# Molecular dynamics model of hydrogen diffusion

## Category: Modeling

Within the computational framework of HyMARC, we are developing high-fidelity interatomic potentials for new materials of interest, using a new molecular dynamics (MD) capability and Sandia supercomputing computing resources to address the statistical problem arising from atomistic simulations of low-probability events, in particular diffusion of hydrogen through solid materials.

The aim of HyMARC is to not only accurately simulate all possible reactions that could occur during the hydriding / dehydriding process using atomistic simulations, but also to generalize our methodologies to enable them to be quickly adapted to new materials. This requires us to develop new interatomic potentials for storage materials that have not been considered in the literature, and to improve the accuracy of existing potentials that usually cannot model chemical reactions and phase transformations. To accomplish this, we are developing Sandia’s analytical bond order potentials (BOP) for new materials. Analytically derived from quantum-mechanical calculations,^{1-5} the fidelity of BOP has been demonstrated for a number of materials, including CdZnTe,^{6,7} Al-Cu,^{8} Cu-H,^{9} and C.^{10} As an example, our carbon BOP^{10} enables molecular dynamics (MD) simulations to capture various atomic reactions between carbon vapor and a copper surface, which results in the correct prediction graphene growth on copper (Figure 1).

Statistics are another challenge for atomistic simulations because an alloy with a given composition can have countless distinct atomic populations on lattice sites. This impacts all thermodynamic and kinetic properties. Using kinetic properties as an example, in the past, atomistic calculations of diffusion energy barriers were usually computed for each atomic jump path. Practical materials often involve thousands of distinct atomic jump paths that are not known a priori. The problem is compounded during hydriding and dehydriding processes, in which the structure is evolving. Even if all atomic jump paths are considered, it is still unclear how thousands of atomic jump events are related to the overall diffusion behavior seen in experiments. Sandia’s large-scale computing resources allow us to determine an overall diffusion energy barrier and an overall pre-exponential factor from the Arrhenius equation constructed from MD simulation of the mean-square displacement of the diffusing species at different temperatures. An example of the Arrhenius plots obtained from such MD simulations of hydrogen diffusion in palladium is shown in Fig. 2. The highly converged linear Arrhenius plots validate that the overall diffusion energy barrier accounting for all atomic jump paths can be accurately determined. They also validate that atoms are able to move around and reach dynamical equilibrium during MD simulations. Because atoms stay for the correct residence time at each lattice site they visit during an MD simulation, performing a large number of time-averaged simulations can resolve the statistical issue of atomistic simulations, provided that sufficient computing resources are available.

**Status: **Available for use in collaboration with HyMARC.

**References**

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