koro 5 chap one

CHEMICAL SENSORS

SIMULATION AND MODELING

VOLUME 5: ELECTROCHEMICAL SENSORS

CHEMICAL SENSORS

SIMULATION AND MODELING

VOLUME 5: ELECTROCHEMICAL SENSORS

EDITED BYGHENADII KOROTCENKOV

GWANGJU INSTITUTE OF SCIENCE AND TECHNOLOGYGWANGJU, REPUBLIC OF KOREA

MOMENTUM PRESS, LLC, NEW YORK

Chemical Sensors: Simulation and Modeling Volume 5: Electrochemical SensorsCopyright © Momentum Press®, LLC, 2013

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording or any other—except for brief quotations, not to exceed 400 words, without the prior permission of the publisher.

First published by Momentum Press®, LLC222 East 46th Street, New York, NY 10017www.momentumpress.net

ISBN-13: 978-1-60650-596-0 (hard back, case bound)ISBN-10: 1-60650-596-3 (hard back, case bound)ISBN-13: 978-1-60650-598-4 (e-book)ISBN-10: 1-60650-598-X (e-book)DOI: 10.5643/9781606505984

Cover design by Jonathan PennellInterior design by Derryfi eld Publishing, LLC

10 9 8 7 6 5 4 3 2 1

Printed in the United States of America

v

CONTENTS

PREFACE xiii

ABOUT THE EDITOR xvii

CONTRIBUTORS xix

PART 1: SOLID-STATE ELECTROCHEMICAL SENSORS

1 SURFACE AND INTERFACE DEFECTS IN IONIC CRYSTALS 3N. F. Uvarov

1 Introduction 31.1 Solid Electrolytes and Electrodes for Electrochemical Sensors:

A Brief Overview 31.2 Surface and Interface Properties of Ionic Solids 6

2 Calculation of the Surface Potential and Surface Defects Using the Stern Model 8

2.1 Description of the Model 82.2 Pure Crystals of the NaCl Type 102.3 Surface Potential in NaCl Crystals Containing Divalent Cations 132.4 Comparison with Experimental Data 152.5 Surface Potential and Concentration of Point Defects on Grain

Boundaries of Superionic Oxide Ceramics 152.6 Surface Disorder in Terms of Energy Diagrams 232.7 Defects on Interfaces 25

3 Size Effects in Nanocomposite Solid Electrolytes 29

4 Applications in Sensors 30

5 Conclusions 34

References 34

vi CONTENTS

2 SOLID-STATE ELECTROCHEMICAL GAS SENSORS 41C. O. ParkI. LeeD. R. LeeJ. W. FergusN. MiuraH. J. Yoo

1 Introduction 41

2 Electrode Potentials 42

3 Types of Electrochemical Sensors 463.1 Equilibrium Potentiometric Sensors 463.2 Mixed Potentiometric Sensors 493.3 Amperometric Sensors 53

4 Applications 574.1 Oxygen Sensors 574.2 Carbon Dioxide Sensors 644.3 NOx Sensors 664.4 SOx Sensors 764.5 Hydrogen Sensors 77

Acknowledgments 86

References 86

PART 2: ELECTROCHEMICAL SENSORS FOR LIQUID ENVIRONMENTS

3 MODELING AND SIMULATION OF IONIC TRANSPORT PROCESSES THROUGH IDEAL ION-EXCHANGE MEMBRANE SYSTEMS 95

A. A. Moya

1 Introduction 95

2 Theoretical Description 982.1 Ionic Transport in Ideal Ion-Exchange Membrane Systems 982.2 Electric Current Perturbations 1012.3 Analytical Solutions 102

3 The Network Model 106

4 Network Simulation 1084.1 Transient Response 1094.2 Electrochemical Impedance 113

5 Conclusion 121

Nomenclature 122

CONTENTS vii

Appendix 123

Acknowledgments 124

References 124

4 MECHANISM OF POTENTIAL DEVELOPMENT FOR POTENTIOMETRIC SENSORS, BASED ON MODELING OF INTERACTION BETWEEN ELECTROCHEMICALLY ACTIVE COMPOUNDS FROM THE MEMBRANE AND ANALYTE 131

R.-I. Stefan-van Staden

1 Introduction 131

2 The Membrane–Solution Interface 132

3 Membrane Confi guration 132

4 New Theoretical Model for Potential Development Based on Membrane Equilibria 133

5 Mechanism of the Potential Development 134

6 Modeling—A Theoretical Approach to Predict the Response and Mechanism of Potential Development 137

7 Selectivity of Potentiometric Sensors: Explanation through Membrane Equilibria 149

7.1 Infl uence of the Composition of the Membrane on the Selectivity of Potentiometric Sensors 150

8 Conclusions 151

References 152

5 COMPUTER MODELING OF THE POTENTIOMETRIC RESPONSE OF ION-SELECTIVE ELECTRODES WITH IONOPHORE-BASED MEMBRANES 155

K. N. Mikhelson

1 Introduction 155

2 Physical Models of Ionophore-Based Membranes 1582.1 Levels of ISE Membrane Modeling 1582.2 One-Dimensional Approach to ISE Membrane Modeling 1602.3 Segmented Model of the ISE Membrane 1612.4 Integral Model of the ISE Membrane 164

3 Computer Modeling for the Phase Boundary Theory 1663.1 Description of the ISE Response in Mixed Solutions

Containing Differently Charged Ions 1663.2 Description of Apparently Non-Nernstian Response Slopes

of Ion-Selective Electrodes 168

viii CONTENTS

4 Modeling Using the Multispecies Approximation 1704.1 The Essence of the Multispecies Approximation 1704.2 System of Equations for Implementation of the Multispecies

Model 1714.3 Selected Results of Modeling Using the Multispecies

Approximation 1745 Diffusion Layer Model: Example of Local Equilibrium Modeling 179

6 Advanced Nonequilibrium Modeling in Real Time and Space 181

7 Conclusions 194

Acknowledgments 194

References 195

6 MODELS OF RESPONSE IN MIXED-ION SOLUTIONS FOR ION-SENSITIVE FIELD-EFFECT TRANSISTORS 201

Sergio Bermejo

1 Introduction 201

2 ISFET Basics 2022.1 Principles of Electrochemical Operation 2022.2 Structures and Materials 206

3 Electrochemical Models 2113.1 The Metal–Solution Junction 2113.2 The Oxide–Solution Junction 2193.3 Membrane-Based ISFETs 2253.4 A General Approach for ISFET Modeling in Mixed-Ion Solutions 232

4 Conclusions 242

Appendix: SPICE Models 242

References 243

PART 3: ELECTROCHEMICAL BIOSENSORS

7 NANOMATERIAL-BASED ELECTROCHEMICAL BIOSENSORS 251N. Jaffrezic-Renault

1 Introduction 251

2 Nanomaterials: Fabrication, Chemical and Physical Properties 2522.1 Conducting Nanomaterials 2522.2 Nonconducting Nanomaterials: Magnetic Nanoparticles 254

CONTENTS ix

3 Conception and Modeling of Amplifi cation Effect in Nanomaterial-Based Enzyme Sensors 255

3.1 AuNPs-Based Amperometric Sensors 2553.2 CNT-Based Amperometric Sensors 2583.3 MNP-Based Amperometric Biosensors 2623.4 Potentiometric Sensors 2653.5 Conductometric and Impedimetric Biosensors 265

4 Conception and Modeling of Amplifi cation Effect in Nanomaterial-Based Immunosensors 267

4.1 AuNP-Based Amperometric Immunosensors 2674.2 AuNP-Based Potentiometric Sensors 2724.3 Impedimetric Sensors 2734.4 Conductometric Sensors 276

5 Conception and Modeling of Amplifi cation Effect in Nanomaterial-Based DNA Biosensors 277

5.1 Amperometric Sensors 2775.2 Impedimetric Sensors 283

6 Conclusion 284

References 285

8 ION-SENSITIVE FIELD-EFFECT TRANSISTORS WITH NANOSTRUCTURED CHANNELS AND NANOPARTICLE-MODIFIED GATE SURFACES: THEORY, MODELING, AND ANALYSIS 295

V. K. Khanna

1 Introduction 295

2 Structural Confi gurations of the Nanoscale ISFET 2972.1 The Nanoporous Silicon ISFET 2972.2 The CNT ISFET 2982.3 The Si-NW ISFET 299

3 Physics of the Si-NW Biosensor 2993.1 Basic Principle 2993.2 Analogy with the Nanocantilever 3003.3 Preliminary Analysis of Micro-ISFET Downscaling to

Nano-ISFET 3013.4 Single-Gate and Dual-Gate Nanowire Sensors 3043.5 Energy-Band Model of the NW Sensor 305

4 Nair-Alam Model of Si-NW Biosensors 3074.1 The Three Regions in the Biosensor 3074.2 Computational Approach 308

x CONTENTS

4.3 Effect of Nanowire Diameter (d ) on Sensitivity at Different Doping Densities, with Air as the Surrounding Medium 310

4.4 Effect of Nanowire Length (L ) on Sensitivity at Different Doping Densities, with Air as the Surrounding Medium 310

4.5 Effect of the Fluidic Environment 3104.6 Overall Model Implications 315

5 pH Response of Silicon Nanowires in Terms of the Site-Binding and Gouy-Chapman-Stern Models 316

6 Subthreshold Regime as the Optimal Sensitivity Regime of Nanowire Biosensors 321

7 Effective Capacitance Model for Apparent Surpassing of the Nernst Limit by Sensitivity of the Dual-Gate NW Sensor 324

8 Tunnel Field-Effect Transistor Concept 326

9 Role of Nanoparticles in ISFET Gate Functionalization 3289.1 Supportive Role of Nanoparticles 3289.2 Direct Reactant Role of Nanoparticles 330

10 Neuron-CNT (Carbon Nanotube) ISFET Junction Modeling 332

11 Conclusions and Perspectives 334

Dedication 335

Acknowledgments 335

References 335

9 BIOSENSORS: MODELING AND SIMULATION OF DIFFUSION-LIMITED PROCESSES 339

L. Rajendran

1 Introduction 3391.1 Enzyme Kinetics 3391.2 Basic Scheme of Biosensors 3401.3 The Nonlinear Reaction-Diffusion Equation and Biosensors 3401.4 Types of Biosensors 3421.5 Michaelis-Menten Kinetics 3431.6 Non–Michaelis-Menten Kinetics 3431.7 Importance of Modeling and Simulation of Biosensors 344

2 Modeling of Biosensors 3452.1 Michaelis-Menten Kinetics and Potentiometric Biosensors 3452.2 Michaelis-Menten Kinetics and Amperometric Biosensors 3462.3 Michaelis-Menten Kinetics and Amperometric Biosensors

for Immobilizing Enzymes 348

CONTENTS xi

2.4 Michaelis-Menten Kinetics and the Two-Substrate Model 3492.5 Non–Michaelis-Menten Kinetics 3532.6 Other Enzyme Reaction Mechanisms 3562.7 Kinetics of Enzyme Action 3612.8 Trienzyme Biosensor 362

3 Microdisk Biosensors 3633.1 Introduction 3633.2 Mathematical Formulation of the Problem 3643.3 First-Order Catalytic Kinetics 3663.4 Zero-Order Catalytic Kinetics 3703.5 For All Values of KM 3723.6 Conclusions 373

4 Microcylinder Biosensors 3734.1 Introduction 3734.2 Mathematical Formulation of the Problem 3744.3 Analytical Solutions of the Concentrations and Current 3764.4 Comparison with Limiting Case of Rijiravanich’s Work 3784.5 Discussion 3794.6 Conclusions 3814.7 PPO-Modifi ed Microcylinder Biosensors 382

5 Spherical Biosensors 3835.1 Simple Michaelis-Menten and Product Competitive

Inhibition Kinetics 3835.2 Immobilized Enzyme for Spherical Biosensors 3855.3 Conclusion 386

Appendix: Various Analytical Schemes for Solving Nonlinear Reaction Diffusion Equations 386

A. Basic Concept of the Variational Iteration Method 386 B. Basic Concept of the Homotopy Perturbation Method 387 C. Basic Concept of the Homotopy Analysis Method 388 D. Basic Concept of the Adomian Decomposition Method 391

References 392

INDEX 399

xiii

PREFACE

This series, Chemical Sensors: Simulation and Modeling, is the perfect comple-ment to Momentum Press’s six-volume reference series, Chemical Sensors: Fundamentals of Sensing Materials and Chemical Sensors: Comprehensive Sensor Technologies, which present detailed information about materials, technologies, fabrication, and applications of various devices for chemical sensing. Chemical sensors are integral to the automation of myriad industrial processes and every-day monitoring of such activities as public safety, engine performance, medical therapeutics, and many more.

Despite the large number of chemical sensors already on the market, selec-tion and design of a suitable sensor for a new application is a diffi cult task for the design engineer. Careful selection of the sensing material, sensor platform, technology of synthesis or deposition of sensitive materials, appropriate coatings and membranes, and the sampling system is very important, because those deci-sions can determine the specifi city, sensitivity, response time, and stability of the fi nal device. Selective functionalization of the sensor is also critical to achieving the required operating parameters. Therefore, in designing a chemical sensor, de-velopers have to answer the enormous questions related to properties of sensing materials and their functioning in various environments. This fi ve-volume com-prehensive reference work analyzes approaches used for computer simulation and modeling in various fi elds of chemical sensing and discusses various phenomena important for chemical sensing, such as surface diffusion, adsorption, surface reactions, sintering, conductivity, mass transport, interphase inter actions, etc. In these volumes it is shown that theoretical modeling and simulation of the pro-cesses, being a basic for chemical sensor operation, can provide considerable assistance in choosing both optimal materials and optimal confi gurations of sensing elements for use in chemical sensors. The theoretical simulation and model ing of sensing material behavior during interactions with gases and liquid surroundings can promote understanding of the nature of effects responsible for high effectiveness of chemical sensors operation as well. Nevertheless, we have to understand that only very a few aspects of chemistry can be computed exactly.

xiv PREFACE

However, just as not all spectra are perfectly resolved, often a qualitative or ap-proximate computation can give useful insight into the chemistry of studied phe-nomena. For example, the modeling of surface-molecule interactions, which can lead to changes in the basic properties of sensing materials, can show how these steps are linked with the macroscopic parameters describing the sensor response. Using quantum mechanics calculations, it is possible to determine parameters of the energetic (electronic) levels of the surface, both inherent ones and those introduced by adsorbed species, adsorption complexes, the precursor state, etc. Statistical thermodynamics and kinetics can allow one to link those calculated surface parameters with surface coverage of adsorbed species corresponding to real experimental conditions (dependent on temperature, pressure, etc.). Finally, phenomenological modeling can tie together theoretically calculated characteris-tics with real sensor parameters. This modeling may include modeling of hot plat-forms, modern approaches to the study of sensing effects, modeling of processes responsible for chemical sensing, phenomenological modeling of operating char-acteristics of chemical sensors, etc.. In addition, it is necessary to recognize that in many cases researchers are in urgent need of theory, since many experimental observations, particularly in such fi elds as optical and electron spectroscopy, can hardly be interpreted correctly without applying detailed theoretical calculations.

Each modeling and simulation volume in the present series reviews model-ing principles and approaches particular to specifi c groups of materials and de-vices applied for chemical sensing. Volume 1: Microstructural Characterization and Modeling of Metal Oxides covers microstructural characterization using scanning electron microscopy (SEM), transmission electron spectroscopy (TEM), Raman spectroscopy, in-situ high-temperature SEM, and multiscale atomistic simulation and modeling of metal oxides, including surface state, stability, and metal oxide interactions with gas molecules, water, and metals. Volume 2: Conductometric-Type Sensors covers phenomenological modeling and computational design of conductometric chemical sensors based on nanostructured materials such as metal oxides, carbon nanotubes, and graphenes. This volume includes an over-view of the approaches used to quantitatively evaluate characteristics of sensitive structures in which electric charge transport depends on the interaction between the surfaces of the structures and chemical compounds in the surroundings. Volume 3: Solid-State Devices covers phenomenological and molecular model-ing of processes which control sensing characteristics and parameters of various solid-state chemical sensors, including surface acoustic wave, metal-insulator-semiconductor (MIS), microcantilever, thermoelectric-based devices, and sensor arrays intended for “electronic nose” design. Modeling of nanomaterials and nano-systems that show promise for solid-state chemical sensor design is analyzed as well. Volume 4: Optical Sensors covers approaches used for modeling and simu-lation of various types of optical sensors such as fi ber optic, surface plasmon resonance, Fabry-Pérot interferometers, transmittance in the mid-infrared region,

PREFACE xv

luminescence-based devices, etc. Approaches used for design and optimization of optical systems aimed for both remote gas sensing and gas analysis cham-bers for the nondispersive infrared (NDIR) spectral range are discussed as well. A description of multiscale atomistic simulation of hierarchical nanostructured materials for optical chemical sensing is also included in this volume. Volume 5: Electrochemical Sensors covers modeling and simulation of electrochemical pro-cesses in both solid and liquid electrolytes, including charge separation and transport (gas diffusion, ion diffusion) in membranes, proton–electron transfers, electrode reactions, etc. Various models used to describe electrochemical sensors such as potentiometric, amperometric, conductometric, impedimetric, and ion-sensitive FET sensors are discussed as well.

I believe that this series will be of interest of all who work or plan to work in the fi eld of chemical sensor design. The chapters in this series have been prepared by well-known persons with high qualifi cation in their fi elds and therefore should be a signifi cant and insightful source of valuable information for engineers and researchers who are either entering these fi elds for the fi rst time, or who are al-ready conducting research in these areas but wish to extend their knowledge in the fi eld of chemical sensors and computational chemistry. This series will also be interesting for university students, post-docs, and professors in material science, analytical chemistry, computational chemistry, physics of semiconductor devices, chemical engineering, etc. I believe that all of them will fi nd useful information in these volumes.

G. Korotcenkov

xvii

ABOUT THE EDITOR

Ghenadii Korotcenkov received his Ph.D. in Physics and Technology of Semiconductor Materials and Devices in 1976, and his Habilitate Degree (Dr.Sci.) in Physics and Mathematics of Semiconductors and Dielectrics in 1990. For a long time he was a leader of the scientifi c Gas Sensor Group and manager of various national and international scientifi c and engineering projects carried out in the Laboratory of Micro- and Optoelectronics, Technical University of Moldova. Currently, Dr. Korotcenkov is a research professor at the Gwangju Institute of Science and Technology, Republic of Korea.

Specialists from the former Soviet Union know Dr. Korotcenkov’s research results in the fi eld of study of Schottky barriers, MOS structures, native oxides, and photoreceivers based on Group III–V compounds very well. His current research interests include materials science and surface science, focused on nanostructured metal oxides and solid-state gas sensor design. Dr. Korotcenkov is the author or editor of 11 books and special issues, 11 invited review papers, 17 book chapters, and more than 190 peer-reviewed articles. He holds 18 patents, and he has presented more than 200 reports at national and international conferences.

Dr. Korotcenkov’s research activities have been honored by an Award of the Supreme Council of Science and Advanced Technology of the Republic of Moldova (2004), The Prize of the Presidents of the Ukrainian, Belarus, and Moldovan Academies of Sciences (2003), Senior Research Excellence Awards from the Technical University of Moldova (2001, 2003, 2005), a fellowship from the International Research Exchange Board (1998), and the National Youth Prize of the Republic of Moldova (1980), among others.

xix

CONTRIBUTORS

Nikolai F. Uvarov (Chapter 1)Institute of Solid State Chemistry and Mechanochemistry Siberian Branch of the Russian Academy of SciencesNovosibirsk 630128, Russia

Chongook Park (Chapter 2)Department of Materials Science & EngineeringKAISTDae-jeon 305-701, South Korea

Inkun Lee (Chapter 2)Department of Materials Science & EngineeringKAISTDae-jeon 305-701, South Korea

Dearo Lee (Chapter 2)Department of Materials Science & EngineeringKAISTDae-jeon 305-701, South Korea

Jeffrey Fergus (Chapter 2)Materials Research and Education CenterAuburn UniversityAuburn, Alabama 36849-5341, USA

Norio Miura (Chapter 2)Art, Science and Technology Center for Cooperative Research Kyushu UniversityFukuoka 816-8580, Japan

xx CONTRIBUTORS

Hyungjun Yoo (Chapter 2)Department of Electrical Engineering KAISTDae-jeon 305-701, South Korea

Antonio Ángel Moya Molina (Chapter 3)Departamento de Física Universidad de Jaén, Campus de las LagunillasJaén 23071, Spain

Raluca-Ioana Stefan-van Staden (Chapter 4)Laboratory of Electrochemistry and PATLAB BucharestNational Institute of Research for Electrochemistry and Condensed Matter Bucharest 060021, Romania

Konstantin N. Mikhelson (Chapter 5)Ionometry Laboratory, Chemical FacultySt. Petersburg State UniversitySt. Petersburg, Russia

Sergio Bermejo (Chapter 6)Department of Electronic Engineering Universitat Politècnica de Catalunya (UPC) Barcelona 08034, Spain

Nicole Jaffrezic-Renault (Chapter 7)Institute of Analytical Chemistry, UMR CNRS 5280Claude Bernard University Lyon 1Villeurbanne 69100, France

Vinod Kumar Khanna (Chapter 8)MEMS & Microsensors CSIR—Central Electronics Engineering Research Institute Pilani 333031 (Rajasthan), India

L. Rajendran (Chapter 9)Department of MathematicsThe Madura College (Autonomous)Madurai 625011, Tamil Nadu, South India

PART 1

SOLID-STATE ELECTROCHEMICAL SENSORS

3DOI: 10.5643/9781606505984/ch1

CHAPTER 1

SURFACE AND INTERFACE DEFECTS IN IONIC CRYSTALS

N. F. Uvarov

1. INTRODUCTION

1.1. SOLID ELECTROLYTES AND ELECTRODES FOR ELECTROCHEMICAL SENSORS: A BRIEF OVERWIEW

Among all known gas sensors, electrochemical sensors are the most compact, economical, and suitable for developing gas-sensing devices. They have wide appli cation for control of air quality and impurity concentration in biotechnology, medical, brewing technologies, and in various industrial, chemical, and biologi-cal processes. The action of electrochemical sensors is based on clearly known fundamental principles, and they are reliable and easily calibrated. Solid-state electrochemical gas sensors exhibit some outstanding properties which makes them of special ineterst for applications. A prime example is yttria-stabilized zir-conia potentiometric sensors used to control the air-to-fuel ratio in automobile engines. These sensors contain all-solid-state electrochemical components; they are extremely robust and operate for a long time even after exposure to tempera-tures as high as 1000°C. There are two main types of electrochemical gas sensors: potentiometric and amperometric ones. The fi rst type operate as concentration or chemical cells; with the second type one measures the electrical current value

4 CHEMICAL SENSORS – SIMULATION AND MODELING: VOLUME 5

through the cell as a function of the concentration of the gas to be analyzed. In all cases the electrochemical cell includes two metallic or semiconducting sensitive electrodes and a solid electrolyte in between.

Solid electrolytes are necessary components of electrochemical sensors. Solid electrolytes with conductivity higher than 10−3 S/cm are classifi ed as superionic conductors. By conductivity level, superionic conductors are close to molten salts. However, in contrast to the latter, they have unipolar conductivity. The high ionic conductivity of superionic conductors is due to a high concentration of point defects, vacancies or interstitial ions, in one of the sublattices of the ionic compound. The defects may be structurally ordered or distributed randomly, resulting in “sublattice melting.” At present there are known many superionic conductors which exhibit conductivity via various cations (H+, Li+, Na+, Ag+) or anions (F−, O2−, S2−) (Hangenmuller and Van Gool 1978; Chebotin and Perfi liev 1978; Salamon 1979; Vashishta et al. 1979; Chandra 1981; Takahashi 1989; Hull 2004; Thangadurai and Weppner 2006; Ishihara 2009). A general strategy to create new superionic compounds and to control their transport properties is to search for suitable host phases and then dope them with aliovalent ions in order to increase the concentration of extrinsic defects. This approach traditional works fairly for some host crystal lattices which are capable of carrying solute at tens of mole percent defects without global structural reconstruction. As a rule, such compounds have structurally disordered high-temperature phases, and doping allows one to stabilize them at low temperatures. Examples of such structures are -AgI, -Li3PO4, -Li4SiO4, perovskites, fl uorites, tysonites, pyrochlores, and structures related to them (Hull 2004). The most widely used solid oxygen-ion conductor, yttria-stabilized zirconia (YSZ), has a fl uorite structure containing 5–10 mol% anionic vacancies in the oxygen sublattice. The situation with proton solid conductors is more complicated. High-temperature proton conductors (with the range of high conductivity of 700–1000 K) may be obtained by dissolution of water or hydrogen in some acceptor-doped perovskite-related oxides contain-ing oxygen vacancies, e.g., BaCeO3, BaZrO3, etc. (Kreuer 2003; Norby 2009). In low-temperature proton conductors (stable below 400 K), conductivity is due to the presence of hydrate water in the crystal structure. There is a special class of intermediate-temperature proton conductors including acid salts such as CsHSO4, CsH2PO4, etc., which have high proton conductivity in high-temperature phases (at 400–500 K) with dynamical disorder of hydrogen bonds in the anionic sublattice (Haile 2001; Ponomareva 2011).

The choice of solid electrolyte for use in the sensor is determined by a particu-lar mechanism of electrode processes taking place on the electrodes. The main types of electrode processes which may proceed in gas sensors are reported else-where (Fabry and Siebert 1997; Park et al. 2003; Bhoga and Singh 2007). For sta-ble operation of the sensor, it is preferable if gas species to be detected participate in an electrode reaction with an ionic species presenting in a solid electrolyte. As

SURFACE AND INTERFACE DEFECTS IN IONIC CRYSTALS 5

a result, in potentiometric sensors, equilibrium is established between gas species and ionic species. In amperometric sensors, the electrode reactions proceed in stationary mode, providing steady current from one electrode to another through the solid electrolyte. For example, oxygen-containing molecules can be easily oxi-dized (hydrocarbons, CO, N2O, NO, SO2, etc.) or reduced (O2, H2O, CO2, N2O, NO, etc.) electrochemically on electrodes in the cell with solid oxide electrolytes. These reactions are complex and include several preliminary stages such as adsorption, dissociation, diffusion, or formation of intermediates (Chebotin and Perfi liev 1978; Verkerk et al. 1983; Adler 2004; Sunarso et al. 2008). This is why the kinetics and specifi c mechanism of summary electrode reactions depend mostly on the chemi-cal nature and morphology of the electrode material.

To control gas-sensing properties of electrochemical sensors, semiconduct-ing oxide electrodes may be used instead of traditional metallic electrodes such as Pt or Pd. Using standard approaches of defects chemistry, one can control the nonstoichiometry of oxides, dominating related physical and chemical properties, including electrical conductivity and catalytic activity (Kröger 1964; Schoonman 1997; Tuller 2003). It is important that the oxide electrode have high ionic con-ductivity together with electronic conductivity. The use of such mixed electronic-ionic conductors (MIECs) as electrodes leads to a strong extension of the triple electrode boundary (gas–electrode–electrolyte) up to full surface of solid electro-lyte. This results in a strong decrease in the specifi c surface resistance of the electrode and, in the case of a solid oxide fuel cell, enhances the specifi c current and power values of the cell. In the case of gas sensors, the use of MIECs offers a possibility to vary the catalytic properties of the electrode material (Adler 2004), control the rate of a particular chemical stage of the process, and achieve higher selectivity of the sensors toward detection of a given gas.

Solid electrolytes and electrode materials are usually prepared in polycrystal-line form and contain a large number of grain boundaries. These planar defects can be electrically active, resulting in the blocking of charge carriers. This ef-fect is attributed to depletion of charge carriers resulting from the compensation of electrically charged grain boundary cores by adjacent space charge regions of opposite charge. Depending on the charge of the grain boundary core, defect concentrations of one type can be dramatically depressed, whereas others are dramatically enhanced. Solid electrolytes should be sintered at high tempera-tures to diminish the contribution of grain boundaries to overall resistivity of the electrolyte. In nanocrystalline solids, the grain size is less than the space charge length. This can lead to size effects, when properties of the solid differ dra-matically from those exhibited by materials with identical composition but with larger grains or wider fi lm spacings. Similarly, thin fi lms are susceptible to the chemi sorption of gaseous species and the consequent depletion or accumulation of charge carriers in the fi lm. Such phenomena are important for the design and operation of semiconducting oxide gas sensors. Thus, the infl uence of surface-


and interface- related defects on the transport properties of ionic conductors and oxide-conducting materials is an area of growing interest.

1.2. SURFACE AND INTERFACE PROPERTIES OF IONIC SOLIDS

Surface or interfacial phenomena play an important role in solid-state ionics. Space charge regions formed by point defects and impurity ions localized on the crystal surfaces or grain boundaries strongly infl uence the transport properties of real ceramic materials and contribute to the electrode polarization. The sur-face potential value depends on adsorption of the gaseous species and therefore strongly infl uences the sensitivity and selectivity of gas sensors.

According to the model of Frenkel and Kliever (FK model) (Frenkel 1946; Grimley 1950; Kliever and Koehler 1965a, 1965b), the surface potential, a key parameter defi ning space charge properties in pure ionic crystals, is determined mainly by the difference in formation energies of the individual defects in the bulk of the crystal. Defects having higher energy accumulate on the surface, whereas the oppositely charged ones form the space charge inside the crystal near the sur-face. Impurities of bivalent cations infl uence the surface potential of ionic crystals, and in some cases an isoelectric point exists (Kliever and Koehler 1965a, 1965b), i.e., a temperature at which the surface potential changes sign. The existence of isoelectric points in doped alkali halide crystals has been experimentally proved by studies of dislocation charge (Urusovskaya 1969; Whitworth 1975; Tallon et al. 1985). Although the FK model is relatively simple and representative, it has an essential disadvantage: This model includes only bulk parameters and does not take into account explicitly the specifi c characteristics of the surface. Attempts to solve this problem have been made by Poeppel and Blakely (the PB model) (Poeppel and Blakely 1969; Blakely and Daniluk 1973), who have studied the infl uence of a limited number of surface sites on the surface potential. Macdonald et al. (1980) substantially improved the model by taking into consideration statistics of surface defects and calculating the surface potential and double-layer capacitance in AgCl. It was shown that the thermodynamic equilibrium of surface defects in terms of the lattice gas model leads to Langmuir adsorption of the defects on the surface.

On the other hand, an alternative approach has been proposed by Lifschitz and Geguzin, who postulated that the surface potential is determined only by parameters of species located on the surface of the crystal (Lifschits et al. 1967). This approach was extended by Chebotin et al. (1984) by consideration of the elementary mechanism of surface disordering. In fact, both these models are vari-ants of the Stern model of the electrochemical double layer on electrodes in con-tact with liquid electrolytes (Stern 1924).

In papers of Maier (1987, 1995) the space charge model was represented in terms of level diagrams for standard chemical and electrochemical potentials of


point defects in both the bulk and surface, including the case of composite solid electrolytes. More sophisticated approaches (i.e., a combination of the FK and Stern models) have been considered by Jamnik et al. (1995) and Khaneft et al. (Khaneft et al. 1990a, 1990b; Khaneft 1992); their models take into account the defect chemistry in the bulk and the surface core. It was again shown that the space charge potential is determined by the difference between the core and bulk standard chemical potentials of individual defects.

Space charge regions localized on the crystal surfaces or grain boundaries strongly infl uence the transport properties of real ceramic materials. In superionic oxides of the MIV

1-cMeIIIcO2-c/2 type the grain boundaries are known to have strong

blocking effect on conductivity. The effect is caused by the depletion of the grain-boundary space charge layer (SCL) in anionic vacancies due to the positive sign of the surface potential on the grain boundary (Heyne 1983; Maier 1986; Burgraaf and Winnbust 1988; Tschöppe 2001a; Guo et al. 2002, 2003; Kim and Maier 2003; Guo and Wasser 2006). The value of the surface potential at intergrain boundar-ies as estimated using the Mott-Schottky model from the conductivity data varies from 0.2–0.3 V for Zr1-xYxO2-x/2 (Guo et al. 2002; Guo and Wasser 2006) to 0.3–0.9 V for heavily doped CeO2 (Tschöppe 2001; Tschöppe et al. 2001, 2004; Kim and Maier 2003; Guo et al. 2003). The barrier height is determined by the value of the electrical potential on the grain boundary, which is an analog of the surface potential. In contrast to classical ionic crystals, in superionic oxides the defect formation energies are close to zero (Goodenough 2003), while the concentrations of impurities and oxygen vacancies are very high. In this case, the conventional FK and PB models are not effective, and only the Stern model is applicable.

Interface defects play an important role in transport properties of composite solid electrolytes, a promising new class of ionic conductors with high ionic con-ductivity. The combination of high conductivity with the enhanced mechanical strength together with the wide prospects for the purposeful modifi cation of the electrolyte properties by varying the type and concentration of the dopant makes these composites promising materials for real electrochemical systems. Since the fi rst report on the effect of heterogeneous doping on ionic conductivity (Liang 1973), many reviews have been published devoted to the description and the anal-ysis of the ion transport in polycrystalline and composite solid electrolytes (Shahi and Wagner 1981; Wagner 1985, 1989; Maier 1985, 1987, 1989a, 1995, 2002, 2003, 2004, 2005; Khandkar and Wagner 1986; Chen 1986; Shukla et al. 1986; Dudney 1989; Uvarov et al. 1992; Uvarov 1996, 2007a, 2008a, 2011; Agrawal and Gupta 1999; Yarostalvtsev 2000; Uvarov and Vanek 2000; Jamnik and Maier 2003; Heitjans and Indris 2003; Schoonman 2005). The increase in the ionic con-ductivity upon heterogeneous doping can be explained within the framework of the space charge model proposed by Wagner and Maier (Jow and Wagner 1979; Maier 1985). This model allows the interpretation of many phenomena observed in composites and is the best suited for the explanation of experimental data for


composites containing oxides with relatively coarse grains. However, the space charge model in its classical version is correct only for ideal crystals in contact with vacuum or a structure-free medium and obviously ignores the real features of the interphase contact, namely, changes in the structures of ionic crystals (e.g., for epitaxial contacts), the effect of elastic strains, the formation of disloca-tions, etc. Moreover, if the surface concentration of defects is suffi ciently high, it is impossible to ignore the interaction between the defects, which results in their ordering and the formation of superstructures and even metastable surface phases. It is known that the conductivity of composites increases as the size of dopant particles increases. Hence, composites with nanosized grains (about 10 nm) are of particular interest for practice. Obviously, uniform mixing of such an oxide with an ionic component should produce a nanocomposite the properties of which depend strongly on the energy of surface interaction and the peculiarities of the interface between the phases. For composites with coarse-grained addi-tives, the presence of surfaces or interphase contacts has virtually no effect on the bulk properties of the ionic salt; hence, the increase in the conductivity is of purely surface nature. However, in many cases, it still remains unclear whether the enhanced conductivity is caused primarily by the specifi c interactions at the interface or by the trivial increase in the surface conductivity as such. To answer this question, information on the conductivity of polycrystals is necessary. In nanocomposites, virtually all volume of the ionic salt is located at the interface, leading to formation of disordered interface-stabilized phases not inherent to the pure salt.

The aim of this chapter is to review surface and interface properties of ionic crystals in terms of the surface/interface defects and quasi-chemical mechanisms of their formation. For this purpose a classic variant of the Stern model is used for the case of strong adsorption of point defects on the surface for ordinary ionic crystals of the NaCl type (Uvarov 2007b, 2008a) and superionic oxides (Uvarov 2007b, 2008b, 2008c). Surface- and interface-related properties of different ionic systems are also analyzed, with an emphasis on size effects in nanocomposites.

2. CALCULATION OF THE SURFACE POTENTIAL AND SURFACE DEFECTS USING THE STERN MODEL

2.1. DESCRIPTION OF THE MODEL

Due to the lattice distortion associated with the assymetric fi eld at the surface, all characteristics of point defects and impurity ions located on the surface dif-fer from those in the bulk. The difference is the reason for the specifi c adsorption (positive or negative) of defects at the crystal surface. If the adsorption energies gi of oppositely charged defects are different, then an excess number of defects


that have the most negative value of gi appear on the surface. Defects of the op-posite charge form a diffuse layer, or space charge layer (SCL), under the surface. According to the Stern model, the surface charge QS is determined by the sum of contributions made by all defects adsorbed on the surface. In the simplest case of the Langmuir adsorption isotherm, the surface charge is given by the expression (Stern 1924)

1

,,

1 expi i SS i S i

ii

N g qQ q Nn kT

−

∞

⎡ ⎤Δ + ϕ⎛ ⎞= ⋅ + ⋅⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦∑ (1.1)

where NS is the concentration of available surface sites (adsorption centers), q is the effective charge of the defect, n∞ is the concentration of the defects in the bulk of the crystal, N is the total number of sites of the crystal lattice, and the summation is done over all possible charged defects of i type. As follows from Eq. (1.1), the surface charge is determined by both the bulk properties (n∞,i) and surface- related parameters [the adsorption energies gi and the surface potential S, which is approximately equivalent to the potential at the inner Helmholtz layer (IHL) in electrochemistry]. The surface charge is balanced by the charge of the SCL, Qd, formed under the crystal surface. If the probability of fi nding an ion at a particular point depends on the local potential through a Boltzmann distribution, ni(x) ni,∞∙exp[–q(x)/kT], then the charge density distribution and the potential gradient must satisfy the Poisson-Boltzman equation. The solution of this equa-tion is the Gouy-Chapman formula for the charge of the SCL,

1/2

1, exp 1i S

d ii

qQ A nkT

−∞

⎧ ⎫⎡ ⋅ ϕ ⎤⎪ ⎪⎛ ⎞= ⋅ ⋅ − −⎨ ⎬⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎪ ⎪⎩ ⎭∑ (1.2)

where A (20kT )1/2; S–1 is the potential of the outer Helmholtz layer (OHL).In superionic conductors, due to the high concentration of charged defects,

the thickness of the SCL is very small, of the order of 1–3 nm. This strongly re-stricts the applicability of the Gouy-Chapman model. In a special case when the concentration of the impurity ions is constant throughout the crystal up to the OHL, the Mott-Schottky approximation may be used and the charge of the SCL is given by (Gurevich and Pleskov 1983; Wasser 1995)

( ) ( )1/21/20 12d c SQ q n −= εε ⋅ ϕ (1.3)

The characteristic length of the SCL estimated by the Mott-Schottky model is several times larger than for the Gouy-Chapman case.

Thus, both charges, i.e., QS and Qd, are defi ned by the surface potential. One can determine its value from the condition of overall neutrality, QS + Qd 0, i.e.,


by solving the transcendental equation derived by summing the right-hand parts of (1.1) and (1.2) or (1.3).

2.2. PURE CRYSTALS OF THE NaCl TYPE

First, let us consider the case of an ideally pure crystal of the NaCl type. As follows from Eqs. (1.2) and (1.3), the surface potential depends on temperature, concen-tration of the surface sites NS, partial energies of adsorption gi, and the concen-tration of the i defects in the bulk of the crystal, xi. The equilibrium concentration, n0, of Schottky defects in pure MX is given by Arrhenius dependence,

00 0 exp

2g

n n n NkT

+ − ⎛ ⎞= = = −⎜ ⎟⎝ ⎠ (1.4)

where n+ and n− are the concentrations of the anion and cation vacancies, respec-tively; N0 is the total volume concentration of MX molecules; g0 h0 − T·S0 is the Gibbs energy of the formation of the Schottky defect determined by the defect formation enthalpy h0 and the entropy S0. From Eqs. (1.2), (1.3), and (1.4) one can express the Stern equation for a NaCl-type crystal as follows:

1 1

0 01 exp 1 exp2 2

S SS

g g e g g ee NkT kT kT kT

− −− +⎧ ⎫⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞Δ − ⋅ φ Δ + ⋅ φ⎪ ⎪⋅ ⋅ + + − + +⎢ ⎥ ⎢ ⎥⎨ ⎬⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎪ ⎪⎩ ⎭

00 exp sh

4 2Sg eA N

kT kT⋅ φ⎛ ⎞ ⎛ ⎞= ⋅ ⋅ − ⋅ ±⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(1.5)

Here g+ and g− are values of the adsorption energy for anion vacancy and cation vacancy, respectively, and sh is the hyperbolic sine. General analysis of this equation shows that the character of the S(T ) curves essentially depends on the values of gi, g0, and NS. If adsorption energies are positive (g− > 0, g+ > 0), then the surface is depleted by defects and practically uncharged, hence the surface potential is close to zero. In the case of negative adsorption energies (g− < 0, g+ < 0), both cationic and anionic vacancies are accumulated on the surface, resulting in formation of negative (at │g−│ > │g+│) or positive (at │g−│ < │g+│) surface charge. For simplicity of data presentation, all entropy terms in g0, g+, and g− are taken equal to zero. Theoretical temperature dependencies of the surface potential are plotted in Figures 1.1a–1.1d. The curves were obtained at different values of g+ < 0 and NS; g0 and g− were taken to be equal to 1.0 and −0.1 eV, respectively.


Functions S(T ) for various NS calculated at a low value of the adsorption en-ergy, g+ −0.2 eV, are presented in Figure 1.1a. Analysis of the data shows that in this case the surface potential tends to zero at T → 0 and increases monotoni-cally with temperature. The temperature dependence S(T ) of this type cannot be interpreted in terms of the FK and PB models (Kliever and Koehler 1965a; Poeppel and Blakely 1969), but it is well approximated by the following expression ob-tained from Eq. (1.5) for small potentials eS/kT << 1:

00

0

2 exp exp exp4S SgkT g gN N

AN kT kT kT

+ −⎡ ⎤⎛ ⎞ ⎛ ⎞Δ Δ ⎛ ⎞ϕ ≈ ⋅ ⋅ − − − ⋅ ⋅ −⎢ ⎥ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦ (1.6)

A similar equation was reported earlier by Lifshitz and Geguzin (Lifschits et al. 1967). It is seen that the surface potential is determined not only by the difference

Figure 1.1. Dependence of the surface potential on temperature as a function of ∆g+ and NS at constant g0 1.0 eV and ∆g− −0.1 eV. Graphs (a), (b), (c), and (d) correspond to values of ∆g+ equal to −0.2, −0.3, −0.4, and −0.6 eV, respectively. Theoretical curves (1), (2), (3), (4), (5), (6), and (7) are calculated at NS values of 1 × 1012, 3 × 1012, 1 × 1013, 3 × 1013, 1 × 1014, 3 × 1014, and 1 × 1015 cm−2, respectively. (Reprinted with permission from Uvarov 2007b. Copyright 2007 Pleiades Publishing, Ltd.)


between g+ and g− but also depends on the defect formation energy g0. The value of S increases linearly with NS and proportionally to the square root of the concentration of Schottky defects in the bulk of the crystal. Thus at low S the process of the formation of the surface charge is limited not only by the concentra-tion of available surface sites, but also by the defect density in the diffuse layer.

At suffi ciently high values of the adsorption energy, │g+│ > g0/4 (g+ < 0), the shape of the S(T ) curves changes substantially. As seen from Figures 1.1b, 1.1c, and 1.1d, in this case, at low temperatures S tends to a limiting value S* which does not depend on NS. At high values of │g+│ and │g+│ > │g−│, anion vacancies prevail in the surface adsorption layer, and Eq. (1.5) may be rewritten in the form

0 00exp exp exp

2 4 2S S

Sg g e g ee N A NkT kT kT kT

+⎛ ⎞Δ + ⋅ ϕ ⋅ ϕ⎛ ⎞ ⎛ ⎞⋅ ⋅ − − ≈ ⋅ ⋅ − ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠ (1.7)

From this equation one fi nds that at T → 0, S → S*, where the value of S* is given by

02*3 4S

ge g +⎛ ⎞⋅ ϕ = ⋅ −Δ −⎜ ⎟⎝ ⎠ (1.8)

For example, in the case of g+ −0.4 eV, g− −0.1 eV, and g0 1.0 eV, the value of S* is equal to 0.10 V (Figure 1.1c). The surface potential may increase or de-crease with the temperature as a function of g+ and NS values. At very high values of │g+│, temperature dependencies of the surface potential (this situation is il-lustrated in Figure 1.1d for g+ −0.6 eV) resemble ones obtained by PB (Poeppel and Blakely 1969), who have shown that at low NS the number of surface sites becomes a limiting factor and S falls to zero with temperature, whereas at high NS the function S(T ) tends to a high-temperature limit given by Eq. (1). A similar limiting value obtained in frames of the Stern model is equal to

S (g− − g+)/2e (1.9)

This expression becomes identical to the equation proposed by Frenkel and Kliever (Kliever and Koehler 1965a). Thus, at suffi ciently high values of │g+│and NS, the FK, PB, and Stern models lead to qualitatively the same result.

In both cases of low and high adsorption energies [Eqs. (1.6) and (1.9), respec-tively], the surface potential is determined by the difference between the partial adsorption energies of the oppositely charged defects. The dependencies S f (g− − g+) obtained by the variation of g+ at fi xed values of g− are shown in Figures 1.2a and 1.2b for values of g0 1.0 and 2.0 eV, respectively. The general character


of the S curves does not depend on the absolute value of g0 but is determined by the gi/g0 ratio and temperature. From this plot one can see that the surface potential values approximate to ones described by Eq. (1.9) at extreme values of NS ≈ 1015 cm2 and at suffi ciently high values of │g− − g+│.

Similar analysis may be done for the case when the surface is enriched in cationic vacancies (g+, g− < 0; │g−│ > │g+│). In this case the value of the sur-face potential is negative and the term g+ in Eq. (1.8) is be substituted for g−.

2.3. SURFACE POTENTIAL IN NaCl CRYSTALS CONTAINING DIVALENT CATIONS

Concentration of the defects in an MX crystal containing divalent cations may be calculated on the basis of a classical approach (Kröger 1964) from known values of the molar fraction of the impurity, c, the formation energy of Schottky defects, g0, and the Gibbs energy, gass, of the formation of dipole complexes [VM − MNa]

x. In order to obtain realistic values of the surface potentials and compare our results

Figure 1.2. Dependence of the surface potential φS on the value of (∆g− − ∆g+)/2e for g0 1.0 eV (a) and g0 2.0 eV (b) at T 500 K. Theoretical curves (1), (2), (3), (4), and (5) are calculated at NS values of 1 × 1011, 1 × 1012, 1 × 1013, 1 × 1014, and 1 × 1015 cm−2, respectively. Solid lines are calculated with Eq. (9). (Reprinted with permission from Uvarov 2007b. Copyright 2007 Pleiades Publishing, Ltd.)


with those obtained earlier, g0 and gass are taken in the form g0 2.12 − 6.4∙keV, gass 0.4 eV (Kliever and Koehler 1965a). The surface of pure NaCl is known to be charged positively (Urusovskaya 1969; Tallon et al. 1985), however, no reliable experimental data on S in NaCl are available in the literature. In this work we have used in calculations the values g+ −0.2 eV and g− −0.51 eV; the energy of the impurity segregation was taken to be zero. Temperature dependencies of S calculated with the above parameters as a function of NS and c are presented in Figures 1.3a and 1.3b. As one can see, the presence of the impurity atoms has a dramatic effect on the surface potential. On the temperature dependencies S(T ) there are isoelectric points, Te, where S changes sign. The value of Te does not depend on the concentration of the surface sites NS (Figure 1.3a) and is defi ned by the molar fraction of the impurity (Figure 1.3b). Similar effects have been reported earlier (Kliever and Koehler 1965; Kliever 1965; Tallon et al. 1985) on the basis of the FK model. It should be noted that in NaCl the effect of the impurity becomes appreciable at extremely small (less then 0.01 ppm) concentration of impurity.

Figure 1.3. Temperature dependence of S in NaCl doped with bivalent impurities obtained from Stern model at ∆g+ −0.2 eV; ∆g− −0.51 eV: (a) at constant concentration of dopant c 1 ppm and different concentrations of surface sites at NS: 1011, 1012, 1013, 1014, and 1015 cm−2, curves 1, 2, 3, 4, and 5, respectively; (b) at constant concentration of surface sites NS 1015 cm−2 and different concen-trations of the dopant: 0.01, 0.1, 1, 10, and 100 ppm, curves 1, 2, 3, 4, and 5, respectively. (Reprinted with permission from Uvarov 2007b. Copyright 2007 Pleiades Publishing, Ltd.)


2.4. COMPARISON WITH EXPERIMENTAL DATA

At present, reliable data on the surface potential are available only for the silver ha-lides AgCl and AgBr (Wonnel and Slifkin 1995). The FK model has been employed for their interpretation, and the following values of defect formation energies for interstitial cations (g0

+) and cationic vacancy (g0−) have been obtained (in eV):

AgCl: g0+ 1.34 − 22.0·kT g0− 0.13 + 12.2·kT (1.10a)

AgBr: g0+ 0.86 − 14.5·kT g0− 0.30 + 7.2·kT (1.10b)

(additional small kT∙ln 2 terms are omitted). The reported values of the forma-tion entropy for interstitial cations seem to be exceptionally high, whereas the corresponding values for cationic vacancies are negative, which is not typical for vacancies in solids. The Stern model was then applied for the interpretation of the experimental data mentioned above. The calculated curves were obtained using Eqs. (1.1) and (1.2). The concentration of Frenkel defects was estimated using data reported in the literature (Poeppel and Blakely 1969; Blakely and Daniluk 1973; Wonnel and Slifkin 1995): g0 1.44 − 9.7∙keV, gass 0.2 eV for AgCl and g0 1.10 − 7.6∙keV, gass 0.4 eV for AgBr; the concentration of bivalent metal impurities in the both cases was taken as 100 ppm and NS was ranged within 1013–1015 cm−2. In all our calculations we have neglected the infl uence of the adsorption energy of the impurity, i.e., the energy of segregation.

The results of the calculations are illustrated in Figure 1.4; theoretical curves were obtained for different NS values using the following parameters:

AgCl: g− −0.18 − 6∙kT g+ ≈ 0 + 2∙kT (1.11a)

AgBr: g− −0.05 − 10∙kT g+ ≈ 0 + 0∙kT (1.11b)

The analysis of the data shows that the concentration of the surface sites is nearly 1014 cm−2. The surface potential in silver halides is determined mainly by the ad-sorption energies of cationic vacancies, g−. These values may be evaluated with more or less appropriate accuracy, whereas values of g+ may be estimated only roughly. Nevertheless, obtained entropy values of 6–10 kT seem to be more reli-able than those estimated by the FK model.

2.5. SURFACE POTENTIAL AND CONCENTRATION OF POINT DEFECTS ON GRAIN BOUNDARIES OF SUPERIONIC OXIDE CERAMICS

In contrast to ordinary ionic crystals, the concentration of defects in superionic conductors is high, comparable to the total number of ions. In this case the value


of defect formation energy is assumed to be zero and the oxide MIV1-cMeIII

cO2-c/2 may be regarded as extrinsic ion conductor. Oxygen vacancies VO

•• form as a re-sult of the dissolution of the MeIII

2O3 in the MIVO2 matrix to compensate for the effective negative charge of MeIII cations in the crystal lattice:

MeIII2O3 ↔ 2MeM′ + VO

•• + 3OOx (1.12)

With decreasing temperature, defects may undergo association into complexes. The association effects have been reported to be responsible for the change in the slope of the Arrhenius plot for conductivity in superionic oxygen conductors (Goodenough 2003; Wang et al. 1981; Arachi et al. 1999). It is of interest to in-vestigate an infl uence of the complexes formed on the surface potential value. For simplicity it is assumed that only electrically neutral complexes are formed.

2MeM′ + VO•• ↔ [2MeM′ + VO

••]x (1.13)

Then the bulk concentrations of defects may be calculated at any temperature from known values of the dopant concentration c and the free energy of the

Figure 1.4. Experimental values of S in AgCl (a) and AgBr (b) in comparison with theoretical values obtained using the Stern model for NS 1015, 1014, 1013, and 1012 cm−2, curves (1), (2), (3), and (4), re-spectively, and concentration of Me2+ impurities of 100 ppm. Values of the adsorption energies used in calculations are pointed out in expressions (1.11a and 1.11b). (Experimental data from Wonnel and Slifkin 1995; theoretical curves have been reported in Uvarov 2007b.)


complex dissociation gdis using a standard procedure (Kröger 1964). For the asso-ciation constant of dipole complexes Kd we used the expression Kd exp(-gass/kT ), where gass was varied from 0 to −0.4 eV.

The surface of solid solution MIV1-cMeIII

cO2-c/2 may adsorb defects, just as is the case with common ionic crystals. For this situation the Stern equation may be represented in the form:

11

••O M

21 12 1 exp 1 exp[V ] [Me ]

S SS

g e g ee NkT kT

−−+ −⎧ ⎫⎡ ⎤⎡ ⎤⎛ ⎞ ⎛ ⎞Δ + ϕ Δ − ϕ⎪ ⎪⎢ ⎥⋅ ⋅ ⋅ + − +⎢ ⎥⎨ ⎬⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠′⎢ ⎥⎢ ⎥⎣ ⎦⎪ ⎪⎣ ⎦⎩ ⎭

( )

1/2••1 1

1 0 M O2

sign [Me ] exp 1 [V ] exp 1S SS

e eA NkT kT

− −−

⎧ ⎫⎡ ϕ ⎤ ⎡ ϕ ⎤⎛ ⎞ ⎛ ⎞′= ϕ ⋅ ⋅ ⋅ ⋅ − + ⋅ − −⎨ ⎬⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦⎩ ⎭ (1.14)

for Gouy-Chapman SCLs, and

11

••O M

21 12 1 exp 1 exp[V ] [Me ]

S SS

g e g ee NkT kT

−−+ −⎧ ⎫⎡ ⎤⎡ ⎤⎛ ⎞ ⎛ ⎞Δ + ϕ Δ − ϕ⎪ ⎪⎢ ⎥⋅ ⋅ ⋅ + − +⎢ ⎥⎨ ⎬⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠′⎢ ⎥⎢ ⎥⎣ ⎦⎪ ⎪⎣ ⎦⎩ ⎭

0 0sign( ) 4S Se cN= ϕ ⋅ εε ⋅ ϕ (1.15)

for Mott-Schottky SCLs. Here NS is the concentration of the surface sites available for the adsorption of oxygen vacancies, which is twice as large as the correspond-ing value for impurity cations; g+ and g− are the adsorption energies of the oxy-gen vacancies and the impurity cations, respectively; N0 3 × 1022 cm−3 is the total volume concentration of M ions; 100. Defect concentrations in the bulk of the crystal, [VO

••] and [MeM′], are interrelated by a ratio [MeM′] 2[VO••]; the sign of the

right-hand members is chosen to be opposite to the sign of the left-hand member. For simplicity it is assumed that S S−1, i.e., the change in electric potential takes place in the diffuse layer only. In spite of the fact that such approximation is rough, it suffi ces for qualitative evaluations. The results of the calculation of the surface potential with Eqs. (1.14) and (1.15) are presented and discussed below.

Gouy-Chapman SCL. Figure 1.1 shows the temperature dependencies of the surface potential in MIV

1-cMeIIIcO2-c/2 calculated from Eq. (1.14) for c 0.10 and

different values of g+ and g−. For simplicity it was assumed that the entropy terms in the free Gibbs energies (g± h± − T S±) were also put to be zero, and practically all surface sites are supposed to be available for the adsorption of the defects: NS 1015 cm−2. The surface potential is very small if both g± > 0, and becomes measurable only when at least one of the g± terms is negative. As seen from Figure 1.5, the surface potential is determined by values of g− and


g+ similarly to ordinary ionic crystals of the NaCl type. Analysis of the S curves shows that at low temperatures the surface potential tends to zero. At high tem-peratures the absolute values of the surface potential are limited by a parameter S* obtained by extrapolation of the high-temperature parts of the S(T ) curves to the ordinate. Values of S* may be estimated from Eq. (1.6) for the case of high potentials when one term in the sum of two exponentials can be neglected. In this case Eq. (1.6) may be rewritten in the following forms:

••O 0 M

22 [V ] exp [Me ] exp

2S S

Sg e ee N A N

kT kT

+⎡ ⎤⎛ ⎞Δ + ϕ ϕ⎛ ⎞′⋅ ⋅ ⋅ − ≈ ⋅ ⋅ ⋅⎢ ⎥ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎢ ⎥⎣ ⎦ (1.16)

for S >0 (in this case g+ < 0, │ g+│ > │ g−│), and

••M 0 O[Me ] exp [V ]expS S

Sg e ee N A N

kT kT

−⎛ ⎞Δ − ϕ ϕ⎛ ⎞′⋅ ⋅ ⋅ − ≈ ⋅ ⋅ −⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ (1.17)

Figure 1.5. Temperature dependence of the surface potential in MIV1-cMeIII

cO2-c/2 calculated from Eq. (1.14) at c 0.10; NS 1015 cm−2; Gass 0; ∆g− −1 eV, and different values of ∆g+. Dash lines were obtained by extrapolation of the high-temperature parts up to S* values in the limit T → 0. (Data from Uvarov 2008b.)


for S < 0 (when g− < 0, │ g−│ > │ g+│). Under the assumption that all nonexpo-nential terms are weakly dependent on temperature, from Eqs. (1.16) and (1.17) one can fi nd:

S* ≈ −2/5∙g+ (S > 0; g+ < 0) (1.18a)

S* ≈ 1/2∙g− (S < 0; g− < 0) (1.18b)

Values of S* may be used only for rough estimation of upper and lower limits of the surface potential at given g± values. Approximate relation (1.18a) gives more reliable values than Eq. (1.18b).

In superionic oxides MIV1-cMeIII

cO2-c/2, the value of S is positive, hence the fi rst case (1.18a) is realized. At g+ −0.6 eV, │g+│ > │g−│, the absolute val-ues of the surface potential, ~0.2–0.3 V, agrees with the experimental values for Zr1-xYxO2-x/2 obtained from conductivity measurements (Guo et al. 2002; Guo and Wasser 2006), therefore this value of g+ was used in all further calculations. For simplicity it was proposed that g− 0 eV. Figure 1.6 presents the S dependen-cies obtained at various concentrations of the dopant. On the same fi gure, data are plotted for the cases of the complete absence of defects association (for gass 0) and the formation of associates with gass −0.2 eV. The infl uence of the defects association on S(T ) dependencies is visible only at low temperatures; at T > 500 K this effect can be neglected. It is to be noted that the straight lines, obtained by the extrapolation of the high-temperature linear segments of the S(T ) curves to the ordinate, converge at the point S → S*, regardless of the concentration of the dopant.

Mott-Schottky SCL. For comparison, the Stern equation with the Mott-Schottky SCL, Eq. (1.15), was solved with the same parameters g+ and g−. The dependencies of the surface potential on temperature are plotted in Figure 1.7. In contrast to the case of Gouy-Chapman SCL, S values do not decrease with temperature at low temperatures. At high temperatures both Gouy-Chapman and Mott-Schottky models give approximately the same result: at T > 500–700 K, the values of the surface potential calculated using the models differ by less than 5 mV (see Figure 1.7). Therefore, in the practically important case of high tem-peratures, the surface potential values do not depend essentially on the particular form of the (x) function in the diffuse layer and are determined mainly by the adsorption energies of the defects.

Cation segregation at the surface. One would expect that as the surface of the oxide MIV

1-cMeIIIcO2-c/2 is charged positively, it should be enriched in the an-

ionic vacancies VO•• and depleted in negatively charged dopant cations MeM′. This,

however, contradicts many experimental observations. Precise chemical micro-probe analyses with a spatial resolution of less than 1 nm using methods of Auger electron spectroscopy, electron energy-loss spectroscopy, energy-dispersive x-ray


spectroscopy, and x-ray photoelectron spectroscopy show that the surface core is enriched in dopant cations (Ikuhara et al. 1997; Lei et al. 2002; Wilkes et al. 2003; Zhu et al. 2005; Norrman et al. 2006). The Stern model provides a clear explanation of these phenomena. Figure 1.8 shows the dependence of the concen-tration of the defects on the surface (in the inner Helmholz layer at S ≈ S-I) on the total concentration of the dopant, c, at 1000 K for the case g+ = −0.6 eV of positive adsorption at the surface of predominantly oxygen vacancies; the segre-gation energy of the Me cation, g−, is taken to be zero. It is seen that the surface potential increases monotonically with c, and the surface concentration of the oxygen vacancies [VO

••]S is higher than that in the bulk ([VO••] c/2). In parallel,

the concentration of the dopant cations at the surface [MeM′]S increases with c and becomes comparable to the [VO

••]S value at high c. The cation segregation at S > 0 is a peculiarity of the defect adsorption isotherm and Eq. (1.1), which may be repre sented for the case of the adsorption of cations in the form

Figure 1.6. Temperature dependence of the surface potential obtained at various concentrations of dopant in the absence of defects association (for gass 0, solid lines) and formation of associates with gass −0.2 eV (dash-dot lines). Curves 1, 2, 3, 4, and 5 correspond to c 0.001, 0.003, 0.01, 0.03, and 0.1, respectively; ∆g+ −0.6 eV; ∆g− 0 eV; NS 1015 cm−2. Dash lines obtained by rough extrapolation of the high-temperature parts up to S* values in the limit T → 0. (Reprinted with permis-sion from Uvarov 2008b. Copyright 2008 Elsevier.)


MM

M

[Me ][Me ]exp

1 [Me ]S S

S

egkT kT

−′ ⎛ ⎞⋅ ϕΔ′= − +⎜ ⎟⎝ ⎠′− (1.19)

From this equation one fi nds that at positive values of the surface potential, [MeM′]S > [MeM′] even at g− 0 (in this case the surface potential is given by a negative value of g+). At c 0.10, concentrations of both [MeM′]S and [VO

••]S are very high, 0.32 and 0.44, respectively. Nevertheless, the total charge of the surface is determined by an excess charge of the oxygen vacancies. This situation agrees completely with experimental data reported in the literature (see Figure 1.8).

It is interesting to compare Eq. (1.19) with an equation proposed by McLean (1957) for qualitative description of impurity segregation in metals:

[ ] [ ] ( )[ ] ( )

seg

seg

M expM

1 M expS

g kT

g kT

Δ=

+ Δ (1.20)

Figure 1.7. Comparison of S values calculated using Gouy-Chapman (solid lines) and Mott-Schottky (dot lines) models of SCL. Curves (1, 1′), (2, 2′), (3, 3′), (4, 4′) and (5, 5′) correspond to c 0.001, 0.0032, 0.01, 0.032, and 0.1, respectively; ∆g+ −0.6 eV; ∆g− 0 eV; gass 0; NS 1015 cm−2. (Reprinted with permission from Uvarov 2008b. Copyright 2008 Elsevier.)


where [M] and [M]S are concentrations of M atoms in the bulk and on the surface of the crystal; gseg is the segregation energy, i.e., the difference of the energy of the crystal when the M atom is located deep inside the crystal and on the surface. The McLean equation may be applied to ionic crystals. In particular, Eqs. (1.19) and (1.20) become equivalent under the condition

segSegg

kT kT

− ⋅ ϕΔΔ = − + (1.21)

In metals the surface potential is close to zero, whereas in ionic crystals it gives an additional (positive or negative) contribution to the segregation energy. Nevertheless, similar to metals, the segregation of impurity atoms (ions, defects) in ionic crystals is defi ned mainly by the corresponding adsorption energies g+ and g−.

A possible reason for the difference in the defect adsorption energies is the difference in excess elastic energy of the crystals accumulated at formation of the defects. Kingery (1984) proposed the following relation between the segregation energy and the size of the impurity atom dissolved in the crystal:

Figure 1.8. Defect concentrations in the bulk ([MeM′ ], [VO••]), on the surface ([VO

••]S, [MeM′ ]S), and the surface potential (ϕS) at 1000 K as a function of the composition of solid solution MIV

1-cMeIIIcO2-c/2.

Values calculated from Eq. (1.6) at ∆g+ −0.6 eV; ∆g− 0 eV; gass −0.4 eV; NS 1015 cm−2. Symbols correspond to experimental data on the surface concentration [MeM′ ]S reported in the literature. (Data from Uvarov 2008b.)


( )21 2seg 1 2

1 2

244 3

KGr rg r r

Gr Krπ

Δ ⋅ −+

(1.22)

where K is the bulk modulus of the solute; G is the shear modulus of the solvent, and r1 and r2 are the ionic radii of the solvent and solute, respectively. From this equation it follows that, in oxides containing impurity cations, the segregation energy of the dopant cations increases with the relative difference in cationic radii of the host oxide and the dopant, rcat

2. The segregation energy of oxygen vacan-cies is defi ned by the difference in the radius of the oxygen anion and the effective radius of the oxygen vacancy, rO

2. In superionic oxides of MIV1-cMeIII

cO2-c/2 type, the surface potential is positive, which can be explained by a high volume change at the formation of extra oxygen vacancies when rO

2 > rcat2.

2.6. SURFACE DISORDER IN TERMS OF ENERGY DIAGRAMS

The results of calculations of the surface potential may be summarized as follows:

1. The surface potential is nonzero only if at least one of gi < 0 and is de-termined by the difference in the defect adsorption energies g− and g+ of positively and negatively charged dominant defects. If g− g+, then S 0.

2. The surface potential increases monotonically with NS value. 3. In pure ionic crystals the temperature behavior of S depends on the value

of g, where g is the most negative of the g+ and g− energies, and differs for two cases:

(a) │g│ < g0/4; the surface potential is small, S increases monotonically with the temperature and rises as a function of the defect concentration in the bulk and NS.

(b) │g│> g0/4; the case of high surface potentials. The values of S may increase or decrease with temperature as a function of NS values. At suffi ciently high values of adsorption energy │g│and NS, the surface potential decreases with temperature and does not depend on the defect concentration.

4. At high NS and │g│the surface potential tends to the value of S ≈ (g− − g+)/2e, which can be regarded as the upper limit. It is to be noted that this expression is formally similar to the equation S ≈ − (g− − g+)/2e obtained in frames of the FK approach, where g− and g+ are the defect formation energies in the bulk of the crystal.

5. In MX crystals doped with MeX2, the situation is more complicated: S val-ues depend on the type, the concentration of the impurity ions (given by the energy of dissociation of complexes [impurity ion − cation vacancy]), and their adsorption energy (or segregation energy) gMe

+. At │g+│ > │g−│ >


│gMe+│ or │gMe

+│ > │g+│ > │g−│ (g+, g−, gMe < 0), an isoelectric point (i.e., temperature where S change sign) exists on the S(T ) dependence.

6. In superionic oxides MIV1-cMeIII

cO2-c/2, values of S are generally bounded by limiting parameters given by values of g+ and gMe

− (the adsorption energy of oxygen vacancies and the segregation energy of Me cations, respectively). The values of S obtained using the Gouy-Chapman and Mott-Schottky mod-els of the SCL differ strongly in the low-temperature limit and tend to level off with a temperature increase. At high temperatures the surface potential does not in practice depend on the particular form of the (x ) function in the SCL and is determined mainly by the adsorption energies of the defects.

7. According to the literature (Heyne 1983; Guo and Maier 2001; Guo and Wasser 2006), in oxides of the MIV

1-cMeIIIcO2-c/2 type the surface potential is

positive, therefore g+ < 0 (g+ > │gMe−│) and the surface should be enriched

in anionic vacancies and depleted in cations. In the Stern model the adsorp-tion of oxygen vacancies and the segregation of extrinsic cations are inter-related, and even at gMe

− 0 a strong segregation of cations takes place on the surface. Nevertheless, the surface as a whole remains positively charged and the diffusion layer is depleted of anionic vacancies.

Figure 1.9. Energy diagrams of surface and bulk defects, charge distribution near the surface, and electrical potential profi les for pure (a, b) and doped (c) ionic crystal MX with Schottky defects. Diagrams obtained in terms of the Stern model. Cases (a) and (b) correspond to the pure crystal with different ∆g+ and ∆g− values. Cases (b) and (c) relate to the MX crystal doped with bivalent impurity MeX2 (dopant concentration equal to c) in intrinsic (b) and extrinsic (c) conductivity regions. (Data from Uvarov 2011.)


Representing the chemical potential of the ith defect, i, in the standard form, i gi

± + kT·ln[ ]i (here [ ]i is the fraction of the defects; the superscript corresponds to the sign of the defect) and taking into account the electrical neutrality condi-tion, one can obtain values of gi

± for all the defects. Physically, each gi± value cor-

responds to the energy necessary for generation of a single defect. One can plot energy diagrams (Figure 1.9) illustrating the difference between the defect ener-gies in the bulk of the crystal and at the surface for MeX2-doped MX crystals in different temperature regions. This diagram differs from the diagrams reported earlier (Maier 1995; 2003; Jamnik et al. 1995) because in the bulk of the crystal in the intrinsic region the defect formation energies for both defects are taken to be equal to g0/2. As seen from the diagram, at negative values of adsorption energies the surface is enriched in defects even in the case of zero surface charge (which is possible at g+ g−). In general, the surface can be considered as an independent subsystem characterized by intrinsic surface disordering with an effective defect formation energy equal to

0 2Sg gg g

+ −Δ + Δ= + (1.23)

The surface is more or less disordered than the bulk, depending on the sign of the second term of this equation.

2.7. DEFECTS ON INTERFACES

Interfaces comprise phase boundaries with more complicated structure defi ned by several interrelated chemical and morphological factors. Chemical factors in-clude the bonding type, the crystal structure of contacting phases, and inter-actions between them. Morphological factors include the type of lattice surfaces, their orientation, and a misfi t between the crystal lattice parameters of adjacent phases. In systems consisting of small particles (or grains), size effects should also be taken into account.

From general conditions of mass and charge conservation it follows that con-centrations of ions are interrelated to fractions of corresponding point defects. As conductivity of ordinary ionic salt MX is carried out by point defects, it is con-venient to express the parameters of the chemical adsorption of ions in terms of the adsorption isotherms of the corresponding defects (including impurity ions) of ith type with the adsorption energies of gi. Chemical adsorption of charged species seems to be a general phenomenon typical for any polar media (includ-ing ionic crystals) and may take place for free surfaces of MX, grain boundary MX–MX, and MX–A interfaces. Therefore the same phenomenological approach based on the Stern model can be applied to surface- or interface-related effects in polycrystalline samples and composites.


In heterogeneous systems consisting of two ionic salts (of the MX–M′X type), there are diffuse layers in both phases. Therefore, for calculation of the surface potential using the Stern model one has to take into account the adsorption of defects belonging to each phase to a common interface. Such a situation is demon strated in the energy diagram depicted in Figure 1.10 for the contact of two intrinsic conductors MX and MX′ with Schottky defects. In this case the surface potential is determined by six independent parameters: (1) the defect formation energies in the bulk of the phases MX and MX′, g01 and g02, respectively; (2) the energies g1

+ and g1− of the defect adsorption for one of the phases (the corre-

sponding adsorption energies for another phase are given by the relations g2+

(g01 + g02)/2 − g1+ and g2

− (g01 + g02)/2 − g1−; (3) the number of active surface

sites, NS; (4) the potential difference between MX and MX′, or Galvani potential, c, which cannot be measured directly. Work is in progress on analysis of the Stern equation for this case. Preliminary estimates show that the following quali-tatively different situations, demonstrated in Figure 1.10, may be realized:

(a) If gi± > 0, then the interface charge is close to zero, and two oppositely

charged diffuse layers may be formed due to the existence of the potential drop between the phases. The potential profi le shown in Figure 1.10a is

Figure 1.10. Energy diagrams of surface and bulk defects, charge distribution, and electrical poten-tial profi les near MX–MX′ (a, b) and MX–A (c) interfaces. Diagrams obtained in terms of the Stern model. Cases (a) and (b) obtained at different values of ∆g+ and ∆g−. (Data from Uvarov 2011.)


typical for classical boundaries between semiconductor and liquid electro-lyte (Gurevich and Pleskov 1983; Sato 1998) and was earlier applied to ex-planation of the interface-related properties of MX–MX′ systems by Maier (1985, 1995).

(b) If gi± < 0, the surface potential and the interface charge are high; the

potential has an extremum at the interface; and two double layers form near the interface in both phases, with the space charge opposite in sign to the interface charge. Such a profi le is presented in Figure 1.10b; it is qualitatively similar to one at the intergrain boundaries of ionic crystals, but the charge distribution is not symmetrical—higher space charge is ac-cumulated in the phase with the lower value of defect formation energy.

These variants correspond to some limiting cases. The real situation is inter-mediate and the interface potential is defi ned by all the independent parameters mentioned above. In the case of doped ionic crystals, one can also take into ac-count the concentration of dopants in the contacting phases and the segregation energy of dopants to the interface. As no data on the interface potential of MX–MX′ systems are available in the literature, it is hard to verify the model.

The defect equilibrium on the interface between an ionic salt MX and an oxide A may be regarded as a chemical adsorption of ions of the MX phase onto the sur-face of the oxide. The concentration of defects inside the bulk of the oxide is neg-ligible, and only the fi rst oxide layer takes part in the interface interaction, which includes pair interactions between ions of MX and A. This results in a change of the defect adsorption energies, the surface potential, and, consequently, the con-centration of point defects in the diffuse layer. The increase in the concentration of the adsorbed ions on the interface (as well as the point defects concentration in the diffuse layer of the ionic crystal) leads to enhancement of the conductivity of the composites. Such a mechanism has been proposed by Maier (1985, 1995). Most of the experimental data reported suggest that the interface interaction con-sists of a selective chemical adsorption of M+ cations, i.e., their shift from the MX bulk to the MX–A interface. Physically, this is equivalent to the change in the ad-sorption energy of positively charged defects (anionic vacancies VX

• or interstitial cations Mi

•) and formation of high positive charge at the interface. As a result, a diffuse layer built of cationic vacancies forms near the interface. The energy dia-gram for the MX–A interface is presented in Figure 1.10c. Selective adsorption of cations can be regarded as interaction of M+ cations as Lewis acid particles with the Lewis base centers O2− or OH− on the surface of the oxide. Therefore, the adsorption energy should depend on the type of cation (the acidity of the cation increases with a decrease in the ionic radius) as well as on the presence and strength of basic groups on the oxide surface. It has been shown (Uvarov 2007a, 2008a, 2011) that lithium salts in systems with alumina exhibit a stronger in-crease in conductivity as compared to rubidium and cesium salts, while iodides


more readily form nanocomposites as compared to chlorides and fl uorides. This suggests that the polarizing ability and the polarizability of ions in the ionic com-ponent play an important role in the surface interaction mechanism. The physi-cal reason for the surface interaction in a composite of the ionic salt–oxide type lies in the trend of both substances to decrease their surface energy due to the interaction of surface ions with the ions of the neighboring phase. Because of the difference in interionic energies and peculiarities of the crystal structures in the interface layers, the ideal structure inherent in individual phases will be distorted in such a way as to provide a gain in the surface energy due to the mutual ap-proach or removal of surface atoms. The relative displacement of ions from their ideal positions is determined by the balance of the interaction energies. In alu-mina and in the majority of the salts MX under discussion, anions exceed cations in size, so it can be expected that for close packing, the interface cations will have the larger free volumes and will be displaced by longer distances than the anions. As a result, in the space between the surface layers, an intermediate, positively charged layer enriched with cations is formed, the charge of which is compen-sated by the cationic vacancies that constitute the diffuse layer. This process may be regarded as a chemical adsorption (Maier 1985, 1995) and may be presented as the following quasi-chemical reaction:

0 ↔ VM′ + (M–A)•S (1.24)

which describes the stage of the surface disordering of MX at the MX–A interface. If an anion is adsorbed on the surface, another reaction may proceed:

0 ↔ Mi• + (X–A)′S (1.25)

0 ↔ VX• + (X–A)′S (1.26)

The isoelectric point of an oxide pE was proposed by Shukla et al. (1988) as a measure of its surface activity. Indeed, equations similar to Eqs. (1.25)–(1.26) may be written for the surface interaction of an oxide with water:

H2O ↔ OH′ + (H–A)•S (1.27)

2H2O ↔ H3O• + (OH–A)′S (1.28)

The fi rst reaction predominates for oxides with pE > 7, for instance, MgO, Al2O3, CeO2; the second prevails for oxides with pE < 7 (ZrO2, SiO2). By analogy with aqueous solutions, one can expect that the surface reaction (1.25) will occur in composites containing basic oxides (pE > 7), whereas for acidic oxides (pE < 7) the interface interaction will follow the mechanism (1.26). The isoelectric point of any oxide changes according to its doping with different dopants or by direct


modifi cation of its surface by acidic or basic agents. This enables one to increase the conductivity of the composite by variation of just its surface properties. A more general approach is to change the Lewis acidity/basity of the oxide surface. Both approaches were successful for the improvement of transport properties of different composites (Saito and Maier 1995).

Recently, we have carried out a comparative study of electrical properties and 7Li NMR data of the composites LiClO4–A (A -Al2O3, -Al2O3, -LiAlO2, -LiAlO2) (Ulihin et al. 2006, 2008). It was shown that the conductivity depends not only on the specifi c surface but also on the chemical nature and the structure of the additive: At the same value of specifi c surface area, composites with -Al2O3 and -LiAlO2 have lower activation energy for conductivity than composites containing -Al2O3 and -LiAlO2 additives. A possible reason for such behavior could be the presence of tetrahedrally coordinated cationic positions in the crystal structure of the -phases. These sites, being located on the surface, seem to be strong basic centers and favor chemical adsorption of lithium cations, leading to enhancement of the concentration of defects in the vicinity of the LiClO4–A interface. It has been recently demonstrated (Ulihin 2009) that the conductivity of composite solid electrolytes LiClO4–A at close values of the specifi c surface area and the volume fraction of oxide increases in a series SiO2–Al2O3–MgO in parallel to an increase in the basicity. That is in agreement with the chemical adsorption approach men-tioned above. Several papers (Nakamura and Saito 1992; Saito et al. 1988; Singh et al. 1995) have reported on conductivity enhancement in composites containing the ferroelectric oxides BaTiO3, LiNbO3, and KTaO3. The effect was proposed to be strengthened due to high dielectric permittivity of the oxide. The concentration of charge carriers in the surface or interface region of MX can be also varied using modifi cation of the surface by electronic donor molecules (Lauer and Maier 1990; Saito and Maier 1995).

3. SIZE EFFECTS IN NANOCOMPOSITE SOLID ELECTROLYTES

When the particle size of a substance becomes smaller than 10–100 nm, its physi-cal properties change appreciably due to size effects. In the last two decades huge progress has been made in research on nanosystems of different types, such as nanostructured pure and composite materials, metal nanoparticles, carbon nano-tubes, mesoporous systems, etc. Size effects may be very strong in nanocom-posite solid electrolytes. In particular, new phases that are not typical for pure components may be stabilized in the nanocomposites. Such effects have been observed in such varied systems as AgI–Al2O3 (Uvarov et al. 1990, 1993, 1996b, 2000a, 2000b, 2000c), Li2SO4–Al2O3 (Uvarov et al. 1994), MNO3–Al2O3 (M Li, Na, K) (Uvarov et al. 1996c), MNO3–Al2O3 (M Rb, Cs) (Uvarov et al. 1996d, 1996e), RbNO3–SiO2 (Lavrova et al. 2000), CsHSO4–SiO2 (Ponomareva et al. 1996, 1998,


2000), LiClO4–A (A Al2O3, LiAlO2, SiO2) (Vinod and Bahnemann 2002; Ulihin et al. 2006, 2008) and may be explained by the occurrence of amorphous phases of the ionic salt in the composites. The existence of the amorphous state is evidenced by the following effects observed in the composites:

1. Strong decrease in the integral intensity of x-ray diffraction peaks attributed to all crystalline phases of MX and appearance of a wide halo on electron diffraction patterns.

2. Diminishing of molar enthalpies of all phase transitions of MX, including the melting enthalpy. Instead, a diffuse peak appears at a temperature much lower than the melting point.

3. Disappearance of abrupt conductivity changes due to phase transitions of MX in the MX–A composites. Arrhenius dependencies of conductivity are nonlin-ear for some composites. Estimates show that the charge carrier concentra-tion in such nanocomposites is comparable to the overall number of cations that is typical for superionic conductors or ion-conducting glasses. This is also confi rmed by the absence of the conductivity change upon melting.

4. Effects 1, 2, and 3 increase systematically with the total number of MX–A interfaces in the composite. This suggests that the amorphous phase is an interface-induced, nonautonomous phase, which occurs only at MX–A interfaces.

The formation of the nanocomposites proceeds spontaneously and the self-dispersion proceeds at noticeable rates even at temperatures substantially below the melting point of MX, i.e., where the ionic salt is in the crystalline state. Due to the solid-phase spreading, the amorphous phase is formed, i.e., the crystal-line phase spontaneously transforms into the amorphous state. It is known that composites MX–A exhibit enhanced conductivity at temperatures below the melt-ing point or superionic phase transition of MX. The properties of nanocomposite systems have been analyzed in detail in several review papers (Heitjans and Indris 2003; Maier 2004, 2005; Schoonman 2005; Uvarov 2007a, 2008a, 2011).

The formation of the amorphous interface-stabilized phase cannot be explained by standard models which involve surface point defect concepts. Nevertheless, one can expect that interface interaction includes the adsorption of ionic species from the ionic salt to the oxide surface. Therefore, at least on a qualitative level, a chemical adsorption concept may be used for a rough estimate of the surface potential and the interface effects in MX–A composites.

4. APPLICATIONS IN SENSORS

There are two main types of resistivity sensors: (1) sensors based on a change of the equilibrium concentration of ionic or electronic defects in the bulk of the


conductor and (2) adsorption sensors the resisitivity of which is determined by surface (or interface) properties of the sensing material. The specifi c features of these sensors can be compared using the examples of binary ionic salts MX and metal oxides.

Sensors of the fi rst type are based on the dependence of the conductivity on the activity of the X (for ionic salt MX) or oxygen (in oxides). This dependence is caused by the variation of equilibrium concentrations of bulk ionic and elec-tronic defects as a function of the component’s activity. In the concentration range where conductivity depends on the oxygen activity, the conductivity is caused by electronic defects which have much higher mobilities than ionic defects. Defect concentrations are commonly represented by Kröger-Vink diagrams (Kröger 1964), i.e., plots of log defect concentration versus log component activity (Figure 1.11), which quantitatively express the variation of defect content within a given phase. The character of the diagram depends on the ratio between the formation enthalpy g0 for ionic defects (Schottky or Frenkel ones) and the band gap Eg. When Eg > g0 (Figure 1.11a), ionic defects prevail, and their equilibrium defi nes the con-centration of electronic defects. In the opposite case, Eg < g0 (Figure 1.11b), defect proerties are defi ned by electron–hole equilibrium. The concentration of electronic and ionic defects in the bulk of the material may be comparable, and the equili-bration time is limited by slow diffusion of ionic defects. To shorten the response

Figure 1.11. Kreger-Vink diagrams for pure ionic salt MX with dominant ionic (a) and electronic (b) defects. Black lines correspond to bulk defects, dot lines correspond to the concentration of surface defects.


time, the sensor should be made as thin fi lms. Similar to oxides, sulfi des may be used for determination of sulfur-containing substances.

Sensors of the second type, operating due to the adsorption phenomena, are more widespread (Lannto 1992; Gopel et al. 1995; Shimizu 1999; Korotchenkov 2007, 2008; Barsan et al. 2007; Wang 2010). Sensitive elements comprise semi-conducting oxides, for example, doped SnO2, ZnO, and TiO2, which show changes in electrical resistivity in the presence of small concentrations of fl ammable gases such as propane, and toxic gases such as carbon monoxide. The sensors detect gases because of a change in electrical resistance which accompanies the reaction between adsorbed species such as O2

−, O− and O2 and the gases to be detected. The chemical adsorption leads to a change in the surface potential which, in turn, results in a resisitivity increase or decrease (as a function of the double-layer structure). Therefore, the surface potential is a key parameter which defi nes the performance of the adsorption-type resisitive sensors, as this parameter defi nes the concentration of the defects (including electronic ones) near the surfaces or grain boundaries. Maier (1989b, 1995) has presented the Kreger-Vink diagram for surface and bulk defects in MX crystals with Frenkel defects. Figure 1.11a shows schematically the Kreger-Vink diagram for a MX crystal with bulk and surface Schottky defects when Eg > g0. One sees that concentrations of electrons and holes deviate signifi cantly from the bulk values. In this case the surface potential is de-termined by the defect adsorption energies as discussed above (see Section 2.2). In particular, the process of the adsorption of intrinsic anionic vacancy may be represented in the form

VX• ↔ VXS

• (1.29)

hereafter, an additional subscript S denotes a species located at the surface. The chemical adsorption of some gaseous species Y at the anionic sites of the surface may be represented by a reaction

Y(g ) + VXS• ↔ YXS

• (1.30)

with formation of a surface acceptor centers YXS•. Reaction (1.30) competes with

(1.29), leading to fi lling the surface by vacancies and results in a change in the surface potential. A qualitatively similar situation takes place in semiconductors MX with Eg < g0 (Figure 1.11b). In this case the surface potential is defi ned by the chemical adsorption (accumulation) of electron donor (MMS′) or acceptor (XXS

•) states at the surface or grain boundaries.

MMSx + e′ ↔ MMS′ (1.31a)

XXSx + e• ↔ XXS

• (1.31b)


XXSx + e• ↔ X(g ) + VXS

• (1.31c)

The formation of “surface impurity” defects YXS• due to reaction (1.30) shifts

equilibrium of the processes (1.31) and affects the surface potental. In contrast to the bulk defects, the concentration of the surface defects may be easily varied, as the surface potential depends not only on specifi c properties of the surface, but also on the type and concentration of adsorbed species. In oxides the chemosorp-tion of oxygen proceeds through the reactions

½O2(g ) + VOS•• + e′ ↔ OOS

• (1.32a)

½O2(g ) + VOS•• ↔ OOS

• + e• (1.32b)

for conductors of n-type and p-type, Eqs. (1.32a) and (1.32b), respectively, with formation of chemisorbed oxygen ions O−(ad) or surface anionic defect OOS

• (in Kreger notation). Concentration of chemisorbed oxygen may be easily affected by adsorption of other reducing or oxidative agents, resulting in a change of the sur-face potential and surface conductivity (or resisitivity).

Similar processes may proceed not only in pure single- and polycrystalline oxides but also in composites where the surface potential forms on the interfaces. Fast response time may be achieved by reducing the crystal size, porosity, or fi lm thickness (allowing an increase in the adsorption surface and the contribution of the surface conductivity). Selectivity is defi ned by the relative value of the adsorp-tion energy of the gas to be detected. It depends on the atomic structure of the adsorption centers and adsorption complex. By variation of the microstructure (orientation and type of grains, porousity, etc.), type and concentration of dop-ants, temperature, and optimal geometry of the sensor, one can fi nely tune ad-sorption properties of the gas-analyte and to gain the best selectivity.

In recent years there has been increased interest in thin-fi lm sensors. Thin fi lms, typically 100 nm thick, of doped tin oxide can be deposited by sputtering, evaporation, sol-gel techniques, etc., with subsequent annealing leading to the development of a nanocrystalline porous structure. Although “thin”-fi lm technol-ogy, in comparison with “thick”-fi lm technology, would appear to offer the advan-tage of relatively lower production costs because of the avoidance of powder and screen-printing paste processing steps, there are drawbacks. Thin fi lms offer a much smaller reactive area than sintered thick-fi lm ceramics, and so the sensitiv-ity of sensors fabricated from them is correspondingly lower; for the same reason, they are more susceptible to surface contamination.

Despite many applications of ceramic gas sensors and great progress manu-facturing techniques, no quantitative models have been proposed for theoretical description of their characteristics. This lack hinders the prediction of optimal materials, dopants, concentrations, and temperatures. The best performance of


sensors is achieved mainly by a trial-and-error strategy. Calculation of the surface potential (or potential profi le on the interface) would open ways to qualitatively describe the surface properties of sensor materials and fi nd new possibilities to improve sensors characteristics.

5. CONCLUSIONS

It has been demonstrated that the Stern model provides a common basis for the quantitative description of the surface and interface effects, including the surface potential formation and the point defects equilibrium at free surfaces and inter-faces. In particular, in classical ionic crystals the model explains describes quali-tatively the absolute values of the surface potential and the presence of isoelectric points. The model correctly describes the defect equilibrium at the interfaces and is applicable to the interfaces in composite solid electrolytes in which the double layer is formed by the point defects in the interface region of the ionic salt. In nanocomposites, structural reconstruction or the formation of interface phases takes place. Analysis of the experimental data shows that in most cases, amor-phous interface phases exist in nanocomposites. Due to their high ionic con-ductivity and other characteristics, the composite solid electrolytes, especially nanocomposites, will fi nd many applications in future technologies, in particular in various gas-sensing devices.

REFERENCES

Adler S.B. (2004) Factors governing oxygen reduction in solid oxide fuel cell cathodes. Chem. Rev. 104(10), 4791–4843. DOI: 10.1021/cr020724o

Agrawal R.C. and Gupta R.K. (1999) Superionic solids: Composite electrolyte phase—An overview. J. Mater. Sci. 34(6), 1131–1162. DOI: 10.1023/A:1004598902146

Arachi Y., Sakai H., Yamamoto O., Takeda Y., and Imanishi N. (1999) Electrical conduc-tivity of the ZrO2-Ln2O3 (Ln lanthanides) system. Solid State Ionics 121(1–4), 133–139. DOI: 10.1016/S0167-2738(98)00540-2

Barsan N., Koziej D., and Weimar U. (2007) Metal oxide-based gas sensor research: How to? Sens. Actuators B 121(1), 18–35. DOI: 10.1016/j.snb.2006.09.047

Bhoga S.S. and Singh K. (2007) Electrochemical solid state g as sensors: An overview. Ionics 13(6), 417–427. DOI: 10.1007/s11581-007-0150-7

Blakely J.M. and Danyluk S. (1973) Space charge regions at silver halide surfaces. Surface Sci. 40(1), 37–60. DOI: 10.1016/0039-6028(73)90050-2

Burggraaf A.J. and Winnubst A. (1988) Segregation in oxide s urfaces, solid electro lytes and mixed conductors. In: Nowotny J. and Dufour L.-C. (eds.), Surface and Near Surface Chemistry of Oxide Materials. Materials Science Monographs, Vol. 47. Elsevier, Amsterdam, 449–477.

Chandra S. (1981) Superionic Solids: Principles and Applicat ions. North-Holland, Amsterdam.Chebotin V.N. and Perfi liev M.V. (1978) Electrochemistry of Solid Electrolytes. Khimiya,

Moscow (in Russian).


Chebotin V.N., Remez I.D., Solovieva L.M., and Karpachev S.V. (1984) Electrical double layer in solid electrolytes—Theory: Oxide electrolytes. Electrochim. Acta 29(10), 1380–1388. DOI: 10.1016/0013-4686(84)87016-4

Chen L. (1986) Composite solid electrolytes. In: Chowdhari B .V.R. and Radhakrishna S. (eds.), Materials for Solid State Batteries. World Scientifi c, Singapore, 69.

Dudney N.J. (1989) Composite solid electrolytes. Annu. Rev. Mater. Sci. 19, 103–120. DOI: 10.1146/annurev.ms.19.080189.000535

Fabry P. and Siebert E. (1997) Electrochemical sensors. In: Gellings P.J. and Bouwmeester H.J.M. (eds.), The CRC Handbook of Solid State Electrochemistry. CRC Press, Boca Raton, FL, chap.10.

Frenkel J. (1946) Kinetic Theory of Liquids. Oxford Unive rsity Press, Oxford, UK.Goodenough J.B. (1993) Oxide-ion electrolytes. Annu. Rev. Ma ter. Res. 33, 91–128. DOI:

10.1146/annurev.matsci.33.022802.091651Gopel W. and Schierbaum K.D. (1995) SnO2 sensors: Current st atus and future prospects.

Sens. Actuators B 26–27(1–3), 1–12. DOI: 10.1016/0925-4005(94)01546-TGrimley T.B. (1950) The contact between a solid and an electrolyte. Proc. R. Soc. (Lond.) A

201, 40–61. DOI: 10.1098/rspa.1950.0043Guo X. and Maier J. (2001) Grain boundary blocking effect in zirconia: A Schottky barrier

analysis. J. Electrochem. Soc. 148(3), E121–E126. DOI: 10.1149/1.1348267Guo X. and Waser R. (2006) Electrical properties of the grai n boundaries of oxygen ion

conductors: Acceptor-doped zirconia and ceria. Prog. Mater. Sci. 51(2), 151–210. DOI: 10.1016/j.pmatsci.2005.07.001

Guo X., Sigle W., Fleig J., and Maier J. (2002) Role of spac e charge in the grain boundary blocking effect in doped zirconia. Solid State Ionics 154–155, 555–561. DOI: 10.1016/S0167-2738(02)00491-5

Guo X., Sigle W., and Maier J. (2003) Blocking brain boundar ies in yttria-doped and un-doped ceria ceramics of high purity. J. Am. Ceram. Soc. 86(1), 77–87. DOI: 10.1111/j.1151-2916.2003.tb03281.x

Gurevich Y.Ya. and Pleskov Yu.V. (1983) Photoelectrochemistr y of Semiconductors. Nauka, Moscow (in Russian).

Haile S.M., Boysen D.A., Chisholm C.R.I., and Merle R.B. (20 01) Solid acids as fuel cell electrolytes. Nature 410, 910–912. DOI: 10.1038/35073536

Hangenmuller P. and Van Gool W. (eds.) (1978) Solid Electrol ytes General Principles, Characterization, Materials, Applications. Academic Press, New York.

Heitjans P. and Indris S. (2003) Diffusion and ionic conduction in nanocrystalline ceramics. J. Phys.: Condens. Matter 15(30), R1257–R1289. DOI: 10.1088/0953-8984/15/30/202

Heyne L. (1983) Interfacial effects in mass transport in ion ic solids. In: Beniere F. and Catlow C.R.A. (eds.), Mass Transport in Solids. Plenum Press, New York, 425–456.

Hull S. (2004) Superionics: Crystal structures and conductio n processes. Rep. Prog. Phys. 67(7), 1233–1314. DOI: 10/1088/0034-4885/67/7/R05

Ikuhara Y., Thavorniti P., and Sakuma T. (1997) Solute segregation at grain boun daries in superplastic SiO2-doped TZP. Acta Mater. 45(12), 5275–5284. DOI: 10.1016/S1359-6454(97)00152-3

Ishihara T. (ed.) (2009) Perovskite Oxide for Solid Oxide Fu el Cells. Springer-Verlag, Dordrecht, The Netherlands.

Jamnik J. and Maier J. (2003) Nanocrystallinity effects in lithium battery materials. Aspects of nano-ionics. Part IV. J. Phys. Chem. Chem. Phys. 5(23), 5215–5220. DOI: 10.1039/B309130A

Jamnik J., Maier J., and Pejovnik S. (1995) Interfaces in so lid ionic conductors: Equilibrium and small signal picture. Solid State Ionics 75, 51–58. DOI: 10.1016/0167-2738(94)00184-T


Jow T. and Wagner J.B. (1979) The effect of dispersed alumin a particles on the electri-cal conductivity of cuprous chloride. J. Electrochem. Soc. 126(11), 1963–-1972. DOI: 10.1149/1.2128835

Khandkar A.C. and Wagner J.B. (1986) Fast ion transport in c omposites. Solid State Ionics 18/19(2), 1100–1104. DOI: 10.1016/0167-2738(86)90316-4

Khaneft A.V., Zhogin I.L., and Kriger V.G. (1990a) The model of formation of Frenkel defects on the surface of ionic crystals. Poverkhnost 6, 65–71 (in Russian).

Khaneft A.V. and Kriger V.G. (1990b) Formation of vacancies on the surface and in the bulk of the ionic crystal. Zh. Fiz. Khim. 64(9), 2424–2429 (in Russian).

Khaneft A.V. (1992) Infl uence of the surface disordering on the formation of Frenkel defects in the ionic crystal. Zh. Fiz. Khim. 66(11), 3037–3044 (in Russian).

Kim S. and Maier J. (2002) On the conductivity mechanism of nanocrystalline ceria. J. Electrochem. Soc. 149(10), J73–J83. DOI: 10.1149/1.1507597

Kingery W.D. (1984) The chemistry of ceramic grain boundarie s. Pure Appl. Chem. 56(12), 1703–1714. DOI: 10.1351/pac198456121703

Kliever K.L. and Koehler J.S. (1965) Space charge in ionic crystals. I. General approach with application to NaCl. Phys. Rev. 140(4), A1226–A1240. DOI: 10.1103/PhysRev.140.A1226

Kliever K.L. (1965) Space charge in ionic crystals—III. Silver halides containing divalent cations. J. Phys. Chem. Solids 27(4), 705–717. DOI: 10.1016/0022-3697(66)90221-6

Korotcenkov G. (2007) Metal oxides for solid-state gas sensors: What determines our choice? Mater. Sci. Eng. B 139(1), 1–23. DOI: 0.1016/j.mseb.2007.01.044

Korotcenkov G. (2008) The role of morphology and crystallographic structure of metal oxides in response of conductometric-type gas sensors. Mater. Sci. Eng. R 61(1–6), 1–39. DOI: 10.1016/j.mser.2008.02.001

Kreuer K.D. (2003) Proton-conducting oxides. Annu. Rev. Mater. Sci. 33(3), 33–59. DOI: 10.1146/annurev.matsci.33.022802.091825

Kröger F.A. (1964) The Chemistry of Imperfect Crystals. North Holland, Amsterdam.L antto V. (1992) Semiconductor gas sensors based on SnO2 thick fi lms. In: Sberveglieri G.

(ed.), Gas Sensors. Kluwer Academic, Dordrecht, The Netherlands, 117–167.Lauer U. and Maier J. (1990) Conductance effects of ammonia on silver chloride boundary

layers. Sens. Actuators B 2(2), 125–131. DOI: 10.1016/0925-4005(90)80021-QL avrova G.V., Ponomareva V.G., and Uvarov N.F. (2000) Nanocomposite ionic conductors

in the system MeNO3–SiO2 (MeRb, Cs). Solid State Ionics 136–137, 1285–289. DOI: 10.1016/0167-2738(00)00590-7

L ee J.S., Adams S., and Maier J. (2000) Transport and phase transition characteristics in AgI:Al2O3 composite electrolytes evidence for a highly conducting 7-layer AgI polytype. J. Electrochem. Soc. 147(6), 2407–2418. DOI: 10.1149/1.1393545

L ee J.S. and Maier J. (1997) Interfacial phase transitions in AgI:Al2O3 composite electro-lytes. In: Negro A. and Montanaro L. (eds.), Proceedings of the International Conference EUROSOLID-97, Politechnico di Torino, 115–122.

L ei Y., Ito Y., Browning N.D., and Mazanec T.J. (2004) Segregation effects at grain boun-daries in fl uorite-structured ceramics. J. Am. Ceram. Soc. 85(9), 2359–2363. DOI: 10.1111/j.1151-2916.2002.tb00460.x

L iang C.C. (1973) Conduction characteristics of the lithium iodide-aluminum oxide solid electrolytes. J. Electrochem. Soc. 120(10), 1289–1292. DOI: 10.1149/1.2403248

L ifschits I.M., Kossevich A.M., and Geguzin Ya.E. (1967) Surface phenomena and diffusion mechanism of the movement of defects in ionic crystals. J. Phys. Chem. Solids 28(5), 783–792, IN1–IN2, 793–798. DOI: 10.1016/0022-3697(67)90007-8


M acdonald J.R., Franceschetti D.R., and Lehnen A.R. (1980) Interfacial space charge and capacitance in ionic crystals: Intrinsic conductors. J. Chem. Phys. 73(10), 5272–5294. DOI: 10.1063/1.439956

M aier J. (1985) Space charge regions in solid two-phase systems and their conduction contribution—I. Conductance enhancement in the system ionic conductor-‘inert’ phase and application on AgC1:Al2O3 and AgC1:SiO2. J. Phys. Chem. Solids 46(3), 309–320. DOI: 10.1016/0022-3697(85)90172-6

M aier J. (1986) On the conductivity of polycrystalline materials. Ber. Bunsenges Phys. Chem. 90(1), 26–33. DOI: 10.1002/bbpc.19860900105

M aier J. (1987) Defect chemistry and conductivity effects in heterogeneous solid electro-lytes. J. Electrochem. Soc. 134(6), 1524–1535. DOI: 10.1149/1.2100703

M aier J. (1989a) Heterogeneous solid electrolytes. In: Chandra S. and Laskar A. (eds.), Superionic Solids and Solid Electrolytes: Recent Trends. Academic Press, New York, 137.

M aier J. (1989b) Kröger-Vink diagrams for boundary regions. Solid State Ionics 32/33, 727–733. D OI: 10.1016/0167-2738(89)90351-2

Ma ier J. (1995) Ionic conduction in space charge regions. Prog. Solid State Chem. 23(3), 171–263. DO I: 10.1016/0079-6786(95)00004-E

Maier J. (2002) Thermodynamic aspects and morphology of nano-structured ion con-ductors: Aspects of nano-ionics. Part I. Solid State Ionics 154–155, 291–301. DOI: 10.1016/0167-2738(02)00499-X

Ma ier J. (2003) Defect chemistry and ion transport in nanostructured materi-als: Part II. Aspects of nanoionics. Solid State Ionics 157(1–4), 327–334. DOI: 10.1016/0167-2738(02)00229-1

Ma ier J. (2004) Ionic transport in nano-sized systems. Solid State Ionics 175(1–4), 7–12. DOI: 10.1016/j.ssi.2004.09.051

Ma ier J. (2005) Nanoionics: Ion transport and electrochemical storage in confi ned systems. Nature Mater. 4(11), 805–815. DOI: 10.1038/nmat1513

Mc Lean D. (1957) Grain Boundaries in Metals. Clarendon Press, Oxford, UK.Na kamura O. and Saito Y. (1992) Interfacial conductivities in Na4Zr2Si3O12/insulator parti-

cle systems. In: Chowdary B.V.R. and Wang W. (eds.), Solid State Ionics: Materials and Applications. World Scientifi c, Singapore, 101.

No rby T. (2009) Proton conductivity in perovskite oxides. In: Ishihara T. (ed.), Perovskite Oxide for Solid Oxide Fuel Cells. Springer-Verlag, Dordrech, The Netherlands, 217–242.

Norrman K., Vels Hansen K., and Mogensen M. (2006) Time-of-fl ight secondary ion mass spectrometry as a tool for studying segregation phenomena at nickel-YSZ interfaces. J. Eur. Ceram. Soc. 26(6), 967–980. DOI: 10.1016/j.jeurceramsoc.2004.12.030

Pa rk C.O., Akbar S.A., and Weppner W. (2003) Ceramic electrolytes and electrochemical sensors. J. Mater. Sci. 38(23), 4639–4660. DOI: 10.1023/A:1027454414224

Poeppel R.B. and Blakely J.M. (1969) Origin of equilibrium space charge potentials in ionic crystals. Surface Sci. 15(3), 507–523. DOI: 10.1016/0039-6028(69)90138-1

Po nomareva V.G., Lavrova G.V., and Simonova L.G. (1999) The infl uence of heterogeneous dopant porous structure on the properties of protonic solid electrolyte in the CsHSO4–SiO2 system. Solid State Ionics 118(3–4), 317–323. DOI: 10.1016/S0167-2738(98)00429-9

Po nomareva V.G., Lavrova G.V., and Simonova L.G. (2000) Effect of silica porous structure on the properties of composite electrolytes based on MeNO3 (MeRb, Cs.). Solid State Ionics 136–137, 1279–1283. DOI: 10.1016/S0167-2738(00)00589-0

Po nomareva V.G., Lavrova G.V., Uvarov N.F., and Hairetdinov E.F. (1996) Composite pro-tonic solid electrolytes in the CsHSO4-SiO2 system. Solid State Ionics 90(1–4), 161–166. DOI: 10.1016/S0167-2738(96)00410-9


Po nomareva V.G. and Lavrova G.V. (2011) Controlling the proton transport properties of solid acids via structural and microstructural modifi cation. J. Solid State Electrochem. 15(2), 213–221. DOI: 10.1007/s10008-010-1227-1

Saito Y., Asai T., Ado K., and Nakamura O. (1988) Ionic conductivity enhancement of Na4Zr2Si3O12 by dispersed ferroelectric PZT. Mater. Res. Bull. 23(11), 1661–1665. DOI: 10.1016/0025-5408(88)90256-5

Sa ito Y. and Maier J. (1995) Ionic conductivity enhancement of the fl uoride conductor CaF2 by grain boundary activation using Lewis acids. J. Electrochem. Soc. 142(9), 3078–3083. DOI: 10.1149/1.2048691

Sa lamon S.B. (ed.) 1979 Physics of Superionic Conductors. Topics in Current Physics, Vol. 15. Springer-Verlag, Berlin.

Sato N. (1998) Electrochemistry at Metal and Semiconductor Electrodes. Elsevier, Amsterdam.Sc hoonman J. (1997) The defect chemistry in solid state electrochemistry. In: Gellings P.J.

and Bouwmeester H.J.M. (eds.), The CRC Handbook of Solid State Electrochemistry. CRC Press, Boca Raton, FL, chap. 5.

Schoonman J. (2005) Nanostructured materials in solid state ionics. Solid State Ionics 135(1–4), 5–19. DOI: 10.1016/S0167-2738(00)00324-6

Sh ahi K. and Wagner J.B. (1981) Enhanced electrical transport in multiphase systems. Solid State Ionics 3/4, 295–299. DOI: 10.1016/0167-2738(81)90101-6

Sh astry M.C.R. and Rao K.J. (1992) Thermal and electrical properties of AgI-based compo-sites. Solid State Ionics 51(3–4), 311–316. DOI: 10.1016/0167-2738(92)90214-A

Sh ukla A.K., Manoharan R., and Goodenough J.B. (1988) Ehancement of ionic conducti-vity by dispersed oxide inclusions: Infl uence of oxide isoelectric point and cation size. Solid State Ionics 26(1), 5–10. DOI: 10.1016/0167-2738(88)90238-X

Sh ukla A.K., Vaidehi N., and Jacob K.T. (1986) Ionic conduction in dispersed solid- electrolytes. Proc. Indian Acad. Sci. (Chem. Sci.) 96(1–2), 533–547.

Sh imizu Y. and Egashira M. (1999) Basic aspects and challenges of semiconductor gas sensors. MRS Bull. 24, 18–24.

Singh K., Lanje U.K., and Bhoga S.S. (1995) Ferroelectric and Al2O3 dispersed Li2CO3 com-posite solid electrolyte systems. In: Extended Abstracts: 10th International Conference on Solid State Ionics, December 3–8, Singapore, 112.

St ern O. (1924) Zur theorie der elektrolytischen doppelschicht. Z. für Electrochem. Angew. Phys. Chem. 30, 508–516.

Sun arso J., Baumann S., Serra J.M., Meulenberg W.A., Liu S., Lin Y.S., and Diniz da Costa J.C (2008) Mixed ionic–electronic conducting (MIEC) ceramic-based membranes for oxy-gen separation. J. Membrane Sci. 320(1–2), 13–41. DOI: 10.1016/j.memsci.2008.03.074

Tak ahashi T (ed) (1989) High Conducting Solid Ionics Conductors: Recent Trends and Applications. World Scientifi c, Singapore.

Tallon J.L., Buckley R.G., Staines M.P., and Robinson W.H. (1985) Vacancy formation parameters from isoelectric temperatures in calcium-doped potassium chloride. Phil. Mag. B 51(6), 635–649. DOI: 10.1080/13642818508243152

Tha ngadurai V. and Weppner W. (2006) Recent progress in solid oxide and lithium ion con-ducting electrolytes research. Ionics 12(1), 81–92. DOI: 10.1007/s11581-006-0013-7

Tschöpe A. (2001) Grain size-dependent electrical conductivity of polycrystalline cerium oxide II: Space charge model. Solid State Ionics 139(3–4), 267–280. DOI: 10.1016/S0167-2738(01)00677-4

Tschöpe A., Sommer E., and Birringer R. (2001) Grain size-dependent electrical conduc-tivity of polycrystalline cerium oxide: I. Experiments. Solid State Ionics 139(3–4), 255–265. DOI: 10.1016/S0167-2738(01)00678-6


Tschö pe A., Kilassonia S., and Birringer R. (2004) The grain boundary effect in heavily doped cerium oxide. Solid State Ionics 173(1–4), 57–61. DOI: 10.1016/j.ssi.2004.07.052

Tuller H.L. (2003) Defect engineering: design tools for solid state electrochemical devices. Electrochim. Acta 48(20–22), 2879–2887. DOI: 10.1016/S0013-4686(03)00352-9

Ulihin A.S., Slobodyuk A.B., Uvarov N.F., Kharlamova O.A., Isupov V.P., and Kavun V.Ya. (2008) Conductivity and NMR study of composite solid electrolytes based on lithium perchlorate. Solid State Ionics 179(27–32), 1740–1744. DOI: 10.1016/j.ssi.2008.02.027

Ulihin A.S., Uvarov N.F., Mateyshina Yu.G., Brezhneva L.I., and Matvienko A.A. (2006) Composite solid electrolytes. Solid State Ionics 177(26–32), 2787–2790. DOI: 10.1016/j.ssi.2006.03.018

Ulihin A.S. and Uvarov N.F. (2009) Electrochemical properties of composite solid electro-lytes LiClO4–MgO. ECS Trans. 16(51), 445–448. DOI: 10.1149/1.3242260

Urusov skaya A.A. (1969) Electric effects associated with plastic deformation of ionic crystals. Sov. Phys. Usp. 11(5), 631–643. DOI: 10.1070/PU1969v011n05ABEH003738

Uvarov N.F., Shastry M.C.R., and Rao K.J. (1990) Structure and ionic transport in Al2O3-containing composites. Rev. Solid State Sci. 4(1), 61–67.

Uvarov N.F., Isupov V.P., Sharma V., and Shukla A.K. (1992) Effect of morphology and particle size on the ionic conductivities of composite solid electrolytes. Solid State Ionics 51(1–2), 41–52. DOI: 10.1016/0167-2738(92)90342-M

Uvarov N.F., Khairetdinov E.F., and Bratel N.B. (1993) Composite solid electrolytes in the system AgI-Al2O3. Elektrokhimiya 29(11), 1406–1410 (in Russian).

Uvarov N.F., Bokhonov B.B., Isupov V.P., and Hairetdinov E.F. (1994) Nanocomposite ionic conductors in the Li2SO4-Al2O3 system. Solid State Ionics 74(1–2), 15–27. DOI: 10.1016/0167-2738(94)90432-4

Uvarov N.F. (1996a) Unusual bulk properties of ionic conductors in nanocomposites. In: Chowdary B.V.R. and Wang W. (eds.), Solid State Ionics: New Developments. World Scientifi c, Singapore, 311.

Uvarov N.F., Hairetdinov E.F., and Bratel N.B. (1996b) High ionic conductivity and unu-sual thermodynamic properties of silver iodide in AgI-Al2O3 nanocomposites. Solid State Ionics 86–88(1), 573–576. DOI: 10.1016/0167-2738(96)00207-X

Uvarov N.F., Hairetdinov E.F., and Skobelev I.V. (1996c) Composite solid electro-lytes MeNO3-Al2O3 (Me Li, Na, K). Solid State Ionics 86–88(1), 577–580. DOI: 10.1016/0167-2738(96)00208-1

Uvarov N.F., Skobelev I.V., Bokhonov B.B., and Hairetdinov E.F. (1996d) Composite solid electrolytes based on rubidium and cesium nitrates. J. Mater. Synthesis Processing 4(6), 391–395.

Uvarov N.F., Vanek P., Yuzyuk Yu.I., Zelezny V., Studnicka V., Bokhonov B.B., Dulepov V.E., and Petzelt J. (1996e) Properties of rubidium nitrate in ion-conducting RbNO3-Al2O3 nanocomposites. Solid State Ionics 90(1–4), 201–207. DOI: 10.1016/S0167-2738(96)00400-6

Uvarov N.F., Politov A.A., and Bokhonov B.B. (2000a) Amorphization of ionic salts in nano-composites. In: Chowdary B.V.R. and Wang W. (eds.), Solid State Ionics: Materials and Devices. World Scientifi c, Singapore, 113.

Uvarov N.F. and Vanek P. (2000b) Stabilization of new phases in ion-conducting nanocompo-sites. J. Mater. Synthesis Processing 8(5–6), 319–326. DOI: 10.1023/A:1011346528527

Uvarov N.F., Vanek P., Savinov M., Zelezny V., Studnicka V., and Petzelt J. (2000c) Percolation effect, thermodynamic properties of AgI and interface phases in AgI–Al2O3 composites. Solid State Ionics 127(3–4), 253–267. DOI: 10.1016/S0167-2738(99)00288-X

Uvarov N.F., Brezhneva L.I., and Hairetdinov E.F. (2000d) Effect of nanocrystalline alumina


on ionic conductivity and phase transition in CsCl. Solid State Ionics 136–137, 1273–1277. DOI: 10.1016/S0167-2738(00)00587-7

Uvarov N.F. and Boldyrev V.V. (2001) Size effects in chemistry of heterogeneous systems. Russ. Chem. Rev. 70(4), 265–284. DOI: 10.1070/RC2001v070n04ABEH000638

Uvarov N.F. (2007a) Ionics of nanoheterogeneous materials. Russ. Chem. Rev. 76(5), 415–434. DOI: 10.1070/RC2007v076n05ABEH003687

Uvarov N.F. (2007b) Surface disordering of classic and superionic crystals: A description in the framework of the Stern model. Russ. J. Electrochem. 43(4), 368–376. DOI: 10.1134/S1023193507040027

Uvarov N.F. (2008a) Composite Solid Electrolytes. Nauka, Novosibirsk (in Russian).Uvarov N.F. (2008b) Estimation of the surface potential in superionic oxide conduc-

tors using the Stern model. Solid State Ionics 179(21–6), 783–787. DOI: 10.1016/j.ssi.2008.01.043

Uvarov N.F. (2008c) Estimation of the surface potential and concentration of surface de-fects in superionic oxides. ECS Trans. 11(33), 207–216. DOI: 10.1149/1.3038924

Uvarov N.F. (2011) Composite solid electrolytes: Recent advances and design strategies. J. Solid State Electrochem. 15(2), 367–389. DOI: 10.1007/s10008-008-0739-4

Vashis hta P., Mundy J.N., and Shenoy G.K. (eds.) (1979) Fast Ion Transport in Solids. Elsevier/North-Holland, New York.

Verker k M.J., Hammink M.W.J., and Burggraaf A.J. (1983) Oxygen transfer on substituted ZrO2, Bi2O3 and CeO2 electrolytes with platinum electrodes, J. Electrochem. Soc. 130(1), 70–78. DOI: 10.1149/1.2119686

Vinod M.P. and Bahnemann D. (2002) Materials for all-solid-state thin-fi lm rechargeable lithium batteries by sol-gel processing. J. Solid State Electrochem. 6(6), 498–501. DOI: 10.1007/s10008-001-0251-6

Wagner J.B. (1985) Composite materials as solid electrolytes. In: Sequeira C.A.C. and Hooper A. (eds.), Solid State Batteries. NATO ASI Series E101. Martinus Nijhoff, Dordrecht, The Netherlands, 77.

Wagner J.B. (1989) Composite solid electrolytes. In: Takahashi T. (ed.), High Conductivity Conductors: Solid Ionic Conductors. World Scientifi c, Singapore, 102

Wang D.Y., Park D.S., Griffi th J., and Nowick A.S. (1981) Oxygen-ion conductivity and defect interactions in yttria-doped ceria. Solid State Ionics 2(2), 95–105. DOI: 10.1016/0167-2738(81)90005-9

Wang C ., Yin L., Zhang L., Xiang D., and Gao R. (2010) Metal oxide gas sensors: Sensitivity and infl uencing factors. Sensors 10(3), 2088–2106. DOI: 10.3390/s100302088

Waser R. (1995) Electronic properties of grain boundaries in SrTiO3 and BaTiO3 ceramics. Solid State Ionics 75, 89–99. DOI: 10.1016/0167-2738(94)00152-I

Whitwo rth R.W. (1975) Charged dislocations in ionic crystals. Adv. Phys. 24(2), 203–304. DOI: 10.1080/00018737500101401

Wilkes M.F., Hayden P., and Bhattacharya A.K. J. (2003) Catalytic studies on ceria lan-thana solid solutions III. Surface segregation and solid state studies. J. Catal. 219(2), 305–309. DOI: 10.1016/S0021-9517(03)00046-0

Wonnel l S.K. and Slifkin L.M. (1995) Subsurface ionic space charges in silver chloride and silver bromide. Solid State Ionics 75, 101–106. DOI: 10.1016/0167-2738(94)00149-M

Yarost alvtsev A.B. (2000) Ion transport in heterogeneous solid systems. Russ. J. Inorg. Chem. 45(suppl. 3), S249–S267.

Zhu J. , Van Ommen J.G., Knoester A., and Lefferts L.J. (2005) Effect of surface compo-sition of yttrium-stabilized zirconia on partial oxidation of methane to synthesis gas. J. Catal. 230(2), 291–300. DOI: 10.1016/j.jcat.2004.09.025

koro 5 chap one

Documents

electrochemical gas

nox sensors

sox sensors

amperometric sensors

oxygen sensors

hydrogen sensors

mixed potentiometric

new yorkchemical sensors