# Accession Number:

## AD0256230

# Title:

## ANALYSIS OF CRYSTAL FACETING AS A LINEAR PROGRAMMING PROBLEM

# Descriptive Note:

# Corporate Author:

## METAL HYDRIDES INC BEVERLY MASS

# Personal Author(s):

# Report Date:

## 1961-12-01

# Pagination or Media Count:

## 1.0

# 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