Structure and melting of Bi nanocrystals embedded in aB2O3−Na2Oglass

A composite material consisting of spherical Bi nanoclusters (nanocrystals and/or liquid nanodroplets) embedded in a $28{\mathrm{Na}}_2\mathrm{O}-72\mathrm{}{\mathrm{B}}_2{\mathrm{O}}_3$ glass was studied by the wide-angle x-ray scattering (WAXS) and small-angle x-ray scattering (SAXS) techniques over the temperature range in which the Bi crystal-liquid transition occurs. Because of the wide radius distribution of Bi clusters and due to the dependence of the melting temperature on crystal radius, the overall transition occurs over a wide range, from 365 up to 464 K. In this transition range, large Bi nanocrystals coexist with small liquid droplets. A weak contraction in a and c lattice parameters of rhombohedral Bi nanocrystals with respect to the bulk crystal was detected. As expected, the average radius of crystalline Bi clusters, deduced from WAXS data, increases for increasing temperatures over the whole solid-to-liquid transition range. The SAXS spectrum recorded at different temperatures within the transition range is essentially invariant, indicating that the radius distribution of Bi nanoclusters (nanocrystals and nanodroplets) is temperature independent. The volume distribution of Bi nanoclusters is a single-mode function with the radius ranging from about 15 up to 41 Å with a maximum at 28 Å. The integral of Bragg peaks of Bi nanocrystals decreases for increasing temperatures as a consequence of the progressive melting of nanocrystals of increasing size. By combining the results of WAXS and SAXS experiments, we determined the melting temperature of the nanocrystals as a function their radius suppressing unwanted size dispersion effects. Our results clearly indicate a linear dependence of the melting temperature on nanocrystal reciprocal radius, thus confirming previous theoretical predictions.