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K. R. Elder

Publications and source records attributed to K. R. Elder.

35 records · Page 2Linked to original sources
arXiv2008

Thermal fluctuations and phase diagrams of the phase field crystal model with pinning

We study the influence of thermal fluctuations in the phase diagram of a recently introduced two-dimensional phase field crystal model with an external pinning potential. The model provides a continuum description of pinned lattice systems allowing for both elastic deformations and topological defects. We introduce a non-conserved version of the model and determine the ground-state phase diagram as a function of lattice mismatch and strength of the pinning potential. Monte Carlo simulations are used to determine the phase diagram as a function of temperature near commensurate phases. The results show a rich phase diagram with commensurate, incommensurate and liquid-like phases with a topology strongly dependent on the type of ordered structure. A finite-size scaling analysis of the melting transition for the $c(2 \times 2)$ commensurate phase shows that the thermal correlation length exponent $ν$ and specific heat behavior are consistent with the Ising universality class as expected from analytical arguments.

cond-mat.mtrl-sci↗
arXiv2008

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.

cond-mat.mtrl-sci↗
arXiv2006

Phase Diagram and Commensurate-Incommensurate Transitions in the Phase Field Crystal Model with an External Pinning Potential

We study the phase diagram and the commensurate-incommensurate transitions in a phase field model of a two-dimensional crystal lattice in the presence of an external pinning potential. The model allows for both elastic and plastic deformations and provides a continuum description of lattice systems, such as for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a mode expansion analysis is used to determine the ground states and the commensurate-incommensurate transitions in the model as a function of the strength of the pinning potential and the lattice mismatch parameter. Numerical minimization of the corresponding free energy shows good agreement with the analytical predictions and provides details on the topological defects in the transition region. We find that for small mismatch the transition is of first-order, and it remains so for the largest values of mismatch studied here. Our results are consistent with results of simulations for atomistic models of adsorbed overlayers.

cond-mat.other↗
arXiv2006

Density Functional Theory of Freezing and Phase Field Crystal Modeling

In this paper the relationship between the density functional theory of freezing and phase field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase field crystal modeling and standard models of binary alloys (i.e., regular solution model). To demonstrate the properties of the phase field crystal formalism a simple model of binary alloy crystallization is derived and shown to simultaneously model solidification, phase segregation, grain growth, elastic and plastic deformations in anisotropic systems with multiple crystal orientations on diffusive time scales.

cond-mat.mtrl-sci↗
arXiv2005

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.

cond-mat.mtrl-sci↗
arXiv2003

Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals

A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated analytically and numerical simulations are presented for a number of important applications including, epitaxial growth, material hardness, grain growth, reconstructive phase transitions and crack propagation.

cond-mat.soft↗
arXiv2002

Instabilities and resistance fluctuations in thin accelerated superconducting rings

The non-equilibrium properties of a driven quasi-one dimensional superconducting ring subjected to a constant electromotive force ({\it emf}) is studied. The {\it emf} accelerates the superconducting electrons until the critical current is reached and a dissipative phase slip occurs that lowers the current. The phase slip phenomena is examined as a function of the strength of the {\it emf}, thermal noise, and normal state resistivity. Numerical and analytic methods are used to make detailed predictions for the magnitude of phase slips and subsequent dissipation.

cond-mat.supr-con↗
arXiv2001

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.

cond-mat.mtrl-sci↗
arXiv2000

Sharp interface limits of phase-field models

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface limit'' from phase field models which have interfaces that are diffuse on a length scale $ξ$. In particular,phase-field equations are mapped onto sharp interface equations in the limits $ξκ\ll 1$ and $ξv/D \ll 1$, where $κ$ and $v$ are respectively the interface curvature and velocity and $D$ is the diffusion constant in the bulk. The calculations provide one general set of sharp interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation and the Kardar-Parisi-Zhang equation.

cond-mat.soft↗
arXiv2000

Conserved Dynamics and Interface Roughening in Spontaneous Imbibition : A Phase Field Model

The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field $α({\bf x})$. The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation $H \sim t^{1/2}$ for the slowing down motion of the average interface position $H$. The interface is found to be superrough, with global roughness exponent $χ\approx 1.25$, indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale $ξ_{\times} \sim H^{1/2}$ arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horv\a'ath and Stanley [Phys. Rev. E {\bf 52} 5166 (1995)] on the temporal scaling of the interface.

cond-mat.dis-nn↗
arXiv1999

Defects, order, and hysteresis in driven charge-density waves

We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, we find that the defect density first increases and then decreases. Furthermore, we find switching phenomena, due to the formation of channels of dislocations. These results are in qualitative accord with recent dynamical x-ray scattering experiments by Ringlandet al. and transport experiments by Lemay et al.

cond-mat.dis-nn↗
arXiv1998

An X-ray Scattering and Simulation Study of the Ordering Kinetics in CuAu

A detailed numerical and experimental study of the ordering of the low temperature tetragonal phase of CuAu is presented. The numerical simulations are based on a coarse-grained free energy derived from electronic structure calculations of CuAu, while the experimental results are obtained from in situ x-ray scattering. Both theoretical and experimental work indicate a subtle kinetic competition between the ordered tetragonal phase and the metastable modulated phase.

cond-mat.stat-mech↗
arXiv1996

Kinetics of Modulated and Ordered Structures in CuAu

A continuum model derived from an atomistic Hamiltonian is used to examine the ordering kinetics in CuAu. A detailed description of the formation of the low and high temperature ordered and modulated superlattice states is given. The metastability of the modulated phase at low temperatures is shown to severely hinder creation of the ordered superlattice. Formation of the modulated superlattice is shown to results in interesting lamellar and labyrinthine structures.

cond-mat.mtrl-sci↗
arXiv1995

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.

cond-mat↗
arXiv1994

Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.

cond-mat↗
arXiv1992

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 $1/4$ in the intermediate time regime.

cond-mat↗