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In this manuscript, we report the density functional theory-based first principles study of the structural and vibrational properties of technologically relevant M′ fergusonite (<i>P</i>2/<i>c</i>)-structured NdTaO₄ and SmTaO₄ under compression. For NdTaO₄ and SmTaO_4, ambient unit cell parameters, along with constituent polyhedral volume and bond lengths, have been compared with earlier reported parameters for EuTaO₄ and GdTaO₄ for a better understanding of the role of lanthanide radii on the primitive unit cell. For both the compounds, our calculations show the presence of first-order monoclinic to tetragonal phase transition accompanied by nearly a 1.3% volume collapse and an increase in oxygen coordination around the tantalum (Ta) cation from ambient six to eight at phase transition. A lower bulk modulus obtained in the high-pressure tetragonal phase when compared to the ambient monoclinic phase is indicative of the more compressible unit cell under pressure. Phonon modes are calculated for the ambient and high-pressure phases with compression for both the compounds along with their pressure coefficients. One particular IR mode has been observed to show red shift in the ambient monoclinic phase, possibly leading to the instability in the compounds under compression.