Enzo Granato

Energetics and atomic mechanisms of dislocation nucleation in strained epitaxial layers

We numerically study the energetics and atomic mechanisms of misfit dislocation nucleation and stress relaxation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Relaxation processes from coherent to incoherent states for different transition paths are studied using interatomic potentials of Lennard-Jones type and a systematic saddle-point and transition-path search method. The method is based on a combination of a repulsive potential minimization and the nudged elastic band method. For a final state with a single misfit dislocation, the minimum-energy path and the corresponding activation barrier are obtained for different misfits and interatomic potentials. We find that the energy barrier decreases strongly with misfit. In contrast to continuous elastic theory, a strong tensile-compressive asymmetry is observed. This asymmetry can be understood as a manifestation of the asymmetry between repulsive and attractive branches of the pair potential, and it is found to depend sensitively on the form of the potential.

Minimum energy paths for dislocation nucleation in strained epitaxial layers

We study numerically the minimum energy path and energy barriers for dislocation nucleation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Stress relaxation processesfrom coherent to incoherent states for different transition paths are determined using saddle point search based on a combination of repulsive potential minimization and the Nudged Elastic Band method. The minimum energy barrier leading to a final state with a single misfit dislocation nucleation is determined. A strong tensile-compressive asymmetry is observed. This asymmetry can be understood in terms of the qualitatively different transition paths for the tensile and compressive strains.

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 reasonable 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.

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

Chiral exponents of the square-lattice frustrated XY model: A Monte Carlo transfer-matrix calculation

N=105

CURRENT-VOLTAGE SCALING OF CHIRAL AND GAUGE-GLASS MODELS OF TWO-DIMENSIONAL SUPERCONDUCTORS

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.

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

Thermal and chiral critical exponents of the fully frustrated [ital XY] model on a square lattice are obtained from a finite-size scaling analysis of the free energy of chiral domain walls. Data were obtained by extensive Monte Carlo transfer-matrix computations for infinite strips of widths up to 14 lattice spacings. Two transfer matrices were implemented, one for each of two principal lattice directions. The results of both are consistent, but the critical exponents differ significantly from the pure Ising values. This is in agreement with other recent Monte Carlo simulations. Our results also support the identification of the critical behavior of this model with that along the line of transitions of simultaneous ordering or becoming critical of Ising and planar rotor degrees of freedom in the [ital XY]-Ising model studied recently.

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer.

The scaling behavior of the current-voltage characteristics of chiral and gauge glass models of disordered superconductors, are studied numerically, in two dimensions. For both models, the linear resistance is nonzero at finite temperatures and the scaling analysis of the nonlinear resistivity is consistent with a phase transition at T=0 temperature characterized by a diverging correlation length

Dynamical transitions and sliding friction in the two-dimensional Frenkel-Kontorova model

\xi \propto T^{-\nu_{T}}

Strain relief in Cu-Pd heteroepitaxy.

and thermal critical exponent