Devolatilization, Batch vs. Rayleigh, and the Limits

Companion to Chapter 12, §12.2.2, Eqs. 12.1–12.5 and Figs. 12.2–12.4. Why volatilization cannot move a rock's δ¹⁸O more than a few per mil, while carbon can run away.

MODEL orange sliders set the physics. VIEW blue sliders only change the plotting window, in the drawer under each chart.

Fig. 12.2 live, rock and fluid vs. reaction progress

batch, δinitial rock = x·δfinal rock + (1−x)·δfluid,  δrock − δfluid = −1000lnαf–rEqs 12.1–12.3
Rayleigh, δf = (δi + 1000)·F(α−1) − 1000Eq 12.4
CaCO₃ + SiO₂ → CaSiO₃ + CO₂, at most 40% of the oxygen leaves, F ≥ 0.6Eq 12.5, calc-silicate limit
rock, Rayleigh rock, batch instantaneous fluid, Rayleigh fluid, batch inaccessible beyond the F limit
MODEL Parameters δ¹⁸O initial rock ‰ 1000lnα (fluid − rock) ‰ F limit for this element F, fraction remaining
VIEW Plot window, view only, does not change the model
rock at chosen F, Rayleigh
rock at chosen F, batch
maximum rock shift at the F limit, Rayleigh
dehydration limits
F ≥ 0.92–0.93 talc, muscovite (Eqs 12.6–12.7)

Published inputs, Eqs 12.1–12.5 with α = 1.006 as drawn in Fig. 12.2, the calc-silicate limit F ≥ 0.6, the dehydration limits F ≥ 0.93 (muscovite + quartz) and 0.92 (talc), and the chapter's conclusion, volatilization reactions cannot change δ¹⁸OWR by more than several per mil under any conditions, larger shifts require infiltration of a fluid or melt. Constructed, the slider defaults. Set the F limit toward 0 to see the carbon or hydrogen case, where the element can be driven out entirely and the residual delta runs away.

Coupled δ¹³C–δ¹⁸O during decarbonation, Figs. 12.3–12.4

Rayleigh decarbonation path batch decarbonation path sample needing infiltration
MODEL Parameters δ¹³C initial carbonate ‰ Δ¹³C (CO₂ − calcite) ‰ sample δ¹⁸O ‰ sample δ¹³C ‰
VIEW Plot window, view only, does not change the model
δ¹⁸O floor of pure decarbonation, Rayleigh at FC → 0
sample inside the envelope?

Published inputs, the coupling, carbon FC runs 1 → 0 while oxygen can lose at most 40% (FO = 1 − 0.4(1−FC) for reaction 12.5), the Δ¹³C(CO₂–calcite) of 2–4‰ at high temperature (Fig. 11.4), and the two field anchors, Notch Peak argillites where δ¹³C drops ~12‰ inside the decarbonation envelope while δ¹⁸O falls 12‰, far beyond the ≤2‰ decarbonation allows (Nabelek et al., 1984), and the Elkhorn two-stage fit, Rayleigh decarbonation then magmatic-fluid mixing (Bowman et al., 1985). Constructed, the oxygen 1000lnα shared with the top panel, the sample point, and the exact trajectory parametrization. Valley (1986) found no contact aureole whose coupled trend is explained by volatilization alone.

Reading the plots. Two controls do all the work. The fractionation sets the slope of the exit path, and the F limit sets how far down it a rock can travel. For oxygen the limit arrives almost immediately, stoichiometry caps decarbonation at 40% loss and dehydration near 8%, so the blue and orange curves barely separate before the shaded wall. For carbon there is no wall, every mole of carbonate carbon can leave as CO₂, so δ¹³C can fall tens of per mil while δ¹⁸O hardly moves, and the coupled trajectory in the lower panel is nearly vertical. A sample left of the envelope is the fingerprint of infiltration, which is why coupled δ¹³C–δ¹⁸O arrays, not either axis alone, diagnose open-system metamorphism. The same lever-rule logic (Box 12.1) explains why prograde biotite δD falls ~30‰ across a dehydration sequence while whole-rock oxygen stays fixed.