Irreversible Island Formation During Deposition: Island Size and Separation Distributions

1992 ◽  
Vol 280 ◽  
Author(s):  
M. C. Bartelt ◽  
M. C. Tringides ◽  
J. W. Evans
Keyword(s):  
Size Distribution ◽  
Rate Equation ◽  
Nucleation And Growth ◽  
Simplified Model ◽  
Island Size ◽  
Deposition Rates ◽  
Island Formation ◽  
Simulation Results ◽  
Precise Simulation

ABSTRACTWe present precise simulation results for a simplified model of irreversible nucleation and growth of islands during deposition. We characterize the scaling of the island and adatom densities, the complete island size distribution, and the adatom-island and island-island separation distributions, with the ratio of diffusion to deposition rates (for fixed coverages,θ<1). We also make some comparisons with rate equation predictions.

Computer Simulation of the Early Stages of Nano Scale SiC Growth on Si

2005 ◽  
Vol 483-485 ◽  
pp. 169-172
Author(s):  
K.L. Safonov ◽  
Yuri V. Trushin ◽  
Oliver Ambacher ◽  
Jörg Pezoldt
Keyword(s):  
Computer Simulation ◽  
Silicon Carbide ◽  
Molecular Beam Epitaxy ◽  
Substrate Temperature ◽  
Size Distribution ◽  
Rate Equation ◽  
Molecular Beam ◽  
Carbon Fluxes ◽  
Island Size ◽  
Nano Scale

Solid source molecular beam epitaxy was applied to create silicon carbide nanoclusters on silicon. The island size distribution can be controlled by an appropriate substrate temperature, carbon fluxes and process times. Rate equation computer simulation was applied to simulate the experimental obtained nano scale nuclei properties.

Transitions in Critical Island Size in Metal (100) and (111) Homoepitaxy: A Self-Consistent Rate Equation Approach

1998 ◽  
Vol 528 ◽  
Author(s):  
Mihail N. Popescu ◽  
Jacques G. Amar ◽  
Fereydoon Family
Keyword(s):  
Rate Equation ◽  
Kinetic Monte Carlo ◽  
Island Size ◽  
Bond Model ◽  
Self Consistent ◽  
Standard Rate ◽  
Simulation Results ◽  
Small Clusters ◽  
Short Range Correlations ◽  
Good Agreement

AbstractA self-consistent rate equation (RE) approach to submonolayer growth for a restricted pair-bond model that is relevant to low and intermediate temperature metal (100) and (111) homoepitaxy is introduced. In contrast to previous standard rate equation results, the transition temperature from i = 1 to a higher critical island size is well predicted along with the average island and monomer densities. It is shown that the method's implicit introduction of short-range correlations between attachment/detachment rates, together with a careful estimate of the escape rates for small clusters, are important factors for a good agreement with the kinetic Monte Carlo simulation results.

Exact Scaling Form for the Island Size Distribution in Submonolayer Epitaxial Growth

1996 ◽  
Vol 440 ◽  
Author(s):  
M. C. Bartelt ◽  
J. W. Evans
Keyword(s):  
Epitaxial Growth ◽  
Size Distribution ◽  
Nucleation And Growth ◽  
Complex Relationship ◽  
Island Size ◽  
The Relationship ◽  
Exact Scaling

AbstractThe exact scaling form is determined for the size distribution of islands created via irreversible nucleation and growth during submonolayer deposition. This form is controlled by a dependence on size of the propensity for islands to “capture” diffusing adatoms. This sizedependence is determined directly from simulations. It reflects a complex relationship between the size of an island, and the area of its cell in a tessellation of the surface based on the island locations. The relationship corresponds to a correlation between island size and separation.

Evolution of cluster size distribution in nucleation and growth processes

1991 ◽  
Vol 136 (3) ◽  
pp. 181-197 ◽  
Author(s):  
J. Bartels ◽  
U. Lembke ◽  
R. Pascova ◽  
J. Schmelzer ◽  
I. Gutzow
Keyword(s):  
Size Distribution ◽  
Cluster Size ◽  
Nucleation And Growth ◽  
Cluster Size Distribution ◽  
Growth Processes

A micromechanistic model of microstructure development during the combustion synthesis process

1995 ◽  
Vol 10 (4) ◽  
pp. 962-980 ◽  
Author(s):  
Yangsheng Zhang ◽  
Gregory C. Stangle
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Combustion Synthesis ◽  
Growth Parameters ◽  
Experimental Studies ◽  
Nucleation And Growth ◽  
Synthesis Process ◽  
Product Phase ◽  
Nucleation Sites ◽  
Rate Of Increase

The influence of the key nucleation and grain growth parameters on (i) the evolution of the microstructure of the product phase (on a microscopic level) and (ii) the combustion synthesis process (on a macroscopic level) were investigated for the combustion synthesis process in the Nb-C system. This work is an integral part of the continuing effort1–3 to develop a more complete theoretical model for combustion synthesis processes in general. In particular, the nucleation and growth of the NbC(s) product phase from the supersaturated liquid Nb/C mixture that appears briefly during the combustion synthesis process was treated in a greater detail by using a decidedly more sophisticated treatment of the nucleation and growth process (as developed in the field of rapid solidification and welding). It was shown that the microstructure of the NbC(s) product phase, including the evolution of the grain size and the size distribution, and the development of the grain's morphology, as well as the combustion wave velocity, are significantly influenced by the total number density of the nucleation sites, nmax, that are present in the system. The grain size distribution was shown to possess a monosize distribution, since during the combustion synthesis process the rate of increase of the degree of local undercooling was very high so that the nucleation process took place (locally) during a very brief period of time. This work provides a sound basis for developing a better control of the microstructure, and for a better understanding and interpretation of the results of related experimental studies.

Numerical Simulation and Analysis on the Impact Effect of Cylindrical Projectile Impacting Shelled Explosive

2013 ◽  
Vol 710 ◽  
pp. 320-324
Author(s):  
Ying Zi Jiang ◽  
Wei Li Wang ◽  
Xue Feng Huang ◽  
Lei Fu ◽  
Zhuang Qing Fan
Keyword(s):  
Numerical Simulation ◽  
Energy Criterion ◽  
Critical Energy ◽  
Simplified Model ◽  
Initiation Point ◽  
4340 Steel ◽  
Simulation Results ◽  
The Impact ◽  
Explosive Detonation ◽  
Critical Initiation

The numerical simulation of shelled Comp.B explosive was studied following the Lee-Tarver ignition and growth model when it was impacted respectively by 4340 Steel, OFHC and 93#W projectile with the same mass; the influences on explosive detonation of the initiation process, the material of projectile and the L/D ratio of projectile were analyzed; the critical initiation speeds of the projectiles of three different materials with different L/D ratio were gained. In order to verify the simulation results, the questions were calculated by the theoretical simplified model, the results of the theoretical calculation and the numerical simulation accorded well based on critical energy criterion. The results show that the capability of igniting explosive, the first is 93#W, the second is OFHC, the last is 4340 Steel; The initiation point were not on the interface of shell and explosive, and the faster of the impacting velocity, the initiation point closer the interface; the bigger of the L/D ratio of projectile, the higher of the critical initiation speed.

A Simplified Model for the Flow Inside Cascade Impactor

2013 ◽  
Author(s):  
Seyyed Mahdi Nemati Mehr ◽  
Salman Sohrabi ◽  
Pedram Falsafi ◽  
Paniz Gorji
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Low Cost ◽  
Mass Difference ◽  
Cascade Impactor ◽  
Computational Method ◽  
Simplified Model ◽  
Unit Value ◽  
Cascade Impactors

In this paper we developed a new mathematical model for the flow inside cascade impactors and via this simplified model, we determined the particle size distribution by a fast and low cost computational method. Using cascade impactors for determining the particle size distribution, one can use comprehensive CFD methods to fully simulate the particle traces. Although the results from those CFD analyses can be very accurate, usually that is not a time and cost efficient routine. In contrast, we showed that by using our proposed calculation we can estimate the particle size distribution very fast and yet with the slight error — comparing to the results from CFD method. Cascade impactors are being used to measure the range of substances moving through an opening and determine the particle size of distributed substances. Air flow containing aerosol entering in each stage, after colliding vertically with a plate will deviate 90 degrees from its original direction. Larger (massive) particles cannot follow the flow because of their larger linear momentum. Hence, they will deviate from the flow and deposit on the plate instead. The mass difference before and after the experiment represents the deposited mass in each stage. By integrating multiple uniquely designed stages into one impactor, we can determine size of particles in the flow. Typical cascade impactors consist of up to ten stages in which different size of aerosols are being separated. This paper presents a simple model for the flow in one single stage of a cascade impactor. Flow inside cascade impactor is approximated by stagnation point potential flow with the stream function of Psi = Axy, and particles are tracked by velocity verlet algorithm. Absorbed particles are associated with unit value; otherwise they are associated with zero. It is assumed that particles in entrance have random size distribution and location. Drag, Saffman and Brownian forces are taken into account in this model for different particle sizes. The results are discussed in detail and compared with data driven from different approaches in the literature.

Spatial Correlations in Growing Films

2000 ◽  
Vol 619 ◽  
Author(s):  
M.C. Bartelt
Keyword(s):  
Size Distribution ◽  
Lattice Gas ◽  
Mean Field ◽  
Film Deposition ◽  
Nucleation Theory ◽  
Spatial Correlations ◽  
Island Size ◽  
Pit Formation ◽  
Free Region ◽  
Lattice Gas Models

ABSTRACTDetailed analyses of non-equilibrium lattice-gas models of island nucleation and growth during film deposition (or etching) have been invaluable in elucidating basic issues in nucleation theory, deviations from mean-field predictions, and experimental observations. Particularly interesting and useful is the behavior of spatial correlations in the adlayer which develop during island (or pit) formation. In particular, a strong depletion in the population of island pairs at separations smaller than the average follows from depletion in the density of diffusing adspecies near islands. This feature delays percolation of clusters of coalesced islands. Another recently discovered and more subtle feature is a strong correlation between the width of the island-free region surrounding an island and the size and growth rate of that island. This direct correlation between island sizes and separations controls the shape of the island size distribution. If incorporated into rate-equation descriptions, it recovers the exact form of the scaling function for the island size distribution.

Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid

2011 ◽  
Vol 1308 ◽  
Author(s):  
Andreas Bill ◽  
Ralf B. Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Growth Rates ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Nucleation And Growth ◽  
Analytic Description ◽  
Silicon Thin Films ◽  
Random Nucleation

ABSTRACTWe present an overview of the theory developed over the last few years to describe the crystallization of amorphous solids. The microstructure of the crystallizing solid is described in terms of the grain size distribution (GSD). We propose a partial differential equation that captures the physics of crystallization in random nucleation and growth processes. The analytic description is derived for isotropic and anisotropic growth rates and allows for the analysis of different stages of crystallization, from early to full crystallization. We show how the timedependence of effective nucleation and growth rates affect the final distribution. In particular, we demonstrate that for cases described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model applicable to a large class of crystallization processes a lognormal type distribution is obtained at full crystallization. The application of the theory to the crystallization of silicon thin films is discussed.

COMPARISON OF FRACTIONAL NOISE DISTRIBUTIONS FOR GENERATING HETEROGENEOUS PERMEABILITY FIELDS IN OIL RESERVOIR SIMULATIONS: A CASE STUDY

Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850066
Author(s):  
MARYAM GHORBANI ◽  
MOHAMMAD REZA KHORSAND MOVAGHAR
Keyword(s):  
Hurst Exponent ◽  
Reservoir Rock ◽  
Rock Properties ◽  
Heterogeneous Reservoirs ◽  
Regionalized Variables ◽  
Geostatistical Models ◽  
Permeability Distribution ◽  
Simulation Results ◽  
Core Permeability ◽  
Precise Simulation

Prediction of reservoir rock properties, especially permeability distribution is needed for precise simulation of heterogeneous reservoirs. Interwell permeability fields have recently been considered for dynamic simulation using geostatistical models and fractal geometries. The geostatistical models employ experimentally observed variograms to characterize the spatial variability of regionalized variables such as permeability. Fractal models can be useful in assessing the spatial correlation of a property because their variogram can be characterized with a single parameter called the Hurst exponent. In this study, based on core permeability data of each well, Hurst exponent (using [Formula: see text] analysis) is assigned locally to each well by means of stream lines and as averaged value for interwell spaces. Then, permeability distributions are created using Fractional Brownian Motion (FBM) and Fractional Gaussian Noise (FGN) models by implementing fast Fourier transform (FFT). Through comparison between simulation results of these models, as well as real grid simulation results, the averaged distribution was shown to give better results over a locally assigned fractal distribution. Furthermore, predictions of field pressure using the FGN model were shown to function better than the FBM model for vertical wells.

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