Pressure dependence of the elastic moduli in aluminum-rich Al-Li compounds

Abstract

I have carried out numerical first-principles calculations of the pressure dependence of the elastic moduli for several ordered structures in the aluminum-lithium system, specifically fcc Al, fcc and bcc Li, L${1}_{2}$${\mathrm{Al}}_{3}$Li, and an ordered fcc ${\mathrm{Al}}_{7}$Li supercell. The calculations were performed using the full-potential linear augmented plane-wave method (LAPW) to calculate the total energy as a function of strain, after which the data were fit to a polynomial function of the strain to determine the modulus. A procedure for estimating the errors in this process is also given. The predicted equilibrium lattice parameters are slightly smaller than found experimentally, consistent with other local-density-approximation (LDA) calculations. The computed elastic moduli are within approximately 10% of the experimentally measured moduli, provided the calculations are carried out at the experimental lattice constant. The LDA equilibrium shear modulus ${\mathit{C}}_{11}$-${\mathit{C}}_{12}$ increases from 59.3 GPa in Al, to 76.0 GPa in ${\mathrm{Al}}_{7}$Li, to 106.2 GPa in ${\mathrm{Al}}_{3}$Li. The modulus ${\mathit{C}}_{44}$ increases from 38.4 GPa in Al to 46.1 GPa in ${\mathrm{Al}}_{7}$Li, then falls to 40.7 GPa in ${\mathrm{Al}}_{3}$Li. All of the calculated elastic moduli increase with pressure with the exception of bcc Li, which becomes elastically unstable at about 2 GPa, where ${\mathit{C}}_{11}$-${\mathit{C}}_{12}$ vanishes.