Identifying the forces that drive a phase transition is always challenging. The hcp-fcc phase transition that occurs in cobalt at ~700 K has not yet been fully understood, although early theoretical studies have suggested that magnetism plays a main role in the stabilization of the fcc phase at high temperatures. Here, we perform a first principles study of the free energies of these two phases, which we break into contributions arising from the vibration of the lattice, electronic and magnetic systems and volume expansion. Our analysis of the energy of the phases shows that magnetic effects alone cannot drive the fcc-hcp transition in Co and that the largest contribution to the stabilization of the fcc phase comes from the vibration of the ionic lattice. By including all the contributions to the free energy considered here we obtain a theoretical transition temperature of 825 K.

We have calculated x-ray photoemission (XPS) spectra and nuclear magnetic resonance (NMR) chemical shifts for amorphous alumina from first principles. We generate models for amorphous structures at three different densities by means of a stochastic quenching procedure. We analyze these structures by calculating radial distribution functions, angle distributions functions, bond lengths, and coordination numbers. Our amorphous models compare well with previous molecular dynamics simulations and experiments. We include in our study, the stable phase of alumina $\alpha$, some of the transition phases, that is, $\theta$, $\gamma$, and $\kappa$, and the hypothetical bixbyite structure for comparison. Our results reproduce both XPS spectra and NMR chemical shifts and suggest that the XPS failure to resolve the different local environments in the different phases of alumina is due to the strong ionicity of the Al-O bond. Our calculated NMR chemical shifts show that the local environments are well resolved. We estimate the broadening of the NMR peaks due to local atomic environment differences in the amorphous phase to be as large as 35 ppm.

We present a study of the structural phase transition and the mechanical and thermodynamic properties of UO${}_2$ by means of the local density approximation (LDA)+$U$ approach. A phase transition pressure of 40 GPa is obtained from theory at 0 K, and agrees well with the experimental value of 42 GPa. The pressure-induced enhancements of elastic constants, elastic moduli, elastic wave velocities, and Debye temperature of the ground-state fluorite phase are predicted. The phonon spectra of both the ground state fluorite structure and high-pressure cotunnite structure calculated by the supercell approach show that the cotunnite structure is dynamically unstable under ambient pressure. Based on the imaginary mode along the $\Gamma$ $-$ $X$ direction and soft phonon mode along the $\Gamma$ $-$ $Z$ direction, a transition path from cotunnite to fluorite has been identified. We calculate the lattice vibrational energy in the quasiharmonic approximation using both first-principles phonon density of state and the Debye model. The calculated temperature dependence of lattice parameter, entropy, and specific heat agrees well with experimental observations in the low temperature domain. The difference of the Gibbs free energy between the two phases of UO${}_2$ has predicted a boundary in the pressure-temperature phase diagram. The solid-liquid boundary is approximated by an empirical equation using our calculated elastic constants.