Anthony Paxton

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.

Bismuth embrittlement of copper is an atomic size effect

Embrittlement by the segregation of impurity elements to grain boundaries is one of a small number of phenomena that can lead to metallurgical failure by fast fracture. Here we settle a question that has been debated for over a hundred years: how can minute traces of bismuth in copper cause this ductile metal to fail in a brittle manner? Three hypotheses for Bi embrittlement of Cu exist: two assign an electronic effect to either a strengthening or weakening of bonds, the third postulates a simple atomic size effect. Here we report first principles quantum mechanical calculations that allow us to reject the electronic hypotheses, while supporting a size effect. We show that upon segregation to the grain boundary, the large Bi atoms weaken the interatomic bonding by pushing apart the Cu atoms at the interface. The resolution of the mechanism underlying grain boundary weakening should be relevant for all cases of embrittlement by oversize impurities.

A quantum-mechanical calculation of the theoretical strength of metals

Abstract We use the local density approximation to density functional theory to re-examine the well-known ‘theoretical strength’ of metals. This is done by calculating ideal twin stress in five b.c.c. transition metals, and in Ir, Cu and Al. This leads us to a first-principles, quantum-mechanical confirmation of the Frenkel model in the theory of plasticity which has previously been thought to have been too oversimplified to be realistic. We discuss this result in the light of the Peierls—Nabarro model and relate it to the deformation behaviour of group-5 and group-6 transition metals. We also include a general analysis of the geometry of the problem that can be readily extended into a number of new areas in the theory of phase transformations.

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.

First-principles determination of the Ni-Al phase diagram

Phase stability in the Ni-Al binary system is investigated using linear muffin-tin orbitals total energy (LMTO) calculations. They provide total energies for the different existing compounds and, using Connolly-Williams inversion, the many-body interactions occurring in the FCC and BCC lattices. These interactions are used in conjunction with the cluster variation method (CVM) to calculate the phase diagram. The computed phase diagram agrees very well with the experimental one.

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.

A bandstructure view of the Hume-Rothery electron phases

The stability of Hume–Rotherys electron phases is studied using modern bandstructure techniques. For these alloys, empirical evidence has shown a strong correlation between the number of valence electrons per atom and the adopted crystal structure. The generally accepted explanation traces the phenomenon to prominent structure in the electron density of states which arises when the free–electron Fermi sphere encounters the Bragg planes at the surface of the Brillouin zone. By applying a rigid band model on the basis of density functional theory to the archetypal system Cu–Zn, we obtain accurate density–of–states functions which are used to critically evaluate the popular models due to Mott and Jones. We also are able to account for the stability of the γ–phase.

WHAT CAN BE LEARNED ABOUT HIGH-TC FROM LOCAL DENSITY THEORY

Abstract The significance of local density band structure results for high T c compounds is critically discussed. It is pointed out that straightforward application of this method can be misleading because of the correlated nature of these materials. However, with LDA numbers can be derived for the parameters appearing in the models in which correlation is treated explicitely. In this way we arrive at the conclusion that despite a large U the high T c materials should be viewed as itinerant materials. Turning to ground state properties, we show that the LDA fails to describe the antiferromagnetism of La 2 CuO 4 and it is pointed out that this may be cured by the inclusion of self interaction corrections. Finally, using a proposed oxygen defect structure for YBa 2 Cu 3 O 7−x and a simple tight binding model based on band structure calculations, we show that jumps and plateaux in the hole counts in the planes and chains occur as a function of x. These features are perfectly correlated with the occurence of the antiferromagnetic, as well as of the 60K and 90K superconducting phases.

Defects in ZnTe, CdTe, and HgTe: Total energy calculations

Total energies for various impurities and defects in HgTe, CdTe, and ZnTe are calculated. Calculations were done using a self‐consistent linear muffin‐tin orbital (LMTO) method within the local density and atomic spheres approximation. We calculate the total energy for substitution on both lattice and interstitial sites, and estimate the lattice strain energies. Estimates of the variation with the alloy predict a linear variation of the substitution energy with the local concentration. We predict that the Te antisite will be more prevalent in all three of the compounds than previously thought. The problem of cross doping during heteroepitaxy on GaAs is predicted to be greater on the cation sublattice.

A tight-binding study of grain boundaries in silicon

Abstract A simple empirical tight-binding model for silicon is propounded and used to compute the atomic and electronic structures of three symmetrical tilt grain boundaries and the intrinsic stacking fault. The ability of the model to describe silicon in a variety of crystal structures is tested and it is shown to be satisfactory for simulating defects in the diamond structure. The effect of charge transfer on the energy and stability of the grain boundaries is assessed. Interatomic forces and energies are computed in real space using a rotationally invariant formulation of the recursion method. Five proposed reconstructions of the (112) symmetrical tilt boundary are studied in detail and good agreement is achieved with results from electron microscopy and diffraction. The (130) and (111) symmetrical tilt boundaries have also been modelled successfully. Comparison is made between the computed electronic structures of the boundaries, reported in this work and by other authors, and experimental measurements of the densities of states at grain boundaries. The existence of band tails and midgap continua in the experimental measurements and the absence of both of these features in the models are two notable points of disagreement. Some fundamental questions about localisation of electronic states at grain boundaries are raised.