A set of efficient numerical algorithms, for accurately computing the forces on dislocations in free-standing thin films, was presented. Firstly, a spectral method was presented for computing the image-stress field of dislocations in an isotropic elastic half-space and a free-standing thin film. The traction force on the free surface was decomposed into Fourier modes by using a discrete Fourier transform, and the resultant image-stress field was obtained by superimposing analytical solutions in the Fourier space. Dislocations which intersected free surfaces were considered; including the use of virtual segments and the associated uniqueness of their solutions. The efficiency of the algorithm was enhanced by incorporating analytical solutions for straight dislocations that intersected free surfaces. A comprehensive algorithm, including a flow diagram, was formulated and the numerical convergence of the algorithms was considered. As a benchmark, the equilibrium orientation of a threading dislocation in a free-standing thin film was computed. Good agreement was found between the predictions of the dislocation dynamics model and those of molecular static simulations and the line tension model.

Modelling Dislocations in a Free-Standing Thin Film. C.R.Weinberger, S.Aubry, S.W.Lee, W.D.Nix, W.Cai: Modelling and Simulation in Materials Science and Engineering, 2009, 17[7], 075007