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Bismuth telluride (Bi₂Te₃) is one of the most intricate materials with its semiconducting, insulating and pressure-induced superconducting properties. Although different theoretical works have been carried out to understand the confusing properties of Bi₂Te₃, information about the high pressure structural, elastic, mechanical and phonon properties of this significant material is still rare. Unlike earlier theoretical approaches, two-body interatomic potentials in the Morse potential form have been employed for the first time to predict the density, phase transition pressure, elastic constants, bulk, shear and Young moduli and elastic wave velocities of Bi₂Te₃ under pressures up to 12 GPa. $\alpha \to \beta$ phase transition pressure of Bi₂Te₃ was found to be 10 GPa. The results of above elastic quantities agree well with experiments and are better than some of the published theoretical data. In addition, the effect of pressure on the phonon dispersion and density of states (DOS) were also evaluated with the same potential and their results are satisfactory, especially for the low-frequency acoustic portions of phonons.

The structural, elastic and thermal properties of $\gamma$-TiAl and ${\alpha }_2$-Ti₃Al phases in the TiAl-based alloy under pressure were reported using CASTEP program based on the density functional theory. The calculated equilibrium parameters and elastic constants are in good agreement with experimental and the available theoretical data. The results indicate that under the same pressure, the ${\alpha }_2$ phase in the direction along $a$-axis is easier to be compressed than the $\gamma$ phase, while the compression along $c$-axis of $\gamma$ phase is larger than that of ${\alpha }_2$ phase; when the pressure is below 20 GPa, both the two phases are elastically stable, but the $\gamma$ phase have higher shear modulus and Young’s modulus, and the ${\alpha }_2$ phase has better ductility and plasticity. Debye temperature, bulk modulus, thermal expansion coefficient and heat capacity of the $\gamma$ phase and ${\alpha }_2$ phase under high pressure and high temperature were also successfully calculated and compared using the quasi-harmonic Debye model in the present work.

The structural stability, elastic, mechanical, optical characteristics and Debye temperature of single crystalline superconductors MPd₂P₂ (M = Y, La) were investigated by using the ab initio technique. We have carried out the plane wave pseudopotential within the generalized gradient approximation (GGA) implemented in the CASTEP computer code. Our investigated results of structural data are in well consistent with the previous experimental data. The bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio v, hardness H, and anisotropic factor A of MPd₂P₂ (M = Y, La) compounds were evaluated from the calculated elastic constants. The analysis of ratio B/G shows that the MPd₂P₂ superconductors are in ductile behavior. The Debye temperatures are also investigated from the elastic constants. Finally, the optical functions including reflectivity, absorption coefficient, loss function, conductivity, refractive index, dielectric function are calculated and analyzed.

The elastic and photocatalytic properties of multiferroic material InFeO₃ under strain are calculated through density functional theory. The calculated results indicate that the intrinsic InFeO₃ and the strained InFeO₃ meet the mechanical stability conditions and hold a relatively larger elastic coefficient than popular multiferroic material BiFeO₃. The calculated bandgap and band edge of InFeO₃ under tensile strain show that InFeO₃ could be a high-efficiency photocatalytic hydrogen production material. InFeO₃ under tensile strain holds the ability of photocatalytic water splitting to produce hydrogen with excellent ferroelectric, mechanical properties and absorption of visible light.

Since crystal structure dictates the resultant physical properties of materials, titled physical features of the P2₁ monoclinic SiGe semiconductors, which are still unclear, have been revealed by density functional theory (DFT). The electronic band gap value with 0.49eV was found to be in the order of previously published cubic and hexagonal closed-packed SiGe semiconductors. Surprisingly, P2₁ monoclinic SiGe has a room temperature Seebeck coefficient of 1500$\mu$V/K which is higher than the reported data of both cubic and hexagonal SiGe alloys. Further, the mechanically stable P2₁ monoclinic phase of the SiGe displays a brittle mechanical character with clear elastic anisotropy has also been deduced. The P2₁ monoclinic phase of the SiGe can be also considered a good high-dielectric material and beneficial for practical applications of IR or UV goals due to its high refractive index.