Mechanical properties of Al$_x$In$_{1-x}$P$_y$Sb$_{1-y}$ quaternary alloy in zinc-blend structure lattice-matched to GaSb substrate are studied under the effects of temperature and pressure. The calculations are done based on empirical pseudopotential method modified with virtual crystal approximation joins compositional disorder impact. Such a model provides analytical data for the compositional dependence of the energy band gaps of Al$_x$In$_{1-x}$P$_y$Sb$_{1-y}$/GaSb system. Our results are presented for the elastic constants ($C_{11}$, $C_{12}$, $C_{44}$), elastic moduli ($B_u$, $Y_0$, $C_s$), internal strain (${\xi}$), bond stretching (${\alpha}$) and bond bending force (${\beta}$) parameters. The alloy of interest is found to be a direct semiconductor within the composition range 0 ${\leq}$ x ${\leq}$ 0.15 and an indirect one for 0.15 ${\le}$ x ${\leq}$ 1. There is a good agreement between our results and the experimental data for its constituents (AlP, AlSb, InP and InSb) which give support for the calculated results of the studied quaternary alloys.

The pressure and composition-dependent electronic properties such as energy band structure, energy bandgaps of pentanary alloy Ga$_x$In$_{1-x}$P$_y$Sb$_z$As$_{1-y-z}$ lattice-matched to InP have been studied. Also, the pressure and composition-dependent of the optical properties as refractive index, high-frequency dielectric constant, static dielectric constant, polarity, covalency, ionicity, susceptibility and reflectivity of the pentanary alloy Ga$_x$In$_{1-x}$P$_y$Sb$_z$As$_{1-y-z}$ have been determined. The empirical pseudo-potential method was used in our calculations. Excellent agreement was obtained between our results and the experimental values at the ambient pressure. Our results for different values of pressure (30, 60, 90 and 120 Kbar) are predictions for the experimental data. The studied properties for the considered alloy may be useful in the design and fabrication of optoelectronic devices.