Herein, we report on the crystal structures of the isostructural ${\text{Ti}}_3{\text{SiC}}_2$ and ${\text{Ti}}_3{\text{GeC}}_2$ phases determined by Rietveld analysis of neutron diffraction data in the $100°$ to $1100°\text{C}$ temperature range. The results show that the Si and Ge atoms vibrate anisotropically with the highest amplitudes and within the basal planes. The equivalent isotropic thermal motion behavior does not differ significantly between the two phases; the anisotropic thermal motion, interatomic distances, and bond angles, however, show strikingly different behavior. Furthermore, while the Ti-Si bonds increase linearly with increasing temperature, the Ti-Ge bonds apparently do not. The anisotropic motion of the Ge atoms in the basal plane with the correlated motion between the Ti and the Ge atoms is invoked as a possible explanation. The volume expansions are $9.0\left(\pm 0.1\right)\times {10}^{-6}{\text{K}}^{-1}$ and $8.7\left(\pm 0.1\right)\times {10}^{-6}{\text{K}}^{-1}$ for ${\text{Ti}}_3{\text{SiC}}_2$ and ${\text{Ti}}_3{\text{GeC}}_2$, respectively; the expansions along the $a$ and $c$ axes are ${\alpha }_{\text{a}}=8.9\left(\pm 0.1\right)\times {10}^{-6}{\text{K}}^{-1}$ and ${\alpha }_{\text{c}}=9.4\left(\pm 0.1\right)\times {10}^{-6}{\text{K}}^{-1}$ for ${\text{Ti}}_3{\text{SiC}}_2$ and ${\alpha }_{\text{a}}=8.5\left(\pm 0.1\right)\times {10}^{-6}{\text{K}}^{-1}$ and ${\alpha }_{\text{c}}=9.2\left(\pm 0.1\right)\times {10}^{-6}{\text{K}}^{-1}$ for ${\text{Ti}}_3{\text{GeC}}_2$. A dramatic increase in error bars and a discontinuity in thermal motion parameters of the ${\text{Ti}}_{\text{II}}$ atoms in ${\text{Ti}}_3{\text{GeC}}_2$ were also observed between 300 and $500°\text{C}$ during both heating and cooling. This discontinuity may in turn explain why the internal friction rises dramatically in that temperature range.

• Received 2 August 2010

DOI:https://doi.org/10.1103/PhysRevB.82.174109