Application of polyhedron model to predict heat capacity of mixed oxides

The heat capacity of mixed oxides can be estimated using a linear summation of the heat capacities of their structural constituent polyhedra. This approach is particularly useful for hygroscopic and volatile oxides, where experimental data can be difficult to obtain. The present work aims to enhance the polyhedron model (PM) by incorporating contributions from second-order transitions, including magnetic and site order-disorders, into C_p and expanding it to include ZnO and PbO-containing systems in comparison to the previous version of the model. A regression analysis was performed over the new dataset consisting of the properties of 85 compounds in the system Li-Na-K-Ca-Mg-Mn-Fe-Pb-Zn-Al-Ti-Si-O to obtain optimized C_p for 20 constituent polyhedra. We validate the updated PM against experimental data, demonstrating an overall improvement between 7 and 9 % in the estimation of C_p compared to the previous version of the model. We also compare the updated model with well-established models in the literature, such as the Neumann-Kopp Rule, and ab-initio calculations. The PM shows higher precision than NKR and the linear summation nature of PM endows the model with simplicity which contrasts with ab-initio calculations. Additionally, the model has demonstrated an inherent self-correction capability relative to the original input values, as shown for K₂Si₄O₉. The model is also applied to predict the heat capacity of 10 compounds in the Na₂O-PbO-SiO₂ and Na₂O-ZnO-SiO₂ systems, where experimental data are lacking.