Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-11T05:11:18.230Z Has data issue: false hasContentIssue false

Cohen's method revisited

Published online by Cambridge University Press:  10 January 2013

Giorgio Spinolo
Affiliation:
INCM, C.S.T.E./CNR, and Department of Physical Chemistry, University of Pavia, I 27100, Pavia, Italy
Filippo Maglia
Affiliation:
INCM, C.S.T.E./CNR, and Department of Physical Chemistry, University of Pavia, I 27100, Pavia, Italy

Abstract

The subject of the paper is the old and well-known linear least squares method for determining the lattice dimension of a crystalline phase from the peak locations of a powder diffraction pattern. Approximations, limits, and extensions of the method are discussed with reference to the assignment of hkl indices to an experimental multiphase pattern.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1999

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

Anselmi-Tamburini, U., and Spinolo, G. (1993). “On the Least-Squares determination of Lattice Dimensions: A Modified Singular Value Decomposition Approach to Ill-Conditioned Cases,” J. Appl. Crystallogr. 26, 58.CrossRefGoogle Scholar
Burnham, C. W. (1991). “LCLSQ: Lattice parameter refinement using correction terms for systematic errors,” Amer. Mineralogist 76, 663664.Google Scholar
Cohen, M. U. (1935). “Precision lattice constants from x-ray powder photographs,” Rev. Sci. Instrum. 6, 68.CrossRefGoogle Scholar
International Tables for X-ray Crystallography (Kynoch, Birmingham, UK, 1967).Google Scholar
Mueller, M. H., Heaton, L., and Miller, K. T. (1960). “Determination of lattice parameters with the aid of a computer,” Acta Crystallogr. 13, 828829.CrossRefGoogle Scholar
Parrish, W., and Wilson, A. J. C. (1967). International Tables for X-ray Crystallography (Kynoch, Birmingham, UK). Vol. II, Sec. 4.7, pp. 216–234.Google Scholar
Spinolo, G., and Tomasi, C. (1997). “Fluorite-related phases in the Bi-rich part of the Bi,Mo/O system,” Powder Diffr. 12, 1619.CrossRefGoogle Scholar
Warren, B. E. (1969). X-ray Diffraction (Dover, New York).Google Scholar
Wilson, A. J. C. (1963). Mathematical Theory of X-ray Powder Diffractometry (Philips Technical Library, Eindhoven).Google Scholar