Simon P.A. Gill

A variational approach to two dimensional grain growth—I. Theory

A variational approach to modelling two-dimensional grain-growth is presented. This variational principle provides the basis for a numerical scheme which uses a cubic polynomial shape function to represent the shape of a grain-boundary. This allows the equilibrium requirement which restricts the orientation of the boundaries at a triple point to be satisfied. Large scale simulations of the evolution of representations of grain structures are presented in an accompanying paper.

A variational approach to two dimensional grain growth - II. Numerical results

Abstract Normal and abnormal grain growth evolution of a two-dimensional network of 1024 grains is investigated using a computer simulation based on the variational principle derived in Part I of this paper. A brief overview of normal grain growth theories is presented and the correlations between these theories and the numerical study discussed. Power law kinetics and a scaling state are found with a grain-growth exponent of β = 0.52 and a second moment of μ 2 = 1.4 respectively. These results are concurrent with expected grain growth behaviour [1] and demonstrate the validity of the variational model.

Modelling microstructure evolution in engineering materials

Abstract In this paper we describe a general thermodynamically consistent variational principle for the rate of evolution of microstructure, which considers the competition between energy dissipation and the rate of change of Gibbs free energy of the system. We describe how numerical and approximate analytical procedures can be developed from the variational principle. Two examples are presented which demonstrate the utility of the approach: the kinetics of precipitate growth in an elastically strained body and the influence of an elastic strain on interdiffusion in a two-component system. Within these examples we pay particular attention to the effect of changes of elastic stored energy on the evolution process. The sensitivity of the morphology of growing phases to the ratio of the driving forces arising from elastic and chemical considerations is explored.

Modelling transient heat conduction in solids at multiple length and time scales: A coupled non-equilibrium molecular dynamics/continuum approach

A method for controlling the thermal boundary conditions of non-equilibrium molecular dynamics simulations is presented. The method is simple to implement into a conventional molecular dynamics code and independent of the atomistic model employed. It works by regulating the temperature in a thermostatted boundary region by feedback control to achieve the desired temperature at the edge of an inner region where the true atomistic dynamics are retained. This is necessary to avoid intrinsic boundary effects in non-equilibrium molecular dynamics simulations. Three thermostats are investigated: the global deterministic Nose-Hoover thermostat and two local stochastic thermostats, Langevin and stadium damping. The latter thermostat is introduced to avoid the adverse reflection of phonons that occurs at an abrupt interface. The method is then extended to allow atomistic/continuum models to be thermally coupled concurrently for the analysis of large steady state and transient heat conduction problems. The effectiveness of the algorithm is demonstrated for the example of heat flow down a three-dimensional atomistic rod of uniform cross-section subjected to a variety of boundary conditions.

Self-organised growth on strained substrates: the influence of anisotropic strain, surface energy and surface diffusivity

The morphological stability of coherent thin films subjected to unequal in-plane biaxial strains is investigated to determine how non-uniform strain states can be used to influence the growth of self-organised island nanostructures. The evolution via surface diffusion is modelled analytically using a small perturbation approach and allows for anisotropies in the surface energy and the surface diffusivity. It is shown that conventional uniform biaxial epitaxy does not provide a driving force towards a particular wavelength as is popularly assumed. This reduces the potential for highly self-organised growth. It is predicted that improvements in island size, shape and spatial distributions can be obtained under certain conditions of anisotropic strain, surface energy and surface diffusivity. This increase in uniformity would be beneficial to the construction of practical devices. Enhancing surface diffusivity anisotropy via the application of an applied strain could offer the most realistic opportunity for controlling the growth of self-assembled structures this way.

Nonequilibrium Molecular Dynamics and Multiscale Modeling of Heat Conduction in Solids

Modeling methodologies for conducting concurrent multiscale simulations in solids at finite temperature are reviewed. The application of such models to the simulation of inhomogeneous thermal problems is of particular interest. Firstly, the basic methods for temperature control of molecular dynamics (MD) simulations are presented. The derivation of fundamental thermophysical properties from the quantum model of phonons is then outlined, and the relevance of classical MD simulation to heat transport phenomena discussed. Progress in fully atomistic modeling of heat transport is reviewed in relation to nonequilibrium molecular dynamics (NEMD) simulation. Different approaches to isothermal finite temperature multiscale modeling are presented. Equations of motion for coarse-grained dynamics are derived and subject to comment. The further requirements of conservation of thermal energy and the approaches to the transport of heat in non-isothermal multiscale simulations are discussed. Recent progress in this relatively new area of modeling is reported and areas for further work identified

An investigation of mean-field theories for normal grain growth

Abstract A method for the formulation of a growth equation for grains undergoing normal curvature-driven grain growth is presented. Comparison with results from a previous numerical simulation by the present authors leads to the proposal of a modified form of Hillerts growth equation. The method is also used to obtain further insights into the kinetics of grain-boundary motion during grain growth which has repercussions for the estimation of the Rhines-Craig constants.

Microstructure and mechanical properties of AZ91 magnesium alloy subject to deep cryogenic treatments

AZ91 magnesium alloy was subjected to a deep cryogenic treatment. X-ray diffraction (XRD), scanning electronic microscopy (SEM), and transmission electronic microscopy (TEM) methods were utilized to characterize the composition and microstructure of the treated samples. The results show that after two cryogenic treatments, the quantity of the precipitate hardening β phase increases, and the sizes of the precipitates are refined from 8–10 μm to 2–4 μm. This is expected to be due to the decreased solubility of aluminum in the matrix at low temperature and the significant plastic deformation owing to internal differences in thermal contraction between phases and grains. The polycrystalline matrix is also noticeably refined, with the sizes of the subsequent nanocrystalline grains in the range of 50–100 nm. High density dislocations are observed to pile up at the grain boundaries, inducing the dynamic recrystallization of the microstructure, leading to the generation of a nanocrystalline grain structure. After two deep cryogenic treatments, the tensile strength and elongation are found to be substantially increased, rising from 243 MPa and 4.4% of as-cast state to 299 MPa and 5.1%.

Composition profiling at the atomic scale in III-V nanostructures by cross-sectional STM

Using cross-sectional STM we have studied the local composition in III/V nanostructures such as GaAs/InGaAs quantum wells, InGaNAs/InP quantum wells and quantum dots, and InAs/GaAs self-assembled quantum dots. We are able to determine the local composition by either simply counting the constituent atoms, measuring the local lattice constant or measuring the relaxation of the cleaved surface due to the elastic field of the buried strained nanostructures.

Confined Capillary Stresses During the Initial Growth of Thin Films on Amorphous Substrates

Changes in substrate curvature indicating the existence of compressive stress in isolated crystallites are commonly observed during the initial stages of thin film deposition of metals on glass or ceramic substrates. Following the suggestion of Abermann et al. (R. Abermann et al., 1978, Thin Solid Films, 52, p. 215), we attribute the origin of this compressive stress to the action of capillary forces during film growth. As new atomic layers are deposited, the capillary forces acting on atoms near the surface are stored as transformation strains in the bulk of the crystallites. To test this concept, we propose three models for evaluating the capillary strains and their induced compressive stresses in a crystalline. A finite element analysis is performed to show that the model predictions agree well with experimental data. ©2002 ASME