Vacancy diffusion along twist grain boundaries in copper
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Vacancy diffusion along twist grain boundaries in copper Miki Nomura, Sing-Yun Lee, and James B. Adams Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801 (Received 22 May 1990; accepted 28 September 1990) Vacancy diffusion along two different high-angle twist grain boundaries (25 and 213) was studied using the Embedded Atom Method (EAM). Vacancy formation energies in all the possible sites were calculated and found to be directly related to the degree of coincidence with the neighboring crystal planes. Optimal migration paths and migration energies were determined and found to be very low. The activation energies for self-diffusion at the boundaries were found to be less than half of the bulk value. Grain boundary diffusion is important because at low temperatures diffusion in polycrystalline materials occurs primarily along grain boundaries and dislocations. EAM calculations by Majid, Bristowe, and Balluffi1 investigating the structure of Au twist grain boundaries were in excellent agreement with their experimental results (to within 0.1 A). The EAM is known to accurately predict activation energies for bulk self-diffusion.2 Thus, the EAM is expected to calculate reliable vacancy formation and migration energies at grain boundaries. Vacancy formation energies at twist and tilt grain boundaries were calculated by Brokman, Bristowe, and Balluffi3 using pair potentials. Their studies showed that formation energies could be quite different from bulk values. Two groups4'5 have used pair potentials for molecular dynamics simulations of diffusion along 25 tilt grain boundaries. The purpose of this paper is to begin a comprehensive study of diffusion along a wide variety of grain boundaries, using the EAM since it includes many body interactions, and therefore, is more reliable than pair potentials. Specifically, we determine the vacancy formation energies for all possible sites, and the optimal migration paths and migration energies for vacancy diffusion. The EAM was developed by Daw and Baskes,6 and for this study we used the standard EAM functions developed by Foiles, Baskes, and Daw.7 The twist grain boundaries were created by rotating two perfect crystals around their [100] axes, with (100) surfaces parallel to the grain boundary. The optimal structures of the grain boundaries were determined by relaxing all the atoms using molecular statics. Periodic boundary conditions were used for the surfaces perpendicular to the grain boundary, and free surfaces were used for the two surfaces parallel to the grain boundary. The lengths of the periodic cells were maintained constant to simulate J. Mater. Res., Vol. 6, No. 1, Jan 1991
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the effect of an infinitely long slab. The slab consisted of 18 atomic layers, each with approximately 200 atoms; smaller slabs with only 11 layers were found to yield nearly identical results. The final structures were very similar to those found by earlier experimental and theoretical studies of A
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