Fig. 2.

Phase diagrams of K-Mn oxide systems at E = 1.2 V. a pH-μ_K slice at 1/R = 0 indicating bulk stabilized phases. b 1/R-μ_K slice at pH = 2 illustrating the size-stabilized phases. c, d Pourbaix grand free-energies versus 1/R, showing the metastable energy landscape of crystal growth where [K⁺] = 10⁻⁶ M (c) and [K⁺] = 0.2 M (d). d is representative of pathways at both [K⁺] = 0.2 M and [K⁺] = 0.33 M due to their similar [K⁺]. The three reaction conditions are referred to as P_K = 0, P_K = 0.2, and P_K = 0.33, respectively, based on their [K⁺]. $\mathrm{d}\left({\Phi }_{\delta -{\mathrm{K}}_{0.33}{\mathrm{MnO}}_{\mathrm{2}}-}{\Phi }_{\alpha -{\mathrm{K}}_{0.125}{\mathrm{MnO}}_{\mathrm{2}}}\right)∕\mathrm{d}{\mu }_{\mathrm{K}}=-0.21$, which means that the driving force for the transformation from the δ to the α phase decreases at a larger [K⁺]. The red and blue arrows indicate the trend that the slope of ${\Phi }_{\delta -{\mathrm{K}}_{0.33}\mathrm{Mn}{\mathrm{O}}_2}$ and ${\Phi }_{\alpha -{\mathrm{K}}_{0.125}\mathrm{Mn}{\mathrm{O}}_2}$ changes with increasing [K⁺]