Muutke küpsiste eelistusi

Solids Far from Equilibrium [Pehme köide]

Edited by
Teised raamatud teemal:
Solids Far from EquilibriumSuurem pilt
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780521177252.html
Märksõnad:
This 1991 book, based on the 1989 Beg-Rohu summer school, contains six sets of pedagogical lectures by respected researchers on the statistical physics of crystal growth. The course views the phenomena of shape and growth from a fresh vantage point, the lectures cover a variety of developments in the field.

Arvustused

"Those interested in statistical physics and applied mathematics will find this a stimulating introduction to this area of research." Mathematical Reviews "...a collection of 6 lectures given by specialists who are among the best in the world...a didactic, self-contained and rather complete introduction to the physics, and mainly statistical physics, of growth." Jacques Villain, , Foundations of Physics

Muu info

This 1991 book, based on the 1989 Beg-Rohu summer school, contains six sets of pedagogical lectures on the statistical physics of crystal growth.
Preface xv
Contributors xvi
Chapter 1 Shape and growth of crystals
P. Nozieres
1 Thermodynamics of interfaces
1(35)
1.1 Interface between two fluids
3(4)
1.2 Solid interfaces
7(10)
1.3 Equilibrium conditions for a curved solid-fluid interface
17(10)
1.4 Equilibrium shapes of crystals
27(9)
2 Crystalline surfaces: facets, steps and kinks
36(38)
2.1 Interaction between steps
40(7)
2.2 Crystal shape viewed as an equilibrium of steps
47(9)
2.3 Crystal facets
56(12)
2.4 Surface melting and crystal shape
68(6)
3 Mobility of the interface
74(30)
3.1 Growth of a vicinal liquid-solid interface
76(5)
3.2 Facet growth at a liquid-solid interface: homogeneous nucleation
81(12)
3.3 Frank-Read sources
93(4)
3.4 Diffusion limited growth at a solid-vacuum interface
97(7)
4 Thermal fluctuations: the roughening transition
104(51)
4.1 Fluctuations of a single step
104(7)
4.2 Fluctuations of the interface
111(3)
4.3 Static renormalization: the Kosterlitz-Thouless transition
114(21)
4.4 Dynamic renormalization
135(9)
4.5 Further comments on the roughening transition
144(7)
Acknowledgments
151(1)
References
152(3)
Chapter 2 Instabilities of planar solidification fronts
B. Caroli
C. Caroli
B. Roulet
1 Introduction
155(6)
2 Thermo-hydrodynamic formalism
161(30)
2.1 The one-phase system: a brief summary
161(8)
2.2 Generalization to two-phase systems. Solidification
169(22)
3 The Mullins-Sekerka instability: free growth of a spherical germ
191(15)
3.1 Free growth of a pure solid
191(1)
3.2 The planar stationary solution
192(3)
3.3 Linear stability of this solution: the Mullins-Sekerka instability
195(5)
3.4 Free growth of a spherical germ
200(3)
3.5 Isothermal spherical growth from a supersaturated melt
203(3)
4 Directional solidification of mixtures: linear stability of the planar front
206(15)
4.1 The planar stationary solution
208(1)
4.2 Linear stability of the planar front (deformation spectrum)
209(3)
4.3 The cellular bifurcation
212(4)
4.4 Experimental studies of the bifurcation diagram
216(5)
5 Directional solidification of mixtures: small amplitude cells
221(19)
5.1 Nature of the bifurcation
221(3)
5.2 Principle of the calculation of the coefficients α1
224(3)
5.3 Theoretical predictions and experimental results on the nature of the bifurcation
227(2)
5.4 The wavevector selection problem. The amplitude equation
229(4)
5.5 Phase diffusion. The Eckhaus instability
233(3)
5.6 The zig-zag instability
236(1)
5.7 Hexagonal cells
236(4)
6 Directional solidification of mixtures: deep cells
240(16)
6.1 Analytic studies of deep cells
241(7)
6.2 Numerical studies
248(1)
6.3 Experimental studies of cell shapes and selection
249(7)
7 Coupling between solutal convection and morphological instability
256(11)
7.1 The uncoupled bifurcations
260(2)
7.2 The coupled bifurcations
262(5)
8 Directional solidification of a faceted crystal
267(30)
8.1 Crenellated stationary front profiles
271(4)
8.2 Local stability of crenellated fronts
275(3)
Acknowledgments
278(1)
References
278(7)
Appendix A Gibbs-Thomson equation for a binary alloy
285(2)
Appendix B The integro-differential front equation
287(1)
B.1 General formalism
287(4)
B.2 Directional solidification of mixtures: the one-sided models
291(3)
B.3 The symmetric model
294(3)
Chapter 3 An introduction to the kinetics of first-order phase transition
J.S. Langer
Preface
297(1)
1 Qualitative Features of First-Order Phase Transitions
298(7)
1.1 Ising ferromagnet
298(3)
1.2 Lattice gas
301(1)
1.3 Binary solution
302(1)
1.4 Some remarks about realistic models
303(2)
2 The droplet model of nucleation
305(6)
2.1 Introduction
305(1)
2.2 The cluster approximation
305(3)
2.3 Nonequilibrium analysis (Becker-Doring theory)
308(3)
3 Continuum models
311(11)
3.1 Introduction
311(1)
3.2 Ising ferromagnet in the continuum limit
312(2)
3.3 Mean-field approximation for the coarse-grained free energy
314(1)
3.4 Thermodynamic equation of motion
315(1)
3.5 Flat interface
316(3)
3.6 Spherical droplet
319(1)
3.7 Domain coarsening
320(1)
3.8 Completion formula
321(1)
4 Continuum model with an Ising-like conserved order parameter
322(8)
4.1 Introduction
322(2)
4.2 Thermodynamic equation of motion
324(1)
4.3 Planar interface
325(1)
4.4 Spherical droplet
326(4)
5 Spinodal decomposition: basic concepts
330(5)
5.1 Introduction
330(1)
5.2 Linear instabilities
331(1)
5.3 The structure factor
332(2)
5.4 Some general observations about the late stages of phase separation
334(1)
6 Fluctuation theory
335(9)
6.1 Introduction
335(1)
6.2 The Langevin approach: basic concepts
336(3)
6.3 The Langevin approach: an illustrative example
339(1)
6.4 The Fokker-Planck equation
340(4)
7 Spinodal decomposition: fluctuations and nonlinear effects
344(8)
7.1 Introduction
344(1)
7.2 Equation of motion for the structure factor
345(2)
7.3 The onset of nonlinear effects
347(2)
7.4 Nonlinear approximations
349(3)
8 Late stages of phase separation
352(13)
8.1 Introduction
352(1)
8.2 The Lifshitz-Slyozov-Wagner theory
353(3)
8.3 Correlations and screening
356(6)
References
362(3)
Chapter 4 Dendritic growth and related topics
Y. Pomeau
M. Ben Amar
1 Introduction
365(3)
2 The moving solidification front
368(6)
3 Effects of surface tension
374(7)
4 Scaling laws for the needle crystal
381(12)
4.1 Scaling law without axial flow
384(2)
4.2 Scaling laws for the growth in a forced flow when ρ < eth < ehy
386(2)
4.3 Scaling laws for the growth with an axial flow such that eth < ρ < ehy
388(2)
4.4 Scaling laws for the growth with an axial flow such that eth < ehy < ρ
390(1)
4.5 Scaling laws for the asymptotic branches
391(2)
5 The integral equation of Nash and Glicksman and its low undercooling limit
393(5)
6 Asymptotes beyond all orders in the geometrical model
398(12)
6.1 Elementary properties
400(2)
6.2 Perturbative solution and boundary layer analysis of its singularity
402(2)
6.3 The WKB contribution `beyond all orders'
404(6)
7 Solution of the integral equations for the needle crystal
410(23)
7.1 Solution of the integral equation for low undercooling
413(6)
7.2 Solution of the integral equation for arbitrary undercooling
419(8)
Conclusion
427(2)
References
429(4)
Chapter 5 Growth and aggregation far from equilibrium
L.M. Sander
Introduction
433(1)
1 Growth and fractals; fractal geometry
434(10)
1.1 Disorderly growth and fractals
434(1)
1.2 Scale-invariance
435(2)
1.3 The fractal dimension
437(1)
1.4 Fractal surfaces
438(1)
1.5 Self-affine fractals
438(2)
1.6 Intersections of fractals
440(1)
1.7 Multifractals
441(3)
2 Model for rough surfaces; the Eden model and ballistic aggregation
444(11)
2.1 Eden growth
445(2)
2.2 Ballistic growth
447(1)
2.3 Surface scaling
448(2)
2.4 Continuum models
450(2)
2.5 The castle-wall model
452(2)
2.6 Higher dimensions
454(1)
3 Diffusion limited aggregation
455(17)
3.1 Simulations
455(3)
3.2 Universality
458(2)
3.3 Experimental manifestations
460(8)
3.4 Theory of DLA
468(4)
4 Cluster-cluster aggregation
472(3)
4.1 Simulations
473(1)
4.2 Cluster size distributions and kinetic equations
474(1)
4.3 Theory; upper critical dimension
474(1)
5 Acknowledgements
475(1)
6 References
476(3)
Chapter 6 Kinetic roughening of growing surfaces
J. Krug
H. Spohn
1 Introduction
479(3)
2 Macroscopic shape
482(7)
2.1 Derivation
482(3)
2.2 Edges, facets and other singularities
485(2)
2.3 The Wulff construction
487(2)
3 Scaling Theory of Shape Fluctuations
489(7)
3.1 Statistical scale invariance
489(3)
3.2 Corrections to scaling
492(2)
3.3 Scaling relations
494(2)
4 Growth models
496(16)
4.1 Eden models
499(3)
4.2 SOS models
502(2)
4.3 Ballistic deposition models
504(6)
4.4 Low temperature Ising dynamics
510(2)
5 Continuum Theory
512(28)
5.1 The Kardar-Parisi-Zhang equation
512(8)
5.2 Directed polymer representation
520(10)
5.3 Numerical results for the KPZ exponents
530(3)
5.4 KPZ type equations without noise
533(7)
6 Driven lattice gases
540(15)
6.1 Steady states
545(3)
6.2 Other one dimensional models
548(3)
6.3 Higher dimensions
551(2)
6.4 Shock fluctuations
553(2)
7 Growth and percolation
555(8)
7.1 First passage percolation
555(4)
7.2 Facets and directed percolation
559(4)
8 An approximation of mean field type
563(10)
8.1 Shape anisotropy for the Eden model
567(2)
8.2 The faceting transition in the Richardson model
569(4)
Acknowledgements 573(1)
References 574(9)
Index 583