6,009 research outputs found
Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
Morphological properties of strained epitaxial films are examined through a
mesoscopic approach developed to incorporate both the film crystalline
structure and standard continuum theory. Film surface profiles and properties,
such as surface energy, liquid-solid miscibility gap and interface thickness,
are determined as a function of misfit strains and film elastic modulus. We
analyze the stress-driven instability of film surface morphology that leads to
the formation of strained islands. We find a universal scaling relationship
between the island size and misfit strain which shows a crossover from the
well-known continuum elasticity result at the weak strain to a behavior
governed by a "perfect" lattice relaxation condition. The strain at which the
crossover occurs is shown to be a function of liquid-solid interfacial
thickness, and an asymmetry between tensile and compressive strains is
observed. The film instability is found to be accompanied by mode coupling of
the complex amplitudes of the surface morphological profile, a factor
associated with the crystalline nature of the strained film but absent in
conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.
Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
The dynamics of phase field crystal (PFC) modeling is derived from dynamical
density functional theory (DDFT), for both single-component and binary systems.
The derivation is based on a truncation up to the three-point direct
correlation functions in DDFT, and the lowest order approximation using scale
analysis. The complete amplitude equation formalism for binary PFC is developed
to describe the coupled dynamics of slowly varying complex amplitudes of
structural profile, zeroth-mode average atomic density, and system
concentration field. Effects of noise (corresponding to stochastic amplitude
equations) and species-dependent atomic mobilities are also incorporated in
this formalism. Results of a sample application to the study of surface
segregation and interface intermixing in alloy heterostructures and strained
layer growth are presented, showing the effects of different atomic sizes and
mobilities of alloy components. A phenomenon of composition overshooting at the
interface is found, which can be connected to the surface segregation and
enrichment of one of the atomic components observed in recent experiments of
alloying heterostructures.Comment: 26 pages, 5 figures; submitted to Phys. Rev.
Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
The fundamental dislocation processes of glide, climb, and annihilation are
studied on diffusive time scales within the framework of a continuum field
theory, the Phase Field Crystals (PFC) model. Glide and climb are examined for
single edge dislocations subjected to shear and compressive strain,
respectively, in a two dimensional hexagonal lattice. It is shown that the
natural features of these processes are reproduced without any explicit
consideration of elasticity theory or ad hoc construction of microscopic
Peierls potentials. Particular attention is paid to the Peierls barrier for
dislocation glide/climb and the ensuing dynamic behavior as functions of strain
rate, temperature, and dislocation density. It is shown that the dynamics are
accurately described by simple viscous motion equations for an overdamped point
mass, where the dislocation mobility is the only adjustable parameter. The
critical distance for the annihilation of two edge dislocations as a function
of separation angle is also presented.Comment: 13 pages with 17 figures, submitted to Physical Review
Comment on: `Pipe Network Model for Scaling of Dynamic Interfaces in Porous Media'
We argue that a proposed exponent identity [Phys. Rev. Lett 85, 1238 (2000)]
for interface roughening in spontaneous imbibition is wrong. It rests on the
assumption that the fluctuations are controlled by a single time scale, but
liquid conservation imposes two distinct time scales.Comment: 1 page, to appear in Phys. Rev. Let
Noise and dynamical pattern selection
In pattern forming systems such as Rayleigh-Benard convection or directional
solidification, a large number of linearly stable, patterned steady states
exist when the basic, simple steady state is unstable. Which of these steady
states will be realized in a given experiment appears to depend on unobservable
details of the system's initial conditions. We show, however, that weak,
Gaussian white noise drives such a system toward a preferred wave number which
depends only on the system parameters and is independent of initial conditions.
We give a prescription for calculating this wave number, analytically near the
onset of instability and numerically otherwise.Comment: 12 pages, REVTEX, no figures. Submitted to Phys. Rev. Let
Phase-field approach to heterogeneous nucleation
We consider the problem of heterogeneous nucleation and growth. The system is
described by a phase field model in which the temperature is included through
thermal noise. We show that this phase field approach is suitable to describe
homogeneous as well as heterogeneous nucleation starting from several general
hypotheses. Thus we can investigate the influence of grain boundaries,
localized impurities, or any general kind of imperfections in a systematic way.
We also put forward the applicability of our model to study other physical
situations such as island formation, amorphous crystallization, or
recrystallization.Comment: 8 pages including 7 figures. Accepted for publication in Physical
Review
DDFT calibration and investigation of an anisotropic phase-field crystal model
The anisotropic phase-field crystal model recently proposed and used by
Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from
microscopic density functional theory for anisotropic particles with fixed
orientation. Further its morphology diagram is explored. In particular we
investigated the influence of anisotropy and undercooling on the process of
nucleation and microstructure formation from atomic to the microscale. To that
end numerical simulations were performed varying those dimensionless parameters
which represent anisotropy and undercooling in our anisotropic phase-field
crystal (APFC) model. The results from these numerical simulations are
summarized in terms of a morphology diagram of the stable state phase. These
stable phases are also investigated with respect to their kinetics and
characteristic morphological features.Comment: It contain 13 pages and total of 7 figure
Amplitude expansion of the binary phase field crystal model
Amplitude representations of a binary phase field crystal model are developed
for a two dimensional triangular lattice and three dimensional BCC and FCC
crystal structures. The relationship between these amplitude equations and the
standard phase field models for binary alloy solidification with elasticity are
derived, providing an explicit connection between phase field crystal and phase
field models. Sample simulations of solute migration at grain boundaries,
eutectic solidification and quantum dot formation on nano-membranes are also
presented.Comment: 11 pages, 8 figure
Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation
The process of pattern formation in the two dimensional Swift-Hohenberg
equation is examined through numerical and analytic methods. Dynamic scaling
relationships are developed for the collective ordering of convective rolls in
the limit of infinite aspect ratio. The stationary solutions are shown to be
strongly influenced by the strength of noise. Stationary states for small and
large noise strengths appear to be quasi-ordered and disordered respectively.
The dynamics of ordering from an initially inhomogeneous state is very slow in
the former case and fast in the latter. Both numerical and analytic
calculations indicate that the slow dynamics can be characterized by a simple
scaling relationship, with a characteristic dynamic exponent of in the
intermediate time regime
Melting at dislocations and grain boundaries: A Phase Field Crystal study
Dislocation and grain boundary melting are studied in three dimensions using
the Phase Field Crystal method. Isolated dislocations are found to melt
radially outward from their core, as the localized excess elastic energy drives
a power law divergence in the melt radius. Dislocations within low-to-mid angle
grain boundaries melt similarly until an angle-dependent first order wetting
transition occurs when neighboring melted regions coalesce. High angle
boundaries are treated within a screening approximation, and issues related to
ensembles, metastability, and grain size are discussed.Comment: 4 pages, 3 figure
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