Structure, electronic density of states and electric field gradients of icosahedral AlCuFe: An ab initio study of the original and a modified Cockayne model

We present a detailed analysis of electronic properties of the Cockayne model of icosahedral AlCuFe, both in its original form and after a structural relaxation using the ab initio density functional approach. The electronic density of states (DOS) and electric field gradients (EFG’s) of the Al and Fe atoms in the original and the relaxed Cockayne models were calculated and compared with available photoemission, Mössbauer, and nuclear quadrupole resonance spectroscopy data. The relaxed and the original models show significantly different electronic properties. Both models are deficient in describing the available experimental data. The DOS’s show two Fe-$d$ peaks, where there is only one such peak in the photoemission spectroscopy data. These models also cannot account for the shape of the Mössbauer spectra. We show that the interchange between 12 Cu and 12 Fe atoms, each belonging to a single symmetry class, results in a smaller number of Cu-Fe nearest-neighbor pairs and a lowering of the total energy by an amount of $\Delta E\sim 50\mathrm{m}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}.$ This “modified” version of the Cockayne model was further relaxed for the final comparison between the calculation and experimental results. The modified model shows a considerable improvement: The DOS has only one Fe-$d$ peak, in agreement with photoemission spectroscopy data, and the calculated EFG’s account very well for the experimental Mössbauer spectra.