Heat capacity and thermodynamic functions of the NZP-structured phosphates M0.5Ti2(PO4)3 (M – Ni, Zn)

Abstract

The temperature dependences of the heat capacities of crystalline phosphates M0.5Ti2(PO4)3 (M – Ni, Zn) have been measured for the first time by the methods of adiabatic vacuum and differential scanning calorimetry over the ranges T = (6.65–614) K and (7.79–650) K, respectively. The heat capacity anomaly below 10 K was observed for Ni0.5Ti2(PO4)3. The heat capacity curve of Zn0.5Ti2(PO4)3 has no anomalies and increases as temperature grows. To define the character of heterodynamics of the phosphates’ structures, we estimated the values of the fractal dimension D in the function of multifractal model of the heat capacity of solids. The corresponding experimental heat capacity data over the temperature range of 35–50 K give D = 3 for the both studied samples, which corresponds to their framework structure. The obtained experimental Cp data were used to calculate the standard thermodynamic functions of the compounds, namely, heat capacities, enthalpies, entropies, and the Gibbs energies. Thermodynamic properties of M0.5Ti2(PO4)3 (M – Ni, Zn) were compared with those for the structurally related phosphates M0.5Zr2(PO4)3 (M – Mg, Ca, Ni, Sr, Ba), NaTi2(PO4)3, AZr2(PO4)3 (A – Na, K, Rb, Cs).