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Application of convex optimization to identification of atomic species from diffraction patterns

Published online by Cambridge University Press:  27 February 2017

Ryoko Oishi-Tomiyasu
Ryoko Oishi-Tomiyasu*
Affiliation:
Faculty of Science, Yamagata University, 1-4-12, Kojirakawa-cho, Yamagata-shi, Yamagata 990-8560, Japan JST PRESTO, 4-1-8, Honcho, Kawaguchi-shi, Saitama 332-0012, Japan
*
a)Author to whom correspondence should be addressed. Electronic mail: ryoko_oishi@sci.kj.yamagata-u.ac.jp
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Abstract

Computational methods and a program to obtain crystal structures that have the perfectly identical diffraction patterns, i.e. structure factors with the same absolute values and the same lattice symmetry are discussed. This is directly related to the uniqueness of solutions in crystal structure determination of single-crystal/powder-crystal samples from diffraction data. In order to solve the problem, it is necessary to solve a system of quadratic equations. The framework of positive-semidefinite programming is used herein to solve the system efficiently.

Keywords

phase retrievalglobal optimizationpositive-semidefinite programmingsystem of quadratic equationsmultiple solutions
Type
Technical Articles
Information
Powder Diffraction , Volume 32 , Supplement S1 , September 2017 , pp. S179 - S185
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Copyright
Copyright © International Centre for Diffraction Data 2017 

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References

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