Nucleated development

A comparison of conventional, Lith and nucleated development is shown in Figure 15. 

Figure 15. A diagrammatic comparison of non-Lith development, conventional Lith development, and nucleated development.

The thermal dehyi-ation of Na2C03.H20 between 336 and 400 K fits the Avrami-Erofeev equation with = 2 (E, = 71.5 kJ mol and., 4 = 2.2 x 10 s [110]). The apparent reduction in rate resulting from an increase of /r(H20) is ascribed to competition from the rehydration reaction. Electron micrographs confirm the nucleation and growth mechanism indicated by the kinetic behaviour, nucleation develops from circular defects that may be occluded solution. 

Molecular clusters are formed due to weakly attractive forces between molecules, the Van der Waals forces. Except under conditions of low temperature, it is difficult to observe and study in the laboratory clusters containing more than a few molecules, so that details about their properties are sparse. Our understanding of the nucleation process consequently relies mainly on theoretical concepts based largely on the principles of statistical mechanics. The theory of homogeneous nucleation developed by Volmer and Weber (1926), Flood (1934), Becker and Doering (1935), and Reiss (1950) assumes that certain thermodynamic properties, such as the molar volume or the surface tension, that can be determined for bulk material... 

The iodine chemistry model INSPECT and the aerosols/chemistry code VICTORIA have been inserted recently. We expect that ESTER-VICTORIA, because it is tightly coupled to the thermalhydraulics, will be easier to run than the old stand-alone version and, in some laboratories at least, may become the standard version. At this stage once the necessary drivers have been developed and tested it should be possible to calculate an entire Phebus test, from bundle to containment and ESTER will be the only European code able to do so. The JRC may then insert models for chemical kinetics and for nucleation developed under SCA, and possibly a special-purpose model for the difficult zone just above the bundle in Phebus. 

The readers who are already acquainted with Chapter 2.1.2 should have a fairly good idea of the physical significance of equation (2.80). However, in the early seventies the exact meaning of this expression was still obscure. Though, one thing was clear an atomistic expression for the stationaiy nucleation rate could be obtained in any particular case of phase formation if the frequencies 6>+ and o). were presented as functions of the supersaturation A/i. The first result ofthis finding was the atomistic theory of electrochemical nucleation developed by Milchev, Stoyanov and Kaischew in 1974 [2.10-2.12] (see also [2.5, 2.62-2.65]). The next Section presents the basic theoretical results obtained by these authors. 

The entropically driven disorder-order transition in hard-sphere fluids was originally discovered in computer simulations [58, 59]. The development of colloidal suspensions behaving as hard spheres (i.e., having negligible Hamaker constants, see Section VI-3) provided the means to experimentally verify the transition. Experimental data on the nucleation of hard-sphere colloidal crystals [60] allows one to extract the hard-sphere solid-liquid interfacial tension, 7 = 0.55 0.02k T/o, where a is the hard-sphere diameter [61]. This value agrees well with that found from density functional theory, 7 = 0.6 0.02k r/a 2 [21] (Section IX-2A). 

The visible crystals that develop during a crystallization procedure are built up as a result of growth either on nuclei of the material itself or surfaces of foreign material serving the same purpose. Neglecting for the moment the matter of impurities, nucleation theory provides an explanation for certain qualitative observations in the case of solutions. 

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, < 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. 

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 ... 

They possess spherical symmetry around a center of nucleation. This symmetry projects a perfectly circular cross section if the development of the spherulite is not stopped by contact with another expanding spherulite. 

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. 

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. 

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