A brief summary of isotopes and fractionation 1. Isotopes are - - PDF document

A brief summary of isotopes and fractionation

• 1. Isotopes are chemically identical, but mechanically different.
• 2. Different masses lead to different bond frequencies...

ν = 1 2π κ µ Hooke's Law

• 3. ...which lead to different zero-point energies...
• 4. Which causes them to react at different rates.

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Isotope Effects verus Fractionation

∆

12C 12C 13C 13C

R P + Q

An Isotope Effect causes Fractionation

For equilibrium rxns:

• HDO + H2 H2O + HD

For nonequilibrium rxns: 2H2O

• 2H2 + O2

E.I.E. = Keq =[HDO][H2] [H2O][HD] α = RH2 / RH2O = 0.30 (i.e., -700‰!) α = RH2 / RH2O = 0.37 (but not consistently applied!) 2HDO

• 2HD + O2

K.I.E. = KH/KD = 2.7 = 0.30

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+e-

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: Good: delta values can usually be added linearly, making mass balance equations straightforward (including blank correction) Bad: delta values are only linear over a small range of absolute abundance so be careful with hydrogen and isotopic labels

Rsamp - Rstd Rstd Rstd 103 δ = ∆R δ =

• r

in ‰ units ‰ implies factor of 103

ntδt = n1δ1 + n2δ2 + ...

0.0 0.5 1.0 400,000

• 1,000

800,000 1,200,000

δ13C (‰) 13C fractional abundance 13C fractional abundance

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0.008 0.010 0.012 0.014

• 200
• 100

100 200 S MOW

Measures of Fractionation

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symbol: defn. used for: 0.8

• 200.0
• 223.1
• 250.0

0.900

• 100.0
• 105.4
• 111.1

0.980

• 20.0
• 20.2
• 20.4

0.990

• 10.0
• 10.1
• 10.1

1.000 0.0 0.0 0.0 1.010 10.0 10.0 9.9 1.020 20.0 19.8 19.6 1.100 100.0 95.3 90.9 1.200 200.0 182.3 166.7 α all ε (α-1)103 kinetic ∆ 1000ln(α) equil. ∆ δA-δB equil. δA+1000 δB+1000

for constant α=1.100

remember delta scale is not linear!

• 200

200 8 9 10 11 12

δ

A - δ B

δ

A

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.

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Figure 2. Cyclostratigraphy and magnetostratigraphy of Ain el Beida with planktonic and benthic 18O and sedimentation rate. Tuning of the sedimentary cyclicity to the 65 N summer insolation and precession curves of the La93(1,1) astronomical solution [Laskar et al., 1993]. Magnetostratigraphy is based on Krijgsman et al. [2004]. Time-equivalent lithologic units in the Mediterranean are shown at the right-hand side of the figure [after Krijgsman et al., 2001]. The initiation of the MSC at 5.96 Ma is indicated by an arrow.

PA1001 VAN DER LAAN ET AL.: LATE MIOCENE STABLE ISOTOPE RECORDS PA1001

Kinetic Fractionations

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.

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reaction coordinate energy CH2D2 CHD2Cl CH2DCl H2DC -- D D2HC -- H α

Open System Fractionation

With only one product, isotopic composition of product is constant.

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"Open" means that reactant is available in unlimited supply. 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).

Q Q P P A

0.5 1.0

yield of P Isotope ratio Reaction Chamber R P R

εP/R δP = δR + εP/R A = αP/R / αQ/R = εP/R − εQ/R

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) Thus we can interpret fo, an important operating condition of the global carbon cycle (and biosphere) from measurements of only 3 quantities. biosphere δa δo δi CO2 inputs carbonate carbon

• rganic carbon

εTOC δi = foδo + (1- fo)δa εTOC = δa − δo δi = fo(δa− εTOC) + δa − foδa = δa − foεTOC fo = δa − δi εTOC

Hayes, Strauss, & Kaufman (1999) Chemical Geology, 161:103-125.

Closed System Fractionation

If the reactant is in limited supply, its composition will change as it is consumed by the reaction.

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Fractionation can be due either to kinetic or equilibrium isotope effects (if P is continually removed). The latter case is often called "Rayleigh Distillation".

B R P A P'

0.5 1.0

yield of P (=f) Isotope ratio R P Fractionation Isotope Effect

Fractionation between pooled product and unconsumed reactant is variable A = f (yield, isotope effect) Fractionation between instantaneously forming product and unconsumed reactant is constant B = f (isotope effect)

ε = (δrf - δro) / ln(1-f)

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Fractionation in Precipitation

δD = 0‰ δD = -76‰ δD = -128‰ δD = -198‰ δD = -53‰ δD = -122‰ Ocean αeq= 0.924 (25°C) αeq= 0.900 (5°C) f = 0.5 f = 0.8 all equilibria at 25°C δD = 0‰ δD = -76‰ δD = -145‰ δD = -237‰ δD = -45‰ δD = -137‰ Ocean αeq= 0.924 (25°C) f = 0.5 f = 0.8 clouds at 5°C Precipitation becomes D-enriched as more rain condenses (farther from the ocean) The effect is exaggerated at colder temperatures because the liquid/vapor fractionation is larger