the crc handbook of solid state electrochemistry 1997 - gellings

The CRC Handbook

of Solid State
Electrochemistry

Edited by

P

.J. Gellings

and

H.J

.M. Bouwmeester

Uni

versity of Twente
Laboratory for Inorganic
Materials Science
Enschede, The Netherlands
CRC Press
Boca Raton New York London Tokyo

Acquiring Editor:

Felicia Shapiro
Project Editor: Gail Renard

Marketing Manager: Arline Massey
Direct Marketing Manager: Becky McEldowney
Cover design: Denise Craig
PrePress: Kevin Luong
Manufacturing: Sheri Schwartz

Library of Congr

ess Cataloging-in-Publication Data

The CRC handbook of solid state electrochemistry / edited by P

.J. Gellings
and H.J.M. Bouwmeester.
p. cm.
Includes bibliographical references and index.
ISBN 0-8493-8956-9
1. Solid state chemistry—Handbooks, manuals, etc. I. Gellings, P.J. II. Bouwmeester, H.J.M.
QD478.C74 1996
541.3

′

7—dc20
96-31466
CIP
This book contains information obtained from authentic and highly regarded sources. Reprinted material is
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Copyright © 1997 by CRC Press, Inc.

ABOUT THE EDITORS

Pr

of. Dr. P.J. Gellings.

After studying chemistry at the University of Leiden (the Neth-
erlands), Prof. Gellings received his degree in physical chemistry in 1952. Subsequently he
worked as research scientist in the Laboratory of Materials Research of Werkspoor N.V.
(Amsterdam, the Netherlands). He obtained his Ph.D. degree from the University of Amster-

dam in 1963 on the basis of a dissertation titled: “Theoretical considerations on the kinetics
of electrode reactions.”
In 1964 Prof. Gellings was appointed professor of Inorganic Chemistry and Materials
Science at the University of Twente. His main research interests were coordination chemistry
and spectroscopy of transition metal compounds, corrosion and corrosion prevention, and
catalysis. In 1991 he received the Cavallaro Medal of the European Federation Corrosion for
his contributions to corrosion research. In 1992 he retired from his post at the University, but
has remained active as supervisor of graduate students in the field of high temperature
corrosion.

Dr

. H.J.M. Bouwmeester.

After studying chemistry at the University of Groningen (the
Netherlands), Dr. Bouwmeester received his degree in inorganic chemistry in 1982. He
received his Ph.D. degree at the same university on the basis of a dissertation titled: “Studies
in Intercalation Chemistry of Some Transition Metal Dichalcogenides.” For three years he
was involved with industrial research in the development of the ion sensitive field effect
transistor (ISFET) for medical application at Sentron V.O.F. in the Netherlands.
In 1988 Dr. Bouwmeester was appointed assistant professor at the University of Twente,
where he heads the research team on Dense Membranes and Defect Chemistry in the Labo-
ratory of Inorganic Materials Science. His research interests include defect chemistry, order-
disorder phenomena, solid state thermodynamics and electrochemistry, ceramic surfaces and
interfaces, membranes, and catalysis. He is involved in several international projects in these
fields.
Copyright © 1997 by CRC Press, Inc.

CONTRIB

UTORS

Isaac

Abrahams

Department of Chemistry

Queen Mary and

Westfield College
University of London
London, United Kingdom

Symeon I. Bebelis

Department of Chemical Engineering

Uni

versity of Patras
Patras, Greece

Henny J

.M. Bouwmeester

Laboratory for Inor

ganic Materials Science

Faculty of Chemical Technology
University of Twente
Enschede, The Netherlands

P

eter G. Bruce

School of Chemistry

Uni

versity of St. Andrews
St. Andrews, Fife, United Kingdom

Anthonie J

. Burggraaf

Laboratory for Inor

ganic Materials Science
Faculty of Chemical Technology
University of Twente
Enschede, The Netherlands

Hans de

Wit

Materials Institute Delft

Delft Uni

versity of Technology
Faculty of Chemical Technology and Materials
Science
Delft, The Netherlands

Pierr

e Fabry

Uni

versité Joseph Fourier
Laboratoire d’Electrochimie et de
Physicochimie des Matériaux et Interfaces
(LEPMI)
Domaine Universitaire
Saint Martin d’Hères, France

Thijs Fransen

Laboratory for Inor

ganic Materials Science
University of Twente
Enschede, The Netherlands

P

aul J. Gellings

Laboratory for Inor

ganic Materials Science
Faculty of Chemical Technology
University of Twente
Enschede, The Netherlands
‡

Deceased

Heinz Gerischer‡

Scientifi

c Member Emeritus of the Fritz Haber
Institute
Department of Physical Chemistry
Fritz-Haber-Institut der Max-Planck-
Gesellschaft
Berlin, Germany

Claes G. Granqvist

Department of

Technology

Uppsala University
Uppsala, Sweden

J

acques Guindet

Uni

versité Joseph Fourier
Laboratoire d’Electrochimie et de
Physicochimie des Matériaux et Interfaces
(LEPMI)
Domaine Universitaire
Saint Martin d’Hères,
France

Abdelkader Hammou

Uni

versité Joseph Fourier
Laboratoire d’Electrochimie et de
Physicochimie des Matériaux et Interfaces
(LEPMI)
Domaine Universitaire
Saint Martin d’Hères,
France

Christian J

ulien

Laboratoire de Ph

ysique des Solides
Université Pierre et Marie Curie
Paris, France

T

etsuichi Kudo

Institute of Industrial Science

Uni

versity of Tokyo
Tokyo, Japan

J

anusz Nowotny

Australian Nuclear Science &

Technology
Organisation
Advanced Materials Program
Lucas Heights Research Laboratories

Menai, Australia

Ilan Riess

Ph

ysics Department
Technion — Israel Institute of
Technology
Haifa, Israel
Copyright © 1997 by CRC Press, Inc.

J

oop Schoonman

Laboratory for

Applied Inorganic Chemistry
Delft University of Technology
Faculty of Chemical Technology and Materials
Science
Delft, The Netherlands

Elisabeth Siebert

Uni

versité Joseph Fourier
Laboratoire d’Electrochimie et de

Physicochimie des Matériaux et Interfaces
(LEPMI)
Domaine Universitaire
Saint Martin d’Hères, (France)

Constantinos G.

Vayenas

Department of Chemical Engineering

Uni

versity of Patras
Patras, Greece

W

erner Weppner

Chair for Sensors and Solid State Ionics

T

echnical Faculty, Christian-Albrechts
University
Kiel, Germany
Copyright © 1997 by CRC Press, Inc.

IN MEMORIAM

Heinz Gerisc

her

1919–1994

On September 14, 1994, Professor Heinz Gerischer died from heart f

ailure. With his
death, the international community of electrochemistry lost the man who most probably was
its most eminent representative. Professor Gerischer was one of the founders of modern
electrochemistry, having contributed to nearly all modern extensions and improvements of
this science.
He was born in 1919 and studied chemistry at the University of Leipzig from 1937 to
1944, presenting his Ph.D. thesis, under the supervision of Professor Bonhoeffer, in 1946.
He worked throughout Germany, was professor of physical chemistry at the Technical
University–Munich, and director of the Fritz-Haber-Institut der Max-Planck-Gesellschaft in
Berlin. He made great contributions to the kinetics of electrode reactions and to the electro-
chemistry at semiconductor surfaces. He also initiated the application of a wide range of
modern experimental methods to the study of electrochemical reactions, including nonelec-
trochemical techniques such as optical and electron spin resonance spectroscopy, and advo-
cated the use of synchroton radiation in surface research. His scientific work was published
in more than 300 publications and was notable for its great originality, clarity of exposition,
and high quality.
We are grateful that we can publish as Chapter 2 of this handbook, what may be Professor
Gerischer’s last publication, in which he again shows his ability to give a very clear exposition
of the basic principles of modern electrochemistry.
Copyright © 1997 by CRC Press, Inc.

PR

EFACE

The idea for this book arose out of the realization that, although e

xcellent surveys and
handbooks of electrochemistry and of solid state chemistry are available, there is no single
source covering the field of solid state electrochemistry. Moreover, as this field gets only
limited attention in most general books on electrochemistry and solid state chemistry, there
is a clear need for a handbook in which attention is specifically directed toward this rapidly
growing field and its many applications.
This handbook is meant to provide guidance through the multidisciplinary field of solid
state electrochemistry for scientists and engineers from universities, research organizations,
and industries. In order to make it useful for a wide audience, both fundamentals and
applications are discussed, together with a state-of-the-art review of selected applications.
As is true for nearly all fields of modern science and technology, it is impossible to treat
all subjects related to solid state electrochemistry in a single textbook, and choices therefore
had to be made. In the present case, the solids considered are mainly confined to inorganic
compounds, giving only limited attention to fields like polymer electrolytes and organic
sensors.
The editors thank all those who cooperated in bringing this project to a successful close.
In the first place, of course, we thank the authors of the various chapters, but also those who
advised us in finding these authors. We are also grateful to the staff of CRC Press — in
particular associate editor Felicia Shapiro and project editor Gail Renard, who were of great
assistance to us with their help and experience in solving all kinds of technical problems.
It is a great loss for the whole electrochemical community that Professor Heinz Gerischer
died suddenly in September 1994 and we remember with gratitude his great services to
electrochemistry. We consider ourselves fortunate to be able to present as Chapter 2 of this
handbook one of his last important contributions to this field.

P

.J. Gellings
H.J.M. Bouwmeester
Copyright © 1997 by CRC Press, Inc.

T

ABLE OF CONTENTS

Chapter 1


Introduction

Henny J

.M. Bouwmeester and Paul J. Gellings

Chapter 2


Principles of Electrochemistry

Heinz Gerischer

Chapter 3

Solid State Background

Isaac

Abrahams and Peter G. Bruce

Chapter 4


Interface Electrical Phenomena in Ionic Solids

J

anusz Nowotny

Chapter 5


Defect Chemistry in Solid State Electrochemistry

J

oop Schoonman

Chapter 6


Survey of Types of Solid Electrolytes

T

etsuichi Kudo

Chapter 7


Electrochemistry of Mixed Ionic–Electronic Conductors

Ilan Riess

Chapter 8


Electrodics

Ilan Riess and J

oop Schoonman

Chapter 9


Principles of Main Experimental Methods

W

erner Weppner

Chapter 10

Electrochemical Sensors

Pierr

e Fabry and Elisabeth Siebert

Chapter 11


Solid State Batteries

Christian J

ulien

Chapter 12


Solid Oxide Fuel Cells

Abdelkader Hammou and J

acques Guindet
Copyright © 1997 by CRC Press, Inc.

Chapter 13


Electrocatalysis and Electrochemical Reactors

Constantinos G.

Vayenas and Symeon I. Bebelis

Chapter 14


Dense Ceramic Membranes for Oxygen Separation

Henny J

.M. Bouwmeester and Anthonie J. Burggraaf

Chapter 15


Corrosion Studies

Hans de

Wit and Thijs Fransen

Chapter 16
Electrochromism and Electrochromic Devices
Claes G. Granqvist
Copyright © 1997 by CRC Press, Inc.

Chapter

1

INTR

ODUCTION

Henny J

. M. Bouwmeester and Paul J. Gellings

I.

Introduction
II. General Scope
III. Elementary Defect Chemistry
A. Types of Defects
B. Defect Notation
C. Defect Equilibria
IV. Elementary Considerations of the Kinetics of Electrode Reactions
References

I.

INTRODUCTION

As in aqueous electrochemistry

, research interest in the field of solid state electrochemistry
can be split into two main subjects:

Ionics:

in which the properties of electrolytes have the central attention

Electr

odics:

in which the reactions at electrodes are considered.
Both fields are treated in this handbook. This first chapter gives a brief survey of the scope
and contents of the handbook. Some elementary ideas about these topics, which are often
unfamiliar to those entering this field, are introduced, but only briefly. In general, textbooks
and general chemical education give only minor attention to elementary issues such as defect
chemistry and kinetics of electrode reactions. Ionics in solid state electrochemistry is inher-
ently connected with the chemistry of defects in solids, and some elementary considerations
about this are given in Section III. Electrodics is inherently concerned with the kinetics of
electrode reactions, and therefore some elementary considerations about this subject are
presented in Section IV. In an attempt to lead into more professional discussions as provided
in subsequent chapters, some of these considerations are presented in this first chapter.

II.

GENERAL SCOPE

The distinction made between

ionics

and

electrodics

is translated into detailed discussions
in various chapters on the following topics:
• electrochemical properties of solids such as oxides, halides, cation conductors, etc.,
including ionic, electronic, and mixed conductors
• electrochemical kinetics and mechanisms of reactions occurring on solid electrolytes,
including gas-phase electrocatalysis.
Copyright © 1997 by CRC Press, Inc.

An important point to note in solid state electrochemistry is that electrolyte and electrode


behavior may coincide in compounds showing both ionic and electronic conduction, the so-
called

mixed ionic–electronic conductors

(often abbreviated to

mixed conductors

).
A review of the necessary theoretical background in electrochemistry and solid state
chemistry is given in Chapters 2 through 5. The fundamentals of these topical areas, which
include structural and defect chemistry, diffusion and transport in solids, conductivity and
electrochemical reactions, adsorption and reactions on solid surfaces, get due attention,
starting with a discussion of fundamental concepts from aqueous electrochemistry in
Chapter 2. Also discussed are fast ionic conduction in solids, the structural features associated
with transport, such as order–disorder phenomena, and interfacial processes. Because of the

great variety in materials and relevant properties, a survey of the most important types of
solid electrolytes is presented separately in Chapter
6. In addition, a detailed account is
provided, in Chapter 7, of the electrochemistry of mixed conductors, which are becoming of
increasing interest in quite a number of applications. Finally, attention is given to electrode
processes and electrodics in Chapter
8, while the principles of the main experimental methods
used in this field are presented in Chapter 9.
In view of the many possible applications in various fields of common interest, a discus-
sion of a number of characteristic and important applications emerging from solid state
electrochemistry follows the elementary and theoretical chapters. In Chapter 10, electrochem-
ical sensors for the detection and determination of the constituents of gaseous (and for some
liquid) systems are discussed. Promising applications in the fields of generation, storage, and
conversion of energy in fuel cells and in solid state batteries are treated in Chapters 11 and
12, respectively. The application of solid state electrochemistry in chemical processes and
(electro)catalysis is considered in detail in Chapter 13, followed by a discussion of (dense)
ceramic mixed conducting membranes for the separation of oxygen in Chapter 14. The
fundamentals of high-temperature corrosion processes and tools to either study or prevent
these are deeply connected with solid state electrochemistry and are considered in Chapter 15.
The application and properties of optical, in particular electrochromic, devices are discussed
in Chapter 16.
We have not attempted to rigorously avoid all overlap between the different chapters, nor
to alter carefully balanced appraisals of fundamental or conceptual issues given in a number
of chapters by different authors. In particular, most chapters devoted to applications also treat
some of the background and underlying theory.

III.

ELEMENTARY DEFECT CHEMISTRY

Some elementary considerations on defect chemistry are presented here, b

ut within the
limits of this introductory chapter, only briefly. For a more extensive treatment, see, in
particular, Chapters 3 and 4 of this handbook.

A.

T

YPES OF DEFECTS

Ion conducti

vity or diffusion in oxides can only take place because of the presence of
imperfections or defects in the lattice. A finite concentration of defects is present at all
temperatures above 0°K arising from the entropy contribution to the Gibbs free energy as a
consequence of the disorder introduced by the presence of the defects.
If x is the mole fraction of a certain type of defect, the entropy increase due to the
formation of these defects is
(1.1)∆sRxx x x=−
()
+−
()
−
()
()
ln ln11
Copyright © 1997 by CRC Press, Inc.

which is the mixing entrop

y of an (ideal) mixture of defects and occupied lattice positions.
If the energy needed to form the defects is E Joule per mole, the corresponding increase of
the enthalpy is equal to:
(1.2)
The change in free enthalpy (or Gibbs free energy) then becomes:
(1.3)
Because in equilibrium g (and of course also

∆

g) must be minimal, we find, by partial
differentiation:
(1.4)
so that, in equilibrium:
(1.5)
or, if x

!

1:
(1.6)
From this we find that, for example, if E = 50 kJ/mol then at 300°K one would have a defect
mole fraction x

≈

2

×

10

–9

, which increases to x

≈

2

×

10

–3

at 1000°K.

At each temperature
a finite, albeit often small, concentration of defects is found in any crystal.
Because the energies needed for creating different defects usually differ greatly, it is often
a good approximation to consider only one type of defect to be present: the

majority defect.

For example, a difference of 40 kJ/mol in the formation energy of two defects leads to a
difference of a factor of about 10

7

between their concentrations at 300°K and of about 10

2

at 1000°K.

The defects under consideration here may be

•

vacant lattice sites, usually called vacancies
• ions placed at normally unoccupied sites, called interstitials
• foreign ions present as impurity or dopant
• ions with charges different from those expected from the overall stoichiometry
In the absence of macroscopic electric fields and of gradients in the chemical potential,
charge neutrality must be maintained throughout an ionic lattice. This requires that a charged
defect be compensated by one (or more) other defect(s) having the same charge, but of
opposite sign. Thus, these charged defects are always present in the lattice as a combination
of two (or more) types of defect(s), which in many cases are not necessarily close together.
Two common types of disorder in ionic solids are Schottky and Frenkel defects. At the
stoichiometric composition, the presence of Schottky defects (see Figure 1.1a) involves
equivalent numbers of cation and anion vacancies. In the Frenkel defect structure (see
∆hxE=⋅
∆∆ ∆ghTsxERTxx x x=−⋅=⋅+
()
+−
()
−

()
()
ln ln11

∂
∂
∆g
x
ERT x x
()
==+
()
−−
()
()
01ln ln
x
x
E
RT1−
=−




exp
x
E
RT
=−





exp
Copyright © 1997 by CRC Press, Inc.

Figure

1.1b) defects are limited to either the cations or the anions, of which both a vacancy
and an interstitial ion are present. Ionic defects which are present due to the thermodynamic
equilibrium of the lattice are called intrinsic defects.
Nonstoichiometry occurs when there is an excess of one type of defect relative to that at
the stoichiometric composition. Since the ratio of cation to anion lattice sites is the same
whether a compound is stoichiometric or nonstoichiometric, this means that complementary
electronic defects must be present to preserve electroneutrality. A typical example is provided
by FeO, which always has a composition Fe

1–x

O, with x > 0.03.

As shown schematically in
Figure 1.2, we see that this is accomplished by the formation of two Fe

3+

ions for each Fe

2+

ion remo

ved from the lattice.
Electronic defects may arise as a consequence of the transition of electrons from normally
filled energy levels, usually the valence band, to normally empty levels, the conduction band.
In those cases where an electron is missing from a nominally filled band, this is usually called
a hole (or electron hole).
The number of electrons and holes in a nondegenerate semiconductor is determined by
the value of the electronic band gap, E

g

.

The intrinsic ionization across the band gap can be
expressed by:
(1.7)
When electrons or electron holes are localized on ions in the lattice, as in Fe

1–x

O, the


semiconductivity arises from electrons or electron holes moving from one ion to another,
which is called

hopping-type semiconductivity

.

FIGURE

1.1.

Schottky and Frenkel defects.

FIGURE

1.2.

Fe

1–x

O as e

xample of a compound with a metal deficit.
′
+
→
←
=
′
[]
×
[]
•
•

eh
Keh
el
0
Copyright © 1997 by CRC Press, Inc.

B.

DEFECT NOTATION

The char

ges of defects and of the regular lattice particles are only important with respect
to the neutral, unperturbed (ideal) lattice. In the following discussion the charges of all point
defects are defined relative to the neutral lattice. Thus only the effective charge is considered,
being indicated by a dot (

•

) for a positi

ve excess charge and by a prime (

′

) for a negative
excess charge. The notation for defects most often used has been introduced by Kröger and
Vink

1

and is gi

ven in Table 1.1. Only fully ionized defects are indicated in this table. For
example, considering anion vacancies we could, besides doubly ionized anion vacancies, V

X

··

,

also have singly ionized or uncharged anion vacancies, V

X

·



or V

X

x

, respecti

vely.

C.

DEFECT EQUILIBRIA

The e

xtent of nonstoichiometry and the defect concentrations in solids are functions of
the temperature and the partial pressure of their chemical components, which are treated
more fully in Chapters 3 and 4 of this handbook.
Foreign ions in a lattice (substitutional ions or foreign ions present on interstitial sites)
are one type of extrinsic defect. When aliovalent ions (impurities or dopes) are present, the
concentrations of defects of lattice ions will also be changed, and they may become so large
that they can be considered a kind of extrinsic defect too, in particular when they form
minority defects in the absence of foreign ions. For example, dissolution of CaO in the fluorite
phase of zirconia (ZrO

2

) leads to Ca

2+

ions occup

ying Zr

4+

sites, and an ef

fectively positively
charged oxygen vacancy is created for each Ca

2+

ion present to preserv

e electroneutrality.
The defect reaction can then be written as:
(1.8)
with the electroneutrality condition or charge balance:
(1.9)
where the symbol of a defect enclosed in brackets denotes its mole fraction. In this case the
concentrations of electrons and holes are considered to be negligible with respect to those
of the substituted ions and vacancies. Consequently, in this situation the mole fraction of
ionic defects is fixed by the amount of dopant ions present in the oxide.
As another example, we consider an oxide MO

2

with Frenk

el defects in the anion
sublattice. As the partial pressure of the metal component is negligible compared with that

T

ABLE 1.1

Kröger–V

ink Notation for Point Defects in Crystals

T

ype of defect Symbol Remarks

V

acant M site V

M

″

Di

valent ions are chosen as example
with MX as compound formula
Vacant X site V

X

··

M

2+

, X

2–

: cation and anion

Ion on lattice site

M

M

x

,

X

X

x

x

: unchar

ged
L on M site L

′

M

L

+

dopant ion

N on M site

N

M

·

N

3+

dopant ion

Free electron

e

′

Free (electron) hole

h

·
Interstitial M ion M

i

··

·

: effective positive charge
Interstitial X ion X

i

″

′

: effective negative charge
CaO Ca O V
Zr O O
→
′′
++
× ••
Ca V
Zr O
′′

[]
=
[]
••
Copyright © 1997 by CRC Press, Inc.

of oxygen under most e

xperimental conditions, nonstoichiometry thus is a result of the
interaction of the oxide with the oxygen in the surrounding gas atmosphere. The Frenkel
defect equilibrium for the oxygen ions can be written as:
(1.10)
for fully ionized defects, as is usually observed in oxides at elevated temperature. The thermal
equilibrium between electrons in the conduction band and electron holes in the valence band
is represented by Equation (1.7). Taking into account the presence of electrons and electron
holes, the electroneutrality condition reads:
(1.11)
If ionic defects predominate, the concentrations of oxygen interstitials O

i

″

and oxygen
vacancies V

O

··

([V

O
··
]
@ [h
·
] and [O
i
″] @ [e′]) are equal and independent of oxygen pressure.
As the oxygen pressure is increased, oxygen is increasingly incorporated into the lattice.
The corresponding defect equilibrium is
(1.12)
This type of equilibrium, which involves p-type semiconductivity, is only possible if cations
are present which have the capability of increasing their valence. As the oxygen pressure is
decreased, oxygen is being removed from the lattice. The corresponding defect equilibrium is
(1.13)
noting that [O
O
×
] ≈ 1.
When only lower oxidation states are available, as in ZrO
2
, an n-type semiconductor is
obtained. Reduction increases the conductivity, and this type of compound is called a reduc-
tion-type semiconductor. Oxidation would involve the creation of electron holes, e.g., in the
form of Zr
5+
, which is energetically very unfavorable because the corresponding ionization
energy is very high, although this could occur in principle at very high oxygen partial

pressures.
IV. ELEMENTARY CONSIDERATIONS OF THE KINETICS
OF ELECTRODE REACTIONS
In this section a simplified account of some basic concepts of the kinetics of electrode
processes is given. We consider a simple electrode reaction:
(1.14)
OOV
KOV
OiO
FiO
×
→
←
′′
+
→
←
′′
[]
×
[
]
••
••
hV eO
Oi
•••
[]
+
[]

→
←
′
[]
+
′′
[]
22
1
2
2
2
2
2
1
2
OO h
Kp Oh
i
ox O i
→
←
′′
+
×=
′′
[]
×
[]
•

•

OOgV e
VeKp
OO
O
red
O
ו•
••
−
=
()
++
′
[]
×
′
[]
=×
1
2
2
2
2
2

1
2
Ox ne d+

→
←
−
Re
Copyright © 1997 by CRC Press, Inc.
where n is the number of electrons transferred in the reaction, Ox is the oxidized form of a
redox couple, e.g., Fe
2+
, O
2
, and H
+
, while Red is the corresponding reduced form, thus
respectively: Fe(metal), OH
–
in aqueous solution or O
2–
in a solid oxide, and H
2
.
The rate of reaction in the two opposite directions is proportional to the anodic current
density i
a
(>0) and the cathodic current density i
c
(<0). In equilibrium these are numerically
equal and the balanced term is called the exchange current density i
0
. The total current density
i

total
= i
a
+ i
c
is equal to zero.
The reaction situation is represented schematically by curve 1 in Figure 1.3. At equilib-
rium, we obtain from the well-known Arrhenius equation for reaction rates:
(1.15)
where A is the pre-exponential factor which contains the factor nF and in general also a factor
depending on the concentration [Ox] for the cathodic and [Red] for the anodic reaction.
When an electric potential difference or overvoltage of magnitude η V is applied between
the electrode and the solution relative to the equilibrium condition, the corresponding situation
is then represented by curve 2 in Figure 1.3. Because of the charge nF transferred in the
reaction, this means that the energy of the reacting species at the electrode is increased by
nFη. Now the activation enthalpies for the anodic and cathodic reaction are no longer equal
and have become, respectively: (∆G
0
act
– αnFη) and (∆G
0
act
+ (1 – α)nFη). Thus the current
densities are given by:
(1.16)
where α is usually called the symmetry factor. For the total current this gives:
(1.17)
FIGURE 1.3. Schematic of free enthalpy–distance curves at equilibrium and with an externally applied potential
+η V with respect to solution.
iiA GRT

ac act
=− = ⋅ −
()
exp ∆
0
iA G nFRT
iA G nFRT
a act
c act
=⋅ − −
()
()
=− ⋅ − + −
()
()
()
exp
exp
∆
∆
0
0
1
αη
αη
iiiifOx nFRTfd nFRT
total a c
=+=
[]
()

()
−
[]
()
−−
()
()
[]
0
1exp Re expαη α η
Copyright © 1997 by CRC Press, Inc.
The factors f([Ox]) and f([Red]) are the concentration-dependent factors mentioned above.
An equation of this form was originally derived by Butler and Volmer for the kinetics of the
hydrogen evolution reaction. Therefore it is called by many authors the “Butler–Volmer
equation,” even when other reactions are considered. Other authors prefer to use more general
names like “current–voltage equation” or “i–V-equation.” For a more complete treatment, see
Chapter 2, Section VIII of this handbook.
For an extensive treatment of electrode processes and electrodics for the case of solid
state electrochemistry, see Chapter 8 of this handbook.
REFERENCES
1. Kröger, F.A. and Vink, H.J., Solid State Phys. 3, 307, 1956.
Copyright © 1997 by CRC Press, Inc.

Chapter 2

PRINCIPLES OF ELECTROCHEMISTRY

Heinz Gerischer

CONTENTS

I. The Subject of Electrochemistry
II. Faraday’s Law and Electrolytic Conductivity
III. The Galvanic Cell at Thermodynamic Equilibrium
IV. Electrostatic Potentials: Galvani Potential, Volta Potential, Surface Potential
V. Electrochemical Equilibrium at Interfaces
VI. Standard Potentials and Electromotive Series
A. Reference Electrodes
B. Electromotive Series
VII. The Electric Double Layer at Interfaces
A. Metal/Electrolyte Interfaces
B. Semiconductor/Electrolyte Interfaces
C. Membrane/Electrolyte Interfaces
VIII. Kinetics of Electron Transfer Reactions at Interfaces
A. General Concepts of Electron Transfer
B. Electron Transfer at Metal Electrodes
C. Electron Transfer at Semiconductor Electrodes
IX. Kinetics of Ion Transfer Reactions at Interfaces
A. Liquid Metals
B. Solid Metals
C. Semiconductors
X. Techniques for the Investigation of Electrode Reaction Kinetics
A. Current and Potential Step
B. Impedance Spectroscopy
XI. Mechanisms of Electrode Reactions and Electrocatalysis
A. Hydrogen Electrode
B. Oxygen Electrode
C. General Remarks
Acknowledgment
References

8956ch02.fm Page 9 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.

I. THE SUBJECT OF ELECTROCHEMISTRY

Electrochemistry covers all phenomena in which a chemical change is the result of electric
forces and, vice versa, where an electric force is generated by chemical processes. It includes
the properties and behavior of electrolytic conductors in liquid or solid form. A great many
of these phenomena occur at interfaces between electronic and electrolytic conductors where
the passage of electric charge is connected with a chemical reaction, a so-called

redox
reaction

. The rate of such a reaction can be followed with great sensitivity as an electric
current. Such contacts constitute the electrodes of galvanic cells which can be used for the
conversion of chemical into electrical energy in the form of batteries or for the generation
of chemical products by electric power (electrolysis).
The properties of the electrodes are at the center of scientific interest. They qualitatively
and quantitatively control the electrochemical reactions in galvanic cells. The properties of
electrolytes are controlled by the concentrations of ions, their mobilities, and the interactions
between ionic particles of opposite charge as well as their interactions with other constituents
of the respective phases (e.g., solvent, membrane matrix, solid matrix). This latter area will,
however, not be dealt with in any detail in this chapter. Emphasis will be given to interfacial
processes. Since the basic laws of electrochemistry were developed in systems with liquid
electrolytes, these relations will be derived and presented in this introduction for such systems.

II. FARADAY’S LAW AND ELECTROLYTIC CONDUCTIVITY

Electrochemical experiments are performed in electrolysis cells which consist of two
electrodes in contact with an electrolyte. The electrodes are electronic conductors which can
be connected to a voltage source in order to drive an electric current through the electrolyte.
In the years 1833–1834, Faraday discovered that the chemical change resulting from the
current is proportional to the amount of electricity having passed through the cell and that
the mass of chemicals produced at the electrodes is in relation to their chemical equivalent:
(2.1)
where

m

is the number of chemical equivalents,

t

the time, F the Faraday constant, and

I

the
current (C · s

-1

). The value of the Faraday constant is F = 96,485 C/mole equivalent, corre-
sponding with the charge of 1 mole of electrons.
The electrolyte contains at least two types of ions with opposite charge. In liquids, all
ions are mobile and contribute to the conductivity. Their mobilities are, however, different,
and their individual contributions to the conductivity can therefore vary over wide ranges. In
solid electrolytes, often only one of the ions is mobile. The transference number, t

i

, charac-
terizes the contribution of each ion to the current in an electrolyte. The knowledge of t

i

for
all components i is therefore important for an understanding of electrolytic processes.
Cations move to the cathode, anions to the anode. If they are not consumed at the
respective electrode at the same rate as they arrive there by ionic migration, they accumulate
or deplete in front of this electrode, and the composition of the electrolyte changes in the
region close to both electrodes in opposite directions. Such changes in composition can be
used for the determination of transference numbers.
The specific conductivity of an electrolyte,

κ

(

Ω

–1

cm

–1

), is connected with the mobilities

of the ions,

u

i

(cm

2

s

–1

V

–1

) and their concentrations,

N

i

(mole cm

–3

), by the relation
(2.2)

dm
dt
I=⋅
1
F
κ= ⋅
()
∑
−−
F
i
zu N cm
ii i
Ω
11

8956ch02.fm Page 10 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.

The transference number of an ion j depends on the mobilities of the other ions
(2.3)
One can determine the individual mobilities,

u

j

, if the transference numbers,

t

i

, and the
concentrations of all mobile ions,

N

i

, are known.
The mobility of an ion is connected with its diffusion coefficient,

D

i

, by the Nernst–Einstein
relation
(2.4)
This diffusion coefficient describes only the self-diffusion of an ion in a homogeneous phase
(obtainable by tracer experiments). If a concentration gradient exists, as is often the case in
electrolyte solutions, the diffusion of all ions is balanced by their electrostatic interaction.
Potential gradients are generated between faster- and slower-moving ions (diffusion poten-
tials) which retard the first and accelerate the latter ions and lead to equal rates of diffusion.
The common diffusion coefficient of a binary salt at low concentration may be used here as
an example. This coefficient is connected to the individual mobilities by
(2.5)
where

z

+

and

z

–

are the charges of the ions and u

+

, u

–

their mobilities. For salt solutions of
higher concentration the relation is more complicated.

1

Ionic mobilities and diffusion coefficients vary with the composition of the respective
phase. In solutions they depend on the concentration and the solvent, in mixtures of salts on
the mole fraction. The interpretation of the properties of electrolytes is a special area of
electrochemistry,

2,3

which shall, however, not be discussed here in detail.
The properties of solid electrolytes are discussed more fully in Chapters 6 and 7 of this
handbook. They of course also get attention in many of the other chapters, in particular
Chapters 3 and 5, while interfacial phenomena are treated more extensively in Chapter 4.

III. THE GALVANIC CELL AT
THERMODYNAMIC EQUILIBRIUM

A galvanic cell can be used to measure the free energy difference of a chemical reaction
if this reaction can be performed in separate steps at two different electrodes. Examples are
the reactions
(2.6A)
(2.6B)
(2.6C)
t
zu
zu
j
jj
ii
i
=
∑
D
RT
z
u
i
i
i

=
()
−
F
.cm s
21
D
zz
zz
uu
uu
RT
±
+−
+−
+−
+−
=
+
⋅
⋅
⋅
+
⋅
F
2
HCl HCl
22
2+→
22

2
Ag Br AgBr+→
22
22 2
HO HO+→

8956ch02.fm Page 11 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.

Reaction (2.6A) can occur in the following steps at the electrodes I and III and in the
electrolyte II, as shown in Figure 2.1.
(2.6A

1

)
(2.6A

2

)
(2.6A

3

)
(2.6A

′

)
If these processes occur reversibly, as indicated in the reaction equations above, the result
is a voltage difference between the electrodes III and I which corresponds with the driving
force of the net reaction (2.6A

′

). The difference in the formulation of Equation (2.6A

′

) from
Equation (2.6A) is indicated by the appearance of the electrons on the two different electrodes
in the net reaction (2.6A

′

). The formation of two HCl molecules is connected with a transfer
of two electrons from phase III to phase I. We know from thermodynamics that the change
in free enthalpy (or Gibbs free energy)

∆

G

for Process (2.3A) is negative. In order to bring
Reaction (2.6A

′

) to equilibrium, this free enthalpy difference must be compensated by the
free enthalpy for the transfer of the corresponding amount of electric charge from phase III
to phase I. This is the energy –2 F

∆

V

per mole electrons. Consequently,
or:
(2.7)
This derivation demonstrates the general relation for the voltage of a galvanic cell,

∆

V

, in
which a chemical reaction with the driving force

∆

G

chem

has reached equilibrium by the
appropriate charge separation. This voltage is described by the Nernst equation for the
electromotive force (emf) of a galvanic cell at equilibrium:
(2.8)

FIGURE 2.1.

Phase scheme of a galvanic cell for the reaction H

2

+ Cl

2

2 HCl.
→
←
Electrode I : H H e
II II I2
22
,
→
←
+
+−
Electrode III : Cl e Cl
II III II2
22
,
+
→
←
−−

Electrolyte II: 2 2 2HCl HCl
II II II
+−
+
→
←
_______________________________
Net reaction : H Cl e HCl e
II II III II I22
222
,,
++
→
←
+
−−
−⋅ + =220F
HCl
∆∆VG
∆
∆
V
G
=−
HCl
F
.
∆
∆
V

G
z
chem
=−
F

8956ch02.fm Page 12 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.

where z is the number of charge equivalents needed for the formation of 1 mol of product.

∆

G

chem

depends on the concentrations (more exactly the activities

a

i

) of the reactants and
products. The equilibrium emf for the reactions (2.6A), (2.6B) and (2.6C) is therefore
(2.9)
(2.10)
(2.11)
In these equations the

∆

G

0

values are the free energy change of the respective reactions
when all participants are in their standard state with the activity

a

0

.*
For the cell (2.6B) the metal is in its standard state if it is pure. If the electrolyte is
saturated with AgBr, its activity is constant and the emf depends only on the activity of Br

2

.
The temperature dependence of the cell voltage is related to the entropy of the reactions.
This relation can be derived directly from Equation (2.8)
(2.12)
The reaction enthalpy is determined by
(2.13)
and the pressure dependence is expressed according to the thermodynamic relations
(2.14)
with

∆

v

the volume change in the reaction. From cell voltage measurements one can often
very precisely determine thermodynamic data of chemical reactions.

IV. ELECTROSTATIC POTENTIALS: GALVANI POTENTIAL,
VOLTA POTENTIAL, SURFACE POTENTIAL

While electric potential differences inside a homogeneous phase can be directly measured
by the work needed for moving an electrically charged probe from one point to another, this

*

a

0

is often set to one and is omitted in the thermodynamic equations. The formulation above should remind the
reader that the standard state can be defined arbitrarily and has to be stated in the thermodynamic data.
∆
∆
V
G
RT
a
a
a
a
a

a
A
=− +














HCl
H
H
Cl
Cl
HCl
HCl
FF
0
00 0
2
2
2

2
2
2
ln
∆
∆
V
G
RT
F
a
a
a
a
B
=− +















AgBr
Br
Br
AgBr
AgBr
F
0
00
2
2
2
2
ln
∆
∆
V
G
RT
a
a
a
a
a
a
C
=− +





















HO O
O
H
H
HO
HO
FF
22
2
2
2
2
2
0

00 0
2
24
ln
∂
∂
∂
∂
∆
∆
∆
V
Tz
G
Tz
S
p,n
chem
p,n
chem
j
j






=−







=
11
FF
∆∆ ∆ ∆
∆
HG SzVT
V
T
chem chem chem
p,n
j
=+ =−−















TF
∂
∂
∂
∂
∆
∆
V
pz
v
T,n
chem
j






=−
1
F

8956ch02.fm Page 13 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.

is not possible if the phase is inhomogeneous in composition and, in particular, if a phase
boundary has to be passed by this probe. The reason is that any probe is exposed not only
to the influence of an electric field, but also to a chemical interaction with the surrounding

matter. If this interaction varies, its variation contributes to the work for the movement of
the probe between two locations. This contribution can be small in single phases with variable
composition; it is, however, of extreme importance for the transfer of a charged particle
through a phase boundary. What can be measured is only the combination of chemical and
electric forces to which a charged particle is exposed. This combination can be represented
by the

electrochemical potential

,

i

,
(2.15)
where µ

i

is the chemical potential in its usual definition:
µ

i

= (

∂

G

/

∂

n

i

)

T,p ,n

j



≠

n

i

(2.16)
for a single phase. The definition of

i

, is, accordingly,
(2.17)
where

ϕ

is the Galvani potential. Any measurement of work for the transfer of a particle with
the charge

z

i

to another phase is a determination of
(2.18)
For a neutral salt the electrical term is canceled in the sum of anions and cations, and
one obtains the chemical potential of the salt. Distribution of a neutral salt between two
different solvents only requires that at equilibrium the chemical potentials become equal,
although electric potential differences may exist at the interface.
Equilibrium at an interface requires, for all charged species which can pass the phase
boundary, that

∆

i

is zero or
(2.19)
where

z

i

has the sign of the charge of the species. At the contact between two different metals,
a contact potential,

∆ϕ

, arising from the different chemical potentials of the electrons in these
metals is generated. Balance of

∆

i

between the two metals requires an excess of electrons
on the phase with the lower chemical potential and a corresponding loss of electrons on the
other side of the contact. This is illustrated in Figure 2.2.
The real measurement of a voltage difference between two electrodes, as in Figure 2.1,
occurs between electronic conductors of equal composition. If the electrodes I and III of
Figure 2.1 are different metals, a contact between metals I and III has to be made on the
other side, and the potential difference would be determined between the open ends of the
same metal.
The reason for the appearance of a Galvani potential difference at the contact between
two phases is not only the accumulation of electric charge of opposite sign at both sides of
˜
µ
˜
µ=µ+
iii
zFϕ
˜

µ
ƒ
µ=






+
≠
i
i
T,p, ,n n
G
n
ji
∂
∂
ϕ
ϕ
F
∆
˜˜˜
µ= µ−µ= µ−µ+ −
()
iIIiIiIIiIi i II I
z F ϕϕ
˜
µ

ϕϕ
II I
II i I i
i
z
−=
µ−µ
F
˜
µ
8956ch02.fm Page 14 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.
an interface; it is also due to the formation of dipole layers in one or both phases directly at
the contact. Polar molecules of the solvent of an electrolyte can be oriented, e.g., by interaction
with a metal surface, and form a dipole layer at the interface. Chemisorption of one type of
ion at the surface of the contacting phase can also result in a dipole layer if the counter ions
remain at a larger distance from the contact. Dipole layers exist on the surface of metals in
contact with vacuum, because the kinetic energy of the electrons in the conduction band
allows the electrons to extend somewhat beyond the last row of positive nuclei of a crystal.
The size of this effect depends on the surface structure and its orientation with respect to the
crystal. One sees this in work function measurements and the so-called Volta potentials above
different surfaces in vacuum or inert gases.
4
Volta potential differences are determined by the work required for moving an electrically
charged probe in vacuum or in an inert gas from one point close to the surface of a condensed
phase I to a point close to the surface of another phase II. The distance of the probe from
the surface should be large enough that all chemical interaction and the effect of electric
polarization (image force) can be neglected. This situation is illustrated for a contact between
two metals in vacuum in Figure 2.3.
The probe may be an electron which shall be moved from point a to point b in Figure 2.3.

The same energy will be required if the probe is moved from point a through the surface of
phase I, through the contact between phase I and phase II, and from there through the surface
of phase II to point b. At the contact we have equilibrium and need no work for the transfer
of the electron between I and II. With the introduction of the electron from point a into
phase I, we gain the chemical binding energy,
I
µ
e–
, and the electrical work for the passage
of the surface dipole layer, –F χ
I
. The passage through the surface of phase II to point b
requires the work to overcome the binding energy
II
µ
e–
and the electrostatic work for passing
the dipole layer F χ
II
. The result yields the definition of the Volta potential difference, ∆ψ,
(2.20)
FIGURE 2.2. Formation of a contact potential between two metals.
FIGURE 2.3. Origin of Volta potential differences between two metals.
∆Gba
ab IIe
–
Ie II I II I
–
→
=µ −µ + −

()
=−
()
−
()
()
FFχχ ψ ψ
8956ch02.fm Page 15 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.
Here, χ is the so-called surface potential corresponding with the electrostatic potential
step resulting from the inhomogeneous charge distribution on the surface. This surface dipole
can be calculated for metals on the basis of more or less refined theories and depends very
much on the band structure. In order to get some idea of the possible size of such surface
potentials, one should realize that a layer of water molecules with each molecule oriented
perpendicular to an atom of a surface with 10
15
atoms per square centimeter would correspond
with a χ potential of about 3.8 V.
Since
II
µ
e–
–
I
µ
e–
= F(ϕ
II
– ϕ
I

), Equation (2.20) yields the connection between the Volta
potential difference between two points in front of different surfaces in vacuum and the terms
∆ϕ and ∆χ
(2.21)
The surface dipole layer is also essential for the measurement of the work function, which
is the energy required to remove an electron from a state in the conduction band where the
probability of occupation by an electron is one half, the Fermi energy, E
F
, into vacuum. Since
the electron has to pass the surface dipole layer in this process, the work function φ is defined
by
(2.22)
where N
A
is Avogadro’s number and e
0
the electron charge, since φ is usually determined in
electron volts.
On metal surfaces χ is negative and, therefore, N
A
× φ is usually larger than – . The
work function can be obtained from photoelectron emission experiments
5
or in relative terms
with the Kelvin method.
6
All such measurements determine the energy to take an electron
from the Fermi energy in the bulk to a position in front of the surface where the chemical
and image force interaction has disappeared, but sufficiently close that the influence of the
surface dipole layer can be considered as the effect of a layer of infinite extension. If one

could measure the energy for the transfer of the electron from the bulk of a closed body to
a point in vacuum at infinite distance where the dipole layer around the body would no longer
affect the energy, one could directly measure . This is indicated in Figure 2.4 for a spherical
body, but, unfortunately, such an experiment cannot be performed.
V. ELECTROCHEMICAL EQUILIBRIUM AT INTERFACES
The simplest electrode reactions are those in which either an ion passes the interface
between an electrolyte and a metal and is incorporated into the metal together with the uptake
of electrons, or in which only the electron passes the interface from an electron donor in the
electrolyte to the metal or from the metal to an electron acceptor. The first case occurs at the
silver electrode of Process (2.6B), the other case occurs in some steps of the electrode
reactions of the Processes (2.6A), (2.6B), and (2.6C). The latter reactions are more complex
and will therefore be discussed later. Instead, the simple redox reaction Ox
+
+ e
–
= Red shall
be used here as an example for the second case.
Equilibrium for the electrode reaction with ion transfer through the interface
(2.23)
where I is the metal phase and II the electrolyte, requires
∆∆∆ψϕχ=+
φχ=−
µ
−
e
A
–
N
e
0

0
µ
e
–
0
µ
e
–
0
MMze
III
z
I
→
←
+
+−
8956ch02.fm Page 16 Monday, October 11, 2004 1:49 PM
Copyright © 1997 by CRC Press, Inc.