Freefermion solution for overall equilibrium crystal shape
Abstract
We generalize the random walk or freefermion 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 nearestneighbour 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