7 research outputs found
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 -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 at low temperatures, the lifetime prefactor diverges
because the transition rates between certain configurations approaches zero
under these conditions. Near 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 and one for .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