First principles calculation of the elastic constants of intermetallic compounds: metastable Al₃Li

We report first principles local density calculations for the metastable Al₃Li intermetallic compound with cubic L1₂ crystal structure using the full-potential linearized augmented plane wave method. From the second derivative of the total energy as a function of volume, and generated tetragonal and trigonal lattice distortions, the elastic constants C₁₁, C₁₂, and C₄₄ were derived yielding C₁₁ = 158 GPa, C₁₂ = 29.4 GPa, and C₄₄ = 57.7 GPa. Because of the very high Young's modulus (E = 141 GPa) compared, for example, to pure Al (E = 66 GPa), it is suggested that Al₃Li plays an important role in strengthening the Al–Li alloys. The calculated Young's modulus appears in good agreement with experimental estimates when the experimental values are extrapolated to 0 K. Although the Young's modulus of Al₃Li is increased in comparison to Al, the calculated bulk modulus is decreased to a value of 72 GPa as compared to pure Al (82 GPa), in agreement with experiment. As a result, the Poisson ratio is reduced to ŝ = 0.173 as compared to the value 1/3 for an isotropic medium. Because of this and the high Young's modulus, the calculated Debye temperature Θ_D at 0 K amounts to 672 K, which is substantially larger than Θ_D for Al, which is about 400 K.