• Occupation Vector: σ = [σ 0 , σ 1 , ...σ N-1 ] is a vector of occupations in a simulation cell. FIG. . a shows the average computing time, per kMC pass (left y-axis, orange lines) and per kMC step (right y-axis, black lines), as a function of total number of atoms for kMC simulations of Na 1+x Zr 2 P x Si 3 -x O 12 , scaling from 1 × 1 × 1 (42 atoms) to 10 × 10 × 10 supercells (42,000 atoms). The details of this model can be found in Ref. . Solid and dashed lines refers to the time consumption with and without Numba, respectively. The LCE model contains 19 unique orbits and 212 possible clusters, with a coupling strength of 12. b shows the relationship between the time consumption and coupling strength between events (defined in Section A) performed on a 8 × 8 × 8 supercell lattice. c describes the effect of basis set size (number of clusters/orbits in LCE model) on simulation time, using the 8 × 8 × 8 supercell.