Nucleation energy relationships

In addition to forming surfaces based on equilibrium energy relationships, nonequilibrium shapes may be determined by the process of nucleation and growth of the material. The nucleation process described in Section 10.6 leads to small islands on the surface. With sufficient atomic mobility these may have surface facets... 

Gibbs considered the change of free energy during homogeneous nucleation, which leads to the classical nucleation theory and to the Gibbs-Tliompson relationship (Mullin, 2001). 

Figures 6.30 and 6.31 present the same information for saturated hydrocarbons. In Figure 6.30, the saturated liquid state is on the lower part of the curve and in Figure 6.31 it is on the upper part of the curve. Below T y, the line width changes, indicating that the liquid probably does not flash below that level. Note that a line has been drawn only to show the relationship between the points a curve reflecting an actual event would be smooth. Note that a liquid has much more energy per unit of volume than a vapor, especially carbon dioxide. Note It is likely that carbon dioxide can flash explosively at a temperature below the superheat limit temperature. This may result from the fact that carbon dioxide crystallizes at ambient pressure and thus provides the required number of nucleation sites to permit explosive vaporization.

Hono et al. [64, 65] confirmed that Cu in both amorphous Fev sSiia.sBgNbsCui and Fe89Zr7B3Cui alloys forms clusters prior to primary crystallization and the Cu clusters act as heterogeneous nucleation sites for bcc-Fe(Si) precipitates. They also confirmed orientation relationships between the Cu clusters and bcc-Fe crystals and concluded that the heterogeneous nucleation of the bcc-Fe phase is due to the lower interfacial free energy for nucleation [66]. 

Thus far, the nucleation equations have been derived with the assumption that the homogeneous interfacial energy, critical cluster size. There is obviously some relationship between surface tension and droplet size, but thus far the theoretical predictions of this relationship and the experimental nucleation data do not seem to be in accord (Walton, 1969). 

In thermodynamic theory of heterogeneous nucleation of solid from vapor,P a nucleus on a substrate is considered to be cap-shaped with a contact angle to the substrate. Young s equation dictates the relationship among the surface and interfacial energies as ... 

The steady two-dimensional diabatic flow is described by the equations for mass, momentum and energy in conservation form (Schnerr and Dohrmann [7], Dohrmann [8]). Real gas effects are not yet included and inviscid fluids are assumed. Here the classical nucleation theory of Volmer [9] is used which gives a good qualitative representation of the behavior of condensing in the supersaturated state (Wegener [iO]). Oswatitsch [11] introduced this theory into the calculation of flow processes, a summary of all basic relationships for compressible flows with heat addition is given by Zierep [12]. To compute the nucleation rate J per unit time and volume, we take... 

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