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Mantle potential temperatures ( T  p ) provide insights into mantle circulation and tests of whether Earth is the only planet to exhibit thermally bi-modal volcanism—a distinctive signature of modern plate tectonics. Planets that have a stagnant lid, for example, should exhibit volcanism that is uni-modal with  T  p , since mantle plumes would have a monopoly on the genesis of volcanism. But new studies of magmatic ferric-ferrous ratios (XFe   2    O  3liq    /   X   FeO    liq$X_{{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{{\text{liq}}}{\text{/}}X_{{\text{FeO}}}^{{\text{liq}}}$   ) ( Cottrell and Kelley 2011 ) and the olivine-liquid Fe-Mg exchange coefficient,  K  D (Fe-Mg) Ol-liq  (or  K  D ) ( Matzen et al. 2011 ) indicate that re-evaluations of  T  p  are needed. New tests and calibrations are thus presented for oxygen fugacity ( f  O 2  ),XFe   2    O  3liq    /   X   FeO    liq$X_{{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{{\text{liq}}}{\text{/}}X_{{\text{FeO}}}^{{\text{liq}}}$   , potential temperature ( T  p ), melt fraction ( F ),  K  D , and peridotite enthalpies of fusion (∆ H  fus ) and heat capacities ( C   P  ). The new models forXFe   2    O  3liq    /   X   FeO    liq$X_{{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{{\text{liq}}}{\text{/}}X_{{\text{FeO}}}^{{\text{liq}}}$    and  f  O 2   reduce error by 25–30%, and residual error for all models appears random; this last observation supports the common, but mostly untested, assumption that equilibrium is the most probable of states obtained by experiment, and perhaps in nature as well. Aggregate 1s error on  T  p  is as high as ~±77 °C, and estimates of  F , and mantle olivine composition, are the greatest sources of error. Pressure and ∆ H  fus  account for smaller, but systematic uncertainties (a constant ∆ H  fus  can under-predict  T  excess  =T  p   plume    −   T  p   ambient$T_{\text{p}}^{{\text{plume}}} - T_{\text{p}}^{{\text{ambient}}}$   ; assumptions of 1 atm can under-predict  T  p ). However, assumptions about whether parental magmas are incremental, accumulated, or isobaric batch melts induces no additional systematic error.

american mineralogist

Special Collection: Olivine: Rates and styles of planetary cooling on Earth, Moon, Mars, and Vesta, using new models for oxygen fugacity, ferric-ferrous ratios, olivine-liquid Fe-Mg exchange, and mantle potential temperature