A comprehensive first-principles study was performed to investigate the elastic and thermodynamic properties of ${\mathrm{U}}_{1-x}{\mathrm{Th}}_x{\mathrm{O}}_2$ $(x=0, 0.25, 0.5, 0.75, 1)$ solid solutions using the DFT+U method, with ${\mathrm{ThO}}_2$ treated under standard DFT. Despite a slight overestimation relative to experimental data, the predicted lattice constants follow the Vegard's law, providing a robust foundation for in-depth analysis. Consistency between the calculated band gaps and previous experimental and theoretical studies further verifies the effectiveness of our approach. Elastic properties, including bulk, shear, and Young's modulus, as well as Poisson's ratio, were predicted, revealing that ${\mathrm{UO}}_2$ is the most incompressible, whereas ${\mathrm{ThO}}_2$ exhibits superior rigidity. All these solid solutions demonstrate good mechanical stability. Elastic anisotropy was characterized using anisotropic indexes and three-dimensional graphs, which indicate that ${\mathrm{ThO}}_2$ exhibits the highest degree of elastic isotropy, followed by ${\mathrm{U}}_{0.5}{\mathrm{Th}}_{0.5}{\mathrm{O}}_2$, while ${\mathrm{UO}}_2$ shows the highest anisotropy. Furthermore, thermodynamic properties, including vibrational free energy, enthalpy, entropy, and specific heat capacity at constant pressure, were computed over a temperature range from 0 to 2000 K. All the compositions exhibit excellent thermodynamic stability. The calculated thermodynamic functions show overall good agreement with available experimental data, particularly for ${\mathrm{U}}_{0.5}{\mathrm{Th}}_{0.5}{\mathrm{O}}_2$. The parameters obtained from this study provide valuable data for future experimental investigations and illustrate the potential of thorium substitution to modulate the performance of conventional ${\mathrm{UO}}_2$ fuels, laying a foundation for further exploration of advanced nuclear fuels.

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• Elasticity
• Entropy
• First-principles calculations
• Specific heat
• Temperature