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Submitted on 1 Jan 1985
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EQUILIBRIUM SHAPE OF CRYSTALS
H. Schulz
To cite this version:
H. Schulz. EQUILIBRIUM SHAPE OF CRYSTALS. Journal de Physique Colloques, 1985, 46 (C3), pp.C3-309-C3-309. �10.1051/jphyscol:1985324�. �jpa-00224641�
JOURNAL DE PHYSIQUE
Colloque C3, suppl6ment au n03, Tome 46, mars 1985 page C3-309
E Q U I L I B R I U M SHAPE OF C R Y S T A L S ~
H.J. Schulz
I n s t i t u t Laue-Langeuin, 156X, 38042 GrenobZe Cedex, France
and Laboratoire de Physique des SoZides, B6t. 510, Universit6 de Paris-Sud, Centre dr0rsay, 91405 Orsay, France
Resume - On d e c r i t l e s mecanismes physiques qui sont responsables de l a forme TKTt=istaux. La t r a n s i t i o n rugueuse d'une face c r i s t a l l i n e donnee i n t e r v i e n t lorsque l ' e n e r g i e l i b r e d'une marche s'annule sur c e t t e surface. En dessous de c e t t e t r a n s i t i o n , des f a c e t t e s de dimensions f i n i e s coexistent avec des por- t i o n s arrondies de l a surface. Prss de l a f r o n t i s r e d'une f a c e t t e , l a forme du c r i s t a l e s t determinee par une interaction longue portee e n t r e marches due aux fluctuations. Une methode simple e s t presentee qui f a i t usage d'une matri- ce de t r a n s f e r t e t permet d'obtenir l a l o i en puissance 3/2 de l a forme du c r i s t a l au voisinage de l a f r o n t i e r e ( l a courbure diverge). Elle permet d'obtenir egalement d ' a u t r e s caracteristiques de 7a forme de l a f a c e t t e . S ' i l y a interaction repulsive L grande portee e n t r e marches, des f a c e t t e s d'ordre de plus en plus &lev& peuvent s e former L basse tempereture, ce qui conduit L un e s c a l i e r du diable L temperature nulle. On donne l a temperature de l a t r a n s i t i o n rugueuse ainsi que sa largeur en fonction des indices (eleves) des faces. S ' i l y a a t t r a c t i o n e n t r e l e s marches, l ' e s c a l i e r du diable d i s p a r a i t en p a r t i e ou completement e t des coins e n t r e d i f f e r e n t e s f a c e t t e s peuvent Otre s t a b l e s a temperature non nu1 l e .
Abstract
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The physical mechanisms governing t h e equilibrium shape of c r y s t a l s a r e described. The roughening t r a n s i t i o n of a given crystal face i s associated with the vanishing of the f r e e energy of a s t e p on t h a t surface. Below the roughening t r a n s i t i o n , f a c e t s of f i n i t e s i z e coexist with rounded parts of the surface. Near t h e boundary of a f a c e t , the shape of the crystal i s determined by a fluctuation-indiced long-range interaction between s t e p s . A simple trans- fer-matrix method i s used t o derive the 3/2-power-law f o r the crystal shape near the boundary (implying diverging curvature), as well as some other fea- tures of the f a c e t shape. If there a r e long-range repulsive interactions between steps, f a c e t s of higher and higher order can form a t low temperatures, leading t o a d e v i l ' s s t a i r c a s e a t T = 0. Formulas f o r t h e width and roughening temperature of the high index faces are given. If there i s a t t r a c t i o n between s t e p s , the devi 1 ' s s t a i r c a s e disappears part1 y or compl e t e l y , and edges between d i f f e r e n t f a c e t s can be stables a t non zero temperatures.* T h e f u l l v e r s i o n o f t h i s paper has been published i n Journal de Physique 5 (1985) 257.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985324
