Wc Mackrodt

Calculated bulk and surface properties of sulfates

Atomistic simulation techniques are used to model a range of sulfates. Two widely different sets of potentials have been developed. The first is based on shell model, electron-gas potentials; the second is a rigid ion model which treats inter- and intra-molecular forces differently. The success of the potential models has been demonstrated by comparing calculated and experimental lattice parameters and elastic constants. The structures and energetics of surfaces of barite (BaSO4) are examined in detail, allowing for the effects of surface relaxation. The two lowest-energy surfaces are {001} and {210} which dominate the calculated equilibrium morphology.

An ab initio Hartree-Fock study of the electron-excess gap states in oxygen-deficient rutile TiO2

Ab initio spin-unrestricted periodic Hartree-Fock calculations have been used to study the electron-excess gap states in rutile TiO2 which result from the formation of oxygen vacancies in the bulk and at the surface of an isolated slab of infinite {110} planes. These states are found to be insulating and occur at ∼ 1–2 eV above the O 2p band edge. It is shown that while the O 2p band undergoes small changes in both width and shape as a result of these defects, it remains essentially spin-paired. On the other hand, gap states associated with these defects are largely spin-polarised states corresponding to excess electron density trapped at bulk vacancies and local Ti 3d1 and Ti 3d2 configurations in both the bulk and at the surface. In the bulk the lowest energy state is one in which the majority of the excess charge is localised at the vacant oxygen site, whereas at the surface the redistribution is essentially at the surface Ti atoms. For the oxygen-deficient {110} surface with an entire plane of missing oxygen atoms, an antiferromagnetic spin arrangement is found consisting of localised spins on the surface titanium atoms.

Ab initio Hartree-Fock calculations of CaO, VO, MnO and NiO

Abstract Ab initio Hartree-Fock calculations are reported of the electronic structures of CaO, VO, MnO and NiO. They are found to be essentially ionic in nature with ground states that are insulating, and, in the case of VO, MnO and NiO, high-spin antiferromagnetic. Calculated lattice parameters, binding energies and bulk moduli compare in accuracy with those for closed-shell oxides such as Li2O, MgO and Al2O3. Differences are found in the upper part of the valence band between VO and MnO and NiO. In VO it is predominantly V(3d) in character, whereas in both MnO and NiO it is O(2p). In the case of NiO this seems to be in accord with oxygen K-edge data for LixNi1−xO.

Direct evidence of O(p) holes in Li-doped NiO from Hartree-Fock calculations

Abstract First-principles periodic Hartree-Fock calculations of the ground state electron distribution and empty oxygen p states in Li 0.125 Ni 0.875 O and Li 0.25 Ni 0.75 O are reported which provide direct evidence of oxygen p holes in Li-doped NiO. Calculated changes in the densities of empty oxygen p states are in good agreement with oxygen K -edge spectra. The empty states of the Li-doped materials provide a theoretical value of the band gap in NiO which, unlike previous estimates, is reasonably close to the observed value of 3.7 eV.

Lattice parameter changes in the mixed-oxide system Ce1–xLaxO2–x/2: a combined experimental and theoretical study

X-Ray diffraction measurements are reported of ceramic samples of the mixed-oxide system Ce1–xLaxO2–x/2 for 0<x<0.9, where x has been determined by EDXA. The solid-state reaction forms a highly crystalline product at an ageing temperature of 1200 °C. The solubility limit of La in the bulk CeO2 at this temperature has been determined as ca. 52% by monitoring the lattice parameter increase and the subsequent appearance of a second La2O3 phase. To model the experimental measurements, atomistic lattice calculations based on electron-gas shell-model potentials have been carried out to estimate the variation of the lattice parameter with La content.

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.

Surface segregation of Ba in MgO

Abstract Surface segregation of Ba in doped polycrystalline and single crystal MgO has been studied by XPS. There is little variation in surface coverage of Ba over a range of bulk doping levels from 7 to 7000 ppm in ceramic pellets equilibrated at 1630 K. This remarkable behaviour is shown to be consistent with surface coverage calculated from heats of segregation derived from ionic model simulations of the surface if due account is taken of the strong variation of the segregation energy with coverage. The coverage of Ba on a MgO(001) single crystal surface doped by indiffusion of Ba deposited onto the crystal from a getter source can be made similar to that of the polycrystalline material. The Ba-segregated MgO(001) surface exhibits a complex LEED pattern.

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...

Ionic solids at high pressures and elevated temperatures: MgO (periclase)

An equation of state for MgO is calculated for conditions of high pressure and temperature using atomistic simulations within the quasiharmonic approximation with two‐body potentials and a simple shell model. It is shown that experimental Hugoniot data can be reproduced accurately; other important properties are also examined including various quantities of geophysical interest. Results for the Helmholtz free energy and internal energy surfaces A(V,T) and U(V,T) are presented in parametrized form.