Interfacial energy crystal-liquid

S, entropy of fusion per volume OsL interfacial energy for liquid-crystal interface... 

Suppose that a spherical nucleus with radius r is present in the liquid. We consider the difference in free enthalpy, AG, between this crystal and an equally large fluid sphere. AG is composed of two components, namely A, the decrease of free enthalpy upon crystallization, and B, the increase in free enthalpy as a result of the formation of the interface. When AGV is the difference in free enthalpy per unit volume between crystal and liquid, and yis the interfacial energy, then ... 

Here y and Sj are the specific free surface energies (- surface energy) and the surface areas of the crystal faces, which contact only the solution y and are the specific free interfacial energies and the surface areas of the faces which contact the foreign substrate and ys is the substrate specific free surface energy (the quantities ys, y, and y2 correspond to yi2, yo, and y23 from -> Equilibrium form of crystals and droplets -> liquid droplets). Substituting the difference y - ys for y - according to the rule of Dupre (- Dupre equation) [ii] one obtains... 

The natural first question to ask is whether the crystal-liquid surface free energy can be measured experimentally by some method that is independent of nucleation kinetics. In gas-liquid nucleation studies, for example, it is routine to measure the surface tension of the liquid and to use its equality with the gas-liquid surface free energy to make predictions of nucleation rates and compare them with experiment. For the liquid-solid transition, the situation is quite different, however. This is true first because the surface tension and the surface free energy are no longer strictly equal due to the possible existence of strains in the crystal. The second reason is that measurements of liquid-solid free energies or interfacial tensions are by no means simple to devise or carry out, and so are available only in certain special cases. These limited experimental data are summarized in this section. 

One of the first and most extensively applied models for the liquid-solid interfacial free energy is that due to Skapski. His approach begins with the assumption that a liquid will wet its crystal, so the contact angle 6 in the three-phase equilibrium between crystal, liquid, and vapor is 0. (This corresponds in Fig. 1 to the replacement of the substrate with the solid, the solid with the liquid, and the liquid with the vapor.) The analog of Eq. (2.15) then has 0 = 0 and cos 0 = 1, so that the result is... 

Where J is the number of nuclei formed per unit time per unit volume Nq is the number of molecules of the crystallizing phase in a unit volume v is the frequency of atomic or molecular transport at the nucleus—liquid interface u is the molecular volume of the crystallizing solute /ig is the interfacial energy per... 

A low nucleation rate. This can be accomplished by having either a small ASf or a large crystal/liquid interfacial energy. The lower ASf and/or the higher 7si, the higher AG. and consequently the more difficult the nucleation. 

Figure 9.4. Schematic showing the variation of interfacial energy in AI2O3 with or without a liquid phase. The interfacial energy represents Kss(Kb) or (ys/ + Ksj/) of a two-dimensional AI2O3 crystal depending on the orientation in 360° (similar to the y-plot of a crystal).

This effect may be understood in terms of the concept of critical nucleus size for growth of crystals. Consider a small particle of material of diameter D immersed in another medium as shown in Fig. 10.23(a). If the particle is a droplet of liquid sitting in another liquid, such that an interfacial energy y exists between the two liquids, then the particle has an excess surface energy which causes a pressure excess 4y/D inside the particle according to Laplace s equation. 

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