Segregation-induced changes in grain boundary cohesion and embrittlement in binary alloys

Abstract

a b s t r a c tGrain boundary embrittlement occurs when a solute enriches at a grain boundary and lowers its cohesive energy. While grain boundary enrichment is often attributed to equilibrium segregation effects, most models of embrittlement consider either the energetics of decohesion or the equilibrium adsorption at the boundary, but not both phenomena together. We develop a model for the change in cohesive energy of a grain boundary of a pure metal upon introduction of solute under conditions of equilibrium segregation prior to fracture. A heuristic grain boundary cohesion map is presented to delineate whether a given solute-solvent pair will exhibit weakening or strengthening of grain boundaries. The analysis helps to clarify that grain boundary embrittlement requires a solute that will both lower the cohesive energy of the boundary and segregate in the first place. The map reasonably captures known metal-metal embrittling pairs.

New nanoscale toughening mechanisms mitigate embrittlement in binary nanocrystalline alloys

“…31 The strength of the alloy comes from a combination of Hall-Petch strengthening as well as traditional and nanoscale solid solution strengthening. 47 In the context of the previous work by Gibson and Schuh, 36 Au is expected to embrittle Pt, consistent with the findings in this study. The present study focuses on identifying the dominant monotonic deformation mechanisms in these alloys and how they contribute to the materials' mechanical properties.…”

“…Pt-Au is expected to be an embrittled system as it has a positive heat of mixing (2.27, as normalized by the gas constant/melting temperature product) and a ratio of surface energies less than one (0.59). 36 Since these are both near threshold values, Au is not expected to strongly embrittle Pt; this is supported by this manuscript, since despite its embrittled nature, the Pt-Au systems did show some plasticity, with mechanisms including dislocation motion, grain boundary migration, localized microstructural transformation and distributed nanocracking.…”

“…29,30,34,35 The potential for grain boundary embrittlement has been explored in the context of thermodynamically stabilized binary alloys by Gibson and Schuh. 36 The Gibson model speculates that an alloying element will be embrittling when two conditions are met: first that the binary pair has a positive heat of mixing, and second that the alloying element has a lower surface energy than that of the base material, promoting the tendency for grain boundary segregation. Furthermore, elemental pairs that have either a higher heat of mixing or lower ratio of surface energies (solute to solvent) are expected to be more embrittling, although the implications of this are not explicitly defined.…”

Application of Machine Learning to Predict Grain Boundary Embrittlement in Metals by Combining Bonding-Breaking and Atomic Size Effects

“…The strengthening energy generally increases with increasing ∆H albeit in individual cases some exceptions can be found [25,26]. Very recently, Gibson and Schuh developed a quantitative model for ∆E SE under conditions of equilibrium segregation and proposed a GB cohesion map to predict whether a given solute-solvent pair will exhibit weakening or strengthening of GBs [27]. Except the similar common feature of ∆C or related quantities with previous modes, the ratio of bonding energies between the solute and solvent, captured by the ratio of their surface energies (RS), was emphasized in their model [27].…”

“…Very recently, Gibson and Schuh developed a quantitative model for ∆E SE under conditions of equilibrium segregation and proposed a GB cohesion map to predict whether a given solute-solvent pair will exhibit weakening or strengthening of GBs [27]. Except the similar common feature of ∆C or related quantities with previous modes, the ratio of bonding energies between the solute and solvent, captured by the ratio of their surface energies (RS), was emphasized in their model [27]. Instead of the traditional one-factor bond-breaking model that relates ∆E SE with relative cohesive energy, Tran et al used a simple two-factor linear model described by the relative metallic radii and the relative difference in cohesive energy, and found it is able to account for most of the variations in the ∆E SE with a value of r 2 > 0.79 [28].The above semi-empirical models and accurate first-principles calculations significantly advance the understanding of solute-induce changes of GB cohesion undoubtedly.…”