Anisotropic corrections of measured integrated Bragg intensities for thermal diffuse scattering – general formula

Abstract

The correction of measured integrated intensities for the first-order thermal diffuse scattering (TDS) is considered on the basis of the existing theory of X-ray thermal diffuse scattering for an elastic wave of long wave length. Generalized formula for the TDS correction ~ is found to be represented by a quadratic form in the Miller indices h, k, land a tensor AlL as ~ = Afllxh 2 + Aflz2k 2 + Af13312 + 2Aflx2hk + 2Aflz3kl+ 2Afl3Jh. All is a tensor introduced in this paper which characterizes the anisotropy of the TDS correction. The form of the tensor Ap is shown to depend only on the crystallographic system. The relation between Ap and the temperature-parameter tensor is presented.

A new theory for X-ray diffraction

“…Since there are as many phonon wavelengths as there are repeat units in any one direction, these satellites merge to produce a redistribution of intensity from the Bragg peak that diminishes in magnitude further from the peak (decreasing in phonon wavelength). The fall in the TDS intensity from a Bragg peak follows a 1/q 2 form (Cochran, 1969) and is an incoherent fraction of the peak intensity (Harada & Sakata, 1974):…”

The consequences of the neglect of TDS correction for temperature parameters

“…(7) (I + ka) By substituting (4), (5) and (7) As discussed previously (Harada & Sakata, 1974), this indicates that within our approximation the position parameters r~ are not affected significantly even if the TDS correction is not applied to the data, but temperature parameters ~ are modified by the amount (k/2) Ap. It should be noted that the tensor form of 13~ obeys the site symmetry of the xth atomic location, while that of AI3 is independent of the atomic species and dependent only on the crystal system.…”

“…The components of AI3 and 13true(acoustic) in the notation of Harada & Pedersen (1968) and Harada & Sakata (1974) …”

“…It will in fact be shown that the relative reduction of the temperature parameters due to neglect of TDS correction is almost the same for any crystal, largely independent of its hardness and depending mainly on the experimental conditions under which the Bragg intensities were measured: the size and shape of the counter aperture, the scan width, the wavelength of the radiation used and the unit-cell dimension of the crystal. In this paper we discuss this problem theoretically on the basis of the formalism of Harada & Sakata (1973, 1974 and then endeavour to test our findings in four different cases. © 1983 International Union of Crystallography…”

“…The consequences of the neglect of TDS correction 0567-7394/83/020202-06501.50 on structure analysis have been discussed by Harada & Sakata (1974) on the basis of their general formalism of TDS correction. They predicted that while the position parameters are little affected, thermal parameters are modified in such a way that the principal axes of the thermal ellipsoids change their directions.…”