Abstract
A conditional probability distribution for triplet invariants is derived for noncentrosymmetric crystals from fourth-order determinantal joint probability distributions. The formula makes use of the entire data set in the computations for each invariant. Test calculations indicate that the formula can be used to help select invariants whose values are distributed close to zero and also to evaluate special invariants associated with seminvariant phases.
Keywords: crystal structure, phase determination, triplet selection, determinantal distributions
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Karle I. L., Wieland T., Schermer D., Ottenheym H. C. Conformation of uncomplexed natural antamanide crystallized from CH(3)CN/H(2)O. Proc Natl Acad Sci U S A. 1979 Apr;76(4):1532–1536. doi: 10.1073/pnas.76.4.1532. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Karle J. Joint probability distribution of the invariants comprising determinantal inequalities: Heuristic derivation. Proc Natl Acad Sci U S A. 1978 Jun;75(6):2545–2548. doi: 10.1073/pnas.75.6.2545. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Karle J. Triplet phase invariants: Formula for centric case from fourth-order determinantal joint probability distributions. Proc Natl Acad Sci U S A. 1979 May;76(5):2089–2093. doi: 10.1073/pnas.76.5.2089. [DOI] [PMC free article] [PubMed] [Google Scholar]