Advanced features: Entropy and Volume grids

Entropy is a measure of the heat content of a thermodynamic system and is the appropriate proxy for heat content in a variable pressure field. Both entropy and volume are "natural" variables for the visualization of magmatic phase equilibria because a magma body evolves as a consequence of heat flow out of the body (the outward flow of entropy) and deformation on the walls of the magma chamber, which controls its volume.

PhasePlot permits the calculation of phase equilibria on entropy-pressure grids, temperature-volume grids, and entropy-volume grids. The calculations are performed by minimizing at each grid point the system enthalpy, Helmholtz free energy, or internal energy, respectively. By default, temperature-pressure grids are calculated by minimization of the Gibbs free energy at each grid point.

To plot entropy on the ordinate or volume on the abscissa:

1. Choose one of the following. Either selection repopulates the axial limits and intervals with suggested values that correspond roughly to derived limits for volume and/or entropy corresponding to default pressure and/or temperature limits.
• Entropy (J/K-kg) from the Ordinate popup
• Volume (cc/kg) from the Abscissa popup
2. Click to populate the grid.

Common problems and suggestions

There are a number of numerical problems that may arise when attempting to calculate phase equilibria on non-default grids. The user should exercise some patience in coaxing these calculations along, and especially in choosing appropriate numerical values for grid limits. In general, calculations require more computing resources on non-default grids, and individual cells in the grid may need to be recomputed after adding appropriate phase suppression constraints or altering numerical convergence constraints, in order to help the program recognize and achieve an equilibrium assemblage.

Keep the following in mind:

• Be patient. Calculations, especially for volume grids, may take a long time to compute. The reason for the delay is that the volume specified for the grid cell may very well be physically impossible, corresponding to a negative system pressure. PhasePlot has to detect this case, and compute a metastable assemblage at finite pressure as an approximation.
• Choose carefully. When entering a new composition, choose entropy or volume limits carefully. It is best to calculate a temperature-pressure grid first for a new composition. After the grid is computed, create a contour plot and display System volume or entropy. Note the maximum and minimum values of these variables from the contour plot, and use them as a guide for setting the maxima or minima for the corresponding volume or entropy grid.
  
• Check status indicators. PhasePlot is more likely to have problems with numerical convergence to a stable assemblage when computing entropy grids and especially when computing volume grids. Check the calculation status indicators for each grid cell carefully. Follow suggestions for improving numerical performance as indicated by the status message displayed in the detailed grid cell popup. Recalculate individually those cells that did not converge to a stable assemblage (Control-click the cell, and choose Use ONLY this grid point to perform this task). Examine the grid as a whole, and check for consistency of phase relations.

Please send feedback if persistent problems occur. Use the "Send Feedback ..." option on the PhasePlot menu. Every effort will be made to try and correct issues related to entropy/volume grids in future releases of PhasePlot.