Temperature dependence of crystal structure of CaGeO₃ high-pressure perovskite phase and experimental determination of its Debye temperatures studied by low- and high-temperature single-crystal X-ray diffraction

Single-crystal X-ray diffraction study of CaGeO₃ perovskite has been conducted over the temperature range of 98 to 1048 K. The crystal begins to deteriorate at a temperature above about 900 K and completely amorphizes by 980 K. The diffraction-intensity distribution and the structure refinements indicate that the Pbnm structure is kept until the occurrence of amorphization. The obtained unit-cell parameters, unit-cell volumes, bond lengths, and displacement parameters increase monotonously with increasing temperature. Thus, no evidence for the existence of the Cmcm high-temperature phase, previously suggested above 520 K, is observed. The Ge-O bond lengths show much smaller thermal expansions than the Ca-O bond lengths; the former ranges between 0.42(2) × 10⁻⁵ K⁻¹ and 0.57(2) × 10⁻⁵ K⁻¹, and the latter between 1.58(4) × 10⁻⁵ K⁻¹ and 3.96(6) × 10⁻⁵ K⁻¹. The Debye temperatures and static disorder components for each constituent atom were determined by applying the Debye model to the temperature dependence of mean square displacements (MSDs) of the atoms. Consequently, no significant static disorder components can be detected in each atom. The Debye temperatures averaged over all directions, obtained from the Debye model fitting to U_eq, yield the harmonic one particle potential coefficients of 4.76(2) eVÅ⁻² for Ca, 11.0(1) eVÅ⁻² for Ge, 5.02(2) eVÅ⁻² for O1, and 5.33(5) eVÅ⁻² for O2. These values become larger in order of Ca < O1 < O2 << Ge, which shows that the one particle potential of Ge is much narrower than that of Ca. This relationship between Ca and Ge is consistent reasonably with bonding stiffness expected from the thermal expansion coefficients of the bond lengths. The anisotropies of MSDs are remarkable in O1 and O2 atoms as a consequence of the strong interaction with adjacent Ge atoms, forming the rigid bonds with these O atoms.

In comparison of the three Pbnm orthorhombic perovskites of CaGeO₃, CaTiO₃, and MgSiO₃, all of these have the BO₆ octahedra more rigid than the AO₁₂ polyhedra (A = Ca or Mg; B = Ge, Ti, or Si) and the tilt angles of BO₆ octahedra are the largest in MgSiO₃ perovskite. These observations indicate that if MgSiO₃ perovskite under high pressures undergoes the same sequence of the high-temperature phase transitions as CaTiO₃ perovskite, the phase boundaries have positive Clapeyron slopes and the phase transition temperatures should become further much higher than those (1512 K for the Pbnm to I4/mcm transition and 1635 K for the I4/mcm to Pm3̄m transition) observed in CaTiO₃ perovskite at ambient pressure. This leads to the conclusion that the high-temperature phase transition to a perovskite phase with different symmetry under high pressures previously suggested in MgSiO₃ perovskite is unlikely.