DERIVATION OF AN INTERSTITIAL POTENTIAL FUNCTION FOR A FACE-CENTERED CUBIC CRYSTAL FROM FIRST PRINCIPLES.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1965
- Accession Number
- AD0616688
Entities
People
- John Eugene Wrobel Jr.
Organizations
- Air Force Institute of Technology