Instructions for using the Binary phase equilibria applet

These instructions are meant for users already familiar with the rudiments of phase equilibria. If you don't know a phase from a component or the significance of Gibbs free energy yet, then you should begin with the Tutorial for a step-by-step introduction to all the concepts involved.


This is a preliminary implementation, very incomplete and subject to change at any time. It provides a representation of phase stability relationships in a binary system with up to 4 phases. The properties of the phases and the P and T scales are given as parameters (you can change them by saving a copy of the Applet page, editing it, and opening it with your browser: phases are given in the param tags as name, g0, S, V, xmin, d2g/dx2 and are separated by semicolons; view the HTML source of the Applet page as an example). P, T, and G scales are presently arbitrary, when the parameters describe real phases it will make sense to attach real numbers to the scales.

To play, click on the P-T projection, the panel at upper-left. The applet will compute and display the G-X diagram in the panel at upper-right and isobaric and isothermal sections in the lower panels. Click-and-drag on the P-T panel to zoom in on the defined rectangle. Shift-click on the P-T panel to unzoom back to the starting scale.

What you see: The P-T panel calculates and plots all three-phase univariant coexistences (red where stable, yellow where metastable) and two-phase coincidences (green where stable, grey where metastable). Click on some of these curves and see the corresponding geometry on the G-X diagram. Where four univariants meet is an invariant point; where a univariant meets a coincidence is a singular point. Try zooming in on these points to see the arrangment of stable and metastable curves around the intersections.

The G-X diagram drawn for a given (P,T) point shows free energy vs. composition for each phase (the form of these curves is assumed to be parabolic) in black. Stable one-phase regions are highlighted in red. All common tangents between pairs of phases are drawn in yellow; these indicate by their endpoints the compositions that can coexist in chemical equilibrium. Stable two-phase regions are indicated by painting the tangent line green. The stable sequence of one and two-phase regions across the diagram is given by the lower envelope of red curves and green tangents and is labelled across the bottom.

The lower panels show isobaric (at left) and isothermal (at right) sections through the selected P and T. The blue lines across the P-T projection show the section lines, and the blue lines on the lower panels show where the two sections intersect at the selected (P,T). Stable one-phase regions are shown in black and labelled by the stable phase; two-phase regions are shown in white and labelled by the coexisting phases. Note that the sequence of one- and two-phase regions along each blue section line is the same and is the same as that labelled across the bottom of the G-X digram as determined by the lower envelope of parabolas and tangents. Univariant three-phase coexistences are marked with red lines; coincident points are not specifically labelled but can be clearly seen where two different one-phase regions touch.

Still to come...

There are more features to label on the P-T diagram (fields, points, etc.). Should the isobaric and isothermal sections show any metastable features, or would that be too messy? Independent zooming on the sections and G-X diagram?

Send suggestions, whines, and flames to Paul Asimow.