4 research outputs found
Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
Here we review the basic concepts and applications of the phase-field-crystal (PFC) method,
which is one of the latest simulation methodologies in materials science for problems, where
atomic- and microscales are tightly coupled. The PFC method operates on atomic length and
diffusive time scales, and thus constitutes a computationally efficient alternative to molecular
simulation methods. Its intense development in materials science started fairly recently following
the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial
studies, dynamical density functional theory and thermodynamic concepts have been linked to
the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we
summarize these methodological development steps as well as the most important applications
of the PFC method with a special focus on the interaction of development steps taken in hard
and soft matter physics, respectively. Doing so, we hope to present today’s state of the art in
PFC modelling as well as the potential, which might still arise from this method in physics and
materials science in the nearby future
Nonlinear hydrodynamic theory of crystallization
We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in
molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a
phenomenology which allows a direct coupling between the free energy functional of the
classical density functional theory and the Navier–Stokes equation. In contrast to the
Ginzburg–Landau type amplitude theories, the dynamic response to elastic deformations is
described by parameter-free kinetic equations. Employing our approach to the free energy
functional of the phase-field crystal model, we recover the classical spectrum for the phonons
and the steady-state growth fronts. The capillary wave spectrum of the equilibrium
crystal–liquid interface is in good qualitative agreement with the molecular dynamics
simulations
Recent developments in modeling heteroepitaxy/heterogeneous nucleation by dynamical density functional theory
Crystallization of supersaturated liquids usually starts by epitaxial growth or by heterogeneous
nucleation on foreign surfaces. Herein, we review recent advances made in modeling
heteroepitaxy and heterogeneous nucleation on flat/modulated surfaces and nanoparticles
within the framework of a simple dynamical density functional theory, known as the phase-field
crystal model. It will be shown that the contact angle and the nucleation barrier are nonmonotonous
functions of the lattice mismatch between the substrate and the crystalline phase.
In continuous cooling studies for substrates with lattice mismatch, we recover qualitatively the
Matthews–Blakeslee mechanism of stress release via the misfit dislocations. The simulations
performed for particle-induced freezing will be confronted with recent analytical results,
exploring thus the validity range of the latter. It will be demonstrated that time-dependent
studies are essential, as investigations based on equilibrium properties often cannot identify the
preferred nucleation pathways. Modeling of these phenomena is essential for designing materials
on the basis of controlled nucleation and/or nano-patterning
Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model
Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows
that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous
precursor forms, and the crystalline phase appears via heterogeneous nucleation in/on the precursor cluster.
Herein, we review recent results by a simple dynamical density functional theory, the phase-field crystal
model, for (precursor-mediated) homogeneous and heterogeneous nucleation of nanocrystals. It will be
shown that the mismatch between the lattice constants of the nucleating crystal and the substrate plays a
decisive role in determining the contact angle and nucleation barrier, which were found to be non-monotonic
functions of the lattice mismatch. Time dependent studies are essential as investigations based on equilibrium
properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential
for designing materials on the basis of controlled nucleation and/or nano-patterning