Correlation between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-Band Occupancy and Crystal Structure in the Rare Earths

Abstract

The rare-earth crystal structure sequence ${\mathrm{hcp}}^{\ensuremath{\rightarrow}}$ Sm-${\mathrm{type}}^{\ensuremath{\rightarrow}}$ double-${\mathrm{hcp}}^{\ensuremath{\rightarrow}}$ fcc observed for decreasing atomic number and increasing pressure is quantitatively correlated with the $d$-band occupancy through the $d$-band energy contribution to the total energy. Self-consistent calculations show that the number of $d$ electrons is very sensitive to the relative size of the ion core. The theory thus accounts for La's anomalous double-hcp structure and the apparent deviations from the electron-per-atom rules exhibited by certain rare-earth Laves phases.