Phase field crystal models with applications to laser deposition: A review.

In this article, we address the application of phase field crystal (PFC) theory, a hybrid atomistic-continuum approach, for modeling nanostructure kinetics encountered in laser deposition. We first provide an overview of the PFC methodology, highlighting recent advances to incorporate phononic and heat transport mechanisms. To simulate laser heating, energy is deposited onto a number of polycrystalline, two-dimensional samples through the application of initial stochastic fluctuations.

study of Au nanoparticle formation in a mechanochemical-aging-based method.

As we strive to perform chemical transformations in a more sustainable fashion, enabling solid-state reactions through mechanochemistry has emerged as a highly successful approach. Due to the wide-ranging applications of gold nanoparticles (AuNPs), mechanochemical strategies have already been employed for their synthesis. However, the underlying processes surrounding gold salt reduction, nucleation and growth of AuNPs in the solid state are yet to be understood.

Direct observation by high resolution transmission electron microscopy of gold(III) particle transformation during aging reduction reaction.

We use a gold nanoparticle synthesis as a model system to study the morphological and compositional changes in gold(III) precursor particles, while reduction is taking place during aging after mechanical activation. Scanning transmission electron microscopy coupled with a high-angle annular dark field detector revealed the nanoscale changes in particle morphology, while electron energy loss spectroscopy mapped the changes in the chemical landscape during the reduction process. Tracking a specific region of interest on the sample grid allowed for comparisons to be made of the same particles across a two day monitoring period.

Multiscale analysis of crystalline defect formation in rapid solidification of pure aluminium and aluminium-copper alloys.

Rapid solidification leads to unique microstructural features, where a less studied topic is the formation of various crystalline defects, including high dislocation densities, as well as gradients and splitting of the crystalline orientation. As these defects critically affect the material's mechanical properties and performance features, it is important to understand the defect formation mechanisms, and how they depend on the solidification conditions and alloying. To illuminate the formation mechanisms of the rapid solidification induced crystalline defects, we conduct a multiscale modelling analysis consisting of bond-order potential-based molecular dynamics (MD), phase field crystal-based amplitude expansion simulations, and sequentially coupled phase field-crystal plasticity simulations.

Orientation Gradients in Rapidly Solidified Pure Aluminum Thin Films: Comparison of Experiments and Phase-Field Crystal Simulations.

Rapid solidification experiments on thin film aluminum samples reveal the presence of lattice orientation gradients within crystallizing grains. To study this phenomenon, a single-component phase-field crystal (PFC) model that captures the properties of solid, liquid, and vapor phases is proposed to model pure aluminium quantitatively. A coarse-grained amplitude representation of this model is used to simulate solidification in samples approaching micrometer scales.

Quantitative phase field simulations of polycrystalline solidification using a vector order parameter.

A vector order parameter phase field model derived from a grand potential functional is presented as an alternative approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit.

Controlling solid-liquid interfacial energy anisotropy through the isotropic liquid.

Although the anisotropy of the solid-liquid interfacial free energy for most alloy systems is very small, it plays a crucial role in the growth rate, morphology and crystallographic growth direction of dendrites. Previous work posited a dendrite orientation transition via compositional additions. In this work we examine experimentally the change in dendrite growth behaviour in the Al-Sm (Samarium) system as a function of solute concentration and study its interfacial properties using molecular dynamics simulations.

Classical nucleation theory in the phase-field crystal model.

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations.

A phase-field-crystal alloy model for late-stage solidification studies involving the interaction of solid, liquid and gas phases.

We present a multiphase binary alloy phase-field-crystal model. By introducing density difference between solid and liquid into a previous alloy model, this new fusion leads to a practical tool that can be used to investigate formation of defects in late-stage alloy solidification. It is shown that this model can qualitatively capture the liquid pressure drop due to solidification shrinkage in confined geometry.

Two-component structural phase-field crystal models for graphene symmetries.

We extend the three-point XPFC model of Seymour & Provatas (Seymour & Provatas 2016 , 035447 (doi:10.1103/PhysRevB.93.

Nanoscale interfacial defect shedding in a growing nematic droplet.

Interfacial defect shedding is the most recent known mechanism for defect formation in a thermally driven isotropic-to-nematic phase transition. It manifests in nematic-isotropic interfaces going through an anchoring switch. Numerical computations in planar geometry established that a growing nematic droplet can undergo interfacial defect shedding, nucleating interfacial defect structures that shed into the bulk as +1/2 point defects.

Analysis of thermodiffusive cellular instabilities in continuum combustion fronts.

We explore numerically the morphological patterns of thermodiffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the recent model of Brailovsky et al. to include distinct process kinetics and reactant heterogeneity.

Incorporating Noise Quantitatively in the Phase Field Crystal Model via Capillary Fluctuation Theory.

A tacit assumption underlying most phase field models of nonequilibrium phase transformations is that of scale separation. Stochastic order parameter field theories utilize noise to separate atomic-scale fluctuations from the slowly varying fields that describe microstructure patterns. The mesoscale distribution of such stochastic variables is generally assumed to follow Gaussian statistics, with their magnitude following fluctuation-dissipation relations.

Phase-Field-Crystal Model for Electromigration in Metal Interconnects.

We propose an atomistic model of electromigration (EM) in metals based on a recently developed phase-field-crystal (PFC) technique. By coupling the PFC model's atomic density field with an applied electric field through the EM effective charge parameter, EM is successfully captured on diffusive time scales. Our framework reproduces the well-established EM phenomena known as Black's equation and the Blech effect, and also naturally captures commonly observed phenomena such as void nucleation and migration in bulk crystals.

Microscopic treatment of solute trapping and drag.

The long wavelength limit of a recent microscopic phase-field crystal (PFC) theory of a binary alloy mixture is used to derive an analytical approximation for the segregation coefficient as a function of the interface velocity, and relate it to the two-point correlation function of the liquid and the thermodynamic properties of solid and liquid phases. Our results offer the first analytical derivation of solute segregation from a microscopic model, and support recent molecular dynamics and numerical PFC simulations. Our results also provide an independent framework, motivated from classical density functional theory, from which to elucidate the fundamental nature of solute drag, which is still highly contested in the literature.

Calculating the role of composition in the anisotropy of solid-liquid interface energy using phase-field-crystal theory.

This work uses Ginzburg-Landau theory derived from a recent structural phase-field-crystal model of binary alloys developed by the authors to study the roles of concentration, temperature, and pressure on the interfacial energy anisotropy of a solid-liquid front. It is found that the main contribution to the change in anisotropy with concentration arises from a change in preferred crystallographic orientation controlled by solute-dependent changes in the two-point density correlation function of a binary alloy, a mechanism that leads to such phenomena as solute-induced elastic strain and dislocation-assisted solute clustering. Our results are consistent with experimental observations in recent studies by Rappaz et al.

New density functional approach for solid-liquid-vapor transitions in pure materials.

A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of solid-liquid-vapor phase transitions within the framework of a single density order parameter. Its equilibrium properties show the most quantitative features to date in PFC modeling of pure substances, and full consistency with thermodynamics in pressure-volume-temperature space is demonstrated. A method to control either the volume or the pressure of the system is also introduced.

Self-assembly via branching morphologies in nematic liquid-crystal nanocomposites.

We demonstrate that the morphological diversity in liquid-crystal hybrid systems is much richer than previously anticipated. More importantly, we reveal the existence of a dual mechanism for self-assembly of nanoparticles via morphological instabilities at phase boundaries. Using numerical simulations, we study the growth of isolated nematic droplets in an isotropic liquid crystal (LC) doped with nanoparticles (NPs) and provide insight into the nature of microstructure evolution in LC hybrids.

Phase-field-crystal model for magnetocrystalline interactions in isotropic ferromagnetic solids.

An isotropic magnetoelastic phase-field-crystal model to study the relation between morphological structure and magnetic properties of pure ferromagnetic solids is introduced. Analytic calculations in two dimensions were used to determine the phase diagram and obtain the relationship between elastic strains and magnetization. Time-dependent numerical simulations in two dimensions were used to demonstrate the effect of grain boundaries on the formation of magnetic domains.

Phase-field-crystal study of solute trapping.

In this study we have incorporated two time scales into the phase-field-crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, K as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where K approaches unity in the limit of infinite velocity. However, with the introduction of wavelike dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by Sobolev [Phys.

Phase-field-crystal model of phase and microstructural stability in driven nanocrystalline systems.

We present a phase-field-crystal model for driven systems which describes competing effects between thermally activated diffusional processes and those driven by externally imposed ballistic events. The model demonstrates how the mesoscopic Enrique and Bellon [Phys. Rev.

Phase-field-crystal methodology for modeling of structural transformations.

We introduce and characterize free-energy functionals for modeling of solids with different crystallographic symmetries within the phase-field-crystal methodology. The excess free energy responsible for the emergence of periodic phases is inspired by classical density-functional theory, but uses only a minimal description for the modes of the direct correlation function to preserve computational efficiency. We provide a detailed prescription for controlling the crystal structure and introduce parameters for changing temperature and surface energies, so that phase transformations between body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and simple-cubic (sc) lattices can be studied.

Effective model hierarchies for dynamic and static classical density functional theories.

The origin and methodology of deriving effective model hierarchies are presented with applications to solidification of crystalline solids. In particular, it is discussed how the form of the equations of motion and the effective parameters on larger scales can be obtained from the more microscopic models. It will be shown that tying together the dynamic structure of the projection operator formalism with static classical density functional theories can lead to incomplete (mass) transport properties even though the linearized hydrodynamics on large scales is correctly reproduced.

Phase-field study of spacing evolution during transient growth.

The primary spacing of a dendritic array grown under transient growth conditions displays a distribution of wavelengths. The average primary spacing is shown, both experimentally and numerically, to evolve between characteristic incubation periods during which the distribution of wavelengths remains essentially stable. Our primary spacing results display a gradual transition period from one spacing range to another, consistent with the fact that the abrupt doubling of spacing predicted by Warren and Langer for an idealized periodic array affects different wavelengths of the distribution at different times.

Phase-field-crystal calculation of crystal-melt surface tension in binary alloys.

A phase field crystal (PFC) density functional for binary mixtures is coarse grained and a formalism for calculating the simultaneous concentration, temperature, and density dependence of the surface energy anisotropy of a solid-liquid interface is developed. The methodology systematically relates bulk free energy coefficients arising from coarse graining to thermodynamic data, while gradient energy coefficients are related to molecular properties. Our coarse-grained formalism is applied to the determination of surface energy anisotropy in two-dimensional Zn-Al films, a situation relevant for quantitative phase field simulations of dendritic solidification in zinc coatings.