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Surface Motion

The quantity tex2html_wrap_inline1250 is the local area dA as a function of the `tilt' tex2html_wrap_inline1254 of the surface z(x,y). For small slopes, the lowest order terms for additional energy due to the tilt goes like: tex2html_wrap_inline1258 . If motion of the surface requires no long-range diffusion, as in grain and antiphase boundaries or domain walls, then gradient flow in the tex2html_wrap_inline1016 inner product is motion by curvature. The small slope approximation to gradient flow appears in the table above and the exact expression appears below. Motion of an interface by surface diffusion has the proximity effect: gradient flow in the tex2html_wrap_inline1064 inner products gives the Mullins surface diffusion equation[10] (the approximate expression appears in Table I).



W. Craig Carter
Tue Sep 30 16:07:27 EDT 1997