Isotopics:

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Isotopics Current Issues in Stable Isotope
Science
BPSC 240 Louis Santiago (2-4951)
santiago_at_ucr.edu Office hours M 1-2 or by
appointment
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SESSION 1. Introduction to Stable Isotopes
1. Introduction to isotopes
2. Isotopes used in ecological studies
3. Stable isotope notation
4. Correct usage of stable isotope expressions
5. Causes of variation in stable isotope
abundances
6. Fractionation factors
7. Rayleigh distillation using fractionation
factors
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Why use stable isotopes?
Non-radioactive TRACERS (of resource type,
origin or flux resource or organismal movements
energy or resource flow) Non-destructive
INTEGRATORS (of system processes of organismal
function of resource tradeoffs spatial and
temporal responses to environment)
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What are isotopes?
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To be or not to be? - A stable isotope that is!
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Partial chart of the elements
Each square represents a nuclide, an isotope
specific atom Atomic number Z
(Protons) Atomic mass Z N (Protons
Neutrons)
8 7 6 5 4 3 2 1
16 8
17 8
18 8
19 8
20 8
15 8
14 8
13 8
16 7
15 7
14 7
12 7
13 7
18 7
17 7
13 6
9 6
10 6
12 6
11 6
14 6
15 6
16 6
8 5
9 5
13 4
12 5
11 5
10 5
Proton Number (Z)
7 4
6 4
9 4
10 4
8 4
11 4
12 4
8 3
7 3
6 3
5 3
9 3
5 2
6 2
3 2
8 2
4 2
3 1
1 1
2 1
0 1 2 3 4 5 6 7
8 9 10 11 12 13
Neutron Number (N)
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Partial chart of the elements
Each row represents nuclides that are isotopes
they share a common number of protons (Z) but
differ in their number of neutrons (N).
8 7 6 5 4 3 2 1
16 8
17 8
18 8
19 8
20 8
15 8
14 8
13 8
16 7
15 7
14 7
12 7
13 7
18 7
17 7
13 6
9 6
10 6
12 6
11 6
14 6
15 6
16 6
8 5
9 5
13 4
12 5
11 5
10 5
Proton Number (Z)
7 4
6 4
9 4
10 4
8 4
11 4
12 4
8 3
7 3
6 3
5 3
9 3
5 2
6 2
3 2
8 2
4 2
3 1
1 1
2 1
0 1 2 3 4 5 6 7
8 9 10 11 12 13
Neutron Number (N)
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Partial chart of the elements
Each row represents nuclides that are isobars
they share a common atomic weight (N Z).
8 7 6 5 4 3 2 1
16 8
17 8
18 8
19 8
20 8
15 8
14 8
13 8
16 7
15 7
14 7
12 7
13 7
18 7
17 7
13 6
9 6
10 6
12 6
11 6
14 6
15 6
16 6
8 5
9 5
13 4
12 5
11 5
10 5
Proton Number (Z)
7 4
6 4
9 4
10 4
8 4
11 4
12 4
8 3
7 3
6 3
5 3
9 3
5 2
6 2
3 2
8 2
4 2
3 1
1 1
2 1
0 1 2 3 4 5 6 7
8 9 10 11 12 13
Neutron Number (N)
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Partial chart of the elements
Each row represents nuclides that are isotones
they share a common number of neutrons (N).
8 7 6 5 4 3 2 1
16 8
17 8
18 8
19 8
20 8
15 8
14 8
13 8
16 7
15 7
14 7
12 7
13 7
18 7
17 7
13 6
9 6
10 6
12 6
11 6
14 6
15 6
16 6
8 5
9 5
13 4
12 5
11 5
10 5
Proton Number (Z)
7 4
6 4
9 4
10 4
8 4
11 4
12 4
8 3
7 3
6 3
5 3
9 3
5 2
6 2
3 2
8 2
4 2
3 1
1 1
2 1
0 1 2 3 4 5 6 7
8 9 10 11 12 13
Neutron Number (N)
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Partial chart of the elements
The shaded squares are stable and the un-shaded
squares are unstable or radioactive nuclides.
8 7 6 5 4 3 2 1
16 8
17 8
18 8
19 8
20 8
15 8
14 8
13 8
16 7
15 7
14 7
12 7
13 7
18 7
17 7
13 6
9 6
10 6
12 6
11 6
14 6
15 6
16 6
8 5
9 5
13 4
12 5
11 5
10 5
Proton Number (Z)
7 4
6 4
9 4
10 4
8 4
11 4
12 4
8 3
7 3
6 3
5 3
9 3
5 2
6 2
3 2
8 2
4 2
3 1
1 1
2 1
0 1 2 3 4 5 6 7
8 9 10 11 12 13
Neutron Number (N)
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Stable isotope trends
3 important points
1. Stable isotopes tend to have an N/Z near 1 for
masses less than 20
2. Stable isotopes tend to have an even Z-number
for masses greater than 20
N

N/Z 1
3. Most biologically important elements have
masses less than 20
Z
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What isotopes are used in ecological studies?
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Average terrestrial abundances of the stable
isotopes of elements used commonly (?),
occasionally (?), and rarely (?) in ecological
studies
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Common isotopes
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
The 10 most common isotopes in the solar system
are H gtgt 4He gtgt 16O gt 12C gtgt 20Ne gt 14N gt 24Mg
gt 28Si gt 56Fe gt 32S
The 10 most common isotopes in the solar system
are H gtgt 4He gtgt 16O gt 12C gtgt 20Ne gt 14N gt 24Mg
gt 28Si gt 56Fe gt 32S
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Terrestrial range
Technical Precision
HEAVIER ISOTOPES ARE RARE!
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Terrestrial range
Technical Precision
HYDROGEN HAS THE LARGEST MASS DIFF BETWEEN ISTOPES
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Terrestrial range
Technical Precision
We analyze gases that contain the isotopes of
interest!
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Terrestrial range
Technical Precision
HYDROGEN HAS A LARGE TERRESTRIAL RANGE, BUT ALSO
A RELATIVELY POOR PRECISION
N ITROGEN HAS A SMALLER TERRESTRIAL RANGE, BUT
BETTER TECHNICAL PRECISION
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How do we express these differences in stable
isotope abundance?
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Stable isotope composition is expressed in d
(delta) notation dR in
Rsample
1 x 1000
Rstandard
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Stable isotope composition is expressed in d
(delta) notation dR in
Rsample
1 x 1000
Rstandard
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Stable isotope composition is expressed in d
(delta) notation dR in
Rsample
1 x 1000
Rstandard
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Stable isotope composition is expressed in d
(delta) notation dR in
Rsample
1 x 1000
Rstandard
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The isotope abundance ratios measured and their
internationally accepted reference standards
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The isotope abundance ratios measured and their
internationally accepted reference standards
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The isotope abundance ratios measured and their
internationally accepted reference standards
These values are the ratios of atoms in the
standards and reflect the very low abundance of
the heavier isotope
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Standards
Some other international standards of known d
value Standard Light Antarctic Precipitation
(SLAP) with values dD -428 d18O
-55.5 Greenland Icesheet Precipitation (GISP)
with values dD -189.7 d18O -24.8
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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.

• 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

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Atom notation
Xheavy Xheavy Xheavy
Xlight Xtotal Where X is the FRACTION of the
heavy or light isotope in a mixture.
Atom
100
100

• ? 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

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How do we use and refer to the delta values?
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a LIGHTER sample contains more of the lighter
isotope, relative to another sample a HEAVIER
samples contains more of the heavier isotope,
relative to another sample
a sample DEPLETED IN THE LIGHT ISOTOPE contains
less of the light isotope and more of the heavy
isotope, relative to another sample a sample
ENRICHED IN THE LIGHT ISOTOPE contains more of
the light isotope and less of the heavy isotope,
relative to another sample
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Using the dD signature in H2O as an example
0

• isotopically heavier
• enriched in D (2H)
• depleted in H

dD ()
-200

• isotopically lighter
• depleted in D (2H)
• enriched in H

-400
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So what causes isotope variation?
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Key points about isotopes

• 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
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Key points about isotopes
1. isotopes have the same chemical properties 2.
However, isotopes differ in N (number of
neutrons), and therefore in mass
How do mass differences lead to variation is
isotope abundance?
They influence chemical BEHAVIOR in reactions or
mixtures
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Isotope mass effects
Differences in mass influence
1. 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.

• As well see next, for water composed of
  different isotopes this has a large, measurable,
  and significant influence

2. The RATES at which the isotopes react
Lighter isotopes react faster. Therefore
different isotopes involved in a chemical
reaction display differential representation in
different phases of the reaction
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Physio-chemical differences
Characteristic physical properties of H216O,
D216O, H218O (from Hoefs 1973, 1997)
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Physio-chemical differences
Characteristic physical properties of H216O,
D216O, H218O (from Hoefs 1973, 1997)
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Physio-chemical differences
Isotope effect associated with zero-point
energy (OR Why does H216O have a higher vapor
pressure?)
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Physio-chemical differences
Isotope effect associated with zero-point
energy (OR Why does H216O have a higher vapor
pressure?)
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 A
LOWER VAPOR PRESSURE FOR D-D
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Physio-chemical differences
In summary
? Higher vibrational frequency, the stretching
and compressing of chemical bonds between
atoms, leads to a higher zero point energy and
lower stability
? Isotopes with a higher mass has greater bond
strength
? Molecules with heavier isotopes will be more
stable than light isotopes
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Reaction rate differences
? Differences in mass also influence the RATES at
which the isotopes react
? The lighter isotope reacts at a faster
rate,leading to a heavier d value in the
remaining substrate relative to the product.
-- Therefore, differences in MASS influence RATES
and lead to ISOTOPE FRACTIONATION
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Fractionation
? Both the differences in physiochemical
properties and reaction rates lead to the
REDISTRIBUTION OF ISOTOPES
? This process is known as FRACTIONATION
? Fractionation can be caused by either
BI-DIRECTIONAL or UNIDIRECTIONAL reactions
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Fractionation
BI-DIRECTIONAL REACTIONS
? also known as EQUILIBRIUM FRACTIONATION
? Differences in physio-chemical properties
always allow bi-directional exchange of isotopes
? Differences in reaction rates sometimes result
in the bi-directional exchange of isotopes
? In such a reaction the difference in d value
between the two pools REMAINS CONSTANT only
when there is CONTINUOUS EXCHANGE between the
substrate and the product.
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Fractionation
UNI-DIRECTIONAL REACTIONS
? also known as KINETIC FRACTIONATION
? Differences in physio-chemical properties never
result in uni-directional exchange of isotopes
? Differences in reaction rates sometimes
result in uni-directional exchange of isotopes
? In such a reaction the difference in d value
between the two pools ALWAYS REMAINS CONSTANT.
? referred to as DISCRIMINATION if it is
biologically (enzyme mediated) fractionation
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How does one attach a number to fractionation?
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Fractionation Factors
The d 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
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Fractionation Factors
If a 1, no fractionation is occurring
If a gt 1, there is more of the heavier isotope in
the substrate than before the reaction began
If a lt 1, there is more of the lighter isotope in
the substrate than before the reaction began
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Fractionation Factors
How to relate a and d values
aAB (1000 dA) / (1000 dB)
Derivation
since dA ((RA/RS) 1)1000   aAB ((RA/RS)
1)1000 1000 ((RB/RS) 1)1000
1000   (1000RA / 1000RS) 1000 1000
(1000RB / 1000RS) 1000 1000  
(1000RA / 1000RS) (1000RB /
1000RS)   RA / RB (1000 dA) / (1000 dB)
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Fractionation Factors
How to determine a from an equilibrium equation
aA bB cC dD
Consider a generic chemical equation
The equilibrium constant would be
K1/n (CcDd)/(AaBb)
Now instead of different chemical species,
consider two phases of a compound which exchange
isotopes to establish chemical equilibrium
(H218O)vapor (H216O)liquid (H216O)v
(H218O)l
Substituting in
K1/n ((H216O)v(H218O)l) / ((H218O)v(H216O)l)
(18O/16O)v/(18O/16O)l RA / RB
aAB
If n 1, as in many simple compounds, then aAB
K
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Fractionation Factors
? With an equilibrium equation, a is really an
EQUILIBRIUM CONSTANT - at equilibrium, it will
tell you the distribution of isotopes between
two species.
? 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
? In a multi-step process, equilibrium
fractionations are ADDITIVE
? In a multi-step process, kinetic fractionations
are NOT ADDITIVE
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More fractionation terminology
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.
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More fractionation terminology
Isotopic enrichment a. In the geological
literature eAB (aAB 1)1000 b. In the
biological literature eAB 103lnaAB   Isotopic
separation (big Delta, D) a. In the geological
literature DAB 103lnaAB ? da db 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. DAB (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
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What causes a to vary?
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Temperature dependence of a
This graph shows that fractionation increases as
the temperature decreases!
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Temperature dependence of a
At 20º
1.0092
a18O 18O / 16OLiquid
18O / 16OVapor 1.0092 9.2
aD D / HLiquid D / HVapor
1.0740 74
1.074
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Temperature dependence of a
At 80º
1.0092
a18O 18O / 16OLiquid
18O / 16OVapor 1.0055 5.5
1.0055
aD D / HLiquid D / HVapor
1.038 38
1.074
1.038
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Tying together isotope fractionation
concepts Rayleigh distillation
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Rayleigh distillation
Rayleigh distillation describes the observed
patterns of ISOTOPE FRACTIONATION as a liquid
pool evaporates such as in cloud formation
Rayleigh distillation is an EQUILIBRIUM
FRACTIONATION process which creates differences
in d values
This fractionation is due to the different
PHYSIO-CHEMICAL BEHAVIORS of the isotopes.
60
Rayleigh distillation
As Rayleigh distillation proceeds, the signatures
of both the accumulated vapor mass and the
remaining water change. The pattern is dependent
on whether you have an OPEN or a CLOSED
system.
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Rayleigh distillation
In an open system, the vapor is removed as soon
as it forms.
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
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Rayleigh distillation
In a closed system, the vapor pool is in
continuous contact with the liquid pool
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Rayleigh distillation
For all systems, if distillation is complete, the
accumulated vapor mass must have a d value equal
to the initial water mass
However OPEN vs. CLOSED systems display different
instantaneous d offsets betweens the two pools
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Rayleigh distillation
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
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
B
C
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Rayleigh distillation
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
D
E
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Uni-directional reaction patterns
Rayleigh distillation is an equilibrium process.
However, similar rules apply to UNI-DIRECTIONAL
REACTIONS.
With uni-directional reactions the important
distinction is between FINITE and INFINITE
amounts of substrate
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Uni-directional reaction patterns
If FINITE amounts of substrate exist, the
creation of product noticeably changes the d
value of the remaining substrate
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
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Uni-directional reaction patterns
If INFINITE amounts of substrate exist, the
conversion of substrate to product does not
noticeably change the d value of the remaining
substrate
Therefore the d values of the substrate and
product remain constant over time and are always
related by the fractionation factor a
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Change in cloud temperature as condensate forms
d18O in a cloud vapor and condensate plotted as a
function of the fraction of remaining vapor in
the clouds for a Rayleigh process.
(liquid H2O)
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How can Stable Isotopes be used as a tool?
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