Structural phase stability in third-period simple metals

Extensive phase-stability calculations for the fcc, hcp, and bcc structures of Na, Mg, Al, and Si are reported both near 1 atm and under high pressure, where Si becomes a natural member of this set of third-period simple metals Calculations for each element have been carried out by two entirely different first-principles techniques: the generalized pseudopotential theory (GPT) and the linear-muffin-tin orbitals (LMTO) method. The two techniques give results in good qualitative agreement for Mg, Al, and Si, and predict sequences of high-pressure structural phase transitions for these elements which arise from the lowering and partial filling of the initially empty 3d band under compression. Detailed analysis shows that major trends in the phase stability of the third-period metals are correlated with specific features both in the LMTO one-electron densities of states and in the GPT interatomic pair potentials. Quantitative comparisons between the two theoretical techniques, as well as with available experimental data and other recent calculations, are further used to assess the accuracy of the approximations employed by these methods in calculating structural energy differences.