Closure temperature in cooling bi-mineralic systems: I. Definition and with application to REE-in-two-pyroxene thermometer

Abstract

Closure temperature is an important concept to many diffusion related problems involving cooling. The basic idea and formulation were outlined in the seminal work of Dodson for cooling mono-mineralic systems. The Dodson's equation has been widely used to calculate closure temperatures for igneous and metamorphic rocks that contain more than one mineral. The purpose of this study is to examine closure temperatures in cooling bi-mineralic systems and to investigate the physical meaning of temperatures calculated using the REE-in-two-pyroxene thermometer. We conduct numerical simulations of diffusive redistribution of trace elements between two coexisting minerals under prescribed cooling using temperature-dependent diffusion coefficients and mineral-mineral partition coefficients. Following Dodson's treatment, the closure temperature in bi-mineralic systems can be defined by the evolution of either average trace element concentrations in the two minerals or their ratio. The latter defines an effective partition coefficient. Closure temperatures calculated based on the two definitions are compared for a range of cooling rates, grain sizes, mineral proportions, and temperature-dependent partition coefficients and diffusion coefficients. Temperatures defined by the effective partition coefficient are recommended. Application to diffusive redistribution of rare earth elements (REE) in orthopyroxene-clinopyroxene systems demonstrates that closure temperature differences among REE are small and hence their average value may be used as the closure temperature for the cooling two-pyroxene system. The average closure temperature of REE in the two-pyroxene system is essentially the same as the temperature calculated using the REE-in-two-pyroxene thermometer and practically independent of pyroxene modal abundance in the system. Differences in temperatures calculated using the REE-and major element-based two-pyroxene thermometers can be used to infer cooling rate of two-pyroxene bearing mafic and ultramafic rocks.

Formation of fast-spreading lower oceanic crust as revealed by a new Mg–REE coupled geospeedometer

“…The basis of geospeedometry using bulk closure temperatures was initially defined by Dodson (1973) for diffusion in a single crystal and has recently been extended to polycrystalline petrological systems (e.g., Eiler et al, 1992;Ehlers and Powell, 1994;Yao and Liang, 2015;Liang, 2017). In general, the bulk closure temperature (T c ) of an element of interest ( j) in two coexisting minerals (α and β) can be described as,…”

Spatial variations in cooling rate in the mantle section of the Samail ophiolite in Oman: Implications for formation of lithosphere at mid-ocean ridges

“…Using approximate solutions to diffusion equations 272 for bimineralic systems, Liang (2014) showed that for two minerals, diffusive reequilibration 273 13 rates follow the "minor's rule", which states the mineral with the lesser amount of a trace 274 element in the system controls the reequilibration timescale. This idea was further explored in 275 numerical simulations of REE redistribution in two pyroxene systems by Yao and Liang (2015), 276 and by Liang (2015), who developed a generalized closure temperature equation for bimineralic 277 systems. These studies found that, except in peridotites with very little cpx ( / <0.05, 278…”

Thermal state and structure of lithospheric mantle beneath the Xing'an Massif, northeast China: Constraints from mantle xenoliths entrained by Cenozoic basalts

“…The closure temperature is the effective temperature at which a mineral ceases diffusive exchange of an element (or component) with other phases in a system at a given cooling rate (Dodson, ). The T REE reflects the average closure temperatures for the diffusive exchange of REE + Y between clinopyroxene and orthopyroxene and probably also approximates the magmatic temperature (Liang et al, ; Yao & Liang, ). Major‐element thermometry yields much lower temperatures than T REE in a cooling process, due to differences in the closure temperature between the trivalent and divalent cations in pyroxenes.…”

“…The disparity between T REE and major‐element temperatures is pervasive for Keluo mantle xenoliths (Figure ) and is thus not an artificial result. These temperature discrepancies may be related to large grain size or the cooling process experienced by the sample (Liang et al, ; Yao & Liang, ). At a given cooling rate, the smaller the grains, the more completely the system attains chemical re‐equilibrium, meaning that T REE more closely approximates the major‐element temperatures.…”

“…fusive exchange of REE + Y between clinopyroxene and orthopyroxene and probably also approximates the magmatic temperatureYao & Liang, 2015). Major-element thermometry yields much lower temperatures than T REE in a cooling process, due to differences in the closure temperature between the trivalent and divalent cations in pyroxenes.Samples from theAershan and Nuomin regions yield consistent major-element temperatures and T REE and overlap with the composition of well-equilibrated continental peridotites reported by Liang et al (2013).…”