Relationship between the parting limit for de-alloying and a particular geometric high-density site percolation threshold

Abstract

The parting limit or de-alloying threshold for electrolytic dissolution of the more reactive component from a homogeneous fcc binary alloy is usually between 50 and 60 at%. The system that has been most studied, dissolution of Ag from Ag–Au, shows a parting limit close to 55 at% Ag. Here, Kinetic Monte Carlo (KMC) simulations of ‘Ag–Au’ alloys and geometric percolation modeling are used to study the relationship between this parting limit and the high-density site percolation thresholds p _c(m) for an fcc lattice, subject to the rule that atoms with coordination greater than nine are prevented from dissolution. The value of p _c(9) is calculated from geometric considerations to be 59.97 ± 0.03%. In comparison, using KMC simulations with no surface diffusion and no dissolution allowed for ‘Ag’ atoms with more than nine total neighbors, the parting limit is found to be slightly lower (58.4 ± 0.1%). This slight discrepancy is explained by consideration of the local atomic configurations of ‘Ag’ atoms – a few of these configurations satisfy the percolation requirement but do not sustain de-alloying, while a larger number show the converse behavior. There is still, however, an underlying relationship between the parting limit and the percolation threshold, because being at p _c(9) guarantees a percolation path in which successive ‘Ag’ atoms share at least one other ‘Ag’ neighbor. With realistic kinetics of surface diffusion for ‘Au’, the parting limit drops to 54.7 ± 0.3% because a few otherwise inaccessible dissolution paths are opened up by surface diffusion of ‘Au’.

Keywords:

• alloys
• atomistic simulation
• clusters
• corrosion

Acknowledgements

Research at the Department of Chemical Engineering, University of Toronto, was funded by NSERC (Canada) and UNENE, the University Network of Excellence in Nuclear Engineering. The industrial sponsors of R.C. Newman's Chair within UNENE are AECL, Ontario Power Generation and Bruce Power. J. Erlebacher's contribution is funded by the NSF (USA) under grant DMR-0705525.

Notes

¹If there are no metal ions present in the electrolyte, there is – formally – no equilibrium to refer to, but as we are usually dealing with conditions that are far from equilibrium, this rarely creates complexities. For this case, rather than refer to an actual equilibrium potential, we can just express Tafel's Law as (E–E*) = b log(i/i*), where i* is the anodic current density at an arbitrary electrode potential E*.