Introduction to Geochemistry

Isotopes
• Isotopes have different ## of neutrons,
and thus a different mass
• Affect on reactions in small, but real, and
provides another measurement of
reactions – affected by similar
physicochemical parameters!
• Also a critical tracer – the isotopes can be
used to track molecules in a reaction!

• 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’, the
reactant remaining is ‘light’
• Isotope fractionation occurs for isotopic
exchange reactions and mass-dependent
differences in the rates of chemical
reactions and physical processes
Fractionation

Fractionation Factor, a
• R is the ratio of heavy to light isotopes
• a, or fractionation factor, is the ratio between
reactant and product
products
ts
reac
R
R tan

a

Why a ratio???
• 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!!

Isotope Standards
• VSMOW – Vienna Standard Mean Ocean
Water – bunch of ocean water kept in
Austria – O and H standard
• PDB – Pee Dee Belemnite – fossil of a
belemnite from the Pee Dee formation in
Canada – C and O
• CDT – Canyon Diablo Troilite –meteorite
fragment from meteor crater in Arizona,
contains FeS mineral Troilite – S
• AIR – Atmospheric air - N

Measuring Isotopes
• While different, isotopes of the same element
exist in certain fractions corresponding to
their natural abundance (adjusted by
fractionation)
• We measure isotopes as a ratio of the
isotope vs. a standard material (per mille ‰)
3
standard
standard
18
10








 

R
R
R
O
sample

b
a
a
b
R
R

a
Where Ra is the ratio of
heavy/light isotope and a is
the fractionation factor
‰
a
b
b
a
a
b 


 

a
ln
103

 is “delta”, and is the isotope ratio of a particular
thing (molecule, mineral, gas) relative to a
standard times 1000. sometimes called ‘del’
 is “delta” and is the difference between two
different isotope ratios in a reaction:
AB = A - B
3
standard
standard
18
10








 

R
R
R
O
sample

Many isotopers are very sensitive about misuses of isotope terminology.
Harmon Craig’s immortal limerick says it all:
There was was a young man from Cornell
Who pronounced every "delta" as "del"
But the spirit of Urey
Returned in a fury
And transferred that fellow to hell

Equilibrium vs. Kinetic fractionation
• Fractionation is a
reaction, but one in
which the free energy
differences are on the
order of 1000x smaller
than other types of
chemical reactions
• Just like other chemical
reactions, we can
describe the proportion
of reactants and
products as an
equilibrium or as a
kinetic function

Because the kinetic energy for heavy and light
isotopes is the same, we can write:
In the case of 12C16O and 13C16O we have:
Regardless of the temperature, the velocity of
12C16O is 1.0177 times that of 13C16O, so the
lighter molecule will diffuse faster and
evaporate faster.
L
H
H
L
m
m
v
v

0177
.
1
994915
.
27
99827
.
28


H
L
v
v

Equilibrium Fractionation
• For an exchange reaction:
½ C16O2 + H2
18O ↔ ½ C18O2 + H2
16O
• Write the equilibrium:
• Where activity coefficients effectively cancel
out
• For isotope reactions, K is always small,
usually 1.0xx (this K is 1.047 for example)
)
(
)
(
)
(
)
(
2
18
2
1
2
16
2
16
2
1
2
18
O
H
O
C
O
H
O
C
K 

WHY IS K DIFFERENT FROM
1.0?
Because 18O forms a stronger covalent bond
with C than does 16O.
The vibrational energy of a molecule is given by
the equations:
H
O
H

h
E l
vibrationa 2
1

m
k


2
1
 kx
F 

Thus, the frequency of vibration depends
on the mass of the atoms, so the energy
of a molecule depends on its mass.

• The heavy isotope forms a lower energy
bond; it does not vibrate as violently.
Therefore, it forms a stronger bond in
the compound.
• The Rule of Bigeleisen (1965) - The
heavy isotope goes preferentially into
the compound with the strongest bonds.

Temperature effects on
fractionation
• The fractionation factors, a, are affected
by T (recall that this affects EA) and
defined empirically:
• Then,
• As T increases,  decreases – at high T 
goes to zero
B
T
A
a
b 

 2
6
3 10
ln
10 a
Where A and B are constants
determined for particular reactions
and T is temp. in Kelvins
a
b
b
a
a
b 


 

a
ln
103

FRACTIONATION DURING
PHYSICAL PROCESSES
• Mass differences also give rise to
fractionation during physical processes
(diffusion, evaporation, freezing, etc.).
• Fractionation during physical process is a
result of differences in the velocities of
isotopic molecules of the same compound.
• Consider molecules in a gas. All molecules
have the same average kinetic energy, which
is a function of temperature.
2
2
1 mv
Ekinetic 

Using isotopes to get information on
physical and chemical processes
• Fractionation is due to some reaction,
different isotopes can have different
fractionation for the same reaction, and
different reactions have different
fractionations, as well as being different at
different temperatures and pressures
• Use this to understand physical-chemical
processes, mass transfer, temperature
changes, and other things…

Equilibrium Fractionation II
• For a mass-dependent reaction:
• Ca2+ + C18O3
2-  CaC18O3
• Ca2+ + C16O3
2-  CaC16O3
• Measure 18O in calcite (18Occ) and water
(18Osw)
• Assumes 18O/16O between H2O and CO3
2- at
some equilibrium
T ºC = 16.998 - 4.52 (18Occ - 18Osw) + 0.028 (18Occ-18Osw)2

Empirical Relationship between Temp. &
Oxygen Isotope Ratios in Carbonates
At lower temperatures, calcite
crystallization tends to incorporate a
relatively larger proportion of 18O
because the energy level (vibration)
of ions containing this heavier isotope
decreases by a greater amount than ions
containing 16O.
As temperatures drop, the energy level
of 18O declines progressively by an
amount that this disproportionately
greater than that of the lighter 16O.

Distillation
• 2 varieties, Batch and Rayleigh distillation
dependent on if the products stay in contact
and re-equilibrate with the reactants
• Batch Distillation:
f = i – (1 – F) 103lnaCO2-Rock
where the isotope of the rock (i) depends on
it’s initial value (f) and the fractionation factor
• Rayleigh Distillation
f - i =103(F(a – 1) – 1)

RAYLEIGH DISTILLATION
Isotopic fractionation that occurs during
condensation in a moist air mass can be
described by Rayleigh Distillation. The equation
governing this process is:
where Rv = isotope ratio of remaining vapor, Rv° =
isotope ratio in initial vapor, ƒ = the fraction of
vapor remaining and a = the isotopic
fractionation factor
1

 a
f
R
R o
v
v

Effect of Rayleigh
distillation on the
18O value of water
vapor remaining in
the air mass and of
meteoric precipitation
falling from it at a
constant temperature
of 25°C.
Complications:
1) Re-evaporation
2) Temperature
dependency of a

ISOTOPE FRACTIONATION IN THE
HYDROSPHERE
Evaporation of surface water in equatorial regions
causes formation of air masses with H2O vapor
depleted in 18O and D compared to seawater.
This moist air is forced into more northerly, cooler air
in the northern hemisphere, where water
condenses, and this condensate is enriched in 18O
and D compared to the remaining vapor.
The relationship between the isotopic composition of
liquid and vapor is:
  3
3
18
18
10
10 

 v
l
v
l O
O 
a


Assuming that 18Ov = -13.1‰ and av
l(O) =
1.0092 at 25°C, then
and assuming Dv = -94.8‰ and av
l(H) = 1.074
at 25°C, then
These equations give the isotopic composition
of the first bit of precipitation. As 18O and D
are removed from the vapor, the remaining
vapor becomes more and more depleted.
Thus, 18O and D values become increasingly
negative with increasing geographic latititude
(and altitude.
  00
0
3
3
18
0
.
4
10
10
1
.
13
0092
.
1 





l
O

  00
0
3
3
8
.
27
10
10
8
.
94
074
.
1 





l
D


Map of North
America
showing
contours of the
approximate
average D
values of
meteoric surface
waters.

Because both H and O occur together in water, 18O and D
are highly correlated, yielding the meteoric water line
(MWL): D  818O + 10

Deviation from MWL
• Any additional fractionation process which
affects O and D differently, or one to the
exclusion of the other will skew a water
away from the MWL plot
• These effects include:
– Elevation effects - (D -8‰/1000m, -4‰/ºC)
– Temperature (a different!)
– Evapotranspiration and steam loss
– Water/rock interaction (little H in most rocks)

Iron Isotopes
Earth’s Oceans 3 Ga had no
oxygen and lots of Fe2+,
cyanobacteria evolved,
produced O2 which oxidized
the iron to form BIFs – in time
the Fe2+ was more depleted
and the oceans were stratified,
then later become oxic as they
are today
This interpretation is largely based on iron
isotopes in iron oxides and sulfide minerals
deposited at those times (Rouxel et al., 2005)

Experiments
• Fe2+ and
FeSmackinawite at
equilibrium,
separate physically
(filter) and measure
each component:
From Butler et al., 2005 EPSL 236 430-442

Fe –isotope exchange with a particle
• Particles coarsen via
Ostwald ripening or
topotactic alignment –
how fast can isotopes
exchange with Fe in a
xstal actively getting
bigger?
• At certain size internal
Fe2+ does not
exchange…
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Fe2+
Guilbaud et al., 2010 EPSL 300 174-183

What can we get from using
multiple isotopes?
• Many isotope systems have more than 2
stable isotopes – 56Fe, 57Fe, 58Fe; 32S, 33S,
34S, 36S
• Looking at multiple isotopes can provide
new insight on multiple processes,
especially useful for complicated reaction
pathways, also helps get at equilibrium v.
kinetic processes, and mass-dependent v.
independent processes…

• Tracing S-isotopic fractionation from
different communities of organisms
(Sulfate-reducers, sulfur
disproportionation, phototrophic S oxid.)
From Zerckle et al., 2009 GCA 73, 291-306

S isotopes and microbes
• The fractionation of H2S formed from
bacterial sulfate reduction (BSR) is affected
by several processes:
– Recycling and physical differentiation yields
excessively depleted H2S
– Open systems – H2S loss removes 34S
– Limited sulfate – governed by Rayleigh process,
enriching 34S
– Different organisms and different organic
substrates yield very different experimental 34S
• Ends up as a poor indicator of BSR vs. TSR

Mass-independent fractionation
• Mass effects for 3 stable isotopes
(such as 18O, 17O, and 16O) should
have a mass-dependent relationship
between each for any process
• Deviation from this is mass-
independent and thought to be
indicative of a nuclear process
(radiogenic, nucleosynthetic,
spallation) as opposed to a physico-
chemical process
• Found mainly associated with
atmospheric chemistry, effect can be
preserved as many geochemical
reactions in water and rock are mass-
dependent

S-isotopic evidence of Archaen
atmosphere
• Farquar et al., 2001; Mojzsis et al., 2003
found MIF signal in S isotopes (32S, 33S,
34S) preserved in archaen pyrites
precipitated before 2.45 Ga
• Interpreted to be signal from the photolysis
of SO2 in that atmosphere – the reaction
occurs at 190-220nm light, indicating low
O2 and O3 (which very effficiently absorb
that wavelength)

Volatilization
• calcite + quartz = wollastonite + carbon dioxide
CaCO3 + SiO2 = CaSiO3 + CO2
• As the CO2 is produced, it is likely to be expelled

• Other volatilization reaction examples…

Oxygen isotopes and climate
/Kepler’s laws

How do we know how warm it
was millions of years ago?
• Ice cores: bubbles contain
samples of the atmosphere
that existed when the ice
formed. (ancient pCO2)
• Marine isotopes: oxygen
isotopes in carbonate
sediments from the deep ocean
preserve a record of
temperature.
• The records indicate that
glaciations advanced and
retreated and that they did so
frequently and in regular
cycles.

Oxygen isotopes and paleoclimate
• Oxygen has three stable isotopes: 16O, 17O, and 18O. (We
only care about 16O and 18O.)
• 18O is heavier than 16O.
• The amount of 18O compared to 16O is expressed using
delta notation:
• Fractionation: Natural processes tend to preferentially
take up the lighter isotope, and preferentially leave
behind the heavier isotope.
18O ‰ = 18O/16O of sample -18O/16O of standard
18O/16O of standard
 1000

• Oxygen isotopes are fractionated during evaporation
and precipitation of H2O
– H2
16O evaporates more readily than H2
18O
– H2
18O precipitates more readily than H2
16O
• Oxygen isotopes are also fractionated by marine
organisms that secrete CaCO3 shells. The organisms
preferentially take up more 16O as temperature
increases.
18O is heavier than 16O
H2
18O is heavier
than H2
16O

Ocean
H2
16O, H2
18O
Evaporation favors
H2
16O H2
18O
Precipitation favors
H2
18O
…so cloud water
becomes
progressively more
depleted in H2
18O as
it moves poleward…
H2
18O
… and snow and
ice are depleted in
H2
18O relative to
H2
16O.
Land
Ice
Carbonate sediments in equilibrium
with ocean water record a 18O signal which
reflects the 18O of seawater and the reaction
of marine CaCO3 producers to temperature.
CaCO3

• As climate cools, marine
carbonates record an
increase in 18O.
• Warming yields a
decrease in 18O of marine
carbonates.
JOIDES Resolution
Scientists examining
core from the ocean
floor.

Long-term
oxygen isotope
record
Ice cap begins to
form on Antarctica
around 35 Ma
This may be related
to the opening of
the Drake passage
between Antarctica
and S. America
From K. K. Turekian, Global Environmental
Change, 1996

Drake
passage
• Once the Drake passage had formed, the
circum-Antarctic current prevented warm ocean
currents from reaching Antarctica

O isotopes during the last 3 m.y.
Kump et al., The Earth System, Fig. 14-4
• Climatic cooling accelerated during the last 3 m.y.
• Note that the cyclicity changes around 0.8-0.9 Ma
− 41,000 yrs prior to this time
− 100,000 yrs after this time

after Bassinot et al. 1994
O isotopes—the last 900 k.y.
• Dominant period is ~100,000 yrs during this time
• Note the “sawtooth” pattern..

Ice Age Cycles:
100,000 years between ice ages
Smaller cycles also recorded every
41,000 years
*,
19,000 - 23,000 years
*This was the dominant period prior to
900 Ma

NOAA
Milutin Milankovitch,
Serbian mathematician
1924--he suggested solar energy changes and
seasonal contrasts varied with small variations
in Earth’s orbit
He proposed these energy and seasonal
changes led to climate variations

Before studying Milankovitch cycles, we need
to become familiar with the basic characteristics
of planetary orbits
Much of this was worked out in the 17th century
by Johannes Kepler (who observed the planets
using telescopes) and Isaac Newton (who
invented calculas)

r’
a
r
r’ + r = 2a
a = semi-major axis
(= 1 AU for Earth)
First law:
Planets travel around the sun in elliptical orbits
with the Sun at one focus
Kepler’s Laws
Minor axis
Major axis

Ellipse:
Combined distances to two fixed points (foci) is fixed
r’
a
r
r’ + r = 2a
• The Sun is at one focus

Aphelion
Point in orbit furthest from the sun
ra
ra = aphelion distance
Earth (not to scale!)

Aphelion
Point in orbit furthest from the sun
Perihelion
Point in orbit closest to the sun
rp
rp = perihelion distance
Earth

Eccentricity
e = b/a so b = ae
a = 1/2 major axis (semi-major axis)
b = 1/2 distance between foci
a
b

Eccentricity
e = b/a
a = 1/2 major axis
Sun-Earth distances
Aphelion: a + ae = a(1 + e)
Perihelion: a – ae = a(1 – e)
a
b

Eccentricity
e = b/a
a = 1/2 major axis
Sun-Earth distances
Aphelion: a(1 + e)
Perihelion: a(1 – e)
a
b
Today:
e = 0.017
Range:
0 to 0.06
Cycles: 100,000 yrs

Kepler’s Second Law
2nd law: A line joining the Earth to the Sun sweeps
out equal areas in equal times
Kump et al., The Earth System, Box Fig. 14-1
Corollary: Planets
move fastest when
they are closest to
the Sun

Kepler’s Third Law
• 3rd law: The square of a planet’s period, P, is
proportional to the cube of its semi-major axis, a
• Period—the time it takes for the planet to go
around the Sun (i.e., the planet’s year)
• If P is in Earth years and a is in A.U., then
P2 = a3

Other characteristics of Earth’s orbit vary as well.
The three factors that affect climate are 

http://www.geo.lsa.umich.edu/~crlb/COURSES/205/Lec20/lec20.html
Eccentricity
(orbit shape)
100,000 yrs
&400,000 yrs
Obliquity
(tilt--21.5 to 24.5o)
41,000 yrs
Precession
(wobble)
19,000 yrs
& 23,000 yrs

Meredith G. Hastings
University of Washington
Joint Institute for Study of the Atmosphere and Ocean &
Department of Atmospheric Sciences
GEOS-CHEM Users Meeting, April 4-6 2005
Modeling the oxygen isotopic
composition of nitrate

NO NO2
O3
h
HNO3
OH
(nitric acid, aka
nitrate NO3
-)
(ozone)
(hydroxyl
radical)
SOURCES
NOx
PAN
organics
temp
O3 (dark)
O3
Nitrogen oxides = NOx = NO+NO2
isotopes of NO3
- reflect
sources and chemistry of NOx

Objective
 goal is to model oxygen isotopic composition of NO3
-
 oxygen isotopes are a record of the oxidants that react with NOx prior
to NO3
- deposition
 will use simulations to diagnose NOx chemistry across environments and
through time
today: quick intro to oxygen isotopes (17O)
qualitative evaluation of NOx chem from obs.
plans for modeling 17O of NO3
-

Stable Isotopes of Oxygen
 denote isotopes in form 16O where 16 is the mass number, or
neutrons+protons
 O : 16O 99.763% 17O 0.0375% 18O 0.1995%
 definition of delta ():
18O = [
(18O/16O)sample
-1]
* 1000 (per mil ‰ units)
(18O/16O)std
 std for O is VSMOW (Vienna-Standard Mean Ocean Water)

Stable Isotopes of Oxygen
 Tracer of chemical processing (interaction with oxidants) in
atmosphere
 17O ≈ 0.5*18O mass dependent fractionation
17O ≈ 17O - 0.5*18O mass independent fractionation
 17O of OH and H2O = 0‰
17O of tropospheric O3 ≈ 35‰

18O (‰ vs SMOW)
17O
(‰ vs SMOW)
mass-dependent
fractionation line
17O/18O≈0.5
17O=0
atmospheric NO3
-
17O
17O > 0
0
20 40 60 80 100
10
30
40
50
20
60

25
10
5
50
75
100
10 20 50 100
SO4
CO
N2O
H2O2
NO3
CO2 strat.
O3
trop.
O3
strat.
18O
17O
17O of different atmospheric species
(courtesy B. Alexander)
mass-dependent
fractionation line
17O=0

NOx/NO3
- Chemistry
 NO3
- deposition represents the major sink of reactive
nitrogen oxides (NOx = NO + NO2) from the atmosphere
 importance of different pathways of HNO3 production vary
diurnally and seasonally
NO + O3 NO2 + O2
NO2 + hv NO + O
O + O2 O3
NO2 + OH HNO3
NO2 + O3 NO3 + O2
NO3 + NO2 N2O5
N2O5 + H2O 2HNO3
M
M
M
aerosol

17O of NO3
- in Princeton Rain
15.0
20.0
25.0
30.0
35.0
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan
2001 2002
17O in winter
17O in summer
17O in spring

17O of atmospheric NO3
-
NO + O3 NO2 + O2
NO2 + hv NO + O
O + O2 O3
NO2 + OH HNO3
NO2 + O3 NO3 + O2
NO3 + NO2 N2O5
N2O5 + H2O 2HNO3
M
M
M
aerosol
(winter)
(summer)
17O 17O
(O3 has high 17O, OH
acts to dilute this signal)
(more influence of O3 in
heterogeneous chemistry)
 the oxygen isotopic composition of NO3
- reflects the oxidation pathway of NOx

Modeling 17O of NO3
-
 First need proportion of NO oxidized by O3 vs. HO2, ROx,
other oxidants
 Determine 17O of NO2
17O of trop O3 = 35 ± 3‰ (f(T,P); strat O3 > 40‰)
17O of HO2 = 0.9 - 1.8‰
17O of H2O/OH/ROx/O2 = 0‰
NO + O3 NO2 + O2
NO + HO2 NO2 + OH
NO + ROx NO2 + RO
NO2 + hv NO + O(3P)

Modeling 17O of NO3
-
 Use 17O of NO2 and proportions of HNO3 produced by
different pathways to determine 17O of HNO3, i.e.,
NO2 + OH HNO3
NO2 + O3 NO3 + O2
NO3 + HC/DMS HNO3 + …
NO3 + NO2 N2O5
N2O5 + H2O 2HNO3
M
aerosol
(R1)
(R2)
(R3)
17O HNO3 (R1) = 2/3 17NO2 + 1/3 17OH
17O HNO3 (R2) =2/3 17NO2 + 1/3 17O3
17O HNO3 (R3) = 1/3 17NO2 + 1/2 17NO3 + 1/6 17H2O
where 17NO3 = 2/3 17NO2 + 1/3 17O3

Initial Plans/Implications
 create most efficient scheme for determining 17O with
chem1d to start
 use GEOS-CHEM with full chemistry (w/ aerosols) to
simulate global 17O HNO3 fields
Sensitivity of 17O to gas-phase concs?
Can we predict seasonal cycle? (tests
heterogeneous chemistry param.; gN2O5)
How much variability do we predict among
environments? Where should we aim to do meas.?
Interpret ice core measurements of 17O!

Training in Stable Isotope Methods, Mass Spectrometery
& Isotopology
Goal: provide some of the fundamentals needed to understand isotopes and
their use in the biological sciences
Six sessions:
1. Fundamentals of isotope physics & chemistry
2. Case studies of how stable isotopes have been applied in natural systems
3. Sampling issues: what, where, how and help! of isotope sample collection
and preparation
4. The isotope ratio mass spectrometer: how it works and how you make it
work for your research
5. Correcting your data - tour de Excel!
6. Discussion about isotope applications & your work - the questions
you face and the challenges you need to resolve
» Introductions: who you are, what you do, why isotopes?

TODAY: Introduction to Stable Isotopes
1. Introduction to isotopes
2. Isotopes used in ecological studies
3. Stable isotope notation
6. Fractionation factors
4. Correct usage of stable isotope expressions
7. Rayleigh distillation: using fractionation factors
5. Causes of variation in stable isotope abundances

Why use stable isotopes?
» They are non-radioactive TRACERS of resource
origin, fate and flux including:
1. organismal movements
2. energy or resource flow across levels of ecological
organization
» They are non-destructive and non-disruptive
INTEGRATORS of ‘system’ processes including:
1. organismal function/tradeoffs
2. spatial and temporal responses to environment

History of Isotopy:
• 1914 Fredrick Soddy proposed that any place on
periodic table can be occupied by more than one
kind of atom
He proposed isotope ---- meaning “same place”
Isotopes  Nuclides of single element having
different atomic weights
•Presently more than 2500 nuclides are known from
~110 elements

To be or not to be? - A stable isotope that is!

Nuclear Entities
These entities are of greatest interest to us

An atom is composed of three types of particles:
PROTONS, NEUTRONS, and ELECTRONS
Each element has a unique number of protons, its atomic
number. The number of protons (Z) determines many of
the chemical and physical properties associated with an
atom.
The atomic mass is the sum of protons and neutrons
(N), particles with nearly identical weights. (Electrons,
negatively charged particles, have insignificant weight –
to ecologists!)
Atoms First:
The atomic number = Z (Protons)
The atomic mass = Z + N (Protons + Neutrons)

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1
Neutron Number (N)
Proton
Number
(Z)
Each square represents a nuclide, an isotope specific atom
Atomic number = Z (Protons): bottom left of each atom
Atomic mass = Z + N (Protons + Neutrons): top left of each atom
O O O O O O O O
N N N N N N N
C C C C C C C C
B B B B B B
Be Be Be Be Be Be Be
Li Li Li Li Li
He He He He He
H H H
Partial chart of the elements

O O O O O O O O
N N N N N N N
C C C C C C C C
B B B B B B
Li Li Li Li Li
He He He He He
H H H
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Neutron Number (N)
Proton
Number
(Z)
Each green row represents nuclides that are isotopes: they
share a common number of protons (Z) but differ in their
number of neutrons (N).
isotopes

O O O O O O O O
N N N N N N N
C C C C C C C C
B B B B B B
Li Li Li Li Li
He He He He He
H H H
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Neutron Number (N)
Proton
Number
(Z)
isobars
Each green row represents nuclides that are isobars: they share
a common atomic weight (N + Z).

O O O O O O O O
N N N N N N N
C C C C C C C C
B B B B B B
Li Li Li Li Li
He He He He He
H H H
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1
Neutron Number (N)
Proton
Number
(Z)
isotones
Each green row represents nuclides that are isotones: they
share a common number of neutrons (N).

O O O O O O O O
N N N N N N N
C C C C C C C C
B B B B B B
Li Li Li Li Li
He He He He He
H H H
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Neutron Number (N)
Proton
Number
(Z)
The shaded squares are stable and the un-shaded squares are
unstable or radioactive nuclides.
-decay occurs along
the line of isobars

N/Z = 1
1. Stable isotopes tend to
have an N/Z near 1 for
masses less than 20
N
Z
2. Stable isotopes tend to
have an even Z-number for
masses greater than 20
3. Most biologically
important elements have
masses less than 20
3 important points:
C
H
O
N
Stable isotope trends

What isotopes are
used in ecological
studies?

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
17O 0.037
18O 0.204
Magnesium 24Mg 78.70
25Mg 10.13
26Mg 11.17
Silicon 28Si 92.21
29Si 4.70
30Si 3.09
Sulfur 32S 95.00
33S 0.76
34S 4.22
36S 0.014
Chlorine 35Cl 75.53
37Cl 24.47
Potassium 39K 93.10
40K 0.0118
41K 6.88
Calcium 40Ca 96.97
42Ca 0.64
43Ca 0.145
44Ca 2.06
46Ca 0.0033
48Ca 0.18
Iron 54Fe 5.82
56Fe 91.66
57Fe 2.19
58Fe 0.33
Copper 63Cu 69.09
65Cu 30.91
Zinc 64Zn 48.89
66Zn 27.81
67Zn 4.11
68Zn 18.57
70Zn 0.62
Strontium 84Sr 0.56
86Sr 9.86
87Sr 7.02
88Sr 82.56
Average terrestrial abundances of the stable isotopes
of elements used commonly (), occasionally (), and
rarely () in ecological studies

When we see this list of isotopes used in ecological
studies, note that it includes many of the most common
isotopes in the solar system:
Common isotopes
The 10 most common isotopes in the solar system are:
H >> 4He >> 16O > 12C >> 20Ne > 14N > 24Mg > 28Si > 56Fe > 32S
The isotopes we study occur
throughout the solar system and
are important in lots of processes!

Element
Isotope
Atomic
weight Relative
Abundance
(%)
Elemental
Relative
Mass
Difference
Molecular Relative Mass
Difference
 ‰ ppm ‰ ppm
Hydrogen
(Deuterium)
1H1
1H2
(D)
1.0078
2.0141 99.984
0.0156
D/H
100%
1HD / 1H1H
(3/2)
50%
700 109 0.25 0.17
Carbon 6C12
6C13
12.0000
13.0034 98.892
1.108
13C / 12C
8.3%
13C 16O 16O / 12C 16O 16O
(45/44)
2.3%
100 1123 0.05 0.56
Nitrogen 7N14
7N15
14.0031
15.0001 99.635
0.365
15N/ 14N
7.1%
15N 14N / 14N 14N
(29/28)
3.6%
50 181 0.1 0.72
Oxygen 8O16
8O17
8O18
15.9949
16.9991
17.9992
99.759
0.037
0.204
18O / 16O
12.5%
12C 16O 18O / 12C 16O 16O
(46/44)
4.5%
100 200 0.1 0.20
Sulphur 16S32
16S33
16S34
16S36
31.9721
32.9714
33.9679
35.9671
95.02
0.76
4.22
0.014
34S / 32S
6.3%
34S 16O 16O / 32S 16O 16O
(66/64)
3.1%
100 4580 0.2 9.16
Terrestrial
range
Technical
Precision
HEAVIER ISOTOPES
ARE RARE!

Element
Isotope
Atomic
weight
Relative
Abundance
(%)
Elemental
Relative Mass
Difference
Difference
 ‰ ppm ‰ ppm
Hydrogen
(Deuterium)
1H1
1H2
(D)
1.0078
2.0141
99.984
0.0156 D/H
100%
1HD / 1H1H
(3/2)
50%
700 109 0.25 0.17
Carbon 6C12
6C13
12.0000
13.0034
98.892
1.108
13C / 12C
8.3%
13C 16O 16O / 12C 16O 16O
(45/44)
2.3%
100 1123 0.05 0.56
Nitrogen 7N14
7N15
14.0031
15.0001
99.635
0.365
15N/ 14N
7.1%
15N 14N / 14N 14N
(29/28)
3.6%
50 181 0.1 0.72
Oxygen 8O16
8O17
8O18
15.9949
16.9991
17.9992
99.759
0.037
0.204
18O / 16O
12.5%
12C 16O 18O / 12C 16O 16O
(46/44)
4.5%
100 200 0.1 0.20
Sulphur 16S32
16S33
16S34
16S36
31.9721
32.9714
33.9679
35.9671
95.02
0.76
4.22
0.014
34S / 32S
6.3%
34S 16O 16O / 32S 16O 16O
(66/64)
3.1%
100 4580 0.2 9.16
HYDROGEN HAS THE
LARGEST MASS DIFF
BETWEEN ISTOPES
Terrestrial
range
Technical
Precision

Element
Isotope
Atomic
weight
Relative
Abundance
(%)
Elemental
Relative
Mass
Difference
Molecular Relative
Mass Difference
 ‰ ppm ‰ ppm
Hydrogen
(Deuterium)
1H1
1H2
(D)
1.0078
2.0141
99.984
0.0156
D/H
100%
1HD / 1H1H
(3/2)
50%
700 109 0.25 0.17
Carbon 6C12
6C13
12.0000
13.0034
98.892
1.108
13C / 12C
8.3%
13C 16O 16O / 12C 16O 16O
(45/44)
2.3%
100 1123 0.05 0.56
Nitrogen 7N14
7N15
14.0031
15.0001
99.635
0.365
15N/ 14N
7.1%
15N 14N / 14N 14N
(29/28)
3.6%
50 181 0.1 0.72
Oxygen 8O16
8O17
8O18
15.9949
16.9991
17.9992
99.759
0.037
0.204
18O / 16O
12.5%
12C 16O 18O / 12C 16O 16O
(46/44)
4.5%
100 200 0.1 0.20
Sulphur 16S32
16S33
16S34
16S36
31.9721
32.9714
33.9679
35.9671
95.02
0.76
4.22
0.014
34S / 32S
6.3%
34S 16O 16O / 32S 16O 16O
(66/64)
3.1%
100 4580 0.2 9.16
Terrestrial
range
Technical
Precision
We analyze gases that
contain the isotopes
of interest!

Element
Isotope
Atomic
weight
Relative
Abundance
(%)
Elemental
Relative
Mass
Difference
Difference
 ‰ ppm ‰ ppm
Hydrogen
(Deuterium)
1H1
1H2
(D)
1.0078
2.0141
99.984
0.0156
D/H
100%
1HD / 1H1H
(3/2)
50%
700 109
0.25+ 0.17
Carbon 6C12
6C13
12.0000
13.0034
98.892
1.108
13C / 12C
8.3%
13C 16O 16O / 12C 16O 16O
(45/44)
2.3%
100 1123
0.05 0.56
Nitrogen 7N14
7N15
14.0031
15.0001
99.635
0.365
15N/ 14N
7.1%
15N 14N / 14N 14N
(29/28)
3.6%
50 181
0.1 0.72
Oxygen 8O16
8O17
8O18
15.9949
16.9991
17.9992
99.759
0.037
0.204
18O / 16O
12.5%
12C 16O 18O / 12C 16O 16O
(46/44)
4.5%
100 200
0.1 0.20
Sulphur 16S32
16S33
16S34
16S36
31.9721
32.9714
33.9679
35.9671
95.02
0.76
4.22
0.014
34S / 32S
6.3%
34S 16O 16O / 32S 16O 16O
(66/64)
3.1%
100 4580
0.2 9.16
Terrestrial
range
Technical
Precision
HYDROGEN HAS A LARGE
TERRESTRIAL RANGE,
BUT ALSO RELATIVELY
LOW PRECISION
NITROGEN HAS A SMALLER
TERRESTRIAL RANGE, BUT
BETTER TECHNICAL
PRECISION

Expressing differences
in stable isotope
abundance

Element
Isotope
Relative
Abundance
(% atoms)
Hydrogen
(Deuterium)
1H1
1H2
(D)
99.984
0.0156
Carbon 6C12
6C13
98.892
1.108
Nitrogen 7N14
7N15
99.635
0.365
Oxygen 8O16
8O17
8O18
99.759
0.037
0.204
1.0860% 13C 1.0805% 13C
Are these relevant?
Absolute isotope abundances
are found at the third decimal
leading to small relative differences

Stable isotope composition is expressed in  (delta)
notation:
R in ‰ = Rsample
–1 x 1000
Rstandard

notation:
–1 x 1000
Rstandard
R is the isotope ratio of the HEAVY / LIGHT isotopes in
either your sample or a standard
i.e. D/H, 13C/12C , 15N/14N , 18O/16O
and is a very small number

notation:
–1 x 1000
Rstandard
Delta notation indicates the isotope ratio in your
sample relative to a standard.
If the isotope ratio in your sample equals the
standard, Rsample/Rstandard = 1 and R = 0‰
The International Atomic Energy Association (IAEA)
maintains a set of standards used for stable isotope
measurements.

notation:
–1 x 1000
Rstandard
Because Rsample never deviates much
from Rstandard (natural variation in isotope ratios is
limited), [(Rsample / Rstandard)-1] is a small number.
In order to make the variation more apparent, one
multiplies the value by 1000, thereby expressing the
value in per mil (parts per thousand ; ‰) notation

Isotope Ratio
Measured
Standard Abundance Ratio
of reference
standard
2H (D) 2H/1H (D/H) V-SMOW: “Vienna-Standard Mean
Ocean Water”
1.5575 x 10-4
13C 13C/12C V-PDB: Vienna-PeeDee Belemnite” 1.1237 x 10-2
15N 15N/14N N2-atm: atmospheric gas 3.677 x 10-3
18O 18O/16O V-SMOW
V-PDB
2.0052 x 10-3
2.0672 x 10-3
34S 34S/32S CDT: a troilite (FeS) from the
“Canyon Diablo” meteorite
4.5005 x 10-2
The isotope abundance ratios measured and their
internationally accepted reference standards

Isotope Ratio
Measured
Standard Abundance Ratio
(R) of reference
standard
2H (D) 2H/1H (D/H) V-SMOW: “Vienna-Standard
Mean Ocean Water”
1.5575 x 10-4
13C 13C/12C V-PDB: “Vienna-PeeDee
Belemnite” [a fossil]
1.1237 x 10-2
15N 15N/14N N2-atm: atmospheric gas 3.677 x 10-3
18O 18O/16O V-SMOW
V-PDB
2.0052 x 10-3
2.0672 x 10-3
34S 34S/32S CDT: a triolite (FeS) from the
“Canyon Diablo” meteorite
4.5005 x 10-2

Isotope Ratio Measured Standard Abundance Ratio of
reference standard
(w/ 95% CI)
2H (D) 2H/1H (D/H) V-SMOW 1.5575 x 10-4 ± .001
13C 13C/12C V-PDB 1.1237 x 10-2 ± .0009
15N 15N/14N N2-atm 3.677 x 10-3 ± .00081
18O 18O/16O V-SMOW
V-PDB
2.0052 x 10-3 ± .00043
2.0672 x 10-3 ± .0021
17O 17O/16O V-SMOW
V-PDB
373 x 10-6 ± 15
379 x 10-6 ± 15
34S 34S/32S CDT 4.5005 x 10-2
These
values are
the ratios
of atoms in
the
standards
and reflect
the very low
abundance
of the
heavier
isotope

Some other international standards of known  value:
Standard Light Antarctic Precipitation (SLAP) with values:
D = -428‰ 18O = -55.5‰
Greenland Icesheet Precipitation (GISP) with values:
D = -189.7‰ 18O = -24.8‰
Standards

Working standards are:
 used on a regular (daily) basis
 homogeneous
 well matched to your analyses
 easily obtained or made
 easily corrected back to the international standards
Working standards
The internationally accepted reference standards are
obviously in limited supply, expensive, and cannot be used
as the daily reference standard in labs around the world.
Instead isotope labs employ WORKING STANDARDS.

1.0860% 13C = 13C -23‰
1.0805% 13C = 13C -28‰
delta notation
Those same two leaves have more interpretable isotope
“values” in delta notation.

delta notation
A quick note, to be elaborated on in lecture 5:
 You can’t do chemical calculations with  units.
 They are just for comparative purposes.
 That said, for small ranges of  units “you are
allowed” to be sloppy.

Xheavy Xheavy
Xheavy + Xlight Xtotal
Where X is the FRACTION of the heavy or light isotope
in a mixture.
Atom % notation
 Unlike delta notation, atom % notation does not accentuate
small changes in isotope abundance.
 You will NOT see this notation used in the NATURAL
ABUNDANCE stable isotope literature
 You WILL see this notation used if you are working with
ENRICHED stable isotope methods
•100 = •100
Atom % =

Using and
referring to the
delta values

a LIGHTER sample contains more of the lighter isotope,
relative to another sample
a HEAVIER samples contains more of the heavier isotope,
Some comparative terms:
LIGHT vs. HEAVY SAMPLES
DEPLETED vs. ENRICHED SAMPLES
a sample “DEPLETED” IN THE HEAVY ISOTOPE contains
less of the heavy isotope and more of the light isotope,
a sample “ENRICHED” IN THE LIGHT ISOTOPE contains
more of the light isotope and less of the heavy isotope,

Using the D signature in H2O as an example:
0
-200
-400
D
(‰)
 isotopically heavier
 enriched in D (2H)
 depleted in H
 isotopically lighter
 depleted in D (2H)
 enriched in H
such values are found in
warm climates, at low
elevation and low
latitudes, evaporated
water
such values are found in
cold climates, at high
elevation and high
latitudes

Some causes of
variation in stable
isotope values

Isotope Effects
Urey’s Axiom: “The heavy isotopes concentrate in the
compound in which the element is most strongly held”
If Urey is correct then this implies that issues such as:
 Bond-strength,
 Mass of an element, isotope or atom,
 Rates of a chemical reaction (chemical behavior),
 System properties (open vs. closed),
 Etc. …….
Could all have effects on isotope distributions in the materials
we measure and help explain the variation in stable isotope
composition (e.g., variation in ).

1. Chemical properties of any element are largely
determined by the number and configuration of
electrons (e-)
 Since isotopes have the same number and
configuration of electrons . . . . .
isotopes have the same chemical properties
13CO2 is chemically identical to 12CO2
Key points about isotopes

1. isotopes have the same chemical properties
2. However, isotopes differ in then number of neutrons, N
they possess, and therefore in mass
How do mass differences lead to
variation is isotope abundance?
Key points about isotopes
Mass differences
influence chemical BEHAVIOR
in reactions or mixtures

Isotope mass effects
Differences in mass influence:
 As we’ll see next, for water composed of different
isotopes this has a large, measurable, and significant
influence.
Lighter isotopes react faster. Therefore different
isotopes involved in a chemical reaction display
differential representation in different phases of the
reaction
2. The PHYSIO-CHEMICAL properties of molecules
composed of different isotopes
That is, factors including vapor pressure, boiling
temperature, freezing point, and melting point are
affected by the isotope composition of a molecule.
1. The RATES at which the isotopes react

Property H2
16O D2
16O H2
18O
Density (20ºC, in g cm-2) 0.997 1.1051 1.1106
Temperature of greatest density (ºC) 3.98 11.24 4.30
Melting point (@760 Torr, in ºC) 0.00 3.81 .028
Boiling point (@760 Torr, in ºC) 100.00 101.42 100.14
Vapor pressure (@100ºC, in Torr) 760.00 721.60 758.07
Viscosity (@20ºC, in centipoise) 1.002 1.247 1.056
Molar volume (@20ºC, in cm3/mole) 18.049 18.124 18.079
Characteristic physical properties of H2
16O, D2
16O, H2
18O
(from Hoefs 1973, 1997)
Physio-chemical differences

Interatomic distance
Isotope effect associated with zero-point energy
ABSOLUTE ZERO
ZERO POINT ENERGY
LEVELS (ZPEs)
D-D
H-H
DISSOCIATED ATOMS
{Morse Potential Curve}
Differences in ZPEs are the
fundamental cause of equilibrium
isotope fractionation

Interatomic distance
Isotope effect associated with zero-point energy
D-D
H-H
EL = 103.2
EH = 105.3
THESE VALUES
ARE THE AMOUNT
OF ENERGY
REQUIRED TO
BREAK THE BOND;
MORE ENERGY IS
NEEDED TO BREAK
THE D-D BOND
THAN THE H-H
BOND, LEADING
TO ISOTOPE
EFFECTS
DISSOCIATED ATOMS

In summary:
 Bond strengths are proportional to isotope mass, so an
isotope with a higher mass has a higher bond strength
 Molecules with heavier isotopes will be more stable than
light isotopes but diffuse more slowly
 Higher vibrational frequency, the stretching and
compressing of chemical bonds between atoms, leads to
a higher zero point energy and lower stability
Therefore, partial vaporization of a liquid pool will lead
to increased concentration of the lighter isotope in the
vapor phase

 Differences in mass also influence the RATES
at which the isotopes react
 The lighter isotope reacts at a faster
rate,leading to a heavier  value in the
remaining substrate relative to the product.
Reaction rate differences
-- Therefore, differences in MASS influence
RATES and lead to ISOTOPE FRACTIONATION

Fractionation
 Fractionation can be caused by either
BI-DIRECTIONAL or UNIDIRECTIONAL
reactions
 Both the differences in physiochemical
properties and reaction rates lead to the
REDISTRIBUTION of ISOTOPES
 This process is known as FRACTIONATION

Types of fractionation
1. Exchange/equilibrium [BI-directional]
• Complete back-reaction
• Product/reactant offset by constant
fractionation factor
2. Kinetic [UNI-directional] = “biological”
• Incomplete back-reaction (extreme case-
Rayleigh distillation)
• Product and reactant  can evolve in concert
(closed system), or product composition
determines reactant composition (open
system)
3. Transport/Diffusion [UNI-directional]
• Subset of kinetic fractionation reactions
involving flux along a concentration gradient

BI-DIRECTIONAL REACTIONS:
 Known as EQUILIBRIUM FRACTIONATION
 In such a reaction the difference in  value
between the two pools REMAINS CONSTANT
when there is CONTINUOUS EXCHANGE
between the substrate and the product
Fractionation
 Differences in physio-chemical properties
and sometimes reaction rates (very fast) allow
bi-directional exchange of isotopes

Fractionation
An example on an EQUILIBRIUM REACTION:
CO2 + H2O  H2CO3
Or alternatively: CO2  H2O
since we are interested in the exchange of oxygen atoms
between CO2 and H2O
Initially the H2O and CO2 have
different isotope compositions, but
as they exchange 18O and 16O’s back
and forth they reach an equilibrium. If
fractionation occurs that the concentration
of each isotope species will not be the same in
both the H2O and CO2 pools [in this case,if the
initial 18O of H2O is –12.95‰ the CO2’s 18O
will be 28.83‰ - we’ll see this next]

UNI-DIRECTIONAL REACTIONS:
 Known as KINETIC FRACTIONATION
 Referred to as DISCRIMINATION if it is
biologically (enzyme mediated) fractionation
Fractionation
 Differences in physio-chemical properties and
reaction rates never result in uni-directional
exchange of isotopes (there is no back-reaction)

Attaching a number
to “fractionation”

The  values of the substrate and the product
are related to one another through a:
FRACTIONATION FACTOR, a
a defines the relationship between the
substrate (A) and product (B) in either an
equilibrium or kinetic reaction such that,
aAB= RA / RB [R is the isotope ratio]
Fractionation Factors

If a = 1, no fractionation is occurring
If a > 1, there is more of the heavier isotope in
the substrate than before the reaction
began
If a < 1, there is more of the lighter isotope in
the substrate than before the reaction
began

aAB = [((RA/RS) –1)•1000] + 1000
[((RB/RS) –1)•1000] + 1000
= [(1000•RA / 1000•RS) – 1000] + 1000
[(1000•RB / 1000•RS) – 1000] + 1000
= (1000•RA / 1000•RS)
(1000•RB / 1000•RS)
= RA / RB = (1000 + A) / (1000 + B)
How to relate a and  values:
Derivation:
We know: aAB = RA/RB
In addition: aAB = (1000 + A) / (1000 + B)
And since: A = ((RA/RS) –1)•1000
Actual value

In other words you can calculate a using:
aAB = RA/RB
aAB = (1000 + A) / (1000 + B)
-or-

 With kinetic fractionation it is the same idea, except
aAB = k1 / k2, where k1 and k2 are the RATE
CONSTANTS for the two isotopic species
 With an equilibrium equation, a is really an
EQUILIBRIUM CONSTANT - at equilibrium, it will tell
you the distribution of isotopes between two species.
 In a multi-step process, kinetic fractionations are NOT
ADDITIVE
 In a multi-step process, equilibrium fractionations are
ADDITIVE

Fractionation
Adding isotope stoichiometry to our equilibrium reaction example, we get:
(CO16O)gas + (H2
18O)liquid <=> (CO18O)gas + (H2
16O)liquid
 this is the equilibrium equation for each atom
 you need to empirically determine the quantities of each species
 once you have these numbers, you can calculate the fractionation factor,
because:
K = ((CO18O)g•(H2
16O)l) / ((CO16O)g•(H2
18O)l)
= (18O/16O)g/(18O/16O)l
= RA / RB or
a = RA / RB

Fractionation Factors…
What is the a-constant in our equilibrium example?
H2O  CO2
where: 18OH2O = -12.95‰
18OCO2 = 28.83‰
therefore: RH2O = 0.001979
RCO2 = 0.002063
(18O/16O)water RA 0.001979
(18O/16O)carbon dioxide RB 0.002063
= = 0.95939
=

Converting delta units to atom%, of the heavier isotope:
Switching between delta units and atom %
+ 1
100
1
* RR
atom% =
On a spreadsheet: atom% = 100/((1/(((/1000)+1)*RR))+1)
For 13C: RR = 0.0112372
15N: RR = 0.0036765
SMOW 2H RR = 0.00015575
18O PDB RR = 0.002067
18O SMOW RR = 0.0020052
34S RR = 0.045005
(Colorado Plateau Stable
Isotope Lab Web Site)
(Europe Sci. Handout)
(Finnigan MAT Isodat Manual)
+ 1

1000

Calculating RA from atom%
You’ve now calculated Atom% 18O
Atom% 16O = 1 – Atom% 18O
RA = Atom% 18O / Atom% 16O

In our kinetic example: CO2 + H2O  carbohydrate
What is the a-constant of the enzyme?
If the CO2 being used has a value of –12.4‰ and
the carbohydrates have a value of -28‰, we can
calculate that they have atomic ratios of 0.01110
and 0.01092 respectively.
Next:
(13C/12C)carbon dioxide RA 0.01110
(13C/12C)carbohydrate RB 0.01092
= = 1.01605
=

There are many other terms which tell you the ‘per mil’
difference between compound A and compound B.
 Some are used in the biological literature and others in
the geological literature.
 Although the numbers they yield are not identical, they
are close approximations of one another.
 When you work up numbers it is very important that you
indicate which calculation you are using.
More fractionation terminology

By definition: AB = A - B
 and you should therefore use the
previous equations to obtain A and B
from a to calculate AB

Isotopic enrichment
a. In the geological literature: eAB = (aAB – 1)•1000
b. In the biological literature: eAB = 103lnaAB
Isotopic separation (big Delta, )
a. In the geological literature: AB = 103lnaAB  a – b
Isotope discrimination
a. Used in the biological literature and refers specifically to enzyme-
mediated fractionation where A is the source and B is the product
b. AB = (aAB – 1)•1000
It is much better to use the (aAB – 1)•1000 calculation. There is no mathematical reason to use an
equation with “ln”
By definition: AB = A - B
 and you should therefore, use the previous equations to
obtain A and B to calculate AB
But you will also see a jumble of other calculations, like:

aAB (aAB–1)•1000 1000*lnaAB A - B
Equilibrium
example
0.95939 - 42.33 - 40.61 - 41.77
Kinetic
example
1.01605 16.05 15.92 16.4
Just to compare some  numbers:
It is very important to know what
terminology is being used!

TEMPERATURE:
A key cause for
variation in a

1.0092
1.074
a18O = [18O / 16O]Liquid
[18O / 16O]Vapor
1.0092 = 9.2‰
aD = [D / H]Liquid
[D / H]Vapor
1.0740 = 74‰
At 20º:
Temperature dependence of a

1.0055
1.038
a18O = [18O / 16O]Liquid
[18O / 16O]Vapor
1.0055 = 5.5‰
aD = [D / H]Liquid
[D / H]Vapor
1.038 = 38‰
At 80º:
1.0092
1.074
Temperature dependence of a

Tying together
isotope fractionation
concepts:
Rayleigh distillation

Rayleigh distillation
• Rayleigh fractionation occurs when a parent mass is
depleted by equilibrium fractionation to a phase
continually removed. The  values of all elements that
show mass dependent fractionation are affected; the
process occurs in all natural systems.
• The equation describing Rayleigh processes is:
R = R0f(1-a)
R and R0 are the ratios at t and at t=0
f is the fraction remaining at t
a is the fractionation factor
“Condensation example”

Rayleigh distillation is an
EQUILIBRIUM
FRACTIONATION process
which creates differences in 
values
This fractionation is due to
the different PHYSIO-
CHEMICAL BEHAVIORS of the
isotopes
WATER & Rayleigh distillation
Rayleigh distillation describes
the observed patterns of
progressive ISOTOPE
FRACTIONATION such as when
a liquid pool evaporates (e.g.
during cloud formation)
This is a classic Rayleigh
Plot; A, B and C are for
an OPEN system; D and E
for a CLOSED system

As Rayleigh distillation
proceeds, the isotope
values of both the
accumulated vapor mass
and the remaining water
change. The pattern is
dependent on whether
the system is “OPEN” or
“CLOSED”
In this example ∆18O
is -9.8‰ (a = 1.0098)
“Evaporation example”

D = 18O of water in a
CLOSED system
E = 18O of vapor in a
CLOSED system” E
D
In a closed system,
the vapor pool is in
continuous contact
with the liquid pool

a
a
a
E
D
In a CLOSED system the
two pools never differ by
more than a because as
distillation proceeds, the
isotopes in the two pools
will always equilibrate
with one another

A = remaining water in
OPEN system (liquid)
B = instantaneous vapor
in OPEN system
C = accumulated vapor
fraction being removed
from the OPEN system
A
B
C
In an open system, the
vapor is removed as soon
as it forms.
The initial a is -9.8
}

A
B
C
However, in an OPEN
system, since the
accumulated vapor (C) is not
in contact with (A), these
two pools are related to one
another by a only at the
start of the distillation
process.
a
a
a
a
a
In either an OPEN or a
CLOSED system, the
remaining liquid pool (A) and
instantaneous vapor (B) must
be related to one another by
the fractionation factor, a

For both systems, if
distillation is complete,
the accumulated vapor
mass (C & E) must have a
 value equal to the initial
water mass
However OPEN vs.
CLOSED systems display
different instantaneous 
offsets betweens the two
pools

 in cloud vapor and
condensate plotted as
a function of the
fraction of remaining
vapor in the clouds
follows the same
Rayleigh process as
evaporation
Rayleigh fractionation from rainfall
rain
cloud
total
rain
“Condensation example”

(liquid H2O)
18O in a cloud vapor and
condensate plotted as a
function of the fraction of
remaining vapor in the clouds
for a Rayleigh process.
The increase in
fractionation with the
decreasing temperature
is taken into account
Change in cloud temperature as condensate forms
A twist: as evaporation
proceeds, the temperature
of the remaining cloud
decreases.

Uni-directional reaction patterns
Rayleigh distillation can also
be applied (similar rules) to
UNI-DIRECTIONAL (Kinetic)
REACTIONS (but they act the
opposite from what we just saw)
With uni-directional
reactions the important
distinction is between
FINITE and INFINITE
amounts of substrate
ONCE AGAIN
CUMULATIVE
PRODUCT
INSTANTANEOUS
PRODUCT
SUBSTRATE

a a a
If INFINITE amounts of
substrate exist, the
conversion of substrate to
product does not
noticeably change the 
value of the remaining
substrate (now ‘open’)
Therefore the  values of
the substrate and product
remain constant over time
and are always related by
the fractionation factor a

If FINITE amounts of
substrate exist, the
creation of product will
change the  value of the
remaining substrate (now
‘closed’)
a
Therefore, the value of
both the substrate and the
instantaneous product will
change over time, although
they will always be related
to one another by the
fractionation factor a
a
a

How can Stable
Isotopes be used
as a tool?
On to some case studies in isotope ecology

Mistake Recommended Expressions Explanation
Referring to the symbol  as
del
Since the time of the early Greeks, the name
of this symbol has been and remains delta
The word del describes either of two things in mathematics:
an operator () of the partial derivative sign ()
13C composition 13C value; or carbon isotope composition A composition of values is not possible
Isotopically depleted water 18O (or D) depleted water Water is not depleted (or enriched) in isotopes
Heavy (light) 18O values High (low) 18O values As number,  values are either high or low
Depleted 13C value low 13C value (relative to another value) 13C values are numbers and cannot be depleted
Oxygen isotopes in chert;
inferred from carbon isotopes;
isotopes of soil water
Oxygen isotope ratio (composition) of chert;
inferred from carbon isotope measurements;
isotopic composition of soil water
Such mistakes are a carryover from loose oral communication
The isotopic composition of
water was 18O = - 4.3‰
The 18O value of the water was - 4.3‰ A matter of redundancy
The isotopic value changed;
the carbon value changed
The isotopic composition changed; the 13C
value changed
The phrase “isotopic value” is ambiguous. Does it mean a
ratio? A delta value?
Enriched (depleted)
carbonates
Depleted carbon source
Isotopically heavy (light) carbonates;
(relatively) 18O-rich carbonates;
(relatively) 13C-poor carbonates
Low 13C source; source with a low 13C value
These phrases culled from the literature make no sense. More
importantly, the words enrich and deplete are overused and
much abused. These words should be reserved for describing a
process that changes the content of the heavy isotope of some
element in the substance being considered
The isotopic signature of the
rock was 18O = 5.7 ‰
The 18O value of the rock was 5.7 ‰. Thus
this rock has the oxygen isotope signature of
the mantle
The word signature should apply to the isotopic composition
of a significant reservoir like the mantle, the ocean, or a major
part of the system being studied, not to the isotopic
composition of ordinary samples
15, 18 , 13 , etc.
15, 18, 13, etc.
-15, -13 , -18 etc.
15N, 18O , 13C, etc. Introduction of new symbolism that saves one character of
space is unnecessary at best and confusing at worst.
The mineral equilibrated with
the fluid
The mineral exchanged with the fluid Isotopic equilibrium, may not have been attained during the
process being described
Sulfur was measured The sulfur isotope composition was measured Confusing because the sulfur content of a rock or mineral may
be understood

Referring to the
symbol  as del
Since the time of the early
Greeks, the name of this
symbol has been and
remains delta
The word del describes either of
two things in mathematics: an
operator () of the partial
derivative sign ()

del
13C composition 13C value; or carbon
isotope composition
A composition of values is not
possible

del
Isotopically
depleted water
18O (or D) depleted water Water is not depleted (or enriched)
in isotopes

del
Heavy (light)
18O values
High (low) 18O values As number,  values are either high
or low

del
Depleted 13C
value
low 13C value (relative to
another value)
13C values are numbers and
cannot be depleted

del
Oxygen isotopes
in chert; inferred
from carbon
isotopes; isotopes
of soil water
Oxygen isotope ratio
(composition) of chert;
inferred from carbon
isotope measurements;
isotopic composition of
soil water
Such mistakes are a carryover
from loose oral communication

del
The isotopic
composition of
water was 18O =
- 4.3‰
The 18O value of the
water was - 4.3‰
A matter of redundancy

del
water was 18O = - 4.3‰
The isotopic
value changed;
the carbon value
changed
The isotopic composition
changed; the 13C value
changed
The phrase “isotopic value” is
ambiguous. Does it mean a ratio? A
delta value?

del
water was 18O = - 4.3‰
value changed
Enriched
(depleted)
carbonates
Depleted carbon
source
Isotopically heavy (light)
carbonates;
(relatively) 18O-rich
carbonates;
(relatively) 13C-poor
carbonates
Low 13C source; source
with a low 13C value
These phrases culled from the
literature make no sense. More
importantly, the words enrich and
deplete are overused and much
abused. These words should be
reserved for describing a process
that changes the content of the
heavy isotope of some element in
the substance being considered

del
water was 18O = - 4.3‰
value changed
Enriched (depleted)
carbonates
Depleted carbon source
Isotopically heavy (light) carbonates;
(relatively) 18O-rich carbonates;
(relatively) 13C-poor carbonates
Low 13C source; source with a low 13C value
These phrases culled from the literature make no sense. More
importantly, the words enrich and deplete are overused and
much abused. These words should be reserved for describing a
process that changes the content of the heavy isotope of some
element in the substance being considered
The isotopic
signature of the
rock was 18O =
5.7 ‰
The 18O value of the rock
was 5.7 ‰. Thus this rock
has the oxygen isotope
signature of the mantle
The word signature should apply
to the isotopic composition of a
significant reservoir like the
mantle, the ocean, or a major part
of the system being studied, not to
the isotopic composition of
ordinary samples

Introduction to Geochemistry

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