Solute partitioning under continuous cooling conditions as a cooling rate indicator

Abstract

A mathematical model is developed to describe the concentration profiles as a function of time of a solute dissolved in two coexisting finite phases under continuous cooling conditions. A temperature‐dependent partitioning of the solute between the two phases is included. The model relates to the use of experimentally determined solute profiles to infer the rates at which various rocks cooled. The model employs finite difference equations and the Thomas tridiagonal method to solve the appropriate differential equations describing the solute partitioning. To illustrate the application of the model, the partitioning of zirconia between coexisting ilmenite and ulvöspinel is considered. It is shown that cooling rates can be calculated not only from solute concentration profiles within the grains but also from the ratio of the solute concentrations at a given distance on both sides of the interface or from the ratio of the average solute concentrations in the two phases. The cooling rates of a suite of Apollo 15 Elbow Crater gabbros are calculated from measured ratios of concentrations at 10 μm from the interfaces between the phases. A comparison is made of calculated concentration ratios 10 μm from the interface and cooling rates for equilibrium versus uniform initial concentrations. It is shown that the Elbow Crater gabbros could not have had a uniform concentration profiles at the previously suggested initial temperature of 1350 K. Also considered are the effects of the initial temperature, the grain sizes, and the diffusion coefficients of Zr in the phases on the calculated cooling rates. Finally, suggestions are made for other systems where the present model can be applied to estimate the thermal histories of rocks.

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

“…4a. It is very similar to those of Lasaga et al (1977), Onorato et al (1981), Liang (2007, 2012), and Liang (2014) for diffusive redistribution of a chemical component between two minerals. To focus on the definition of closure temperature for cooling bi-mineralic systems, we consider a simplified problem of a trace element diffusive exchange between two minerals (A and B) in a 1-D geometry subject to prescribed cooling (Eq.…”

“…In the empirical and analytical equations of Ehlers and Powell (1994) and Powell and White (1995), closure temperatures for bi-mineralic systems depend only on diffusion parameters of the mineral that has a slower diffusion rate for the element of interest. In general, diffusive exchange of an element of interest between two minerals depends on diffusion coefficients and partition coefficients of the element in the two minerals, grain sizes and volume fractions of individual minerals (Lasaga et al, 1977;Onorato et al, 1981;Eiler et al, 1992;Liang, 2014). Thus, one would expect that these factors also affect the closure temperatures of bi-mineralic systems.…”

“…Attempts have been made to investigate closure temperatures for cooling bi-mineralic and poly-mineralic systems (e.g., Lasaga et al, 1977;Onorato et al, 1981;Lasaga, Fig. 1.…”

Near conductive cooling rates in the upper-plutonic section of crust formed at the East Pacific Rise

“…Hence, there will be a temperature, Tc, at which diffusion becomes too slow for measurable Mg loss from the plagioclase. This closure temperature (Tc) depends on the distance from the interface (Dodson, 1986;Onorato et al, 1981), such that the rims of a plagioclase crystal will be able to maintain equilibrium Mgconcentrations down to lower temperatures than the core of the crystal, leading to the development of a closure profile that is convex upwards for a continuous cooling history. Faak et al (2014) show how the evolution of the resulting concentration profile of Mg in plagioclase depends on the cooling history.…”

Fe–Mg interdiffusion rates in clinopyroxene: experimental data and implications for Fe–Mg exchange geothermometers

“…10) using the geothermometer by pairing either the compositions at the core of each crystal 12 (under the assumption that they have not been reset, referred to as core-core temperatures 13 henceforth), or the compositions at the rims of the two crystals (rim-rim thermometry). See 14 Onorato et al (1981) for more details on the evolution of calculated temperatures at different 15 points of the crystal in such a cooling system. 16 We consider two examples for peak temperatures corresponding to cases that may arise 17 in mantle (1300 °C) and crustal metamorphic (900 °C) samples, respectively.…”