Despite the fact that the impurity atoms are continuously implanted, C m starts to decrease and eventually drops below the concentration threshold C C . Growth As soon as C m drops below C C , no new particles are formed and the existing ones grow by incorporation of newly implanted
impurity atoms. The growth of NPs is driven by the transport of the monomers to the particle/matrix interface, i.e., by diffusion, and then by their absorption and incorporation into the particle via interface interactions. The growth rate dR/dt of a spherical particle of radius R(t) can be Belinostat mw thus described by a general expression, which includes both diffusion and interface absorption [26–29]: (2) where k is the rate of monomer absorption at the particle surface, ϵ -1 = DV a /k is the screening length which compares bulk diffusion to surface integration effect, D is the diffusion coefficient of Pb atoms in Al, and V a is the molar volume of Pb precipitates. To retrieve the particle growth law in the growth regime, we assume R ≫ R C . The product ϵR = kR/DV a is the key parameter determining the growth mechanism. When kR ≪ DV a , the interface integration is the rate-determining step. In this case, integration of Eq. (2) reveals that the particle
size increases linearly with time during the growth regime, i.e., R∝t, with a slope of k(C m - C ∞). On the other hand, when kR ≫ DV a , the growth is purely diffusion limited and presents different kinetic behavior as R 2∝t with a slope of 2DV a (C m - C ∞). While, if kR is comparable with DV a , the growth rate is determined by both diffusion and interface absorption, the Epigenetics Compound Library precipitates evolve as (ϵR 2 + 2R) ∝t. For ion implantation with a constant current density since implantation fluence f∝t, it can be seen that the scaling law of the average particle radius R with implantation
fluence f provides a distinct signature for distinguishing the growth kinetics of the embedded NPs. In addition, the important values of the Resminostat absorption rate k (in the interface kinetic limited case) and the diffusion coefficient D (in the diffusion limited case) during implantation can be deduced. Size evolution of Pb nanoparticles Due to the extremely small value of C ∞ for Pb in Al (0.19 at.% at 601 K) [30], the supersaturation and nucleation regimes should already be finished after a short implantation time, i.e., at a low implantation fluence. It was observed that Pb NPs with average radius about 2.1 nm are formed with an implantation fluence of 7 × 1015 cm-2 and a current density at 2.0 μAcm-2 (Figure 6). Thus, the upper limit of the critical monomer concentration for particle nucleation to occur C C can be MLN4924 in vitro estimated to be 6 at.% in Al, i.e., 6.2 × 10-3 mol/cm3, by assuming that all the implanted Pb atoms (7 × 1015 cm-2) are dissolved monomers in the Al layer (Figure 4). In addition, since C m < C C in the growth regime, one can safely assume the upper limit of C m = C C = 6.