Mechanisms and kinetics of the migration of grain boundaries containing extended defects

A full understanding of the basic processes of grain boundary migration is a fundamental prerequisite for predictive models of microstructural evolution in polycrystalline materials in processing and in service. In a detailed study of the kinetics of a $\left[111\right] \mathrm{\Sigma }7$ symmetric tilt boundary, we have previously shown that defect-free, flat grain boundaries, below their roughening temperature, can be strictly immobile in the experimental limit. Here we present the results of molecular dynamics simulations of grain boundaries containing a variety of “defects.” These simulations show that the presence of some of these defects restores the mobility of flat boundaries, even well below the roughening transition temperature. These defects fundamentally alter the mesoscale mechanism of grain boundary migration from one involving homogeneous nucleation to a heterogenous process. At the atomistic level, the crystal lattice reorients via coordinated shuffling of groups of atoms. In the case of flat boundaries, these shuffles must accumulate to form critically stable nuclei, but in the case of boundaries containing defects the shuffling of a small number of atoms at the defects can be sufficient, fundamentally altering the mechanism and kinetics of migration.

Figure 1

The unrelaxed of the grain boundary structures used in our simulations. The different symbols denote atoms in different close-packed layers. The solid lines indicate the size of the per atom stress in the direction perpendicular to the grain boundary as a means of visualizing the boundary structure. The polygons in the boundary highlight the basic structural unit of the flat $\mathrm{\Sigma }7$ boundary. The dashed lines indicate $\left\{1\overline{1}0\right\}$ planes for reference. For the Step and Asymmetric boundaries, the insets show detailed cross sections through the boundary, with one half of the bicrystal removed and atoms colored according to their coordinate perpendicular to the boundary to emphasize the out-of-plane features.

Figure 2

Mobility data for the grain boundary migration simulations. (a) The grain boundary velocity as a function of driving force at $600\text{K}$ for the four different boundaries. The inset shows the same data but presented as a nominal mobility ($\equiv v/P$) with linear fits to the data. (b) An Arrhenius presentation of the simulation results for a driving force of 5 meV/atom. The solid lines are linear best fits or fits based on the island nucleation model of migration kinetics. The inset shows the same data on linear scales. Except where indicated, lines are a guide for the eye only.

Figure 3

Snapshots of migrating boundaries containing structural defects. Atoms in one half of the bicrystal are not shown. The atoms are colored according to their position perpendicular to the grain boundary surface to emphasize the role of out-of-plane features in the migration process (color scales are arbitrary and vary between defects). Time scales for the migration process along with the temperatures and driving forces used are marked in the figure.

Figure 4

The patterns of atomic rearrangement in migration simulations at three different temperatures. The initial and final positions are shown by open (red) and filled (blue) symbols, respectively. Black arrows show hops confined to a single close-packed plane. Green vectors show atoms hopping between different planes. A “string” [23] of anomalous jumps at 400 K is highlighted (in orange). In all cases a rigid translation has been applied to the final atom positions to clarify the pattern of rearrangement (see Appendix).

Figure 5

The energy barriers for atomic rearrangement of 21 atoms derived from NEB calculations over a range of driving forces (each symbol corresponds to a single replica). The inset shows the barriers for no force and the maximum driving force with the energy change due to the artificial driving force subtracted out.

Figure 6

The energy barriers for grain boundary migration as a function of driving force for the different boundaries. The dashed line is the prediction of the island model of migration kinetics. The solid line shows the barrier for the ordered shuffle of 21 atoms from the disfavored crystal orientation to the favored.

Figure 7

The atomistic mechanism of grain boundary migration. The top row of figures shows the hops undertaken by atoms as the grain boundary sweeps through from left to right. Open (red) circles indicate the initial positions, filled (blue) circles the final positions. The bottom row of figures shows histograms of the length in Å of the atomic hops. The figures on the left show the raw data from the migration simulation. The figures on the right are the result of shifting the final positions of the atoms by a fixed translation. Data are for a simulation with $T=400$ K and $P=25$ meV/atom (250 MPa).

Figure 8

The migration paths of a group of seven nonequivalent atoms in the CSL cell (left) during a dynamical simulation and (right) as predicted by the NEB calculation. The trajectories are colored (from red through green to blue) according to time from initial (open symbols) to fully migrated positions (closed symbols). In the case of the NEB calculations, the reaction coordinate stands as a proxy for time.

Figure 9

The reaction coordinate as a function of time for individual atoms in the minimal groups identified by differently shaped symbols in Fig. 8. Data from the dynamical simulations [solid (red) lines] are compared with the predictions of the NEB calculations [dashed (blue) lines], for which the overall reaction coordinate of the NEB cell is used as a proxy for time.