Ab initio calculation of phase diagrams of ceramics and minerals

Abstract

A range of methods, based on Monte Carlo and lattice dynamics simulations, are presented for the calculation of the thermodynamic properties of solid solutions and phase diagrams. These include Monte Carlo simulations with the explicit interchange of cations, the use of the semigrand-canonical ensemble and con®gurational bias techniques, hybrid Monte Carlo/molecular dynamics, and a new con®gurational lattice dynamics technique. It is crucial to take account of relaxation of the local atomic environment and vibrational effects. Examples studied are (i) the enthalpy and entropy of mixing, the phase diagram and the spinodal of MnO/MgO. The available experimental data disagree widely for this system; (ii) the enthalpy of mixing of CaO/MgO, where the size mismatch between the cations is considerably larger than in (i); (iii) the postulated high-pressure orthorhombic to cubic phase transition in (Mg,Mn)SiO 3 perovskite, where we show that impurity cations can have a much larger effect than that expected from a mean-®eld treatment or linear interpolation between endmember compounds. {Basis of a presentation given at Materials Discussion No. 3, 26±29

Molecular modelling of rare earth element complexation in subduction zone fluids

“…Oganov and Ono, 2004;Tsuchiya et al, 2004), and to the structural and thermodynamic properties of upper mantle minerals (e.g. Allan et al, 2001;Lavrentiev et al, 2003) and properties of silicate melts (e.g. Karki et al, 0016-7037/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved.…”

Monte Carlo simulations of Fe-Cr solid solution

“…Exchange MC simulations (MCX), introduced recently [6], solve this problem for systems with configurational disorder by allowing explicit change of atomic configurations. In an event, a random choice is made regarding whether to attempt a random exchange between a pair of (different) atoms, or a random displacement of an atom, or a random change in the volume of the simulation box.…”

Non-empirical phase equilibria in the Cr–Mo system: A combination of first-principles calculations, cluster expansion and Monte Carlo simulations

“…The large vibrational effect is more likely to be found in the systems where there is a large mismatch in the atomic radius between the atomic species [21,43] (and thus a large size mismatch in the lattice constants of the crystal structures between thee atomic species). The CreMo system is such a case where the Cr atomic radius is 1.249 Å, while Mo atomic radius is 1.363 Å [49], and the lattice constants of the pure Cr bcc crystal are 2.88 Å, while they are 3.15 Å for the Mo bcc crystal [4].…”