Using defects to store energy in materials – a computational study

Energy storage occurs in a variety of physical and chemical processes. In particular, defects in materials can be regarded as energy storage units since they are long-lived and require energy to be formed. Here, we investigate energy storage in non-equilibrium populations of materials defects, such as those generated by bombardment or irradiation. We first estimate upper limits and trends for energy storage using defects. First-principles calculations are then employed to compute the stored energy in the most promising elemental materials, including tungsten, silicon, graphite, diamond and graphene, for point defects such as vacancies, interstitials and Frenkel pairs. We find that defect concentrations achievable experimentally (~0.1–1 at.%) can store large energies per volume and weight, up to ~5 MJ/L and 1.5 MJ/kg for covalent materials. Engineering challenges and proof-of-concept devices for storing and releasing energy with defects are discussed. Our work demonstrates the potential of storing energy using defects in materials.


DEFECT FORMATION ENERGY CALCULATIONS
The defect formation energy E F is computed under the assumption that defects do not interact with each other, so that E F is the energy to form an isolated defect. Figure S7 shows the convergence of E F , achieved by employing supercells with a single defect and progressively increasing the supercell size to remove spurious image interactions 2 . The formation energy is then obtained by extrapolating the results to the N → ∞ limit. These extrapolated results, used in Figure 3 of the main text, are given below in Table S1. Note that since the defects studied here are neutral (i.e., not charged), no additional corrections due to the periodic boundary conditions are necessary. Next, we provide additional details on the calculations carried out in this work.
Graphene: we use a hexagonal 2-atom unit cell with an experimental lattice constant of 2.46Å and a 60×60×1 k-point grid. For the n × n × 1 supercells with the Stone-Wales defect, we use k-point grids of 10×10×1, 9×9×1, 8×8×1, and 6×6×1 for supercells with n = 6, 7, 8, and 10, respectively. A 20Å vacuum in the layer-normal direction is included in the simulation cell in all cases. The relaxed structure is shown in Fig. S2.
Graphite: we use a hexagonal 4-atom unit cell with experimental lattice constants of a = 2.46Å and c = 6.708Å. The k-point grid for the unit cell is 60×60×8. For the vacancy, we use the following n × n × 1 supercells: n=4 (63 atoms, 15×15×8 k-point grid), n=5 (99 atoms, 12×12×8 k-point grid), and n=6 (143 atoms, 10×10×8 k-point grid). For the interstitial, we use the following n×n×1 supercells: n=4 (65 atoms, 16×16×8 k-point grid), n=5 (101 atoms, 12×12×8 k-point grid), and n=6 (145 atoms, 10×10×8 k-point grid). For the Frenkel pair, we use the following n×n×1 supercells: n=5 (100 atoms, 12×12×8 k-point   Table   S1. These extrapolated formation energies are in very good agreement (within 5−10 %) with available experiments and previous calculations (Table S2). We find vacancy formation energies in the 4−8 eV range for the covalently bonded materials studied here, which are greater than the typical 0.5−4 eV values for metals 3 ; for example, the vacancy formation energy computed here for tungsten is ∼3 eV. Our computed interstitial formation energies span a wide range, with values of 3−21 eV. The FP formation energy also varies widely (4.5−17.5 eV) for the materials studied here. In certain metals, FPs are stable against recombination only if the interstitial is at a minimum distance away from the vacancy 4,5 .
For instance, the FP in tungsten is not stable 5 in our simulation cell and recombines upon DFT relaxation. For this reason, the FP formation energy in tungsten is estimated using the value for the IFP, namely, the sum of the vacancy and interstitial formation energies.
We use the same approach to obtain E FP in other materials for which we used computed FP formation energies taken from the literature (Table S3). The defect formation energies computed here, together with values taken from the literature for materials not studied here with DFT (Table S3), form the basis to compute the energy stored in defects.