Discrete-Event Analytic Technique for Surface Growth Problems

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete events that take place on the interface and its elementary local-site configurations. We construct theoretical probability distributions of deposition events at saturation for surfaces generated by selected growth rules. These distributions are then used to compute measurable physical quantities. Despite the neglect of temporal correlations, our approximate analytical results are in very good agreement with numerical simulations. This discrete-event analytic technique can be particularly useful when applied to quantification problems, which are known to not be suited to continuum methods.Comment: 4 pages, 7 figures, published 17 Feb. 200

Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for $|H|/J>2$ and one for $|H|/J<2$.Comment: published versio

Crystallization of a supercooled liquid and of a glass - Ising model approach

Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with four-spin interaction. We monitor the morphology of crystals which grow after placing crystallization seeds in a supercooled liquid. Defects in such crystals constitute an intricate and very stable network which separate various domains by tensionless domain walls. We also show that the crystallization which occurs during the continuous heating of the glassy phase takes place at a heating-rate dependent temperature.Comment: 7 page

Nucleation of Al3Zr and Al3Sc in aluminum alloys: from kinetic Monte Carlo simulations to classical theory

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of Al3Zr and Al3Sc. These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test di erent mean-field approximations (Bragg-Williams approximation as well as Cluster Variation Method) for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small L12 clusters.Comment: submitted to Physical Review B (2004