Previous investigators have shown that natural chromium-bearing spinel solid solutions adhere closely to the general formula (Mg, Fe++) (Cr, Al, Fe+++)2O4 and may therefore be graphically portrayed in a triangular prism, the length of which represents the ratios MgO/FeO, and the cross section the relative proportions of Cr2O3, Al2O3, and Fe2O3. In this paper, theoretical expressions are derived whereby the prism may be "contoured" for conditions of isothermal–isobaric equilibrium according to (a) the spinel compositions that may coexist with olivine or pyroxene having specific MgO/FeO ratios; (b) the activity ratios of Cr/Al, Cr/Fe+++, or Al/Fe+++ that obtain in the environments in which the spinel solid solutions form, and (c) the oxygen fugacities that accompany formation of spinel in systems containing olivine (forsterite–fayalite) and orthopyroxene (enstatite–ferrosilite). Rough "working" values for the thermochemical coefficients involved are estimated from limited calorimetric data and chemical analyses of spinel–olivine and spinel–orthopyroxene pairs.

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