Binding Energies in the Growth of Crystal Nuclei from Metallic Atoms

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Abstract
First order perturbation theory has been employed to compute the binding energies of various geometrical configurations of three to eight atoms of sodium. It has been assumed that in the metal lattice the binding is essentially homopolar. It has been shown that the growth of a unit cell probably proceeds via the diatomic molecule to a square, a fifth atom adding along a cube edge, a sixth at the body center and the cell completed by location of atoms at the remaining cube corners. The unit cell is still a very unstable unit, a result in agreement with high vapor pressures and solubility of finely divided particles, and with the concept of active centers on reaction surfaces. The fifth order secular equation employed to determine the energies of configurations of five and six atoms has been made more amenable to use in calculations. A fourteenth order secular equation, with similar characteristics, has been employed for the cases of seven and eight atoms. Approximate calculations with copper atoms instead of sodium give similar results but indicate that higher activation energies of nuclei formation may obtain in this case. The percentage of the total binding assigned to interchange is shown to be an important factor. The calculations indicate that the net effect of interchange forces in homopolar crystals is to increase the potential energy. The crystal structure is stable only because of the coulombic and van der Waals' forces. When applied to hydrogen (90 percent interchange) it is shown that a metallic lattice is utterly unstable.