We report ab-inito density functional theory calculation of phonons in cubic phase of ZrW 2 O 8 in the entire Brillouin zone and identify specific anharmonic phonons that are responsible for large negative thermal expansion (NTE) in terms of translation, rotation and distortion of WO 4 and ZrO 6 . We have used density functional calculations to interpret the experimental phonon spectra as a function of pressure and temperature as reported in literature. We discover that the phonons showing anharmonicty with temperature are different from those showing anharmonicity with pressure although both are of similar frequencies. Only the latter phonons are associated with NTE. Therefore the cubic and/or quadratic anharmonicity of phonons is not relevant to NTE but just the volume dependence of frequencies. The calculations are able to reproduce the observed anomalous trends, namely, the softening of the low frequency peak at about 5 meV in the phonon spectra with pressure and its hardening with temperature, while both the changes involve a compression of the lattice. Earlier neutron scattering data [9] as well as theoretical [8] estimates of the anharmonicty of the phonons in ZrW 2 O 8 using interatomic potential model indicated that modes of energy below 8 meV are responsible for observed NTE. However estimates based on the Raman spectroscopy showed [7] that several modes nearly upto 50 meV contribute to NTE. The large disagreement in the energy range as well as nature of the low-energy modes in previous works indicated the need for understanding of NTE behaviour in ZrW 2 O 8 using ab-inito calculations. Recently ab-initio calculations of zone center phonon modes have been published [6]. However the authors concluded [6] that one should fully explore the nature of the phonons in the entire Brillouin zone for understanding the mechanism of NTE in cubic ZrW 2 O 8 . Here we report such a comprehensive calculations and identify specific zoneboundary modes that are highly anharmonic. The calculations are able to reproduce the observed NTE in cubic ZrW 2 O 8 as well as anomalous trends of the phonon spectra with increase in temperature and pressure.Important soft modes were identified in cubic ReO 3 [13] and ScF 3 [14] at M and R-points in the Brillouin zone respectively. These modes show simultaneously both large negative Grüneisen parameter as well as large quadratic anharmonicity, the former leading to NTE and latter to the temperature dependence. In case of ZrW 2 O 8 , we find that the modes that show large negative Grüneisen parameter contribute to NTE are not necessarily the same as those showing cubic and/or quadratic anharmonicity and significant temperature dependence. This finding means that the modes found anharmonic in temperature dependent measurements are not necessarily relevant to NTE.The first-principle calculations of lattice dynamics have been performed using Vienna Ab-initio Simulation Package (VASP) [15,16].The generalized gradient approximation (GGA) exchange correlation given by Perdew Becke and Ern...
We report a comparative study of the dynamics of to understand the large shift of the phonon frequencies of these solids with pressure and temperature. In particular, the quartic component of the anharmonic term in the crystal potential is able to account for the temperature dependence of the phonon modes.
We present temperature dependent inelastic neutron scattering measurments, accompanied byabinitio calculations of phonon spectra and elastic properties as a function of pressure to understand anharmonicity of phonons and to study the mechanism of negative thermal expansion and negative linear compressibility behaviour of ZnAu2(CN)4. The mechanism is identified in terms of specific anharmonic modes that involve bending of the Zn(CN)4-Au-Zn(CN)4 linkage. The high-pressure phase transition at about 2 GPa is also investigated and found to be related to softening of a phonon mode at the L-point at the Brillouin zone boundary and its coupling with a zone-centre phonon and an M-point phonon in the ambient pressure phase. Although the phase transition is primarily driven by a L-point soft phonon mode, which usually leads to a second order transition with a 2×2×2 supercell, in the present case the structure is close to an elastic instability that leads to a weakly first order transition.
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