 
Summary: Grooving of a grain boundary by evaporationcondensation below
the roughening transition
H. A. Stonea
and M. J. Aziz
Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
D. Margetis
Department of Mathematics, Massachusetts Institute of Technology (MIT), Cambridge,
Massachusetts 01239
Received 23 September 2004; accepted 4 April 2005; published online 6 June 2005
The development of surface grooves at grain boundaries that intersect a planar surface is analyzed
for the case that the evolution occurs below the thermodynamic roughening transition by
evaporationcondensation processes. The dynamics are described by a nonlinear partial differential
equation that has a similarity solution, so the resulting groove profile is described by a nonlinear
ordinary differential equation. An approximate analytical solution to the nonlinear problem is
obtained and is in excellent agreement with the numerical solution. The depth and width of the
groove varies as t1/2
, where t is time, analogous to the classical results valid above the
thermodynamic roughening temperature. In addition, the approximate analytical solution provides
an explicit relation between the groove width and the dihedral angle, and is in sufficiently good
agreement with the numerical results as to make such numerical solutions unnecessary for this
