Nucleation, growth and

Two mechanisms of phase separation are nucleation and growth and spin-odal decomposition. The theory of spinodal decomposition was developed by Cahn and HilUard [71]. In the region of the phase diagram inside the spinodal, phase separation leads to the formation of microregions with compositions that deviate from the system composition by a very small amount. 

Morphological data showing that IPNs are highly heterogeneous structures allowed Sperling et aL [72-74] to propose the mechanism of IPN formation called nucleation and growth. A thermodynamic theory of IPN morphology has been developed in [74]. Its main assiunption is that there are two separate states of polymer I and polymer II separated one from another. In state 2, the 

Sperling has studied theoretical conditions for the formation of domains in sequential IPNs using cross-linking degree for each network, as well as thermodynamics of mixing and interfacial tension for sequential IPNs, where separation occurs by the nucleation mechanism. The derivation of the basic equation for IPN domain diameters is based on a physical model of sequential IPNs, according to which polymer II, which is formed in a swollen network I, constitutes a spherical core and is in a contracted (deformed) state, while polymer I surrounds the core and is in an expanded (deformed) state. 

Several assumptions were made for this derivation (1) a thermodynamic equilibrium process exists throughout the development of the domain formation (2) the domains are spheres with identical diameters (3) the polymer networks obey Gaussian statistics and (4) a sharp interfacial boundary exists between the two phases (we have to note that the validity of these assumptions is rather questionable). The authors present the process of domain formation in the following way (Fig. 6) [75]. 

Initially, in state 1, network I is completely separated from monomer II. In state 2, the polymer network is swollen with the monomer mixture II. The path from state 1 to state 2 is accompanied by the mixing of polymer I and 

We have already used at several places in this chapter, the notion of nucleation and growth. We discuss this extremely important concept in some more detail here. When a melt - which for simplicity is of a single component glass-forming material - is cooled below its melting point slowly, it crystallizes at an undercooling equal to T -Tct) T. The crystallization involves two processes - one, the nucleation and the other, the growth of the crystals. Nucleation is the step in which, by virtue of thermal fluctuations alone the constituent particles order spontaneously into a tiny units called embryo. These embryos redissolve spontaneously 

Once again the net change in the total energy w during the formation of the nuclei would be 

We also note that at the edge of the nuclei the equalization of forces requires that 

Upon substitution of this condition into the expression for w, one can calculate the value of Wmax by differentiating the expression with respect to r as before. In fact rc can be found to be equal to AGy, which is the same as that for homogeneous nucleation. However, Wmax for heterogeneous nucleation Wmax hetero) works out to be, 

AGv is given by, AGy = A// - TAS. Under conditions of constant pressure, and only slightly below the melting point, we can assume that A// and AS to be temperature independent so that d AG)l6.T = - AS. This can be integrated from to Ter (temperature of crystallization) so that 

Conventional electrodeposition from solutions at ambient conditions results typically in the formation of low-grade product with respect to crystallinity, that is, layers with small particle size, largely because it is a low-temperature technique thereby minimizing grain growth. In most cases, the fabricated films are polycrystalline with a grain size typically between 10 and 1,000 nm. The extensive grain boundary networks in such polycrystalline materials may be detrimental to applications for instance, in semiconductor materials they increase resistivity 

---

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. 

The following two sections will focus on epitaxial growth from a surface science perspective with the aim of revealing the fundamentals of tliin-film growth. As will be discussed below, surface science studies of thin-film deposition have contributed greatly to an atomic-level understanding of nucleation and growth. 

Lewis B and Anderson J C 1978 Nucleation and Growth of Thin Films (New York Academic)... 

Venables J A, Spiller G D T and Hanbucken M 1984 Nucleation and growth of thin-films Rep. Prog. Phys. 47 399... 

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

Kortan A R, Hull R and Opila R L 1990 Nucleation and growth of CdSe on ZnS quantum orystallite seeds and vise versa in inverse mioelle media J. Am. Chem. Soc. 112 1327... 

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 ... 

The development of the principles of nucleation and growth eady in the twentieth century (2) ultimately led to the discovery that certain nucleating agents can induce a glass to crystallize with a fine-grained, highly uniform microstmcture that offers unique physical properties (3). The first commercial glass-ceramic products were missile nose cones and cookware. 

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... 

Gas AntisolventRecrystallizations. A limitation to the RESS process can be the low solubihty in the supercritical fluid. This is especially evident in polymer—supercritical fluid systems. In a novel process, sometimes termed gas antisolvent (GAS), a compressed fluid such as CO2 can be rapidly added to a solution of a crystalline soHd dissolved in an organic solvent (114). Carbon dioxide and most organic solvents exhibit full miscibility, whereas in this case the soHd solutes had limited solubihty in CO2. Thus, CO2 acts as an antisolvent to precipitate soHd crystals. Using C02 s adjustable solvent strength, the particle size and size distribution of final crystals may be finely controlled. Examples of GAS studies include the formation of monodisperse particles (<1 fiva) of a difficult-to-comminute explosive (114) recrystallization of -carotene and acetaminophen (86) salt nucleation and growth in supercritical water (115) and a study of the molecular thermodynamics of the GAS crystallization process (21). 

Crystal Morphology. Size, shape, color, and impurities are dependent on the conditions of synthesis (14—17). Lower temperatures favor dark colored, less pure crystals higher temperatures promote paler, purer crystals. Low pressures (5 GPa) and temperatures favor the development of cube faces, whereas higher pressures and temperatures produce octahedral faces. Nucleation and growth rates increase rapidly as the process pressure is raised above the diamond—graphite equiUbrium pressure. 

Precipitatioa (2,13—17) techniques employ a combination of nucleation and growth iaduced by adding a chemical precipitant, or by changing the temperature and/or pressure of the solution. Chemical homogeneity is controlled by controlling the rate of precipitation. FFeterogeneous precipitation iavolves the precipitation of a soHd of different composition from the solution, and the composition of the precipitate may change as precipitation continues. Coprecipitation iavolves the simultaneous precipitation of similar size cations ia a salt as a soHd solutioa. 

Sol-Gel Techniques. Sol-gel powders (2,13,15,17) are produced as a suspension or sol of coUoidal particles or polymer molecules mixed with a Hquid that polymerizes to form a gel (see Colloids SoL-GELtechnology). Typically, formation of a sol is foUowed by hydrolysis, polymerization, nucleation, and growth. Drying, low temperature calciaation, and light milling are subsequently required to produce a powder. Sol-gel synthesis yields fine, reactive, pseudo-crystalline powders that can be siatered at temperatures hundreds of degrees below conventionally prepared, crystalline powders. 

Formation. CoUoid formation involves either nucleation and growth phenomena or subdivision processes (6,21,24—29). The former case... 

Along with operating variables of the crystallizer, nucleation and growth determine such crystal characteristics as size distribution, purity, and shape or habit. 

---