Beta eucryptite (LiAlSiO4) shows one-dimensional super-ionic conductivity as well as anisotropic thermal expansion behavior. We have performed inelastic neutron scattering measurements in beta eucryptite over 300 to 900 K and calculated the phonon spectrum using ab initio density functional theory method. The calculated energy profile for cooperative lithium ion displacements indicates preferential movement of Li ion along the hexagonal c-axis in the high temperature phase. However, the energy barrier for Li ion diffusion is significantly reduced when a Schottky defect is introduced in the crystal. Further, the anisotropic stress dependence of the phonon spectrum is calculated to obtain the thermal expansion behavior along various axes. The calculations show that the Gruneisen parameters of the low-energy phonon modes around 10 meV have large negative values and govern the negative thermal expansion behavior both along the a and c axes. On the other hand, anisotropic elasticity along with anisotropic positive values of the Gruneisen parameters of the high-energy modes in the range 30 to 70 meV are responsible for positive thermal expansion in the a-b plane and negative expansion along the c-axis. The analysis of the polarization vectors of the phonon modes sheds light on the mechanism of the anomalous thermal expansion behavior. We extend the study to discuss the relationship of the soft phonons in the Brillouin zone with the observed high-pressure and high-temperature phase transitions as reported in the literature.
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