Experimental considerations in measurements of diffuse scattering

Abstract

A brief review is given of the Boric-Sparks method of measuring and separating the diffuse scattering in alloys due to local displacements of atoms from lattice sites. Experimental techniques are reviewed with particular emphasis on simple computer controls, dead time, monochromators and specimens. After this, sources of error in the measurements are discussed and simple methods for assessing these errors presented. Equations for estimating higher-order terms than those included by Boric and Sparks are presented. It now appears that a thorough analysis of the errors needs to be made for each measurement prior to its publication. As this kind of experiment is readily automated and easily analyzed for errors with modern computers, this should now become standard procedure. It is also suggested that intensities in electron units be kept on file and made available when requested, as is done with structure factors.

A structural study of the alloy Cu3Au above its critical temperature

“…As has been mentioned earlier, the temperature correction applied in this study is only an approximation; the temperature factor should vary with the value of lmn (Walker & Keating, 1963;Hayakawa et al, 1975). However, calculation showed that the changes in intensity with such a variation were much less than the statistical error.…”

“…(A typical data point was 3200 counts, but in the symmetry separation some five of these points are involved.) The evaluation of errors in the separation of the data with the technique employed here have been discussed by Gragg, Hayakawa & Cohen (1973) and Hayakawa, Bardhan & Cohen (1975). In both the separation and inversion, it is assumed that in the displacement terms the scattering factor ratios, ( fco ( _fAo fA.-fc ) and fAu--fCu) ' are constant [see equations (4)- (12)].…”

Equations for diffuse scattering from disordered alloys with h.c.p. structure

“…Hayakawa, Bardhan & Cohen (1975) suggest the inclusion of higher powers of u in the expansion of exp (iK. u) for observing the direct effect of temperature factors, common to all contributions of diffuse scattering.…”

Equations for diffuse scattering from materials with multiple sublattices

“…The techniques are still evolving; see Sparks & Boric (1966), Boric & Sparks (1971), Gragg & Cohen (1971), Gragg, Hayakawa & Cohen (1973), Williams (1974), Hayakawa, Bardhan & Cohen (1975), Tibballs (1975) for the latest procedures, techniques and error analyses. Currently, there is considerable interest in such diffuse scattering from other materials, such as oxides and carbides, where diffuse scattering can provide information about clustering or local order of the high density of point defects or of ions in solid solution in such materials; examples are the recent studies by Brunel & Bergevin (1969), Chudinova, Kuz'kina & Shivrin (197.0, 1971), Billingham, Bell & Lewis (1972), Andersson, Gjonnes & Tafto (1974).…”