Return to aqueous electrolyte page

Quaternary systems

According to the phase rule, a system with four independent components has F=6-P degrees of freedom. An invariant point in a quaternary system thus contains 6 different phases in equilibrium with each other. An invariant point can for example consist of a vapor phase, a liquid phase, and four solid phases in equilibrium with each other.

A quaternary system with three phases (solid-liquid-vapor) in equilibrium with each other has three degrees of freedom. If the temperature is fixed, two degrees of freedom remain. A phase diagram isotherm showing a quaternary system with a vapor phase and a liquid phase requires therefore an area to mark the concentration range in which a solid phase is in equilibrium with the other two phases. A line is needed to mark concentrations where two solid phases are in equilibrium with liquid and vapor. An isotherm for a quaternary system is therefore a three-dimensional diagram.

It is customary to show this type of diagrams as Jänecke projections (E. Jänecke, "über eine neue Darstellungsform der wässerigen lösungen", Z. anorg. Chem., 51(1906)132-157). Jänecke projections are contour plots, where the water content is shown as contours. Alternatively, as it is done on these pages, the water content can be shown as numbers (weight percent water) at grid intersections.

For quaternary systems with two cations and two anions the charge fraction of each cation and each anion can be varied between zero and one. Thus the diagram becomes square. The quaternary (Na⁺,K⁺)-(Cl^-,SO₄^2-)-H₂O system is an example of this. In systems with three cations and one anion or one cation and three anions, the Jänecke projection is triangular.