THE CONDITIONAL PROBABILITY DISTRIBUTION OF CRYSTAL STRUCTURE INVARIANTS.

Abstract

New methods for solving complex noncentrosymmetric crystal structures have been developed at NRL. A vital part of the method involves evaluating the structure invariants cos(phi(sub vector h(sub 1)) + phi (sub vector h (sub 2)) + phi (sub vector h (sub 3))), where vectors ((h sub 1) + (h sub 2) + (h sub 3)) = 0, directly from the normalized structure factor amplitudes. The theoretical conditional probability distribution of cos(phi(sub vector h (sub 1)) + phi (sub vector h (sub 2)) + phi (sub vector h (sub 3))) and the theoretical expected values of the structure invariants are essential to this computation. This report tabulates the conditional distribution and the expectations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 31, 1970
Accession Number
AD0712767

Entities

People

  • Herbert A. Hauptman
  • J. Harrison Hancock
  • Janet E. Fisher

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Computations
  • Crystal Structure
  • Crystals
  • Mathematics
  • Probability
  • Probability Distributions

Readers

  • Linear Algebra
  • Materials Science and Engineering.
  • Neural Network Machine Learning.