In situ study of the kinetics of growth of Pb nanoparticles embedded in a PbO–B₂O₃ glass

The process of growth of liquid Pb nanoparticles embedded in a lead borate glass was investigated by transmission electron microscopy (TEM) and by in situ small-angle X-ray scattering (SAXS) during isothermal annealing at different temperatures within the 649–679 K range. A TEM study at room temperature of the glass–Pb nanoparticle composite, previously subjected to isothermal annealing, showed the presence of a number of nearly spherical Pb nanocrystals with some size dispersion. The analysis of several series of experimental SAXS curves recorded in situ, for increasing periods of time of isothermal annealing at different temperatures, allowed the authors to determine time and temperature dependences of the radius distribution functions of the growing spherical Pb nanoparticles. Since all selected annealing temperatures were higher than the melting temperature of bulk Pb, the Pb nanoparticles were in all cases in the liquid state during the whole growth process. A fast increase in the total volume of Pb droplets was observed during the initial stages of annealing, which indicated that the Pb droplets grow because of the incorporation of Pb atoms dispersed in the glass matrix. For more advanced stages of droplet growth, when the concentration of Pb atoms becomes close to its equilibrium concentration, the time dependences of the average radius, number density and total volume of Pb droplets are those predicted by the classical theory of coarsening proposed by Lifshitz–Slyosov–Wagner. Furthermore, it has been established that the Pb nanodroplets preserve their spherical shape and their relative dispersion in size through the whole coarsening process and that the activation energy for diffusion of Pb atoms and growth of Pb droplets embedded in the studied glass is E_a = 2.65 ± 0.09 eV per atom.