Crystal structure, phase stability and elastic properties of the Laves phase ZrTiCu 2

Abstract

The crystal structure of the ternary Laves phase ZrTiCu 2 with unusual stoichiometry has been determined from combined refinement of X-ray powder, X-ray single crystal and neutron powder intensity data. The derived structure is of type MgZn 2 (space group P6 3/ mmc) with lattice parameters a = 0.51491(3) nm, c = 0.82421(8) nm. Crystal symmetry and composition reveal a high degree of atomic disorder, because Ti and Zr atoms share the 4f sites, whereas Ti and Cu atoms are found at the 6h sites. The 2a sites, however, are exclusively occupied by Cu. Lattice parameters for alloys Zr 1− x Ti 1− x Cu 2+2 x (annealed at 800 °C) as a function of the concentration of Cu for a constant ratio of Zr/Ti = 1 vary in a nonlinear way, which is consistent with the described complex atomic substitution mechanism. At a load of 2 N the micro-hardness was measured to be 7.5 ± 0.3 GPa, which is significantly larger than for most of the binary Ti–Cu or Zr–Cu phases. By a density functional theory ab initio approach the site preferences of Zr, Ti and Cu were calculated indicating that a random mixture of Ti and Cu atoms at the 6h lattice sites is a key factor to stabilize the proposed structure, which is unique for a Laves phase. Lattice parameters, elastic constants and shear moduli for polycrystalline ZrTiCu 2 were also derived. The Vickers hardness of 6.2 GPa was estimated by applying a correlation between shear modulus and hardness. Data as calculated by the ab initio approach are in good agreement with the experimental findings.