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Lecture 30
STABLE ISOTOPE APPLICATIONS I: HIGH
TEMPERATURES
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.
TEMPERATURE DEPENDENCE OF
EQUILIBRIUM FRACTIONATIONS
In Lecture 27, we found that the transla- tional and rotation contributions to the parti- tion function do not vary with temperature. In our example calculation at low tempera- ture, we found the vibrational contribution varies with the inverse of absolute tempera- ture. At higher temperature, the e - h^ ν /kT^ term in equation 26.35 becomes finite and this re- lationship breaks down. As a result, the temperature dependence of the equilibrium constant can generally be described as:
ln K = A
B
T^2
where A and B are constants. At infinite temperature, the fractionation is unity; i.e., ln K ≈ 0. Because of the nature of this tem- perature dependency, fractionation of stable isotopes at mantle temperatures will usually be small. This is one reason why stable iso- topes are useful tracers of crustal assimila- tion and recycling. It must be emphasized that the simple cal- culations in Lecture 27 are applicable only to a gas whose vibrations can be approximated by a simple harmonic oscillator. Real gases show fractionations that are complex func- tions of temperature, with minima, maxima, inflections, and crossovers.
TABLE 30.1. COEFFICIENTS OXYGEN ISOTOPE
FRACTIONATION AT LOW TEMPERATURES:
ΔQZ-φ = A + B × 106 /T^2 φ Α Β Feldspar 0 0.97 + 1.04b* Pyroxene 0 2. Garnet 0 2. Olivine 0 3. Muscovite – 0.60 2. Amphibole – 0.30 3. Biotite – 0.60 3. Chlorite – 1.63 5. Ilmenite 0 5. Magnetite 0 5.
- b is the mole fraction of anorthite in the feldspar. This term therefore accounts for the compositional dependence discussed above. From Javoy (1976).
TABLE 30.2. COEFFICIENTS FOR OXYGEN ISOTOPE
FRACTIONATIONS AT ELEVATED TEMPERATURES
(600° – 1300°C)
Cc Ab An Di Fo Mt Qz 0.38 0.94 1.99 2.75 3.67 6. Cc 0.56 1.61 2.37 3.29 5. Ab 1.05 1.81 2.73 5. An 0.76 1.68 4. Di 0.92 3. Fo 2. Coefficients are for mineral pair fractionations expressed as: 1000 α = B× 106 /T^2 where B is given in the Table. Qz: quartz, Cc: calcite, Ab: albite, An: anorthite, Di: diopside, Fo: forsterite, Mt: magnetite. For example, the fractionation between albite and diopside is 1000αΑλ−Δι = 1.81× 106 /T^2 (T in kelvins). From Chiba, et al. (1989).
Lecture 30 238 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 frequencies and have a tendency to incorporate the heavy iso- tope preferentially. For example, quartz (SiO 2 ) is typically the most 18 O-rich mineral and magnetite the least (O is bonded to Si4+ in quartz and Fe2+^ and Fe3+^ in magnetite). The covalent bonding of the basic mineral structure is most important in determining fractionations: the bonding between Si and O is largely covalent, the bonding between Fe and O is largely ionic. Substitution of cations in a primarily ionic site in silicates has less isotopic ef- fect. Thus, for example, we would expect rela- tively 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. per mil at room temperature. The substitution of Al for Si in plagioclase is somewhat more important (substitution of Ca for Na is much less important), leading to a 1.1 permil frac- tionation between anorthite and albite at room temperature. Table 30.1 lists the parameters for the temperature dependence of silicate and oxide fractionation factors at low temperatures. Carbonates tend to be very 18 O rich because O is bonded to a small, highly charged atom, C4+. The fractionation relative to water, ∆^18 O (the ∆ is the difference rather than the fraction) is about 30 for calcite. The cation (i.e., Ca or Mg in carbonate) has a secondary role (because of the effects of its mass on vibrational fre- quency). The ∆^18 O decreases to about 25 for Ba (about 3 times the mass of Ca). Crystal structure usually plays a secondary role. The ∆^18 O between aragonite and calcite is of the order of 0.5 permil. But there apparently is a large fractionation (10 permil) of C be- tween graphite and diamond at room tempera- ture. Pressure effects turn out to be small, 0. permil at 20 kbars and less. The reason should be fairly obvious: there is no volume change is
TABLE 30.3. 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 30.1. Calculated oxygen isotope fractionation for several mineral pairs as a function of temperature (from O’Neil, 1986).
Lecture 30 240
! " 1000 ln # Qz $% = A +
B
T
2 &^10
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 30.1 may be used to obtain the fractionation between any of the two phases shown. The other isotope that has been used extensively for geothermometry of igneous and metamorphic rocks is sulfur. Its principal application has been in determining the temperature of deposition of sul- fide ores, most of which precipitate from hydrous fluids. Sulfur may be present in fluids as any one of several species. Since isotope fractionation depends on bond strength, the predicted order of 34 S en- richment is: SO 42 !> SO 32 !> SO 2 > SCO > Sx ~ H 2 S ~HS^1 –^ > S^2 –^ (Ohmoto and Rye, 1979). Figure 30. shows the temperature dependence of fractionation factors between H 2 S and other phases, and Table 30.3 lists coefficients for the equation:
! " 1000 ln # $% H 2 S = A +
B
T
2 &^10
CO 2 and other carbon–bearing species are ubiquitous in meteoric and hydrothermal waters. Carbon- ates often precipitate from such solutions and the fractionation between carbon-species provides yet another opportunity for geothermometry. Figure 30.3 shows carbon isotope fractionation factors be- tween CO 2 and other carbon bearing species as a function of temperature. The figure includes fractionation factors both calculated from the- ory and observed vibrational frequencies (cal- cite, carbonate ion, carbon monoxide, methane) and empirical determined values (dolomite, bi- carbonate ion, and carbonic acid). Table 30. lists coefficients for a third degree polynomial expression of temperature dependence.
The Importance of Equilibrium
All geothermometers are based on the appar- ently contradictory assumptions that complete equilibrium was achieved between phases dur- ing, or perhaps after, formation of the phases, but that the phases did not re-equilibrate at any subsequent time. The reason these assump- tions can be made and geothermometry works at all is the exponential dependence of reaction rates on temperature. Isotope geothermome- ters have these same implicit assumptions about the achievement of equilibrium as other systems. The importance of the equilibrium basis of the geothermometry must be emphasized. Be- cause most are applied to relatively low tem- perature situations, violation of the assumption that complete equilibrium was achieved is common. We have seen that isotopic fraction- ations may arise from kinetic as well as equilib- rium effects. If reactions do not run to comple- Figure 30.3. Fractionation factors for distribution of carbon isotopes between CO 2 and other carbon-bear- ing species as a function of temperature. From Oh- moto and Rye (1979).
Lecture 30 241 tion, the isotopic differences may re- flect kinetic effects as much as equilib- rium effects. Other problems can result in incorrect temperature as well: the system may partially re-equilibration at some lower temperatures during cool- ing; free energies of isotope exchange reactions are low, meaning there is lit- tle 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 particularly slow at tem- peratures well below the melting point. Equilibrium between solid phases will thus generally depend on reaction of these phases with a fluid. Of course, this is true of ‘conventional’ chemical reactions as well, and metamorphism generally occurs in the presence of a fluid. Figure 30.4 compares sphalerite–galena sulfur isotope temperatures with fluid-inclusion homoge- nization temperatures. Excluding the Pine Point data, the best fit to the data is fairly close to that ex- pected from the fractionation factors listed in Table 30.3: Δsp-gn = 0.73 × 106 /T^2. Many of the points fall off the expected curve, indicating disequilibrium. Ohmoto and Rye (1979) noted a number of factors that may contribute to the lack of fit, such as impure mineral separates used in the analysis; for exam- ple, 10% of the galena in sphalerite and visa versa would result in an estimated temperature of 215°C if the actual equilibration temperature was 145°C. Different minerals may crystallize at different times and dif- ferent temperatures in a hy- drothermal system and hence would never be in equilibrium. In general, those minerals in direct contact with each other give the most reliable temperatures. Real disequilibrium may also occur if crystallization is ki- netically controlled. The generally good fit to the higher temperature sulfides and poor fit to the low tem- perature ones suggests kinetics may indeed be an important factor. Javoy (1976) suggested a graphical method to test for oxygen-isotope equilibrium based on a rear- rangement of 30.2. Choosing a ubiq- uitous index mineral, for example quartz, we may rewrite 30.2 for each quartz-mineral pair as:
∆Qz-φ – AQz-φ = BQz-φ × 106 /T^2 30.
TABLE 30.4 ISOTOPE FRACTIONATION FACTORS OF
CARBON COMPOUNDS WITH RESPECT TO CO 2
1000 Ln α = A × 108 /T^3 + B × 106 /T^2 + C × 103 /T + D
φ Α B C D T°C Range CaMg(CO 3 ) 2 - 8.914 8.737 - 18.11 8.44 ≤ 600 Ca(CO 3 ) - 8.914 8.557 - 18.11 8.24 ≤ 600 HCO 1 – 3 0 - 2.160^ 20.16^ - 35.7^ ≤^290 CO 2 – 3 - 8.361^ - 8.196^ - 17.66^ 6.14^ ≤^100 H 2 CO 3 0 0 0 0 ≤ 350 CH 4 4.194 - 5.210 - 8.93 4.36 ≤ 700 CO 0 - 2.84 - 17.56 9.1 ≤ 330 C - 6.637 6.921 - 22.89 9.32 ≤ 700 From Ohmoto and Rye (1979). Figure 30.4. Comparison of temperatures determined from sphalerite–galena sulfur isotope fractionation with fluid-in- clusion homogenization temperatures. J: Creede, CO, S: Sunnyside, O: Finlandia vein, C: Pasto Bueno, G: Kuroko. From Ohmoto and Rye (1979).
Lecture 30 243 strictly true of stable isotope ratios, 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. De- gassing does significantly affect stable isotope ratios, particularly those of carbon and hydrogen, which compromises the value of magmas as a mantle sample. Once oxides begin to crystallize, fractional crystallization will affect oxygen isotope ratios, although the result- ing changes are at most a few per mil. Finally, weathering and hy- drothermal processes can affect stable isotope ratios of basalts and other igneous rocks. Because hy- drogen, carbon, nitrogen, and sul- fur are all trace elements in basalts but are quite abundant at the Earth’s surface, these elements are particularly susceptible to weath- ering effects. Even oxygen, which constitutes nearly 50% by weight of silicate 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 composition might vary, has proved to be more difficult than expected. One ap- proach has been to use basalts as samples of mantle, as is done for radiogenic isotopes. Relatively little isotope 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, assimi- lation of crustal rocks by magmas and oxygen isotope exchange dur- ing weathering complicate the situation. An alternative is to use direct mantle samples such as xenoliths occasionally found in basalts, although these are consid- Figure 30.6. Oxygen isotope ratios in olivines and clinopyroxenes from mantle peridotite xenoliths. Data from Mattey et al. (1994).
