Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T07:01:41.112Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bricogne, G. (1991). “A Multisolution Method of Phase Determination by Combined Maximization of Entropy and Likelihood. III. Extension to Powder Diffraction Data,” Acta Crystallogr. A 47, 803–829.CrossRefGoogle Scholar
Bricogne, G. (1993). “Direct Phase Determination by Entropy Maximization and Likelihood Ranking: Status Report and Perspective,” Acta Crystallogr. D 49, 37–60.Google Scholar
Carvalho, C. A. M., and Hashizume, H. (1992). “Optimization of a Maximum-Entropy Program for Powder Diffraction,” Report of RLEMTIT, Tokyo Institute of Technology, Vol. 17, 47–61.Google Scholar
Cascarano, G., Favia, L., and Giacovazzo, C. (1992). “SIRPOW.91-a Direct-Method Package Optimized for Powder Data,” J. Appl. Crystallogr. 25, 310–317.CrossRefGoogle Scholar
Collins, D. M. (1982). “Electron Density Images from Imperfect Data by Iterative Entropy Maximization,” Nature (London) 298, 49–51.CrossRefGoogle Scholar
Estermann, M., McCusker, J. B., and Baerlocher, C. (1992). “Ab Initio Structure Determination from Severely Overlapping Powder Diffraction Data,” J. Appl. Crystallogr. 25, 539–543.CrossRefGoogle Scholar
Gilmore, C. J., Henderson, K., and Bricogne, G. (1991). “A Multisolution Method of Phase Determination by Combined Maximization of Entropy and Likelihood. IV. The Ab Initio Solution of Crystal Structures from their X-Ray Powder Data,” Acta Crystallogr. A 47, 842–846.CrossRefGoogle Scholar
Gull, S. F., and Daniell, G. J. (1978). “Image Reconstruction from Incomplete and Noisy Data,” Nature (London) 272, 686–690.CrossRefGoogle Scholar
Gull, S. F., Livesey, A. K., and Sivia, D. S. (1987). “Maximum Entropy Solution of a Small Centrosymmetric Crystal Structure,” Acta Crystallogr. A 43, 112–117.CrossRefGoogle Scholar
Hiraguchi, H., Hashizume, H., Fukunaga, O., Takenaka, A., and Sakata, M. (1991). “Structure Determination of Magnesium Boron Nitride, Mg3BN3, from X-Ray Powder Diffraction Data,” J. Appl. Crystallogr. 24, 286–292.CrossRefGoogle Scholar
Hiraguchi, H., Hashizume, H., Sasaki, S., Nakano, S., and Fukunaga, O. (1993). “Structure of High-Pressure Polymorph of Mg3BN3 Determined from X-Ray Powder Data,” Acta Crystallogr. B 49, 478–483.CrossRefGoogle Scholar
Jansen, J., Peschar, R., and Schenk, H. (1992). “On the Determination of Accurate Intensities from Powder Diffraction data. II. Estimation of Intensities of Overlapping Reflections,” J. Appl. Crystallogr. 25, 237–243.CrossRefGoogle Scholar
Ohsumi, K., Hagiya, K., and Ohmasa, M. (1991). “Development of a System to Analyse the Structure of a Submicrometre-Sized Single Crystal by Synchrotron X-Ray Diffraction,” J. Appl. Crystallogr. 24, 340–348.CrossRefGoogle Scholar
Sakata, M., and Sato, M. (1990). “Accurate Structure Analysis by the Maximum-Entropy Method,” Acta Crystallogr. A 46, 263–270.CrossRefGoogle Scholar
Shankland, K., Gilmore, C. J., Bricogne, G., and Hashizume, H. (1993). “Maximum Entropy Solution of a Small Centrosymmetric Crystal Structure. VI. Automatic Likelihood Analysis via the Student t Test, with an Application to the Powder Structure of Magnesium Boron Nitride, Mg3BN3,” Acta Crystallogr. A 49, 493–501.CrossRefGoogle Scholar
Sivia, D. S., Hamilton, W. A., and Smith, G. S. (1991). “Analysis of Neutron Reflectivity Data: Maximum Entropy, Bayesian Spectral Analysis and Speckle Holography,” Physica B 173, 121–138.CrossRefGoogle Scholar
Skilling, J. (1989). “Classical Maximum Entropy,” in Maximum Entropy and Bayesian Methods (Kluwer, Amsterdam), pp. 45–52.CrossRefGoogle Scholar