Isotope Geochemistry Measuring Isotopes While different isotopes of the same element exist in certain fractions corresponding to their natural abundance adjusted by Where R is the ratio of fractionation a Ra b heavy light isotope and is Rb the fractionation factor We measure isotopes as a ratio of the isotope vs a standard material per mille a Rsample Rstandard O Rstandard 18 3 a b 103 a b 10 ln a b Fractionation A reaction or process which selects for one of the stable isotopes of a particular element 3 selects a a If the process for the heavier 10 ln b a b b isotope the reaction product is heavy the reactant remaining is light Isotope fractionation occurs for isotopic exchange reactions and mass dependent differences in the rates of chemical reactions and physical processes Temperature effects on fractionation The fractionation factors are affected by T recall that this affects EA and defined empirically 6 A 10 103 ln ba B 2 T Then 3 a b Where A and B are constants determined for particular reactions and T is temp in Kelvins a b 10 ln a b As T increases decreases at high T goes to zero Equilibrium vs Kinetic fractionation Fractionation is a reaction but one in which the free energy differences are on the order of 1000x smaller than other types of chemical reactions Just like other chemical reactions we can describe the proportion of reactants and products as an equilibrium or as a kinetic function FRACTIONATION DURING PHYSICAL PROCESSES Mass differences also give rise to fractionation during physical processes diffusion evaporation freezing etc Fractionation during physical process is a result of differences in the velocities of isotopic molecules of the same compound Consider molecules in a gas All molecules have the same average kinetic energy which is a function of temperature Ekinetic 2 mv 1 2 Because the kinetic energy for heavy and light isotopes is the same we can write vL mH vH mL In the case of 12C16O and 13C16O we have vL 28 99827 1 0177 vH 27 994915 Regardless of the temperature the velocity of 12C16O is 1 0177 times that of 13C16O so the lighter molecule will diffuse faster and evaporate faster Equilibrium Fractionation For an exchange reaction C16O2 H218O C18O2 H216O 1 Write the equilibrium 18 16 K C O2 2 H O2 1 2 C 16O2 H 18O2 Where activity coefficients effectively cancel out For isotope reactions K is always small usually 1 0xx this K is 1 047 for example WHY IS K DIFFERENT FROM 1 0 Because 18O forms a stronger covalent bond with C than does 16O The vibrational energy of a molecule is given by the equations Evibrational 1 2 h O H H 1 2 k m F kx Thus the frequency of vibration depends on the mass of the atoms so the energy of a molecule depends on its mass The heavy isotope forms a lower energy bond it does not vibrate as violently Therefore it forms a stronger bond in the compound The Rule of Bigeleisen 1965 The heavy isotope goes preferentially into the compound with the strongest bonds Equilibrium Fractionation II For a mass dependent reaction Ca2 C18O32 CaC18O3 Ca2 C16O32 CaC16O3 Measure 18O in calcite 18Occ and water 18Osw Assumes 18O 16O between H2O and CO32 at some equilibrium T C 16 998 4 52 18Occ 18Osw 0 028 18Occ 18Osw 2 Empirical Relationship between Temp Oxygen Isotope Ratios in Carbonates At lower temperatures calcite crystallization tends to incorporate a relatively larger proportion of 18O because the energy level vibration of ions containing this heavier isotope decreases by a greater amount than ions containing 16O As temperatures drop the energy level of 18O declines progressively by an amount that this disproportionately greater than that of the lighter 16O Distillation 2 varieties Batch and Rayleigh distillation dependent on if the products stay in contact and re equilibrate with the reactants Batch Distillation f i 1 F 103ln CO2 Rock where the isotope of the rock i depends on it s initial value f and the fractionation factor Rayleigh Distillation f i 103 F 1 1 RAYLEIGH DISTILLATION Isotopic fractionation that occurs during condensation in a moist air mass can be described by Rayleigh Distillation The equation governing this process is o 1 Rv Rv f where Rv isotope ratio of remaining vapor Rv isotope ratio in initial vapor the fraction of vapor remaining and a the isotopic fractionation factor Effect of Rayleigh distillation on the 18O value of water vapor remaining in the air mass and of meteoric precipitation falling from it at a constant temperature of 25 C Complications 1 Re evaporation 2 Temperature dependency of Using isotopes to get information on physical and chemical processes Fractionation is due to some reaction different isotopes can have different fractionation for the same reaction and different reactions have different fractionations as well as being different at different temperatures and pressures Use this to understand physical chemical processes mass transfer temperature changes and other things Volatilization calcite quartz wollastonite carbon dioxide CaCO3 SiO2 CaSiO3 CO2 As the CO2 is produced it is likely to be expelled Other volatilization reaction examples ISOTOPE FRACTIONATION IN THE HYDROSPHERE Evaporation of surface water in equatorial regions causes formation of air masses with H2O vapor depleted in 18O and D compared to seawater This moist air is forced into more northerly cooler air in the northern hemisphere where water condenses and this condensate is enriched in 18O and D compared to the remaining vapor The relationship between the isotopic composition of liquid and vapor is Ol Ov 10 10 18 l v 18 3 3 Assuming that 18Ov 13 1 and vl O 1 0092 at 25 C then Ol 1 0092 13 1 10 10 4 0 0 00 18 3 3 and assuming Dv 94 8 and vl H 1 074 at 25 C then Dl 1 074 94 8 103 103 27 8 0 00 These equations give the isotopic composition of the first bit of precipitation As 18O and D are removed from the vapor the remaining vapor becomes more and more depleted Thus 18O and D values become increasingly negative with increasing geographic latititude and altitude Map of North America showing contours of the approximate average D values of meteoric surface waters Because both H and O occur together in water 18O and D are highly correlated yielding the meteoric water line MWL D 8 18O 10 Deviation from MWL Any additional fractionation process which affects O and D differently or one to the exclusion of the other will skew a water away from the MWL plot These effects include Elevation effects D 8 1000m 4 C Temperature different