The crystal stabilities of ␣-and ␤-boron are studied theoretically by the density-functional calculations. The ground-state properties and thermodynamic properties are calculated by the pseudopotential method. These calculated thermodynamic properties include the effect of atomic disorder, observed experimentally, as well as the effect of phonons. The pressure dependence of the free energy is also studied. At zero temperature, it is found that ␣-boron is more stable than ␤-boron. This does not change even if the zero-point energy and atomic disorders are considered. The contribution of these effects to the energy is small at T = 0 K. However, these effects eventually cause a phase transition to ␤-boron at high temperatures. By considering the phonon contribution as the chief source of the temperature dependence of the free energy, 970 K is obtained as the transition temperature, which is in qualitative agreement with the experimental value of 1400 K. The difference between these values could be attributed to anharmonic effects. The effect of thermal expansion on the transition temperature is insignificant. At finite pressures, the stability of various polymorphs can be determined mainly using the atom density. The basic feature underlying all the above properties is that ␣-boron is dense, while ␤-boron is dilute. For ␤-boron, an energetic consideration shows that the disorder in the atom arrangement is inherent. The present calculations reveal a small change in bond length for specific intericosahedral bonds, which is caused by an atomic disorder.

Articles you may be interested inEffect of stirring on the growth rate anisotropy of the metastable α-glycine single crystals AIP Conf.The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry Abstract. This paper describes the crystal stability of α-rhombohedral and β -rhombohedral boron. Our study includes structural optimization, pressure dependence and phonon calculation, which are followed by thermodynamic considerations. The properties at the zero temperature are discussed, so that α-boron is stable in terms of the electronic structure at zero temperature and phonon contribution. As temperature is increased, the effect of the phonon contribution tends to relatively lower the thermodynamic potential of β -boron. Furthermore the diluted phase (β -boron) is thermodynamically more stable than the dense phase (α-boron) at high temperatures through the volume contribution to the enthalpy.

Phase diagram of boron is theoretically studied, with focusing mainly on difference between α and β phases. The melting curve is calculated by the pressure dependence of the bulk modulus of solid. It is found that the gradient of the melting curve is inverted at a high pressure. Based on this finding, a promising method to obtain good-quality crystals of α phase is proposed.

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From a theoretical standpoint, we propose that the addition of oxygen enhances the luminescence for codoping europium and magnesium in gallium nitride. From the additional oxygen, donor levels are created to an energy range between the europium f*-level and the conduction band, whereas magnesium acceptor levels are between the europium f-level and the valence band. Because the donor and acceptor levels form exciton paths from the host bands to Eu luminescent levels, the luminescence must be efficiently promoted.