Potassium diffusion in melilite: Experimental studies and constraints on the thermal history and size of planetesimals hosting CAIs

Among the calcium-aluminum-rich inclusions (CAIs), excess ⁴¹K (⁴¹K*), which was produced by the decay of the short-lived radionuclide ⁴¹Ca (t_1/2 = 0.1 Myr, has so far been detected in fassaite and in two grains of melilites. These observations could be used to provide important constraints on the thermal history and size of the planetesimals into which the CAIs were incorporated, provided the diffusion kinetic properties of K in these minerals are known. Thus, we have experimentally determined K diffusion kinetics in the melilite end-members, åkermanite and gehlenite, as a function of temperature (900-1200 °C) and crystallographic orientation at 1 bar pressure. The closure temperature of K diffusion in melilite, T_c(K:mel), for the observed grain size of melilite in the CAIs and cooling rate of 10-100 °C/Myr, as calculated from our diffusion data, is much higher than that of Mg in anorthite. The latter was calculated from the available Mg diffusion data in anorthite. Assuming that the planetesimals were heated by the decay of ²⁶Al and ⁶⁰Fe, we have calculated the size of a planetesimal as a function of the accretion time t_f such that the peak temperature at a specified radial distance r_c equals T_c(K:mel). The ratio (r_c/R)³ defines the planetesimal volume fraction within which ⁴¹ K* in melilite grains would be at least partly disturbed, if these were randomly distributed within a planetesimal. A similar calculation was also carried out to define R versus t_f relation such that ²⁶Mg* was lost from ∼50% of randomly distributed anorthite grains, as seems to be suggested by the observational data. These calculations suggest that ∼60% of melilite grains should retain ⁴¹K* if ∼50% of anorthite grains had retained ²⁶Mg*. Assuming that t_f was not smaller than the time of chondrule formation, our calculations yield minimum planetesimal radius of ∼20-30 km, depending on the choice of planetesimal surface temperature and initial abundance of the heat producing isotope ⁶⁰Fe.