Bismuth embrittlement of copper is an atomic size effect

Embrittlement by the segregation of impurity elements to grain boundaries is one of a small number of phenomena that can lead to metallurgical failure by fast fracture(1). Here we settle a question that has been debated for over a hundred years(2): how can minute traces of bismuth in copper cause this ductile metal to fail in a brittle manner? Three hypotheses for Bi embrittlement of Cu exist: two assign an electronic effect to either a strengthening(3) or weakening(4) of bonds, the third postulates a simple atomic size effect(5). Here we report first principles quantum mechanical calculations that allow us to reject the electronic hypotheses, while supporting a size effect. We show that upon segregation to the grain boundary, the large Bi atoms weaken the interatomic bonding by pushing apart the Cu atoms at the interface. The resolution of the mechanism underlying grain boundary weakening should be relevant for all cases of embrittlement by oversize impurities.

Electromigration of vacancies in copper

The total current-induced force on atoms in a Cu wire containing a vacancy are calculated using the self consistent one-electron density matrix in the presence of an electric current, without separation into electron-wind and direct forces. By integrating the total current-induced force, the change in vacancy migration energy due to the current is calculated. We use the change in migration energy with current to infer an effective electromigration driving force F-e. Finally, we calculate the proportionality constant rho* between F-e and the current density in the wire.

Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper

First-principles calculations of the Sigma 5(310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However, numerical results show a striking equivalence between the alkali metal Na and the semimetal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unraveled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the net reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.

Boron in copper: A perfect misfit in the bulk and cohesion enhancer at a grain boundary

Using first principles electronic structure methods, we calculate the effects of boron impurities in bulk copper and at surfaces and grain boundaries. We find that boron segregation to the Sigma5(310)[001] grain boundary should strengthen the boundary up to 1.5 ML coverage (15.24 at./nm2). The maximal effect is observed at 0.5 ML and corresponds to boron atoms filling exclusively grain boundary interstices. In copper bulk, B causes significant distortion both in interstitial and regular lattice sites, for which boron atoms are either too big or too small. The distortion is compensated to a large extent when the interstitial and substitutional boron combine together to form a strongly bound dumbbell. Our prediction is that bound boron impurities should appear in a sizable proportion if not dominate in most experimental conditions. A large discrepancy between calculated heats of solution and experimental terminal solubility of B in Cu is found, indicating either a significant failure of the density functional approach or, more likely, strongly overestimated solubility limits in the existing B-Cu phase diagram.