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

Abstract

First principles calculations of the Σ5(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 rôle 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.

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

“…We further identify mechanisms responsible for grain boundary strengthening within the framework of the "ghost impurity cycle" proposed in our previous work. 8 The cycle admits the occupation of both substitutional and interstitial positions by impurity atoms at the interface, a feature that is fully exploited in the present study.…”

“…8, the change of W sep at the A → D step describes grain boundary weakening due to some host-host bonds being broken ͓"host removal" ͑HR͒ mechanism͔. Transition D → C corresponds to the distortion of the atomic structure of pure boundary and surface caused by impurity ͓"substitutional structure" ͑SS͒ mechanism͔.…”

“…We used the local density approximation ͑LDA͒ in the parametrization of von Barth and Hedin, 21 which was modified by Moruzzi et al 22 Other parameters ͑k-point meshes, real space meshes, etc.͒ were the same as in Ref. 8 to which the reader is referred for further details.…”

“…The largest strengthening effect is observed at 0.5 ML, at which W sep increases by 0.5 J / m 2 and becomes as large as 3.81 J / m 2 . This can be compared to twice the surface energy of pure Cu, 8 2␥ 310 s = 4.42 J / m 2 , which provides an upper bound for W sep above which a grain boundary would become stronger than a bulk.…”

Self-assembly of Sn-3Ag-0.5Cu Solder in Thermoplastic Resin Containing Carboxyl Group and its Interconnection

“…8 Despite the advantages and extensive research performed on these solders to date, Sn-58Bi solder has an inherent drawback, i.e., its reliability declines as a function of thermal history. [21][22][23][24][25][26][27] Additionally, Sn-52In solder is expensive. Accordingly, Sn-3Ag-0.5Cu solder has been recommended by the Japan Electronics and Information Technology Industries Association (JEITA), and is widely used in FC interconnections.…”