Na+ ion conductivity can be improved by the substitution of an Mg atom for an Al atom to form a nonstoichiometric Na+ β-alumina. We performed a first principles study to investigate the most stable substitution site of an Mg atom and the resulting structural change of the nonstoichiometric Na+ β-alumina. Al atoms were classified as four different layers in the spinel block that are separated by conduction planes in the nonstoichiometric Na+ β-alumina. The substitution of an Mg atom for an Al atom at a tetragonal site was more favorable than that at an octahedral site. The substitution in the spinel block was more favorable than that close to the conduction plane. This result was well explained by the volume changes of the polyhedrons, by the standard deviation of the Mg-O distance, and by the comparison with bulk MgO structure. Our result indicates that the most preferable site for the Mg atom was the tetrahedral site at the spinel block in the nonstoichiometric Na+ β-alumina.

Density functional theory was utilized to investigate the growth of an indium nanowire on a Si (001) buckled surface. A site between the edge of two Si dimers is most favorable when the first In atom is adsorbed on the surface at an adsorption energy level of 2.26 eV. The energy barriers for migration from other sites to the most favorable site are low. When the second In atom is adsorbed next to the first In atom to form an In dimer perpendicular to the Si dimer row, the adsorption energy is the highest among all adsorption sites. The third In atom prefers either of the sites next to the In dimer along the In dimer direction. The fourth In atom exhibited the same tendency showed by the second atom. The second and fourth In adsorption energy levels are higher than the first and third levels as the In atoms consume the third valence electron by forming In dimers. Therefore, the In nanowire grows perpendicular to the Si dimer row on the Si (001) surface, as it satisfies the bonding of the three valence electrons of the In atoms.

Tetragonal-Ni1-xPdxSi/Si (001) structure was studied by using density functional theory (DFT). An epitaxial interface between 2×2×4 (001) tetragonal-NiSi supercell and 1×1×2 (001) Si supercell was first constructed by adjusting the lattice parameters of B2-NiSi structure to match those of the Si structure. We chose Ni atoms as a terminating layer of the B2-NiSi; the equilibrium gap between the tetragonal-NiSi and Si was calculated to be 1.1 Å. The Ni atoms in the structure moved away from the original positions along the z-direction in a systematic way during the energy minimization. Two different Ni sites were identified at the interface and the bulk, respectively. The two Ni sites at the interface have 6 and 7 coordination numbers. The Ni sites with coordination number 6 at the interface were located farther away from the interface, and were more favorable for Pd substitution.