Full Elasticity Tensor from Thermal Diffuse Scattering

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.

Figure 1

Graphical rendering of measured diffuse scattering and calculated TDS. Considered cases are calcite at $T=170\mathrm{K}$ for a ROI of $q\in [0.03,0.15]$ (top panels), MgO with $q\in [0.06,0.15]$ at $T=90\mathrm{K}$ (middle panels), and with the multitemperature method at $T=90$, 120 K (bottom panels). Each image shows a cross section of the reciprocal space, in the neighborhood of the selected Bragg peak, and for a given $q_z=\mathrm{\Delta }{Q}_z/|{\mathit{a}}^{*}|$. The data are grouped by pairs, with the experimental and calculated intensity distribution on the left-hand and right-hand side, respectively. The scattering intensity is shown on a linear color scale from black (zero) to white (given maximal intensity $I_{\max }$). The reverse interpolation, which is only used for graphical rendering, results in some artifacts; for example, some intensity remains outside the ROI. The stripes visible at $hkl=\overline{2},\overline{2},4$ and 0, $\overline{2}$, 4 are due to the finite angular steps in the measurement, and each stripe corresponds to the contribution of a single diffraction pattern.