A model for ferromagnetism observed at ambient temperature in films of oxides such as ZnO is proposed and evaluated. The ferromagnetic moment in the model arises from electrons trapped at negatively charged vacancies in an n-type oxide. These vacancies are capable of trapping either one or two electrons. Trapped electrons are described by a one-band Hubbard Hamiltonian where the Hubbard U is the effective electron-electron repulsion for a pair of electrons in a vacancy. Ferromagnetism is known to exist in the Hubbard model applied to periodic three-dimensional (3D) lattices, provided the Hubbard U parameter exceeds the defect bandwidth W and the filling is away from half or complete filling. Hybrid and local-density approximation density-functional theory calculations are used to evaluate Hubbard model parameters for electrons trapped in defects in ZnO. They are also used to calculate magnetic exchange couplings of well-separated, singly negatively charged defects, which are induced by a conduction band electron. Strong ferromagnetic coupling between defects is found in these total-energy calculations over a range exceeding 10Å when the defects have a large, positive Hubbard U value. Hubbard U values for oxygen (V O ), zinc (V Zn ), and zinc-oxygen complex (V ZnO ) vacancies in various charge states are estimated from defect transition levels. V

We investigate phase separation including elastic coherency effects in the bulk and at surfaces and find a reduction of the solubility limit in the presence of free surfaces. This mechanism favours phase separation near free surfaces even in the absence of external stresses. We apply the theory to hydride formation in nickel, iron and niobium and obtain a reduction of the solubility limit by up to two orders of magnitude at room temperature in the presence of free surfaces. These effects are concisely expressed through a solubility modification factor, which transparently expresses the long-ranged elastic effects in a terminology accessible e.g. to ab initio calculations.

Transition levels of defects are commonly calculated using either methods based on total energies of defects in relevant charge states or energy band single particle eigenvalues. The former method requires calculation of total energies of charged, perfect bulk supercells, as well as charged defect supercells, to obtain defect formation energies for various charge states. The latter method depends on Janak's theorem to obtain differences in defect formation energies for various charge states. Transition levels of V Zn , V O , and V ZnO vacancy defects in ZnO are calculated using both methods. The mean absolute deviation in transition level calculated using either method is 0.3 eV. Relative computational costs and accuracies of the methods are discussed.

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface, that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structural defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band (CI-NEB) method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, Cinsertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.