In this work, we performed the calculations based on density functional theory with different exchange and correlation energy approximations and employed the method of the constant force within the harmonic approximation, to study the phonon and thermodynamic properties of the three MWO₄ (M = Ca, Sr or Ba) compounds with scheelite-type structure. In the first part of the work, we carried out an analysis of the performance of the local density approximation (LDA) and generalized gradient approximation of the Perdew-Burke-Ernzerhof revised for solids (GGA-PBEsol) on the computed phonon density of states, specific heat at constant volume, entropy and Gibbs free energy of the scheelite BaWO₄ compound. Comparisons between calculated and experimental data showed that the GGA-PBEsol approach exhibited better performance. In the second part of the work, we extended the study of the thermodynamic properties to the SrWO₄ and CaWO₄ compounds, which are not presented in the literature, using the GGA-PBEsol approximation. It was found that the magnitude of the specific heat at the constant volume at high temperature respects the following order: BaWO₄ > CaWO₄ > SrWO₄. Moreover, it was verified a relation between M²⁺ ionic radius in the scheelite MWO₄ (M = Ba, Sr or Ca) and their entropy, Gibbs energy, and Helmholtz free energy.

在这项工作中，我们根据密度泛函理论以不同的交换和相关能量近似值进行了计算，并采用了谐波近似中的恒力方法，研究了三个MWO ₄（M = Ca， Sr或Ba）具有白钨矿型结构的化合物。在工作的第一部分中，我们根据计算的声子态密度对固体的修正的Perdew-Burke-Ernzerhof（GGA-PBEsol）的局部密度近似（LDA）和广义梯度近似的性能进行了分析。 ，白钨矿BaWO _4的恒定体积比热，熵和吉布斯自由能化合物。计算数据和实验数据之间的比较表明，GGA-PBEsol方法表现出更好的性能。在工作的第二部分中，我们使用GGA-PBEsol近似将热力学性质的研究扩展到了SrWO ₄和CaWO ₄化合物中，但文献中未列出。据发现，比热的在高温下的方面按以下顺序恒定体积的大小：钨酸钡₄  > CaWO ₄  > SrWO ₄。此外，还证实了白钨矿MWO ₄中的M ²⁺离子半径（M = Ba，Sr或Ca）与它们的熵，吉布斯能和亥姆霍兹自由能之间的关系。