Theory of elastic constants of cubic transition metals and alloys

We have from first principles calculated the elastic constants (${\mathit{C}}_{11}$, ${\mathit{C}}_{12}$, and ${\mathit{C}}_{44}$) of all nonmagnetic cubic d transition metals, and obtained good agreement with experimental data. We show that the trend exhibited by the tetragonal shear constant in the transition metals can be simply understood. In particular, we show that .ul4 the trend of the tetragonal shear constant, C', of cubic transition metals and alloys is determined by the energy difference between the fcc and bcc structures of a given system, which in turn is determined by band filling. This finding is in turn due to the result that these systems have a Bains path with similar shape, and our ``canonical'' Bains path illustrates this behavior. The trend of C' is further studied by including selected alloys (thereby obtaining a finer tuning of band-filling effects). The scaling of C' with the bcc-fcc energy difference is found to hold also for the studied alloys (roughly), and the calculated C' is found to agree well with available experimental data.