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Advances in Materials Science and Engineering
Volume 2012 (2012), Article ID 520967, 5 pages
http://dx.doi.org/10.1155/2012/520967
Research Article

Integral Solution of the Interface Profile of Grain Boundary Grooving by Surface Diffusion

1Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
2Shaanxi Key Laboratory for Condensed Matter Structure and Properties, Northwestern Polytechnical University, Xi'an 710072, China
3Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 23 June 2012; Revised 14 October 2012; Accepted 15 October 2012

Academic Editor: Pavel Lejcek

Copyright © 2012 Caifang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In polycrystalline thin films, formation of grain boundary grooving is investigated widely due to its effects on their properties. Infinite series solution of the interface of grain-boundary grooving by surface diffusion has been obtained. In this paper, with Fourier transform, a novel integral solution of the profile of grain boundary grooving is derived. Numerical examples are taken to test the performance of the integral solution. According to the numerical examples, we find that the novel solution is in accordance with the infinite series solution.