Structure and dynamics: an atomic view of materials
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Edition: | [Reprint.] |
| Series: | Oxford master series in physics
1 : condensed matter physics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 334 S. Ill., graph. Darst. |
| ISBN: | 9780198506782 |
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MARC
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| 100 | 1 | |a Dove, Martin T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Structure and dynamics |b an atomic view of materials |c Martin T. Dove |
| 250 | |a [Reprint.] | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a XXII, 334 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford master series in physics |v 1 : condensed matter physics | |
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| 830 | 0 | |a Oxford master series in physics |v 1 : condensed matter physics |w (DE-604)BV017064373 |9 1 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017605099 | ||
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| adam_text | Contents
Symbols xix
1
Introduction
1
1.1
Observations
1
1.1.1
Microscópio
and macroscopic properties of solids
1
1.1.2
Physical characteristics of crystals
1
1.1.3
Physical properties of crystals
2
1.1.4
Thermodynamic properties of crystals
8
1.1.5
So what do some simple observations tell us?
10
1.2
Length scales and time scales
12
1.3
Tools of the trade
13
1.3.1
Theoretical and mathematical tools
13
1.3.2
Experimental tools
15
1.3.3
Special tools and concepts for the study of the structure
and dynamics of crystals
16
Summary of chapter
17
Further reading for Chapter
1 17
2
Structure of materials
18
2.1
Introduction
18
2.2
Crystal structures of the elements
19
2.2.1
Close-packed metals
19
2.2.2
Body-centred cubic packing
25
2.2.3
Simple cubic packing
25
2.2.4
Crystal structures of elements with covalent bonding
26
2.2.5
Diatomic molecular structures and other molecular
elements
27
2.2.6
Summary of the structures of the elements
29
2.3
Crystal structures of some simple inorganic compounds
29
2.3.1
Diatomic compounds
29
2.3.2
Ionic packing
31
2.3.3
Crystals with general formula AXm
,
and the general idea
of coordination polyhedra
32
2.4
The perovskite family of crystal structures
35
2.4.1
The ideal perovskite structure
35
2.4.2
Ferroelectric phase transitions in perovskites
37
2.4.3
Rotational phase transitions
38
2.4.4
Effects of chemical variation
39
2.4.5
Variations on the perovskite theme
40
χ
Contents
2.5
Organie
crystals
40
2.6
Disordered materials
41
2.6.1
The importance of structural disorder
41
2.6.2
Orientational disorder in molecular crystals
41
2.6.3
Orientational disorder in framework structures
42
2.6.4
Fast-ion conductors
43
2.6.5
Liquid crystals
43
2.7
Glasses and amorphous phases
44
2.7.1
Glasses and structural disorder
44
2.7.2
Quantifying short-range order
45
2.7.3
Amorphous and crystalline phases of silica
47
2.8
Conclusions
48
Summary of chapter
49
Further reading
50
Exercises
50
Formal description of crystal structures
52
3.1
Introduction
52
3.2
Crystal structure: lattices, unit cell, and atomic coordinates
53
3.2.1
Definition of the crystal lattice
53
3.2.2
The unit cell
54
3.2.3
Lattices, lattice parameters, and symmetry: the seven
crystal systems
54
3.2.4
Volume of the unit cell
56
3.2.5
Conventional and primitive lattices: The
14
Bravais
lattices
56
3.2.6
Atomic coordinates
57
3.2.7
Crystal structure as the convolution of the lattice and the
atomic basis
58
3.3
Crystal symmetry
1.
Point-symmetry operations
61
3.3.1
Point symmetry
61
3.3.2
The four point symmetry operations
61
3.3.3
Combination of symmetry operations
64
3.3.4
The
32
crystallographic point groups
65
3.4
Application of the formalism of point groups
66
3.4.1
Symmetry of the crystal
66
3.4.2
Symmetry breaking transformations
68
3.5
Crystal symmetry
2.
Translational symmetry and space groups
70
3.5.1
Translational symmetry
70
3.5.2
Enumeration of the space groups
72
3.6
Breaking the rules: aperiodic structures, incommensurate
materials, and quasicrystals
73
3.6.1
Incommensurate or modulated structures
73
3.6.2
Quasicrystals
74
Summary of chapter
74
Further reading
75
Exercises
76
Contents xi
The reciprocal lattice
78
4.1
The concept of the reciprocal lattice
78
4.2
Definitions
79
4.2.
ł
Geometry of the reciprocal lattice and its link to the
crystal lattice
80
4.2.2
Relationship between real and reciprocal lattice
parameters
81
4.2.3
Interplanar spacing and the reciprocal lattice parameters
82
4.2.4
Reciprocal lattice vectors and atomic structure
82
4.3
Non-primitive lattices
82
4.3.1
Some general principles and practical methods
82
4.3.2
Primitive and non-primitive lattices: application to bcc
and fee lattices
85
4.4
The reciprocal lattice as the Fourier transform of the crystal lattice
86
4.5
Reciprocal space and the Brillouin zone
87
Summary of chapter
89
Further reading
90
Exercises
90
Atomic bonding in crystals
91
5.1
Bonding and the variety of crystal structures
91
5.2
Thermodynamic preamble: the context of the binding energy
91
5.3
Lattice energy
94
5.4
Models of bonding
96
5.4.1
Coulomb energy
96
5.4.2
Repulsive interactions
98
5.4.3
Combination of Coulomb and Born-Mayer interactions:
example of alkali halides
98
5.4.4
Dispersive interactions: binding in molecular crystals
99
5.4.5
Shell models
100
5.4.6
Hydrogen bonds
101
5.4.7
Empirical representations of
co
valent
and metallic
bonding
102
5.5
Quantum mechanical view of chemical bonding
105
5.5.1
The need to take a proper quantum-mechanical view
105
5.5.2
Born-Oppenheimer approximation
106
5.5.3
Bloch s theorem for electrons in a periodic structure
106
5.5.4
Simple view of bonding in molecules
107
5.5.5
Tight-binding methods
108
5.5.6
Electron-electron interactions: Hartree-Fock and beyond
110
5.5.7
Representation of electronic wave functions
112
5.5.8
Practical calculations of binding energies from quantum
mechanics
114
Summary of chapter
114
Further reading
115
Exercises
115
xii Contents
Diffraction
117
6.1 Basics
of diffraction
117
6.1.1
Use
of
radiation
beams
117
6.1.2
Bragg slaw
118
6.1.3
Single-crystal and powder
diffraction
measurements
118
6.1.4
Diffraction
and crystal
structures
119
6.2
Beams of
radiation
and measurement of
diffraction
patterns 1
19
6.2.1
Laboratory X-ray methods
119
6.2.2
Measurement of the intensity of scattered X-ray beams
120
6.2.3
Synchrotron X-ray sources
122
6.2.4
Neutron beams
123
6.2.5
Comparison of the characteristics of X-ray and neutron
beams
126
6.2.6
Beams of electrons
129
6.3
Basics of the theory of diffraction
129
6.3.1
The wave equation
129
6.3.2
Scattering of radiation from two particles
130
6.3.3
Scattering of radiation from a collection of particles
132
6.4
Scattering of radiation from a continuous distribution of
particles
133
6.4.1
General principle
133
6.4.2
X-ray atomic scattering factor
133
6.4.3
Neutron scattering factors
134
6.5
Diffraction and Fourier analysis
134
6.5.1
Scattering processes as Fourier transforms
134
6.5.2
Fourier transforms and convolution
135
6.6
Application: the structure of glasses revealed by neutron
scattering
136
6.7
Diffraction from crystalline materials
138
6.7.1
Fourier transform of the perfect crystal
138
6.7.2
The effect of particle size on the diffraction pattern
140
6.7.3
The inverse transform: obtaining the electron
density from X-ray diffraction measurements of the
structure factor
140
6.7.4
The phase problem
141
6.8
Effects of symmetry on diffraction patterns
142
6.8.1
Friedel slaw
142
6.8.2
Point symmetry of diffraction patterns
144
6.8.3
Centre of symmetry
145
6.8.4
Systematic absences
145
6.8.5
Determination of space-group symmetry
147
6.9
Solution of the phase problem and determination of crystal
structure
149
6.9.1
The origin of the phase problem
149
6.9.2
Historical review of attempts to bypass the phase
problem
149
6.9.3
Direct methods to overcome the phase problem
150
6.9.4
Refinement of the crystal structure
151
Contents xiii
Summary of chapter
152
Further reading
153
Exercises
154
7
Physical properties
156
7.1
Overview
156
7.1.1
Crystal anisotropy
156
7.1.2
An introduction to tensors
157
7.1.3
Field and matter tensors
158
7.2
First-rank tensors
158
7.3
Second-rank tensors
158
7.3.1
Basic ideas
158
7.3.2
Stress as a second-rank tensor
160
7.3.3
Strain as a second-rank tensor
160
7.3.4 45°
rotation of the strain tensor and the conversion
between tensile and shear strain
161
7.3.5 Voigt
notation
162
7.3.6
Principal axes
163
7.3.7
Symmetry and second-rank matter tensors
164
7.3.8
Example of zero thermal expansion
164
7.4
Third-rank tensors
165
7.4.1
Piezoelectricity
165
7.4.2
Use of
Voigt
notation for third-rank tensors
169
7.4.3
Transformations of third-rank tensors
169
7.5
Fourth-rank tensors
171
7.5.1
A hierachy of higher-order tensors
171
7.5.2
The elasticity tensors
171
7.6
Induced changes in matter tensors
172
7.6.1
Basic ideas
172
7.6.2
Refractive index, the electro-optic effect, and the
photoelastic effect
172
Summary of chapter
173
Further reading
173
Exercises
173
8
Lattice dynamics
175
8.1
Why do we need to consider dynamics?
175
8.2
The harmonic approximation
175
8.3
Lattice vibrations of one-dimensional monatomic crystals
176
8.3.1
The linear chain model
176
8.3.2
Sound waves
-
vibrations with long wavelengths
177
8.3.3
Vibrations with shorter wavelengths: general features
178
8.3.4
Vibrations with shorter wavelengths: the special case of
λ
=
2я
178
8.3.5
Vibrations with shorter wavelengths: the general case
179
8.3.6
Extension of model of monatomic chain to include
distant neighbours
180
8.3.7
Reciprocal lattice, the Brillouin zone, and allowed
wave vectors
181
xiv Contents
8.3.8
Three-dimensional monatomic crystals:
general principles
182
8.4
Dispersion curves in face-centred cubic materials
183
8.4.1
Dispersion curves of neon
183
8.4.2
Dispersion curves of lead
187
8.4.3
Dispersion curves of potassium
187
8.5
Lattice vibrations of crystals with several atoms in the unit cell
189
8.5.1
The basic model
189
8.5.2
Solution for small wave vector
190
8.5.3
General result
192
8.5.4
Generalization for more complex cases: atomic motions
193
8.5.5
Generalization for more complex cases:
the dynamical matrix
194
8.5.6
Lattice dynamics of ionic crystals
196
8.5.7
The lattice dynamics of the alkali halides
197
8.5.8
The lattice dynamics of quartz
198
Summary of chapter
199
Further reading
200
Exercises
200
9
Thermodynamics and lattice dynamics
202
9.1
The quantization of lattice vibrations
202
9.1.1
Phonons: the quanta of harmonic lattice vibrations
202
9.1.2
The Bose-Einstein relation,
η(ω, Τ)
203
9.1.3
High-temperature behaviour
204
9.1.4
Heat capacity
204
9.1.5
Phonon free energy and entropy
205
9.2
Thermodynamic functions for crystals
206
9.2.1
Thermodynamic functions
206
9.2.2
The Einstein model
206
9.2.3
Density of states
207
9.2.4
Density of states for acoustic modes
207
9.2.5
Debye model of heat capacity
208
9.2.6
Example of thermodynamic functions of
fluorite, CaF2
209
9.3
Atomic displacements
211
9.3.1
Normal mode coordinates
211
9.3.2
Vibrational energy and amplitude
211
9.3.3
Recasting the crystal Hamiltonian
212
Summary of chapter
213
Further reading
214
Exercises
214
10
Experimental methods for measurements of vibrational
frequencies
216
10.1
Introduction
216
10.2
Basic ideas of spectroscopy
217
10.3
Neutron scattering techniques
219
10.3.1
Neutrons for
spectroscopie
measurements
219
Contents xv
10.3.2 Neutron
scattering experimental methods: the triple-axis
spectrometer
219
10.3.3
General formalism of neutron scattering
222
10.3.4
Applications of neutron inelastic scattering
226
10.4
Inelastic X-ray scattering
228
10.5
Light scattering
228
10.5.1
Basic idea of Raman scattering
228
10.5.2
Mechanism of Raman scattering
229
10.5.3
Applications of Raman spectroscopy
230
10.5.4
Brillouin scattering
231
10.6
Infrared absorption spectroscopy
231
Summary of chapter
233
Further reading
234
Exercises
234
11
Anharmonic interactions
236
11.1
Introduction
236
11.2
Thermal conductivity
239
11.3
Thermal expansion
241
11.3.1
Theory
241
11.3.2
Example: calculation of thermal expansion in
fluorite
243
11.4
Temperature dependence of phonon frequencies
244
Summary of chapter
245
Further reading
246
Exercises
246
12
Displacive phase transitions
247
12.1
Introduction to displacive phase transitions
247
12.1.1
Importance of thermodynamic analysis
249
12.1.2
Various types of displacive phase transitions
250
12.2
Quantitative description of displacive phase transitions:
the concept of the order parameter
252
12.2.1
The general definition of the order parameter
252
12.2.2
Examples of order parameters for specific phase
transitions
254
12.2.3
Order parameters in other phase transitions
255
12.2.4
Experimental measurements of order parameter
255
12.2.5
First- and second-order phase transitions
256
12.3
Landau theory of displacive phase transitions
258
12.3.1
Qualitative behaviour of the free energy
258
12.3.2
Expansion of the free energy function for a second-order
phase transition
259
12.3.3
Calculation of properties for a second-order phase
transition
259
12.3.4
First-order phase transitions
261
12.3.5
The range of validity of Landau theory
262
12.4
Soft mode theory of displacive phase transitions
263
12.4.1
Basic idea of the soft mode
263
xvi Contents
MA.
2
Ferroelectric soft modes
264
12.4.3
Zone boundary (antiferroelectric) phase transitions
265
12.4.4
Ferroelastic phase transitions
266
12.4.5
Incommensurate phase transitions
266
12.5
Lattice dynamical theory of the low-temperature phase
267
12.5.1
Lattice dynamical theories
267
12.5.2
Potential energy of the crystal
267
12.5.3
Phonon free energy
268
12.5.4
Full free energy and the Landau free energy
function
269
12.5.5
Low-temperature behaviour
269
Summary of chapter
270
Further reading
272
Exercises
272
A Real crystals!
274
A.1 Reality against ideality
274
A.2 Point defects
275
A.2.1 Vacancies: Schottky defects
275
A.2.2 Interstitial defects: Frenkel defects
276
A.2.3 Coupled charge substitutions and vacancies
276
A.2.4 Colour centres
276
A.2.5 Diffusion and atomic mobility
276
A.3 Large-scale imperfections
277
A.3.1 Dislocations
277
A.3.2 Grain boundaries
277
A.3.3 Domains and domain walls
278
A.3.4 Surfaces and surface reconstructions
278
Summary of appendix
279
Further reading
279
В
Fourier analysis
280
B.
1
Fourier transforms as the extension of Fourier series
280
B.2 One-dimensional Fourier transform
280
B.3 Some one-dimensional Fourier transforms
281
B.3.1 Dirac
S
function
281
B.3.2 Slit function
281
B.3.3 Symmetric exponential function
281
B.3.
4
Gaussian function
282
B.4 Convolution theorem
282
Summary of appendix
283
Further reading
283
С
Schœnflies
representation of the point groups
284
C.I The
Schœnflies
and International systems
284
C.2 Schoenflies labelling of non-cubic point groups
284
C.3 Schoenflies labelling of the cubic point groups
285
Summary of appendix
285
Further reading
285
Contents xvii
D
Rhombohedral,
trigonal, and hexagonal unit cells
286
Summary of appendix
286
Further reading
286
E
Space groups
287
E.
1
Space group symbols
287
E.2 Defining symmetry
288
E.3 General and special positions
289
E.4 The International Tables of Crystallography
290
E.5 Relating general equivalent positions to actual atomic positions
290
Summary of appendix
291
Further reading
291
F
Lattice energy minimization
292
Summary of appendix
292
G
Some notes on the variational theorem
293
Summary of appendix
294
Further reading
294
H
Ewald
sphere
295
Summary of appendix
297
Further reading
297
I The Wilson plot
298
Summary of appendix
299
Further reading
299
J
Diffraction from
isotropie
materials
300
J.
1
Basic diffraction equations
300
J.2
Isotropie orientational
averages
300
J.3 Pair distribution functions
301
J.4 Reverse Fourier transform
302
J.5 General approach to analysis of diffraction data
303
Summary of appendix
303
Further reading
303
К
Calculation of physical properties
304
K.
1
Expansion of the crystal energy
304
K.2 Equilibrium condition and the elastic constant tensor
304
K.3 Piezoelectric and dielectric tensors
305
Summary of appendix
306
Further reading
306
L
Partition function: some key
resulte
307
L.
1
The definition and use of the partition function
307
L.2 The free energy
307
L.3 Some results
308
L.3.1 Heat capacity
308
xviii Contents
L.3.2
Susceptibility
308
Summary of appendix
309
Further reading
309
M
Lattice sums
310
Summary of appendix
310
Further reading
310
N
Mean-square atomic displacement and temperature factors
311
Summary of appendix
313
Further reading
313
Solutions to exercises
314
References
326
Index
331
|
| any_adam_object | 1 |
| author | Dove, Martin T. |
| author_facet | Dove, Martin T. |
| author_role | aut |
| author_sort | Dove, Martin T. |
| author_variant | m t d mt mtd |
| building | Verbundindex |
| bvnumber | BV035549165 |
| callnumber-first | Q - Science |
| callnumber-label | QC176 |
| callnumber-raw | QC176 |
| callnumber-search | QC176 |
| callnumber-sort | QC 3176 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 1000 |
| ctrlnum | (OCoLC)552406106 (DE-599)BVBBV035549165 |
| dewey-full | 530.41 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.41 |
| dewey-search | 530.41 |
| dewey-sort | 3530.41 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | [Reprint.] |
| format | Book |
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| id | DE-604.BV035549165 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:40:11Z |
| institution | BVB |
| isbn | 9780198506782 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017605099 |
| oclc_num | 552406106 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XXII, 334 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford master series in physics |
| series2 | Oxford master series in physics |
| spelling | Dove, Martin T. Verfasser aut Structure and dynamics an atomic view of materials Martin T. Dove [Reprint.] Oxford [u.a.] Oxford Univ. Press 2008 XXII, 334 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford master series in physics 1 : condensed matter physics Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 s DE-604 Oxford master series in physics 1 : condensed matter physics (DE-604)BV017064373 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017605099&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dove, Martin T. Structure and dynamics an atomic view of materials Oxford master series in physics Festkörperphysik (DE-588)4016921-2 gnd |
| subject_GND | (DE-588)4016921-2 |
| title | Structure and dynamics an atomic view of materials |
| title_auth | Structure and dynamics an atomic view of materials |
| title_exact_search | Structure and dynamics an atomic view of materials |
| title_full | Structure and dynamics an atomic view of materials Martin T. Dove |
| title_fullStr | Structure and dynamics an atomic view of materials Martin T. Dove |
| title_full_unstemmed | Structure and dynamics an atomic view of materials Martin T. Dove |
| title_short | Structure and dynamics |
| title_sort | structure and dynamics an atomic view of materials |
| title_sub | an atomic view of materials |
| topic | Festkörperphysik (DE-588)4016921-2 gnd |
| topic_facet | Festkörperphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017605099&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017064373 |
| work_keys_str_mv | AT dovemartint structureanddynamicsanatomicviewofmaterials |