Surface Evolution by Vapor Transport

Vapor transport differs from surface diffusional transport, where the flux is always in the surface plane. For both surface diffusion and vapor transport, the diffusion potential at the surface is proportional to the local value of 7sk if the surface free energy is isotropic. For surface diffusion, the interface normal velocity is related to a derivative (i.e., the divergence of the flux). Also, the total volume is conserved during surface diffusion. For vapor transport, the interface normal velocity is directly proportional to the vapor flux, and the total number of atoms is not necessarily conserved. 

Crystal growth from the vapor phase has been treated in Chapter 12. An expression for the net atom flux, Jv, gained at a macroscopically flat crystal surface during growth from the vapor has been obtained in Exercise 12.2 in the form of Eq. 12.27. To treat surfaces possessing nonuniform curvature, this relationship can be generalized in the form 

The first-order expansion employed will be valid under all usual conditions. 

The normal growth velocity of a local region of the surface with curvature k can then be found by using Eqs. 14.14 and 14.15  

In the common situation where the surface contains undulations but is macroscop-ically flat, Pamb will be well approximated by Peq(n = 0), so that 

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