M. C. Warren

Structure and elasticity of MgO at high pressure

Abstract The structural and elastic properties of MgO periclase were studied up to 150 GPa with the first-principles pseudopotential method within the local density approximation. The calculated lattice constant of the B1 phase over the pressure range studied is within 1% of experimental values. The observed B1 phase of MgO was found to be stable up to 450 GPa, precluding the B1-B2 phase transition within the lower mantle. The calculated transition pressure is less than one-half of the previous pseudopotential prediction but is very close to the linearized augmented plane-wave result. All three independent elastic constants, c11, c12, and c44, for the B1 phase are calculated from direct computation of stresses generated by small strains. The calculated zero-pressure values of the elastic moduli and wave velocities and their initial pressure dependence are in excellent agreement with experiments. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 15 GPa and then increasing from 15 to 150 GPa. Longitudinal and shear-wave velocities were found to vary by 23 and 59%, respectively, with propagation direction at 150 GPa. The character of the anisotropy changes qualitatively with pressure. At zero pressure longitudinal and shear-wave propagations are fastest along [111] and [100], respectively, whereas above 15 GPa, the corresponding fast directions are [100] and [110]. The Cauchy condition was found to be strongly violated in MgO, reflecting the importance of noncentral many-body forces.

Elasticity of hexagonal BeO

We study the elastic properties, electronic structure, and equation of state of BeO using a first-principles pseudopotential method within the gradient-corrected approximation of the density functional theory. Comparison of the calculated and experimental properties of BeO shows good agreement for all the properties studied here: ground-state structure, linear and bulk compressibilities, and elastic moduli. Calculations are also performed with the local density approximation and the differences in elastic properties are interpreted in terms of a uniform compression. Analysis of the pressure effect on the lattice parameters and on the atomic coordinates shows that the structure changes are close to isotropic from zero to 100 GPa.

Elastic properties of TiB2 and MgB2

We study the elastic properties, electronic structure and equation of state of titanium diboride and magnesium diboride using a first-principles pseudopotential method. We show that the results of the calculations carried out using the gradient-corrected approximation of the density-functional theory are in excellent agreement with the most recent experimental data. These results confirm that early reports of anomalously high elastic anisotropy of TiB2 were based on erroneous experimental data for the off-diagonal components of the elastic coefficients tensor. Present results for TiB2 are more accurate than previously reported Hartree-Fock calculations. Predicted elastic properties of the recently discovered superconductor, MgB2, are presented and compared to contradictory experimental estimates of bulk and linear compressibilities.

Practical methods in ab initio lattice dynamics

A popular method of extracting phonon frequencies from ab initio calculations is to find the equilibrium structure of a material and then build up the matrix of force constants by calculating forces acting due to small displacements of the atoms. If the range of the force constants is assumed to be short, as it typically is in parametrized force-model calculations, the entire dispersion relation can be evaluated from data taken from small ab initio calculations. In this paper we highlight the practical difficulties introduced by low-symmetry structures with free internal parameters and present practical solutions to them. By way of example, we present a number of calculations where solution of these problems is essential. These include ab initio calculation of phonon dispersion in a non-centrosymmetric structure (silver gallium diselenide) and good agreement between calculations and neutron scattering data for a structure with free internal parameters (germanium sulphide).

Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions

Abstract The structural and thermodynamic properties of minerals are strongly affected by cation site-ordering processes. We describe methods to determine the main interatomic interactions that drive the ordering process, which are based on parameterizing model Hamiltonians using empirical interatomic potentials and/or ab initio quantum mechanics methods. The methods are illustrated by a number of case study examples, including Al/Si ordering in aluminosilicates, Mg/Ca ordering in garnets, simultaneous Al/Si and Mg/Al ordering in pyroxenes, micas and amphiboles, and Mg/Al non-convergent ordering in spinel using only quantum mechanical methods.

Monte Carlo methods for the study of cation ordering in minerals

Abstract This paper reviews recent applications of Monte Carlo methods for the study of cation ordering in minerals. We describe the program Ossia99, designed for the simulation of complex ordering processes and for use on parallel computers. A number of applications for the study of long-range and short-range order are described, including the use of the Monte Carlo methods to compute quantities measured in an NMR experiment. The method of thermodynamic integration for the determination of the free energy is described in some detail, and several applications of the method to determine the thermodynamics of disordered systems are outlined.

Calculation of the elastic constants of the Al2SiO5 polymorphs andalusite, sillimanite and kyanite

Abstract Based on quantum mechanical calculations we predict the elastic constants of kyanite at 0 K. The reliability of the prediction has been evaluated by computing the elastic constants of andalusite and of sillimanite and comparing them to experimentally determined values. The computed bulk moduli of andalusite (145 GPa) and of sillimanite (159 GPa) are constistent with experimental values. Only two of the computed elastic contants c13 of andalusite and c23 of sillimanite differ from the experimental values by more than 11%. As the parameter-free model is transferable, the predictions for the bulk modulus, B = 178 GPa, and the elastic constants of kyanite are believed to be equally reliable. In contrast to the promising results of our quantum mechanical calculations, the agreement with experimental values is poor for elastic properties derived from a transferable empirical core-shell model.

Theoretical investigation of bonding in diaspore

The bulk modulus of diaspore, alpha -AlOOH, has been obtained from density functional theory based calculations. The value obtained, B = 148 GPa, is consistent with that previously obtained from elastic constant measurements, but in strong disagreement with values derived from high pressure x-ray diffraction experiments. A Mulliken bond population analysis of the electronic structure implies that the Al-O bonds are significantly covalent, in contrast to findings based on an earlier x-ray diffraction study. On compression, the main change is the increase in the hydrogen-bond strength.

Rigid unit modes and the negative thermal expansion in ZrW2O8

Abstract ZrW2O8 has a negative coefficient of thermal expansion from 0.3 K to its decomposition temperature around 1050 K. The negative thermal expansion is isotropic and is not disrupted by the structural phase transition at 430 K. A complicated distribution in reciprocal space of Rigid Unit Mode (RUM) phonons has been found for ZrW2O8 using Lattice Dynamics. The RUMS are very low energy phonons which cause collective rotations of ZrO6 octahedra and WO4 tetrahedra within the crystal structure. These distortions enable ZrW2O8 to contract upon heating.

Bulk and key surface structures of hematite, magnetite, and goethite: A density functional theory study

Abstract The iron oxides hematite, magnetite, and goethite were studied with density functional theory to establish a consistent set of structures for both the bulk mineral and key surfaces, characterize surface relaxation, and predict and test calculated scanning tunneling microscopy (STM) images. Spinpolarized, plane-wave pseudopotential calculations were carried out on recognized terminations of the hematite (0001) and goethite (010) surfaces and on two terminations of magnetite (111), derived from bulk structures optimized with the same simulation parameters. In the bulk, geometry optimizations having different spin configurations were compared, to find that even without an on-site Coulomb correction, the expected spin states were found to have lowest energy: antiferromagnetic in hematite and goethite and ferrimagnetic in magnetite. However, magnetite shows a conducting minority spin. All four surfaces showed structural relaxation consistent with previous work. The ½-monolayer termination (octahedral and tetrahedral Fe) of magnetite (111) underwent slightly more relaxation than the ¼-monolayer termination, with consequently lower surface energy. A calculated STM image for ¼-monolayer magnetite is compared to an observed image at positive bias and suggests that the tetrahedral Fe dominates the image. STM images are predicted for hematite and goethite to aid interpretation of future experimental work.