Thermodynamics of Nucleation and Interfaces

let us consider an epitaxial layer of a few monolayer thickness on a substrate with 2 diameter. The volume of such a layer is in the order of 10 cm, corresponding to a mole number in the order of 10. The interface area amounts to a few 10 m. Thus, the volume contribution is in the order of a few tens or hundreds of Joule, and the interface energy is about four orders of magnitude lower. 

For an isothermal, isobaric system of unchanging size and composition, ydA = w is the reversible work required to incrementally create additional surface. The energy of a surface can be altered by a change in either y or A. Changes in the 

Interface energies are of importance when a new phase is emerging. In crystal-growth practice one is predominantly concerned with heterogeneous nucle-ation because commonly a substrate or a seed crystal is required in order to force the growth in a specified crystallographic direction and to lower the supersaturation required for crystallization to occur. 

When a nucleus of a crystalline film F is formed from atoms leaving a nutrient phase N and depositing onto a substrate S, volume of F and two new interfaces, those between the film and the nutrient and the film and the substrate, are formed, while the area of another one, that between the substrate and the nutrient, diminishes. Consequently, the associated total change in free energy is given by 

The superscripts refer to the different interfaces, r is a mean dimension, and the a s are factors accounting for the nucleus geometry. Assuming the nucleus shape to be a spherical cap with the curved surface area Oi r, the projected circular area a2 on the substrate and the volume a3t, these factors are a = j 2— 3cos0 + cos 0), i = 27t(l — cos 0), and U2 = n sin 0, and 0 is the contact or wetting angle. 

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