Structure and energetics of long-period tilt grain boundaries using an effective Hamiltonian

We have investigated the atomic structures of 44 〈110〉 symmetric tilt grain boundaries (GB’s) with atomistic simulations using an embedded-atom method (EAM) potential for aluminum. The focus has been on examining the efficacy of the structural unit model in the context of very long period boundaries. Our studies, which have been carried out using two EAM potentials, of both the equilibrium and metastable structures of a number of boundaries, reveal that geometric arguments inherent in the structural unit model must be supplemented by energetic considerations. An effective Hamiltonian is introduced to this end which computes the energy of a string of structural units using two-body potentials between individual units. The potentials are calculated via a least-squares fit to the results of full atomistic represented by the effective Hamiltonian. Results based on as few as 16 inputs are very encouraging and clearly demonstrate the effectiveness of this method. This scheme lends itself to a straightforward extension to GB structure calculations at finite temperatures using Monte Carlo techniques