Temperature dependence of crystal structure of CaGeO₃high-pressure perovskite phase and experimental determination of its Debye temperatures studied by low- and high-temperature single-crystal X-ray diffraction

Abstract

Single-crystal X-ray diffraction study of CaGeO 3 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 CaGeO 3 , CaTiO 3 , and MgSiO 3 , all of these have the BO 6 octahedra more rigid than the AO 12 polyhedra (A = Ca or Mg; B = Ge, Ti, or Si) and the tilt angles of BO 6 octahedra are the largest in MgSiO 3 perovskite. These observations indicate that if MgSiO 3 perovskite under high pressures undergoes the same sequence of the high-temperature phase transitions as CaTiO 3 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 Pm3m transition) observed in CaTiO 3 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 MgSiO 3 perovskite is unlikely.

Variable–temperature single–crystal X–ray diffraction study of SrGeO₃ high–pressure perovskite phase

“…On the other hand, Figure 3 shows that the diffraction peaks begin to broaden at a temperature higher than 323 K and completely disappear by 448 K. This observation agrees well with the results of Andrault et al (1996), who reported that the SrGeO 3 perovskite, metastable at ambient pressure, amorphized near 500 K and that the amorphous phase began to recrystallize to the thermodynamically stable pseudowollastonite phase at a higher temperature. A similar observation was reported for the CaGeO 3 orthorhombic perovskite, which amorphizes near 923 K (Durben et al, 1991;Nakatsuka et al, 2015b).…”

“…Assuming a harmonic OPP, V OPP ðuÞ ¼ ðq=2Þhu 2 i d (Willis and Pryor, 1975), the OPP coefficient q, corresponding to the force constant, is related to the Debye temperature Θ D (Nakatsuka et al, 2015b):…”

A new high-pressure strontium germanate, SrGe2O5

“…In particular, it is noteworthy that in both tetrahedral and octahedral coordination, the Ge-O bonds in SrGe 2 O 5 are still more covalent than the Si-O bonds in SrSi 2 O 5 . Such strong covalency of the Ge-O bonds in SrGe 2 O 5 affects atomic thermal vibrations, as was also discussed in SrGeO 3 cubic perovskite Nakatsuka et al, 2016) and CaGeO 3 orthorhombic perovskite (Nakatsuka, Kuribayashi et al, 2015). Indeed, the displacement ellipsoids of the O atoms largely elongate toward the direction of 'void space' in the structure, which is not filled with GeO 6 octahedra and GeO 4 tetrahedra, so that their thermal vibrations avoid interactions with adjacent Ge atoms (Fig.…”

“…Meanwhile, germanates have frequently been employed as model substances for the corresponding silicates (e.g. Nakatsuka et al, 2005Nakatsuka et al, , 2016Nakatsuka, Kuribayashi et al, 2015;Koganemaru et al, 2013) because they exhibit similar phase transformations to those of silicates at lower pressures. Phase and structural studies of germanates have thus provided important insights into phase transformations of silicate minerals in the Earth's interior.…”

Phase stability of iron germanate, FeGeO3, to 127 GPa

“…In case of the germanate system, MgGeO 3 , MnGeO 3 and ZnGeO 3 form pPv upon heating to ~63 GPa (Hirose et al 2005), ~60 GPa (Tateno et al 2006) and ~115 GPa (Yusa et al 2014) respectively. Post-perovskite has not been observed in CaGeO 3 (Nakatsuka et al 2015) and…”