The structure of Sn alloyed with Hg ͑10 at. %͒ was studied under pressure up to 66 GPa with energydispersive x-ray diffraction using synchrotron radiation. The ambient pressure simple hexagonal (hP1) phase transformed at 15 GPa to a body-centered tetragonal (tI2) phase similar to the high-pressure forms of Sn and InBi. The axial ratio, c/a, of the tI2 phase increased with pressure up to a maximum value of c/aϷ0.92 at about 40 GPa and remained nearly constant upon further compression to 55 GPa. At pressures above 55 GPa, a second phase transition, probably to an orthorhombic phase, was observed. The structural trends observed are discussed in terms of a Fermi-sphere-Brillouin-zone interaction. ͓S0163-1829͑99͒04709-8͔

The simple alkali metal Na, that crystallizes in a body-centred cubic structure at ambient pressure, exhibits a wealth of complex phases at extreme conditions as found by experimental studies. The analysis of the mechanism of stabilization of some of these phases, namely, the low-temperature Sm-type phase and the high-pressure cI16 and oP8 phases, shows that they satisfy the criteria for the Hume-Rothery mechanism. These phases appear to be stabilized due to a formation of numerous planes in a Brillouin-Jones zone in the vicinity of the Fermi sphere of Na, which leads to the reduction of the overall electronic energy. For the oP8 phase, this mechanism seems to be working if one assumes that Na becomes divalent metal at this density. The oP8 phase of Na is analysed in comparison with the MnP-type oP8 phases known in binary compounds, as well as in relation to the hP4 structure of the NiAs-type.

The program BRIZ has been developed for displaying Brillouin zones and Fermi sphere configurations. The underlying physics relates to the nearly-free-electron model for simple sp-metals. A Brillouin zone boundary near the Fermi level provides formation of the energy gap and leads to the lowering of the structure energy. Consideration of the Brillouin zone with respect to a free-electron Fermi sphere and zone filling by electron states provides useful information for phase structure stability and physical properties.

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InBi is studied by energy-dispersive diffraction with synchrotron radiation in a diamond-anvil cell under pressure up to 75 GPa. Three phase transitions are observed from its initial tetragonal structure tP4 with c/aϷ0.95 to another tP4 structure with c/aϷ0.65 typical for the ␤-Np structure, than to a disordered tetragonal body-centered structure tI2, and finally some hints are obtained for a transition to a cubic body-centered structure cI2. All these transformations are reversible with large hysteresis. InBi(tI2), phase III, shows initially a steep increase in c/a from 0.91 to 0.94, in the pressure range from 20 to 30 GPa, and a nearly constant value of about 0.96 above 55 GPa. Hints for the possible stability of a new phase IV are noticed in the present experiments on decompression from 75 GPa as admixture of new lines to phase III giving strong indications for a first-order phase transition with large hysteresis. The origin of the tetragonal distortion and the transformation to a cubic phase are discussed from the point of view of nesting the Fermi sphere in the Brillouin zone. ͓S0163-1829͑98͒00110-6͔ PHYSICAL REVIEW B