Michael W. Finnis

A stabilization mechanism of zirconia based on oxygen vacancies only

Abstract The microscopic mechanism leading to stabilization of cubic and tetragonal forms of zirconia (ZrO2) is analyzed by means of a self-consistent tight-binding model. Using this model, energies and structures of zirconia containing different vacancy concentrations are calculated, equivalent in concentration to the charge compensating vacancies associated with dissolved yttria (Y2O3) in the tetragonal and cubic phase fields (3.2 and 14.4% mol, respectively). The model is shown to predict the large relaxations around an oxygen vacancy, and the clustering of vacancies along the 111 directions, in good agreement with experiments and first principles calculations. The vacancies alone are shown to explain the stabilization of cubic zirconia, and the mechanism is analyzed.

Point defects and chemical potentials in ordered alloys

Abstract We discuss the thermodynamics of point defects in an ordered A m B n alloy for small deviations from the stoichiometric composition. The concentrations of the two kinds of antisite and vacancy are function of three basic energies of formation and of the stoichiometry. We derive general formulae for them which can be solved numerically. Analytic formulae for the chemical potentials are derived in terms of the point-defect concentrations. Simple analytic formulae are derived for the concentrations which are valid when the constitutional defects (which dominate at low temperatures) continue to dominate the thermally excited defects of the same type at higher temperatures. The energies entering these formulae are defined in a general way, suitable for ab initio or semiempirical methods of calculation. We illustrate the results with calculations for NiAl using three different central N-body potentials. A significant effect is due to the temperature dependence of the formation energies.

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals. This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.

Theoretical and experimental investigations of structures and energies of Σ = 3, [112] tilt grain boundaries in copper

Abstract Using atomistic computer simulations, symmetric and asymmetric Σ = 3 tilt grain boundaries in Cu were investigated. Equilibrium energies and structures were calculated by static and dynamic energy minimization. A semi-empirical N-body potential served as a model of the interatomic forces in Cu. The atomistic structure of the grain boundary inclined at about 84° to the {111} twin boundary was investigated by high-resolution transmission electron microscopy (HRTEM). Plotted against the inclination angle Φ112 of the boundary plane, the calculated grain boundary energies increase monotonically up to Φ112 ≈ 73°. At larger inclination angles the data indicate an energy minimum at about 80°. The computer simulations predic that boundaries equilibrated at temperatures near T = 0K are planar for inclination angles σ112 < 73°, but consist of a three-dimensional layer of predominantly body-centred-cubic (bcc) Cu for inclination angles greater than 73°. In all three-dimensional boundaries by bcc layer ...

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free-energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behavior above the transition temperature.

Atomistic study of structural correlations at a liquid–solid interface

Abstract Structural correlations at a liquid–solid interface were explored with molecular dynamics simulations of a model aluminium system using the Ercolessi–Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium crystalline positions while liquid atoms were free to move. The density profile at the interface was investigated for different substrate crystallographic orientations and temperatures. An exponential decay of the density profile was observed, ρ ( z )∼e − κz , leading to the definition of κ as a quantitative measure of the ordering at the liquid solid interface. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found.

Atomistic and electronic structure of Al/MgAl2O4 and Ag/MgAl2O4 interfaces

Abstract For the first time, very precise experimental data on the atomistic structure of a metal/oxide interface were obtained by quantitative high-resolution transmission electron microscopy (HRTEM). They are compared with the results of ab initio density-functional theory (DFT) calculations for the same real interface structure, performed without the need for introducing artificial coherency strains. The model system of this study is the coherent (001)-oriented interface between Al and MgAl2O4 in parallel orientation. By means of quantitative HRTEM we determined the relative translation of the two crystals with picometre precision, and also within this error limit our ab initio calculations correctly predict the experimental structure. The electron density distribution obtained by the calculations indicates a directional bonding between the metal and the oxide beyond the concept of the image charge model. Furthermore, we have carried out ab initio DFT calculations for the (001) interface between Ag and MgAl2O4. Since this interface has the same crystallography as Al/MgAl2O4, comparison of the electron density distribution reveals the net effect of the electron configuration in the metal on the nature of the metal oxide adhesion.

Ordering at Solid-Liquid Interfaces Between Dissimilar Materials

In an earlier report we explored structural correlations at a liquid-solid interface with molecular dynamics simulations of a model aluminium system using the Ercolessi-Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium fcc crystalline positions while liquid atoms were free to move. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found. In the present paper we extend this study to the case of a fixed bcc substrate in contact with liquid aluminium. We find surprisingly similar results for the density profiles of both (100) and (110) substrates. However, there is a far greater in-plane ordering in the (100) than for the (110) system. For the (100) substrates we observe adsorption of liquid atoms into the terminating plane of the bcc (100) substrate, effectively transforming the bcc (100) plane into an fcc (100) plane.

Insight into gallium behavior in aluminum grain boundaries from calculation on Σ=11 (113) boundary

Gallium impurities affect the atomic processes and material properties of aluminum metal to a high degree. Various ab initio calculations have been performed on a Sigma = 11 (113) symmetric tilt boundary in aluminum with and without some gallium substitutions. A simple interpretation of the results emerges, which can be applied to grain boundaries in general. The calculations relate to the energetics of gallium substitution on various sites, local relaxation effects, vibrational frequencies and a barrier to grain boundary migration

A Density Functional Study of Interactions at the Metal–Ceramic Interfaces Al/MgAl2O4 and Ag/MgAl2O4

Ab-initio density functional calculations were performed on the geometric and the electronic structures of coherent cube-on-cube interfaces between spinel (MgAl 2 O 4 ) and the two metals Al and Ag. The calculations were carried out in the local density approximation (LDA) employing norm-conserving pseudopotentials and a mixed basis set of plane waves and local orbitals. The cohesive properties of the bulk materials are determined in good agreement with experiment. Four different high-symmetry translation states between the metal atoms and an Al-O or a Mg termination layer of the spinel are investigated at the unrelaxed interface distance. For Al a marked preference for the on-top O position on the Al-O layer is found, whereas for Ag the hollow-site positions are slightly preferred over the on-top O position on the Al-O layer. An optimization of the interface distance yields a distinct energy minimum at 1.90 A for Al/MgAl 2 O 4 on the on-top O site, in very good agreement with experiment. For Ag the total-energy curves of the different adhesion sites intersect and enable a low-energy dissociation path.