The significant known hydrated borate mineral assemblages (principally of the western United States) in the system Na₂O-CaO-MgO-B₂O_3-H₂O are expressible in three ternary composition diagrams. Phase rule interpretation of the diagrams is consistent with observation, if the activity of H₂O is generally considered to be determined by the geologic environment. The absence of conflicting tie-lines on a diagram indicates that the several mineral assemblages of the diagram were formed under relatively narrow ranges of temperature and pressure.

The known structural as well as empirical formulas for the minerals are listed, and the more recent (since 1960) crystal structure findings are discussed briefly.

Schematic Gibbs free energy-composition diagrams based on known solubility-temperature relations in the systems Na₂B₄O₇-H₂O and Na₂B₄O₇-NaCl-H₂O, are highly useful in the interpretation and prediction of the stability relations in these systems; in particular these diagrams indicate clearly that tincalconite, although geologically important, is everywhere a metastable phase. Crystal-chemical considerations indicate that the same thermodynamic and kinetic behavior observed in the Na₂B₄O₇-H₂O system will hold in the Ca₂B₆O₁₁-H₂O system. This conclusion is confirmed by the petrologic evidence.

The chemical relations among the mineral assemblages of a ternary diagram are expressed by a schematic “activity-activity” diagram. These activity-activity diagrams permit the tracing-out of the paragenetic sequences as a function of changing cation and H₂O activities.