A combination of experimental and topological constraints indicates that critical equilibria play an important role in determining the pyroxene-liquid phase relations along the Mg2Si2O6-CaMgSi2O6 (enstatite-diopside) join and in natural lherzolites. Topological constraints do not permit the three-pyroxene equilibrium, orthopyroxene + diopside = pigeonite, to intersect either of the two melting equilibria, pigeonite + diopside = liquid or pigeonite = orthopyroxene + liquid in the enstatite-diopside join. Thus, with increasing pressure, pigeonite cannot abruptly replace diopside on the solidus of simplified lherzolites in this join. A supercritical low-Ca clinopyroxene, however, can replace diopside with increasing pressure along the solidus in the following manner: As the temperature of the solidus sweeps up the orthopyroxene + diopside two-phase held, the solidus crosses that region of the two-phase field where the diopside-rich Limb of the two-phase held is inflected sharply toward enstatite by the proximal top of the metastable pigeonite + diopside solvus; once the solidus is at a higher temperature than the top of the metastable solvus, the diopside coexisting with orthopyroxene becomes supercritical and its Ca content drops rapidly but continuously.In the natural system and its synthetic analogs pigeonite may replace augite on the Iherzolite solidus (orthopyroxene + augite + olivine + plagioclase + liquid) at constant pressure and decreasing Mg' [MgO/(MgO + FeO)] as the solidus liquid, which becomes less aluminous, intersects the liquid coexisting with orthopyroxene + pigeonite + augite, which becomes more aluminous with decreasing Mg'. However, with Mg' and the normative feldspar composition of the liquid nearly constant, the solidus liquid becomes sufficiently more aluminous with increasing pressure to prevent the three-pyroxene equilibrium from overtaking and intersecting the Iherzolite solidus. Thus, in the natural system as in the enstatite-diopside join, pigeonite does not replace augite abruptly. Rather, the replacement of augite by low-Ca clinopyroxene with increasing pressure is relatively gradual and is influenced by the presence of a pseudoternary pigeonite + augite solvus. Experimental evidence suggests that the top of the solvus emerges from the local solidus at 13-15 kbar and forms a critical end point to the pigeonite + augite + olivine liquidus boundary. The emergence of the critical end point distorts both the remaining liquidus boundaries and the clinopyroxene solid-solution surface, such that the CaO content of the clinopyroxene (now supercritical) coexisting with orthopyroxene decreases more rapidly with further increases in pressure. The critical end point migrates to the orthopyroxene-wollastonite join in just a few kilobars and completely eliminates the pigeonite + augite + olivine liquidus boundary curve by similar to 18 kbar.
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