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’.