7,919 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.
Closing the gap between atomic-scale lattice deformations and continuum elasticity
Crystal lattice deformations can be described microscopically by explicitly
accounting for the position of atoms or macroscopically by continuum
elasticity. In this work, we report on the description of continuous elastic
fields derived from an atomistic representation of crystalline structures that
also include features typical of the microscopic scale. Analytic expressions
for strain components are obtained from the complex amplitudes of the Fourier
modes representing periodic lattice positions, which can be generally provided
by atomistic modeling or experiments. The magnitude and phase of these
amplitudes, together with the continuous description of strains, are able to
characterize crystal rotations, lattice deformations, and dislocations.
Moreover, combined with the so-called amplitude expansion of the phase-field
crystal model, they provide a suitable tool for bridging microscopic to
macroscopic scales. This study enables the in-depth analysis of elasticity
effects for macro- and mesoscale systems taking microscopic details into
account.Comment: 9 pages, 7 figures, Supporting Information availabl
Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
One of the major difficulties in employing phase field crystal (PFC) modeling
and the associated amplitude (APFC) formulation is the ability to tune model
parameters to match experimental quantities. In this work we address the
problem of tuning the defect core and interface energies in the APFC
formulation. We show that the addition of a single term to the free energy
functional can be used to increase the solid-liquid interface and defect
energies in a well-controlled fashion, without any major change to other
features. The influence of the newly added term is explored in two-dimensional
triangular and honeycomb structures as well as bcc and fcc lattices in three
dimensions. In addition, a finite element method (FEM) is developed for the
model that incorporates a mesh refinement scheme. The combination of the FEM
and mesh refinement to simulate amplitude expansion with a new energy term
provides a method of controlling microscopic features such as defect and
interface energies while simultaneously delivering a coarse-grained examination
of the system.Comment: 14 pages, 9 figure
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
Elder, Nathan (6)
HQ Co. 92nd Infantry Divisionhttps://dh.howard.edu/prom_corres/1035/thumbnail.jp
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