The chemical properties of an element are primarily determined by the number of protons in the nucleus (the atomic number, which also determines the configuration of the electron cloud. Nucleii also contain neutrons, and atoms having the same atomic number can appear in forms with different numbers of neutrons. These differing forms are known as isotopes of the element. Isotopic proxies have proved to be a versatile source of information about past climates. Some isotopes are unstable, and decay into other elements; these can be used as "clocks," to determine when things happened. The original, and most famous, such application is radiocarbon dating, which makes use of the decay of the form of carbon having a molecular weight of 14 (carbon-14, or 14C. Stable isotopes do not decay, and instead provide a tracer of past chemical reactions in which the substance participated. For elements heavier than Helium the stable isotopic composition of a planet is determined primarily by the synthesis of the elements in the supernova explosion which gave birth to the material eventually incorporated into the Solar system. The isotopic ratio can in some cases be further changed by the process of planetary formation. For example, oxygen has three stable isotopes: 18O, 17O and 16O, the latter of which is by far the most common. About 1 in 500 atoms of oxygen on Earth are 18O, which is nearly the same ratio as found in the Sun and which presumably represents the composition of the primordial Solar nebula. 17O is less commonly used as a proxy because it is so much rarer than 18O (only 1 in 2500 oxygen atoms on Earth), but variations in its composition are readily detectable with modern measurements, and have important specialized uses. Hydrogen has two stable forms: Deuterium (D) which has a proton and a neutron, and normal hydrogen (H) which has only a proton. About one hydrogen molecule in 6500 occurring in Earth's ocean water is D. This differs from the 1:1700 ratio in the outer Sun, because Deuterium is destroyed by nuclear fusion in the Sun and in the early Solar nebula; curiously, the composition of the outer Sun is nearly the same as Jupiter. The stable isotopes of carbon are 13C and 12C, of which the latter is by far the more common. About 1 in 100 carbon atoms on Earth are 13C. The carbon isotopic system attracts particular attention because carbon is the basis of organic chemistry - the stuff of life as we know it. Stable isotopes of S, N, Ar and many other elements have proved useful as proxies. In fact, it is hard to think of any measureable isotopic ratio that hasn't proved useful as a proxy for some aspect of climate or atmospheric composition.
The utility of isotopes as climate proxies derives from what they tell us about processes that sort them out into different reservoirs. Isotopes of an element have nearly the same chemical and physical behavior, but not exactly the same behavior. The subtle differences come about in part because, at a given temperature, the molecules of the lighter isotopes have a higher typical velocity than those of the heavier isotopes, since all molecules have the same mean kinetic energy at any given temperature. Among other things, this means that lighter isotopic forms of a substance evaporate more readily than heavier ones, so that the vapor phase of a substance is typically depleted in heavy isotopic forms relative to the condensed phase with which it is in contact. We will find this effect particularly useful in the interpretation of water isotopes, but a very similar process applies to the gradual "evaporation" of a planet's atmosphere into outer space, and can be used to constrain the proportion of atmosphere that has been lost in such a fashion.
The rate at which a given element or a molecule containing that element undergoes chemical reactions also depends on the isotope involved. Other things being equal, heavier isotopes would tend to react more slowly, because they have lower speeds and therefore lower collision rates with other reactants than their lighter, nimbler cousins. However, there are more subtle effects involved that can either enhance or retard reaction rates. Specifically, the difference in molecular weight between isotopes can affect the characteristic vibration frequencies of molecule bonds, and this can in turn affect the probability that colliding reactants will stick together. Very often, the degree of preference for one isotopic form over another - the degree of fractionation occurring between reactant pool and reaction product - depends on the temperature at which the reaction is taking place. When this is so, the isotopic composition of the product provides a useful paleo-thermometer. In Section 1.3 we stated that "certain aspects" of the chemical composition of zircons constrained the temperature of Hadean water with which the zircons were in contact; with this cryptic phrase, we were in fact referring to the ratio of 16O to 18O in the Hadean zircons which, like all silicate minerals, contain oxygen (their chemical formula is ZrSiO4). Similarly, it was the oxygen isotopic ratio of cherts (later confirmed by silicon isotopic ratios) that was used to constrain Archaean temperatures in Section 1.3. A problem with all such paleothermometers is that fractionation is relative to the isotopic composition of the reactant pool, so that one needs to know the likely composition of the reactant pool in order to infer temperatures from the reaction product (e.g. the cherts or zircons), which are preserved long after the pool of reactants have been dissipated.
Biochemistry also has isotopic preferences. Photosynthetic Earth life (even of the sort that doesn't produce oxygen) prefers the lighter forms of carbon, so that organic material of photosynthetic origin is enriched in 12C and depleted in 13C relative to the inorganic carbon left behind. A record of the isotopic composition of inorganic carbon is preserved in carbonate minerals (e.g. CaCO3) precipitated out and deposited on the ocean floor, with or without the help of shell-forming organisms. Organic material is directly preserved in sedimentary rocks such as shales. For example, the organic material in the Isua shales is presumed to be of biological origin because its carbon is isotopically light - enriched in 12 C relative to the average composition of carbon on Earth. Respiration - eating organic matter and combining it with oxygen to release energy - does not fractionate carbon to any significant extent, so the isotopic signature imprinted by photosynthesis is carried over to those of us creatures in the non-photosynthetic organic realm.
The simplest kind of isotopic fractionation to characterize is equilibrium fractionation. To keep things concrete, we'll illustrate the concept using oxygen isotopes. Consider two physically or chemically distinct substances, each of which contains oxygen atoms. For example, the two substances could consist of water in its vapor phase and water in its liquid phase. Alternately, the two substances might be different chemical compounds containing oxygen, such as calcium carbonate (CaCO3) and water (H2O), or silica (SiO2) and water; the latter pair leads to the chert-based paleothermometer mentioned earlier. Each of the two substances will have some initial ratio of 18O to 16O. Now imagine bringing the two substances into contact, whereupon the two substances exchange heavier and lighter forms of oxygen, changing the initial ratios. After a very long time, the isotopic ratios in each substance will reach equilibrium and stop changing. At that point, we can define the equilibrium fractionation factor f12 via the relation r'1 = 71,2^2 (1.4)
where r1 is the ratio of 18 O to 16 O in the first substance after equilibrium has been reached, and r2 is the corresponding ratio for the second substance. The fractionation factors differ for different pairs of substances, but typically (though not invariably) exhibit the following characteristics:
• The fractionation factor is typically quite close to unity
• The fractionation factor deviates most from unity at low temperatures, and approaches unity as temperature increases
• The deviation of the fractionation factor from unity increases as the contrast between the masses of the two isototopes increases (e.g. more fractionation for 18O vs 16O than for 17O
For example, the oxygen in silica (SiO2) is isotopically heavy in comparison with the oxygen in the water with which it is in equilibrium; the fractionation factor is 1.036 at 20C but falls to 1.018 at 100C. Similarly, oxygen in liquid water is isotopically heavy in comparsion to that in the water vapor with which it is in equilbrium; in this case, the fractionation factor is 1.01 at 20C and falls to 1.005 at 100C. It is the temperature dependence of the fractionation that makes it possible to use isotopic ratios as paleothermometers. Some kinds of fractionation appear to operate in nearly the same way whether the reactions happen within organisms or inorganically.
This appears to be the case for carbonate precipitation, which fractionates in much the same way regardless of whether it happens inorganically or in shell-forming organisms. Other forms of fractionation, such as the fractionation of carbon isotopes in photosynthesis, are more inherently biologically mediated, though even in such cases the fractionation factors tend to be similar across broad classes of organisms sharing the same biochemical pathways.
Isotopic composition is usually described using S notation, which is defined as follows. Let ta be the ratio of the number of molecules of isotope A in a sample to the number of molecules of the dominant isotope. Typically, ta will be a rather small number. Next let ta,s be the isotopic ratio for a standard reference sample. Isotopic composition is invariably reported relative to a standard because the analytical instruments currently in use cannot measure the absolute composition to very high accuracy, but they can measure the difference relative to a standard very accurately; the standard is an actual physical substance, natural or manufactured, which can be put into the analytical instrument and serve as a basis for comparison. The choice of standard is a matter of convention, and there are various standards typically used in different contexts. For example, the standard for oxygen and hydrogen isotopes in ice or water is usually taken to be VSMOW, which stands for Vienna Standard Mean Ocean Water. The ratio of 18O to 16O in VSMOW is 1/498.7, and of D to H is 1/6420; this approximates the mean present composition of water in the ocean.
Once one agrees upon a standard, the isotopic composition of a sample can be described in terms of the quantity
Thus, negative values of S indicate that the sample is depleted in isotope A relative to the standard, whereas positive values indicate that the sample is enriched. The S value is usually expressed as a per mil, or parts-per-thousand, value. For example, a S value of .001 would usually be expressed as 1 per mil or 1%o. A difference of 1%ois often equivalent to a miniscule variation in isotopic concentration, requiring high analytical precision to measure. For example, for the case of S18O, a 1%odifference is equivalent to changing the ratio of 18O molecules to 16O molecules by .001 • 498 7, or a hair over 2 parts per million. Deuterium (D) is even tougher. For deuterium, a difference of 1%oamounts to a change in the D to H ratio of only 0.16 parts per million, though the challenge is offset by the fact that fractionation in the D/H system is considerably stronger than fractionation in the 18O/16O system owing to the lesser relative mass contrast in the latter case.
Carbonate minerals (e.g. CaCO3 or MgCO3) are important recorders of the oxygen and carbon isotopic composition of past environments. For carbonates, the isotopic composition is usually reported relative to the PDB standard, named after a mineral powder made from a naturally occurring fossil carbonate (the "Peedee Belemnite") The physical powder standard no longer exists, so it has been supplanted by a synthetic equivalent, known as VPDB. It is important to keep the standards in mind when interpreting the isotopic literature. Oxygen isotopes occur in both carbonate and water, and so can be reported relative to either the VSMOW or VPDB standard. The conversion between the two is given by
A useful rule of thumb to keep in mind when interpreting oxygen isotopes in marine carbonates is that a carbonate reading zero relative to VPDB would be in equilibrium with water having zero S18O(VSMOW), if the carbonate formed at a temperature of around 18C. This means that a carbonate S18O(PDB) of "around" zero goes along with the waters in which they formed having S18O(VSMOW) of "around" zero. Later, we'll clarify just what we mean by "around," and how that depends on temperature.
Having introduced the 6 notation and the VPDB standard, we are now in a position to get more quantitative about the things to be learned from the stable isotopes of carbon preserved in carbonates. The quantity of interest is 513C, reported relative to the VPDB reference. Carbon dioxide is cooked out of carbonates in the interior of the Earth, and outgases from volcanoes, subduction zones and the mid-ocean ridge with 613C « —6%o. In a steady state, the flux of carbon in this carbon dioxide is balanced by the burial of carbon in the form of inorganic carbonates (e.g. CaCO3 and organic carbon (schematically CH2O). In the long run, most of this burial is in sea-floor sediments, since whatever forms on land tends to eventually get washed into the ocean. Note that even carbonate precipitated biologically in the form of shells of organisms is considered inorganic material, and acts pretty much (though not exactly) like inorganically precipitated carbonate. There are some kinds of recently evolved plants that use photosynthetic pathways that fractionate carbon very little, but for the most part, photosynthetically produced organic carbon has 513C values that are about 25%olower than that of the carbon dioxide reservoir from which the photosynthetic organisms make their substance. For example, CO2 in the atmosphere today has 513C « —8%o, while land plants have 513C values running from -32%oto -25%oand marine organic carbon has 513C « —25%o. Fossil fuels, which are made from ancient land plants (in the case of coal) or marine organisms (in the case of oil) have 513C « —25%o.
If forg is the fraction of carbon which is buried in the form of organic carbon, 6o is the 513C of carbon outgassed from the Earth's interior, 6org is the 513C of the organic carbon buried and 5carb is the 513C of the carbonate carbon buried, then mass balance implies
If data from both organic and carbonate sediments are available, this formula can be used directly to infer forg. It is instructive, however, to make use of the intrinsic fractionation between inorganic carbon and photosynthetically produced organic carbon to infer the isotopic compositions of the two burial fluxes as a function of forg. Note that because photosynthetic fraction is relative to the composition of the inorganic carbon pool, it is incorrect to assume that 6org « — 25%o. It could be considerably heavier, if the inorganic pool has very positive 513C. Let's consider two limiting cases. Suppose that forg « 1, so that nearly all of the carbon outgassed from the Earth's interior is intercepted by photosynthesis and buried as organic carbon. In that case, mass balance requires that 6org « 6o « —6%o. This can only happen if the inorganic carbon pool consists of isotopically heavy carbon with 513C « (—6 + 25)%o = 19%o. Since the carbonate that precipitates from an inorganic carbon pool tends to be isotopically heavier than the pool itself, the trickle of carbonate precipitated in this situation will have 513C in excess of 19%o. The precise value depends on aspects of ocean chemistry we will not pursue here. In the opposite limit, when forg « 0 and there is little organic carbon burial, then 6carb « 6o « —6%o. The inorganic carbon pool this carbonate precipitates from is somewhat isotopically light compared to the carbonate itself, and the organic carbon fractionates relative to that value, yielding 6org < (—6 — 25)%o = —31%o. The typical situation over the past two billion years has been for Scarb to be somewhat positive, between 2%oand 5%o, while 6org hovers around -22%o. There are periods, however, when carbon isotopes undergo considerable excursions from the typical situation. These carbon isotope excursions provide an important window into big events in the carbon cycle.
The above picture applies only when the carbon cycle is in a steady state. When any part of the carbon cycle is significantly out of equilibrium - for example, when one is building up a new pool of stored organic carbon in land plants and soils - the simple input-output isotopic calculation no longer works. One must then do a detailed accounting of the flows of carbon between the various reservoirs involved, and the attendent isotopic fractionations. This can be a very intricate process, especially since the fractionations involved are generally temperature dependent. There are other important aspects of the isotopic carbon cycle we have swept under the rug, such as the important information that can be gained from vertical gradients of 513C in carbonates.
There is another biological process that can leave a distinct mark on the carbon isotopic record, namely methanogenesis. When there is oxygen around, organic matter generally gets decomposed into CO2 by respiration. In anaerobic environments, methanogens get the goodies instead, and turn organic matter into CH4. This is a multi-step process, each step of which fractionates carbon. The result is CH4 which is much lighter isotopically than the organic feedstock from which it was produced. Biologically produced methane today has 513C values on the order of -50 . When the atmosphere-ocean system is rich in oxygen, as has been the case for the past half billion years, methanogenesis plays a very minor role in the carbon cycle and usually leaves little imprint in the isotopic record. A possible exception to this general rule may occur as a result of gradual accumulation of large amounts of methane in the form of exotic ices called clathrates, which can form in ocean floor sediments and under arctic permafrost laters. If some event occurs which suddenly releases this stored methane into the atmosphere or ocean, the isotopically light methane quickly oxidizes into CO2 which works its way into the carbonates. The net result is a negative carbonate carbon isotope excursion, the magnitude of which tells us something about the quantity of methane released relative to the net carbon in the ocean-atmosphere system.
At present, the arsenal of climate proxies is much more limited for other planets than it is for Earth. Biologically mediated proxies are obviously not in the cards for planets that seem to have no biology, but many of the abiological proxies used on Earth would be equally useful on other planets; cherts on Mars would provide much the same kind of information as cherts have provided on Earth. The use of these chemical proxies is limited primarily by the weight and power consumption of analytical instruments needed to carry out some of the analyses that are typically done on Earth materials. The same constraint applies to many of the means of determining chronology based on radioactive decay. Such techniques can be applied to other planets with a preserved geological record (notably Mars), but must await sample return missions. Meanwhile, a considerable amount has been accomplished by remote-sensing from planetary orbiters, and from low-power instrumentation on landers. The landforms of Mars have been imaged in great detail, and constitute a proxy for past climates with regard to occurence of water and glacial activity. The minerology of the surface can be determined by a range of remote-sensing techniques, so a fair amount is known about the occurence of clay minerals (a signature of water and weathering) in the ancient crust of Mars, and other minerals such as the iron compound hematite also tell us something about the aqueous environment of Early Mars. On all planets, a study of the isotopic composition of atmospheric gases (possible by in situ and remote spectroscopic means) provides valuable information on the source of the atmosphere and how much has been lost over time, insofar as lighter isotopes escape to space more readily than heavy isotopes. With sample return missions and improved robotic exploration, the future promises a rich expansion in planetary proxy studies, not least the prospect of drilling the Martian polar glaciers to see what climate mysteries they record.
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