Crystallization kinetics of polydisperse colloidal hard spheres. II. Binary mixtures

In this paper we present measurements of the crystallization kinetics of binary mixtures of two different sized hard sphere particles. The growth of the Bragg reflections over time were analyzed to yield the crystallite scattering vector, the total amount of crystal, and the average linear crystal size. It was observed that a particle size distribution skewed to higher sized particles has a less detrimental effect on the crystal structure than a skew to smaller sized particles. In the latter case we observe that initial crystallite growth occurs at only a small number of sites, with further crystallization sites developing at later times. Based on these measurements we elaborate further on the previously proposed growth mechanism whereby crystallization occurs in conjunction with a local fractionation process in the fluid, which significantly affects the kinetic growth of crystallites in polydisperse systems.

Figure 1

Structure factors for all samples studied shown in the fluid phase (dashed line) at time $\tau ={\tau }_o$ and the final structure factor measured at the end of the experimental run (solid line) at time ${\tau }_f$. Note that ${\tau }_o\ne 0$, as experiments are begun after allowing the tumbled sample to stop flowing. The $x$ scale is the scattering vector $q$ in units $\mu {\mathrm{m}}^{-1}$.

Figure 2

Crystallinity $X\left(\tau \right)$ as a function of log reduced time for all samples composed of predominantly small particles $(x⩽0.01)$.

Figure 3

Scattering vector of the position of the main reflection as a function of log reduced time for all samples composed of predominantly small particles $(x⩽0.01)$. The final error bars show the absolute uncertainty due to calibration of the detector angle [13].

Figure 4

Average linear crystal dimension $L\left(\tau \right)$ as a function of time for all samples composed of predominantly small particles $(x⩽0.01)$.

Figure 5

Crystallinity $X\left(\tau \right)$ as a function of log reduced time for samples composed of predominantly large particles $(x⩾0.897)$ at volume fractions (a) $\varphi =0.52$, (b) $\varphi =0.53$, (c) $\varphi =0.54$, and (d) $\varphi =0.55$. All data have been normalized to the final value of the X1[0.55] sample. The slope of the dashed lines are the growth coefficients of rapid conversion $\mu$ and the initial period ${\mu }_{\mathrm{i}}$ as referred to in the text.

Figure 6

Average crystallite size $L\left(\tau \right)$ as a function of log reduced time for samples composed of predominantly large particles $(x⩾0.897)$ at volume fractions (a) $\varphi =0.52$, (b) $\varphi =0.53$, (c) $\varphi =0.54$, and (d) $\varphi =0.55$.