
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