Pressure and temperature dependence of EXAFS Debye-Waller factors in diamond-type and white-tin-type germanium

Abstract

Extended X-ray absorption fine-structure (EXAFS) spectra near the Ge K-edge in diamond- and white-tin-type Ge under high temperature and high pressure were measured using a cubic-anvil-type apparatus (MAX90) with synchrotron radiation from the Photon Factory, Tsukuba, Japan. Pressure values up to 10.6 GPa were estimated on the basis of the isothermal equation of state of the diamond-type Ge within an accuracy of 0.4 GPa. Pressures for the same cell assembly were also determined by X-ray diffraction experiment using the NaCl scale. The diamond-type Ge is of great advantage to the pressure calibrant of EXAFS measurements at elevated temperature because a harmonic approximation can be applied up to 900 K. By the phase transition from diamond-to white-tin-type phases, with an increase in coordination number, Ge-Ge distances increase. A sixfold-coordinated Ge atom in the white-tin-type structure has crystallographically non-equivalent two kinds of nearest-neighbour distances [2.530 (8) Å and 2.697 (8) Å at 12.8 GPa]. The harmonic effective interatomic potential, V(u) = 1/2αu2, was evaluated from the contribution to the thermal vibration, where u is the deviation of the bond distance from the location of the potential minimum. The potential coefficient, α, at 0.1 MPa is essentially temperature independent and is 9.06 eV Å-2. At 9 GPa the potential coefficient is 9.71 eV Å-2. The effective interatomic potential is influenced not only by pressure but also by changes in coordination number. The high-pressure white-tin-type phase has a broader potential and a relatively larger mean square amplitude of vibration than the diamond-type phase.