where rS = 1.00 nm is the mean radius of the structurally disordered region and rA = 3.00 nm is the mean radius of the activated region where the graphitic structure is mostly conserved but the symmetry-breaking structure enhances the D band. CA = 4.2 and CS = 0.87 are parameters that describe the strength of the influences of the structurally disordered and activated regions on the intensity of the D band, respectively. The ID/IG of NPC (θ-Al2O3) is 2.12 and the mean distance between the defects in NPC (RNPC) can be estimated to be 1.64 nm by solving Eq. 3 for ID/IG(R) = 2.12.