Physical chemistry of ionic materials ions and electrons in solids

Physical Chemistry of Ionic Materials: Ions and Electrons in Solids.Joachim Maier Copyright  2004 John Wiley & Sons, Ltd... 2.1.6 Two-body potential functions 2.2 Many atoms in contact:

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Physical Chemistry of Ionic Materials: Ions and Electrons in Solids.

Joachim Maier Copyright  2004 John Wiley & Sons, Ltd ISBNs: 0-470-99991-1 (HB); 0-470-87076-1 (PB)

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Contents

1 Introduction

1.1 Motivation

1.2 The defect concept: Point defects as the main actors

2 Bonding aspects: From atoms to solid state

2.1 Chemical bonding in simple molecules

2.1.1 Ideal covalent bonding

2.1.2 Polar covalent bonding

2.1.3 The ionic bonding

2.1.4 Metallic bonding

2.1.5 Further intermediate forms of chemical bonding

2.1.6 Two-body potential functions

2.2 Many atoms in contact: The solid state as a giant molecule

2.2.1 The band model

2.2.2 Ionic crystals

2.2.3 Molecular crystals

2.2.4 Covalent crystals

2.2.5 Metallic crystals

2.2.6 Mixed forms of bonding in solids

2.2.7 Crystal structure and solid state structure

4.2 The formalism of equilibrium thermodynamics

4.3 Examples of equilibrium thermodynamics

4.3.1 Solid-solid phase transition

4.3.2 Melting and evaporation

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4.3.5 Phase equilibria and mixing reactions

4.3.6 Spatial equilibria in inhomogeneous systems

4.3.7 Thermodynamics of elastically deformed solids

4.3.8 The thermodynamic functions of state of the perfect solid

5 Equilibrium thermodynamics of the real solid

5.1 Preliminary remarks

5.2 Equilibrium thermodynamics of point defect formation

5.3 Equilibrium thermodynamics of electronic defects

5.4 Higher-dimensional defects

5.4.1 Equilibrium concentration

5.4.2 Dislocations: Structure and energetics

5.4.3 Interfaces: Structure and energetics

5.4.4 Interfacial thermodynamics and local mechanical equilibria 5.5 Point defect reactions

5.5.1 Simple internal defect equilibria

5.5.2 External defect equilibria

5.8.4 Defect thermodynamics of the interface

5.8.5 Examples and supplementary comments

6 Kinetics and irreversible thermodynamics

6.1 Transport and reaction

6.1.1 Transport and reaction in the light of irreversible

thermodynamics 6.1.2 Transport and reaction in the light of chemical

kinetics 6.2 Electrical mobility

6.2.1 Ion mobility

6.2.2 Electron mobility

6.3 Phenomenological diffusion coefficients

6.3.1 Ion conduction and self-diffusion

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Contents

6.5 Diffusion kinetics of stoichiometry change

6.6 Complications of matter transport

6.7.3 Phenomenological rate constants

6.7.4 Reactivity, chemical resistance and chemical capacitance 6.8 Catalysis

6.9 Solid state reactions

6.10.2 Nonequilibrium structures in time and space

6.10.3 The concept of fractal geometry

7 Solid state electrochemistry:

Measurement techniques and applications

7.1 Preliminary remarks:

Current and voltage in the light of defect chemistry

7.2 Open circuit cells

7.3.3 Bulk and phase boundary effects

7.3.4 Stoichiometry polarization

7.3.5 Coulometric titration

7.3.6 Impedance spectroscopy

7.3.7 Inhomogeneities and heterogeneities:

Many-point measurements and point electrodes 7.4 Cells generating current

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in general for inhomogeneous and heterogeneous systems They are discussed briefly

at the end of this chapter, but are, above all, significant for the discussion of thedistribution of charge carriers in boundary layers (see Section 5.8) and for kinetics

in general (Chapter 6) Consideration of surfaces and thus of morphology is shifted

to Section 5.4

According to Fig 1.2 we decompose thermodynamic functions into contributionsthat arise from (chemically)2 perfect solids and contributions that are brought in bydefects At this point we are now interested in the equilibrium thermodynamics ofthe (chemically) perfect state Our aim is to sketch the free enthalpy of the perfectsolid with the aid of the previous chapters on chemical bonding and phonons, as well

as to consider relevant aspects of the thermodynamic formalism and its application

to solids, in particular in view of interactions with the chemical environment.Let us first build up the necessary thermodynamic apparatus Readers familiar withsolid state thermodynamics can omit this chapter

4.2 The formalism of equilibrium

thermodynamics

The aim of thermodynamics is to express functions of state such as Gibbs energy(free enthalpy) in terms of state variables and to obtain relevant information on theequilibrium state Both the first and second laws make statements concerning thevariation of a particular extensive state function of a given system with regard to

1 Later we essentially use the intensive parameters temperature and chemical component tentials (component partial pressures) as variables Note that fixing the particle numbers in a given equilibrium system of given pressure or of given volume also defines the component partial pressures.

po-2 The addendum "chemical" is intended to emphasize that phonons are elements of the perfect solid as it is defined here On the other hand, "chemical" at this point also includes effects that can, with some justification, be regarded as crystallographic.

Physical Chemistry of Ionic Materials J Maier

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Physical Chemistry of Ionic Materials: Ions and Electrons in Solids

alkaline earth elements, 45

alkaline earth halide, 51, 63, 69, 113ff,

114, 151ff, 159, 242, 245, 412

alkaline earth oxide, 78, 92, 378, 412

alkaline earth stannate, see perovskite,

see proton conductor

alkaline earth titanate, see perovskite

associate, 174, 185, 193, 200ff, 327f attractor, 270, 382ff

autocatalysis, 386ff band, 35ff, 54ff, 126ff band bending, 222 band gap, 40ff, 126ff, 192, 213, 266,

404, 419 band model, 36ff, 54ff, 202ff, 222ff band structure, 48, 125ff, 191

band-band transition, see electron

transfer

barium oxide, see alkaline earth oxide barium titanate, see perovskite

battery, 481ff, 487ff high performance, 290, 481ff lead, 492

lithium, 481ff, 487ff metal-air, 481, 488, 494 Na-S, 289, 492f

Ni-Cd, 492 nickel hydride, 494 rocking chair, 491f silver, 488

zebra, 493 zinc, 488f, 494 bismuth, 33 bismuth oxide, 352 Bjerrum concept, 201 Bloch wave, 40 Boltzmann distribution, 66, 80, 117ff,

124fT, 217ff

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boundary phase transition, 261

brick layer model, 474

caesium chloride structure, 62

caesium hydrogen sulfate, 261, 287

calcium fluoride, see alkaline earth

halide

capacitance chemical, ambipolar, 83, 301, 344, 361f, 445ff, 451, 458f

double-layer, 428ff electrical, 403, 426ff phase boundary, 428ff, 438ff space charge, 440ff, 458ff

capacitor, see supercapacitor, see

ca-pacitance Carter equation, 377 catalysis, 351, 362ff cell

battery, see battery

electrochemical, 399ff, 424ff, 481ff equilibrium, 404ff

fuel, see fuel cell

galvanic, 48 Iff photoelectrochemical, 419f polarization, 418ff

transference, 413

cerates, see perovskite, see proton

con-ductor ceria, 248, 287, 352, 430, 434f, 484f

cerium oxide, see ceria

chaos, 388f

charge transfer, see transfer reaction

chemical potential, 75ff, 119ff, 134,

146ff, 155ff, 177ff, 200ff, 217ff, 268ff, 399ff

chemical relaxation, 312ff chlorine molecule, 26, 32, 56 chromium oxide, 92

climbing, 138 close-packing of spheres, 62, HOff cluster, 32, 35, 260

cluster compounds, 32, 61 cobalt oxide, 310, 363, 397, 490f colloids, 217

colour centres, 206f concentration ambipolar, 302, 326f, 336, 451

conduction band, 35ff, see band

conduction electron, 14ff, 125ff

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cybernetics, see system analysis

Dalton composition, see intrinsic

electronic, see conduction tron, see hole, see conduction

elec-electron line, 108, 134ff plane, 108, 134ff, 217ff point, 14ff, 108ff, 155ff defect cluster, 208

defect formation atomistics, 109ff thermodynamics, 109ff, 155ff defect notation, 16f

defect strength, 210 degeneracy, 123, 130ff degree of freedom composition (variance), 149 interface crystallography, 144

of motion, 65 degree of influence, 225ff dehydrohalogenation, 365f delta function, 309, 463

demixing, see phase separation

density functional, 50 density of states, 38ff, 45 effective, 125

depolarization chemical, 417f diamond, 44ff, 57ff, 70f, 109f, 126 dielectric constant, 110, 210ff, 223ff,

426 diffusion, 20, 268ff, 444ff chemical, 332ff tracer, 332ff diffusion coefficient charge, 283, 295ff, 305ff, 331 chemical, ambipolar, 300ff, 305fT, 312f, 368ff, 444ff, 490

Fick's law, 279 random walk, 280 tracer, 296ff, 305ff diffusion potential, 409 diode characteristic, 433

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heterogeneous, see S-theorem

homogeneous, see C-theorem

double tangent construction, 95ff

268ff, 338ff, 367, 399ff electronegativity, 28ff, 31, 133 elliptical integrals, 257

EMF, see cell voltage

energy internal, 72ff kinetic, 25f, 36ff energy eigenvalue, 25ff, 37ff enstatite, 61

enthalpy, 75, 83 entropy, 74ff, 210, 217ff, 270ff, 382ff entropy production, 270ff, 382ff, 403 equilibrium conditions, 74, 81ff, 93ff,

101, 120ff, 217ff, 404ff equivalent circuit, 424ff, 444ff, 462ff EVD, 376

ex situ parameter, 144, 179, 183f, 194 exchange flux density, 435ff

exchange rate, 278, 343, 350ff, 435 exchange reactivity, 361

exciton, 207 extrinsic, 125ff, 161ff, 177ff faceting, 151

fellow traveller effect, 248 Fermi energy, 39, 126ff Fermi function, 133 Fermi level, 222 Fermi-Dirac distribution, 80, 119f,

125, 130ff, 215f Fick's law, 272ff, 275fT, 279, 307ff filter, (electro-) chemical, 418 fluorite structure, 62

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Helmholtz layer, 439f Henryan normalization, 77, lOOf Herring's relation, 151

heterogeneities, 217ff, 268f, 367ff, 473ff heterogeneous solid electrolytes, 240ff high temperature electrolysis, 419

high temperature superconduction, see

cuprate high temperature, SOFC, 485ff hole

atomic, see vacancy

electron-, 14ff, 125ff hollandite, 290f

Hooke's law, 34, 138 hybrid, 27

hydrocarbon, 27, 32, 56, 60, 364ff,

418ff, 48 Iff hydrogen (atom, molecule, molecule-

ion), 23ff, 44, 90, 196, 482ff hydrogen bonds, 29, 56

hydrogen chloride, 29, 56

I-regime, 167 impact ionization, 390f impedance, see impedance spectro-

scopy impedance spectroscopy, 462ff inclusion, 153

indium antimonide, 49, 126, 292 insulator, 40ff

interaction defect, 200ff, 319ff electron, 50 electron-phonon, see Cooper pair

orbital, see bonding

intercalation, 489ff interface, 108, 134ff, 217ff, 332ff interface core, 143f, 217ff, 333

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lanthanum gallate, see perovskite

lanthanum manganate, see perovskite

lanthanum nickel hydride, 494

Laplace transformation, 307, 464ff lattice energy, 52, 56, 58, 105f lattice molecule, 109, 119, 122ff, 155,

303, 429f, 453f lever rule, 95ff

Liesegang phenomenon, 391 life-time semiconductor, 230

ligand field effect, see crystal field

ef-fect limiting current, 437, 483 Lindemann's relation, 71 line of dislocation, 137 line tension, energy, 255 Lippmann's equation, 148 lithium, 468, 487ff

lithium cells, see battery lithium cobaltate, 490f, 498

lithium halide, see alkali halide

lithium manganate, 490f, 498 lithium nickelate, 490f, 498 lithium nitride, 289f, 497 lithium sulfate, 290 lithium vanadate, 490f living systems, 385ff Ljapunov function, 379, 384 macrostructure, 63

Madelung constant, 5Iff, 21 If Madelung energy, 51ff, 21 If Magneli phases, 208

magnesia, 54f, 92, 205, 377, 414 magnesium metal, 33, 45

magnesium oxide, see alkaline earth

oxide, see magnesia

manganese oxide, 97, 363, 412, 488 mass

effective, 132

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Index

mass action law, 82ff, 120ff, 146ff,

155ff, 177ff, 200ff, 217ff

mass transport, see diffusion

master equation, see rate equation

mixed alkali effect, 322

mixed bonding forms, 53

266f Nasicon, 85, 289ff, 412 native, 18, 155ff, 161ff, 186 neighbouring phase, 19, 161ff, 217ff,

338ff, 362ff, 367ff, 399ff NEMCA effect, 364, 419 Nernst voltage, 406ff Nernst-Einstein equation, 274 Neumann's relation, 151 nickel, 373, 397, 410, 484, 493, 499 nickel arsenide, 62

nucleation, 148f, see phase formation,

375 number of states, 45 Ohm's law, 272, 274, 282f, 418ff Onsager relations, 271, 386 orbitals, 26ff

oscillating reaction, 384, 388f Ostwald ripening, 148, 381 overlap integral, 25

oxide, 12, 16ff, 55, 78f, 92, 340ff,

352, 362ff, 404ff, 412, 414, 419, 424ff

oxygen, 14ff, 79, 89ff, 108ff, 268ff, 399ff paddle wheel mechanism, 290

pair bonding energy, 53, 58, 96, 105f partition sum, 66

PEEK, 258 Peierls distortion, 44, 293 Peierls energy, 138

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498 potential function, 33ff Born-Mayer, 33 Lennard-Jones, 33, 56, 57 Mie, 33ff, 53, 56, 65 Morse, 33

P-regime, 167 primary cell, 481, 487ff proton conductor, 115, 194ff, 215, 258,

291f, 304, 331, 376, 407, 416,

419, 486 pseudo potential, 49

P T C R effect, 262ff P-theorem, activity rule, 168, 205 pulsating mercury drop, 391 pyrochlore, 175f, 485

quasi-stationarity, 338ff, 374 quenching process, 194f Raoultian normalization, lOOf rate constant

apparent (solid state reaction), 370ff

effective, 347ff, 437 elementary, 269ff, 283ff, 306, 338ff rate equation, 269ff, 430ff

reaction constant effective, 344 reaction coupling, 340 reaction equilibrium, 81ff, 93ff, 120ff,

155fT, 220 reaction progress variable, 81 reaction rate, 82, 268ff, 270ff, 278,

324f, 338ff, 362ff, 367ff, 430ff reactivity, 342, 361

reactor, electrochemical, 419f reciprocal space, 42

recombination centres, 367 relaxation, llOff, 312ff, 319ff, 332, 472 www.pdfgrip.com

Tiêu đề	Physical Chemistry of Ionic Materials: Ions and Electrons in Solids
Tác giả	Joachim Maier
Trường học	John Wiley & Sons, Ltd.
Chuyên ngành	Physical Chemistry
Thể loại	book
Năm xuất bản	2004

Định dạng
Số trang	538
Dung lượng	21,54 MB