1. (a) Bulk modulus and (b) hardness of MgAl₂O₄ under various temperatures (experimental data obtained from the literature^[19])B_T and B_M denote the bulk modulus of bonds in tetrahedra and octahedra, respectively; B is the bulk modulus of MgAl₂O₄ crystal; H_T and H_M represent the hardness of bonds in tetrahedra and octahedra, respectively; H is the hardness of MgAl₂O₄ crystal

2. Temperature dependence of Young’s modulus of MgAl₂O₄ (experimental data obtained from literature^[16,20])

3. Predicted value of the heat capacity of MgAl₂O₄ (experimental data obtained from literature^[22,23,24])

4. Comparison of prediction with experimental data (a) of Ghosh, et al^[17], (b) Boniecki, et al^[18] of the temperature dependent fracture strengths of MgAl₂O₄

5. Comparison of prediction with experimental data of temperature dependent fracture toughnesses of MgAl₂O₄^[16-18,27]

6. Temperature dependence of (a) inversion parameter, (b) anion parameter, (c) lattice constant, and (d) averaged bond length for MgAl₂O₄^[12,25,29] R_T and R_M denote the bond length in tetrahedra and octahedra, respectively (1 Å=0.1 nm)

7. Ratio of bond valence to bond length of MgAl₂O₄ under various temperatures $S _{Ave}^{T}/ R_{T}$ and $ S _{Ave}^{M}/ R_{M}$ represent the ratio of bond valence to bond length in tetrahedra and octahedra, respectively