(332g) Adaptive Grid-Based Method for Mapping Cavity Connectivity in Thermal Crystals and Amorphous Materials

The cavities in ideal, zero Kelvin crystal structures are straightforwardly charactized by the largest sphere that can be placed in each void. For example, in an fcc crystal it is well-known that the largest sphere that can fit in an octahedral (O) site has a diameter 0.414 times the atomic diameter [1]. This method, however, does not account for the non-spherical shape of each void nor does it account for fluctuations in the size and shape of the cavity at finite temperatures. Additionally, it is not adaptable to amorphous materials in which the cavity centers are not easily identifiable.

We develop an adaptive grid-based method for computing the size and shape of cavities in thermal crystals and amorphous materials. We identify pathways connecting cavities by launching stochastic trajectories and compute the energy barrier for an absorbed atom to hop between connected cavities using the nudged elastic band (NEB) method. We calibrate our methodology by analyzing a zero Kelvin fcc crystal. The resultant cavity map has one O site and two tetrahedral (T) sites per atom, with each O site connected to eight nearest neighbor T sites. We demonstrate the sensitivity of our results to two adjustable parameters, the probe diameter and the number of trajectories. Finally, we present cavity maps for an ensemble of amorphous configurations for a binary Lennard-Jones mixture [2].

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Document release number LLNL-ABS-821430.

Figure. (a) An fcc unit cell showing O and T sites in blue and red, respectively. (b) The connectivity map for (a) showing that each O site is connected to 8 T sites. (c) An amorphous configuration showing six cavities. (d) The connectivity map for (c) showing how the cavities are connected.

References

1. Fukai, Yuh. The metal-hydrogen system: basic bulk properties. Vol. 21. Springer Science & Business Media, 2006.
2. Kob, Walter, and Hans C. Andersen. "Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function." Physical Review E5 (1995): 4626.