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Details of cleavage energy calculations in a GB. (a) Initial structure of two grains adjacent to each other. (b) Variation in total energy of the system as the distance of separation between the two grains is progressively increased, until it levels off at a distance of separation of . (c) Corresponding structure when the grains are separated by . (d) Initial position of dopant atom (in red) along the GBs.
Charge density plots of (a) pure Ni (b) Cr along GB and (c) S along GB. Charge localization induced by S and bond sharing induced by Cr may attribute to their weakening/strengthening behaviors, respectively.
Calculated cleavage energies for GB in Ni, with impurities at interstitial sites, at a concentration of . Numbers in parentheses indicate cleavage energies when selected dopants as Hf and S are put in substitutional sites at GBs.
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