Contribution of vacancies to relaxation in amorphous materials: A kinetic activation-relaxation technique study

The nature of structural relaxation in disordered systems such as amorphous silicon ($a$-Si) remains a fundamental issue in our attempts at understanding these materials. While a number of experiments suggest that mechanisms similar to those observed in crystals, such as vacancies, could dominate the relaxation, theoretical arguments point rather to the possibility of more diverse pathways. Using the kinetic activation-relaxation technique, an off-lattice kinetic Monte Carlo method with on-the-fly catalog construction, we resolve this question by following 1000 independent vacancies in a well-relaxed $a$-Si model at 300 K over a timescale of up to one second. Less than one percent of these survive over this period of time and none diffuse more than once, showing that relaxation and diffusion mechanisms in disordered systems are fundamentally different from those in the crystal.

Figure 1

Change in vacancy volumes upon minimization. Volumes of vacancies created from the initial model are in blue and volumes after minimization are in red. Positive pressure is compressive while negative pressure is tensile. Inset: histogram showing the distribution of relaxed volumes for the 453 vacancies surviving relaxation.

Figure 2

Formation energy (eV) as a function of original atomic pressure and atomic von Mises stress of the atom that was removed.

Figure 3

Histogram showing the lifetime of the vacancies that were annihilated. Inset: distribution of lifetimes of stationary vacancies as a function of the activated barrier of the annihilation event (first event where vacancy ceases to be present). The blue line represents the Boltzmann factor at a temperature of 300 K.

Figure 4

(a) Initial and final configurations of a typical vacancy diffusion event. (b) Initial and final configurations of a typical vacancy annihilation event. Green (peach, orange) atoms are threefold (fourfold and fivefold) coordinated. Small black dots indicate the center of the vacancy. See text for details.