The end members used in MELTS are spinel (MgAl2O4), hercynite (FeAl2O4), magnetite (Fe3O4), chromite (FeCr2O4), and ulvöspinel (Fe2TiO4). Dependent end members -- magnesiochromite (MgCr2O4), magnesioferrite (MgFe2O4), and qandilite (Mg2TiO4) -- may also be input. All molar proportions will be converted to the MELTS independent end members on submission.
It is assumed that Ti4+ and Cr3+ cations occupy only the octahedral site, so the FeCr2O4 and Fe2TiO4 end members are always normally ordered. The standard state ordering state in the volume model is normal for MgAl2O4 and FeAl2O4, and inverse for Fe3O4. The ordering state may be input as site occupancy or calculated using the MELTS ordering model. Alternatively, the ordering state may assumed to be normal or inverse, to the extent allowed by the stoichiometry; where appropriate equipartition will be assumed for isovalent cations (i.e. Mg2+ and Fe2+; Al3+ and Fe3+).
As formulated, Vtotal = Videal + Vexcess where Videal is a function of the conditions at which the volume is measured (Pv, Tv). On the other hand, Vexcess depends on the equilibrium ordering state, which may reflect different conditions (Ps, Ts). Output will be as follows:
- If the model is used to calculate the volume of spinels at crustal or mantle conditions (i.e. the MELTS ordering model is used with Pv = Ps, and Tv = Ts) then derivatives of Videal, Vexcess and Vtotal will be displayed.
- If the site occupancy is input or assumed (i.e. the MELTS ordering model is not used) then Ps and Ts are unknown; in this case only derivatives of Videal will be output.
- If, for example, the model is used to calculate the volume at ambient conditions of a spinel that was previously annealed (i.e. the MELTS ordering model is used but Pv ≠ Ps or Tv ≠ Ts) then derivates of Videal will be with respect to Pv and Tv and derivates of Vexcess will be with respect to Ps and Ts.