Sillimanite is one of the aluminosilicate polymorphs (Al2SiO5). To balance this formula, you find that the aluminum must be in both 6+ and 4+ oxidation states. Thus the more accurate formula looks like Al6+Al4+Si4+O5. The Al6+ all reside in octahedral coordination, while the Al4+ and Si4+ mix on tetrahedral sites. There are two symmetrically distinct tetrahedral sites per unit cell called T1 and T2. There are four formula units per unit cell and thus there are 8 total T-sites in the unit cell, four T1 and four T2 filled with 4 Al4+ and 4 Si4+. In fully disordered sillimanite the Al4+ and Si4+ are evenly distributed over these tetrahedral sites (two of each element in each of the two T-sites). Calculate the entropy of configuration (Smixing) for fully disordered sillimanite at 0K. Recall, S = klnΩtotal and Ωtotal = Ωsite1Ω site2