  In this paper, we performed a detailed theoretical study of structural,
elastic and electronic properties of two germanides LuAuGe and ScAuGe by means
of first-principles calculations using the pseudopotential plane-wave method
within the generalized gradient approximation. The crystal lattice parameters
and the internal coordinates are in good agreement with the existing
experimental and theoretical reports, which proves the reliability of the
applied theoretical method. The hydrostatic pressure effect on the structural
parameters is shown. The monocrystalline elastic constants were calculated
using the stress-strain technique. The calculated elastic constants of the
MAuGe (M = Lu, Sc) compounds meet the mechanical stability criteria for
hexagonal crystals and these constants were used to analyze the elastic
anisotropy of the MAuGe compounds through three different indices.
Polycrystalline isotropic elastic moduli, namely bulk modulus, shear modulus,
Young's modulus, Poisson's ratio, and the related properties are also estimated
using Voigt-Reuss-Hill approximations. Finally, we studied the electronic
properties of the considered compounds by calculating their band structures,
their densities of states and their electron density distributions.
