Crystal surface energy

The amount of enthalpy per mole associated with the finite crystal surface energy (a) reduces the equilibrium enthalpy for the infinite crystal (AHq). Thus, from... 

Approaches used for crystallization in homopolymers may be used to calculate the change in melting temperature due to finite crystal thickness (Thompson-Gibbs equation), lamellar crystal surface energies (Flory-Vrij theory), and growth rates (kinetic nucleation theory). Details can be obtained from [1]. 

The immobility of the surface atoms of a refractory solid has the consequence that the surface energy and other physical properties depend greatly on the immediate history of the material. A clean cleavage surface of a crystal will have a different (and probably lower) surface energy than a ground, abraded, heat-treated or polished surface of the same material. 

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. 

The uncertainties in choice of potential function and in how to approximate the surface distortion contribution combine to make the calculated surface energies of ionic crystals rather uncertain. Some results are given in Table VII-2, but comparison between the various references cited will yield major discrepancies. Experimental verification is difficult (see Section VII-5). Qualitatively, one expects the surface energy of a solid to be distinctly higher than the surface tension of the liquid and, for example, the value of 212 ergs/cm for (100)... 

Factors Affecting the Surface Energies and Surface Tensions of Actual Crystals... 

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

Calculate the surface energy at 0 K of (100) planes of radon, given that its energy of vaporization is 35 x 10 erg/atom and that the crystal radius of the radon atom is 2.5 A. The crystal structure may be taken to be the same as for other rare gases. You may draw on the results of calculations for other rare gases. 

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. 

Microcrystals of SrS04 of 30 A diameter have a solubility product at 25°C which is 6.4 times that for large crystals. Calculate the surface tension of the SrS04-H20 interface. Equating surface tension and surface energy, calculate the increase in heat of solution of this SrS04 powder in joules per mole. 

Ichimiya A, Ohno Y and Horio Y 1997 Structural analysis of crystal surfaces by reflection high energy electron diffraction Surf. Rev. Left 4 501-11... 

Feibelman P J 1987 Force and total-energy calculations for a spatially compact adsorbate on an extended, metallic crystal surface Phys. Rev. B 35 2626... 

Mag., 25(1), 131 (1972)] conclude that these measurements are valid when 50 percent corrections are added for the bending energy of the crystal. Kuznetzov ranks other materials by a relative wear test. His results substantiate the efficiencies given earlier. Attempts to measure efficiency of the grinding process by calorimetiy involve errors that exceed the theoretical surface energy of the material being ground. 

The approximate calculation of the surface energies of metals as a function of crystal structure described earlier uses the enthalpy of sublimation, s, and the co-ordination number to calculate the energy as a function of the atomic concentration on the surface. The atomic areas of the principal configurations are as follows ... 

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