Abstract
Thermal fluctuations in a low-angle, symmetric tilt boundary composed of a series of dislocations of identical Burgers vectors are studied. At zero temperature the grain boundary is composed of equally spaced, coplanar, straight dislocations. At nonzero temperatures the dislocations are allowed to fluctuate a small distance both in and out of the zero-temperature plane. The energy of a sinusoidal fluctuation is shown to be linear in wave number for oscillations both parallel and perpendicular to the dislocations. These excitations give rise to a decrease in the ¦θ ln ¦θ ∥ term of the grain-boundary free energy, where θ is the angle of misorientation between the two grains, linearly proportional to temperature. The grain boundary considered here, with these fluctuations, is argued to be smooth, not rough.
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