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Register a new userHydrodynamic theory of freezing: Nucleation and polycrystalline growth
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Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Toth et al., J. Phys.: Condens. Matter 26, 055001 (2014)], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.
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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 (Granasy 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 Granasy 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 polycrystal-line solidification obtained using an atomistic phase-field model.
The nucleation and growth of CdS nanoparticles within a polymer matrix was followed by in-situ synchrotron X-ray diffraction. The nanoparticles form by effect of the thermolysis of thiolate precursors at temperatures between 200 and 300 Celsius degrees. Above 240 Celsius degrees the precursor decomposition is complete and CdS nanoparticles grow in the polymer matrix forming a nanocomposite with interesting optical properties. The nanoparticle structural properties (size and crystal structure) depend on the annealing temperature.(abridged version)
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 absence of grain coalescence. Two distinct generalizations of the theory established earlier are considered. A closed analytic expression of the grain size distribution useful for experimental studies is derived for anisotropic growth rates. The main difference from the isotropic growth case is the appearance of a constant prefactor in the distribution. The second generalization considers a Gaussian source term: nuclei are stable when their volume is within a finite range determined by the thermodynamics of the crystallization process. The numerical results show that this generalization does not change the qualitative picture of our previous study. The generalization only affects quantitatively the early stage of crystallization, when nucleation is dominant. The remarkable result of these major generalizations is that the non-equilibrium grain size distribution is robust against anisotropic growth of grains and fluctuations of nuclei sizes.
In this paper the relationship between the density functional theory of freezing and phase field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase field crystal modeling and standard models of binary alloys (i.e., regular solution model). To demonstrate the properties of the phase field crystal formalism a simple model of binary alloy crystallization is derived and shown to simultaneously model solidification, phase segregation, grain growth, elastic and plastic deformations in anisotropic systems with multiple crystal orientations on diffusive time scales.
We investigated the homogenous nucleation of the stoichiometric B2 and B33 phases in the Ni50Zr50 alloy using the persistent embryo method and the classical nucleation theory. The two phases become very close competitors at large supercoolings, which is consistent with the experimental observations. In the case of the B2 phase, the linear temperature dependence of the solid-liquid interface (SLI) free energy extrapolated to the melting temperature leads to the same value as the one obtained from the capillarity fluctuation method (CFM). In the case of the B33 phases, the SLI free energy is also a linear function of temperature at large supercoolings but the extrapolation to the melting temperature leads to a value which is considerably different from the CFM value. This is consistent with the large anisotropy of the SLI properties of the B33 phase nearby the melting temperature observed in the simulation of the nominally flat interface migration.
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