Interface Equations for Capillary Rise in Random Environment

We consider the influence of quenched noise upon interface dynamics in 2D and 3D capillary rise with rough walls by using phase-field approach, where the local conservation of mass in the bulk is explicitly included. In the 2D case the disorder is assumed to be in the effective mobility coefficient, while in the 3D case we explicitly consider the influence of locally fluctuating geometry along a solid wall using a generalized curvilinear coordinate transformation. To obtain the equations of motion for meniscus and contact lines, we develop a systematic projection formalism which allows inclusion of disorder. Using this formalism, we derive linearized equations of motion for the meniscus and contact line variables, which become local in the Fourier space representation. These dispersion relations contain effective noise that is linearly proportional to the velocity. The deterministic parts of our dispersion relations agree with results obtained from other similar studies in the proper limits. However, the forms of the noise terms derived here are quantitatively different from the other studies

Equilibrium Shape and Size of Supported Heteroepitaxial Nanoislands

We study the equilibrium shape, shape transitions and optimal size of strained heteroepitaxial nanoislands with a two-dimensional atomistic model using simply adjustable interatomic pair potentials. We map out the global phase diagram as a function of substrate-adsorbate misfit and interaction. This phase diagram reveals all the phases corresponding to different well-known growth modes. In particular, for large enough misfits and attractive substrate there is a Stranski-Krastanow regime, where nano-sized islands grow on top of wetting films. We analyze the various terms contributing to the total island energy in detail, and show how the competition between them leads to the optimal shape and size of the islands. Finally, we also develop an analytic interpolation formula for the various contributions to the total energy of strained nanoislands.Comment: 9 pages, 7 figure

Dynamics near the Surface Reconstruction of W(100)

Using Brownian molecular dynamics simulation, we study the surface dynamics near the reconstruction transition of W(100) via a model Hamiltonian. Results for the softening and broadening of the surface phonon spectrum near the transition are compared with previous calculations and with He atom scattering data. From the critical behavior of the central peak in the dynamical structure factor, we also estimate the exponent of the power law anomaly for adatom diffusion near the transition temperature.Comment: 8 pages, 8 figures, to appear in Phys. Rev.

Equilibrium shape and dislocation nucleation in strained epitaxial nanoislands

We study numerically the equilibrium shapes, shape transitions and dislocation nucleation of small strained epitaxial islands with a two-dimensional atomistic model, using simple interatomic pair potentials. We first map out the phase diagram for the equilibrium island shapes as a function of island size (up to N = 105 atoms) and lattice misfit with the substrate and show that nanoscopic islands have four generic equilibrium shapes, in contrast with predictions from the continuum theory of elasticity. For increasing substrate-adsorbate attraction, we find islands that form on top of a finite wetting layer as observed in Stranski-Krastanow growth. We also investigate energy barriers and transition paths for transitions between different shapes of the islands and for dislocation nucleation in initially coherent islands. In particular, we find that dislocations nucleate spontaneously at the edges of the adsorbate-substrate interface above a critical size or lattice misfit.Comment: 4 pages, 3 figures, uses wrapfig.sty and epsfig.st

Dynamical transitions and sliding friction of the phase-field-crystal model with pinning

We study the nonlinear driven response and sliding friction behavior of the phase-field-crystal (PFC) model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed layers on a substrate under the action of an external driving force at finite temperatures, allowing for both elastic and plastic deformations. We derive general stochastic dynamical equations for the particle and momentum densities including both thermal fluctuations and inertial effects. The resulting coupled equations for the PFC model are studied numerically. At sufficiently low temperatures we find that the velocity response of an initially pinned commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The main features of the nonlinear response in the PFC model are similar to the results obtained previously with molecular dynamics simulations of particle models for adsorbed layers.Comment: 7 pages, 8 figures, to appear in Physcial Review

Stress release mechanisms for Cu on Pd(111) in the submonolayer and monolayer regimes

We study the strain relaxation mechanisms of Cu on Pd(111) up to the monolayer regime using two different computational methodologies, basin-hopping global optimization and energy minimization with a repulsive bias potential. Our numerical results are consistent with experimentally observed layer-by-layer growth mode. However, we find that the structure of the Cu layer is not fully pseudomorphic even at low coverages. Instead, the Cu adsorbates forms fcc and hcp stacking domains, separated by partial misfit dislocations. We also estimate the minimum energy path and energy barriers for transitions from the ideal epitaxial state to the fcc-hcp domain pattern.Comment: 4 pages, 4 figure

Diffusive Spreading of Chainlike Molecules on Surfaces

We study the diffusion and submonolayer spreading of chainlike molecules on surfaces. Using the fluctuating bond model we extract the collective and tracer diffusion coefficients D_c and D_t with a variety of methods. We show that D_c(theta) has unusual behavior as a function of the coverage theta. It first increases but after a maximum goes to zero as theta go to one. We show that the increase is due to entropic repulsion that leads to steep density profiles for spreading droplets seen in experiments. We also develop an analytic model for D_c(theta) which agrees well with the simulations.Comment: 3 pages, RevTeX, 4 postscript figures, to appear in Phys. Rev. Letters (1996

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

Glassy phases and driven response of the phase-field-crystal model with random pinning

We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then finally a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes