ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
A magic determinant is a Karle-Hauptman determinant in which the phases of reflexions forming the elements are expressed in magic-integer representation. By means of appropriate algorithms, which are described, magic determinants may be found, up to order 30, which have a high content of large E's. The value of the magic determinant depends on the values of the independent variables (usually two) in terms of which the magic-integer-represented phases are defined. Maxima are sought in a map of magic-determinant values and these give trial values for the constituent phases. These phases may be refined by maximizing one or more of the largest eigenvalues of the matrix of elements. Applications to five different structures are described and the usefulness and limitations of the magic-determinant concept are discussed. It is concluded that Karle-Hauptman determinants, chosen in the way described, provide a very discriminating figure of merit. However, the structure factors they contain usually provide a rather poor base for subsequent phase development and this limits the usefulness of the magic-determinant approach.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739478001825
Permalink