A comparison of theoretical and experimental profiles for thermally-induced grain-boundary grooving

Michigan State University, Materials Science and Mechanics Department, East Lansing, MI 48824, USA

Corresponding author: casee@egr.msu.edu

Received: 24 June 1999
Revised: 16 September 1999
Accepted: 20 September 1999
Published online: 15 December 1999

Abstract

Thermally-induced grain boundary grooving has typically been characterized experimentally by either (1) optical interferometry (OI) or (2) reference line (RL) technique. For the OI technique, groove angle and groove width are reported and for the RL technique, groove angle, width and depth are reported. Even recent Atomic Force Microscope (AFM) studies of grain boundary grooving report their results in terms of groove angle, width, and depth exclusively. These measurements have been interpreted in terms of Mullins' 1957 theory on grain boundary grooving, which includes a derivation of the grain boundary groove profile. However, analyzing the groove depth, width, and angle uses only a small fraction of the groove profile information provided by Mullins' theory. In contrast to the literature, this study uses AFM data from thermal grooving in polycrystalline alumina to make a detailed comparison between Mullins' equation (and a modified form of Mullins' equation) for the entire groove profile rather than just the groove width or groove angle, thus providing a more rigorous and comprehensive test of theory. In addition, despite the wider and deeper grooves produced by microwave annealing, the modified form of Mullins' equation fits well both the microwave and conventionally annealed groove profiles.