First-Principles Structural, Mechanical, and Thermodynamic Calculations of the Negative Thermal Expansion Compound Zr<inf>2</inf>(WO<inf>4</inf>)(PO<inf>4</inf>)<inf>2</inf>

The negative thermal expansion (NTE) material Zr2(WO4)(PO4)2 has been investigated for the first time within the framework of the density functional perturbation theory (DFPT). The structural, mechanical, and thermodynamic properties of this material have been predicted using the Perdew, Burke and Ernzerhof for solid (PBEsol) exchange-correlation functional, which showed superior accuracy over standard functionals in previous computational studies of the NTE material α-ZrW2O8. The bulk modulus calculated for Zr2(WO4)(PO4)2 using the Vinet equation of state at room temperature is K0 = 63.6 GPa, which is in close agreement with the experimental estimate of 61.3(8) at T = 296 K. The computed mean linear coefficient of thermal expansion is -3.1 × 10-6 K-1 in the temperature range ∼0-70 K, in line with the X-ray diffraction measurements. The mean Grüneisen parameter controlling the thermal expansion of Zr2(WO4)(PO4)2 is negative below 205 K, with a minimum of -2.1 at 10 K. The calculated standard molar heat capacity and entropy are CP0 = 287.6 and S0 = 321.9 J·mol-1·K-1, respectively. The results reported in this study demonstrate the accuracy of DFPT/PBEsol for assessing or predicting the relationship between structural and thermomechanical properties of NTE materials.