The First Principle Calculations For The Crystal Structure And Thermodynamics Propertites Of Metal Vanadium And Lead-Tin Alloy

Based on the density functional theory (DFT) and density functional perturbation theory (DFPT) of the first principle, with exchange-correlation potential used the generalized gradient approximation (GGA). The lattice structure, energies, electronic bands and density of states (DOS), phonon spectrum and density of states (DOS) of the metal Vanadium are optimized and calculated. Then using the calculated phonon DOS, the heat capacity, the entropy, the bulk modulus, the Gruneisen parameter and the coefficient thermal expansion of Vanadium are attained in standard condition(298.5K,1atm), which of them are compared and well matched with experimental results.Then, using the relation between crystal structure and energy, the melting temperature of the metal Vanadium is directly obtained in the range of0-40GPa after analyzed the solid-liquid phase transition mechanism. All calculations are compared with the experimental results, and significantly better than the result acquired by V. Sorkin et al employing molecular modeling approach.Followed by using the relation between crystal structure and energy as well as phonon dispersion once again, the structure phase transition of Vanadium under high pressures are discussed and studied. Firstly, using the relations between crystal structure and energy in different pressures, it is easily to find that the structure energy corresponding to body-centered cubic (BCC) structure is not the minimum in130GPa and begin to change from BCC to the rhombic structure. However, when the pressure is320GPa, BCC structure reoccurs again, and phase transition disappears. Secondly, in order to verification the results of phase transition above by using the relations of phonon dispersion in different pressures again. When the pressure is70GPa, the transverse acoustics phonon mode begin to show softening and lead to mechanical properties unstable, implying to occur to phase transition also. While the pressure is up to500GPa, the transverse acoustics are not returned to the situation where at ambient conditions. So, it is forecasted that the pressure from the rhombic structure to the BCC is higher than500GPa, which is compared with some relevant papers.Finally, Based on the density functional theory (DFT) and density functional perturbation theory (DFPT) of the first principle, with exchange-correlation potential used the local density approximation (LDA). By employing the virtual crystal method, the lattice structure, energies, electronic bands and density of states (DOS), phonon spectrum and density of states (DOS) of the Lead-Tin alloy are optimized and calculated. Then using the calculated phonon DOS, the heat capacity, the entropy, the free energy and the inner energy of Pb-Sn are gained in standard condition (298.5K, latm), which of them are compared and well matched with experimental results. Also, using the relation between crystal structure and energy, the melting temperature of the Pb-Sn alloy is directly obtained in the range of0-1.6GPa after discussed the solid-liquid phase transition mechanism, all of the calculations are compared with the experimental results. At the same time, those results of Pb-Sn alloy are carefully compared with lead.