International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.4, p. 278

Section 3.4.4.5.1. SVD-Index

A. Altomare,a* C. Cuocci,a A. Moliternia and R. Rizzia

aInstitute of Crystallography – CNR, Via Amendola 122/o, Bari, I-70126, Italy
Correspondence e-mail:  angela.altomare@ic.cnr.it

3.4.4.5.1. SVD-Index

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This commercial indexing program (Coelho, 2003a[link]), which uses the Monte Carlo method, is part of the TOPAS (Coelho, 2003[link]b) suite from Bruker AXS. The reciprocal-cell parameters in equation (3.4.2)[link] are found by using, in an iterative way, the singular value decomposition (SVD) approach (Nash, 1990[link]) to solve linear equations relating (hkl) values to d spacings. The method is particularly useful in cases for which there are more equations than variables. All the observed lines in the powder pattern are involved in the indexing procedure. It is claimed that the program is relatively insensitive to impurity peaks and missing high d spacings; it performs well on data with large diffractometer zero errors.

More recently, two indexing methods have been introduced in TOPAS: LSI (least-squares iteration), an iterative least-squares process which operates on the d-spacing values extracted from reasonable-quality powder diffraction data, and LP-Search (lattice parameter search), a Monte Carlo based whole-powder-pattern decomposition approach independent of the knowledge of the d-spacings (Coelho & Kern, 2005[link]).

References

Coelho, A. A. (2003a). Indexing of powder diffraction patterns by iterative use of singular value decomposition. J. Appl. Cryst. 36, 86–95.Google Scholar
Coelho, A. A. (2003b). TOPAS. Version 3.1 User's Manual. Bruker AXS GmbH, Karlsruhe, Germany.Google Scholar
Coelho, A. A. & Kern, A. (2005). Discussion of the indexing algorithms within TOPAS. IUCr Commission on Powder Diffraction Newsletter, 32, 43–45.Google Scholar
Nash, J. C. (1990). Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol: Adam Hilger.Google Scholar








































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