Isotope fractionation in silicate melts by thermal diffusion

Abstract

Arising from F. Huang, P. et al. Nature 464, 396–400 (2010)10.1038/nature08840; Huang et al. reply

It was recently shown that relatively large (compared to analytical precision) steady state thermal isotope fractionations are produced in silicate melts whenever temperature differences are maintained for a sufficiently long time^1,2. Huang et al.³ reported new data on thermal isotopic fractionation of magnesium, calcium, and iron in silicate liquids, and claimed (1) that thermal isotopic fractionations in silicate liquids are independent of composition and temperature, and (2) that their “results lead to a simple and robust framework for characterizing isotope fractionations by thermal diffusion in natural and synthetic systems”. Here I consider whether the data and arguments presented by Huang et al.³ support their claims. In summary, I caution against assuming (on the basis of the data presented by Huang et al.³) that the thermal isotopic fractionations are independent of temperature and composition, or that a framework of the type claimed has been found.

Main

Huang et al.³ reported new data on thermal isotopic fractionation of magnesium, calcium and iron in silicate liquids that extend the earlier results^1,2 to a larger temperature range and to compositions other than basalt. The magnesium isotopic composition versus temperature reported by Huang et al.³ for molten andesite and basalt are shown in Fig. 1. The local slope in such a plot determines the thermal-diffusion isotopic sensitivity Ω, defined as the magnitude of isotopic fractionation per temperature offset, and expressed in units of ‰ °C⁻¹ amu⁻¹ (here amu indicates atomic mass unit). If Ω is independent of temperature, the data would fall on straight lines, which is clearly not the case for the andesite experiments (squares in Fig. 1), where the slope of the isotopic fractionations versus temperature shows that Ω_Mg varies from about 0.05 ‰ °C⁻¹ amu⁻¹ for T > 1,450 °C to about 0.02 ‰ °C⁻¹ amu⁻¹ for T < 1,450 °C. Despite this, Huang et al.³ imply in their figure 1 that Ω_Mg = 0.03 ‰ °C⁻¹ amu⁻¹ with an uncertainty of only ±10%. The iron isotope data reported by Huang et al.³ also show large variations of Ω_Fe with temperature.

Figure 1: Isotopic fractionation of magnesium as a function of temperature.

Data are taken from table 1 in Huang et al.³. Shown are values for molten Mount Hood andesite (squares for data from a 46-h experiment, circles for data from a 168-h experiment), and for molten mid-ocean-ridge basalt (diamonds for data from a 264-h experiment). The isotopic fractionations are given as . The figure shows that in the case of andesite, Ω_Mg is not constant, but rather decreases by a factor of more than two between T > 1,500 °C and T < 1,500°C. The data for basalt are too few to support a conclusion to the effect that Ω_Mg is independent of composition.

PowerPoint slide

Huang et al.³ claim to have cast their experimental observations in a theoretical framework. This ‘theoretical framework’ is simply a parameterization of an assumed, not theoretically derived, functional form for the mass dependence of a quantity they call ΔS_T, which, like Ω, is proportional to the slope of the thermal isotope fractionations versus temperature. The assumed expression for ΔS_T is , where X and Y are the mass of two isotopes of an element of valence Z and ionic radius a. The three quantities c, α and β were adjusted such that the calculated ΔS_T reproduces three values of ΔS_T taken from their experiments. Leaving aside the issues of what specific value of ΔS_T to choose, given its variation with temperature, which is proportional to the slope of δ²⁶Mg versus temperature shown in Fig. 1, or that all the elements considered have the same Z, using a parameterization with three free parameters to fit three data does not constrain and validate the functional form of the parameterization. One can, however, test the proposed parameterization by calculating ΔS_T for all the major elements of basalt (magnesium, calcium, iron, silicon and oxygen) and comparing these to the experimental data reported by Richter et al.². As might be expected, the parameterization works reasonably well in reproducing the measured ΔS_T for magnesium, calcium and iron; however, when applied to oxygen and silicon, the calculated values and the measured values differ by more than a factor two for oxygen and more than a factor of ten for silicon.

I caution against assuming (on the basis of the data presented by Huang et al.³) that thermal isotope fractionations in silicate liquids are independent of temperature and composition or that they have found “a simple and robust framework for characterizing isotope fractionations by thermal diffusion in natural and synthetic systems”.