121 research outputs found
Phase field theory of polycrystalline solidification in three dimensions
A phase field theory of polycrystalline solidification is presented that is
able to describe the nucleation and growth of anisotropic particles with
different crystallographic orientation in three dimensions. As opposed with the
two-dimensional case, where a single orientation field suffices, in three
dimensions, minimum three fields are needed. The free energy of grain
boundaries is assumed to be proportional to the angular difference between the
adjacent crystals expressed here in terms of the differences of the four
symmetric Euler parameters. The equations of motion for these fields are
obtained from variational principles. Illustrative calculations are performed
for polycrystalline solidification with dendritic, needle and spherulitic
growth morphologies.Comment: 7 pages, 4 figures, submitted to Europhysics Letters on 14th
February, 200
Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Gránásy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Gránásy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystalline solidification obtained using an atomistic phase-field model
Nonequilibrium steady states in fluids of platelike colloidal particles
Nonequilibrium steady states in an open system connecting two reservoirs of
platelike colloidal particles are investigated by means of a recently proposed
phenomenological dynamic density functional theory [M. Bier and R. van Roij,
Phys. Rev. E 76, 021405 (2007)]. The platelike colloidal particles are
approximated within the Zwanzig model of restricted orientations, which
exhibits an isotropic-nematic bulk phase transition. Inhomogeneities of the
local chemical potential generate a diffusion current which relaxes to a
nonvanishing value if the two reservoirs coupled to the system sustain
different chemical potentials. The relaxation process of initial states towards
the steady state turns out to comprise two regimes: a smoothening of initial
steplike structures followed by an ultimate relaxation of the slowest diffusive
mode. The position of a nonequilibrium interface and the particle current of
steady states depend nontrivially on the structure of the reservoirs due to the
coupling between translational and orientational degrees of freedom of the
fluid
Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: I. Transitions in the one-phase liquid region
The published version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsThe phase field theory (PFT) has been applied to predict equilibrium interfacial properties and nucleation barrier in the binary eutectic system Ag-Cu using double well and interpolation functions deduced from a Ginzburg-Landau expansion that considers fcc (face centered cubic) crystal symmetries. The temperature and composition dependent free energies of the liquid and solid phases are taken from CALculation of PHAse Diagrams-type calculations. The model parameters of PFT are fixed so as to recover an interface thickness of approximately 1 nm from molecular dynamics simulations and the interfacial free energies from the experimental dihedral angles available for the pure components. A nontrivial temperature and composition dependence for the equilibrium interfacial free energy is observed. Mapping the possible nucleation pathways, we find that the Ag and Cu rich critical fluctuations compete against each other in the neighborhood of the eutectic composition. The Tolman length is positive and shows a maximum as a function of undercooling. The PFT predictions for the critical undercooling are found to be consistent with experimental results. These results support the view that heterogeneous nucleation took place in the undercooling experiments available at present. We also present calculations using the classical droplet model classical nucleation theory (CNT) and a phenomenological diffuse interface theory (DIT). While the predictions of the CNT with a purely entropic interfacial free energy underestimate the critical undercooling, the DIT results appear to be in a reasonable agreement with the PFT predictions.This work has been supported by the Hungarian Academy of Sciences under Contract No. OTKA-K-62588 and by the ESA PECS Contract Nos. 98005, 98021, and 98043
Nucleation and Bulk Crystallization in Binary Phase Field Theory
We present a phase field theory for binary crystal nucleation. In the
one-component limit, quantitative agreement is achieved with computer
simulations (Lennard-Jones system) and experiments (ice-water system) using
model parameters evaluated from the free energy and thickness of the interface.
The critical undercoolings predicted for Cu-Ni alloys accord with the
measurements, and indicate homogeneous nucleation. The Kolmogorov exponents
deduced for dendritic solidification and for "soft-impingement" of particles
via diffusion fields are consistent with experiment.Comment: 4 pages, 4 figures, accepted to PR
Relaxation dynamics in fluids of platelike colloidal particles
The relaxation dynamics of a model fluid of platelike colloidal particles is
investigated by means of a phenomenological dynamic density functional theory.
The model fluid approximates the particles within the Zwanzig model of
restricted orientations. The driving force for time-dependence is expressed
completely by gradients of the local chemical potential which in turn is
derived from a density functional -- hydrodynamic interactions are not taken
into account. These approximations are expected to lead to qualitatively
reliable results for low densities as those within the isotropic-nematic
two-phase region. The formalism is applied to model an initially spatially
homogeneous stable or metastable isotropic fluid which is perturbed by
switching a two-dimensional array of Gaussian laser beams. Switching on the
laser beams leads to an accumulation of colloidal particles in the beam
centers. If the initial chemical potential and the laser power are large enough
a preferred orientation of particles occurs breaking the symmetry of the laser
potential. After switching off the laser beams again the system can follow
different relaxation paths: It either relaxes back to the homogeneous isotropic
state or it forms an approximately elliptical high-density core which is
elongated perpendicular to the dominating orientation in order to minimize the
surface free energy. For large supersaturations of the initial isotropic fluid
the high-density cores of neighboring laser beams of the two-dimensional array
merge into complex superstructures.Comment: low-resolution figures due to file size restrictions, revised versio
On the growth and form of spherulites
Many structural materials (metal alloys, polymers, minerals, etc.) are formed
by quenching liquids into crystalline solids. This highly non-equilibrium
process often leads to polycrystalline growth patterns that are broadly termed
"spherulites" because of their large-scale average spherical shape. Despite the
prevalence and practical importance of spherulite formation, only rather
qualitative concepts of this phenomenon exist. The present work explains the
growth and form of these fundamental condensed matter structures on the basis
of a unified field theoretic approach. Our phase field model is the first to
incorporate the essential ingredients for this type crystal growth:
anisotropies in both the surface energy and interface mobilities that are
responsible for needle-like growth, trapping of local orientational order due
to either static heterogeneities (impurities) or dynamic heterogeneities in
highly supercooled liquids, and a preferred relative grain orientation induced
by a misorientation-dependent grain boundary energy. Our calculations indicate
that the diversity of spherulite growth forms arises from a competition between
the ordering effect of discrete local crystallographic symmetries and the
randomization of the local crystallographic orientation that accompanies
crystal grain nucleation at the growth front (growth front nucleation or GFN).
The large-scale isotropy of spherulitic growth arises from the predominance of
GFN.Comment: 14 pages, 11 figure
Infrared and differential-scanning-calorimetry study of the room-temperature cubic phase of RbC60
We present differential-scanning-calorimetry curves and infrared spectra taken during the temperature cycling of stoichiometrically pure RbC60 powder. In addition to the three known phases (high-temperature fcc, ortho-I, and ortho-II), we see evidence for an intermediate structure around 300 K, observed previously by ESR and x-ray diffraction. This phase is obtained both by quenching from high temperature and by warming up the ortho-II structure. Its infrared spectrum is identical to that of the high-temperature fcc phase, indicating a structure containing C-60(-) monomers
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
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 fundaments 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.Comment: 95 pages, 48 figure
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