Thermal expansion modeling of framework-type Na[AsW2O9] and K[AsW2O9

Abstract

We report lattice thermal expansion of two alkali metal arsenotungstates possessing framework-type structures. Rietveld refinement analysis of the temperature-dependent neutron time-of-flight diffraction data revealed that K[AsW2O9] exhibits positive thermal expansion in the a- and c-directions, and negative thermal expansion in the b-direction. Opposite, the isostructural Na[AsW2O9] shows positive thermal expansion in all three directions. Using the quasi-harmonic approximation DFT calculations demonstrate that both acoustic and optic negative mode Grüneisen parameters contribute to the phonon density of states (PDOS). The lattice thermal expansion was fitted using Grüneisen first order approximation for the zero pressure equation of state at 0K, where the vibrational energy was calculated using the Debye-Einstein-Anharmonicity model. The thermodynamic Grüneisen parameter accounts for the isothermal anharmonicity while an anharmonicity parameter measures the isochoric anharmonicity. The magnitude and the sign of the cross-linking values (linear compressibility multiplied by axial Grüneisen parameter) helped understand the associated axial negative thermal expansion.