Melting and freezing temperatures of confined Bi nanoparticles over a wide size range

Abstract

The size dependences of the melting and freezing temperatures, T m and T f, respectively, of spherical Bi nanoparticles embedded in a sodium borate glass were determined by applying a new experimental procedure based on the combined and simultaneous use of small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). This experimental procedure is particularly useful for materials in which a widely polydisperse set of nanoparticles are embedded. The results provide additional and stronger evidence supporting the main previous conclusions: (i) the melting and freezing temperatures both decrease linearly for increasing reciprocal radius (1/R); and (ii) the effect of undercooling is suppressed for Bi nanoparticles with radii smaller than a critical value equal to 1.8 nm. These results confirm a previously proposed low-resolution structural model for Bi nanocrystals below their melting temperature and with radius R > 1.8 nm, which consists of a crystalline core surrounded by a disordered shell. In the present work, a number of samples with different and partially overlapping radius distributions were studied, allowing the determination of T m(R) and T f(R) functions over a wide range of radii (1 < R < 11 nm). Comparison of the experimentally determined T m(R) and T f(R) functions corresponding to different samples indicates good reproducibility of the experimental results. This allowed the verification of the robustness of the experimental procedure based on in situ combined use of SAXS and WAXS for determination of the radius dependence of the melting and freezing temperatures of spherical nanoparticles in dilute solution.