Accession Number : AD0616688

Title :   DERIVATION OF AN INTERSTITIAL POTENTIAL FUNCTION FOR A FACE-CENTERED CUBIC CRYSTAL FROM FIRST PRINCIPLES.

Descriptive Note : Master's thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING

Personal Author(s) : Wrobel,John Eugene ,Jr.

Report Date : FEB 1965

Pagination or Media Count : 114

Abstract : An interstitial potential function for an fcc crystal was derived by series expansions of 1/r in terms of Fourier exponentials, Legendre polynomials and cubic harmonics of the type alpha. In particular, a function having the form of an empirical function suggested by J. C. Slater and P. DeCicco of M.I.T. was derived by the series expansions. This derived function not only gives the Slater-DeCicco empirical constants in terms of known functions, but also generates higher order terms. The series expansion for the interstitial potential is found to converge very poorly. For example, after five hundred terms, it is convergent to only three significant places. Furthermore, the function is not entirely analytical, being expressed in terms of the number of lattice points in an fcc reciprocal lattice for a given wave vector magnitude. These numbers are not analytical functions of the wave vectors but a simple method for determining them is given. (Author)

Descriptors :   (*CRYSTAL LATTICES, POTENTIAL THEORY), FUNCTIONS(MATHEMATICS), FOURIER ANALYSIS, POLYNOMIALS, HARMONIC ANALYSIS, SERIES(MATHEMATICS), CRYSTAL SUBSTRUCTURE, VECTOR ANALYSIS, BESSEL FUNCTIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE