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 chapter "Environmental Isotopes" by Clark and Fritz (1997)

Definitions

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.

Isotope Terminology

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 calculated by:

(in ‰) = (R_sample/R_standard - 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. Harmon Craig's immortal limerick says it all:

There was was a young man from Cornell
Who pronounced every "delta" as "del"
But the spirit of Urey
Returned in a fury
And transferred that fellow to hell

There are several commonly used ways for making comparisons between the d values of two materials. The first three are preferred.

• 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 than -20‰)
• 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).

Basic Principles

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 equilibrium reaction.

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 = R_A/R_B

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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