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Using a density functional theory-phase field dislocation dynamics model, we reveal a strong inverse relationship between the dislocation equilibrium core width and the normalized intrinsic stacking fault energy for nine face centered cubic (fcc) metals, in quantitative agreement with experiments but not with conventional continuum models. In addition, we show that due to an anomalous feature in its γ-surface, platinum has a fundamentally different core structure and a much wider equilibrium core width than expected. Based on ab initio electronic structure calculations, we attribute this anomaly to distinct differences in the directionality of charge transfer in platinum.