Quantitative analyses of the electron spin resonance behavior using an integrable model

•An asymmetric electron spins resonance spectrum model was established.•The effectiveness of this model is confirmed by results of twenty experimental validations.•Spin concentration in materials can be estimated due to this integrable model.•The quantitative relationship between chemical composition and double integral of ESR intensity was searched.•Good application results are obtained. Electron spin resonance (ESR) is a spectroscopic method employed to detect distinct species of materials, for example, organic free radicals, transition metal ions, triplet-state molecules, and some point-defect in materials. However, many experimental ESR results of materials have not been theoretically explained due to the lack of a reliable and accurate ESR model. To quantitatively analyze the ESR behavior, we established an asymmetric ESR spectrum model in this study. The effectiveness of this model was confirmed by the results of twenty experimental validations. Because this ESR spectrum model is integrable, spin concentration in materials can be estimated using this model. Furthermore, the quantitative relationships between chemical composition and the double integral of ESR intensity were investigated in this study. The proposed ESR model may expand the application of ESR.