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Saito Y. — Statistical physics of crystal growth
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Название: Statistical physics of crystal growthАвтор: 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: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 185Добавлена в каталог: 01.12.2013Операции: Положить на полку |
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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
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