1

Faculty of Engineering
Department of Eng. Geology
Principles of Geochemistry
Chapter 4: Isotopic of Geochemistry
Lecture 5: Stable Isotopes
Lecturer: Dr. Abdullahi Osman Goyle
Nov 4th, 2023
 Introduction

❑ Stable isotopes geochemistry is concerned with

variation in the isotopic compositions of elements
arising small differences in the chemical
behavior of different isotopes of an element.
❑ These can provide a very large amount of useful
information about chemical (both geochemical
and biochemical) processes.
❑ Traditionally, the principle elements of interest
in stable isotope geochemistry were H, C, N, O,
and S.
❑ Over the last two decades, Li and B have also
become “staples” of isotope geochemistry.
 Stable Isotopes

❑ These elements have several common characteristics:

o They have low atomic mass.
o They form bonds with a high degree of covalent character.

❑ It was once thought that elements not meeting these criteria would not show
measurable variation in isotopic composition.
❑ However, as new techniques have become available, geochemists have begun
to explore isotopic variations of many more elements, including
Mg, Si, Cl, Ca, Ti, Cr, Fe, Zn, Cu, Ge, Sr, Mo and U.
❑ Isotopic variations are much smaller in these elements.
 Fractionation

❑ The masses of these elements are

subject to mass-dependent fractionation
❑ Fractionation can be define as a
reaction or process which selects for one
of the stable isotopes of a particular
element.
❑ If the process selects for the heavier
isotope, the reaction product is ‘heavy’
❑ If the process selects for the light
isotope, the reaction product is ‘light’
 Isotopes of Major Elements of interest
Element Isotope Abundance (%)

Hydrogen 1H 99.985
2H 0.015
Carbon 12C 98.89
13C 1.11
Nitrogen 14N 99.63
15N 0.37
Oxygen 16O 99.759
18O 0.204
Sulfur 32S 95.00
33S 0.76
34S 4.22
36S 0.014
 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.
❑ Two classes of basic mechanisms exist for fractionating
isotopes:
❑ 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.
Fractionation on Earth
 Equilibrium Isotope Fractionation

❑ Equilibrium isotope fractionation controls the distribution of isotopes in the

case that a system approaches thermodynamic equilibrium.

• Tends to be most relevant for high temperature problems

• Igneous and (to a certain extent) metamorphic rocks
• Tends to be less important in processes involving gas phases, biological
reactions, or transport

❑ Isotopes distribute themselves among compounds in a way that

minimizes the energy of the system.
 Theory of equilibrium isotopic fractionation

❑The energy of a diatomic molecule is a function of its vibrational frequency

(v): = ½h v.

❑h (Plank’s constant) = 5.626176x10-34J/Hz

❑ When a light isotope is replaced by a heavier one in a diatomic molecule,

the vibrational frequency decreases; which results in the energy of the
molecule decrease.
❑This decrease in the energy results in strengthening the covalent bond.
❑A consequence of molecule containing the heavy isotope are more stable &
less reactive than those with the light ones.
 Theory of equilibrium isotopic fractionation: Example

1HCl 2HCl

E (vib) = ½(hv) ≈ 17,900 J/mol E (vib) = ½(hv) ≈ 12,800 J/mol

1HF 2HF

E (vib) = ½(hv) E (vib) = ½(hv)

≈ 24,800 J/mol ≈ 17,900 J/mol
 Equilibrium fractionation

❑ For an exchange reaction

½ C16O2 + H2 18O ½ C18O2 + H2 16O
❑ For isotope reactions, K is always small, usually 1.
❑ This K is 1.047
❑ Because 18O forms a stronger covalent bond with C that does 16O
❑ The heavy isotope forms a lower energy bond; it does not vibrate as
violently.
❑ The rule of Bigeleisen states: the heavy isotope goes preferentially into the
compound with the strongest bonds.
 Isotope Standards

❑ Differences between 2 isotopes of one element is very small

❑ To measure them individually with enough precision is difficult to
impossible for most isotope systems
❑ By comparing a sample ratio to a standard ratio, the difference between
these two can be determined much more precisely.
❑ There are many isotope standards:
o VSMOW: Vienna Standard Mean Ocean Water.
• For O and H standard
o PDB: Pee Dee Belemnite: fossil of a belemnite from the Pee Dee formation
USA. It is for C and O
o CDT: Canyon Diablo Troilite: meteorite fragment from meteor crater in
Arizona. For S
 Fractionation Factor, 𝜶

❑ While different, isotopes of the same element exist in certain fractions

corresponding to their natural abundance we can calculate fractionation
factor 𝜶 as shown below:
Rreactants
𝜶= R
products
❑ R is the ratio of heavy to light isotopes
❑ 𝜶 or fractionation factor, is the ratio between reactant and product
H2Owater H2Ovapor
( 18O/16O)
𝜶 18Owater-vapor = 18 16 water
( O/ O)vapor
 Measuring Isotopes

❑ We measure isotopes as a ratio of the isotopes vs. standard material (per

mille %)

Rsample−RStandard
𝜹18O = × 103 %o
RStandard
❑ 𝜹 is “delta”, and is the isotope ratio of a particular thing (Molecule, mineral,
gas) relative to a standard times 1000.
(18O/16O) − ( 18O/16O)
sample VSMOW
𝜹18O = × 1000
(18O/16O)VSMOW
 Isotope ratios

Element Ratio Absolute ratio Standard Notation

Oxygen 18O/16O 2.0052 × 10-3 VSMOW 𝜹18O
Hydrogen 2H/1H 1.557 × 10-4 VSMOW 𝜹D
Carbon 13C/12C 1.122 × 10-2 PDB 𝜹13C
Nitrogen 15N/14N 3.613 × 10-3 Air 𝜹15N

VSMOW: Vienna standard mean ocean water: (𝜹18O)sea = ~ 0

18O/16O) 18O/16O) (𝜹18O)lake = -4
( sample− ( VSMOW
𝜹18O = 18 × 1000 (𝜹18O)SiO2 = + 10
( O/16O)VSMOW
 Fractionation between phases

❑ ∆ is “delta” and is the difference between two different isotope ratios in a

reaction:
∆A-B = 𝜹A - 𝜹B
❑ ∆: fractionation between phases
❑ If we have a rock contains quartz and magnetite, both will have their own
isotope ratios.
❑ ∆ =(𝜹18O)SiO2 - (𝜹18O)Fe3O4
❑ 𝜶 : fractionation factor
(𝜹18O)SiO2
𝜶=
(𝜹18O)Fe3O4

∆ ≈ (ln 𝜶) × 103
 Fractionation between phases

❑ As the value of 𝜹 for a sample increases, the relative abundance of the

rare (heavy) also isotope increase.
for carbon isotopes
As the value of 𝜹13C increases There is enrichment in
i.e., “becomes more positive” 13C

As the value of 𝜹13C decreases There is depletion in

i.e., “becomes more negative” 13C
 Temperature dependence on fractionation

❑ The fractionation factors, 𝜶, are affected by T and defined empirically:

B × 10 6
a
103 ln 𝜶b = A +
T2
❑ Where A and B are constants determined for particular reactions and T is
temp. in Kelvins
❑ Then,
103 ln 𝜶ab ≈ 𝜹a - 𝜹b = ∆ a
b

❑ For a range of minerals, the constants of A and B in this equation have

been found.
 Temperature dependence

The table below shows the constants for some minerals. (quartz reference)

Mineral A B
Pyroxene 0 2.75
Garnet 0 2.88
Olivine 0 3.91
Muscovite -0.6 2.20
Amphibole -0.30 3.15
Magnetite 0 5.57
 Example

If we have a rock sample which is mixture of magnetite, quartz, and olivine,

And we assumed that we separated out the magnetite and quartz grains of this
rock and analyzed the oxygen isotope composition. If we get that it is 2 per mil
and 10 per mil respectively.
At what temperature did these minerals equilibrate?
Solution
Given: 𝜹18Oquartz = 10 %o , 𝜹18Omagnetite = 2 %o

B × 10 6
103 ln 𝜶 = A +
T2
103 ln 𝜶 = 𝜹quartz - 𝜹mineral
B × 106 5.57 × 106
𝜹quartz - 𝜹magnetite = A + 2 = 10 – 2 = 0 +
T T2
 Solution

5.57 × 106
8=
T2
T = 834 K (561 oC)
❑ In some cases, we can’t find quartz. But with a few
changes, we can still find the equilibration temperature
based on any two minerals in the rock.
❑ Assume that we analyzed the magnetite and the olivine
grains in this sample and we got 4.4 per mil in the
olivine and 2 per mil in the magnetite. What will be the
T at which the minerals equilibrate?
❑ Solution:
❑ Given: 𝜹18Omagnetite = 2 % 𝜹18Oolivine = 4.4 %
 Solution

B × 106 B ×106
𝜹quartz - 𝜹magnetite = A + ⇒ 𝜹quartz = A + + 𝜹magnetite
T2 T2
B × 106 B ×106
𝜹quartz - 𝜹olivine = A + 2 ⇒ 𝜹quartz = A + 2 + 𝜹olivine
T T
B ×106 5.57 × 106
For magnetite: 𝜹quartz = A + + 𝜹magnetite = +2
T2 T2
B ×106 3.91 × 106
For olivine : 𝜹quartz = A + 2 + 𝜹olivine = 2 + 4.4
T T
Equate the two equations:
3.91 × 106 5.57 × 106 3.91 × 106 5.57 × 106
+ 4.4 = +2⇒ + 4.4 – 2 =
T2 T2 T2 T2
3.91 × 106 5.57 × 106 5.57 × 106 3.91 × 106
2 + 2.4 = 2 ⇒ 2.4 = 2 -
T T T T2
(5.57 × 106) − (3.91 × 106)
2.4 = 2 = T = 832 K (559 oC)
T
 Kinetic isotopic fractionation

❑ Kinetic effect can enhance fractionation arising.

❑ Consider the evaporation to the gas phase of water composed for simplicity
of only the two most common forms, H2O16 and H2O18. At chemical
equilibrium we would predict:

❑ Yet, because H2O16 moves faster than H2O18, thereby enhancing the level of
H2O16 enrichment during evaporation of water to a moving parcel of
atmosphere over a body of water.
❑ This process occurs on Earth as H2O evaporates from the oceans, since the
atmosphere is rarely saturated with respect to H2O. The opposite process
occurs during condensation of H2O liquid or solid from the atmosphere.
 Kinetic isotopic fractionation

Relative to a standard (oceanic water)

+ve The sample is enriched in the heavy

isotopes
-ve The sample is depleted in the heavy
isotopes

❑ When water evaporates at equilibrium under constant P, isotopic

composition of the vapor differs from that of the remaining water due to
isotope fractionation during the evaporation
 Kinetic isotopic fractionation

❑ Lightest water (H216O) evaporates

preferentially relative to the heaviest
molecule (D218O)
❑ heaviest molecule in water vapor
condenses preferentially relative to
lightest molecule, so:
❑ Depleted in D & 18O relative to sea
water.
❑ Condensate enriched in D & 18O
relative to the vapor.