. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography a. EQUILIBRIUM b. GROWTH Fig. 7. The generation and growth of a step in a face by the emergence of a screw dislocation. tion probability per unit time, the equivalent of the desorption constant used by Hobbs and Scott; it is the reciprocal of the residence time t. Thus, from Eq. (5), KD = 1/V = Ds/xs-, and the solu- tion to Eq. (19) is tcosh(.v/.vs) " 1 , (20) cosh(.v0)J which assumes that the outer boundaries are growing steps which act a
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography a. EQUILIBRIUM b. GROWTH Fig. 7. The generation and growth of a step in a face by the emergence of a screw dislocation. tion probability per unit time, the equivalent of the desorption constant used by Hobbs and Scott; it is the reciprocal of the residence time t. Thus, from Eq. (5), KD = 1/V = Ds/xs-, and the solu- tion to Eq. (19) is tcosh(.v/.vs) " 1 , (20) cosh(.v0)J which assumes that the outer boundaries are growing steps which act as infinitely good sinks for excess ad- molecules, , 5«(±x0/2)=0. Molecules diffuse to each step of height h, enter the step, and provide for its advance at a rate v given by »«(2Q/h)xap8F tanh(.r0), (21) an expression which cares for the case of a limited fetch. Note that this expression degenerates to the simplified equation given by Hallett (1961) and by Hobbs and Scott when .rs<$Cxo. In general, however, each step will have neighboring steps which compete for the supply of adsorbed molecules so that the full expression [Eq. (21)] is necessary. b. Step sources The development leading to Eq. (21) gives an idea of how steps interact on a surface characterized by. the parameter .v,, provided that the steps exist in the first place. Remember that, without a continual source of steps somewhere on the surface, steps will simply advance to the crystal edge and disappear, stopping further growth. This means that, since regeneration of steps by two-dimensional nucleation, with ensuent growth, is energetically improbable at the low super- saturations normally present during growth, a mecha- nism other than two-dimensional nucleation must be responsible for the growth which is observed (Cabrera and Burton, 1949). The most likely mechanism is that first proposed by Frank (1949) and based upon the emergence of screw dislocations at the surface. This spiral step mechanism d
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