Gd Barrera

Negative thermal expansion

There has been substantial renewed interest in negative thermal expansion following the discovery that cubic ZrW2O8 contracts over a temperature range in excess of 1000 K. Substances of many different kinds show negative thermal expansion, especially at low temperatures. In this article we review the underlying thermodynamics, emphasizing the roles of thermal stress and elasticity. We also discuss vibrational and non-vibrational mechanisms operating on the atomic scale that are responsible for negative expansion, both isotropic and anisotropic, in a wide range of materials.

Ab initio calculation of phase diagrams of ceramics and minerals

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 configurational bias techniques, hybrid Monte Carlo/molecular dynamics, and a new configurational 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)SiO3 perovskite, where we show that impurity cations can have a much larger effect than that expected from a mean-field treatment or linear interpolation between end-member compounds.

SHELL - a code for lattice dynamics and structure optimisation of ionic crystals

This paper describes Shell, a program which uses lattice statics and quasiharmonic lattice dynamics to calculate analytically the free energy of a crystal, and its derivatives with respect to both internal and external strains, at a given temperature and pressure. These quantities can be used to perform efficient fully dynamic structure optimisation of unit cells containing hundreds of ions. Interactions are via short-ranged spherically symmetric pairwise and three-body potentials as well as the usual Coulomb terms, and polarizability effects may be accounted for by use of the shell model. Application of the code to the rutile phase of MgF2 is briefly described.

Free energy of formation of defects in polar solids

A more exact method than hitherto available, based on lattice statics and quasi-harmonic lattice dynamics, is presented for the direct minimisation of the free energies of periodic solids with very large unit cells. This is achieved via the calculation of analytic derivatives of the vibrational frequencies with respect to all external and internal variables. The method, together with large defective supercells, is used to calculate the free energies of defects in MgO as a function of temperature. A major advantage of the supercell approach is that constant-volume and constant-pressure quantities are calculated independently. This allows a critical appraisal of the common approximations used for many years: (i) to convert constant-volume defect parameters to constant-pressure and (ii) to justify the use of static calculations at constant volume in the interpretation of experimental data obtained at constant pressure and at high temperatures. Defect enthalpies show only a small variation with temperature and differ by ca. 2% from the internal energy change in the static limit. An assessment is also made of the commonly used ZSISA approximation, in which the free energy at each temperature is minimised with respect to external strains only, simultaneously determining the internal strains by minimising the static lattice energy.

Ionic solids at elevated temperatures and high pressures: MgF2

A combination of periodic Hartree–Fock theory, quasiharmonic lattice dynamics, and molecular dynamics is used to study the behavior of MgF2 at elevated temperatures and/or high pressures. Particular attention is paid to the pressure-induced transition from the rutile to the fluorite structure in view of earlier theoretical estimates of the transition pressure, which differ widely. It is shown that previously reported potentials obtained by fitting to empirical data fail to reproduce thermodynamic properties. To rectify this, a new set of consistent two-body potentials has been derived from ab initio periodic Hartree–Fock calculations. Lattice dynamics calculations in the quasiharmonic approximation based on these potentials has been used to study the two phases of MgF2 at high T and P. The resulting transition pressure and that obtained directly from Hartree–Fock calculations in the static limit are both ⩽30 GPa, which is close to the experimental value but appreciably lower than a previous molecular dyna...

Lithium oxide and superionic behaviour—A study using potentials from periodic ab initio calculations

Abstract A simple general methodology for obtaining interionic potentials from periodic ab initio calculations is presented, using periodic Hartree-Fock theory as implemented in the program crystal . To test the approach, two-body potentials are generated for Li2O. Results obtained from our new potential are compared with those from previously suggested empirical potentials, paying most attention to the possibility of superionic behaviour in this material at high temperatures. The application of ab initio Hartree-Fock theory, lattice statics, lattice dynamics and molecular dynamics is able to provide a consistent picture of a superionic transition in lithium oxide at 1100 K. Details of the mechanism of the transition are discussed with the aid of the calculated dispersion curves at high temperature, and individual molecular dynamics trajectories.

Semigrand-canonical ensemble simulations of the phase diagrams of alloys

We show how Monte Carlo simulations with the explicit interchange of atoms and the use of the semigrand-canonical ensemble, can be used to calculate phase diagrams for alloys. We illustrate our approach with the system Pd/Rh using the embedded atom method with potential parameters derived from ab initio density functional calculations. Our techniques take full account of local structural distortion, clustering and thermal effects.

Structure and energetics of Cu-Au alloys

The structures and energetics of Cu-Au alloys over a wide range of temperatures are studied using a combination of quasi-harmonic (QH) lattice dynamics and Monte Carlo (MC) simulations at constant temperature and constant pressure. The many-body potential used is fitted to room-temperature experimental data taking vibrational contributions into account. Transitions to the disordered phases are studied using MC simulations in which not only anisotropic deformation of the unit cell and atomic movements are allowed, but also exchange of atoms of different type is explicitly considered. Our calculations reproduce all characteristic features of the order-disorder transitions, including the characteristic peaks in the plots of heat capacity as a function of temperature.

Simulation of metals and alloys using quasi-harmonic lattice dynamics

Abstract This work describes the implementation of a new program, EAMLD, that allows the calculation of static and vibrational contributions to the free energy of metals and alloys using lattice dynamics (LD) within the quasi-harmonic (QH) approximation. Many-body interactions are taken into account by using potentials of the Embedded Atom Method (EAM) form. The free energy is calculated as a function of both the macroscopic and internal degrees of freedom, allowing the study of complex crystals and crystal surfaces and imperfections. Examples include the temperature dependence of the elastic coefficients of Au, the surface energies of Cu and the thermal expansion of Cu3Au.

Evaluation of thermodynamic properties of solids by quasiharmonic lattice dynamics

Quasiharmonic lattice dynamics is a simulation technique complementary to Monte Carlo and molecular dynamics. Quantum effects are readily taken into account, and high precision does not normally require long runs. Vibrational stability is a sensitive test of interatomic potentials, and details of the vibrational motion reveal mechanisms for phase transitions or for thermal expansion. The major computational task is usually to find the equilibrium geometry at a given T, P; this done, calculating free energy, heat capacity, thermal expansion, etc., is rapid and accurate. For three-dimensional ionic crystals and slabs, our code SHELL calculates analytically first derivatives of the free energy with respect to all strains, internal as well as external; this gives a full minimization of the free energy so efficient that large unit cells can be used, allowing applications to defects and disordered systems. Various applications are discussed: MgF2, including the rutile/fluorite transition; negative thermal expansion in ZrW2O8; anisotropic expansion of polyethylene at very low temperatures; surface free energies for MgO; defect energies and volumes in MgO; and a new method for obtaining free energies and phase diagrams of disordered solids and solid solutions, applied to MnO/MgO and CaO/MgO.