Abstract
The phase pure synthesis of Ti${}_{3}$AlC${}_{2}$ MAX phase is quite difficult and some additives are required to get a phase pure Ti${}_{3}$AlC${}_{2}$ such as Sn. In this study, Sn doped Ti${}_{3}$AlC${}_{2}$ MAX phase has been investigated taking into account the experimental synthesis conditions where some Sn atoms could replace Al atoms in the structure. For this purpose, Ti${}_{3}$Al${}_{1-x}$Sn${}_{x}$C${}_{2}$ with x ranging from 0 to 1 with 0.1 interval has been studied using the first principles method and the results show that all compositions are thermodynamically stable. The electronic properties of these compositions have been studied using band filling theory in detail. Also, the mechanical properties of these compounds such as shear modulus, Poisson's ratio, Young's modulus, sound wave velocities, polarization of the sound waves, enhancement factor, the power flow angle and etc. have been obtained with the varying directions and the three-dimensional mechanical properties have been visualized.
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