Geol. 656 Isotope Geochemistry

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1 ISOTOPE FRACTIONATION IN THE HYDROLOGIC SYSTEM AND BIOSPHERE HYDROGEN AND OXYGEN ISOTOPE RATIOS IN THE HYDROLOGIC SYSTEM We noted above that isotopically light water has a higher vapor pressure, and hence lower boiling point than isotopically heavy water. Let's consider this in a bit more detail. Raoult's law states that the partial pressure, p, of a species above a solution is equal to its molar concentration in the solution times the standard state partial pressure, p, where the standard state is the pure solution. So for example: p = p o H 16 2 O H 16 2 O [ H 16 2 O] 20.1a and p = p o H H O H 18 2 O 2 O [ ] 20.1b Since the partial pressure of a species is proportional to the number of atoms of that species in a gas, we can define α, the fractionation factor between liquid water and vapor in the usual way: α l /v = p H 2 18 O / p H 2 16 O [H 2 18 O]/[H 2 16 O] By solving 20.1a and 20.1b for [H 16 2 O] and [H 18 2 O] and substituting into 20.2 we arrive at the relationship: 20.2 α l /v = p o H 18 2 O 20.3 o p H 16 2 O Interestingly enough, the fractionation factor for oxygen between water vapor and liquid turns out to be just the ratio of the standard state partial pressures. The next question is how the partial pressures vary with temperature. According to classical thermodynamics, the temperature dependence of the partial pressure of a species may be expressed as: d ln P dt = ΔH RT where T is temperature, H is the enthalpy or latent heat of evaporation, and R is the gas constant. Over a sufficiently small range of temperature, we can assume that H is independent of temperature. Rearranging and integrating, we obtain: ln p = ΔH + const 20.5 RT We can write two such equations, one for [H 16 2 O] and one for [H 18 2 O]. Dividing one by the other we obtain: ln p o H 18 2 O = A B o p H RT 16 2 O where A and B are constants. This can be rewritten as: α = ae -B/RT 20.7 Over a larger range of temperature, H is not constant. The fractionation factor in that case depends on the inverse square of temperature, so that the temperature dependence of the fractionation factor can be represented as: /8/09

2 lnα = A B T Figure 20.1 shows water-vapor and ice-vapor fractionation factors for oxygen. Over a temperature range relevant to the Earth's surface, the fractionation factor for oxygen shows an approximately inverse dependence on temperature. Hydrogen isotope fractionation is clearly non-linear over a large range of temperature. Given the fractionation between water and vapor, we might predict that there will be considerable variation in the isotopic composition of water in the hydrologic cycle, and indeed there is. Furthermore, these variations form the basis of estimates of paleotemperatures and past ice volumes. Let's now consider the question of isotopic fraction in the hydrosphere in greater detail. As water vapor condenses, the droplets and vapor do not remain in equilibrium if the precipitation occurs and the droplets fall out of the atmosphere. So the most accurate description of the condensation process is Rayleigh distillation, which we discussed above. To a first approximation, condensation of water vapor will be a function of temperature. As air rises, it cools. You may have noticed the base elevation of clouds is quite uniform on a given day in a given locality. This elevation represents the isotherm where condensation begins. At that height, the air has become supersaturated, Figure Temperature dependence of fractionation factors between vapor and water (solid lines) and vapor and ice (dashed lines) for various species of water.! 18 O Equilibrium Rayleigh T, C Figure Calculated dependence of δ 18 O on temperature based on equ We assume the water vapor starts out 10 per mil depleted in δ 18 O. and condensation begins, forming clouds. Water continues to condense until equilibrium is again achieved. Further condensation will only occur if there is further cooling, which generally occurs as air rises. The point is that the parameter ƒ, the fraction of vapor remaining, can be approximately represented as a function of temperature. To explore what happens when water vapor condenses, lets construct a hypothetical model of condensation and represent ƒ as hypothetical function of temperature such as: 234 4/8/09

3 ƒ = T Since T is in kelvins, this equation means that ƒ will be 1 at 273 K (0 C) and will be 0 at 223 K ( 50 C). In other words, we suppose condensation begins at 0 C and is complete at 50 C. Now we also want to include temperature dependent fractionation in our model, so we will use equation Realistic values for the constant a and B are and J/mole respectively, so that 20.7 becomes: 20.9 α = e /RT Substituting 20.9, and R=8.314J/mol-K into equation 19.69, our model is: δ 18 O v =1000 T e /T So we predict that the isotopic composition of water vapor should be a function of temperature. We can, of course, write a similar equation for equilibrium condensation. Figure 20.3 shows the temperature dependence we predict for water vapor in the atmosphere as a function of temperature (we have assumed that the vapor begins with δ 18 O of -10 before condensation begins). Of course, ours is not a particular sophisticated model; we have included none of the complexities of the real atmosphere. It is interesting to now look at some actual observations to compare with our model. Figure 20.3 shows the global variation in δ 18 O in precipitation, which should be somewhat heavier than vapor, as a function of mean annual air temperature. The actual observations show a linear dependence on temperature and a somewhat greater range of δ 18 O than our prediction. This reflects both the ad hoc nature of our model and the complexities of the real system. We did not, for example, consider that some precipitation is snow and some rain, nor did we consider the variations that evaporation at various temperatures might introduce. Along with these factors, distance from the ocean also appears to be an important variable in the isotopic composition of precipitation. The further air moves from the site of evaporation (the ocean), the more water is likely to have condensed and fallen as rain, and therefore, the smaller the value of ƒ. Topography also plays an important role in the climate, rainfall, and therefore in the isotopic composition of precipitation. Mountains force air up, causing it to cool and the water vapor to condense. Thus the water vapor in air that has passed over a mountain range will be isotopically lighter than air on the ocean side of a mountain range. These factors are illustrated in the cartoon in Figure Figure Variation of δ 18 O in precipitation as a function of mean annual temperature /8/09

4 Hydrogen as well as oxygen isotopes will be fractionated in the hydrologic cycle. Indeed, δ 18 O and δd are reasonably well correlated in precipitation, as is shown in Figure The fractionation of hydrogen isotopes, however, is greater because the mass difference is greater. Figure 20.6 shows the variation in oxygen isotopic composition of meteoric surface waters in the North America. The distribution is clearly not purely a function of mean annual Figure Cartoon illustrating the process of Rayleigh fractionation and the increasing fractionation of oxygen isotopes temperature, and this illustrates the role of the factors discussed above. in rain as it moves inland. We will return to the topic of the hydrologic system in a future lecture when we discuss paleoclimatology. ISOTOPE FRACTIONATION IN THE BIOSPHERE As we noted, biological processes often involve large isotopic fractionations. Indeed, biological processes are the most important cause of variations in the isotope composition of carbon, nitrogen, and sulfur. For the most part, the largest fractionations occur during the initial production of organic matter by the so-called primary producers, or autotrophs. These include all plants and many kinds of bacteria. The most important means of production of organic matter is photosynthesis, but organic matter may also be produced by chemosynthesis, for example at mid-ocean Figure Northern hemisphere variation in δd and δ 18 O in ridge hydrothermal vents. Large fractions of both carbon and nitrogen occur precipitation and meteoric waters. The relationship between δd and δ 18 O is approximately δd = 8δ 18 O After Dansgaard (1964). during primary production. Additional fractionations also occur in subsequent reactions and up through the food chain as hetrotrophs consume primary producers, but these are generally smaller. CARBON ISOTOPE FRACTIONATION DURING PHOTOSYNTHESIS The most important of process producing isotopic fractionation of carbon is photosynthesis. As we earlier noted, photosynthetic fractionation of carbon isotopes is primarily kinetic. The early work of Park and Epstein (1960) suggested fractionation occurred in several steps. Subsequent work has elucidated the fractionations involved in these steps, which we will consider in more detail here /8/09

5 For terrestrial plants (those utilizing atmospheric CO 2 ), the first step is diffusion of CO 2 into the boundary layer surrounding the leaf, through the stomata, and internally in the leaf. The average δ 13 C of various species of plants has been correlated with the stomatal conductance (Delucia et al., 1988), indicating that diffusion into the plant is indeed important in fractionating carbon isotopes. On theoretical grounds, a 4.4 difference in the diffusion coefficients is predicted ( 12 CO 2 will diffuse more rapidly; see Lecture 27) so a fractionation of 4.4 is expected. Marine algae and aquatic plants can utilize either dissolved CO 2 or HCO 3 for photosynthesis: CO 2(g) CO 2(aq) + H 2 O H 2 CO 3 Η + +HCO 3 An equilibrium fractionation of +0.9 per mil is associated with dissolution ( 13 CO 2 will dissolve more readily), and an equilibrium +7 to +12 fractionation (depending on temperature) occurs during hydration and dissociation of CO 2. Thus, we expect dissolved HCO 3 to be about 8 to 12 per mil heavier than atmospheric CO 2. At this point, there is a divergence in the chemical pathways. Most plants use an enzyme called ribulose bisphosphate carboxylase oxygenase (RUBISCO) to catalyze a reaction in which ribulose bisphosphate reacts with one molecule of CO 2 to produce 2 molecules of 3-phosphoglyceric acid, a compound containing 3 carbon atoms, in a process called carboxylation (Figure 20.7). Energy to drive this reaction is provided by another reaction, called photophosphorylation, in which electromagnetic energy is used to dissociate water, producing oxygen. The carbon is subsequently reduced, carbohydrate formed, and the ribulose bisphosphate regenerated. Such plants are called C 3 plants, and this process is called the Benson-Calvin, or Calvin, cycle. C 3 plants constitute about 90% of all plants and include algae and autotrophic bacteria and comprise the majority of cultivated plants, including wheat, rice, and nuts. There is a kinetic fractionation associated with carboxylation of ribulose bisphosphate that has been determined by several methods to be in higher terrestrial plants. Bacterial carbolaxylation has different reaction mechanisms and a smaller fractionation of about 20. Thus for terrestrial plants a fractionation of about 34 is expected from the sum of the fraction. The actual observed total fractionation is in the range of 20 to 30. The disparity between the observed total fractionation and that expected from the sum of the steps presented something of a conundrum. The solution appears to be a model that assumes the amount of carbon isotope fractionation expressed in the tissues of plants depends on ratio the concentration of CO 2 inside plants to that in the external environment. The model may be described by the equation: Figure Variation of average δ 18 O in precipitation over North America. δ 18 O depends on orographic effects, mean annual temperature, and distance from the sources of water vapor. Figure Ribulose bisphosphate (RuBP) carboxylation, the reaction by which C 3 plants fix carbon during photosynthesis /8/09

6 Δ = a + (c i /c a )(b a) where a is the isotopic fractionation due to diffusion into the plant, c i is the interior CO 2 concentration, c a is the ambient or exterior CO 2 concentration, and b is the fractionation occurring during carboxylation. According to this model, where an unlimited amount of CO 2 is available Figure Phosphoenolpyruvate carboxylation, (i.e., when c i /c a 1), carboxylation alone causes fractionation. At the other extreme, if the concentration the reaction by which C 4 plants fix CO 2 during photosynthesis. of CO 2 in the cell is limiting (i.e., when c i /c a 0), essentially all carbon in the cell will be fixed and therefore there will be little fractionation during this step and the total fractionation is es- Figure Chemical pathways in C 4 photosynthesis. sentially just that due to diffusion alone. Both laboratory experiments and field observations provide strong support for this model. More recent studies have shown that Rubisco enzyme exists in at least 2 different forms and that these two different forms fractionate carbon isotopes to differing degrees. Form I, which is by far the most common, typically produces the fractionation mentioned above; fractionation produced by Form II, which appears to be restricted to a few autotrophic bacteria and some dinoflagellates, can be as small as The other photosynthetic pathway is the Hatch-Slack cycle, used by the C 4 plants, which include hotregion grasses and related crops such as maize and sugarcane. These plants use phosphoenol pyruvate carboxylase (PEP) to initially fix the carbon and form oxaloacetate, a compound that contains 4 carbons (Fig. 20.8). A much smaller fractionation, about -2.0 to -2.5 occurs during this step. In phosphophoenol pyruvate carboxylation, the CO 2 is fixed in outer mesophyll cells as oxaloacetate and carried as part of a C 4 acid, either malate or asparatate, to inner bundle sheath cells where it is decarboxylated and refixed by RuBP (Fig. 20.9). The environment in the bundle sheath cells is almost a closed system, so that virtually all the carbon carried there is refixed by RuBP, so there is little fractionation during this step. C 4 plants have average δ 13 C of -13. As in the case of RuBP photosynthesis, the fractionation appears to depend on the ambient concentration of CO 2. This dependence can be modeled as: Δ = a + (b 4 + b 3 φ a)(c i /c a ) where a is the fractionation due to diffusion of CO 2 into the plant as above, b 4 is the fractionation during transport into bundle-sheath cells, b 3 is the fractionation during carboxylation (~ 3 ), φ is the fraction CO 2 leaked from the plant. A third group of plants, the CAM plants, have a unique metabolism called the Crassulacean acid metabolism. These plates generally use the C 4 pathway, but can use the C 3 pathway under certain conditions. These plants are generally adapted to arid environments and include pineapple and many cacti, they have δ 13 C intermediate between C 3 and C 4 plants. Terrestrial plants, which utilize CO 2 from the atmosphere, generally produce greater fractionations than marine and aquatic plants, which utilize dissolved CO 2 and HCO 3, together referred to as dissolved inorganic carbon or DIC. As we noted above, there is about a +8 equilibrium fractionation between dissolved CO 2 and HCO 3. Since HCO 3 is about 2 orders of magnitude more abundant in seawater than dissolved CO 2, many marine algae utilize this species, and hence tend to show a lower net fractionation during photosynthesis. Diffusion is slower in water than in air, so diffusion is often the rate-limiting step. Most aquatic plants have some membrane-bound mechanism to pump DIC, which 238 4/8/09

7 can be turned on when DIC is low. When DIC concentrations are high, fractionation in aquatic and marine plants is generally similar to that in terrestrial plants. When it is low and the plants are actively pumping DIC, the fractionation is less because most of the carbon pumped into cells is fixed. Thus carbon isotope fractionations can be as low as 5 in algae. The model describing this fractionation is: Δ = d + b 3 (F 3 / F 1 ) where d is the equilibrium effect between CO 2 and HCO - 3, b 3 is the fractionation associated with carboxylation, and (F 3 /F 1 ) is the fraction of CO 2 leaked out of the cell. Though the net fractionation varies between species and depends on factors such as light intensity Figure Dependence of δ 13 C of algae and bacterial on CO 2 concentration and moisture stress, higher C 3 plants have average bulk δ 13 C values of -27 ; algae and lichens are typically -12 from hydrothermal springs in Yellowstone National Park. Carbon isotope to 23. In aquatic systems where the ph is lower than in fractionation also depends on the ph of seawater, CO 2 becomes a more important species and the water, because this determines the algae can in some cases utilize this rather than HCO 3. species of carbon used in photosynthesis. In those cases, the total fractionation will be greater. An interesting illustration of this, and the effect of the CO 2 concentration on net fractionation is shown in Figure 20.9, which shows data on the isotopic composition of algae and bacteria in Yellowstone hot springs. Some fractionation is also associated with respiration (the oxidation of carbohydrate to CO 2 ), but the net effect is uncertain. Not surprisingly, the carbon isotope fractionation in C fixation is also temperature dependent. Thus higher fractionations are observed in cold water phytoplankton than in warm water species. However, this observation also reflects a kinetic effect: there is generally less dissolved CO 2 available in warm waters because of the decreasing solubility at higher temperature. As a result, a larger fraction of the CO 2 is utilized and there is consequently less fractionation. Surface waters of the ocean are generally enriched in 13 C because of uptake of 12 C during photosynthesis (Figure 20.11). The degree of enrichment depends on the productivity: biologically productive areas show greater enrichment. Deep water, on the other hand, is depleted in 13 C (perhaps it would be more accurate to Figure Depth profile of total dissolved inorganic carbon and δ 13 C in the say it is enriched in 12 C). Organic matter falls through the water column and is decomposed and "remineralized", North Atlantic. i.e., converted in inorganic carbon, by the action of bacteria, enriching deep water in 12 C. Thus biological activity acts to "pump" carbon, and particularly 12 C from surface to deep waters. Essentially all organic matter originates through photosynthesis. Subsequent reactions convert the photosynthetically produced carbohydrates to the variety of other organic compounds utilized by or /8/09

8 ganisms. Further fractionations occur in these reactions. These fractionations are thought to be kinetic in origin and may partly arise from organic C-H bonds being enriched in 12 C and organic C-O bonds are enriched in 13 C. 12 C is preferentially consumed in respiration (again, because bonds are weaker and it reacts faster), which would tend to enrich residual organic matter in 13 C. Thus the carbon isotopic composition of organisms becomes more positive moving up the food chain. Interestingly, although the energy source for chemosynthesis is dramatically different than for photosynthesis, the carbon-fixation process is similar and still involves the Calvin cycle. Not surprisingly then, carbon fractionation during chemosynthesis is similar to that during photosynthesis. Some chemosynthetic bacteria, notably some of the symbionts of hydrothermal vent organisms, have Rubisco Form II, and hence show smaller fractionations. NITROGEN ISOTOPE FRACTIONATION IN BIOLOGICAL PROCESSES Nitrogen is another important element in biological processes, being an essential component of all amino acids and proteins. As in the case of carbon, most of terrestrial nitrogen isotopic variation results from biological processes. These processes, however, are considerably more complex because nitrogen exists in more forms and more oxidation states. There are five important forms of inorganic nitrogen: molecular nitrogen (N 2 ), nitrate (NO + 3 ), nitrite (NO + 2 ), ammonia (NH 3 ), and ammonium (NH - 4 ). Equilibrium isotope fractionations that can be quite large occur between these five forms. Except for the ammonium ammonia reaction, the reactions between these forms are all redox reactions and they are predominantly biologically mediated. Significant kinetic fractionations occur during these biological mediated reactions. Heterotrophs get their nitrogen from what they eat and there is only a slight difference, generally around 1 or 2, between animals and what they eat. Autotrophs, including algae, plants and bacteria, must assimilate nitrogen from the environment. Plants and algae cannot assimilate and utilize N 2, they must used some type of fixed nitrogen, which can be any of the remaining 4 forms listed above. The dirty work of converting nitrogen to ammonia (and from there to other forms of nitrogen), a process called fixation, is done by bacteria, including photosynthetic ones. This involves only a small fractionation of -3 to +1. Reduced nitrogen (e.g., ammonia) is the form of nitrogen that is ultimately incorporated into organic matter by autorophs (it is ultimately incorporated into organic molecules as NH 2 amine groups). There is a fractionation of up to -20 when autotrophs uptake of ammonium ( 14 N is taken up preferentially), the extent depending on the ammonium abundance. When ammonium is abundant, fractionation tends to be large, when it is not, most available ammonium is taken up and there is little fractionation (Figure 20.12). Most plants, including many marine algae, can utilize oxidized nitrogen, NO 3 and NO 2, as well as reduced nitrogen. In these cases, nitrogen must first be reduced by the action of reductase enzymes. δ 15 N fractionations of 0 to trogen Cycle. Table 20.1 Nitrogen Isotopic Fractionation in the Exogenic Ni- 24 have been measured for the assimilation of NO 3. N 2 fixation N 2 2NH 3 <2 Reaction Fractionation There is a small fractionation when + NH 3 NH to 33 that ammonium is subsequently incorporated into organic molecules. Nitrification NH NO 3-15 to -35 There are two principle reactions by which ammonia is incorporated into organic matter: formation of glutamate from α-ketoglutarate via the Denitirification Nitrate reduction NO - 3 N 2 NO NH 4-5 to to -35 glutamate dedhydrogenase reaction, and formation of glutamine from glutamate via the enzyme glutamine synthetase. A positive fractionation (i.e., the product is enriched in 15 N) of +2 to +4 has been 240 4/8/09

9 measured for the glutamate dedhydrogenase reaction, and the fractionation for the glutamine synthetase reaction is also expected to be positive, because N is bound more strongly in the product than in ammonia. The net result of these various fractionations is that organic nitrogen is usually heavier than atmospheric nitrogen. The isotopic compositions of marine particulate nitrogen and nonnitrogen-fixing plankton are typically 3 to +12 δ 15 N. Terrestrial plants unaffected by artificial fertilizers generally have a narrower range of +6 to +13 per mil. Legumes (and a few other kinds of plants) are a special case. While they cannot fix nitrogen, they have symbiotic bacteria in their root nodules that can. As a result, legumes have distinctly lower δ 15 N than other terrestrial, in the range of 2 to +4. Marine blue-green algae range from -4 to +2, with most in the range of -4 to -2. A caveat to all this most fixed nitrogen in ecosystems now derived from artificial fertilizers. These fertilizers contain ammonia derived from atmospheric N 2 through the Haber process, in which there is little isotopic fractionation. Consequently, modern plants, particularly those raised on artificial fertilizers, have lower δ 15 N. OXYGEN AND HYDROGEN ISOTOPE FRACTIONATION BY PLANTS Oxygen is incorporated into biological material from CO 2, H 2 O, and O 2. However, both CO 2 and O 2 are in oxygen isotopic equilibrium with water during photosynthesis, and water is the dominant form. Therefore, the isotopic composition of plant water determines the oxygen isotopic composition of plant material. The oxygen isotopic composition of plant material seems to be controlled by exchange reactions between water and carbonyl oxygens (oxygens doubly bound to carbon): C = 16 O + H 2 18 O! C = 18 O + H 2 16 O Figure Dependence of nitrogen isotope fractionation by bacteria and diatoms on dissolved ammonium concentration. Fractionations of +16 to +27 (i.e., the organically bound oxygen is heavier) have been measured for these reactions. Consistent with this, cellulose from most plants has δ 18 O of +27±3. Other factors, however, play a role in the oxygen isotopic composition of plant material. First, the isotopic composition of water varies from δ 18 O 55 in Arctic regions to δ 18 O 0 in the oceans. Second, less than complete equilibrium may be achieved if photosynthesis is occurring at a rapid pace, resulting in less fractionation. Finally, some fractionation of water may occur during transpiration, with residual water in the plant becoming heavier. Hydrogen isotope fractionation during photosynthesis occurs such that the light isotope is enriched in organic material. In marine algae, isotope fractionations of 100 to 150 have been observed, which is similar to that observed in terrestrial plants: 86 to Among terrestrial plants, there appears to be a difference between C 3 and C 4 plants. The former fractionations of 117 to 121, while fractionations -86 to 109 have been observed in C 4 plants. However, little is known in detail about the exact mechanisms of fractionation. As is the case for oxygen, variations in the isotopic composition of available water and fractionation during transpiration are important in controlling the hydrogen isotopic composition of plants. This is illustrated in Figure /8/09

10 Figure Isotopic Fractionations of hydrogen during primary production in terrestrial plants. After Fogel and Cifuentes (1993). BIOLOGICAL FRACTIONATION OF SULFUR ISOTOPES Though essential to life, sulfur is a minor component is living tissue (C:S atomic ratio is about 200). Plants take up sulfur as sulfate and subsequently reduce it to sulfide and incorporate into cysteine. There is apparently no fractionation of sulfur isotopes in transport across cell membranes and incorporation, but there is a fractionation of +0.5 to 4.5 in reduction process, referred to as assimilatory sulfate reduction. This is substantially less than the expected fractionation of about -20, suggesting that nearly all the sulfur taken up by primary producers is reduced and incorporated into tissue. Sulfur, however, plays two other important roles in biological processes. First, sulfur in the form of sulfate can act as an electron acceptor or oxidant, and is utilized as such by sulfur-reducing bacteria. This process, in which H 2 S is liberated, is called dissimilatory sulfate reduction and plays an important role in biogeochemical cycles, both as a sink for sulfur and source for atmospheric oxygen. A large fractionation of +5 to 46 is associated with this process. This process produces by far the most significant fractionation of sulfur isotopes, and thus governs the isotopic composition of sulfur in the exogene. Sedimentary sulfate typically has δ 34 S of about +17, which is similar to the isotopic composition of sulfate in the oceans (+20), while sedimentary sulfide has a δ 34 S of 18. The living biomass has a δ 34 S of 0. The final important role of sulfur is a reductant. Sulfide is an electron acceptor used by some types of photosynthetic bacteria as well as other bacteria in the reduction of CO 2 to organic carbon. Most unique among these perhaps are the chemosynthetic bacteria of submarine hydrothermal vents. They utilize H 2 S emanating from the vents as an energy source and form the base of the food chain in these unique ecosystems. A fractionation of +2 to 18 is associated with this process. REFERENCES AND SUGGESTIONS FOR FURTHER READING Bowen, R., Isotopes in the Earth Sciences, Elsevier, Essex, 647, Broecker, W. and V. Oversby, Chemical Equilibria in the Earth, McGraw-Hill, New York, 318 pp., 1971 (Chapter 7). Dansgaard, W., Stable isotopes in precipitation, Tellus, 16, , Faure, G., Principles of Isotope Geology, 2 nd ed., J. Wiley & Sons, New York, 589 p., Ferronsky, V. I., and V. A. Polyakov, Environmental Isotopes in the Hydrosphere, ed., 466 pp., John Wiley and Sons, Chichester, Fogel, M. L., and M. L. Cifuentes, Isotope Fractionation during Primary Production, in Organic Geochemistry: Principles and Applications edited by M. H. Engel and S. A. Macko, p , Plenum, New York, Hoefs, J., Stable Isotope Geochemistry, 3 rd ed., Springer-Verlag, Berlin, 241p O'Leary, M. H., Carbon isotope fractionation in plants, Phytochemistry, 20, , Park, R. and S. Epstein, Carbon isotope fractionation during photosynthesis, Geochim. Cosmochim. Acta, 21, , /8/09