Structural and elastic properties of β-brass

First-principles calculations have been made for the 50–50 ordered alloy CuZn, β-brass, of the energy per atom in tetragonal structure as a function of the tetragonal lattice parameters a and c. A full-potential electronic-structure program was used with both the local-density approximation (LDA) and the generalized gradient approximation (GGA). Both formulations confirm the existence of a shallow energy minimum (the ground state) at c/a = 1 (β-brass has CsCl structure), and reveal the occurrence of a shallow secondary minimum at approximately c/a = 1.26. With decreasing electronic charge on the Zn atom this minimum becomes deeper, and moves toward larger c/a values, reaching the value c/a = 21/2 when one full electron is taken away from Zn, i.e., when Zn is replaced with Cu. The three elastic constants of β-brass have been calculated and compared with experiment. The large elastic shear anisotropy of β-brass discussed by Clarence Zener in 1947 has been confirmed in this work, although the anisotropy is not quite as large as the then available experimental data indicate.