Lecture 14: Stable Isotopes and Climate

• Questions– How do different isotopes of the same element get

fractionated from one another?– What can we learn about geology from measurements of

stable isotope ratios in rocks?– What can we learn about the history of climate from such

measurements in ice, water, fossils, and sediments?• Tools

– Thermodynamics and kinetics• Reading:

– Albarède, Chapter 2 (again)

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The stable isotopist’s periodic table• We are interested here in elements that have more than one non-

radiogenic isotope, for which the mass difference between isotopes is a significant fraction of the atomic mass, and which have enough interesting chemistry to fractionate the isotopes

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H

Li

Na

K

Rb

Cs

Fr

Be

Mg

Ca

Sr

Ba

Ra

Sc

Y

Ti

Zr

Hf

Rf

V

Nb

Ta

Db

Cr

Mo

W

Sg

Mn

Tc

Re

Bh

Fe

Ru

Os

Hs

Co

Rh

Ir

Mt

Ni

Pd

Pt

Cu

Ag

Au

Zn

Cd

Hg

Ga

In

Tl

Ge

Sn

Pb

As

Sb

Bi

Se

Te

Po

Br

I

At

Kr

Xe

Rn

B

Al

C

Si

N

P

O

S

F

Cl

Ne

Ar

He

La

Ac

Ce

Th

Pr

Pa

Nd

U

Pm

Np

Sm

Pu

Eu

Am

Gd

Cm

Tb

Bk

Dy

Cf

Ho

Es

Er

Fm

Tm

Md

Yb

No

Lu

Lr

1

2

3

4

5

6

7

IA IIA IIIA IVA VA VIA VIIA VIIIA

IIIB IVB VB VIB VIIB VIIIB IB IIB

Lanthanides

Actinides

1

3

11

19

37

55

87

4

12

20

38

56

88

21

39

22

40

72

104

23

41

73

105

24

42

74

106

25

43

75

107

26

44

76

108

27

45

77

109

28

46

78

29

47

79

30

48

80

5

13

31

49

81

6

14

32

50

82

7

15

33

51

83

8

16

34

52

84

9

17

35

53

85

10

18

36

54

86

2

57

89

58

90

59

91

60

92

61

93

62

94

63

95

64

96

65

97

66

98

67

99

68

100

69

101

70

102

71

103

Standard Repertoire

Limited or recent use only

The stable isotopist’s periodic table• Traditional stable isotope chemistry focuses entirely on the light

elements (H, Li, B, C, N, O)• More recently analytical tools have become precise enough to

enable work on the small anomalies in heavier metals

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Element # isotopes Δm/m Abundances (%)

H 2 1 99.985, 0.015Li 2 1/6 7.5, 92.5B 2 1/10 19.9, 80.1C 2 1/12 98.89,1.11N 2 1/14 99.634,0.366O 3 2/16 99.762,0.038,0.2Mg 3 2/24 78.99,10.0,11.01Si 3 2/28 92.23,4.67,3.10S 4 4/32 95.02,0.75,4.21,0.02Cl 2 2/35 75.77,24.23Fe 4 4/54 5.85,91.75,2.12,0.28

Delta notation• Stable isotope ratios are almost always expressed in -notation:

δ = ( )x1000Rsample-Rstandard

RStandard

e.g.,

The x1000 implies that the units on δ are parts per thousand, permil, or ‰

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Theory of Isotope Fractionation• Fractionation refers to the partial separation of two isotopes of the same

element, producing reservoirs with different ratios of the isotopes. These differences are called isotopic anomalies.

• Two classes of basic mechanisms and two strange ones exist for fractionating isotopes:– The two basic mechanisms are:

• equilibrium isotope fractionation, which is due to differences in bond energies of isotopes in compounds

• kinetic isotope fractionation, which is due to differences in average velocity or reaction rates of different isotopes

• Both depend only on the mass of the isotope and are called mass dependent fractionation; both will fractionate, say 18O/16O about twice as much as 17O/16O

– The strange mechanisms are mass-independent fractionation; one depends on quantum mechanical symmetry terms that occur for molecules like O3 and SO2 and reflects only the identity (not mass) of atoms, so fractionates 17O and 18O equally. The other depends on isotope-specific wavelengths of photo-dissociation reactions and is thought perhaps to have been relevant in the solar nebula.

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Equilibrium Isotope Fractionation

• Equilibrium isotope fractionation controls the distribution of isotopes in the case (obviously) that a system approaches thermodynamic equilibrium.– Tends to be most relevant for high temperature problems

• Igneous and (to a certain extent) metamorphic rocks• Some meteoritic processes• Hydrothermal interactions

– Tends to be less important in processes involving gas phases, biological reactions, or transport

• Largest fractionations occur between states of a particular element with very different chemical bonding environments– Different oxidation states: N0 vs. N-3 vs. N+5...

– Different bonding partners: H2 vs. H2O vs. CH4...

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ClCl HH

• • Isotopes distribute themselves among compounds in a way that minimizes the Isotopes distribute themselves among compounds in a way that minimizes the energy of the system. The sensitivity to mass comes in through the vibrational energy of the system. The sensitivity to mass comes in through the vibrational modes of interatomic bondsmodes of interatomic bonds

• • Vibrations are quantized, E(vib) = hVibrations are quantized, E(vib) = h(n+1/2) n=0,1,2,3(n+1/2) n=0,1,2,3• • 1/2•h1/2•h is called the Zero-Point Energy (ZPE) is called the Zero-Point Energy (ZPE)• • Vibrational frequency Vibrational frequency depends on “spring constant” and reduced mass: depends on “spring constant” and reduced mass:

Theory of equilibrium isotopic fractionationTheory of equilibrium isotopic fractionation

Bond length

Energy

n=1, E(vib)=3/2•h=0, ( )=1/2•n E vib h

Bond length

Energy

isotopically lightmolecule

isotopically heavymolecule

ν =1

2πkμ

,μ =m1m2m1+m2

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Theory of equilibrium isotopic fractionation: example11HHCl Cl = 8.97•10 = 8.97•101313 Hz Hz 22HHCl Cl = 6.43•10 = 6.43•101313 Hz Hz

E(vib) = 1/2•hE(vib) = 1/2•h ≈ ≈ 17,900 J/mol17,900 J/mol

E(vib) = 1/2•hE(vib) = 1/2•h ≈ ≈ 12,800 J/mol12,800 J/mol

11HHF F = 12.41•10 = 12.41•101313 Hz Hz 22HHF F = 8.99•10 = 8.99•101313 Hz Hz

E(vib) = 1/2•hE(vib) = 1/2•h ≈ ≈ 24,800 J/mol24,800 J/mol

E(vib) = 1/2•hE(vib) = 1/2•h ≈ ≈ 17,900 J/mol17,900 J/mol

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Theory of equilibrium isotopic fractionation, example

22HCl + HCl + 11HF HF 11HCl + HCl + 22HFHF

At Equilibrium, for H-isotope exchange between HF and HCl:At Equilibrium, for H-isotope exchange between HF and HCl:

GG00 ≈ ≈ E(vib) = E(vib)E(vib) = E(vib)productsproducts – E(vib) – E(vib)reactantsreactants

E(vib) E(vib) productsproducts = 17,900 J/mol ( = 17,900 J/mol (11HCl) + 17,900 J/mol (HCl) + 17,900 J/mol (22HF) HF) E(vib) E(vib) reactantsreactants = 12,800 J/mol ( = 12,800 J/mol (22HCl) + 24,800 J/mol (HCl) + 24,800 J/mol (11HF)HF)

E(vib) = –1,800 J/mol, driving the reaction to the right and E(vib) = –1,800 J/mol, driving the reaction to the right and concentrating concentrating 22H in HF (by a factor of 2 at 25 ºC)!H in HF (by a factor of 2 at 25 ºC)!

• • Need to consider all energy levels, not just ground state Need to consider all energy levels, not just ground state (Boltzmann statistics), as well as entropy terms, both of which (Boltzmann statistics), as well as entropy terms, both of which give give smaller fractionations at high temperaturesmaller fractionations at high temperature

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Temperature dependence of equilibrium isotope effects

αA−B =RARB

10

€

ΔA−B ≡ δA −δB ≈1000lnα A−B

Theory of kinetic isotope effects

• Kinetic isotope effects occur in fast, incomplete, or unidirectional processes like evaporation, diffusion, and biological reactions

• Consider an ideal gas. Every molecule has, on average, the same kinetic energy E = 1/2 mv2

• The average velocities of two molecules with different masses due to isotopic substitution therefore follow the relationship

• Hence the light isotopic species will diffuse faster in the gas phase.– e.g., this is one way to enrich 235U relative to 238U, but in the

form of the gas molecule UF6, the diffusivity ratio implies only (352/349)1/2 = 4‰ separation per cycle

v1v2

=m2m1

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Theory of kinetic isotope effectsKinetic fractionation effects can be much larger than equilibrium fractionations. This is the result of two factors:• Equilibrium fractionation factors depend on the imbalance between forward rate constants and reverse rate constants for different isotopes; kinetic factors depend only on the forward rates. Both rates are likely to be faster for light isotopes, so reverse reaction diminishes the fractionation.• The open-system effect, whereby both the distillate and the residue can become very fractionated.

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Theory of kinetic isotope effects

We can see kinetic isotope effects resulting from hydrothermal alteration of igneous rocks initially in equilibrium and in metamorphic rocks as a result of partial devolatilization

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More on hydrothermal alteration• Hydrothermal alteration of rocks is pervasive

– Any place that igneous rocks are emplaced and cooled to the point where fracture is possible, water is likely to get in

– Resulting patterns depend on composition of water (seawater vs. meteoric, plus latitude dependence), temperature, and water-rock ratio

– “Fresh” igneous rocks mostly acquire odd isotope signatures by assimilating altered ones

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Stable isotope thermometry I• Equilibrium fractionation factors are temperature dependent. Therefore measurements of isotope fractionation between coexisting phases presumed to have equilibrated with one another define the temperature at which they equilibrated.• Several common mineral pairs have been calibrated by laboratory exchange experiments.• The general problem is that equilibrium is most readily achieved at high temperature but the isotope thermometers are most sensitive at low temperature!

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Stable isotope thermometry II• In general minerals exchange more readily with a free water phase than with each other:

– so it is easiest to calibrate fractionation factors relative to water and

– most reasonable to assume equilibrium between mineral and water in natural settings

T(°C) =16.9−4.2ΔCaCO3−H2O+0.13ΔCaCO3−H2O2

A reversal experiment

Epstein et al (1953) produced the first useful such calibration for biogenic calcite and water and thereby founded the field of isotope paleothermometry:

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Stable Isotope thermometry III

Sediment-core records of the isotopic composition of biogenic calcite are available at various resolutions and record lengths covering the last 70 Ma. Though there are vital effects that modify the CaCO3-H2O fractionation, these are small.

Problem: we have only the calcite, not the H2O from which it precipitated. So how much of the δ18O variation is due directly to temperature (which controls fractionation between calcite and H2O) and how much due to the change in δ18O of seawater?

Why does seawater δ18O change? Because of the growth and decay of ice sheets…

But why is ice so light in 18O?

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Stable isotopes and the Hydrologic Cycle• The ice-seawater difference reflects general aspects of the

fractionation of oxygen (and hydrogen) isotopes by the hydrologic cycle– These are mostly kinetic factors, since evaporation and

precipitation of water vapor, rain, and snow are nearly Rayleigh processes

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Stable isotopes and the Hydrologic Cycle

• The more rain you pull out of a cloud, the lighter the isotopes in the cloud become and the lighter the next increment of rain gets– Since low temperature lowers solubility,

air that reaches cold places has become very dry and very light

– Since water vapor originates in the ocean, by the time clouds get far inland they become very light

– So there is a continental effect superimposed on a latitudinal gradient

– Tests to distinguish interaction with seawater from meteoric water are much more sensitive some places than others!

19 18O map

Stable isotopes and the Hydrologic Cycle• Since hydrologic processes involve only mass fractionation, the hydrogen isotopes and oxygen isotopes co-vary quite closely, defining the meteoric water line D = 8 * 18O + 10

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D map

Isotope Paleoclimatology• First indication that climate variations in the Pleistocene are

cyclic and that there have been more ice ages than can be seen in geological evidence came from deep sea sediment cores measured by Emiliani (1966), but he had no timescale:

Calibration showed that the major glacial-interglacial cycle has a period of 100,000 years, modulated by ~20 ka and ~40 ka oscillations

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Isotope Paleoclimatology• The marine isotope record can be deconvolved into temperature

(i.e., calcite-H2O) and ice volume (i.e. 18Owater) signals if we know the variation of sea level, which directly measures how much water is tied up ice sheets on land

Some data on this from 14C or U-Th dating of coral terraces

Answer: about 1 ‰ from each effect

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Isotope Paleoclimatology• Why are ice ages quasi-periodic?

Because they are driven by periodic variations in solar forcing resulting from quirks of the Earth orbit, called Milankovitch cycles

• These mostly affect the seasonality of sunlight, not the total amount received

Precession

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Isotope Paleoclimatology

• The so-called Milankovitch hypothesis (Hays, Imbrie, & Shackleton) argues that ice ages are driven by summer insolation at 65°N.

• Why? Because ice sheets can only grow if snow that falls during winter lasts through the summer without melting and the big high-latitude continental areas are in the northern hemisphere.

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Isotope Paleoclimatology

• The Milankovitch curve fits the phases and relative power in the 20, 40, and 100 ka cycles well but it has at least three shortcomings:– The forcing functions are

sinusoidal but the response is sawtoothed (fast warmings), which requires a nonlinear coupling mechanism

– The amplitude of the climate swings is much bigger than one expects from fairly small changes in forcing (another nonlinear clue)

– And, ice-core data indicate very high amplitude variability at much higher frequencies

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Isotope Paleoclimatology• Ice core records from Greenland provide annual time resolution(!)

but only constrain climate at high latitude and only go back one ice-age cycle (4 in Antarctica but no annual bands there)

• Why is the time resolution so much better? Because sediment cores suffer from bioturbation, slow sedimentation, and poor time control

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Isotope Paleoclimatology• Ice core records record

extraordinary stability of the Holocene and very high-amplitude rapid fluctuations during the late Pleistocene

• Are these fluctuations just analytical noise? No, they match up in both Greenland summit cores (GRIP and GISP)

• Are they just a local Greenland effect? No, they correlate with worldwide indicators

• These are called Heinrich events and their cause is poorly understood

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Mass-independent Effects• Looking at three isotopes of the same element, all mass-dependent

fractionation (whether equilibrium or kinetic) should displace samples along the same line (e.g., slope 1/2 in δ17O-δ18O space)

• Clayton and Mayeda (1974) demonstrated that different classes of meteorites define different such lines, but that all objects from a given parent body (e.g., earth-moon system) share a common line

• But chondrites show a BIG depletion in 16O along a line with slope one, originally interpreted as a nucleosynthetic effect, i.e. imperfect mixing into solar system of some pure 16O material from a separate stellar source

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Mass-independent Effects• But Thiemens and coworkers discovered in the 1980’s that certain reactions

involving ozone (O3) can fractionate isotopes independent of mass due to a quantum mechanical symmetry effect (there are more distinct states for 18O16O16O or 17O16O16O than for 16O16O16O; explained in detail by Gao and Marcus (2001) in a prize-winning Caltech thesis)

• No real mechanism has been proposed, but the possibility of mass-independent chemical effects casts doubt on the need for nucleosynthetic explanation of the three O-isotope heterogeneity of the solar system/

O2+O=O3

O3

O

O2

• The symmetry mechanism also works for SO2 and has been invoked to explain anomalies in Δ33S ~ δ33S–δ34S in Archaean rocks, when presumably atmosphere was more reducing and H2SO4 less dominant

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