Elasticity of TiO₂ rutile to 1800 K

Abstract 

The ambient pressure elastic properties of single-crystal TiO₂ rutile are reported from room temperature (RT) to 1800 K, extending by more than 1200 ºK the maximum temperature for which rutile elasticity data are available. The magnitudes of the temperature derivatives decrease with increasing temperature for five of the six adiabatic elastic moduli (C _ij ). At RT, we find (units, GPa): C ₁₁=268(1); C ₃₃=484(2); C ₄₄=123.8(2); C ₆₆=190.2(5); C ₂₃=147(1); and C ₁₂=175(1). The temperature derivatives (units, GPa K⁻¹) at RT are: (∂C ₁₁/∂T) _P =−0.042(5); (∂C ₃₃/∂T) _P =−0.087(6); (∂C ₄₄/∂T) _P =−0.0187(2); (∂C ₆₆/∂T) _P =−0.067(2); (∂C ₂₃/∂T) _P =−0.025; and (∂C ₁₂/∂T) _P −0.048(5). The values for K _S (adiabatic bulk modulus) and μ (isotropic shear modulus) and their temperature derivatives are K _S =212(1) GPa; μ=113(1) GPa; (∂K _S /∂T) _P =−0.040(4) GPa K⁻¹; and (∂μ/∂T) _P =−0.018(1) GPa K⁻¹. We calculate several dimensionless parameters over a large temperature range using our new data. The unusually high values for the Anderson-Gròneisen parameters at room temperature decrease with increasing temperature. At high T, however, these parameters are still well above those for most other oxides. We also find that for TiO₂, anharmonicity, as evidenced by a non-zero value of [∂ln (K _T )/∂lnV] _T , is insignificant at high T, implying that for the TiO₂ analogue of stishovite, thermal pressure is independent of volume (or pressure). Systematic relations indicate that ∂² K _S /∂T∂P is as high as 7×10⁻⁴ K⁻¹ for rutile, whereas ∂²μ/∂T∂P is an order of magnitude less.