Full Elasticity Tensor from Thermal Diffuse Scattering

Abstract

We present a method for the precise determination of the full elasticity tensor from a single crystal diffraction experiment using monochromatic x rays. For the two benchmark systems calcite and magnesium oxide, we show that the measurement of thermal diffuse scattering in the proximity of Bragg reflections provides accurate values of the complete set of elastic constants. This approach allows for a reliable and model-free determination of the elastic properties and can be performed together with crystal structure investigation in the same experiment

Structural, elastic and vibrational properties of celestite, SrSO4, from synchrotron x-ray diffraction, thermal diffuse scattering and Raman scattering

“…In the case of SrSO 4 their are nine independent elastic coefficients to be fitted simultaneously together with the background. This is significantly higher than the two benchmark systems previously studied with this method: calcite (six values) and MgO (three values) [21]. The ST method was used successfully for calcite, where the crystal was of very high quality.…”

“…This will allow us to address the temperature dependence of the elastic moduli, see discussion in Ref. [21].…”

“…The quantitative analysis of the thermal diffuse scattering is based on a fit of the three-dimensional distribution of the intensity of scattered x-rays in the vicinity of Bragg reflections [21]. Assuming the adiabatic and harmonic approximation, the intensity of X-rays inelastically scattered from phonons for a single-phonon process is given by:…”

Implications of X-ray thermal diffuse scattering in integrated Bragg intensities of silicon and cubic boron nitride

“…It is important to integrate a voxel of a size comparable to an experimental situation, since the contribution elsewise is grossly over-or underestimated. The choice of voxel size is based on the definition of the Bragg peaks of MgO by Wehinger et al (2017). The integration area is calculated from the experimental conditions described by Niepö tter et al (2015).…”

“…In general the elastic constants are unknown and analysis of the peak shape or voxel size is seldom done. However, increased attention has recently been devoted to extracting dynamic models and elastic constants from TDS data, thereby promoting TDS into a desired scattering feature (Welberry et al, 2012;Wehinger et al, 2017). Theoretical advances, where quantum mechanical computations have become faster and the lattice dynamical expression simpler, have aided this more constructive attitude towards TDS (Xu & Chiang, 2005).…”