Hume-Rothery electron concentration rule across a whole solid solution range in a series of gamma-brasses in Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga, Ni–Zn and Co–Zn alloy systems

Abstract

The aim of the present work is to examine if the Hume-Rothery stabilisation mechanism holds across whole solid solution ranges in a series of gamma-brasses with especial attention to the role of vacancies introduced into the large unit cell. The concentration dependence of the number of atoms in the unit cell, N, for gamma-brasses in the Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga, Ni–Zn and Co–Zn alloy systems was determined by measuring the density and lattice constants at room temperature. The number of itinerant electrons in the unit cell, e/uc, is evaluated by taking a product of N and the number of itinerant electrons per atom, e/a, for the transition metal element deduced earlier from the full-potential linearised augmented plane wave (FLAPW)-Fourier analysis. The results are discussed within the rigid-band model using as a host the density of states (DOS) derived earlier from the FLAPW band calculations for the stoichiometric gamma-brasses Cu5Zn8, Cu9Al4 and TM2Zn11 (TM = Co and Ni). A solid solution range of gamma-brasses in Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga and Ni–Zn alloy systems is found to fall inside the existing pseudogap at the Fermi level. This is taken as confirmation of the validity of the Hume-Rothery stability mechanism for a whole solute concentration range of these gamma-brasses. An exception to this behaviour was found in the Co–Zn gamma-brasses, where orbital hybridisation effects are claimed to play a crucial role in stabilisation.