# Status messages

The following messages are displayed in the subtitle of the Phase Detail popover associated with calculation results for a given grid cell. These messages describe the state or condition that caused exit from the phase equilibrium algorithm.

### Successful termination status messages

**Optimal residual norm**

Convergence of the phase equilibrium algorithm has been verified by locating a sufficiently zero gradient and positive definite second derivative matrix of the operative thermodynamic potential. No residual supersaturations remain. The system is unquestionably in the equilibrium state.

**Residual norm less than optimal**

Convergence of the phase equilibrium algorithm has been verified by locating a near zero gradient and positive definite second derivative matrix of the operative thermodynamic potential. No residual supersaturations remain. The system is likely in the equilibrium state. The "zero" in the energy gradient is less than the "Residual norm relative tolerance for sub-optimal quadratic convergence" (fourth adjustable algorithmic parameter box in the Advanced panel of User Preferences), but greater than the "Residual norm relative tolerance for optimal quadratic convergence" (third adjustable algorithmic parameter box).

**Minimal energy computed**

Convergence of the phase equilibrium algorithm occurred because a lower minimum in the operative thermodynamic potential could not be found. The gradient of that potential may not be "zero," but the second derivative matrix is positive definite. No residual supersaturations remain. The system is likely in the equilibrium state. Test this by scanning the phase list in the Grid cell details popover for negative chemical affinities, which indicate residual supersaturations. The minimal energy test for convergence can be disabled by checking the "Prevent minimal energy test for convergence" algorithmic options box in the Advanced panel of User Preferences. The criteria for minimal energy convergence can be set in the seventh adjustable algorithmic parameter box ("Relative convergence criteria for estimation of the minimum during a linear search step") in the Advanced panel of User Preferences.

**Trivial case with no quadratic search**

Convergence of the phase equilibrium algorithm occurred because there are no computations to perform. Generally a single phase is stable and no residual supersaturations remain. The system is likely in the equilibrium state. Test this by scanning the phase list in the Grid cell details popover for negative chemical affinities, which indicate residual supersaturations. Please file a bug report documenting conditions if residual saturations are found in conjunction with this status message. File the bug report by using the "Send Feedback ..." option on the PhasePlot menu.

**No search direction. Row and column constraints are equal**

Convergence of the phase equilibrium algorithm occurred because the phase rule is satisfied exactly. The gradient of the operative thermodynamic potential may not be "zero," and the second derivative matrix may not be positive definite. The system is likely in an equilibrium state if there are no residual supersaturations. Test this by scanning the phase list in the Grid cell details popover for negative chemical affinities, which indicate residual supersaturations. If an apparent disequilibrium solution has been generated by PhasePlot, then try suppressing phases that are not anticipated to form in the stable equilibrium state (Examine converged equilibrium phase relations in neighboring cells for a clue as to what stable assemblage is likely). Do this suppression from the Constraints dialog. Please file a bug report documenting conditions if an equilibrium assemblage cannot be achieved by phase suppression. File the bug report by using the "Send Feedback ..." option on the PhasePlot menu.

### Questionable or unsuccessful termination status messages

**Quadratic algorithm did not converge in <N> iterations (rNorm: <value>)**

Convergence of the phase equilibrium algorithm failed because the "zero" in the operative thermodynamic potential gradient is less than the "Residual norm relative tolerance for sub-optimal quadratic convergence" (4th adjustable algorithmic parameter box in the Advanced panel of User Preferences). The reported <N> gives the number of major iterations attempted by the convergence algorithm and <value> is the gradient residual norm achieved when the algorithm exited. If <value> is reasonably close to the target value for sub-optimal quadratic convergence, then try increasing the number of allowed quadratic iterations (5th adjustable algorithmic parameter box in the Advanced panel of User Preferences). If that procedure fails to result in an equilibrium solution, then try relaxing the sub-optimal convergence criteria. Often, that approach will push the algorithm past a particularly difficult numerical problem and result in achieving a verifiable equilibrium state. Remember to reset the default values back to their original values for subsequent calculations.

**Addition/removal cycling for phase <phase> detected**

Convergence of the phase equilibrium algorithm failed because the <phase> cycled in and out of the stable assemblage more times than allowed by the "Maximal number of phase inclusion/phase removal cycles permitted" (13th adjustable algorithmic parameter box in the Advanced panel of User Preferences). Try two approaches to dealing with this situation. First, alter the maximal number of cycles and see if an equilibrium state can be achieved. If that approach does not work and the phase that is cycling is not anticipated to be part of the final equilibrium assemblage (examine converged equilibrium phase relations in neighboring cells for a clue as to what stable assemblage is likely), then suppress the phase from the Constraints dialog. Please file a bug report documenting conditions if an equilibrium assemblage cannot be achieved by phase suppression. File the bug report by using the "Send Feedback ..." option on the PhasePlot menu.

**The linear search direction has *zero* length**

Convergence of the phase equilibrium algorithm failed because a "downhill" step towards the minimum was found in the operative thermodynamic potential, yet a solution proceeding in that direction is infeasible. This seeming contradiction can arise if the concentration of a component in a phase approaches "zero." Various approaches may be tried to rectify the situation. All involve altering algorithmic behavior via the Advanced panel of User Preferences). First, try checking the option "Make 'zero' steplength linear searches non-fatal." If that fails to solve the problem, then try lowering the "Minimum allowed steplength in a linear search" or the "Minimum molar concentration of a component in a phase." Failing this approach please file a bug report documenting conditions that generated the problem. File the bug report by using the "Send Feedback ..." option on the PhasePlot menu. Remember to reset the default back to their original values for subsequent calculations.

**Molar redistribution was not successful (solid)**

Convergence of the phase equilibrium algorithm failed because an attempt was made to remove a phase from the assemblage and the composition of this phase could not be reassigned to the remaining phases in the assemblage without violating the bulk composition constraint on the system. This error will only occur if a liquid phase is absent from the system. Proceed cautiously by checking "Make failure in element redistribution non-fatal" in the algorithmic options section of the Advanced panel of User Preferences. Otherwise, suppress any phases that are not likely to occur in the final equilibrium assemblage (examine converged equilibrium phase relations in neighboring cells for a clue as to what stable assemblage is likely) using the Constraints dialog. Failing this approach please file a bug report documenting conditions that generated the problem. File the bug report by using the "Send Feedback ..." option on the PhasePlot menu. Remember to reset the defaults back to their original values for subsequent calculations.

**Molar redistribution was not successful (liquid)**

Convergence of the phase equilibrium algorithm failed because an attempt was made to remove a liquid from the assemblage and the composition of this liquid could not be reassigned to the remaining phases in the assemblage without violating the bulk composition constraint on the system. Proceed by checking "Make failure in element redistribution non-fatal" in the algorithmic options section of the Advanced panel of User Preferences. If this action fails to solve the problem please file a bug report documenting conditions. File the bug report by using the "Send Feedback ..." option on the PhasePlot menu.

**The hessian is rank deficient**

Convergence of the phase equilibrium algorithm failed because the algorithm encountered a phase rule violation on the way to identifying the stable equilibrium assemblage. This error can occur only if the box "Make rank deficient quadratic solutions fatal" is checked in the algorithmic options section of the Advanced panel of User Preferences. Uncheck the box and recompute the cell.