Imaging grain boundary grooves in hard-sphere colloidal bicrystals

Colloidal particles were sedimented onto patterned glass slides to grow three-dimensional bicrystals with a controlled structure. Three types of symmetric tilt grain boundaries between close-packed face-centered-cubic crystals were produced: $\mathrm{\Sigma }5\left(100\right),\mathrm{\Sigma }17\left(100\right)$, and $\mathrm{\Sigma }3\left(110\right)$. The structure of the crystals and their defects were visualized by confocal microscopy, and characterized by simple geometric measurements, including image difference, thresholding, and reprojection. This provided a quick and straightforward way to detect the regions in which the atoms are mobile. This atomic mobility was higher at the grain boundaries and close to the solid-liquid interface. This method was compared to the more conventional analysis based on the calculation of the local order parameter of the individual particles to identify the interface. This was used in turn to identify the presence of grooves at the grain-boundary–liquid triple junction for every type of grain boundary, except for the twin $\left[\mathrm{\Sigma }3\right(110\left)\right]$, for which no groove could be detected. Images of these grooves were processed, and the angle linking the grain boundary energy to the solid-liquid interfacial energy was measured. The resulting values of the grain boundary energy were compared to estimates based on the density deficit in the boundary.

Figure 1

Definition of the geometry of the groove at the grain-boundary–liquid triple junction.

Figure 2

Confocal images of the templates: $\mathrm{\Sigma }3\left(110\right)$ (left), $\mathrm{\Sigma }17\left(100\right)$ (middle), and $\mathrm{\Sigma }5\left(100\right)$ (right).

Figure 3

Projection of the order parameter of all particles in the $\mathrm{\Sigma }5\left(100\right)$ bicrystal. The grain boundary is perpendicular to the plane of the figure, and the template is at the bottom. The color bar indicates the order parameter (0–24).

Figure 4

Projection of particles with order parameters less than the threshold order parameter (11) in the $\mathrm{\Sigma }5\left(100\right)$ bicrystal.

Figure 5

Difference between two consecutive confocal microscopy images of the same location taken two minutes apart. (a) Slice close to the template at the bottom of the sample and (b) slice close to the liquid-solid interface. The grain boundary is horizontal in the middle of the images. Some particles have moved, leading to characteristic black and white patterns like the one shown as a zoomed inset in (a).

Figure 6

Projected view of the mobility in a $\mathrm{\Sigma }5\left(100\right)$ (a) and in a $\mathrm{\Sigma }17\left(100\right)$ grain boundary (b). Grooves can be observed at the solid-liquid interface grain boundary triple line.

Figure 7

Projected view of the mobility in a $\mathrm{\Sigma }3\left(110\right)$ grain boundary. No groove can be observed.

Figure 8

Effect of the threshold used in the analysis of the position of the solid-liquid interface. The particles are colored according to their order parameter and are also shown. Interface positions corresponding to different threshold values for the (OP) and for the IP procedures are indicated.

Figure 9

Comparison of the two best thresholds using the OP and the IP procedures.

Figure 10

Fitting of the experimental groove profile.

Figure 11

Time dependence of the two contributions, ${\alpha }_1$ and ${\alpha }_2$, to the groove angle $\alpha$ of the $\mathrm{\Sigma }5$(100) boundary. The contributions fluctuate more than the total angle.

Figure 12

Average value of the density in the plane perpendicular to the grain boundary (lower densities for darker gray levels). Note that the density is smaller at the grain boundary, at all heights $Z$.

Figure 13

Average Voronoi volumes of the particles of the $\mathrm{\Sigma }5\left(100\right)$ boundary projected onto the $x\text{−}z$ plane.