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

The Mn–Cr decay system, in which Mn decays to Cr (t1/2 = 3.7 Ma) has been widely used to construct Cr/Cr vs. Mn/Cr isochrons and thus determine relative ages of early solar system objects or events, assuming that the initial Cr isotopic ratio, (Cr/Cr)o, equals ( Mn/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 MgAl2O4 end-member composition, as a function of temperature and oxygen fugacity (f(O2)). 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(O2) in the range of f(O2) of around ±2 log units relative to that of the wüstite–magnetite buffer. The difference in the D(Cr) between the two stocks and the observed D(Cr) vs. f(O2) 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(O2) conditions, respectively. Assuming a homogeneous semi-infinite matrix, the closure temperature (Tc) of Cr diffusion in spinel has been calculated as a function of grain size, cooling rate, peak temperature (To) and f(O2). Also the dependence of D(Cr) and Tc(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 Tc 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 Tc(Cr) and Tc(Mn) for the estimation of the (Mn/Mn)o ratio from an internal isochron defined by these minerals. Finally, we discuss the problem of determining the Tc for an internal isochron in relation to the individual Tc(Cr) for spinel, olivine and orthopyroxene. 2015 Elsevier Ltd. All rights reserved.