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Chapter 9
Stable Isotope Geochemistry II: High
Temperature Applications
INTRODUCTION
Stable isotopes have a number of uses in high temperature geochemistry (i.e., igneous and meta- morphic geochemistry), which we will treat in the next several lectures. Perhaps the most important of these is geothermometry, i.e., deducing the temperatures at which mineral assemblages equilibrated. This application makes use of the temperature dependency of fractionation factors. Other important applications include reconstructing ancient hydrothermal systems, detecting crustal assimilation in mantle-derived magmas, and tracing recycled crust in the mantle. These applications primarily involve O isotopes. Before discussing these subjects, let's briefly review the factors governing isotopic frac- tionation.
T EMPERATURE DEPENDENCE OF E QUILIBRIUM F RACTIONATIONS
In Chapter 8, we found that the translational and rotation contributions to the partition function do not vary with temperature. In our example calculation at low temperature, we found the vibrational contribution varies with the inverse of absolute temperature. At higher temperature, the e -h^ ν /kT^ term in equation 8.35 becomes finite and this relationship breaks down. It higher temperature, the equilibrium constant becomes generally proportional to the inverse square of temperature:
ln K = A +
B
T
Figure 9.01. a. Comparison of quartz-mineral fractionation factors estimated from the difference in oxygen site potential (Vqtz – Vmineral) and experimentally observed fractionation factors at 1000 K. b. Comparison of fractionation factors estimated through the increment method, which also considers cation mass, and experimentally observed fractionation factors at 1000 K. From Chacko, et al. (2001).
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where A and B are constants. At infinite temperature, the fractionation is unity; i.e., ln K ≈ 0. Because of the nature of this temperature dependency, fractionation of stable isotopes at mantle temperatures will usually be small. This is one reason why stable isotopes are useful tracers of crustal assimilation and recycling. It must be emphasized that the simple calculations in Chapter 8 are applicable only to a gas whose vi- brations can be approximated by a simple harmonic oscillator. Real gases show fractionations that are complex functions of temperature, with minima, maxima, inflections, and crossovers.
Compositional and Structural Dependence of Equilibrium Fractionations
The nature of the chemical bond is of primary important in determining isotope fractionations. In general, bonds to ions with a high ionic potential and low atomic mass are associated with high vibrational fre- quencies and have a tendency to incorporate the heavy isotope preferentially. This point is illustrated by the site-potential method of estimating fractionation factors (Smyth, 1989). The site potential is simply the energy required (e.g., in electron volts) to remove an atom from its crystallographic site and is a meas- ure of bond strength. Figure 9.01a shows that the there is a strong correlation between the difference in oxygen site potential in minerals and the fractionation factor between those two minerals. The solid line shows that silicates plot along a line with the equation ∆1000K (qtz-mineral) = 0.751 (V (^) qtz –V (^) mineral ). Ox- ides (and to a less extent, apatite and calcite) fall off this correlation. The deviation in the case of calcite and apatite probably reflects the more strongly covalent nature of oxygen bonds in those minerals. In the case of the oxides, it reflects the vary- ing mass of the cation, as cation mass af- fects bond strength. In silicates, oxygens are primarily bound to Si and secondarily to other cations. However, in oxides such as rutile, perovskite, and magnetite, oxy- gen is bound primarily to Fe or Ti, which of course have very different masses than Si. The “increment method” of estimat- ing fractionation factors (e.g., Zhang,
- takes account of the cation ion mass. As Figure 9.01b shows, this method produces and improved agree- ment of calculated and experimentally observed fractionation factors for the ox- ides. Substitution of cations in a primarily ionic site in silicates has only a minor ef- fect on fractionation factors. Thus, for example, we would expect relatively little O isotopic fractionation between K- feldspar and Na-feldspar. This turns out to be the case: the fractionation is of the order of 0.1 per mil at room temperature. The substitution of Al for Si in plagio- clase is somewhat more important (sub- stitution of Ca for Na is much less im- portant), leading to a 1.1 permil frac- tionation between anorthite and albite at room temperature. Table 9.01 lists the
Figure 9.02. Calculated oxygen isotope fractionation for several mineral pairs as a function of temperature (from O’Neil, 1986).
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ciently invariant over a range of geologically interesting temperatures that as a practical matter they can be described as constants. We have also noted that at temperatures close to room temperature and below, the form of equation 9.01 changes to K ∝ 1/T. Because of the dependence of the equilibrium constant on the inverse square of temperature, stable isotope geothermometry is employed primarily at low and moderate temperatures, that is, non-mag- matic temperatures. At temperatures greater than 800°C or so (there is no exact cutoff), the fractiona- tions are often too small for accurate temperatures to be calculated from them. In principal, a temperature may be calculated from the isotopic fractionation between any phases provided the phases achieved equilibrium and the temperature dependence of the fractionation factor is known. Indeed, there are too many isotope geothermometers for all of them to be even mentioned here. We can begin by considering silicate systems. Figure 9.02 shows fractionation factors between various silicates and oxides as a function of temperature. Tables 9.01 and 9.02 list coefficients A and B for temperature dependence of the fractionation factor between quartz and other common silicates and oxides when this temperature dependence is expressed as:
Δ ≅ 1000 ln α Qz − φ = A +
B
T^2
× 106 9.0 2
with temperature expressed in Kelvins. Recall that fundamental rule of thermodynamics states that if phases A and C and A and B are in equilibrium with each other, then C is also in equilibrium with B. Thus Table 9.01 may be used to obtain the fractionation between any of the two phases shown. The other isotope that has been used exten- sively for geothermometry of igneous and metamorphic rocks is sulfur. Its principal application has been in determining the tem- perature of deposition of sulfide ores, most of which precipitate from hydrous fluids. Sul- fur may be present in fluids as any one of several species. Since isotope fractionation depends on bond strength, the predicted or- der of 34 S enrichment is: SO 42 −^ > SO 32 −^ > SO 2 > SCO > Sx ~ H 2 S ~HS^1 –^ > S^2 –^ (Ohmoto and Rye, 1979). Figure 9.03 shows the temperature dependence of fractionation factors between H 2 S and other phases, and Table 9.03 lists co- efficients for the equation:
Δ ≅ 1000 ln αφ− H 2 S = A +
B
T^2
× 106 9.0 3
CO 2 and other carbon–bearing species are ubiquitous in meteoric and hydrothermal waters. Carbonates often precipitate from such solutions and the fractionation between carbon-species provides yet another oppor- tunity for geothermometry. Figure 9.0 4 shows carbon isotope fractionation factors between CO 2 and other carbon bearing spe- cies as a function of temperature. The figure includes fractionation factors both calculated from theory and observed vibrational fre- quencies (calcite, carbonate ion, carbon mon-
Figure 9.03. Relationship of S isotope fractionation be- tween H 2 S and other sulfur-bearing species and tem- perature. From Ohmoto and Rye (1979).
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oxide, methane) and empirical determined values (dolomite, bicarbonate ion, and car- bonic acid). Table 9 .04 lists coefficients for a third degree polynomial expression of temperature dependence.
The Importance of Equilibrium
All geothermometers are based on the apparently contradictory assumptions that complete equilibrium was achieved be- tween phases during, or perhaps after, formation of the phases, but that the phases did not re-equilibrate at any subsequent time. The reason these assumptions can be made and geothermometry works at all is the exponential dependence of reaction rates on temperature. Isotope geother- mometers have these same implicit as- sumptions about the achievement of equi- librium as other systems. The importance of the equilibrium basis of the geothermometry must be empha- sized. Because most are applied to rela- tively low temperature situations, violation of the assumption that complete equilib- rium was achieved is common. We have seen that isotopic fractionations may arise from kinetic as well as equilibrium effects. If reactions do not run to completion, the isotopic differences may reflect kinetic ef- fects as much as equilibrium effects. Other problems can result in incorrect tempera- ture as well: the system may partially re- equilibration at some lower temperatures during cooling; free energies of isotope ex- change reactions are low, meaning there is little chemical energy available to drive the reaction to equilibrium. Indeed, isotopic equilibrium probably often depends on other reactions occurring which mobilize the element involved in the exchange. Solid-state exchange reactions are particu- larly slow at temperatures well below the melting point. Equilibrium between solid phases will thus generally depend on reac- tion of these phases with a fluid. Of course, this is true of ‘conventional’ chemi- cal reactions as well, and metamorphism generally occurs in the presence of a fluid.
TABLE 9.03. COEFFICIENTS FOR SULFUR ISOTOPE
FRACTIONATION:
Δφ−H 2 S = A + B × 106 /T^2 (T IN KELVINS)
φ Β A T°C Range CaSO 4 6.0±0.5 5.26 200 - 350 SO 2 – 0.5±0.5 4.7 350 - 1050 FeS 2 0.4±0.08 200 - 700 ZnS 0.10±0.05 50 - 705 CuS – 0.4±0. Cu 2 S – 0.75±0. SnS – 0.45±0. MoS 2 0.45±0. Ag 2 S – 0.8±0. PbS – 0.63±0.05 50 - 700 From Ohmoto and Rye (1979)
Figure 9.04. Fractionation factors for distribution of car- bon isotopes between CO 2 and other carbon-bearing species as a function of temperature. From Ohmoto and Rye (1979).
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in plagioclase affects O isotope fractionation factors because the nature of the bond with oxygen. The composition of a CO 2 bearing solution, however, should not affect isotopic fractionation between calcite and dissolved carbonate because the oxygen is bonded with C regardless of the presence of other ions (if we define the fractionation as between water and calcite, some effect is possible if the O in the car- bonate radical exchanges with other radicals present in the solution).
STABLE ISOTOPE COMPOSITION OF THE MANTLE Before we can use stable isotope ratios as indicators of crustal assimilation and tracers of crustal recy- cling, we need to define the stable isotopic composition of “uncontaminated” mantle. It is, however, important to recognize from the outset that, in a strict sense, there may be no such thing. We found in our consideration of radiogenic isotope ratios that no samples of “primitive” mantle have been recov- ered: the mantle, or at least that portion sampled by volcanism, has been perva- sively processed. A very considerable amount of oceanic crust has been sub- ducted during this time, perhaps ac- companied by sediment. As we shall see, the stable isotopic composition of the oceanic crust is extensively mod- ified by hydrothermal processes and low temperature weathering. Sub- duction of this material has the poten- tial for modifying the stable isotopic composition of the mantle. Thus while we will attempt to use stable isotope ratios to identify “contamination” of mantle by subduction, we must recog- nize all of it may have been “contami- nated” to some degree. Other problems arise in defining the stable isotope composition of the man- tle. We relied heavily on basalts as mantle samples in defining the radio- genic isotope composition of the man- tle. We could do so because radiogenic isotope ratios are not changed in the magma generation process. This will not be strictly true of stable isotope ra- tios, which can be changed by chemical processes. The effects of the melting process on most stable isotope ratios of interest are small, but not completely negligible. Degassing does signifi- cantly affect stable isotope ratios, par- ticularly those of carbon and hydrogen, which compromises the value of mag- mas as a mantle sample. Once oxides begin to crystallize, fractional crystalli- zation will affect oxygen isotope ratios,
Figure 9.06. Oxygen isotope ratios in olivines and cli- nopyroxenes from mantle peridotite xenoliths. Data from Mattey et al. (1994).
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although the resulting changes are at most a few per mil. Fi- nally, weathering and hydrothermal processes can affect stable isotope ratios of basalts and other igneous rocks. Because hy- drogen, carbon, nitrogen, and sulfur are all trace elements in basalts but are quite abundant at the Earth’s surface, these elements are particularly susceptible to weathering effects. Even oxygen, which constitutes nearly 50% by weight of sili- cate rocks, is readily affected by weathering. Thus we will have to proceed with some caution in using basalts as samples of the mantle for stable isotope ratios.
Oxygen
Assessing the oxygen isotopic composition of the mantle, and particularly the degree to which its oxygen isotope com- position might vary, has proved to be more difficult than ex- pected. One approach has been to use basalts as samples of mantle, as is done for radiogenic isotopes. Relatively little iso- tope fractionation occurs during partial melting, so the oxygen isotopic composition of basalt should the same as that in the mantle source within a few tenths per mil. However, assimila- tion of crustal rocks by magmas and oxygen isotope exchange during weathering complicate the situation. An alternative is to use direct mantle samples such as xenoliths occasionally found in basalts, although these are considerably rarer than are basalts. Figure 9.06 shows the oxygen isotope composition of oli- vines and clinopyroxenes in 76 peridotite xenoliths analyzed by Mattey et al. (1994) using the laser fluorination technique. The total range of values observed is only about twice that ex- pected from analytical error alone, suggesting the mantle is fairly homogeneous in its isotopic composition. The difference between co-existing olivines and clinopyroxenes averages about 0.5 per mil, which is consistent with the expected frac- tionation between these minerals at mantle temperatures. Mattey et al. (1994) estimated the bulk composition of these samples to be about +5.5 per mil. Figure 9.07 shows the distribution of δ^18 O in selected basalts from 4 different groupings. To avoid the weathering problems we discussed above, Harmon and Hoefs (1994) included only submarine basaltic glasses and basalts that had less than 0.75% water or had erupted historically in their compilation. There are several points worth noting in these data. MORB are significantly more homogeneous than are other basalts. MORB have a mean δ^18 OSMOW of +5.7‰ and a standard deviation of ±0.2‰. Thus the depleted upper mantle appears to be a compara- tively homogeneous and well-mixed reservoir for oxygen, just as it is for other elements. Oceanic is- land basalts, which presumably sample mantle plumes, are slightly less enriched in 18 O (mean δ^18 OSMOW = +5.5‰), and are also more variable (1σ = 0.5‰). The histogram shown excludes Iceland, because Ice- landic basalts are quite anomalous in their low δ^18 O (mean ~ 4.5‰). This has been shown to be due primarily to assimilation of older basaltic crust that has equilibrated with meteoric water, which is quite (^18) O depleted at the latitude of Iceland. There is, however, some evidence to suggest even primary Ice-
Figure 21.7 of MORB (+5.7). After Harmon and Hoefs (1994).
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δ^13 C of - 6.5 and a standard deviation of 1.7. Hawaiian basalts appear to have slightly heavier carbon. Xenoliths in oceanic island basalts are also slightly heavier than MORB. Whether this reflects a real dif- ference in isotopic composition or merely the effect of fractionation is unclear. The most CO 2 - rich MORB samples have δ^13 C of about – 4. Since they are the least degassed, they presumably best repre- sent the isotopic composition of the depleted mantle (Javoy and Pineau, 1991). If this is so, there may be little difference in carbon isotopic composition between MORB and oceanic islands sampled thus far (which include only Hawaii, Reunion, and Kerguelen). Gases released in subduction zone volcanos have δ^13 C that ranges from 0 to – 10‰, with most values being in the range of – 2 to – 4‰, comparable to the most gas-rich MORB (Javoy, et al., 1986). Continental xenoliths are more heterogeneous in carbon isotopic composition than other groups, and the meaning of this is unclear. Carbonatites have some- what lighter carbon than most MORB. Diamonds show a large range of carbon isotopic compositions (Figure 9.08). Most diamonds have δ^13 C within the range of - 2 to - 8‰, hence similar to MORB. However, some diamonds have much lighter carbon. Based on the inclusions they contain, diamonds can be divided between peridotitic and eclogitic. Most peridotitic diamonds have δ^13 C close to – 5‰, while eclogitic diamonds are much more isotopically variable. Most, though not all, of the diamonds with very negative δ^13 C are eclogitic. Many diamonds are isotopically zoned, indicating they grew in several stages. Three hypotheses have been put forward to explain the isotopic heterogeneity in diamonds: pri- mordial heterogeneity, fractionation effects, and recycling of organic carbon from the Earth’s surface into the mantle. Primordial heterogeneity seems unlikely for a number of reasons. Among these is the absence of very negative δ^13 C in other materials, such as MORB, and the absence of any evidence for primordial heterogeneity from the isotopic compositions of other elements. Boyd and Pillinger (1994) have argued that since diamonds are kinetically sluggish (witness their stability at the surface of the Earth, where they are thermodynamically out of equilibrium), isotopic equilibrium might not achieved during their growth. Large fractionations might therefore occur due to kinetic effects. However, these kinetic fractionations have not been demonstrated, and fractionations of this magnitude (20‰ or so) would be surprising at mantle temperatures. On the other hand, several lines of evidence support the idea that isotopically light carbon in some diamonds had its origin as organic carbon at the Earth’s surface. First, such diamonds are primarily of eclogitic paragenesis, eclogite is the high pressure equivalent of basalt. Sub- duction of oceanic crust continuously carries large amounts of basalt into the mantle. Oxygen isotope heterogeneity observed in some eclogite xenoliths suggests these eclogi- tes do indeed represent subducted oceanic crust. Second, the nitrogen isotopic composi- tion of isotopically light diamonds are anomalous relative to nitrogen in other man- tle materials yet similar to nitrogen in sedi- mentary rocks.
Hydrogen
Like carbon, hydrogen can be lost from ba- salts during degassing. On the one hand, the problem is somewhat less severe than for carbon because the solubility of water in ba- salt is much greater than that of CO 2. Basalts
Figure 9.09. Effect of degassing and post-eruptive processes on the water content and δD of basalts. From Kyser and O’Neil (1984).
