Abstract

Although many formulations of plagioclase + liquid equilibria have been calibrated in the last decade, few models specifically address the issue of temperature (T) prediction. Moreover, for those that do, T error is not addressed, greatly limiting their use as geothermometers. Several recent models of plagioclase-liquid equilibria are thus tested for their ability to recover T from their calibration data, and predict T from experiments not used for calibration. The models of Sugawara (2001) and Ghiorso et al. (1995, 2002) outperform earlier calibrations. These models perform reasonably well at T > 1100 °C, though recovery and prediction of T is less precise for hydrous compositions. In addition, these models cannot be integrated with geo-hygrometers, or other mineral-melt thermometers and barometers; the following expression predicts T with up to 40% greater precision:

 
\begin{eqnarray*}&&\frac{10^{4}}{\mathit{T}(K)}\ =\ 6.12\ +\ 0.257\ ln\ \left(\frac{[Ab^{pl}]}{[Ca^{liq}(Al^{liq})^{2}(Si^{liq})^{2}]}\right)\ {-}\ 3.166[Ca^{liq}]\ +\ 0.2166[H_{2}O^{liq}]\\&&{-}\ 3.317\left[\frac{Al^{liq}}{Al^{liq}\ +\ Si^{liq}}\right]\ +\ 1.216[Ab^{pl}]^{2}\ {-}\ 2.475\ {\times}\ 10^{{-}2}[\mathit{P}(kbar)]\end{eqnarray*}
(1)

Because these thermometers are pressure (P) sensitive, a temperature-sensitive barometer was also developed

 
\begin{eqnarray*}&&\mathit{P}(kbar)\ =\ {-}42.2\ +\ 4.94\ {\times}\ 10^{{-}2}\ [\mathit{T}\ (K)]\ +\ 1.16\ {\times}\ 10^{{-}2}\ \mathit{T}\ (K)\ ln\left(\frac{[Ab^{pl}Al^{liq}Ca^{liq}]}{[An^{pl}Na^{liq}Si^{liq}]}\right).\\&&{-}\ 382.3[Si^{liq}]^{2}\ +\ 514.2[Si^{liq}]^{3}\ {-}\ 19.6ln[Ab^{pl}]\ {-}\ 139.8[Ca^{liq}]\\&&+\ 287.2[Na^{liq}]\ +\ 163.9\ [K^{liq}]\end{eqnarray*}
(2)

In these models, T is in Kelvins and P is in kbar. Anpl and Abpl are the fractions of anorthite and albite in plagioclase, calculated as cation fractions: An = CaO/(CaO + NaO0.5 + KO0.5) and Ab = NaO0.5/(CaO+NaO0.5+KO0.5). Terms such as Alliq refer to the anhydrous cation fraction of Al in the liquid; H2O in Equation 1 is in units of wt%. Errors on these models are comparable to those for clinopyroxene thermobarometers: In Equation 1, R = 0.99 and the standard error of estimate (SEE) is 23 K; for Equation 2, R = 0.94 and the SEE is 1.8 kbar. The models successfully recover mean pressures for experimental data that are not used for calibration, and are furthermore able to recover near-1-atm P estimates for volcanic rocks from Kilauea, Hawaii, which are thought to have crystallized at or very near Earth’s surface.

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