Stable Isotopes – Physical Fundamentals

Lecture outline: 1) principles of stable isotope fractionation 2) equilibrium fractionation 3) kinetic fractionation 4) mass-independent fractionation

9/27/12

spectrometer light intake

Annual layers in a tropical ice cap

Introduction to Stable Isotope Geochemistry

Stable Isotope geochemistry

is concerned with variations of the isotopic compositions of elements arising from physicochemical processes (vs. nuclear processes).

fractionation

refers to the change in an isotope ratio that arises as a result of a chemical 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 Characteristics of a useful stable isotope system: 1.

large relative mass difference between stable isotopes (  m/m) 2.

abundance of “ rare ” isotope is high (0.1-1%) 3.

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

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

Notation

We can define a

fractionation factor

(  ):  

R R B A

Where R A , R B are the isotope ratios in two phases (ex. carbonate and water, or water vapor and water, etc) NOTE:   is close to 1 because ratios differ by parts per thousand approaches 1 as temperature increases We define a measurement reporting convention (  or “ delta ” units):  18

O

    18

O

/

16

O

 

spl

  18

O

/

16

O

18

O



std

/

16

O



std

 

*1000

Note that ‘ deltas ’ are named after the heavy isotope So each isotopic measurement is reported relative to a

standard

Fractionation types

There are three types of isotope fractionation: 1.

equilibrium fractionation 2.

3.

kinetic fractionation mass-independent fractionation (far less important)

Equilibrium fractionation -

arises from the translational, rotational, and

vibrational

1. molecules in gases and liquids 2. 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: motions of

most imp.



CO

2 

H O



R R CO

2 

1.0233

at 25 ° C, so 18 O/ 16 O is larger in CO 2 than in H 2 O at equilibrium

From William White

’

s (Cornell) upcoming Geochemistry textbook

Equilibrium fractionation (cont)

Effect of vibrational E in harmonic oscilllator model So why does equilibrium fractionation occur?

a molecule with a heavy isotope sits at a lower zero point energy level than the same molecule with all light isotopes bonds with high potential energies are broken more readily bond strengths vary for light and heavy isotopes of an element Which bond is broken most easily?

zero point energy

What about temperature?

the difference in zero point energies for light vs. heavy molecules decreases with increasing T bond strengths converge at high T, fractionation factor goes to 1 at high T

Temperature-dependence of equilibrium fractionation

From these plots we can see that: 1.

α varies inversely with T 2.

the harmonic oscillator model approximation holds up well: 

1

T

for T<200C 

1

T

2 for T>200C So at colder temperatures, isotopes will be more heavily fractionated.

Composition-dependence of equilibrium fractionation

IMPORTANT rule of thumb

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

Ex: 18 O in carbonates - heavily enriched in carbonate because O tightly bonded to small, highly charged C 4+ , vs. weaker H + - so  18 O cal-water =  18 Ocarb  18 Owater = 30 ‰ Ex: quartz (SiO 2 ) most enriched mineral Lattice configuration (aragonite vs. calcite) plays a secondary role (  18 O arag-cal =0.5‰) Chemical substitutions in the lattice (ie. Ba instead of Ca) also have a small effect:  18 O Ba-cal-water = 25‰ (vs. 30‰ for Ca-cal

)

Kinetic fractionation

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

E k



1

mv

2

2

Consider two molecules of CO 2 : 12 C 16 O 2 (mass = 12 + 2*16 = 44) and 13 C 16 O 2 (mass = 13 + 2*16 = 45) if their energies are the same, then:

1 2

2 

1 2

2 and the ratio of their velocities is:

v A v B

  

m B m A

 1/ 2  

assuming ideal gas

45

 1/ 2 

1.011

44

SO… 12 C 16 O 2 can diffuse 1.1% further than 13 C 16 O 2 in a given amount of time

This can be observed as gas moves through a fine capillary tube ( 12 C 16 O 2 arrives first).

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

Kinetic fractionation (cont)

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  13 C) and bacterial reduction (low  34 S))

NOTE

: The tell-tale sign of kinetic fractionation is fractionation that is directly proportional to the mass difference (  m).

You can identify a kinetic process by comparing  values for different isotope systems ie. 18 O/ 16 O vs. 13 C/ 12 C (2/1) 18 O/ 16 O vs. 17 O/ 16 O (2/1)

Mass-independent fractionation

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

mass-independent

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