201 research outputs found
Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic
Monte Carlo (MC) simulations of lattice models are a widely used way to
compute thermodynamic properties of substitutional alloys. A limitation to
their more widespread use is the difficulty of driving a MC simulation in order
to obtain the desired quantities. To address this problem, we have devised a
variety of high-level algorithms that serve as an interface between the user
and a traditional MC code. The user specifies the goals sought in a high-level
form that our algorithms convert into elementary tasks to be performed by a
standard MC code. For instance, our algorithms permit the determination of the
free energy of an alloy phase over its entire region of stability within a
specified accuracy, without requiring any user intervention during the
calculations. Our algorithms also enable the direct determination of
composition-temperature phase boundaries without requiring the calculation of
the whole free energy surface of the alloy system
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
Using bond-length dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys
A model is tested to rapidly evaluate the vibrational properties of alloys
with site disorder. It is shown that length-dependent transferable force
constants exist, and can be used to accurately predict the vibrational entropy
of substitutionally ordered and disordered structures in Au-Cu, Au-Pd, and
Cu-Pd. For each relevant force constant, a length- dependent function is
determined and fitted to force constants obtained from first-principles
pseudopotential calculations. We show that these transferable force constants
can accurately predict vibrational entropies of L1-ordered and disordered
phases in CuAu, AuPd, PdAu, CuPd, and PdAu. In
addition, we calculate the vibrational entropy difference between
L1-ordered and disordered phases of AuCu and CuPt.Comment: 9 pages, 6 figures, 3 table
The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics
A longstanding limitation of first-principles calculations of substitutional
alloy phase diagrams is the difficulty to account for lattice vibrations. A
survey of the theoretical and experimental literature seeking to quantify the
impact of lattice vibrations on phase stability indicates that this effect can
be substantial. Typical vibrational entropy differences between phases are of
the order of 0.1 to 0.2 k_B/atom, which is comparable to the typical values of
configurational entropy differences in binary alloys (at most 0.693 k_B/atom).
This paper describes the basic formalism underlying ab initio phase diagram
calculations, along with the generalization required to account for lattice
vibrations. We overview the various techniques allowing the theoretical
calculation and the experimental determination of phonon dispersion curves and
related thermodynamic quantities, such as vibrational entropy or free energy. A
clear picture of the origin of vibrational entropy differences between phases
in an alloy system is presented that goes beyond the traditional bond counting
and volume change arguments. Vibrational entropy change can be attributed to
the changes in chemical bond stiffness associated with the changes in bond
length that take place during a phase transformation. This so-called ``bond
stiffness vs. bond length'' interpretation both summarizes the key phenomenon
driving vibrational entropy changes and provides a practical tool to model
them.Comment: Submitted to Reviews of Modern Physics 44 pages, 6 figure
Point-charge electrostatics in disordered alloys
A simple analytic model of point-ion electrostatics has been previously
proposed in which the magnitude of the net charge q_i on each atom in an
ordered or random alloy depends linearly on the number N_i^(1) of unlike
neighbors in its first coordination shell. Point charges extracted from recent
large supercell (256-432 atom) local density approximation (LDA) calculations
of Cu-Zn random alloys now enable an assessment of the physical validity and
accuracy of the simple model. We find that this model accurately describes (i)
the trends in q_i vs. N_i^(1), particularly for fcc alloys, (ii) the magnitudes
of total electrostatic energies in random alloys, (iii) the relationships
between constant-occupation-averaged charges and Coulomb shifts
(i.e., the average over all sites occupied by either or atoms) in the
random alloy, and (iv) the linear relation between the site charge q_i and the
constant- charge-averaged Coulomb shift (i.e., the average over all sites with
the same charge) for fcc alloys. However, for bcc alloys the fluctuations
predicted by the model in the q_i vs. V_i relation exceed those found in the
LDA supercell calculations. We find that (a) the fluctuations present in the
model have a vanishing contribution to the electrostatic energy. (b)
Generalizing the model to include a dependence of the charge on the atoms in
the first three (two) shells in bcc (fcc) - rather than the first shell only -
removes the fluctuations, in complete agreement with the LDA data. We also
demonstrate an efficient way to extract charge transfer parameters of the
generalized model from LDA calculations on small unit cells.Comment: 15 pages, ReVTeX galley format, 7 eps figures embedded using psfig,
to be published in Phys. Rev.
Interatomic potentials for atomistic simulations of the Ti-Al system
Semi-empirical interatomic potentials have been developed for Al, alpha-Ti,
and gamma-TiAl within the embedded atomic method (EAM) by fitting to a large
database of experimental as well as ab-initio data. The ab-initio calculations
were performed by the linear augmented plane wave (LAPW) method within the
density functional theory to obtain the equations of state for a number of
crystal structures of the Ti-Al system. Some of the calculated LAPW energies
were used for fitting the potentials while others for examining their quality.
The potentials correctly predict the equilibrium crystal structures of the
phases and accurately reproduce their basic lattice properties. The potentials
are applied to calculate the energies of point defects, surfaces, planar faults
in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al
system, the proposed potentials provide reasonable description of the lattice
thermal expansion, demonstrating their usefulness in the molecular dynamics or
Monte Carlo studies at high temperatures. The energy along the tetragonal
deformation path (Bain transformation) in gamma-TiAl calculated with the EAM
potential is in a fairly good agreement with LAPW calculations. Equilibrium
point defect concentrations in gamma-TiAl are studied using the EAM potential.
It is found that antisite defects strongly dominate over vacancies at all
compositions around stoichiometry, indicating that gamm-TiAl is an antisite
disorder compound in agreement with experimental data.Comment: 46 pages, 6 figures (Physical Review B, in press
First-principles calculation of the effect of strain on the diffusion of Ge adatoms on Si and Ge (001) surfaces
First-principles calculations are used to calculate the strain dependencies
of the binding and diffusion-activation energies for Ge adatoms on both Si(001)
and Ge(001) surfaces. Our calculations reveal that the binding and activation
energies on a strained Ge(001) surface increase and decrease, respectively, by
0.21 eV and 0.12 eV per percent compressive strain. For a growth temperature of
600 degrees C, these strain-dependencies give rise to a 16-fold increase in
adatom density and a 5-fold decrease in adatom diffusivity in the region of
compressive strain surrounding a Ge island with a characteristic size of 10 nm.Comment: 4 pages, 4 figure
Configurational Thermodynamics of Alloyed Nanoparticles with Adsorbates
Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core–shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having O-coverage up to a monolayer, we fully detail the core–shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design
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