Modelling Solid Nucleation and Growth In Supercooled Liquid

1999 ◽  
Vol 580 ◽  
Author(s):  
J.P. Leonard ◽  
James S. Im
Keyword(s):  
Random Number ◽  
Thermal Evolution ◽  
Supercooled Liquid ◽  
Nucleation And Growth ◽  
Nucleation Kinetics ◽  
Time Step ◽  
Si Films ◽  
Solid Nucleation ◽  
Random Nature ◽  
Induced Crystallization

AbstractIn this paper, we present a numerical model that incorporates algorithms to simulate nucleation and growth in supercooled liquid in a manner that properly accounts for the stochastic nature of nucleation. The basis of our model relies on a discretization of space and time to address thermal evolution, rapid growth of the undercooled interface, and nucleation in supercooled liquid. The present formulation of nucleation permits the spatially and temporally random nature of the phenomenon to be manifested in the transformation and resultant microstructure. This is accomplished by (1) calculating the probability of nucleation in each and every liquid node during each time step using the Poisson expression, and (2) triggering nucleation if and only when the random number assigned to a node for the time step is less than the calculated nucleation probability. No empirical or deterministic conditions for nucleation are imposed; nucleation occurs spontaneously and solely based on nucleation kinetics. We demonstrate the effectiveness of the overall model by analyzing conditions similar to those encountered in pulsed laser-induced crystallization of thin Si films, and discuss the generality of the proposed stochastic formulation of nucleation.

scholarly journals A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170327 ◽  
Author(s):  
Eugenya V. Makoveeva ◽  
Dmitri V. Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Description ◽  
Supercooled Liquid ◽  
Intermediate Stage ◽  
Nucleation And Growth ◽  
Time Dependent ◽  
Supersaturated Solution ◽  
Nucleation Kinetics ◽  
Type Integral ◽  
Laplace Type

This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Aluminum-Induced Crystalization of Amorphous Silicon Films Deposited by Megnetron Sputtering

2013 ◽  
Vol 690-693 ◽  
pp. 1655-1658
Author(s):  
Jun Qian ◽  
Wei Min Shi ◽  
Jing Jin ◽  
Ji Rong Li ◽  
Yang Liao
Keyword(s):  
Raman Spectroscopy ◽  
Magnetron Sputtering ◽  
Amorphous Silicon ◽  
Energy Dispersive Spectroscopy ◽  
Nucleation And Growth ◽  
X Ray Diffraction ◽  
X Ray ◽  
Annealing Procedure ◽  
Si Films ◽  
Induced Crystallization

Aluminum–induced crystallization of sputtered a-Si under two-step annealing procedure on glass substrate is studied. A 200 nm thick a-Si film was deposited by magnetron sputtering on glass and a Al film of 150 nm was sputtered on top. The samples were annealed under two-step annealing procedure. Nucleation and growth of grains were followed by optical microscopy (OM), X-ray diffraction (XRD), Raman spectroscopy, and energy dispersive spectroscopy (EDS). Continuous (111) oriented poly-Si films were obtained with a Raman Peak at 520.8cm-1. The different annealing periods is discussed.

A New Experimental Method for Investigating the Nucleation Kinetics of Solids in Supercooled Liquid Si

1995 ◽  
Vol 398 ◽  
Author(s):  
H. Jin Song ◽  
James S. Im
Keyword(s):  
Thin Film ◽  
Experimental Method ◽  
Supercooled Liquid ◽  
Isothermal Transformation ◽  
Frequency Range ◽  
Nucleation Kinetics ◽  
Detection Techniques ◽  
Wide Range ◽  
Solid Nucleation ◽  
Kinetics Of

ABSTRACTIn this paper, we first describe and then demonstrate the soundness of a new experimental method that is designed to deliver a wide range of accurately measured nucleation rates of solids in supercooled liquid Si. The method utilizes thin-film processes, as well as laser-quenching and detection techniques, in order to first induce isothermal transformation and then extract the corresponding solid nucleation rates over a frequency range potentially greater than ten orders of magnitude. The technological and scientific gains that can result from acquiring such information are discussed.

A Model for Silicon Dendrite Growth During Laser/Plasma Deposition from a Silane Discharge

1986 ◽  
Vol 75 ◽  
Author(s):  
Harold M. Anderson ◽  
Philip J. Hargis
Keyword(s):  
Laser Plasma ◽  
Plasma Deposition ◽  
Dendritic Structure ◽  
Negative Temperature ◽  
Supercooled Liquid ◽  
Interface Temperature ◽  
Laser Fluences ◽  
Krf Laser ◽  
Si Films ◽  
Tip Radius

AbstractA model for dendrite growths in polycrystalline Si films formed during laser/plasma deposition with a silane discharge and a pulsed KrF laser has been developed. The model assumes a thin (less than 10 nm) amorphous silicon (a-Si) film is deposited on a substrate prior to phase transformation due to laser heating. The observed dendritic structure of the overall polycrystalline Si films is attributed to Si crystals shooting from an excessively supercooled Si liquid bath. Supercooled liquid forms since the melting point for a-Si can be reached at relatively low KrF laser fluences. Latent heat evolved at the solid-liquid interface induces an interface temperature higher than that of the melt and the requisite negative temperature gradient for absolute bath supercooling. Since the formation of an undercooled liquid by fast melting a-Si is also an important first step in explosive crystal regrowth studies, these results may have important implications for crystal growth and transient annealing. A conical approximation model is used in this study to characterize the stability of the dendrite tip in terms of local temperature gradients, i.e., the degree of undercooling at the tip of the parabolic dendrite. The degree of undercooling and hence the tip radius appears to be significantly affected by small changes in the laser fluence. Stability criteria lead to a relationship between regrowth velocity, V, and the tip radius, R, of the form VR2= constant. The size and stability of the dendrite tip is determined from a balance between the destabilizing force due to thermal diffusion and the stabilizing capillary force. Based on the observed tip radii formed at laser fluences from 0.13 to 0.25 J/cm2, the model predicts regrowth velocities in a range between 2.0 and 20 m/s – values consistent with transient annealing studies of a-Si

Monte Carlo Simulation of Precipitate Nucleation and Growth: Time Dependent Results

1988 ◽  
Vol 141 ◽  
Author(s):  
James P. Lavine ◽  
Gilbert A. Hawkins
Keyword(s):  
Monte Carlo ◽  
Crystalline Silicon ◽  
Three Dimensional ◽  
Nucleation Site ◽  
Nucleation And Growth ◽  
Lattice Points ◽  
Growth Time ◽  
Decay Kinetics ◽  
Time Step ◽  
Oxygen Atoms

AbstractA three-dimensional Monte Carlo computer program has been developed to study the heterogeneous nucleation and growth of oxide precipitates during the thermal treatment of crystalline silicon. In the simulations, oxygen atoms move on a lattice with randomly selected lattice points serving as nucleation sites. The change in free energy that the oxygen cluster would experience in gaining or losing one oxygen atom is used to govern growth or dissolution of the cluster. All the oxygen atoms undergo a jump or a growth decision during each time step of the anneal. The growth and decay kinetics of each nucleation site display interesting fluctuation phenomena. The time dependence of the cluster size generally differs from the expected 3/2 power law due to the fluctuations in oxygen arrival at and incorporation in a precipitate. Competition between growing sites and coarsening are observed.

Poly-Si films with low aluminum dopant containing by aluminum-induced crystallization

2010 ◽  
Vol 53 (1) ◽  
pp. 111-115 ◽  
Author(s):  
ChengLong Wang ◽  
DuoWang Fan ◽  
ChengBin Wang ◽  
ZhongRong Geng ◽  
HaiLin Ma ◽  
...  
Keyword(s):  
Si Films ◽  
Induced Crystallization ◽  
Aluminum Induced Crystallization

scholarly journals Pseudo Random Number Generation through Reinforcement Learning and Recurrent Neural Networks

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 307
Author(s):  
Luca Pasqualini ◽  
Maurizio Parton
Keyword(s):  
Reinforcement Learning ◽  
Random Number ◽  
Short Term Memory ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Time Step ◽  
Software Applications ◽  
Pseudo Random Number ◽  
Markov Decision ◽  
Partially Observable

A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate the quality of PRNGs by checking statistical properties of the generated sequences. These sequences are commonly represented bit by bit. This paper proposes a Reinforcement Learning (RL) approach to the task of generating PRNGs from scratch by learning a policy to solve a partially observable Markov Decision Process (MDP), where the full state is the period of the generated sequence, and the observation at each time-step is the last sequence of bits appended to such states. We use Long-Short Term Memory (LSTM) architecture to model the temporal relationship between observations at different time-steps by tasking the LSTM memory with the extraction of significant features of the hidden portion of the MDP’s states. We show that modeling a PRNG with a partially observable MDP and an LSTM architecture largely improves the results of the fully observable feedforward RL approach introduced in previous work.

Sign in / Sign up

Export Citation Format

Share Document