Numerical Simulation of Grain Boundary Grooving By Level Set Method

Details Numerical Simulation of Grain Boundary Grooving By Level Set Method Numerical Simulation of Grain Boundary Grooving By Level Set Method

2000-01-31

arxiv.org/abs/cond-mat/0001449v1

Physics

Condensed Matter

Materials Science

Submitted to the Journal of Computational Physics (19 pages, 8 Postscript figures, 3 tables, 29 references)

Scientific paper

10.1006/jcph.2001.6760

A numerical investigation of grain-boundary grooving by means of a Level Set method is carried out. An idealized polygranular interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. The surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface curvature gradients, and a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional Hamilton-Jacobi type equation. The results obtained are in good agreement with both Mullins' analytical "small slope" solution of the linearized problem (W.W. Mullins, 1957) (for the case of an isolated grain boundary) and with solution for the periodic array of grain boundaries (S.A. Hackney, 1988).

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