Accession Number : AD0256230

Title :   ANALYSIS OF CRYSTAL FACETING AS A LINEAR PROGRAMMING PROBLEM

Corporate Author : METAL HYDRIDES INC BEVERLY MASS

Personal Author(s) : MULLINS,W.W. ; SEKERKA,R.F.

Report Date : DEC 1961

Pagination or Media Count : 1

Abstract : The principal purpose of this paper is to present a geometrical construction that yields the minimum free energy a planar crystal surface may achieve by faceting, that is, by breaking up into orientations other than the one originally present. A comparison of this problem with the well known one of predicting the equilibrium shape of a crystal shows that both require the minimization of the surface free energy but that the constraints differ; in the equilibrium shape problem the volume of material is constant; in the present faceting problem the average orientation of the surface remains constant and equal to that of the original plane. The Wulff construction solves the equilibrium shape problem; it will be shown to also determine the solution of the faceting problem. The work represents an extension of certain results due to Herring who has given a construction which yields the free energy of a surface faceted in a specified mode, but has not considered the minimum problem. (Author)

Descriptors :   *CRYSTALS, *LINEAR PROGRAMMING, CRYSTAL STRUCTURE, ENERGY, MEASURE THEORY, SURFACE PROPERTIES

Distribution Statement : APPROVED FOR PUBLIC RELEASE