A new estimate of the chondrule cooling rate deduced from an analysis of compositional zoning of relict olivine

Compositional zoning in chondrule phenocrysts records the crystallization environments in the early solar nebula. We modeled the growth of olivine phenocrysts from a silicate melt and proposed a new fractional crystallization model that provides a relation between the zoning profile and the cooling rate. In our model, we took elemental partitioning at a growing solid-liquid interface and time-dependent solute diffusion in the liquid into consideration. We assumed a local equilibrium condition, namely, that the compositions at the interface are equal to the equilibrium ones at a given temperature. We carried out numerical simulations of the fractional crystallization in one-dimensional planar geometry. The simulations revealed that under a constant cooling rate the growth velocity increases exponentially with time and a linear zoning profile forms in the solid as a result. We derived analytic formulae of the zoning profile, which reproduced the numerical results for wide ranges of crystallization conditions. The formulae provide a useful tool to estimate the cooling rate from the compositional zoning. Applying the formulae to low-FeO relict olivine grains in type II porphyritic chondrules observed by Wasson and Rubin, we estimate the cooling rate to be ∼200-2000 K s^–1, which is greater than that expected from furnace-based experiments by orders of magnitude. Appropriate solar nebula environments for such rapid cooling conditions are discussed.