Size-dependent melting and freezing and thermal expansion of Pb nanoparticles in lead-borate glass

We investigated the thermal behavior of Pb nanocrystals and Pb nanodroplets embedded in lead-borate glass by small-angle X-ray scattering (SAXS). Analyzing the SAXS intensities recorded in situ during the heating and cooling processes we determined the dependence on the radius of the melting and freezing temperatures of Pb nanoparticles embedded in the glass. Modeled SAXS intensity functions yielded several parameters associated with the theoretical functions characterizing the relationships between nanoparticle radius and melting and freezing temperatures. The temperature-dependent SAXS intensity profiles were further employed to determine the thermal expansion coefficients of Pb nanocrystals and nanodroplets within the glass matrix. Our findings reveal that the coefficient of thermal expansion for solid Pb nanocrystals exceeds that of bulk Pb crystals, underscoring distinctive thermal behavior at the nanoscale. Conversely, the coefficient of thermal expansion for liquid Pb nanodroplets is notably lower than that observed for bulk liquid Pb.