First-Principles Simulations and Z-Contrast Imaging of Impurities at <001> Tilt Grain Boundaries in Mgo
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ABSTRACT First-principles density-functional calculations were used to study the effects of Ca impurities on the 1=5 (310) tilt grain boundaries in MgO. An equilibrium structure and two metastable structures of the grain boundaries in pure MgO have been established. The calculations further demonstrated that Ca impurities segregate at particular sites in the metastable grain boundary and induce a structural transformation. This result is consistent with atomic resolution Z-contrast imaging. The calculations also found that the impurities at the grain boundaries do not induce states in the band gap. The mechanism of the transformation is also discussed. INTRODUCTION Impurity segregation in grain boundaries not only changes the chemistry of the grain boundaries, but may change the structure also. Thus, the mechanical, electrical and optical properties of polycrystalline materials can be altered in a dramatic way [1-5]. Theoretical simulations have been used extensively to model grain boundaries and understand effects of impurities on grain boundaries. Recently, we have directly observed the structure of an impurity segregated tilt grain boundary in MgO by the use of Z-contrast imaging. High spatialresolution electron energy loss spectroscopy demonstrated that the impurity is Ca. The structure we observed disagrees with the model proposed by empirical potential calculations for a grain boundary in pure MgO. In the present paper, we report first-principles density-functional calculations of the effects of Ca impurities on the 1=5 (310) tilt grain boundaries in MgO and demonstrate that Ca segregation induces a structural transformation of the grain boundary. METHOD The calculations were based on density functional theory with the exchange-correlation energy treated in the local density approximation [6,7]. Norm-conserving Pseudopotentials were defined on a real-space grid. The calculations were performed using the code CASTEP. An energy cutoff of 600 eV was used, and the integration over the Brillouin zone was performed using three special k points chosen according to the Monkhorst-Pack scheme. For each geometry the electronic wave functions were first relaxed by the conjugate gradient scheme of Payne et al. [8]. Atoms were then fully relaxed according to the Hellman-Feynman forces until the largest force on any ion in any direction was less than 0.1 eV/A. The cell dimensions were optimized until the largest displacement was less than 0.01 A. We used periodic supercells that contain two oppositely oriented 1=5 (310) grain boundaries. The grain boundaries are parallel to the {310} plane of the original crystalline lattice. They have a periodicity of one conventional lattice parameter (a=4.211 A) in the direction and a periodicity of 6.64 A in the direction perpendicular to axis. The two grain boundaries are separated by 13.4 A, twice the distance between neighboring dislocation cores, and each cell contains 40 Mg and 40 0 atoms.
181 Mat. Res. Soc. Symp. Proc. Vol. 492 0 1998 Materials Research Society
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