Enstatite exchange between orthopyroxene and clinopyroxene

The two-pyroxene thermometer is the temperature dependence of enstatite exchange between coexisting orthopyroxene and clinopyroxene:

Mg₂Si₂O₆ (opx) = Mg₂Si₂O₆ (cpx)

The enstatite–diopside solvus is temperature-sensitive from about 900 to 1400 °C at 1 bar (Atlas, 1952; Boyd & Schairer, 1964) and at 30 kbar (Davis & Boyd, 1966). Boyd (1973) read temperature from Ca# = Ca/(Ca+Mg) in low-Fe clinopyroxene. That graphical solvus interpolates as a second-order polynomial, T (°C) = −0.7639 Ca#² + 33.135 Ca# + 1097.1.

Mixing models

Wood & Banno (1973) added a mixing model so CaO and FeO could shift pyroxene activities, with Mg²⁺ and Fe²⁺ assumed to partition equally onto M1 and M2. Later microprobe work (Nehru & Wyllie, 1974; Mori & Green, 1975, 1976; Lindsley & Dixon, 1976) showed the Davis & Boyd solvus was systematically off at low temperature. Lindsley & Dixon (1976) also found a real pressure effect: diopside Ca rises by 0.11 ± 0.01 mol % per kbar between 5 and 35 kbar. Howells & O’Hara (1975) tied the high-temperature limb to pressure and silica activity.

Wells (1977) updated Wood & Banno with those experiments and argued that the pressure effect was still smaller than analytical uncertainty. The Wells equation was the working thermometer through the late 1970s. Nickel & Brey (1984), using reversals to 60 kbar, showed it is good from 1000–1300 °C and 5–30 kbar, but overestimates T outside that window and underestimates T at higher pressure. Their reformulation uses KD = X(en)cpx / X(en)opx with an explicit P term (T in K, P in kbar).

Bertrand & Mercier (1985) inverted the synthetic data iteratively and kept a simple form. Carlson & Lindsley (1988) went the other way: a full thermodynamic model of non-ideal pyroxene components. Brey & Köhler (1990) preferred fewer fitted parameters. Because ln KD of En(opx) = En(cpx) is curved in T while (ln KD)² is nearly linear (Ehrenberg, 1979), they fit (ln KD)² on natural peridotite, in the spirit of Bertrand & Mercier.

Taylor (1998)

Taylor (1998) extended the compositional range with experiments at 10–35 kbar and 1050–1260 °C on peridotite enriched in Na₂O and TiO₂. Nimis & Grütter (2010) prefer Taylor (1998) over Brey & Köhler (1990) two-pyroxene because it agrees with the Brey & Köhler Ca-in-opx thermometer and reproduces high-Na experiments. The Brey & Köhler two-pyroxene thermometer overestimates T when Na in clinopyroxene is treated poorly.

Hygrohodos solves peridotite temperature with the Taylor (1998) two-pyroxene calibration (T_TA98), iterated with the Al-in-opx pressure.