Embrittlement of Metals by Trace Impurities

Embrittlement by the segregation of impurity elements to grain boundaries leads to failure by fast fracture. A question that has been debated over hundred years is How can minute traces of bismuth cause this ductile metal to fail in a brittle manner Three hypotheses for this embrittlement exist. 

Two of them assign an electronic effect to either a strengthening or weakening of the interatomic bonding, the third one postulates a simple atomic-size effect. Distinguishing between these proposed mechanisms would be very difficult using direct experiments. 

The authors of [30] have performed the first-principles calculations that allowed them to support a size effect expHcitly and to reject the electronic hypotheses. 

The work of fracture may be characterized by a critical energy-release rate for cleavage G . A crack propagates in the absence of a plastic strain if the equality ( deav 2y holds, where ys is the surface energy. If a nucleation and motion of dislocations occur at the tip of the crack the stress concentration relives. A critical 

The local density approximation to density functional theory allowed one to find out that for a typical grain boundary in pure copper = 3.10 J m. Upon segregation of one monolayer of bismuth to the same grain boundary decreases 

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