Iron from the sky

Most meteorites are stony, but about one in twenty falls observed are irons: masses of iron–nickel metal, often with a few per cent of cobalt and traces of phosphorus, sulphur and carbon. Their composition and structure show that most are pieces of the metallic cores of small planets, a few tens to a few hundred kilometres across, that melted early in the history of the Solar System, separated into metal core and rocky mantle, and were later broken apart by collisions (Buchwald 1975).

When a polished slice of most iron meteorites is etched with dilute acid, a striking pattern appears: long bands crossing one another in three or four directions, outlined by thin bright lamellae, with fine-grained areas between them. The pattern was described first by William Thomson in Naples in 1804 and independently by Alois von Widmanstätten in Vienna in 1808, and carries the second name (Buchwald 1975).

Kamacite and taenite

Iron–nickel metal has two main crystal forms. Taenite (γ) is face-centred cubic and can hold a lot of nickel; kamacite (α) is body-centred cubic and holds little, at most around 7 % nickel at the relevant temperatures. Above roughly 700–900 °C, depending on composition, a meteoritic metal with 5–15 % nickel is entirely taenite, often as single crystals metres across. On slow cooling it enters a two-phase field of the iron–nickel phase diagram: kamacite begins to form, at a temperature that is lower the more nickel the metal contains.

The kamacite grows as plates parallel to the four sets of octahedral {111} planes of the parent taenite crystal, which is why the bands cross in up to four directions and why such meteorites are called octahedrites. For a kamacite plate to grow, the nickel it rejects must diffuse away into the neighbouring taenite. Nickel diffusion slows enormously as the temperature falls, and below about 400 °C the structure is effectively frozen. The width of the kamacite bands therefore records how long the metal spent in the temperature range where nickel could still move, that is, how fast it cooled.

Diffusion and time

Diffusion in solids follows the Arrhenius law, $D(T) = D_0\,e^{-Q/RT}$, where $Q$ is an activation energy and $R$ the gas constant. A useful rule from Fick’s laws is that in a time $t$ atoms spread over a characteristic distance $x \approx \sqrt{2Dt}$.

import math

# Arrhenius law for nickel diffusing in taenite (fcc Fe-Ni):
# D = D0 · exp(−Q / RT), D0 = 2.25e-6 m²/s, Q = 245 kJ/mol.
R, D0, Q = 8.314, 2.25e-6, 245e3
def D(T_c):
    return D0 * math.exp(-Q / (R * (T_c + 273.15)))

for T in (900, 700, 600, 500, 400):
    print(f"{T} °C: D = {D(T):.1e} m²/s")

# Fick's characteristic length x ≈ √(2Dt), held at 700 °C.
YEAR = 3.156e7
print()
for label, t in (("one day", 86400), ("one year", YEAR), ("a century", 100 * YEAR),
                 ("a million years", 1e6 * YEAR)):
    x = math.sqrt(2 * D(700) * t)
    print(f"{label:16s} at 700 °C: x ≈ {x * 1e6:8.2f} µm")
# 900 °C: D = 2.8e-17 m²/s
# 700 °C: D = 1.6e-19 m²/s
# 600 °C: D = 5.0e-21 m²/s
# 500 °C: D = 6.3e-23 m²/s
# 400 °C: D = 2.2e-25 m²/s
#
# one day          at 700 °C: x ≈     0.17 µm
# one year         at 700 °C: x ≈     3.17 µm
# a century        at 700 °C: x ≈    31.67 µm
# a million years  at 700 °C: x ≈  3166.99 µm

Between 900 °C and 400 °C the diffusion coefficient falls by a factor of a hundred million. At 700 °C, nickel moves a fraction of a micrometre in a day and a few micrometres in a year. Bands a fraction of a millimetre wide need hundreds of thousands to millions of years.

import math

R, D0, Q = 8.314, 2.25e-6, 245e3
D = lambda T_k: D0 * math.exp(-Q / (R * T_k))
YEAR = 3.156e7

def fick_length(rate_K_per_Myr, T_hi=700.0, T_lo=400.0, steps=3000):
    """√(2∫D dt) for steady cooling from T_hi to T_lo (°C)."""
    dT = (T_hi - T_lo) / steps
    integral = sum(D(T_hi + 273.15 - (i + 0.5) * dT) for i in range(steps)) * dT
    seconds_per_kelvin = 1e6 * YEAR / rate_K_per_Myr
    return math.sqrt(2 * integral * seconds_per_kelvin)

for rate in (1, 10, 100, 1000, 10000):
    x = fick_length(rate)
    print(f"{rate:6d} K/Myr: {300 / rate:8.3f} Myr from 700 to 400 °C, "
          f"diffusion length ≈ {x * 1e3:5.2f} mm")

# A laboratory furnace cooled at 1 K per hour over the same range:
x_lab = fick_length(1.0 * 24 * 365.25 * 1e6)
print(f"lab, 1 K/hour: {x_lab * 1e6:.2f} µm")
#      1 K/Myr:  300.000 Myr from 700 to 400 °C, diffusion length ≈ 17.40 mm
#     10 K/Myr:   30.000 Myr from 700 to 400 °C, diffusion length ≈  5.50 mm
#    100 K/Myr:    3.000 Myr from 700 to 400 °C, diffusion length ≈  1.74 mm
#   1000 K/Myr:    0.300 Myr from 700 to 400 °C, diffusion length ≈  0.55 mm
#  10000 K/Myr:    0.030 Myr from 700 to 400 °C, diffusion length ≈  0.17 mm
# lab, 1 K/hour: 0.19 µm

This simple estimate lands in the right range. Cooling at hundreds to thousands of kelvin per million years gives diffusion lengths of a few tenths of a millimetre to a couple of millimetres, the scale of the bands; a laboratory furnace, even cooled slowly for a year, gives a fraction of a micrometre. That is why a true Widmanstätten pattern cannot be produced artificially, and why its presence is one of the strongest signs that a piece of metal is meteoritic.

The width of the bands depends on nickel content as well as cooling rate, because metal richer in nickel begins to form kamacite at a lower temperature, where diffusion is already slower. Fine bands therefore do not mean slow cooling: the fine octahedrites of group IVA cooled faster than the medium octahedrites of group IIIAB. A detailed model, first developed by Goldstein and Short, treats nucleation temperature, nickel content and cooling rate together (Goldstein and Short 1967).