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Saito Y. — Statistical physics of crystal growth
Saito Y. — Statistical physics of crystal growth

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Название: Statistical physics of crystal growth

Автор: Saito Y.

Аннотация:

This book gives a systematic overview on the scientific fundamentals of crystal growth from the classical phenomenological description to the recent theoretical contributions of statistical physics such as studies on surface roughening and on the pattern formation in the diffusion-limited growth.

The book emphasizes physical concepts as well as mathematical details, and is intended to serve as lecture notes for postgraduate courses.



Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 185

Добавлена в каталог: 01.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-parameter      26 27
Absolute stability      107
Activation energy      see "Energy barrier"
Adjoint operator      148 151
Adsorbed atom      20 30 46—51 58—62
Aggregation      82—85
Alloy growth      101—120
Amplification rate      61 78—81 95 106-110
Amplitude modulation      109
Angle of normal vector      13—17 33 86 90 113 143 144
Anisotropy      14—17 86—90 93 113 150-152
Anisotropy, factor      150
Anisotropy, strength of      14 86 92 151
Arc length      14 33 143
Archemedes's spiral      51 145
Aspect ratio      75
Attachment kinetics      58
Bacteria colonies      82
Berg effect      120—122
Bifurcation, subcritical      109
Bifurcation, supercritical      109
Body-centered solid-on-solid (BCSOS) model      137
Boltzmann weight      6 9 24 38 53 100
Boundary element method      88 111 119 123 153—156
Boundary integral      148 149 155
Brownian motion      39
Capillary effect      86—100
Capillary effect, length      68 86 105 113 117 150 160
Cellular structure      111
chemical potential      6 8 9 22
Chemical potential, difference      6—9 21 24 52 55
Coexistence curve      4 22
Compact      83 84
Compact, dendrite CD      99
Compact, seaweed CS      99
Concentration distribution around polygon      121
Concentration distribution in solution      103 158
Concentration distribution of adsorbed atom      46—51 61
Conservation law      48 62 68 73 76 104 149 153 157
Convective stability      94
Convex envelope      99
correlation length      29 132 137
Critical curve      137
Critical nucleus size      52
Critical point      16
Critical radius      14 51 72 145
Critical velocity      106
Critical wavenumber      107
Cumulant      134
Curvature      14 61 68 143 150 158
Curvature in spherical coordinate      80
Curvature, radius      15 117 143
Cusp, singularity      41
Cusp, structure      111
Dendrite      66 111
Dendrite in a channel      97
Dendrite, asymmetric      98
Dendrite, free      86
Dendrite, irregular      82 99
Dendrite, regular      86 100
Dendrite, symmetric      88 97
Dendrite, three-dimensional      90—93 97
Dendrite, tip      86
Dendrite, two-dimensional      86—90 93—97 153
Dense branched morphology DBM      99
Deposition      8 46 59
Deposition, critical rate      60 64
Deposition, flux      8 46 48
Desolvation      9
Desorption      8
Detailed balance      24 53
Diffusion, chemical      46 66 82 99 101 116 121
Diffusion, constant      6 47 104 149 150
Diffusion, dimensionless field      68 104 157
Diffusion, edge      20
Diffusion, equation      47 66 68 104 148 156 157
Diffusion, equation in parabolic coordinate      73 76
Diffusion, equation in spherical coordinate      71
Diffusion, length      69 77 84 93 105 117 148 157
Diffusion, length in solid      149
Diffusion, length local      95
Diffusion, surface      20 30 46 59 82
Diffusion-limited aggregation, DLA      66 83
Diffusional instability      60 62 77 105 121
dispersion relation      62 79 82 106
Doublon      98 100
Eckhaus, boundary      110
Eckhaus, instability      108
Eigenvalue      40 110 145 151
Eigenvalue, equation      40 110 145 151
Eigenvector      40 151
Einstein — Stokes relation      6
Electrochemical deposition      82 85
Electrostatic potential      121
Elliptic paraboloid      75
Energy barrier for desolvation      9
Energy barrier for diffusion      6
Energy barrier for surface diffusion      46
Energy, interatomic      3 21 24 31 124
Energy, interface      10
Enthalpy      4
entropy      4
Entropy, reduction      38 39
Equiconcentration      121
Equilibrium shape      10—17 41 100
Equipartition law      34
Error function      70 75
Euler — Lagrange equation      11
Eutectic growth      114 157
Eutectic Jackson — Hunt theory      119 157
Eutectic point      114
evaporation      46 59
Exact solution      137
Exponential integral function      75
F model      30 139
Facet      22 42 120 121
Facet, arm      123
Facet, size      42
Faceting transition      20 41 42
FIN      92 97
Fixed point      137
Force balance      116 159
Four-fold symmetry      150
Fractal      82 84 95 101
Fractal, dendrite FD      101
Fractal, dimension      83
Fractal, forest      84
Fractal, seaweed FS      101
Free energy of step      13 17 28 30—34 38—42 50 133 137 139
Free energy of surface      11 22 38 41 43 86—93 111 116
Free energy, barrier for nucleation      53
Free energy, density      11
Free energy, inequality      130
Gas density      84
Gaussian model, continuous      128
Gaussian model, discrete (DG)      124
Gibbs free energy      4
Gibbs — Thomson effect      18 50 59 77 88 104 117
Green's function      148 153 156
Green's function, lattice      129
Green's theorem      148
Growth, law from melt      7
Growth, law from solution      9
Growth, law from vapor      8
Growth, law, linear      7 8 9 52 56
Growth, law, parabolic      52
Growth, rate      72 75
Growth, rate by spiral      51
Growth, rate by two-dimensional nucleation      55
Growth, rate of dendrite      152
Growth, rate of eutectics      119
Growth, shape      17 18
Gruber — Mullins model      39
Hamiltonian      24
Hamiltonian of continuous model      133
Hamiltonian of Gaussian model      124
Hamiltonian of Ising model      16 21
Hamiltonian of modified Gaussian model      129
Hamiltonian of SOS model      24 31 124
Hamiltonian, effective      131
Heat conduction      7 66 102
Heat conduction, flux      77
Height      23 29 124 133
Height, continuous      128 130
Height, correlation      135
Height, difference correlation      29 33 124 129 133
Height, integer      23 124
Height, long wavelength component      134
Height, short wavelength component      134
Hele-Shaw cell      90 95 101 114
Hertz — Knudsen formula      8 30 52 56
Hysteresis      109
ICE      2 120
Ice, rule      139
Integro-differential equation      148 151 152 155
Interatomic bond      20 24 31 99 124 139
Interface supercooling      69 117 159
Ising model      16 21 26 37 100 124
Isotherm      77
Ivantsov parabola      72-76 88 150
Ivantsov parabola, relation      74 86 88 92 93
Kinetic coefficient      7-9 18 25 59 67 68 120 155
Kinetic resistivity      72
Kinetics-limited growth      46
Kink      20 30 38
Kink, density      31 33
Kink, energy      33
Kuramoto — Sivashinsky equation      64
Lamellar, periodicity      118
Lamellar, structure      114 157
Landau coefficient      108
Landau — Ginzburg expansion      108
Laplace equation      83 121
Laplacian in parabolic coordinate      146
Latent heat      4 7 20 66 104 117 158
Lattice gas model      16 21 99
Legendre transformation      12
Lifetime of adatom      46
Linear interpolation      153
Linear response      17
Linear stability analysis      61 79 105 151
Liquidus line      102 117 158
Liquidus line, slope of      103 117
Local equilibrium      47 59 68 72 74 76 77 104 115 142 149 153 157
Master equation      24
Maximum velocity      100 151
Maxwell distribution      7
Melt growth      7 66
Melting temperature      4 27 66 72
Microscopic solvability      see "Solvability condition"
Minimum undercooling hypothesis      119 160
Miscibility gap      115 157
Mobility      63
Modified Bessel function      141 148 150
Molecular beam epitaxy      7
Monte Carlo, dynamical      25
Monte Carlo, simulation of DLA in a finite-density gas      85
Monte Carlo, simulation of growth shape      99
Monte Carlo, simulation of roughening      22—26 30 56 124-128
Monte Carlo, simulation of steps      64
Monte Carlo, step      25
Morphology, phase diagram      98 100
Morphology, transition      99 100
Most unstable mode      80 95
Moving frame      69 148 153 156
Mullins — Sekerka instability      77 88 93
Multinucleation growth      55
Multiple-mesh method      153
Neutral curve      107 110
Noise, amplification      97
Noise, effect on dendrite      93
Noise, origin of sidebranches      94
Normal gradient      122 153
Normal vector      11 12 38 61 143 146
Normal velocity      61 67 95 147 153
Nucleation, rate      54 55
Nucleation, two-dimensional      30 52 123
One-sided model      59 67 88 153 157
Orientation dependence      see "Anisotropy"
Oscillation instability      120
Parabolic coordinate      73 76 146
Parabolic crystal      72 74 93
Parity breaking      119
Partition coefficient      103
Partition function      32 36 39 128
Pattern formation      66
Peclet number      75 150
Periodic boundary condition      155
periodic structure      102 155
periodicity      114 160
Periodicity of sidebranch      95
Perturbation expansion, first order      134
Perturbation expansion, second order      135
phase diagram      102 114
Phase diagram, morphological      98 100
Phase field model      152
Phase modulation      110
Phase transition      3 26 132
Phase transition of surface      20
Phase transition, first-order      5
Phase transition, liquid-crystal      4
Polyhedral crystal      1 120
Quasi stationary approximation      89 106 148 157
Radial velocity      144
Random walk      46
Rate equation      53
Reflection electron microscope      31
Relaxation dynamics      25
Renormalization group, equation      136
Renormalization group, theory      29 133
Renormalization group, trajectory      136
Roughening temperature      27 30 33 37 41 56 133 137 139
Roughening transition      20 29 41 133
Roughening transition, exact solution      29 137
Roughening transition, mean field approximation      26 29
Roughening transition, multilayer model      28
Roughening transition, renormalization group theory      29 133
Roughening transition, single layer model      26
Roughening transition, variational method      129
Roughness      7 21
Scaling form      69
Scaling relation      88 119 151
Scanning tunneling microscope      22 31
Schroedinger equation      150
Schwoebel effect      59
Screw dislocation      30 46
Segregation coefficient      103
Self-similarity      83
Separatrix      137
Sidebranch      93-97
Sidebranch, correlation of      94
Simulation      120
Simulation by boundary element method      see "Boundary element method"
Simulation by Monte Carlo method      see "Monte Carlo"
Single nucleation growth      58
Singular face      38 120
Singular perturbation method      88 150
Six vertex model      30 139
Slow dynamics      63
Snow      2 120 123
1 2
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