Showing papers by "Adrian P. Sutton published in 2008"

Interatomic potentials for strontium titanate: An assessment of their transferability and comparison with density functional theory

Abstract: The technological importance of polycrystalline strontium titanate $({\text{SrTiO}}_{3})$ is directly linked to its interfacial and grain boundary properties, which are at present poorly understood. A complete understanding (including links with experiment) requires information from many length scales, including electronic and atomistic, up to microstructural and macroscopic. In addition, the size and complexity of many general grain boundaries makes first-principles simulations prohibitively expensive. We have tested the ability of a number of interatomic potentials from the literature to accurately describe at least the structures of some simple grain boundaries in ${\text{SrTiO}}_{3}$. The potentials we have tested are of three types: rigid ion model with either fixed formal or partial charges and shell model. We have also performed a detailed density functional theory (DFT) study of the same boundaries and used this data (interface structures and energies) to validate the interatomic potentials. Our conclusion is that none of the potentials can reproduce the energy ordering of the boundaries predicted by the DFT calculations. The boundary structures produced by some of the potentials do however agree reasonably well with the DFT structures. We discuss the implications of our findings for ionic oxide grain boundary research and critically examine the rigid ion and shell model approximations.

Phase-field model of interfaces in single-component systems derived from classical density functional theory

Abstract: Phase-field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived from first principles. In single-component systems, the free energy is a functional of a ``phase field,'' which is an order parameter often referred to as the crystallinity in the context of grain boundaries, but with no precise definition as to what that term means physically. We present a derivation of the phase-field model by Allen and Cahn from classical density functional theory first for crystal-liquid interfaces and then for grain boundaries. The derivation provides a clear physical interpretation of the phase field, and it sheds light on the parameters and the underlying approximations and limitations of the theory. We suggest how phase-field models may be improved.

Phase field modelling of interfaces from first principles

Abstract: Phase field modelling is a technique in (computational) material science that utilises diffuse interface constructions to simulate the dynamics of microstructural evolution. To date, phase field modelling of crystalline interfaces has been guided mainly by phenomenology and symmetry considerations, rather than microscopic physics. The central equation of motion minimises a free energy with respect to the phase field, which is considered as a space and time dependent, coarse-grained, continuous degree of freedom of the system. However, it is neither clear how to interpret the phase field microscopically, nor how to derive the equation of motion from atomic interactions. Based on the (classical) density functional theory by Haymet and Oxtoby, we derive the phase field model by Allen and Cahn, which is commonly used for modelling crystalline interfaces. In the present article, we summarise the physical implications of the various observables and parameters as well as the underlying approximations.