^{1,a)}, Dirk G. A. L. Aarts

^{1}and Roel P. A. Dullens

^{1}

### Abstract

We experimentally investigate the dynamics of particles constituting grain boundaries in a two-dimensional colloidal crystal, using video-microscopy. A clear plateau in the mean square displacement of the grain boundary particles is found, followed by an upswing indicative of cage breaking. The van Hove correlation functions and the non-Gaussian parameter show that grain boundary particle dynamics are highly heterogeneous. Furthermore, we identified clusters of cooperatively moving particles and analyzed the time-dependence of the weight-averaged mean cluster size. We find good correlation between the behavior of the mean square displacement, and the time dependence of the non-Gaussian parameter and the cluster size, as also reported for various supercooled systems. Our results therefore provide experimental support for the similarity between particle dynamics in grain boundaries and in supercooled liquids as suggested by recent computer simulations.

We thank Paddy Royall for useful discussions, Michael Juniper for critically reading the manuscript and the EPSRC for financial support.

I. INTRODUCTION

II. EXPERIMENTAL METHODS AND DATA ANALYSIS

A. Colloidal model system

B. Single particle dynamics

C. Interface localization

D. Identification of grain boundary particles

III. RESULTS AND DISCUSSION

A. Dynamics of the grain boundary particles

B. Cooperative motion and cluster size distributions

IV. CONCLUSION

### Key Topics

- Grain boundaries
- 46.0
- Colloidal systems
- 15.0
- Cluster dynamics
- 10.0
- Glasses
- 7.0
- Bulk crystals
- 5.0

## Figures

(a) An orientational Voronoi plot of the grain boundary, where the color of each cell represents the local orientation parameter of the corresponding particle, as indicated by the color scale. The shaded band around the interface (solid line) represents the distance criterion for locating the GB particles (see Sec. II D). The inset on the top shows an image of a small part of the grain boundary. The inset on the left shows a typical tangent-hyperbolic fit to the local orientation parameter profile for a single bin. (b) The mean square displacement for the selection *n* _{ c } ≠ 6 (×), for (◯), for 12σ (△), and for the bulk crystal particles (□). The inset shows a segment of the GB, with particle positions plotted over a period of 2500 s.

(a) An orientational Voronoi plot of the grain boundary, where the color of each cell represents the local orientation parameter of the corresponding particle, as indicated by the color scale. The shaded band around the interface (solid line) represents the distance criterion for locating the GB particles (see Sec. II D). The inset on the top shows an image of a small part of the grain boundary. The inset on the left shows a typical tangent-hyperbolic fit to the local orientation parameter profile for a single bin. (b) The mean square displacement for the selection *n* _{ c } ≠ 6 (×), for (◯), for 12σ (△), and for the bulk crystal particles (□). The inset shows a segment of the GB, with particle positions plotted over a period of 2500 s.

Mean square displacements for the grain boundary particles ⟨*r* ^{2}⟩ (○), split into, along the boundary, ⟨*x* ^{2}⟩ (□), and perpendicular to it, ⟨*y* ^{2}⟩ (△), and for the bulk crystal in the *x* (×) and *y* (⋄) directions.

Mean square displacements for the grain boundary particles ⟨*r* ^{2}⟩ (○), split into, along the boundary, ⟨*x* ^{2}⟩ (□), and perpendicular to it, ⟨*y* ^{2}⟩ (△), and for the bulk crystal in the *x* (×) and *y* (⋄) directions.

(a) Self part of the van Hove correlation function along (*x*) and perpendicular (*y*) to the grain boundary for the grain boundary particles (○) and the bulk crystalline particles (□), for *t* = 200 s. The solid lines are Gaussian fits to the data. (b) Non-Gaussian parameters for the motion along the grain boundary (*x*, □), perpendicular to it (*y*, △), and for the bulk crystalline particles in *x* (○) and *y* (⋄).

(a) Self part of the van Hove correlation function along (*x*) and perpendicular (*y*) to the grain boundary for the grain boundary particles (○) and the bulk crystalline particles (□), for *t* = 200 s. The solid lines are Gaussian fits to the data. (b) Non-Gaussian parameters for the motion along the grain boundary (*x*, □), perpendicular to it (*y*, △), and for the bulk crystalline particles in *x* (○) and *y* (⋄).

Typical cluster of moving particles (to scale) in the grain boundary illustrating the cooperative nature of the particle motion. The light spheres are the particle positions at *t* _{0} = 0 s and the dark spheres are the positions at *t* = 200 s.

Typical cluster of moving particles (to scale) in the grain boundary illustrating the cooperative nature of the particle motion. The light spheres are the particle positions at *t* _{0} = 0 s and the dark spheres are the positions at *t* = 200 s.

(a) Probability distribution, *P*(*n*), of cluster sizes, *n*, for different times: *t* = 1 s (□), *t* = 5 s (○), *t* = 10 s (⋄), *t* = 220 s (△), and *t* = 1050 s (×). (b) The normalized weight-averaged mean cluster size, *S*, as a function of the observation time window, *t*.

(a) Probability distribution, *P*(*n*), of cluster sizes, *n*, for different times: *t* = 1 s (□), *t* = 5 s (○), *t* = 10 s (⋄), *t* = 220 s (△), and *t* = 1050 s (×). (b) The normalized weight-averaged mean cluster size, *S*, as a function of the observation time window, *t*.

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