Here again is the result obtained on the previous page with equals-signs added to remind us that these are equations:
| Phase | SiO2 | Al2O3 | K2O | H2O | |
| 1 Qz | = | 1 | 0 | 0 | 0 |
| 1 Sil - 1 Qz | = | 0 | 1 | 0 | 0 |
| 2Ms - 3 Qz - 3 Sil | = | 0 | 0 | 1 | 2 |
| 1 Water | = | 0 | 0 | 0 | 1 |
| 1 Mc - 1 Qz +1 Sil - 1 Ms +1 Water | = | 0 | 0 | 0 | 0 |
Notice that the right side of the bottom equation is 0. Extracting this equation from the table we have:
1 Mc - 1 Qz +1 Sil - 1 Ms + 1 Water = 0
which upon rearranging reads:
1 Mc +1 Sil +1 Water = 1 Qz + 1 Ms
This is the desired equation among the five phases! If more phases made from the four components were added, the Gaussian Elimination procedure would lead to addtional rows below for which the right side of the equation is 0 and, therefore, more reactions.
The example shown here was selected to be relatively simple. Additional phases require more steps, but a computer can do those steps quickly. In some cases, the order of the rows or columns might need to be changed to get an answer. But again, the computer can be coded to make that adjustment.
Two tools are available on this website to identify possible equations among a group of phases using the Gaussian Elimination method. Figure 01 provides pulldown lists of end member phases of known compositions that can be selected by you for reaction identification. Figure 02 asks you to upload a file with phases and their compositions and then identifies possible reactions among those phases.
Both of these tools also look for reactions among subgroups of phases from the group selected or uploaded. For n phases there are 2n possible groups, so this is a good task for a computer. The code checks all the possible phase groups and the reactions found may not all be mathematically independent of one another. Note also that the Gaussian Elimination method requires that there be more phases than components. In some cases, you may need to enter one or more additional phases to get the results you seek. For example, add Qz to And, Ky, and Sil if you want to see all the aluminosilicate reactions.
A spreadsheet that uses Gaussian Elimination to identify reactions for 3- and 4-component systems created for teaching by Dexter Perkins is available for downloading on this SERC website page along with a pdf file with his explanation of the process.
