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Based on density functional theory the noncentrosymmetric superconductorMo_3Al_2C in its well established {\beta}-Mn type ($P4_{1}32$) crystalstructure is investigated. In particular, its thermodynamical and dynamicalstabilities are studied by calculating lattice vibrations within the harmonicapproximation. It is found that the fully stoichiometric compound isdynamically unstable. However, compounds with carbon vacancies, i.e.,Mo_3Al_2C_{1-x}, can be dynamically stabilized for vacancy concentrations x >0.09. By means of a simple thermodynamical model we estimate x ~ 0.13-0.14 forMo_3Al_2C_{1-x} at the experimental preparation temperatures. The influence ofthe carbon vacancy concentration on the electronic structure is investigated.

Density functional theory study of phase stability, vibrational and electronic properties of $Mo_3Al_2C$