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First-principle calculations have been adopted in order to reveal and deeply understand the structural, electronic, elastic, thermodynamic, and vibrational properties of full-Heusler X2TiAl (X = Au, Ru, and Zr) alloys in theL21phase. The fundamental physical properties such as bulk modulus, its pressure derivative, anisotropy factor, shear modulus, Poisson’s ratio, Cauchy pressure, elastic constants, heat capacity, thermal expansion coefficient, and Young’s modulus are obtained and compared with the literature. Debye temperature and Grüneisen parameter are also evaluated over the temperature range of 0–1500 K. Electronic band structures and their partial density of states and phonon dispersion curves are presented for all alloys and used to interpret the electronic and mechanical properties and stabilities of alloys in theL21phase.

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