Structural and electronic properties of the liquid polyvalent elements. III. The trivalent elements

We present ab initio calculations of the atomic structure, the electronic density of states, and the photoemission intensities of the trivalent metals Al, Ga, In, and Tl. The investigations are based on pseudopotential-derived interatomic forces, molecular-dynamics simulations for the atomic structure, and self-consistent linear-muffin-tin-orbital supercell calculations for the electronic structure and photoelectron spectra. This study extends similar work on the liquid di- and tetravalent elements W. Jank and J. Hafner, Phys. Rev. B 41, 1497 (1990); 42, 6926 (1990). We show that the trend from a close-packed structure in liquid Al to a somewhat more loosely packed atomic arrangement in liquid Ga, but then a return to more close-packed structure in the heavy elements arises from a modulation of the random packing of atoms by the Friedel oscillations in the potential and the damping of these oscillations by relativistic effects. Relativistic effects are also responsible for the formation of a pseudogap separating the s- and p-orbital-dominated parts of the valence band.