Phonon density of states of Sn in textured SnO under high pressure: Comparison of nuclear inelastic x-ray scattering spectra to a shell model (art..: PRB 74, 094303)

H. GIEFERS; S. KOVAL; G. WORTMANN; W. STURHAHN; E. E. ALP; M. Y. HU

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

Año: 2006 vol. 74 p. 1 - 12

0163-1829

Phonon density-of-state in textured SnO <!-- @page { size: 21cm 29.7cm; margin: 2cm } P { margin-bottom: 0.21cm } --> The local phonon density of states (DOS) at the Sn site in SnO is studied at pressures up to 8 GPa with 119Sn nuclear-resonant inelastic x-ray scattering (NRIXS) of synchrotron radiation at 23.88 keV. The preferred orientation (texture) of the SnO crystallites in the investigated samples is used to measure NRIXS spectra preferentially parallel and almost perpendicular to the c-axis of tetragonal SnO. A subtraction method is applied to these NRIXS spectra to produce projected local Sn DOS spectra as seen parallel and perpendicular to the c-axis of SnO. These experimentally obtained local Sn DOS spectra,both in the polycrystalline case as well as projected parallel and perpendicular to the c-axis, are compared with corresponding theoretical phonon DOS spectra, derived from dispersion relations calculated with a recently developed shell-model. Comparison between the experimental projected Sn DOS spectra and the corresponding theoretical DOS spectra enables us to follow the pressure-induced shifts of several acoustic and optic phonon modes. While the principal spectral features of the experimental and theoretical phonon DOS agree well at energies above 10 meV, the pressure behaviour of the low-energy part of the DOS is not well reproduced by the theoretical calculations. In fact, they exhibit, in contrast to the experimental data, a dramatic softening of two low-energy modes, their energies approaching zero around 2.5 GPa, clearly indicating the limitations of the applied shell-model. These difficulties are obviously connected with the complex Sn-O and Sn-Sn bindings within and between the Sn-O-Sn layers in the litharge structure of SnO. We derived from the experimental and theoretical DOS spectra a variety of elastic and thermodynamic parameters of the Sn sublattice, such as the Lamb-Mössbauer factor, the mean force constant, Debye temperatures as well as the vibrational contributions to the Helmholtz free energy, specific heat, entropy, and internal energy. We found, in part, good agreement between these values, for instance for the Grüneisen parameters for some selected phonon-modes, especially for some optical modes studied recently by Raman spectroscopy [Wan04]. We discuss in detail a possible anisotropy in the elastic parameters resulting from the litharge-type structure of SnO, for instance for the Lamb-Mössbauer factor, where we can compare with existing data from 119Sn-Mössbauer spectroscopy.