Stable Isotopes – Physical Fundamentals 9/27/12

Lecture outline:1) principles of stable isotope fractionation

2) equilibrium fractionation

3) kinetic fractionation

4) mass-independent fractionation

spectrometer lightintake

Annual layers in a tropical ice cap

Introduction to Stable Isotope Geochemistry

Stable Isotope geochemistry is concerned with variations of the isotopic compositionsof elements arising from physicochemical processes (vs. nuclear processes).

Characteristics of a useful stable isotope system:1. large relative mass difference between stable isotopes (Δm/m)2. abundance of “rare” isotope is high (0.1-1%)3. element forms variety of compounds in natural system

Examples: 2H/1H, 7Li/6Li, 11B/10B, 13C/12C, 15N/14N, 18O/16O, 26Mg/24Mg,30Si/28Si, 34S/32S, 37Cl/36Cl, 40Ar/36Ar, 44Ca/40Ca, 56Fe/54Fe

- note convention of putting the heavy isotope above the light isotope

fractionation refers to the change in an isotope ratio that arises as a result of achemical or physical process.Occurs during:

- isotopic exchange reactions in which the isotope are redistributed among different molecules containing that element- unidirectional or incomplete reactions - physical processes like evaporation/condensation, melting/crystallization, adsorption/desorption, diffusion

Notation

18 16 18 16

18

18 16

/ /*1000

/spl std

std

O O O OO

O O

We can define a fractionation factor (α):

AA B

B

R

Rα Where RA, RB are the isotope ratios in two phases

(ex. carbonate and water, or water vapor and water, etc)

NOTE: α is close to 1 because ratios differ by parts per thousand α approaches 1 as temperature increases

We define a measurement reporting convention ( or “delta” units):

So each isotopic measurement is reported relative to a standard

Note that ‘deltas’ are named after the heavy isotope

Fractionation typesThere are three types of isotope fractionation:1. equilibrium fractionation2. kinetic fractionation3. mass-independent fractionation (far less important)

Equilibrium fractionation- arises from the translational, rotational, and vibrational motions of

1. molecules in gases and liquids2. atoms in crystal lattices

- energy of these motions is mass-dependent- systems will move to the lowest energy configuration- usually largest in covalent bonds, minimal in ionic bonds

Ex:

From William White’s (Cornell)upcoming Geochemistrytextbook

most imp.

at 25°C, so 18O/16O is larger in CO2

than in H2O at equilibrium

2

2 2

2

1.0233COCO H O

H O

R

Rα

Equilibrium fractionation (cont)So why does equilibrium fractionation occur?

- a molecule with a heavy isotope sitsat a lower zero point energy level than the same molecule with all light isotopes

- bonds with high potential energiesare broken more readily

- bond strengths vary for light and heavyisotopes of an element

What about temperature?- the difference in zero point energies

for light vs. heavy molecules decreaseswith increasing T

- bond strengths converge at high T,fractionation factor goes to 1 at high T

Which bond is brokenmost easily?

zero point energy

Effect of vibrational E in harmonic oscilllator model

Temperature-dependence of equilibrium fractionation

harmonic

oscillla

tor model

harmonic oscilllator m

odel

data

data

From these plots we can see that:1. α varies inversely with T2. the harmonic oscillator model

approximation holds up well:

11T

α for T<200C

for T>200C2

11T

α

So at colder temperatures,isotopes will be more heavilyfractionated.

Composition-dependence of equilibrium fractionation

IMPORTANT rule of thumb: the heavy isotope will be concentrated in the phase in whichit is most strongly bound (or lowest energy state). Solid>liquid>water, covalent>ionic, etc.

Ex: 18O in carbonates- heavily enriched in carbonate because O tightly bonded to small, highly charged C4+, vs. weaker H+

- so Δ18Ocal-water = 18Ocarb-18Owater = 30‰Ex: quartz (SiO2) most enriched mineral

Lattice configuration (aragonite vs. calcite) plays a secondary role (Δ18Oarag-cal=0.5‰)

Chemical substitutions in the lattice (ie. Ba instead of Ca) also have a small effect:Δ18OBa-cal-water = 25‰ (vs. 30‰ for Ca-cal)

Kinetic fractionation- arises from fast, unidirectional, incomplete reactions (many biologically-mediated rxns)

21

2kE mv

Consider two molecules of CO2: 12C16O2 (mass = 12 + 2*16 = 44)and 13C16O2

(mass = 13 + 2*16 = 45)

if their energies are the same, then:

and the ratio of their velocities is:

2 21 1

2 2A A B Bm v m v

1/ 2 1/ 245

1.01144

A B

B A

v m

v m

SO… 12C16O2 can diffuse 1.1% further than 13C16O2 in a given amount of time

In reality, gas are not ideal, velocity difference is reduced by collisions, reduced fractionation

assumingideal gas

This can be observed as gas moves through a fine capillary tube (12C16O2 arrives first).

1. Velocities of gas molecules are different- kinetic energies of molecules of ideal gas are equal- so differences in mass (heavy vs. light isotopes) must be compensated for by velocity

2. Lighter isotope will be preferentially reacted (back to vibrational E plot) - easier to break C-H bonds than C-D bonds- when reactions do not go to equilibrium, lighter isotope will be enriched in products

- usually very large kinetic fractionations in biologically-mediated rxns(ex: photosynthesis (low 13C) and bacterial reduction (low 34S))

Kinetic fractionation (cont)

NOTE: The tell-tale sign of kinetic fractionation is fractionation that is directly proportional to the mass difference (Δm).You can identify a kinetic process by comparing values for different isotope systems ie. 18O/16O vs. 13C/12C (2/1)18O/16O vs. 17O/16O (2/1)

Thiemens and Heidenreich, 1983; Theimens, 1999 (review)

mass-independent

Mass-independent fractionation

Observed in meteorites and in atmospheric photo-chemical reactions,mechanism unknown.