Table Of ContentS E L E C T E D B Y G R E N O B L E S C I E N C E S
Solid-State
Electrochemistry
Essential Course Notes
and Solved Exercises
Abdelkader Hammou & Samuel Georges
Solid-State Electrochemistry
Abdelkader Hammou Samuel Georges
(cid:129)
Solid-State Electrochemistry
Essential Course Notes and Solved Exercises
123
Abdelkader Hammou Samuel Georges
Laboratoire d’Electrochimie et de Laboratoire d’Electrochimie et de
Physico-chimie des Matériaux et des Physico-chimie des Matériaux et des
Interfaces Interfaces
PHELMA PHELMA
Saint-Martin-d’Hères, France Saint-Martin-d’Hères, France
This translation has been supported by UGA Éditions, publishing house of Université
Grenoble Alpesandthe régionAuvergne-Rhône-Alpes.https://www.uga-editions.com/.
ISBN978-3-030-39658-9 ISBN978-3-030-39659-6 (eBook)
https://doi.org/10.1007/978-3-030-39659-6
Translated, revised and adapted from “Electrochimie des solides”, A. Hammou/S. Georges, EDP
Sciences,2011.
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Grenoble Sciences
The French version of this book received the “Grenoble Sciences” label.
“Grenoble Sciences” directed by Professor Jean Bornarel, was between 1990
and 2017 an expertising and labelling centre for scientific works, with a na-
tional accreditation in France. Its purpose was to select the most original high
standard projects with the help of anonymous referees, then submit them to
reading comittees that interacted with the authors to improve the quality of the
manuscripts as long as necessary. Finally, an adequate scientific publisher was
entrusted to publish the selected works worldwide.
About this Book
This book is translated, revised and adapted from Électrochimie des solides
– Exercices corrigés avec rappels de cours by Abdelkader Hammou & Samuel
Georges, EDP Sciences, Grenoble Sciences Series, 2011, ISBN 978-2-7598-0658-4.
The Translation from original French version has been performed by:
Brett Kraabel, Physical Sciences Communication.
The reading committee of the French version included the following members:
2 J.M. Bassat, CNRS research director, Bordeaux
2 J. Fouletier, professor at Grenoble Alpes University
2 R.N. Vannier, professor at the ENS of Chemistry, Lille
and K. Girona, PhD student
V
Preface
The electrochemistry of solids is a relatively young field that only really caught
on in the 1950s. Its particularity resides in the multidisciplinary nature of its
content, which associates electrochemistry, solid-state chemistry (organic and
inorganic), and physical chemistry. The principal goal is to synthesize and
characterize materials susceptible for use in devices that exploit their electro-
chemical properties. The materials studied are either electrolytes or electrode
materials, which are two major families of materials.
2 The electrolytes discussed are solid oxide or halide solutions in the crys-
talline state [(ZrO ) (Y O ) , β alumina, (SrCl ) (KCl) …], or glassy
2 1−x 2 3 x 2 1−x x,
state (SiO -K O, LiI, Li P S ...) and organic-polymer-salt complexes
2 2 4 2 7,
(POE-LiTFSI). In this work, we mainly study the structural characteristics
(i.e., phases, crystalline structure) and the ionic transport properties (i.e.,
electrical conductivity, transport modes, ionic domain). The experimental
results are analyzed by considering the properties under study as a function
of temperature, of the nature and concentration of structural defects (va-
cancies, interstitials, impurities, dopants) present in the phase, and of the
chemical potential of the basic constituents of the phase. An example of the
latter is oxygen in the case of solid oxide electrolytes; in this case, Brouwer
diagrams are frequently used. Finally, note that, in most solid electrolytes,
the conductivity derives only from one ionic species.
2 Electrode materials are made of metals (Li, Na, Ag, Pt, …) as well as ox-
ides (La Sr MnO , FePO , WO , …), composites (Ni-YSZ), or sul-
1−x x 3−δ 4 3
fides (TiS , MoS , …). Research in this field focuses primarily on deter-
2 2
mining the electrical conductivity and identifying and studying the kinetics
of the electrode reactions and the durability of the electrode-electrolyte
interface. As is the case with aqueous solutions, the results are interpreted
by relying on the polarization due to adsorption-desorption, to diffusion
and migration of electroactive species, and to charge transfer.
VII
VIII Solid-State Electrochemistry
Today, the international electrochemistry community is well structured, with
regular conferences and a large volume of significant publications in electro-
chemical journals (Journal of the Electrochemical Society, Journal of Power
Sources, Solid State Ionics, Ionics) and in solid-state chemistry journals (Journal
of Materials Science, Journal of the European Ceramic Society, Journal of the
American Ceramic Society, …). Teaching texts in this field, however, are few
and take the form of courses, of chapters written by specialists, or of proceedings
of conferences dealing with the solid-state electrochemistry.
The origin of this collection of exercises is the desire to provide a work tool in
the form of exercises to satisfy the need expressed by doctoral students in our
laboratory and by participants in the continuing-education courses on solid-state
electrochemistry organized by our group at the Laboratoire d’Électrochimie
et de Physicochimie des Matériaux et des Interfaces of Grenoble (LEPMI). To
the best of our knowledge, no such work exists to this day. Our goal is thus to
fill a void by allowing readers to familiarize themselves, by solving problems,
with the notions presented in Solid-State Electrochemistry. These problems
cover essentially
2 the notation of defects in ionic crystalline solids with the focus on the no-
tion of effective charge,
2 the evolution of the stoichiometry as a function of temperature, of the dop-
ing level, and of the chemical potential of the basic constituents of the
materials under study, in particular by using Brouwer diagrams,
2 methods to measure electrochemical quantities (conductivity, transport
number, electrode polarization) such as impedance measurements, dilato-
coulometry, and drawing current-voltage curves,
2 the study of several applications involving solid electrolytes, such as fuel
cells, batteries, and sensors.
The essential skills required to solve these exercises are presented in the form
of course notes. These are given at the outset of each chapter. To delve deeper
into a question, one should consult the specialized books and articles in the
(non-exhaustive) bibliography that appears at the end of this book. The pub-
lications from which some of the exercises in this book were constructed also
appear in the bibliography.
We hope that our contribution will illuminate with a less arduous light this field
towards which we hope to attract a larger public.
Preface IX
We are grateful to Professor Jacques Fouletier and Professor Pierre Fabry for hav-
ing provided us with a certain number of the exercises proposed herein; exercises
that were used in the exam for the Master II diploma in Electrochemistry and
Materials from the Université Grenoble Alpes. We also thank Elisabeth Siebert,
Cécile Rossignol, and Jean-Louis Souquet for reading the original manuscript,
discussing the pertinence of the exercises, and especially for taking time out
from their schedule to verify the answers. Finally, our gratitude goes out to all
our colleagues who, after reading the manuscript, gave us their opinion and
constructive recommendations; in particular Rose-Noëlle Vannier, Jean-Marc
Bassat, and Jacques Fouletier, as well as Kelly Girona.
Table of contents
Base quantities, units, and symbols from the international system (IS) ..........1
Chapter 1 – Description of ionic crystals ............................................................7
Course notes ...........................................................................................................7
1.1 – Definitions .......................................................................................................7
1.1.1 – The perfect crystal ...............................................................................7
1.1.2 – The real crystal ....................................................................................7
1.1.3 – Structure elements and effective charge ..............................................8
1.2 – Reactions and equilibria ..................................................................................9
1.2.1 – Atomic disorder and electronic disorder..............................................9
1.2.2 – Writing the reactions..........................................................................10
1.2.3 – Presence of foreign atoms .................................................................10
1.2.4 – Equilibrium with the environment.....................................................11
1.3 – Brouwer diagram ...........................................................................................11
1.3.1 – Equilibria ...........................................................................................11
1.3.2 – Electroneutrality relation and the Brouwer approximation ...............12
1.3.3 – Diagram for MX crystal ...................................................................13
2
1.3.4 – Case of solid solution (MX ) (DX) ..............................................13
2 1−x x
1.4 – Stoichiometry and departure from stoichiometry ..........................................14
Exercises ..............................................................................................................15
Exercise 1.1 – Notation for structure elements and structure defects ....................15
Exercise 1.2 – Notation for doping reactions .........................................................16
Exercise 1.3 – Sitoneutrality and expression of chemical formulas .......................18
Exercise 1.4 – Calculation of defect concentrations...............................................18
Exercise 1.5 – Doping strontium fluoride ...............................................................18
Exercise 1.6 – Variation of the concentration of structure defects
in pure zirconium dioxide ZrO as a function of oxygen partial pressure ...19
2
XI
XII Solid-State Electrochemistry
Exercise 1.7 – The non-stoichiometry of iron monoxide .......................................20
Exercise 1.8 – Departure from stoichiometry of barium fluoride BaF .................21
2
Exercise 1.9 – Crystallographic and thermodynamic study
of thorium dioxide ThO ...............................................................................22
2
Solutions to exercises .............................................................................................24
Solution 1.1 – Notation for structure elements and structure defects .....................24
Solution 1.2 – Notation for doping reactions .........................................................25
Solution 1.3 – Sitoneutrality and notation for chemical formulas ..........................28
Solution 1.4 – Calculation of defect concentrations ...............................................30
Solution 1.5 – Doping strontium fluoride ...............................................................31
Solution 1.6 – Variation of the concentration of structure defects
in pure zirconium dioxide ZrO as a function of oxygen partial pressure ...32
2
Solution 1.7 – The non-stoichiometry of iron monoxide .......................................33
Solution 1.8 – Departure from stoichiometry of barium fluoride BaF ..................35
2
Solution 1.9 – Crystallographic and thermodynamic study
of thorium dioxide ThO ...............................................................................39
2
Chapter 2 – Methods and techniques ..............................................................47
Course notes .........................................................................................................47
2.1 – Complex impedance spectroscopy ................................................................47
2.1.1 – Time domain: principal passive linear dipole devices
in sinusoidal regime ...........................................................................47
2.1.2 – Complex notation ..............................................................................47
2.1.3 – Graphical representation of complex impedance ..............................48
2.1.4 – Other dipole devices ..........................................................................51
2.1.5 – Physical meaning of complex impedance spectra .............................52
2.2 – Methods to measure transport number ..........................................................52
2.2.1 – Electromotive force method ..............................................................52
2.2.2 – Using the results of total conductivity ...............................................53
2.2.3 – Tubandt method .................................................................................54
2.2.4 – Dilatocoulometric method to measure cationic transport number ....55
2.2.5 – Electrochemical semipermeability ....................................................56
2.2.6 – Blocking electrode method ................................................................57
Exercises ..............................................................................................................59
Exercise 2.1 – Determination of conductivity by four-electrode method ..............59
