Ternary error diagrams: Graphical representation of errors in ternary system compositions

A new technique is described for graphically presenting the errors between predicted and measured ternary compositions. The ternary error diagram is constructed using three axes, one for each of the errors associated with each component. Each of the three axes is rotated by 120 degrees about the origin with respect to the other two axes. When plotted on the diagrams, each point represents the error in the ternary composition predicted by a model compared with the actual experimentally determined composition. The better the agreement is between the model predictions and the experimental data, the closer the data point will be to the diagram's origin. Also presented is a new measure for quantifying the accuracies of a model's predictions compared to observed compositions. The use of the graphical technique is illustrated in the context of modeling ion-exchange equilibrium behavior in three-component systems.