First-principles thermodynamics of transition metals: W, NiAl, and PdTi

We apply the pseudopotential density-functional-perturbation theory approach along with the quasiharmonic approximation to calculate the thermal expansion of tungsten and two important metallic alloys NiAl and PdTi. We derive the theory for anisotropic crystal structures and test the approximation that the anisotropic effects of thermal expansion are equivalent to negative pressure-this simplifies the calculation enormously for complex structures. Throughout, we find excellent agreement with experimental results.