Precise determination of crystal lattice parameters

Abstract

Precision X-ray methods for absolute and relative determination of crystal lattice parameters (interplanar distances) are described and compared, including the X-ray divergent-beam (Kossel) technique, the Bond method, the Renninger method, the back reflection method, the interference method, and the method of standards. It is shown that for most of the considered methods, a relative accuracy of ∼ 10−5 – 10−6 for determining the lattice parameters is usually achievable, with the last two methods giving a much greater accuracy, at the level of ∼ 10−8 – 10−9 .

The development of an approach for the precision determination of thermal strain tensor elements for single crystals using the example of t-Ag0.8Li0.2InSe2

“…9 The existing methods for refining the UCP of single crystals are considered in the most comprehensive way in the review. 13 These methods allow relative errors of no more than 10 −6 –10 −9 to be obtained but require complex experimental setups and radiation sources with special parameters. The purpose of our work was to create an approach for precision in single crystal UCP determination that can be used on any laboratory diffractometer and synchrotron radiation station equipped with a 2D detector, without changing their design.…”

“…[9][10][11] For these purposes, specially developed precision single crystal UCP determination methods are used, for example, the Bond method, which allows for the reduction of the UCP determination relative error to several ppm. 12 There are other approaches; 13 however, separate devices or special designs of experimental stations and special radiation sources are required for their implementation, as well as for the Bond method. Therefore, currently, they are scarcely used.…”

Synergistic effect of montmorillonite and nano-Sb2O3/brominated polystyrene on the flame retardancy of polypropylene matrix composites

“…X-ray diffraction (XRD) patterns of samples were recorded at room temperature by Ultima IV XRD (Rigaku Corporation of Japan) with 2θ diffraction angle range from 2° to 10° at 2°/min of scanning speed. The value of interplanar distance was calculated by Bragg’s law 14 …”

Using diffraction losses of X-rays in a single crystal for determination of its lattice parameters as well as for monochromator calibration

“…In the present paper, we analyse the spectra measured previously (Polikarpov et al, 2018;Zhang et al, 2019) and we show that by careful analysis of glitches the unit-cell (UC) parameters of crystalline optics, used in transmission geometry, can be accurately determined. Usually, the UC parameters are determined from some diffraction experiments with X-rays or electrons -for a rather complete and recent review of the methods used for UC parameter determination see Lider (2020). Some of the methods can reach a precision of da=a = 1 Â 10 À9 (Stoupin & Shvyd'ko, 2011;Toellner et al, 2011).…”

“…Some of the methods can reach a precision of da=a = 1 Â 10 À9 (Stoupin & Shvyd'ko, 2011;Toellner et al, 2011). However, to get such high precision the absolute X-ray energy has to be known very accurately [for example, using a 57 Fe Mossbauer radiation source (Lider, 2020)]. In addition, most of the methods require precise goniometers or rather complicated experimental geometry.…”