Free-fermion solution for overall equilibrium crystal shape
Abstract
We generalize the random walk or free-fermion method of Yamamoto, Akutsu and Akutsu to obtain a simple explicit solution for the overall equilibrium crystal shape of a simple cubic crystal at temperatures, T, low with respect to the nearest-neighbour coupling, E. The thermal rounding of the corners and of the edges of the cube appears to be qualitatively different : at the corners the width of the rounded, vicinal surface and its radius of curvature are estimated to be of order (k_B T/E) R, where 2 R is the diameter of the crystal. As the distance l from the corner along an edge increases, the width of the vicinal surface and transverse radius of curvature decrease as exp (-l/k_B T/ER) reaching an exponentially small value at the middle of the edge. On the other hand, the radius of curvature parallel to an edge grows as exp (l/k_B T/ER), so that the product of two principal curvatures remains constant up to a numerical factor. A qualitative explanation of the results is presented, based on the strong dependence of the stiffness of the steps on their orientation with respect to the axes of the crystal.
- Publication:
-
Journal de Physique I
- Pub Date:
- March 1991
- DOI:
- 10.1051/jp1:1991139
- Bibcode:
- 1991JPhy1...1..373M