In materials below the melting point, most of the dynamics occurs via activated processes: in that regime, barriers separating different states are high compared to the average thermal energy and can be crossed only with the help of rare thermal fluctuations. Diffusion of defects and impurities is an example of such activated processes. In simple materials, such as elemental crystals, the nature of these mechanisms can be identified from the symmetries of the problem. For more complex materials, such as ceramics and glasses, however, this is not feasible because the number of possible local environments increases rapidly with the complexity of the structure. To study relaxation and diffusion in these materials, it is therefore necessary to sample a large number of representative events.
We present here a numerical method designed to sample activated processes with characteristic time scales much beyond the reach of standard simulation methods such as molecular dynamics and real space Monte Carlo. The activation-relaxation technique (ART) [1,2] defines moves directly in the configurational energy landscape. A configuration is first brought from a local minimum to a nearby saddle point, determining the energy barrier for the event (activation). The configuration is then relaxed into a new minimum, completing the trajectory (minimization). The advantage of this approach is that it does not impose a set of pre-determined atomic rearrangements; atoms move in response to the physical trajectory defined on the potential energy surface. In our simulations, we find events involving the displacement of one to hundreds of atoms, crossing barriers as low as a few hundredth of an eV and as high as 5 or even 10 eV. Contrary to real-space simulations, the numerical effort required to find a saddle point is independent of its activation energy; it is thus possible to sample a very wide range of time scales.
The activation-relaxation technique provides an efficient tool for structural optimization since it can go over barriers that are difficult to reach by other techniques. We have used ART to produce low energy configurations of a-Si, metallic glasses and a-GaAs[3,4]. In this case, the details of the trajectory are not very important and the name of the game is to find the lowest energy configuration produced. For many systems, we believe that ART is more efficient than standard algorithms such as molecular dynamics. It provides, moreover, a completely different optimization schedule and can serve as a check for possible biases in the method of preparation. In the case of metallic glasses and cells of up to 216 atoms of a-GaAs, ART even produced partial or total crystallization although, due to the non-polynomial nature of the search in high dimension, ART is unlikely to crystallize larger unit cells.
Because the trajectory linking different minima is close to the physical trajectory, it is also possible to use the events created by ART to study the nature of activated mechanisms in these materials. We have recently concentrated on two materials, a-Si and v-SiO2, that present both similarities and numerous differences. Creating several thousands of events in unit cells containing 1000 atoms and more in both cases, we can extract some general understanding of the microscopic mechanisms associated with relaxation and diffusion.
Many activated processes in a-Si  involve local topological rearrangements that preserve the perfect tetrahedral coordination of the environment. These ``perfect events'' involve bond exchanges between neighbor atoms, in the spirit of the Wooten, Winer and Weaire (WWW) bond switching mechanism . Although first introduced as an artificial step to numerically amorphize silicon, this mechanism appears to be the basis for most topological rearrangements in our simulations, including events in which defects are involved.
In contrast with these results, our simulations indicate that perfect mechanisms do not play any major rôle in v-SiO2 . Because of the additional constraint on chemical ordering, SiO2 requires the close involvement of coordination defects to rearrange itself topologically.
Much work remains to be done to understand in details the above results
and to establish more strongly the activation-relaxation technique. In
spite of this, ART has already provided many new insights and promises
many more in the near future.
Acknowledgements: This work was done in collaboration with S
W. de Leeuw and L.J. Lewis. It is supported in part by the NSF, grant number
DMR-9805848. Some of the computations were done on the Cray T3E of HPAC,