Structural parameters, elastic constants, and thermodynamic properties of ordered and disordered solid solutions of ZrHf alloys are investigated through first-principles calculations based on density-functional theory （DFF）. The special quasi-random structure （SQS） method is used to model the disordered phase as a single unit cell, and two lamella structures are generated to model the ordered alloys. Small strains are applied to the unit cells to measure the elastic behavior and mechanical stability of ZrHf alloys and to obtain the independent elastic constants by the stress-strain relationship. Phonon dispersions and phonon density of states are presented to verify the thermodynamic stability of the considered phases. Our results show that both the ordered and disordered phases of ZrHf alloys are structurally stable. Based on the obtained phonon frequencies, thermodynamic properties, including Gibbs free energy, entropy, and heat capacity, are predicted within the quasi-harmonic approximation. It is verified that there are no obvious differences in energy between ordered and disordered phases over a wide temperature range.
The first-principles calculations are performed to investigate the adsorption of O2 molecules on an Sn（lll） 2 × 2 surface. The chemisorbed adsorption precursor states for O2 are identified to be along the parallel and vertical channels, and the surface reconstructions of Sn（111） induced by oxygen adsorption are studied. Based on this, the adsorption behaviours of O2 on X（111） （X=Si, Ge, Sn, Pb） surfaces are analysed, and the most stable adsorption channels of O2 on X（111） （X=Si, Ge, Sn, Pb） are identified. The surface reconstructions and electron distributions along the most stable adsorption channels are discussed and compared. The results show that the O2 adsorption ability declines gradually and the amount of charge transferred decreases with the enhancement of metallicity.
