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

Abstract

Extended X-ray absorption ®ne-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 diamondtype 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-tintype phases, with an increase in coordination number, GeÐGe distances increase. A sixfoldcoordinated Ge atom in the white-tin-type structure has crystallographically non-equivalent two kinds of nearest-neighbour distances [2.530 (8) A Ê and 2.697 (8) A Ê at 12.8 GPa]. The harmonic effective interatomic potential, V(u) = 1/2u 2 , 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 coef®cient, , at 0.1 MPa is essentially temperature independent and is 9.06 eV A Ê À2 . At 9 GPa the potential coef®cient is 9.71 eV A Ê À2 . The effective interatomic potential is in¯uenced 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 diamondtype phase.

High-pressure EXAFS measurements of crystalline Ge using nanocrystalline diamond anvils

“…The pressure evolution of σ 2 for the nearest neighbor shells are reported in Fig.5 (b). In the diamond phase, ambient pressure values σ 2 1 = (6 ± 1)10 −3Å 2 and σ 2 2 ∼ σ 2 3 = (15 ± 5)10 −3Å 2 are in good agreement with previous EXAFS data 11,17 . These reflect a first shell correlation stronger than expected, whereas higher coordination shell values approach those measured by X-ray diffraction (empty square in Fig.5 (b)).…”

“…The quality of the collected data appears comparable to those obtained outside the DAC, and represents an evident increase of the extent of k-range available. Previous high pressure EXAFS experiments performed on this system limited the results to the first shell 16,17 . Results obtained with the quantitative analysis provided information up to the third shell for the diamond phase and up to the fourth shell for the β-Sn phase, demonstrating that the employment of ND anvils offers evident advantages for coupling EXAFS and DAC techniques.…”

Local structure of magnetite and maghemite and chemical shift in Fe K-edge XANES

“…The relative comparison of results by precise EXAFS analyses has an accuracy that can determine the thermal expansion coefficient (Yoshiasa et al, 1999a). Decreases in the average distances and σ 2 values for spinel -type Fe 3−δ O 4 solid -solutions were consistent with the estimated δ values.…”

“…The EXAFS interference function, χ(k), was extracted from the measured absorption spectrum using a standard procedure (Maeda, 1987;Yoshiasa et al, 1999a;Yoshiasa et al, 1999b). The radial structural function was obtained by Fourier transform over the k range of 2.5 -11.5 Å −1 (Fig.…”

Thermodynamic properties of semiconductor compounds studied based on Debye-Waller factors

“…Semiconductors are important materials in technological and electronic applications, the DWFs of which are the subject of many interesting papers [7][8][9][10][11][12][13][14][15][16][17][18]. For Si the MSRD has been studied by XAFS calculation [7] and by XAFS experiment [8][9][10].…”