where ν 0 is the attempt frequency, which we set as a characteristic value of 1 × 10 13 Hz for both lithium vacancies and lithium interstitials, and a is the hop distance which we take as nearest-neighbour Li-Li distance of 2.67 Å. ∆E X is the potential energy barrier for defect species X to hop between adjacent defect sites, for which we use the barrier heights calculated by Emly et al. of ∆E Lii = 0.17 eV, ∆E VLi = 0.34 eV , which gives a ratio D * Lii /D * VLi ≈ 10 3 at T = 298 K. To calculate the ionic conductivity of Li 3 OCl using eq. ( ) we require the lithium vacancy and lithium interstitial concentrations under typical operating conditions. Crucially, these defect concentrations can differ from the values predicted under typical synthesis conditions (300 °C to 360 °C under vacuum) that we have presented in sections III B and III C. Both lithium vacancies and lithium interstitials are highly mobile even at room temperature, and some proportion of lithium vacancy-interstitial pairs will recombine as the temperature is decreased. Electron and hole pairs may also recombine upon cooling, although in a wide-gap system σ / S cm -1