Nucleation and growth theories

Stoyanov S and Kashchiev D 1981 Thin film nucleation and growth theories a confrontation with experiment Current... 

Using this thermodynamic picture, classic nucleation and growth theory was used to describe the phase transformation that occurs in these materials, despite the relatively unique synthesis method that is employed. The governing equation for homogeneous nucleation that describes the change in free energy associated with the formation of a spherical crystalline nucleus in an amorphous host is as follows ... 

B. Lewis, "Nucleation and Growth Theory" in Crystal Growth, BJl. Pamplin, Ed., Pergamon Press, Oxford (1980). 

C.G. Pope, Nucleation and Growth Theory in Zeolite Synthesis. Microporous Mesoporous... 

It is important to recognize that the driving force of the new phase formation will not be the same at different stages of polymer film deposition, neither it will be the same for polymer molecules with different MWs. In order to better understand the situation, let us use the usual approach adopted in nucleation and growth theory and consider formation of a spherical nucleus with a radius r on the surface of a foreign substrate (foreign means there is no specific interaction, like chemical bond formation, between the deposited molecules and the substrate). The work of new phase formation W can be expressed as follows ... 

The details of nucleation and growth theory are given in many standard textbooks on kinetics and phase transformations see the books on interfaces in Chapter 15 and on phase transformations in Chapter 25. 

Journal of Crystal Growth. An international journal that publishes articles that deal with aU aspects of crystal growth, from nucleation and growth theories to apparatus and instrumentation. 

Nucleation and growth theories constitute a very attractive methodology in solid state physics to describe phenomena related to phase transitions. In this view, a new phase is pictured as growing out from a small finite-sized droplet. Typical examples are liquid bubbles formed from a gaseous phase (e.g., rain droplets), gas bubbles forming under close-to-critical liquids (e.g., boiling water), or crystallization in amorphous liquids (e.g., in silica-based semiconductors or organic polymers) [69]. 

Lewis, B. (1980) Nucleation and growth theory. In Crystal Growth, 2nd edn., B.R. Pamplin (ed.), Pergamon Press, Oxford, 23-63. 

Nucleation and growth theory is at the heart of the DP method. For a general introduction to this theory we refer to the literature [15, 16]. In summary, the... 

Three reactions occur when a Ti02-opacified porcelain enamel frit is fired crystallization of anatase, crystalllization of rutile, and inversion of anatase to rutile. The concepts of nucleation and growth theory have been applied to these three reactions to develop an overall kinetic law of transformation which predicts the concentrations of anatase and of rutile as function of the firing conditions. This theoretical development has been found to agree with the results of quantitative X-ray studies. 

Since nucleation and growth theory is phenomenological in nature, the physical reasoning involved in the development of the theory will be emphasized here, and the mathematical details will be discussed elsewhere ). The theory begins with the postulate that in the unfired glass there are a number Nq of potential sites for nucleation, or embryos as they are sometimes called, per unit volume. This postulate was first made by Avrami ( ) around 1940 in treating a different problem. As will be seen, the mathematical formalism follows Avrami in many respects, although the postulates do not. 

For this set of PE-h-PS diblock copolymers, several polymer nucleation and growth theories were applied to overall DSC isothermal crystallization rate data [61, 130,269,270]. These results indicate that the behavior of the PE-6-PS system is complex. Although the Lauritzen-Hoffman theory was developed for describing crystal growth only, it has been employed to describe overall crystallization data since it is capable of fitting the data remarkably well [269]. In these cases, such as when isothermal crystallization kinetics data obtained by DSC is employed, the energy barrier for crystallization reflected in Kg (denoted by us in this case KJ) contains contribution from both primary nucleation and crystal growth. 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

In spite of these obstacles, crystallization does occur and the rate at which it develops can be measured. The following derivation will illustrate how the rates of nucleation and growth combine to give the net rate of crystallization. The theory we shall develop assumes a specific picture of the crystallization process. The assumptions of the model and some comments on their applicability follow ... 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

Before discussing such theories, it is appropriate to refer to features of the reaction rate coefficient, k. As pointed out in Sect. 3, this may be a compound term containing contributions from both nucleation and growth processes. Furthermore, alternative definitions may be possible, illustrated, for example, by reference to the power law a1/n = kt or a = k tn so that k = A exp(-E/RT) or k = n nAn exp(—nE/RT). Measured magnitudes of A and E will depend, therefore, on the form of rate expression used to find k. However, provided k values are expressed in the same units, the magnitude of the measured value of E is relatively insensitive to the particular rate expression used to determine those rate coefficients. In the integral forms of equations listed in Table 5, units are all (time) 1. Alternative definitions of the type... 

Mathematical expressions for the N G model can be derived from the classical theory for the nucleation and growth of two-dimensional hlms [Schmickler, 1996]. Two regimes are distinguished ... 

The hydrogen absorption/desorption kinetics are usually analyzed by applying the JMAK (Johnson-Mehl-Avrami-Kolmogorov) theory of phase transformations, which is based on nucleation and growth events [166-168] where a is the fraction transformed at time t or alternatively for hydrides the fraction absorbed... 

A series of nucleation and growth models was developed by, for example, Bewick et al. (11), Armstrong and Harrison (16), and Scharifker and Hills (17). Amblart et al. (18) have shown that nickel epitaxial growth starts with the formation of three-dimensional epitaxial crystallites. An electrochemical model for the process of electroless metal depositions (mixed-potential theory) was suggested by Paunovic (14) and Saito (14b). 

Solids undergoing martensitic phase transformations are currently a subject of intense interest in mechanics. In spite of recent progress in understanding the absolute stability of elastic phases under applied loads, the presence of metastable configurations remains a major puzzle. In this overview we presented the simplest possible discussion of nucleation and growth phenomena in the framework of the dynamical theory of elastic rods. We argue that the resolution of an apparent nonuniqueness at the continuum level requires "dehomogenization" of the main system of equations and the detailed description of the processes at micro scale. 

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