Thermal Diffused Scattering (TDS) – a new tool for determining single crystal elasticity at high-pressure condition

Abstract:

X-ray thermal diffuse scattering (TDS) has been used to determine phonon dispersion relation of solids since 1940s (Wehinger et al. 2013; Ding et al. 2006; Xu and Chiang 2005). However, its application in high-pressure mineral physics has not been widely recognized. Sound velocities of Earth materials at relevant high pressure (P) and temperature (T) conditions are essential for interpreting seismic data, which provides by now the most accurate image of the Earth interior. Comparing with other commonly used techniques for measuring sound velocities in the high-pressure mineral physics community, it has significant advantages and disadvantages. Firstly, it could be used for measuring any single crystals at extreme P-T conditions using diamond anvil cell (DAC), not limited to transparent samples or nuclear resonant isotopes; Secondly, single-crystal elastic constants could be obtained through TDS, and hence directional dependences of sound velocities are available; Finally, experimental setup for TDS measurement is very easy, essentially identical to what is used for routine high-pressure single-crystal X-ray diffraction experiments. However, TDS is much less straightforward in data interpretation, which usually involves micro force constant modeling between the nearest neighbor atoms. We developed dependable data collection procedures for TDS measurement under high-pressure conditions. Measurements with single-crystal Si and foresterite under ambient and high-pressure conditions are successful. Using the python code package we developed for analyzing TDS data, we successfully reproduced the previously determined single-crystal elastic moduli of Si and foresterite using Brillouin spectroscopy and ultrasonics. The experimental uncertainty of the single crystal elastic moduli determined from TDS approach is within 4% or better.