Extended Data Fig. 4: Determination of the effective activation energy using isoconversional principle.

a, Flynn−Wall−Ozawa (FWO) method^54,55. b, Kissinger-Akahira-Sunose (KAS) method^56,57. c, Calculated effective activation energy (\({E}_{\alpha }\)) as a function of conversion rate (\(\alpha \)). The theoretical basis of these analyses roots in the isoconversional principle^31,32, presuming that for any given chemical reaction, the reaction rate at a constant extent of conversion should only depend on temperature. It is hence possible to evaluate the effective activation energy (\({E}_{\alpha }\)) for individual conversion rate (\(\alpha \)) in a model-free manner, without priori assumption of the reaction model. For a non-isothermal process (in this case, continuous heating), the generalized kinetic rate theory states: \({\rm{d}}\alpha \,/{\rm{d}}t=k(T)f(\alpha )\), where \(k(T)\) is the rate constant, whose temperature dependency closely follows Arrhenius law: \(k(T)={k}_{0}\exp (\,-\,Q/{RT})\), and \(f(\alpha )\) represents a complex function of \(\alpha \). When a constant heating rate is utilized during a TGA measurement: \(\beta ={\rm{d}}T\,/{\rm{d}}t\), a further correlation can be set: \({\rm{d}}\alpha \,/{\rm{d}}T=({\rm{d}}\alpha \,/{\rm{d}}t)({\rm{d}}t\,/{\rm{d}}T)=(1/\beta )({\rm{d}}\alpha \,/{\rm{d}}t)\) and the generalized rate equation hence becomes: \({\rm{d}}\alpha /{\rm{d}}T=({k}_{0}/\beta )\exp (\,-\,Q/{k}_{{\rm{B}}}T)f(\alpha )\), whose temperature integration is: \(g(\alpha )=\int (1/f(\alpha )){\rm{d}}\alpha =({k}_{0}/\beta )\int \exp (\,-\,Q/{k}_{{\rm{B}}}T){\rm{d}}T\). The FWO method takes the integration with Doyle’s approximation^54,55, leading to: \(\mathrm{ln}(\beta )=\mathrm{ln}({k}_{0}\,{E}_{\alpha }/Rg(\alpha ))-5.3305-1.052({E}_{\alpha }/R{T}_{\alpha })\), thus by evaluating the slope on the \(\mathrm{ln}\left(\beta \right)v.s.\left(1/{T}_{\alpha }\right)\) plot per each \(\alpha \), the effective activation energy can be obtained. The KAS method^56,57, on the other hand, takes a linear integration that brings about: \(\mathrm{ln}(\beta /{T}_{\alpha }^{2})=\mathrm{ln}({k}_{0}\,{E}_{\alpha }/Rg(\alpha ))-({E}_{\alpha }/R{T}_{\alpha })\), and thus on the \(\mathrm{ln}(\beta /{T}_{\alpha }^{2}){v}.s.\,(1/{T}_{\alpha })\) the effective activation energy can be determined at each \(\alpha \). The presence of a non-constant \({E}_{\alpha }\) throughout an \(\alpha \) range of 0.05–0.85 proves the onsets of more than one reaction process at play, as further revealed in the main text using in situ SXRD.