Formation of nanoclusters through silver reduction in glasses: The model

The system of equations describing the formation of silver nanoclusters through the reduction of ionic silver in the course of thermal processing of silver containing glasses in hydrogen is formulated and solved numerically. The processes of the clusterization of neutral silver within the glass and at the surface, and the growth of the nanoclusters are modeled with the account of different mobilities and concentrations of the participating species. The influence of the variation of diffusion coefficients of Ag0 atoms, Ag+ and H+ ions as well as concentration of Ag+ ions in the glass matrix. It is shown that concentration distribution of neutral hydrogen (H0) strongly depends on the relationship between concentration of Ag+ ions (CAg+) and concentration of neutral hydrogen at the glass surface (C1), as well as between diffusion coefficients of silver and hydrogen ions. When DAg+ ≪ DH+ and CAg+ ≫ C1, the total hydrogen concentration profile (CHtot = CH0 + CH+) is defined by silver ion diffusion coefficient DAg+. Concentration of neutral silver, CAg0, represents a bell-shaped depth distribution, whose maximum moves to the depth linearly with t1/2 with the rate depending both on the diffusion coefficient of neutral silver, DAg0, and neutral hydrogen, DH0. It is shown that the depth position of the maximum coincides with the frontier of the layer filled by clusters. The kinetics of the cluster radius growth in the bulk of the glass also depends both on DAg0 and DH0 and essentially deviated from the kinetic law R2 ∼ t predicted earlier in the assumption of time-independent oversaturation. The kinetics of Ag cluster growth on the glass surface turned out independent of the DAg0 diffusion coefficient.