Particle-swarm-optimization-assisted rate equation modeling of the two-peak emission behavior of non-stoichiometric 
CaAl_xSi_(7-3x)/4N_3:Eu^2+ phosphors

We examined non-stoichiometric CaAl(x)Si((7-3x)/4)N(3):Eu(2+) phosphors that were intentionally prepared with x = 0.7-1.3 to identify the origin of the deconvoluted Gaussian components that constitute the emission spectra of stoichiometric CaAlSiN(3):Eu(2+) phosphors. The Al/Si molar ratio around the Eu(2+) activator caused the deconvoluted Gaussian peaks. The Eu(2+) activator sites in Al-rich environments gave rise to the lower-energy emission peak, while those in Si-rich environments were related to the higher-energy emission peaks. Active energy transfer from the Eu(2+) activator site in the Si-rich environment to the Eu(2+) activator site in the Al-rich environment was confirmed. Particle swarm optimization was employed to estimate the nine unknown decision parameters that control the energy transfer process. All of the decision parameters were estimated within the range of reasonable values.