Time-evolution of grain size distributions in random nucleation and growth crystallization processes

  title={Time-evolution of grain size distributions in random nucleation and growth crystallization processes},
  author={Anthony V Teran and Ralf B. Bergmann and Andreas Bill},
  journal={Physical Review B},
We study the time dependence of the grain size distribution $N(\mathbf{r},t)$ during crystallization of a $d$-dimensional solid. A partial differential equation, including a source term for nuclei and a growth law for grains, is solved analytically for any dimension $d$. We discuss solutions obtained for processes described by the Kolmogorov-Avrami-Mehl-Johnson model for random nucleation and growth (RNG). Nucleation and growth are set on the same footing, which leads to a time-dependent decay… 

Figures and Tables from this paper

Nonequilibrium grain size distribution with generalized growth and nucleation rates
We determine the non-equilibrium grain size distribution during the crystallization of a solid in $d$ dimensions at fixed thermodynamic conditions, for the random nucleation and growth model, and in
Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid
We 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
Simulation of phase transformation kinetics in thin films under a constant nucleation rate
Abstract The classic framework of Johnson-Mehl-Avrami-Kolmogorov (JMAK) has been commonly used in studies of thin film phase transformation kinetics despite its inherent limitation to transformations
The Grain Size Distribution in Crystallization Processes With Anisotropic Growth Rate
The grain size distribution allows characterizing quantitatively the microstructure at different stages of crystallization of an amorphous solid. We propose a generalization of the theory we
Kinetics of phase transformations with heterogeneous correlated-nucleation
We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation
Kinetics of dissolution-precipitation reaction at the surface of small particles: modelling and application
  • M. Tomellini
  • Materials Science
    Journal of Materials Science
  • 2011
In the framework of the theory of phase transformations with position-dependent nucleation rate, a model has been developed aimed at describing the dissolution-precipitation reaction at the surface
Pleomorphism and multidirectional combination of Si crystal nucleation during solidification
Research on the structural properties of silicon crystal nucleation during solidification has been the subject of numerous classic studies in condensed matter physics and material science. The
A revisited Johnson–Mehl–Avrami–Kolmogorov model and the evolution of grain-size distributions in steel
The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For
Nucleation of silicon nanocrystals in a remote plasma without subsequent coagulation
We report on the growth mechanism of spherical silicon nanocrystals in a remote expanding Ar plasma using a time-modulated SiH4 gas injection in the microsecond time range. Under identical
Thin film phase transformation kinetics: From theory to experiment
Abstract The Level-set method simulation is used to address the effect of finite size on kinetics of thin film phase transformations. The results are first interpreted using the classic


Evaluation of time-dependent grain-size populations for nucleation and growth kinetics.
  • Crespo, Pradell
  • Materials Science, Medicine
    Physical review. B, Condensed matter
  • 1996
A statistical mean-field model is presented for a completely degenerated system, based on the same assumptions as the Kolmogorov-Johnson-Johnson (KJMA) model, that is to say, randomly distributed active nucleation sites which grow isotropically and collision resulting in a growth stop at the interface.
Numerical model of solid phase transformations governed by nucleation and growth : Microstructure development during isothermal crystallization
A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal
Nucleation and growth in one dimension.
  • Ben-Naim, Krapivsky
  • Mathematics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
The Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model is studied in one dimension and it is shown that the system reaches complete coverage in a finite time and that the near-critical behavior of the system is robust.
Modeling of Growth and Impingement of Spherical Grains
A model was developed to simulate the growth and impingement of spherical grains, which are frequently encountered in the solidification, recrystallization and other processes in association with
Stochastic modeling of nucleation and growth in a thin layer between two interfaces
Abstract A stochastic modeling method is presented for the analysis of nucleation and growth in a thin layer between two interfaces. In this layer, nucleation occurs randomly and growth stops at the
Pattern formation by growing droplets: The touch-and-stop model of growth
We investigate a novel model of pattern formation phenomena. In this model spherical droplets are nucleated on a substrate and grow at constant velocity; when two droplets touch each other they stop
Scaling relations for grain autocorrelation functions during nucleation and growth.
  • Axe, Yamada
  • Physics, Medicine
    Physical review. B, Condensed matter
  • 1986
It is found that while such scaling relations are no longer exact in late stages of growth, they continue to provide accurate simple approximations.
Direct measurement of the free-energy barrier to nucleation from the size distribution of dendritic crystallites in a-Si thin films.
  • Kumomi, Shi
  • Materials Science, Medicine
    Physical review. B, Condensed matter
  • 1995
A model-independent method is developed based on the dynamic scaling of the cluster size distribution and other universal kinetics in the early stages of nucleation and growth to determine the free-energy barrier to nucleation of the amorphous-to-crystalline transformation in a-Si thin films.
Nucleation in the pre-coalescence stages: universal kinetic laws
Abstract This article is devoted to a detailed summary of recent results on the dynamic scaling of the cluster size distribution (CSD) and other universal kinetic laws in the pre-coalescence stages
On the origin of logarithmic-normal distributions: An analytical derivation, and its application to nucleation and growth processes
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributions in nature and describes a large number of physical, biological and even sociological phenomena.