A brief summary of isotopes and fractionation 1 Isotopes are chemically identical but mechanically different 2 Different masses lead to different bond frequencies 1 2 Hooke s Law 3 which lead to different zero point energies 4 Which causes them to react at different rates IL001 Isotope Effects verus Fractionation 12C 12C 13C 13C An Isotope Effect R For equilibrium rxns P For nonequilibrium rxns HDO H2 H2O HD 0 30 E I E Keq HDO H2 Q H2O HD RH2 RH2O 0 30 i e 700 2H2O 2HDO K I E KH KD 2 7 Fractionation causes e 2H2 O2 2HD O2 RH2 RH2O 0 37 but not consistently applied IL002 Delta Notation Introduced in 1948 by Harold Urey partly for conciseness and partly to emphasize that we measure relative isotope ratios very accurately but absolute isotope ratios only poorly All delta values are relative Defining accuracy can be a bit tricky Slight confusion over its definition Rsamp Rstd 103 Rstd R Rstd or in units implies factor of 103 Good delta values can usually be added linearly making mass balance equations straightforward including blank correction nt t n1 1 n2 2 Bad delta values are only linear over a small range of absolute abundance so be careful with hydrogen and isotopic labels 13C 200 1 200 000 100 800 000 0 100 200 0 008 0 010 13 400 000 S MOW 0 1 000 0 012 0 014 C fractional abundance 0 0 0 5 1 0 13 C fractional abundance IL004 Measures of Fractionation defn used for A 1000 B 1000 1 103 1000ln A B all kinetic equil equil 0 8 0 900 0 980 0 990 1 000 1 010 1 020 1 100 1 200 200 0 100 0 20 0 10 0 0 0 10 0 20 0 100 0 200 0 223 1 105 4 20 2 10 1 0 0 10 0 19 8 95 3 182 3 250 0 111 1 20 4 10 1 0 0 9 9 19 6 90 9 166 7 12 for constant 1 100 11 dA dB symbol 10 9 8 200 0 200 dA remember delta scale is not linear IL006 Equilibrium Fractionations Fractionations can exist between different phases of the same compound as well as between different compounds Equilibrium isotope effects are usually temperature dependent but pressure independent Fractionations form basis for thermometry Normal EIE means heavy isotope accumulates in stronger bond or light isotope is more volatile and fractionation decreases with T There are exceptions Equil isotope effects are difficult to measure direclty but can be predicted from calculations at least for simple molecules Equilibrium fractionations can be measured directly by equilibrating materials at constant T IL005 PA 1001 VA N DE R L A A N E T A L L AT E MIOCE NE STA B L E ISOT OPE R E COR DS F igur e 2 Cyclostratigraphy and magnetostratigraphy of A in el B eida with planktonic and benthic 18O and sedimentation rate Tuning of the sedimentary cyclicity to the 65 N summer insolation and precession curves of the L a93 1 1 astronomical solution Laskar et al 1993 Magnetostratigraphy is based on K rijgsman et al 2004 Time equivalent lithologic units in the Mediterranean are shown at the right hand side of the figure after K rijgsman et al 2001 T he initiation of the MSC at 5 96 Ma is indicated by an arrow PA 1001 Kinetic Fractionations H2DC D CH2D2 D2HC H energy CH2DCl CHD2Cl reaction coordinate Kinetic isotope effects can be rationalized in terms of the potential energy barrier of the reaction The lower the barrier the faster the reaction Kinetic isotope effects are usually independent of both temperature and pressure KIE s are typically constant for a particular reaction Normal KIE means light isotope reacts more rapidly There are very few known exceptions and nearly all involve D H Kinetic isotope effects are easy to measure directly but cannot generally be predicted from theory Kinetic fractionations can be tricky to measure in natural systems because fractionation often depends on reaction yield IL012 Open System Fractionation Open means that reactant is available in unlimited supply With only one product isotopic composition of product is constant R P R P R P R P With two or more products isotopic composition depends on relative yield of each product Isotopic mass balance must be maintained what goes in must come out R Q Reaction Chamber P Q A P R Q R Isotope ratio A P R Q R P 0 0 5 1 0 yield of P IL013 Example of Open System Fractionation At the broadest level inputs to the global C cycle weathering volcanism must match outputs buried carbonate and organic matter a CO2 inputs i biosphere o carbonate carbon TOC organic carbon i fo o 1 fo a TOC a o i fo a TOC a fo a a fo TOC fo a i TOC Hayes Strauss Kaufman 1999 Chemical Geology 161 103 125 Thus we can interpret fo an important operating condition of the global carbon cycle and biosphere from measurements of only 3 quantities Closed System Fractionation If the reactant is in limited supply its composition will change as it is consumed by the reaction Fractionation R P Isotope Effect Isotope ratio Fractionation between pooled product and unconsumed reactant is variable A f yield isotope effect R A B Fractionation between instantaneously forming product and unconsumed reactant is constant B f isotope effect P P 0 0 5 yield of P f 1 0 rf ro ln 1 f Fractionation can be due either to kinetic or equilibrium isotope effects if P is continually removed The latter case is often called Rayleigh Distillation IL014 Fractionation in Precipitation D 128 D 76 f 0 5 eq 0 924 25 C D 198 f 0 8 D 53 D 0 Ocean D 122 all equilibria at 25 C Precipitation becomes D enriched as more rain condenses farther from the ocean D 145 D 76 eq 0 924 25 C D 0 Ocean f 0 5 D 237 f 0 8 eq 0 900 5 C D 45 D 137 clouds at 5 C The effect is exaggerated at colder temperatures because the liquid vapor fractionation is larger IL016