Determination of the melting temperature of spherical nanoparticles in dilute solution as a function of their radius by exclusively using the small-angle X-ray scattering technique

Abstract

In this investigation the dependence on radius of the melting temperature of dilute sets of spherical nanocrystals with wide radius distributions was determined by a novel procedure exclusively using the results of small-angle X-ray scattering (SAXS) measurements. This procedure is based on the sensitivity of the SAXS function to small and rather sharp variations in the size and electron density of nanocrystals at their melting temperature. The input for this procedure is a set of experimental SAXS intensity functions at selected q values for varying sample temperatures. In practice, the sample is heated from a minimum temperature, lower than the melting temperature of the smallest nanocrystals, up to a temperature higher than the melting temperature of the largest nanocrystals. The SAXS intensity is recorded in situ at different temperatures during the heating process. This novel procedure was applied to three samples composed of dilute sets of spherical Bi nanocrystals with wide radius distributions embedded in a sodium borate glass. The function relating the melting temperature of Bi nanocrystals with their radius – determined by using the procedure proposed here – agrees very well with the results reported in previous experimental studies using different methods. The results reported here also evidence the predicted size-dependent contraction of Bi nanocrystals induced by the large surface-to-volume ratio of small nanocrystals and an additional size-independent compressive stress caused by the solid glass matrix in which liquid Bi nanodroplets are initially formed. This last effect is a consequence of the increase in the volume of Bi nanoparticles upon crystallization and also of differences in the thermal expansion coefficients of the crystalline phase of Bi and the glass matrix. This additional stress leads to a depression of about 10 K in the melting temperature of the Bi nanocrystals confined in the glass. The procedure described here also allowed the determination of the specific masses and thermal expansion coefficients of Bi nanoparticles in both liquid and crystalline phases.