  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 semi metal 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 unravelled.
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 nett
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.
