EES 471 Chemistry Stable Isotope Chemistry Theory Questions

Oxygen isotope exchange at 500˚C in a closed-system containing differing relativeproportions of quartz and garnet (almandine)
A. Consider the mass-balance relationships controlling garnet O-isotope composition in a closed
system with coexisting, fully equilibrated garnet and quartz (SiO2), using a fractionation factor
for 500˚C. You should produce a plot of the d18O of the garnet (y-axis; assuming initial garnet
d18OVSMOW = +5‰ for all calculations) as a function of the garnet/(garnet+quartz) O massbalance and the initial (pre-heating) d18O of the quartz (ranging from -15 to +25‰). Use the O
mass-balance as the x-axis [(moles of garnet O)/(moles garnet O + moles of quartz O)] and plot
the garnet d18O for differing initial quartz d18O. Assume that the garnet is pure almandine in
composition (that is, the Fe+2-rich version of garnet, that is: Fe2+3Al2Si3O12).
B. Carefully evaluate which fractionation factors to use in this consideration, stating your
preferred source and why you selected it.
C. For “real rocks” containing only these two minerals (such rocks do exist) that you believe
experienced prolonged heating at 500˚C, how would you go about demonstrating O isotope
equilibrium?
D. For “real rocks” containing the two phases, what would you expect for the case where O
isotope equilibrium is not achieved during this heating (and how could you test this?)?
Z.D. Sharp Principles of Stable Isotope Geochemistry
Abstract
Principles of Stable Isotope Geochemistry is written as a textbook to accompany a
one semester course in Stable Isotope Geochemistry. There are 13 chapters, each dealing
with a specific subtopic of the field. Other than Chapters 1 and 2 – introduction and
definitions – most of the remaining chapters can be read without reliance on the
preceding ones. It is also hoped that the book will serve as a general reference volume
for researchers in the field.
Principles of Stable Isotope Geochemistry has been organized in such a way that
major concepts are explained and accompanied by numerous examples. In most cases, the
first published examples are used for illustration, giving both a broad base of
understanding and an appreciation for the historical development of the field. Chapters
are organized according to broad classifications. In some cases this is done by discipline
such as Chapter 4 – Hydrology and in others by isotope, such as Chapter 10 – Sulfur.
The new revised version is online. In this way, it can be modified as new
advances are made in the field. Comments regarding errors, omissions or suggestions for
improvements are welcome in order to keep the book up to date. This new online version
is free of charge, available in PDF format. A hardcopy is also available.
Table of Contents
Chapter 1: Introduction
Chapter 2: Terminology, Standards and Mass Spectrometry
Chapter 3: Equilibrium Isotope Fractionation
Chapter 4: The Hydrosphere
Chapter 5: The Oceans
Chapter 6: Biogenic Carbonates: Oxygen
Chapter 7: Carbon in the Low-Temperature Environment
Chapter 8: Low Temperature Minerals, Exclusive of Carbonates
Chapter 9: Nitrogen
Chapter 10: Sulfur
Chapter 11: Igneous Petrology
Chapter 12: Metamorphic Petrology
Chapter 13: Extraterrestrial Materials
Appendix 1: Standard Reference Materials for Stable Isotopes
Appendix 2: Sample calculation of the correction procedure for adjusting measured
isotope data to accepted IAEA reference scales
Z.D. Sharp Principles of Stable Isotope Geochemistry
About the cover: A Metropolitan Vickers MS 2 mass spectrometer, bought by the Ecole
de Géologie, Nancy France in 1958 for analyses of Pb, and later Rb/Sr at the CNRS,
Nancy. Similar mass spectrometers were used for oxygen isotope analyses. The mass
spectrometer consists of a copper vertical tube pumped by a diffusion pump (bottom
center). The flight tube cuts through the central vacuum tube, allowing it to be pumped
essentially at both ends. This is the predecessor of the early VG Micromass
spectrometers. Photograph by Andreas Pack.
Sharp, Z.D. Principles of Stable Isotope Geochemistry
About the cover: A Metropolitan Vickers MS 2 mass spectrometer, bought by the Ecole
de Géologie, Nancy France in 1958 for analyses of Pb, and later Rb/Sr at the CNRS,
Nancy. Similar mass spectrometers were used for oxygen isotope analyses. The mass
spectrometer consists of a copper vertical tube pumped by a diffusion pump (bottom
center). The flight tube cuts through the central vacuum tube, allowing it to be pumped
essentially at both ends. This is the predecessor of the early VG Micromass
spectrometers. Photograph by Andreas Pack.
7/4/2017 About the cover
Chapter 1
INTRODUCTION
Contents
1.1 About this book ………………………………………………………………………………………………. 1
1.2 Historical Background …………………………………………………………………………………….. 1
1.3 Scope of the Discipline ……………………………………………………………………………………. 5
1.3.1 What are stable isotopes? …………………………………………………………………………… 6
1.3.2 Which elements and why? …………………………………………………………………………. 8
1.4 Abundances of the Rare Isotopes of Light Elements ……………………………………………. 9
1.5 Characteristics of Elements that Undergo Significant Isotopic Fractionation………… 10
1.6 Applications in the Earth Sciences ………………………………………………………………….. 12
1.7 Isotope Effects ……………………………………………………………………………………………… 13
1.7.1 Kinetic isotope effects……………………………………………………………………………… 13
1.7.2 Equilibrium isotope effects ………………………………………………………………………. 14
References …………………………………………………………………………………………………………. 16
Sharp, Z.D. Principles of Stable Isotope Geochemistry
Chapter 1
INTRODUCTION
1.1 About this book
The first edition of this book was written as a general introduction to stable
isotope geochemistry. It was meant primarily as a guide and general resource for an
upper division and graduate level stable isotope course. Since it was first published in
2007, the scope of stable isotopes has grown tremendously. New fields, not envisioned in
the first edition, have developed and blossomed, and existing fields have grown
considerably. The motivation for the original book was to provide a useful, inexpensive
textbook that could also be used as foundation for new practitioners to the field. However
things are changing so fast that it is impossible to keep up with new developments using
the traditional publishing format. Turn-around times are too long, and the cost to the enduser are too high. This new ‘live’ edition is meant to overcome these problems. The book
is online and freely available to all. Because it is electronic, it can be (and hopefully will
be) modified easily and frequently, so that new developments can be incorporated as they
become available. It is my hope that this ‘live’ version will remain up-to-date and be a
valuable no-cost resource for stable isotope practitioners around the world.
1.2 Historical Background
The published early ‘discussions’ by scientists studying the structure of the atom
and significance of isotopes make for remarkable reading. The early practitioners,
including J.J. Thomson, E. Rutherford, F. Soddy and F.W. Aston, J. Chadwick, G.
Gamow and others were generally concerned with radioactivity – the spontaneous
disintegration of large atoms to smaller fragments. But in their efforts to understand the
structures of atoms, they were also keenly aware of departures of elemental masses from
Aston’s ‘whole number rule’ – the idea that all elements have masses that are multiples of
the mass of hydrogen. In a round-table discussion by E. Rutherford, F. W. Aston, J.
Chadwick, and others, Rutherford states: “The essential point brought out in the earlier
work of Dr. Aston was that the masses of the elements are approximately expressed by
whole numbers, where oxygen is taken as 16-with the exception of hydrogen itself. But
the real interest, as we now see it, is not the whole number rule1 itself, but rather the
departures from it” (Rutherford et al., 1929). Of particular interest was the element Cl,
with a mass of 35.5. In an earlier ‘discussion’ in 1921, J.J. Thomson stated “Mr. Aston,
who has measured the atomic weight of chlorine by a different method, cannot find any
chlorine – or any other substance – with an atomic weight of 35.5, but he does find
substances with atomic weights of 35 and 37. Accepting the numbers on both sides, there
does not seem to be any explanation other than that either chlorine is a mixture of these
two substances of atomic weight 35 and 37, or else that, in the discharge tube which Mr.
Aston employs to measure the atomic weight, some decomposition or integration – or
both – of the chlorine atom has occurred.” (Thomson et al., 1921). Aston had identified
the two isotopes of Cl, masses 35 and 37. There was no problem with his mass
1
The whole number rule is that the masses of the elements are multiples of the mass of hydrogen or as
Rutherford states above, relative to oxygen with a mass of 16.
1-1
Chapter 1. Introduction
spectrograph! In 1931 James Chadwick published the results of his discovery of the
neutron in the modestly titled paper “Possible existence of a neutron” (Chadwick, 1931),
and the fundamental building blocks of atoms were firmly in place.
The first suggestion that physical chemical processes could cause isotopic
fractionation of light elements in natural substances was made in 1925 by British
scientists H. Briscoe and P. Robinson (Briscoe and Robinson, 1925). Before that time, it
was generally assumed that the isotopic compositions of all substances were
homogeneously distributed throughout the Earth. Briscoe and Robinson observed a
variation in the atomic weight of boron in minerals from various localities. They
proposed that processes like solution, crystallization, melting, and volatilization would
likely cause such isotopic variations in nature. In the following year the eminent Russian
scientist V. Vernadsky suggested that isotopic fractionation of the light elements should
occur in living matter as well, but there were no experimental or natural data to support
this hypothesis at that time. Variations in the hydrogen and oxygen isotope ratios of water
in the hydrologic cycle of the Earth were recognized crudely as early as the mid-1930s on
the basis of precise density measurements (Gilfillan, 1934). In that same decade, H.
Urey2 and his colleagues at Columbia University were conducting experiments and
developing the theory for isotope exchange reactions and equilibria (Urey and Greiff,
1935), and A. Nier and his colleagues at the University of Minnesota were making
significant improvements to Aston’s early mass spectrometer designs, and were
discovering variations in the stable isotope ratios of several light elements in natural
materials (Fig. 1.1).
Probably the first bona fide
application of light stable isotope
measurements to a major geochemical
problem was published by F. Wickman
(1941) who calculated the total amount of
bitumen and coal in the Earth on the basis of
carbon isotope analyses of these materials.
Titles of several articles written in the 1930s
and 1940s show clearly that the power of
stable isotope measurements in resolving
problems in earth science was recognized
long ago by outstanding scientists
throughout the world (Table 1.1).
Light stable isotope geochemistry as
we know it today arguably began in 1946.
During that year, Harold Urey traveled to
several prominent universities in Europe to
deliver a lecture sponsored annually by the
Royal Society of London. Urey presented
results of calculations of the isotopic Fig. 1.1. Nier’s 60° sector mass spectrometer, 1947.
fractionation of stable isotope ratios of the From Rankama (1954).
2
H.C. Urey (1893-1981) won the Nobel Prize in chemistry in 1934 for his discovery of deuterium. He is
considered the father of modern stable isotope geochemistry.
1-2
Sharp, Z.D. Principles of Stable Isotope Geochemistry
light elements among ideal gases and simple aqueous ions from spectroscopic data and
the methods of statistical mechanics. The results of his calculations, published in the now
classic paper entitled The Thermodynamic Properties of Isotopic Substances (Urey, 1947)
remain to this day a valuable resource for isotope fractionation factors of simple
compounds. At this lecture in Zurich in December of 1946, the renowned
crystallographer Paul Niggli wondered if it might be possible to determine the fresh water
or marine origin of ancient deposits of limestone, coral or shells from oxygen isotope
analysis of the carbonate. At that time it was already known that 18O/16O ratios of marine
limestones were about 3% higher than those of the ocean and that ocean water was
isotopically heavier than fresh waters. Prompted by Niggli’s remarks, Urey turned his
attention to the temperature coefficient of the oxygen isotope fractionation between
CaCO3 and H2O. On the basis of estimates made from his calculations, he concluded that
this coefficient might be large enough to determine the temperatures of ancient oceans
from oxygen isotope analyses of CaCO3 in fossil shells. As Urey recounted the story
later: “I suddenly found myself with a geological thermometer in my hands.” And the
games began.
Table 1.1. Selected early publications in stable isotope chemistry and
geochemistry.
Year
Title
Reference
1921
1932
Discussion on isotopes
A hydrogen isotope of mass 2 and its concentration.
1934
1935
The natural separation of the isotopes of hydrogen.
Isotopic exchange equilibria.
1936
The relative atomic weight of oxygen in water and
air.
Isotopic composition of rain water.
Thomson et al. Proc. Roy. Soc. Lond. 99, 87-104
Urey, H.C., Brickwedde, F.G. and Murphy, G.M.,
Phys. Rev. 40, 1.
Dole, M., J. Amer. Chem. Soc. 56, 999.
Urey, H.C. and Greiff, L.J., J.Amer. Chem.
Soc. 57, 321
Dole, M., J. Chem. Phys. 4. 268-275.
1939
1940
1941
1941
1947
1947
1949
A mass spectrometer for routine isotope abundance
measurements
Determination of the isotopic composition of
[hydroxyl] waters in metamorphic rocks and minerals.
On a new possibility of calculating the total amount of
coal and bitumen.
Calculation of equilibrium constants for isotopic
exchange reactions.
The thermodynamic properties of isotopic substances
Natural variations in the isotopic content of sulfur
and their significance.
1950
Isotopic composition of oxygen in silicate rocks.
1951
Carbonate-water isotopic temperature scale.
1951
Relative abundance of oxygen and carbon isotopes in
carbonate rocks.
Variation in the relative abundance of carbon isotopes in
plants.
The geochemistry of the stable carbon isotopes.
1952
1953
Teis, R.V., Compt. Rend. Acad. Sci. U.R.S.S. 23,
674.
Nier, A.O. Rev. Sci. Inst. 11, 212-216
Vernadsky, W.I., Vinogradov, A.P., and
Teis, R.V., Compt. Rend. Acad. Sci. U.R.S.S. 31,
573.
Wickman, F.E., Geol. Fören. i Stockholm
Förh. 63, 419.
Bigeleisen, J., Mayer, M.G. J. Chem. Phys. 15,
261-267.
Urey, H.C. J. Chem. Soc. 562-581.
Thode, H.G., MacNamara, J. and Collins,
C.B., Can. J. Res. 27B, 361.
Baertschi, P., Nature 166, 112.
Baertschi, P. and Silverman, S.R., Geochim.
Cosmochim. Acta 1, 4-6.
Epstein, S., Buchsbaum, R., Lowenstam, H.,
Urey, H.C. J. Geol. 62, 417-426.
Baertschi, P., Nature 168, 288.
Wickman, F.E., Geochim. Cosmochim. Acta, 2,
243.
Craig, H., Geochim. Cosmochim. Acta, 3, 53-92.
1-3
Chapter 1. Introduction
The overall precision of the isotopic measurements required to make temperature
estimates that were meaningful in paleoclimatology was not attainable in the 1940s. At
that time the precision of mass spectrometric measurements of 18O/16O ratios was about a
factor of ten less than required to determine temperatures to ± 0.5oC. In addition, there
was no reproducible technique for extracting CO2 from CaCO3, and there were no
experimental data relating the oxygen isotope fractionation between calcium carbonate
and water to temperature. Urey was not to be deterred from proceeding with this
ambitious project, and he assembled an outstanding group of young scientists to work on
it. This research team included postdoctoral fellow Sam Epstein, doctoral students
Harmon Craig, and John McCrea, paleontologist Heinz Lowenstam and an electronics
engineer Charles McKinney. By 1950, this group had successfully improved the
precision of the Nier isotope ratio mass spectrometer (Nier, 1947; McKinney et al., 1950)
by the necessary factor of 10, developed reproducible analytical extraction methods for
biogenic carbonates and established standards and protocols that are still being followed
for the most part today. The development of the oxygen isotope paleotemperature scale
(Urey et al., 1948; Epstein et al., 1951; Urey et al., 1951) has been heralded as one of the
outstanding scientific achievements of the twentieth century.
Concurrent with work on oxygen isotope analyses of carbonate shells, members
of the Chicago group conducted survey studies of oxygen isotope variations in silicate
rocks and minerals (Baertschi, 1950; Baertschi and Silverman, 1951), carbon isotope
variations in nature (Craig, 1953), stable isotope ratios of natural waters (Epstein and
Mayeda, 1953; Friedman, 1953) and oxygen isotope compositions of biogenic phosphates
(Tudge, 1960). Important early stable isotope research was also conducted in Hamilton,
Ontario on sulfur isotope ratios of rocks and minerals (Thode, 1949), in Copenhagen on
oxygen isotope variations in natural waters (Dansgaard, 1954), and in Moscow on
oxygen and sulfur isotope ratios of rocks and minerals (Vinogradov and Dontsova, 1947;
Trofimov, 1949). Tom Hoering and his group in Arkansas investigated isotopic variations
of nitrogen and chlorine in natural substances (Hoering, 1956; Hoering and Moore, 1958;
Hoering and Parker, 1961). Within a few short years, it was recognized that oxygen
isotope fractionations between cogenetic minerals were large enough to register
temperatures of formation of high-temperature rocks (Clayton and Epstein, 1958) and
that hydrogen and oxygen isotope measurements of rocks and minerals were powerful
petrologic tools (Taylor and Epstein, 1962).
From these beginnings, stable isotope research has blossomed to the point where
thousands of isotope ratio mass spectrometers are in operation in laboratories all over the
world. Stable isotope measurements are being made to resolve problems in many diverse
fields including geochemistry, climatology, hydrology, plant physiology, ecology,
archaeology, meteorology, meteoritics, palaeobiology, bacteriology and the origin of life.
Almost all the early achievements in the field of isotope geology were made by
gifted chemists and physicists who developed the theory and techniques, improved the
mass spectrometers and extraction methods, and thought and wrote about many
fundamental scientific questions of geologic interest. It is well to keep in mind that,
despite developments in isotope ratio mass spectrometry, most notably very stable
electronics and increased sensitivity of sources, there have been only modest
improvements in the overall precision of modern stable isotope analyses over those made
in the early 1950s. There are certainly exceptions to this claim. Sample sizes have come
1-4
Sharp, Z.D. Principles of Stable Isotope Geochemistry
down considerably and some of the more exotic, cutting-edge analyses could not have
been made on the early machines. Most importantly however, the ease of analysis has
improved dramatically. Thanks to the efforts of the mass spectrometer manufacturers to
produce more user-friendly machines, many types of analyses that used to take the better
part of a day can now be done in minutes. This has opened up the field of stable isotopes
to a whole new class of researchers, particularly biologists, who need large numbers of
analyses to see through the inherent variability of natural populations.
The new rapid techniques do not necessarily translate to better precision or
accuracy. The old laborious extraction techniques for a stable isotope analysis were
developed by analytical chemists who were very concerned about reproducible,
quantitative chemical reactions. I have been asked by students whether the ‘old’ data are
any good and can be used. I would say that data from much of the old literature is as good
or better than data collected today. (The only question would be whether the old data are
calibrated to known reference materials).
It is instructive to read the early papers. One comes to the enlightening realization
that many questions being examined with the aid of stable isotope measurements today
were already addressed by these early workers. Similar or identical conclusions reached
from analyses of several or even only a few carefully selected materials 40-50 years ago
are reappearing in recent publications that may contain hundreds of analyses, many of
them superfluous. It is worthwhile, both from an historical standpoint and as proper
scientific procedure to be aware of pertinent observations and conclusions published in
the older literature. In this spirit, I have made an attempt to cite primary references
whenever possible in this book.
1.3 Scope of the Discipline
Stable isotope measurements have an extremely wide range of applications and
the principles employed are relatively easy to grasp. There are gross similarities between
some of the approaches and scientific goals of stable isotope geochemistry and other
geochemical systems. The basic principle of stable isotope geochemistry was first
recognized by Briscoe and Robinson (1925) when they identified differences in the boron
isotope ratios of natural materials. The fundamental principle is this: In any multiphase
system, there is a preferential fractionation of isotopes, with one phase preferentially
incorporating the heavy (or light) isotope relative to other coexisting phases. This
isotope fractionation is due to subtle differences in the masses and thermodynamic
properties of the different isotopes, and occurs in both equilibrium and kinetic processes.
Evaporation of water into undersaturated air and incorporation of CO2 during
photosynthesis are examples of irreversible kinetic processes with large isotope
fractionations. High temperature crystal growth and mineral recrystallization are
processes that often approach thermodynamic equilibrium and have generally smaller
isotopic fractionations. Unlike the kinetic fractionations, equilibrium fractionations
follow well-understood thermodynamic rules. The traditional isotopic systems apply to
the elements H, C, N, O, S. Recent analytical advances have added a whole host of
additional elements to the isotope geochemists arsenal, including B, Cl, Si and the ‘nontraditional’ isotopes of Li, Mg, Ca, Cr, Fe, Cu, Zn, Se, and Mo (Johnson et al., 2004;
Teng et al., 2017). Given that most natural materials contain one or more of these
elements, the applications of stable isotopes to natural systems are extraordinarily broad
1-5
Chapter 1. Introduction
based, with new ideas being developed all the time. Figure 1.2 gives a broad-brush
overview of the various fields and types of applications of stable isotopes.
Petrology
Paleoclimate
soil
lake
marine
Tree Rings
volatiles
Paleoaltitude
Paleoatmosphere
metamorphic
igneous
ice cores
carbonates
sources/
assimilation
fluid/rock
ratios
cooling rates
precipitation
sources
organics
water chemistry
orographic
effects
cloud
dynamics
evapotranspiration
temperature
Planetary
Science
productivity
ocean
circulation
diagenesis
thermometry
Hydrology/
Oceanography
groundwater
sedimentary
early solar
system
processes
authigenic
minerals
astrobiology
paleo
modern
food
web
evolution
fluid sources
chondrites
differentiated
bodies
Paleontology
diet
meteorite
classification
nucleosynthesis
metabolism
environment
climate
Fig. 1.2. Examples of the types of fields that are studied using stable isotopes.
1.3.1 What are stable isotopes?
In the most simple description, atoms consist of the subatomic particles protons,
electrons and neutrons. Protons are positively charged, electrons are negatively charged
and neutrons have no charge. The mass of a neutron is about equal to that of a proton and
the mass of an electron is negligible relative to protons and neutrons (Table 1.2). The
mass of an atom, therefore is determined by the total number of protons and neutrons.
An element is defined by the number of protons in its nucleus. In a neutral atom,
the number of protons is balanced by an equal number of electrons which are present as a
negatively charged cloud around the nucleus. The configuration of the electron cloud
imparts to the atom its gross chemical properties. For a given element, the number of
protons (atomic number Z) is always the same, but the number of neutrons (neutron
number N) may vary. The mass number A is the sum of Z + N (Table 1.3). The number
of neutrons in the nucleus of an element does not affect the gross chemical properties of
the element and its compounds, but mass differences due to changing N can cause subtle
chemical and physical differences which results in isotopic fractionation. It is these small
differences comprise the subject of this discipline.
1-6
Sharp, Z.D. Principles of Stable Isotope Geochemistry
An isotope3 of a given element differs from another isotope of the same element
by the number of neutrons in its nucleus. Most elements in the Periodic Table have two
or more naturally occurring isotopes (either stable or radioactive) but 21 elements,
including fluorine and sodium, are monoisotopic. The nucleus of the single natural
isotope of fluorine, contains 9 protons (Z = 9) and 10 neutrons (A = 19). Oxygen has
three naturally occurring isotopes: 16O with 8 protons and 8 neutrons, 17O with 8 protons
and 9 neutrons, and 18O with 8 protons and 10 neutrons.
Table 1.2. Charge and mass of the proton, neutron and electron.
Particle
Charge
Mass (g)
Mass (amu)
Proton
Neutron
Electron
+1
0
-1
1.6726219 × 10-24
1.6749275 × 10-24
9.1093836 × 10-28
1.0072766
1.0086654
0.000548597
Consider the three isotopes of hydrogen. Protium has one proton, one electron
and a mass of 1.0078 atomic mass units, or amu. The nucleus of deuterium, a second
isotope of hydrogen, contains one proton and one neutron. It has almost the same
chemical properties as protium, but a mass of 2.0141 amu (Fig. 1.3), equal to the
additional mass of a neutron less the nuclear binding energy of deuterium. Tritium, the
third naturally occurring isotope of hydrogen, has one proton and two neutrons in its
nucleus and thus has a mass of ~3 amu. Whereas both protium and deuterium are stable
isotopes of hydrogen, the additional neutron in tritium imparts instability to the nucleus
so that tritium is radioactive with a half life of 12.3 years. Neither protium nor deuterium
will undergo spontaneous radioactive decay, although strictly speaking, any nuclide4
could undergo spontaneous decay, but the probability of such decay is negligible for
these so-called stable isotopes. For example, 50V, which was assumed to be stable,
actually has a half-life of 1.5×1017 y, far longer than the age of the Universe. The three
isotopes of hydrogen have very similar chemical properties but different masses, and
these slight differences in mass result in slightly different strengths of bonds to other
elements. These slight differences in mass and bond strengths are responsible for
fractionation of the different isotopes between coexisting phases undergoing a physical or
chemical reaction and provide the foundation for all of stable isotope geochemistry.
An example of important effects that can arise as a result of small differences in
bond strengths is provided by the chemical and physical properties of the various
isotopologues of water (Table 1.4), where an ‘isotopologue’ refers to the mass of a given
compound. Although the physical and chemical properties of the isotopologues of water
are clearly distinct and large, pure isotopologues are not found in nature. Rather, there
exist mixtures of the end-member isotopologues which are each determined by the
3
The word isotope was coined in 1913 by Frederick Soddy, an English scientist who was awarded the
1921 Nobel Prize in chemistry for his investigations into the origin and nature of isotopes.
4
Truman Kohman of Carnegie Mellon University coined the word nuclide as a general term for a specific
isotope. Including those artificially produced, there are >2500 known nuclides and most of them are
radioactive. That is, stable isotopes are relatively rare in nature.
1-7
Chapter 1. Introduction
isotopes of the elements in the compound. Isotopic variations that occur in our Solar
System are much smaller than the isotopic differences between artificially produced pure
isotopologues.
Table 1.3 Isotopic abundances and relative atomic masses of the pertinent elements in
stable isotope geochemistry. Symbols for the main elements in the discipline are
emboldened.
Symbol
Atomic
Neutron
Mass
Abundance
Atomic Weight
Number
number
Number (per cent)
(12C = 12.)
Z
N
M
H
D
Li
1
1
3
B
5
C
6
N
7
O
8
Si
14
S
16
Cl
17
0
1
3
4
5
6
6
7
7
8
8
9
10
14
15
16
16
17
18
20
18
20
1
2
6
7
10
11
12
13
14
15
16
17
18
28
29
30
32
33
34
36
35
37
99.985
0.015
7.42
92.58
19.78
80.22
98.89
1.11
99.63
0.37
99.759
0.037
0.204
92.21
4.70
3.09
95.0
0.76
4.22
0.014
75.53
24.47
1.007825
2.0140
6.01512
7.01600
10.0129
11.00931
≡12.
13.00335
14.00307
15.00011
15.99491
16.99914
17.99916
27.97693
28.97649
29.97376
31.97207
32.97146
33.96786
35.96709
34.96885
36.96590
1.3.2 Which elements and why?
It often comes as a surprise to learn that classical stable isotope geochemistry
concerns, for the most part, variations in the stable isotope ratios of only five elements:
H, C, N, O, and S (or SNOCH). Although small in number, these elements comprise the
bulk of tissues in living organisms. The isotope ratios of Si and Cl in natural materials
were first measured in 1954 (Allenby, 1954) and 1961 (Hoering and Parker, 1961),
respectively, but only recently has interest in these systems jumped substantially. The
most unexpected developments in stable isotope geochemistry is the explosive rise in the
non-traditional isotopes of metals, including Li, B, Mg, Ca, Ti, V, Cr, Fe, Cu, Zn, Se, Sr,
and Mo (Johnson et al., 2004). Most of these isotope ratios are measured using multicollector inductively coupled plasma mass spectrometer (MC-ICP-MS) and to a lesser
1-8
Sharp, Z.D. Principles of Stable Isotope Geochemistry
extent thermal ionization mass spectrometry (TIMS) or secondary ion mass
spectrometery (SIMS). The isotopic variability in these systems is generally low (except
for Li, which has enormous fractionations), but the analytical methodologies allow for
differences of less than 0.1‰ to be measured with confidence.
Except for certain stable isotope relations in extraterrestrial materials and gases in
the upper atmosphere of Earth, stable isotope geochemistry deals mainly with those
Fig. 1.3. Cartoon of the three isotopes of hydrogen. All have one proton (red sphere) and one electron but
differ in the number of neutrons in the nucleus (blue sphere). The three isotopes have very similar chemical
properties, but they have very different relative masses and subtly different bond strengths. This phenomenon
gives rise to hydrogen isotope fractionation in physical and chemical reactions.
isotopic variations that arise either from isotopic exchange reactions or from massdependent fractionations that accompany biological and physical chemical processes
occurring in nature or in the laboratory. While ultimately quantum mechanical in origin,
such isotope effects are governed by kinetic theory and the laws of thermodynamics.
Natural variations in the stable isotope ratios of heavy elements of geological interest like
Sr, Nd, and Pb involve nuclear reactions and are governed by other factors including the
ratio of radioactive parent and daughter, decay constants, and time.
1.4 Abundances of the Rare Isotopes of Light Elements
Isotopic ratios of the most of the elements of primary interest for light stable
isotope geochemistry are written conventionally as the ratio of the heavy (and rare)
isotope to the light (and more abundant) isotope as in 18O/16O, 34S/32S, etc. Early workers
wrote these ratios in the opposite sense and reported values of absolute ratios. For
example, 12C/13C or 32S/34S ratios were reported as relatively large numbers like 91.16
and 22.51, respectively. With our present knowledge of the absolute stable isotope ratios
of certain international reference standards, it is now possible to compare these old
analyses with modern analyses of similar materials. There is no accepted convention for
writing isotopic ratios of other elements of geochemical interest. Sometimes the heavier
1-9
Chapter 1. Introduction
isotope is the more abundant isotope and is still written in the numerator, as in 11B/10B. In
other cases the lighter isotope is written in the numerator regardless of its relative
abundance, as in 3He/4He. The moderately heavy isotope systems violate the ‘rare is
heavy’ rule. Johnson et al. (2004) recommend that all isotope systems should report
‘heavy/light’ isotope ratios to be consistent with the traditional stable isotope terminology.
He isotopes will remain forever an exception. The traditional 3He/4He nomenclature,
where the R value is the 3He/4He ratio of a sample relative to the 3He/4He ratio of air (Ra
= 1.4 × 10-6) will live on.
Table 1.4 Chemical and physical properties of three of the nine isotopologues of water.
(From Hutchinson, 1957 and Handbook of Chemistry and Physics)
Property
H216O
D216O
Boiling Point (°C)
Freezing Point (°C)
Density at 0°C (gm/cm2)
Vapor Pressure at 20°C (bars × 102)
Temperature of Maximum Density (°C)
Critical Temperature (°C)
Critical Pressure (bars)
Ionization Product, Kw at 25°C
Dielectric Constant at 20°C
Surface Tension at 19°C (dynes/cm)
Viscosity at 20°C (centipoise)
Refractive Index, ηd at 20°C
Representative Solubilities at 25°C
(g/g of water)
NaCl
BaCl2
100.00
0.00
0.999841
2.3379
4.0
374.1
220.6
1 × 10-14
80.36
73.66
1.009
1.33300
101.42
3.82
1.10469
2.0265
11.6
371.5
221.5
0.3 × 10-14
79.755
72.83
1.260
1.32844
0.359
0.357
0.305
0.289
H218O
2.3161
The elements under discussion in this text have one common isotope, like 16O or
S, and one or more rare isotopes, like 17O, 18O, or 33S, 34S, and 36S whose average
abundances range from fractions of a per cent to a few per cent. The isotopic abundances
and relative atomic weights of elements whose isotopic ratios vary as a result of massdependent processes are given in Table 1.3. Note that boron and chlorine are exceptions
to the general rule given above concerning disparity in the abundances of the heavy and
light isotopes of an element. In these two cases the abundances of the rare isotopes 10B
and 37Cl are relatively high at 19.78 and 24.47 per cent, respectively.
32
1.5 Characteristics of Elements that Undergo Significant Isotopic Fractionation
The named elements share several characteristics that are not possessed by other
elements whose isotopic ratios are not fractionated to any significant extent in nature or
in the laboratory. These characteristics, enumerated below, are only observed
characteristics and are not rigorously tied to theoretical principles.
1-10
Sharp, Z.D. Principles of Stable Isotope Geochemistry
1. They have a relatively low atomic mass. Significant mass-dependent isotopic
variations in terrestrial materials have been looked for but not clearly
demonstrated in heavier elements like Cu, Sn, and Ag. These heavier elements do
have small fractionations that can now be measured with sufficient precision to
have geological relevance, but they generally only have a total range in nature of
a few per mil or less.
2. The relative mass difference between the rare (heavy) and abundant (light)
isotope is large. Compare, for example, the values of 8.3 per cent and 12.5 per
cent for the pairs 13C-12C and 18O-16O, respectively, with the value of only 1.2 per
cent for 87Sr-86Sr. The relative mass difference between D (deuterium) and H
(protium) is almost 100 per cent and hydrogen isotope fractionations are
accordingly about ten times larger than those of the other elements of interest. The
condition of large relative mass difference is by no means sufficient to promote
isotopic fractionation; the 48Ca/40Ca ratio varies little in terrestrial rocks despite
the large relative mass difference between the isotopes (only that of D-H is
larger).
3. They form chemical bonds that have a high degree of covalent character.
Elements like K, Ca, and Mg that occupy cation sites in minerals form ionic
bonds to other elements and experience little or no site preference that could give
rise to significant isotopic fractionations. Mg2+, for example, is almost always
surrounded by the same atomic environment in nature: an octahedron of oxygen.
Nonetheless, small Ca isotope variations observed in biogenic carbonates may
have an origin in mass dependent fractionation.
4. They can exist in more than one oxidation state (C, N, S), form a wide variety of
compounds (notably O), and are important constituents of naturally occurring
solids and fluids. Some of the largest fractionations in nature arise from
differences in the nature of the chemical bonds to elements in different oxidation
states as in the carbon isotope fractionation between CO2 and CH4, and sulfur
isotope fractionation between sulfide and sulfate. Silicon occurs in a number of
naturally occurring compounds, but is almost always bonded to the same element
(oxygen) in one oxidation state (+4). Consequently its isotopic ratios vary little in
nature, outside of biological processes. Hydrogen is also bonded exclusively to
oxygen in inorganic minerals as -OH groups but its isotopic composition is
influenced greatly by the other ions bonded to the OH oxygen (Mg2+, Al3+, Fe2+,
etc.).
5. The abundance of the element and rare isotope is sufficiently high (tenths to a few
atom per cent) to assure the ability to make precise determinations of the isotopic
ratios by mass spectrometry. Measurements of isotopic ratios in materials at trace
levels are difficult. Large amounts of material are needed and problems with
blanks and contamination become quite serious. With recent advances in the
sensitivity of conventional isotope ratio mass spectrometers and the introduction
of continuous flow mass spectrometers, low abundance is less of an issue than it
1-11
Chapter 1. Introduction
has historically been. The abundance of the rare isotope still separates certain
elements, such as He, which has a rare isotope abundance of 0.000137 %, from
the elements commonly considered the ‘light stable isotopes’.
1.6 Applications in the Earth Sciences
Stable isotope measurements have been applied successfully to the resolution of
fundamental problems in the earth sciences, human sciences, biological sciences and
several subdisciplines of chemistry. Applications in the earth sciences can be broadly
classified into four main types:
1. Thermometry
2. Tracers
3. Reaction mechanisms
4. Chemostratigraphy
Formation temperatures of rock, mineral and gas systems
are determined on the basis of temperature-dependent
equilibrium fractionations of the isotopic ratios between
two or more cogenetic phases. Stable isotope thermometry
has played a major role in studies of paleoclimatology.
Recent development of ‘clumped isotopes’ results in a
single-mineral thermometer.
Large reservoirs like the ocean, the mantle, meteoric waters
and organic matter have distinct stable isotope signatures
that can be used to trace the origin of rocks, fluids, plants,
contaminants, and food sources. Isotopic ratios can also be
used as biomarkers.
Distinctions can be made between diffusion and
recrystallization, open and closed systems, and bacterial
and thermogenic processes. Certain isotope values can be
used to identify kinetic, non-equilibrium processes.
Abrupt changes (excursions) in the stable isotope ratios of
minerals and organic matter in ocean sediments and certain
other terrestrial materials are used as stratigraphic markers,
indicators of ocean productivity, and atmospheric
chemistry.
The applications of stable isotopes are driven partly by technology and partly by
the changing interests in scientific disciplines. Some applications, such as the new nontraditional isotopes, are exciting and high profile, but are also very difficult analytically
and costly. An MC-ICP-MS is a very expensive instrument and clean labs are also
required for many of the non-traditional measurements. This necessarily limits the
number of practitioners in the field. On the other hand, the oxygen and hydrogen isotope
ratio of waters can now be measured using low-cost desktop laser spectroscopy devices.
As a result, far more researchers are able to measure waters than exotic non-traditional
isotopes. The fields are also driven by the science, and interests wax and wane in
different disciplines. Climate change concerns drive more people towards water issues
and paleoclimate, so research in these fields has increased. Some fields, have ‘matured’
and consequently, related publications have decreased. There are also completely new
techniques which have led to large number of unanticipated study fields. These include
1-12
Sharp, Z.D. Principles of Stable Isotope Geochemistry
triple isotope analyses of sulfur and oxygen and most notably, the single mineral
carbonate thermometer based on ‘clumped isotopes’ (Eiler, 2007).
1.7 Isotope Effects
1.7.1 Kinetic isotope effects
Kinetic isotope effects are common both in nature and in the laboratory and their
magnitudes are comparable to and often much larger than those of equilibrium isotope
effects. Kinetic isotope effects are irreversible, and normally associated with fast,
incomplete, or unidirectional processes like evaporation, diffusion, and dissociation
reactions. Biological reactions such as photosynthesis are clearly irreversible, defying
tradition thermodynamics which assume chemical equilibrium. Isotope effects attendant
on diffusion and evaporation are explained (in part) by the different translational
velocities possessed by the different isotopic forms of molecules as they move through a
phase or across a phase boundary. Classical kinetic theory tells us that the average kinetic
energy (K.E.) per molecule is the same for all gases at a given temperature. Consider, for
example, the molecules 12C16O and 12C18O that have molecular weights of 28 and 30,
respectively. Equating their kinetic energies at some T
and
(
)
(
)
K.E. 12 C16 O = K.E. 12 C18 O
(1.1)
K.E. = ½mv2
(1.2)
where m is mass and v is velocity. Substituting the masses of these isotopologues of CO,
the above equations reduce to
½(28)(v28)2 = ½(30)(v30)2
(1.3)
v 28 = 30 / 28v 30 = 1.035v30.
(1.4)
That is, regardless of T, the average velocity of 12C16O molecules is 3.5 per cent greater
than the average velocity of 12C18O molecules in the same system.
Such velocity differences can lead to isotopic fractionations in a variety of ways.
For example, isotopically light molecules will preferentially diffuse out of a system and
leave the reservoir enriched in the heavy isotope. On average, more 12CO2 molecules than
13
CO2 molecules strike the surfaces of leaves and enter the stomates, an effect partially
responsible for the low 13C/12C ratios of plants relative to other carbon-containing
substances in nature. In the case of evaporation, the greater average translational
velocities of isotopically lighter water molecules allow them to break through the liquid
surface preferentially and diffuse across a boundary layer, resulting in an isotopic
fractionation between vapor and liquid that is superimposed on the equilibrium isotopic
fractionation between liquid and gaseous H2O. Attesting to this phenomenon is the fact
that water vapor over the oceans or over a large lake has 18O/16O and D/H ratios that are
significantly lower than the ratios that would obtain at equilibrium (at 100% relative
humidity). These lower ratios arise from kinetic isotope effects associated with
evaporation.
1-13
Chapter 1. Introduction
While it is important to be aware of kinetic isotope effects, they are relatively rare
in high-temperature processes occurring on Earth. By contrast, transient processes can
occur whereby differing rates of isotopic exchange between coexisting minerals
themselves, or between the minerals and an external fluid, can result in assemblages that
are grossly out of isotopic equilibrium. Such examples are explained, not by kinetic
isotope effects, but rather by a series of equilibrium isotope exchange reactions that have
not gone to completion.
1.7.2 Equilibrium isotope effects
Equilibrium isotope effects can be considered in terms of the effect of atomic
mass on bond energy. Substituting a light for heavy isotope in a molecular site does not
affect the nuclear charges or electronic distribution of the molecule. It does, however,
affect the bond strength. The energy required to break a bond is slightly higher for a
heavy isotope than it is for a light one. This subtle difference in bond strength results in a
predictable isotope fractionation between any two phases. The magnitude of this
equilibrium isotopic effect is related to the bonding environment of the phases in
question. Most importantly, the fractionation is dependent on temperature, so that for
appropriate systems, such as calcite-water, the equilibrium oxygen isotope fractionation
between the two phases is a function of temperature alone.
Equilibrium isotopic fractionations between two substances or between two
phases of the same substance is the basis of stable isotope thermometry. The temperature
dependence on isotope fractionation spawned the first major application of stable isotope
chemistry to geological problems: the calcite oxygen isotope thermometer. first used for
paleotemperature estimates over 50 years ago (Urey et al., 1948; Epstein et al., 1951;
Urey et al., 1951). Figure 1.4 illustrates the equilibrium oxygen isotope fractionations
between selected silicate minerals as a function of temperature. The fractionation
between any two phases (roughly given by the difference in the isotopic composition of
the two phases) generally follows a 1/T2 relationship (T in Kelvins). This means that the
fractionations become smaller with increasing temperature and that the temperature
dependence on the fractionation becomes greater at lower temperatures. The calcite-water
fractionation is 28.8 ‰ at 25°C, but less than 1‰ at 600°C. The inverse temperature
relationship means that a thermometer becomes more precise at lower temperature. The
calcite-water thermometer has a precision of better than 1/2°C at room temperature,
whereas the precision for quartz-mineral fractionations at metamorphic temperatures is an
order of magnitude less precise (Fig. 1.4). (That said, being able to constrain the
temperature of metamorphism to ±10°C is a remarkable achievement. Fractionations of
not only oxygen isotopes, but those of hydrogen, carbon, nitrogen and sulfur have been
used successfully over the years to place constraints on formation temperatures of both
high and low temperature systems in nature. These concepts are discussed in more detail
in later chapters of this text.
1-14
Sharp, Z.D. Principles of Stable Isotope Geochemistry
10
1000lnα (mineral-water)
Oxygen
5
qu a rtz
a lbite
0
w h o le ro c
k
ga rne t
-5
-10
250
ite
m agne t
350
450
550
650
750
850
Temperature (°C)
Fig. 1.4. Oxygen isotope fractionation between selected minerals as a function of temperature. In addition
to oxygen, regular variations occur for most isotopic systems, including hydrogen, carbon, nitrogen and
sulfur. Under certain circumstances to be discussed later, knowledge of the δ18O values of two cogenetic
phases allows the temperatures of formation to be determined. Note: 1000lnαa-b ≈ δa – δb.
1-15
Chapter 1. Introduction
References
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et Cosmochimica Acta 5, 40-48.
Baertschi, P. (1950) Isotopic composition of the oxygen in silicate rocks. Nature 166,
112-113.
Baertschi, P. and Silverman, S.R. (1951) The determination of relative abundances of the
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Briscoe, H.V.A. and Robinson, P.L. (1925) A redetermination of the atomic weight of
boron. Journal of the Chemical Society, Transactions 127, 696.
Chadwick, J. (1931) Possible existence of a neutron. Nature 192, 312.
Clayton, R.N. and Epstein, S. (1958) The relationship between O18/O16 ratios in
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Craig, H. (1953) The geochemistry of the stable carbon isotopes. Geochimica et
Cosmochimica Acta 3, 53-92.
Dansgaard, W. (1954) The O18-abundance in fresh water. Geochimica et Cosmochimica
Acta 6, 241-260.
Eiler, J.M. (2007) “Clumped-isotope” geochemistry—The study of naturally-occurring,
multiply-substituted isotopologues. Earth and Planetary Science Letters 262, 309327.
Epstein, S., Buchsbaum, R., Lowenstam, H. and Urey, H.C. (1951) Carbonate-water
isotopic temperature scale. Journal of Geology 62, 417-426.
Epstein, S. and Mayeda, T.K. (1953) Variation of 18O content of waters from natural
sources. Geochimica et Cosmochimica Acta 4, 213-224.
Friedman, I. (1953) Deuterium content of natural water and other substances. Geochimica
et Cosmochimica Acta 4, 89-103.
Gilfillan, E.S.J. (1934) The isotopic composition of sea water. Journal of the American
Chemical Society 56, 406-408.
Hoering, T. and Parker, P.L. (1961) The geochemistry of the stable isotopes of chlorine.
Geochimica et Cosmochimica Acta 23, 186-199.
Hoering, T.C. (1956) Variations in the nitrogen isotope abundance, [Chap. 6] of Nuclear
Processes in Geologic Settings. Natl. Research Council, Comm. Nuclear Sci., Nuclear
Sci. Ser. Rept. no. 19, 39-44.
Hoering, T.C. and Moore, H.E. (1958) The isotopic composition of the nitrogen in
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Johnson, C.M., Beard, B.L. and Albarède, F. (2004) Overview and General Concepts, in:
Johnson, C.M., Beard, B.L., Albarède, F. (Eds.), Geochemistry of Non-Traditional
Stable Isotopes. Mineralogical Society of America, Washington, D.C., pp. 1-24.
McKinney, C.R., McCrea, J.M., Epstein, S., Allen, H.A. and Urey, H.C. (1950)
Improvements in mass spectrometers for the measurement of small differences in
isotope abundance ratios. Review of Scientific Instruments 21, 724-730.
Nier, A.O. (1947) A mass spectrometer for isotope and gas analysis. Review of Scientific
Instruments 18, 398-411.
Rankama, K. (1954) Isotope Geology. McGraw-Hill Book Co., Inc., New York.
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Sharp, Z.D. Principles of Stable Isotope Geochemistry
Rutherford, E., Aston, F.W., Chadwick, J., Ellis, C.D., Gamow, G., Fowler, R.H.,
Richardson, O.W. and Hartree, D.R. (1929) Discussion on the structure of atomic
nuclei. Proceedings of the Royal Society of London, Series A 123, 373-390.
Taylor, J., H.P. and Epstein, S. (1962) Relationship between O18/O16 ratios in coexisting
minerals of igneous and metamorphic rocks Part 2. Application to petrologic
problems. Geological Society of America Bulletin 73, 675-694.
Teng, F.-Z., Watkins, J.M. and Dauphas, N. (2017) Non-Traditional Stable Isotopes,
Reviews in Mineralogy and Geochemistry. Mineralogical Society of America, p. 885.
Thode, H.G. (1949) Natural variations in the isotopic content of sulphur and their
significance. Canadian Journal of Research 27B, 361.
Thomson, J.J., Aston, F.W., Soddy, F., Merton, T.R. and Lindeman, F.A. (1921)
Discussion on isotopes. Proceedings of the Royal Society of London, Series A 99, 87104.
Trofimov, A. (1949) Isotopic constitution of sulfur in meteorites and in terrestrial objects.
Doklady Akademii nauk SSSR 66, 181-184.
Tudge, A.P. (1960) A method of analysis of oxygen isotopes in orthophosphate; its use in
the measurement of paleotemperatures. Geochimica et Cosmochimica Acta 18, 81-93.
Urey, H.C. (1947) The thermodynamic properties of isotopic substances. Journal of the
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Urey, H.C., Epstein, S., McKinney, C. and McCrea, J. (1948) Method for measurement
of paleotemperatures. Bulletin of the Geological Society of America (abstract) 59,
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and temperatures of the Upper Cretaceous of England, Denmark, and the southeastern
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Urey, H.C. and Greiff, L.J. (1935) Isotopic exchange equilibria. Journal of the American
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Vinogradov, A.P. and Dontsova, E.I. (1947) Izotopnyi sostav kisloroda
alyumosilikatnykh gornykh porod. Doklady Akademii nauk SSSR, 83-84.
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1-17
Chapter 2
TERMINOLOGY, STANDARDS AND MASS SPECTROMETRY
Contents
2.1 Overview ……………………………………………………………………………………………………….. 1
2.2 Isotopes, Isotopologues, Isotopomers, and Mass Isotopomers ………………………………. 1
2.2.1 ‘Isotope’ vs. ‘Isotopic’ ………………………………………………………………………………. 2
2.3 The Delta Value ……………………………………………………………………………………………… 2
2.4 The Fractionation Factor  ………………………………………………………………………………. 8
2.5 1000ln, , and the  Value …………………………………………………………………………… 10
2.6 Reference Standards………………………………………………………………………………………. 12
2.6.1 Hydrogen……………………………………………………………………………………………….. 13
2.6.2 Carbon …………………………………………………………………………………………………… 17
2.6.3 Nitrogen ………………………………………………………………………………………………… 17
2.6.4 Oxygen ………………………………………………………………………………………………….. 18
2.6.5 Sulfur…………………………………………………………………………………………………….. 19
2.6.6. Silicon ………………………………………………………………………………………………….. 19
2.6.7. Chlorine………………………………………………………………………………………………… 20
2.7 Isotope Ratio Mass Spectrometry ……………………………………………………………………. 20
2.7.1 Components of a mass spectrometer………………………………………………………….. 21
2.7.1.1 The ion source ………………………………………………………………………………….. 22
2.7.1.2. The analyzer ……………………………………………………………………………………. 23
2.7.1.3. Collector assembly …………………………………………………………………………… 25
2.7.1.4 Dual inlet mass spectrometer inlet system ……………………………………………. 26
2.7.2 Gas Chromatograph Isotope Ratio Mass Spectrometry (GC-IRMS) ……………… 27
2.7.3 Gases measured in isotope ratio mass spectrometry …………………………………….. 28
2.7.4 Relations between measured and desired isotopic ratios ………………………………. 29
2.8 Laser absorption mass spectroscopy ………………………………………………………………… 30
REFERENCES ………………………………………………………………………………………………….. 33
Sharp, Z.D. Principles of Stable Isotope Geochemistry
Chapter 2
TERMINOLOGY, STANDARDS AND MASS SPECTROMETRY
2.1 Overview
Most of the accepted terms and symbols used in stable isotope geochemistry are
precise and were developed by the earliest workers who gave the matter considerable
thought. Arguably, some of the terms could be improved, and some recent workers have
unilaterally coined new symbols and expressions for reasons known only to themselves.
Unfortunately this practice has caused considerable confusion among new workers and
more and more improper usage is finding its way into the literature and into oral
presentations. In this text the terms established by the founders of our discipline will be
used, both in homage to them and because these terms are, for the most part, logical and
grammatically correct. In Table 2.1 a number of terms and phrases are presented that are
considered to be mistakes, with the reasons why they are unacceptable, and
recommended alternatives. All examples were culled from the literature. Although some
of these common mistakes can be seductive in their simplicity, they should be avoided, in
part to preserve the historical purity of the discipline but, most importantly, because they
are indeed mistakes and not simply a matter of style.
In this chapter, the nomenclature commonly used in stable isotope geochemistry
is developed, the mysterious and arcane standardization protocols and reference standards
are explained and the principles of the mass spectrometer are presented.
2.2 Isotopes, Isotopologues, Isotopomers, and Mass Isotopomers
Most definitions of the word isotope include something to the extent ‘one of two
or more forms of an element’ due to differing numbers of neutrons. Or ‘one of two or
more atoms having the same atomic number but different mass numbers’. However these
definitions fail to describe monoisotopic elements such as fluorine. A better definition
might be ‘a particular form of an element defined by a specific number of neutrons’ or ‘a
variety an element with a fixed number of neutrons”. In applications to natural processes,
we are obviously not concerned with monoisotopic elements, so perhaps both definitions
are equally valid.
All stable isotope studies report the stable isotope composition of a particular
element in a molecule or compound. For example, we measure the carbon isotope
composition of CO2 or calcite, and the hydrogen isotope composition of water. According
to recommendations made in 1994 by the International Union of Pure and Applied
Chemistry (IUPAC), isotopologues are molecules that differ from one another only in
isotopic composition. It is therefore appropriate to talk about the different ‘isotopologues’
of water, but not the different ‘isotopes’ of water because water doesn’t have isotopes – its
constituent elements H and O do. Writing about ‘water isotopes’ may sound short and
concise, but it is wrong. Just as petrologists don’t talk about ‘rock isotopes’, so
hydrologists should avoid talking about ‘water isotopes’.
Isotopologues can have the same or different masses. For example, 12C17O has the
same mass as 13C16O. Although they have the same mass, they are distinctly different
isotopologues of carbon monoxide. The word isotopologue, when used with care, is the
2-1
Chapter 2. Terminology, Standards and Mass Spectrometry
appropriate term to describe molecules that are encountered in stable isotope
geochemistry and will be employed frequently in this text.
Isotopomers (contraction of isotopic isomers) are isotopologues that differ from
one another only in the positions or locations of the isotopic elements. Studies of
isotopomers is common in pharmaceutical and biochemical research, where the position
of atoms provides important information about metabolic processes. Isotopomers always
comprise the same number of each isotope and thus always have the same mass. They
differ from one another in the positions or locations of the isotopic elements and thus the
connection to isomerism. Two different isotopic forms of acetaldehyde provide an
example of isotopomers: CH2DCH=O and CH3CD=O. They have the same isotopic
composition, but the D atom is bonded to the methyl group carbon in the first case and to
the carboxyl carbon in the second. Isotopic forms of nitrous oxide (15N14NO and
14 15
N NO), and ozone (16O18O16O and 18O16O16O) are among the few isotopomers studied
by stable isotope geochemists (e.g., Michalski and Bhattacharya, 2009). In mass
spectrometry, the expression mass isotopomer, normally an organic compound, is used to
describe a family of isotopologues that have the same mass. Because mass isotopomers
are collected simultaneously on the same collectors of a mass spectrometer, they pose a
problem in isotopic analysis. The molecules 13C16O and 12C17O are mass isotopomers that
each have mass 29.
2.2.1 ‘Isotope’ vs. ‘Isotopic’
These two words appear to be used randomly and interchangeably because the
proper use of one or the other is not immediately clear. My mentor, Jim O’Neil, was
confronted with this dilemma as a U.S.G.S. employee. He consulted the Technical
Reports Unit at the USGS for guidance. After some research, it was decided that ‘isotope’
is used when modified and ‘isotopic’ is used as a stand-alone adjective. One therefore
should write “The oxygen isotope composition of . . .” and “The isotopic composition of .
. .”. In the first case, ‘oxygen’ modifies ‘isotope’ and in the second ‘isotopic’ stands
alone.
2.3 The Delta Value
Relative differences in isotopic ratios can be determined far more precisely than
absolute isotopic ratios. McKinney et al. (1950) introduced the delta () notation to report
stable isotope data for all materials except certain extraterrestrial materials whose
isotopic ratios and variations are occasionally so large that absolute ratios are used in
publications (see Chapter 13). The delta value is given by1
 R  Rstd
   x
 Rstd

  1000

2.1a
1
Some people have suggested that the ‘× 1000’ part of the definition of delta should be left out. The delta
numbers would then be very small, and they would be reported in per mil (‰), percent (%) or per meg
(ppm), with the actual  value being multiplied by 1,000, 100 or 106, respectively. There is some sense to
this argument, but the 50+ years of defining the delta with the ×1000 part has worked wonderfully, and as
the saying goes ‘if it ain’t broke, don’t fix it’.
2-2
Sharp, Z.D. Principles of Stable Isotope Geochemistry
or equivalently

 R
   x 1  1000
 Rstd 
2.1b
where R is the ratio of the abundance of the heavy to light isotope, x denotes the sample,
and std is an abbreviation for standard. For the elements, hydrogen, carbon, nitrogen,
oxygen, sulfur,, silicon and chlorine, R is given by 2H/1H (or D/H), 13C/12C, 15N/14N,
18
O/16O (and 17O/16O), 34S/32S (and 33S/32S, 36S/32S), 30Si/28Si (and 29Si/28Si), and
37
Cl/35Cl, respectively. The notation 2H/1H is strictly correct for hydrogen isotope ratios
(Coplen, 1994) and is used almost exclusively in the hydrological literature, but, for
historical reasons, D/H is routinely used by many workers in geological studies.
Delta values are reported in per mil, or parts per thousand, and the symbol for per
mil is ‰. A positive  value means that the ratio of heavy to light isotope is higher in the
sample than it is in the standard, and a negative  value has the opposite meaning. A
sample with a 18O value of +19.7‰ has an 18O/16O ratio that is 19.7 per mil, or 1.97 per
cent, higher than that of the standard. Similarly, a negative D value of –65.2‰ means
that the D/H ratio of the sample is 65.2 per mil or 6.52 per cent lower than that of the
standard. The  value is computed from the intensities of ion signals measured in the
Table 2.1. Common Mistakes in Terminology and Phraseology
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 and science: an
operator () or the partial derivative ()
13C composition
13C value; carbon isotope composition
Isotopically depleted water
18
Stable water isotopes have been
widely used as tracers. . .
Stable O and H isotope ratios in water
have been used. . .
heavy (light) 18O values
high (low) 18O values
Isotopically negative
relatively low  values
13C values are numbers and a
composition of numbers has no
meaning.
A given sample of water is neither
depleted nor enriched in isotopes.
Only elements have isotopes. It is the H
and O that has the isotopes, not H2O.
As numbers, -values can be high or
low, positive or negative, but not heavy
or light.
Isotopic ratios are not negative or
positive; they are lower or higher than
those of the standards.
depleted 13C value
low 13C value (relative to another)
enriched (depleted) carbonates.
isotopically heavy (light) carbonates
enriched (depleted) compositions
(relatively) 18O-rich or 13C-poor
carbonates
depleted carbon reservoir
reservoir of (isotopically) light carbon
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
O (or D) depleted water
13C values are numbers and, as such,
they cannot be depleted or enriched.
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 the
element in some substance.
Such written mistakes are a carryover
from loose oral communication.
2-3
Chapter 2. Terminology, Standards and Mass Spectrometry
The isotopic composition of the
water was 18O = 4.3‰.
The isotopic value changed.
The 18O value of the water was
4.3‰.
The isotopic composition changed. The
18O value changed.
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.
15, 18, 13, etc.;
15N, 18O, 13C, etc.
15
18
13
   etc.;
151813, etc.
Sulfur was measured
The 13C content of . .
In general the water isotopes are
valuable proxies of temperature
variations in high latitudes
. . . using data assimilation of
water-isotope ratios . .
the sulfur isotope composition was
measured
The 13C/12C ratio of ..
In general the isotopologues of water
are valuable proxies of temperature
variations in high latitudes
Same as above
A matter of redundancy.
The phrase isotopic value is
ambiguous. R?, ? Which element?
The word signature should be used to
describe 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 of new symbols that save
one character of space is unnecessary
at best and confusing at worst.
Misleading because the sulfur content
of a rock or mineral may be understood.
13C content refers to how much 13C
there is in a rock. A sample of coal has
a lot of 13C (high 13C content) but a low
13C/12C ratio compared to most
materials.
Water does not have isotopes. It is
composed of H and O that have
multiple isotopes.
Just as it would be wrong to say “using
data of fish-isotope ratios” so it is wrong
to say ‘water-isotope ratios’.
mass spectrometer (see section 2.8). Mass spectrometric analyses of pure gases other than
H2 are reproducible to  0.01‰ or better. Excellent reproducibility like this does not
necessarily represent the precision of an actual sample because errors can be introduced
from the collection and chemical preparation procedures employed. To get a true
precision of ± 0.01‰ requires extreme care. Reporting a precision for an analysis based
on the precision obtained on the measurement of the gas in a mass spectrometer will
always result in a precision that is higher than the actual precision of the overall analysis
and should be avoided. Oxygen isotope compositions are reported using the symbol 18O,
those of carbon by 13C, and so forth. The symbol  is the lower case Greek letter delta
and is commonly used in many disciplines to express a difference. The unrelated symbol
 (del) crept into the parlance of stable isotope geochemistry about 20-30 years ago,
presumably as some kind of abbreviation for the correct word delta2. This incorrect usage
should be abandoned because the word del has been used for centuries to denote the
symbol , the partial derivative sign and is not the greek letter ‘delta’.
The delta notation provides a very convenient means to express the small relative
differences in isotopic ratios between samples and standards that are measured by
isotope ratio mass spectrometry. The effective precision of a stable isotope measurement
is much higher than is immediately apparent from the stated precision of a  value, which
in the best case is 0.01‰. For example, the absolute 18O/16O ratio of one of the
international reference standards SMOW is (2005.20±0.45)10-6. This ratio was
I first encountered students using  in place of  because the symbol took only one stroke of a keyboard
(on a Mac) instead of two for the . Needless to say, this was not a convincing reason to abandon the
correct notation.
2
2-4
Sharp, Z.D. Principles of Stable Isotope Geochemistry
determined by comparing the isotopic value of a sample of SMOW to synthetic mixtures
of pure D218O and H216O (Baertschi, 1976b), and is known to five significant figures, or
to four parts in 105. The 18O/16O ratio of a gas whose 18O value is +2.06‰ relative to
SMOW (18O of SMOW = 0.00‰ by definition) is 0.00200933, the value obtained by
substituting 2.06 in equation 2.1
18
2.06 
O / 16 O sample  2005.20  10 6
2005.20  10 6
1000 ,
2.2
A 18O value of +2.05‰ corresponds to an absolute ratio of 0.002009311, different from
a 18O value of +2.06‰ by ±0.00000002. Obviously, given the uncertainties in the
absolute value of our reference, the absolute ratio is not known anywhere near the
calculated precision. Nevertheless, by accepting a value for the absolute 18O/16O ratio of a
reference standard (SMOW in this case), we can determine relative differences in the
18
O/16O ratios of two substances at the remarkable level of two parts in the eighth decimal
place! The ability to determine relative differences in small isotopic ratios at this level of
precision makes stable isotope measurements among the most precise attainable in all of
geochemistry.
The delta scale leads to some interesting peculiarities which fortunately, for the
most part, can be ignored. Consider the oxygen isotope composition of a gas, given by


δ 18 O  


 O O
 O O
18
16
sample
18
16
standard


 11000


2.3.
If we have a sample with no 18O, then the 18O/16O ratio of the sample is 0, and the
D18O value is -1000‰. The isotope scale ‘bottoms out’ at -1000‰. At the other
extreme, a sample containing only 18O has a 18O/16O ratio of ∞, and the 18O value is
∞‰. The  value of a mixture of two materials can be approximated by taking the
average of the two delta values of the unmixed materials in their relative proportions, and
in practice, this works well, although mathematically it is not correct. Just consider
mixing equal proportions of pure H218O and pure H216O. The mixture has a composition
of H16O18O, with a 18O value of 497753‰, but if we were just to take the average of the
two endmember delta values (-1000 and ∞‰), the answer would not be correct.
Fortunately, the rare isotope is generally in low concentrations, so that for most
geological applications we can use delta values additively because the denominator (the
common isotope) has a fraction close to 1.
Isotopic compositions of samples are measured relative to the isotopic
composition of a reference gas, the working standard, in a mass spectrometer. To
convert the  value of sample X from one scale (reference standard A – the working gas 
value) to another scale (reference standard B – the international standard  value), the
following equation is used:
2-5
Chapter 2. Terminology, Standards and Mass Spectrometry
 X B =  X-A +  A B + 0.001 X-A   A-B 
2.4.
This simple calculation, analogous to converting temperatures on the Celsius scale to
temperatures on the Fahrenheit scale, is made in every stable isotope laboratory in the
world3. Laboratory working standards are calibrated relative to international reference
standards, precious materials which are distributed to qualified workers by the
International Atomic Energy Agency (IAEA) or the National Institute of Standards and
Technology (NIST). In most stable isotope laboratories there are supplies of gases like
CO2, N2, H2, etc. contained in metal or glass tubes and tanks that are fitted with
appropriate valves to allow aliquots of the gases to be taken for use as working standards
or for calibration purposes. The  values of the gases are well known from repeated
measurements relative to the values of primary or secondary reference standards, which
are analyzed sparingly.
Suppose that the CO2 working standard (WS) used in a given mass spectrometer
13
has a  C value of +4.75‰ relative to the international standard PDB (WS-PDB). When
an unknown sample is analyzed in the mass spectrometer, the difference in the isotopic
composition of the sample and the working standard is measured. If sample X has a 13C
value of 22.32‰ relative to WS (X-WS), the 13C value of X on the PDB scale is
4.75  22.32 + 0.001(4.75)(22.32) = 17.68‰.
2.5
That is,  values are converted from the working standard of the mass spectrometer to
PDB, or to any international reference standard, by simply adding a scaling term
10-3(X-WS)(WS-PDB) to the sum of the two delta values X-WS and WS-PDB. Another
equation (essentially the same equation rearranged in a slightly different format)
frequently used to calculate a scale change like this has, for the case above, the form
1.00475(22.32) + 4.75 = 17.68‰
2.6
The difference of 4.75‰ between the isotopic composition of the working standard and
PDB must be added to the measured raw value (-22.32), but only after the raw value has
been corrected for scale expansion, equivalent in this case to a multiplicative factor of
1.00475 (equal to 1 + 0.001WS-PDB). Note that there is a contraction or expansion of
scales involved in these calculations and this term is directly related to the magnitude of
the difference in  values between the two standards. The size of  values changes from
one scale to another. When converting between scales, one must apply both an additive
and multiplicative factor to the raw data. If the value of a working standard is 12.34‰,
the multiplicative factor is 1.01234 (i.e., 1 + 0.001) and the additive factor is 12.34. If
the  value of another working standard is –6.78‰, the multiplicative factor is 0.99322 (1
+ 0.001  -6.78), which in this case contracts the scale, and the additive factor is –6.78.
The application of this equation is familiar to many geochemists analyzing carbonates.
There are two references scales for oxygen, the SMOW and PDB scale. The value of
3
Certainly, many workers are not aware that such calculations are being made, as the conversion equations
are hidden in the software packages provided with their mass spectrometers.
2-6
Sharp, Z.D. Principles of Stable Isotope Geochemistry
PDB on the SMOW scale (or VPDB on the VSMOW scale) is 30.91‰. In order to
convert a 18O value from the SMOW to PDB scale the equation
18OSMOW = 1.03091×18OPDB + 30.91
2.7
is used.
In order to reduce the size of the multiplicative factor, international reference
standards are prepared with isotopic compositions that are as close as possible to the
range of isotopic compositions of natural materials expected to be analyzed by most
workers. In the same vein, a researcher can choose working standards whose isotopic
compositions are close to those of the materials most commonly met in the research at
hand. If given the choice, it would be better to have a working gas with a higher delta
value (higher proportion of rare isotope) than the sample gas to minimize extrapolation.
The practice of having similar reference and sample gas compositions results in only
small improvements in precision, but is a worthwhile practice in any case.
Over the years, stable isotope geochemists have tacitly developed a certain
uniformity in the presentation of their data. Some notations used in the past have all but
disappeared in the modern literature, but are noted for the sake of completeness. In the
early literature you will see the expressions (O18/O16), O18 (D/H), and so forth, but
these strictly more correct notations soon gave way to the simpler expressions 18O and
D. Prior to the mid-1970s the mass number was always written as a right superscript of
the symbol of the element as in O18, C14, U235, etc. It is for this reason that one usually
hears the element name (or symbol) and number spoken in that order, as in “C-14
dating”, “Sr-90 contamination”, or “delta O-18 values”. Subsequently, IUPAC officially
changed the order in which mass number and symbol are written to allow oxidation states
and other identifying marks to be written to the right of the element symbol. In the early
literature, D and 13C values were often given in per cent rather than in per mil.
Box 2.1 Why
units?
12
C is the official reference mass for atomic mass
Prior to the 1970s, two conventions were used for determining
relative atomic masses. Physicists related their mass spectrometric
determinations to the mass of 16O, the most abundant isotope of
oxygen, and chemists used the weighted mass of all three isotopes
of oxygen 16O, 17O, and 18O. At an international congress devoted to
standardization of scientific weights and measures, the redoubtable
A.O. Nier proposed a solution to these disparate conventions whose
negative consequences were becoming serious. He suggested that
the carbon-12 isotope (12C) be the reference for the atomic mass unit
(amu). By definition, its mass would be exactly 12 amu, a
convention that would be acceptable to the physicists. By adopting
this convention, the average mass for oxygen (the weighted sum of
the three naturally occurring isotopes) becomes 15.9994 amu, a
number close enough to 16 to satisfy the chemists.
2-7
Chapter 2. Terminology, Standards and Mass Spectrometry
2.4 The Fractionation Factor 
The isotopic fractionation factor between two substances A and B is defined as
RA
2.8.
RB
The  value is the ratio of the ratios for the rare to heavy isotope in any two substances A
and B. In terms of  values this expression becomes
A B =
δA
1000 = 1000 + δ A
=
δ
1000 + δ B
1+ B
1000
1+
α A B
2.9.
The  value is a measure of the isotope fractionation between any two phases and is
extremely important in terms of understanding equilibrium isotope exchange. This
concept is the foundation of our field, where the early practitioners realized that the
enrichment of the heavy isotope in one phase relative to coexisting phase in isotopic
equilibrium is a function almost exclusively of temperature. Isotope exchange reactions
are considered in terms of equilibrium thermodynamics in which isotopes of a single
element are exchanged between two substances until equilibrium is reached. (Kinetic
reactions that do not reach equilibrium are important for understanding the mechanisms
of chemical reactions or mineral formation, but should not be considered in terms of the
equilibrium fractionation factor ). The chemical makeup of reactants and products in an
isotope exchange reaction are identical. For the general case of an isotope exchange
reaction between substances A and B, where the subscripts 1 and 2 refer to molecules
totally substituted by the light and heavy isotope, respectively and a and b refer to the
coefficients necessary to balance the reaction, we have
aA1 + bB2 = aA2 + bB1
2.10a.
An example of such a reaction is given by
12
CH4 + 13CO2 = 13CH4 + 12CO2
2.10b.
In a real system, there would be only one methane phase and one CO2 phase, nevertheless
it is thermodynamically valid to consider the components 12CH4 and 13CH4 as making up
the CH4 phase. The equilibrium constant for equation 2.10a the above reaction is written
in the usual way
K=
 A2 a B1 b   A2
 A1 a B2 b B2
A1 
b
B1 
a
2.11.
The terms in parentheses are activities but, in practice, ratios are normally used. The
difference between concentrations and ratios of isotopologues is normally negligible (i.e.
2-8
Sharp, Z.D. Principles of Stable Isotope Geochemistry
the activity coefficient   1), so that substituting ratio for activities is valid. For the
reaction given by equation 2.10b, the equilibrium constant is

K=

13
CH 4
12
CH 4



CO  

CO 
12
13
12
13
13
12
CO2
2
CH 4
CO2
CH 4
2.12.
2
Finally, because the reaction is written with the hydrogen (in methane) and oxygen (in
CO2) as having the same value in the numerators and denominators (we are considering
their isotopic composition fixed), equation 2.12 becomes simply


K=

C
13
C
12
13
C
12
C
methane
2.13,
CO 2
which is identical to the  value
If the isotopes are randomly distributed over all possible sites or positions in
substances A and B, the fractionation factor () is related to the equilibrium constant (K)
for isotope exchange reactions in the following way:
 = K1/ n
2.14
where n is the number of atoms exchanged, normally 1 as in the example above. For the
isotope exchange reaction between CO2 and SiO2, we have
K =α=


18
18
O
16
O
16
O
O
CO2
2.15.
SiO 2
Values of  are normally very close to unity, typically 1.00X, and the fractionation is
often considered informally to be equal to X. As a true thermodynamic equilibrium
constant,  is a function of temperature4, so values of  are meaningful only when
temperature is specified. For example, the sulfur isotope fractionation between sphalerite
(ZnS) and galena (PbS) is 1.00360 at 200°C. It is accepted parlance to state that, at
200°C, (1) the sphalerite-galena fractionation is 3.60 per mil, or (2) sphalerite
concentrates 34S by 3.60 per mil relative to galena5. It is common to report the difference
in the isotopic composition as
4
Chemical thermodynamic reactions are a function of both temperature and pressure. Because the volume
change for the isotope exchange reactions 2.10a is extremely small, pressure can be ignored except in
extreme cases. See Horita et al.(2002).
5
Note that the difference of 3.60‰ is only correct if the 34S value of the galena is 0.
2-9
Chapter 2. Terminology, Standards and Mass Spectrometry
 A B =  A –  B
2.16.
is the upper case symbol for the Greek letter delta and is frequently expressed orally as
“big delta” or “cap delta”.
2.5 1000ln, , and the  Value
For the 34S/32S example mentioned above, if the 34S values of sphalerite and
galena are 3.6‰ and 0.0‰, respectively, then  = 1.0036 and the difference between the
34S values of sphalerite and galena is 3.6‰. It is a useful mathematical fact that
1000ln(1.00X) is approximately equal to X. For our sphalerite-galena example, 1000ln =
3.594. That is, 1000ln is the fractionation between sphalerite and galena. It is close the
difference in the isotopic composition of the two phases, and is independent on their
actual isotopic composition. It is sometimes called the per mil fractionation, but this
terminology is strictly not correct because  is unitless. This logarithmic function has
added theoretical significance. For perfect gases, ln varies as 1/T2 and 1/T in the high
and low temperature regions, respectively. As in any expressions or calculations in
thermodynamics, T is absolute temperature in kelvins.
The fractionation expressed as 1000ln is of prime importance in stable isotope
geochemistry. This quantity is very well approximated by the  value, but it is important
to realize that the two are not exactly the same:
 A B =  A –  B  1000ln A-B
2.17.
That is, merely subtracting  values is a good approximation to the per mil fractionation
given by 1000ln and identical to it within the limits of analytical error when the
individual values of A and B as well as A-B are less than about 10‰. As the
numbers in Table 2.2 indicate however, the differences between A-B and 1000ln
become significant when the fractionations or the  values are greater than 10. For all
fractionations that are assumed to be at thermodynamic equilibrium, 1000ln should be
reported. Reporting the differences in delta values is valid when non-equilibrium
fractionations are being studied, such as in biological processes. A few authors have used
the symbol  to designate an isotopic fractionation and define it as  = (  1)1000.
Again, for small values of , this function is almost identical to 1000ln (Table 2.2). It is
recommended that not be used for equilibrium reactions. Instead  is more commonly
used in kinetic, non-equilibrium processes, where the isotopic composition of two phases
can be measured, but because they are out of chemical equilibrium, do not follow the
rules of classical thermodynamics.
Table 2.2. Comparison between values obtained using different
expressions for isotopic fractionations.
A
B

A-B
A-B
103ln A-B
1.0
5.0
10.0
0.0
0.0
5.0
1.00100
1.00500
1.00498
1.00
5.00
5.00
1.00
5.00
4.98
1.000
4.988
4.963
2-10
Sharp, Z.D. Principles of Stable Isotope Geochemistry
10.0
12.0
15.0
20.0
20.0
30.0
30.0
30.0
30.0
0.0
0.0
0.0
0.0
5.0
5.0
20.0
15.0
10.0
1.01000
1.01200
1.01500
1.02000
1.01493
1.02488
1.00980
1.01478
1.01980
10.00
12.00
15.00
20.00
15.00
25.00
10.00
15.00
20.00
10.00
12.00
15.00
20.00
14.93
24.88
9.80
14.78
19.80
9.950
11.929
14.889
19.803
14.815
24.571
9.756
14.670
19.608
The  function is an integral part of a variety of analytical techniques. For
example, the 18O value of a sample of liquid (l) water is determined by equilibrating the
water with a small amount of CO2 gas at a constant temperature and then measuring the
oxygen isotope composition of the equilibrated CO2 gas in a mass spectrometer. At 25°C,
the fractionation factor  between CO2(gas) and H2Ol is 1.04120. This is approximately
equivalent to stating that CO2 is 40.37‰ (103ln = 40.37‰) heavier than the water with
which it was equilibrated, but the actual 18O value of the water is not equal to the 18O
value of CO2 – 40.37‰. The 18O value of CO2 in equilibrium with H2O is determined
using equation 2.9.
As another example, the isotopic compositions of carbon and oxygen in
carbonates are determined by reacting the carbonates with 100% phosphoric acid and
measuring the CO2 that is released during the decarbonation reaction. All of the carbon is
released during this procedure and the 13C value of the CO2 gas is identical to the 13C
value of the original carbonate. Only 2/3 of the oxygen in the carbonate is transferred to
the CO2 gas. There is a temperature dependent isotopic fractionation between the oxygen
in the evolved CO2 and the oxygen in the original carbonate. To a first-approximation, as
long as the temperature of acid dissolution reaction is held constant, the fractionation
between the carbonate and liberated CO2 is constant. This provides us with the so-called
acid fractionation factor,  for CO2 liberated from a carbonate sample. If we know the
 value between evolved CO2 gas and carbonate at the reaction temperature, we can
calculate the 18O value of the carbonate itself. At 25°C, CO2-calcite) for the
phosphoric acid reaction is 1.01025. That is, the liberated CO2 is about 10‰ heavier than
the calcite. From equation 2.9, we have
  1.01025 
1000  CO2
1000   calcite
2.18.
If the 18O value of the calcite is -6.78‰, then the liberated CO2 gas will have a 18O
value of 3.40‰. Interestingly, this  value is not the same as the equilibrium
fractionation between CO2 and calcite. At 25°C, the equilibrium CO2-calcite value is
1.01258. The 1.01025 value is an empirical determination of the fractionation between a
calcite sample and the CO2 liberated in a non-equilibrium, but repeatable, fractionation
that occurs during acid dissolution. It would probably be more correct to use  for this
equation, because the fractionation is not the same as the equilibrium  value for CO2
and calcite.
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Chapter 2. Terminology, Standards and Mass Spectrometry
2.6 Reference Standards
Very precise comparisons of isotopic compositions of materials can be
determined in a given laboratory, but to allow for accurate intercomparisons of data
obtained in different laboratories, an internationally accepted set of reference standards is
available to all workers in the field. The measured isotopic composition of any substance
should be the same in all laboratories after calibrations have been made with these
international reference standards. Beginning in the 1970s, committees of stable isotope
geochemists convened periodically in Vienna to select standard materials and to establish
protocols for calibrating mass spectrometer analyses and presenting stable isotope data
(Coplen and Clayton, 1973; Coplen et al., 1983; Hut, 1987; Coplen, 1996). These
reference materials (Appendix 1) are available from the National Institute for Standards
and Technology (NIST) in Gaithersburg, Maryland and from the International Atomic
Energy Agency (IAEA) in Vienna. International reference standards are in limited supply
and are not intended for use as working standards. They are provided in small quantities
to allow workers to establish larger supplies of secondary reference materials (solids,
liquids and gases) that in turn can be used on a daily basis as working standards, for
calibrating extraction techniques, and so on.
The history of stable isotope reference materials is long and complex and
unfortunately has led to considerable confusion. The early Chicago group reported 13C
and 18O values of carbonates relative to the carbon and oxygen isotope compositions of
a powdered specimen of Belemnitella americana from the Upper Cretaceous Peedee
formation of South Carolina. They called this calcite standard PDB (PeeDee Belemnite).
When the original supply of this material became exhausted, another sample was
prepared and named PDB II, a standard that was later replaced by PDB III. In each case
the new standard was carefully calibrated against the isotopic composition of the original
sample of PDB. Despite the fact that the original supply of PDB is exhausted, PDB
remains the standard used in reporting all carbon isotope analyses and most of the oxygen
isotope analyses of low-temperature carbonates. Secondary standards have been
developed with isotopic compositions that are calibrated to the original PDB.
The Chicago group also created an Mean Ocean Water by taking the average
ocean water samples collected at depths ranging from 500 and 2000 meters, with the goal
of creating a sample that was representative of the average oxygen isotope composition
of the ocean (Epstein and Mayeda, 1953). Each ocean has a slightly different 18O and
D value (Table 2.3). In order to standardize the average ocean water value, Harmon
Craig compared the 18O and D values of these ocean waters to the National Bureau of
Standards Potomac River water (NBS-1). He coined the term Standard Mean Ocean
Water, or SMOW as the average of the different ocean waters, with  values defined in
terms of NBS 1 by the following relationships:
18
D/H (SMOW) ≡ 1.050 D/H (NBS-1)
O/16O (SMOW) ≡ 1.008 18O/16O (NBS-1)
2.20.
This allowed workers everywhere to standardize their ‘ocean water’ values to the widely
distributed NBS-1 (Fig. 2.1). Ultimately an actual water standard with D and 18O
values equal to the defined SMOW was made by mixing waters with different isotopic
2-12
Sharp, Z.D. Principles of Stable Isotope Geochemistry
compositions. This physical sample is called VSMOW (or V-SMOW), where the V is an
abbreviation for ‘Vienna’, the headquarters for the International Atomic Energy Agency
that distributes the standard. Unfortunately the original VSMOW has been used up, and a
second standard VSMOW2 was made by the IAEA Isotope Hydrology Laboratory in
2006. It is thought to be essentially identical to the original VSMOW (except perhaps for
its 17O value) and is available for distribution through the IAEA. Many other accepted
standards are available from the IAEA, so that standardization procedures are now
relatively routine and stable isotope analyses made anywhere in the world are, for the
most part, easily comparable.
Table 2.3.  18O and D values of the average
deep water samples from the different oceans.
Compilation from Craig (1961).
Location (sample)
Atlantic
Pacific
Indian
NBS-1
D‰
-0.7
+0.9
+0.1
-47.60
18O (‰)
+0.14
+0.04
-0.07
-7.94
A further complication has developed because of the use of non-quantitative
techniques for determining stable isotope ratios. Carbon and nitrogen isotope analyses of
organic matter, and to a lesser extent sulfur isotope analyses, are now made almost
exclusively using an elemental analyzer. This methodology consists of combusting
organic matter (or S-bearing phase) in a helium stream and excess oxygen gas. The C is
converted to CO2, N is converted to N2 and S is converted to SO2. The gases are
separated in a gas chromatograph using He as a carrier gas and measured in ‘continuous
flow mode’ in the mass spectrometer (see section 2.7.2 for a discussion of continuous
flow mass spectrometry). Unfortunately, the measured isotopic composition is often not
the same as the actual composition of the sample due to a number of factors, including
incomplete reaction, contamination from other C and N sources in the organic matter and
fractionation at the open split. Many laboratories and the IAEA have developed standards
that can be used to compare the isotopic compositions of specific isotopic compounds,
including cellulose, benzoic acid and caffeine. An outline of the reference materials for
selected elements is given below.
2.6.1 Hydrogen
In much of the early literature on the abundance of deuterium in natural materials,
a sample of Lake Michigan water was used as a reference standard. The D value of the
Lake Michigan standard is 42.4‰ on the modern VSMOW scale. Today, all hydrogen
isotope analyses are reported relative to VSMOW, a logical geochemical reference
material because ocean water is by far the largest terrestrial reservoir of water. By
definition, the D value of VSMOW is equal to zero. VSMOW has a D/H ratio that is
higher than the ratios of most other materials on Earth, an interesting geochemical fact in
itself. Thus most D values of natural materials on our planet are negative on this scale in
2-13
Chapter 2. Terminology, Standards and Mass Spectrometry
contrast to D values of extraterrestrial substances
which can be extremely positive for reasons
explained in Chapter 13.
SMOW was originally defined relative to
NBS-1 (Fig. 2.1) by equation 2.19. A physical
sample of water with an isotopic composition
equal to SMOW was made by Harmon Craig and
Ray Weiss, who distilled a large sample of ocean
water (Fig. 2.2 and Fig. 2.3) and adjusted its
hydrogen and oxygen isotope compositions to
match SMOW by carefully adding appropriate
amounts of other waters of different isotopic
compositions. This was the original VSMOW
sample. By definition, it has a D value ≡ 0‰ on
the VSMOW scale. Practitioners in the field
should realize that data presented in older
literature using the SMOW reference are identical
to those using the VSMOW or VSMOW2
reference. No additional corrections are needed in
order to compare data reported relative to either
reference. In other words, the D and 18O values
of SMOW and VSMOW are identical6.
All hydrogen isotope ratios are measured
using H2 gas in the mass spectrometer and H2O
gas with laser spectroscopy7 (Table 2.4). The raw
D value of a sample whose D/H ratio is quite
different, say 20-30‰ or more from that of the
Fig. 2.1. Picture of an ampoule (glass breakseal tube) containing NBS-1 standard, a
working standard, will generally be very slightly
reference standard that was formerly
different when measured on different mass
distributed by the National Bureau of
spectrometers. The factor most responsible for
Standards (now NIST).
this effect is the inevitable production of the ion
H3+ (the same mass 3 as DH+) in the source of the
The label reads:
Isotope Reference Sample #1.
mass spectrometer (or non-linearities in the case
PROTIUM OXIDE (Ordinary
of laser spectroscopy). In order to resolve this
Water)
problem, an isotopically light natural water from
Antarctica was selected as an additional reference standard for use in determining the
stretching factor for individual mass spectrometers (see Appendix 2 for further
discussion). The stretching factor is especially important for hydrogen isotope
measurements because the variation in D values of natural materials are about ten times
larger than variations in any other element. This standard was given the acronym SLAP
(Standard Light Antarctic Precipitation) and has a D value of 428‰ on the basis of a
comparison study made in many of the major stable isotope laboratories in the world in
the 1970s. (SLAP2 has a D value of -427.5±0.3‰). In order to calibrate a machine for
6
7
see https://nucleus.iaea.org/rpst/Documents/VSMOW2_SLAP2.pdf for details of VSMOW2
See sections 2.7 and 2.8 for methodological details
2-14
Sharp, Z.D. Principles of Stable Isotope Geochemistry
Fig. 2.2. The ocean pier at the Scripps Institute in San Diego, where Harmon Craig and Ray
Weiss collected water for VSMOW. Photo by author.
Table 2.4. Gases commonly measured in conventional gas source isotope ratio …