布朗大學(xué)同位素地球化學(xué)3.stableisotopefractionation

1、Stable Isotope Fractionation,Topics in this class,Why do isotopic ratios change (fractionate) in nature?Types of stable isotope fractionationHow do we express the isotopic fractionation in a quantitative manner?How

2、 could isotopic fractionation be used for environmental and geological research?,Objectives,Understand the fundamental theory of stable isotope fractionationFamiliar with the types of isotopic fractionationFamiliar w

3、ith different ways to describe fractionation (sometimes confusing),What is isotopic fractionation?,Isotopes of an element have slightly different chemical and physical properties due to the mass differenceIn chemical,

4、physical or biological processes, the reactants and products may have different isotopic ratiosThe changes in isotopic ratios in these processes are called “isotopic fractionation”,Expression of isotopic fractionation,

5、For a process from reactant to product, the isotopic fractionation factor α is defined as:For example, during evaporation, the oxygen isotopic fractionation is expressed as,,There is no fractionation if ? = 1,Key scien

6、tists/events in studying isotopic fractionation in hydrological cycle,Harold Urey, discovered D in 1933 using spectroscopyGianque and Johnson: Discovered 18O in 1929Friedman: found δ18O and δD change in coordinated f

7、ashion in precipitationHarmon Craig: studied δ18O and δD partition in precipitation, established meteoric water line (1961)Later work demonstrates how isotopes are partitioned through other systems, such as 13C in th

8、e carbon cycle,Types of isotope fractionation,Equilibrium isotope fractionationKinetic (non-equilibrium) isotope fractionationDiffusive isotope fractionation (a special case of kinetic isotope fractionation)Non-mas

9、s dependent isotope fractionation,Thermodynamic equilibrium of isotope fractionation,Fractionation can be regarded as an exchange of isotopes between two molecular species or phases that are participating in a reaction

10、H218O+C16O16O ? H216O+C16O18OThe exchange reactions involve breaking of old bonds and formation of new bondsThe strength of bonds formed by the light vs. heavier isotopes is different, resulting in difference in reac

11、tion rates,Zero point energy,The difference in bond strength is a result of different “zero point energy” of isotope species,Bond strength of heavy and light isotopes,The heavy isotope has a stronger bond and require gr

12、eater energy to dissociate than a light isotopeLighter nuclei react more quicklyIn a equilibrium reaction, stronger bonds survive longer, so that usually the heavy isotopic species are partitioned into the more conde

13、nsed phase, e.g., liquid phase in vapor-liquid reactions,Partition functions (Q),Dissociation energy of a molecule is related to its partition function (Q), at vibrational frequency Q = ?-1m3/2∑e-E/kTwhere,? = a

14、 symmetry valuem = massE = the energy state, from zero point energy to the energy of the dissociated molecule (J*mole-1)K = Boltzmann constant (gas constant per molecule)=n?1.380658 ? 10-23JK-1T = thermodynamic tempe

15、rature K,1. Equilibrium constant = α,X + Y* ? X* + Ye.g., H2 + HDO ? HD + H2OK = [X*][Y]/[X][Y*] = {[X*]/[X]}÷{[Y*]/[Y]}= Rx/Ry = α,Concentration ratio = ratio of Q,Rx = [X*]/[X] = Qx* / Qx,C16O2/C16O18O

16、 ? H216O/H218O,Partition function and a,Isotopic distribution in molecules of an equilibrium system is determined by the Q values of each moleculeThe difference in isotopic ratios are proportional to e-DE/TAt higher

17、temperature e-DE/T→1, the fractionation factor a→1,Temperature impact,At higher temperature, the influence of difference in E (zero point energy difference) on Q is smaller, hence the isotopic fractionation between diffe

18、rent isotopic species is smallerAt lower temperatures, ?E plays a greater role in changing the Q, hence larger isotopic fractionation,Requirement of isotopic equilibrium,Chemical equilibrium, forward and backward react

19、ion rates are equalForward and backward reactions have proceeded enough times to mix the isotopes between reactants and productsReactant and product pools must be well mixed. If not, then isotopic equilibrium will ex

20、ist only for the immediately produced reactants and products in the vicinity of reaction site (e.g., air-water interface for vapor-water equilibrium),Redistribution of isotopes of an element among various reactants and p

21、roductsAt equilibrium, isotope ratios in each compound are constantFor example, dissolution of CO2 in H2OCO2 + H2O ? H2CO3 The equilibrium involves exchange of O atoms between CO2 and H2OH218O+C16O16O ? H216O+

22、C16O18OThis process needs to occur many times to ensure full exchange, sometimes stirring is necessary, the exchange also proceeds faster when pH<4.5,Equilibrium isotopic fractionation,At equilibrium,[a=1.0412,

23、 (Friedman and O’Neil, 1977)]Therefore, at equilibrium, d18O of CO2 is ~40‰ higher than d18O of H2O.A global scale example is atmospheric CO2 has d18O about 40±2 ‰ (VSMOW), compared with 0±1‰ for ocean water

24、. This equilibrium is the basis of one way to measure the d18O values of H2O,Another well known, important isotope exchange reaction isThe equilibrium isotope fractionation factorTherefore, calcite is enriched in

25、18O relative to ocean water by +28.6 ‰. (at 25oC)This fractionation is temperature dependent, so it is the basis for paleotemperature reconstruction using the CaCO3 deposited in ocean.,,Natural equilibrium systems,In n

26、atural systems, complete physicochemical equilibrium is seldom maintainedHowever, if the net forward reaction does not greatly exceed the rate of back reaction, it still can be considered to have an isotopic equilibriu

27、mRain-vapor, snow-vapor, can be treated as isotopic equilibrium, even though super saturation in clouds is common,Temperature effect on equilibrium isotope fractionation,There is an inverse relationship between tempera

28、ture and isotopic fractionation factor (?) The general empirical relationship between the fractionation factor and temperature is:103ln?X-Y = aT-2 + bT-1 + cParameters a, b, c have been determined for many syst

29、ems (see the inner cover page of the text),Oxygen and hydrogen isotopic fractionation between different water phases,T and isotopic fractionation,Water – vapor fractionation,T-fractionation in various systems,Kinetic iso

30、tope fractionation,Kinetic isotope fractionation occurs in,Systems out of chemical and isotopic equilibriumForward and backward reaction rates are very differentUnidirectional reactions, or reversible reactions if re

31、action products become physically isolated from the reactantsIn kinetically controlled reactions, the faster the reaction, the smaller the isotopic fractionation. For example, if water freezes rapidly, the 3‰ equilibri

32、um enrichment of ?18O in the ice with respect to the water is reduced towards 1 ‰.,Enzyme-mediated reactions,Most biologically mediated reactions (mostly redox reactions) are unidirectional reactionsThey display reprod

33、ucible kinetic isotope effect in the same conditionsExamples, photosynthesis, biodegradation, methanogenesis,Diffusion of molecules or ions through concentration or temperature gradientsCan be considered as a special

34、 case of kinetic isotopic fractionationFractionation arises from the differences in the diffusive velocities between isotopesFor processes controlled by diffusion only, the mass differences determine the fractionatio

35、n factor,Diffusive isotopic fractionation,During diffusion into a vacuum, the steady-state fractionation is the ratio of the velocities of the two isotopesWhere v=molecular velocity (cm s-1) k=Boltzmann consta

36、nt (gas constant per molecule) =n*1.380658*10-23 JK-1 m=molecular mass (in Kg) T=absolute temperature K,Diffusion into a vacuum,Graham’s Law,,The fractionation factor for two isotopic molecules during diffus

37、ion into a vacuum is given by Graham’s Law:,For 12C16O16O (mass 44) and 12C16O18O (mass 46), the diffusion isotopic fractionation factor is:,In the more common case where a gas or solute is diffusing through another medi

38、um (e.g., Air), the mass of the medium must be take into account, the equation isWhere 28.8 is the average mass of air (79% of N2, 21% of O2, 0.79×28+0.21×32=28.8),Diffusion through a medium,CO2 diffusion

39、in soil,If m*=12CO2, m=13CO2, we can calculate 12CO2 diffuses 4.4% faster than 13CO2, or there is 4.4% carbon isotopic fractionation when CO2 diffuses through air. Examples: Soil gases, some aquifers,Fractionat

40、ion factor (α=RA/RB)Isotope separation: big delta Δ ΔA-B = δA-δB,Expressions of isotope difference between molecules A and B,Enrichment factor ? is defined as?A-B = (RA/RB – 1) * 103 = (α- 1)103When αi

41、s close to 1, say 1.00x, we can verify, 1000ln1.00x ≈x(remember the series: lnx=(x-1)-(x-1)2/2+(x-1)3/3… ) ?A-B = (αA-B-1)*1000 =(1.00x-1)*1000 =x ≈1000ln1.00x =103ln α,,Enrichment factor (?

42、),? and Big Delta,εA-B = (αA-B-1)*1000 =[(1000+δA)/(1000+δA)-1]*1000 ≈ δA-δB = DA-BTherefore, εA-B=(αA-B-1)*1000 ?ΔA-B ≈103ln α,Example of water vapor fractionation,At 25oC, evaporate ocean water

43、 with δ18Ow = 0.0 ‰ VSMOW, the water vapor has δ18Ov = -9.3 ‰ VSMOWThe isotopic separation (?) is: ?18Ow-v = δ18Ow - δ18Ov = 9.30 ‰α18Ow-v = (18O/16O)w/ (18O/16O)v = (1000 + δ18Ow)/ (1000 + δ18Ov) = 1.0093ε18Ow

44、-v = [(18O/16O)w/ (18O/16O)v -1]?1000 = 9.30 ‰,D, ε, and 103lnα,When α is not far from 1, these three values are similar, but discrepancies increase as α departs from 1When D, ε, and 103lnα are used interchangeably to

45、express isotopic differences between A and B, but remember they are approximationsDA-B ≈ εA-B ≈ 103lnαA-BWhen α is large, 103lnα is preferred since it is theoretically related to temperature,Comparison of D, ε, and 1

46、03lnα,Comparison of D, ε, and 103lnα,When α is large,Hydrogen isotope fractionation factor between water and dissolved H2S is large:αH2O-H2S = 2.37 (Galley et al., 1972)103lnα(2H) H2O-H2S = 863 ‰ε(2H) H2O-H2S = (α

47、-1)?103 = 1370 ‰From α18O H2O-H2S =(1000 + δ18OH2O)/ (1000 + δ18OH2S)Assuming δDH2O = 0 ‰ (e.g., ocean water), δ18OH2S=-578 ‰ D(2H) H2O-H2S = δDH2O - δ18OH2S= 578 ‰,Mass-dependent Isotope fractionation,The extent o

48、f isotopic fractionation is proportional to mass difference. There are two types of mass-dependent isotope fractionationA) For different elements, H, O, C, N, S, Si, Sr etc., the larger the mass difference between the

49、isotopic species, the greater the potential for isotopic fractionationB) For the same elements with multiple isotopes (≥3), the large the mass difference between isotopes, the larger the isotopic fractionation in the s

50、ame process16O, 17O, 18O32S, 33S, 34S,Different elements,Fractionation: Δ∝ where MH is the mass of heavier isotope; ML is the mass of lighter isotope.For D/H: Δ∝ (2-1)/1=1For 18O/16O: Δ∝ (18-16)/16=1/

51、8For 86Sr, 87Sr, Δ∝ (87-86)/86=1/86,Hydrogen and oxygen isotope fractionation in the water cycle,In natural processes, the isotope fractionation of hydrogen isotopes is approximately 8 times of oxygen isotope fractiona

52、tion. The global meteoric water line (GMWL) (more discussion in next chapter) is δD=8δ18O+10 The coefficient “8” reflect the fact that fractionation of D/H is about 8 times larger than the 18O/16O, which is exa

53、ctly the mass difference ratio,Same elements: theory of mass dependent fractionation,Urey. 1947: the thermodynamic properties of isotopic substances. J.Chem.Soc. (London), 562-581Original theory for calculating “equili

54、brium isotopic fractionation for the mass dependency of isotopic fractionation. The theory is very complicated and beyond this classHowever, the conclusion is more important to us, which is 17RA/17RB = (18RA/18RB)

55、α (1) Where A and B are two terrestrial substances, or two phases (e.g., water and vapor phases of water etc.); and αis a function of the mass difference of different isotopes,The αis defined bywhere ML, M

56、M, MH are masses for the base, middle and heavy isotopes of the same elementFor example, the 16O, 17O, 18OThis is only slightly different from real measured value, 0.516 (last class),α value,Measured α is slightly

57、 variable for different compounds (5.0 to 5.3)α is independent of temperatureIf in equation (1), if substance B is VSMOW, we have 17RA/17RVSMOW = (18RA/18RVSMOW)α (2)Take natural log, “l(fā)n” on both sides o

58、f the equation, we get ln(17RA/17RSMOW) = αln(18RA/18RSMOW) (3),Since in terrestrial and lunar samples, RS/RVSMOW is fairly close to 1 for oxygen isotopes, and we know, lnx=(x-1)-(x-1)2/2+(x-1)3/3… When

59、 x is close to 1, only the first term on the right will be significant, therefore,lnx≈(x-1)apply this to (3), we have 17RA/17RSMOW -1≈α (18RA/18RSMOW-1), or δ17Os≈ α?δ18Os = 0.517δ18Os,Line of mass dependen

60、t fractionation,Earth, Moon and ordinary chondrites lie on a single chemical fractionation trend, it can be concluded that they were derived from a reservoir homogenized with respect to O isotopes, and that the small dif

61、ference between them are due to chemical fractionations during condensation and accretion processesKinetic process can also be similarly examined to determined the proportionality between 17O/16O variations and 18O/16O

62、 variations.,Non-mass dependent fractionation,,,Ocean water,,Earth materials,,,,Clayton et al., 1973,Mass independent isotope fractionation effect,Nuclear interaction, depending on the nuclear structure. Common in carbon