23 research outputs found
Computer simulation of crystallization kinetics with non-Poisson distributed nuclei
The influence of non-uniform distribution of nuclei on crystallization
kinetics of amorphous materials is investigated. This case cannot be described
by the well-known Johnson-Mehl-Avrami (JMA) equation, which is only valid under
the assumption of a spatially homogeneous nucleation probability. The results
of computer simulations of crystallization kinetics with nuclei distributed
according to a cluster and a hardcore distribution are compared with JMA
kinetics. The effects of the different distributions on the so-called Avrami
exponent are shown. Furthermore, we calculate the small-angle scattering
curves of the simulated structures which can be used to distinguish
experimentally between the three nucleation models under consideration.Comment: 14 pages including 7 postscript figures, uses epsf.sty and
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Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Gránásy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Gránásy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystalline solidification obtained using an atomistic phase-field model
Kolmogorov–Johnson–Mehl–Avrami kinetics for non-isothermal phase transformations ruled by diffusional growth
Abstract We report on the functional form of the rate of
the transformed volume fraction in non-isothermal phase
transitions occurring by nucleation and diffusional growth.
The microscopic growth rate is computed by solving the
diffusion problem for time-dependent diffusion coefficient.
The growth law is further employed in the Kolmogorov–
Johnson–Mehl–Avrami (KJMA) theory for describing the
time dependence of the transformed volume at constant
heating rate. It is demonstrated that the transformation rate
separates in the product of volume fraction and actual
temperature functions. In the framework of the KJMA
approach this factorization is exact. It is also shown that for
real systems (due to the high values of the reduced activation
energies for nucleation and growth), the kinetics is
in excellent agreement with the stretched exponential
function appropriate for isothermal transformations