Effects of Uniaxial Compression on the Third-Zone Fermi Surface of Aluminum

Abstract

The effects of uniaxial compression up to 40 kg/${\mathrm{cm}}^{2}$ on the areas of the [110]-$\ensuremath{\gamma}$ and [100]-$\ensuremath{\beta}$ orbits of the third-zone Fermi surface of aluminum have been determined by means of a de Haas-van Alphen phase-shift technique. Both areas were found to increase under compression, the $\ensuremath{\gamma}$-orbit area by (4.6 \ifmmode\pm\else\textpm\fi{} 0.3) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$%/(kg/${\mathrm{cm}}^{2}$) and the $\ensuremath{\beta}$-orbit area by (3.4 \ifmmode\pm\else\textpm\fi{} 0.7) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$%/(kg/${\mathrm{cm}}^{2}$). The estimates of the errors allow for the possibility of systematic errors. The nearly-free-electron (NFE) and four-orthogonalized-plane-waves (OPW) models for the aluminum Fermi surface were used to calculate the effects of uniaxial compression, hydrostatic pressure, and alloying on the $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ cross sections. The NFE results for both orbits were not at all satisfactory. The predictions of the four OPW model for the stress and pressure derivatives of the $\ensuremath{\gamma}$-orbit area agreed with experiment within the experimental error when the changes in the matrix elements with stress and pressure were obtained from the $q$ dependence of the Heine-Abarenkov form factor. The dependence on alloying, calculated from the four-OPW model on the assumption that the change in matrix elements and volume was negligible, was in equally good agreement with experiment. The results of similar four-OPW calculations for the $\ensuremath{\beta}$ orbit did not agree with experiment quite so well, the discrepancies being roughly twice as large as the experimental error.