Energy Bands in Iron via the Augmented Plane Wave Method

Results of numerical calculations of the band structure of body-centered cubic and face-centered cubic iron are reported; the calculations have been carried out according to the augmented plane wave (APW) method of Slater. A total of 55 points in the $\frac{1}{48}$ of the Brillouin zone has been examined in the bcc case; this provides sufficient information for construction of a density-of-states curve which is presented. For the fcc structure, calculations have been performed at 17 points of high symmetry; no density-of-states curve is calculated.

The potential used is that of Manning and consists of the argon core plus 7 valence electrons. The lattice constants are taken as $a=3.647\mathrm{}\times {10}^{-8\mathrm{}}$ cm for the fcc lattice and $a=2.861\mathrm{}\times {10}^{-8\mathrm{}}$ cm for the bcc lattice. Fortunately, the latter constant is one of the three used by Stern in a modified tight-binding calculation of the cohesive energy and band structure of iron. Rather good agreement is found between the present calculation and Stern's.

The APW method seems a promising one inasmuch as the convergence in terms of number of plane waves is reached in about 40 plane waves (this for a point in the Brillouin zone having $\mathrm{no}$ symmetry). Moreover, the method is one which is quite adaptable to a digital computer and has been programmed for the Whirlwind computer (by Saffren) and for the IBM 704 and 709 computers.