  The structural, electronic, elastic and optical properties of tetragonal
(P4mm) phase of Pb0.5Sn0.5TiO3 (PSTO) and Pb0.5Sn0.5Ti0.5(Zr0.5)O3 (PSTZO) are
examined by first-principles calculations based on the density functional
theory (DFT) using the pseudo-potential plane wave (PP-PW) scheme in the frame
of generalized gradient approximation (GGA). We have calculated the ground
state properties such as equlibrium lattice constants, volume, bulk modulus and
its pressure derivative. From elastic constants, mechanical parameters such as
anisotropy factor, elastic modulus and Poisson's ratio are obtained from the
Voigt-Reuss-Hill average approximation. Rather than their averages, the
directional dependence of elastic modulus, and Poisson's ratio are modelled and
visualized in the light of the elastic properties of both systems. In addition,
some novel results, such as Debye temperatures, and sound velocities are
obtained. Moreover, we have presented the results of the electronic band
structure, densities of states and charge densities. These results were in
favourable agreement with the existing theoretical data. The optical dielectric
function and energy loss spectrum of both systems are also computed. Born
effective charge (BEC) of each atoms for both systems is computed from
functional perturbation theory (DFPT). Finally, the spontaneous polarization is
also determined from modern theory of polarization to be 0.8662 C/m2 (PSTO) and
1.0824 C/m2 (PSTZO).
