Fundamentals of Stable Isotope Geochemistry
The following is a brief review of some of the fundamentals of stable
isotope geochemistry, including definitions,
terminology, basic principles,
standards, and guidelines
on reporting data. The sources of the text are given at the end.
For a more detailed discussion of the fundamentals, see the chapter "Fundamentals
of Isotope Geochemistry" by Kendall and Caldwell (1998) or the
Isotopes" by Clark and Fritz (1997)
Isotopes are atoms of the same element that have the same numbers of
protons and electrons but different numbers of neutrons. The difference
in the number of neutrons between the various isotopes of an element means
that the various isotopes have similar charges but different masses. The
superscript number to the left of the element designation indicates the
number of protons plus neutrons in the isotope. For example, among the
hydrogen isotopes, deuterium (denoted as D or 2H) has one neutron
and one proton. This is approximately twice the mass of protium (1H)
whereas tritium (3H) has two neutrons and is approximately three
times the mass of protium. All isotopes of oxygen have 8 electrons and
8 protons; however, an oxygen atom with a mass of 18 (denoted 18O)
has 2 more neutrons than oxygen-16 (16O).
The original isotopic compositions of planetary systems are a function
of nuclear processes in stars. Over time, isotopic compositions in terrestrial
environments change by the processes of radioactive decay, cosmic ray interactions,
and such anthropogenic activities as processing of nuclear fuels, reactor
accidents, and nuclear-weapons testing. Radioactive (unstable) isotopes
are nuclei that spontaneously disintegrate over time to form other isotopes.
During the disintegration, radioactive isotopes emit alpha or beta particles
and sometimes also gamma rays. The so-called stable isotopes are nuclei
that do not appear to decay to other isotopes on geologic timescales, but
may themselves be produced by the decay of radioactive isotopes. For example,
14C, a radioisotope of carbon, is produced in the atmosphere
by the interaction cosmic-ray neutrons with stable 14N. With
a half-life of about 5730 years, 14C decays back to 14N
by emission of a beta particle; the stable 14N produced by radioactive
decay is called "radiogenic" nitrogen.
In everyday speech, isotopes are still described with the element name
given first, as in "oxygen-18" or "O-18" instead of
"18- oxygen". And many texts, especially older ones that were
typeset without superscripts, show the mass number to the right of the
element abbreviation, as in C-13 or C13 for carbon-13. However, both in
speech and in media, it is becoming more common to put the mass number
before the element name, as is 15N.
The stable isotopic compositions of low-mass (light) elements such as
oxygen, hydrogen, carbon, nitrogen, and sulfur are normally reported as
"delta" (d) values in parts per thousand
(denoted as ‰) enrichments or depletions relative to a standard of known
composition. The symbol ‰ is spelled out in several different ways: permil,
per mil, per mill, or per mille. The term "per mill" is the ISO
term, but is not yet widely used. d values are
(in ‰) = (Rsample/Rstandard - 1)1000
where "R" is the ratio of the heavy to light isotope in the
sample or standard. For the elements sulfur, carbon, nitrogen, and oxygen,
the average terrestrial abundance ratio of the heavy to the light isotope
ranges from 1:22 (sulfur) to 1:500 (oxygen); the ratio 2H:1H
is 1:6410. A positive d value means that the
sample contains more of the heavy isotope than the standard; a negative
d value means that the sample contains less
of the heavy isotope than the standard. A d15N
value of +30‰ means that there are 30 parts-per-thousand or 3% more 15N
in the sample relative to the standard.
In ASCII-only media, the term delta is almost always denoted with the
small Greek letter d. In media lacking this
symbol, it is not- uncommonly replaced informally with the letter "d".
The term d is spelled and pronounced delta
not del. The word del describes either of two mathematical terms: an operator
or a partial derivative.
Many isotopers are very sensitive about misuses of isotope terminology.
Craig's immortal limerick says it all:
There was was a young man from Cornell
Who pronounced every "delta" as "del"
But the spirit of Urey
Returned in a fury
And transferred that fellow to hell
There are several commonly used ways for making comparisons between
the d values of two materials. The first three
- higher vs. lower values
- heavier vs. lighter (the "heavier" material is the one with
the higher value)
- more/less positive vs. more/less negative (eg., -10‰ is more positive
- enriched vs. depleted (remember to state what isotope is in short supply;
eg., a material is enriched in 18O or 16O relative
to some other material).
The various isotopes of an element have slightly different chemical
and physical properties because of their mass differences. For elements
of low atomic numbers, these mass differences are large enough for many
physical, chemical, and biological processes or reactions to "fractionate"
or change the relative proportions of various isotopes. Two different types
of processes -- equilibrium and kinetic isotope effects -- cause isotope
fractionation. As a consequence of fractionation processes, waters and
solutes often develop unique isotopic compositions (ratios of heavy to
light isotopes) that may be indicative of their source or of the processes
that formed them.
Equilibrium isotope-exchange reactions involve the redistribution of
isotopes of an element among various species or compounds. At equilibrium,
the forward and backward reaction rates of any particular isotope are identical.
This does not mean that the isotopic compositions of two compounds at equilibrium
are identical, but only that the ratios of the different isotopes in each
compound are constant. During equilibrium reactions, the heavier isotope
generally becomes enriched (preferentially accumulates) in the species
or compound with the higher energy state. For example, sulfate is enriched
in 34S relative to sulfide; consequently, the sulfide is described
as depleted in 34S relative to sulfate. During phase changes,
the ratio of heavy to light isotopes in the molecules in the two phases
changes. For example, as water vapor condenses (an equilibrium process),
the heavier water isotopes (18O and 2H) become enriched
in the liquid phase while the lighter isotopes (16O and 1H)
tend toward the vapor phase.
Kinetic isotope fractionations occur in systems out of isotopic equilibrium
where forward and backward reaction rates are not identical. The reactions
may, in fact, be unidirectional if the reaction products become physically
isolated from the reactants. Reaction rates depend on the ratios of the
masses of the isotopes and their vibrational energies; as a general rule,
bonds between the lighter isotopes are broken more easily than the stronger
bonds between the heavy isotopes. Hence, the lighter isotopes react more
readily and become concentrated in the products, and the residual reactants
become enriched in the heavy isotopes.
Biological processes are generally unidirectional and are excellent
examples of "kinetic" isotope reactions. Organisms preferentially
use the lighter isotopic species because of the lower energy "costs",
resulting in significant fractionations between the substrate (heavier)
and the biologically mediated product (lighter). The magnitude of the fractionation
depends on the reaction pathway utilized and the relative energies of the
bonds being severed and formed by the reaction. In general, slower reaction
steps show greater isotopic fractionation than faster steps because the
organism has time to be more selective. Kinetic reactions can result in
fractionations very different from, and typically larger than, the equivalent
Many reactions can take place either under purely equilibrium conditions
or be affected by an additional kinetic isotope fractionation. For example,
although evaporation can take place under purely equilibrium conditions
(i.e., at 100% humidity when the air is still), more typically the products
become partially isolated from the reactants (e.g., the resultant vapor
is blown downwind). Under these conditions, the isotopic compositions of
the water and vapor are affected by an additional kinetic isotope fractionation
of variable magnitude.
The partitioning of stable isotopes between two substances A and B can
be expressed by use of the isotopic fractionation factor (alpha):
A-B = RA/RB
where "R" is the ratio of the heavy to light isotope (e.g.,
2H/1H or 18O/16O). Values for
alpha tend to be very close to 1. Kinetic fractionation factors are typically
described in terms of enrichment or discrimination factors; these are defined
in various ways by different researchers.
Isotopic compositions are determined in specialized laboratories using
isotope ratio mass spectrometry. The analytical precisions are small relative
to the ranges in d values that occur in natural
earth systems. Typical one standard deviation analytical precisions for
oxygen, carbon, nitrogen, and sulfur isotopes are in the range of 0.05‰
to 0.2‰; typical precisions for hydrogen isotopes are poorer, from 0.2
to 2.0‰, because of the lower 2H:1H ratio.
Stable Isotope Standards
Various isotope standards are used for reporting isotopic compositions;
the compositions of each of the standards have been defined as 0‰. Stable
oxygen and hydrogen isotopic ratios are normally reported relative to the
SMOW standard ("Standard Mean Ocean Water" (Craig, 1961b)) or
the virtually equivalent VSMOW (Vienna-SMOW) standard. Carbon stable isotope
ratios are reported relative to the PDB (for Pee Dee Belemnite) or the
equivalent VPDB (Vienna PDB) standard. The oxygen stable isotope ratios
of carbonates are commonly reported relative to PDB or VPDB, also. Sulfur
and nitrogen isotopes are reported relative to CDT (for Cañon Diablo
Troilite) and AIR (for atmospheric air), respectively.
VSMOW and VPDB are virtually identical to the now-unavailable SMOW and
PDB standards. However, use of VSMOW and VPDB is preferred (and in some
journals is now required) because their use implies that the measurements
have been calibrated according to IAEA (International Atomic Energy Agency)
guidelines for expression of delta values relative to available reference
materials on normalized permil scales (Coplen,
1996). Laboratories accustomed to analyzing anthropogenic, highly enriched
compounds may report absolute isotope abundances in atomic-weight percent
or ppm instead of ratios in per mil.
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||Kendall, C., Sklash, M.G. and Bullen, T.D. (1995). "Isotope Tracers
of Water and Solute Sources in Catchments", In: S.T. Trudgill (Ed.),
Solute Modelling in Catchment Systems, John Wiley and Sons Ltd.,
New York, pp. 261-303.
||Kendall, C. and Caldwell, E. A. (1998). "Fundamentals
of Isotope Geochemistry", In: C. Kendall and J.J. McDonnell (Eds.),
Tracers in Catchment Hydrology. Elsevier Science, Amsterdam, pp.