Solution model reformulation refers to the way Perple_X handles solution models with missing endmembers. Perple_X '05 does not really do reformulation, rather it generates pseudocompounds over the entire range of compositions that are theoretically possible for a solution model, and then decides which compositions are possible given the endmembers actually present. In contrast, more recent versions of Perple_X reformulate solution models so as to eliminate missing endmembers. In solutions with one independent chemical mixing site (e.g., Gr-Py-Alm garnet) this is straightforward in that there is a one-to-one correspondence between missing and eliminated endmembers. However, reciprocal solutions (i.e., solutions with more than one-independent chemical mixing site, such as in minerals with both Mg-Fe and Tschermaks exchange) are more complicated. For reciprocal solutions reformulation is done by eliminating one or more of the species represented by the missing endmember and this requires elimination of at least one additional endmember. In general there are several ways in which this can be done and it is important for users to understand this in order to control the choices VERTEX makes. Consider the case of a reciprocal solution (A,B)(C,D) with endmembers AC, AD, BC, and BD. Supposing endmember AC is missing, VERTEX has two choices:
Eliminate species A from the model, this requires elimination of endmember AD as well as AC, and results in the solution model B(C,D).
Eliminate species C from the model, this requires elimination of endmember BC as well as AC, and results in the solution model (A,B)C.
Left to make this choice on its own VERTEX will eliminate the species from the first site (as defined in the model input), but the user can control the choice by eliminating an additional endmember (i.e., if endmember BC is excluded, then VERTEX can only make the second choice). In more complex reciprocal solutions choices may require the elimination of different numbers of endmembers, in this case VERTEX is programmed to select choice(s) that eliminate the fewest number of endmembers. Here, again, the user can steer this process by excluding additional endmembers. Returning to the (A,B)(C,D) example, in Perple_X '05 if the endmember AC was missing, then VERTEX would have generated compositions over the AD-BC-BD ternary composition space. In contrast, the current version of Perple_X will reformulate the solution as a simple binary (either B(C,D) or (A,B)D). To get the ternary solution AD-BC-BD or the cross-site binary AD-BC the user must enter these solutions in the solution model data file explicitly as single site mixing models.