A generalized O-element approach for analyzing interface structures

JY Zhang and YP Gao and YZ Wang and WZ Zhang, ACTA MATERIALIA, 165, 508-519 (2019).

DOI: 10.1016/j.actamat.2018.12.005

A correct description of interfacial dislocations is critical to the understanding of physical and mechanical properties of the interfaces and their impact on phase transformation and deformation mechanisms. The O-lattice theory provides a general theoretical framework for determining interfacial dislocation structures. However, for systems having an invariant line (IL) or an invariant plane, the O-elements do not always exist in the three-dimensional (3D) space, which impedes the capability of the O-lattice theory to the interfaces in these systems. To determine the dislocation structures in interfaces for which the O-elements do not extend in the 3D space, we introduce a generalized O-element approach by employing the Moore-Penrose pseudoinverse. The generalized O-elements, as the least square solutions to the O-lattice, play a parallel role as that of the ideal O-elements and extend the candidate locations for the coherent regions between dislocations. Worked examples for dislocation structures in both homo-phase and hetero-phase systems are presented. The predicted interface structures are in good agreement with experimental observations and molecular statics (MS)/molecular dynamics (MD) simulations. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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