A METHOD FOR ESTIMATING TEMPERATURE AND OXYGEN FUGACITY FOR AN ASSEMBLAGE OF CLINOPYROXENE, AENIGMATITE, ILMENITE, AND QUARTZ IN PERALKALIC RHYOLITE

Clinopyroxene, quartz, and ilmenite comprise a common mafic phenocryst assemblage in peralkaline rhyolite (i.e., comendite and pantellerite). When olivine is also part of the assemblage, QUIlF equilibria can be used to estimate temperature (T). If olivine is not present, but aenigmatite is, T and oxygen fugacity (fO₂) may be estimated from clinopyroxene-ilmenite-quartz equilibria (AHQ and FeMgAugIlm from QUIlF) and aenigmatite-ilmenite-quartz equilibria. In this method, the QUILF95 program is used to calculate oxygen fugacities, hematite activities (a_Hem), and ilmenite activities (a_Ilm) over a range of T (600-800°C) at a specified pressure (P, in bars), which defines one line in T-log fO₂ space. Another line can be calculated over the same temperature range for aenigmatite-ilmenite-quartz equilibrium (Aen + O₂ = 2Hem + Ilm + 4Qtz + Na₂SiO₅ (melt); see White et al., 2005, Can. Mineral., 43: 1331-1347, and Macdonald et al., 2011, Lithos, 125: 553-568) from the following equation:

log fO₂ = -22784/T + 8.6654 – 0.2189(P-1)/T + 2 log a_Hem + log a_Ilm,

where units for T are K. This equation assumes unit activities for aenigmatite, silica activity relative to quartz, and the Na₂SiO₅ (melt) component. The slope (m) and intercept (b) of each line (subscript n) can be calculated from basic linear algebra:

[b_n; m_n] = (M_n^TM_n)^-1M_n^Ty_n,

where M is a 5 x 2 matrix with unit values in the first column and temperatures (600, 650, 700, 750, 800) in the second, and y is a 5 x 1 matrix consisting of calculated log fO₂ values. Temperature (T, °C) then equals (b₁ – b₂)/(m₁ – m₂) and log fO₂ equals T(m₁) + b₁.