First Principle Calculations For The Lattice And Thermodynamics Of FCC Metals

Based on the density functional theory (DFT) and the density-functional perturbation theory (DFPT) of first principle, with generalized gradient approximation (GGA), the lattices, energy bands, density of states, and phonon spectrums, are optimized and calculated for the transition metals Ni, Cu, Rh, Pd, Ir, and Au. The relationship of the energy and lattice are discussed.It is shown that, the energy surface for a large atomic number would have one maximum of the simple cubic (SC) structure and two minima of face center cubic (FCC) and body center cubic (BCC) structures;and for a small atomic number it would have with two maxima located on both sides of the SC structure, the SC structure then forms a shallow potential well with a high energy.Nickel is a magnetic element, and others here are not magnetic. All these elements show the metallic features with their wide conduction electronic bands for some bands cross through the Fermi surface. The densities of states (DOS) near the Fermi level are contributed mainly by the bands at the k points on the line L-X-W. The electrons near the L point would be excited by heat or external field following the L-X-W line, and those near the X point following theΓ-X-K line.The calculated phonon spectrum, entropies, heat capacities, bulk modulus, Gruneisen constants and thermal expansion coefficients are in good agreement with the experimental results. The energy of longitudinal acoustic (LA) bands is generally higher than that of transverse acoustic band. The rate of the peak heights for the density of states of TA and LA increases with the atomic number. The DOS peaks of TA and LA for Ir have the same height. And the TA peak of DOS for Pt is slightly higher than the LA peak.The relationship of the energies and lattices are analyzed. Mechanism of the phase transitions from solid to liquid and ferromagnetic to paramagnetic are discussed and the melting temperature Tm and Curie temperature Tc are derived. With compare with the experimental data, the derived melting temperatures for transition metal with FCC lattices and the relationship of the melting temperature with pressure are superior to the results from the atomic simulations using the method of molecular dynamics. It shows the mechanics suggested for the solid-liquid and ferromagnetic-paramagnetic phase transition of transition metals is worth to be studied further.