Modified Fisher Droplet Model

1982 ◽  
Vol 21 ◽  
Author(s):  
J. Marro ◽  
R. Toral
Keyword(s):  
Cluster Size ◽  
Lattice Gas ◽  
Three Dimensional ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Exact Results ◽  
Droplet Model ◽  
Simple Modification ◽  
The Magnetic Field ◽  
Effective Cluster

ABSTRACTWe propose a simple modification of the Fisher droplet model which, unlike classical nucleation theory, reproduces very well some Monte Carlo equilibrium cluster distributions P1 for the three-dimensional Ising or lattice gas model. It then follows that p1(h) /p1(h=0) = A exp(− η l) where η ∝hl/Y, y≃0.45, when the magnetic field h is small enough, as suggested from the consideration of an effective cluster size ly , while η seems rather proportional to h at larger values of the field, as implied by some exact results.

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

Molecular Dynamics Simulation of Nano Cluster-Seed Effects on Heterogeneous Nucleation

2009 ◽  
Author(s):  
Donguk Suh ◽  
Seung-chai Jung ◽  
Woong-sup Yoon
Keyword(s):  
Molecular Dynamics ◽  
Heterogeneous Nucleation ◽  
Three Dimensional ◽  
Seed Mass ◽  
Nucleation Theory ◽  
Dynamics Simulation ◽  
Classical Nucleation Theory ◽  
Supersaturation Ratio ◽  
Order Of Magnitude ◽  
Nano Cluster

A three-dimensional heterogeneous nucleation is simulated by classical molecular dynamics, where the Lennard-Jones gas and solid nano cluster-seed molecules have argon and aluminum properties, respectively. All dimensions of the wall are periodic and a soft core carrier gas within the system controls the temperature rise induced by latent heat of condensation. There are three shapes of cluster-seeds being cube, rod, and sphere, three classes of masses, and the simulation took place under nine supersaturation ratios, making a total of 81 calculations. An analysis of variance was performed under a three-way layout to analyze the cluster-seed and supersaturation ratio effects on the system. For supersaturation ratios above the critical value nucleation rates were evaluated, below growth rates, and overall liquefaction rates were each defined and calculated. Results show that the supersaturation ratio dominantly controls all rates, but seed characteristics are important for the growth of the largest cluster under the critical supersaturation ratio. Overall liquefaction increases subject to an escalation of supersaturation ratio and seed mass. However, the significance of the supersaturation ratio for overall liquefaction suggests that thermal diffusion is more dominant than mass interactions for this system. Homogeneous characteristics are also compared with the heterogeneous system to find that though nucleation may occur for an insufficient supersaturation ratio when a seed is within the system, the addition of a seed does not in fact facilitate the increase in rates of the phenomena at high supersaturation ratios. Finally a comparison with the classical nucleation theory asserts a 3 to 4 order of magnitude difference, which is within the lines of deviation when it comes to theory and molecular simulations.

MONTE CARLO SIMULATION OF NUCLEATION AND GROWTH IN THE 3D NEAREST-NEIGHBOR ISING MODEL

2001 ◽  
Vol 12 (03) ◽  
pp. 345-359 ◽  
Author(s):  
JÜRN SCHMELZER ◽  
D. P. LANDAU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Cluster Size ◽  
Nearest Neighbor ◽  
Ostwald Ripening ◽  
Nucleation And Growth ◽  
Size Distribution Function ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Regular Solutions

Monte Carlo simulations of nucleation and growth processes in an Ising-binary alloy model are presented. The evolution of the cluster size distribution function and its characteristic properties (mean radius and concentration of the clusters) has been investigated from the initial quench into the metastable region of the phase diagram until the establishment of the final equilibrium. All classical stages of nucleation and growth could be observed, the stages of steady-state nucleation, independent growth and Ostwald ripening. A quantitative analysis of the simulational results in terms of the theory of regular solutions shows the validity of classical nucleation theory in the region of the phase diagram considered and provides evidence for a size and structure dependent interfacial tension between the two newly formed phases.

Nucleation and Growth Characteristics of Thin Metal Films

1971 ◽  
Vol 29 ◽  
pp. 216-217
Author(s):  
H. P. Singh ◽  
L. E. Murr
Keyword(s):  
Thin Films ◽  
Three Dimensional ◽  
Metal Films ◽  
Nucleation And Growth ◽  
Growth Characteristics ◽  
Thin Metal ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Thin Metal Films ◽  
Initial Deposition

This paper reports observations of nucleation and growth characteristics of thin metal films vapor deposited onto heated sodium chloride substrates. An attempt is made to explain the differences in nucleation and growth characteristics on the basis of classical nucleation theory.Thin metal films were prepared by vapor deposition onto heated NaCl (001) substrates in a commercial vacuum unit using a constant evaporation rate of approximately 1000 Å/sec. In the case of discontinuous thin films, approximately 200 Å of carbon was deposited for support. Samples for electron microscopy were prepared by standard techniques and were observed at 125 kV. Figs. 1(a) to (c) show a growth sequence of gold thin films characterized by 1) the formation of random, three dimensional, isolated nuclei at initial deposition, and their growth with further deposition predominantly by surface diffusion; 2) coalescence of these nuclei forming bigger islands; 3) the flattening of islands and formation of network structure : and 4) the filling up of these network structures with further deposition forming a continuous film.

The Morphological Stability of Strained Epitaxial Layers

1996 ◽  
Vol 440 ◽  
Author(s):  
B. W. Wessels
Keyword(s):  
Thin Films ◽  
Critical Thickness ◽  
Strain Relaxation ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Epitaxial Layers ◽  
Two Dimensional ◽  
Morphological Stability

AbstractThe morphological stability of strained-layer thin films is analyzed using classical nucleation theory. For the case where strain relaxation occurs by formation of coherent islands, the model predicts that the critical thickness for transition from two-dimensional (2D) to three dimensional (3D) growth depends inversely on the square of the misfit. The predicted dependence of critical thickness on misfit is in agreement with recent experimental studies on the heteropitaxy of III-V compounds.

Two-Phase Eulerian/Lagrangian Model for Nucleating Steam Flow

2002 ◽  
Vol 124 (2) ◽  
pp. 465-475 ◽  
Author(s):  
A. G. Gerber
Keyword(s):  
Three Dimensional ◽  
Low Pressure ◽  
Steam Flow ◽  
Nucleation Theory ◽  
Lagrangian Model ◽  
Classical Nucleation Theory ◽  
Navier Stokes ◽  
Steam Turbines ◽  
Complex Flow ◽  
Two Phase

This paper describes an Eulerian/Lagrangian two-phase model for nucleating steam based on classical nucleation theory. The model provides an approach for including spontaneous homogeneous nucleation within a full Navier-Stokes solution scheme where the interaction between the liquid and gas phases for a pure fluid is through appropriately modeled source terms. The method allows for the straightforward inclusion of droplet heat, mass, and momentum transfer models along with nucleation within complex flow systems as found, for example, in low pressure steam turbines. The present paper describes the solution method, emphasizing that the important features of nucleating steam flow are retained through comparison with well-established 1-D solutions for Laval nozzle flows. Results for a two-dimensional cascade blade and three-dimensional low pressure turbine stage are also described.

Molecular Dynamics Simulation of Three-Dimensional Heterogeneous Nucleation

2011 ◽  
Author(s):  
Donguk Suh ◽  
Kenji Yasuoka
Keyword(s):  
Molecular Dynamics ◽  
Heterogeneous Nucleation ◽  
Homogeneous Nucleation ◽  
Three Dimensional ◽  
Nucleation Theory ◽  
Dynamics Simulation ◽  
Classical Nucleation Theory ◽  
Supersaturation Ratio ◽  
Seed Growth ◽  
Thermodynamic Conditions

Nanoparticle growth based on three-dimensional heterogeneous nucleation was simulated by classical molecular dynamics. To collectively observe the effects of the dimension of seeds and thermodynamic conditions, seed size and system supersaturation ratio were the factors that were examined to see if they influenced the nucleation rates. Two stages were found to exist within the system, where the first stage is from the seed growth and the second from homogeneous nucleation. The Yasuoka-Matsumoto method was used to calculate the rates. The homogeneous nucleation characteristics coincided with the classical nucleation theory, but heterogeneous nucleation showed an irregular form, which at the current state cannot not be fully understood. Kinetic analysis was also performed to calculate the critical nucleus size and better understand the seed growth characteristics. All in all, the seed effects were insignificant to the overall nucleation characteristics for this system.

THREE-DIMENSIONAL ISING NUCLEATION AT LOW TEMPERATURES

1999 ◽  
Vol 10 (05) ◽  
pp. 809-813 ◽  
Author(s):  
DIETRICH STAUFFER
Keyword(s):  
Low Temperatures ◽  
Three Dimensional ◽  
Nucleation Theory ◽  
Classical Nucleation Theory

Simulations at T/Tc = 1/4 agree with classical nucleation theory if the droplets are assumed as small cubes instead of spheres.

scholarly journals Microscopic Evidence for Liquid-Liquid Separation in Supersaturated CaCO3 Solutions

Science ◽  
2013 ◽  
Vol 341 (6148) ◽  
pp. 885-889 ◽  
Author(s):  
Adam F. Wallace ◽  
Lester O. Hedges ◽  
Alejandro Fernandez-Martinez ◽  
Paolo Raiteri ◽  
Julian D. Gale ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Phase Separation ◽  
Liquid Phase ◽  
Lattice Gas ◽  
Solid Phase ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Liquid Separation ◽  
Dynamics Simulations ◽  
Dense Liquid

Recent experimental observations of the onset of calcium carbonate (CaCO3) mineralization suggest the emergence of a population of clusters that are stable rather than unstable as predicted by classical nucleation theory. This study uses molecular dynamics simulations to probe the structure, dynamics, and energetics of hydrated CaCO3 clusters and lattice gas simulations to explore the behavior of cluster populations before nucleation. Our results predict formation of a dense liquid phase through liquid-liquid separation within the concentration range in which clusters are observed. Coalescence and solidification of nanoscale droplets results in formation of a solid phase, the structure of which is consistent with amorphous CaCO3. The presence of a liquid-liquid binodal enables a diverse set of experimental observations to be reconciled within the context of established phase-separation mechanisms.

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