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).

中文翻译：

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NZP 结构磷酸盐 M0.5Ti2(PO4)3 (M – Ni, Zn) 的热容量和热力学函数

摘要 通过绝热真空和差示扫描量热法在 T = (6.65–) 范围内首次测量了结晶磷酸盐 M0.5Ti2(PO4)3 (M – Ni, Zn) 的热容量的温度依赖性。 614) K 和 (7.79–650) K，分别。对于 Ni0.5Ti2(PO4)3，观察到低于 10 K 的热容量异常。Zn0.5Ti2(PO4)3 的热容曲线没有异常，随着温度的升高而增加。为了定义磷酸盐结构的异质动力学特征，我们估计了固体热容多重分形模型函数中的分形维数 D 的值。在 35-50 K 温度范围内的相应实验热容数据给出了两个研究样品的 D = 3，这对应于它们的框架结构。获得的实验 Cp 数据用于计算化合物的标准热力学函数，即热容、焓、熵和吉布斯能量。M0.5Ti2(PO4)3 (M – Ni, Zn) 的热力学性质与结构相关的磷酸盐 M0.5Zr2(PO4)3 (M – Mg, Ca, Ni, Sr, Ba), NaTi2(PO4) 的热力学性质进行了比较)3, AZr2(PO4)3 (A – Na, K, Rb, Cs)。