Thermodynamics of manganese oxides: Sodium, potassium, and calcium birnessite and cryptomelane

), consistent with added stabilization of the layer and tunnel structures at the nanoscale. Surface energies generally decrease with decreasing average manganese oxidation state. A stabilizing enthalpy contribution arises from increasing counter-cation content. The formation of cryptomelane from birnessite in contact with aqueous solution is favored by the removal of ions from the layered phase. At large surface area, surface-energy differences make cryptomelane formation thermodynamically less favorable than birnessite formation. In contrast, at small to moderate surface areas, bulk thermodynamics and the energetics of the aqueous phase drive cryptomelane formation from birnessite, perhaps aided by oxidation-state differences. Transformation among birnessite phases of increasing surface area favors compositions with lower surface energy. These quantitative thermodynamic findings explain and support qualitative observations of phase-transformation patterns gathered from natural and synthetic manganese oxides.