Electron momentum-space densities and Fermi surface ofLi100−xMgx(0<~x<~40)alloys: Compton scattering experiment versus theory

Abstract

Directional Compton profiles (CP's) of ${\mathrm{Li}}_{100\ensuremath{-}x}{\mathrm{Mg}}_{x}(0<~x<~40)$ were measured for (11)12 directions of the momentum transfer q with (0.14) 0.16 a.u. $(\mathrm{a}.\mathrm{u}.=\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}$ units: $\ensuremath{\Elzxh}=e=m=1)$ momentum space resolution using synchrotron x rays, monochromatized to (31) 59 keV (values in brackets refer to $x=0).$ The total experimental valence electron CP's, their second derivatives, and the associated directional differences were compared with the corresponding Korringa-Kohn-Rostoker--coherent-potential-approximation--local-density-approximation (KKR--CPA--LDA) computations. Discrepancies between measurements and calculations are partly traced back to an inadequate treatment of electron correlation effects within the LDA framework. The three-dimensional (3D) valence-electron momentum density, \ensuremath{\rho}(p), as well as the 3D occupation number density $N(\mathbf{k}),$ were reconstructed from experimental data using the Fourier-Bessel method. The reconstructed \ensuremath{\rho}(p)'s exhibit evidence of higher momentum components due to 110 umklapp processes, whose variations with x are in reasonable agreement with the KKR-CPA calculations. The experimental $N(\mathbf{k})$'s provide a direct measure of the Fermi-surface anisotropy and show the presence of necks on the 110 Brillouin-zone boundaries for $x>~13$ in good accord with 2D positron annihilation experiments.