Diffusion kinetics of Cr in spinel: Experimental studies and implications for 53Mn–53Cr cosmochronology

Abstract

The 53 Mn-53 Cr decay system, in which 53 Mn decays to 53 Cr (t 1/2 = 3.7 Ma) has been widely used to construct 53 Cr/ 52 Cr vs. 55 Mn/ 52 Cr isochrons and thus determine relative ages of early solar system objects or events, assuming that the initial Cr isotopic ratio, ( 53 Cr/ 52 Cr) o , equals ( 53 Mn/ 52 Cr) o . With the primary objective of interpretation of these ages within a diffusion kinetic framework, we have determined the tracer diffusion coefficient of Cr in natural spinels, which are very close to the MgAl 2 O 4 end-member composition, as a function of temperature and oxygen fugacity (f(O 2 )). It is found that the diffusion coefficient of Cr, D(Cr), in two stocks of spinels (referred to as cut-gems and gem-gravels) with very similar major element chemistry is consistently different, but the data in each stock yield well defined Arrhenius relations that show a difference of log D of 0.6-1.0, depending on temperature, with the D(Cr) in gem-gravel being higher than that in the cut-gem stock. The D(Cr) was found to have a positive dependence on f(O 2 ) in the range of f(O 2 ) of around ±2 log units relative to that of the wü stite-magnetite buffer. The difference in the D(Cr) between the two stocks and the observed D(Cr) vs. f(O 2 ) relation has been explained in terms of a change of point defect concentration resulting from heterovalent substitution of trace elements and equilibration with the imposed f(O 2 ) conditions, respectively. Assuming a homogeneous semi-infinite matrix, the closure temperature (T c ) of Cr diffusion in spinel has been calculated as a function of grain size, cooling rate, peak temperature (T o ) and f(O 2 ). Also the dependence of D(Cr) and T c (Cr) on the Cr# (i.e. Cr/(Cr + Al) ratio) has been accounted for using available D(Cr) vs. Cr# data in Suzuki et al. (2008). We argue, on the basis of crystal chemical considerations and available diffusion kinetic data for minerals, that the T c for Mn should be much lower than that for Cr in spinel, olivine and orthopyroxene, and discuss the potential implications of the anticipated disparity between T c (Cr) and T c (Mn) for the estimation of the ( 53 Mn/ 55 Mn) o ratio from an internal isochron defined by these minerals. Finally, we discuss the problem of determining the T c for an internal isochron in relation to the individual T c (Cr) for spinel, olivine and orthopyroxene.

Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes

“…From a recent study on diffusion kinetics of Cr and Mn in spinel, olivine, and orthopyroxene, we infer that parent body metamorphism should have affected Mn more than Cr (Posner et al. ). Therefore, metamorphic heating may have caused small‐scale redistribution of Mn and Cr and the scatter of Allende components in the isochron diagram.…”

Diffusion-driven chromium isotope fractionation in ultramafic cumulate minerals: Elemental and isotopic evidence from the Stillwater Complex

“…Soret diffusion could produce large Cr isotopic fractionations, with heavy Cr isotopes preferentially diffusing down the thermal gradient. However, Soret diffusion cannot be responsible for the heavy Cr isotopic compositions observed here in silicate minerals because thermal diffusivity (Lesher and Walker, 1986) is dozens of orders of magnitude faster than that of elemental Cr in minerals (Ganguly et al, 2007;Posner et al, 2016;Jollands et al, 2017). It is thus reasonable to assume that no measurable or long-lasting temperature gradient can occur at the grain scale.…”

“…Chromium diffuses slower than Fe, Mg, and Li, but faster than Ti and Si in silicate minerals (e.g., Ito and Ganguly, 2006;Ganguly et al, 2007;Posner et al, 2016), and magmatic minerals thus commonly present Cr zoning patterns. Indeed, Cr diffusion profiles in olivine, orthopyroxene, and spinel have been used to calculate the cooling rates of meteorites (e.g., Lugmair and Shukolyukov, 1998;Ito and Ganguly, 2006).…”

“…Olivine and pyroxene are the most common silicate minerals in the lithospheric mantle (generally up to >90%), commonly coexisting with chromite in mafic-ultramafic complexes such as layered intrusions and ophiolites, the major hosts of Cr resources on Earth. The kinetics of Cr volume diffusion in olivine (Ito and Ganguly, 2006;Jollands et al, 2017), pyroxene (Ganguly et al, 2007), and chromite (Suzuki et al, 2008;Posner et al, 2016) have been well-documented. Cr diffusion kinetics can yield timescales of magmatic processes and can be used to determine the closure temperatures of the 53 Mn- 53 Cr radiogenic dating system (e.g., Ito and Ganguly, 2006;Ganguly et al, 2007).…”

Millennial storage of near-Moho magma

“…We used the FEniCS (22) finite element code to model 2D diffusion of Cr-Al exchange in spinels, combined with a nested sampling Bayesian inversion (23) to constrain the timescales of mush storage with robust estimates of uncertainty. We derived diffusivity equations for Cr-Al exchange in Cr-spinel that take into account the covariance between the underlying diffusive parameters (24,25) Table S1). We ran the models using Gaussian prior distributions with 1σ uncertainties for temperature (1215 ± 30°C), pressure (0.8 ± 0.14 GPa) (12,18), and ferric iron contents (Fe 3+ /Fetotal) of the system (0.14 ± 0.02) (26).…”