Crystal structure and elastic-constant anomalies in the magnetic 3dtransition metals

Assuming a saturated ferromagnet, the anomalous crystal structures of the magnetic 3d transition elements Fe, Co, and Ni are explained from simple band-filling arguments. The full-potential linear muffin-tin orbital (FP-LMTO) method is used to calculate the elastic constants (${\mathit{C}}_{11}$, ${\mathit{C}}_{12}$, and ${\mathit{C}}_{44}$) for the magnetic and cubic 3d transition metals Cr, Fe, and Ni. For Co calculations of the elastic constants have been performed in the fcc crystal structure (β-Co). Good agreement with the experimental data is found even for Fe and Co which have anomalous elastic constants. The behavior of the elastic shear constant C’ can be understood from the filling of the spin-down 3d band for the ferromagnetic elements. It is shown that C’ correlates with the relative crystal stabilities of the bcc and fcc structures for these elements as has earlier been found for the paramagnetic 4d and 5d metals and alloys.