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Test of maximum-entropy methods to solve a small structure ab initio from powder diffraction data

Published online by Cambridge University Press:  10 January 2013

Naoaki Sudo ,
Hiroo Hashizume  and
Carlos A. M. Carvalho
Naoaki Sudo
Affiliation:
Research Laboratory of Engineering Materials, Tokyo Institute of Technology, Nagatsuta, Midori, Yokohama 227, Japan
Hiroo Hashizume*
Affiliation:
Research Laboratory of Engineering Materials, Tokyo Institute of Technology, Nagatsuta, Midori, Yokohama 227, Japan
Carlos A. M. Carvalho
Affiliation:
Research Laboratory of Engineering Materials, Tokyo Institute of Technology, Nagatsuta, Midori, Yokohama 227, Japan
*
a)To whom all correspondence should be addressed.
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Abstract

Detailed procedures for solving small crystal structures ab initio with the maximum-entropy (ME) methods using X-ray powder diffraction data are described by determining the structure of the low-pressure phase of magnesium boron nitride, Mg3BN3(L), which was previously solved by one of the authors and co-workers using the Patterson method and the direct methods. The simple ME method devised by Gull, Livesey, and Sivia failed to correctly phase the structure-factor data, leading to noninterpretable electron-density maps. This method, maximizing the entropy under the constraints of the observed structure factors with subsequent incorporation of strong extrapolates in the basis set, trapped the solution in a local entropy maximum, from which there is no way to move. The multisolution method of phase determination by entropy maximization and likelihood evaluation, developed by Bricogne and Gilmore, successfully located all the Mg, B, and N atoms in one cycle of phase extension. The correct solution had a highest log-likelihood gain, but a minimum entropy, among the multisolutions generated by phase permutation.

Keywords

maximum-entropy methodstructure determinationpowderphase problemelectrondensity distribution
Type
Research Article
Information
Powder Diffraction , Volume 10 , Issue 1 , March 1995 , pp. 34 - 39
Copyright
Copyright © Cambridge University Press 1995

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