Analytic Approximations to the Coherent Potential for Substitutional Alloys.
Abstract
In the Traveling Cluster Approximation (TCA) method of Coherent Potential Approximation (CPA), the graphs of the corrected cumulant expansion are partially summed in such a way that the Herglotz property of the mean resolvent can be analyzed easily at each stage. A single graph in this approximation may induce a sequence of clusters traveling arbitrarily large distances through the sample. The CPA and the singlesite TCA are known to be exactly equivalent to each other. The TCA in the level of nearestneighbor approximation (TCA(nn)) was applied to both twodimensional and threedimensional alloys in the singleband calculation, with nn interaction, and site diagonal disorder only. The TCA(nn) gives quite satisfactory results when compared with exact calculations for 19 x 20 x 21 site alloys with site diagonal disorder. It gives substructure which does not appear in the results of the CPA, and also gives better band edges of the spectrum.
 Publication:

Ph.D. Thesis
 Pub Date:
 1977
 Bibcode:
 1977PhDT........19R
 Keywords:

 Physics: Condensed Matter;
 Alloys;
 Approximation;
 Coherence;
 Metallurgy;
 Coherent Scattering;
 Crystal Structure;
 Metallography;
 Solid Phases;
 SolidState Physics