On the existence and structure of a mush at the inner core boundary of the Earth

TL;DR

This paper investigates the stability of the inner core boundary of Earth, suggesting that a mushy zone likely exists due to complex thermal and compositional processes, with implications for Earth's inner core structure.

Contribution

It provides a linear stability analysis of the inner core boundary, highlighting the conditions under which a mushy zone can form and estimating its possible thickness and structure.

Findings

The inner core boundary is likely morphologically unstable.

A significant mushy zone could develop, possibly spanning up to the entire inner core radius.

The mushy zone would be thin, with interdendritic spacing possibly only a few meters.

Abstract

It has been suggested about 20 years ago that the liquid close to the inner core boundary (ICB) is supercooled and that a sizable mushy layer has developed during the growth of the inner core. The morphological instability of the liquid-solid interface which usually results in the formation of a mushy zone has been intensively studied in metallurgy, but the freezing of the inner core occurs in very unusual conditions: the growth rate is very small, and the pressure gradient has a key role, the newly formed solid being hotter than the adjacent liquid. We investigate the linear stability of a solidification front under such conditions, pointing out the destabilizing role of the thermal and solutal fields, and the stabilizing role of the pressure gradient. The main consequence of the very small solidification rate is the importance of advective transport of solute in liquid, which tends to remove light solute from the vicinity of the ICB and to suppress supercooling, thus acting against the destabilization of the solidification front. For plausible phase diagrams of the core mixture, we nevertheless found that the ICB is likely to be morphologically unstable, and that a mushy zone might have developed at the ICB. The thermodynamic thickness of the resulting mushy zone can be significant, from $\sim100$ km to the entire inner core radius, depending on the phase diagram of the core mixture. However, such a thick mushy zone is predicted to collapse under its own weight, on a much smaller length scale ($\lesssim 1$ km). We estimate that the interdendritic spacing is probably smaller than a few tens of meter, and possibly only a few meters.