Interlayer vacancy diffusion and coalescence in graphite

Due to the layered nature of graphite, the migration and interaction of point defects in the graphite crystal structure are highly anisotropic, and it is usually assumed that individual mobile lattice vacancies are confined to diffuse on a single plane. We present the results of ab initio calculations based on density functional theory which demonstrate that vacancies can, in fact, move between adjacent planes when they interact with one another via relatively low energy pathways, often with barriers of less than 1 eV. These interlayer transition mechanisms can significantly alter both the kinetics of point-defect aggregation and coalescence and also the resultant morphologies of multivacancy complexes that form as a result of migrating vacancies interacting.

Figure 1

Monovacancy diffusion. (a) Initial structure, (b) saddle point structure, and (c) final structure of the in-plane transition. (d) Initial structure, (e) saddle point structure, and (f) final structure of the transition of an $\alpha$ monovacancy between planes. The upper-layer atoms are white, lower-layer atoms are dark gray, and the moving atom is red. The minimum energy paths for each transition are shown on the right.

Figure 2

Interlayer divacancy coalescence to the in-plane 5-8-5 structure. (a) The $V_{2,1}^{\beta \beta *}$ structure, (b) saddle point structure, and (c) final structure. (d) The $V_{2,1}^{\alpha \beta }$ structure, (e) saddle point structure, and (f) final structure. (g) The $V_{\beta \beta }^{2,1}$ structure, (h) saddle point structure, and (i) final structure. The atom that moves between the layers is red. The minimum energy paths for each transition are shown on the right.

Figure 3

(a) The $V_{2,1}^{\beta \beta *}$ structure with the third-nearest-neighbor lattice positions to the vacancy in the upper layer (labeled 1 or 2).

Figure 4

Coalescence of monovacancy with the $V_{2,1}^{\beta \beta *}$ structure. (a) A monovacancy migrated to a third-nearest-neighbor position labeled with a 1. (b) The resulting structure after a 0.2 eV barrier transition, (c) the saddle point structure for interlayer migration, and (d) the final coplanar trivacancy structure.

Figure 5

Interlayer coalescence of a monovacancy with a coplanar trivacancy. (a), (d), and (g) The three configurations of a monovacancy bound to a trivacancy. (b), (e), and (h) The corresponding saddle points for interlayer migration. (c), (f), and (i) The fully coalesced coplanar quad vacancies. The atom that moves between the layers is red. The corresponding minimum energy paths for each transition are shown on the right.

Figure 6

(a) The structure of an interlayer $V_3-V_3$ complex. (b) The saddle point structure for the collective interlayer migration of the $V_3$. (c) The coplanar $V_6$ loop formed from the movement of the three highlighted (red) atoms between the layers. The minimum energy path is shown on the right.

Figure 7

(a) An interlayer $V_4-V_3$ complex. (b) An in plane $V_7$ loop formed from the movement of the four highlighted (red) atoms between the layers. (c) An in-plane $V_6$ loop in one layer and a monovacancy in the other layer formed from the movement of three of the four highlighted atoms between the layers. The corresponding minimum energy paths for each transition are shown on the right.