Research on the Lattice Stability of Elemental Be, Mg, Ca, Sr, Ba and Ra by the Ultra-Soft Pseudo-Potential Method in First Principles

Lattice constants, total energies, and densities of state of alkali-earth metals Be, Mg, Ca, Sr, Ba and Ra in group IIA with competing crystalline structures were calculated via the Perdew-Burke-Ernzerhof parameterization of generalized gradient approximation with ultra-soft pseudo-potential method (PBE-GGA-USPP) in the density functional theory. The lattice stabilities of Be, Mg, Ca and Sr agree well with those of the Perdew-Wang parameterization of generalized gradient approximation with projector augmented-wave method (PW91-GGA-PAW) in density functional theory and the CALPHAD method. The lattice stability of Ba agrees with that of PW91-GGA-PAW method in first-principles but disagrees with the result of CALPHAD method for the stability of competing hcp and fcc structures. The lattice stability of Ra is calculated and agrees with the experimental fact. Analyses of the electronic structures show that the p state of electrons contributes mainly to the density of state (DOS) for Be and Mg and the d state plays main role in that of Ca, Sr, Ba and Ra.