A relation between the surface energy and the Debye temperature for cubic solids
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It is shown that a phenomenological relation exists between the Debye temperature 6 (in degree Kelvin) and the surface energy T (in ergs/cm2) of cubic solids: 6 = 71.9V(I/M), where M is the atomic weight. This relation is derived theoretically in the Debye isotropic approximation by assuming that the interatomic potential is central. No restrictions are imposed on the range of the potential. The relation is obeyed very well by the observed values of 6 and T in the case of many solids. I. INTRODUCTION
In this paper we have derived a phenomenological relation between the surface energy and the Debye temperature for cubic solids. We find that this relation is obeyed very well by the observed values for many cubic solids. The relation is interesting because it shows a correlation between two apparently different macroscopic parameters of solids at a microscopic level. The surface energy of a solid is related to the total interaction energy of an atom in the solid which is determined by the interatomic potential. On the other hand, the Debye temperature of a solid is related to the interatomic force constants. We show that the two can be related by using the Fourier representation of the interatomic potential and its derivatives. In our derivation, we have assumed the interatomic potential to be central but have not imposed any restriction on the range of the potential. We have assumed a rather simple and crude model for our calculations. We relate the surface energy of a solid to the bond strength of the atoms in the solid in a manner which is similar to calculation of the cohesive energy. Indeed, the cohesive energy of a solid is related to its surface energy through a numerical factor. We have neglected the contribution of the solid state effect, such as surface relaxation, electronic structure of the solid surface, and details of the lattice structure and anisotropy. In our model, all the solid state effects are contained in a single parameter, namely, the Debye temperature. Our relation is, therefore, a phenomenological relation for solids which ignores the finer contributions to the surface energy. However, in spite of the various crude approximations, we obtain a relation between the surface energy and the Debye temperature which is obeyed quite well by many cubic solids.
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attachment from The Ohio State University, Columbus, Ohio. Current address: Materials Reliability Division, National Institute of Standards & Technology, Boulder, Colorado 80303.
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Different phenomenological relations between the surface energy and other parameters of solids have been derived earlier by Gilman1 and Miedema and Dorleign2 (see also Ref. 3). Gilman's relation shows that the surface energy of a solid is proportional to its Young's modulus. We find that the surface energy of a solid is proportional to the square of its Debye temperature. This is consistent with Gilman's relation since the Debye temperature of a solid is proportional to the square root of its Young's modulus. Our relation is
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