Kinetic origin of grain boundary migration, grain coalescence, and defect reduction in the crystallization of quenched two-dimensional Yukawa liquids

The kinetic origin of grain boundary migration, grain coalescence, and defect reduction in the crystallization of quenched two-dimensional Yukawa liquids are numerically investigated. It is found that, in grain coalescence, stick-slip cracking the region in front of the grain boundary into smaller subgrains corotating with small angle, followed by healing, is the key for aligning lattice misorientation and inducing grain boundary stick-slip advance. Cracking is initiated from the weakly interlocked dislocation along its Burgers vector, which in turn causes dislocation motion along the crack. The cascaded scattering and recombination of two dislocations with ${60}^{\circ }$ and ${120}^{\circ }$ Burgers vector angle difference into two and one dislocations are the major processes for dislocation motion and reduction, respectively, in grain boundary migration. A rough grain boundary with large curvature easily supports the above process and induces high grain boundary mobility. Along a straight smooth grain boundary, the parallel Burgers vectors of the string of dislocations hinder defect reduction and induce coalescence stagnation.

Figure 1

(a) Plots of $1/D_f$ versus $t_w$ for runs I and II. The numbers by the gray lines indicate the scaling exponents. (b)–(d) Snapshots of particle configurations at different $t_w$. In the late stage, stringlike defect clusters consisting of five- and sevenfold disclinations, represented by triangles and squares, respectively, can be formed along GBs to accommodate lattice misorientation.

Figure 2

(a) and (b) Sequential color coded plots reflecting bond angle variations in $335{\tau }_0$ interval for the box region of Fig. 1. Cracking into and healing of small clockwise rotating subgrains with rotating directions indicated by arrows, lead to GB migration and lattice realignment. Bond breaking and reconnection occur along the strong shear (green) strips between adjacent corotating subgrains. (c) and (d) The corresponding particle trajectories showing the cooperative vortexlike hopping causing the above cracking-rotating-healing process. (e) The plot of ${\theta }_6$ variation in the $x^{\prime }t$ space, showing the stick-slip advance of the GB along $x^{\prime }$ [line $AB$ in (a)] induced by stick-slip subgrain rotation.

Figure 3

(a) Sequential plots showing recombination of two dislocations with about ${120}^{\circ }$ Burgers vector (indicated by straight arrows) angle difference into a new dislocation, along the cracking (green) strips between three clockwise corotating subgrains, which causes lattice realignment and GB migration. (b) Sequential plots showing scattering of two dislocations with ${60}^{\circ }$ incoming and outgoing Burgers vector angle difference, along cracking strips. The first panels in (a) and (b) are color coded by bond angle change in a $50{\tau }_0$ interval. The gray thick lines indicate GBs. (c) Sketch showing Burgers vectors for the basic dislocation interaction processes. (d) and (e) Temporal evolutions of Burgers vectors of dislocations (moving along or against Burgers vectors), in the regions corresponding to the upper and lower box regions of Fig. 2, respectively, from $t_w=600$ to $1340t_w$. The cascaded recombination and scattering are the dominated processes for defect motion and reduction, and GB migration. The Burgers vector length is one lattice constant.

Figure 4

(a) and (b) Particle and defect configurations at two different $t_w$ in the box region of Fig. 1. (c) The corresponding small fluctuations of GBs at different $t_w$. It shows stagnation of a straight GB along a dislocation string, hindered by the nearly parallel Burgers vectors transverse to the string.

Figure 5

(a) and (b) Temporal evolutions of $|\Delta D_f|$ and $N_r$, and $N_r/\left|\Delta D_f\right|$, respectively, in a $50{\tau }_0$ interval for five runs coded by different colors under the same quenching operation as run I.