Indexing of powder diffraction patterns by iterative use of singular value decomposition

A fast method for indexing powder diffraction patterns has been developed for large and small lattices of all symmetries. The method is relatively insensitive to impurity peaks and missing high d-spacings: on simulated data, little effect in terms of successful indexing has been observed when one in three d-spacings are randomly removed. Comparison with three of the most popular indexing programs, namely ITO, DICVOL91 and TREOR90, has shown that the present method as implemented in the program TOPAS is more successful at indexing simulated data. Also significant is that the present method performs well on typically noisy data with large diffractometer zero errors. Critical to its success, the present method uses singular value decomposition in an iterative manner for solving linear equations relating hkl values to d-spacings.