Atomic size effects in Ni–Al based solid solutions

We have determined the atomic volumes of Ni, Al and Ni vacancies in NiAl by analyzing the variations of lattice parameter with composition. We have also attempted to determine the atomic size factors for the solid-solution strengthening elements: Ti, Hf, and Zr, through lattice parameter measurements of solid-solution alloys. The atomic size factor for Ti is found to be +0.34, indicating a sufficiently large size mismatch to account for significant solid-solution strengthening in this system. We calculated a similar atomic size factor of +0.27 for Ti using lattice parameters that had been computed from first-principles. Lattice contractions and negative atomic size factors were observed for Hf and Zr-containing alloys, suggesting the presence of trapped vacancies. Annealing and slow-cooling experiments minimized these lattice contractions and supported the trapped vacancy hypothesis. Using the approximation that the NiAl(Hf, Zr) lattice parameters vary linearly with composition out to the Heusler phase boundary, we determined size factors of Hf and Zr to be +0.57 and +0.65, respectively.