Energy Relations of the Surface of Solids I. Surface Energy of the Diamond

Abstract

From the known structure of the diamond the total surface energy of the crystal has been calculated in terms of the energy of the carbon-carbon bond, and is found to be: 1.50×10−9EB erg cm−2 for the 111 face, and 2.10×10−9EB erg cm−2 for the 100 face, where EB is the energy in ergs per bond. If the bond energy is assumed to be 90 kcal. mole−1 the values become 5650 erg cm−2 for the 111 face, and 9820 erg cm−2 for the 100 face. The corresponding free surface energies are found to be: 111 face at 25°=5400 erg cm−2 100 face at 25°=9400 erg cm−2. One uncertain feature in the calculation is that involved in the calculation of the decrease in energy caused by the long range binding of the valence bonds in the surfaces. In the 111 face the bonds are 2.517A apart, and are perpendicular to the surface. Thus the bond directions are parallel, while inside the diamond the carbon-carbon distance is only 1.54A, and the bonds meet head on. While in the 111 face there is only one bond per carbon atom, in the 100 face there are two bonds per atom. In the 111 face there are 1.825×1015 bonds per sq. cm−2, with an area of 5.48A2 each, while in the 100 face the corresponding values are 3.158×1015 bonds per cm2 and 3.167A2 per bond. It is concluded that in the 111 face the interaction energy of the type described above is less than one percent and is negligible. Even in the 100 face the interaction should be small. No account was taken of any adjustment of the energy of the unsevered bonds in the surface region. This should cause a greater decrease of energy than the long range binding of the severed bonds. Thus the values of the surface energy calculated in this paper should be considered as maximum values.