GEOL360 Topic 2 : Isotope Geology

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LECTURE NOTES: T2 : ISOTOPE GEOLOGY

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Topic 2 : Isotope Geology

2.1 Introduction Stable isotopes

Radiogenic isotopes*

Tracers: H, C, O, S, N Processes & element cycles

Geochronology Earth history

Isotopes = two or more atoms of the same atomic number but with different atomic masses: same number of protons (Z) but different number of neutrons atomic weight = average mass of atoms for natural isotopic composition * emphasize difference between (non-)radiogenic vs. radioactive, stable vs. unstable… Reference standard for atomic masses is 12C = 12.000 a.m.u. (atomic mass units) e.g. argon Z = 18: e.g. potassium Z = 19:

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Ar 0.34%, 38Ar 0.06%, 40Ar 99.6%, K 93.3%, 40K 0.01%, 41K 6.7%,

atomic wt. = 39.948 atomic wt. = 39.098

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N.B. Ar is “heavier” than K, despite having lighter atomic number 2.2 Geochronology Radioactivity is the spontaneous adjustment of nuclei of unstable atoms to a more stable state, which releases radiation. Radioactive properties are determined only by the nucleus (electron structure is irrelevant). All elements with Z>83 (bismuth) occur in nature only as radioactive isotopes, while elements with Z>92 (uranium) are very unstable, and are not found in nature. Three main forms of radioactive decay, where the parent isotope A decays to the daughter isotope B (see isotope chart h/o) α particles

= He nucleus (2p + 2n)

so

x y

α A   →

x -4 y -2

β particles

= electrons (e-) ordinary β decay: n → p + + e− , so electron capture: p + + e− → n , so

x y x y

β A   →

x y +1 x y -1

β

A  →

B + 42 α

B

B

In addition, all forms of radioactive decay may release γ rays and X-rays (high energy electromagnetic radiation) Radioactive decay is a first-order reaction, so that the number of atoms that decompose per unit time is proportional to the number of atoms present:

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dN = −λN dt


where

N is the number of parent atoms at time t λ is the decay constant, in units of (1/time)

integrate both sides from t=0 to t , and N=N0 to N, so −λt = ln( N ) − ln( N 0 ) , then

N = N 0e− λt and t1 / 2 =

ln(2) λ

where t1/2 is the half-life (the time required for half an initial number of atoms to decay) λ is a constant (unaffected by P, T, X, etc. although electron capture is slightly sensitive to external factors which may alter outer electron distribution) If there is no daughter isotope initially present, then N=P and N0=P+D 1 D so P = ( P + D)e− λt , D = P (e λt − 1) and t = ln(1 + ) P λ in this case we can get the age of a sample simply from measuring D and P, assuming we know the decay constant Most radiogenic systems involve simple parent-daughter decay (Rb-Sr, Sm-Nd, K-Ar, C-N, etc) but a few have extended decay series. e.g. U-Th-Pb system:

238

U -> 206Pb U -> 207Pb 232 Th -> 208Pb 235

14 intermediate isotopes 11 intermediate isotopes 10 intermediate isotopes

2.3 Rb-Sr system 87 37

β Rb   →

87 38

Sr so from equations worked out above,

87

Sr= 87Rb(e λt − 1)

However, there is usually some initial strontium in the material to be analysed: 87

Srmeas = 87Srinitial + 87Rbmeas (e λt − 1)

In addition, it is easier and more accurate to measure ratios of isotopes rather than their absolute abundances, so using a non-radiogenic isotope as the denominator we get: 87 87 87 ( Sr 86 ) meas = ( Sr 86 ) initial + ( Rb 86 ) meas (e λt − 1) Sr Sr Sr

This is the equation of a straight line. To get the age of a sample (t) we need to know λ and (87Sr/86Sr)initial. We can either assume an initial value of (87Sr/86Sr), in which case the calculated age is then called a model age, or measure several samples and fit them with a straight line. The slope of the line will be (eλt-1). If it is a good line it is called an isochron:

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• Can use several different whole-rock samples, in which case the age will only be meaningful if they are a cogenetic suite (i.e. they all crystallized at the same time in the case of igneous rocks, or they all underwent the same P-T-t path in the case of metamorphic rocks) • Can also use different mineral pairs, or whole-rock and mineral separates. λ is known to within 5%, standard value is 1.42 x 10-11 y-1 Analytical uncertainties lead to an age with minimum errors of about ± 2% Note that both Rb and Sr are quite abundant in many major phases of igneous and metamorphic rocks (Rb substitutes for K, Sr substitutes for Ca; see topic 1 for more info) Age interpretation: (i) “true age” – igneous crystallization or prolonged high T metamorphism (or cooling at end of high T metamorphism) (ii) false age – partial resetting from metamorphism similar to closure temperature of Rb-Sr system (ca. 500 to 550 ˚C). This may actually give different mineral and whole-rock isochrons, see below. (iii) false age – interaction with fluids renders data meaningless (both Rb and Sr are quite mobile) The closure temperature of a system is the temperature at which diffusional transfer of the relevant isotopes between the sample of interest and surrounding rocks effectively stops, i.e. the temperature at which the sample becomes “closed” to resetting. It varies with cooling rate, grain size, etc, but a specific system can usually be assumed to have closed within a 50˚C range, e.g. about 500-550˚C for Rb-Sr. An example of partial resetting (interpretation type ii) is given below (Fig. 2.2 in Brownlow):

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Since isotopic exchange between adjacent minerals (mm scale) is easier than exchange between adjacent lumps of rock (m scale or more), a rock heated to about 520˚C may show resetting of mineral isochrons but preserve the original age of crystallization. This sort of data needs to be interpreted carefully… Finally, (87Sr/86Sr)i ratios can be used to investigate Earth history: the crust has higher Rb/Sr than the mantle (recall that Rb is less compatible than Sr) so mantle melts have lower (87Sr/86Sr)i ratios than crustal melts. e.g.

oceanic basalts (87Sr/86Sr)i continental basalts (87Sr/86Sr)i granites (87Sr/86Sr)i

0.702 to 0.707, pure mantle melt wider range, crustal contamination 0.707 to >1.0, crustal melt

Due to the mobility of Rb and Sr in fluids, and the closure temperature which leads to resetting during metamorphism, the Sm-Nd system is more useful. 2.4 Sm-Nd system The principle of this technique is similar to the Rb-Sr technique, so we get similar equations (this time we use non-radiogenic 144Nd as the denominator): α The decay system is 147 λ = 6.54 x 10-12 y-1,  → 143 62 Sm  60 Nd , so 143 Ndmeas =143Ndinitial +147Smmeas (e λt − 1) and the age equation is: 143 ( Nd 144

Nd

143 ) meas = ( Nd 144

Nd

147 ) initial + ( Sm 144

Nd

) meas (e λt − 1)

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Again, either mineral separates from a single rock or a suite of whole-rock samples may be analysed. Sm and Nd are both rare-earth elements (group IIIB of the periodic table), and behave similarly to each other. They are strongly partitioned into accessory phases such as monazite and apatite. In the case of monazite (REE phosphate), they are essential structural consitituents of the mineral. Some Sm and Nd is also found in garnet, olivine and other minerals. Their similar behaviour means there was probably no fractionation during Earth formation by nebular condensation, but some fractionation did occur during crust-mantle differentiation. Although both are incompatible elements, Nd is slightly more incompatible than Sm: [in detail this is because Nd3+ has a larger radius than Sm3+ so it has a lower ionic potential, = charge/radius, so forms weaker ionic bonds: see topic 5] Partial melting ->

melts have higher Sm, higher Nd, lower Sm/Nd ratio solids have lower Sm, lower Nd, higher Sm/Nd ratio

In addition to dating igneous rocks, the Sm-Nd system can be a powerful tool in looking at the evolution of the crust and mantle. Taking representative values of Sm and Nd abundances, 147Sm/144Nd and 143 Nd/144Nd from chondritic meteorites (the Chondritic Uniform Reservoir, or CHUR) to represent the undifferentiated mantle, we can calculate bulk evolution of 143Nd/144Nd vs. time for the crust-mantle system.

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We express the deviation of a sample from the CHUR evolution curve as:

εNd

 143    Nd    144 Nd  sample,t  − 1 × 10 4 , where t is u sually zero (i.e. time of measurement) = 143    Nd   144    Nd CHUR ,t 

Since melting decreases the Sm/Nd ratio of the melt, igneous rocks usually have negative values of εNd. The more differentiated a rock is, and the older it is, the more negative will be its εNd. We can use this to determine the “model age” or “crustal residence age” of a sample, which is the age at which it would have separated from either CHUR or depleted mantle, assuming that its Sm/Nd ratio has remained unchanged since that time. Effectively we backtrack the evolution of the sample in time until its εNd is zero (i.e. it has the same 143Nd/144Nd ratio as CHUR or DM).

 143 Nd   143 Nd   147 Sm  =  144  +  144  (e λt − 1) where t is an arbitrary time in the past  144   Nd today  Nd t  Nd today

and

Nd CHUR

T

 143 1  ( Nd = ln 147 λ ( Sm

144 144

Nd ) sample,today − ( 143 Nd

Nd ) sample,today − ( 147 Sm

144 144

Nd )CHUR ,today

Nd )CHUR ,today

 + 1  

Model ages may be used to constrain the provenance of clastic sediments (the sediments should have the same model age as the source area as long as the Sm/Nd ratio has not been altered during erosion and deposition).

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NB model ages may not correspond to a specific crust formation event: they may result from the mixing of two or more components derived from the mantle at different times – this can be verified using independent evidence, e.g. U-Pb ages 2.5 Stable isotopes There are over 300 naturally occurring isotopes (including both stable and radioactive isotopes) Stable = not radioactive, i.e. does not spontaneously decay Radiogenic = formed by radioactive decay of another isotope. Radiogenic isotopes may be stable (e.g. 87Sr, 143Nd, 208Pb, 207Pb, 206Pb) or unstable (e.g. 214Pb, 210Pb are both intermediates in 238U ⇒ 206Pb). Tin has 10 stable isotopes, while 21 elements have only radioactive isotopes. To be useful to geologists, stable isotopes of the same element must vary in abundance (i.e. ratio) in nature. Fractionation = change in relative abundance. Can occur by physical, chemical or biological processes. Results in small variations in ratios, not total separation. Physical processes e.g. evaporation, diffusion; chemical effects due to difference in mass and hence bonding energies (higher mass ⇒ stronger bonds); biological effects not well understood. Natural variations are found in the isotopic ratios of many elements, particularly the lighter ones. Degree of fractionation depends on relative difference in mass, e.g. 1H/2H much more different than 16O/18O. Fractionation effects are insignificant in the heavy isotopes used in most radiometric dating methods. Equilibrium constant: for any reaction: kA + lB = mC + nD

[C] m [D] n [ A] k [ B] l

the equilibrium constant

K=

e.g. for the reaction

1 3

the equilibrium constant is

[C K= [C

C16O32− + H 2 18O = 13 C18O32− + H 2 16O O32− ]

[H ] [H 1/ 3

18

2− 1 / 3 3

16

O

(C O K= (H

2− 3

18

which can be rewritten as

O]

16 2

O]

18 2

C16O32− )

1/ 3

O H 2 16O)

18

2

N.B. sample analysis measures isotopic ratios. These ratios are reported relative to standards, since differences in ratios can be measured more precisely than absolute ratios.

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( = (

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O 16O)CO 2−

18

The fractionation factor:

α A−B

R = A RB

e.g.,

α CO 2− − H O 3

2

O 16O) H O 3

18

2

1

In general α = K n where n = number of atoms exchanged In this case n=1 (one oxygen atom = 1/3 CO32-) so α=K Equilibrium processes lead to fractionation which can be predicted, or measured to gain information about the process. e.g. formation temperature of CaCO3 precipitated in ocean can be determined by measuring isotopic composition of carbonate. At 273K, α is 1.033 (varies regularly with T): (i) measure 18O/16O of precipitated carbonate (beware biological ppn) (ii) assume 18O/16O of ancient seawater ≈ that of modern oceans (iii) calculate α and compare with experimental data for α as a function of T Note: (a) samples must have formed under eqm conditions with no subsequent alteration: does not work for Paleozoic and older rocks (affected by fluids) (b) O isotopic composition of modern seawater varies geographically by an amount equivalent to 9˚C temperature difference (can still get relative ∆T) (c) use aragonite; calcite is stable form but may be diagenetically recrystallized in which case would have new 18O/16O at this time (d) shells of some organisms do not form in isotopic eqm with seawater (biological effects again) Despite these potential problems, oxygen isotope paleothermometry is used extensively and indicates an overall decrease in ocean temperatures throughout the Tertiary. Disequilibrium processes such as evaporation, diffusion, unidirectional chemical and biological reactions, also lead to fractionation. e.g. water evaporation: H216O molecules have higher average translational velocities than heavier H218O molecules, so they evaporate preferentially. Above oceans, continual evaporation leads to atmospheric depletion in 18O relative to seawater. (If the vapour is saturated then equilibrium fractionation has a smaller effect; α=1.0098 at 0˚C. For example, water condensation is an equilibrium process). For most elements isotopic abundance measurements are made on gaseous species and are reported as a deviation from a standard, using delta notation: R  ∂ ( ‰) =  sample − 1 × 1000 where ‰ is “per mil”, or per thousand  Rstndard 

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Ratios are always presented as heavier element/lighter element ∂ is a value for a single sample relative to a standard. Use ∆ to compare two samples: ∆A-B = ∂A - ∂B ≈ 1000 ln αA-B ≈ αA-B on a ‰ basis and

αA-B = RA/RB = (1000 + ∂A)/(1000 + ∂B)

Standards used in stable isotope analysis: O, H SMOW or V-SMOW: O, C PDB: N:

air

S:

CDT

(Vienna) Standard Mean Ocean Water D/H = 155.76 x 10-6, 18O/16O = 2005.2 x 10-6 Peedee Belemnite C/12C = 1123.75 x 10-5, 18O/16O = 2067.2 x 10-6

13

15

N = 0.36%, 14N = 99.64%; 15N/14N = 0.003676

Cañon Diablo Troilite S/32S = .044994, or 32S/34S ≈ 22.22

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Note that, for example ∂18OSMOW = 0.0 ‰ by definition 2.6 Oxygen and hydrogen isotopes D/H and 18O/16O are linearly related in present day meteoric waters Meteoric Water Line (MWL):

∂D = 8 ∂18O + 10

∂D and ∂18O may vary due to (a) evaporation of seawater (S to A), (b) condensation in clouds (A to P). Both concentrate lighter isotopes in the vapour phase and heavier isotopes in the liquid phase (ocean or rainwater). Fig. 2-15:

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• Atmospheric vapour has more –ve ∂ than atmospheric precipitation • ∂ values of vapour and precipitation are more –ve at higher latitudes (moisture in air at poles came from evaporation of water nearer equator) • ∂ values of vapour and precipitation are more –ve further inland (o/h fig. 2-16) At a specific location, mean isotopic compositions also determined by temperature, altitude, intensity of precipitation, local climate and topography. Present-day ∂ are known for ocean and meteoric waters, and it may be assumed locally that groundwater values ≈ those for meteoric water, unless evaporation is significant. ∂ for other waters is assumed (ancient ≈ modern) or estimated Applications: • Isotopic fractionation between minerals: can be used to estimate temperature of formation or equilibration: ln αmin1-min2 = A + B/T2 where A and B are constants. There is a similar relation for the fractionation factor between minerals and water, and αmin1-min2 is usually found from combining αmin1-water and αmin2-water. Quartz-minerals pairs record equilibration temperatures for metamorphic rocks (beware low-T alteration or re-equilibration). • The source(s) of ore-forming fluids may be constrained either by measuring ∂D and ∂18O in fluid inclusions, or by measuring ∂D and ∂18O of ore minerals, and combining these with αmin-water (known) and the temperature of ore formation (assumed). e.g. most ore bodies show later fluids nearer to MWL, suggesting a mix of magmatic and meteoric waters (o/h fig. 2-20) • Interactions between seawater and oceanic crust secondary hydrated minerals in shallow oceanic crust have higher ∂18O than primary igneous minerals, indicating submarine weathering with high water/rock ratio (o/h fig. 2-23a) greenschist facies minerals at greater depths have lower ∂18O than unaltered basalt, indicating hydrothermal metamorphism • Surface-water / groundwater interactions: e.g. measure ∂D of streams during storm event shows that groundwater contribution to stream flow may be more important than surface run-off (o/h fig. 2-18a: in this case groundwater has different ∂D to meteoric water). e.g. measure ∂18O to determine river water contribution to groundwater in the vicinity of a river (o/h fig. 2-18b: in this case river water from Alps has lower ∂18O than local groundwater). Model using mixing equations:

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2.7 Equations for isotopic mixtures of a single element (Faure ch. 18.5, p. 335) (i) Consider a mixture of two components for a single element. Binary mixture of A and B, then the mixing parameter fA is defined as: fA = WA / (WA + WB) where WA and WB are the weights or volumes of components A and B in the mixture. Concentration of element X in a mixture (M) of components A and B is [X]M = fA ([X]A - [X]B) + [X]B where [X] denotes concentration of X. This is a straight line on a graph of [X] and fA. (ii) Now consider a mixture of two components for two elements. If we have data for two elements, X and Y, then we can get the equation: [Y ]M = [ X ]M

[Y ]A − [Y ]B [ X ]A [Y ]B − [ X ]B [Y ]A + [ X ]A − [ X ]B [ X ]A − [ X ]B

which is the equation of a straight line on a graph of [Y]M vs. [X]M. (iii) Now consider two endmembers A and B, each with different Sr concentrations and 87Sr/86Sr ratios. The Sr concentration of mixture M is: [Sr]M = [Sr]AfA + [Sr]B(1 – fA) and the equation for the 87Sr/86Sr ratio of a binary mixture is:  87 Sr   87 Sr  [Sr] A  87Sr  [Sr] B +  86  (1 − f A )  86  =  86  f A [Sr] M  Sr  M  Sr  A [ Sr] M  Sr  B if the concentrations of Sr are the same in A and B, this simplifies to:  87 Sr   87 Sr   87 Sr   86  =  86  f A +  86  (1 − f A )  Sr  M  Sr  A  Sr  B For mixtures of water containing different O and H isotopic ratios, ∂ values may be used in place of actual ratios, for example: and

∂18OM = ∂18OAfA + ∂18OB(1 - fA) ∂DM = ∂DAfA + ∂DB(1 - fA)

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2.8 Carbon isotopes C is 98.9% 12C, 1.1% 13C, negligible 14C. In nature, ∂13C ranges from +6 to –38 ‰:

-40

-30

δ13C (‰) -20 -10

0

-10

atmospheric CO2 marine bicarbonate marine limestone fresh water limestone reduced carbon (all rock types) carbonatites & diamonds petroleum meteorites higher plants eukaryotic algae cyanobacteria photosynthetic bacteria methanogenic bacteria

-40

-30

-20 -10 δ13C (‰)

0

-10

In general, organic carbon is typically about 25 ‰ lighter (more negative) than inorganic carbon, due to fractionation during photosynthesis (difference between present-day organic and inorganic carbonates). • This difference can be traced back to at least 3.5 Ga, indicating that carbon fixation by autotrophic life forms began at least this long ago. (Autotrophs are organisms that are capable of living exclusively on inorganic materials, water, and an energy source such as sunlight or chemically reduced matter, e.g. plants and some bacteria).

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• Marked variations in ∂13C in organic sedimentary material began at about 2.8 Ga, but these variations are not found in carbonates. Therefore this may represent the beginning of photosynthetic O2 production (recall that most BIFs were deposited between about 2.8 and 2.1 Ga) • Carbon isotopes are also used extensively in investigating modern oceanic chemistry, and in atmospheric chemistry (including sampling methane emitted by grazing cows to investigate their contribution to global warming). Examples of ∂13C measurements applied to ocean chemistry: (a) Gradient from less -ve ∂13C at surface of lakes and oceans to more strongly –ve at depth, due to oxidation of organic carbon to dissolved CO2 (this gradient is stronger in the summer) (b) General correlation between amount of dissolved O2 and ∂13C: more oxidation of organic carbon ⇒ less O2 and lighter carbon (more -ve ∂13C) (c) Most marine limestones and calcareous organisms reflect ∂13C of total dissolved inorganic C in water mass, ∴pelagic limestones give information about surface water, and benthic organisms record ∂13C of deep water. Beware local and regional variations in water ∂13C. (d) ∂13C in primary producers varies with taxon and size, and in general ∂13C becomes less -ve as you move up the food chain (e.g. diatoms have ∂13C ≈ -20.3‰, benthic predators have ∂13C ≈ -16.6 ‰) • Case study: Watanabe et al., 2000. Geochemical evidence for terrestrial ecosystems 2.6 billion years ago. Nature, v. 408, p. 574-578. Micro-organisms known in oceans since at least 3.8 Ga. Oldest undisputed terrestrial fossils are 1.2 Ga microfossils from Arizona. This paper looks at organic matter in a paleosol (carbonaceous ancient soil) from eastern South Africa. Paleosol is ~ 17m thick, developed on a serpentinized dunite (rock made mostly of olivine) between 2.6 and 2.7 Ga. Typical reduced carbon content of Precambrian paleosols is less than 0.1 wt.%; samples from this paleosol contain upo to 0.36 wt.%. Three possible interpretations: (i) graphite formed inorganically during serpentinization (>2.7 Ga) and concentrated by soil formation; but too much hydrogen (H/C