtime changes in the near-Fermi band structure of active materials in electrochemical systems as a function of the state of charge, cycle number, cycling rate and other electrochemical parameters. XPS is a near-surface sensitive technique with its energy discriminating detector sensitive predominantly to the signal electrons emanating from within about one to two inelastic mean free path (IMFP) below the surface. If we consider LiCoO2 as an example, the IMFP is ∼2.5 nm for photoelectrons with about 1 keV of kinetic energy (Fig. 4). With typical XPS setups using an Al Kα fixed energy source (∼1486 eV), the technique will average information from about 5 nm of depth. A standard XPS system will, therefore, not be able to discriminate information from just the top 1–2 nm of the surface. At the same time, because the source energy limits the depth

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Fig. 4. The inelastic mean-free path through a matrix of the LiCoO2 cathode compound.

sensitivity to ∼5 nm, a standard XPS system will not be able to access information more than 5 nm below the surface. In other words, even though XPS in known to be a “surface sensitive” technique, a fixed energy XPS system does not provide true surface information, but is also not “bulk sensitive” enough to probe beyond about 5 nm. This problem can be resolved with a tunable energy synchrotron X-ray source. Since the degree of surface sensitivity depends on the kinetic energy of those emanating electrons, a synchrotron source allows XPS to have variable depth sensitivity. By varying the photon energy, one can change the kinetic energy and, therefore, the IMFP of a specific photo-emitted core electron allowing the degree of surface sensitivity to be tuned. IMFP tuned XPS will likely be used increasingly in the interrogation of near-surface chemical states in batteries, super capacitors and other energy storage and conversion systems where the surfaces and interfaces play a vital role. Though some key in-situ experiments with high pressure XPS systems have been demonstrated as proofs of concept with the aid of high-end differential pumping instrumentation, the method is ultimately limited by the short IMFP of the signal electrons, and truly operando XPS experiments with liquid electrolytes, as a result, will be very difficult to design. Traditionally, XPS requires high or ultra-high vacuum in the sample analysis chamber in order to have appreciable electron yield reach the detector. Like soft X-ray spectroscopy, the vacuum requirement places severe restrictions on the feasibility of in-situ or operando experiments. Recent developments have led to the

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proliferation of ambient pressure XPS (APXPS), sometimes referred to as high pressure XPS, tools which can reach pressures of 130 mbar; Their history and mechanisms for achieving such performance are detailed by Starr and co-workers.3 For Li-ion battery materials specifically, APXPS finds application for gas/solid surface interactions; meaning lithium-oxygen reactions for Li-air batteries are prominent examples of insight gained from APXPS. For example, Lu et al. used in-situ APXPS to study the reaction products of Lix V2 O5 as the battery was discharged in the presence of a low pressure of oxygen.4 Their study was the first to provide evidence of reversible lithium peroxide formation, an important step in understanding the redox mechanisms of Li–O2 chemistry. However, APXPS is not required for all in-situ XPS studies. For example, Yao et al. studied the thermal stability of Li2 O2 and Li2 O using a heated stage inside of a laboratory-scale XPS instrument, allowing the outgassing to dissipate before analysis at normal XPS chamber pressures.5 Naturally, APXPS has a wide range of application for the study of surface catalysis and surface species beyond Li-air batteries. Another review by Crumlin et al. provides similar information but within the broader context of electrochemical devices, spanning fuel cells to Li-oxygen batteries.6 5. Design of XAS Experiments for Batteries 5.1. The Complementary Aspects of XAS Using Hard Versus Soft X-rays In X-ray parlance, “soft” X-rays refer to photons with < 2 keV energy, whereas “hard” X-rays typically implies > 4 keV energy, leaving little choice but to refer to the narrow 2–4 keV region in between to be referred as “tender” X-rays. There are some specific advantages to characterizing battery materials using both soft and hard X-rays. Let us take the commercially successful LiCoO2 cathode as an example. The X-ray absorption near-edge spectra (XANES) of the O K-edge in LiCoO2 will show a pre-edge corresponding to t2g , and empty eg states followed by empty continuum states. At a slightly higher

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Fig. 5. The relationship between the energy diagram for LiCoO2 and the XAS spectral features for the O K-, the Co K-, and the Co L-edges.

soft X-ray energy, and possibly at the same synchrotron beam line, one can access the complementary Co L-edge, providing direct d orbital information. The t2g , and eg states are also present as minor features of the Co K-edge spectra (Fig. 5). Soft X-ray XAS is, uniquely, a combined probe of multiple, relevant orbitals. In Li batteries the most common non-lithium metals found are the 3d transition metals (TMs henceforth). The K-edge XAS of Co probes their fully empty 4sp orbitals (Fig. 5) that are less relevant to the TM 3d. Since the TM 3d orbitals are highly sensitive to the oxidation state of the TM ions, we can follow the shifts in the edge and changes in amplitude to follow the changes in their local electronic structure operando. On the other hand, at the soft X-ray energies, the attenuation length of the X-ray photons may be forbiddingly small to penetrate standard packaging materials for batteries. Operando cells at these energies would have serious design challenges as a result. The same is not true of the hard X-ray energy photons whose penetrative power is high enough make the design of operando cells to be far less complicated. Also, the extended X-ray absorption fine structure (EXAFS) is only practically available from the Co K-edge in the hard X-ray region.

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This is because at the soft X-ray energies multiple core emissions can be closely spaced in energy (the O K-, the Co L3 -, and L2 -edges in this example) and so the EXAFS functions from each overlap and complicate data analysis, whereas at hard X-ray emissions, the core emissions are likely to be more spaced out (there are no core electron emissions above the Co K-edge in LiCoO2 for example). Therefore, the typical wide bandwidth of energy range required for the effective EXAFS analysis is more likely to be available for core emissions at the hard X-ray range. Being aware of the specific advantages and disadvantages of soft and hard X-rays, one should strive to use both in order to gain multiple perspectives from batteries. In the section below, the specific advantages of soft and hard X-rays are discussed. These are some advantages of soft X-rays for XAS of Li battery materials — • Probes relevant final states: As discussed above, soft X-rays allow us to probe more meaningful electronic states for battery compounds. At these energies dipole selection rule allowed transitions to empty 2p and 3d states of oxygen and 3d transition metals, respectively. By probing those states directly one can identify changes in the M–O chemical bond directly (Fig. 5). • More surface sensitive: The issue here is very similar to what was discussed above regarding the information depth in XPS. When reviewing characterization tools for electrode materials particular attention should be paid to the relative surface sensitivities of various options. For XAS measured in electron yield mode, the IMFP of the Auger electrons are low compared to those for higher energy transitions, if such is available. In LiCoO2 , for example, one has the option of conducting a higher energy K-edge XAS (Co 1s → 4p) using hard X-rays or a lower energy Co L–edge (Co 2p → 3d) using soft X-rays (Fig. 5). In the former, the IMFP of the Auger electrons is ∼20 Å while, in the latter, the IMFP is ∼4.5 Å. Choosing the soft X-ray option ensures that the information is coming mainly from the top unit cell as opposed to the top 5 unit cells that would be reported using the hard X-rays. • Higher energy resolution: The core hole lifetime (t) for an electron transition in inversely proportional to the uncertainty in the

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transition energy (E) due to Heisenberg uncertainly principle. Since the corehole lifetime is inversely related to the transition energy, the soft X-ray transitions will have narrower E. In other words, soft X-ray spectra naturally have better energy resolution than hard X-ray ones. Practically speaking, the difference between the core-hole lifetime limited resolutions could be a difference between a few tenths of eVs at soft X-ray energies versus a few eVs at the hard X-ray ones. So, the XANES features are necessarily sharper with core electrons binding energies in the soft X-ray range compared to corresponding ones at hard X-ray energies. On the other hand, for EXAFS, a few eVs of resolution is sufficient for high quality analysis. There are some inherent advantages of using hard X-rays for XAS studies — • Higher penetration: Hard X-rays are quite penetrative and so operando cells can be designed even for the soft end of the hard X-ray range so that one may probe even early transition metals such as vanadium. • Access to wide bandwidth EXAFS: In the hard X-ray regime the electron transitions are well separated in energy which generally translates to a wide bandwidth of EXAFS information. While Co L-edge EXAFS is not easily obtainable since the EXAFS from L3 and L2 transitions overlap with one another except for the narrow energy range between the two transitions, Co K-edge in LiCoO2 does not have interference from any other higher energy transitions. In the Li[Co,Ni]O2 cathode, the Ni K-edge is sufficiently removed from the Co K-edge that neither one interferes with the other. As an example of the rich local structural information obtainable from XAS using hard X-rays, Figs. 6(a) and 6(b) show the changes in the XANES and the EXAFS, respectively, during the charge/discharge of a LiCoO2 -based cell.7 The XANES in Fig. 6(a) shows the Co K-edge position shift to higher binding energy during charging since more energy is required to photoionize Co, as it gets oxidized to compensate for the excess negative charge present, when

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Fig. 6. (a) Operando measurements of XANES (showing oxidation and reduction behavior) and (b) EXAFS (providing the local atomic structure around Co atoms in LiCoO2 ) during the charge (lower arrow in a, b) and discharge (upper arrow in a, b) of LiCoO2 -based batteries.7 Reproduced with permission of The Electrochemical Society.

Li is titrated out of LiCoO2 during battery charging. Meanwhile, the R-space data obtained from the EXAFS region (Fig. 6(b)), shows the first two peaks corresponding to the M–O and the M–M bonds, respectively, while the 3rd peak, M–O2 corresponds to the oxygen atoms from the next plane. The fact that M–O1 and M–M is very stable while M–O2 exhibits contraction and expansion during charge and discharge, respectively, points to the in-plane rigidity and the inter-planar “breathing” during the cycling of Li(1−x) CoO2 . One can see from this example that in-situ XAS is a powerful tool for examining atomistic mechanisms in batteries. 6. A Detailed Discussion of Operando XAS Experiments for the Study of Batteries XAS is the mainstay characterization technique of synchrotrons, because of its unique requirement for a variable energy photon

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source. At a synchrotron, the full spectrum of X-rays, from soft to tender to hard, has been used to study all types of Li-ion battery materials. Soft X-rays require ultrahigh vacuum conditions because of the high attenuation of low energy X-rays by ambient gases. Traditionally, the ultrahigh vacuum (UHV) requirement makes in-situ or operando experiments with battery materials incompatible because of the liquid electrolyte. However, use of a solid-state electrolyte and battery design bypasses that challenge and can offer great insight into the role of oxygen in Li-ion battery materials, as demonstrated by Petersburg et al.8 Through this design simultaneous collection of the partial electron yield and fluorescence X-ray yield, corresponding to the surface and bulk of the battery electrode, the oxygen and cobalt showed significantly different chemical environments. In an example of medium operando spectroscopy, Cuisinier et al. were the first to find detailed evidence of the sulfur species involved in the redox chemistry of Li–S batteries, which have garnered significant attention in the battery research community.9 It is important to note that their work used extremely porous carbon nanospheres of 220 nm diameter as a framework, which provided a highly uniform electrochemical response and excellent cycle stability. Most importantly, the nanospheres trap specific sulfur species in the pores but act as a bulk electrode, allowing the researchers to minimize the bulk sulfur X-ray self-absorption effects. These types of modifications to traditional sample architectures are common for in-situ and operando experiments in order to maximize the effectiveness of the spectroscopy. Hard X-rays, consisting of several keV photons, are frequently used to study transition metal cations in Li-ion battery materials. Besides the information that XAS itself provides, it can also add insights to information from other X-ray techniques. For example, Wang et al. investigated the structural changes in Li1−x FePO4 using in-situ XRD during charging.10 However, in-situ hard XAS and exsitu soft XAS were able to track the oxidation state of the Fe cation, and thus Li content, in the bulk and on the surface, respectively, indicating that the timing of the phase transition delay caused by

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charging is later than that observed in XRD. Ouvrard and co-workers later confirmed the phenomenon but with time and spatial resolution, confirming the phase change delay and heterogeneity through isosbestic points and linear combination fit while spatial mapping suggested that the percolation of conductive grains is responsible for the phenomena observed.11 Like Wang et al., a specially devised electrochemical cell was used to perform the operando experiments. Similarly, Mn–based electrodes can also be studied during charging and discharge, by using common stainless steel CR2032 coin cells with basic modifications. Lowe et al. used synchrotron XRD and XAS to track each conversion step of Mn in LiMn3 O4 , following the phase formed after each lithiation reaction and identifying where the charge storage was occurring.12 As seen in the examples above, having a custom cell design, simple or complex, is common for insitu and operando experiments, particularly with respect to energy range, the vacuum requirements, if any, and the desired region of study. In-situ and operando XAS provide unique information about battery redox reactions that can often help explain unexpected or undesirable phenomena, more so when combined with other X-ray or characterization techniques. A specific study of RuO2 as a prototype electrode material for an alternative battery design that uses conversion instead of intercalation to store lithium by Hu et al. combined XANES and EXAFS with in-situ pair distribution function (PDF), another synchrotron X-ray based technique, and nuclear magnetic resonance (NMR) to explain how such a conversion electrode architecture can have additional capacity for Li-ion storage.13 The versatility of XAS in sensitivity to chemical species of various oxidation states and in spatial resolution, whether laterally for mapping or between surface and bulk, is a powerful leveraging tool for characterization, especially under in-situ or operando conditions. 6.1. Information in XANES and XAS At this point, we should first discuss the information content in XAS spectroscopy in more detail. The XANES region is strongly influenced by unoccupied valence and conduction band structure

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and, therefore, sensitive to chemical bonds. The region beyond that, EXAFS, is strongly influenced by the type and geometric position of neighboring atoms. This delineation mostly helps in the standardized treatment of XAS data, though the physics between the XANES and EXAFS regions is, of course, continuous. Above its ionization energy an electron, emerging from its initial state of a specific orbital of a specific element in the sample, can be in resonance with various empty final states. The final states are the local mixed orbitals representing the chemical bonds, such as molecular orbitals (MOs), and the electron transitions produce the XANES spectrum, with the X-ray absorption proportional to the transition probability between the initial atomic state and the final states:

2

r ∗ ik· 3

µ ∝
ψf ˆ · r e ψi d r
, (1) where µ is absorption, ψi and ψf are the initial and final states, and ˆ is the electric field vector of the incident synchrotron photon. With higher kinetic energy, the photoelectron can be treated as a plane wave that scatters from the neighboring atoms. The interference between the outgoing and backscattering electron waves in this region set up a standing wave. As the photoelectron kinetic energy increases, its wavelength decreases, and consequently, the phase shift between the outgoing and returning waves changes at the location of the absorber atom. This phase shift, in turn, affects the probability of X-ray absorption by the absorber atom, with no phase shift (constructive interference between the outgoing and backscattered wave) causing a maximum X-ray absorption, and a phase shift of λ/2 (destructive interference) causing a minimum X-ray absorption. Because the average distance between the absorber and the neighboring atoms does not change, the waves will progressively go in and out of phase, as the kinetic energy increases. The XANES and EXAFS data should both be collected whenever possible since the information obtained from each of the regions is somewhat different. Energy shifts in the XANES region point to oxidation or reduction of the absorbing atom and, in some cases,

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concurrent changes in absorber-nearest-neighbor bond length, while the changes in the intensity are caused by changes in the density of final state. Oscillations in the EXAFS region can be converted from energy-space to k-space (momentum space) and Fourier transformed to real space to obtain a function that is proportional to the radial distribution function. The EXAFS oscillations in k-space, χ(k), can be represented by the sum of contributions from all the scattering paths of the photoelectrons: χ(k) =

 Nj j

rj2

S20 ∗

Fj exp( − 2rj /λ)exp( − 2σj2 k 2 ) sin[2k ∗ rj + φ(k)]), k (2)

where Nj is the coordination number of atoms at a distance rj and Nj /rj is the approximation of the partial radial distribution function (PRDF), S20 is the many-electron overlap factor, Fj is the backscattering amplitude, exp(−2σj2 k2 ) is the Debye–Waller factor representing the Gaussian distribution of atomic neighbor positions due to static and thermal disorder in the material. Finally, the sin[2k × rj + ϕ(k)] represents oscillations with [2k × rj + ϕ(k)] being the phase of the electron. The χ(k) function, and the corresponding Fourier transform χ(r) can be calculated for a model cluster using several freelyavailable codes. It is self-evident that the EXAFS oscillations are rich with local structural information, that can be gleaned by fitting experimentally measured χ(k) with that simulated from a model. 6.2. Reaction Mechanisms The reaction at a battery electrode, in the first-order approximation, is the equilibration of the electrode atomic environment to the Nernst potential in the presence or absence of an external bias. The equilibrium reactions are diffusion limited and take place in the 102 millisecond to 102 seconds timescale depending on the diffusing species and the diffusion length. Measurement of near-equilibrium atomic and electronic structure in electrochemical devices such as Li-ion batteries, therefore, does not require higher time resolution than a millisecond.

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The mechanics of Li forward titration and reverse titration experiments can be monitored by speciation at high time resolution using XAS. If scanning only the near-edge (XANES) portion of the XAS spectra, unique spectra can be obtained at a rate of a scan per minute routinely and as rapidly as in 10s of milliseconds using rapid scanning XAS where the monochromator and the associated detector electronics sweep continuously through energy. Spectra from such experiments must be deconstructed to reveal the significant common components between them and the relative weights of each of those components. Reaction kinetics can then be obtained by following the rate of change of the weights of the deconstructed components. When a set of spectra represent a single reaction pathway, i.e., a single reaction is converting reactants to products as is the case on a voltage “plateau” in the charge/discharge curves of Li batteries, then each XAS spectrum can be represented as a linear combination of the two end spectra of the series. Identification of the electronic structure (such as oxidation state) and the atomic structure (local symmetry and coordination) of the end structure can be done by “fingerprinting” spectral signatures with those of reference compounds.a Linear component analysis (LCA) is an analytical tool that can be used to investigate the kinetics of intercalation or conversion reactions in Li batteries. LCA should be carried out on the XANES region as well as the EXAFS region (post Fourier transformed to R-space) to obtain complementary information on chemical bonding and the atomic structure changes during the reaction. Leifer et al. showed very convincingly the conversion reaction during the lithiation of Ag2 V4 O11 (SVO) to LixAg2 V4 O11 .14 An XAS dataset marked by crossover points, or isosbestic points, in the X-ray absorption function evidences a single reaction path. Conversely, the presence of isosbestic points is a quick indication

a It should be noted that since XANES spectra are simultaneously sensitive to

oxidation state, bond length and local symmetry, care must be taken to distinguish between these effects.

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Fig. 7. Manganese absorption edge for Li1−x Ni1/3 Mn1/3 Co1/3 O2 as a function of the extent of de-lithiation. Isosbestic points are marked with  symbols while the nearly-isosbestic point is labeled with ◦.

that the reaction involving a particular element in a Li battery has proceeded through a single reaction. Isosbestic points result from the basic fact that if, in a reaction, the reactants and the products have equal absorption co-efficients at a specific energy (i.e. αE1(A) = αE1(B)), and the sum of the concentration of reactants plus products remains fixed, then at all stages of the reaction the absorption coefficient remains constant. It follows a corollary, that a true single reaction would mean that every intersection points in the dataset should be isosbestic. The simultaneous presence of isosbestic and nearly-isosbestic intersections (as at ∼6561 eV in Fig. 7) means that the spectra are dominated by a single reaction pathway but are still affected by the presence of a minor side reaction. For large XAS datasets (such as in operando experiments) during charge/discharge reactions in batteries where single reaction paths are not self-evident (no isosbestic points in the XANES region, for example) principal component analysis (PCA) can be used as a fully objective analytical tool. PCA provides the answer to the question of how many minimum spectral components are necessary to reconstruct any spectrum in the dataset and, therefore, how many independent chemical species (with unique chemical signatures) are contained in overall reaction. PCA is based on the singular value decomposition (SVD) algorithm in linear algebra. SVD is based on the theorem that any m × n

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Fig. 8. The relationship between a set of XAS data expressed as a matrix [A] and its principal components [B] through the eigen values [v] and the transverse of the weightings [w].

matrix A, with m rows n columns, can be represented as a product of m × n column-orthogonal matrix B, an n × n diagonal matrix V with elements that are positive or zero, and the transpose of an n × n orthogonal matrix w (Fig. 8). For further details, readers are referred to the work of Ressler and references therein.15 PCA can be applied to a set of XAS spectra since such a dataset can be expressed as an m×n matrix. In the analysis of a set of XANES spectra, the column vector (α1j , β2j , χ3j , . . . , µmj ), where 1 ≤ j ≥ n, represents one XANES spectrum out of the total set of n spectra. The output matrix B therefore also has n columns, but the ones that are important are those for which vij = 0. It can, therefore, be determined from the eigenvalues in matrix V how many eigenvectors ∼columns in B are sufficient to reconstruct the experimental spectra. While PCA has been applied to the analysis of XAS datasets, specifically in the area of catalysis, it is an analytical technique that can be applied to any spectroscopic technique. In the study of Li batteries, however, PCA is currently underutilized, with infrared,16 neutron diffraction17 and two XAS studies7,18 evidenced by a literature survey. In the first of the two XAS works cited, Alamgir and others7 show a very effective use of PCA in an in-situ study of the delithiation of a thin-film LiCoO2 -based Li battery. They infer that two separate reactions occur during delithiation, which allows them to rule out Co oxidation as the only charge compensation reaction

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Fig. 9. The XANES of the Co K-edge as a function of the Li content. The left inset shows the smaller s-to-d transition that carries Co d-band occupancy information.7 Reproduced with permission of The Electrochemical Society.

occurring during the charging of the battery. The implication of this finding was that there was the possibility of charge compensation occurring with a non-cobalt species over a portion of the Li deintercalation reaction. A close look at the Co XANES (Fig. 9) showed that, based on the changes in the spectral features, the set of spectra could be divided into two sections as a function of the extent of Li deintercalation. This is more clearly seen in Fig. 10 which amplifies the s → d pre-edge feature. Formation of a d-electron hole, according to Eq. (1) would result in an increase in the density of unoccupied states and therefore an increase in the peak amplitude. In Fig. 10, we see that the peak amplitude shows dramatic change in behavior in the x ≤ 0.25 and the x ≥ 0.37 regions. The EXAFS from the same dataset Fourier transformed to realspace is shown in Fig. 11. The function in Fig. 11 is proportional to

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Fig. 10. XANES shows us that for x > 0.37, charge compensation occurs through Co d-hole formation.

the radial distribution function around Co atoms, for Li(1−x) CoO2 for 0.12 ≤ x ≤ 0.7. One can clearly see changes occurring at the Co–O and Co–Co coordination shells as represented by their respective distances in Fig. 12. Alamgir et al. were the first to deduce from in-situ data, the presence of oxygen holes (responsible for the oxygen neighbor 2 in Fig. 12) in the x ≤ 0.25 region where we see fewer Co holes. Future XAS work on reactions in batteries and other electrochemical systems look very promising using traditional (edge shifts, fingerprinting, R-space fitting) as well as non-traditional (LCA, isosbesticity, and PCA) analytical schemes. 7. Other Synchrotron X-ray Methods Applied to Battery Chemistries 7.1. Synchrotron Based X-ray Diffraction (XRD) XRD using synchrotron radiation provides structural information based on the coherence between repeated structural units in the

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Fig. 11. The distribution of nearest neighbors of Co is being shown as a function of Li. It is clear from the asymmetric shape of the Co–O peak during early delithiation that it is composed of subpeaks (at more than one distinct Co–O distance).7 This observation is analyzed further in Fig. 12. Reproduced with permission of The Electrochemical Society.

Fig. 12. The near neighbor distances to the nearest oxygen and Co species around Co centers as a function of Li content are being compared here. While the relative changes can be compared, the absolute distances require a backscattering phase shift correction.7 Reproduced with permission of The Electrochemical Society.

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material but not necessarily on the subtleties of the structure within the units. Without long-range structural repetition, the coherence of the scattered X-rays is limited. This dependence on long-range order is a fundamental weakness of XRD in studying nanostructures. With decreasing dimensions of nanostructured electrode materials, the coherence-dependent signal intensity will diminish accordingly to the vanishingly small limit of the Debye– Scherrer equation. This is all the more true if there is an inherent disorder within the nanostructures themselves. Still, crystal phase identification is a very worthwhile exercise when one is following the chemical reactions within a battery and so XRD studies needs to be carried out to complement XAS whenever possible. Early work by Amatucci et al. reported in-situ XRD studies to understand de-lithiation mechanism for the prototypical LiCoO2 20 cathode to CoO19 2 using a specially designed in-situ cell. The work of Amatucci and co-workers follows that of earlier work on Lix TiS2 by Dahn,21 and was succeeded by a host of other in-situ diffraction studies by other researchers. Some of the highly cited early work done using in-situ XRD include: the analysis of the structure of synthesized amorphous vanadates by Denis et al.,22 the study of the Li intercalation reaction into nanostructured anatase TiO2 by Van De Krol and co-workers,23 the structural transition in Lix Mn2 O4 by Mukerjee et al.24 The penetrative power of hard X-rays can be used to great effect to construct tomographical diffraction slices through a real battery. Collecting this data during battery operation allows for the construction of an electrochemical landscape over intrabatteryspaceandreactiontime.25 Rijssenbeek and co-workers have demonstrated very elegantly the use of synchrotron “white” beam (full bandwidth of X-rays) to conduct in-situ energy dispersive Xray diffraction (EDXRD). With the highly penetrative hard X-rays, the experimental cell design is very forgiving and so, similar in-situ experiments can be conducted on fully assembled batteries during cycling.

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7.2. Bridging between Soft and Hard X-ray Regimes: Perspectives on X-ray Raman Inelastic X-ray Raman scattering (XRS)26 is a less common type of synchrotron X-ray core-hole spectroscopy, although its theoretical understanding has been known for several decades.27 Its recent development is owed to the proliferation of 3rd generation synchrotron sources.28 Generally, it is comparable to XAS in the type of information it generates,29 but it is unique in that it can probe low atomic number (Z) elements using high energy X-rays.26 Examining the local atomistic structure from the perspective of low Z atoms usually requires low energy X-rays that are strongly absorbed and scattered by other heavier atoms, such as those in the battery packaging or the ambient atmosphere. As a result, any XAS experiment studying low Z atomic edges without the use of ultrahigh vacuum has significant challenges associated with it. With high energy X-rays, however, light elements can be studied under high pressure30 or liquid environments.31 For example, XRS can probe C and Li, as well as O in water.32 Additionally, since it uses high energy X-rays, XRS probes length-scales on the order of the bulk, whereas soft X-ray spectroscopy for the study of light elements is surface-limited. These unique attributes of XRS have situated the technique to fill in the gap left among other core-hole spectroscopies. XRS relies on a non-resonant, inelastic scattering event in which an incident photon with energy E0 is scattered by interacting with the sample and yields a photon with energy Ef , where the energy lost in the interaction is E = E0 − Ef . The energy lost in the photon-matter interaction is transferred to exciting a core electron to an unoccupied state. Since the core hole excitation mechanism is the same as that of XAS, the same information on local atomistic structure can be obtained by using XRS. The distinction between XRS and XAS is that the cause of the core electron excitation is E, not the incident photon energy E0 , meaning that penetrative, high energy X-rays can still probe elements that normally would require medium or low energy X-rays. However, the flexibility in incident photon energy comes at the cost of signal quality and resolution, since the cross-section of XRS is much smaller compared to more common scattering events,

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Fig. 13. The variation in intensity of different scattering events obtained by using an incident photon energy of 8,900 eV for (a) and (b) and 8,400 eV for (c) shows the low intensity of Raman scattering. Reprinted with permission from Ref. 26. Copyright 1989 by the American Physical Society.

such as Rayleigh and Compton scattering, as shown in Fig. 13.26 Additionally, the energy shift required for a specific excitation must be significantly greater than the energy of the Compton scattered Xrays, as a commonly encountered problem is loss of the XRS signal due to an overwhelming Compton background. More acquisition time is also required because of the decay in signal intensity at high energy shift, which then elevates the issue of radiation damage. Mathematically, the transition probability for an XRS event is described by Eq. (3)26   4π3 e4 h (1 + cos2 θ) × | f |exp(iqr)|i|2 δ(Ef − Eo − h(vi − vj )), w= m2 vi vj (3) where vi and vj are the frequencies of the incident and scattered photons, θ is the scattering angle, q is the momentum transfer, r is

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the distance to the nucleus, and f | and i| are the final and initial states, respectively. The integrand is only significant when r < the core hole radius. Since the dipole approximation is valid when qr 1, the equation reduces to:  Handbook of Solid State Batteries Downloaded from www.worldscientific.com by NATIONAL UNIVERSITY OF SINGAPORE on 10/27/15. For personal use only.

w=

 64π5 e4 h (1 + cos2 θ) sin2 (θ/2)| i|r|f |2 . m2 c2

(4)

In Eq. (4), the matrix element is the same as the matrix element in the equation for dipole X-ray absorption.26,29 This explains why the core hole excitation mechanism is the same as in XAS and allows us to obtain an XAS spectrum using XRS. Due to the low cross-section for the Raman scattering event, the X-ray source must be extremely bright in order for the experiment to achieve an energy resolution and signal quality comparable to what is considered standard for XAS. Therefore, an XRS experiment necessitates a 3rd generation or newer synchrotron X-ray source, such as the APS at Argonne National Laboratory or the newly constructed NSLS-II at Brookhaven National Laboratory. The second requirement is a detector-analyzer system that can capture a significant amount of the inelastically scattered X-rays. The system consists of multiple large cylindrically- or spherically-bent crystals, typically several cm in diameter, arranged on concentric Rowland circles to redirect and focus the energy shifted X-rays onto a detector. Because of the high energy of the scattered X-rays and the geometry of the optics, the detector-analyzer system can be set up under ambient conditions with adequate space for in-situ experimental equipment. With the requirements of a high brightness synchrotron X-ray source and a specialized detector-analyzer system, only a few facilities are capable of XRS. At APS, Beam line 18-ID has developed a reasonably high resolution (1 eV) system, which has demonstrated the capability to study C in graphite, Li in LiOH·H2 O, and O in water. 32,33 The proposed Inelastic X-ray Scattering (IXS) beam line at NSLS-II would initially achieve a resolution of 1 meV with a micronsized beam spot, with an ultimate goal of reaching 0.1 meV energy resolution and at least 0.1 nm−1 in momentum resolution. The beam

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line begins commissioning in 2014, and is scheduled to open for user access in June 2015.34 There are numerous advantages of using XRS as a characterization technique for battery materials. Firstly, as a technique that uses a synchrotron X-ray source, it is capable of varying the incident photon energy to create a sufficiently strong energy transfer to excite the core electron of key elements within a range of several keV. Since the energy range of 6 to 9 keV also encompasses the K-edge of common transition metals used in Li-ion electrodes, an experiment which conducts both transition metal XAS and low Z element XRS can be envisioned. Secondly, elemental specificity in XRS can be leveraged to obtain surface or near-surface information in thin film samples where different elements may be present in different layers, such as coatings that contain low Z elements. Thirdly, the penetrating power of the high energy X-rays enables in situ and operando study of low Z elements, such as at elevated temperatures. In particular, probing the local atomistic structure of Li would provide unique insight into the intercalation reactions during charging and discharging, as well as information highly relevant to the formation of the solid-electrolyte interphase. Most importantly, XRS, as a technique that probes low Z elements in the bulk, fulfills a critical gap in information left between in-situ XPS, which can only probe low Z elements at the surface, and in-situ XAS, which can only probe higher Z elements in the bulk. 8. Conclusion and Future Directions This chapter provides an overview about various X-ray synchrotron based spectroscopic techniques and their applicability to battery electrode materials to obtain detailed information about in their local structure, oxidation state and crystalline order under in-situ as well as ex-situ conditions. Most notable among them is the XAS method at variable X-ray energies, where detailed structural and bonding information can be obtained from XANES and EXAFS analysis. Energy dispersive white light XRD and X-ray absorption based tomographic methods under in-situ conditions can provide chemical as well as morphological changes occurring in battery electrode

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materials under operating conditions. Recent developments in soft X-ray methods and XRS would enable studying low Z materials that are otherwise not possible using hard x-rays or otherwise require UHV condition. With the advent of new high flux 3rd generation synchrotron sources that promise spatial resolution in the less than 10 nm range, new advances are possible with spectroscopy, diffraction and imaging. Simultaneous imaging, diffraction and XAS, for example, can be imagined from nanoscopic domains. Synchrotron sources will begin to compete with routine electron microscopes on the imaging and nano-diffractions front while providing the full spectrum of additional benefits of the synchrotron beam: its continuous energy range, high brightness and polarization. Synchrotron methods will play an increasingly important role for studying the surface and interfacial phenomena related to batteries and other electrochemical devices. References 1. M. K. Song, S. Park, F. M. Alamgir, J. Cho and M. Liu, Mater. Sci. Eng. 72(11) (2011) 203–252. 2. S. Y. Lai, D. Ding, M. Liu and F.M. Alamgir, ChemSusChem 7(11) (2014) 3078–3087. 3. D. E. Starr, Z. Liu, M. Havecker, A. Knop-Gericke and H. Bluhm, Investigation of solid/vapor interfaces using ambient pressure X-ray photoelectron spectroscopy, Chem. Soc. Rev. 42(13) (2013) 5833–5857. 4. Y. C. Lu, E. J. Crumlin, G. M. Veith, J. R. Harding, E. Mutoro, L. Baggetto, N. J. Dudney, Z. Liu and Y. Shao-Horn, Sci. Rep. (2012), 2. 5. K. P. C. Yao, D. G. Kwabi, R. A. Quinlan, A. N. Mansour, A. Grimaud, Y. L. Lee and Y. C. Lu,Y. Shao-Horn, J. Electrochem. Soc. 160(6) (2013) A824–A831. 6. E. J. Crumlin, H. Bluhm and Z. Liu, J. Electron Spectrosc. Relat. Phenom. 190 (2013) 84–92. 7. F. M. Alamgir, E. Strauss, M. denBoer, S. Greenbaum, J. F. Whitacre, C. C. Kao and S. Neih, LiCoO2 , J. Electrochem. Soc. 152(5) (2005) A845– A849. 8. C. F. Petersburg, R. C. Daniel, C. Jaye, D. A. Fischer and F. M. Alamgir, J. Synchrotron Radiat. 16(5) (2009) 610–615. 9. M. Cuisinier, P. E. Cabelguen, S. Evers, G. He, M. Kolbeck, A. Garsuch, T. Bolin, M. Balasubramanian and L. F. Nazar, J. Phys. Chem. Lett. 4(19) (2013) 3227–3232.

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10. X. J. Wang, C. Jaye, K. W. Nam, B. Zhang, H. Y. Chen, J. Bai, H. Li, X. Huang, D. A. Fischer and X. Q. Yang, J. Mater. Chem. 21(30) (2011) 11406–11411. 11. G. Ouvrard, M. Zerrouki, P. Soudan, B. Lestriez, C. Masquelier, M. Morcrette, S. Hamelet, S. Belin, A. M. Flank and F. Baudelet, J. Power Sources 229 (2013) 16–21. 12. M. A. Lowe, J. Gao and H. D. Abruna, J. Mater. Chem. A 1(6) (2013) 2094–2103. 13. Y. Y. Hu, Z. Liu, Z. K. W. Nam, O. J. Borkiewicz, J. Cheng, X. Hua, M. T. Dunstan, X. Yu, K. M. Wiaderek, L. S. Du, K. W. Chapman, P. J. Chupas, X. Q. Yang and C. P. Grey, Nat. Mater. 12(12) (2013) 1130–1136. 14. N. D. Leifer, A. Colon, K. Martocci, S. G. Greenbaum, F. M. Alamgir, T. B. Reddy, N. R. Gleason, R. A. Leising and E. S. Takeuchi, J. Electrochem. Soc. 154(6) (2007) A500–A506. 15. T. Ressler, J. Wong, J. Roos and I. L. Smith, Environ. Sci. Technol. 34(6) (2000) 950–958. 16. H. Park, S. R. Kwon, Y. M. Jung, H. S. Kim, H. J. Lee and W. H. Hong, Chem. Commun. 42 (2009) 6388–6390. 17. M. A. Rodriguez, M. H. Van Benthem, D. Ingersoll, S. C. Vogel and H. M. Reiche, Powder Diffr. 25 (2010) 143–148. 18. W. S. Yoon, K. Y. Chung, J. McBreen, K. Zaghib and X. Q. Yang, Electrochem. Solid State Lett. 9(9) (2006) A415–A417. 19. G. G. Amatucci, J. M. Tarascon and L. C. Klein, J. Electrochem. Soc. 143(3) (1996) 1114–1123. 20. M. Morcrette, Y. Chabre, G.Vaughan, G. Amatucci, J. B. Leriche, S. Patoux, C. Masquelier and J. M. Tarascon, Electrochim. Acta 47(19) (2002) 3137–3149. 21. J. R. Dahn and R. R. Haering, Solid State Communn. 40(3) (1981) 245–248. 22. S. Denis, E. Baudrin, M. Touboul and J. M. Tarascon, J. Electrochem. Soc. 144(12) (1997) 4099–4109. 23. R. Van de Krol, A. Goossens and E. A. Meulenkamp, J. Electrochem. Soc. 146(9) (1999) 3150–3154. 24. S. Mukerjee, T. R. Thurston, N. M. Jisrawi, X. Q. Yang, J. McBreen, M. L. Daroux and X. K. Xing, J. Electrochem. Soc. 145(2) (1998) 466–472. 25. J. Rijssenbeek, Y. Gao, Z. Zhong, M. Croft, N. Jisrawi, A. Ignatov and T. Tsakalakos, J. Power Sources 196(4) (2011) 2332–2339. 26. K. Tohji and Y. Udagawa, Phys. Rev. B 39 (1989) 7590–7594. 27. (a) B. Davis and P. Mitchell, Phys. Rev. 32(3) (1928) 331–335; (b) D.P. Mitchell, Phys. Rev. 33(3) (1929) 871–878. 28. J. A. Soininen, J. J. Rehr, A. Mattila, S. Galambosi and K. Hamalainen. AIP Conf. Proc. 882 (2007) 102–104. 29. Y. Mizuno and Y. Ohmura, J. Phys. Soc. Jpn. 22(2) (1967) 445–449.

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30. Y. Meng, H. K. Mao, P. J. Eng, T. P. Trainor, M. Newville, M. Y. Hu, C. Kao, D. Shu, D. Hausermann and R. J. Hemley, Nat. Mater. 3(2) (2004) 111–114. 31. P. Wernet, D. Nordlund, U. Bergmann, M. Cavalleri, M. Odelius, H. Ogasawara, L. A. Näslund, T. K. Hirsch, L. Ojamäe, P. Glatzel, L. G. M. Pettersson and A. Nilsson, Science 304(5673) (2004) 995–999. 32. U. Bergmann, P. Glatzel and S. P. Cramer, Microchem. J. 71(2–3) (2002) 221–230. 33. S. Anders, J. Diaz, J. W. Ager, R. Yu Lo and D. B. Bogy, Appl. Phys. Lett. 71(23) (1997) 3367–3369. 34. NSLS. IXS: Inelastic X-ray Scattering 2014. Available at http://www. bnl.gov/ps/nsls2/beamlines/overviews/IXS.asp.

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Chapter 4

Analytical Electron Microscopy — Study of All Solid-State Batteries Ziying Wang and Ying Shirley Meng Department of NanoEngineering UC San Diego La Jolla, CA 92093-0448, USA

This chapter focuses on the recent development and optimization of analytical electron microscopy to understand the dynamic changes in the bulk and interfaces of electrodes and electrolytes within all solidstate batteries. Three major aspects are covered: (1) design and fabrication of all solid-state batteries that remain functional after careful focused ion beam (FIB) processing; (2) enablement of in-situ biasing in both FIB/SEM and transmission electron microscope and/or scanning transmission electron microscope (TEM/STEM); and (3) development of the fundamental understanding of the dynamic chemical and electronic processes at the solid/solid interfaces of electrode/electrolyte by high resolution imaging and electron energy loss spectroscopy (EELS). Our goal is to apply analytical microscopy to gain new insights that can help us make significant inroads towards understanding the basic science of ion transport, charge transfer and related phase transformations in electrochemical systems at the nanometer scale.

1. Introduction In-situ electrochemical operation in the ultra-high vacuum column of a Transmission Electron Microscopy (TEM) has been pursued by two major strategies. In one strategy, a “nano-battery” is fabricated from an all-solid-state thin film battery using a focused ion beam (FIB). The electrolyte is either polymer based or ceramic based without any liquid components. The second strategy involves liquid electrolytes. 109

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Although the latter approach more closely resembles the actual operating conditions of the widely-used functional battery, the extreme volatility of the organic electrolytes presents a significant challenge for designing an in-situ cell suitable for the vacuum environment of the TEM. Ionic liquids can be used to replace the conventional polycarbonate based electrolytes without the tedious silicon nitride window sealing cell setup. More recently, it has been reported that Li2 O can be used as a low-voltage electrolyte for lithiation in Si/Sn/Ge and FeF2 electrode materials.1–4 However, Li2 O is unstable upon high voltage charging. Therefore, it would not be suitable for high voltage delithiation of transition metal oxides, a common class of materials used as the positive electrode in lithium-ion batteries. Significant progress has been made in the past few years on the development of in-situ electron microscopy for probing nanoscale electrochemistry. Both strategies mentioned above are pursued in the research community. Yamamoto et al. reported the dynamic visualization of electric potential in an all solid-state battery by electron holography and electron energy loss spectroscopy (EELS).5 They emphasized the need for thicker electrolyte while preparing the cross-section using FIB to avoid short-circuiting during the biasing process. Their experimental set up consisted of an electrolyte that was too thick (90 µm) and only a smaller portion of the cross-section was thinned down to be observed in the TEM while the whole stack was biased. In spite of the in-situ observation in TEM, the problem with this configuration was that the thinner part (∼60 nm) observed in TEM had higher resistance than other parts of the cross-section and led to very minimal electrochemical activity. More recently, there has been tremendous progress on in-situ studies using Si nanowires,1, 6 Ge nanowires,3 and SnO2 nanowires7, 8 as anode materials. Ionic liquid was mostly used as electrolyte. A schematic of the experimental set up is shown in Fig. 1. With a similar setup, Feng et al.2 successfully used Li2 O as the electrolyte and lithiated FeF2 , a conversion type electrode material. A novel “necking” phenomenon was revealed in the nano-composite materials by this in-situ TEM technique. Despite the success of in-situ biasing experiments of individual nanowires and nanoparticles, there are several drawbacks to the

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Fig. 1. From Ref. 2, (a) schematic of the electrochemical cell used for in-situ TEM measurements. (b) Time-lapse images from a collection of particles that react with lithium coming from the lower right. The reaction proceeds immediately in region (I), but is delayed and absent in regions (II) and (III), respectively. Scale bar, 10 nm.

approach, such as: 1. The chemistry of individual nano-materials seems to be unique and generalizing the results to an electrochemically active system is debatable (particularly when the individual and ensemble effects of nano-materials are different). 2. Ionic liquid is of low vapor pressure, and use of IL in the UHV column may induce long-term damage to the microscopes. 3. Electrode/electrolyte interface is very important in energy storage devices, which cannot be addressed directly by these studies. Considering the above points, our approach has unique advantages because our starting point is an electrochemically active solidstate battery stack. This type of all solid-state sample can be used to study the interface effects in-situ while monitoring electrochemical and structural changes with high spatial resolution. We demonstrate that the FIB processed cross-section is still electrochemically active and in-situ TEM can be used as an advanced tool to monitor the electrode/electrolyte interface during the operation of the battery. 2. FIB Fabrication and Electrochemical Biasing of Nano-Batteries The eventual success of in-situ analytical TEM depends on the fabrication of less than 100 nm thick all solid-state lithium-ion

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batteries that are electrochemically active. As one of the few methods capable of such fabrication, FIB technique has been used for TEM specimen preparation and semiconductor circuit editing quite extensively.9, 10 Major concerns with FIB have been the surface damage, re-deposition, and preferential sputtering due to high current density.11, 12 Several articles on the FIB damage to materials during preparation of specimens have proposed possible methods to reduce this damage.13–16 FIB fabrication of electrochemically functional all solid-state nano-batteries depends on two main factors: Limitation of structural damage caused by high ion beam current and avoidance of shorting caused by re-deposition during milling processes. Using an all solid-state battery with Si, LiPON, and LiCoO2 as anode, electrolyte, and cathode respectively as the typical system, functional nano-batteries have been fabricated using a two-step procedure with a specific set of beam parameters. The successful preservation of electrochemical functionality depends on several parameters; most importantly, the ion beam current and the pixel dwell time. For typical FIB fabrications, beam energy and current are given more importance compared to pixel dwell time. Here, we demonstrate that pixel dwell time to be a very important parameter. To reduce the fabrication time and damage induced by FIB, a twostep fabrication process was utilized. The first step is a high current (≤2.8 nA) milling process followed by a low current (0.28 nA) crosssection cleaning process while maintaining the 30 kV incident beam. During the first step high current leads to a large amount of redeposition across the stack and the second step cleans the crosssection. Figures 2(a) and 2(b) shows the cross-section SEM images of the Si/LIPON/LiCoO2 battery stack which clearly depicts the effect of this two-step fabrication process. High ion beam current (>0.28 nA) during the surface cleaning process tends to heat the amorphous electrolyte and worsen re-deposition across the stack. The second important parameter is the pixel dwell time, defined as how long the ion beam dwells on each pixel during a scanning process. Higher dwell time also leads to heating and increasing re-deposition, causing loss of electrochemical activity of the battery stack. Figure 3 shows the effect of pixel dwell time on the

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Fig. 2. SEM images of the all solid-state battery (effect of two-step fabrication process). (a) After step one: Milling process. (b) After step two: Cross-section cleaning.17

Fig. 3. Electrochemical voltage profile of all solid-state batteries fabricated by FIB. (a) 100 ns pixel dwell time, (b) 1 µs pixel dwell time, (c) 10 µs pixel dwell time. (d) and (e) show the typical dimensions of a nano-battery from top-view and side-view.17

electrochemical activity of a sputtered micro-battery stack fabricated by FIB. The stack was charged under constant current mode (typically with a current density of about 100 µA/cm2 ) in-situ in a FIB system. The normal size of the nano-batteries fabricated is a 2 µm×10 µm rectangle with the thickness of the whole battery stack. In Fig. 3(a), the charging profile for a nano-battery fabricated using 100 µs pixel dwell time shows hardly any voltage, indicating shorting across the stack. Figure 3(b) shows the charging curve for a nano-battery fabricated using 1 µs pixel dwell time, and the voltage was lower than the expected 3.6 V. Figure 3(c) shows the charging profile for a nano-battery fabricated using 100 ns pixel dwell time and the voltage raised to 3.6 V. For all the three cases, the charging

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current density was 100 µA/cm2 . Nano-batteries fabricated using 100 ns pixel dwell time are highly consistent and repeatable with 3.6 V voltage plateau which agrees well with the voltage profile of macro-batteries in literature.18 Subsequent to the successful nanobattery fabrication, we scaled down to fabricate even thinner nanobatteries. The specific procedures of electrochemically biasing the batteries inside the FIB are fairly simple and straight forward. A micron slab consisting of the whole battery stack is lifted out of the all solid-state thin film battery using typical TEM sample preparation procedures.9 The liftout procedure must be conducted with the aforementioned maximum FIB current setting and pixel dwell time parameters. Once this sample is mounted on a typical OmniProbe copper grid for TEM samples via Pt-welding, a small cleaning cross-section is used to expose the whole battery stack near the welding area. Afterwards, a second Pt-welding is used to connect the previous Pt-weld (which is connected to the Cu grid) to the exposed Au-bottom current collector. This ensures an electrical connection from the FIB stage to the cathode of the nano-battery. In order to isolate the top anode Silicon layer, cleaning cross-sections are applied from a side-view to remove a portion of the battery down to the lithium cobalt oxide layer. Finally, the nano-battery is milled to the desired size by cleaning cross-sections from the top-view. The anode connection is made by physically contacting the Omniprobe micromanipulator to the top surface of the nano-battery. Most FIB models will support outside electrical connections to the stage and omniprobe via electrical ports, hence establishing electrical connections from the nano-battery to an external battery cycler. Figure 4 demonstrates the procedures involved in the fabrication and biasing of a nano-battery. 3. Beam Damage Control in TEM/STEM After the successful fabrication of nano-batteries with careful FIB parameter control, electron beam damage under scanning transmission electron microscope (STEM) and EELS with a highly focused

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Fig. 4. (a) Mounting of nano-battery after the liftout. (b) Cleaning cross-section to expose battery layers and Pt-welding for electrical connection. (c) Electrical contact to the nano-battery after cleaning the cross-section.

electron beam must be controlled and minimized in order to extract useful analytical information. The most critical aspect related to the non-destructive lithium transport evaluation in electron microscopes is the stability of the solid-electrolyte under the intense electron beams. Current densities in modern STEM imaging and EELS have increased significantly due to high focusing capabilities of the modern microscopes, leading to e-beam damage of nanomaterials.19–22 Materials, depending on their physical and thermal properties respond to e-beam dosage in different ways with threshold doses for damage-less imaging. E-beam dose is calculated by multiplying the current density and the exposure time in each pixel and indicated by the number of electrons/nm2 . Threshold doses reported in literature vary from as small as 5 × 102 e− /nm2 for 100 keV incident energy of the electrons to about 107 e− /nm2 for 200 keV.20–23 The contributing factors for the e-beam induced damages are: (i) atomic displacements, (ii) e-beam sputtering, (iii) ebeam heating, (iv) electro-static charging, and (v) radiolysis.19 At high incident energies, most of the energy lost by the electrons is due to inelastic scattering which can eventually heat up the sample locally if the thermal conductivity of the sample is low.19 For electrically-insulating samples at high current densities, lateral migration of ions is possible due to electrostatic charging induced electric fields across the samples.19 Similarly, radiolysis (e-beam degradation) induced mass loss is also possible. For example, fluorine loss in AlF3 and metallic Al-nanoparticle formation has

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been observed due to radiolysis.19 Lithium phosphorous oxynitride (LIPON) is amorphous, electronically non-conducting and has low thermal conductivity. LIPON is a commercialized solid electrolyte and has been used in all solid-state batteries for a long time now.24, 25 Among the above-mentioned aspects of damage, e-beam heating, electrostatic charging and radiolysis are all relevant for this work considering the physical, electrical and thermal properties of the solid electrolyte LIPON. In this chapter, we report the stability of LIPON under both high flux electron and ion beams and present how the beam induced instability can affect the functionality of the nano-batteries and quantitative analysis of EELS data. This type of analysis must be conducted for any solid electrolyte since they are intrinsically susceptible to beam damage. LIPON is highly sensitive to both e-beam and ion beam damage. Large electron dose leads to decomposition of the electrolyte which is not desirable for the functionality of the battery. The mechanism of LIPON damage can be attributed to three factors (i) electrostatic charging, (ii) beam heating and (iii) radiolysis. Figure 5 shows the STEM images recorded after EELS mapping in the region indicated

Fig. 5. Electron dose effect on LiPON during STEM/EELS mapping at various dosage. (a) and (b) show no observable damage while (c) and (d) show formation of voids in LiPON.17

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by the box in each image. Figures 5(a) and 5(b) show that the LIPON is undamaged while 5(c) and 5(d) show that the LIPON is damaged as seen by the dark contrast in most of the pixels. The legends in each figure indicate the electron dose used for EELS mapping which clearly shows that there is a threshold dose of about 0.5×107 e− /nm2 , below which no damage can be observed. Both the cathode and anode have very high threshold and do not show any damage at this dose level. These are representative images from many observations and irrespective of pixel size and dwell time. Beyond the threshold dose, damage can be observed. This damage also manifests significant changes in the EELS spectrum edge of elements, more specifically on the Li K-edge. The damaged region shows lower intensity for Li K-edge (as shown in Fig. 6 and the inset) for the spectra collected from the same sample but with different electron doses. The lower intensity of lithium

Fig. 6. Electron dose effect on EELS signal of Li-edge. Larger dose not only damages the LIPON, but also decreases the Li signal intensity.

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Fig. 7. The series of images from (a) to (f) shows the evolution of electrolyte damage as the small voids begin to cluster together to form large voids.

K-edge indicates that high electron dose induced damage causes lithium loss. This could be due to localized heating and/or by the electrostatic charging induced electric field which can drive away lithium in LIPON. It is important to note that LIPON has high lithium-ion conductivity at high temperatures.26 Figure 7 shows a series of bright field TEM images recorded at regular time intervals demonstrating the time evolution of damage in the LIPON electrolyte. Electrolyte damage is in the form of small voids which cluster to form a large void as shown by the low magnification image in Fig. 7(f). Similar bubble formation was observed during imaging in a scanning electron microscope operated at 10 kV with equal to or longer than 10 µs dwell time. Such a bubble formation in LIPON is plausibly due to dissociation of N2 at higher dose; this is typically referred as radiolysis. Radiolysis is predominant in polymers and ionic crystals such as NaCl with similar dose thresholds.27 Consequently, imaging with SEM needs to be minimized during FIB fabrication processes to avoid electrolyte damage. Furthermore, LIPON electrolyte is highly sensitive to air/moisture specifically when its cross-sections are thinned down to 100 nm. Swollen electrolyte layer filled with voids was observed if the FIB prepared samples were not transferred to the TEM as soon

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as possible (preferably less than 15 minutes). This highlights the importance of immediate transfer of nano-batteries from FIB to TEM for in-situ TEM biasing experiments.

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4. Design of TEM/STEM Biasing Holders The strict thinness requirements of TEM samples coupled with the need for electronic biasing of the solid-state batteries demand the creation of new TEM/STEM sample holder designs that fulfill these needs. These designs must accommodate the individual and separate electrical connections to the cathode and anode of the thin battery sample and the sample holder must have the electrical connections outside of the TEM where it could be connected to a potentiostat. Through exploratory work, a few experimental designs and new TEM holders have emerged and been tested. These designs include TEM holder designs from NanoFactory and ProtoChips, as both manufacturers produce TEM holders capable of electrically biasing the TEM sample. The main components of successful electrical biasing of the TEM sample include the large TEM holder, sample carrier (where the TEM sample is mounted), and electrical connections from the sample to the sample carrier then finally to the outside end of the TEM holder. Many designs navigate through these obstacles with their own challenges. At the time of this writing, the NanoFactory designs have been used the most for experimentation. Firstly, a design which includes a thinned solid-state battery electrically connected to a sample carrier that serves as connectors to both the cathode and anode (separately of course) is used. The first design is illustrated in Fig. 8 for clarifications. The semi-circular gold coated pad is a custom-made pad from TEMwindows.com with about a 2.85 mm diameter and a 200 nm surface coating of SiN. The spacing between the two gold pads is 50 micron. The sample carrier is cut horizontally at the square window so that there will be easy access while working with FIB. Secondly, a design in which the sample carrier makes one electrode connection and a piezo-controlled tip makes the second

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Fig. 8. First NanoFactory design with connections to both the cathode and anode. (a) The thin film battery sample is mounted on a SiN grid with two gold pads which is wired to the connections of the sample carrier. (b) The sample carrier is then loaded on to the TEM holder with jaws that make pin hold connections to the sample carrier. Figures courtesy of NanoFactory.

electrode connection is also explored. This design is illustrated in Fig. 9 for clarifications. The technical difficulties with this design lie with the piezo-controlled tip used for connection. When the TEM holder is placed within the TEM, the connection must be made with the tip using manual controls of the piezo-tip. Since the TEM beam will only provide a two-dimensional planar view of the solid-state battery, the depth information can only be obtained via trial and error. This process takes time and considerable skill to execute properly without physically damaging the solid-state battery. Models made by NanoFactory, such as the Multimodal

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Fig. 9. (a) shows the electrical connection schematic of the nano-battery, (b) shows an overall view of the second NanoFactory design with connection to one electrode and a piezo-controlled connection to the second electrode. Courtesy of Brookhaven National Lab.

Optical NanoProbe, are suitable for electric biasing of solid-state thin battery in TEM column. One connection is made via the piezocontrolled tip and the second connection is simply made through the OmniProbe grid, which is conducting and is contacting the Oring that holds it in place. The TEM holder itself will have leads connecting to the O-ring and piezo-controlled tip separately. There are some advantages of one design over the other. The first design ensures contact to both electrodes, but the physical dimension of the SiN gap requires the nano-battery to be quite large, which can be difficult to work with using FIB. The second design is not limited by physical dimension restrictions, but the connection needs to be made in the TEM without a stereo view, which can be tricky due to lack of depth information. In addition to the NanoFactory design, the ProtoChips Aduro TEM holder is also capable of electrically biasing TEM holders. Such designs have not been experimented with by our group but serve as potential alternatives. However, there are also other potential challenges that these TEM holder designs do not address. For example, the inability to protect the TEM sample from atmospheric conditions during sample carrier mounting on the TEM holder or sample transfer from FIB to TEM can be detrimental to lithiumion battery electrode components that are sensitive to air moisture,

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Fig. 10. Future designs of TEM holder with vacuum sealable capability for in-situ TEM as envisioned by the authors.

especially in the super thinned state. In our opinion, the next generation TEM holders for in-situ TEM will comprise of designs that eliminate the presence of air exposure conditions. A sample design by us is illustrated in Fig. 10. The most important part of this design is a pair of closable doors on both sides of the frame that enclose the TEM sample carrier and keep the contents in vacuum. These doors (drawn with green parts) should be controlled remotely via radio frequency signals or similar technology, allowing opening and closing inside FIB or TEM to permit access. In the open door state, the sample carrier will be out of plane of the frame, allowing FIB interactions such as ion beam milling, Pt welding, and OmniProbe manipulations, which would be blocked by the frame top otherwise. While the doors are closing, the sample carrier will shift back in plane with the frame and allow full closure. Ideally, the sample carrier (white part) should be separable from the connection (orange part) for changing of the sample carriers. The sample carrier can allow multiple connections (eight connections denoted here) while it will be inserted into the orange connector. On the bottom side, there is a central rod that will fit into the slots of any standard modern SEM/FIB machines and other pin holes for the electrical connections. Once the samples are prepared and the vacuum doors closed, this TEM holder head can be connected to the rest of the TEM holder with an inverted part

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that will make all the necessary connections with the TEM holder head. With the future physical fruition of this design, many new capabilities will be available for in-situ TEM experiments without the constraints of air exposure. 5. In-situ Analytical Characterization of Nano-Batteries using Imaging, Diffraction, and Spectroscopy With the successful fabrication of functional solid-state nanobatteries using appropriate FIB fabrication parameters and careful electron-beam damage control under the TEM, many analytical characterization techniques can be conducted in-situ to observe the dynamics of lithiation processes in solid-state batteries. The foremost technique enabled is the in-situ TEM imaging of the nano-battery cross sections for in-situ morphological changes. In many battery chemistries, expansion of solid-state electrodes is of great importance to the performance of the battery. For example, amorphous silicon will expand in volume about 170% when lithiated to ∼Li2.5 Si and over 280% when fully lithiated to Li3.75 Si,28 causing stress in the electrode. Contrast changes in a two-phase interface propagating will provide kinetic rate information about the phase transformation. Additionally in certain solid-state battery setups, which include conversion electrodes such as FeF2 , significant morphological changes can also be observed.2 Electron diffraction also provides information for structural changes occurring in the electrodes during charging and discharge. Almost all electrodes will have some form of phase transformation during cycling that affects the performance of the cell. For instance, amorphous-crystalline interfaces present large interfacial strains within the electrodes, which could lead to pulverization and loss of capacity as in the case of silicon.29–32 More importantly, spectroscopic characterization, which provides chemical information, can be enabled with in-situ analytical TEM. Coupled with the spatial resolution of STEM mode, detailed analysis can be carried out in situ, mapping out the chemical concentration of elements of interest as lithiation progresses. The

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Fig. 11. (a) The series of images show the propagation of an a-Lix Si phase into a-Si at a speed of about 0.06 nm/s.28 (b) The series of images show the conversion reaction of FeF2 particles into Fe nanoparticles imbedded in a LiF matrix.2

main technique providing such information is EELS included in many of today’s modern TEMs.33 It takes advantage of the difference in kinetic energy of the primary electrons after inelastic scatterings through the sample to identify the elemental composition of the material. When conducted in STEM mode of the TEM, EELS can couple nanometer-scale spatial resolution with elemental identification, providing a powerful technique that allows scientists to envision the lithium-ion transport movement across the solid electrolyte. Interesting phenomenon, such as interfacial accumulation, can be easily identified with EELS Li-K edge elemental mapping. Figure 12 demonstrates combined imaging and chemical analysis capability with high spatial resolution. The TEM sample is fabricated from a thin film solid-state battery consisting of SnO2 (anode)/Li3.4 V0.6 Si0.4 O4 (LVSO electrolyte)/LiNi0.5 Mn1.5 O4 (cathode) deposited by pulsed laser deposition (PLD).34 Lithium concentration mapping produced by EELS analysis will provide insight into the interfacial phenomena that are of high importance

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Fig. 12. (a) TEM image of the solid-state battery cross-section. (b) shows the respective elemental mappings of nickel, vanadium, and lithium. (c) shows the lithium concentration mapping using Li–K edge.34

in solid-state batteries. EELS is also capable of providing valuable oxidation state information of transition metal ions after careful analysis of fine structure peaks. For example, the L3 /L2 peak ratio of Cobalt will be an indication of the oxidation state of Cobalt. Elemental Cobalt will have a L3 /L2 peak ratio of about 3.77 whereas higher oxidation Cobalt will have a ratio of 2.90 at Co2+ and 2.43 at a mixture of Co3+ and Co2+ .35 An alternative to STEM/EELS is the energy filtered TEM. Conducted in the TEM mode, primary electrons passing through the sample are filtered by a magnetic prism to form contrast images formed by electrons of a specific energy. When the selected energy range is at the energy loss edge of a specific element, the resulting image shows a concentration map of the selected element.36 The advantage of this technique is the absence of concentrated electronbeam compared to the focused probe of STEM mode; however, the image will only contain a limited energy range constraining the chemical information to one element at a time. It nevertheless will not carry the spectroscopic information that can be used to identify oxidation states as the intensities within the energy range are integrated together. Of course, each technique will present different information with its own advantages and disadvantages. Careful planning and preparation will allow the users to fully utilize these techniques available in-situ within the TEM.

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With all the conditions properly managed, analytical electron microscopy of solid-state thin film batteries can be quite a powerful tool to analyze the interfacial phenomena present during the operation of thin film batteries. In a recent ex-situ STEM/EELS study,17 the cathode/electrolyte and anode/electrolyte have both been shown to accumulate lithium. In the model system, the cell is constructed as lithium cobalt oxide, lithium phosphorus oxynitride, and amorphous silicon as cathode, electrolyte, and anode respectively. Upon overcharging of the anode to over three times its theoretical capacity to about 260 µAh/cm2 , various additional interfaces form at the anode/electrolyte interface. Firstly, lithium plating occurs at the copper (current collector) and silicon interface to compensate for the extra capacity. Secondly, an inter-diffused interface of silicon and phosphorus forms, which could correspond to irreversible reactions between the anode and electrolyte. Detailed electron energy loss spectrums shown in Fig. 13 demonstrates the presence of lithium and phosphorus signals at position 0, while in the interface between silicon and LiPON, additional silicon signals are seen at position 1–2. In the silicon layer, lithium and silicon signals corresponds to the formation of lithiated silicon at position 3–4. Finally, from position 5–7, we only see lithium K-edge which is evidence for lithium plating.

Fig. 13. (a) Annular Dark Field STEM image of the anode/electrolyte interface in a sample charged to 260 µAh/cm2 . (b) Electron Energy Loss Spectra recorded from 8 different sites along the interface.17

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Fig. 14. (Color online) High loss EELS of the interfacial LCO layer (black) and bulk LCO layer (red). The O–K pre-edge is severely diminished in the interfacial LCO layer indicating Co-O bonding and coordination changes.

With further study, the cathode/electrolyte interface showed a short range ordered lithium cobalt oxide layer between LiPON and bulk lithium cobalt oxide that accumulated lithium along with chemical bonding changes upon charging. Upon charging, ex-situ EELS analysis showed O–K pre-edge disappearance (Fig. 14) in this interfacial layer indicating oxygen vacancy formation as the O–K pre-edge is heavily influenced by the bonding between transition metal ion and oxygen. O–K edge electron energy loss spectrum probes unoccupied 2p orbitals of oxygen. Since the transition metal 3d electrons are hybridized with the oxygen 2p electrons, analysis of the edge along with the pre-edge provide information about energy splitting and type of coordination of the transition metal including presence of oxygen vacancies.37 Li–K edge concentration mappings also show lithium accumulation within this layer contributing to possible capacity loss. Interestingly, our recent in-situ EELS analysis only shows a shifting of O–K pre-edge suggesting oxygen vacancy formation is not kinetically favored.38 These findings demonstrate the unique analytical information STEM/EELS characterization can provide with high spatial resolution and chemical sensitivity.

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More importantly, the difference between in-situ and ex-situ analysis clearly points to the dynamic information that can be lost in ex-situ experiments.

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6. Future Perspectives — Opportunities and Challenges Once the in-situ analytical electron microscopy of solid-state batteries technique matures with further studies, many experimental opportunities are open for analysis of different interfacial phenomena that are not present in other types of systems such as nanowires and nanoparticles. The most immediate progression is the introduction of different chemistries for electrodes and/or electrolytes. Other types of intercalation materials such as LiNi0.5 Mn1.5 O4 high voltage spinel, and lithium excess layered material are of interest as they have unique structural and chemical changes during electrochemical operations. For example, lithium excess material has been shown to undergo surface transition from layered structure to spinel structure with transition metal migration.39 With a solidstate battery configuration, this surface phase transformation could be monitored by in-situ TEM to obtain dynamic information of the transition metal migration. Different types of electrolytes could be explored, such as the recently discovered LLZO (Garnet) and LLTO (Perovskite) structures. Their interfaces with the electrode materials remain largely unknown at the time this chapter was written. Future experiments will also include observations with high temporal resolution. In-situ EELS mapping could help visualize the lithium concentration during charging and demonstrate lithium transport at the interfaces in real time. Morphological and structural changes are very important with conversion materials and the solid-state battery setup will provide a closer representation of electrode operation in a full cell rather than just the material itself. Dynamic transition metal and anion bonding changes can be monitored by in-situ high loss EELS through the bulk of the electrode with high spatial resolution. Changes in the O–K edge will reflect changes in the transition metal and oxygen bonding, while transition metal L3 /L2 edge ratios will reflect its oxidation state. All these characterizations provide a wide range of information about

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the mechanism and dynamics of chemical changes in the electrode in a full cell environment. However, the community will face many fabrication and technical challenges to enable in-situ STEM/EELS characterization with high temporal resolution. With more frequent e-beam scanning, there is a higher dosage of electrons on the sample. Selecting solidstate electrolytes that can withstand such intense beam exposure is of vital importance to push the limits of in-situ STEM/EELS analysis. Certain Garnet type, Perovskite type, and amorphous materials could function as electrolytes that survive higher doses of electron beam without decomposition. Additionally, the biasing current is still too high for lower charge/discharge rate experiments. Even at the pico-ampere range, the current density is still on the orders of 100 µA/cm2 which corresponds to about 1C (one hour charge/discharge). Near-equilibrium reactions will require slower rates; hence femto-ampere potentiostats will be needed to bias the samples given their nano-sized area. A second strategy is to use Dynamic TEM for the characterization of solid-state batteries. This technique has been under intense development in recent years, though typically used in biological beam-sensitive samples. Nanosecond time-scale Dynamic TEM requires high intensity electron beams in a short nanosecond pulse, and Dynamic TEM achieves such requirements by introducing laser stimulated photoemission electron source to generate excess of 2 × 109 photo-emitted electrons in a single 15-ns bunch. Such capabilities enable observation of transient morphological and diffraction changes with high temporal resolution that can be missed in conventional TEM.40–43 We expect that the battery community will greatly benefit from the advancement in DTEM. In summary, high temporal resolution STEM/EELS characterization will provide critical new insights of dynamic interfacial phenomena that would shed light on the design and optimization of future solid-state batteries, a safer and more reliable energy storage technology. Acknowledgments Z.W. and Y.S.M. acknowledge the funding support for the development of the all-solid-state battery and the in-situ FIB and TEM

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biasing design by the U.S. Department of Energy, Office of Basic Energy Sciences, under Award Number DE-SC0002357.

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28. J. W. Wang et al., Nano Lett. (2013) 709–715. 29. X. H. Liu et al., ACS Nano 6 (2012) 1522–1531. 30. S. W. Lee, M. T. McDowell, L. A. Berla, W. D. Nix and Y. Cui, Proc. Natl. Acad. Sci. U. S. A. 109 (2012) 4080. 31. K. J. Zhao et al., J. Electrochem. Soc. 159 (2012) A238. 32. J. W. Wang et al., Nano Lett. 13 (2013) 709–715. 33. R. F. Egerton, Reports on Progress in Physics 72 (2009) 016502. 34. Y. S. Meng et al., Elec .Chem. Soc. Interface. 20 (2011) 49–53. 35. B. D. Yuhas, D. O. Zitoun, P. J. Pauzauskie, R. He and P. Yang, Angewandte Chemie 118 (2006) 434–437. 36. P. A. Midgley and M. Weyland, Ultramicroscopy 96 (2003) 413–431. 37. J. Graetz et al., J. Phys. Chem. B 106 (2002) 1286–1289. 38. Z. Wang et al., Manuscript in Preparation. (2014). 39. B. Xu, C. R. Fell, M. Chi and Y. S. Meng, Energy and Environmental Science 4 (2011) 2223–2233. 40. J. S. Kim et al., Science 321 (2008). 41. J. E. Evans, K. L. Jungjohann, N. D. Browning and I. Arslan, Nano Lett. 11 (2011) 2809–2813. 42. M. R. Armstrong et al., Ultramicroscopy 107 (2007) 356–367. 43. T. LaGrange et al., Ultramicroscopy 108 (2008) 1441–1449.

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Li-ion Dynamics in Solids as Seen Via Relaxation NMR∗ Viktor Epp† and Martin Wilkening‡,§

Graz University of Technology Christian Doppler Laboratory for Lithium Batteries Stremayrgasse 9, A–8010 Graz, Austria ‡ [email protected] and † [email protected]

Various time-domain nuclear magnetic resonance (NMR) techniques are highly useful to study Li-ion dynamics in solid electrolytes and electrode materials from an atomic-scale point of view. In particular, by combining lithium NMR techniques being sensitive to Li jump processes on different length scales and time scales detailed information on activation energies, jump rates and diffusion pathways can be collected. This helps understand the relationship between local structure and dynamic parameters and assists in developing new materials for solid-state energy storage. In this chapter, we will review recent examples where NMR relaxation has been successfully applied to both highly conducting solid electrolytes and selected anode materials.

1. Introduction The development of electric vehicles and portable devices such as smartphones and computers as well as the advent of stationary energy storage systems pose significant challenges to currently developed rechargeable batteries.1–15 Certainly, electrochemical energy storage is expected to offer increased power and capacity as well as safety and longevity. Towards this end, solid-state batteries, ∗ DFG Forschergruppe 1277: Mobility of Lithium Ions in Solids. § Corresponding author.

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using either Li, Na,16–24 Mg25–29 or even F ions30–34 as charge carriers, are among the great hopes of energy storage research. Compared to conventional lithium-ion batteries equipped with liquid electrolytes,12, 35 an all-solid-state system using a nonpolymer solid electrolyte features superior characteristics also with regard to service life and thermal stability.36–38 It is widely known that liquid electrolytes have plenty of drawbacks such as toxicity, flammability and instability when in contact with the electrode material. However, so far, they proved largely irreplaceable with solid-state counterparts. For these reasons, scientists from complementary disciplines such as solid-state chemistry, physics and materials sciences are searching feverishly for solids suitable to act as powerful electrolytes and electrode materials. Solid electrolytes, in particular, should possess attributes that include the following: (i) High ionic (bulk) conductivity at ambient and sub-ambient temperature, (ii) Low interfacial and/or grain boundary resistance, (iii) Good electronic insulator, (iv) Thermal and electrochemical stability, (v) Li+ transference number close to one, (vi) Good mechanical strength, (vii) Better compatibility with electrodes, (viii) Environmentally friendly. Finding a material having all the characteristics mentioned may prove a challenging task and much more research is required until all these features are integrated. All-solid-state batteries may solve many aspects related to the reliability of Li-ion technology, such as the gas build-up that may occur inside a Li-ion cell or possible shortcircuits due to Li dendrite formation. It is expected that they will also have an impact on the specific capacity and power capabilities. Indeed, thin solid electrolyte films may be used and novel battery technologies, such as printing or other deposition techniques, can easily be implemented. Besides the important fact of electrochemical stability (i), electronically insulating solid electrolytes (ii), in particular, are to show

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an extremely good ionic conductivity around ambient temperature (ii). In concreto, specific ion conductivities σ in the order of 10−3 to 10−2 S cm−1 , or even better and transport numbers close to one (iv) are necessary to realize powerful and competitive batteries. Such values are comparable with poorly conducting liquid-based materials. Importantly, a small activation energy of the relevant longrange ion transport process is needed to ensure a sufficiently fast Li hopping even at lower temperatures. Often, this requirement is linked to defect-rich structures39 modified by appropriate doping, local disorder or (artificial) nano-size effects.40, 41 Generally, it is influenced by a large number of vacant sites being available for the charge carriers to move over long distances. The site fraction of intrinsic defects in thermal equilibrium depends on temperature and amounts to about 10−4 near the melting point as a maximum.42, 43 Compared to liquids, with diffusion coefficients approximately in the order of 10−8 m2 s−1 , the corresponding values in most of the Li-containing solids usually are orders of magnitude lower. Fast ion conductors form an exception. Their diffusion coefficients may reach values normally found in, e.g. (poorly conducting, organic-based) liquid electrolytes. Over the past years, many single-phase and multi-phase, nanoand microcrystalline lithium, fluorine and sodium conducting solids20, 34, 39, 44–49 have been identified and thoroughly characterized by complementary nuclear and non-nuclear techniques as well as electrochemical methods. Some of the most prominent examples are Li3 N,50–54 Li3 PO4 :Li4 SiO4 ,55, 56 BaF2 ,57 MSnF4 (M = Ba, Pb),34, 58–64 Na-beta-alumina,65–67 and many others.39 These also include those having been studied at the early stages of a research area that is today known as solid state ionics.68–70 However, most of them do not meet all of the necessary criteria [(i) to (viii), see above] to be employed as solid electrolytes. For instance, many of them lack a sufficiently high ionic diffusivity (or conductivity) as well as electrochemical stability. Recently, promising new candidates were considered which show extremely high ion conductivities and negligible electronic contributions.45, 71–76

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β

Fig. 1. (Color Online) Total conductivity of selected solid Li-ion conductors studied recently and during the past; for comparison, also some of the commonly used liquid electrolytes are included. For the sake of clarity, in Fig. 2 a cut-out is shown including the most important solid electrolytes with high Li+ conductivity near ambient temperature. Data were taken from the literature: αLi2 SO4 77 ; LISICON (Li14 Zn(GeO4 )4 )78 ; Li-β-alumina79 ; Li10 GeP2 S12 72 ; s-Li3 N (pure, sintered)50 ; d-Li3 N (doped with H)51 ; tetragonal LLZ (Li7 La3 Zr2 O12 )80 ; cubic LLZ (Li7 La3 Zr2 O12 with 0.9 wt% Al added)81 ; LiBSO (0.3 LiBO2 –0.7 Li2 SO4 , thin film)82 ; LiPON (lithium phosphorous oxynitride, thin film);83 PEO:LiClO4 84 ; LiBF4 :EMIBF4 ;85 LiPF6 :EC:PC86 ; LiPF6 :EC:PC:PVDF:HFP.87

In Figs. 1 and 2, the temperature dependence of σ for a small selection of Li ion conductors is shown;a in Fig. 1 also a Note that these two figures do not represent an Arrhenius diagram since σ instead

of σT is plotted versus the inverse temperature.

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Fig. 2. (Color Online) A selection of suitable Li ion conductors to develop lithiumbased batteries. The figure complements the previous one and highlights solids exhibiting fast ion transport near ambient temperature. Data presented were taken from the literature, see also some of the References of Fig. 1: Li3.25 Ge0.25 P0.75 S4 ;88 glass Li2 S:SiS2 :Li3 PO4 ;89 glass Li2 S:SiS2 :Li4 SiO4 ;90 glass Li2 S:SiS2 :P2 S5 :LiI;91 glass Li2 S:P2 S5 ;92 Li7 P3 S11 ;92 LiSiPO (Li4 SiO4 :Li3 PO4 solid solution);56 LATPO (Li1.3Al0.3 Ti1.7 (PO4 )3 crystal);93 Li3 InBr6 ;94 LLTO (La0.51 Li0.34 TiO2.94 , bulk conductivity).95

the conductivity values for commonly used liquid electrolytes are displayed. In particular, the fast ion conductor Li3x La2/3−x TiO3 has been extensively studied by relaxation NMR by Bohnke and coworkers.96 Recently, Li diffusion in (Li2 S)7 (P2 S5 )3 was investigated by pulsed-field echo NMR spectroscopy.97 The developments of bulk-type solid-state rechargeable lithium batteries with sulfide glass-ceramics have been summarized by Hayashi and Tatsumisago,

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recently.45 For comparison, an overview of Na-ion conductors20 as well as (solid) polymer electrolytes1 can be found elsewhere. In many cases it is useful to underpin results from AC and DC conductivity spectroscopy with those from other techniques. Many of the electrolytes shown in Figs. 1 and 2 have been the subject of intense conductivity studies. In particular, extremely fast Li-ion conductors are increasingly investigated by NMR methods.53, 98–102 In general, the application of complementary methods, such as mass tracer43, 103, 104 or neutron reflectometry,105–107 being able to probe different motional correlation functions, greatly helps us to understand the fundamental nature of ion transport. Unfortunately, the well-known tracer method using a radioactive marker43 is difficult to apply because of the very short-living radioactive Li isotopes.108–110 However, apart from beta-radiation detected 8 Li NMR,42, 52, 111–116 classical relaxation NMR, taking advantage of the superb receptivity of the stable isotope 7 Li (spin–3/2 nucleus), represents the method of choice for temperature-variable relaxation measurements in both liquids117 and solids.42, 53, 98 In particular, such studies also include field cycling measurements.118–127 Occasionally, additional 6 Li (spin–1) NMR measurements are extremely helpful for the interpretation of relaxation transients and the corresponding R1ρ rates measured as a function of both resonance frequency and temperature.98 In doing so, light can be thrown on the nature of the underlying relaxation mechanisms, i.e. whether they are driven by magnetic dipolar or electric quadrupolar interactions.80, 128, 129 It is often useful to subdivide methods being capable to study solid-state diffusion into microscopic and macroscopic ones (see Table 1) as done by Heitjans.111 Whereas microscopic methods probe diffusion parameters such as jump rates of ions and barrier heights for elementary jump processes, macroscopic methods are sensitive to long-range diffusion.42, 102 NMR investigations in solids span the range of jump rates τ −1 from 10−2 to 109 s−1 in the case of the microscopic methods, while macroscopic NMR techniques, such as magnetic field gradient techniques (FG-NMR),143 which may be static or pulsed,54, 144–147 cover diffusion coefficients in the range 10−14 m2 s−1 to 10−11 m2 s−1 .

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Table 1. Some of the typical nuclear and non-nuclear methods to probe diffusion of small atoms or ions in solids; here, subdivided into micro- and macroscopic ones. Macroscopic

Microscopic

Nuclear

tracer diffusion field gradient NMRa

NMR relaxation (e.g. T1(ρ) , T2 ) beta-NMRb 1D and 2D exchange NMRc quasi-elastic neutron scattering Mössbauer spectroscopy

Non-nuclear

DC conductivity mechanical relaxation

AC conductivity

a Using a static or pulsed field gradient. b For example, taking advantage of the NMR-active isotope 8 Li.111 c High-resolution NMR technique carried out at fast magic angle spinning

(MAS); 2D MAS NMR is, in particular, useful to probe site-specific Li residence times if a sufficiently good spectral resolution can be achieved.130–142 This is in dia- as well as in paramagnetic compounds the case where Fermi contact interactions govern NMR shifts.

Fig. 3. NMR time-domain methods, including high-resolution (2D) exchange spectroscopy and the respective time scales they are sensitive to. (MA: motional averaging, i.e. line narrowing).

Figure 3 briefly illustrates the timescales to which the different relaxation NMR techniques are sensitive. In general, spin-lattice relaxation (SLR) measurements, labeled in Fig. 3 with the time constant T1 , are usually performed in the so-called laboratory frame of reference. Temperature-variable SLR

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NMR is able to probe extremely fast Li motional processes with rates in the order of some MHz. Slower Li diffusion processes, however, can be detected with the so-called spin-lock technique42, 96, 99, 148–153 (1/T1ρ ≡ R1ρ ) where the external magnetic field B0 , corresponding to resonance frequencies in the MHz range, is formally replaced with a magnetic field B1 which is characterized by (angular) locking frequencies ω1 in the kHz range. Even slower jump processes can be probed via NMR line shape measurements (or spin–spinrelaxation (SSR) experiments (1/T2 ≡ R2 )) as well as by means of 2D exchange NMR130, 131, 134, 142 (see also the References in footnote c of Table 1). Stimulated echo NMR, that is, spin-alignment echo (SAE) NMR, complements the set of available techniques.98, 154–161 SAE NMR was originally developed to investigate deuteron (spin– 1) dynamics.126, 143, 162–164 In the last decade, however, it was also successfully extended to probe jump rates and diffusion pathways of other spin–3/2 and spin–1 quadrupole nuclei such as 9 Be,165–168 7 Li98, 154–161, 165–171 and 6 Li as well.116, 155, 172 1.1. Basics of NMR Relaxation 1.1.1. Influence of diffusion on NMR resonance lines Recording static NMR line shapes as a function of temperature represents one of the easiest ways to collect first information on how fast Li spins diffuse in a solid.42, 173, 174 The method is also suitable for the fast screening of solid electrolytes.175 In general, the NMR line width ν is related to the SSR rate R2 quantifying the decay of a transverse magnetization My (t), i.e. perpendicular to the external magnetic field B0 . A transverse magnetization can be generated simply with a 90° radio-frequency pulse. y denotes that My (t) is sampled as free induction decay (FID) in the rotating frame of reference. In the simplest case the transients My (t) follow either exponential or Gaussian shaped functions depending on the sample temperature and diffusivity of the nuclei under investigation. In the latter case also a Gaussian shaped NMR resonance line is obtained after Fourier transformation of My (t).

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At low temperatures the FIDs of solids proceed on a very short time scale compared to those measured in liquids. Accordingly, broad NMR lines with widths in the kHz range are obtained. This is due to the fact that the nuclei in a solid are much less mobile than in the liquid state. They are exposed to slightly different dipolar magnetic fields leading to a distribution of resonance frequencies around the mean value ω0 /2π being the resonance frequency which is related to B0 via B0 = ω0 /γ with γ being the magnetogyric ratio of the probe nuclei. To eliminate dead time receiver effects and to record also NMR intensities owing to electric quadrupole interactions, which in the case of 7 Li may span up to several tens of kHz, echo techniques can be applied (see Fig. 4).

Fig. 4. (Color Online) (a) The saturation recovery pulse sequence used to probe the SLR NMR rates R1 : A train of closely spaced rf-pulses (π/2)x (n ≈ 10) destroys the (initial) longitudinal magnetization (Mz = Meq ) so that Mz = 0 at t = 0. The subsequent recovery of Mz (t) is probed with a single π/2-pulse which is sent after a variable relaxation delay t = td . (b) The pulse sequence of the spin-lock technique to record the rotating-frame NMR rates R1ρ : Immediately after the π/2-pulse the magnetization Mρ pointing along the (−y ) − axis is locked by the field B1 . The decay of Mρ(−y ) is then probed by plotting the height (or area) of the free induction decay (FID) as a function of the locking pulse length tlock .99 In a simplified manner (c) and (d) depict the pulse sequences to record SSR NMR rates and stimulated echo decay curves. See text for further explanation.

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At sufficiently low temperatures, at which translational ion dynamics can be regarded as frozen, i.e. in the rigid-lattice regime, the jump rate τ −1 of the ion is much smaller than the line width ν. Hence, ν and R2 are independent of temperature. Usually, the rigid-lattice value of R2 is of the order of 104 s−1 . At higher temperatures, however, the nuclei start moving and local magnetic fields are averaged. With increasing diffusivity the transverse relaxation process is slowed down and, thus, the FIDs proceed on a longer time scale similar to the case which is present in liquids. Consequently, the corresponding NMR line starts to narrow. The beginning of this motional narrowing indicates the onset of ion motions with residence times τ of the order of the inverse line width 1/ν. At even higher temperatures, i.e. in the regime of extreme narrowing, the line width reaches once again a temperature independent value due to inhomogeneities of the external magnetic field B0 . In Fig. 5, this behavior is exemplarily shown for polycrystalline Li7 BiO6 being a moderate Li ion conductor which has been primarily studied by stimulated echo NMR.176 Owing to the weaker dipole–dipole interactions in the case of 6 Li, as compared to 7 Li, the rigid lattice line widths differ from each other. This also affects the characteristic temperature at which moving of the spins starts averaging dipolar interactions. Note that the inflexion point of the 7 Li NMR MN curve is slightly shifted towards higher T. The lines are to guide the eye. A rough estimation of the activation energy according to the semi-empirical model introduced by Hendrickson and Bray177 yields 0.45 eV. This is in fair agreement with results from SAE NMR (0.54 eV).176 Such discrepancies might be traced back to dynamical heterogeneities.178 1.1.2. Influence of diffusion on NMR SLR The primary observable in an NMR experiment is the magnetization M being proportional to the sum of the nuclear magnetic moments of the sample. In thermal equilibrium M = Mz is parallel to the external magnetic field B0 , i.e. Mz = M0 . Using an external radio frequency field the direction of the magnetization with respect to B0 can be changed, i.e. nuclear spins can be “reversed”. The transition

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6

Li 58 MHz

14

28 °C

–10 °C –60 °C

7

10 fwhm (Hz)

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6 °C

extreme narrowing

rigid lattice

12

143

Li

8

ca. 450 meV

6

6 4

Li

2 0

-15

-10

-5

0

5

10

15

150

200

250

300

frequency (kHz)

T (K)

(a)

(b)

350

400

450

(a) 6 Li NMR lines of polycrystalline Li7 BiO6 recorded at the temperatures

Fig. 5. indicated; (Color Online) (b) motional narrowing of the Li NMR line widths as a function of temperature. In general, measurements of the NMR line widths allow the estimation of jump rates and activation energies using, e.g., the (semi-)empirical models first presented by Abragam as well as Hendrickson and Bray. However, in a more precise way this is possible via SLR or SAE NMR. MN starts when the mean Li jump rates reaches the order of the rigid lattice line width; therefore, jump rates in the order of kHz can be measured. Usually this translates into conductivity values in the order of 10−8 to 10−6 S cm−1 .

probability will be maximum when this external radio frequency ω1 is in resonance with the Larmor precession frequency of the nucleus given by ω0 = γB0 .42, 173 Immediately after excitation with a radio frequency pulse, the spin-system starts to relax to its state of thermal equilibrium. This so-called SLR process can be recorded when the recovery of the magnetization vector M along the axis defined by the magnetic field B0 is monitored as a function of waiting (or delay) time t = td . Usually, an inversion or a saturation recovery pulse sequence153 (see Fig. 4) is used for this purpose.42 In the simplest case Mz (t) follows an exponential Mz (t)/M0 = 1 − exp (−td /T1 )

(1)

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with 1/T1 ≡ R1 being the SLR rate, which is a function of temperature. Besides other effects, the relaxation process is induced by internal fluctuating fields due to the temperature dependent motion of the nuclei. These fields may be dipolar magnetic from neighboring nuclei as well as quadrupolar electric from local electric field gradients. The fluctuations of an internal field are described by a correlation function G(t). According to the model introduced by Bloembergen, Purcell and Pound (BPP),179 for random jump diffusion G(t) is assumed to be a simple exponential G(t) = G(0) exp (−|t|/τc ).

(2)

τc is the correlation time, which is within a factor of the order of unity equal to the mean residence time τ between two successive jumps of the nucleus. The Fourier transform of G(t), to which R1 is related, is the spectral density function J(ω). It has a Lorentzian shape when G(t) is an exponential. Most importantly, SLR becomes effective when J(ω) has intensities at the resonance frequency.42 1/T1 ≡ R1 ∝ J(ω0 ) ≈ G(0)

2τc . 1 + (ω0 τc )2

(3)

The temperature dependence of τc in Eq. (3) is typically given by an Arrhenius relation τc = τ0 exp (EA /(kB T)),

(4)

where τ0 is the pre-exponential factor and EA the activation energy of the diffusion process. T is the absolute temperature and kB denotes Boltzmann’s constant. Thus, for a given Larmor frequency ω0 , the socalled diffusion induced relaxation rate R1 diff , measured at ω = ω0 , first increases with increasing T (low–T range, ω0 τ  1), passes through a maximum at a specific temperature Tmax and decreases then with still increasing temperature (high-T range, ω0 τ  1)). Taking into account the frequency dependence of R1 diff the behavior can be summarized as follows:
high-T /kB T), if T  Tmax (ω0 ) exp (Ea R1 diff (ω0 , T) ≈ (5) −β low-T /kB T), if T  Tmax (ω0 ). ω0 exp (−Ea

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0.5

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0

0.62

(a)

(b)

Fig. 6. (Color Online) (a) Arrhenius plot of the 7 Li NMR relaxation rates of garnettype Li7 La3 Zr2 O12 crystallizing with tetragonal symmetry. The rates nicely illustrate the behavior of R1 and R1ρ as a function of temperature. In (b) the R1 rates are compared with the temperature dependence of R2 . Deviations from BPP-type behavior manifest in β < 2. Note that the data points marked with dots were excluded from the BPP-type fits shown as solid lines in (a).

As an example, the SLR NMR rates of the solid electrolyte Li7 La3 Zr2 O12 are shown in the Arrhenius plot of Fig. 6. Tmax (ω0 ) decreases with decreasing Larmor frequency. Especially in disorhigh-T

is larger than Elow-T , so that an asymmetric dered materials Ea a diffusion induced rate peak is observed, which is in contrast to simple BPP behavior assuming uncorrelated motion and leading to a symmetric maximum of R1 diff in the Arrhenius plot. This is also the case when the complex Li dynamics in garnet-type Li7 La3 Zr2 O12 is analyzed (see Fig. 6(a)).80 In the (ideal) BPP case the exponent β is 2, whereas several models for SLR in disordered ion conductors such as the coupling concept,180 the jump relaxation model 181 and the dynamic structure model182 as well as the assumption of a distribution of jump correlation times183 predict 1 < β ≤ 2, which is often found experimentally. Thus, the parameter β links the frequency dependence of R1 diff to the asymmetry of the peak, i.e. the two activation energies are related via β according to high-T

Elow-T = (β − 1)Ea a

.

(6)

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In the case of Li7 La3 Zr2 O12 (Fig. 6) this relation is well fulfilled when R1ρ rates are considered. NMR relaxation entails an almost model independent access to the diffusion parameters. It is given when τc is read out via the maximum condition, ω0 τc = 0.62 (BPP behavior), for several diffusion induced relaxation rate peaks recorded at different Larmor frequencies ω0 which cover preferably a large range.156 This includes also the measurement of SLR NMR rates recorded in the rotating frame of reference R1ρ where the relaxation of the spins is probed in the presence of a weak locking field B1 which usually corresponds to (angular) frequencies ω1 in the kHz range (see above).148–152 The spin-lock pulse sequence is schematically sketched in Fig. 4.153 In a first approximation results from SLR measurements in the rotating frame of reference can be interpreted in the same way as those obtained in the laboratory frame of reference. However, the maximum condition is given by ω1 τc ≈ 0.5. Since ω1 is in the order of several kHz the diffusion-induced rate peak is shifted towards much lower T making the method attractive to study slower Li motions. In Fig. 6, the rates R1 and R1ρ were measured at 77 MHz and 30 kHz respectively. The relatively low value of Tmax in the case of R1ρ enables access to the high-T flank of the rate peak yielding the activation energy describing long-range ionic motion. Here, for tetragonal Li7 La3 Zr2 O12 this yields 0.5 eV; this result is in perfect agreement with that obtained by macroscopic DC conductivity measurements.80 Let us note that dimensionality effects influence the slope of the high temperature flank.42, 184 Spatially confined 1D and 2D diffusion,157, 185–188 which is often found in layer structured materials, for example, lead to a smaller slope in the limit ω0 τ  1 (and ω1 τ  1 as well) than expected for 3D motion. Moreover, in contrast to 3D diffusive motion, in the high-T limit the SLR rates for 1D and 2D diffusion do depend in a characteristic way42, 186 on resonance frequency, as is outlined below. Lastly, it is worth noting that the corresponding microscopic diffusion coefficient can be calculated from the Einstein–Smoluchowski relation D(NMR) = 2 /(6τ),

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which is here written in its form for 3D uncorrelated motion.  denotes the average jump length which can be estimated from the lattice parameters of the crystals. D values obtained from NMR can be compared with those estimated from DC conductivity measurements. The DC conductivity σDC is directly related to the long-range diffusion coefficient DDC via the Nernst–Einstein relation DDC =

σDC kB T , Nq2

(7)

where q denotes the charge and N the number density of charge carriers. σDC T also follows Arrhenius behavior according to   σDC T = A exp −Ea,DC /(kB T) . (8) Finally, the self-diffusion coefficient D is linked to DDC via the relations Dtracer = Hr DDC and Dtracer = fD where Dtracer is the so-called tracer diffusion coefficient and Hr as well as f represent the Haven ratio and the correlation factor connecting Dtracer with D. This yields, Dtracer = Hr

σDC kB T = f 2 /(6τ), Nq2

(9)

6kB T · σDC , Nq2 2

(10)

which gives, τ −1 = (Hr /f )

directly relating the motional correlation rate τ −1 available by NMR with σDC . Assuming Hr ≈ 1 and uncorrelated motion (f = 1) the ratio Hr /f is of the order of unity. 1.1.3. 7 Li SAE NMR — probing single-spin hopping correlation functions via stimulated echoes In addition to NMR relaxometry and here included for the sake of completeness, Jeener–Broekaert echoes189 can be used to study spinalignment echo (SAE) decay rates.98, 154, 167 SAE NMR gives direct

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access to single-spin motional correlation functions. Although developed by Spiess et al. to study translational and rotational jump processes of deuterons, as mentioned above,126, 143, 162, 163 the method is increasingly used to probe slow Li+ motions98, 102, 172 as well as Ag+ dynamics as shown by Vogel, Eckert and co-workers.172, 190, 191 It can be applied to both the 7 Li and 6 Li nucleus.98, 116, 155, 172 In particular, Vogel et al. have shown how to use 109Ag three- and fourtime correlation functions to shed light on dynamic heterogeneities and dynamic lifetimes of the moving spins in crystalline phases.172 The principle of SAE NMR is very similar to that of exchange NMR. A presentation of the technique in greater depth is given by Wu et al. and Böhmer et al. elsewhere.98, 102, 167, 192 Here, we would like to point out just the basic idea. In the ideal case, SAE NMR enables the direct determination of Li jump rates τ −1 , see above, as well as access to geometric information on the diffusion pathway of the Li ions. Diffusion parameters obtained by SAE NMR, although recorded with an atomic-scale method, compare well with those from DC conductivity measurements.155, 193 The latest example to document this agreement took advantage of the slow Li exchange process in Li2 TiO3 .194 The three-pulse sequence to record 7 Li SAE NMR decay functions, from which the diffusion-controlled decay rates can be extracted, is depicted in Fig. 4(d). The first two pulses, separated by the evolution time tp generate the stimulated echo whose intensity is monitored as a function of tm . During this mixing time the echo intensity decreases if the jumping ions visit sites characterized by different electric field gradients (EFGs). Quadrupolar SLR and/or spin-diffusion can also contribute to the echo decay.155, 161 Echo decay and thus ion diffusivity is coded in terms of changing quadrupole frequencies the spins are exposed to during hopping through the crystal lattice. The quadrupole frequency is a measure for the interaction of the quadrupole moment of the Li spin with an EFG.173 The latter is produced by the electric charge distribution in the direct neighborhood of the nucleus under investigation. Thus, jumping between electrically inequivalent sites is used to directly probe Li ion hopping rates.

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In other words, the resulting decay curve represents a correlation function which reflects the probability to find an ion initially marked by a site-specific quadrupole frequency at another site characterized by the same frequency at a later time. In the following, selected results from 7 Li SAE NMR, that is, the temperature dependence of Li decay rates, will be shown for Lix TiS2 158 and Li4+x Ti5 O12 .193 It is worth noting that SAE NMR has been successfully applied to study Li dynamics in Nb bearing garnet-type oxides being promising electrolytes for solid-state rechargeable batteries.195

2. Case Studies on Crystalline and Nanocrystalline Li Ion Conductors 2.1. Layer-Structured Materials: Spatially Confined Lithium Diffusion Layer-structured materials play one of the major roles in lithiumion battery chemistry.2, 196 Insertion hosts offer the possibility to reversibly accommodate and release lithium ions. In many cases, Li ion diffusion in the van-der-Waals gap of a series of transition metal oxides and sulfides is rather fast. 2.1.1. Titanium disulfide — a model system for 2D diffusion Titanium disulfide is known as a prominent intercalation host which has been studied in the early stages of research on rechargeable batteries.2, 196–199 Although later replaced by transition metal oxides, it is an exceptionally good model system to be studied by SLR and SAE NMR spectroscopy. Layer-structured titanium disulfide, crystallizing with the CdI2 structure, is a semiconductor and has a hexagonal close-packed sulfur lattice with the titanium ions in octahedral sites between alternating sulfur sheets.196 The TiS2 sheets are stacked directly on top of one another resulting in the sulfur anion stacking sequence ABAB. Li may easily be intercalated at any concentration x to form a stage-1 compound h-Lix TiS2 (0 < x ≤ 1).196 The intercalated Li atoms are at rest at the octahedral sites 1b as shown in Fig. 7(a) which illustrates the crystal structure.

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Fig. 7. (Color Online) (a) Crystal structure of hexagonal Lix TiS2 . (b) Temperature dependence of the diffusion-induced SLR NMR rates, R1 diff (9.97 MHz) and R1ρ diff (5.2 kHz), of 7 Li in h-Li0.7 TiS2 .156, 157 For comparison, the Li jump rates τ −1 directly measured by SAE NMR are also shown.156, 157

Exemplarily, the diffusion-induced SLR NMR rate peaks, R1 (1/T) and R1ρ (1/T), of the hexagonal modification are shown in the Arrhenius plot of Fig. 7(b).157 The data can be used (i) to extract both activation energies and jump rates for the Li hopping process and (ii), when frequency-dependent measurements are considered, to collect information on the dimensionality of the motional process, that is, to obtain geometric properties of the dynamic process. While Li motion is 3D in the cubic modification of TiS2 , the SLR NMR rates of the hexagonal (1T) polymorph reveal typical characteristics for low-dimensional diffusion as expected for Li hopping which is anticipated to be restricted to the van-der-Waals gap of Lix TiS2 . In particular, a distinct frequency dependence of the SLR NMR rates in the limit ω0(1) τc  1 shows up clearly indicating low-dimensional (here 2D) motion.185 This is underpinned by careful inspection of the corresponding R1ρ (1/T) peaks revealing that the high-temperature flank is characterized by a smaller slope than the low-T side for which ω0(1) τc  1 holds.156, 157 As mentioned above, this agrees well with J(ω0(1) ) for 2D diffusion.184, 200

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The dashed lines in Fig. 7(b) represent fits according to this expression using J2D (ω0(1) , τ) ∝ R1 (ω0(1) , τ) with J2D (ω0(1) , τ) ∝ τ ln(1 + 1/(ω0(1) τ)β ). Interestingly, the best fits are obtained when β ≈ 2 is valid. This is in agreement with the result obtained when the R1 rates on the low-T flank are analyzed as a function of frequency. Thus, correlation effects seem to play a minor role in the investigated sample and a BPP-type relaxation behavior shows up on the low-T side. Irrespective of the 2D-fits shown in Fig. 7(b), the low-T flank points to an activation energy of approximately 0.37 eV for Li hopping in h-Li0.7 TiS2 .156, 157 This value is in very good agreement with that one which was deduced from the Arrhenius plot in Fig. 8. The solid line shown corresponds to τ −1 = 6.3(1) × 1012 s−1 exp (−0.41(1)eV/kB T); the pre-factor obtained

Fig. 8. (Color Online) (a) Li jump rates for h-Li0.7 TiS2 versus reciprocal temperature. Jump rates were obtained from the various diffusion-induced SLR NMR relaxation peaks at different resonance frequencies (
: 9.97, 19.2, 27.9 and 77.7 MHz) and locking frequencies (◦: 2.1, 5.2 and 10 kHz), respectively.157 For comparison, Li jump rates deduced from analyzing 7 Li spin-alignment NMR echoes (•: 155 MHz) are also shown.156, 157 Furthermore, 1/τ (H #) can be estimated from R2 data. A single diffusion process is observed over a relatively large temperature −1 from spin-alignment echo NMR recorded at two radio range. b) Li jump rates τSAE frequencies (77.7 MHz (
), 155 MHz (◦)) For comparison, R2 (77.7 MHz (H #)) as well as R1 (77.7 MHz (
)) are also shown.156, 157

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is in good agreement with values expected for phonon frequencies which usually range from 1012 s−1 to 1014 s−1 . Li jump rates shown in Fig. 7 were determined at the temperatures where the SLR NMR rate peaks measured at different frequencies pass through their maxima. To calculate the rates, the conditions ω0 τc ≈ 1 and ω1 τc ≈ 0.5, respectively, were used. Furthermore, in Fig. 7 Li jump rates are included which were measured by 7 Li SAE NMR; the technique is per se sensitive to very slow Li exchange processes between electrically inequivalent sites.154, 156, 159, 162, 201 These may be identified with two sites in the van-der-Waals gap, namely the octahedral one (1b), normally occupied by Li and the tetrahedral one (2d).157 According to quantum chemical calculations, the electric field gradient at the tetrahedral site differs from that at the octahedral one by a factor of three.202 In agreement with calculations of Bredow et al.203 SAE NMR measurements of final state amplitudes have shown that the elementary step for Li self-diffusion in Lix=0.7 TiS2 is predominantly governed by the diffusion pathway 1b → 2d → 1b . This pathway, as has been shown by recent calculations of van der Ven and coworkers,204 is the preferred one if di-vacancies are present. Certainly, the smaller x the larger the number fraction of di-vacancies which can be formed. Interestingly, when x reaches 1, direct hopping between the sites 1b and 1b becomes energetically favoured. Let us note that the activation energy calculated for the two-step diffusion pathway with the intermediate occupation of the tetrahedral site 2d is in excellent agreement with that experimentally probed via SAE NMR and SLR NMR.203 It has also been found for analogous lithium-bearing dichalogenides.205, 206 For comparison with SLR NMR, the measured 7 Li SAE NMR −1 rates τSAE ≈ τ −1 are also included in Fig. 7 (b). It is clearly seen that the SLR NMR rates of the low-T flanks and SAE NMR probe the same activation energy.156, 157 As expected, the decay rates of the SAE NMR experiments, which were obtained from two-time correlation functions recorded at 77.7 and 155 MHz, are independent of the magnetic field used to record the data (Fig. 8 (b)). They are solely governed by Li diffusion below 200 K. It is worth noting that in this

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temperature range, which is identical with the rigid-lattice regime, neither NMR spin-lattice nor NMR SSR, recorded at the same Larmor frequency, is able to probe such slow diffusive motions. Note that for SLR NMR carried out at 77.7 MHz the diffusion-induced low-T flank is expected to show up at even higher T. Additionally, the large range of frequencies and correlation (or jump) rates probed by R1 and R1ρ studiesb can be further extended by R2 measurements. As can be seen from Fig. 8 (b) at about 240 K the SSR rates R2 start to decrease and τ −1 is given by τ −1 ≈ 1/T20 = 1/100 µs where 1/T20 ≡ R20 denotes the spin-spin relaxation rate in the rigid-lattice regime that shows up below 200 K. The lithium jump rate estimated is also included in Fig. 8(a). Altogether, in the case of h-Li0.7 TiS2 correlation rates have been covered over nine decades156, 157 which, as far as NMR studies of Li ion conductors are concerned, seems to have been exceeded up to now only in a beta-NMR investigation of Li3 N.52, 111 Remarkably, a single diffusion process is observed up to 500 K. For comparison with other fast Li ion conductors, at room temperature the rate τ −1 of hexagonal Lix=0.7 TiS2 is in the order of 106 s−1 . According to the Einstein–Smoluchowski equation this translates into a selfdiffusion coefficient DNMR of 10−14 m2 s−1 which represents a good approximate value, if not a benchmark, also for other layerstructured transition metal oxides such as LiCoO2 . As will be shown below, by now there are promising solid electrolytes known which exhibit higher diffusion coefficients at even lower temperatures. Lastly, by comparing the Li jump rates in hexagonal Lix TiS2 with those of the cubic modification as it has been done by Heitjans and co-workers,185 it turned out that Li diffusion in the layered material is by about one order of magnitude faster than in the other polymorph.158 Thus, among other effects, the dimensionality of a translational dynamic process, to which frequency-dependent SLR

b Note that the gap in the dynamic window of R and R 1 1ρ measurements can be closed in certain cases by β-NMR R1 measurements207 and by field cycling NMR relaxometry as well.118

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Fig. 9. (Color Online) 7 Li SLR NMR rates R1ρ of layer-structured Lix NbS2 with x = 0.7.188 The rates were recorded in the rotating frame of reference using two different locking frequencies, viz 5 kHz and 20 kHz. The solid lines show fits using Richards’ spectral density function for 2D diffusion giving an activation energy of 0.43 eV and a pre-exponential factor in the order of 1012 s−1 . Note that any nondiffusive background effects, showing up at high and low temperatures, respectively, could be well approximated with a power law according to R1ρ ∝ T κ .

NMR rates are sensitive to, seem to play an important role for Li diffusion. 2.1.2. Lithium niobium sulfide and lithium borohydride: 2D Li diffusion as probed by frequency-dependent NMR relaxation Besides titanium disulfide also Lix NbS2 (3R modification) has been recently investigated by frequency-dependent 7 Li NMR spectroscopy taking advantage of the spin-lock technique to record R1ρ rates.188 A typical result is shown in Fig. 9. As expected, with increasing ω1 /2π the peaks shift towards higher T indicating increasing Li diffusivity, see Fig. 9. The SLR NMR rates probed are in good agreement with Richards’ prediction184, 200 for a diffusion process strictly confined to two dimensions. Particularly, in Fig. 10 they are shown versus locking frequency; the linear dependence observed at high temperatures, that is, in the limit ω1 τc  1, once again reveals a 2D diffusion process taking place between the NbS2

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(a)

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155

(b)

(Color Online) Frequency-dependence of the 7 Li SLR NMR rates of layer-

Fig. 10. structured Lix=0.7 NbS2 recorded on the high-T side (a) as well as on the low-T flank (b) of the diffusion-induced rate peaks shown in Fig. 9.188 A logarithmic frequency dependence is in agreement with 2D diffusion. In the limit ω1 τ  1 deviations from BPP-type behavior (β = 2) show up manifesting in a β value of β ≈ 1.8.

sheets. For comparison, in the low-T limit, which is characterized by β ω1 τc  1, the corresponding rates follow R1ρ ∝ ω1 . The frequency exponent turns out to be smaller than 2 as it is expected for correlated motion.181, 182, 208, 209 Keep in mind that β is a measure for the deviation from simple BPP-type relaxation behavior.42, 185 Apart from transition metal sulfides other polycrystalline examples showing low-dimensional Li motion, which have been probed by frequency-dependent SLR NMR, are extremely rare.157, 186, 187 In many cases, Li diffusivity is too slow so that the high-temperature flank cannot be reached either due to technical limitations or decomposition of the materials. In other cases interfering non-diffusive background rates dominate SLR NMR and mask the diffusioninduced contribution. Interestingly, the hexagonal modification of LiBH4 ,210, 211 being recently also evaluated as an electrolyte in an all-solid-state lithium battery,212 shows negligible non-diffusive background effects and a high Li diffusivity.213–215 Orthorhombic LiBH4 reversibly transforms into the highly conducting hexagonal form at ca. Thex/ortho = 380 K.216 The 2D nature of Li diffusion in the layered form was probed by both 7 Li and 6 Li

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Fig. 11. (Color Online) (a) Purely diffusion-induced 6 Li SLR NMR rates of hexagonal LiBH4 (P63 mc) whose structure is depicted in (b).187 The frequencydependent rates point to low-dimensional Li diffusion in the hydride; (c) a static 7 Li NMR spectrum revealing the (mean) electric-quadrupolar interactions of the Li spins in LiBH4 .

NMR relaxometry.187 In the case of LiBH4 , the experimental limit for relaxation NMR is given by the relatively low melting point Tm of the hydride; fortunately it is still high enough that a sufficiently large range of the high-T flanks could be probed. The lines shown in Fig. 11 indicate the difference between the 2D and 3D response of SLR NMR. They indicate that the NMR response is in line with the model introduced by Richards’184 for low-dimensional diffusion. 2.1.3. Graphite-based anodes: Li diffusion in ordered LiC6 Considering anode materials in lithium-ion batteries, graphite is certainly the most used negative electrode material. Though precisely studied by temperature-variable beta-NMR112, 217, 218 and QENS219 in the past, quite recently 7 Li SLR NMR measurements in the rotating frame of reference have been carried out to probe Li motions in ordered LiC6 near room temperature.220 Interestingly, in the stage-1 compound (see Fig. 12) Li self-diffusion is lower than expected. Many layer-structured cathode materials show even higher diffusivities compared to the LiC6 . Certainly, Li hopping is expected to increase in diluted samples such as LiC12 . The diffusion-induced SLR rate peak shown in Fig. 13(a) points to a

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Fig. 12. (Color Online) Crystal structure of LiC6 ; (a) view along the ab-plane, (b) view along the c-axis.220 Arrows indicate possible Li diffusion pathways. Mainly in-plane Li self-diffusion takes place between the graphene sheets making LiC6 an interesting model system to study 2D lithium diffusion.

self-diffusion coefficient D in the order of 1.9 × 10−15 m2 s−1 at 314 K. Considering the activation energy probed via NMR this corresponds to 5 × 10−16 m2 s−1 at 293 K.220 In Fig. 13(a), the Arrhenius behavior of R1 , R1ρ , and R2 is shown.220 From SLR NMR in the rotating frame of reference the activation energy of 0.55 eV can be deduced which is in good agreement with that obtained from background-corrected temperaturevariable SSR NMR rates (see Fig. 13(a)). As expected, relatively strong non-diffusive background relaxation superimposes the R1ρ (1/T) peak. Non-diffusive contributions to longitudinal relaxation arise from the interaction of the Li spins with conduction electrons. At sufficiently low temperatures, when R1 in the lab frame becomes less influenced by lithium diffusion, the rates depend almost linearly on temperature which is a clear indication of such interactions. This is also corroborated by NMR chemical shift measurements; the isotropic Knight shift is approximately 42 ppm when referenced to aqueous LiCl.220, 221 As expected, the 7 Li NMR spectrum of a powder sample is characterized by a

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ρ

Fig. 13. Arrhenius plot of the various NMR relaxation rates of LiC6 : (a) SSR rates recorded at 166 MHz; (b) NMR SLR rates measured with the spin-lock technique at 14 kHz; (c) SLR rates acquired with the saturation recovery pulse sequence in the laboratory frame of reference.220 (b) Two selected 7 Li NMR spectra recorded with the solid echo technique at 228 K, that is, in the rigid lattice regime and at 295 K.220

dipolarly broadened central transition whose width is in agreement with Li ions located between the carbon layers with six nearest Li neighbors at a distance of 4.3 Å. Since Li occupies electrically equivalent sites in LiC6 the powder spectrum (Fig. 13) is composed of a single pattern owing to the interaction of the quadrupole moment of the Li spins with a non-vanishing electric field gradient. The situation is very similar to that of hexagonal LiBH4 presented above. However, the NMR spectrum of LiC6 is broadened by homonuclear dipole–dipole interactions at low T, i.e. in the rigid lattice regime. These become averaged with increasing Li motion, see Fig. 13(b). Coming back to Fig. 13, the data points labeled with R1 ,corr represent rates which have been corrected for any non-diffusive background relaxation. They reveal an activation energy of only 0.25 eV being much lower than that deduced from R1ρ and R2 . However, they are comparable with values estimated from NMR

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line shape analyses.220 Most likely, correlation effects and localized jump processes lead to this result while long-range Li diffusion is clearly governed by an activation barrier of approximately 0.55 eV. This value is in good agreement with those calculated by Toyoura et al.222, 223 for different types of in-plane Li diffusion mechanisms including, for example, the interstitial mechanism illustrated in Fig. 12(b). Lastly, Li jump rates of LiC6 which were deduced from various NMR relaxation methods are plotted in Fig. 14.220 Interestingly, a uniform Arrhenius behavior is found spanning a dynamic range T (˚C) 9

200

100

8

50

20

0

-25

-50 LiC6

8

Li β -SLR NMR oriented sample

}

7 log10(1/π / 1/s)

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6

powder sample (this work)

0.

55

5

eV

7

Li SLR 7

Li SSR MN

4

crystal orientations

3 2

onset of MN

||

2.0

2.5

3.0

3.5

4.0

4.5

(1/K)

Fig. 14. (Color Online) Lithium diffusion in ordered LiC6 . The Li jump rates shown were obtained from complementary time-domain NMR methods. Angulardependent 8 Li beta-NMR measurements were carried out on highly oriented pyrolytic graphite112 ; the orientations refer to the c-axis of the crystals. The data points named “MN” were estimated from the onset of motional line narrowing or from the inflexion point of the narrowing curve.220 Analyzing the maximum of the R1ρ (1/T) peak serves as a highly reliable way to determine hopping rates, in general. Altogether, the data points can be approximated with a single Arrhenius relation characterized by 0.55 eV and a pre-factor of approximately 1 × 1014 s−1 , which agrees well with the typical regime of phonon frequencies.

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of many decades and including the relevant temperature range for battery applications. As an illustration, decreasing the temperature from 293 to 268 K (− 5 °C), Li self-diffusivity is slowed down by a factor of 10. Such key figures are crucial for the safe and efficient operation of graphite-based ion batteries. In particular, at freezing temperatures the performance of a battery is then additionally limited and controlled to a large extent by slow Li diffusion within the host material. 2.2. Non-Graphitic Anode Materials There is considerable interest to replace graphite with alternative anode materials including, in particular, titanium oxides5 or siliconbased14 compounds. Besides the various polymorphs of TiO2 which can be prepared with quite different morphologies in nanostructured forms,5, 224 lithium titanate, Li4 Ti5 O12 (LTO)225–227 shows several advantages when used as anode material. However, the quite high, but flat insertion potential of 1.55 V (versus metallic Li) reduces the final voltage of the cell when it is combined with common cathode materials. The zero-strain oxide can accommodate Li ions up to the composition Li7 Ti5 O12 . Apart from LTO, silicon is attractive because of its extremely high theoretical capacity compared to other Li alloys.14 Considerable volume expansion during the formation of Li–Si alloys is one of the major drawbacks that one has to bring under control.228, 229 2.2.1. NMR relaxation rates of polycrystalline Li4+x Ti5 O12 In Fig. 15, the 7 Li NMR SLR rates, recorded at several kHz with the spin-lock technique, are shown for Li4+x Ti5 O12 with x = 0 and x > 0.232 The samples with Li excess were prepared either chemically by treatment with n-butyllithium or electrochemically in Li half cells. Whereas Li diffusion is rather slow in the original sample with x = 0,193 Li insertion, which is accompanied by a transfer of Li ions231 residing from the initial 8a sites to vacant 16c sites (see also the crystal structure depicted in Fig. 16(b)), drastically promotes Li diffusivity.230, 232 This is reflected by a significant shift of the diffusion-induced relaxation rate peak towards lower T. 7 Li NMR

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Fig. 15. (Color Online) (a) NMR SLR rates of microcrystalline Li4+x Ti5 O12 with x = 0 and x > 0. A large increase in Li diffusivity is observed during Li insertion and the diffusion-induced rate peak is shifted towards lower temperatures. In the case of x = 0 it cannot be probed below T ≈ 500 K. (b) NMR line widths of the three samples shown in (a). In agreement with NMR relaxometry, onset of motional narrowing of the Li-rich samples starts at significantly lower T as compared to the situation with x = 0.

line widths measurements, carried out at the same Larmor frequency (77.7 MHz), fully agree with the observations from rotating-frame SLR NMR.230 Note that the increase in Li ion dynamics is in line with a decrease in activation energy; starting with 0.76 eV (as deduced from R1ρ ) the activation energy is only 0.43 eV when the Li content has increased from x = 0 to x ≈ 1.7. Interestingly, the manner Li is inserted, either chemically or electrochemically, does not influence the Li ion diffusion parameters of LTO. Moreover, the NMR rate peaks of the samples with x > 0 can be approximated with a BPP-type179 spectral density function. Hence, correlation effects seem to be almost absent as opposed to the examples mentioned above. A rather high Li+ hopping activation energy of LTO with x = 0 has also been corroborated by (DC) conductivity spectroscopy and stimulated echo, that is, SAE NMR, which is able to probe long-range ion dynamics.102, 193 Recent measurements point to a value of 0.85 eV that classifies the host-anode LTO as a rather poor

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Fig. 16. (Color Online) (a) Li diffusion coefficients of LTO (and Li7 BiO6 ) which have been obtained from DC conductivity measurements as well as from 7 Li SAE NMR.102 (b) Crystal structures of LTO and Li7 BiO6 . Note that increasing x to x ≈ 1.6 has an enormous influence on Li diffusivity. The diffusion coefficient of Li5.7 Ti5 O12 obtained from the SLR NMR rate peak shown in Fig. 15 (a) also shown () and highlighted by the dashed arrow.

ion conductor.233, 234 For comparison, in Fig. 16 diffusion coefficients D, obtained from SAE NMR via conversion of the corresponding decay rates, are compared with D values from DC conductivity measurements. The good agreement shows that SAE NMR is able to probe long-range ion dynamics from a microscopic, that is, an atomic-scale point of view. Similar results were obtained for layerstructured Li7 BiO6 and Li2 TiO3 102, 176, 194 ; the corresponding results from the two complementary methods are also included in Fig. 16. For a better illustration, the drastic increase of Li diffusivity in LTO because of Li insertion is indicated by the dashed arrow pointing to the diffusion coefficient D deduced from rotating-frame SLR NMR on Li5.7 Ti5 O12 . Quantitatively this corresponds to an increase of D by five orders of magnitude which certainly has its impact on the good performance of LTO as an anode material. While Li diffusion is rather slow in LTO, the situation is completely different in Li silicides which are widely considered as high-capacity anode materials.228, 235–237 Recent NMR results on one

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Fig. 17. (Color Online) (a) Crystal structure of Li12 Si7 consisting of Y-shaped Si4 stars and Si5 rings. (b) The NMR signal of the Li ions (Li(6)) centered between the ¨ rings reveals planar Huckel aromaticity of the Si rings.241 (c) 6 Li 2D MAS NMR spectrum of Li12 Si7 (88 MHz and 30 kHz spinning frequency)241 : The NMR signal upfield shifted towards −17 ppm (referenced to aqueous LiCl) gives evidence for an aromatic ring current of the pentadienyl-analogue Si5 units. A very slow exchange process with most of the other ions is observed. This is reflected by the presence of off-diagonal intensities when the spectrum is recorded at a relatively large mixing time of 1 s.

of the most interesting binary compounds, viz single-phase Li12 Si7 , will be briefy discussed in the next section. 2.2.2. Very fast Li ion dynamics in (high capacity) Li–Si binary alloys The use of Si-based anode materials leads to a variety of different Li–Si compounds formed during charging the battery.14 These also include amorphous products.237–239 A recent NMR study on Li-ion diffusivity on polycrystalline Li12 Si7 (Fig. 17), which has been carefully prepared by solid-state reaction, revealed extremely fast Li-ion dynamics at temperatures far below 300 K.240 Most interestingly, the SLR NMR rates, recorded in the rotating frame of reference, clearly show the existence of at least three dynamically quite different relaxation processes (Fig. 18). This corresponds to a stepwise activation of different diffusion mechanisms whereby the fastest one seems to show the characteristics of a one-dimensional motional process.240 The features for 1D diffusion include, in particular, a slope (here, 0.09 eV) of the high-temperature flank which is expected to be

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Fig. 18. (Color Online) (a) Arrhenius plot of the diffusion-induced SLR NMR rates of polycrystalline Li12 Si7 recorded in both the laboratory (77.7 and 155.4 MHz) and rotating frame of reference (39 and 12.4 kHz).240 Dashed lines are to guide the eye. The pronounced maximum recorded in the lab frame is consistent with those of R1ρ showing up below 200 K. (b) Lithium jump rates deduced from the peak maxima shown in (a).240 An activation energy of 0.18 eV for the fastest diffusion process corresponds to 0.09 eV which can be deduced from the corresponding high-temperature flanks of the relaxation rate peaks.

half the one (0.18 eV) of the Arrhenius plot shown in Fig. 18(b). Note that the jump rates in Fig. 18(b) were directly estimated from the maxima of the SLR NMR peaks. Such a very small activation energy of only 0.18 eV is in good agreement with the ultra-fast Li hopping probed in the Zintl phase. Additionally, in contrast to 2D diffusion, for which R1(ρ) diff ∝ ln (τω0(1) ) is valid in the limit ω0(1) τ  1, the diffusion-induced SLR rates of a 1D process −0.5 should be proportional to τ 0.5 ω0(1) . Indeed, in the present case a −0.4 ω0(1) -dependence has been observed.240 This gives clear evidence for a channel-like hopping process which has, so far, not been documented by NMR relaxometry.

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Interestingly, apart from the exceptional dynamic properties of Li12 Si7 , the Zintl phase exhibits some unique electric-magnetic properties due to the complex crystal structure being composed of Y-shaped Si4 stars and Si5 rings. The Li ions sandwiched between these pentadienyl analogue Si5 -rings seem to be tightly bound. They are involved in a slow Li exchange process which can be made visible by high-resolution 6 Li MAS NMR techniques (see Fig. 17(c)).241 Most interestingly, these ions show a telltale upfield NMR shift241 which is a hallmark of (Hückel) aromaticity. Aromaticity, which is primarily found for carbon-containing compounds, is due to the impact of magnetically induced ring currents on the NMR chemical shifts of nearby nuclei, the respective signals are either pushed upfield when located near the interior of the rings or downfield when residing on their periphery. The investigation of further Li–Si Zintl phases as well as the characterization of Li dynamics in Li-silicides formed in batteries is currently an attractive NMR topic. 2.3. Oxides and Sulfides as Promising Solid Electrolytes As outlined in the introduction, extremely fast ion conduction is a prerequisite for a powerful and reliable solid electrolyte. In recent years some very promising candidates have been introduced which include, for example, garnet-type49, 74, 81, 242–245 and argyrodite-type Li-containing oxides and sulfides.71, 246–251 Besides synthesizing new materials with exceptional properties, the improvement of known materials with initially poor Li+ conduction by, e.g. nanostructuring or interface-engineering,252, 253 might also help develop new functional electrolytes.254–264 As an example, the introduction of structural disorder and large volume fractions of interfaces252 by high-energy ball milling174, 265 lead to an increase of the Li ion conductivity of LiTaO3 (and LiNbO3 ) by many orders of magnitude.266, 267 When used as thin films, such structurally disordered materials including nanocrystalline ceramics or even nanoglasses174, 268 may represent interesting solid electrolytes. In particular, this might hold also for so-called nanocrystalline dispersed ion conductors264, 269, 270 or nanocomposites271 which consist of e.g. an Li+ ion conductor and a nano-sized insulator. Composites

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of Li2 O and insulators such as Al2 O3 or B2 O3 have been studied by relaxation NMR recently.264, 272–274 In such two-phase materials, Liions take advantage of fast ion conduction pathways generated by the hetero-contacts of adjacent crystallites.

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2.3.1. Li ion conducting garnets The first publication of Weppner and Thangadurai74 on Li-ion conductivity in garnet-type Li7 La3 Zr2 O12 (LLZ) crystallizing with cubic symmetry stimulated once more many research groups to work on LLZ and related compounds.245 While Li diffusion is only moderate in the tetragonal form of LLZ,80, 275 the cubic modification, which seems to be significantly stabilized at ambient temperature by the introduction of Al, reveals a much higher conductivity. Note that phase-pure tetragonal LLZ transforms into the cubic modification at elevated temperatures.80 However, no abrupt change of Li diffusivity is accompanied with this transformation as revealed by NMR.80 Thus, besides structural stabilization, doping with Al and of course, with other ions,75, 242, 243 greatly pushes Li ion mobility towards high values. Presumably, this is connected to a rearrangement of Li ions having access to multiple sites in Al-doped LLZ. In Fig. 19 selected 7 Li NMR line shapes are shown which have been recorded under static conditions at the temperatures indicated.81 The sample used for NMR investigations contains approximately 5 wt.% Al. Motional narrowing proceeds in a heterogeneous way. Already at relatively low temperatures a small subset of Li ions is mobile on the NMR time scale defined by the rigid lattice line widths. This is reflected by the emergence of a narrowed NMR line on top of the dipolarly broadened Gaussian line fully determining the spectrum at T = 173 K. At 220 K the area fraction Af of the highly mobile ions takes a value of approximately 20%. With increasing T this fraction continuously increases until the NMR line in the regime of extreme narrowing (373 K) is predominantly governed by a Lorentzian shape. In other words, at low temperatures NMR line shapes sense a distribution of Li sub-ensembles while at higher T, a single spin system governs the NMR response. The fluent transition from

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Fig. 19. (Color Online) Temperature-variable 7 Li NMR spectra of Al-doped cubic LLZ prepared by Janek and co-workers,81 via solid-state reaction. The NMR central lines reveal a so-called heterogeneous narrowing owing to dynamically different spin reservoirs.

heterogenous dynamics to homogeneous mobility is expected to show up also in SLR NMR. Indeed, the shape of the rate peaks of R1 and R1ρ (see Fig. 20), and thus also the type of the underlying motional correlation functions, strongly differ from each other.81 Besides the general fact that the two methods should not necessarily probe the same motional correlation function, they are applied in two different temperature regimes where spin dynamics might differ. While Li hopping below 400 K leads to a strict R1 (1/T) Arrhenius behavior characterized by only 0.12 eV, the corresponding R1ρ rates, which were measured at locking frequencies whose values are comparable to that of the rigid-lattice line width, reveal an extremely broad rate maximum covering a large temperature range.

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Fig. 20. (Color Online) (a) 7 Li NMR relaxation rates of cubic Li7 La3 Zr2 O12 recorded in the laboratory and rotating frame of reference at the frequencies indicated.81 For comparison, also SSR rates (R2 ) have been included. (b) Li jump rates determined from the NMR relaxation rate peaks and estimated from motional narrowing (MN) and R2 .81 Moreover, jump rates deduced from impedance spectroscopy are also shown. Note that the right axis refers to Li jump rates read out from the modulus representation of impedance data.

The origin of such behavior could be the superposition of different NMR relaxation rate peaks. Whereas at the lowest temperatures nondiffusive and weakly temperature-dependent background effects show up, above 400 K both rates R1 and R1ρ pass into the same hightemperature flank with an activation energy of 0.34 eV (Fig. 20). For comparison, almost the same value is probed via DC conductivity (Fig. 20(b)), thus giving strong evidence that this value determines long-range ion transport in the bulk. 2.3.2. Li-containing argyrodite-type conductors A few years ago a new class of Li-containing sulfides and selenides was introduced by Deiseroth and co-workers.71 Preliminary conductivity measurements showed an Li conductivity comparable with that recently reported for the channel-structured sulfide prepared by Kanno et al.72 It turned out that the Li-bearing argyrodites, which have been investigated by NMR relaxometry as yet,128 served as excellent model systems to probe extremely fast Li motional processes greatly exceeding those in Al-doped LLZ.

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Fig. 21. (Color Online) (a) 7 Li NMR line widths of three Li-containing argyrodites (Li7 PSe6 , Li6 PSe5 Cl, and Li6 PS5 Br).128 An extremely fast Li hopping process is responsible for the line narrowing process starting at temperatures as low as 87 K. So far, Li dynamics with similar hopping rates have been only rarely detected. (b) Arrhenius plot of the NMR relaxation rates probed at locking frequencies in the kHz range. Data refer to the samples shown in (a).128

This is clearly visible when the motional narrowing curves of Fig. 21 are regarded.128 For the Br-sample averaging of dipolar interactions sets in at an extremely low temperature as low as 87 K. The corresponding 7 Li NMR relaxation rate peak recorded in the rotating frame of reference shows up at Tmax = 167 K. These results give strong evidence that Li jump rates are of the order of 105 s−1 at Tmax . Such fast Li translational motions would correspond to R1 rate peaks showing up around room temperature or below and indeed, this is exactly found and illustrated in the Arrhenius plot of Fig. 22.128 When recorded at a Larmor frequency of ω0 /2π = 116 MHz the rate R1 (1/T) passes through a maximum at 263 K. As expected, reducing the resonance frequency from 116 to 44 MHz in the case of 6 Li, the rate peak can be shifted towards even lower T, viz 238 K. According to the maximum condition being valid at the peak maximum, ω0 τc ≈ 1, the correlation rate τc−1 is close to 109 s−1 near ambient temperature. According to Eq. (10) such a high value translates into an Li ion conductivity in the order of

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Fig. 22. (Color Online) 7 Li and 6 Li NMR relaxation rates of polycrystalline Li6 PS5 Br which have been recorded at the frequencies indicated.128 R1 (1/T) rates pass through characteristic maxima at temperatures slightly lower than ambient. From the (frequency-independent) high-temperature flank of the R1ρ (1/T) peaks an activation energy of only 0.2 eV can be deduced. Altogether, this points an Li conductivity in the order of 10−2 S cm−1 near 300 K, thus, representing liquid-like Li diffusivity in a rigid solid.

10−2 S cm−1 . Correspondingly, the activation energy probed via the high-temperature flank of the R1ρ (1/T) peaks turns out to be rather low guaranteeing fast ion conduction even in the sub-ambient temperature regime. The dynamic parameters found by NMR for Li6 PS5 Br are comparable to those of Li10 GeP2 S12 which is currently one the fastest Li ion conductor known (see Fig. 1).72 It is worth noting that the 6 Li NMR rates are much lower than the 7 Li ones recorded at a higher Larmor frequency of 116 MHz. This is simply due to the fact that diffusion-induced longitudinal relaxation is driven by quadrupolar interactions rather than by magnetic dipole–dipole interactions. The latter would yield much smaller difference in absolute rates. In the case of electric quadrupolar

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SLR the quadrupolar moment of the moving spin, either a spin3/2 or a spin-1 nucleus, interacts with non-vanishing and sitespecific electric field gradients produced by the electric charge distribution at the nuclear site. Since the quadrupolar moment of 6 Li is much smaller than that of 7 Li, the resulting interaction is weaker accordingly. A much less pronounced difference is expected for pure dipolar interactions.80, 129 Interestingly, Li diffusivity increases in the order Li7 PSe6 < Li6 PSe5 Cl < Li6 PS5 Br. Most likely this is the result of local disorder and stress introduced via suitable substitutions of Br for sulfur anions. This facilitates localized jump processes and, as a consequence thereof, also long-range ion transport. The situation is in contrast to a perfectly dense packed anion sub-lattice giving less freedom for the ions to easily move over long distances. A similar situation may be found also in the doped garnets. In Al-doped cubicLLZ the ions have access to a number of vacant crystallographic sites enabling them to use multiple diffusion pathways within an irregularly formed energy landscape. 2.4. Nanostructured Oxides Prepared by High Energy Ball Milling Synthesizing new materials with exceptionally good transport properties is one approach to develop new types of batteries and improve existing ones. Certainly, another route is to modify the morphology of known ion conductors in order to enhance their diffusion parameters while the overall chemical composition remains roughly untouched. Such routes include the synthesis of nanostructured and in particular, nanocrystalline materials by both bottom-up or top-down approaches such as high-energy ball milling.254, 255, 262, 265 Single-phase and two-phase materials might take advantage of Li-ions located in the large volume fraction of (structurally disordered) interfacial regions.262 As an example, Dudley and co-workers recently reported on high Li-ion diffusivity in nanoporous β-Li3 PS4 with a high surface-to-bulk ratio.76 This has led to the development of core-shell cathode materials showing excellent cycling performance in a solid-state battery.276

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Fig. 23. (Color Online) 7 Li NMR spectra of microcrystalline and nanocrystalline LiTaO3 .266 The latter has been prepared by high-energy ball milling of the µm-sized starting material in a shaker mill. The mean crystallite size is about 20 nm; 7 Li NMR reveals a partially disordered structure being responsible for fast ion transport.

In so-called dispersed ion conductors262, 270 highly mobile ions might be found in those regions formed by adjacent nm-sized crystallites differing in chemical composition, that is, an Li-ion conductor such as Li2 O on the one hand and ionically insulating materials such as Al2 O3 or B2 O3 on the other hand.264, 272 Moreover, such non-trivial size effects, which are based on the formation of space charge zones257 merging into each other, are found also for non-Li-ion conductors.270, 277 One of the most prominent examples are epitaxially grown alternating layers of BaF2 and CaF2 .278 Many others, especially those containing Ag as the main charge carrier,256 can be mentioned. The following two examples refer to Li-ion conductors and are used here to exemplarily illustrate the potential of nanocrystalline ceramics to serve as solid electrolytes. An almost entire collection can be found in some of the recently published reviews.262 2.4.1. Single-phase nanocrystalline LiTaO3 Lithium tantalate266 and lithium niobate267, 279–282 as well are known to be poor ion conductors at room temperature. However, the introduction of defects via high energy ball milling, i.e. extensive mechanical treatment in ball mills, enables the preparation of nanocrystalline powders showing improved ion dynamics.266, 267

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Fig. 24. (a) X-ray powder diffraction patterns of micro- and nanocrystalline LiTaO3 prepared by high-energy ball milling.266 (b) High-resolution TEM of nanocrystalline LiTaO3 mechanically treated for 16 h in a shaker mill.266 The sample consists of nm-sized crystallites with diameters in the order of 20 nm and less.

As an example, in Fig. 23 the 7 Li NMR spectra of microcrystalline and nanocrystalline LiTaO3 are compared.266 Li occupies a single crystallographic site in LiTaO3 which results in a well-defined quadrupole powder pattern (see inset of Fig. 23). It illustrates the structurally ordered state of the sample from an atomic-scale point of view. In contrast, mechanical treatment and, thus, the associated introduction of defects leads to a quadrupolar powder pattern due to a distribution of electrically inequivalent sites generated. Structural disorder and the presence of nm-sized crystallites can also be made visible by X-ray powder diffraction (XRPD) and high-resolution transmission electron microscopy (TEM),266 see Fig. 24. While the XRPD pattern of the source material, i.e. before milling, shows sharp reflexes, that of the ball-milled material is largely affected by broadening of the intensities due to reduced crystallite size, strain and disorder as well. Abrasion of Al2 O3 from the vial set used to treat the starting material has negligible influence on the Li-ion transport parameters which have been probed by 7 Li NMR.266 In Fig. 25 7 Li NMR SLR behavior and line narrowing curves are shown for some selected samples.266 The poor ionic diffusivity of

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Fig. 25. (Color Online) (a) 7 Li NMR line narrowing of selected samples of LiTaO3 , non-treated and treated (30 min, 16 h) in a high-energy ball mill.266 (b) 7 Li NMR SLR rates of micro- and nanocrystalline LiTaO3 recorded in the laboratory frame of reference at 77.72 MHz.266

microcrystalline LiTaO3 is reflected by the absence of any narrowing of the Li NMR central transition up to 525 K at least. This drastically changes when the oxide is ball milled. Even after a short period of 30 min significant motional narrowing sets in, which is in line with an increase of the initially low ion conductivity (10−8 S cm−1 at 670 K) by three to four orders of magnitude. An increase of another order of magnitude occurs when the milling time is increased to 16 h. 7 Li NMR spectra of the corresponding sample undergo motional narrowing already starting at temperatures as low as 300 K. A similar behavior is found for LiNbO3 ; in that case, a nanocrystalline sample resembles diffusion behavior of amorphous LiNbO3 .283 The same trend is observed via 7 Li NMR SLR (Fig. 25). Whereas the rates of the microcrystalline sample simply show a non-diffusive relaxation background, those of the sample mechanically treated for 16 h pass over into the diffusion-induced low-T flank of an NMR rate peak. Converting the slope into an activation energy results in 0.37 eV. This value is comparable to that activation energy which can be determined from AC conductivity measurements also performed in the MHz range.266 DC conductivity measurements yield 0.64 eV.266 This value reflects long-range rather than shortrange Li dynamics. Although the conductivity obtained is by far

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extremely high, mechanical treatment and soft synthesis routes in general, offer easily applicable techniques to purposefully manipulate ion dynamics in solids.

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2.4.2. Two-phase nanocrystalline Li2 O:Al2 O3 Since the earlier work by Liang et al.269 many two-phase systems, or dispersed ion conductors,261, 270, 277, 284, 285 have been studied to explore the effect of hetero-contacts on Li ion conductivity.260, 261 The original system investigated by Liang et al. was LiI:Al2 O3 ; they observed that Li-ion conductivity in the composite passes through a maximum at a certain content of insulator added.269 Some years ago Indris et al. prepared a nanocrystalline two-phase composite (1 − x)Li2 O:xB2 O3 and studied conductivity and Li diffusivity.264, 273 Together with the group of Bunde and co-workers264, 272 they were able to explain the conductivity maximum observed by the application of percolation theory.286 At a given volume fraction of the insulator, throughgoing, i.e. non-stoping, and highly conducting pathways are formed which are responsible for the enhanced longrange Li ion transport probed by DC conductivity σDC . In a nanocrystalline composite the volume fraction of interfacial regions is large enough that ions residing in or near these areas can be probed by 7 Li NMR spectroscopy.273 Indeed, the temperaturevariable NMR spectra of (1 − x)Li2 O:xAl2 O3 reveal a characteristic two-component line shape (see Fig. 26) reflecting the ions in the interior of the grains and those located in the interfacial regions.274 Asimilar effect has also been observed for nanocrystalline Lix TiS2 .287, 288 The latter are either generated by homo-contacts (Li2 O:Li2 O) or so-called hetero-contacts (Li2 O:Al2 O3 ), i.e. contacts between two chemically different materials.260 While σDC passes through a maximum as a function of insulator content, its increase manifests in a different but consistent way in 7 Li NMR spectra. The more insulator is added, the more hetero-contacts are formed per volume fraction Li2 O. Therefore, referred to the total number of Li spins, an increasing number fraction is expected to reside in the interfacial regions. Indeed, this behavior is illustrated in Fig. 27.260, 274

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Fig. 26. (Color Online) (a) 7 Li NMR spectrum of nanocrystalline Li2 O being composed of a broad Gaussian shaped line (Li ions in the bulk) and a motionally narrowed component which reflects Li ions in the large volume fraction of interfacial regions.260 (b) Simplified sketch of the two different regions where the dynamically distinct Li spin reservoirs are located.260 (c) Crystal structure of Li2 O,260 the cubic oxygen environment in the anti-fluorite structure leads to a vanishing electric field gradient at the Li sites. Thus, the spectrum in (a) solely reflects central transitions.

Fig. 27. (Color Online) 7 Li NMR spectra of nanocrystalline (1 − x)Li2 O: xAl2 O3 .260, 274 The larger the insulator content Al2 O3 , the more hetero-contacts (bold lines) are generated per volume fraction Li2 O. The conductivity σDC (x) is expected to show a maximum when through going diffusion pathways are formed (see (b)).

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To sum up, nanostructuring single-phase materials by highenergy ball-milling as well as the preparation of two-phase nanocrystalline dispersed ion conductors271 represent a promising route to manipulate ion dynamics and to direct it towards enhanced diffusivities. The concept might also work for ion conductors showing an increased ionic conductivity from the outset, particularly when materials have been combined which greatly differ in crystal structure and hardness, for example. 3. Summary and Outlook Nuclear magnetic resonance serves as a highly versatile tool to probe Li-ion diffusion, that is, translational dynamics, over a broad length scale and time scale. The present chapter focuses on several experimental examples that were used to illustrate how relaxation NMR can be applied to characterize Li-ion hopping in solids. In particular, the measurement of diffusion-induced SLR rates is highly useful to characterize extremely fast Li translational dynamics in solid electrolytes. The SLR rate R1 is per se sensitive to correlation rates in the order of 109 s−1 corresponding to ionic conductivities ranging from 10−3 S cm−1 to 10−2 S cm−1 . Slower motions can be probed by measuring SLR NMR in the rotating frame of reference, line-shape analyses and SAE NMR. In certain cases relaxation NMR, and line shape measurements in particular, is able to quantify dynamic heterogeneities. When SLR NMR is carried out as a function of Larmor frequency, 2D diffusion can be differentiated from the 3D one. Usually, this discrimination is based on models introducing spectral density functions bearing a frequency dependence of the SLR rates in the high-temperature limit. So far, ideal 2D (as well as 1D) Li diffusion has only rarely been documented. It is one of the topics within an Austro-German Research Unit 1277 Mobility of Li Ions in Solids funded by the German Science Foundation (DFG). With an eye towards future studies, the combination of SLR NMR with field gradient NMR techniques and/or field-cycling NMR measurements arouse the interest of those groups working in this field. It nicely illustrates how many complementary

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methods are available taking advantage of the interactions of Li spins with magnetic (and electric) fields. Comparing results from dynamic (time-domain) NMR with those from multi-dimensional high-resolution NMR, which is able to investigate both structure and site-specific dynamics, a powerful set of techniques has been made available during the last decades to characterize Li bearing solids. In this way, NMR spectroscopy can certainly accept the challenge to explore structure-property relationships and thus, to understand Li-ion transport from different viewpoints. This might help us to discover new (nanostructured) materials and manipulate known ionic conductors to advance all-solid-state lithium-ion batteries. Acknowledgment We thank our present and former colleagues at the Graz University of Technology and the Leibniz University Hannover for collaborations, joint papers and many fruitful discussions on Li-ion transport in solids. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) (DFG Research Unit 1277, grant no. WI3600/2-1 and 2-2 as well as 4-1 and 4-2), and by the Austrian Federal Ministry of Economy, Family and Youth, and the Austrian National Foundation for Research, Technology and Development. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

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155. S. Faske, H. Eckert and M. Vogel, Phys. Rev. B. 77 (2008) 104301. 156. M. Wilkening, W. Küchler and P. Heitjans, Phys. Rev. Lett. 97 (2006) 065901. 157. M. Wilkening and P. Heitjans, Phys. Rev. B. 77 (2008) 024311. 158. M. Wilkening and P. Heitjans, Diff. Fundam. 2 (2005) 60. 159. M. Wilkening, A. Kuhn and P. Heitjans, Phys. Rev. B. 78 (2008) 054303. 160. M. Wilkening, C. Lyness, A. R. Armstrong and P. G. Bruce, J. Phys. Chem. C. 113 (2009) 4741. 161. M. Wilkening, J. Heine, C. Lyness, A. R. Armstrong and P. G. Bruce, Phys. Rev. B. 80 (2009) 064302. 162. H. W. Spiess, J. Chem. Phys. 72 (1980) 6755. 163. F. Fujara, S. Wefing and H. Spiess, J. Chem. Phys. 84 (1986) 4579. 164. M. Lausch and H. W. Spiess, J. Magn. Res. 54 (1983) 466. 165. X.-P. Tang, R. Busch, W. Johnson and Y. Wu, Phys. Rev. Lett. 81 (1998) 5358. 166. X.-P. Tang, U. Geyer, R. Busch, W. Johnson and Y. Wu, Nature. 402 (1999) 160. 167. X.-P. Tang and Y. Wu, J. Magn. Res. 133 (1998) 155. 168. F. Qi, T. Jörg and R. Böhmer, Solid State Nucl. Magn. Res. 22 (2002) 484. 169. F. Qi, G. Diezemann, H. Böhm, J. Lambert and R. Böhmer, J. Magn. Res. 169 (2004) 225. 170. F. Qi, C. Rier, R. Böhmer, W. Franke and P. Heitjans, Phys. Rev. B. 72 (2005) 104301. 171. S. Faske, B. Koch, S. Murawski, R. Küchler, R. Böhmer, J. Melchior and M. Vogel, Phys. Rev. B. 84 (2011) 024202. 172. C. Brinkmann, S. Faske, B. Koch and M. Vogel, Z. Phys. Chem. 224 (2010) 1535. 173. A. Abragam, The Principles of Nuclear Magnetism, (Clarendon, Oxford, 1961). 174. P. Heitjans, E. Tobschall and M. Wilkening, Eur. Phys. J. — Special Topics. 161 (2008) 97. 175. J. G. Schiffmann, J. Kopp, G. Geisler, J. Kroeninger and L. van Wüllen, Solid State Nucl. Magn. Reson. 49–50 (2013) 23–25. 176. M. Wilkening, C. Mühle, M. Jansen and P. Heitjans, J. Phys. Chem. B. 111 (2007) 8691. 177. J. R. Hendrickson and P. J. Bray, J. Magn. Res. 9 (1973) 341. 178. M. Storek, R. Böhmer, S. W. Martin, D. Larink and H. Eckert, J. Chem. Phys. 137 (2012) 124507. 179. N. Bloembergen, E. M. Purcell and R. V. Pound, Phys. Rev. 73 (1948) 679. 180. K. L. Ngai, Comments Solid State Phys. 9 (1980) 141. 181. K. Funke, Prog. Solid State Chem. 22 (1993) 111.

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182. A. Bunde, W. Dieterich, P. Maass, and M. Meyer, in Diffusion in Condensed Matter — Methods, Materials, Models, eds. P. Heitjans and J. Kärger, Chapter 20, pp. 813–856. Springer, Berlin, (2005). 183. E. Goebel, W. Müller-Warmuth, H. Olyschläger and H. Dutz, J. Magn. Res. 36 (1979) 371. 184. P. M. Richards, in Topics in Current Physics, ed. M. B. Salamon, Springer, Berlin, 15 (1979). 185. W. Küchler, P. Heitjans, A. Payer and R. Schöllhorn, Solid State Ion. 70/71 (1994) 434. 186. A. F. McDowell, C. F. Mendelsohn, M. S. Conradi, R. C. Bowman and A. J. Maeland, Phys. Rev. B. 51 (1995) 6336. 187. V. Epp and M. Wilkening, Phys. Rev. B. 82 (2010) 020301. 188. V. Epp, S. Nakhal, M. Lerch and M. Wilkening, J. Phys.: Condens. Matter. 25 (2013) 195402. 189. J. Jeener and P. Broekaert, Phys. Rev. 157 (1967) 232. 190. M. Vogel, C. Brinkmann, H. Eckert and A. Heuer, Phys. Chem. Chem. Phys. 4 (2002) 3237. 191. M. Vogel, C. Brinkmann, H. Eckert and A. Heuer, J. Non-Cryst. Solids. 307 (2002) 971. 192. R. Böhmer, J. Magn. Res. 147 (2000) 78. 193. M. Wilkening, R. Amade, W. Iwaniak and P. Heitjans, Phys. Chem. Chem. Phys. 9 (2006) 1239. 194. B. Ruprecht, M. Wilkening, R. Uecker and P. Heitjans, Phys. Chem. Chem. Phys. 14 (2012) 11974. 195. B. Koch and M. Vogel, Solid State Nucl. Magn. Res. 34 (2008) 37. 196. M. S. Whittingham, Prog. Solid State Chem. 12 (1978) 41. 197. M. S. Whittingham, R. Chen, T. Chirayil and P. Zavalij, Solid State Ion. 94 (1997) 227. 198. M. S. Whittingham, Solid State Ion. 134 (2000) 169. 199. B. Silbernagel and M. Whittingham, J. Chem. Phys. 64 (1976) 3670. 200. P. M. Richards, Solid State Commun. 25 (1978) 1019. 201. M. Wilkening and P. Heitjans, Defect Diffus. Forum. 237–240 (2005) 1182. 202. T. Bredow, P. Heitjans, and M. Wilkening, Phys. Rev. B. 70 (2004) 115111. 203. W. Bensch, T. Bredow, H. Ebert, P. Heitjans, S. Indris, S. Mankovsky and M. Wilkening, Progr. Solid State Chem. 37 (2009) 206. 204. A. Van der Ven, J. C. Thomas, Q. Xu, B. Swoboda and D. Morgan, Phys. Rev. B. 78 (2008) 104306. 205. C. Ramírez, R. Adelung, L. Kipp and W. Schattke, Phys. Rev. B. 73 (2006) 195406. 206. C. Ramírez, R. Adelung, R. K. L. Kipp and W. Schattke, Phys. Rev. B. 71 (2005) 035426.

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207. P. Heitjans, A. Körblerin, H. Ackermann, D. Dubbers, F. Fujara and H.-J. Stöckmann, J. Phys. F. 15 (1985) 41. 208. K. Ngai, Phys. Rev. B. 48(18) (1993) 13481. 209. M. Meyer, P. Maass and A. Bunde, Phys. Rev. Lett. 71 (1993) 573. 210. A. Soloninin, A. Skripov, A. Buzlukov and A. Stepanov, J. Solid State Chem. 182(9) (2009) 2357. 211. R. L. Corey, D. T. Shane, R. C. Bowman and M. S. Conradi, J. Phys. Chem. C. 112 (2008) 19784. 212. K. Takahashi, K. Hattori, T. Yamazaki, M. M. K. Takada, S. Orimo, H. Maekawa and H. Takamura, J. Power Sources. 226 (2013) 61. 213. M. Matsuo, Y. Nakamori, S. Orimo, H. Maekawa and H. Takamura, Appl. Phys. Lett. 91 (2007) 224103. 214. H. Maekawa, M. Matsuo, H. Takamura, M. Ando, Y. Noda, T. Karahashi and S. Orimo, J. Am. Chem. Soc. 131 (2009) 894. 215. T. Ikeshoji, E. Tsuchida, T. Morishita, K. Ikeda, M. Matsuo, Y. Kawazoe and S. Orimo, Phys. Rev. B. 83 (2011) 144301. 216. M. Matsuo, H. Takamura, H. Maekawa, H. Li and S. Orimo, Appl. Phys. Lett. 94 (2009) 084103. 217. P. Freiländer, P. Heitjans, H. Ackermann, B. Bader, G. Kiese, A. Schirmer and H.-J. Stöckmann, Z. Naturforsch. 41a (1986) 109. 218. A. Schirmer and P. Heitjans, Z. Naturforsch. 50a (1995) 643. 219. A. Magerl, H. Zabel and I. S. Anderson, Phys. Rev. Lett. 55 (1985) 222. 220. J. Langer, V. Epp, P. Heitjans, F. A. Mautner and M. Wilkening, Phys. Rev. B. 88 (2013) 094304. 221. M. Letellier, F. Chevallier and F. Béguin, J. Phys. Chem. Solids. 67 (2006) 1228. 222. K. Toyoura, Y. Koyama, A. Kuwabara, F. Oba and I. Tanaka, Phys. Rev. B. 78 (2008) 214303. 223. K. Toyoura, Y. Koyama, A. Kuwabara and I. Tanaka, J. Phys. Chem. C. 114(5) (2010) 2375. 224. A. Armstrong, G. Armstrong, J. Canales, R. Garcia and P. Bruce, Adv. Mater. 17 (2005) 862. 225. M. Thackeray, J. Electrochem. Soc. 142(8) (1995) 2558. 226. E. Ferg, R. Gummow, A. de Kock and M. Thackery, J. Electrochem. Soc. 141 (1994) L147. 227. L. Kavan and M. Grätzel, Electrochem. Solid State Lett. 5 (2002) A39. 228. M. Obrovac and L. Christensen, Electrochem. Solid State Lett. 7(5) (2004) A93. 229. J. Dahn, W. McKinnon, R. Haering, W. Buyers and B. Powell, Can. J. Phys. 58 (1980) 207. 230. M. Wilkening, W. Iwaniak, J. Heine, V. Epp, A. Kleinert, M. Behrens, G. Nuspl, W. Bensch and P. Heitjans, Phys. Chem. Chem. Phys. 9 (2007) 6199.

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231. M. Wagemaker, D. R. Simon, E. M. Kelder, J. Schoonman, C. Ringpfeil, U. Haake, D. Lützenkirchen-Hecht, R. Frahm and F. M. Mulder, Adv. Mater. 18(23) (2006) 3169. 232. M. Wagemaker, E. R. H. van Eck, A. P. M. Kentgens and F. M. Mulder, J. Phys. Chem. B. 113(1) (2009) 224. 233. W. Iwaniak, J. Fritzsche, M. Zukalova, R. Winter, M. Wilkening and P. Heitjans, Def. Diff. Forum. 289–292 (2009) 565. 234. J. Haetge and P. Hartmann and K. Brezesinski and J. Janek and T. Brezesinski, Chem. Mater. 23(19) (2011) 4384. 235. C. Chan, H. Peng, G. Liu, K. McIlwrath, X. F. Zhang, R. A. Huggins and Y. Cui, Nature Nanotechn. 3(1) (2008) 31. 236. M.-H. Park, M. G. Kim, J. Joo, K. Kim, J. Kim, S. Ahn, Y. Cui and J. Cho, Nano Lett. 9(11) (2009) 3844. 237. J. Li and J. R. Dahn, J. Electrochem. Soc. 154(3) (2007) A156. 238. A. Netz, R. A. Huggins and W. Weppner, J. Power Sources. 119–121 (2003) 95. 239. P. Limthongkul, Y.-I. Jang, N. J. Dudney and Y.-M. Chiang, Acta Mater. 51 (2003) 1103. 240. A. Kuhn, P. Sreeraj, R. Pöttgen, H.-D. Wiemhöfer, M. Wilkening and P. Heitjans, J. Am. Chem. Soc. 133 (2011) 11018. 241. A. Kuhn, P. Sreeraj, R. Pöttgen, H.-D. Wiemhöfer, M. Wilkening and P. Heitjans, Angew. Chem. Inter. Ed. 50(50) (2011) 12099. 242. E. Rangasamy, J. Wolfenstine and J. Sakamoto, Solid State Ion. 206 (2012) 28. 243. J. L. Allen, J. Wolfenstine, E. Rangasamy and J. Sakamoto, J. Power Sources. 206 (2012) 315. 244. S. Narayanan, V. Epp, M. Wilkening and V. Thangadurai, RSC Adv. 2(6) (2012) 2553. 245. V. Tangadurai, S. Narayanan and D. Pinzaru, Chem. Soc. Rev. 43 (2014) 4714. 246. S. T. Kong, O. Gün, B. Koch, H. J. Deiseroth, H. Eckert and C. Reiner, Chem. — Eur. J. 16 (2010) 5138. 247. O. Pecher, S.-T. Kong, T. Goebel, V. Nickel, K. Weichert, C. Reiner, H.-J. Deiseroth, J. Maier, F. Haarmann and D. Zahn, Chem. Euro. J. 16 (2010) 8347. 248. S. Boulineau, M. Courty, J.-M. Tarascon and V. Viallet, Solid State Ion. 221 (2012) 1. 249. S. Boulineau, J.-M. Tarascon, J.-B. Leriche and V. Viallet, Solid State Ion. 242 (2013) 45. 250. R. P. Rao, N. Sharma, V. K. Peterson and S. Adams, Solid State Ion. 230 (2013) 72.

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251. R. P. Rao and S. Adams, Phys. Status Solidi A — Appl. Mater. Sci. 208(8) (2011) 1804. 252. H. Gleiter, Acta Mater. 48 (2000) 1. 253. H. Gleiter, Beilstein J. Nanotechn. 4 (2013) 517. 254. M. Pooley and A. Chadwick, Rad. Eff. Def. Solids. 158 (2003) 197. 255. S. L. P. Savin, A. V. Chadwick, L. A. O’Dell and M. E. Smith, Solid State Ion. 177 (2006) 2519. 256. J. Maier, Nature Mater. 4(11) (2005) 805. 257. J. Maier, Progr. Solid State Chem. 23(3) (1995) 171. 258. J. Maier, Solid State Ion. 175 (2004) 7. 259. J. Maier, Z. Phys. Chem. Inter. Ed. 217(4) (2003) 415. 260. P. Heitjans and M. Wilkening, Mat. Res. Bull. 34(12) (2009) 915. 261. P. Heitjans and M. Wilkening, Def. Diff. Forum. 283–286 (2009) 705. 262. P. Heitjans and S. Indris, J. Phys. Condens. Matter. 15(30) (2003) R1257. 263. P. Heitjans and S. Indris, J. Mater. Sci. 39 (2004) 5091. 264. S. Indris and P. Heitjans and H.E. Roman and A. Bunde, Phys. Rev. Lett. 84 (2000) 2889. 265. S. Indris, D. Bork and P. Heitjans, J. Mater. Synth. Proc. 8(3–4) (2000) 245. 266. M. Wilkening, V. Epp, A. Feldhoff and P. Heitjans, J. Phys. Chem. C. 112(25) (2008) 9291. 267. P. Heitjans and M. Masoud and A. Feldhoff and M. Wilkening, Faraday Discuss. 134 (2007) 67. 268. A. Kuhn, M. Wilkening and P. Heitjans, Solid State Ion. 180(4–5) (2009) 302. 269. C. C. Liang, J. Electrochem. Soc. 120 (1973) 1289. 270. P. Knauth, J. M. Debierre and G. G. Albinet, Solid State Ion. 121(1–4) (1999) 101. 271. P. Knauth and J. Schoonman, eds., Nanocomposites: Ionic Conducting Materials and Structural Spectroscopies. (Springer, Berlin, 2008). 272. S. Indris, P. Heitjans, M. Ulrich and A. Bunde, Z. Phys. Chem. 219(1) (2005) 89. 273. S. Indris and P. Heitjans, J. Non-Cryst. Solids. 307 (2002) 555. 274. M. Wilkening, S. Indris and P. Heitjans, Phys. Chem. Chem. Phys. 5(11) (2003) 2225. 275. J. Awaka, N. Kijima, H. Hayakawa and J. Akimoto, J. Solid State Chem. 182 (2009) 2046. 276. Z. Lin, Z. Liu, N. J. Dudney and C. Liang, ACS Nano. 7(3) (2013) 2829. 277. J. Debierre, P. Knauth and G. Albinet, Appl. Phys. Lett. 71(10) (1997) 1335. 278. N. Sata, K. Eberman, K. Eberl and J. Maier, Nature. 408(6815) (2000) 946. 279. K. N. A. M. Glass and T. J. Negran, J. Appl. Phys. 49 (1978) 4808. 280. M. Masoud and P. Heitjans, Def. Diff. Forum. 237–240 (2005) 1016.

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281. D. Bork and P. Heitjans, J. Phys. Chem. B. 102(38) (1998) 7303. 282. D. Bork and P. Heitjans, J. Phys. Chem. B. 105(38) (2001) 9162. 283. M. Wilkening, D. Bork, S. Indris and P. Heitjans, Phys. Chem. Chem. Phys. 4 (2002) 3246. 284. P. Heitjans, S. Indris and M. Wilkening, Nanocomposites: Ionic Conducting Materials and Structural Spectroscopies, Dynamical aspects of nanocrystalline ion conductors studied by NMR. Springer, Berlin, (2008). 285. P. Knauth, J. Electroceram. 5 (2000) 111. 286. A. Bunde, W. Dieterich and E. Roman, Phys. Rev. B. 55(1) (1985) 5. 287. R. Winter and P. Heitjans, J. Non-Cryst. Solids. 293 (2001) 19. 288. R. Winter and P. Heitjans, J. Phys. Chem. B. 105(26) (2001) 6108.

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Chapter 6

Crystalline Inorganic Solid Electrolytes: Computer Simulations and Comparisons with Experiment M. D. Johannes

Materials Science and Technology Division US Naval Research Laboratory Washington, DC 20375, USA

N. A. W. Holzwarth

Department of Physics Wake Forest University Winston-Salem, NC 27106, USA

This chapter presents examples of the use of first principles computer simulations in the study of two families of solid electrolyte materials — namely the family of Li phosphate, phospho-nitride, and thiophosphate materials and the family of Li oxide garnet materials. The simulation work together with related experimental studies of these solid electrolytes supports the continued development of all-solid-state battery technology.

1. Introduction and Overview The use of crystalline solids as electrolytes in battery applications has a long history as discussed in several review articles and monographs.1, 2 The purpose of this chapter is to describe examples of the use of first-principles calculations in the development of two families of solid electrolyte materials — namely Li phosphates and thiophosphates (Sec. 2) and Li oxide garnets (Sec. 3). Beyond 191

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the scope of this chapter, there have been quite a few successful first-principles studies of other electrolytes. For example, the recent experimental discovery of Li10 GeP2 S12 as a superionic conductor by Kamaya et al.3 has generated significant experimental and theoretical work including a study of the phase and electrochemical stability and Li+ conductivity by Ong et al..4 1.1. Computational Methods The computations discussed in this work are based on so-called “first-principles” electronic structure methods. The term “firstprinciples” implies a series of well-developed approximations to the exact quantum-mechanical description of a material with Ne electrons and NN nuclei. Denoting the electron coordinates by {r i } (i = 1, 2, . . . , Ne ) and nuclear coordinates by {Ra } (a = 1, 2, . . . , NN ), the many-particle Schrödinger equation takes the form H({ri }, {Ra })
α ({ri }, {Ra }) = Eα
α ({ri }, {Ra }),

(1)

where H denotes the quantum mechanical Hamiltonian, Eα and
α ({ri }, {Ra }) denote the energy eigenvalue and the corresponding eigenfunction, respectively. The solution of Eq. (1) with NN Ne coupled variables, is intractable for all but the smallest systems. The analysis of Born and Oppenheimer,5 noting that the electron mass is 10−3 times smaller than the nuclear mass, leads to an approximate separation of the nuclear and electronic motions. Operationally, the nuclei are treated as classical particles with interaction energies consistently determined by expectation values of the electronic Hamiltonian. The electronic Hamiltonian and the corresponding Schrödinger equation should be solved for each set of nuclear positions {Ra }. The solution of the Born–Oppenheimer electronic Schrödinger equation is further approximated with the use of density functional theory developed by Kohn, Hohenberg, and Sham,6, 7 treating the Ne electrons in a self-consistent mean-field due to both the electrons and nuclei. The reliability of density functional theory in the representation of real materials depends on the development of the exchange-correlation functional form. While this remains an active area of research, the local density

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approximation (LDA)8 and the generalized gradient approximation (GGA)9 often work well, particularly for modeling the ground state properties of solid electrolytes. In density functional theory, the electronic energy of a system of Ne electrons can be expressed as a sum of contributions:

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E(ρ, {Ra }) = EK + Eee + Exc + EeN + ENN ,

(2)

representing the electronic kinetic energy, the coulombic electronelectron repulsion, the exchange-correlation energy, the electron– nuclear interaction energy, and the nuclear–nuclear interaction energies respectively. The electron density ρ(r) is self-consistently determined from Kohn–Sham single particle wavefunctions for each state n: H

KS

ψn = n ψn

where ρ(r) =

Ne


|ψn (r)|2

(3)

n=1

at self-consistency. The Kohn–Sham Hamiltonian is determined from the functional derivative H KS =

∂E(ρ, {Ra }) . ∂ρ(r)

(4)

In addition to well-controlled mathematical and physical approximations, numerical approximations are needed to solve the density functional equations. There are many successful numerical schemes many of which grew from the frozen-core approximation10 and the refinement of the pseudopotential formalism11 with the development of first-principles pseudopotentials.12, 13 A significant boost to the field was contributed by Car and Parrinello14 who showed that within the Born–Oppenheimer approximation, the self-consistent electronic structure algorithm could be efficiently coupled to the adjustment of the nuclear coordinates for structural and molecular dynamics studies. In addition to the adjustment of the nuclear coordinates, techniques were developed to allow for variable simulation cells in order to simulate the effects of pressure, stress, or phase transitions.15–17 Response function methods and density-functional perturbation theory methods were developed

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by Gonze,18, 19 allowing for the exploration of materials properties in the vicinity of equilibrium including the dynamical matrix and phonon modes. The efficiency and accuracy of the pseudopotential approach was significantly improved with the introduction of so-called ultra-soft pseudopotentials (USPP) by Vanderbilt20 and the projector-augmented plane wave (PAW) method by Blöchl.21 An invaluable contribution to the success of computational studies of materials, particularly those discussed in this chapter, has been the development of several open source software projects such as ABINIT22 and QUANTUM ESPRESSO.23 These codes make use of many of the state-of-the-art formalism developments including those listed above. These projects promote scientific productivity by reducing the duplication of coding efforts and by allow developers and users to share in the implementation and debugging of a common code system. For the simulations in Sec. 2, the pseudopotential data files were generated using the ATOMPAW package24 and the USPP package.20 For the simulations in Sec. 3, the Vienna Ab Initio Software Package (VASP) was used.25, 26 Also important is the development of visualization tools. For this work, OpenDx,27 XCrySDen,28, 29 and VESTA30 were used. For solid electrolytes which are electronically insulating and which operate in their ground electronic states, the calculation of the electronic energy E(ρ, {Ra }) using density functional theory (Eq. (2)) works quite well. By using constrained optimization of the energy E(ρ, {Ra }) over the nuclear coordinates {Ra }, it is possible to study structural parameters of stable and meta-stable structures. A reasonable estimate of the heat of formation H of each compound material can be computed from the ground state energies at zero temperature
H ≈ E(ρ, {Ra }) − νe Ee (ρ, {Ra }), (5) e

where E(ρ, {Ra }) denotes the computed electronic energy of the material per formula unit, νe denotes the number of atoms of element “e” in the formula unit, and Ee (ρ, {Ra }) denotes the energy per atom in its standard state of the element as defined in the CRC Handbook31 or the NIST JANAF Thermochemical Tables.32 In practice, the calculation of E(ρ, {Ra }) is subject to an arbitrary

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reference energy which depends on the details of the code and of the pseudopotential datasets. If the electronic energy calculations for E and Ee are evaluated consistently with accurate convergence criteria, the ambiguity of the total energy disappears from the evaluation of Eq. (5). These measured and computed heats of formation are useful in quantifying the expected stability of the materials in various structures and compositions. The first-principles approach can be extended to simulate ion mobilities. For example, the “nudged elastic band”33–35 method (NEB) can be used to estimate the migration energy Em . The basic assumptions of this approach34 are that the ion diffusion is slow enough so that the process is well described by Boltzmann statistics and that the diffusion rate is controlled by ion trajectories which pass through harmonic regions of the potential energy surface near minima and saddle points which represent transition states of the system. The computational effort is thus focused on finding the saddle points of the potential energy surfaces between local minimum energy configurations. Each of the diffusion paths considered is approximated by a series of transitions between pairs of local minima corresponding to meta-stable configurations. The search for the saddle point is implemented by assuming several intermediate “images” between each pair of local minima. Each of the images is relaxed until the forces perpendicular to the minimum energy path are less than the prescribed tolerance level. The energies between each pair of local minima is determined by interpolating between the energies of the images and Em is determined from the difference between the highest and lowest energy along the path. The migration energy is related to the temperature dependent ionic conductivity σ(T) with an Arrhenius relation36, 37 σ(T) =

K −EA /kT e , T

(6)

where the prefactor K depends on the material and k denotes the Boltzmann constant. In the case of a material with few intrinsic defects, the activation energy includes both the ion migration energy Em and also the “formation" energy Ef associated with the creation of a defect. The usual case is that Ef is the energy to create a

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vacancy-interstitial pair and the activation energy is given by

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1 EA = Em + Ef . 2

(7)

This method was used to analyze the Li ion conductivity in Subsec. 2.3. In addition, the dynamics of Li ion diffusion subject to temperature were carried out using molecular dynamics (MD) simulations with the energies and forces derived from first principles (VASP) calculations at each time step. The results from MD simulations provide a convenient comparison to the NEB calculations from a more integrated, statistical point of view. While NEB calculations specifically evaluate the activation barrier by calculating the energy curve along a real-space trajectory, MD simulations are statistical and the activation barrier extracted is an “effective” barrier — essentially the average barrier experienced by the movement of all Li-ions in the simulation. The mean squared displacement of the Li-ions < x2 > is measured as a function of time and the diffusion constant, D can be extracted via the following: D=

1 d( < x2 > ) 6 dt

(8)

where the factor of 6 comes from the three-dimensionality of the diffusion path. This analysis was used in Subsec. 3.5. Because diffusivity is activated, performing MD evaluations of < x2 > at various temperatures and fitting to an Arrhenius plot will yield an activation barrier of the form D = D0 e−EA /kT .

(9)

A comparison of EA derived in this manner from MD to NEB results can provide an estimate of Ef and also can reveal whether there is a single or perhaps many different Li ion paths accessed during diffusion. In principle, one advantage of the MD approach is that the prefactor D0 is also determined, while the corresponding prefactor K of Eq. 6 is not computed in the NEB approach.

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1.2. Validation It is always important to ask the question: How reliable are computer simulations in describing real materials. Typically, it has been reported41 that results obtained using the LDA exchange-correlation functional8 tend to underestimate the lattice parameters by 2% while results obtained using the GGA exchange-correlation functional9 tend to overestimate the lattice parameters by 1%. On the other hand, for most materials, the fractional coordinates computed for the non-trivial site positions are nearly identical (within 0.1%) for LDA and GGA calculations in comparison with experiment. Similar findings have been reported in the literature for a wide variety of computational studies of insulating, non-transition metal materials. One quantitative indication of the accuracy of the calculations is the comparison of computed and measured lattice vibration modes. Fortunately, there have been several reports of experimental measurements of Raman and infrared absorption spectra of crystalline Li3 PO4 38–40, 42–44 ; therefore our simulations of the zone center phonon modes serve as a validity check the calculations. Figure 1

ν

ν

Fig. 1. Comparison of experimental and calculated Raman spectra for γ-Li3 PO4 (left) and β-Li3 PO4 (right). The experimental measurements were performed at room temperature (RT) and at liquid nitrogen temperature (NT). Exp. A was taken from Ref. [38] and Exp. B and C were taken from Ref. [39], and Exp. D was taken from Ref. [40]. These are compared with calculated results using PAW and USPP formalisms and LDA and GGA exchange-correlation functionals.

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shows the spectra of Raman active modes calculated using the LDA and GGA exchange-correlation functions and USPP20 and PAW24 pseudopotential datasets compared with various experimental measurements for the γ and β structures. There is variation among the various experimental measurements for γ-Li3 PO4 , some of which can be attributed to temperature and some attributed to resolution. In terms of comparing experiment to the calculations, it is striking that for frequencies ν > 600 cm−1 , the results calculated using the LDA functional are in good agreement with experiment, while the agreement deteriorates at lower frequencies. These high-frequency modes are mainly due to internal vibrations of the PO4 tetrahedra. The lack of agreement for the lower frequency modes is likely to be due to numerical error which is reflected in the differences between the two LDA calculations using USPP and PAW datasets. The good agreement between the simulations and experiment for the higher frequency vibrational modes of these materials motivated the choice of the LDA functional for most the simulation studies on the Li phosphates and thiophosphates covered in this review (Sec. 2).41, 45–53 On the other hand, for the simulations of garnet oxide materials discussed in Sec. 3 of this review, a sensitivity to more accurate lattice parameters motivated the choice of the GGA functional.54 2. Li Phosphate, Phospho-Nitride and Thiophosphate Crystalline Electrolytes The thin-film solid electrolyte LiPON developed at Oak Ridge National Laboratory (ORNL),55–63 is a very widely used solid electrolyte for thin-film batteries and a number of other related technologies.64 In addition to studies at ORNL, there has been considerable research65–68 on the preparation and properties of LiPON materials. One of the outstanding attributes of LiPON electrolytes is its long-term stability in contact with a pure lithium anodes.69 By contrast, several other electrolyte candidates, such as for example lithium silicates and lithium silicate/phosphate composites, have been found63 to react with lithium anode films. LiPON electrolytes

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have the composition of Lix POy Nz . The LiPON electolytes with the highest ionic conductivities (10−6 S/cm) have a glassy structure and a range of values of 0.2 ≤ z ≤ 0.7 representing the ideal nitrogen contribution.55, 65, 70 At the present time, we know of no experimental evidence that crystalline members of the LiPON family of materials can approach the conductivities of the LiPON glasses, however, a systematic study of the LiPON family of crystalline materials49 has proven useful for developing an understanding of the fundamental structures and properties of LiPON electrolytes. Meanwhile, the structurally and chemically related Li thiophosphate family of materials have recently received attention as promising candidates for solid-state electrolytes71–81 where increased ionic conductivities as large as 10−3 S/cm have been reported. These materials are characterized by the composition Liv PSw . The comparison between the crystalline Li phosphates and corresponding thiophosphates has provided further insight into solid electrolyte development. Subsection 2.1 presents the energetics of lithium phosphates, lithium phospho-nitrides, and lithium thiophosphates and related compounds. In order to facilitate comparisons between materials and comparisons of calculations with experiment, the material energies are expressed in terms of the heats of formation. Subsection 2.2 details the structural forms such as phosphate and thiophosphate monomers, dimers, and chains found from experiment and computation in view of their relative stabilities. Subsection 2.3 reviews the calculated and experimental Li-ion conduction properties of these materials. 2.1. Heats of Formation The estimation of the heat of formation H as given in Eq. (5) has been been carried out for a large number of Li phosphate, Li phospho-nitride, and Li thiophosphate crystals as listed in Table 1. For these materials, the elemental reference states are given as follows. Li is referenced to solid Li in its body-centered cubic structure which is modeled directly. P is referenced to its “white" structural form. Since this structure is difficult to model directly, the calculations first simulated the structure of “black" phosphorus in

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¯ P31m (#162) P1¯ (#2) P1¯ (#2) ¯ P31m (#162) P1¯ (#2)

−29.72 −33.97 −33.18 −12.42 −11.59

Li7 P3 O11 Li7 P3 S11

P1¯ (#2) P1¯ (#2)

−54.84 −20.01

LiPO3 LiPN2 s1-Li2 PO2 N SD-Li2 PO2 N

P2/c (#13) ¯ (#122) I 42d Pbcm (#57) Cmc21 (#36)

−12.75 −3.65 −12.35 −12.47

Cmc21 (#36) P63 /mmc (#194) C2/c (#15) R3c (#161) Fdd2 (#43) P1¯ (#2) Pnma (#62) Pna21 (#33)

−5.80 −0.94 (−0.45∗ ) −3.02 (−3.32∗ ) −15.45 (−15.53∗ ) −15.78 −1.93 −2.45 (−2.33) −4.84 (−4.71∗ )

Li3 N Li2 O Li2 O2 Li3 P Li2 S Li2 S2

P6/mmm (#191) ¯ (#225) Fm3m P63 /mmc (#194) P63 /mmc (#194) ¯ (#225) Fm3m P63 /mmc (#194)

−1.60 (−1.71∗ ) −6.10 (−6.20∗ ) −6.35 (−6.57∗ ) −3.47 −4.30 (−4.57) −4.09

LiNO3 Li2 SO4

¯ (#167) R3c P21 /c (#14)

−5.37 (−5.01∗ ) −14.63 (−14.89∗ )

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Li4 P2 O6 Li4 P2 O7 Li5 P2 O6 N Li4 P2 S6 Li4 P2 S7

SD-Li2 PS2 N N 2 O5 P3 N5 h-P2 O5 o-P2 O5 P2 S5 P4 S3 SO3

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−21.23 −21.20 (−21.72∗ ) −8.37 −8.28

Structure

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Pmn21 (#31) Pnma (#62) Pmn21 (#31) Pnma (#62)

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H (eV/FU)

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H (eV/FU)

Material

200

Table 1. Calculated heats of formation for Li phosphates, phospho-nitrides, and thiophosphates and related materials. The structural designation uses the the notation defined in the International Table of Crystallography85 based on structural information reported in the International Crystal Structure Database.86 The heats of formation H (eV/FU) are given in units of eV per formula unit. When available from Refs. [31] and [32], experiment values are indicated in parentheses. Those indicated with “*" were used fitting the O and N reference energies as explained in the text.

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its orthorhombic structure (Cmce (#64))82 and the white P reference energy was determined by adding the experimental value31 of the heat of formation for white P relative to black P of 39.3 kJ/mol. S is referenced to its orthorhombic structure (α-S8 — Fddd (#70))83 which is modeled directly. O and N are referenced to their gaseous molecular forms. For these, additional steps had to be taken because, while the Kohn–Sham formalism using the LDA exchange-correlation functional is known to do an excellent job of comparing the energies of materials in the solid state, molecular energies are treated less well. Accordingly, an approach similar to that of Wang et al.84 was used. That is, a least squares fit to standard heats of formation for N and O containing compounds having enthalpy data as indicated with “*" in Table 1 was used to set the reference energies of O and N. While all calculations are based on results for idealized crystals corresponding to experimental temperatures of 0 K, we estimate that the additional heat and work needed to bring the materials to the standard temperature of 298.15 K is negligible compared to the overall error of the calculational methods. The results of our calculations of the total energies of all of the materials of this study, including the materials used in the fit, are given in Table 1. The calculated results agree with the available experimental results within 0.5 eV. Similar tables have been reported in earlier work47, 49, 51, 53 ; small differences in the calculated values of H are indicative of variations in the computational details and in the accuracy of the experimental heats of formation used for the O and N standards. (In fact, the heats of formation quoted in Refs. [31] and [32] often lack specific structural information.) It is expected that relative energies between structurally and chemically similar materials are considerably more accurate than the overall error. For each material listed in Table 1 the optimization calculations were initiated with indicated crystal structure. For most of the materials, the crystal structures were reported in the International Crystal Structure Database (ICSD)86 and/or in original experimental references. However, as explained in Subsec. 2.2, a few of material structures listed in Table 1 are hypothetical in the sense that they have not (yet) been experimentally realized, although their

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idealized structures are readily accessible through computation. The results of Table 1 are useful for understanding the structural and compositional stabilities of these materials.

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2.2. Structural Forms of Crystalline Electrolytes For the Li phosphate, phospho-nitride, and thiophosphate electrolytes of this study, Table 2 lists the lattice parameters corresponding to the structural optimization energies reported in Table 1. While the calculated lattice constants are typically 2% smaller than the experimental values, with a few exceptions, the calculated results for lattice shapes and internal parameters are in good agreement with experiment. A striking property of the Li phosphate, phospho-nitride, and thiophosphate electrolytes is their structural similarities and their compositional patterns. For the LiPON materials, having the general composition Lix POy Nz , the stoichiometry is generally restricted to the relation x = 2y + 3z − 5. This implies the formal ionic charges of Li+1 , O−2 , N−3 , and P+5 which is consistent with most of the existent LiPON materials. For the Li thiophosphate materials the general composition is Liv PSw . The restricted relationship consistent with the Li phosphates is v = 2w − 5 implying the formal ionic charges of Li+1 , S−2 , and P+5 . This relationship is followed by many of the Li thiophosphates with some interesting exceptions such as Li4 P2 S6 . While a wide variety of structural forms have been reported, a useful categorization is monomer, dimer, and chain structures. These are discussed in more detail below. 2.2.1. Monomer-Structured Materials The category of monomer structures includes Li3 PO4 and Li3 PS4 both of which have been observed in several structural forms, including the orthorhombic structures having space groups Pmn21 (#31) and Pnma (#62). Following the naming conventions of the previous literature, β-Li3 PO4 refers to the Pmn21 structure and γ-Li3 PO4 refers to the Pnma structure. By contrast for lithium thiophosphate, γ-Li3 PS4 refers to the Pmn21 structure and β-Li3 PS4 refers to the Pnma structure.88

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Material

b

c

α

β

γ

a

b

c

α

β

γ

5.99 7.57 10.28 12.86 8.36 8.43 10.67 9.54 12.01 4.76 5.95 12.92 4.47 5.33 8.87 11.46

5.13 6.43 6.00 7.81 6.98 7.16 8.80 4.97 6.15 4.76 5.95 5.27 4.47 4.67 5.30 6.30

4.74 6.06 4.82 5.94 5.11 4.83 5.79 10.39 12.23 5.36 6.37 16.19 7.24 9.13 4.65 4.91

90 90 90 90 112 110 111 103 102 90 90 90 90 90 90 90

90 90 90 90 90 90 90 116 114 90 90 99 90 90 90 90

90 90 90 90 104 101 91 72 72 120 120 90 90 90 90 90

6.23 7.71 10.49 12.82 8.56

5.23 6.54 6.12 8.22 7.11

4.86 6.14 6.93 6.12 5.19

90 90 90 90 111

90 90 90 90 90

90 90 90 90 103

12.50

6.03

12.53

103

113

74

6.07 13.07 4.58

6.07 5.41 4.58

6.58 16.45 7.12

90 90 90

90 99 90

120 90 90

9.07

5.40

4.69

90

90

90

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a

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β-Li3 PO4 [87] γ-Li3 PS4 [88] γ-Li3 PO4 [89] β-Li3 PS4 [88] Li4 P2 O7 [90] Li5 P2 O6 N Li4 P2 S7 Li7 P3 O11 Li7 P3 S11 [74] Li4 P2 O6 Li4 P2 S6 [91] LiPO3 [92] LiPN2 [93] s1 -Li2 PO2 N SD-Li2 PO2 N [52] SD-Li2 PS2 N

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Table 2. Calculated and measured lattice constants (in Å) and angles (in degrees) for Li phosphate, phospho-nitride, and thiophosphate crystals. When available, the experimental reference is listed in [ ] brackets.

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Key

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β-Li3 PO4

γ-Li3 PS4

Fig. 2. Ball and stick diagram for the Pmn21 structures of β-Li3 PO4 and γ-Li3 PS4 (2 formula units per unit cell) from computational results. The key shown at the left indicates the ball convention used throughout Sec. 2.

Calculations find the lowest energy structure for these materials to be the ones having the Pmn21 space group.87, 88 These structures are well-defined in the sense that the Wyckoff sites are fully occupied. While the lattice constants of β-Li3 PO4 are approximately 80% of those of γ-Li3 PS4 , the fractional coordinates of the two materials are nearly identical. Figure 2 shows a ball and stick diagram of these two structures. The detailed structures of the Pnma materials are more complicated than those of the Pmn21 materials. In γ-Li3 PO4 shown in Fig. 3, the structure is described by full occupancy of the crystallographic sites.89 A comparison with Fig. 2 shows that a crude approximation to the Pnma structure can be derived from the Pmn21 structure by switching the a and b axes and then doubling the unit cell along the a axis. Additional differences are due to the orientation of the phosphate or thiophosphate tetrahedra along the c-axis. For Li3 PS4 in the Pnma structure, further complication comes from the fact that experimental analysis of β-Li3 PS4 finds that some of the Li sites are partially occupied88, 94 — namely the site labeled “b” in the Wyckoff notation is found to have an occupancy of 70% while the site labeled “c” is found to have an occupancy of 30%. In simulations of idealized perfect crystal structures, a structure

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β-Li3 PS4

Fig. 3. Ball and stick diagram for the Pnma structures of γ-Li3 PO4 and β-Li3 PS4 (4 formula units per unit cell) from idealized computational results.

with full occupancy of the “b" site was found to have the lowest energy. This is the structure reported in Tables 1 and 2 and shown in Fig. 3. The differences between the structures of γ-Li3 PO4 and the idealized β-Li3 PS4 structure shown in Fig. 3 are due primarily to the differences in the Li site positions.53 2.2.2. Dimer-Structured Materials Li phosphate dimer structures have been found in the P1¯ (#2) structure with 26 atoms in the unit cell.90 In this structure, two phosphate groups are connected with a “bridging" O forming Li4 P2 O7 crystals. This structure having 2 formula units per unit cell is visualized in Fig. 4 together with a hypothetical nitrogenated analog based on the same structure but with N replacing the bridging O and with the addition of an extra Li ion to maintain charge neutrality. At this time, Li5 P2 O6 N remains a hypothetical idealization of a possible LiPON structure, having a stoichiometry close to the range of typical prepared films.57 The thiophosphate dimer material Li4 P2 S7 has been studied in its glassy form.95 Although the crystalline form may not exist in nature, it was possible to create a metastable computer model of

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a

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a c

c

b

b

Fig. 4. Ball and stick diagrams for the P1¯ structures of Li4 P2 O7 and Li5 P2 O6 N (2 formula units per unit cell) from computational results.

a

a

c

b

b

c

Fig. 5. Ball and stick diagrams for the P1¯ structures of hypothetical Li4 P2 S7 and the meta-stable superionic conductor Li7 P3 S11 (both with 2 formula units per unit cell) from computational results.

this structure, based on the phosphate analog as visualized in Fig. 5. While Li4 P2 S7 is not known to crystallize alone, the dimer has been shown to play an important role in the the meta-stable so-called superionic ceramic material Li7 P3 S11 which has been identified in the P1¯ structure.74, 96 This structure, visualized in Fig. 5 is composed of dimer and monomer substructures.51 For completeness, the lithium phosphate analog Li7 P3 O11 is also listed in Tables 1 and 2, even though its physical realization seems unlikely. For the Li thiophosphates, a different dimer form — Li4 P2 S6 with trigonal symmetry — has been synthesized91 and appears

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¯ Fig. 6. Ball and stick diagrams for the P31m structures of (a) Li4 P2 O6 and (b) Li4 P2 S6 (1 formula unit per unit cell) from computed results.

to be a stable decomposition product of other Li thiophosphate electrolytes.74 The crystal structure of Li4 P2 S6 was described by Mercier et al.91 as hexagonal P63 /mcm (#193) with half occupancy of the P (4e) sites. The electronic structure calculations of the 6 possible configurations of this unit cell find the lowest energy configuration ¯ to be described by the P31m (#162) structure which is a subgroup of the original space group. This structure and its phosphate analog are visualized in Fig. 6. In contrast to the other materials, an interesting characteristic of the optimized Li4 P2 S6 and Li4 P2 O6 structures is the presence of a direct bond between two P ions,47 indicating a more covalent configuration than the P+5 ionic state assumed for other phosphates and thiophosphates. While Li4 P2 S6 has been reported in several studies, Li4 P2 O6 is not known to exist. The heat of formation table results are consistent with the observed stability of Li4 P2 S6 +S compared to Li4 P2 S7 and of Li4 P2 O7 relative to Li4 P2 O6 +O. 2.2.3. Chain-Structured Materials Crystals of LiPO3 are characterized by infinite linear chains of phosphate, where in each formula unit, two O’s make tetrahedral bonds with P, while the third O is involved with a bridge bond between two phosphate groups. LiPO3 can be prepared from a Li2 OP2 O5 glass by heating97 and its crystal structure was analyzed92

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Fig. 7. Ball and stick diagrams for (a) LiPO3 in the P2/c structure (20 formula units per unit cell) and (b) s1-Li2 PO2 N in the Pbcm structure (4 formula units per unit cell) from the calculated results. For each crystal diagram, a view of a horizontal chain axis is also provided for a single phosphate or phospho-nitride chain.

to have the space group P2/c (#13) with 100 atoms per primitive unit cell. Figure 7 shows a ball and stick model of the structure, showing the arrangement of the chains using lattice parameter labels consistent with Ref. [92]. A visualization of the chain structure itself is also given in the figure, showing the chain to be twisted about its axis with a periodicity of 10 phosphate groups. The possibility of substituting N for O in natural LiPO3 was studied computationally.49 Starting with the P2/c structure of natural LiPO3 , the 20 bridging oxygens were substituted with nitrogens and 20 additional Li atoms were introduced into the structure to maintain charge neutrality. The relaxation results were remarkable; showing that the nitrided chain has a very stable structure with a periodicity of (PO2 N)2 groups. The first optimized structure obtained from the simulation was called s1 -Li2 PO2 N and was found to have 24 atoms per unit cell having the space group Pbcm (#57) which is visualized in Fig. 7. The most intriguing structural feature of the simulated structure of s1 -Li2 PO2 N compared to its parent LiPO3 material, is the regularization of the chain structure with a planar −P–N–P–N− backbone which is also visualized in Fig. 7. In 2013, a form of Li2 PO2 N was experimentally realized by Senevirathne et al.52 The

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Fig. 8. Ball and stick diagram of SD-Li2 PO2 N in the Cmc21 structure (2 formula units per unit cell) from the calculated results.

synthesized material called SD-Li2 PO2 N has the Cmnc21 (#36) space group and differs from the s1 structure by the arrangement of the phosphate chains. Interestingly, it is structurally similar98 to Li2 SiO3 . The solid=state synthesis of SD-Li2 PO2 N used the reaction 1 1 (10) Li2 O + P2 O5 + P3 N5 → Li2 PO2 N, 5 5 which is predicted to be exothermic from the computed heats of formation given in Table 1. SD-Li2 PO2 N is visualized in Fig. 8. It is tempting to ask the question whether a similar thiophosphonitride material could exist. Accordingly, computational studies of SD-Li2 PS2 N find a metastable structure and the results are recorded in Tables 1 and 2. At this time there is no evidence that this structure has be physically realized and, according to the heat of formation table, the exothermicity of the reaction analogous to Eq. (10) is smaller than the expected calculational error. For completeness, LiPN2 which was prepared and analyzed experimentally93, 99 was also studied computationally49 and its ¯ (#122) energy and lattice results are listed in Tables 1 and 2. Its I 42d structure with 2 formula units per unit cell is more complicated than the chain structures discussed in this section. 2.3. Li Ion Mobilities in Crystalline Electrolytes The Li ion conductivities in many of the crystalline Li phosphates, phospho-nitrides and thiophosphates have been studied

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Table 3. Calculated migration energies (Ecal m ) for Li-ion vacancies (vac) and interstitials (int), vacancy-interstitial formation energies (Ecal ) and corresponding f

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the activation energies (Ecal A ) for crystalline materials computed using the NEB method in idealized supercells. When available, experimental activation energies exp EA are also listed together with additional information including the literature reference indicated in [ ] brackets. For γ-Li3 PO4 , results for different crystallographic directions are quoted to compare with single crystal experiment; in other cases, only the minimum energies are given. All energies are given in eV.

Material

vac Ecal m

int Ecal m

Ecal f

β-Li3 PO4 0.7 0.4 γ-Li3 PO4 0.7, 0.7 0.4, 0.3 Li2.88 PO3.73 N0.14 Li3.3 PO3.9 N0.17 Li1.35 PO2.99 N0.13 LiPO3 0.6 0.7

2.1 1.7

LiPN2 SD-Li2 PO2 N γ-Li3 PS4 β-Li3 PS4 Li7 P3 S11

2.5 2.0 0.8 0.0 0.0

0.4 0.4 0.3 0.2 0.2

0.8

0.5

1.2

Ecal A

exp

EA

1.4 1.3, 1.1 1.23, 1.14 0.97 0.56 0.60 1.2 1.4 0.76–1.2 1.7 0.6 1.4 0.6 0.7 0.5 0.2 0.4 0.2 0.1

Reference

(sngl. cryst.) [100] (poly cryst.) [58] (amorphous) [58] (amorphous) [101] (poly cryst.) [97] (amorphous) [97] (poly cryst.) [99] (poly cryst.) [52] (poly cryst.) [102] (nano cryst.) [103] (poly cryst.) [76]

experimentally and computationally. Some of these results are summarized in Table 3 in terms of the activation, migration, and formation energies discussed in Eqs. (6) and (7). In this table for γ-Li3 PO4 , results for different crystallographic directions are quoted to compare with single crystal experiment; in other cases, only the minimum migration energies are given. From the results reported in Table 3, the calculated and measured activation energies for crystalline γ-Li3 PO4 and for crystalline LiPO3 are in reasonably good agreement. In both of these crystals, the activation energy for ionic conduction is dominated by a large formation energy Ef . For results on amorphous preparations of the exp same materials, the reported values of EA are much smaller and consistent with the assumption that the samples have temperature independent reservoirs of Li defect sites so that EA ≈ Em . The exp fact EA ≈ Ecal m for LiPN2 and SD-Li2 PO2 N suggests that those

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samples also have significant temperature independent reservoirs of Li defect sites. In contrast to the Li phosphates and phospho-nitrides, the ionic conductivities of Li thiophosphates are significantly higher, consistent with the computer modeling results which indicate that the Li thiophosphates have generally smaller migrations energies Ecal m . In addition, several configurations of Li-ion vacancy-interstitial pairs have been found to have negligible formation energies Ecal f . cal Small values of Ecal m and Ef are consistent with the generally small activation energies for ion conduction measured for these materials. In addition to the bulk ionic conductivity, practical electrolytes must also form stable interfaces with the electrode materials. Modeling of idealized interfaces of electrolytes with pure Li films find53 that Li phosphate/Li interfaces are stable while Li thiophosphate/Li interfaces are not. Further modeling work is needed to investigate this issue.

3. Li Oxide Garnet Electrolytes Metal oxide materials have been investigated for their utility as solid electrolytes for Li ion batteries for more than 25 years. Stability against a Li metal anode, an electronic band gap with a technologically suitable magnitude (minimum of 4.5 eV), chemical stability under operating voltages and temperatures and high ionic conductivity are among the essential characteristics for battery usage. Very few materials satisfy all of these criteria simultaneously. Many potential materials are unstable against Li metal,104–111 while others readily undergo decomposition.112–114 Garnet-structured oxides, such as Li5 La3 M4 O12 (M=Ta,Nb),115 have been shown to have conductivities rivaling LiPON, but only the Ta version is stable against Li and has a conductivity of ∼10−6 S/cm. This is still a full three orders of magnitude lower than traditional liquid electrolytes. 3.1. Two-Phase Garnet Oxides Recently, a new garnet oxide material, Li7 La3 Zr2 O12 (LLZO), was shown to have a conductivity as high as σ = 1.9x10−4 S/cm, while

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Fig. 9. (Color online) Crystal structure of tetragonal (left) and cubic (right) phases of LLZO. Dark gray (large) spheres are Zr, red spheres are O, and tiny grey spheres are La. All Li positions are included, although in the cubic phase not all are occupied. The Li(1) atoms are gold, Li(2) are white, and Li(3) are pink.

also remaining stable against Li.116, 117 Unfortunately, the synthesis of this material produced two distinct phases: a cubic one with the observed high conductivity and a tetragonal one with a much lower conductivity of σtetra = 1.63x10−6 S/cm.118 The determining factor between phases was, for many years, unknown. Thus progress toward practical usage of this material was hampered by the appearance of the unwanted tetragonal phase during synthesis. In Fig. 9, the two phases are shown. The tetragonal phase has an ordered Li sublattice with three distinct symmetry sites, Li(1), Li(2) and Li(3), all fully filled. The cubic phase has only two distinct Li sites, but both of them are partially filled, leading to overall disorder on the Li sublattice. In 2011, Geiger et al.119 noted that if the material was synthesized in Pt crucibles, only the tetragonal phase emerged, whereas synthesis in the more common alumina crucibles produced a mix of tetragonal and cubic phases. This lead to the hypothesis that accidental incorporation of Al must contribute to the emergence of the cubic, high-conductivity form of LLZO. By intentionally incorporating Al during synthesis, Rangasamy et al.120 proved the correctness of the hypothesis and established a critical Al concentration of 0.20 moles per formula unit for achieving

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the high=conductivity cubic phase. These two results significantly clarified the experimental landscape, but simultaneously raised interesting fundamental questions: (1) By what mechanism does Al cause the structural lattice transition? and (2) Why is it accompanied by a two=order-of-magnitude increase in conductivity?

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3.2. Dopant Site Preference To answer these questions, it was first necessary to determine where in the lattice Al sits. Density functional theory calculations of defect site preference show that Al strongly prefers to enter the Li sublattice and that the Li(1) site is the lowest energy position. Li(2) and Li(3) sites in the tetragonal lattice are significantly less favorable by 1.42 eV and 1.23 eV respectively. This large energy barrier virtually guarantees that, at least at reasonably low concentrations, dopant Al will be located at Li(1) sites. Since Al has a 3+ valency and Li has a 1+ valency, a second defect or defects are necessary to achieve charge balance. Calculations show that the lowest energy=compensating defect is a Li vacancy. In addition to the Li(1) displaced by Al, two of these vacancies are necessary to balance the system. These vacancies preferentially occupy the Li(2) or Li(3) sites with equal probability, based on defect calculations, with the formation of a Li(1) site vacancy being 0.1 eV higher in energy. The near equality of all vacancy formation energies indicates Li(1) vacancies are likely present along with those at Li(2) and Li(3) sites in Al-doped LLZO. Addition of Al3+ during synthesis therefore produces a Li=deficient compound with one Al defect at a Li(1) site and two further Li vacancies in the Li sublattice. Note that the Li(1) site functions as a “crossroads" for the Li-ion pathways so that any immobile ion occupying this site would be expected to hinder Li ion diffusion. The arrangement of the Al-induced vacancies is a major factor in the shape of the lattice itself,54 but the precise distribution of vacancies was twice determined experimentally with very different results. In Fig. 10, the Li sublattice in the cubic and tetragonal cells is shown with the Wyckoff position labels of the Li(1) tetrahedral and Li(2)/Li(3) octahedral sites labeled.

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Fig. 10. The Li sublattices of cubic (a) and tetragonal (b). The Li(1) atoms are the larger gold spheres in both structures, with Li(2) in white and Li(3) in dark gray. The very small gold spheres in the tetragonal structure are tetrahedrally coordinated sites, i.e. Li(1) which become fully unoccupied during the cubic to tetragonal phase transition. The crystallographic site notations for each cell type the are given in black.

One determination showed Li(1) sites being nearly fully occupied, while Li(2) sites, which have three times the multiplicity, being about 1/3 occupied.121 A second investigation found both Li(1) and Li(2) sites were each approximately half=filled.122 First principles of molecular dynamics simulations found site occupancies of 0.47 and 0.46 for Li(1) and Li(2) respectively, favoring the Xie et al. findings. Furthermore, these calculations showed that once an Li(1) site was occupied, the surrounding four Li(2) sites were always empty and that no nearest neighbor Li(2)–Li(2) pairs were simultaneously occupied. This is due to the short distances between these neighbors and the resulting strong Coulomb repulsion between two ionized Li atoms. Because of the geometry of the crystal, this puts a hard constraint on the occupation of the Li(1) sites as a function of overall Li content in the system. For an occupation x of the three Li(1) sites available per formula unit, there are 4x unoccupied Li(2) sites out of the 12 available per formula unit. Therefore, if Li(1) sites were nearly fully occupied as in Awaka et al.,121 there would be 0.94 × 3 = 2.82 Li located at the Li(1) site and 4 × 2.82 = 11.28 mandatory vacancies

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in the Li(2) sublattice. This leaves only 0.72 Li(2) sites available for occupation, yielding an overall Li concentration of 3.54, far below the observed concentration of 0.65–0.70. As the Li concentration decreases, for instance as a function of Al doping, more Li(1) sites may be occupied, provided four nearby Li(2) vacancies are available.

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3.3. The Role of Dopant-Induced Vacancies In addition to elucidating the Li distribution in Al-doped LLZO, density functional calculations reveal that disorder on the Li sublattice is the driving force behind the tetragonal to cubic transition and that there is a critical number of vacancies necessary for disorder to occur. Relaxed stoichiometric LLZO (i.e. 7 Li per formula unit) is always tetragonal, regardless of the starting configuration of the lattice parameters. By randomly removing Li and compensating with a uniformly charged positive background to eliminate the complicating effects of Al itself (to be discussed later), it can be shown that the system will relax away from tetragonal to either cubic or orthorhombic, depending on the particular Li configuration calculated. Since in reality the Li is mobile and entropy effects are present, this indicates that random vacancies alone are sufficient to drive the system into a cubic ground state. To pinpoint the critical concentration of vacancies necessary to stabilize the cubic phase, the energy difference between a constrained tetragonal and constrained cubic cells with identical vacancy configurations were calculated. All internal coordinates along with the lattice parameters (subject only to the symmetry constraint) were calculated for 40 randomized vacancy configurations per vacancy concentration. The results are shown in Fig. 11 using both the mean and lowest energy configurations of the 40 calculations. The transition occurs when the line crosses zero and, as can be seen in the figure, the critical concentration occurs somewhere between 0.39 and 0.43 vacancies per formula unit, in remarkable agreement with the experimentally determined number of 0.41 per formula unit.120 To further verify that the cubic ground state is stabilized upon creation of vacancies in the Li sublattice, Bernstein et al.54 used a variable cell shape version of molecular dynamics, and added 0.25

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Fig. 11. Energy difference between tetragonal and cubic structures as a function of vacancy number, for minimum energy configuration (solid line) and mean configuration energy (dashed line). This figure was reproduced from Ref. 54 with permission.

vacancies per formula unit, a number above both the theoretically and experimentally determined critical concentration. The vacancies were inserted randomly into the ordered, tetragonal unit cell. Within 5–10 ps of simulation time, the system spontaneously converted to cubic. Thereafter, it experienced some fluctuation between cubic and tetragonal states, settling permanently into a cubic, Li-disordered ground state after 30 ps. As can be seen in Fig. 12 (top panel) the ratios ax /az and ay /az drop from above 1.0 to very near 1.0, indicating a cubic phase. When this drop occurs, there is a concurrent change in the distribution of the Li. The Li(1) tetrahedral sites and Li(2)/Li(3) octahedral sites have different crystallographic notations in the two different symmetry cells (cubic and tetragonal). However, it is possible to map every site in the tetragonal cell onto a corresponding site in the cubic cell (Fig. 12 bottom panel). In doing this, we can understand how the Li shifts in concert with the phase transition. There is a sharp drop in the occupancy of the 16f and 32g sites associated with the tetragonal symmetry. These are octahedrally coordinated Li(2)/Li(3) sites in the tetragonal unit cell. In the cubic cell, these correspond to Li(2) sites with the 96h symmetry label. As 96h experiences neither an increase nor decrease coincident with the

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Fig. 12. Evolution over time of structural and site occupation quantities for a sample system with nvac = 2 at T = 600 K. Top: unit cell shape (ax /az blue, ay /az red) and volume (black). Middle: 96hc (black) and 16ft +32gt (red) lattice site occupation. Bottom: 24dc (black), 8at (red) and 16et (blue with symbols) lattice site occupations. This figure was reproduced from Ref. 54 with permission.

phase transition, it can be assumed that the non-Li(1) site occupancy remains relatively constant. On the other hand there is also a clear dip in the originally fully occupied tetrahedral Li(1) sites with the 8a label in the tetragonal cell (Fig. 12 bottom panel). This drop is accompanied by an increase in the originally fully unoccupied 16e symmetry sites of the tetragonal cell. Again the overall occupancy of these sites when projected in the cubic cell (24d) remains constant. Therefore, the disorder can be gauged not only by the change in the lattice constants, but the sudden occupation of formally empty 16e octahedral sites in the “tetragonal" cell, which concurrently transitions to cubic. 3.4. Fundamental Mechanisms of the Phase Transition First principles calculations have also illuminated the fundamental underlying mechanism that causes the cubic state to stabilize upon vacancy creation. The link between Li distribution and lattice

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symmetry suggests that Li ordering, perhaps driven by Coulomb repulsion, breaks the symmetry and the lattice distorts as a consequence. However, a point-charge model shows that the energy of the tetragonal distortion actually increases the overall energy compared to a Li-ordered cubic cell, indicating that Coulombic forces between ions are not the full story. Calculations with full Li stoichiometry clearly reproduce the energy advantage of the tetragonal over cubic phase with Li ordering, but interestingly, show that disorder even with stoichiometric Li content is favored over order if symmetry is cubic. Thus it is clear that there is an energy gain associated with the lattice distortion itself, rather than a simple response to Li order. By analyzing pair distribution functions of various ions in both cubic and tetragonal ordered cells, it is clear that the La-O distances are extremely rigid. This is perhaps not surprising since the 3+ and 2− formal vacancies are large and likely to interact strongly. Li ordering causes the oxygen ions to shift somewhat (preserving La-O distances) and this results in a distortion of the ZrO6 octahedra. In the cubic cell, the Zr-O bond lengths are 2.130 ± 0.02 Å and O-Zr-O bond angles are 180◦ ± 4.0◦ . The relaxation to a tetragonal cell relieves this distortion, restoring the octahedra to a uniform Zr-O bond length of 2.125 ± 0.005 Å and a O-Zr-O bond angle of 180◦ ±0.01◦ . Since the Zr-O bonds are expected to be at least partially covalent, this should produce an energy change unrelated to Coulombic forces. To quantitatively estimate the covalent bond distortion contribution to the overall energy lowering, we parametrize the calculated total energies of the ordered tetragonal cell as a function of Zr-O bond length and O-Zr-O bond angle by computing the energies for small displacements of an O atom and fitting to an harmonic approximation. Using the observed changes between cubic and tetragonal ZrO6 octahedra, we find the energy lowering upon tetragonal distortion due to relief of ZrO6 distortion accounts for nearly all of the energetic difference between a Li-ordered cubic and tetragonal cell, as can be seen in Fig. 13. From this, it can be concluded that covalent bonding is an essential component of the tetragonal distortion. This suggests a possible doping scheme for stabilizing the desired (high=conductivity) phase

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Fig. 13. Relaxed energies for 10 disordered cells with cell parameters constrained to be precisely cubic (left) and allowed to relax freely (second from left). Energies for the experimental Li ordering in a cubic cell (center) and a relaxed to tetragonal cell (second from right). The energy difference between cubic-ordered and tetragonalordered arising from bending/stretching of the covalent Zr-O bonds in the harmonic model (right). This figure was reproduced from Ref. 54 with permission.

through replacement of some (or all?) of the Zr with an element that bonds more weakly with the surrounding oxygen atoms. 3.5. Li Diffusion In addition to static DFT calculations, first principles molecular dynamics calculations were performed to gauge the Li mobility and understand its connection to Al-doping and phase change. The strict ordering of Li ions in the tetragonal phase is an obvious hindrance to movement through the lattice. Thus the very low ionic conductivity is unsurprising. Once the Al3+ ions have created two vacancies on the Li sublattice, there is considerably more freedom of movement. The mean squared displacement as a function of time, along with the best linear fit, are shown in Fig. 14 for a stoichiometric cubic cell, a stoichiometric tetragonal cell, a cell doped with 0.25 Al per formula unit and a cell with the same number of vacancies as the Al-doped cell, but without the Al ion itself. For the cubic cell, the lattice constants are constrained to be equal, but otherwise unconstrained. To gauge the effect of the Al ion itself, a cell with an equal number of vacancies in the Li sublattice, but without the Al ion was created, with a uniform (“jellium") compensating positive background to balance the charge. As can be seen in the figure, the actual shape of the lattice has little to no effect on the diffusivity, provided the system is

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Mean squared displacement (Ang2)

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60

Li6.5La3Zr2O12 (jellium)

50

Li6.25Al0.25La3Zr2O12 Li7La3Zr2O12 cubic

40

Li7La3Zr2O12 tetragonal 30

20

10

0

0

50

100

Time (ps)

Fig. 14. The averaged mean squared displacement of Li-ions in LLZO with various doping schemes at 800 K. “Jellium" refers to the creation of vacancies with a uniform compensating background charge. Solid lines are the best linear fit to the data; the diffusivity is easily calculable from their slopes via Eq. 8.

stoichiometric (Li7 La3 Zr2 O12 ). With 0.25 Al ions per formula unit, the cell parameters become quickly cubic (not shown) and the diffusivity is dramatically increased. With an equal number of vacancies but without actual Al ions in the system, the diffusivity is markedly increased again. This indicates that the immobile Al ions, sitting at the crossroads site of the Li sublattice, have a “blocking" effect on the diffusivity. 3.6. Optimizing the Doping Scheme Since there is no practical way to create vacancies without real compensating ions, alternate dopant ions that create vacancies but are physically located away from the Li sublattice are highly desirable. One possibility is Ta4+ which goes into the lattice at the Zr4+ site. Although Ta is less efficient than Al in creating vacancies (each Ta ion creates one vacancy whereas each Al creates two) it more efficiently increases the diffusivity. As can be seen in Fig. 15, adding

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Mean squared displacement (Ang2)

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Li6.875La3Zr1.875Ta0.125O12

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Li6.75La3Zr1.75Ta0.25O12

0.375

Li6.625La3Zr1.625Ta0.375O12

40

Li6.25Al0.25La3Zr2O12 30

0.5 0.25

20

0.125 10

0

0

50

100

Time (ps)

Fig. 15. The averaged mean squared displacement of Li ions in LLZO with different levels of Ta doping compared to Al doping, at 800 K in each case. The solid lines are the best linear fit to the data.

0.25 vacancies per formula unit via Ta doping yields approximately the same diffusivity as adding 0.5 vacancies via Al doping. Ta doping of the LLZO structure should therefore be considered the most efficient way to achieve high conductivity. Experiments have shown that Ta readily enters the lattice at the Zr site, the resulting phase is cubic, and the conductivity is high.123 Careful conductivity measurements to quantitatively establish its effect on conductivity remain to be done. Further computational work on this class of materials reveals that the room temperature conductivity should be extremely high, superseding that of Al-doped LLZO.124 4. Concluding Remarks The good agreement between first principles methodologies and the several instances of predictive power, point towards a future in which solid electrolyte materials will be greatly improved and perhaps even developed from the ground up using computational methodologies. The work in this chapter on phosphate and oxide

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electrolytes shows that understanding the connection between structure, electronic structure and performance is well within the realm of computational possibility. The range of crystalline forms and breadth of substitutional possibilities in the known classes of solid electrolytes alone is daunting to consider from a synthesis and testing point of view. By providing the crucial link between atomicscale, quantum mechanical phenomena and measurable properties, simulations of solid electrolytes can be used to streamline the process and point the way towards optimized, useful materials. Acknowledgements The work by MDJ was funded by the Office of Naval Research (ONR) through the Naval Research Laboratory’s Basic Research Program. Computational resources were provided by the DoD High Performance Computing Center. This work benefited heavily from collaborations with Noam Bernstein, Khang Hoang and Jeff Sakamoto. The work by NAWH was supported by NSF grant DMR-1105485. Computations were performed on the Wake Forest University DEAC cluster, a centrally managed resource with support provided in part by the University. Collaborations with current and previous research assistants and associates Yaojun A. Dun, Xiao Xu, Nicholas Lepley and Ahmad Al-Qawasmeh are gratefully acknowledged. References 1. R. A. Huggins, Advanced Batteries; Materials Science Aspects, (Springer Science + Business Media, LLC, 233 Spring Street, New York, NY 10013, USA, 2009). 2. K. Takada, Progress and prospective of solid-state lithium batteries, Acta Materialia. 61(3) (Feb., 2013) 759–770. 3. N. Kamaya, K. Homma, Y. Yamakawa, M. Hirayama, R. Kanno, M. Yonemura, T. Kamiyama, Y. Kato, S. Hama, K. Kawamoto and A. Mitsui, A lithium superionic conductor, Nature Materials 10(9) (2011) 682–686. 4. S. P. Ong, Y. Mo, W. D. Richards, L. Miara, H. S. Lee and G. Ceder, Phase stability, electrochemical stability and ionic conductivity of the

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Li10±1 MP2 X12 (M=Ge, Si, Sn, Al or P and X = O, S or Se) family of susperionic conductors, Energy & Environmental Science 6 (2013) 148–156. M. Born and K. Huang, Dynamical Theory of Crystal Lattices, (Oxford at the Clarendon Press, Oxford University Press, Ely House, London.I, 1954). P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Physical Review 136 (1964) B864–B871. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Physical Review 140 (1965) A1133–A1138. J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B. 45 (1992) 13244– 13249. J. P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. Erratum — Phys. Rev. Let. 78 (1997) 1396. U. von Barth and C. D. Gelatt, Validity of the frozen-core approximation and pseudopotential theory for cohesive energy calculations, Phys. Rev. B. 21 (1980) 2222–2228. J. C. Phillips and L. Kleinman, New method for calculating wave functions in crystal and molecules, PRB 116 (1959) 287–294. D. R. Hamann, M. Schlüter and C. Chiang, Norm-conserving pseudopotentials, Phys. Rev. Lett. 43 (1979) 1494–1497. G. P. Kerker, Non-singular atomic pseudopotentials for solid-state applications, J. Phys. C: Solid St. Phys. 13 (1980) L189–L194. R. Car and M. Parrinello, Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett. 55 (1985) 2471–2474. H. C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature, The Journal of Chemical Physics 72(4) (1980) 2384. M. Parrinello and A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, Journal of Applied Physics 52(12) (1981) 7182. R. M. Wentzcovitch, Invariant molecular-dynamics approach to structural phase transitions, Physical Review B 44(5) (1991) 2358. X. Gonze, First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugategradient algorithm, Physical Review B 55(16) (1997) 10337. X. Gonze and C. Lee, Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Physical Review B 55(16) (1997) 10355.

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20. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41 (1990) 7892–7895. USPP code is available from the website http://www.physics.rutgers.edu/ ∼dhv/uspp/. 21. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953–17979. 22. X. Gonze, B. Amadon, P. M. Anglade, J. M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Cote, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. J. T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G. M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. J. Verstraete, G. Zerah and J. W. Zwanziger, Abinit: First-principles approach to material and nanosystem properties, Computer Physics Communications 180(12) (2009) 2582–2615. Code is available at the website http://www. abinit.org. 23. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari and R. M. Wentzcovitch, Quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21(39) (2009) 394402 (19pp). Available from the website http://www.quantum-espresso.org. 24. N. A. W. Holzwarth, A. R. Tackett and G. E. Matthews, A Projector Augmented Wave (PAW) code for electronic structure calculations, Part I: Atompaw for generating atom-centered functions, Computer Physics Communications. 135 (2001) 329–347. Available from the website http://pwpaw.wfu.edu. 25. G. Kresse and J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 111169. 26. G. Kresse and J. Furthmuller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci. 6(1) (1996) 15–50. 27. OpenDX — The Open Source Software Project Based on IBM’s Visualization Data Explorer — is available from the web site http:// www.opendx.org.

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the frequencies reported in this paper were obtained by manually digitizing the unlabeled peaks. Y. A. Du and N. A. W. Holzwarth, Mechanisms of Li+ diffusion in crystalline Li3 PO4 electrolytes from first principles, Phys. Rev. B. 76 (2007) 174302 (14 pp). P. Tarte, Isomorphism and polymorphism of the compounds Li3 POi4 , Li3AsO4 and Li3 VO4 , Journal of Inorganic and Nuclear Chemistry 29 (1967) 915–923. T. Riedener, Y. Shen, R. J. Smith and K. L. Bray, Pressure induced phase transition and spectroscopy of Mn5+ - doped Li3 PO4 , Chemical Physics Letters 321 (2000) 445–451. R. J. Smith, Y. Shen and K. L. Bray, The effect of pressure on vibrational modes in Li3 PO4 , J. Phys.: Condens. Matter 14 (2002) 461–469. Y. A. Du and N. A. W. Holzwarth, Effects of O vacancies and N or Si substitutions on Li+ migration in Li3 PO4 electrolytes from first principles, Phys. Rev. B 78 (2008) 174301. Y. A. Du and N. A. W. Holzwarth, Li ion migration in Li3 PO4 electrolytes: Effects of O vacancies and N substitutions, ECS Transactions 13 (2008) 75–82. N. A. W. Holzwarth, N. D. Lepley and Y. A. Du, Computer modeling of lithium phosphate and thiophosphate electrolyte materials, Journal of Power Sources 196 (2011) 6870–6876. Y. A. Du and N. A. W. Holzwarth, First principles simulations of Li ion migration in materials related to LiPON electrolytes, ECS Trans. 25(36) (2010) 27–36. Y. A. Du and N. A. W. Holzwarth, First-principles study of LiPON and related solid electrolytes, Phys. Rev. B 81 (2010) 184106 (15pp). N. D. Lepley and N. A. W. Holzwarth, Computer modeling of crystalline electrolytes — lithium thiophosphates and phosphates, Transactions of the Electrochemical Society 35(14) (2011) 39–51. N. D. Lepley and N. A. W. Holzwarth, Computer modeling of crystalline electrolytes — lithium thiophosphates and phosphates, Journal of the Electrochemical Society 159 (2012) A538–A547. K. Senevirathne, C. S. Day, M. D. Gross, A. Lachgar and N. A. W. Holzwarth, Anew crystalline LiPON electrolyte: Synthesis, properties and electronic structure, Solid State Ionics 333 (2013) 95–101. N. D. Lepley, N. A. W. Holzwarth and Y. A. Du, Structures, Li+ mobilities and interfacial properties of solid electrolytes Li3 PS4 and Li3 PO4 from first principles, Phys. Rev. B 88 (2013) 104103 (11 pp). N. Bernstein, M. D. Johannes and K. Hoang, Origin of the Structural Phase Transition in Li7 La3 Zr2 O12 , Phys Rev Lett. 109(20) (2012) 205702. N. J. Dudney, Thin=film micro-batteries, Interface 17(3)(3) (2008) 44–48.

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69. B. Wang, J. B. Bates, F. X. Hart, B. C. Sales, R. A. Zuhr and J. D. Robertson, Characterization of thin-film rechargeable lithium batteries with lithium cobalt oxide cathodes, Journal of the Electrochemical Society 143(10) (1996) 3203–3213. 70. N. J. Dudney, Addition of a thin-film inorganic solid electrolite (Lipon) as a protective film in lithium batteries with a liquid electrolyte, Journal of Power Sources 89 (2000) 176–179. 71. F. Mizuno, A. Hayashi, K. Tadanaga and M. Tatsumisago, New lithium-ion conducting crystal obtained by crystallization of Li2 S– P2 S5 glasses, Electrochemical and Solid-State Letters 8 (2005) A603–A606. 72. F. Mizuno, A. Hayashi, K. Tadanaga and M. Tatsumisago, New, highly ion-conductive crystals precipitated from Li2 S–P2 S5 glasses, Adv. Mater. 17 (2005) 918–921. 73. F. Mizuno, T. Ohtomo, A. Hayashi, K. Tadanaga and M. Tatsumisago, Lithium ion conducting solid electrolytes prepared from Li2 S, elemental P and S, Solid State Ionics 177 (2006) 2753–2757. 74. H. Yamane, M. Shibata, Y. Shimane, T. Junke, Y. Seino, S. Adams, K. Minami, A. Hayashi and M. Tatsumisago, Crystal structure of a superionic conductor Li7 P3 S11 , Solid State Ionics 178 (2007) 1163–1167. 75. A. Hayashi, Preparation and characterization of glassy materials for all-solid-state lithium secondary batteries, Journal of the Ceramic Society of Japan 115 (2007) 110–117. 76. M. Tatsumisago and A. Hayashi, Preparation of lithium ion conducting glasses and glass-ceramics for all-solid-state batteries, Journal of Non-Crystalline Solids 354 (2008) 1411–1417. 77. K. Minami, A. Hayashi and M. Tatsumisago, Electrical and electrochemical properties of the 70Li2 S·(30 − x)P2 S5 ·xP2 O5 glass-ceramic electrolytes, Solid State Ionics 179 (2008) 1282–1285. 78. A. Hayashi, K. Minami, F. Mizuno and M. Tatsumisago, Formation of Li+ superionic crystals from the Li2 S-P2 S5 melt-quench glasses, J. Mater. Sci. 43 (2008) 1885–1889. 79. A. Hayashi, K. Minami and M. Tatsumisago, High lithium ion conduction of sulfide glass-based solid electrolytes and their application to all-solid-state batteries, Journal of Non-crystalline Solids 355 (2009) 1919–1923. 80. J. Trevey, J. S. Jang, Y. W. Jung, C. R. Stoldt and S.-H. Lee, Glassceramic Li2 S–P2 S5 electrolytes prepared by a single step ball billing process and their application for all-solid-state lithium-ion batteries, Electrochemistry Communications 11 (2009) 1830–1833. 81. Z. Liu, W. Fu, E. A. Payzant, X. Yu, Z. Wu, N. J. Dudney, J. Kiggans, K. Hong, A. J. Rondinone and C. Liang, Anomalous high ionic

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95. J. A. D. G. Schmedt and H. Eckert, High-resolution double-quantum 31 P NMR: A new approach to structural studies of thiophosphates, Chem. Eur. J. 4 (1998) 1762–1767. 96. Y. Onodera, K. Mori, T. Otomo, A. C. Hannon, S. Kohara, K. Itoh, M. Sugiyama and T. Fukunaga, Crystal structure of Li7 P3 S11 studied by neutron and synchorotron X-ray powder diffraction, J. Phys. Soc. Jpn. 79 (2010) 87–89. Suppl. A; Proc. 3rd Int. Conf. Physics of Solid State Ionics (ICPSSI-3). 97. B. K. Money and K. Hariharan, Lithium ion conduction in lithium metaphosphate based systems, Applied Physics A 88 (2007) 647–652. 98. K.-F. Hesse, Refinement of the crystal structure of lithium polysilicate, Acta Cryst. B 33 (1977) 901–902. 99. W. Schnick and J. Luecke, Lithium ion conductivity of LiPN2 and Li7 PN4 , Solid State Ionics 38 (1990) 271–273. 100. A. K. Ivanov-Shitz, V. V. Kireev, O. K. Mel’nikov and L. N. Demainets, Growth and ionic conductivity of γ-Li3 PO4 , Crystallography Reports 46 (2001) 864–867. 101. F. Muñoz, A. Durán, L. Pascual, L. Montagne, B. Revel and A. C. M. Rodrigues, Increased electrical conductivity of LiPON glasses produced by ammonolysis, Solid State Ionics 179 (2008) 574–579. 102. M. Tachez, J.-P. Malugani, R. Mercier and G. Robert, Ionic conductivity of and phase transition in lithium thiophosphate Li3 PS4 , Solid State Ionics 14 (1984) 181–185. 103. Z. Liu, W. Fu, E. A. Payzant, X. Yu, Z. Wu, N. J. Dudney, J. Kiggans, K. Hong, A. J. Rondinone and C. Liang, Anomalous high ionic conductivity of nanoporous β-Li3 PS4 , Journal of the American Chemical Society 135(3) (2013) 975–978. 104. H. Y.-P. Hong, Crystal structure and ionic conductivity of Li14 Zn (GeO4 )4 and other new Li+ superionic conductors, Materials Research Bulletin 13(2) (1978) 117–124. 105. H. Aono, N. Imanaka and G.-y. Adachi, High Li+ conducting ceramics, Accounts of Chemical Research 27(9) (1994) 265–270. 106. A. D. Robertson, A. R. West and A. G. Ritchie, Review of crystalline lithium-ion conductors suitable for high temperature battery applications, Solid State Ionics 104(1–2) (1997) 1–11. 107. A. K. Padhi, Mapping of Transition Metal Redox Energies in Phosphates with NASICON Structure by Lithium Intercalation, J Electrochem Soc. 144(8) (1997) 2581. 108. Y. Inaguma, C. Liquan, M. Itoh, T. Nakamura, T. Uchida, H. Ikuta and M. Wakihara, High ionic conductivity in lithium lanthanum titanate, Solid State Commun. 86(10) (1993) 689–693.

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109. H. Kawai, Lithium Ion Conductivity of A-Site Deficient Perovskite Solid Solution La0.67−x Li3x TiO3 , J Electrochem Soc. 141(7) (1994) L78. 110. O. Bohnke, Mechanism of ionic conduction and electrochemical intercalation of lithium into the perovskite lanthanum lithium titanate, Solid State Ionics 91(1–2) (1996) 21–31. 111. P. Birke, Electrolytic Stability Limit and Rapid Lithium Insertion in the Fast-Ion-Conducting Li0.29 La0.57 TiO3 Perovskite-Type Compound, J Electrochem Soc. 144(6) (1997) L167. 112. U. V. Alpen, A. Rabenau and G. H. Talat, Ionic conductivity in Li3 N single crystals, Appl. Phys. Lett. 30(12) (1977) 621. 113. Y.-F. Y. Yao and J. T. Kummer, Ion exchange properties of and rates of ionic diffusion in beta-alumina, Journal of Inorganic and Nuclear Chemistry 29(9) (1967) 2453–2475. 114. G. Farrington, B. Dunn and J. Briant, Li+ and divalent ion conductivity in beta and beta" alumina, Solid State Ionics 3–4 (1981) 405–408. 115. V. Thangadurai, H. Kaack and W. Weppner, Novel fast lithium ion conduction in garnet-type Li5 La3 M2 O12 (M = Nb, Ta), J. Am. Ceram. Soc. 86(3) (2003) 437–440. 116. R. Murugan, V. Thangadurai and W. Weppner, Fast lithium ion conduction in garnet-type Li7 La3 Zr2 O12 , Angew Chem Int Edit. 46(41), 7778–7781, (2007). 117. S. Ohta, T. Kobayashi and T. Asaoka, High lithium ionic conductivity in the garnet-type oxide Li7−x La3 (Zr2−x , Nbx )O12 (x=0–2), J. Power Sources 196(6) (2011) 3342–3345. 118. J. Awaka, N. Kijima, H. Hayakawa and J. Akimoto, Synthesis and structure analysis of tetragonal Li7 La3 Zr2 O12 with the garnet-related type structure, J. Solid State Chem. 182(8) (2009) 2046–2052. 119. C. A. Geiger, E. Alekseev, B. Lazic, M. Fisch, T. Armbruster, R. Langner, M. Fechtelkord, N. Kim, T. Pettke and W. Weppner, Crystal Chemistry and Stability of Li7 La3 Zr2 O12 Garnet: A Fast Lithium-Ion Conductor, Inorg Chem. 50(3) (2011) 1089–1097. 120. E. Rangasamy, J. Wolfenstine and J. Sakamoto, The role of Al and Li concentration on the formation of cubic garnet solid electrolyte of nominal composition i Li7 La3 Zr2 O12 , Solid State Ionics 206 (Jan., 2012), 28–32. 121. J. Awaka, A. Takashima, K. Kataoka, N. Kijima, Y. Idemoto and J. Akimoto, Crystal Structure of Fast Lithium-ion-conducting Cubic Li7 La3 Zr2 O12 , Chem Lett. 40(1) (2011) 60–62. 122. H. Xie, J. A. Alonso, Y. Li, M. T. Fernandez-Diaz and J. B. Goodenough, Lithium Distribution in Aluminum-Free Cubic Li7 La3 Zr2 O12 , Chem Mater. 23(16) (2011) 3587–3589.

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123. J. L. Allen, J. Wolfenstine, E. Rangasamy and J. Sakamoto, Effect of substitution (Ta, Al, Ga) on the conductivity of Li7 La3 Zr2 O12 , Journal of Power Sources 206 (May, 2012) 315–319. 124. L. J. Miara, S. P. Ong, Y. Mo, W. D. Richards, Y. Park, J. M. Lee, H. S. Lee and G. Ceder, Effect of Rb and Ta Doping on the Ionic Conductivity and Stability of the Garnet Li7+2x−y (La3−x Rbx )(Zr2−y Tay )O12 (0 ≤ x ≤ 0.375, 0 ≤ y ≤ 1) Superionic Conductor: A First Principles Investigation, Chem Mater. 25(15) (2013) 3048–3055.

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Chapter 7

Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport and Mechanical Strength Wyatt E. Tenhaeff

Department of Chemical Engineering University of Rochester Rochester, NY 14627, USA

Sergiy Kalnaus

Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge, TN 37831, USA

1. Introduction Several promising lithium-conducting solid electrolytes have been discovered, many of which were discussed in the preceding chapter. Other excellent reviews discussing solid electrolytes and solid-state lithium batteries are also available.1, 2 Generally, solid electrolytes can be sorted into two classes: inorganic ceramics and glasses and organic macromolecules (e.g. polymers). Given the demand for battery cells in high power applications and the interest in automotive applications, the research community has placed a strong emphasis on discovering solid materials with ever increasing Li+ conductivities. In fact, solid lithium-ion conductors have been 235

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discovered with lithium conductivities comparable to those of conventional carbonate-based liquid electrolytes for lithium-ion batteries.3 The room temperature ionic conductivity of Li10 GeP2 S12 and 1M LiPF6 in ethylene carbonate/dimethyl carbonate (1:1 w/w) is 1.2 × 10−2 and 1.1 × 10−2 S cm−1 , respectively.3, 4 To be practically relevant in lithium battery cells, though, solid electrolytes should satisfy several other requirements. The following list is not intended to be exhaustive but rather highlight additional considerations when designing solid-state batteries. Properties of ideal lithium-ion conductors: 1. High Li+ conductivity. For high power capabilities. 2. Negligible electronic conductivity. To minimize internal selfdischarge. 3. Unity transference number. To eliminate charge polarization losses. 4. Chemical compatibility with anode and cathode. Reaction of electrolyte with either electrode is detrimental, often leading to resistive interfaces or mixed ionic/electronic conductivities. 5. Wide electrochemical window. Desired to maximize the cell’s energy density. 6. Thin. Must minimize internal resistance for power and added mass/volume for gravimetric/volumetric energy density. 7. Stiff and tough, flaw tolerant. To suppress the formation and intrusion of Li metal dendrites while accommodating cyclinginduced volume changes. 8. Processible, manufacturable. For high throughput manufacturing of full cells in industrial production lines. 9. Inexpensive, synthesized from abundant elements. To lower cell cost. Comparing the inorganic and polymeric electrolytes, ceramic electrolytes offer advantages in requirements #1 and #3–5. The primary drawbacks of ceramics are associated with their manufacturing and incorporation with other components in the cell. Ceramic electrolyte membranes are commonly synthesized via conventional solid-state synthesis methods. Other techniques, such as sol-gel syntheses, can be employed, but the membrane sintering step, required regardless

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Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport 237

of the synthesis technique, is quite slow compared to the conventional slurry coating processes employed for lithium-ion batteries. Other solid-state fabrication approaches utilize powder compacting, in which powdered cathode and solid electrolytes are pressed into a dense compact and integrated with a metal electrode, typically Li metal or a Li alloy. It appears that cold-pressing is sufficient for sulfide-based electrolytes, while oxide-based electrolytes require high temperature annealing. Powder compacting may offer more rapid fabrication, but interfacial compatibility issues remain a significant challenge.2, 5–9 Polymer electrolytes offer ease of processing. Various industrial manufacturing techniques can rapidly and economically produce thin electrolyte layers. Discoveries in novel polymer compositions and structures, as well as large plasticizing anions for lithium salt, have led to polymer electrolytes with compelling Li+ conductivities.10–13 One key drawback to polymer electrolytes is their mechanical properties. Monroe and Newman showed that the shear modulus of a polymer electrolyte needs to be two times the shear modulus of lithium to inhibit dendrites.14 Also, toughness is required to accommodate volume changes during cycling. In polymer electrolytes, Li+ transport is associated with segmental motion. A fraction of the lithium cations (ideally all) are complexed to Lewis bases within the polymer host. In the case of linear poly(ethylene oxide) (PEO), the Lewis base is the ether oxygen. The polymer segmental motion must be high such that Li+ can transport from one complexation site to another. High conductivities are achieved when the polymer electrolyte is completely amorphous and operating at temperatures well above its glass transition temperature. The transport behavior of amorphous polymer electrolytes can be discussed in terms of free volume concepts, and the temperature dependence is well described by the Vogel–Tamman–Fulcher (VTF) equation.10 In this temperature region, the polymer electrolytes are better described not as solids but viscous liquids. Accordingly, they do not possess the mechanical properties required to inhibit Li dendrites. To improve the mechanical properties of polymer electrolytes, Weston and Steele pioneered the investigation of composite polymer

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electrolytes (CPE) where rigid alumina fillers were mixed into a polymer electrolyte.15 Since their study, the development of CPE has been a widely investigated approach to overcome the mechanical property limitations of polymer electrolytes. Beyond improving the mechanical properties of the electrolytes, composites with insulating fillers can provide enhanced conductivities and interfacial stabilities with the electrodes. Generally, the optimal filler concentration to achieve maximum ionic conductivity is approximately 10 wt%.16 This filler concentration does not provide enough stiffening to surpass the shear modulus threshold where lithium dendrites can be inhibited. As the fraction of insulating filler is increased, there is a drop in conductivity which can be considered a dilution effect. Lithium cations cannot transport through the bulk of the insulating filler phase, and these high loadings also increase the tortuosity for transport as the cations must diffuse around the non-conductive fillers. To circumvent these limitations, solid polymer composite electrolytes where the fillers are rigid glass or ceramic lithium ion conductors are being studied. With conductive fillers, the premise is that the composites can be loaded with much higher concentrations of the stiff inorganic phase to meet the mechanical properties requirements without sacrificing high Li+ conductivities. In this chapter, the progress toward fabricating solid CPE will be discussed. In Sec. 2, the literature on “conventional” solid polymer composite electrolytes filled with stiff insulating phases will be reviewed. Experimental efforts to synthesize and characterize the composites with conductive fillers will be reviewed in Sec. 3. Section 4 covers lithium transport phenomena at interfaces between two solid electrolytes. Finally, the modeling approaches to identify optimal composite microstructures for enhanced conductivities and mechanical properties will be highlighted in Sec. 5. 2. Polymer Composites with Insulating Fillers The research in the area of composite electrolytes with the particulate filler gained strength since the initial observations of significant improvements in mechanical properties by addition of small-sized

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Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport 239

grains of ceramic oxides.15 Typical experiments involved mixtures of PEO-based polymers with lithium salt and insulating inorganic particulate fillers. Since the conductivity of amorphous polyether phase can be three orders of magnitude higher than in crystalline polyether phase,17 the experiments were performed at temperatures where PEO is amorphous (above 60◦ C). Addition of the hard phase was envisioned as an approach to improve the mechanical properties of PEO-based electrolyte, which behaves as a viscous liquid at elevated temperatures. Direct application of such electrolyte in a lithium-ion cell would encounter the problems characteristic of liquid electrolytes. Weston and Steele characterized the behavior of lithium perchlorate-polyethylene oxide (LiClO4 –PEO) with addition of inert filler, α-alumina, in the high temperature range (100◦ C to 150◦ C).15 It was determined that the optimal volumetric loading for maintaining conductivity and improving mechanical stability at 100◦ C was 10 vol%. This amount of filler had negligible effect on overall conductivity of the composite, but the mechanical stability improved at the same time. This suggested possible use of this system in polymer batteries operating at high temperatures. It should be mentioned, that addition of higher volumetric loadings of Al2 O3 filler (50 vol%) in the experiments resulted in significant decrease of ionic conductivity, the values of which became much lower than expected from the Maxwell–Wagner EMT.15 This effect was explained by agglomeration of alumina particles resulting in insulating barriers within the polymer. It should be noted that rather large alumina particles (40 µm) were used in these experiments.15 Further investigations of polymer composites with inert fillers confirmed the above findings.18–25 The main purpose once again was improvement of mechanical strength of the polymer at the temperatures above 60◦ C. Croce et al. performed electrochemical analysis of (PEO)8 LiClO4 + Al2 O3 composites and compared the results to the cycle performance of pure (PEO)8 LiClO4 at 100◦ C.21 Electrochemical cycling was done in a cell where the composite electrolyte was sandwiched between metallic lithium foil and TiS2 . It was determined that conductivity of such composite system is

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comparable to that of a pure polymer electrolyte provided the particle size is sufficiently small (smaller than 5 µm), and the highest conductivity was obtained at 10 wt% loading of the ceramics filler. The results of C/5 cycling in the configuration described above show successful cycling up to 150 cycles; at the same time the cell containing the polymer electrolyte alone was cycled only 35 times before it failed due to shorting caused by Li dendrites.21 Similar reports were produced for mixtures of (PEO)8 LiClO4 and γ-LiAlO2 , where the maximum of conductivity was also observed at 10 wt% filler.22, 24, 25 Detailed investigations suggested that the particle size together with the loading fraction plays an important role in overall conductivity behavior. Wieczorek and co-workers produced a systematic study of PEO-NaI electrolytes mixed with alumina and silica powders of different sizes.19, 20, 23 The experiments were done with a range of mono-dispersed θ-Al2 O3 particle diameters: 2 µm, 4 µm, and 7 µm. It was determined that the maximum conductivity was achieved at 10 wt% to 20 wt% with the smallest particles, and the conductivity remained stable over a long period of time.20 The results of these early studies are summarized in Table 1. It should be mentioned that the reported conductivities of the pure polymersalt electrolytes have a significant degree of scatter; therefore, in addition to the absolute values of the CPE conductivity, the values normalized to the conductivity of polymer (when available) are reported in Table 1 in order to emphasize the effect of dispersoid addition. In order to reduce the amount of data, only the results at 10 wt% are shown. Figure 1 further illustrates the particle size effect by displaying the data from Table 1. The conductivities corresponding to two characteristic temperatures are shown, one being above the amorphous transition and one below; 100◦ C and 25◦ C correspondingly. As can be seen the benefit of addition of dispersoid particles in terms of conductivity increase is evident only for very small particle sizes — a narrow band below 2 µm (Fig. 1). As the particle size increases the conductivity of the composite has the value close to that of polymer-salt system alone (normalized conductivity is close to 1).

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Table 1. 10 wt%.

Maximum conductivity of different CPEs with inert fillers achieved at

Polymer Electrolyte

Additive

(PEO)10 -NaI (PEO)8 -LiClO4

SiO2 α−Al2 O3

(PEO)10 -NaI

θ-Al2 O3

(PEO)8 -LiClO4 (PEO)8 -LiClO4 (PEO)8 -LiClO4

γ-LiAlO2 β -Al2 O3 γ−LiAlO2

Size, µm

σ25 S cm−1

σ100 S cm−1

— 40.0 2.0 4.0 7.0 0.5 13 1.0

6.81e–06 2.95e–07 6.16e–06 4.56e–07 6.10e–08 4.58e–07 — —

1.82e–03 6.03e–04 1.55e–03 9.02e–04 1.16e–03 1.11e–03 1.66e–03 9.54e–04

σ25 σPol

σ100 σPol

20.4 0.88 18.4 1.48 0.18 45.8 — —

1.20 0.78 1.04 0.60 0.78 9.57 1.12 1.15

Refs. 23 15 20 22 21 25

Notes: σ25 — conductivity of composite electrolyte at 25◦ C (room temperature). σ100 — conductivity of composite electrolyte at 100◦ C. σPol — conductivity of polymer at the corresponding temperature.

Fig. 1.

Effect of dispersoid particle size on conductivity at 10 wt% of additive.

In order to explain this behavior it was proposed that addition of ceramic dispersoid prevents polymer recrystallization.24, 25 Presence of ceramic particles prevents re-arrangement of polymer chains to a more ordered stable state; this effect is more pronounced if the particle size becomes close to the polymer chain length.25 Apparently there exists an optimal concentration of particles, beyond which

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agglomeration occurs thus creating the regions free of filler which readily recrystallize. Experiments involving NMR, X-ray diffraction and resistivity measurements of the composite electrolytes appear to confirm the above hypothesis. The samples containing pure PEO-based electrolyte and the samples containing polymer mixed with inorganic filler were annealed to 100◦ C, then quenched to 30◦ C. Subsequent resistance measurements were performed as a function of time. It was shown that the resistance of pure (PEO)8 LiClO4 increased dramatically after cooling, while the samples with dispersoid particles maintained their low resistance characteristic of amorphous system.24 In the experiments with PEO-NaI + Al2 O3 the longtime degree of crystallinity was studied using X-ray diffraction experiments, and it was determined that addition of ceramic powder resulted in increased content of amorphous phase in comparison to pure PEO.20 It is interesting to note that the measurements of PEONaI with highly conductive NASICON ceramics produced values of composite conductivity nearly identical to those obtained from the mixture of the same polymer electrolyte with inert filler. Moreover, no percolation was observed with NASICON particles.19 While it was confirmed that addition of NASICON powders to the polymer electrolyte decreased the degree of crystallinity,19, 20 similarly to the effect from addition of aluminum oxide, there was no other benefit derived from highly conductive properties of NASICON. It was suggested that direct conduction through NASICON grains could not take place due to formation of passivating layer on the particle surface since rather high interfacial resistance was observed.19 (see Sec. 3 for discussion on composites with conductive ceramic reinforcement). The initial observations of improved conductivity with addition of fine dispersed inert filler were followed by increased research in this area. The experiments continued with mostly PEO-based polymer electrolytes mixed with Al2 O3 ,26–33 TiO2 ,27, 33–35 ZrO2 ,36 and SiO2 23, 28, 30, 37 In the majority of cases, conductivity enhancements relative to the polymer matrix alone were observed. Unlike the original early studies where the addition of dispersant was viewed

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as a way to strengthen a polymer at high temperatures,15, 21 the later investigations shifted towards moving the operating temperature down while using the fillers as plasticizers to increase the amount of amorphous phase in the composite.27 Based on the previous results on the effect of particle size on conductivity enhancement, the experiments mostly involved particulate ceramics with nano-sized particles. The results from some of the studies are summarized in Table 2. Table 2.

Room temperature conductivity of PEO-LiX with different dispersoids.

Polymer Electrolyte

Additive

(PEO)8 -LiClO4 (PEO)8 -LiClO4

TiO2 Al2 O3

1.3 × 10−2 5.8–03

(PEO)20 -LiClO4 (PEO)20 -LiClO4 (PEO)20 -LiClO4 (PEO)20 -LiClO4

α-Al2 O3 Al2 O3 TiO2 a TiO 2

(PEO)20 -LiClO4

b TiO

(PEO)20 -LiBF4 (PEO)20 -LiCF3 SO3 (PEO)20 -LiCF3 SO3

γ-LiAlO2 γ-LiAlO2 γ-LiAlO2

(PEO)20 -LiBF4

c S-ZrO

(PEO)20 -LiClO4 (PEO)20 -LiClO4

c S-ZrO

(PEODME)-LiClO4 SiO2 (PEODME)-LiClO4 Al2 O3 (PEODME)-LiClO4 TiO2 (PEODME)-LiClO4 a TiO2 (PEO)9 -LiCF3 SO3 (PEO)9 -LiCF3 SO3 (PEO)9 -LiCF3 SO3 (PEO)9 -LiCF3 SO3

σ25 σPol

10 10

7.0 × 10−6 4.0 × 10−6

70.0 27, 28 40.0

0.90 5.0 × 10−2 2.0 × 10−2 2.0 × 10−2

10 10 10 10

3.6 × 10−5 7.6 × 10−6 9.7 × 10−6 1.1 × 10−5

117.8 24.6 31.3 34.9

2.0 × 10−2

10

1.1 × 10−5

34.9

4.0 4.0 4.0

20 10 20

2.0 × 10−7 3.0 × 10−8 1.0 × 10−7

— 0.38 1.25

26

2

2.5 × 10−2

10

3.5 × 10−8

0.58

38

2

2.5 × 10−2 2.5 × 10−02

5 10

4.8 × 10−6 2.1 × 10−6

20.0 11.43

36

7.0 × 10−3 1.3 × 10−2 2.1 × 10−2 10 × 10−12

10 10 10 10

7.1 × 10−6 4.5 × 10−6 5.8 × 10−6 7.4 × 10−6

5.29 3.39 4.37 5.56

30

3.96 × 10−6 9.91 × 10−6 6.58 × 10−5 7.00 × 10−5

7.14 17.9 118.8 126.1

29

2

c S-ZrO

Al2 O3 Al2 O3 Al2 O3 Al2 O3

Loading (wt%)

σ25 S cm−1

2

Size, µm

basic>acidic>filler free,40 which once again contradicts the data in Fig. 2. Similar results were obtained by Egashira et al. using (PEO)20 -LiBF4 with Al2 O3 where the maximum gain in ionic conductivity was observed for neutral filler while the lowest conductivity was found in samples with acidic alumina (the conductivities distributed as neutral>basic>filler free>acidic).31 It is reasonable to suggest that other factors may play an important role in CPE conductivity behavior thus inflating the amount of variables involved in the problem. Detailed work by Syzdek et al. demonstrates rather insignificant role of surface acidity on conductivity of composites made with alumina and titania powders in PEO-LiClO4 .33 It was determined that the processing of powders plays a crucial role in overall performance of the composite, making direct comparison of results from multiple studies challenging. For instance, a high degree of agglomeration of nano-sized Al2 O3 fillers following acid treatment was observed where agglomerates in tens of micrometers range were still present even after prolonged sonication, as shown in Fig. 3.33 Interestingly, the highest conductivity was observed in samples with alumina grains of approximately 1 µm in size, exceeding the conductivity of composites with nano-sized fillers (Table 2).

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Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport 247

Fig. 3. SEM micrograph showing agglomerates of nano-TiO2 in polymer electrolyte. Reprinted from Ref. 33 with permission from Elsevier.

Results by Bac et al. demonstrate significant influence of salt concentration in polymer electrolyte on effective conductivity and lithium transference number.30 The experiments involved poly(ethylene oxide)dimethyl ether (PEODME) with LiClO4 and different dispersoid fillers (Al2 O3 , TiO2 , and SiO2 ). It was determined that the benefits of adding the ceramics particles were evident at very specific ranges of salt concentrations (10−3 to 10−2 mol/kg and 0.5 to 1 mol/kg) where somewhat modest enhancements in conductivities were observed (Table 2 lists the values at 10−2 mol/kg). At all other concentrations (the overall range investigated was from 10−3 to 10 mol/kg), the conductivity of the electrolyte with ceramics additive was very close to that of the PEODME-LiClO4 matrix. Acid treatment of titania particles increased the conductivity only slightly, from 5.8 × 10−6 to 7.4 × 10−6 S/cm.30 While most of the work used the filler concentration of 10 wt% following the early studies,15, 21, 22, 24 further investigations show that the optimal filler loading is not necessarily 10 wt% for all combinations of polymer, salt, and filler. In a very detailed study, Dissanayake et al. investigated the effect of both filler concentration and particle size on the conductivity of (PEO)9 -LiCF3 SO3 (lithium triflate, LiTf) and Al2 O3 .29 The results suggest very strong

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Fig. 4.

Conductivity measurements in (PEO)9 -LiTf + xAl2 O3 system.29

correlation between the surface area of the filler and maximum conductivity enhancement, with the enhancements being more pronounced at higher temperatures. The representative cases from the study in Ref. 29 are shown in Fig. 4, and the room temperature conductivity values are placed in Table 2. As can be seen from Fig. 4 the conductivity maxima can be achieved at two different values of filler concentration, depending on the particle size and temperature. It should be noted, that one set of experiments in Ref. 21 involved large particles but having high degree of porosity with an average pore size of 5.8 nm. Effectively these fillers have the largest specific surface area, and the composite can be considered as a nanocomposite with 5.8 nm grains. Apparently, the larger grains produce bimodal conductivity behavior — one optimum being at approximately 10 wt%. The peaks merge together with decreasing

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Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport 249

Fig. 5. Room temperature conductivity in (PEO)9 -LiTf + xAl2 O3 system with different particle sizes.29

particle sizes (increasing surface areas). The results from room temperature measurements are arranged separately in Fig. 5. 3. Polymer Composites with Conductive Fillers Compared to the literature on solid polymer nanocomposite electrolytes employing insulating nanoparticles as fillers,41 there are vastly fewer reports where the stiff inorganic filler is itself a Li+ conductor. However, a few research groups have explored the concept of these mixed phase composite electrolytes where both phases conduct Li cations. These groups highlight slightly different rationales for the study of these composites, but it seems that they all recognize the difficulty of creating and maintaining interfacial contact between rigid solids, e.g. the solid electrolyte and electrode.42–52 The polymeric phase is viewed as an important component that facilitates interparticle contact, while providing some mechanical flexibility and processing ease. Invariably, the polymeric phase in these studies consisted of a dissolved Li salt in a polymer based on an EO motif. PEO with dissolved LiX, where X is a soft anion, is the archetypical lithium ion polymer electrolyte. Early reports by Skaarup et al. in the late 1980s emphasized composite systems consisting of Li3 N in PEO-LiTf.42 The authors

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recognized the importance of interfacial charge transfer between the polymeric and ceramic phase; hence they fabricated composites using Li3 N grains with average particle sizes of 50–100 µm. A series of composites were characterized where the polymeric volume fraction was varied; the optimal volume fraction of PEO-LiCF3 SO3 was 5–10 vol%. At 5 vol% polymer, the conductivity at 30◦ C was circa 10−4 S cm−1 , which is 1000X the conductivity of the polymer electrolyte but 4X smaller than the Li3 N conductivity. Above 70◦ C, the activation energy, 0.27 eV, was consistent with the activation energy of pure Li3 N. Below the melting temperature of the polymeric phase, the activation energy was 0.17 eV. This reduction was not explained, but it is important to note that a large increase in activation energy was not observed, as is the case for pure PEO-LiTf. For neat PEO-LiTf, the activation energy increases to 1.3 eV below its crystallization temperature. The authors concluded that the limiting transport process is not within the polymeric phase. As the volume fraction of polymer electrolyte was increased, a corresponding drop in conductivity and increase in activation energy were observed. Above 70◦ C, the activation energies of Li3 N and pure PEO-LiTf were reported as 0.27 and 0.54 eV, respectively. From 16 to 64 vol% polymer, the conductivity dropped by several orders of magnitude, and the activation energy became 0.6 eV. Interestingly, the activation energy was essentially constant over the entire temperature range. Since the activation energy remained constant at 0.6 eV throughout the entire temperature range, it was concluded that the polymer’s microstructure must be modified within the interfacial regions. Symmetrical cells of the composite with Li metal electrodes were prepared and cycled galvanostatically. Compared to sintered Li3 N, dendrites formed at lower currents in the Li3 N/PEO-LiCF3 SO3 composites. Unfortunately, extensive characterization of symmetric cells or the incorporation of the material into full solid-state cells was not reported. In a later report, Skaarup et al. communicated their findings on sulfide glass (1.2 Li2 S–1.6 LiI-B2 S3 ) with grain sizes of 25– 75 µm in PEO-LiCF3 SO3 and polyethylene (PE).43 PE was used to further confirm the role of the polymeric phase in these composites.

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Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport 251

Fig. 6. Schematic representation of polymer composite electrolyte (terminology of original authors was mixed phase electrolyte). White region is the inorganic phase; the black region is the polymer electrolyte. Reprinted from Ref. 42 with permission from Elsevier.

Given that PE is electrically and ionically insulating, the authors were surprised to observe similar transport behavior using PE and PEO: LiTf. Optimal volume fractions for both polymer matrices were approximately 10 vol%. The conductivity at 25◦ C was about 10−5 S cm−1 , and the activation energies were 0.34 eV, which is consistent with the activation energy of the sulfide glass. These results suggested that the polymeric phase contributes little to charge transport. Rather, its primary role is to act as a binder for the inorganic particles. Optimal results were obtained using micronized PE wax with a volume fraction of 10.9%. The authors assumed this composition provided the best binding properties, providing intimate, stable interparticle contact between the sulfide glass grains. This was an important finding because PE, being a saturated hydrocarbon, is chemically inert in contact with Li metal. In 1989, Aono showed that trivalent substitutions of Ti4+ in the lithium titanium phosphate system [Li1+x Mx Ti2−x (PO4 )3 ] while maintaining a NASICON crystal structural leads to improvements in ion conductivities several orders of magnitude. Optimal lattice conductivities of 3 × 10−3 S cm−1 were achieved substituting Al

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to yield a composition of Li1.3Al0.3 Ti1.7 (PO4 )3 (LATP).53 However, like Li3 N and other solid electrolytes, this system is chemically unstable in contact with Li metal due to the presence of Ti4+ . Due to the higher Li+ conductivities, several groups have tried to integrate LATP into solid-state batteries with Li metal electrodes. An Australian group investigated mixtures of LATP with an ethylene oxide(EO)/propylene oxide (PO) copolymer containing dissolved LiCF3 SO3 .45 The copolymer had a molecular weight of 5000 g mol−1 and trihydroxyl functionality; the EO:PO ratio was 3:1. At a LATP loading of 66 wt%, the composite’s conductivity was approximately an order of magnitude higher than the polymer electrolyte’s but lower than that of an optimally sintered LATP membrane. A later study confirmed conductivity enhancements in composites containing 40 vol% LATP.47 This study also compared transport in composites fabricated with “fine” and “medium”sized LATP powders. Mid-frequency semicircles observed in the Nyquist impedance plots were ascribed to transport at the interface between LATP and the polymeric phase. Comparing the Nyquist plots of composites fabricated with “medium” and “fine” LATP at the same filler concentrations, they observed much larger interfacial impedances for the “fine” particles. Moreover, the overall composite conductivity did not increase significantly using the “fine” particles, while the composites with “medium” particles had an appreciable conductivity increase at high filler loadings (>20 vol%). The authors convincingly argue that interfacial impedance severely limits Li+ transport throughout the composite’s microstructure. The authors also qualitatively described a dramatic improvement in the composite’s conductivity after a minor exposure to atmospheric humidity. The effect of moisture absorption was further quantified subsequently.48 The composites were exposed to the laboratory atmosphere and allowed to absorb moisture from the air. After nine days of exposure, the composite’s conductivity increased by a factor of 70. The conductivities of the polymer electrolyte and LATP exposed to the lab environment for the same length of time increased by factors of five and six, respectively. Thus, the authors suggested that the absorbed moisture dramatically altered

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Designing Solid Polymer Composite Electrolytes for Facile Lithium Transport 253

the interfacial behavior. While this approach is unfeasible for real electrolyte materials to be integrated with Li-ion anodes or Li metal, which require rigorously dried components, it is an interesting result that highlights the importance of the interfacial region in these composites. They also performed these experiments where the atmosphere was saturated with the vapors of protic and aprotic polar solvents and obtained similar results. Many of these solvents (e.g. methanol and acetonitrile) absorbed quite readily into the composites, representing more than 20% of the composite by mass. Like water, however, methanol and acetonitrile are both unsuitable solvents for lithium batteries. The importance of the interfacial transport was later corroborated by Inda et al.52 They fabricated composites of NASICON powders mixed with a PEO/poly(propylene oxide) copolymer and LiTFSI. The role of the average particle size was investigated. In one composite, the average particle size was 1.5 µm and in the other, the average particle diameter was 5 µm. Composites with the 5 µm powders had the highest conductivity. Solid-state batteries were built using these composite electrolytes, a LiCoO2 cathode, and Li4 Ti5 O12 anode. Consistent with the conductivity results, the best battery performance in terms of capacity and capacity retention over 10 cycles was observed for the cells employing composites with average particles sizes of 5 µm. In the preceding studies, ceramic particulate fillers randomly dispersed within a polymer electrolyte matrix comprised the composite microstructures. Wang et al. presented an intriguing alternative design consisting of ceramic electrolyte fibers dispersed in polymer electrolyte matrices.50 The ceramic composition was the perovskite-type lithium lanthanum titanate: Li0.35 La0.55 TiO3 (LLTO). The motivation for employing fibers was to improve the mechanical properties relative to dispersed particulate composites, as well as reduce the high resistance interfacial area between polymer and ceramic. Li transport should be favorable within the high aspect ratio fibers where diffusion can occur unimpeded by the polymer–ceramic interface. However, a uniform sheath of polymer electrolytes around the LLTO fibers was an important requirement

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due to the chemical instability of LLTO with Li metal. The reduction potential for Ti4+ in LLTO is approximately 1.5 V versus Li/Li+ . Composites consisting of dispersed LLTO particles were compared to composites filled with chopped LLTO fibers. For a given LLTO loading, the overall composite conductivity was higher using fibers versus dispersed particulates. Facile intra-fiber transport of Li+ cations was promoted as one reason for these higher conductivities. Another likely contribution is the differences in interfacial area. The characteristic lengths of the LLTO fibers and particles were 250 µm and 5 × 10−2 : the concentrated region. The conductivity still increases with x but less rapidly. The activation energy decreases linearly with x, while above the percolation threshold, some defects aggregate in clusters and do not participate in the conduction anymore. Only free defects are mobile, however the presence of the clusters induce a large distribution of energy barrier for anion jump and can favor anions mobility. Réau et al.,47 have described a similar conductivity mechanism depending on x as described above for doped BaF2 . A deep analysis of ionic conductivity has been made by Ure.48 He could determine the migration enthalpy of F interstitial ions or F vacancies in pure and doped CaF2 crystals (see Table 1). Wang and Grey28 have studied YF3 -doped CaF2 by NMR spectroscopy and could identify the F anions in different interstitial positions. From variable temperature 19 F MAS NMR studies they found that F1 and F2 ions are mobile at low temperature and F3 and Fn ions are also mobile at high temperature.

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Table 1. Ionic conductivities and activation energies of rare earth doped fluorite-type compounds.

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Compound CaF2 Ca0.65 La0.35 F2.35 Ca0.65 Ce0.35 F2.35 Ca0.65 Pr0.35 F2.35 Ca0.65 Gd0.35 F2.35 Ca0.65 Tb0.35 F2.35 Ca0.65 Dy0.35 F2.35 Ca0.65 Ho0.35 F2.35 Ca0.65 Y0.35 F2.35 Ca0.7 Yb0.3 F2.3 Ca0.8 Lu0.2 F2.2 SrF2 Sr0.69 La0.31 F2.31 Sr0.64 Ce0.36 F2.36 Sr0.68 Pr0.32 F2.32 Sr0.64 Nd0.36 F2.36 Sr0.83 Gd0.17 F2.17 Sr0.8 Tb0.2 F2.2 Sr0.79 Dy0.21 F2.21 Sr0.9 Ho0.1 F2.1 Sr0.8 Y0.2 F2.2 Sr0.84 Er0.16 F2.16 Sr0.75 Lu0.25 F2.25 BaF2 Ba0.6 La0.4 F2.4 Ba0.74 Ce0.26 F2.26 Ba0.74 Pr0.26 F2.26 Ba0.86 Nd0.14 F2.14 Ba0.8 Gd0.2 F2.2 Ba0.94 Tb0.06 F2.06 Ba0.9 Dy0.1 F2.1 Ba0.7 Ho0.3 F2.3 Ba0.7 Tm0.3 F2.3 Ba0.85 Lu0.15 F2.15

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Conductivity at 160◦ C (S cm−1 )

Reference

7 × 10−11 1.11 × 10−6 2.48 × 10−6 2.51 × 10−6 8.37 × 10−5 1.64 × 10−5 1.47 × 10−5 5.17 × 10−6 1.57 × 10−7 1.12 × 10−8 1.61 × 10−9 2 × 10−11 4.61 × 10−5 7.4 × 10−5 5.33 × 10−5 4.77 × 10−5 5.01 × 10−8 1.51 × 10−8 4.49 × 10−9 1.54 × 10−9 1.35 × 10−9 5.69 × 10−10 8.07 × 10−10 2 × 10−10 5.95 × 10−5 5.62 × 10−6 1.76 × 10−6 9.57 × 10−7 1.3 × 10−6 2.33 × 10−6 7.04 × 10−7 1.34 × 10−6 4.53 × 10−7 1.72 × 10−6

29 36

29 37

29 32

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3.2. Tysonite-type Fluorides

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3.2.1. Structure of tysonite-type fluorides Nominally pure or undoped rare-earth fluorides (RF3 ) crystallize in two different structures at room temperature. One is based on trigonal tysonite-type (P-3c1) and another is based on orthorhombic βYF3 (Pnma) type. The RF3 with large cations (La–Nd) adopt tysonitetype structure whereas the RF3 with smaller cations (Sm–Lu, Y) adopt the orthorhombic structure.14 Further, two modifications exists in the tysonite-type structure: hexagonal phase (P63/mmc)49 and trigonal phase (P-3c1).51 The hexagonal phase is built up of two compositionally different layers. One layer is built up of only fluoride ions (F1) (4f, 1/3, 2/3, 0.57) and the other layer is built-up of fluoride ions (F2, 2b, 0, 0, 1/4) as well as metal ions (2c, 1/3, 2/3, 41 ) in the same plane. These two layers are stacked alternatively perpendicular to the c-direction. The ratio between F1 and F2 is 2:1. The following compounds adopt the hexagonal tysonite-type structure: ThOF2 ,51 BiO0.1 F2.8 ,52 and Bi1−x Bax F3−x (0.05 ≤ x ≤ 0.17)53 and R1−x Mx F3−x solid solutions (R = Gd–Er; M = Ca, Sr: 0.07 ≤ x ≤ 0.33).55 It was suggested that the hexagonal phase is stabilized by the doping of heterovalent M2+ cation in RF3 (R = Gd-Er) by creating the anion vacancies. In the trigonal phase (Fig. 3) the F1 sublattice remains the same with a small displacement in the position. However, the F2 lattice splits into F2 and F3. F2 atoms slightly move out of the Ln–F plane because of very small F–F distances between the fluorine and Ln–F layers. The ratio of fluoride ions in the trigonal phase is F1:F2:F3 = 12:4:2. High-resolution 19 F MAS NMR studies confirmed the existence of three fluorine sites F1:F2:F3 in the LaF3 structure.54 The following phases adopt the trigonal tysonite-type structure: RF3 (R = La-Nd) and solid solutions on their basis R1−x Mx F3−x (M = Ca, Sr, Ba and R = La–Nd).53 3.2.2. Ionic conductivity in tysonite-type fluorides The ionic conductivity is found to increase in tysonite-type single crystals in the following order LaF3 < NdF3 < PrF3 < CeF3 .14 Among

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Crystal structure of trigonal tysonite.

these tysonite-structured rare earth trifluorides, LaF3 is of particular interest since its mechanism of conductivity is representative of many rare-earth trivalent fluorides. In the case of LaF3 , conductivity is slightly anisotropic with a higher conductivity parallel to the caxis than perpendicular to this c-axis for temperatures up to 415 K.56 The activation energies are 0.46 eV for transfer perpendicular to the c-axis, and 0.43 eV for transfer in parallel to the c-axis. The anisotropy disappears above 415 K and the activation energy of 0.26 eV observed indicates a change in the conductivity mechanism from a vacancy mechanism within the F1 fluorine subsystem to a mechanism with exchange of F vacancies between the F1 subsystem and the F2–F3 subsystem.57 The anisotropy disappeared in the doped samples suggesting that exchange between F1, F2, F3 sublattices occurs at low temperatures. As for the fluorite-type compounds, the conductivities are drastically improved by doping with heterovalent fluorides. Most of the published works report on R1−y My F3−y compounds (R = La or Ce and M = Ba, Sr or Ca) which are obtained by mixing RF3 with MF2 in different concentrations.

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Fig. 4. Variation of the conductivity at 293 K as a function of the ionic radius rM2+ in the series of solid solutions: (1) La0.95 M0.05 F2.95 , (2) Pr0.95 M0.05 F2.95 , and (3) Nd0.95 M0.05 F2.95 (M = Ca, Sr, Ba).57 Reproduced with permission of Springer.

The solubility limit of the M2+ ions in the La1−y My F3−y is 23 mol% for Ca, 17 mol% for Sr and 14 mol% for Ba.53 Figure 4 shows the conductivity of R0.95 M0.05 F2.95 system for different doping ions. SrF2 was found to be a suitable dopant for LaF3 , PrF3 and NdF3 exhibiting improved conductivity.57 However, in the case of CeF3 , CaF2 was found as the most effective dopant. Takahashi et al. have obtained higher conductivity values for doped CeF3 compared to LaF3 .58 The conductivity was greatly improved by doping with 5 mol% of BaF2 , SrF2 or CaF2 , the highest conductivity was obtained for Ce0.95 Ca0.5 F2.95 with 1.2 · 10−2 S.cm−1 at 573 K. The formation of F interstitials in tysonite-type crystal is very unlikely because the interstitial sites in the tysonite structure are very small (0.84 Å while for F anion, radius is 1.19 Å).59 For the compositions studied, the introduction of bivalent cations should lead to the formation of vacancies. Further, vacancies on the F1 sublattice were observed in a neutron diffraction study of La1−x Bax F3−x in agreement with the increase in F1 mobility on BaF2 doping.50 The intrinsic defects in the tysonite structure are the Schottky defects (cation vacancy associated with anion vacancy) and the anion conduction is a vacancy mechanism. For low concentration of dopant, the conductivity increases with y and the activation energy decreases. This is mainly related to the formation of an increasing number of defects which are free to migrate. The conductivity reaches a maximum at the percolation threshold (ca.

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y = 0.07 for BaF2 in LaF3 ). From this value, the activation energy remains somehow constant but the conductivity decreases because the vacancy migration is hindered by the presence of too many defects.

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3.2.3. Effect of nanostructuring in tysonite-type fluorides Although most of the work was done on single crystals, a few works have been published on polycrystalline LaF3 . Sobolev et al.61 prepared La0.8 Ca0.2 F2.8 by ball milling. Different milling conditions were applied using a planetary mill but the ionic conductivity seemed not much affected by them. The reported values are close to 5 · 10−4 S·cm−1 at 200◦ C but the activation energy is higher than reported for doped LaF3 single crystals. By contrast with fluoritetype fluorides (e.g. CaF2 ), the conductivity has not been improved with nanoparticles of LaF3 . Rather, the conductivity decreases and the activation energy increases compared to single crystal.62 Similar results were obtained by Reddy and Fichtner in the case of nanocrystalline LaF3 and LaF3 doped with BaF2 .9 Figure 5 shows

Fig. 5. Arrhenius plot for the ionic conductivity of nanocrystalline La1−x Bax F3−x (0≤ x ≤ 0.15).9 Reproduced with permission of Royal Chemical Society.

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the Arrhenius plot for the ionic conductivity of nanocrystalline La1−x Bax F3−x (0 ≤ x ≤ 0.15). Much less conductivities and high activation energies were observed compared to corresponding single crystals compositions reported. This contrary behavior compared to fluorite-type compounds is not yet understood, but it is likely that the situation at the grain boundaries plays a decisive role. 3.2.4. Ion conduction mechanism in tysonite-type fluorides As mentioned earlier in the tysonite-type structure, fluoride ions are positioned in three distinct sites, F1, F2, F3, in the ratio of 12:4:2. The F2 and F3 sites are located in the mixed layers. Usually, they are taken as quasi-equivalent F2,3 sites. Earlier 19 F NMR experiments indicate that only the F1 ions are mobile at low temperatures and that exchange between the F1 and F2–F3 sublattices occurs only at higher temperatures.60 These 19 F NMR studies could not resolve the difference between F2 and F3 sites and treated them as dynamically equal. However, Wang and Grey studied the ion conduction mechanism by high-resolution 19 F MAS NMR experiments on LaF3 and La0.99 Sr0.01 F2.99 .54 This method is in fact able to resolve the difference between F2 and F3 ions. Figure 6(a) shows the 19 F MAS NMR spectra of LaF3 in the temperature range 24–266◦ C. At room temperature they observed the three fluorine sites F1, F2 and F3. The exchange between F1 and F3 started at 73◦ C. At 266◦ C, F1 peak shifted by 4.2 ppm while the F3 peak almost disappeared. Thus, until 266◦ C exchange is possible only between F1–F1 and F1–F3. No F1–F2 exchange was observed. Figure 6(b) shows the 19 F MAS NMR spectra La0.99 Sr0.01 F2.99 . In the case of La0.99 Sr0.01 F2.99 the F1– F3 exchange started at much lower temperature compared to pure material and the F3 peak completely disappeared at 198◦ C. Above 198◦ C, the F1–F2 exchange was observed and by 266◦ C the F2 peak completely disappeared. Hence, the F1, F2 and F3 sites in LaF3 are dynamically non-equivalent. In summary, at low temperature exchanges occur only among the F1 sites, at higher temperature there is an exchange between F1 and F3 and at even higher temperature there is exchange between F1 and F2. Heterovalent doping greatly decreases the onset

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Fig. 6. 19 F variable-temperature MAS NMR spectra of (a) LaF3 , (b) La0.99 Sr0.01 F2.99 , collected with a spinning speed of 23 kHz. *= spinning sideband. 19 F spectra were referenced to CCl3 F at 0 ppm. Adapted with permission from Ref. 54. Copyright (1997) American Chemical Society.

temperature for fluoride diffusion. The order of activation energies for fluoride ion jump pathways is F1–F19V versus Li+ /Li.27 Al–stabilized cubic LLZO does not consist of any redox active species at lower potentials and is therefore inherently stable both chemically and electrochemically against metallic Li. Cyclic voltammetry indicates that metallic Li can be reversibly plated and stripped in a Cu–LLZO– Li cell (Fig. 8). The lack of activity from 0 to 6V also suggests no oxidation occurs at higher potentials. Further detailed potentiostatic studies are needed confirm the higher potential stability though. Although there are a few relatively recent examples demonstrating stability against metallic Li, there is a need for comprehensive kinetic characterization of the charge/discharge behavior of solid state half cells. The impetus for doing so is to demonstrate the utility of SCOs in solid-state batteries. For example, conventional Li-ion batteries are charged and discharged at current densities in the 1 mA/cm2 range. Typically, Li-ion cell impedances are in the 10−6 S/cm) at 298 K and some but not extensive reactivity between the SCO and electrodes. The previous section discussed mechanical property considerations of free-standing SCO membranes. Indeed, the relatively brittle nature of oxides will not only complicate handling and large scale fabrication of membranes but also of integration into solidstate cells/batteries. Bonding SCO membranes to dense electrodes will likely require high temperature processing to form chemical bonds between components. Likewise, shear stresses arise if there are significant disparities in thermal coefficients of expansion between components. The magnitude of the stresses may be reduced by geometric parameters such as the stack height and aspect ratio, but in general smaller dimensions minimize strain to reduce stress. Additionally, the introduction of a sintering aid or low melting temperature interphase could lower fabrication temperatures to decrease thermo-mechanical stresses upon cooling. Ohta et al. recently identified Li3 BO3 as a compound that reduced the fabrication temperature to allow the fabrication of LLZO/LCO cells at or below 700◦ C.51 In addition to lowering the processing temperature, the solid state cell performance was maintained and the interfacial impedance was low enough to allow cycling studies. Other groups have used similar strategies to interpose a metal oxide interlayer between cathodes and the solid electrolyte. For example, LiNbO3 or LLTO have been used as a buffer layer to form a low impedance and chemically stable interface between LCO and sulfide electrolytes.52, 53 The same approach could be effective for SCOs. Further work is required to mature this approach. The application will determine the solid-state cell or battery design primarily striking a balance between energy and power density.54 Vehicle electrification will likely require different formats based on fully electric versus hybrid electric vehicles. Microelectronics will also have unique performance requirements. Whatever the case, the cell component materials and dimensions will control the charge/discharge power density. Depending on the electrode type, one charge carrier, such as Li-ions, electrons or metallic Li atoms in

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Li anodes, will limit the rate performance. For example, assuming the interfacial impedance is relatively low, the self-diffusivity of Li may limit the rate capability of solid state cells employing metallic Li anodes. In other words, stripping Li in relatively thick Li anodes (several microns) at high current densities may result in Kirkendall diffusion voids causing abrupt spikes during discharge. Similarly, polarization will result if metal oxide Li insertion electrodes have poor Li-ion, electronic or both types of conduction. As a guide, consider a conventional Li-ion cell that consists of a liquid electrolyte to transport ions through a percolative pore network that permeates the entire cell stack. The liquid electrolyte delivers Li–ions to individual particles such as graphite for the anode or LCO (LiCoO2 ), NMC (LiNi0.33 Mn0.33 Co0.33 O2 ), or LMO (LiMn2 O4 ) for the cathode. Because the liquid electrolyte has a relatively high conductivity, it is the solid state transport in the Li–ion host electrode particles that limit the total ionic current during cycling. The solid state transport is governed by the intrinsic solid-state diffusivity and the Li host electrode particle diameter, which can range from hundreds of nanometers to approximately ten microns in diameter. Additionally, most Li–ion host electrode materials have relatively low electronic conductivity with the exception of LCO and graphite. To address this, conductive additives such as carbon black are added to make an electrically conductive composite electrode. Likewise, if similar electrode materials are to be used in solid-state batteries, novel design and fabrication technologies must be developed to address mixed transport issues. Many reports describing examples of solid-state batteries involve sputtered electrodes and/or electrolytes.55 Sputtering allows for the fabrication of discrete, relatively dense layers ranging from hundreds of nanometers to microns thick. This level of precision enables component dimensions that match the range of particle size or maximum diffusion distance in conventional Li-ion cells, which again is important to control the maximum diffusion distance in the electrodes. However, in the context of vehicle electrification and cost, battery packs will weigh hundreds of kilograms, thus perhaps favoring bulk-scale fabrication approaches. Conversely, it

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Fig. 10. (a) Integration of amorphous interphase(s) (could be the same or different based on the electrode formulations) between a SCO and insertion electrodes, (b) an amorphous, ionically conducting amorphous interphase could reduce the stack sintering temperature and increase interface strength, (c) Li-ion migration is facilitated by the amorphous interphase between the SCO and layered cathode. The amorphous interphase eliminates the need for precise crystallographic alignment between components, thus reducing interface impedance.

may be feasible to coat battery components with relatively thin intermediate layers to reduce interfacial impedance and enhance bonding. For example, micron-scale components could be bound together with an ionically conducting, low melting temperature material that forms low impedance interfaces (Fig. 10). Depending on the electrode and SCO selection, the amorphous interphase can consist of different formulations (as indicated by layers “1” and “2” in Fig. 10). An alternative route may be to emulate conventional Li-ion cell technology by replacing the liquid electrolyte with the solid electrolyte. Tarascon et al. have recently demonstrated that this approach is effective in solid state sulfide electrolyte-based thick film batteries.56 Electrode and electrolyte powders are blended together

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(a)

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(b)

Fig. 11. A sintering aid facilitated solid-state cell fabrication. (a) LCO particles bound together and to a LLZO membrane using a sintering aid at 700◦ C. (b) Half-cell cycling data demonstrates the efficacy of this approach. Reprinted with permission from Ref. 51.

to make composite electrodes that are then hot pressed to a layer of electrolyte. Compared to SCOs, sulfide electrolytes have the added benefit of significantly lower elastic moduli to facilitate sintering and densification at lower temperatures, which can prevent deleterious reactions between the electrodes and the electrolyte. Returning back to the SCOs, the powder processing approach could be a viable approach. The primary challenge, however, will be establishing processing technology to densify the electrode-electrolyte blend without causing deleterious chemical reactions. Unlike the sulfide electrolytes, SCOs will likely require elevated temperatures to sinter as described above. One potential remedy is to pursue an approach reported by Ohta et al. where a sintering aid (Li3 BO3 ) was used to sinter LCO to previously densified LLZO at 0.5, and appears to be associated with the added oxygen replacing the nbS in the glass. Redrawn from Ref. 154.

all-sulfide lithium thiogermanate glass. A full description of these spectra and their structural interpretation has been given,83,153 but it is observed as shown in Fig. 6(a) that the added O first substitutes at the bS position, presumably because it can be bonded to the stronger Lewis acid in the glass, Ge+4 over Li+ . In this case, the Li+ conductivity increase in this system, Fig. 8, occurs in a compositional region where the added oxygen is only replacing the bS units. The conductivity activation energy decreases and the conductivity increases in this same compositional region can be understood if the added oxygen at the bridging position, Fig. 6(a), actually increases the interstitial doorway radius, rD , that characterizing the size of the interstitial region, see Figs. 7(a) and 10, between equilibrium cation sites. We have quantified this effect by determining the effective interstitial doorway radius from neutron and x-ray diffraction studies and a sharp increase in the rD value is observed

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Fig. 9. Composition dependence of the calculated values of the rD , strain activation energy, Es and total conductivity activation energy, Etot for ternary oxy Li2 S + GeS2 + GeO2 -sulfide glasses. The rapid increase in the conductivity, Fig, 8, appears to be associated with a decreasing strain energy arising from an increasing doorway radius caused by the added oxygen replacing the bS positions, Fig. 6, above. At higher O additions, the doorway radius, rD , finally decreases below that of the pure all-sulfide glass, x >0.5, and appears to be associated with the added oxygen replacing the nbS in the glass. Redrawn from Ref. 154.

for the first addition of oxygen to the binary 0.5Li2 S + 0.5GeS2 glass, see Fig. 9. We have therefore suggested that this increase in rD works to decrease the volumetric requirements for the Li+ conduction, thereby effectively decreasing the volumetric strain energy for conduction in these glasses. Hence, rather than increasing the coulombic binding energy as might be expected, the added oxygen decreases the strain energy for conduction. We have also measured the available free-volume for conduction, not shown here, and find that indeed the free-volume in these glasses increases with the first O additions to these glasses. However, this effect of replacing bS units cannot persist beyond the available concentration of bS and, as such, Fig. 8 above shows that the conductivity eventually falls below that of the original pure all-sulfide glass at x = 0.5 where all of the bS positions have been replaced. Beyond this composition, the added O must create nbO and as such now the dopant Li+ ions must interact with the higher

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binding energy of the nbO site and the conductivity must fall. This structural argument suggests that the beneficial effect of added O may only occur when there are available bS to replace. It seems that this hypothesis has not so far been examined. Indeed, beyond the limited studies of Tatsumisago and his co-workers and those of the author, the field of mixed oxy-sulfide glasses has not been fully examined and perhaps remains a fertile field of study. Further, there also appears to be no studies of mixed anion seleno-sulfido or seleno-oxo glasses in the open literature to determine the more compositionally broader veracity of these observations and models developed by the author and his students. While the author admits the review of the various structures of FIC sulfide and oxy-sulfide glasses has been brief, it is hoped that the broad aspects of this field have been provided and the significant citations to the literature can be helpful to the reader to learn more about the interesting and important structures of these glasses. We now turn to a brief discussion of the models of conductivity and the conductivity activation energy to lay a framework for the more significant discussion of the composition dependence of the conductivity in these glasses and glass-ceramics. 3. General Mechanisms of Ion Conduction in Glass The general agreement on the role of added modifiers and dopant salts to a typical sulfide glass is to create structure breaking cation — anion sites where the anion is (typically) nbS and alkali conduction requires the thermally activated hopping of the alkali ion from one nbS structure to another. A two dimensional simplified interpretation of this hopping mechanism is shown in Fig. 10. In order for the alkali ion to move to the adjacent cation site, it is generally understood that there are two energy barriers that it must overcome, see for example reference.158 The first energy barrier arises from the coulombic charge attraction energy that results from the cation — anion attractive potential; the smaller the cation and the anion, the larger is the attractive potential and the larger the coulombic energy barrier that must be overcome. Likewise, for larger cations,

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Fig. 10. Simplified two dimensional representation of the ion conduction energetics as a weakly bound alkali ion, +, hops from one equilibrium cation site, nbS, to another. To do so, the mobile cation must overcome two energy barriers, the longer range coulombic binding energy, EC , and the shorter range volumetric strain energy, ES . Redrawn from Ref. 158.

e.g. Rb+ and Cs+ , and larger anions, e.g. S− and Se− , the coulombic potential energy well of the cation will be smaller and therefore the coulombic energy barrier that must be overcome will be smaller. This coulomb energy barrier, Ec , is often also termed the “creation” energy barrier to suggest that the cation must first dissociate away from the attractive potential of the anion in order for the cation (or anion) to be available for ionic conduction. Because the alkali cation carries volume, this volume must be accommodated in the structure of the glass during conduction events. Because this volumetric strain energy, Es , acts only when the cation moves away from its equilibrium site, this energy barrier is a very short range energy barrier and acts only as the cation attempts to move out of its coordination sphere at the equilibrium cation site. For these reasons, this strain energy barrier is also often called the migration energy barrier. This energy barrier is viewed as being active only when the cation migrates away from the equilibrium site and so it is often associated with the energy barrier to the mobility, µ, of the mobile cation (or anion).

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From the description above, it is not only necessary for there to be large concentrations of the mobile cation species, n, in Eq. 2 below, but that these mobile ions must also have high ionic mobilities, µ in Eq. 2.

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 σ0 −Eact σ(T) = n(T)eZµ(T) ≡ exp T kT

(2)

To achieve large values of both the number density n and mobility µ, the energy barriers for each of these terms must be small, see Eq. 3a and 3b. As described above, the cation size dependence of both of these two energy barriers are opposite. That is, while small cations would be expected to have small volumetric strain energies, they would also be expected to have larger coulombic binding energies. This effect is shown in Fig. 11. Hence, depending upon the specific details of the glass structure, the most conductive cation (or anion) may be different for different glasses. However, it is most commonly observed that only the small cations Li+ and Na+ have significant conductivities in the glassy state for either oxide or sulfide glass chemistries. While Se and Te based glasses are beyond the scope of this review, it is also true that there are almost no reports

Fig. 11. Cation radius dependence of the coulombic binding energy, EC , which decreases (at constant alkali ion concentration and anion radius) with cation radius, and the cation radius dependence of the volumetric strain energy, ES , that increases with cation radius. Both calculations were done using Equations 7 and 8 for a typical sulfide glass.

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of alkali ion conduction in the these glasses beyond the first reports by Pradel et al. on Li2 Se + SiSe2 glasses.159–161 The two parts of the total activations energy, Eact , the coulombic binding energy and the strain energy, respectively, are shown in Eq. 3 below.       (a) n(T) = n0 exp −EC RT (b) µ(T) = µ0 (T) exp −ES RT (3) In Eq. 3a and 3b, Ec and Es , as described above, are the creation (coulomb) and migration (strain) activation energy terms, respectively, and sum to the total measured conductivity activation energy, Eact, Eq. (4), Eact = EC + ES

(4)

For completeness, from activated rate theory of conduction in the linear electric field regime, Eq. (5) gives the full form of the zero frequency limit of the conductivity, σd.c. (T).
 −Eact n0 Za Zc e2 λ2 ν0 exp (5) σd.c. (T) = 6kT kT Equating Eqs. (2), (3) and (5) shows that, σ0 =

n0 Za Zc e2 λ2 ν0 6k

(6)

While a complete treatment is beyond the scope of the review here, it is important to review at least one of the models of these activation energies due originally to Anderson and Stuart162 that the author and his co-workers have found to give not only a good understanding of the atomic level description of these activation energies, but also can be used in a predictive manner for glasses of high ionic conductivity. We begin with the coulomb binding energy, Ec .128 Eq. 7 shows that the coulombic binding energy has four separate contributions. First, the simplest part of the binding energy describes the difference in coulombic potential energy at − the equilibrium site (r+ Na +rS ) and at the transition point halfway − between the two equilibrium cation sites, (r+ Na + rS + λ/2). The

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second component of the coulombic binding energy recognizes that the charge separation of the anion and the cation takes place in a glass of permittivity ε0 ε∞ . Finally, the third component of the coulombic binding energy corrects for the fact that the charge separation of the cation and anion also is affected by the many bodied nature of the coulombic potential where all cations and anions contribute to the coulomb potential energies of the mobile cations through an effective Madelung constant, MD .  1 MD ZC ZA e2 1   − (7) EC = 4πε0 ε∞ rNa+ + rS− rNa+ + rS− + λ/2 The MD value, of course, cannot be determined a priori for a glass because the long range disorder will give rise to a distribution of MD values, but values typical of compounds related to the glass composition being studied would be expected as a first approximation. However, these MD values would be different for each and every cation and anion in the glass structure and could in principle be calculated only once the full structure of glass is determined. Such structures cannot of course be fully determined, but given the 1/r dependence of the MD values, those distances much farther than 10 atomic distances from the anion or cation of interest would make less and less contribution to the MD values at each site. It might be expected that computer simulations of glass structures by molecular dynamics (MD) or reverse Monte Carlo (RMC) simulations of systems of a few thousand atoms will yield relatively good predictions of the MD values of glass structure. The author and his collaborators are in the process of calculating such MD values from MD simulations and will report on these in the near future. The migration energy ES has been approximated by McElfresch et al.163 as an improvement over the first attempt by Anderson and Stuart162 and is given in Eq. 8. ES = πG

2 λ rNa+ − rD 2

(8)

McElfresch approximated the strain energy as the energy necessary to dilate a cylindrical volume of length λ/2 from its initial radius rD out to the radius necessary to accommodate the conducting ion,

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r+ Na in the case of a sodium ion, through an isotropic medium with shear modulus, G. In the expressions for the coulombic binding energy and the volumetric strain energy, it is clear why the sulfide glasses typically have many orders of magnitude higher conductivities than a corresponding oxide of the same overall alkali ion concentration. Due to the larger ionic radius of the sulfide ion the coulombic binding energy is smaller because not only is the 1/r distance term smaller, but the higher atomic polarizability of the sulfide anion creates significantly larger relative dielectric permittivity than for oxide glasses. The sulfide glasses have smaller volumetric strain energies due in part to the weaker chemical bonding of the sulfide glasses giving rise to significantly smaller mechanical moduli and the larger sulfide anions would pack in the glass structure at larger distances in the first coordination sphere around the alkali cation giving rise to larger interstitial doorway radii, rD . Having now reviewed a significant part of the general compositional characteristics of sulfide ion conducting glasses and reviewed the general characteristics of the activation energies for ion conduction in glass and having motivated why sulfide glasses have such higher ionic conductivities than typical oxide glasses, we now turn to a review of some of the more recent and important data on the composition dependence of specific sulfide glasses and glass ceramics. The lighter and more mobile Li+ and Na+ cations are considered first and then some (but not all) of the heavy alkali cations in pure sulfide glasses are considered. The review is completed by considering recent results on sulfide glass-ceramic materials. 4. Sulfide Glass Solid Electrolytes 4.1. Binary Sulfide Alkali Ion Conducting Glasses 4.1.1. Binary Alkali Thiophosphate Glasses 4.1.1.1. Lithium systems While covalent sulfide glasses such as As2 S3 have been known and studied for more than 50 years, alkali ion doped ionic glasses appear to be much more recent. It appears that the very first

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report of a lithium (or sodium) doped sulfide glass was made in 1980 in the research group of Levasseur who reported on the compositional series of glasses LiX + Li4 P2 S7 as an analogue to the well-studied LiX + LiPO3 series reported on extensively by Malugani and co-workers.61,111,116,117,164 Even for this composition, the glass forming character is quite limited and rapid quenching is required to yield this composition as a glass. This arises presumably because at this stoichiometry, Li4 P2 S7 , there is a relatively high melting point compound that rapidly and congruently crystallizes out of the melt. All of these melts must optimally be melted inside sealed tube ampoules, typically glassy silica, to prevent molecular P4 S10 units from sublimating from the melt and atmospheric moisture and water from reacting with the melt. This sublimation is most significant for the high P2 S5 composition, typically x Li2 S 400◦ C) heated where in the case of over heat treating at 550◦ C, a significantly lower conductivity of ∼10−6 (
cm)−1 and a significantly higher conductivity activation energy of ∼50 kJ/mole is obtained. In order to further optimize the glass crystallization processing conditions, these authors have explored a more traditional two step, lower temperature nucleation and higher temperature growth, glass crystallization process.105 As perhaps expected from the fine powdered nature of the MCM glasses and also for finely ground MQ glass powders, crystallization processes were dominated by surface nucleation and growth processes. By comparison, for the MQ bulk glasses, bulk nucleation and growth processes were the dominant crystallization processes. From their experiments, an optimized two-step process for the highest conductivity 70 mole% Li2 S + 30 mole% P2 S5 composition was found to be a nucleation step of 30 minutes at 210◦ C followed by a growth step of 1 hour at 280◦ C was observed to yield the highest Li+ ion conductivity glass-ceramic over a single glasscrystallization process of 280◦ C for one hour. This higher conductivity was attributed to decreasing the interparticle and interfacial impedance of the polycrystalline glass ceramic. Even still, the Li+ ion conductivity of the optimized glass-ceramic had a conductivity of ∼5.2 × 10−3 (
cm)−1 at room temperature compared to the single step glass ceramic value of 4 × 10−3 (
cm)−1 , only a modest increase for a longer and multi-step glass-crystallization process. From the expected phase diagram for the Li2 S + P2 S5 system, compounds are expected and known for Li4 P2 S7 (66.7 mole% Li2 S) and Li3 PS4 (75 mole% Li2 S). Hence, the highest conductivity glass ceramic composition being found at 70 mole% Li2 S would suggest that it exists as a mixed phase, the lever rule suggesting 60 mole% Li4 P2 S7 and 40 mole% Li3 PS4 . However, rather than a mixture of these two crystalline phases, both powder XRD and singlecrystal XRD were consistent with the formation of a new metastable phase Li7 P3 S11 that is comprised of a mixture of the two

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Fig. 28. 010 plane projection of the crystal structure for highly conducting Li7 P3 S11 phase formed on glass crystallization 70Li2 S + 30P2 S5 glass. Taken with permission from Ref. 260. 3− thio-phosphate anions, P2 S4− 7 and PS4 . Figure 28 shows a portion of the crystal structure of Li7 P3 P11 along the [010] direction that shows 3− 260 the presence of the P2 S4− 7 and PS4 anions. + While positions for the Li were reported for this structure, presumably due the rapid motion of the Li+ ions in this solid electrolyte, the authors could not definitively determine the Li+ positions, their occupancies and the presence or otherwise of interstitial sites. A principal reason for this appears to be that these authors used x-ray synchrotron radiation which is known to scatter weakly off low Z elements such as Li. Further, these researchers appear to not have examined the material at sufficiently low temperature such that the Li+ ions would be effectively frozen into their equilibrium positions. Low temperature neutron diffraction could be used to resolve these problems and perhaps could be used to fully identify the Li+ ion positions in this solid electrolyte. A further increase in the Li+ ion conductivity of this electrolyte was recently reported by these workers. They overcame an earlier observation where Li2 S and P2 S5 chemically reacted in the solid state formed the identified Li7 P3 S11 phase directly, but produced a poorly conducting phase with Li+ ion conductivity of only ∼10−6

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(
cm)−1 at room temperature. In a new third approach, these authors reacted the Li2 S and P2 S5 at high temperature 700◦ C in the liquid state followed by rapidly quenching the liquid to the glassy state followed by the glass crystallization process described above.261 In this two-step process where the liquid state of the Li7 P3 S11 phase was accessed, the measured room temperature Li+ ion conductivity of 17 × 10−3 (
cm)−1 with an activation energy of ∼17 kJ/mole were observed. These authors found that in these high temperature processed glass-ceramics, the inter-granular interfacial impedance was further decreased to yield a glass-ceramic with a Li+ ion conductivity 17/5.2 = 3.2 times higher than the best glass ceramic they had previously obtained. This improved behavior may arise from more complete chemical reaction of the constituents in a more rigorously dry and oxygen free environment arising from the vacuum sealed SiO2 tube preparation method the authors reported using. Finally, in an effort to better understand and therefore control the glass crystallization process and to ultimately produce a glass

Fig. 29. Dependence of the geometric and the density of mixed phases on the sintering (glass crystallization) temperature for the composition 0.80Li2 S + 0.20P2 S5 MCM glasses while pressuring at 186 or 232 MPa as identified on the figure. Redrawn and used with permission from Ref. 262.

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ceramic with an optimal microstructure, Berbano and co-workers262 have investigated hot-pressing routes to more fully dense glass ceramics, see Fig. 29. As perhaps expected, these authors observed that they could indeed achieve higher density glass ceramics using hot pressing techniques of MCM powder starting materials. So far it seems, however, that these authors have not measured the d.c. Li+ ion conductivities of these hot pressed glass ceramic materials.262 6. Conclusions and Outlook As described in this chapter, tremendous progress has been made in developing new kinds and types of glassy and glass-ceramic solid sulfide and oxy-sulfide electrolytes. The conductivities, especially those of Li+ electrolytes, are now as high as, or in some cases exceed, those of the typical liquid electrolytes that are in common use today in many if not all lithium ion batteries. The low ionic conductivity of typical oxide glasses and glass ceramics that has limited the utilization of these solid electrolytes in batteries has essentially been overcome by new sulfide and mixed oxy-sulfide glass and glass ceramic chemistries. The ionic conductivity of these new electrolytes is sufficiently high so that the electrolytes are now device enabling, rather than device limiting. New highly scalable MCM processing techniques have opened up new avenues of mass production that have the potential to enable these new sulfide and oxy-sulfide solid electrolytes to be used in large scale, low cost manufacturing to enable new types of high performance and safe all-solid state batteries. The tremendous advantage that these highly conducting solid electrolytes have in opening up the temperature range of operation to significantly higher and significantly lower operating temperatures and in dramatically reducing the fire hazards presented by traditional liquid electrolyte lithium batteries make them very attractive electrolytes for such next generation solid state batteries. The new challenges that these solid electrolyte batteries present are a direct result of their advantageous chemistries that lead to their ability for large scale low cost facile MCM manufacturing and their

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high ionic conductivity. However, through careful compositional optimization, it has been shown that mixed oxy-sulfide and mixed glass former compositions can be used to dramatically improve the chemical and electrochemical stability and as such, it can be envisioned that soon new compositions and chemistries will be developed that will enable these shortcomings to be overcome. Indeed, significant progress has already been made in making these sulfide materials relatively inert in normal dry-room battery operations. Given the tremendous progress that has been made in increasing the conductivity of these solid electrolytes and in improving their chemical and electrochemical stability combined with new low cost routes to large scale manufacturing of them in high yield and in high purity, it is perhaps reasonable to conclude that future research in solid state battery chemistry will need to focus on developing high capacity anode and cathode chemistries that will take full advantage of the high conductivity and high electrochemical stability that these solid electrolytes present. These are subjects of the other chapters of this book and the reader is encouraged to peruse these chapters to learn more about the progress that has been made in these areas. Acknowledgments The author would like to thank the editors of this volume for the invitation to write this chapter and for their patience as he completed his work on it. Their help has been enormous and their patience beyond compare as they helped me work through this chapter during a year of unprecedented travel and other commitments. Thanks for your great help, it is very much appreciated. The author would like to thank the many funding agencies, Department of Energy, National Aeronautics and Space Agency, the Office of Naval Research, the Defense Advanced Research Projects Agency, and especially the National Science Foundation Ceramics Program of the Division of Materials Research and in particular the current Program Director Dr. Lynnette Madsen, who have helped support the author and his many students in their research on the

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subject of ion conducting glasses, ceramics, and glass ceramics. The author gratefully acknowledges the NSF for his current NSF DMR grant 1304977 and his current NSF CBET grant 1438223 and the past support from the NSF over the past nearly 30 years. The author would like to thank and acknowledge the help and support of his many post-doctoral, graduate, and undergraduate researchers of his GOM group at Iowa State University for their untiring work to help many of the research advances possible in the author’s research group. He would like to thank and acknowledge the many collaborators at Iowa State and around the world for their significant contributions to nearly all aspects of this work. In particular, he would like to thank Professors Ferdinando Borsa and Ivar Svare for their long-standing collaboration on the use of NMR techniques in the study of FICGs. Finally, the author would like to thank his former Ph.D. mentor Professor C. Austen Angell who helped begin the author’s study of fast ion conducting glasses 35 years ago. His mentoring and help has led to a fruitful and enjoyable career in studying these very interesting and now very useful materials. References 1. E. Seddon, E. J. Tippett, W. E. S. Turner, J. Soc. Glass Technol., 16 (1932) 450. 2. J. R. Hendrickson, P. J. Bray, Phys. Chem. Glasses, 13 (1972) 43. 3. W. M. Risen, Jr., G. B. Rouse, J. M. Gordon, Phys. Non-Cryst. Solids, Int. Conf., 4th, (1977) 473. 4. M. D. Ingram, C. T. Moynihan, A. V. Lesikar, J. Non-Cryst. Solids, 38&39 (1980) 371. 5. H. Jain, H. L. Downing, N. L. Peterson, J. Non-Cryst. Solids, 64 (1984) 335. 6. A. Q. Tool, C. G. Eichlin, J. Opt. Soc. Am., 8 (1924) 419. 7. A. Q. Tool, D. B. Lloyd, Bur. Standards Fuels and Furnaces, 6 (1928) 353. 8. A. Q. Tool, J. B. Saunders, J. Research Natl. Bur. Standards, 42 (1949) 171. 9. A. H. Dietzel, Phys. Chem. Glasses, 24 (1983) 172. 10. K. Hughes, J. O. Isard, Phys. Electrolytes, 1 (1972) 351. 11. I. M. Hodge, M. D. Ingram, A. R. West, J. Amer. Ceram. Soc., 59 (1976) 360.

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12. M. D. Ingram, C. A. Vincent, Annual Reports of the London Chemical Soc., A (1977) 23. 13. A. Levasseur, B. Cales, J. M. Reau, P. Hagenmuller, C. R. Hebd. Seances Acad. Sci., Ser. C, 285 (1977) 471. 14. T. Minami, H. Nambu, M. Tanaka, J. Am. Ceram. Soc., 60 (1977) 467. 15. M. Lazzari, B. Scrosati, C. A. Vincent, J. Am. Ceram. Soc., 61 (1978) 451. 16. A. Levasseur, B. Cales, J. M. Reau, P. Hagenmuller, Mater. Res. Bull., 13 (1978) 205. 17. T. Minami, M. Tanaka, Kagaku (Kyoto), 33 (1978) 122. 18. R. J. Charles, J. Amer. Ceram. Soc., 46 (1963) 235. 19. P. M. Sutton, J. Amer. Ceram. Soc., 47 (1964) 188. 20. K. Otto, M. E. Milberg, J. Amer. Ceram. Soc., 51 (1968) 326. 21. P. B. Macedo, C. T. Moynihan, R. Bose, Phys. Chem. Glasses, 13 (1972) 171. 22. V. Provenzano, L. P. Boesch, V. Volterra, C. T. Moynihan, P. B. Macedo, J. Amer. Ceram. Soc., 55 (1972) 492. 23. H. A. Schaeffer, J. Mecha, J. Amer. Ceram. Soc., 57 (1974) 535. 24. D. P. Button, R. P. Tandon, H. L. Tuller, D. R. Uhlmann, J. Non-Cryst. Solids, 42 (1980) 297. 25. C. C. Hunter, M. D. Ingram, Solid State Ionics, 14 (1984) 31. 26. H. L. Tuller, D. P. Button, Transp.-Struct. Relat. Fast Ion Mixed Conduct., Proc. Risoe Int. Symp. Metall. Mater. Sci., 6th, (1985) 119. 27. M. Balkanski, R. F. Wallis, I. Darianian, J. Deppe, Mater. Sci. Eng., B1 (1988) 15. 28. F. A. Fusco, H. L. Tuller, NATO ASI Series, Series B: Physics, 199 (1989) 321. 29. B. Barrau, J. M. Latour, D. Ravaine, M. Ribes, Silic. Ind., 44 (1979) 275. 30. B. Barrau, M. Ribes, M. Maurin, A. Kone, J. L. Souquet, J. Non- Cryst. Solids, 37 (1980) 1. 31. B. Barrau, J. L. Souquet, M. Ribes, C. R. Seances Acad. Sci., Ser. C, 290 (1980) 353. 32. J. P. Malugani, G. Robert, Solid State Ionics, 1 (1980) 519. 33. J. P. Malugani, G. Robert, C. R. Seances Acad. Sci., Ser. C, 290 (1980) 251. 34. M. Ribes, B. Barrau, J. L. Souquet, J. Non-Cryst. Solids, 38–39 (1980) 271. 35. J. L. Souquet, Solid State Ionics, 5 (1981) 77. 36. J. L. Souquet, E. Robinel, B. Barrau, M. Ribes, Solid State Ionics, 3–4 (1981) 317. 37. S. S. Susman, L. Boehm, K. J. Volin, C. J. Delbecq, Solid State Ionics, 5 (1981) 667.

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38. M. Ribes, B. Carette, M. Maurin, Journal de Physique, Colloque, (1982) 403. 39. B. Carette, M. Maurin, M. Ribes, M. Duclot, Solid State Ionics, 9–10 (1983) 655. 40. B. Carette, M. Ribes, J. L. Souquet, Solid State Ionics, 9–10 (1983) 735. 41. A. Levasseur, C. Delmas, Comm. Eur. Communities, [Rep.] EUR, (1984) 67. 42. A. Pradel, T. Pagnier, M. Ribes, Solid State Ionics, 17 (1985) 147. 43. S. J. Visco, P. Spellane, J. H. Kennedy, J. Electrochem. Soc., 132 (1985) 751. 44. J. H. Kennedy, Y. Yang, J. Solid State Chem., 69 (1987) 252. 45. V. K. Deshpande, A. Pradel, M. Ribes, Mater. Res. Bull., 23 (1988) 379. 46. J. H. Kennedy, Z. Zhang, J. Electrochem. Soc., 135 (1988) 859. 47. W. Burckhardt, B. Rudolph, Solid State Ionics, 36 (1989) 153. 48. H. Eckert, J. H. Kennedy, A. Pradel, M. Ribes, J. Non-Cryst. Solids, 113 (1989) 287. 49. J. H. Kennedy, Z. Zhang, J. Electrochem. Soc., 136 (1989) 2441. 50. S. M. Martin, J. A. Sills, J. Non-Cryst. Solids, 135 (1991) 171. 51. S. W. Martin, D. R. Bloyer, T. Polewik, Ceram. Trans., 20 (1991) 147. 52. M. Menetrier, A. Hojjaji, C. Estournes, A. Levasseur, Solid State Ionics, 48 (1991) 325. 53. J. P. Duchange, J. P. Malugani, G. Robert, Prog. Batteries Sol. Cells, 4 (1982) 46. 54. R. Mercier, J. P. Malugani, B. Fahys, J. Douglade, G. Robert, J. Solid State Chem., 43 (1982) 151. 55. J. P. Malugani, G. Robert, Solid State Ionics, 1 (1980) 519. 56. J. P. Malugani, G. Robert, Mater. Res. Bull., 14 (1979) 1075. 57. J. P. Malugani, G. Robert, Mater. Res. Bull., 14 (1979) 1075. 58. M. Doreau, A. Abou El Anouar, G. Robert, Journal de chimie physique, 78 (1981) 223. 59. R. Mercier, J. P. Malugani, B. Fahys, G. Robert, Solid State Ionics, 5 (1981) 663. 60. G. Robert, J. P. Malugani, Fr. Demande, 7 pp (1981). 61. G. Robert, J. P. Malugani, A. Saida, Solid State Ionics, 3/4 (1981) 311. 62. M. Ribes, B. Carette, M. Maurin, J. Phys., Colloq., (C9), 403–6 (1982). 63. B. Carette, M. Ribes, J. L. Souquet, Solid State Ionics, 9–10 (1983) 735. 64. B. P. Carette, A. Kone, J. L. Souquet, M. R. Ribes, M. Maurin, Fr. Demande, 10 pp (1983). 65. H. Wada, M. Menetrier, A. Levasseur, P. Hagenmuller, Mater. Res. Bull., 18 (1983) 189.

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88. K. S. Sidhu, S. Singh, S. S. Sekhon, S. Chandra, A. Kumar, Phys. Chem. Glasses, 32 (1991) 255. 89. A. Pradel, C. Rau, D. Bittencourt, P. Armand, E. Philippot, M. Ribes, Chem. Mater., 10 (1998) 2166. 90. A. Pradel, N. Kuwata, M. Ribes, J. Phys.: Condensed Matter, 15 (2003) S1561. 91. R. Christensen, J. Byer, T. Kaufmann, S. W. Martin, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol., Part B, 50 (2009) 237. 92. M. J. Haynes, C. Bischoff, T. Kaufmann, S. W. Martin, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol., Part B, 50 (2009) 144. 93. R. Christensen, G. Olson, J. Byer, S. Martin, J. Non-Cryst. Solids, To be submitted. 94. R. Christensen, G. Olson, W. Martin Steve, J. Phys. Chem. B, 117 (2013) 16577. 95. R. Christensen, G. Olson, W. Martin Steve, J. Phys. Chem. B, 117 (2013) 2169. 96. C. Bischoff, K. Schuller, N. Dunlap, S. W. Martin, J. Phys. Chem. B, 118 (2014) 1943. 97. C. Bischoff, K. Schuller, S. W. Martin, J. Phys. Chem. B, 118 (2014) 3710. 98. M. Tatsumisago, S. Hama, A. Hayashi, H. Morimoto, T. Minami, Solid State Ionics, 154–155 (2002) 635. 99. A. Hayashi, S. Hama, F. Mizuno, K. Tadanaga, T. Minami, M. Tatsumisago, Solid State Ionics, 175 (2004) 683. 100. F. Mizuno, A. Hayashi, K. Tadanaga, M. Tatsumisago, Electrochem. Solid-State Lett., 8 (2005) A603. 101. T. Ohtomo, F. Mizuno, A. Hayashi, K. Tadanaga, M. Tatsumisago, Solid State Ionics, 176 (2005) 2349. 102. Y. Seino, K. Takada, B. C. Kim, L. Zhang, N. Ohta, H. Wada, M. Osada, T. Sasaki, Solid State Ionics, 176 (2005) 2389. 103. A. Hayashi, K. Minami, F. Mizuno, M. Tatsumisago, J. Mater. Sci., 43 (2008) 1885. 104. J. Trevey, Y. S. Jung, S.-H. Lee, ECS Trans., 16 (2009) 181. 105. K. Minami, A. Hayashi, M. Tatsumisago, J. Am. Ceram. Soc., 94 (2011) 1779. 106. A. Hayashi, K. Noi, A. Sakuda, M. Tatsumisago, Nature Communications, 3 (2012) 1843/1. 107. M. Tatsumisago, A. Hayashi, Solid State Ionics, 225 (2012) 342. 108. B. E. Warren, J. Am. Ceram. Soc., 24 (1941) 256. 109. A. Levasseur, J. C. Brethous, J. M. Reau, P. Hagenmuller, Mater. Res. Bull., 14 (1979) 921.

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110. A. Levasseur, M. Kbala, J. C. Brethous, J. M. Reau, P. Hagenmuller, M. Couzi, Solid State Commun., 32 (1979) 839. 111. J. P. Malugani, G. Robert, Mater. Res. Bull., 14 (1979) 1075. 112. J. P. Malugani, R. Mercier, B. Fahys, G. Robert, J. Solid State Chem., 45 (1982) 309. 113. T. Minami, T. Shimizu, M. Tanaka, Solid State Ionics, 9–10 (1983) 577. 114. P. P. Tsai, M. Greenblatt, J. Non-Cryst. Solids, 103 (1988) 101. 115. M. D. Ingram, Philos. Mag. B, 60, 729–40 (1989). 116. J. P. Malugani, A. Wasniewski, M. Doreau, G. Robert, C. R. Hebd. Seances Acad. Sci., Ser. C, 287 (1978) 455. 117. J. P. Malugani, A. Wasniewski, M. Doreau, G. Robert, A. Al Rikabi, Mater. Res. Bull., 13 (1978) 427. 118. S. W. Martin, J. Amer. Ceram. Soc., 74 (1991) 1767. 119. Y. M. Moustafa, J. Mater. Sci. Mater. Electron., 6 (1995) 135. 120. M. Ganguli, M. H. Bhat, K. J. Rao, Solid State Ionics, 122 (1999) 23. 121. P. S. S. Prasad, A. N. D. Rani, S. Radhakrishna, Mater. Chem. Phys., 25 (1990) 487. 122. J. R. Min, J. Wang, L. Q. Chen, R. J. Xue, W. Q. Cui, J. K. Liang, Physica Status Solidi A: Applied Research, 148 (1995) 383. 123. A. Pradel, C. Rau, D. Bittencourt, P. Armand, E. Philippot, M. Ribes, Chem. Mater., 10 (1998) 2162. 124. D. Y. Seung, A. Levasseur, M. Couzi, Phys. Chem. Glasses, 39 (1998) 295. 125. P. Kluvanek, R. Klement, M. Karacon, J. Non-Cryst. Solids, 353 (2007) 2004. 126. D. Larink, H. Eckert, S. W. Martin, J. Phys. Chem. C, 116 (2012) 22698. 127. D. Larink, H. Eckert, M. Reichert, S. W. Martin, J. Phys. Chem. C, 116 (2012) 26162. 128. R. Christensen, G. Olson, S. W. Martin, J. Phys. Chem. B, 117 (2013) 16577. 129. R. Christensen, J. Byer, G. Olson, S. W. Martin, J. Non-Cryst. Solids, 358 (2012) 583. 130. R. Christensen, J. Byer, G. Olson, S. W. Martin, J. Non-Cryst. Solids, 358 (2012) 826. 131. G. E. Jellison, Jr., Phys. Chem. Glasses, 19 (1978) 52. 132. P. J. Bray, S. Feller, G. E. J. Jellison, Y. H. Yun, J. Non-Cryst. Solids, 38–39 (1980) 93. 133. P. J. Bray, F. Bucholtz, A. E. Geissberger, I. A. Harris, Nuclear Instrum. Meth., 199 (1982) 1. 134. P. J. Bray, A. E. Geissberger, F. Bucholtz, I. A. Harris, J. Non-Cryst. Solids, 52 (1982) 45.

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135. P. J. Bray, J. F. Emerson, D. Lee, S. A. Feller, D. L. Bain, D. A. Feil, J. Non-Cryst. Solids, 129 (1991) 240. 136. L. van Wullen, W. Muller-Warmuth, Solid State Nucl. Magn. Res., 2 (1993) 279. 137. J. W. Zwanziger, R. E. Youngman, M. Braun, Borate Glasses, Crystals & Melts, [Proceedings of the International Conference on Borate Glasses, Crystals & Melts], 2nd, Abingdon, UK, July 22–25, 1996, (1997) 21. 138. P. J. Bray, W. J. Dell, Journal de Physique, 43 (1982) 131. 139. G. El-Damrawi, W. Muller-Warmuth, H. Doweidar, I. A. Gohar, J. NonCryst. Solids, 146 (1992) 137. 140. J. W. Mackenzie, A. Bhatnagar, D. Bain, S. Bhowmik, C. Parameswar, K. Budhwani, S. A. Feller, M. L. Royle, S. W. Martin, J. Non-Cryst. Solids, 177 (1994) 269. 141. S. A. Feller, J. Kottke, J. Welter, S. Nijhawan, R. Boekenhauer, H. Zhang, D. Fei, C. Parameswar, K. Budhwani, M. Affatigato, A. Bhatnagar, G. Bhasin, S. Bhowmik, J. Mackenzie, M. Royle, in: Borate Glasses, Crystals, and Melts, 1996, pp. 246. 142. J. M. Roderick, D. Holland, A. P. Howes, C. R. Scales, J. Non-Cryst. Solids, 293–295 (2001) 746. 143. H. Yamamoto, N. Machida, T. Shigematsu, Solid State Ionics, 175 (2004) 707. 144. J. P. Malugani, G. Robert, R. Mercier, Mater. Res. Bull., 15 (1980) 715. 145. T. Minami, K. Imazawa, M. Tanaka, J. Non-Cryst. Solids, 42 (1980) 469. 146. A. Hayashi, H. Yamashita, M. Tatsumisago, T. Minami, Solid State Ionics, 148 (2002) 381. 147. A. Hayashi, R. Komiya, M. Tatsumisago, T. Minami, Solid State Ionics, 152–153 (2002) 285. 148. A. Hayashi, M. Tatsumisago, T. Minami, J. Electrochem. Soc., 146 (1999) 3472. 149. K. Minami, A. Hayashi, S. Ujiie, M. Tatsumisago, Solid State Ionics, 192 (2011) 122. 150. Y. Kim, J. Saienga, S. W. Martin, J. Phys. Chem. B, 110 (2006) 16318. 151. Y. Kim, S. W. Martin, Solid State Ionics, 177 (2006) 2881. 152. Y. Kim, J. Saienga, S. W. Martin, J. Non-Cryst. Solids, 351 (2005) 3716. 153. Y. Kim, J. Saienga, S. W. Martin, J. Non-Cryst. Solids, 351 (2005) 1973. 154. Y. Kim, J. Saienga, S. W. Martin, J. Phys. Chem. B, 110 (2006) 16318. 155. I. Seo, S. W. Martin, Inorg. Chem., 50 (2011) 2143. 156. C. Julien, S. Barnier, M. Massot, N. Chbani, X. Cai, A. M. LoireauLocac’h, M. Guittard, Materials Science & Engineering, B: Solid-State Materials for Advanced Technology, B22 (1994) 191.

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157. B. Barrau, M. Ribes, M. Maurin, A. Kone, J. L. Souquet, J. Non-Cryst. Solids, 37 (1980) 1. 158. S. W. Martin, C. A. Angell, J. Non-Cryst. Solids, 83 (1986) 185. 159. V. Michel-Lledos, A. Pradel, M. Ribes, Eur. J. Solid State Inorg. Chem., 29 (1992) 301. 160. A. Pradel, V. Michel-Lledos, M. Ribes, H. Eckert, Solid State Ionics, 53–56 (1992) 1187. 161. A. Pradel, G. Taillades, M. Ribes, H. Eckert, J. Non-Cryst. Solids, 188 (1995) 75. 162. O. L. Anderson, D. A. Stuart, J. Am. Ceram. Soc., 37 (1954) 574. 163. D. K. McElfresh, D. G. Howitt, J. Am. Ceram. Soc., 69 (1986) C. 164. J. P. Malugani, B. Fahys, R. Mercier, G. Robert, J. P. Duchange, S. Baudry, M. Broussely, J. P. Gabano, Solid State Ionics, 9–10 (1983) 659. 165. G. Robert, J. P. Malugani, A. Saida, Solid State Ionics, 3–4 (1981) 311. 166. M. Tatsumisago, A. Hayashi, Functional Materials Letters, 1 (2008) 31. 167. M. Tatsumisago, F. Mizuno, A. Hayashi, J. Power Sources, 159 (2006) 193. 168. F. Mizuno, T. Ohtomo, A. Hayashi, K. Tadanaga, M. Tatsumisago, Solid State Ionics, 177 (2006) 2753. 169. F. Mizuno, A. Hayashi, K. Tadanaga, M. Tatsumisago, Solid State Ionics, 177 (2006) 2721. 170. A. Hayashi, Y. Ishikawa, S. Hama, T. Minami, M. Tatsumisago, Electrochem. Solid-State Lett., 6 (2003) A47. 171. A. Hayashi, S. Hama, T. Minami, M. Tatsumisago, Electrochem. Commun., 5 (2003) 111. 172. F. Mizuno, S. Hama, A. Hayashi, K. Tadanaga, T. Minami, M. Tatsumisago, Chem. Lett., (2002) 1244. 173. F. Mizuno, A. Hayashi, K. Tadanaga, M. Tatsumisago, Adv. Mater. (Weinheim, Ger.), 17 (2005) 918. 174. S. W. Martin, J. Amer. Ceram. Soc., 71 (1988) 438. 175. C. Bischoff, K. Schuller, M. Haynes, S. W. Martin, J. Non-Cryst. Solids, 358 (2012) 3216. 176. S. S. Berbano, I. Seo, C. M. Bischoff, K. E. Schuller, S. W. Martin, J. NonCryst. Solids, 358 (2012) 93. 177. Z. Zhang, J. H. Kennedy, H. Eckert, J. Amer. Chem. Soc., 114 (1992) 5775. 178. Y. Kawamoto, M. Nishida, Phys. Chem. Glasses, 18 (1977) 19. 179. Y. Kawamoto, M. Nishida, J. Non-Cryst. Solids, 20 (1976) 393. 180. J. H. Kennedy, S. Sahami, S. W. Shea, Z. Zhang, Solid State Ionics, 18–19 (1986) 368.

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181. S. Sahami, S. W. Shea, J. H. Kennedy, J. Electrochem. Soc., 132 (1985) 985. 182. J. H. Kennedy, Y. Yang, J. Solid State Chem., 69 (1987) 252. 183. H. Eckert, Z. Zhang, J. H. Kennedy, J. Non-Cryst. Solids, (1988). 184. J. H. Kennedy, Z. Zhang, Solid State Ionics, 28–30 (1988) 726. 185. J. H. Kennedy, Z. Zhang, J. Electrochem. Soc., 135 (1988) 859. 186. H. Eckert, J. H. Kennedy, A. Pradel, M. Ribes, J. Non-Cryst. Solids, 13 (1989) 287. 187. H. Eckert, Z. Zhang, J. H. Kennedy, Mater. Res. Soc. Symp. Proc., 135 (1989) 259. 188. J. H. Kennedy, Mater. Chem. Phys., 23 (1989) 29. 189. A. Pradel, M. Ribes, Mater. Chem. Phys., 23 (1989) 121. 190. A. Pradel, M. Ribes, M. Maurin, Solid State Ionics, 28–30 (1988) 762. 191. A. Pradel, M. Ribes, Solid State Ionics, 18–19 (1986) 351. 192. H. Takahara, M. Tabuchi, T. Takeuchi, H. Kageyama, J. Ide, K. Handa, Y. Kobayashi, Y. Kurisu, S. Kondo, R. Kanno, J. Electrochem. Soc., 151 (2004) A1309. 193. H. Morimoto, H. Yamashita, M. Tatsumisago, T. Minami, J. Ceram. Soc. Jpn., 108 (2000) 128. 194. H. Morimoto, H. Yamashita, M. Tatsumisago, T. Minami, J. Am. Ceram. Soc., 82 (1999) 1352. 195. A. Hayashi, K. Tadanaga, M. Tatsumisago, T. Minami, Y. Miura, J. Ceram. Soc. Jpn., 107 (1999) 510. 196. Y. Yoneda, N. Machida, T. Shigematsu, Funtai oyobi Funmatsu Yakin, 49 (2002) 799. 197. A. Pradel, M. Ribes, Solid State Ionics, 18–19 (1986) 351. 198. J. Cho, S. W. Martin, Ceram. Transactions, 65 (1996) 85. 199. H. Peng, N. Gu, N. Machida, T. Shigematsu, Electrochimica Acta, 48 (2003) 1893. 200. C. Bischoff, K. Schuller, S. P. Beckman, S. W. Martin, Phys. Rev. Lett., 109 (2012) 075901/1. 201. I. Seo, S. W. Martin, RSC Advances, 1 (2011) 511. 202. I. Seo, S. W. Martin, Acta Mater., 59 (2010) 1839. 203. I. Seo, S. W. Martin, ECS Trans., 28 (2010) 287. 204. D. Le Messurier, V. Petkov, S. W. Martin, Y. Kim, Y. Ren, J. Non-Cryst. Solids, 355 (2009) 430. 205. W. Yao, S. W. Martin, Solid State Ionics, 178 (2008) 1777. 206. W. Yao, K. Berg, S. Martin, J. Non-Cryst. Solids, 354 (2008) 2045. 207. J. Saienga, S. W. Martin, J. Non-Cryst. Solids, 354 (2008) 1475. 208. Y. Kim, H. Hwang, K. Lawler, S. W. Martin, J. Cho, Electrochim. Acta, 53 (2008) 5058.

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209. J. Saienga, Y. Kim, B. Campbell, S. W. Martin, Solid State Ionics, 176 (2005) 1229. 210. B. Meyer, F. Borsa, D. M. Martin, S. W. Martin, Phys. Rev. B: Condens. Matter Mater. Phys., 72 (2005) 144301/1. 211. Q. Mei, S. W. Martin, Phys. Chem. Glasses, 46 (2005) 51. 212. Y. Kim, J. Saienga, S. W. Martin, J. Non-Cryst. Solids, 351 (2005) 1973. 213. C. R. Nelson, S. A. Poling, S. W. Martin, J. Non-Cryst. Solids, 337 (2004) 78. 214. B. Meyer, F. Borsa, S. W. Martin, J. Non-Cryst. Solids, 337 (2004) 166. 215. Q. Mei, B. Meyer, D. Martin, S. W. Martin, Solid State Ionics, 168 (2004) 75. 216. Q. Mei, J. Saienga, J. Schrooten, B. Meyer, S. W. Martin, Phys. Chem. Glasses, 44 (2003) 178. 217. Q. Mei, J. Saienga, J. Schrooten, B. Meyer, S. W. Martin, J. Non-Cryst. Solids, 324 (2003) 264. 218. M. Qiang, K. Young Sik, W. M. Steve, J. Non-Cryst. Solids, submitted (2002). 219. I. Svare, F. Borsa, D. R. Torgeson, S. W. Martin, Phys. Rev. B: Condens. Matter, 48 (1993) 9336. 220. I. Svare, S. W. Martin, F. Borsa, Phys. Rev. B: Condens. Matter Mater. Phys., 61 (2000) 228. 221. K. H. Kim, D. R. Torgeson, F. Borsa, J. Cho, S. W. Martin, I. Svare, Solid State Ionics, 91 (1996) 7. 222. I. Svare, F. Borsa, D. R. Torgeson, S. W. Martin, J. Non-Cryst. Solids, 172–174 (1994) 1300. 223. I. Svare, F. Borsa, D. R. Torgeson, S. W. Martin, Phys. Rev. B: Condens. Matter Mater. Phys., 48 (1993) 9336. 224. G. N. Greaves, S. J. Gurman, C. R. A. Catlow, A. V. Chadwick, S. Houde-Walter, C. M. B. Henderson, B. R. Dobson, Philos. Mag. A, 64 (1991) 1059. 225. A. Levasseur, J. C. Brethous, M. Kbala, P. Hagenmuller, Solid State Ionics, 5 (1981) 651. 226. A. E. Geissberger, F. L. Galeener, Struct. Non-Cryst. Mater., Proc. Int. Conf., 2nd, (1983) 381. 227. J. G. Edwards, P. W. Gilles, Adv. Chem. Ser., No. 72 (1968) 211. 228. A. S. Gates, J. G. Edwards, Inorg. Chem., 16 (1977) 2248. 229. D. E. Hintenlang, P. J. Bray, J. Non-Cryst. Solids, 69 (1985) 243. 230. V. I. Svergun, Y. K. Grinberg, V. M. Kuznets, T. A. Babushkina, Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, (1970) 1448. 231. M. Menetrier, A. Hojjaji, C. Estournes, A. Levasseur, Solid State Ionics, 48 (1991) 325.

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232. H. Eckert, W. Mueller-Warmuth, W. Hamann, B. Krebs, J. Non-Cryst. Solids, 65 (1984) 53. 233. H. Eckert, Z. Zhang, J. H. Kennedy, Mater. Res. Soc. Symp. Proc., 135 (1989) 259. 234. Z. Zhang, J. H. Kennedy, J. Thompson, S. Anderson, D. A. Lathrop, H. Eckert, Appl. Phys. A, 49(1) (1989) 41. 235. S. W. Martin, D. R. Bloyer, J. Am. Ceram. Soc., 73 (1990) 3481. 236. M. Royle, J. Cho, S. W. Martin, Borate Glasses, Cryst. Melts, [Proc. Int. Conf.], 2nd, (1997) 279. 237. K. H. Kim, D. R. Torgeson, F. Borsa, J. P. Cho, S. W. Martin, I. Svare, G. Majer, J. Non-Cryst. Solids, 211 (1997) 112. 238. J. Cho, S. W. Martin, J. Non-Cryst. Solids, 170 (1994) 182. 239. M. Royle, J. Cho, S. W. Martin, J. Non-Cryst. Solids, 279 (2001) 97. 240. S. Hwang, C. Fernandez, J. Amoureux, J. Han, J. Cho, S. Martin, M. Pruski, J. Amer. Chem. Soc., 120 (1998) 7337. 241. S. W. Martin, J. Cho, T. Polewik, S. Bhowmik, J. Amer. Ceram. Soc., 78 (1995) 3329. 242. J. A. Sills, S. W. Martin, D. R. Torgeson, J. Non-Cryst. Solids, 168 (1994) 86. 243. J. Kincs, J. Cho, D. Bloyer, S. W. Martin, ASTM Spec. Tech. Publ., STP 1249 (1994) 185. 244. D. R. Bloyer, J. Cho, S. W. Martin, J. Amer. Ceram. Soc., 76 (1993) 2753. 245. H. K. Patel, S. W. Martin, Phys. Rev. B: Condens. Matter Mater. Phys., 45 (1992) 10292. 246. H. K. Patel, S. W. Martin, Solid State Ionics, 53–56 (1992) 1148. 247. S. W. Martin, T. Polewik, J. Amer. Ceram. Soc., 74 (1991) 1466. 248. S. W. Martin, D. R. Bloyer, T. Polewik, Ceram. Trans., 20 (1991) 147. 249. S. W. Martin, D. R. Bloyer, J. Amer. Ceram. Soc., 74 (1991) 1003. 250. J. Cho, S. W. Martin, J. Non-Cryst. Solids, 298 (2002) 176. 251. J. Cho, S. W. Martin, J. Non-Cryst. Solids, 194 (1996) 319. 252. J. Cho, S. W. Martin, J. Non-Cryst. Solids, 190 (1995) 244. 253. J. A. Sills, S. W. Martin, D. R. Torgeson, J. Non-Cryst. Solids, 175 (1994) 270. 254. J. Cho, S. W. Martin, J. Non-Cryst. Solids, 182 (1994) 248. 255. J. Cho, S. W. Martin, B. Meyer, K. H. Kim, D. R. Torgeson, J. Non-Cryst. Solids, 270 (2000) 205. 256. A. Levasseur, R. Olazcuaga, M. Kbala, M. Zahir, P. Hagenmuller, C. R. Seances Acad. Sci., Ser.2, 293 (1981) 563. 257. H. Yamashita, A. Hayashi, H. Morimoto, M. Tatsumisago, T. Minami, Y. Miura, J. Ceram. Soc. Jpn., 108 (2000) 973. 258. S. W. Martin, W. Creighton, M. Marple, to be published.

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Glass and Glass-Ceramic Sulfide and Oxy-Sulfide Solid Electrolytes

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259. A. Hayashi, T. Fukuda, H. Morimoto, T. Minami, M. Tatsumisago, J. Mater. Sci., 39 (2004) 5125. 260. H. Yamane, M. Shibata, Y. Shimane, T. Junke, Y. Seino, S. Adams, K. Minami, A. Hayashi, M. Tatsumisago, Solid State Ionics, 178 (2007) 1163. 261. Y. Seino, T. Ota, K. Takada, A. Hayashi, M. Tatsumisago, Energy & Environmental Science, 7 (2014) 627. 262. S. S. Berbano, M. Mirsaneh, M. T. Lanagan, C. A. Randall, Int. J. Appl. Glass Science, 4 (2013) 414.

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Chapter 15

Crystalline Polymer Electrolytes Yuri G. Andreev, Chuhong Zhang and Peter G. Bruce∗ School of Chemistry University of St Andrews North Haugh, St Andrews, Fife, Scotland KY16 9ST, UK ∗[email protected]

In this chapter, we describe crystalline ion-conducting complexes formed by akali metal salts and poly(ethylene oxide). A variety of factors influencing the conductivity of such complexes are presented. Electrochemical testing of these materials in lithium and sodium rechargeable batteries demonstrate that crystalline polymer/salt complexes can be used as electrolytes in all-solid-state energy storage devices.

1. Introduction Since their discovery by Wright1 and the realization of their potential as solid ionic conductors by Armand,2 polymer/salt complexes have been the subject of intense study for over 40 years.3, 4 During the first 30 years, amorphous polymer/salt complexes formed by alkali metal salts and poly(ethylene oxide) (PEO), CH3 O(CH2 CH2 O)n CH3 , or its various derivatives were the main focus of research since only such complexes were known to conduct ions and thus serve as polymer electrolytes (PE) in a variety of electrochemical devices. Amorphous PE’s operate only above their glass transition temperature, Tg , and their conductivity mechanism is explained in terms of the dynamic bond percolation theory.5 According to this theory, ion transport is promoted by local segmental motion of polymer chains which repeatedly creates new coordination sites for cations to migrate through. The mechanism of ion transport in amorphous 503

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PE’s cannot operate in crystalline polymer/salt complexes. Thus, crystalline complexes were considered to be insulators, while major scientific efforts were directed towards suppression of crystalline constituents of commonly encountered phase blends. In the meantime, the work of elucidating the structure of crystalline polymer/salt complexes continued to provide information about the short-range order in their amorphous counterparts, since it had been demonstrated that the arrangement of the nearest neighboring atoms was independent of the degree of long-range order.6 We shall begin by describing the discovery of ionic conductivity in crystalline polymer/salt complexes, followed by a presentation of their crystal structures, the factors that influence the magnitude of the conductivity ending with some comments on the future direction of research. 2. Discovery of Crystalline Polymer Electrolytes The research on crystalline polymer/salt complexes took a significant turn when a new and powerful structure determination method from powder diffraction data was developed,7, 8 which led to solution of the crystal structures of PEO6 :LiXF6 (X = P, As, Sb).9, 10 Each of these isostructural complexes, Fig. 1, contains cylindrical tunnels formed by pairs of polymer chains. Lithium cations reside within the tunnels and are coordinated by six ether oxygens, three from each chain, from both chains while the anions are located in the space between the tunnels. Such a structural arrangement immediately suggested possible Li+ transport along the tunnels, which was readily confirmed by variable-temperature conductivity measurements, Fig. 2, establishing the existence of crystalline PE’s. The later discovery of PEO8 :MAsF6 (M = Na, K, Rb) expanded the field of crystalline PE’s.11 The structure of the 8:1 complexes is distinct from that of the 6:1 complexes. The alkali metal cations are contained within tunnels formed from only one helical polymer chain. The cations are coordinated by eight ether oxygens and the anions are located in the inter-tunnel space and not involved in coordination, Fig. 3.

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Fig. 1. (Color online) The structure of PEO6 :LiAsF6 . Left, view of the structure showing rows of Li+ ions perpendicular to the page. Blue spheres, lithium; white spheres, arsenic; magenta, fluorine; light green, carbon in chain 1; dark green, oxygen in chain 1; pink, carbon in chain 2; red, oxygen in chain 2 (hydrogen atoms not shown). Right, view of the structure showing the relative positions of the chains and their conformation.

Fig. 2. Ionic conductivity of crystalline PEO6 :LiAsF6 (triangles) and PEO8 :NaAsF6 (circles) as a function of temperature.

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Fig. 3. (Color online) The structure of PEO8 :NaAsF6 . Left, view of the structure showing rows of Li+ ions perpendicular to the page. Violet spheres, sodium; white spheres, arsenic; magenta, fluorine; green, carbon; red, oxygen (hydrogen atoms not shown). Right, view of the structure showing the relative positions of the chains and their conformation.

A common feature of all crystalline PE’s is a linear dependence of the logarithm of conductivity with the inverse temperature, see Fig. 2, like that in ceramic ionic conductors, and distinctly different from the non-linear temperature dependence in amorphous PE’s described by a Vogel–Tamman–Fulcher equation. Such linear behavior is adequately described by an Arrhenius equation and suggests the ion-hopping mechanism of conductivity. It should be mentioned here that the observed change of the slope in the conductivity dependence of PEO8 :NaAsF6 at ∼25◦ C is associated with a phase change in the crystalline complex. Also worth noting is that the conductivity of the sodium complex is over an order of magnitude higher than that of the lithium PE. The ratio of the cations and anions involved in the charge transport is different in Li- and Na-based crystalline PE’s. Only Li+ cations diffuse in PEO6 :LiXF6 , along the tunnels formed by PEO. Molecular dynamics simulations reveal that the polymer chains “breathe” to ease the ion transport without disrupting the integrity of the crystal structure, thus the dynamics of the chains plays an important role in promoting conductivity by opening bottlenecks

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between static sites.12, 13 The cations hop through coordination sites found in the structure of each tunnel and formed by either six (site occupied by Li+ in the structure) or four (vacant site in the structural model) ether oxygens. In PEO8 :NaAsF6 , however, 60% of charge is carried by anions at temperatures above ambient. This proportion increases to over 80% below room temperature. Conductivity of the early crystalline lithium PE’s was not sufficient for applications in electrochemical devices. As a result, research was carried out to understand the factors that influence the level of ionic conductivity, revealing ways by which it can be increased. Let us consider them in turn. 3. Crystal Structure Unlike amorphous PEO/salt complexes, their crystalline counterparts form only at certain discrete compositions, traditionally labeled as n:1, where n is the number of ether oxygens per cation. Structures of many crystalline complexes, with n between 1 and 4, were established prior to discovery of the ion-conducting 6:1’s and 8:1’s with hexafluoride anions. The common feature of all structures with n ≤ 4 is that both ether oxygens and anions coordinate the cations, Fig. 4.

Fig. 4. (Color online) Fragments of the structures of (from left to right) PEO: NaCF3 SO3 .14 PEO3 :LiAsF6 ,15 PEO4 :KSCN.16 showing cation coordination. Violet spheres, sodium/potassium; light blue spheres, lithium; yellow spheres, sulfur; dark blue spheres, nitrogen; white spheres, arsenic; magenta, fluorine; green, carbon; red, oxygen.

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Fig. 5. (Color online) The structure of β-PEO6 :LiAsF6 . Left, view of the structure showing chain and ion arrangements. Blue spheres, lithium; white spheres, arsenic; magenta, fluorine; green, carbon; red, oxygen (hydrogen atoms not shown). Right, fragment of the structure showing conformation of the PEO chains and coordination of cations by ether oxygens.

Strong binding between the cations and the coordinating anions can inhibit ion transport. However, successful diffusion of ions in an ordered environment is possible only via pathways connecting the sites occupied by the potentially mobile ions. Such pathways also require intermediate vacant coordination sites if the sites populated by ions are too far apart to enable hopping. The profound effect of crystal structure on ionic conductivity of PE’s can be demonstrated by comparing two polymorphs of PEO6 :LiAsF6 . In addition to the structure shown in Fig. 1, hereafter referred to as α phase, a complex with the same chemical composition can be obtained with a different atomic arrangement, β phase, Fig. 5.17 Each Li+ ion in the β phase is coordinated by six ether oxygens from a turn of a single non-helical PEO chain. The shortest lithium–lithium distance is 7.5 Å, compared to 5.4 Å in the α phase. Unlike the α phase, Li+ ions in the β phase are arranged

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in a zigzag fashion and there are no intermediate coordination sites to sustain cation hopping. The AsF− 6 anions form columns and do not coordinate the cations. Thus the ionic conductivity is likely to be largely anionic and is 10 times lower than that of the α polymorph.17

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4. Molecular Weight of the Polymer The first crystalline PE’s with Li hexafluoride salts were synthesized using commercially available PEO of the average molecular weight (Mw) 100,000 Da. Further investigation revealed that complexes with the same structure form within the average Mw of PEO ranging from several million down to at least 750 Da. However, the crystallite size (dimensions of the region with perfect crystallographic order) increases on reduction of the Mw.18 The dependence is linear, Fig. 6, only at low weights up to ∼2000 Da, above which it rapidly plateaus. The trend of increasing crystallite size with decreasing molecular weight is as expected for polymer crystallization. 2000 Da is below the entanglement limit for PEO and hence chain lengths corresponding to the molar masses below should grow larger crystals, unimpeded by chain entanglement which causes disorder. The exact arrangement at the junctions of neighboring PEO chains in the structure cannot be directly established by diffraction studies, since

Fig. 6. Crystallite size of PEO6 :LiXF6 (X = P, As, Sb) as a function of molecular weight of the polymer.

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Fig. 7. Ionic conductivity of PEO6 :LiSbF6 at 25◦ C (triangles) and 40◦ C (circles) as a function of molecular weight of the polymer.

even at 750 Da the average individual chain in the structure of PEO6 :LiAsF6 spreads over 33 Å — almost twice the value of the longest unit cell edge, 17.5 Å, of the complex. This and the fact that the crystallite size is greater than 2500 Å (no broadening of the diffraction peaks) make the polymer chains appear crystallographically infinite. Like the crystallite size, ionic conductivity in PEO6 :LiXF6 also increases on reduction of the Mw, Fig. 7, by four orders of magnitude in the range from 2000 to 750 Da. The increase in crystallite size results in fewer grain boundaries per unit length and this is expected to increase conductivity, but not by four orders of magnitude. It may be that accompanying the growth of larger crystallites there is better alignment of the chains within the crystals which reduces the barriers to Li+ transport at lower Mw’s of the polymer. Such changes are consistent with the non-linearity of the dependence shown in Fig. 7.

5. Doping Doping is a well-established means of changing electrical properties of solids. A variety of doping strategies were tested in an attempt to improve the ionic conductivity of crystalline PE’s.

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5.1. Isovalent Anionic Doping While it is common to increase the conductivity of hopping ionic conductors by introducing additional vacancies or interstitials, as discussed later, there is precedent for enhanced conductivity due to isovalent doping in ceramic ionic conductors, specifically AgI.19 Conductivity increases by three orders of magnitude on replacing 20 mol% of I− with Br− . The substituting ion changes the potential energy of the conducting ion and hence the energetics of defect creation as well as ion mobility. It is possible to replace up to 5 mol% of the hexafluorarsenate anions in PEO6 :LiAsF6 by bis(trifluoromethanesulphonyl)imide (TFSI), N(SO2 CF3 )− 2 , without changing the crystal structure of the host complex and without any evidence of amorphization, despite the significant difference in the shape and size between the two anions. The conductivity of such the PEO6 :(LiAsF6 )0.95 (LiTFSI)0.05 complex is 1.5 orders of magnitude higher than of the pristine, undoped, PE, Fig. 8.20 It appears that differences in shape, size and charge distribution of the doping anion do not have to be substantial in order to provide

Fig. 8. Ionic conductivity of crystalline PEO6 :LiAsF6 (•), PEO6 :Li(AsF6 )0.9 (SbF6 )0.1 (), PEO6 :(LiSbF6 )0.99 (Li2 SiF6 )0.01 (
), PEO6 :(LiAsF6 )0.95 (LiTFSI)0.05 (), (PEO0.75 G40.25 )6 : LiPF6 () as a function of temperature [G4 = CH3 O (CH2 CH2 O)4 CH3 ].

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significant increase in conductivity. PEO6 :Li(AsF6 )1−x (SbF6 )x complex at x = 0.9 and x = 0.1 has over an order of magnitude higher conductivity than the undoped ones, at x = 0 or x =1 , see Fig. 8.21 The only discerning difference between the two anions is the ionic − radius — 1.67 Å (AsF− 6 ) and 1.81 Å (SbF6 ). However, like in the case of AgI, subtle strains caused by the size difference between the two + XF− 6 anions is sufficient to disrupt the potential around the Li ions, enhancing the conductivity. 5.2. Aliovalent Anionic Doping Introduction of vacancies or interstitial ions are the dominant methods of increasing conductivity of ceramic superionic conductors. The latter strategy was applied to crystalline PE’s by means of partial 2− replacement of SbF− 6 anions with divalent SiF6 in the corresponding 22 6:1 complex. Less than 5 mol% of the antimony hexafluoride anions + can be replaced by SiF2− 6 , with additional Li ions (to maintain electroneutrality) most likely occupying the four-coordinate sites in the tunnel formed by the PEO chains, Fig. 9, located between the six-coordinate sites occupied by lithiums in the structure of

Fig. 9. (Color online) Aliovalent doping of PEO6 :LiSbF6 . Left, fragment of the undoped structure showing unoccupied four-coordinate sites. Right, same fragment 2− with one of the SbF− 6 anions replaced by SiF6 and the vacant site occupied by + Li (dark blue sphere). White spheres, antimony; magenta spheres, fluorine; blue spheres, lithium; yellow sphere, silicon; green, carbon; red, oxygen.

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PEO6 :LiSbF6 . The conductivity of PEO6 :(LiSbF6 )0.98 (Li2 SiF6 )0.02 , see Fig. 8, is just over an order of magnitude higher than that of the undoped complex.

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5.3. Polymer Doping For ion transport to occur, point defects (vacancies or interstitials) are required. Polymer chain ends are a likely source of point defects in crystalline PE’s. To probe this, the number of chain ends must be increased. This can be achieved by using mixtures of PEO and glymes — commercially available monodispersed poly(ethylene oxide) with fewer repeat units — during the synthesis of crystalline complexes. The major hurdle to be overcome with doping by glymes is phase segregation. Short-chain monodispersed polymers readily form crystalline complexes with alkali metal salts that have different structure and not necessarily good ionic conductors. At present only one 6:1 complex, in which the tunnel enclosing the cations is formed by a 3:1 mixture of PEO (Mw 1000 Da) and tetraglyme, has been reported, (PEO0.75 G40.25 )6 :LiPF6 [G4 = CH3 O(CH2 CH2 O)4 CH3 ].23 The conductivity of this complex is one and a half orders of magnitude higher than that of the PEO6 :LiPF6 , see Fig. 8. 6. Polymer Chain Ends Once the role of the PEO chain ends in ionic conductivity of crystalline PE’s had been established, the influence of the size of the end groups was investigated. In addition to the PEO6 :LiPF6 complex with PEO (Mw = 1000 Da) chains terminated by methyl groups, –CH3 , complexes with the same polymer terminated by −C2 H5 and –C3 H7 were prepared. It turns out that slightly bulkier end groups, –C2 H5 , increase the conductivity of the complex by an order of magnitude, Fig. 10,24 while the conductivity drops significantly at temperatures below 50◦ C, when even larger groups, –C3 H7 , are used to terminate the polymer, with noticeable increase of the activation energy (change in the slope of the temperature dependent conductivity in Fig. 10). Powder diffraction patterns, Fig. 11, confirm that all three complexes have the same structure but

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Fig. 10. Ionic conductivity of crystalline PEO6 :LiPF6 prepared with PEO terminated by –CH3 (circles), –C2 H5 (up triangles) and –C3 H7 (down triangles) as a function of temperature.

Fig. 11. X-ray powder diffraction patterns PEO6 :LiPF6 prepared with PEO terminated by various end groups. Although the structure is the same for all three groups, broader peaks in the pattern from the complex with the bulkiest ends indicate significant reduction of the crystallite size.

the crystallite size is significantly smaller (broader Bragg peaks) in the complex prepared with C3 H7 -terminated PEO. Thus, chain ends that are moderately larger than –CH3 create greater local structural disorder, which is beneficial for the conductivity increase, however

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Fig. 12. Mass spectrum of polydispersed PEO (Mw = 1000 Da). Numbers above the peaks represent the number of EO units in the corresponding chains.

once the size of the terminal groups increases further, the longrange crystal order becomes disrupted, which is detrimental for conductivity. 7. Dispersity of Polymer Chain Lengths Polydispersity is an inherent feature of polymer materials. A typical distribution of chain lengths in commercial PEO of 1000 Da average Mw is shown in Fig. 12. Synthesis of truly monodispersed PEO is a formidable challenge. However, it is possible to synthesize PEO of selective Mw’s which closely approach monodispersity. PEO6 :LiPF6 complex with monodispersed polymer of 22 EO repeat units, Mw = 1015 Da, has the same structure as the 6:1 complex prepared with polydispersed PEO. Only the lattice parameters in the two complexes are slightly different, which is manifested by small shifts in the diffraction peak positions, Fig. 13. With dispersity of the polymer length being the sole distinction, it is the arrangement of the chain ends that causes the observed change in the unit cell size when a monodispersed PEO is used. If the chain ends of the monodispersed polymer were distributed randomly along the tunnels such an arrangement would effectively mimic the complex with polydispersed PEO and

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Fig. 13. (Color online) X-ray powder diffraction patterns PEO6 :LiPF6 prepared with polydispersed (black) and monodispersed (red) PEO. Peak shifts indicate change in the unit cell sizes.

no change in the lattice parameters would take place. However, coincidence of all ends of the polymer chain pairs forming the tunnels, see Fig. 1, imposes a greater impact on the structure, which is likely to change the lattice parameters both in the direction of the tunnels’ axes and perpendicular to them. There are two possible patterns of how the PEO chain ends can be arranged in the structure of the 6:1 complex prepared with a monodispersed polymer. The first one implies the highest degree of coincidence — junctions of chain ends coincide in all neighboring tunnels, forming planes throughout the crystallites. The second pattern precludes formation of such planes, limiting coincidence of chain ends of the two polymer strands only within individual tunnels. The “planes” model inevitably entails a change in crystal symmetry of the complex. However, no experimental evidence of superstructure in the monodispersed complex has been obtained. In addition, MD simulations of the first model indicate that the blocks of tunnels containing uninterrupted polymers are unlikely to be aligned perpendicular to the planes of chain ends but instead are canted with respect to each other.25 The consequence of such a canted arrangement would be reduction of the crystallite size from 2500 Å down to ∼40 Å (the overall length of an individual PEO

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Fig. 14. Schematic representation of part of the PEO6 :LiXF6 crystal structure prepared with polydispersed (top) and monodispersed (bottom) PEO. Polymer chains are represented by the solid black lines, Li+ ions — by grey circles.

chain in the complex), manifested by pronounced peak broadening in the powder diffraction pattern. This is not supported by the experimental data, see Fig. 13. Thus, the only plausible model of the chain ends arrangement in the 6:1 complex prepared with a monodispersed PEO, which explains the change in the unit cell dimensions while preserving the crystallite size, is the coincidence of the ends on both sides of individual tunnels but with no registry between tunnels. Coincidence of chain ends may explain the lower conductivity of the PEO6 :LiPF6 complex, when monodispersed polymer is used,24 Fig. 14, because there are fewer occurrences of such defects along the same length of the tunnel than in the 6:1 structure with polydispersed PEO. 8. Conduction in Crystalline Polymer Electrolytes Although our understanding of ion transport in PE’s is far from complete, the studies described previously have permitted the statement of some key features. Ionic conductivity in crystalline polymers resembles that in ceramic electrolytes more closely than amorphous polymers above Tg . The ion motion involves hopping between neighboring sites along the polymer tunnels and hence requires defects, vacancies and interstitials. The tunnels are composed of chains of finite length. Chain ends are natural sources of point defects, where one might expect missing cations or cations located outside the tunnels, paired with the anions. Increasing the magnitude (size of chain end

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groups) of the disorder at the chain ends can increase conductivity proportionally to an increase in the number of defects (conductivity σ = nqµ, n — number of carriers; q — charge; µ — mobility). However, since this is a 1D conductor, too much disruption of the tunnel continuity at the chain ends will compromise the mobility of the ions along the tunnels. As a consequence, a balance has to be struck and of course this highlights the importance of searching for 2D and 3D crystalline PE structures where defects are much less likely to impede ion transport. Despite the limitations of the 1D structure, investigation of the factors influencing the ionic conductivity of crystalline PE’s led to conductivities approaching that of the best amorphous PEO:salt complexes, with the advantage of higher Li+ transport numbers in the ordered, crystalline, complexes. To make further improvements a detailed knowledge of the mechanism of conductivity in crystalline PE’s is required. Work to better establish the conduction mechanism is currently under way. 9. Crystalline Polymer Electrolytes in Lithium and Sodium Ion Batteries Solid electrolyte holds the key to all-solid-state electrochemical devices. Ionic conductivity is not the only criteria of importance for the application of solid electrolytes in lithium-ion batteries. The electrolyte/electrode interface is critical and this is a major problem for ceramic electrolytes.3, 4 PE’s offer potentially superior interfacial properties with solid intercalation electrodes. Crystalline PE, (PEO0.75 G40.25 )6 :LiPF6 , which has the highest conductivity at room temperature reported so far (see Fig. 8), was tested in a lithiumion cell. Linear voltammetry established the electrochemical stability window between ∼4.5 V (cathodic polarization) and 1.5 V (anodic polarization) versus Li+ /Li (Fig. 15), which is consistent with expectations for an ether-based electrolyte. The results of galvanostatic cycling of a cell with LiFePO4 as a cathode and Li-metal as anode are shown in Fig. 16. The cycling

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Fig. 15. Linear sweep voltammograms of (left) (PEO0.75 G40.25 )6 :LiPF6 and (right) PEO8 :NaAsF6 at 45◦ C. Scan rate 1 mV s−1 . Stainless steel working electrode.

Fig. 16. (Color online) Charge–discharge curves of all-solid-state batteries consisting of (PEO0.75 G40.25 )6 :LiPF6 polymer electrolyte, LiFePO4 cathode and (left) Li metal anode at 45◦ C, (right) VO2 (B) anode at 25◦ C, at a rate of C/20. Capacities are based on the LiFePO4 cathode expressed as C rate, where 1C corresponds to 170 mAhg−1 (the theoretical capacity of LiFePO4 ). Insets are discharge capacity of corresponding cells at various current densities.

reveals good capacity retention at various current densities (see inset in Fig. 16). The load curve is dominated by a plateau at ∼3.5 V, as expected for the two phase intercalation reaction associated with LiFePO4 /FePO4 .26 The capacity does decrease significantly with increasing rate. From the current density in mAcm−2 at each rate we calculated the IR drop from the electrolyte resistance and this is 20 mV at C/20 rising to 80 mV at C/5. Examining the load curve in Fig. 16, it is unlikely the IR drop alone can account for

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the reduction in capacity at higher rate. As such, there must be significant interfacial resistance. As the polymer electrolyte is not of course stable in contact with Li, we replaced it with VO2 (B), the potential of which versus Li+ /Li is 2.45V and hence lies within the stability window of the electrolyte. Galvanostatic cycling of a cell constructed with VO2 (B) (anode) and LiFePO4 (cathode) is shown in Fig. 16. The overall cell potential is as anticipated, based on the voltages of the two electrodes, as is the shape of the overall load curve, which is dominated by plateaus on charge and discharge with good capacity retention (see inset in Fig. 16). The cell is cathode-limited and the capacities are therefore based on the mass of the cathode. Unlike LiFePO4 , there is no phase change associated with lithium intercalation/de-intercalation in VO2 (B) during charge and discharge.27 Linear voltammetry of the crystalline PEO8 :NaAsF6 complex revealed an electrochemical stability window between ∼4.5 V (cathodic polarization) and 1.0 V (anodic polarization) versus Na+ /Na (see Fig. 15). A rocking-chair battery with Na0.44 MnO2 as both cathode and anode electrodes demonstrated sustainable cycling (Fig. 17).

Fig. 17. Charge-discharge curves for a Nax MnO2 /PEO8 :NaAsF6 /Nax MnO2 cell (x0 = 0.44) at 45◦ C, rate C/6. Numbers indicate cycles.

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The data demonstrate successful operation of crystalline PE’s in lithium and sodium ion batteries. If the conductivity of such electrolytes could be increased further, the advantageous interfacial properties of such materials could represent a significant advance towards safe lithium and sodium ion batteries in the longer term. Future research of crystalline PE’s will be focused on establishing detailed mechanism of ionic conduction in such complexes. The conductivity mechanism will pave the way for design of PE’s with the composition and the structure optimized for ionic conduction. In addition, new types of crystalline PE’s with 2D and 3D pathways for ion transport are likely to deliver a major increase of conductivity. References 1. D. E. Fenton, J. M. Parker and P. V. Wright, Polymer 14 (1973) 589. 2. M. B. Armand, J. M. Chabagno and M. J. Duclot, in Fast Ion Transport in Solids, eds. P. Vashishta, J. N. Mundy and G. K. Shenoy (North-Holland, 1979) p. 131. 3. F. M. Gray and R. S. O. Chemistry, Polymer Electrolytes (Royal Society of Chemistry, 1997). 4. C. Sequeira and D. Santos, Polymer Electrolytes: Fundamentals and Applications (Woodhead Publ Ltd, Cambridge, 2010). 5. S. D. Druger, M. A. Ratner and A. Nitzan, Solid State Ion. 9–10 (1983) 1115. 6. R. Frech, S. Chintapalli, P. G. Bruce and C. A. Vincent, Chem. Commun. (1997) 157. 7. Y. G. Andreev, P. Lightfoot and P. G. Bruce, Chem. Commun. (1996) 2169. 8. Y. G. Andreev, P. Lightfoot and P. G. Bruce, J. Appl. Crystallogr. 30 (1997) 294. 9. G. S. MacGlashan, Y. G. Andreev and P. G. Bruce, Nature 398 (1999) 792. 10. Z. Gadjourova, D. M. Marero, K. H. Andersen, Y. G. Andreev and P. G. Bruce, Chem. Mat. 13 (2001) 1282. 11. C. H. Zhang, S. Gamble, D. Ainsworth, A. M. Z. Slawin, Y. G. Andreev and P. G. Bruce, Nat. Mater. 8 (2009) 580. 12. D. Brandell, A. Liivat, A. Aabloo and J. O. Thomas, J. Mater. Chem. 15 (2005) 4338. 13. D. Brandell, A. Liivat, H. Kasemagi, A. Aabloo and J. O. Thomas, J. Mater. Chem. 15 (2005) 1422. 14. Y. G. Andreev, G. S. MacGlashan and P. G. Bruce, Phys. Rev. B 55 (1997) 12011.

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15. I. Martin-Litas, Y. G. Andreev and P. G. Bruce, Chem. Mat. 14 (2002) 2166. 16. P. Lightfoot, J. L. Nowinski and P. G. Bruce, J. Am. Chem. Soc. 116 (1994) 7469. 17. E. Staunton, Y. G. Andreev and P. G. Bruce, J. Am. Chem. Soc. 127 (2005) 12176. 18. Z. Stoeva, I. Martin-Litas, E. Staunton, Y. G. Andreev and P. G. Bruce, J. Am. Chem. Soc. 125 (2003) 4619. 19. K. Shahi and J. B. Wagner, Appl. Phys. Lett. 37 (1980) 757. 20. A. M. Christie, S. J. Lilley, E. Staunton, Y. G. Andreev and P. G. Bruce, Nature 433 (2005) 50. 21. S. J. Lilley, Y. G. Andreev and P. G. Bruce, J. Am. Chem. Soc. 128 (2006) 12036. 22. C. H. Zhang, E. Staunton, Y. G. Andreev and P. G. Bruce, J. Am. Chem. Soc. 127 (2005) 18305. 23. C. Zhang, E. Staunton, Y. G. Andreev and P. G. Bruce, J. Mater. Chem. 17 (2007) 3222. 24. E. Staunton, Y. G. Andreev and P. G. Bruce, Faraday Discuss. 134 (2007) 143. 25. A. Liviat, D. Brandell, A. Aabloo and J. O. Thomas, Polymer 48 (2007) 6448. 26. A. K. Padhi, K. S. Nanjundaswamy and J. B. Goodenough, J. Electrochem. Soc. 144 (1997) 1188. 27. G. Armstrong, J. Canales, A. R. Armstrong and P. G. Bruce, J. Power Sources 178 (2008) 723.

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Polymer Electrolytes∗ Sabina Abbrent

Institute of Macromolecular Chemistry CAS Prague, Czech Republic

Steve Greenbaum

Hunter College of the City University of New York New York, NY, 10065 USA

Emanuel Peled and Diana Golodnitsky

Tel Aviv University 69978 Israel

This chapter discusses polymer electrolytes, their characterization, and their application in solid-state batteries. The concept of a material that acts as both the physical separator and the electrolyte while maintaining good contact with the electrodes through many charge/discharge cycles has motivated research on polymer electrolytes for over three decades. Beginning with poly(ethylene oxide) (PEO) as a host matrix for lithium salts, which is still the focus of many investigations, this review covers a variety of solvent (liquid)-free systems as well as plasticized or gel electrolytes. Several strategies for improving mechanical and electrical properties such as forming blends, organic/inorganic composites, or copolymerization are also described. Some of the most commonly used characterization tools are briefly discussed, including thermal analysis, X-ray diffraction, electrical impedance, and vibrational and nuclear magnetic resonance spectroscopies. Finally, a brief survey of power source applications of polymer electrolytes ranging from microbatteries to large format electric vehicle batteries is given. ∗ The editors note that this chapter takes a broad view to encompass the wide

diversity of polymer based materials and processing; focused topics including composite electrolytes, crystalline polymers, and 3D microbatteries are discussed fully in other chapters. Similarly, other chapters delve more deeply into several key characterization methods. 523

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1. Introduction Lithium-metal polymer (LMP) batteries are considered one of the most promising candidates to exploit the full energy of the Li+ /Li electrochemical couple for electric vehicle and other applications. The ultimate goal in the development of a polymer electrolyte for LMP batteries is to allow high performance operation with a high specific energy density. More recently the prospect of dispensing almost entirely with the bulky cathode (up to 70% of the total battery mass) leading to a corresponding increase in gravimetric energy density has led to the concept and pursuit of the lithium–air battery, which also requires a robust solid ionic conductor.1–3 To reach these targets, it is very important to take into account the ionic transport, electrochemical and interfacial properties of the polymer electrolyte. To date, poly(ethylene oxide) (PEO)-based polymer electrolytes have been regarded as one of the most suitable electrolytes for lithium batteries. They are also attractive for lithium-ion batteries because of their dual functions as electrolyte and separator. Despite over 30 years of worldwide research on polymer electrolytes (PEs) since their initial discovery,4,5 the requirement of sufficiently high cationic conductivity for lithium battery applications still remains somewhat elusive.6−9 Furthermore, there is still considerable scientific controversy about the very nature of the ion transport mechanism and the precise factors governing cation–anion interactions in polymer–salt complexes based on PEO, the most widely studied host polymer. This chapter is organized as follows: First, a discussion of some of the technical details regarding the kinds of applications for which solid-state power sources using PEs will be presented. Next is a survey of the main classes of PEs (e.g. solvent-free, gels, etc.) and experimental approaches to synthesize and characterize them. This is followed by discussions of the ion transport mechanisms and electrochemical stability of the PE against Li and in the working cell. The final section will address the degree to which PEs have successfully been incorporated into solid-state batteries and capacitors and the outstanding issues which must be confronted in order to more fully realize the potential contribution of PEs to these important applications.

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2. Applications of Polymer Electrolytes There are many strong motivations for replacing standard liquid electrolytes in a wide variety of large format, consumer and microelectronics battery uses. Among these are processability, dimensional and thermal stability, ability to maintain an intact electrode/ electrolyte interface during the volume changes associated with cycling, preventing electrolyte leakage, and suppression of concentration gradient of ionic species and dendrite growth in metal anode cells. Additional advantages in stability make certain polymer electrolytes attractive for advanced battery development, such as for air batteries. Large format batteries will play an increasing role in electric grid storage/leveling as renewable but intermittent energy sources (i.e. solar and wind) are exploited, and are already in use in gasoline/electric hybrid and plug-in vehicles. The greater storage demands of all-electric cars require novel materials and battery design schemes without sacrificing safety. The inherent dimensional stability of PEs over porous polymer separators containing a high fraction of flammable liquid electrolyte becomes a paramount factor for cell sizes appropriate to electric car batteries. Military portable power also demands high volumetric and gravimetric energy density, as well as often harsh operating conditions, in particular mechanical shock and vibration. The use of PEs can deliver all of these benefits. The development and use of lithium-ion batteries in consumer electronics (i.e. cell phones, laptop computers, etc.) must be regarded as an unqualified success. However, there is still room for improvement, especially in view of increasing power demands associated with exponentially increasing functionality in current and future devices. Again, the combined roles of separator and electrolyte in the PE can lead to an increase in energy density (provided that the ionic conductivity is sufficient) to help meet these needs. Although early use of rechargeable lithium metal batteries in cell phones was discontinued after spectacular and well-publicized failures10,11 the energy density advantage of returning to a lithium anode can be made safer by a PE that suppresses the formation and growth

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of dendrites.12−16 The recent development of Si/Li alloys17−20 with comparable energy density is also a promising strategy, and the ability of PEs to maintain contact with the electrode during significant volume changes is an attractive attribute. 3D microbatteries, designed for powering miniature devices such as microelectromechanical systems (MEMS) and small sensors use novel concepts to pack high charge capacity into remarkably small area footprints by folding the planar geometry into a thick laminate or network. As a result, the total current path and in particular, the Li ion diffusion length remains relatively small. Thus, low ionic conductivity is less of a hindrance and the advantages of polymer conformal coating methods, including electrodeposition, can then be utilized to provide both separator and electrolyte functions.21−29 Because of recent advances and relevance to this volume, 3D microbatteries will be introduced in this chapter, but the editors note that other chapters present much more details for the materials and devices. As mentioned above, world-wide research on lithium–air batteries is gathering speed and intense interest. Paramount technical problems which need to be overcome are protection of the lithium metal anode and facilitation of the oxygen reduction reaction (ORR).2,30−37 Related to the latter concern is the stability of the 2− 2− species associated electrolyte to the very reactive O− 2 , O2 and O 38 with the ORR. Because traditional carbonate electrolytes have proved to be unstable in this environment, the prospect of using PEs appears attractive.38 Another cell chemistry offering significant energy density but receiving much less attention than lithium–air is sodium–air, in which much the same concerns about ORR would also apply. An advantage of sodium–air, however is that the cell can be run at moderately elevated temperature (∼100◦ C) where the sodium electrode is in the molten phase, which would eliminate dendrite formation upon charging.39 Polymer materials also serve as the mechanical separator in conventional Lithium-ion technology. Separators have undergone material evolution throughout the years and may consist nowadays of high-tech materials, such as ion-exchange membranes, electrolyte

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films, non-woven fabrics and various porous nanomaterials.40 The distinction between a conventional battery separator typically consisting of a microporous polyolefin (typically polyethylene, polypropylene or a combination of these two) filled with liquid electrolyte and solid polymer electrolytes (SPEs) discussed below can be subtle, but is related primarily to the degree of phase separation and thus to the degree that the liquid electrolyte leakage is inhibited. While the use of liquid electrolyte will always raise the issue of leakage and related safety concerns, improvements toward the safe use of liquid electrolytes continues through tighter cell designs electrode coating for capacity enhancement,41 further improvement of separators42−45 and of the liquid electrolyte itself.46 3. Survey of Polymer Electrolytes Classification can follow several schemes, but here we separate the dry polymers which are free of solvent, from those containing some amount of a liquid forming either a plasticized or gel structure. These dry and plasticized polymer electrolytes are further tailored by forming composite and hybrid materials comprised of two or more distinct phases which may include inorganic compounds or glass. The composite structures differ further in scale, from nano- to micro-meters, and also their dispersion and connectivity. 3.1. Solvent-free SPEs PEO salt electrolytes The most studied SPE consists of high molecular mass (∼5 × 106 amu) PEO, corresponding to about 105 monomer repeat units, complexed with an alkali metal salt. It is widely recognized that the polar ether oxygen configuration in the helical PEO structure have an optimal spacing to coordinate the Li ions (in the case of Li electrolytes). The work of Bruce and others 47−50 has shown that a wide variety of well-defined crystalline compounds having different EO/Li ratios can be formed. However, most PEO salt complexes are heterogeneous, containing a mix of crystalline and amorphous phases, which may also include regions of uncomplexed PEO. The

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high molecular mass results in chain entanglements which impart solid-like properties to these materials, but local segmental motions occur enabling some mobility to the ions. A typical composition PEOn LiX investigated for battery applications is n (the ratio of EO monomer units to Li ions) ranging from 10 to 20. The optimal value of n depends on the application, most importantly the temperature of operation. A low value usually yields rigid structures with a high degree of crystallinity and/or an amorphous component with a high glass transition temperature and thus unsuitable for ambient temperature, whereas a high value of n reduces the number of mobile ions. The criteria that determine which lithium salt to use (i.e. which anion, X) are mainly those that factor into solubility of the salt in PEO. Thus X is preferably a large singly charged and “soft” anion 2− (the with highly delocalized charge such as ClO− 4 or N(SO2 CF3 ) latter often abbreviated as TFSI) in order to limit ion-pairing.51 Simultaneously, Li+ –polymer interaction must be sufficiently strong to promote complexation but not so strong as to inhibit exchange between polymer segments and thus transport.6 Nonetheless, this scheme usually results in a weak anion–polymer interaction which imparts a higher anion than cation conductivity. Although this does not seriously limit the applicability of these materials, much effort has been given to strategies to promote the Li+ ion transference number (i.e. the fraction of current carried by the cations) as will be mentioned below. The semi-crystalline or amorphous phases resulting when lithium salts are dissolved in PEO usually have conductivities below the necessary values at ambient temperatures.52 It is well established that it is ion migration through the amorphous phases which gives rise to the ionic conductivity of the material.53−60 Such a mobility mechanism is free-volume dependent and essentially coupled to the segmental mobilities of the polymer. Many strategies have been proposed to overcome the electrical and mechanical limitations of PEO Li salt complexes. Polymer blending is one possible approach to improve polymer electrolyte performance. The main advantages of blend-based

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polymer electrolytes are simplicity of preparation and easy control of physical properties by changing the composition of blended polymer matrices.61 In addition, mechanical properties in these systems can be relatively easily controlled by varying the amount of the added polymer.62−64 Typically, a comparatively inert polymer which enhances the mechanical integrity of the blend is added to the PEO, which itself is complexed with the electrochemically active ion.65,66 In principle, miscibility in polymer blends can be achieved through favorable intermolecular interactions between blending components. Compatibility can also be enhanced via ion–dipole interaction from the used salt.67,68 PEO is a good proton acceptor which forms hydrogen bonds with many proton donors like poly(vinyl phenol) (PVPh),69 poly(methyl vinyl ether–maleic acid) (PMVE-MAc)70 or poly(acrylic acid).71 However, miscibility in the binary PEO-based blends can also be achieved via specific dipole–dipole interactions with non-proton donors like poly(vinyl acetate),72 poly(trimethylene carbonate)73,74 and different acrylates such as poly(n-butyl methacrylate),75 poly(methyl methacrylate)76,77 or polyacrylate.78 PEO-based electrolytes blended with many commercial polymers have been studied with good results including polyvinylidene fluoride (PVdF),79,80 poly(acrylonitrile) (PAN),81,82 polysulfone,83 polyurethanes,84,85 polysiloxanes86−88 and polyphosphazenes.89−91 Simultaneously blended polymer electrolytes between these commercial polymers themselves have also been studied such as polyethylmethacrylate with PVC,92 polymethylmethacrylate with for instance PVC,93−95 natural rubber96 or polyvinilidene fluoride (PVDF-HFP)97 or PVDF itself with an amorphous hyperbranched polyether (PHEMO)98 or triblock copolymer PPG–PEG– PPG diamine.61 A more sophisticated means of altering the properties of PEO polymer electrolyte is copolymerization which can be defined as attaching another entity to the backbone of the original polymer chain compared to single blending of two individual chains, as illustrated in Fig. 1. Such process requires either direct synthesis of such combined polymer chains or polymerizable monomer entities.

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Fig. 1. Three types of copolymers, from the left blended, block and random. Borrowed with permission from.99

In both cases a wide variety of possible copolymers can be achieved based on first the physical attachment of the individual units and second their actual chemical composition. Figure 1 displays examples of the most elementary co-polymer type with the two monomer entities attached either in blocks or randomly. While a random copolymer will result in a less structured system with decreased possibility of ordering,100 a block copolymer is capable of creating both homogeneous and heterogeneous systems with various chemical as well as physical properties depending on the ratio and type of the individual constituent polymers.58 Copolymerization with PEO is usually intended to decrease crystallinity and further enhance ionic mobility of the resulting electrolyte system.101−103 Homogeneous systems often exhibit single phase behavior.104−106 On the other hand, heterogenous, often phase separated systems investigated include PEO copolymers with polyisoprene,107,108 polystyrene.107,109−113 several polyacrylates,114−122 polyethylene,123,124 PAN,125 polyurethane126 or as depicted in Fig. 1, butyroacetone.99 Copolymerization to PEO is not restricted to linear systems; many side-chains consisting of monomer or oligomer units have been investigated, added randomly or in blocks depending on the desired result. Such side-chains of these so-called graft copolymers have been shown to greatly influence mechanical and physical properties of the resulting electrolyte material.127,128 Chemical

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structure of the side-chains gives the copolymers names such as comb-branched,129,130 double-comb,131,132 star-branched,133,134 hyper-branched135,136 or dendronized137 which can be further divided into linear dendritic, star dendritic and dendritic star copolymers. Furthermore, copolymerization is again not restricted to PEO, with both PVDF and acrylates being used as the basis of these allsolid polymer systems.97,138−140 Hybrid electrolytes containing inorganic copolymers based on aluminium,141 silicon, mostly siloxanes,86,142−149 phosphorus150,151 including alkyl phosphates,152,153 phosphonates154 and phosphazenes,155,156 sulfur,83,157 fluorine158 or boron159−163 have been widely investigated for their favorable mechanical as well as fireretarding properties.164 Cross-linking is an alternative approach to achieve mechanical strength in polymer electrolytes providing anchoring points for the chains and, therefore, restraining excessive movement of polymer segments. The linking process is usually random thus also decreasing ordered structures in the system.165 Such materials usually involve linkable short-chain PEO moieties166−168 as well as a wide variety of siloxanes.169−174 Single lithium-ion conducting polymers The previously cited recognition that most PEO:LiX complexes are better anion than cation conductors, which causes undesirable electrode polarization effects, has also led to various approaches to suppress the anionic conductivity, thereby enhancing the Li+ transference number. In principle, such a “single ion conductor” could be realized by tethering the anion to the polymer chain, as in the case of a polyelectrolyte. However given the strong cation– anion interactions, this usually has the effect of vastly decreasing the Li+ mobility as well.175,176 To suppress cation–anion interaction, thus facilitating Li+ transport, the use of anionic groups with highly delocalized charge has been successfully demonstrated, one recent example being SO2 N−SO2 CF3 attached to a polystyrene chain.175

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Another strategy that has met with some success in mitigating cation transference is to add anionic traps to the PEO LiX electrolyte, examples of these being boron compounds,177 linear or cyclic aza-ether compounds,178 or larger trapping agents such as calixpyrrole.179 In all of these cases, substantial improvement in Li+ transference was achieved. However, due to factors such as longterm stability and cost, among others, this strategy has not been pursued at the commercial level, although Hitashi Corp. claims to be preparing new type of batteries with this technology.180 Dispersed particle composite and hybrid polymer electrolytes (HPEs) Efforts to improve electrolyte materials have also focused on the introduction of nanosized particles into the dry polymer matrix. Since the first introduction of such ceramic fillers by Weston and Steel,181 several reports have indicated improvements in the ionic conductivity, due to the enhanced segmental motion of amorphous regions, and enhanced interfacial stability of PEO-based polymer electrolytes.182−188 Such composite electrolytes, also referred to as nanocomposite electrolytes or dispersed particle electrolytes, will be further discussed in a dedicated chapter [editors’ note]. Typical particles include: nano-oxides such as magnesium oxide (MgO),183,189 titania (TiO2 , rutile or anatase),190 alumina (Al2 O3 ),183,184,191 silica (SiO2 ),192−194 LiAlO2 165,195−199 or zirconium dioxide (ZrO2 )200 ; also carbon nanotubes (CNTs),201−204 as well as different organic nanomaterials205,206 and other fine particles such as clay and kaolin.207,208 Such electrolytes, generally refer to the incorporation of inorganic particles, while the term hybrid electrolytes is usually applied to a group of gel electrolytes where an inert polymer membrane is soaked with a liquid electrolyte indicating an intermediate system, not solid but not liquid. These will be discussed in the next section. A third class of composites, providing an even finer distinction, is functional nanocomposites or hybrid organic–inorganic materials or ormolytes (organically modified electrolytes) having organically substituted inorganic components such as for example –Si–O–Si–O– backbones such as polysiloxane,209 ureasil,210−212

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alkoxysilane213 or modified aluminosilica214 within the polymer matrix. These are typically prepared by sol–gel technology.215−218 The advantage of these systems is the introduction of an inorganic network into the polymer matrix which provides simultaneously an amorphous structure and good thermal, mechanical, and chemical stability.219 Liquid crystal (LC) containing polymers Another way to achieve higher lithium conductivities while improving mechanical properties of the resulting PEO-based electrolyte material is generation of a liquid crystalline phase within the polymer matrix. Such LCs are functional materials that can form selforganized anisotropic structures.220 The dynamic and anisotropic properties of LCs can help to develop anisotropic ion-transporting materials. The macroscopic alignment in layers of molecules consisting of ion-conductive oligo(ethylene oxide) sections and ioninsulating mesogenic rod sections lead to the formation of 2D ion conductors.221−224 3.2. Plasticized and Gel Polymer Electrolytes (GPE) While PEO complexes still garner much scientific attention, alternative strategies for preparing flexible polymeric ion conductors have been conceived, executed, and even developed commercially. Principal among these are GPE or plasticized polymer electrolytes.9,225−227 In the GPE, a polymer matrix is softened by an organic liquid most often a carbonate and the electrolyte is uniformly mixed to form a pseudo single phase. This makes the materials safer electrolytes for capacitors and batteries, because they prevent liquid electrolyte leakage, suppress the evaporation of the solvent, and lower the flammability.226 Various polymers have been investigated as matrices for GPEs the most important are described below. Enhancement of mechanical properties of the membranes without seriously compromising their ionic conductivity can also be accomplished by several means, including blending with other polymers, copolymerization, and crosslinking.

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PVdF based gel electrolytes Many groups have investigated gel electrolytes based on PVdF either pure,228−230 blended62,66,231,232 or crosslinked227,233 using many different preparation techniques. Perhaps the most widely studied GPE is based on a copolymer of PVdF and hexafluoropropylene (HFP), imbibed with a carbonate-Li salt electrolyte. This technology was pioneered by Bellcore Corp. (now Telcordia Technologies).234 Chief attractions of PVdF-HFP are that the copolymer cannot dissolve in the carbonate liquid electrolyte owing to its strongly electron-withdrawing functional group (–C–F), which also provides good electrochemical stability and non-combustibility. Furthermore, it has a fairly high dielectric constant (ε = 8.4) that assists in greater dissociation of the Li salt. In the polymer, the HFP units reduce the crystallinity of the polymer improving its solubility in a variety of solvents and lowering its melting temperature.226,235 The Bellcore technology has enjoyed some success in lithium-ion polymer electrolyte configurations, but cannot be used with lithium metal as an anode because of the general instability of fluorinated polymers against Li.236 Gels based on PEO Introduction of a plasticizer to the semi-crystalline PEO system has resulted in a sharp decrease of the crystallites and so higher mobility of the system through increased free volume of the conducting amorphous phase.225 The plasticizers are most often carbonates such as PC or EC, but also short chain-PEOs, so-called polyethylene glycols or PEGs,237 anion-cryptands238,239 and many others. The importance of the choice of lithium salt used has also been demonstrated and widely discussed, above all by M. Armand.240,241 Attempts to further increase cation mobility of the PEO-based systems comprise various approaches such as using blends,109,184,242 copolymers,243,244 combbranch polymers245 and cross-linked ‘networks’.246−248 All these enhancements have been achieved either by reducing the crystallinity of polymers or by lowering the glass-transition temperature of these polymer gel systems.

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Poly (acrylonitrile) (PAN) compositions PAN-system was first investigated in the 1980’s by Watanabe249 and Abraham.250 The evolution of PAN-based electrolytes has been described in detail in Ref. 225. It was concluded that similar to PVdF, the PAN host does not participate in the ionic transport mechanism but acts only as a matrix for structural stability. Conducting properties are then highly dependent on the type of plasticizer and salt used,251−255 or on the properties of the polymer matrix after combination with other polymers.256,257 Systems with high ionic conductivities of 10−3 S cm−1 at room temperature (RT), and a good electrochemical stability were reported. Poly(methacrylate)s (PMA) systems The advantage of methacrylates is the possibility of crosslinking through the double bond breakage activated by UV-source or heat. One or two methacrylate groups can be attached to any length of for instance PEO-unit and thus chain polymerization or 3D crosslinking can be obtained. Arbitrary blends of chain length and type can be polymerized with a multitude of polymer frames with different physical and chemical properties.94,248,258−262 Composite GPEs As in the case of PEO salt complexes, the addition of inorganic oxide nanofillers to gel electrolytes based on various polymer systems has also been reported.263−270 In these composite GPEs, the ceramic particles promote electrochemical properties of the polymer electrolytes, presumably only by physical actions without directly contributing to the lithium-ion transport process. However, it has been reported that lithium containing ceramic filler particles such as LiAlO2 could also enhance the number of charge carriers by facilitating suitable surface modifications of particles271,273 with resulting unique advantages in terms of controlling the final morphology of the system.273

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Ionic liquids GPEs More recently, the exponentially growing list of ionic liquids (IL) and their applications has led to their incorporation into gel electrolytes. Such combination of ionic liquids with polymer networks results in quasi-solid materials with enhanced electrochemical and thermal stability.240,274 The carbonate derivatives normally used in GPEs are highly volatile and flammable, while ionic liquids are molten salts with high thermal stability, non-volatility, non-flammability, and high ionic conductivity at an ambient temperature.275,276 In the past few years many groups have focused on IL systems in GPEs reporting promising results.122,277−280 From one side ILs act as charge carriers; from the other they behave like low-weight molecular organic solvents endowed with a dipole moment,281 acting either as the main conductivity medium supported in a polymer membrane or as a plasticizing component in polymer electrolytes. A further substantial benefit of ILs is their enhanced safety factor due to low volatility, reactivity, and wide electrochemical window.6,282 In the first scenario, the ILs are incorporated into a polymer host, most commonly PVdF-HFP along with a lithium salt (i.e. the source of Li+ ions for battery applications). The lithium salt anion most commonly studied is TFSI, which is usually the same IL anion.122,283−285 Some studies have also explored the effect of adding alkyl carbonates to the polymer/IL/Li salt gel, which under ideal circumstances preserves the safety factor of the IL component while improving ionic conductivity and promoting stable SEI formation.240,286 The improvement in conductivity results from a lowering of the local viscosity to a certain extent through partial carbonate — Li+ solvation thereby mitigating the strong Li+ — anion interaction.287 In the second scenario, as an additive to PEO/Li salt complexes, ILs have been shown to improve both the conductivity and the Li+ transference number.288−292 Many different types of ionic liquids have been prepared and investigated including protic ILs based on N-methylpyrrolidine-acetic acid293 or asymmetrical dicationic ionic liquids based on both imidazolium and aliphatic ammonium.294

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HPEs Another class of polymer electrolytes considered consists of standard and, in some cases novel, liquid electrolytes immobilized in a polymeric matrix. These materials evolved from the classic Celgard systems using liquid electrolyte and a mechanical separator between the electrodes.40 The passive purely mechanical separators have been replaced by highly functional membranes that are able to act as a liquid media holder and a separator at the same time. Very similar to GPEs, these systems differ in retaining separate solid and liquid phases within the systems and are therefore called hybrid or wet systems.295 Usually a self-standing dry polymer membrane is created and later soaked with liquid electrolyte solution. Many different approaches to obtain a safe, efficient, compatible material have appeared in the literature using various types or blends of polymers,43,92,296,297 composites273,298,299 ionic liquids281 and complex liquid electrolytes.300 The method of preparation is also important for the properties of the resulting material as discussed below. 4. Preparation Methods for Polymer Electrolytes Depending on the type of polymer electrolyte to be prepared a variety of preparation methods are used. The most common means of preparing PEOn LiX PEs is to dissolve both polymer and salt in a suitable solvent, for example, acetonitrile or methanol, cast the solution onto a PTFE surface (which facilitates film removal) and remove the solvent by a combination of vacuum and elevated temperature. Obviously for lithium battery applications, care must be taken to remove water from the polymer, salt, and solvent, prior to casting and then from the film during the drying procedure. Other synthesis methods have also been developed, for example hot-pressing a mixture of PEO and salt without the use of solvent.155,194,301 There are a number of preparation methods for gel electrolytes in use, the main ones being casting, phase inversion, and electrospinning.302 In the casting process, porous membranes are

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prepared by dissolving the polymer in a suitable solvent such as acetone and mixing with a plasticizer, for example, dibutyl phthalate (DBP). After solvent evaporation, the plasticizer is extracted with another solvent and the polymer membrane is assembled into the battery which is then activated by adding liquid electrolyte, which swells the polymer into the gel form. The added complexity and cost of the DBP extraction step has led to the development of the other methods, which have largely replaced casting. The phase inversion method is based on the precipitation of the porous polymer through either the interaction of a suitable solvent/non-solvent combination, or through solvent evaporation or cooling.225,303 Electrospinning has been demonstrated as an effective means to produce large surface area microporous polymers with a fully interconnected pore structure.188,304−306 Many polymer materials can be designed by blending polymerizable monomers, either using heat or irradiation (UV-light) technique. Monomers of chosen chemistry are mixed with salt, plasticizer, composite and/or ionic liquid and the ready-made blend to which proper amount of suitable initiator was added is heated or irradiated long enough to assure polymerization. Novel strategies, processing of oriented systems Despite over 25 years of research and development of non-crystalline polyether based solid electrolytes with low glass transition temperatures, there remains a conductivity plateau of about 10−5 S/cm (at ambient temperature), still over an order of magnitude too low for applications. Studies by Bruce et al.,307 Wright et al.,49 and our group308,309 have shown that crystalline-phase conductivity can be significant, if the helical chain structures through which the Li+ ions can hop are oriented. Some PEO:LiX complexes of the same nominal concentration exhibit higher conductivity in their crystalline than their amorphous phases.307 [The editors note that another chapter in this volume is dedicated to these exceptional crystalline polymers.] Our groups have demonstrated that chain alignment through mechanical stretching can produce a nearly two order of magnitude increase in ionic conductivity, with an anisotropy that

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favors conduction along the stretch direction, corresponding to the helical axis.308 It has also been shown that chain orientation and enhanced ion transport perpendicular to the film plane can be achieved by solvent casting the polymer under applied strong and inhomogeneous magnetic field.309 Unfortunately, the largest enhancements through polymer chain orientation occur in the most salt-concentrated materials, where the baseline conductivity is rather low, so that even the enhanced values are still too low for practical applications. Nonetheless, these efforts indicate another possible avenue of obtaining sufficiently conducting PEs. An approach that combines suppressing the crystalline phase with orientation has been described by Teeters and co-workers, where PEO–Li salt complexes confined in nanoporous inorganic filtration membranes demonstrated a nearly two order of magnitude increase in ionic conductivity compared to the bulk material.310 Despite the limited ambient temperature conductivity of PEO Li salt complexes, commercial attempts to use them in electrical vehicle batteries have met with some success, as will be described later.

5. Characterization and Mechanisms PEs are complex and often heterogeneous materials and investigation of their properties as a function of composition and morphology has been a continuing challenge. The following discussion highlights just a few of the many analytical methods used to characterize PEs that now largely form the basis of our current understanding. Very often, as in most materials science investigations, several methods are used simultaneously, each and every one adding a piece to the puzzle. Several of these methods are described in more detail and for a wider variety of materials in other chapters [editors’ note]. 5.1. Thermal Analysis Detailed knowledge of the thermal properties of the final material as well as its individual components is necessary in order to produce a reliable device stable which is workable at a range of temperatures.

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Typically, two different techniques are used: Differential scanning calorimetry (DSC) and Thermal gravimetric analysis (TGA). Normally, overall thermal stability and thermodynamic changes in a material such as the melting and crystallization temperatures (first-order transitions) are measured by the DSC technique. For electrolytes, even partial crystallization of the polymer matrix will have large impact on mechanical and dynamic properties of the material as it will change the free volume of the amorphous polymer phase where all or most ionic motion is presumed to occur.311 Primarily though this mobility depends on the glass transition temperature (Tg ) of the amorphous phase, this thus being the most important thermal property of polymer electrolyte material measurable with DSC. It is at this second-order transition that chain mobility significantly changes and its value therefore primarily determines ionic mobility in the material at ambient temperatures.312 Lowering of Tg is the synonym for increasing ionic mobility in a polymer material and can be accomplished by blending or co-polymerization of the matrix and/or by addition of plasticizing agents as has been described above. DSC technique can here function as a quick and easy estimate of material properties when optimizing the composition of a new system. TGA is used to evaluate the stability of the measured material. While DSC mostly observes reversible thermodynamic transitions, TGA reveals the temperature of material decomposition and degradation. The temperature and process of evaporation of liquid components can also be observed. 5.2. Rheology Rheology measurements of the material can be used to predict practical use temperatures, impact properties, energy dissipation, stiffness and many other performance properties. In the most usual set of experiments strain and stress are measured and expressed in terms of Young’s Modulus (Tensile Modulus), which describes how much a material will stretch (i.e. how much strain it will undergo) as a result of a given amount of stress. Stress (σ) is graphed against strain (ε) showing the toughness of a material (i.e. how

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much it resists stress, in J m−3 ) equal to the area under the curve, between the y-axis and the fracture point. The different regions of the resulting curve reveal the intrinsic properties of the measured material, showing the elastic region where the ratio of stress to strain (Young‘s modulus) is constant, plastic region, where the rate at which extension is increasing is going up, and the material has passed the elastic limit and will no longer return to its original shape. The material will ‘give’ and extend more under less force. Finally, reaching the fracture point, the material breaks/fractures and the curve ends and the ultimate tensile strength of the material is reached. Also, elasticity, the property of an object or material which will restore it to its original shape after distortion and yield strength or the yield point, the amount of stress that a material can undergo before moving from elastic deformation into plastic deformation can be estimated. With proper equipment rheological properties can be measured continuously as the material undergoes temperatureinduced changes from amorphous to crystalline; solid to molten and vice versa. Dynamic rheology is used to measure the elastic (G ) and viscous  (G ) moduli of a sample. Typically, the frequency dependence of G and G is measured to understand the extent of structure formation within the sample. For disperse systems with no particle flocculation, G is greater than G over the entire range of frequencies. For weakly flocculated systems, the presence of particle structures introduces both viscous and elastic effects into the rheological response. Thus, the moduli show a weaker dependence on frequency, and the elastic modulus G often exceeds the viscous modulus G at high frequencies. If the particles flocculate into a volume-filling network structure, the moduli, G and G are independent of frequency, and the materials is classified as a gel, i.e. shows predominantly elastic properties with G > G .192,313,314 Changes of the mechanical properties of electrolyte material by rheology experiments have been studied as a function of type of polymer material315,316 and varied types and concentrations of monomers,244 fillers,192,317−319 salts and plasticizers.244,320 In combination with electrochemical measurements the applicability of the materials is revealed.66 The

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rheological properties of PEs are directly involved in important considerations such as processability and cell assembly, and the ability to suppress dendrite growth in Li metal batteries.

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5.3. Vibrational — IR and Raman Spectroscopy Techniques Infrared and Raman spectroscopic measurements provide spectra showing bands originating from vibrations of individual bonds or groups in a molecule, thus focusing on the molecular rather than macroscopic level. Vibrations caused by stretching, scissoring, rocking and wagging of individual groups are highly conformationsensitive and therefore the presence or absence of such modes makes it possible to distinguish between different coordination situations or changing phases occurring in the samples. Absorption of electromagnetic radiation in the IR region is possible if the frequency of the radiation, ν, corresponds to the frequency of a normal mode of vibration. The region of interest in absorption spectroscopy thus corresponds to the IR portion of the electromagnetic spectrum between wavelengths 2 and 25 µm. It should be noted that not all normal modes are IR active. Only an oscillating dipole can absorb electromagnetic radiation of matching frequency. The second way in which electromagnetic radiation may interact with a vibrating molecule is by scattering of the irradiated light. There will be both elastic scattering (Rayleigh scattering) and inelastic scattering (Raman scattering), the latter involving a change in frequency corresponding to the excitation or the deexcitation of a vibrational mode. Only a few photons, approximately 1 in 108 –109 , undergo Raman scattering, which is why much more sophisticated instrumentation is necessary compared to the relatively simple IR equipment. As for IR absorption, not all the normal modes are Raman active. Only modes that induce a change in the polarizability, α, are Raman active that is (dα/dq) = 0 is a condition for the Raman process. Accordingly, the selection rules for Raman and IR are different and the two techniques provide complementary information.321 In PE research these techniques are mainly applied when detailed information of coordination of individual species is sought as such

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determination of preferential coordination of lithium can be decisive for the resulting conductivity of the whole system.66,190,203,322 In combination with other methods specific information can be obtained such as for example in combination with TGA the exact products of thermal degradation can be identified.323 5.4. Diffraction Techniques Diffraction measurements give information about the morphology of a system and about long range ordering, phases and structures. X-ray scattering at low angles gives an insight into the ordering of large scale structures within a system. Heterogeneity caused by differences in density distributed over a polymer film, such as periodically repeating crystalline and amorphous regions, can be revealed. Also, the mean distance between crystalline regions in a material can be resolved.113,324−326 Wide-angle X-ray diffraction (XRD) measurements reveal the detailed long-range atomic arrangement in a material. Therefore, the detailed structure and relative amount of a crystalline component of or within a sample can be determined.63,199,327−330 In situ measurements enable the study of dynamic intercalation processes and structural changes of both electrolyte and its interface that occur during charge/discharge process.331,332 Neutron diffraction is useful especially when details on structural positions of lighter atoms such as lithium and hydrogen are needed,330,333,334 although the requirements for specially designed nuclear reactor rules out frequent availability of neutron scattering equipment. Modeling techniques, some of which are described later, are often applied in order to extrapolate and finalize the structures and filling in the missing atoms. 5.5. Scanning Electron Microscopy (SEM) SEM makes it possible to actually visualize the structure of electrolyte materials and measure different features within. It is usually used to obtain details of microstructure features such as crystallites,10,176 size and shape of composite particles,201,206,267

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structure of membrane porosity232,297 and also for detailed interface morphology.26,29

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5.6. Conductivity Measurements Ionic conductivity of a material can be conveniently measured by impedance spectroscopy. A small AC current pulse with a range of frequencies (ω) is sent through a sample enclosed between two blocking electrodes, and the voltage response of the cell is observed. From this, the impedance, Z(ω), and the bulk ionic conductivity can be calculated. When performing impedance spectroscopy measurements, no salt concentration gradients or depletion of the salt from the bulk occurs. The response of an ionic conductor placed between two blocking electrodes can often be modeled by an equivalent circuit as shown in Fig. 2(a). Here, Rs represents the resistance of the bulk and is caused by the response of individual ionic species to the applied current. Cg is the geometric capacitance. The impedance, Z(ω), is usually represented in a complex plane plot, and results in a single semicircle and a vertical line increasing in impedance with decreasing frequency (Fig. 2(b)). The mid-frequency intercept with the real axis of impedance represents the resistance associated with

Fig. 2. (a) Equivalent circuit representing the impedance spectrum of an electrolyte — blocking electrode cell, where Cdl is the electrode double layer capacitance, Cg is the geometric capacitance, and Rs is resistance associated with ion conduction in the electrolyte. (b) A representative complex plane plot of an ideal electrolyte-blocking electrode cell. The bulk resistance is estimated from the midfrequency intercept with the real axis (Rs ).

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ion conduction. If the thickness of the electrolyte and the area of the electrodes are known, the ionic conductivity can be readily measured.335 The ionic conductivity, σ, of a polymer electrolyte is for a given temperature generally expressed as

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σ(T) =




ni qi µi ,

(1)

i

where ni is the number of charge carriers, qi their charge and µi their mobility. The temperature dependence of the conductivity of charged species is mostly derived from their motion being a thermally activated process. However, if the equilibrium of the polymer electrolyte changes with temperature, for example due to ion dissociation, pairing, or higher aggregate formation the number n and charge q of the ionic species (i.e. including aggregates) will also be temperature dependent. From Eq. (1) it is clear that an increase in number of charge carriers, e.g. due to a change in the salt concentration, should result in an increase in the ionic conductivity. However, the large ability of PEO polymers to dissolve salts allows highly concentrated solutions. As a consequence, for such solutions it is often possible to reach an optimum concentration, beyond which a further addition of salt will lead to a decrease in ionic conductivity.336 First, due to the close proximity of ionic species in concentrated solutions, there is a frequent occurrence of both contact and solvent separated ion-pairs or higher aggregates, thus decreasing the concentration of charge carriers, or reducing their mobility. Second, further addition of salt to an already concentrated sample will lead to stiffening of the polymer backbone, through ion-induced crosslinking and thus to reduction of the ionic mobility of the system.51 Temperature Dependence Ionic transport is a thermally activated process, which is also closely coupled to the dynamics and the mobility of other components of the system. The dynamics of the polymer chain and the solvent are

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therefore important for the conductivity of a polymer electrolyte. It has been shown that the temperature dependence of conductivity in these systems is closely coupled to the segmental motion of the polymer. The temperature dependence of the conductivity, σ, in semicrystalline polymer electrolytes has been described by the Arrhenius relation   EA σ = σ0 . exp − , (2) RT where the conduction mechanism involves a thermally activated step, characterized by the activation energy, EA . The ionic conductivity in fully amorphous polymer electrolytes (or semicrystalline PEs with a significant amorphous fraction) is often expressed by the Vogel–Tammann–Fulcher (VTF) equation   EA − 12 σ = AT exp − , (3) R(T − T0 ) where T0 is correlated to the glass transition temperature (Tg ), of the polymer chain, and is typically around 40 K lower than Tg .5,219 The conductivity mechanism for ionic transport in polymer electrolytes has been described by the dynamic bond percolation theory.56 The theory suggests that cations move by hopping between vacant coordination sites along the polymer backbone. These vacant coordination sites emerge and disappear due to the motions of the polymer chains. The mobility of the cations is then strongly dependent on the dynamics of the system and the cation–polymer interactions. When a plasticizer is added to the system both the dynamics and the coordination situation are changed. These changes can be studied by a wide range of experimental techniques such NMR, FTIR Spectroscopy and Impedance Spectroscopy. Also, for the oriented crystalline PEs described previously,307−310 the ionic conductivity is not strongly coupled to the host polymer segmental motion. An important practical consideration is that the ionic conductivity of PEO-based electrolytes has been known to depend strongly on the thermal treatment protocol and to decrease slowly as a

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function of aging. The instability of the conductivity is usually attributed to the slow re-crystallization kinetics of PEO and Li– PEO complexes.337 Another problem occurring in all-solid-state systems is high interfacial electrode/electrolyte resistance caused by “point-type” contacts. Because of the rigid and rough surface of the polymer–electrolyte films, only a fraction of the lithium electrode (θ) is in intimate contact with the PE.338 It is well known that in Li/solid PEs and CPE cells, θ  1 at near-ambient temperatures. Preheating of the cells is typically used to eliminate the deleterious effect of poor electrode/electrolyte interfacial contacts on the precision of conductivity tests. Considering the fact that polymer electrolytes are intrinsic part of an intended battery system, it is obvious that its compatibility with all materials used is paramount.339 This involves particularly the electrodes, where stability, compatibility and possible sidereactions and their causes and consequences at the interfaces are extensively researched. Electrochemical measurements are used to study electrochemical stability and reactions occurring on the electrolyte surface during cell-recycling often in combination with one or several spectroscopic methods.340−343 Another electrochemical interface study involves grain boundaries of the above discussed surface modified nanoparticles that has been shown to change ionic character during the charge-discharge cycle thus actively contributing to the process.344,345 5.7. Nuclear Magnetic Resonance From the “early days” (late 1970’s) of PEs, nuclear magnetic resonance (NMR) spectroscopy has been successfully and productively applied to investigate ion–polymer coordination and ionic mobility.62,346−350 The relevant nuclei include 7 Li and 19 F, for probing the environments and mobility of the ions, and 1 H and 13 C for the polymer. Recently, with renewed interest in sodium batteries, 23 Na is returning to the scene as well. One of the hallmarks of any ionic conductor is the observation of motional line narrowing of the nuclear resonance corresponding to the mobile ion (i.e. 7 Li) and this diagnostic commonly reported during the initial studies

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of PEs remains in use today.79,351,352 In fact, this approach was the first to establish unambiguously that ionic conduction is strongly coupled to polymer segmental motion occurring above the glass transition temperature (Tg ) in the amorphous phase of the PE.353,354 As discussed previously, this finding has driven the PE community to focus on the development of amorphous materials with low Tg . This remains the predominant approach with the exceptions cited above, namely, finding suitable surface-functionalized fillers that interact with the ions or examples of oriented crystalline structures, which in both cases involves some decoupling of the polymer and ionic motions. NMR is also a powerful method to probe ion and polymer dynamical process over a span of some 10 orders of magnitude (in time or frequency) from spin-lattice relaxation to pulsed field gradient diffusion. After NMR excitation, the return to thermal equilibrium magnetization along the applied static field direction is characterized by spin-lattice or longitudinal relaxation time T1 . It is the process of energy transfer from the excited nucleus to the surroundings or the lattice, usually meaning the neighboring molecules, that returns the nuclear spin system to thermal equilibrium. Since the first comprehensive treatise of relaxation published over 60 years ago,355 measurements of T1 as a function of temperature have provided a useful molecular level probe of dynamics because the most effective relaxation mechanisms, whether mediated by nuclear dipole–dipole, quadrupole, or electron spins (in samples containing paramagnetic centers), must have significant spectral density components close to the NMR frequency. Thus T1 is very sensitive to motional processes with a time-scale of ∼10−10 s. As a typical example of relaxation behavior in a PEO–lithium salt complex, Fig. 3 displays the T1 data for PEO20 LiBETI (where BETI is N(SO2 CF2 CF3 )2 .356 Both the 7 Li and 19 F values, and of the latter, for resolved resonances from the CF2 and CF3 groups of the anion, are plotted. The 7 Li T1 minimum occurs somewhat above RT while the 19 F T minima, though not observed due to the limited temperature 1 range, are expected to occur at much lower temperature. The CF3 resonance is characterised by the highest T1 values (presumably on

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19

F (CF3)

19

F (CF2)

7

Li F (CF3)

19 19

F (CF2)

7

Li

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T1 (s)

1

0.1 2.6

2.8

3.0

3.2

3.4

3.6

1000/Temp (1/K)

Fig. 3. T1 vs. temperature of filler-free (solid markers) and 10% wt. SiO2 (empty markers) P(EO)20 LiBETI polymer electrolytes.

the high temperature side of the minimum) because of the rapid fluoromethyl group rotation about its symmetry axis. The effect of added nanosized SiO2 filler on the T1 values is relatively small but observable. Regarding motional processes more directly related to longrange ionic transport, pulsed field gradient NMR has been used to measure molecular and ionic self-diffusion coefficients since the mid-1960s and has become a relatively common tool to characterize PEs.357−363 One of the frequent observations in such studies is that the total ionic conductivity calculated from the Nernst–Einstein Nq2 (D +D

)α

Li anion equation, σcalc = , where N the number of ions per kT unit volume, q the charge of the ions, α the degree of dissociation, k is the Boltzmann constant, T the absolute temperature, and DLi and Danion are the diffusion coefficients of cation and anion, respectively, frequently agrees with the experimentally measured conductivity for only α < 1. That is, correlated motion of associated ions that contributes to the NMR signal decay with D is evaluated and it does not contribute to the net conductivity. An example of a diffusion NMR investigation of a gel electrolyte system containing an ionic liquid is displayed in Fig. 4.287

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Fig. 4. Arrhenius plots of the self-diffusion coefficients of Li, P13, and TFSI in the 1M LiTFSI/P13TFSI/PVDF-HFP and 1 M LiTFSI/0.2EC+0.8P13TFSI/PVDF-HFP polymer gel electrolyte membranes. Reproduced with permission from Ref. 287.

The host polymer is PVdF-HFP, the ionic liquid is 1-methyl-3propylpyrrolidinium (P13 ) TFSI and the LiTFSI concentration is 1M. All three mobile species, IL cation, anion, and Li+ are probed by 1 H, 19 F, and 7 Li NMR respectively. The Li diffusion coefficient is the lowest among all species as expected from its tendency toward ion association due to its high charge density. The effect of adding ethylene carbonate (EC) to the gel is dramatic as depicted in Fig. 4 in which the Li diffusion now exceeds that of the other ions. Because EC is a good SEI former in standard lithium-ion batteries,225,226,302 it is reasonable to incorporate it into the gel electrolyte. However as shown here, there is clearly another benefit in that it apparently solvates the Li+ ions and mitigates their interaction with the anions. More sophisticated NMR experiments revealing greater structural and in some cases dynamical details are possible using 2D techniques, where two different nuclei can be studied not only simultaneously but also in dependence on each other, i.e. how they are correlated. This discussion goes beyond the scope of this review

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but many of these techniques are described and discussed in the context of PEs in previous review articles of the authors.364,365

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5.8. Modeling and Theory Molecular dynamics (MD) simulations have been applied by many different research groups attempting to clarify crystal structures or stability of coordination species in a wide range of electrolyte materials,366 non-aqueous liquid electrolytes367,368 as well as SPEs. Multitude of MD studies concentrate on different systems based on short chain PEO47,329,369−376 but also based on other polymers,377,378 polymers containing nano-particles,379−381 plasticisers382 or other cations besides lithium, especially sodium.383,384 Monte Carlo (MC) simulations have been less frequently used, but have contributed to the field of polymer electrolytes and revealed the limiting step in ion conduction in polymer matrices by the development and testing of the dynamic bond percolation theory.56 MC has also been used to model the Li+ adsorption on a metal electrode from a liquid electrolyte,385,386 and helped to explain the conduction mechanisms in polymer electrolytes mentioned above.387−390 Ab initio calculations can only be applied to much smaller systems and are thus directed to probe properties dependent on local phenomena. The major benefit of ab initio calculations compared to MD or MC, apart from the inclusion of electrons and thereby electronic properties directly, is that the results are independent of any previously developed force-field and that local phenomena are treated undisturbed. The use of ab initio methods also allows the collection of different basic physical properties such as local and global minima on potential energy surfaces, bond strengths, interaction strengths or charge distributions.391 In PE research ab initio calculations have been applied to study properties of battery materials either alone,392−394 in conjunction with experimental techniques such as NMR or IR or Raman spectroscopies241,322,395,396 or in order to serve further simulations with necessary input data.397,398

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6. Implementation of Polymer Electrolytes in Solid-State Batteries

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6.1. Microelectronic Batteries The rapidly growing billion-dollar-scale market for microelectronics, where the requirements for the amount of energy stored on a given footprint (J/mm2 ) take precedence over energy per unit mass (Wh/kg) or volume (Wh/L), requires on-board power delivery on exceptionally small geometric scales. Typical 2D battery configurations were originally designed for devices of dimensions larger by a factor of a thousand or even a million. As a consequence, miniaturisation based on conventional rechargeable-battery technologies becomes highly problematic. Furthermore, the key components of most conventional Li-ion batteries (electrolytes, separators) cannot survive the integration process during micro-fabrication, as a result of the high temperature of solder reflow (260◦ C). Solid LIPON thin-film Li-ion batteries, although more amenable to the microfabrication process than is liquid-electrolyte Li-ion technology, often fall short of the energy demands of MEMS/NEMS devices399 and low-footprint capacity. To maximize the energy storage per geometric area, one is forced to seek space in 3D, and this leads to investigations of 3D design for microelectrode arrays. The increased area of electrolyte/electrode contacts in these 3D electrode designs significantly facilitates “ionic transfer” by reducing the tortuosity of the migration pathway. The achievement of conformal coating of the complex 3D-electrode structures of the cell by polymer electrolyte constitutes a great challenge, since the electrolyte must have the appropriate electrochemical properties in addition to the mechanical properties needed to withstand the pressures of second-electrode formation, sealing of the cell, and changes in the electrode volumes during the operation of the cell. Typical methods of PE casting are inapplicable for highaspect-ratio 3D-MB architectures. Several approaches to prepare polymer electrolytes and composite electrolytes for 3D batteries are presented here. Other chapters provide a more complete discussion of 3D designs and thin electrolytes [editors’ note].

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Spin coating and vacuum infiltration of polymer electrolytes Successive steps of spin coating and vacuum can be used to insert the membrane into the high-aspect-ratio perforated substrates. For the preparation of a 3D (HPE),400 a commercially available PVDF2801 copolymer (Kynar) was chosen as binder, and fumed silica as filler for the polymer membrane, as in the Bellcore process. The ionic conductivity of a membrane soaked in either tetraglyme or EC:DMC-based electrolyte with Li-imide salt, was 1–3 mS.cm−1 at RT. The interfacial lithium/HPE resistance (RSEI ) of 6–10 ohm.cm−2 was stable for 3000 hours. Conformal coating were obtained on the microchannels of the perforated silicon, Foturan and glasscapillary arrays, however the thickness of the membrane and its morphology depend on the type of solvent, pore former (PC or PEG), concentration of solids in the casting slurry, and drying conditions. The membranes cast from cyclopentanone were transparent or slightly translucent with smooth homogeneous surface and bulk. The membrane cast from acetone has less uniform morphology, with surface irregularities and sometimes trapped air bubbles. This was explained400 by extremely fast evaporation of the solvent. While this hybrid electrolyte did not ensure conformal coating of the cathode in microchannels, the Li/HPE/MoOx Sy -on-Si 3D cell ran for 100 charge/discharge cycles with 0.06%/cycle capacity loss and 100% Faradaic efficiency. SPEs for 3D microbatteries were synthesized by researchers from Uppsala University.24,29,401 A thin-film electrolyte of a 2:1 blend of polyetheramine (glyceryl poly(oxypropylene)) and cross-linked oligomeric poly(propylene oxide) diacrylate with LiTFSI for 3DMB ensures good mechanical stability and conformal coating on complex surfaces like porous LiFePO4 cathodes. The electrolyte showed conductivities of 3.45 × 10−6 and 5.80 × 10−5 S cm−1 at RT and 60◦ C, respectively. Electrolytes of about 2 µm-thick cast on LiFePO4 cathodes and cycled against metallic lithium, displayed stable discharge capacities of 8 mAh/g at RT, and 120 mAh/g at 60◦ C.24 Thin and pinhole-free 3D-polymer electrolyte layers based on oligomeric polyetheramine substituted with a methacrylic group at one of its three chain ends exhibited good electrochemical and

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chemical stability up to 4 V versus Li/Li+ .29 High-molecular-weight poly(trimethylene carbonate) (PTMC) as a new host material for Liion SPE was synthesized through bulk ring-opening polymerization of the cyclic monomer to yield a high-molecular-weight polymer. The most conductive systems were found at [Li+ ]:[carbonate] ratios of 1:13 and 1:8, which showed electrochemical stability up to 5.0 V versus Li/Li+ and an ionic conductivity on the order of 10−7 Scm−1 at 60◦ C. Electropolymerization of polymer electrolytes The deposition of polymer electrolytes into and onto nanostructures by electrochemical techniques is the most convenient way to ensure the desired filling and/or coating of the nanostructures. Indeed, electropolymerization is a particularly powerful way of controlling the deposition of different polymers into various porous materials.402,403 Very recently, the use of electrodeposition to fill TiO2 nanotubes with a layer of poly(methylmethacrylate)-polyethylene oxide, (PMMA-(PEO)475) has been reported.404 The electropolymerization of MMA-(PEO)475 monomer from aqueous solution containing LiTFSI was carried out by cyclic voltammetry (CV). A homogeneous copolymer layer 6 nm in thickness was deposited on the inner and outer walls of the nanotube. The presence of LiTFSI was confirmed by XPS. Another example of the use of electropolymerization for the preparation of polymer electrolytes for 3D-MBs was proposed by Owens et al.404 PAN films were grown on glassy carbon, nickel foam and MnO2 substrates by cathodic electropolymerization of acrylonitrile in acetonitrile with tetrabutylammonium perchlorate (TBAP) as the supporting electrolyte. The electronic-barrier properties of the films were confirmed by impedance spectroscopy of carbon |PAN| Hg cells. The ionic resistance of the films varied from 200 kOhm.cm2 in the dry state to 1.4 Ohm.cm2 when plasticized with 1 M LiPF6 in propylene carbonate. A galvanic cell was prepared by successive electrodepositions of MnO2 and PAN on a carbon substrate, with the use of liquid lithium amalgam as the top contact. The cell showed a stable open-circuit potential and behaved normally under the galvanostatic intermittent-titration technique test (GITT).

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Electrophoretic deposition of polymer electrolytes A novel approach of conformal electrophoretic deposition (EPD) of hybrid and solid polymer-in-ceramic and ceramic-in-polymer electrolytes for 3D-MBs has been recently proposed.405,406 The electrolytes are composed of zirconia and polyethylene imine or lithium aluminate and PEO. The authors found that the EPD process of pristine and composite polymer–ceramic films follows a simple linear relationship between time and mass of the deposit for the tested ranges of values of the relevant parameters. Addition of PEI polymer to the suspension improved film adhesion to planar and 3D-perforated silicon substrates and reduced the film roughness to less than 2 µm, even at long deposition times. The relative content of PEO and LiAlO2 in the membrane depends on the type of solvent and composition of the suspension. Films deposited at 50 V are smoother, conformal and more uniform than those prepared at 100, 150 and 200 V. To gain a phenomenological understanding of the EPD process for a system of charged colloidal particles covered with a polyelectrolyte (PE), the authors developed a model for the electric potential on the basis of the Poisson–Boltzmann (PB) relation.407 They simulated a set of scenarios in an attempt to present the influence of pH, surface potential, PE density, and the PE brush length on the electric-potential and charge-distribution profiles as a function of distance from the solid-surface/brush interface, where ‘brush’ is one of the possible PE configurations. It was found that at high density of adsorbed PEI molecules the repulsion forces eliminate coagulation between corona-like “soft” particles and form smoother films. On the other hand, the repulsion causes prolonged (or delayed) soft particle–electrode interaction for migration and oscillation in the neighborhood of a minimum-potential-energy-surface electrode. Time of Flight Secondary Ion Mass Spectroscopy (TOFSIMS) spectra and positive-ion-species images showed homogeneous lateral and depth distribution of the polymer binder in electrophoreticallydeposited composite films. Electrophoretic deposition of a modified composite PEOceramic film on the 3D perforated silicon substrate405 was carried

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Fig. 5. ESEM images of 3D perforated silicon coated by gold current collector and composite zirconia-based film, (a) planar and cross-sectional SEM micrographs at different magnifications (b, c).

out with the use of the homemade-deposition setup, which provides continuous flow of the suspension through the microchannels. The thickness of the substrate was 400 µm, the diameter of a single channel was 50 µm, and the interhole spacing was 20 µm. The perforated substrates were prepared with the use of the deep reactive ion-etching (DRIE) method. Planar (Figs. 5(a)) and cross-sectional SEM micrographs at different magnifications (Figs. 5(b) and 5(c)) of the PEI-modified YSZ film deposited on the gold-coated, perforated silicon chip show that the morphology of the 3D deposit inside long narrow channels is similar to that obtained on the planar surfaces. The ionic conductivity of electrophoretically deposited PEOLiAlO2 composite, with impregnated 0.3 M LiTFSI-PYR14 TFSI ionicliquid electrolyte is 1–3 mS/cm at 30 to 60◦ C and comparable to that of commercial battery separators.406 The conductivity of quasi-solid plasticized PEO-in-LiAlO2 electrolyte is 0.2 mS/cm at RT and does not change up to 100◦ C. The temperatureindependent ionic conductivity of quasi-solid polymer-in-ceramic electrolyte and the very low apparent activation energy indicate that the interfacial ceramic/polymer ion-conduction path is favored. Conformal coating of the 3D electrode materials by thinfilm, polymer–ceramic composites is beneficial for high-power battery operation, since these electrolytes are able to prevent hightemperature thermal runaway and significantly improve battery safety.

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6.2. Consumer Electronics Although many challenges for battery development still remain,408 a large number of manufacturers have presented viable working products.409,410 A very concise overview of battery types and producers and the different types and technologies is available online.411 One of the first PE battery producers in the US was Bellcore. Their patented battery design is also known as plastic lithium-ion cell (PLION)234 based on microporous plasticized PVdF-HFP based polymer electrolyte which serves both as separator and electrolyte. In PLION cells, the anode and cathode are laminated onto either side of the gellable membrane. Many battery designs produced world-wide are derived from this technology such as Motorola and Mitsubishi Electric, where separate adhesive layer (PVdF) is applied to the separator and used to bond the electrode and the separator films, using in the first case the hot, liquid electrolyte as an in situ PVdF plasticizer.40 On the other hand, Sanyo, Sony, and Panasonic started commercial production on lithium-ion batteries based on GPE technology in 2002. Sony reported the use of a thin, liquid electrolyte-plasticized PAN layer directly applied either to the electrode or the separator surfaces as an effective ion-conductive adhesive, while Sanyo technology is based on the injection of the mixture of an electrolyte solution and a precursor of PEO followed by heating the cell to polymerize the PEO precursor. The electrolyte solution consists of the solvent mixture of EC, DEC and LiN(SO2 C2 F5 )2 .412 In 2009, however, Sony also launched production of high-power, Long-life Lithium-Ion Secondary Battery based on random PVDF/HFP (a mixture of low and high MWs) as the polymer matrix, PC and EC as a solvent mixture and LiPF6 , a modified anode consisting of graphite particles coated with amorphous carbon and olivinetype lithium iron phosphate as the cathode material.413 Lithium-ion polymer batteries used and patented by Apple, Inc. are said to have enabled the manufacturing of curved and irregular shape designs to be used in new generation Apple products.414

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6.3. Electric Vehicles Only a few organizations are working towards polymer electrolyte batteries for vehicles, although eliminating the use of flammable liquid electrolytes may improve safety and performance. In Canada, Hydro-Québec together with Grafoid Inc. have patented several battery components applicable for high-power as well as high energy batteries.415,416 In collaboration with 3M, Hydro-Québec intends to produce personal and public transportation vehicles.417 Bolloré Group, French national distributor of oil and petroleum, has developed a unique technology based on slightly modified PEO for electric lithium metal polymer (LMP) batteries. It now operates in stationary and mobile applications (electric buses and cars, Autolib’) for electric batteries. It also has a leading position through IER in terminals and access control and identification systems for transport.418 To maintain its leading position, Toyota has announced a bold plan to commercialize solid-state batteries around 2020 and lithium air batteries — which offer a five-fold increase for the same weight — are said to follow several years later.419 7. Summary and Outstanding Issues Limiting Application Today’s lithium-ion batteries, found in nearly all consumer electronics and made almost exclusively in Asia, will require additional technological advances before they can be applied widely to tomorrow’s electric vehicles. Still needed are improvements in safety, especially considering the hazards of flammable liquid electrolytes in large batteries, and durability, along with cost reductions. Novel configurations such as 3D microbatteries with unprecedented energy density will also benefit by continued improvement in polymer electrolyte properties and processing ability. Although a number of successful applications of polymer electrolyte batteries have been developed, there are many more that await the advent of a solventfree system with an order-of-magnitude higher ionic conductivity than currently exists. These outstanding issues must be confronted in order to more fully realize the potential contribution of PEs to these important applications.

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Acknowledgment

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The authors acknowledge the U.S. Office of Naval Research for previous support on oriented polymer electrolytes reviewed herein and the U.S. Department of Energy for more recent support during the time this article was prepared. The authors also thank the U.S.Israel Binational Science Foundation for support. References 1. M. Armand and J. M. Tarascon, Building better batteries, Nature 451 (2008) 652–657. 2. G. Girishkumar, B. McCloskey, A. C. Luntz, S. Swanson and W. Wilcke, Lithium-Air Battery: Promise and Challenges, J. Phys. Chem. Lett. 1 (2010) 2193–2203. 3. Z. Rao and S. Wang, A review of power battery thermal energy management Renew. Sust. Energ. Rev. 15 (2011) 4554–4571. 4. D. E. Fenton, J. M. Parker and P. V. Wright, Complexes of alkali metal ions with poly(ethylene oxide), Polymer 14 (1973) 589. 5. M. B. Armand, J. M. Chabagno and M. J., D. in Fast Ion Transport in Solids, eds J. N. Mundy, P. Vashishta and G. K Shenow, p. 131, (Elsevier Science Ltd, New York, 1979). 6. M. B. Armand, P. G. Bruce, M. Forsyth and S. Bruno, in Energy Materials, (eds. D. O’Hare, D. W. Bruce R. I. Walton), Ch. 1, (John Wiley & Sons, Ltd., New York, 2011). 7. G. Ceder, G. Hautier, A. Jain and S. P. Ong, Recharging lithium battery research with first-principles methods, MRS Bull. 36 (2011) 185–191. 8. B. Scrosati and Garche, J. Lithium batteries: Status, prospects and future, J. Power Sources 195 (2010) 2419–2430. 9. V. Di Noto, S. Lavina, G. A. Giffin, E. Negro and B. Scrosati, Polymer electrolytes: Present, past and future, Electrochim. Acta 57 (2011) 4–13. 10. T. Yoshida, et al., Electrodeposition of inorganic/organic hybrid thin films, Adv. Funct. Mater. 19 (2009) 17–43. 11. M. Burris, Lithium-ion battery safety, (2013) http://components. about.com/od/Components/a/Liionsafety.htm. 12. Y. Takei, K. Takeno, H. Morimoto and S.-I. Tobishima, Effects of nonaqueous electrolyte solutions mixed with carbonate-modified siloxane on charge–discharge performance of negative electrodes for secondary lithium batteries, J. Power Sources 228 (2013) 32–38.

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27. M. Roberts, et al., 3D lithium ion batteries-from fundamentals to fabrication, J. Mater. Chem. 21 (2011) 9876–9890. 28. J. F. M. Oudenhoven, L. Baggetto and P. H. L. Notten, All-solid-state Lithium–ion microbatteries: A review of various three-dimensional concepts, Adv. Energy Mater. 1 (2011) 10–33. 29. B. Sun, I. Y. Liao, S. Tan, T. Bowden and D. Brandell, Solid polymer electrolyte coating from a bifunctional monomer for threedimensional microbattery applications, J. Power Sources 238 (2013) 435–441. 30. K. M. Abraham and Z. Jiang, A polymer electrolyte-based rechargeable Lithium/oxygen battery, J. Electrochem. Soc. 143 (1996) 1–5. 31. T. Ogasawara, A. Debart, M. Holzapfel, P. Novak and P. G. Bruce, Rechargeable LI2O2 electrode for lithium batteries, J. Am. Chem. Soc. 128 (2006) 1390–1393. 32. A. Debart, A. J. Paterson, J. Bao and P. G. Bruce, Alpha-MnO2 nanowires: A catalyst for the O2 electrode in rechargeable lithium batteries, Angew. Chem. Int. Ed. 47 (2008) 4521–4524. 33. C. O. Laoire, S. Mukerjee, K. M. Abraham, E. J. Plichta and M. A. Hendrickson, Influence of nonaqueous solvents on the electrochemistry of oxygen in the rechargeable Lithium–air battery, J. Phys. Chem. C 114 (2010) 9178–9186. 34. B. Kumar, et al., A solid-state, rechargeable, long cycle life Lithium–air battery, J. Electrochem. Soc. 157 (2010) A50–A54. 35. T. Zhang, et al., A novel high energy density rechargeable lithium/air battery, Chem. Commun. 46 (2010) 1661–1663. 36. J.-S. Lee, et al., Metal–air batteries with high energy density: Li–air versus Zn–air, Adv. Energy Mater. 1 (2011) 34–50. 37. M. Zhang, et al., Water-stable lithium anode with Li1.4Al0.4Ge1.6 (PO4)3–TiO2 sheet prepared by tape casting method for lithium–air batteries, J. Power Sources 235 (2013) 117–121. 38. J. Hassoun, F. Croce, M. Armand and B. Scrosati, Investigation of the O2 Electrochemistry in a Polymer Electrolyte Solid-State Cell, Angew. Chem. Int. Edi. 50 (2011) 2999–3002. 39. E. Peled, D. Golodnitsky, H. Mazor, M. Goor and S. Avshalomov, Parameter analysis of a practical lithium- and sodium-air electric vehicle battery, J. Power Sources 196 (2011) 6835–6840. 40. P. Arora and Z. Zhang, Battery separators, Chem. Rev. 104 (2004) 4419– 4462. 41. C. Sisbandini, D. Brandell, T. Gustafsson and L. Nyholm, The mechanism of capacity enhancement in LiFePO4 cathodes through polyetheramine coating, J. Electrochem. Soc. 156 (2009) A720–A725.

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42. D.-W. Kim, B. Oh, J.-H. Park and Y.-K. Sun, Gel-coated membranes for lithium-ion polymer batteries, Solid State Ion. 138 (2000) 41–49. 43. Y. Wang, J. Travas-Sejdic and R. Steiner, Polymer gel electrolyte supported with microporous polyolefin membranes for lithium ion polymer battery, Solid State Ion. 148 (2002) 443–449. 44. Y.-B. Jeong and D.-W. Kim, Effect of thickness of coating layer on polymer-coated separator on cycling performance of lithium-ion polymer cells, J. Power Sources 128 (2004) 256–262. 45. S. Santhanagopalan, P. Ramadass and J. Zhang, Analysis of internal short-circuit in a lithium ion cell, J. Power Sources 194 (2009) 550–557. 46. A. Chakrabarti, R. Filler and B. K. Mandal, Synthesis and properties of a new class of fluorine-containing dilithium salts for lithium-ion batteries, Solid State Ion. 180 (2010) 1640–1645. 47. C. Zhang, E. Staunton, Y. G. Andreev and P. G. Bruce, Doping crystalline polymer electrolytes with glymes, J. Mater. Chem. 17 (2007) 3222–3228. 48. A. M. Christie, S. J. Lilley, E. Staunton, Y. G. Andreev and P. G. Bruce, Increasing the conductivity of crystalline polymer electrolytes Nature 433 (2005) 50–53. 49. P. V. Wright, Y. Zheng, D. Bhatt, T. Richardson and G. Ungar, Supramolecular order in new polymer electrolytes, Polymer Int. 47 (1998) 34–42. 50. S. H. Chung, Y. Wang, S. G. Greenbaum, D. Golodnitsky and E. Peled, Uniaxial stress effects in poly(ethylene oxide) – LiI polymer electrolyte film: A 7Li nuclear magnetic resonance study, Electrochem. Solid State Lett. 2 (1999) 553–555. 51. D. Golodnitsky, in Encyclopedia of Electrochemical Power Sources, eds. G. Juergen, et al., pp. 112–128, (Elsevier, New York, 2009). 52. B. Scrosati, F. Croce and S. Panero, Progress in lithium polymer battery R&D, J. Power Sources 100 (2001) 93–100. 53. M. D. Ingram, et al., Activation energy-activation volume master plots for ion transport behavior in polymer electrolytes and supercooled molten salts, The J. Phys. Chem. B 109 (2005) 16567–16570. 54. Z. Stoeva, C. T. Imrie and M. D. Ingram, Effect of pressure on ion transport in amorphous and semi-crystalline polymer electrolytes, Phys. Chem. Chem. Phys. 5 (2003) 395–399. 55. M. C. Wintersgill, J. J. Fontanella, J. P. Calame, D. R. Figueroa and C. G. Andeen, Dielectric relaxation in poly(ethylene oxide) complexed with alkali metal perchlorates, Solid State Ion. 11 (1983) 151–155. 56. S. D. Druger, M. A. Ratner and A. Nitzan, Polymeric solid electrolytes: Dynamic bond percolation and free volume models for diffusion, Solid State Ion. 9–10, Part 2 (1983) 1115–1120.

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410. S. Santhanagopalan and Z. Zhang, in Batteries for Sustainability, ed. R. J. Brodd, Ch. 6, 135–194, (Springer, New York, 2013). 411. Energy source guides: Battery business in the world (2013), Available at http://energy.sourceguides.com/businesses/byP/batP/batt/btora/ btora.shtml. 412. A. Froloff, Development of Lithium Polymer Batteries with Gel Polymer Electrolyte, (Sanyo Energy Corp., 2001). 413. K. Oiyama, (Sony Corporation). 414. M. Campbell, Apples research into curved battery technology points to new iOS products designs (2013), Available at http://appleinsider.com/articles/13/05/02/apples-research-into-curved-batterytechnology-points-to-new-ios-products-designs. 415. Grafoid Inc., Grafoid Inc. Announces R&D agreement With hydroQuebec’s IREQ for next generation LFP-graphene batteries, (2012) http://www.marketwatch.com / story / grafoid-inc-announces-rdagreement-with-hydro-quebecs-ireq-for-next-generation-lfp-graphene-batteries-2012-11-26. 416. HydroQuébec. Materials for battery manufacturing, (2010) http:// www.hydroquebec.com/innovation/en/pdf/10408A_MateriauxBatteries_PRESS.pdf. 417. 3M. Lithium Polymer Battery: 3M and hydro-quebec are paving the way for electric vehicle success (2013), http://www.prnewswire.co. uk/news-releases/lithium-polymer-battery-3m-and-hydro-quebecare-paving-the-way-for-electric-vehicle- success-156289395.html. 418. Group, B. Electricity storage and solutions, (2013) http://www. bollore.com/en-us/activities/electricity- storage-and-solutions. 419. T. Global, Research progress: Next generation secondary batteries (2013), Available at http://www.toyota-global.com/innovation/environmental_technology/next_generation_secondary_batteries.html.

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Chapter 17

All Solid-State Thin Film Batteries Jie Song

Materials Science and Engineering Program & Texas Materials Institute The University of Texas at Austin Austin, TX 78712, USA

William West

Nagoya University Nagoya 464-8603, Japan

All solid-state thin film batteries offer numerous advantages over conventional batteries where a small footprint and very thin profile are required, such as applications for on-board micro-chip power for micro-sensors, small medical implantable devices, radio frequency identification (RFID) cards, among many others. Thin film batteries also offer outstanding cycle life and safety relative to conventional lithium-ion cells, albeit at a cost of high substrate and packaging mass compared to the mass of active electrode material. The thin film battery components can be fabricated by a wide range of deposition and patterning technologies, most of which are compatible with microelectronic fabrication techniques. Many different materials can be used for the anode, cathode and electrolyte, which offer flexibility for tailoring the performance of the cells to a particular application. With ongoing advancements in low power electronics and energy harvesting, coupled with new developments in higher energy thin film electrodes and higher conductivity thin film solid electrolytes, the future prospects are excellent for widespread applications of thin batteries.

1. Introduction Thin film battery cells represent an important subset within the class of solid-state battery technologies. These cell designs take advantage of the inherent benefits of solid-state batteries such as negligible 593

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flammability and tolerance to excursions in temperature extremes while providing a number of unique advantages of a very thin cell profile where a conventional cell may be too large or heavy. Stateof-the-art thin film batteries offer numerous benefits such as: • Exceptionally long calendar life for storage over the entire range of state-of-charge • Very high cycle life at deep discharge, which exceeds conventional lithium-ion batteries by more than an order of magnitude • High rate capability • Very low self-discharge rate • The ability to be prepared in a variety of shapes and form factors • The absence of any appreciable growth of solid electrolyte interphase (SEI) or lithium dendrite formation allowing for incorporation of very high specific capacity thin film lithium metal anodes However, as with any battery cell design, the cell-level specific energy is limited by the mass of the active electrode material, and in thin film battery designs the active mass of the electrodes is typically a factor of ten or more lower mass than the substrate. As such, the cell-level specific energy of thin film batteries is usually much lower than conventional lithium-ion cells and it is unlikely that thin film batteries will supplant conventional lithium ion cells in applications such as energy storage for electric vehicles where battery specific energy is of the utmost importance. Rather, thin film batteries find applications for providing energy storage for: • • • • •

Radio frequency identification (RFID) and other “smart” cards Small implantable medical devices Wireless microsensors Microelectromechanical systems (MEMS) devices On-chip (e.g. static random access memory) back-up power

As new developments in ultra-low power electronics and miniaturization of MEMS devices are achieved, it is anticipated that thin film batteries will find an ever-widening suite of applications.

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Based on benefits and potential applications, thin film batteries have been a focus of study in the battery community since at least the early 1980s.1 As described below, during the past four decades a wide range of anodes, electrolytes, cathodes, substrates and encapsulants as well as deposition methodologies have been examined and reported. It is noteworthy that a key turning point in the advancement of the field was the identification of the thin film electrolyte lithium phosphorous oxynitride (Lipon) by Bates et al. at Oak Ridge National Laboratory (ORNL).2,3 This solid electrolyte provided a number of important advantages over prior electrolyte systems including outstanding electrochemical stability against lithium metal and higher voltage cathodes such as LiCoO2 , ease of preparation, negligible electronic conductivity and comparatively good lithium ion conductivity. To date, Lipon remains the electrolyte employed in virtually all commercially-fabricated thin film batteries. It should be noted here that the nomenclature for thin film batteries historically has been somewhat unclear, and phrases such as “thin film batteries”, “thin film microbatteries” or “microbatteries” have been used interchangeably to describe the same basic technology. In this chapter, we adopt the usage of the phrase “thin film batteries” to describe cells fabricated with a total thickness on the order of 100 µm or less, with footprints on the scale of 1 cm2 . Only for thin film batteries with footprints on the scale of 100 µm × 100 µm or less do we refer to the cells as “thin film microbatteries” or “microbatteries”.

2. Fabrication Methods The fabrication of a thin film battery consists of deposition of thin films of the battery components and thin film patterning. To deposit thin films of the battery components, various well-established deposition techniques can be applied. The most common techniques include thermal evaporation, pulsed laser deposition (PLD), sputter deposition, sol–gel deposition, chemical vapor deposition (CVD) and electrochemical deposition. Thermal evaporation, sputtering, and PLD belong to the class of physical vapor deposition (PVD)

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processes; CVD, sol–gel deposition and electrochemical deposition are chemical processes. Thermal evaporation is a process wherein a solid material is heated inside a vacuum chamber below approximately 1×10−6 Torr (1.3 × 10−4 Pa) to a temperature which generates appreciable vapor pressure. These evaporated particles are then free to condense on a substrate typically placed above the deposition source. Two methods are predominantly used for heating the source material, namely resistive heating and electron beam (e-beam) heating. Resistive heating is the most common technique for vaporizing materials at temperatures below about 1500◦ C, while focused e-beams are most commonly used for temperatures above 1500◦ C.4 PLD is a thin film deposition technique where a high-power, pulsed laser, such as the KrF excimer laser (ca. 1 J/pulse), is focused inside a vacuum chamber onto a target of the desired composition. A schematic of PLD is shown in Fig. 1. The ablated materials are then collected on nearby sample surfaces to form thin films. This process can occur in high vacuum or in the presence of a background gas, such as oxygen, which is commonly used when depositing oxides in order to fully oxygenate the deposited films. PLD is applicable to almost any material, particularly compounds that are difficult

Fig. 1. A typical PLD system is shown above. The ablated material is collected on substrates in the form of thin films.

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or impossible to produce in thin-film form by other techniques. Many different types of targets such as powders, sintered pellets, and single crystals can be used in PLD. Because of the extremely high heating rate of the target surface (ca. 108 K/s) by pulsed laser irradiation, the stoichiometry of the target can be retained in the deposited film. The narrow angular distribution of the ablated species limits the area of uniform thin films, but rotating both the target and substrate has been reported to help produce large uniform films.5 Sputter deposition is a PVD method that produces thin films by cathode sputtering. In the cathode sputtering process a metered gas such as argon, oxygen or nitrogen, is introduced into a vacuum chamber and is then ionized by an electric field which generates a self-sustaining plasma. Positively charged ions, such as Ar+ , O+ 2, + or N2 , created by the loss of electrons within the plasma, are then accelerated by a high electric field towards a target. Because the ions contain adequate kinetic energy, atoms or molecules are ablated from the target material. The stream of ablated material generated from the sputtered target passes through the chamber and deposits onto the substrate as a film or coating. Several types of sputtering systems are typically employed for thin film deposition including direct current (DC) sputtering, radio frequency (RF) sputtering and magnetron sputtering.6 In the DC sputtering system, a highvoltage DC power source is used to pass current through the target. It is generally used for sputtering conductive materials. For non-conductive thin films including non-metals and insulators an alternating current (AC) with a typical frequency of 13.56 MHz, or “RF”, is applied. In the magnetron sputtering system, a magnetic field is superimposed parallel to the cathode surface. The electrons in the plasma circle around the magnetic field lines and stay near the target surface, thereby increasing the current density which leads to an increased plasma density at the target surface. This effectively increases the sputtering rate at the target. Combinations of these techniques including DC magnetron and RF magnetron (Fig. 2) are used for the production of thin films. Sol–gel deposition is a wet chemical technique often applied to produce films of metal oxides. It involves the formation of a

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Fig. 2. Schematic of reactive RF magnetron sputtering system.7 Reproduced from Ref. 7, copyright 2007 with permission from Elsevier.

viscous solution of precursors and use of coating technologies, like spray coating, dip coating or spin coating. The sol–gel fabrication of thin films has gained much interest because of its simplicity, low processing temperature, stoichiometry control and ability to produce chemically homogenous films. The sol–gel deposition can be applied on a planar surface or on a 3-D structure. CVD involves flowing a precursor gas or gases into a chamber containing one or more heated substrates to be coated. Chemical reactions occur on and near the hot surfaces, depositing a film composed of individual, non-volatile product molecules on the substrate. This is accompanied by the production of chemical by-products that are exhausted out of the chamber along with unreacted precursor gases. CVD processes do not necessarily require vacuum or high energy inputs, and have been practiced commercially prior to PVD methods. Many variants of CVD processing have been researched and developed including atmospheric pressure (APCVD), low-pressure (LPCVD), plasmaenhanced (PECVD), atomic layer (ALD), and laser-enhanced (LECVD) chemical deposition.8 In order to define the physical boundaries of the deposited thin film components, both mechanical masks and photolithography

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Fig. 3. Photographs of thin film batteries patterned by mechanical masks (left)9 and microfabrication procedures (center and right).11 Reprinted From Ref. 9, Copyright 2000, with permission from Elsevier; reprinted from Ref. 11, © IOP Publishing. Reproduced with permission from IOP Publishing. All rights reserved.

may be employed (Fig. 3). Most of the thin film batteries reported in literature were realized with mechanical masks often made of stainless steel.9 The entire process is carried under a controlled atmosphere so as to ensure chemical stability of the materials, but this method does not allow dimensions below several decades of mm2 of active area and it is difficult to be used for mass production. Microfabrication procedures compatible with standard integrated circuit (IC) technology, such as thin film deposition, photolithography, and reactive etching, have been used to prepare thin film batteries and microbatteries.10,11 These procedures have enabled automated manufacturing and test processes which may make thin film batteries easier and more cost effective to use in high volume designs. Photolithography is the process that transfers a pattern using light or electrons onto a substrate, usually a wafer. The steps involved in the photolithographic process are wafer cleaning, barrier layer formation, photoresist application, soft baking, mask alignment, exposure and development, and hard-baking. In the process a light source is typically used to transfer an image from a patterned mask to a photosensitive layer (photoresist or resist) that has been deposited on a substrate or thin film. This same pattern is later transferred into the substrate or thin film (layer to be etched) using either a positive or negative etch process. In the construction of microsystems, photolithography is used at any point in the process where a pattern needs to be defined on a layer. This occurs several times during the fabrication of a microsystem device as layers build upon layers.12

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Fig. 4. Cross-section of a thin-film battery with a two-dimensional (2D) (left)13 and three-dimensional (3D) structure (right).14 Reprinted from Ref. 13, Copyright 2005, with permission from Elsevier; Reprinted from Ref. 14, Copyright © 2007, Wiley-VCH Verlag Gmbh & Co. KGaA, Weinheim.

3. Components of Thin Film Batteries Schematics illustrating the layout of thin film batteries with twoor three-dimensionality are shown in Fig. 4. Multi-layers are prepared on substrates which could be silicon wafers, alumina plates, metal foils and plastics. The components of a cell include current collector, cathode film, solid-state electrolyte film, anode film and the protective coating. 3.1. Cathodes Layered Crystal Structure LiCoO2 is the most frequently used cathode material in commercial lithium-ion batteries due to its high specific capacity (140 mAh g−1 ), high operating electrode potential (ca. 4 V), long cycle-life, and ease of preparation usually involving deposition followed by a single heat treatment at high temperature (ca. 700◦ C). Deposition methods include sputtering,15−19 PLD,20,21 CVD,22−24 ALD25 and wet chemical routes including electrostatic spray pyrolysis26,27 and sol–gel deposition.28−31 Among these methods, DC and RF magnetron sputtering are the most widely used techniques for LiCoO2 thin-film preparation. Numerous reports on the LiCoO2 system have been published regarding the relationship between structure, electrochemical properties and deposition parameters such as working pressure, Ar/O2 ratio, sputter power, bias voltage, and other variables.15,16,19

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In general, three crystalline phases of LiCoO2 can be found in thin films depending upon deposition conditions and postannealing treatments.21 The high-temperature phase, HT-LiCoO2 , is hexagonal with the α-NaFeO2 structure (space group R-3m). Li and Co ions are fully ordered, occupying octahedral sites in alternating [111] layers within a face-centered cubic (fcc) oxygen sublattice. A partially ordered phase of the same composition, referred as LT-LiCoO2 , has a modified spinel structure similar to that of Li2 Ti2 O4 , and is composed of an fcc oxygen network with alternating cation layers of Li0.25 Co0.75 and Li0.75 Co0.25 in the [111] spinel direction. Another rock-salt LiCoO2 phase exists usually in asprepared thin films deposited at lower temperatures, which has a completely random cation ordering with the fcc oxygen sublattice.32 HT-LiCoO2 is well-known for its layered structure with highly reversible lithium-ion extraction and insertion. Heat treatment is regarded as the most effective method to get HT-LiCoO2 thin films with high crystallinity either during deposition or with a postannealing process15,33 (Fig. 5). Heat treatments using a conventional furnace or rapid thermal annealing process in room air at high temperature greater than 600◦ C has been widely adopted.34,35 However, heat treatment at high temperature is likely to cause film cracks and voids due to differences in the thermal expansion coefficients between the LiCoO2 thin film and the substrate. This can further lead to micro-shorts when the solid-state electrolyte and anode are subsequently deposited. Crack-free LiCoO2 thin films were prepared by applying a two-step treatment with a combination of substrate heating at 300◦ C during sputtering and a rapid thermal annealing process at 650◦ C.36 Thin films prepared at low temperature were also investigated in order to be compatible with integrated silicon-based devices or flexible polymer substrates.17,18,37 LiCoO2 thin films have a strong orientation dependence which plays a large role in their performance especially with regard to rate capability. This is because only 2D diffusion paths are available in layered LiCoO2 . As shown in Fig. 6, the intercalation pathway of the (003) plane is horizontal to the substrate surface, while that of the (110) plane is almost vertical with respect to the substrate surface.38

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Fig. 5. Discharge curves for Li|LiCoO2 cell with LiCoO2 films annealed in O2 atmosphere at 500, 600 and 700◦ C for 2 h. The LiCoO2 films were prepared by RF magnetron sputtering from a LiCoO2 target.15 Reprinted from Ref. 15, Copyright 2004, with permission from Elsevier.

Fig. 6. Lithium-ion diffusion and intercalation pathways in LiCoO2 thin film layers oriented to various lattice planes.34 Reproduced from Ref. 34 with permission from The Electrochemical Society.

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Differences in orientation result in lithium-ion diffusivities that vary by a few orders of magnitude. The (104)-oriented thin film exhibits ˜ Li value than that of the a larger Li+ chemical diffusion coefficient D 39 (003) oriented thin film. The crystalline lattice growth of LiCoO2 thin films is determined by the competition between the surface energy and volume strain energy.34,40 The orientation of LiCoO2 thin films can be controlled by thickness,34,39 deposition method41 and substrate temperature during deposition.38 LiNiO2 thin films42,43 have been considered as an alternative to LiCoO2 , but the serious problems with LiNiO2 are stoichiometry control, structural stability, cation disorder, and poor cycling performance. Other alternative layered cathode materials based on the substitution of metal ions into the LiNiO2 system are LiNi0.5 Mn0.5 O2 ,12,44 LiNi0.8 Co0.2 O2 ,45,46 LiNi1/4 Mn1/2 Co1/3 O47 2 and Li[Li0.2 Mn0.54 Co0.13 Ni0.13 ]O2 .48 These thin films were deposited for thin film batteries with methods similar to those used in LiCoO2 thin films. Spinel Crystal Structure LiMn2 O4 has a spinel structure and belongs to the Fd3m(O7h ) space group with cubic lattice parameter a = 8.239.49 In the spinel structure, half of the octahedral sites (16d) are occupied by the Mn ions forming a 3D framework of edge-sharing MnO6 octahedra; lithium ions occupy tetrahedral interstices (8a), which share common faces with four neighboring empty octahedral sites at the 16c position. One Li can be either removed from LiMn2 O4 at 4.1 V vs Li+ /Li leading to λ-MnO2 or inserted at 3 V leading to Li2 MnO4 (Fig. 7). Both processes exhibit theoretical capacities of 148 mAh g−1 . Thin films based on the spinel LiMn2 O4 cathode have been prepared by various methods such as PLD,50−54 RF sputtering,55,56,62 sol–gel spin coating,57 electrostatic spray deposition58 and CVD.59 In conventional liquid electrolyte lithium-ion cells, it has been shown that stoichiometric LiMn2 O4 bulk material suffers capacity loss during cycling due to structural Jahn–Teller distortion and manganese dissolution in the electrolyte.60 However, excellent cycling performance was observed in LiMn2 O4 thin films prepared

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Fig. 7. Typical discharge curves of a thin film battery at various current densities at 25◦ C and 100◦ C with a LiMn2 O4 cathode prepared by RF sputtering.62 Reproduced from Ref. 62 with permission from The Electrochemical Society.

by sputtering or sol–gel methods.61−63 This is because a thin film of LiMn2 O4 can easily relax the strain generated from volume expansion/contraction and Jahn–Teller distortion during cycling.61 Moreover, transition metal dissolution into the solid electrolyte is expected to be negligible. When a Lix Mn2−y O4 thin film is incorporated in a solid-state thin film lithium battery, it gives a specific capacity of 260–280 mAh g−1 between 4.5–1.5 V with the reduction of Mn from the +4 to +3 oxidation state; thousands of cycles have been achieved between 4.5–2.5 V at 25◦ C with little loss of capacity.62 LiNi0.5 Mn1.5 O4 has a spinel structure similar to that of LiMn2 O4 with Ni and Mn either randomly or orderly occupying the octahedral sites. It shows a high voltage at 4.7 V vs. Li+ /Li corresponding to the Ni2+ /Ni4+ redox couple. Decomposition of the electrolyte is avoided when LiNi0.5 Mn1.5 O4 thin films are employed in a solidstate thin film battery. LiNi0.5 Mn1.5 O4 thin films exhibit a high

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Fig. 8. Typical charge/discharge curves for PLD LiNi0.5 Mn1.5 O4 thin film on a stainless steel substrate cycled between 3 and 5 V with a current of 20 µA/cm2 .64 Reproduced from Ref. 64 with permission from The Electrochemical Society.

volumetric energy density of 308 µWh cm−2 µm−1 which makes it a very attractive cathode material for thin film lithium batteries. LiNi0.5 Mn1.5 O4 thin films have been prepared by PLD,64−66 electrostatic spray pyrolysis67 and sol–gel spin coating.68,69 Olivine Crystal Structure Olivine LiFePO4 has been extensively studied and developed in recent years for the next generation of liquid electrolyte lithium-ion batteries because of its high structural stability, relatively high specific capacity (∼170 mAh g−1 ), long cycle life, and good thermal stability.70,71 However its low ionic and electronic conductivity (as low as 10−9 S cm−1 ) was initially viewed as a limitation to its application in high-rate batteries.72 The now well-known excellent rate performance of LiFePO4 was demonstrated by reducing the active particle size to the nano-scale and coating them with carbon. LiFePO4 thin-film electrodes with a thickness of a few hundred nanometers or several micrometers can be also used for thin film batteries especially for low power applications. LiFePO4 thin films have been prepared by PLD,73,74 and RF magnetron

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sputtering.75,76 In order to increase electronic conductivity, codeposition of LiFePO4 /C, and LiFePO4 /Ag were investigated.77,78 LiCoPO4 , another olivine-structured thin film has been prepared by magnetron sputtering41,79 as a cathode for thin film batteries. It exhibits a charge/discharge plateau of 4.8 V with a theoretical capacity of 167 mAh g−1 . However, its intrinsic low electronic conductivity of around 10−10 to 10−9 S cm−1 and low practical discharge capacity make it a poor cathode for thin film batteries. Amorphous and Crystalline V2 O5 V2 O5 has received much attention as a cathode material for lithiumion batteries throughout the last few decades. It offers relatively high specific capacity (147 mAh g−1 at 2.6–4.0 V, 294 mAh g−1 at 2.0–4.0 V), fast lithiation and good safety80 which has led to research on film growth and applications in thin film batteries. Cystalline V2 O5 has an orthorhombic structure that belongs to the Pmnm space group.81 It is usually described as made up of chains of edge-sharing VO5 square pyramids. These chains are linked together via corner sharing. V2 O5 thin films show two distinct voltage plateaus at 3.4 V and 3.2 V vs. Li+ /Li when cycled in the voltage range of 2.6–4.0 V

Fig. 9. The first charge/discharge curves of as-deposited LiFePO4 films by RF magnetron sputtering at different Pt substrate temperatures: (1) 25, (2) 300, (3) 400 and (4) 500◦ C.76 Reprinted with permission from Ref. 76. Copyright 2009 American Chemical Society.

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Fig. 10. Charge/discharge curves of ∼30 nm thick V2 O5 film deposited by ALD.87 Reprinted with permission from Ref. 87. Copyright 2012 American Chemical Society. Table 1. Comparison of cathode thin films for thin film batteries (volumetric capacity, voltage range and volumetric energy density).

Cathode Type

Theoretical gravimetric capacity (mAh g−1 )

Volumetric capacity (µAh cm−2 µm−1 )a

Voltage range (V)

Energy density µWh cm−2 µm−1

LiCoO2 LiMn2 O4 LiNi0.5 Mn1.5 O4 LiFePO4 V2 O5

137 (0.5 Li+ per f.u.) 148 (1 Li+ per f.u.) 147 170 147 (1 Li+ per f.u.)

68 64 65 61 50

4.2−3.0 4.3−3.5 5.0−3.5 4.0−3.0 4.0−2.6

256 254 308 208 163

a Using the volume of a unit cell, the volumetric capacity can be calculated.

(Fig. 10). This corresponds to the phase transformation sequence of α−ε−δ. In the extended potential window of 1.8–4.0 V V2 O5 has poor cycling stability with rapidly decreasing capacity.82 Crystalline or amorphous V2 O5 thin films can be deposited by DC reactive sputtering,83 RF magnetron reactive sputtering,84 thermal evaporation,85 PLD,86 ALD,87 CVD88 and sol–gel methods.89 Though the volumetric capacity and volumetric energy density of V2 O5 films are low compared with LiCoO2 or LiMn2 O4 (Table 1), one advantage of V2 O5 films as the cathode of thin film lithium batteries

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is that they are generally deposited at room temperature84 which enables the deposition of thin film batteries on flexible polymer substrates. Another limitation for use in thin film batteries is that it is almost exclusively prepared in the unlithiated state, necessitating a lithium or lithium alloy anode in full cell.

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3.2. Electrolytes Electrolytes for thin film batteries, both inorganic and polymer electrolytes, are discussed in greater detail in other chapters of this book, and as such are covered only briefly here. Thin film solid electrolytes are required to have a high ionic conductivity (>10−7 S cm−1 ), a negligible electronic conductivity, and be electrochemical stable in contact with the anode and cathode electrodes. Desirable properties of thin film electrolytes include minimal reactivity with oxygen and moisture, ease of conformal and pin-hole free deposition, and mechanical robustness. Inorganic Electrolytes Glassy, thin-film electrolytes are generally used in thin film batteries because they provide a large, electrochemically active interface. An added benefit to using thin film techniques (sputtering, PLD, etc.) to deposit the electrolyte is that they preferentially deposit the amorphous phase of the electrolyte. Ion-conducting glasses generally consist of network formers which are covalent oxides or sulfides such as SiO2 ,90 P2 O5 ,91 B2 O3 ,92 GeS93 2 etc. and network modifiers, such as Li2 O or Li2 S. The network formers create strongly cross-linked macromolecular chains which facilitates amorphous glass formation when quenched from a liquid or vapor phase. The network modifiers chemically react with the network formers leading to a decrease of the average length of the macromolecular chains.94 It has been reported that incorporation of nitrogen into the oxide network or addition of another network former can enhance the ionic conductivity and electrochemical stability of glassy electrolytes. The most well-known example is Lipon.91 The incorporation of nitrogen into the Li2 O–P2 O5 glassy system increases

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Fig. 11. Illustration of two ways that nitrogen can be incorporated into Li2 O–P2 O5 glassy system.102 Reprinted with permission from Ref. 102. Copyright 2008, American Vacuum Society.

cross-linking between the chains of PO4 tetrahedron due to the substitution of non-bridging oxygen ion in the glass network by doubly (P−N = P) and triply (P−N < P) coordinated nitrogen as shown in Fig. 11. This effectively stabilizes the Lipon film in contact with lithium metal and increases the ionic conductivity to about 3.3× 10−6 S cm−1 .91 Lipon films are typically deposited by RF magnetron sputtering from a Li3 PO4 target in nitrogen plasma.91,95−97 The composition and ionic conductivity vary with the sputter power, the partial nitrogen pressure and substrate temperature.95,97,98 Lipon films deposited by PLD,99 ion beam assisted deposition (IBDA),100 E-beam evaporation101 and plasma-assisted directed vapor deposition (PA-DVD)102 have also been reported. Mixed former effect has been also employed by adding boron or silicon to other network formers showing greatly increased ionic conductivity as well as improved chemical durability. For example, glasses of the Li4 SiO3 – Li3 BO3 system show improved conductivities compared with those of the end members.90,103 Some attempts have been reported of combining the above approaches, viz. the nitrogen incorporation and mixed former effect which has shown an increase in ionic conductivity of 1.24 × 10−5 S cm−1 .90 A number of solid-state electrolytes having perovskite structure such as Li0.35 La0.55 TiO3 (LLTO), NASICON structure such as LiTi2 (PO4 )3 (LTP) and garnet-like structure such as Li7 La2 Zr2 O12 (LLZ) have been reported with high bulk ionic conductivity in

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the range of ∼10−3 to 10−4 S cm−1 . However, the preparation of these bulk electrolytes usually involves high temperatures (often >1000◦ C) which is prone to failure of thin film lithium batteries resulting from the development of stress and interlayer diffusion. Amorphous thin film electrolytes of LLTO, LTP and LLZ have been investigated for thin film lithium batteries because of their denser microstructure, negligible grain boundary effect, and improved chemical stability.26,104−107 The amorphous electrolytes deposited by E-beam evaporation, sol–gel, RF sputtering or PLD show significantly lower ionic conductivity compared to the bulk materials. As shown in Table 2, Li2.9 La0.68 ZrO8 thin films prepared by RF sputtering have an ionic conductivity of 4.0 × 10−7 S cm−1 ,107 and Li0.5 La0.5 TiO3 thin film deposited by PLD shows a conductivity of 2×10−5 S cm−1 .104 Research efforts towards preparing thin films of these solid electrolytes with properties commensurate with the bulk properties continues and serves as an opportunity for breakthrough development. Sulfide-based solid electrolytes exhibit high ionic conductivity of more than 10−3 S cm−1 at 25◦ C and good electrochemical stability.108,109 The ionic conductivity of amorphous 80Li2 S–20P2 S5 thin films prepared by PLD is 7.9 × 10−5 S cm−1 .29 High-quality amorphous Li2 S–GeS2 thin films with an ionic conductivity as high as 1.7 × 10−3 S cm−1 , deposited by RF sputtering, did not show any cracks and pits on the surface and the ionic conductivities of the thin films are 2–3 orders of magnitude higher than the values reported for Lipon thin films93 (Fig. 12). The sulfide-based solid electrolytes are very sensitive to moisture, which causes structural changes and generates H2 S gas.110 Thin film batteries using sulfidebased electrolytes require handling in an inert gas atmosphere with robust encapsulations. Polymer electrolytes Dry polymer electrolytes that do not contain any flammable organic liquids unlike gel polymer electrolytes show great technological potential for use in thin/flexible all solid-state thin film batteries. A solid-state thin film battery was first reported in 1989 using a

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Table 2. The chemical composition, conductivities at 25◦ C and activation energies of some Li+ thin-film, inorganic electrolytes and dry polymer electrolytes used in thin film batteries. Electrolyte film

Film composition

Li2 O–P2 O5

Li2.9 PO3.3 N0.46 (Lipon) Li2.9 Si0.45 P1.0 O1.6 N1.3 Li3.09 BO2.53 N0.52 N/A

Li2 O–SiO2 – P2 O5 Li2 O–B2 O3 Li2 O– V2 O5 -SiO2 Li2 O– B2 O3 –P2 O5

40Li2 O– 30B2 O3 – 30P2 O5 Li−La−Zr−O Li2.9 La0.68 ZrO8 Li–La–Ti–O Li0.5 La0.5 TiO3 Li−Al−Ti− Li1.3Al0.3 P−O Ti1.7 (PO4 )3 Li2 S–P2 S5 80Li2 S·20P2 S5 Li2 S–GeS2 Li6 GeS5 tris N/A (2-methoxyethoxy) vinylsilane -LiClO4 LiClO4 /poly PEO/LiClO4 (ethylene =18:1 oxide)(PEO) poly(ethylene N/A oxide) (PEO) and LiCF3 SO3 PEALi:O = 1:20 PPGDA− and LiTFSI PEA:PPGDA = 2:1 PEO based [Li]/[EO] = BAB block 0.05 copolymer

σLi+ at 25◦ C (S cm−1 )

Ea (eV)

Ref.

RF sputtering

3.3 × 10−6

0.54

91

RF sputtering

1.24 × 10−5

0.48

90

RF sputtering

2.3 × 10−6

0.49

92

RF sputtering

1.0 × 10−6

N/A

110

RF sputtering

1.22 × 10−6

0.49

102

RF sputtering PLD RF sputtering

4.0 × 10−7 2 × 10−5 2.46 × 10−5

0.70 N/A 0.32

107 104 26

PLD RF sputtering plasma polymerization

7.9 × 10−5 1.22 × 10−3 10−5 − 10−6

0.45 N/A N/A

29 93 113

Spin coating

1 × 10−4

N/A

114

Evaporation

3 × 10−4

N/A

115

casting

3.5 × 10−6

N/A

116

casting

2 × 10−4

N/A

117

Deposition method

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Fig. 12. A comparison of Arrhenius plots of ionic conductivities between Li2 S– GeS2 thin films and Lipon thin films.93 Reproduced from Ref. 93 with permission from The Electrochemical Society.

polymer electrolyte film prepared by plasma polymerization from tris(2-methoxyethoxy) vinylsilane and LiClO4 . This dry polymer electrolyte film demonstrated a conductivity between 10−5 and 10−6 S cm−1 at room temperature.113 A dry polymer with a complex of LiClO4 /poly(ethylene oxide)(PEO) was prepared by spin coating and exhibited a high ionic conductivity.114 Various other complex dry polymer electrolytes have been developed for thin film lithium batteries.115−118 Polymer electrolyte films can be produced using various methods, including spin coating or casting from a polymer solution,114,117 evaporation methods,115 and in-situ plasma polymerization techniques.113 3.3. Anodes Most thin film batteries report using lithium metal as the anode33,79,119 because it provides the lowest potential among all the anode materials and a high theoretical specific capacity of 3869 mAh g−1 . The lithium thin film is usually deposited by thermal evaporation of lithium metal under vacuum,33 which is complicated by the fact that it is highly moisture sensitive. The lithium thin film

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can also be in-situ electroplated at the anode current collector on the initial charge in a “lithium free” thin film battery, provided the cathode is prepared in the discharged (lithiated) state.120,121 High quality encapsulants are of course required to avoid the reaction of lithium with moisture when lithium metal is used as an anode. Other alternative anodes to lithium metal have been reported. Graphitized carbonaceous thin films prepared by plasma-assisted CVD122 or repeated substrate induced coagulation123 were explored as the anode for thin film batteries. Li4 Ti5 O12 with a spinel structure (Li[Li1/3 Ti5/3 ]O4 ) is another anode that has been employed. This anode undergoes very minor volumetric changes ( 0.75 in Lix CoO2 . This is when the current in the reference cell starts to move between electrode bases (see Fig. 17), and can be seen as a voltage gain for the optimized cell during the discharge process. For example, the optimized cell with a current density of 4 A/m2 is operating at the same voltage as the reference cell with 2 A/m2 if x > 0.85. Thus, twice as high current can be achieved in the optimized cell during this part of the discharge cycle. Since the optimization of the geometry is only affecting the second half of the discharge cycle, it can be questioned if it is necessary to conduct any optimization procedure. However, the 3D-MBs are considered for systems requiring high current densities, thus rendering these effects very important. When the devices operate with high current pulses, the active material surface is depleted very rapidly, which in turn leads to a situation where the battery must operate under conditions where its overall state-of-charge (SOC) is high, although the local SOC at the electrode–electrolyte interface is low. Under such conditions, the optimized geometry display significant advantages since the energy dissipated during charge transport is considerably smaller than for the reference cell. However, it remains to be seen if it is possible fabricate these kinds of cell with unevenly distributed electrode material. Contributions from several research groups indicate that when producing electrode coatings, it is not only possible, but maybe even likely, to achieve these kinds of depositions rather than completely uniform coatings.110 For example, Notten et al. fabricated an electrode with slightly thicker material coating at the tips of the plates than at the bottoms of the trenches.19 Lethien et al.111 synthesized an interdigitated 3D-MB half-cell of silicon nanopillars coated with LiFePO4 and LiPON layers, so that the tips of the pillars had a material coating distribution similar to what was achieved in the simulations presented here. Lafont et al. used electrostatic spray pyrolysis to prepare LiNi0.5 Mn1.5 O4 coated trenches,110 also resulting in a seemingly non-uniform electrode coating. Hopefully, theoretical work explaining the ionic transport in 3D-MBs with non-uniformly coated electrodes can simplify future experimental

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work, and accelerate the research and development in this area by helping to overcome the problems associated with the non-optimal 3D-battery geometries.

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5. Conclusion and Future Outlook In this chapter, computer simulations of the 3D-MB architectures have been discussed. Primarily the 3D-trench and 3D-interdigitated geometries have been simulated, and the ionic transport properties during battery operation investigated. It has then been demonstrated that the major differences when utilizing a 3D-geometry as compared to a conventional 2D-design originates in the dimensionality of the ionic transport. In a conventional battery, the ionic transport is 1D in nature since the ions move straight between the electrodes. This means that the cell can generally be described by 1D geometrical and mathematical models. However, 3D electrodes need detailed 3D geometrical models, leading to longer computational times and more complex mathematical descriptions. As a rule of thumb for FEM simulations, the demand for computer memory increases by ∼n2 , where n is the number of nodes. Therefore, method development based on a fundamental understanding of the electrochemistry in the battery systems is likely to play an important role to significantly decrease the computational time. The early simulations of the 3D-trench geometry demonstrated the impact of the electrode conductivity on the ionic transport and the current density distribution in the cell. A constant concentration gradient and a uniform current density in the electrolyte, which are common attributes of thin-film batteries, proved to be impossible to achieve when using electrodes of standard Li-ion battery materials such as LiCoO2 and LiC6 . These simulations demonstrated a highly non-uniform current density distribution and material utilization in the 3D-trench geometry, seriously affecting its discharge dynamics and reducing the estimated cell performance. However, when the conductivity of the positive electrode was increased at least to ca. 25% of the negative electrode conductivity, almost all effects of the non-uniform current density distribution disappeared.

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Furthermore, an almost uniform electrochemical activity can be achieved if 3D metal current collectors are coated with the electrode materials. The electrode tips then remain slightly more active areas, with the tip of the negative electrode being the most active due to the high electrical conductivity of graphite. However, studies of the discharge dynamics have demonstrated that even electrodes with equal conductivities caused non-uniform material utilization. The electrode geometry itself influences the discharging process, since the electrode tips are utilized faster than the bases due to local surface area differences. These results have shown the basic tools for investigating ionic transport properties in the 3D-MB. They also identify the basic tools for further improvements of the 3D-MB: manipulations with the material parameters and/or the shape of the electrodes. One of the key features of the 3D-MB is the surface area gain. The area gain is much larger in the 3D-interdigitated than in the 3D-trench geometry, since the pillar sides facing the neighbors contribute to the surface area gain as well. Therefore, the interdigitated geometry is more favorable to use and higher battery currents can be reached, although this increases the complexity of the geometry due to different possible electrode pillar arrangements. To find the electrode configuration with maximum possible performance, i.e. the cell with uniform electrochemical activity over the electrode surface area, a few mathematical optimization strategies have been employed. The topology optimization of the 3D-MB conducted by the level-set method can provide a useful tool for future studies. Indeed, the topology optimization suggested a geometry which demonstrated uniform electrode material utilization and an almost stationary current density distribution. It is in this context interesting to note that polymer electrolytes seem to display some significant advantages as compared to liquid electrolytes. While a higher conductivity makes it possible to use higher currents, the polymer electrolyte enables constructing the battery with a more uniform current density distribution. The simulations carried out of 3D-MBs so far have merely scratched the surface in the understanding of ionic transport in these

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systems. Experimentally, there are many more possible geometries investigated than those considered in the published studies. Future studies could well continue with simulations of other 3D-MB architectures, for example the 3D-concentric or the aperiodic geometries. More details should also be implemented to the mathematical models. For example, the resistivity of the SEI film layer has not yet been implemented in any of the published works. Improvements may also be achieved by incorporating concentration dependent diffusion coefficients into the models. Furthermore, as the number of reported prototype cells increases, simulations estimating the performance of experimental cells can be conducted and compared to realistic data, which has perhaps been the major drawback of the studies done so far. Many of these prototypes have demonstrated problems — for example the interdigitated cell by Min et al.29 which worked only for a couple of cycles and thereafter short-circuited, or the aperiodic geometry,112 which demonstrated similar problems. Since the basic properties of the ionic transport in the 3D-microsystems have been identified in the early studies described here, the bottlenecks for the performance of the experimental geometries can be identified and possible solutions can be suggested. Furthermore, when the optimal electrode material distribution in these geometries is identified, possible problematic locations in the cells can subsequently be identified easily. The main focus of the future 3D-MB studies should therefore be connecting theoretical and experimental work. Abbreviations and Symbols MEMS 3D-MB LHS RHS FEM PDE MD SEI

Microelectromechanical systems 3D-microbattery Left-Hand Side Right-Hand Side Finite Element Method Partial Differential Equation Molecular Dynamics Solid Electrolyte Interface

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a c D F H, h, d, dc i0 J k r R T V Voc z j 0 t+  n

Specific area of an electrode (m−1 ) Concentration (mol/m3) Diffusion coefficient (m2 /s) Faraday constant (96 485 C/mol) Geometrical parameters of the cell Exchange current density (A/m2 ) Ionic flux density (mol/(m2 s)) Rate constant (A/(m2 (mol/m3 )3/2 )) Normalized resistance of the cell ( m2 ) Universal gas constant (8.314 J/(mol K)) Absolute Temperature (K) Volume of the electrolyte (m3 ) Open circuit voltage (V) Charge number Current density (A/m2 ) Transference number of Li+ ions in the electrolyte Unit normal vector

Greek letters α ε η σ φ  τ

Transfer coefficient Porosity of the electrodes Surface overpotential in the battery (V) Conductivity (S/m) Electrical potential (V) Geometrical region of the problem (m) Pseudo time, representing the optimization step

Subscripts Li PF6 0 a c i

Li+ ions PF− 6 ions Corresponding to constant initial value or boundary condition Anodic Cathodic Defined when used

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j l s

Defined when used Liquid phase (electrolyte) Solid phase (electrode material)

Superscripts p n ∗

Positive electrode Negative electrode Electrodes

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83. C. Zhu, X. Li, L. Song and L. Xiang, J. Power Sources 223 (2013) 155. 84. C. Hellwig, S. Sörgel and W. G. Bessler, ECS Trans. 35 (2011) 215. 85. G. -H. Kim, K. Smith, K. -J. Lee, S. Santhanagopalan and A. Pesaran, J. Electrochem. Soc. 158 (2011) A955. 86. N. Baba, H. Yoshida, M. Nagaoka, C. Okuda, S. Kawauchi, Meet. Abstr. MA2012-02 (2012) 477. 87. T. G. Zavalis, M. Behm and G. Lindbergh, J. Electrochem. Soc. 159 (2012) A848. 88. J. -L. Zang and Y. -P. Zhao, Int. J. Eng. Sci. 61 (2012) 156. 89. R. T. Purkayastha and R. M. McMeeking, Comput. Mech. 50 (2012) 209. 90. L. Greve and C. Fehrenbach, J. Power Sources 214 (2012) 377. 91. S. Golmon, K. Maute and M. L. Dunn, Comput. Struct. 87 (2009) 1567. 92. G. Turon Teixidor, B. Y. Park, P. P. Mukherjee, Q. Kang and M. J. Madou, Electrochimica Acta 54 (2009) 5928. 93. V. Zadin, D. Brandell, H. Kasemägi, A. Aabloo and J. O. Thomas, Solid State Ion. 192 (2011) 279. 94. V. Zadin, H. Kasemägi, A. Aabloo and D. Brandell, J. Power Sources 195 (2010) 6218. 95. V. Zadin and D. Brandell, Electrochimica Acta 57 (2011) 237. 96. V. Zadin, D. Brandell, H. Kasemägi, J. Lellep and A. Aabloo, J. Power Sources 244 (2013) 417. 97. T. F. Coleman and Y. Li, Math. Program. 67 (1994) 189. 98. T. F. Coleman and Y. Li, SIAM J. Optim. 6 (1996) 418. 99. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, (Addison-Wesley, 1989). 100. S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Science 220 (1983) 671. 101. M. P. Bendsøe and O. Sigmund, Topology Optimization: Theory, Methods, and Applications, (Springer, 2003). 102. S. J. Osher and F. Santosa, J. Comput. Phys. 171 (2001) 272. 103. M. Y. Wang, X. Wang and D. Guo, Comput. Methods Appl. Mech. Eng. 192 (2003) 227. 104. Z. Liu, J. G. Korvink and R. Huang, Struct. Multidiscip. Optim. 29 (2005) 407. 105. C. Zhuang, Z. Xiong and H. Ding, Comput. Methods Appl. Mech. Eng. 196 (2007) 1074. 106. Z. Luo, L. Tong and H. Ma, J. Comput. Phys. 228 (2009) 3173. 107. E. Olsson and G. Kreiss, J. Comput. Phys. 210 (2005) 225. 108. E. Olsson, G. Kreiss and S. Zahedi, J. Comput. Phys. 225 (2007) 785. 109. V. Zadin, H. Kasemägi, A. Aabloo and D. Brandell, ECS Meet. Abstr. 1003 (2010) 684.

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Electrochemical Simulations of 3D-Battery Architectures

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110. U. Lafont, A. Anastasopol, E. Garcia-Tamayo and E. Kelder, Thin Solid Films 520 (2012) 3464. 111. C. Lethien, M. Zegaoui, P. Roussel, P. Tilmant, N. Rolland and P. A. Rolland, Microelectron. Eng. 88 (2011) 3172. 112. P. Johns, M. J. Lacey, M. R. Roberts, G. Enany and J. R. Owen, 18th Int. Conf. Solid State Ion. (2011) 302.

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Chapter 22

Silver Ion Conducting Electrolytes and Silver Solid-State Batteries Kevin Kirshenbaum∗ , Roberta A. DiLeo†,‡ , Kenneth J. Takeuchi†,‡ , Amy C. Marschilok†,‡ and Esther S. Takeuchi∗,†,‡ ∗ Energy

Sciences Directorate Brookhaven National Laboratory Upton, NY 11973, USA † Department

of Materials Science and Engineering Stony Brook University Stony Brook, NY 11794, USA ‡ Department

of Chemistry Stony Brook University Stony Brook, NY 11794, USA

Silver ion conducting electrolytes are being explored as a material to be used in solid state batteries. This chapter provides a review of the advances in silver ion conducting solid electrolytes over the last 20 years. We discuss the advances that have been made in the synthesis of new electrolyte materials and provide conductivity values for new electrolytes reported. We then turn to a summary of the models of the origin and enhancement of silver ion conductivity in solid electrolytes with focus on those that have been proposed more recently. Finally, we review the progress of solid state batteries and include values for the reported energy density and voltage of the cells.

1. Introduction The goal of this chapter is to discuss the improvements in silver ion conducting solid state electrolytes and silver solid state batteries

779

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Material

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0.8 AgI + 0.2 Al2 O3 0.8 AgI + 0.2 Al2 O3 , compressed at 550 Mpa AgI (bulk, beta phase) 0.7 AgI + 0.3 Al2 O3 (mesoporous) AgBr 0.7 AgBr + 0.3 Al2 O3 (mesoporous) 0.8 AgI + 0.2 Al2 O3 (high pressure synthesis, before heating) 0.8 AgI + 0.2 Al2 O3 (high pressure synthesis, after heating) 0.8 AgI + 0.2 SnO2 0.4 AgI + 0.4 Ga2 S3 +0.2 GeS2 0.5 AgI + 0.25Ag2 S + 0.25 GeS2 0.6 AgI + 0.4 AgPO3

Ionic Conductivity at 25◦ C (S/cm)

Activation Energy (eV)

3.0 × 10−5 1.0 × 10−4

Refs. 13 13

6.0 × 10−7 3.1 × 10−3 3.3 × 10−7 2.5 × 10−4 ∼10−1

0.42 0.23 0.34 0.28 0.26

37 37 37 37 101

∼10−3

0.40

101

2.0 × 10−4 6.34 × 10−6 2.0 × 10−2 2.0 × 10−2

0.383 0.17

102 103 104 34, 105, 106

that have occurred over the last 20 years. Thematically, the silver ion conducting materials are organized by their crystalline or amorphous nature. First, an overview of electrolyte development is provided, followed by a brief discussion of relevant theories describing ion mobility and a review of the current state of the art in silver solid-state batteries (Table 9). Following the text are tables organized by material composition providing ionic conductivity and activation energy for many silver ion conductors (Tables 1–8). The authors have made an effort to include all silver ion conductors reported in the literature since 1993. For ionic conductivities of materials reported before this time, see Refs. 1 and 2. Also included in this chapter is a table identifying the components (anode, cathode, electrolyte), use condition (current drain) and output parameters (open circuit voltage, energy density, capacity) of reported silver solid-state batteries.

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Table 2. Ionic conductivities and activation energies of AgI with Ag2 O and other additives.

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Material 0.3 AgI + 0.4 Ag2 O + 0.2 P2 O5 + 0.1 Fe2 O3 0.6 AgI + 0.27 Ag2 O + 0.13 (B2 O3 + V2 O5 ) 0.6 AgI + 0.27 Ag2 O + 0.13 (B2 O3 + MoO3 ) 0.6 AgI + 0.4 (0.67 Ag2 O + 0.33 B2 O3 ) 0.67 AgI + 0.33 (0.67 Ag2 O + 0.33 V2 O5 ) 0.5 AgI + 0.25 Ag2 O + 0.25 CrO3 0.64 AgI + 0.16 Ag2 O + 0.21 MoO3 0.64 AgI + 0.16 Ag2 O + 0.21 (0.1 ZnO + 0.9 MoO3 ) 0.5 AgI + 0.33 Ag2 O + 0.17 (0.5 TeO2 + 0.5As2 O5 ) 0.6 AgI + 0.27 Ag2 O + 0.13 (0.7 TeO2 + 0.3 P2 O5 ) 0.6 AgI + 0.27 Ag2 O + 0.13 (0.6 TeO2 + 0.4 V 2 O5 ) 0.67 AgI + 0.23 Ag2 O + 0.1 (0.3 SeO2 + 0.7 P2 O5 ) 0.6 AgI + 0.27 Ag2 O + 0.13 (0.5 SeO2 + 0.5 As2 O5 ) 0.67 AgI + 0.23 Ag2 O + 0.1 (0.8 SeO2 + 0.2 V 2 O5 ) 0.6 AgI + 0.27 Ag2 O + 0.13 (0.4 SeO2 + 0.6 MoO3 ) 0.6 AgI + 0.2 Ag2 O + 0.16 MoO3 + 0.04 V 2 O5 0.6 AgI + 0.24 Ag2 O + 0.16 (0.1 MoO3 + 0.9 V 2 O5 ) 0.6 AgI + 0.26 Ag2 O + 0.15 (0.6 MoO3 + 0.4 As2 O5 ) 0.20 Ag2 S + 0.8 (0.4 Ag2 O + 0.6 P2 O5 ) 0.15 Ag2 S + 0.85 (0.3 Ag2 O + 0.7MoO3 )

Ionic Conductivity at 25◦ C (S/cm)

Activation Energy (eV)

∼2 × 10−3 1.76 × 10−3 1.34 × 10−3 6.73 × 10−4 9.0 × 10−3 ∼1 × 10−2 2.0 × 10−2 3.2 × 10−2

0.31 0.35 0.31 0.21 0.27

1.12 × 10−2

0.16

111

1.59 × 10−2

0.14

111

1.72 × 10−2

0.12

111

2.93 × 10−2

Refs. 107 89 89 108 109 88 110 110

83

1.65 × 10−2

0.23

112

2.63 × 10−2

0.22

81

3.12 × 10−2

85

2.3 × 10−3

113

1.9 × 10−2

0.33

87

1.65 × 10−2

0.35

87

∼5 × 10−6 1.02 × 10−6

∼0.52 0.55

114 33

2. Electrolyte Development The search for new solid silver ion conducting electrolytes has led to the discovery of many different types of ionic conductors. In

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Table 3. Ionic conductivities and activation energies of silver conducting electrolytes with CuI.

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Material 0.3 Cu0.75Ag0.25 I + 0.35 Ag2 O + 0.35 MoO3 0.4 Cu0.95Ag0.05 I + 0.45 Ag2 O + 0.15 B2 O3 0.4 Cu0.75Ag0.25 I + 0.3 Ag2 O + 0.3 SeO2 0.4 Cu0.75Ag0.25 I + 0.4 Ag2 O + 0.2 V2 O5 0.35 Cu0.95Ag0.05 I + 0.33 Ag2 O + 0.33 CrO3 0.3 Cu0.75Ag0.25 I + 0.47 Ag2 O + 0.23 P2 O5 0.3 CuI + 0.47 Ag2 O + 0.23 P2 O5 0.45 CuI + 0.55 (2 Ag2 O + 0.7 V2 O5+ 0.3 B 2 O3 ) 0.35 CuI + 0.65 Ag2 CrO4 0.50 CuI + 0.50 Ag3 PO4 0.55 CuI + 0.45 Ag4 P2 O7

Ionic Conductivity at 25◦ C (S/cm) 1.7 × 10−3 2.1 × 10−3 1.4 × 10−3 1.3 × 10−3 1.1 × 10−3 1.15 × 10−4 1.33 × 10−2 3.56 × 10−3 2.83 × 10−3 10−4 –10−3 10−4 –10−3

Activation Energy (eV)

147◦ C).4 A possible rationale for the high ionic conductivity associated with the α-AgI phase is the relatively large number of vacant holes in equivalent-energy

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783

Ionic conductivities and activation energies of AgI:AgCl-based elec-

Material

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0.75 AgI + 0.25 AgCl 0.8 (0.75 AgI + 0.25 AgCl) + 0.2 Fe2 O3 0.7 (0.75 AgI + 0.25 AgCl) + 0.3 Al2 O3 0.7 (0.75 AgI + 0.25 AgCl) + 0.3 (0.83 Ag2 O + 0.17 B2 O3 ) 0.85 (0.75 AgI + 0.25 AgCl) + 0.15 CeO2 0.8 (0.75 AgI + 0.25 AgCl) + 0.2 (Ag2 O + MoO3 ) 0.7 (0.75 AgI + 0.25 AgCl) + 0.3 (Ag2 O + WO3 ) 0.7 (0.75 AgI + 0.25 AgCl) + 0.3 (Ag2 O + B 2 O3 ) 0.75 (0.75 AgI + 0.25 AgCl) + 0.25 (Ag2 O + CrO3 ) 0.7 (0.75 AgI + 0.25 AgCl) + 0.3 (Ag2 O + B2 O3 + WO3 ) 0.8 (0.75 AgI + 0.25 AgCl) + 0.2 SnO2 0.8 (0.75 AgI + 0.25 AgCl) + 0.20 (Ag2 O + V 2 O5 ) 0.7 (0.75 AgI + 0.25 AgCl) + 0.3 KI

Ionic Conductivity at 25◦ C (S/cm)

Activation Energy (eV)

3.1 × 10−4 1.5 × 10−3 9.2 × 10−4 2.23 × 10−2

0.234 0.12 0.074

Refs. 102, 120 121 95 122

1.2 × 10−3 6.0 × 10−3

123 124

4.0 × 10−3

125

4.4 × 10−3

0.225

2.0 × 10−3

126 127

2.76 × 10−2

0.04

128

8.4 × 10−4 9.0 × 10−3

0.147

102 129

5.9 × 10−3

130

positions for Ag ions to occupy.5 Because of the high ratio of structurally and energetically equivalent available positions to the number of Ag ions, the movement of Ag ions through the crystal in the presence of an electric field is greatly facilitated. Because of this highly desired increase in Ag ion conductivity, many researchers have attempted to stabilize the alpha phase at ambient temperature or otherwise alter the composition AgI to increase the ion conductivity. In this section, several strategies to increase the ion conductivity in AgI-based materials will be discussed, including: i. Creating nanostructures of AgI without changing its chemical composition.

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Table 5. Ionic conductivities and activation energies of silver conducting electrolytes containing other Halides. Ionic Conductivity at 25◦ C (S/cm)

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Material 0.45 AgCl + 0.05 Ag2 O + 0.2 MoO3 + 0.3 P2 O5 0.2 CdI2 + 0.8 (Ag2 O + B2 O3 ) 0.2 CdI2 + 0.8 (1.75 Ag2 O + 0.7 V2 O5 + 0.3 B 2 O3 ) 0.25 PbI2 + 0.75 (Ag2 O + WO3 ) Ag2 O + P2 O5 + (20%) ZnI2 Ag2 O + P2 O5 + (20%) CdI2 Ag2 O + P2 O5 + (20%) CdCl2 Ag2 O + P2 O5 + (20%) CdBr2 Ag2 O + P2 O5 Ag2 O + P2 O5 + (15%) LiCl Ag2 O + P2 O5 + (15%) NaCl Ag2 O + P2 O5 + (5%) MgCl2 Ag2 O + P2 O5 + (5%) PbCl2 Ag2 O + P2 O5 + (5%) CuCl2 0.4 SbI3 + 0.6 Ag2 WO4 0.4 SbI3 + 0.6 Ag2 SO4

Activation Energy (eV)

2.5 × 10−3 3.0 × 10−2 5.25 × 10−4

0.3

131

0.288

30 132

7.4 × 10−3 6.22 × 10−4 1.25 × 10−4 4.64 × 10−5 1.17 × 10−4 8.51 × 10−7 8.91 × 10−5 6.45 × 10−5 8.12 × 10−6 7.41 × 10−6 3.80 × 10−6 5.7 × 10−2 2.1 × 10−3

133 134 134 134 134 92 92 92 92 92 92 135 136

Table 6. Ionic conductivities and activation energies of silver conducting electrolytes based on RbAg4 I5 and similar materials.

Material RbAg4 I5 RbAg4 I5 nanowires (K3 Rb)0.25Ag4 I5 KAg4 I5 KAg4 I5 (AgI)3.9 (CuI)0.1 (KI) (AgI)3.2 (CdI2)0.4 (KI)

Ionic Conductivity at 25◦ C (S/cm) ∼0.2 0.117 ∼0.2 ∼0.2 1.12 × 10−2 2 × 10−2 (at 1 kHz) 1.5 × 10−1 (at 1 kHz)

Refs.

Activation Energy (eV)

Refs.

0.045 0.171 0.062

52 137 52 52 130, 138 138 138

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Table 7. Ionic conductivities and activation energies of other silver ion conductors.

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Material Ag3 SnI5 Ag4 PbI6 Ag2 HgI4 Ag13 I4 (AsO4 )3 Ag3 ITeO4 Ag4 I2 SeO4 Ag9 I3 (SeO4 )2 (IO3 )2 Ag7 I4 PO4 Ag19 I15 P2 O7 Ag8 I4 V2 O7 Ag5 IP2 O7 Ag10 Te4 Br3

Ionic Conductivity at 25◦ C (S/cm) 1.0 × 10−4 ∼2 × 10−5 1 × 10−7 6.4 × 10−6 7.4 × 10−5 1.6 × 10−3 7.1 × 10−5 1.9 × 10−2 9.0 × 10−2 8.6 × 10−4 3.0 × 10−6 1.4 × 10−2

Activation Energy (eV)

0.41 0.27 0.22 0.45

0.24 0.28 0.37

Refs. 139 139 139 140 141 141 142 143 143 55 23 144

ii. Inclusion of additional inert phases. iii. Partial or complete anion or cation substitution (ex: AgBr and AgCl, and (Ag,Cu)I). iv. New materials that form as byproducts from one of the above attempts, for example, Ag8 I4 V2 O7 which forms from a combination of AgI, Ag2 O and V2 O5 . v. Exploring crystalline ionic conductors such as RbAg4 I5 and related compounds. After the discovery of the ionic conductor AgI, a large research effort was put forward to modify and improve on the Ag ion conductivity, ionic transfer number, and the stability of the electrolyte. Regarding Ag ion conductivity, each of the above strategies has met with some success; for strategies i–iv, Ag ion conductivities of bulk AgI were increased by several orders of magnitude. The largest effect was observed with strategy v; the Ag ion conductivity increased to approx. 0.3 S/cm in RbAg4 I5 and is comparably high in other crystalline ionic condcutors that remain in the alpha phase.

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Material

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9in x 6in

0.98 (0.9 PEO + 0.1 AgNO3) + 0.02 PVP 0.9 PEO + 0.1 AgNO3 0.8 PEO + 0.2 AgNO3 0.95 (0.9 PEO + 0.1 AgNO3 )+ 0.05 SiO2 PEO50AgCF3 SO3 + 5% MgO PEO with AgSCN PEO-AgSCN with (20 wt%) SiO2 PEO-AgSCN with (10 wt%) Fe2 O3 PEO-AgSCN with (10 wt%) Al2 O3 PEO with (15%) Ag2 SO4 AgClO4 in POEM-g-PDMS AgCF3 SO3 in POEM-g-PDMS 20% AgNO3 in polyvinyl alcohol 6% AgCF3 SO3 in PPG PPG4–AgCF3 SO3 + 5% Al2 O3 Pure Chitosan Chitosan with AgCF3 SO3 0.25[(PVP)Me]I + 0.75 AgI 0.25[(PVP)H]I + 0.75 AgI 0.25[(PVP)Bu]I + 0.75 AgI

Ionic Conductivity at 25◦ C (S/cm)

Refs.

8.0 × 10−6 4.0 × 10−6 9.2 × 10−3 8.8 × 10−6 2.0 × 10−6 1.3 × 10−6 3.0 × 10−5 1.1 × 10−5 8.8 × 10−4 7.0 × 10−4 ∼3 × 10−5 ∼4 × 10−6 ∼7 × 10−7 ∼1 × 10−5 6.2 × 10−4 1.73 × 10−10 4.25 × 10−8 6.0 × 10−3 2.0 × 10−4 2.0 × 10−4

46 145 146 145 43 47, 147 47 47 47 77 148 148 149 150 151 152 152 153 153 153

AgI nanostructures The high Ag ion conductivity of alpha-AgI has been associated with an increased Ag ion disorder 7 and a decrease in migration pathway barriers.8–10 In an effort to achieve this conduction increase at room temperature, various nanostructures of AgI have been produced, the goal of which is to either stabilize alpha-AgI or otherwise provide conduction pathways. Several reports by a group at the Max Planck Institute in Stuttgart have presented conductivity data for nanoplates, nanotetrahedra, and nanorods with room temperature conductivities on the order of 10−3 , 10−5 , and 10−7 , respectively.11, 12 They attribute this increase in conductivity to an increase in the cation lattice disorder, allowing for better ion conduction through

Ag + SE

Ag + SE

Iodide:graphite: SE :TAAI‡ Iodide:graphite: SE:TAAI Iodide:graphite: SE TAAI Iodine:graphite

Ag + SE

Iodine:graphite:SE

Ag + SE

Iodine:graphite:SE + TAAI iodide:graphite: SE:TAAI Iodide:carbon: SE:TMAIa Iodine:graphite: SE + TAAI

Ag + SE Ag + SE

Ag + SE Ag + SE Ag + SE

Silver selenovanadate (AgI–Ag2 O–(SeO2 +V2 O5 ) Silver selenovanadate (AgI–Ag2 O–(SeO2 +V2 O5 ) Silver selenoarsanate (AgI–Ag2 O–(SeO2 +As2 O5 ) AgI–Ag2 O–(SeO2 +P2 O5 )

Refs.

0.687

1.18-2.62

2.67–5.89

81

0.652–0.676

2.3–4.29

0.626–0.663

0.7–1.7

1.69-3.85

82

0.636–0.672

3.14–4.12

7.0–9.2

83

0.684–0.686

0.65–1.16

1.25–2.55

84

0.684–0.686

0.81–1.31

1.76–2.86

84

0.658–0.667

1.56–1.60

3.50–3.65

84

0.654–0.652

4.24–5.22

7.54–9.27

85

2.5–11

86

2–4

87

60AgI–26.67Ag2 O– 13.33(0.3SeO2 +0.7P2 O5 ) 60AgI–26.67Ag2 O– 13.33(0.3SeO2 +0.7P2 O5 ) 60AgI–26.67Ag2 O– 13.33(0.3SeO2 +0.7P2 O5 ) 60% AgI+26.67% Ag2 O+13.33% (0.4SeO2 +0.6MoO3 ) AgI–Ag2 O–B2 O3 -MoO3

0.640–0.686

AgI–Ag2 O–(MoO3 + V2 O5 )

0.673–0.675

0.9–1.8

81

page 787

787

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Capacity (mAh)

9in x 6in

Ag + SE

OCV† (V)

Energy Density (Wh/kg)

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Cathode

Solid Electrolyte (SE)∗

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Composition, use, and performance parameters of silver solid state batteries. Silver Ion Conducting Electrolytes and Silver Solid-State Batteries

Anode

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Table 9.

Ag + SE Ag + SE Ag + SE Ag + SE Ag Ag Ag Ag

Refs.

0.660–0.670

1.0–1.8

2.4–4.2

87

2.9–3.2

6.8–7.3

50AgI–25Ag2 O–25CrO3 60AgI–20Ag2 O–20CrO3 70AgI–15Ag2 O–15CrO3 30CuAgI–35Ag2 I–35MoO3

0.619

1.13

2.37

88 88 88 91

40CuAgI–45Ag2 O–15B2 O3

0.617

6.55

12.84

91

40CuAgI–30Ag2 O–30SeO2

0.634

1.81

3.76

91

40CuAgI–40Ag2 O–20V2 O5

0.627

2.77

5.05

91

35CuAgI–32.5Ag2 O–32.5CrO3

0.620

0.88

1.87

91

Ag2 O–P2 O5 Ag2 O–P2 O5 –LiCl Ag2 O–P2 O5 –NaCl Ag2 O–P2 O5 –MgCl2

0.298 0.668 0.653 0.611

92 92 92 92

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Ag + SE Ag + SE Ag + SE Ag + SE

AgI–Ag2 O–(MoO3 + As2 O5 )

Capacity (mAh)

9in x 6in

Iodine:graphite: SE + TAAI Iodine:graphite Iodine:graphite: TMAI Iodine:graphite: TMAI Iodine-phenothiazine CTCb :graphite Iodine-phenothiazine CTC:graphite Iodine-phenothiazine CTC:graphite Iodine-phenothiazine CTC:graphite Iodine-phenothiazine CTC:graphite Iodine:graphite Iodine:graphite Iodine:graphite Iodine:graphite

OCV† (V)

Energy Density (Wh/kg)

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Ag + SE

Solid Electrolyte (SE)∗

11:19

Cathode

(Continued)

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Anode

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Notes: ∗ SE — solid electrolyte. † OCV — open circuit voltage. ‡ TAAI — tetraalkyl ammonium iodide. a TMAI — tetramethyl ammonium iodide. b CTC — charge transfer complex.

9.6–10.4

0.680 0.621–0.628

4.79–5.41 5.84–6.45

8.5–9.3 9.9–10.4

94 94

0.685 0.603 0.608 0.630

0.0352

0.0882 2.96 2.96 2.96

95 96 96 96

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(AgI0.75AgCl0.25 )(1−s) :(Al2 O3 )x Ag6 I4 MoO4 Ag6 I4 CrO4 30CuI–70Ag2 OMoO3

5.6–6.24

92 92 93

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20CdI2 –80[xAg2 O–y(0.7V2 O5 -0.3B2 O3 )] 20CdI2 –80[xAg2 O–y(0.7V2 O5 –0.3B2 O3 )]

0.597 0.588 0.684

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Ag2 O–P2 O5 –PbCl2 Ag2 O–P2 O5 –CuCl2 CdI2 –Ag2 O–V2 O5 –B2 O3

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Iodine:graphite Iodine:graphite Iodide:graphite: SE (2 ratios) Iodine:graphite: SE Iodine:graphite: SE:TAAI Iodine:graphite Iodine-Ph-CTC:SE Iodine-Ph-CTC:SE Iodine-Ph-CTC:SE

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Ag Ag Ag + SE

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Fig. 1. Crystal structure of α-AgI. The I-anions form a BCC lattice while the Ag+ ions occupy several of a number of equivalent-energy sites. The Ag+ ions tend to occupy the tetrahedral sites while diffusion occurs through the octahedral and trigonal sites. Adapted from Refs. 2, 6, 7.

vacancies. In another study, pressure up to 550 MPa was applied to bulk AgI.13 Through the application of pressure, dislocation defects were introduced in AgI which provided conduction pathways and increased the conductivity to 10−4 S/cm. In a study by Makiura et al., by decreasing the dimension of the AgI particles to 10 nm, not only was the alpha phase stabilized at lower temperatures (approx. 40◦ C upon cooling), but the conductivity of AgI in the beta/gamma phase at 25◦ C was increased to 1.5 × 10−2 S/cm.14 These results were recently confirmed by another study.15 Together, these studies provide a potential route to not only increase conductivity, but also to stabilize alpha-AgI at low temperatures. Anion or cation substitution in AgI By substituting another monovalent cation for Ag+ or a different halide for I− , the ionic conductivity of the resulting ionic substance is affected in several ways. In studies where Cu+ was partially

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substituted into AgI, at low concentrations the low temperature (in the beta/gamma phase) ionic conductivity increases, but the high temperature (alpha phase) conductivity decreases.16 The authors point out that there is still a search for a complete microscopic description, however they also attribute this change in conductivity to the “change in ionicity of Ag–I bond and increase in strength of p-d hybridization”. At high concentrations, Cu+ substitution actually raises beta-alpha transition temperature from 147◦ C to 360◦ C at x = 0.9 ((1 − x)AgI: xCuI) and at x > 0.50, the material no longer conducts Ag+ ions, but begins to conduct Cu+ ions.17 With halide substitution the transition temperature into the alpha phase can decrease; for example, in (1 − x)AgI: xAgCl, at the optimal conducting concentration (x = 0.25) the glassy transition temperature decreases to 135◦ C from 147◦ C found in pure AgI.18 Thus, at ambient temperature an enhancement in ion conductivity is observed, although the alpha phase is not accessed. In a study involving the AgI–AgBr system an increase in ionic conductivity with substitution of AgBr was attributed to a decrease in host lattice polarizability19 rather than the availability of vacant sites for silver ions. This decrease in polarizability decreases the activation energy for ionic motion allowing for higher ionic mobility. The greatest ionic conductivity enhancements result from cationic substitution forming crystals of the form MAg4 I5 where M = Rb, K, NH4 or other ions. RbAg4 I5 and KAg4 I5 have room temperature ionic conductivities of ∼0.3 S/cm, some of the highest discovered to date. This extremely high ionic conductivity is due to the fact that these materials are in the alpha phase at room temperature and have a large number of vacant sites for the Ag+ ions to occupy; RbAg4 I5 , for example, has 16 Ag ions spread nonuniformly across 56 sites.5 Figure 2 presents the crystal structure of RbAg4 I5 as reported by Bradley and Greene,20 and similar structures were published by Geller21 and Hull et al.22 with slight discrepancies in the discussion of the occupancy of the Ag+ sites (see Ref. 22 for a more complete discussion of occupancy). The bonds shown between Ag+ sites as well as the shaded regions point to possible openings for Ag+ ion mobility.

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Fig. 2. Crystal structure of RbAg4 I5 . Obtained from ICDD #28503. Crystallographic information from Ref. 20. Shaded bars highlight adjacent silver ion sites (i.e. intersite distances less than 2 Å) that provide potential pathways for ion movement.

Other Crystalline Ag ion conductors Finally, studies involving crystalline Ag ion conductors exist that do not fit into any of the above categories. Typically the materials of interest were formed by combining AgI with another silver salt. Crystallography studies report that the anions in these systems, including both iodide and oxides, create large conduction pathways for Ag+ ions.9, 23 2.2. Amorphous Ag Ion Conductors AgI combines a large, polarizable anion and a smaller, mobile cation in a crystalline lattice to yield good ion conductivity. Specifically, a large number of energy and structurally similar sites available for cation occupancy and open channels for the cations to travel through result in good ion conductivity. Ag ion conducting materials are also observed with glasses that contain Ag+ ions with polarizable oxides, creating pathways for Ag+ ions to move. Further, in application glass ionic conductors can have several advantages over crystalline ion

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conductors. First, glasses have no preferred growth direction and so the conductance is isotropic, which allows for less orientation demands. Also, ion conductance is not interrupted by discrete grain boundaries and planar defects. Finally, a wide range of materials can be used to create these glasses in continuous ion ratios, allowing for a large number of possible materials. Ag conducting glasses are made by rapidly quenching a mixture of glass-formers and either a silver halide or chalcogenide salt, or both. X-ray diffraction (XRD) is then used to determine that these materials are indeed glasses, with an observed absence of diffraction peaks. These mixture are typically of the form: AgX + Ag2 Y + AM ON , where X is a halide, Y is a chalcogenide (O, S, or Se), and AM ON is one of many possible materials known as glass formers including (but not limited to) B2 O3 , Al2 O3 , Fe2 O3 , V2 O5 , As2 O5 , P2 O5 , MoO3 , CrO3 , WO3 , SeO2 , TeO2 , CeO2 , and SnO2 . Additionally, other halide materials such as CdI2 and SbI3 can be used as the glass-formers in place of or in addition to the AM ON component. The silver salt AgX disperses in the glass former AM ON and the + Ag ions are mobile. A large amount of silver salts can be added to these glass formers and still retain the glassy structure; in many cases the optimal conductivity is reached when the amount of AgI in the mixture reaches almost 50%. Ag2Y, is a glass modifier and is often combined with the glass former to generate the amorphous ion conductor. Amorphous ion conductors can be made without a glass modifier, however it has been observed that materials with a modifier added generally have higher conductivities. The glass former forms a strong network of long chains of oxides such as BO3 and VO4 . The glass modifier attaches to these, breaking the long chains and reducing the size of the structure.24–29 In amorphous glasses, when two or more glass formers (AM ON components) are mixed, there can be an enhancement of ionic conductivity known as the mixed glass former effect. In these cases, the total ionic conductivity of the subsequent glass is increased over the conductivity of either constituent separately. The reason for the improvement of ion conductivity in glassy materials remains subject

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to debate, but there have been several studies to suggest that the local charge conditions can strongly affect the conductivity. In a 2011 study, keeping the Ag content constant, glass nanocomposites of 0.20CdI2 –0.80 (0.50 Ag2 O–0.50 (xB2 O3 –(1 − x)P2 O5 )) were made as a system where Ag–I coordination should remain constant.30 It was found that ionic conductivity increased with B2 O3 concentration which correlated with the increase of BO3 and decrease of BO4 complexes, which the authors claim influences the mobility of Ag+ ions. The salt AgX may be more than just the source of mobile Ag+ and may act to increase the ion conductivity as well. In a study by Swenson and Börjesson, the authors observed that adding a halide salt a glass increased the volume of the glass network.31 They found a cubic scaling relation between the volume and ionic conductivity that strongly suggests that the conductivity increases when the pathways for conduction can be increased. Other studies have appeared in the literature involving ion conductivity and glasses. For example, a study32 reported a similar correlation between Ag–I distance and ionic conductivity. By measuring the extended X-ray absorption fine structure (EXAFS) spectrum the authors were able to determine Ag–I distances for 24 different AgI glasses. They found that as the distance between Ag and I increased, the activation energy decreased and conductivity increased for these materials. This strongly suggests that it is possible to “open” conduction pathways by adjusting the contents of the glass formers and thereby increase conductance. Similar results have been found in other glassy systems.33 Further, there appears to be a correlation between ion conductivity and flexibility in glasses.34 Finally, models to describe this behavior of conductance on volume will be discussed in the following section. Ag-ion conducting composites A composite of AgI and an insulator can result in an ion conducting composite. Other reviews have also described this type of composite in depth.1, 35 In general, composite electrolytes are solid systems containing multiple distinct phases, frequently two crystal phases or a crystalline and a glass phase together. For example, insulating

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oxides have been dispersed in AgI or AgCl and have been found to enhance the ionic conductivity. In one early study by Shahi and Wagner, Al2 O3 was added to AgI whereupon they observed that smaller Al2 O3 particles led to a larger increase in ionic conductivity.36 Presumably, the increased surface area of the Al2 O3 either allows for more conduction pathways or somehow lowers the energy required for the Ag ion to hop from one site to the next. In a more recent study, the increase in conductivity in AgI and AgBr with 30% mesoporous Al2 O3 is attributed to the space-charge model, which states that Ag ions are adsorbed at the surface of the oxide which leads to a high number of anion defects in those regions and this more vacancies for the mobile Ag ions,37 however, stacking defaults in hexagonal beta-AgI can also contribute to enhanced ion conductivity. Finally, in addition to the study on AgI discussed above,13 plastic deformation was shown to enhance the conductivity and stabilize the defects against annealing in AgCl/Al2 O3 composites, indicating that the defects themselves play a crucial role in the enhancement of ionic conductivity.38, 39 Doped polymer electrolytes Doped polymer electrolytes are reminiscent in concept of amorphous Ag ion conductors. Although the initial focus was on Li-ion conduction for use in batteries, studies involving Ag ion conducting systems have become more common over the last decade. Silver doped polymer electrolytes are formed by combining a silver salt with a polar polymer matrix using several possible methods. The variety of preparation is a notable advantage of ion conducting polymers; traditionally they are prepared using the solgel, solution cast, or electro-deposition methods, however a solventfree, hot-pressed method has also been shown to be successful40 as well as thin film production.41 Doped polymers are also being considered for use in high energy density batteries,42 and because of their low weight may be useful is many applications. Finally, doped polymers can be relatively inexpensive, are readily available, and have mature associated science and technology. There are, however, several disadvantages to ion conducting polymer electrolytes. In general, they have a lower ionic

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conductivity and can have very low transference numbers (as low as tcation ∼ 0.2 in Ref. 43). It is also important to specify tcation as both cations and anions can be mobile. Also, polymer electrolytes can form passive layers between the electrolyte and electrode making applications more difficult. Doped polymer electrolytes display the best properties in the amorphous phase, and so to reduce or prevent crystallization during processing of the polymers they can be irradiated with gamma rays to introduce cross-linking.41 To improve the conductivity of polymers up to 10−3 S/cm, polymer electrolytes can be plasticized,44–46 however these can suffer from a reduction in mechanical strength. To counteract this, polymers may be copolymerized with another low glass temperature, Tg , polymer. In addition to enhancing the physical properties of the polymer, it was shown that the addition of inert filler material such as an insulating oxide improves the ionic conduction properties; studies in which 10–20% (by weight) of SiO2 , Al2 O3 , and Fe2 O3 were added to optimally-conducting PEO-AgSCN showed an enhancement of the ionic conductivity by a factor of 10.47 This effect may be explained by the space-charge-layer model.

3. Ion Mobility Directed understanding of ion conductivity in solid electrolytes is critical towards important applications such as battery science and technology. Phenomenological studies can provide direction for optimization of known materials, however a more complete and directed understanding of the microscopic mechanism of ion conductivity can lead to the targeted synthesis and/or application of new ion conducting materials. In the following sections, some of the current models for ion mobility with a focus on studies published within the last 20 years will be briefly discussed. The models discussed up to 1989 are thoroughly reviewed in Ref. 35, which includes a detailed description of interface models such as the space charge layer model. For more information of the models discussed here as well as

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additional proposed theories, previous review articles have covered this topic with detail beyond the scope of this review.1, 7, 48–51

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3.1. Crystalline Ag Ion Conductors Ion conduction in the alpha phase of AgI is most often attributed to the two Ag+ ions occupying vacant sites with similar energies.7 Because the Ag+ ions can move relatively freely among these sites, ion conduction in this system has been referred to as liquid-like. Other materials in the alpha phase, like RbAg4 I5 , have a similar crystal structure, with ions able to move between a large number of vacant sites.21, 52 Although all of the vacant sites should be occupied, reverse Monte Carlo simulations show that Ag+ ions preferentially occupy the tetrahedral Ag+ sites and conduction between unit cells occurs at trigonal and octahedral sites.6 These calculations are substantiated by diffuse scattering measurements on a single crystal of alpha-AgI.53 At room temperature, the beta-AgI forms, where the Ag+ ions become more closely packed and less mobile. Instead of having a large number of vacant, similar energy sites for Ag+ ions, beta-AgI has three crystallographically distinct sites: two types of tetrahedral sites and one type of octahedral site. In the previous section, we listed several AgI-based compounds that were still crystalline and in the beta phase, yet had an increase in ionic conduction. It was shown that small additions of oxides in AgI are insoluble and therefore not actually doping and contributing to the enhancement of conductivity.54 In beta-AgI, the enhancement of ionic conductivity is due to an increase in point defects, called Frenkel disorder.8, 36 These defects are believed to increase the number of vacancies within a crystal thereby increasing conductivity. Ag+ ions are also transported through a crystal via ion pathways. Because of the complex structure of most Ag+ ion conductors, ion pathways can be difficult to envision directly from crystallographic data for anything more complex than a cubic structure like alpha AgI. For beta AgI, however, pathways may be determined from the anion positions (which are well-defined) using the bond valence (or valence sum) method.8, 10, 23, 55 This method can be applied

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to any crystalline system: Ag+ ion pathways were determined for Ag8 I4 V2 O7 , Ag26 I18 W4 O16 , and Ag16 I12 P2 O7 .5, 56 Experimental verification of these pathways can be difficult, however a study providing evidence for conducting pathways in the amorphous system 0.5 AgI: 0.5 AgPO3 may provide a potential route to observing these pathways.57 3.2. Glassy Ag Ion Conductors One of the earliest reports of ionic conducting glasses was reported by Kunze in 1973,58 however it was not until much later that Minami showed that since the melt is cooled quickly to form the glass, the structure of the melt is often maintained in the glass to a large extent, and because the conductivity is sensitive to the structure, the conductivity of the glass is close to that of the melt. Below the melting temperature there is a jump to lower conductivity, however if the properties of the glass can be maintained (rather than converting completely to those of the crystal), the conductivity of the glass can be closer to that of the melt.59 This glass modifier was discussed in the previous section: the glass modifier maintains the glass properties and inhibits crystal formation. Because glasses are highly disordered, models that apply to crystalline ion conductivity may be incomplete or inappropriate for glass ion conductivity. This section contains a summary of some of the models associated with amorphous glass ionic conductors. Please consult specific review articles for more details of each model. Space-charge-layer model In ionic conductors that have been interspersed with insulators, an enhancement of the conductivity at the interface is observed that can be explained by an increase in surface defects relative to the bulk leading to the formation of a space-charge layer.60 This enhancement of conductivity was shown to be proportional to the surface area of the insulating particles.61, 62 More recently, Monte Carlo simulations have found that the critical concentrations obtained using percolation models are in agreement with experimental results.63 Although this model had some considerable success in certain electrolyte

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systems, there are a few problems trying to extend it to all systems. Dudney showed that although this model can be used to explain the enhancement of conductivity in AgCl–Al2 O3 composites, it is not enough to explain that seen in LiI–Al2 O3 and AgI-Al2 O3 silver ion conductors.35, 64

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Anderson-Stuart (A-S) model Anderson and Stuart proposed a model65 in which the measured activation energy for cation migration, Ea , is actually made up of two components, Eb and Es (i.e. Ea = Eb + Es ). Eb is the binding energy that holds the cation in the network and Es is the electrostatic strain energy that comes from ion movement. This model predicts that the increase of ionic conduction with temperature comes from an increase in mobility, which has been supported by neutron scattering studies.66 Weak-electrolyte model Ravaine and Souquet67 propose that the number of mobile ions is not what one would expect from stoichiometric considerations. Instead, only some of the ions are mobile, and to promote an immobile ion into a mobile state requires an energy equal to the activation energy, Ea . This energy is made up of the enthalpy of dissociation, H/2, and the migration energy, Em , that are identical to the binding energy and strain energy of the A-S model, respectively. Structural unpinning number model With the observation that the transport relaxation times are much faster than the anion relaxation, the Ag+ ions can be said to be “unpinned” from their initial lattice positions and able to move about the sublattice. Shastry and Rao68 introduced the structural unpinning number (SUN), S, with S = C (Z∗ χa ) (Vm /N) where C = 1.0 cm−3.5 (a constant to make S dimensionless), Z∗ is the charge of the ion, χa is the molecular or anionic electronegativity, Vm is the molar volume of the glass and N is the molar number of ions.

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Conductivity and activation energy can be expressed in terms of the structural unpinning number: log (σ) =

log (σ0 ) [1 − exp ( − aS)]

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log (Ea ) = −aS + log (kT) + log ( log (1/σ0 )), where σ0 is the conductivity of the undoped glass and a is a constant determined by the slope of ln (Ea ) versus S. The SUN model focuses on the microscopic origins of cation transport and provides insight into the origin of the conductivity and activation energy. Unfortunately, this model does not account for the jump in the conductivity at the beta-alpha transition. Cluster bypass model Ingram et al.69 suggested that the glasses might form macrodomains, ordered clusters of glass material on the order of a few nanometers. In this model, the preferred conduction pathways still retain the structural properties of the melt and are embedded between the glass molecules. This model correctly explains the mixed alkali effect and may help rationalize the ion conducting pathways observed in 0.5 AgI: 0.5 AgPO3 .57 Specifically, field ion microscopy was used to observe Ag+ ion emission from the surface of the electrolyte at discrete, nanometer-sized points which corresponded to ion conduction channels. It would be interesting to repeat this measurement on single crystalline samples to determine if the positions of the conduction channels agree with the theoretical values obtained from bond-valence calculations.10 Dynamic Structure Model (DSM) The DSM70, 71 starts with the experimental observations that the glass structure is not completely frozen until far below the glass transition temperature, Tg , mobile cations are able to determine their own glassy environment, and that transport is a hopping process. This model leads to the cation memory effect in which cations hop

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between sites and can convert these sites to their own environment, which would lead to correlations in the ion hopping.

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Mixed barrier model Schuch et al.72 provided insight into the mixed glass former effect (described above) where mixing two or more glass formers increases conductivity. In this model, there is a spatial distribution of activation barriers for ion jumps, and this kinetic barrier is decreased upon mixing. Bond valence calculations As with crystalline ion conductors, bond valence calculations based on reverse Monte Carlo methods can be used to calculate ion pathways through the electrolyte,56, 73 although with more difficulty than in the crystalline state. The authors have successfully used this model to reproduce the mixed alkali effect, as well as gain insight regarding the stability of the pathways with respect to time and temperature. 3.3. Doped Polymer Ion Conduction Polymer electrolytes are chemically very different than crystalline or amorphous electrolytes, and as such, with the exception of polymers with insulating particles added, few of the theories of ion conduction that apply to materials like AgI will apply to polymers. In the case of polymers with added insulators, theories that describe the interaction of conductor and insulator may still apply (for example, the space-charge-layer model described above). Polymer electrolytes typically have a crystalline and an amorphous phase, with ion conduction occurring primarily in the amorphous phase.41 A notable observation is that the temperature dependence of the conductivity of polymer electrolytes does not follow the same as in crystalline and glass electrolytes. In crystalline and glass electrolytes, the conductivity typically takes the Arrhenius form of: σ(T) ∝ exp( − Ea /T),

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Fig. 3. Schematic drawing of the free volume model. The rate of ion conduction is proportional to the probability that a hole will open (Ph ) and that the ion will jump into the newly opened hole before it closes (Pj ). Adapted from Ref. 74.

where Ea is the activation energy. Polymer electrolytes, however, often show conductivity of the form of the Vogel–Tamann–Fulcher (VTF) equation: 
B −1/2 σ (T) ∝ T , exp T − T0 where T0 is an experimentally determined temperature typically below the glass transition temperature, Tg . Several explanations for this relationship have been proposed and will be discussed briefly below. Free volume model Developed initially for glassy electrolytes, the free volume model states that there are locations into which carriers can hop, and that the probability of vacant sites leads to this temperature dependence of the conductivity.74, 75 In this model (Fig. 3), holes are formed by thermal fluctuations and above some critical hole volume particles can move into the vacant volume. Dynamic disorder/dynamic bond percolation model These models consider conduction as particles hopping between sites. Conduction happens when pathways between these sites are open, and that these pathways between vacant sites can fluctuate between “forbidden” and “allowed”.76 Renewing environments model This model is closely related to the dynamic bond percolation model, however here carriers do not hop between sites, rather they are subject to a dissipative force and a random force and move in

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with classical (Langevin) motion.76, 77 An ion is located within a certain confining region, however this confining environment is able to rearrange (called “renewal”) after some time, with renewals occurring after some average time, τ. This model is mainly focused on single ion transport, which applies Ag ion conductors, but may not be useful for other ionic conducting electrolytes. This model was extended more recently by Maitra and Heuer to predict the chain length dependence on the diffusion constant in PEO:LiBF4 .42 Additional methods to describe the microscopic transport of ions in polymer electrolytes are briefly discussed below. Modified Poisson–Nernst–Planck (PNP) theory Van Soestbergen et al.78 use a simplified version of PNP theory (see references in Ref. 79) to describe the motion of ions in polymeric electrolytes and epoxies. This numerical model yields similar information as the more standard RC circuit analysis, however PNP theory can actually be used to explain various microscopic phenomena such as charge transfer across interfaces and the buildup of a diffusive layer and requires fewer assumptions than RC circuit analysis. Lewis acid-base model As discussed above, the addition of inactive filler materials such as Al2 O3 , SiO2 , and Fe2 O3 improve the structural and ionic conducting properties of polymer electrolytes. One way to explain these results is to consider the Lewis acid-base characteristics of the ions and polymers. In this way, polymer electrolytes are seen to interact with the added oxides, with the oxides enhancing cross-linking between polymer segments and preventing the polymer from reorganizing.43, 80 The Lewis acid-base interactions may also increase the salt dissociation and provide greater ion mobility or concentration. 4. Silver Solid-State Batteries Thus far, this chapter has focused on the development of solidstate electrolytes. In this section, the preparation and performance

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of batteries made with solid-state electrolytes will be reviewed. The development of silver solid-state batteries is still an emerging area of research, with opportunities for future developments in this field. Most silver-ion conducting solid electrolytes used in solid state batteries include a matrix host material of Ag2 O or AgI–Ag2 O materials. Several groups have investigated doping effects within this matrix including CdI2 , chlorides, and various vanadates, arsenates, and phosphates. Performance metrics of conductivity, open circuit voltage, capacity, and shelf-life are measured to determine the effects of such doping and compared with theoretical or thermodynamically determined values. As the chemistry of the battery highly influences the performance, the configuration of the cathode is often a point of study in many of these solid-electrolyte investigations. Cathodes often comprise iodine and graphite to aid in conductivity, in addition to mixing in the solid electrolyte of interest. In many works a commonly used cathode additive is a tetraalkyl ammonium iodide (TAAI), where some studies have included the effect of alkyl length on battery performance. While the addition of TAAI initially causes reductions in open circuit voltage, it ultimately aids battery performance by increasing stability and shelf-life. A number of the works from the last 20 years summarized below show incremental improvements in battery performance as the cathode chemistry is optimized for a given solid electrolyte under investigation. Early studies of solid electrolyte systems suggest that silver selenovanadate (SSV) glassy electrolyte systems give high conductivity and the composition of these systems were studied to determine performance in solid state batteries by characterizing open-circuit voltage, polarization and discharge capabilities. An electrolyte of 66.67% AgI–23.07%Ag2 O–10.26%[0.8SeO2 +0.2V2 O5 ] gave the highest conductivity of previously studied related systems for doped solid electrolytes and because the chemical composition of the battery greatly influences the battery performance this electrolyte was studied in the presence of many cathode chemistries.81 The cathode comprises varying weight ratios of iodide, graphite, solid electrolyte and TAAI. The fabrication of the best performing batteries was determined by down-selecting to the optimized

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performance as each additional material was added to the cathode starting from iodide:graphite (I:C) mixtures to which the SSV system was added, after which TAAI was added. The open circuit voltage was observed to increase as a function of increasing temperature, and with the addition of graphite, solid electrolyte, and TAAI there is a stable voltage range between 27–60◦ C. Batteries with a 7:3 cathode composition (I:C) yield higher discharge capacity and specific energy, while still maintaining mechanical integrity in the pellet form. In this system, as in many others to follow, the addition of the solid electrolyte and TAAI in the cathode improves energy density over the batteries containing cathodes with only iodine and graphite.81 Further pursuit of this type of solid electrolyte design inspired the investigation of silver selenoarsanate (AgI–Ag2 O– (SeO2 +As2 O5 )) compounds in comparison to the selenovanadate systems. With TAAI present in the cathodes the open circuit voltage is in a similar range to the selenovanadates between 0.663 and 0.626 V. However, the energy density is not maintained with this electrolyte and its range from 0.7–1.7 Wh/kg is even lower than batteries with cathodes where no solid electrolyte is present.82 Additional solid electrolytes within the same family include (AgI– Ag2 O–(SeO2 +P2 O5 )) (SSP) based solid electrolytes. Cathodes and anodes of a similar nature were prepared with the inclusion of solid electrolyte and TAAI into the cathode. The conductivity and battery performance metrics were quite good compared to the vanadate and arsenate systems, with increased energy density, while maintaining a comparable open circuit voltage.83 Similarly, other groups have explored the optimization of the electrolyte constituents of the SSP electrolytes and the effect with varying cathode composition. In this study 60%AgI–26.67%Ag2 O–13.33%(0.3SeO2 +0.7P2 O5 ) solid electrolyte was synthesized and batteries were fabricated, measuring the pertinent metrics. In this work, the open circuit voltage was seen to decrease from 0.686 V to 0.658 V with addition of solid electrolyte and then TAAI into the cathode. However, the discharge capacity and the energy density improve with the addition of the solid electrolyte and the TAAI for a given optimized ratio of iodine and graphite in the initial cathode composite.84

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An adaptation of this electrolyte system includes a molybdate variation, specifically, 60%AgI+26.67%Ag2 O+13.33%(0.4SeO2 +0.6MoO3 ) was studied. As noted previously TAAI was used to reduce the tarnishing action of molecular iodide. The cathode composition with this electrolyte giving the best performance has an energy density of 3.08 Wh/kg without the addition of TAAI. Once TAAI is added, in order to reduce iodine activity, even higher energy densities, over 4 Wh/kg, are realized. The X-ray diffraction (XRD) and battery performance of this AgI-based electrolyte support the idea that amorphous solid-electrolytes with high ionic conductivity are more suitable than their crystalline counterparts.85 Additional adaptations include a silver boromolybdate, AgI–Ag2 O– B2 O3 –MoO3 , solid electrolyte. The transport number of silver ions in this electrolyte is close to unity, which is consistent with similar systems. The expected open circuit voltage range from 0.640–0.686 V remains constant over 6 months of testing these devices which suggests good shelf-life. Improvements in cell performance are attributed to improved surface area contact between electrode and electrolyte as the electrolyte is included in both the anode and cathode composites. Capacities range from 2.5–11 mAh depending on the cell composition, where the use of TMAI causes a 4-fold increase in capacity at 11 mAh.86 Further variations of the molybdate system have included investigations of silver molybdovanadate AgI–Ag2 O–(MoO3 + V2 O5 ) and silver molybdoarsenate AgI–Ag2 O– (MoO3 + As2 O5 ) as solid electrolytes. Similar to other studies looking at the effect of composition ratio and the addition of TAAI on performance, these authors noted a similar open circuit voltage to other molybdate systems on the order of 0.660–0.675 V, however, the energy density of these two systems at a maximum of 1.8 Wh/kg were much lower than other molybdate-based electrolytes.87 A majority of these cited works use a similar synthesis method to obtain the silver-conducting solid electrolyte, which is described as a melt-quenching method after which a powder is obtained and pressed into a pellet. Limited studies have shown the potential for low- or roomtemperature processing to eliminate high temperature techniques

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that are not compatible with unstable materials. One such approach that has been reported is the mechanochemical synthesis of a solid electrolyte containing AgI, Ag2 O, and CrO3 ; this mechanical approach is compared with conventional high temperature meltquenching techniques in this work.88 XRD results confirm that milling techniques can dissolve silver iodide in an Ag2 O-CrO3 matrix suitable for electrolyte testing, and ion transport numbers are near unity for all the ball-milled samples, which is consistent with melt-quench prepared materials. Limited battery characterization has shown that up to 500 µA/cm2 of current can be drawn without significant polarization for optimized samples of the ball-milled solid electrolytes. The electrical and structural properties of the ball-milled amorphous samples are in good agreement with those of quenched samples, and energy densities are reported between 2.9–3.2 Wh/kg.88 As there are small subtleties in many of these systems the determination of metrics such as open circuit voltage and capacity must be accurate in order to appropriately evaluate new electrolytes. While discovering new materials is of predominant focus, there is focus on testing techniques, as described by this work, in which the authors develop a new testing method and set-up to remove high input impedance devices for testing of conventional solid-state batteries. This compact discharge-polarization unit is used to characterize solid-state batteries with ((CH3 )4 N)2Ag13 I15 , silver borovanadate AgI–Ag2 O–B2 O3 –V2 O5 , and silver boromolybdate AgI–Ag2 O–B2 O3 –MoO3 electrolytes. Cells of various compositions, including solid electrolyte and TMAI in cathode were fabricated, tested, and demonstrated the accuracy of this new testing method by producing the same open circuit voltage values within ±2 mV for each electrolyte type.89 In an effort to increase the conductivity of silver-conducting solid electrolytes, doping with an additional metal was an approach used by several groups. A pseudo-ternary system 40%(Cu1−xAgx I)45%(Ag2 O)–15%(B2 O3 ) was prepared and characterized to determine its suitability as a solid electrolyte. For this composition, ionic transport values vary between 0.95 and 0.97 depending on the value of x, and XRD confirms the glass-like nature of several

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different electrolyte compositions, suggesting this electrolyte would be promising for silver solid state batteries.90 Specifically, one study has compared Cu1−xAgx I–Ag2 O–Y electrolytes, where Y = MoO3 , B2 O3 , SeO2 , V2 O5 , and CrO3 . Cells with these electrolyte combinations were fabricated and compared across their individually optimized compositions. Furthermore, these authors did not mix the solid electrolyte with the cathode composites but instead used Ag-phenothaizine-I2 cathodes to improve conductivity and maintain shelf-life. The open circuit voltages range from 0.617–0.634 V depending on electrolyte composition at room temperature and are comparable to thermodynamically estimated value for these types of cells. While all these electrolytes provide cells capable of delivering 280 µA/cm2 current densities, the 40%CuAgI–45%Ag2 O–15%B2 O3 electrolyte cell results in the highest capacity, 12.84 mAh, and energy density, 6.55 Wh/kg, of the combinations studied, despite its lower open circuit voltage.91 Within the scope of introducing additional metal ions into silver-conducting solid electrolytes, other metal ions including Li, Na, Mg, Pb, and Cu, have been investigated, by the addition of their respective chlorides. A broad comparison of cells utilizing these doping metal-ions was completed. The amorphous nature for all the studied electrolytes was confirmed by XRD, and electrical characterization was performed. The addition of these electrolyte dopants increases the open circuit voltage in order of cells containing Li>Na>Mg>Pb>Cu. The Li-doped cell gives the best open circuit voltage and lifetime, while the Pb-doped cell has the lowest voltage and shortest lifetime, with the Na, Cu, and Mg falling in between according to electrode potential values. These results suggest divalent metal chlorides may not be suitable as electrolyte dopants as their addition markedly reduces open circuit voltage and cell lives as compared to monovalent metal chlorides.92 An alternative metal doping that has been studied is cadmium in a CdI2 –Ag2 O–V2 O5 – B2 O3 system. In these studies ion transport number, thermoelectric power and discharge curves were used to characterize behavior. This silver-solid electrolyte was doped with CdI2 and the battery was fabricated by mixing solid electrolyte into the anode which was opposite a cathode of iodide:graphite:solid electrolyte. While this

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system is highly disordered it does support stable conduction of silver ions and batteries have open circuit voltages of approximately 0.68 V.93 Additional studies with this same electrolyte system have shown the addition of TAAI to improve polarization behavior as well as the current drain. While there is an initial decrease in the open circuit voltage to 0.628 V, with the addition of TAAI, the energy density does not change and shelf-life is improved.94 While many factors influence the conductive network in glassy solid electrolyte systems, a typical approach is to disperse ultrafine particles into a host matrix, AgI, in the case of many silverconducting electrolytes. This work explores a composite matrix (1 − x)(0.75Agl+0.25Ag(1)-x(Al2 O3 ) as an electrolyte system with characterization of electrical conductivity, to determine effects of molar concentration, preparation methods, and temperature. Both quenched and/or annealed methods were used to synthesize the host and matrix materials and materials were ground to a powder. Silver metal was used as anode from battery fabrication, and cathodes were graphite:iodide, graphite:KI3 , graphite:(CH3 )4 NI3 ; graphite:(C2 H5 )4 NI3 . Immediately it was observed that larger conductivities were possible with the new host matrix as compared to the conventional AgI host, even with large (