Widmanstatten pattern

How can the crystal figure inside an iron meteorite reveal how slowly its parent body cooled?

Cut an iron meteorite, polish the face, and swab it with dilute acid. Out of plain grey metal comes a lattice of interlocking bands, sometimes centimetres long, crossing at fixed angles across the whole slab.

The claim made about that figure is a strange one: not that it shows the meteorite is old, or extraterrestrial, but that it records a rate — how fast, in degrees per million years, a body that no longer exists shed its heat four and a half billion years ago. How can a static pattern in a lump of metal contain a rate at all? A rate is a thing divided by a time, and neither is obviously present.

Start with what the bands are. Iron meteorites are iron-nickel alloys, and at high temperature such an alloy is a single crystalline phase — taenite, face-centred cubic. A whole meteorite is often one enormous crystal of it.

Cool it, and thermodynamics changes its mind. Below a certain temperature the single phase is no longer stable and the alloy separates into two: kamacite, low in nickel and body-centred cubic, and taenite retaining the rest. (Where that begins depends on the bulk nickel content; for common iron meteorites it is somewhere near 700-900 K, a range I am recalling rather than reading off a phase diagram.)

Now the geometry. Kamacite does not appear at random: it nucleates and grows as flat plates on particular planes of the parent taenite crystal — the {111} family, of which there are four sets. Four plate orientations inherited from one parent crystal is what makes the pattern a pattern, coherent across ten centimetres rather than a jumble of local grains. Hence the name for these meteorites, octahedrites.

Here is where the rate enters. Kamacite holds less nickel than the alloy it grows from. So every increment of plate growth has to reject nickel, and that nickel must move away into the surrounding taenite. It moves by solid-state diffusion, which in a metal near these temperatures is achingly slow.

That makes growth diffusion-limited, and diffusion-limited growth has a signature everyone can derive: a diffusion front advances not in proportion to time but to the square root of it. So the half-thickness w of a kamacite plate goes roughly as the square root of D t, where D is the diffusion coefficient and t the time spent in the growth window.

Now put the cooling rate in. The time available is the temperature interval crossed divided by the rate of crossing it, so t is proportional to one over the cooling rate. Substituting:

w² is proportional to D × ΔT / (cooling rate) — so cooling rate is proportional to 1 / w².

That is the whole inference. A meteorite whose bands are twice as wide as another's cooled roughly four times more slowly — no absolute value needed, because the exponent does the work.

Absolute values are a harder matter, and here I will decline to quote figures. They come out in degrees per million year — extraordinarily slow — but the published numbers span more than an order of magnitude between meteorite groups and have been revised substantially as iron-nickel diffusion coefficients were re-measured. The ordering of meteorites by cooling rate is robust; the numbers attached to them are model-dependent and still moving.

What does slow cooling imply? Conduction gives the second derivation: a body of radius R loses heat on a timescale of about R² over its thermal diffusivity. Read backwards, cooling that slow requires a substantial body with a metal core insulated by a rocky mantle, not a bare lump radiating into space. The pattern is evidence for differentiated asteroids — objects large enough to have melted, separated iron from silicate, and cooled under a blanket.

Can this be falsified? Two ways, both sharp. First, the diffusion model predicts that nickel should be graded across each kamacite-taenite interface — steeply piled up in the taenite next to the plate, tailing off with distance, the frozen record of an unfinished diffusion process. Measure it with an electron microprobe and that is exactly what appears; the characteristic profile is an independent second reading of the same cooling rate, and it agrees with the band widths. A flat, fully-equilibrated profile, or no gradient at all, would destroy the model. Second, the model says no laboratory can make this pattern, because no laboratory can cool anything at degrees per million years. Nobody has. Fast cooling of the same alloy produces quite different, fine-scale structures.

Three refinements, because the simple version is easy to over-read.

First, band width is not a thermometer on its own. Bulk nickel content also controls it, and dramatically: alloys low enough in nickel form a single kamacite crystal with no pattern at all (hexahedrites), and alloys high enough in nickel never enter the plate-forming field on any relevant timescale and show a featureless face (ataxites). So the width must always be read together with the composition. That is the step people skip, and the reason the diagram below puts a gate there.

Second, the etching does not create the structure. The two phases differ in nickel content and so are attacked by acid at different rates; the acid only makes visible a boundary present since the parent body cooled.

Third, "cooling rate" here means the rate at one particular temperature interval, the one in which the plates were growing. A parent body's full thermal history is not a single number, and different methods sample different stages of it. Treating the figure as reporting the object's whole life would be reading more than it says.

• Why the iron meteorite groups sort into distinct cooling-rate clusters, and what that implies about how many parent bodies there were.

Every term the collection defines is gathered in the glossary.