Abundance and Measurement of Stable Isotopes

The discovery of isotopes is best understood in the context of the spectacular advances in physics and chemistry that transpired during the last 200 years. Around the year 1800, compounds and elements had been distinguished. About 39 elements were recognized, and discoveries of new elements were occurring rapidly. At about this time, the chemist John Dalton revived the ancient idea of the atom, a word derived from the Greek “atomos,” which literally means “indivisible.” According to Dalton’s theory, all matter is made of atoms which are immutable and which cannot be further subdivided. Moreover, Dalton argued that all atoms of a given element are identical in all respects, including mass, but that atoms of different elements have different masses. Even today, Dalton’s atomic theory would be accepted by a casual reader, yet later developments have shown that it is erroneous in almost every one of its key aspects. Nevertheless, Dalton’s concept of the atom was a great advance, and, with it, he not only produced the first table of atomic weights, but also generated the concept that compounds comprise elements combined in definite proportions. His theory laid the groundwork for many other important advances in early nineteenth-century chemistry, including Avogadro’s 1811 hypothesis that equal volumes of gas contain equal numbers of particles, and Prout’s 1815 hypothesis that the atomic weights of the elements are integral multiples of the weight of hydrogen. By 1870, approximately 65 elements had been identified. In that year, Mendeleev codified much of the available chemical knowledge in his “periodic table,” which basically portrayed the relationships between the chemical properties of the elements and their atomic weights. The regularities that Mendeleev found directly lead to the discovery of several “new” elements—for example, Sc, Ga, Ge, and Hf—that filled vacancies in his table and confirmed his predictions of their chemical properties and atomic weights. Similarly, shortly after Rayleigh and Ramsay isolated Ar from air in 1894, the element He was isolated from uranium minerals in 1895; the elements Ne, Kr, and Xe were found in air in 1898; and Rn was discovered in 1900.

Igneous Rocks, Meteorites, and Fluid-Rock Interactions

Oxygen is the most important element in common, rock-forming minerals. Earth’s crust and mantle contain about 44 wt. % oxygen, and even with its dense iron core, the bulk Earth is estimated to be approximately 30% oxygen. Considering the low mass and large size of the oxygen atom, the oxygen content is even higher if expressed in terms of vol. % or mol. %. For the above reason, a central problem of stable isotope geochemistry is to explain the distribution of oxygen isotope ratios in rocks. As shown in this chapter, much of the diversity in the abundance ratios is related to interactions of rocks with Earth’s extensive hydrosphere, which is nearly 89 wt. % oxygen. Even though hydrogen is only a minor element in rocks, some discussion of hydrogen isotopes is included here because they provide powerful complementary relationships to evaluate fluid-rock interactions. It has been suspected for centuries, and has now been proven by oxygen isotope data (see later), that Earth and the Moon have very similar origins. In particular, the δ18O values of large rock reservoirs on the Moon and Earth are practically identical. Diverse lunar lithologies have remarkably uniform values ranging only from +5.4 to +6.8 relative to SMOW, with the subset of lunar igneous rocks showing even less variation at +5.7 ± 0.2 (Epstein and Taylor, 1971; Taylor and Epstein, 1973). The same limited range of values is found for the largest lithologic reservoirs on Earth. For example, mid-ocean ridge (MOR) basalts are the most abundant igneous rock type on Earth, and cover practically the entire ocean floor. The δ18O values of these basalts are practically uniform at +5.7 ± 0.5 (Kyser, 1986). Similarly, other mafic lavas, as well as peridotites, pyroxenites, and practically all other mantle materials with the exception of the ophiolites and eclogites, have δ18O values in the restricted range of +5.0 to +8.0. Moreover, no apparent secular trend over geologic time has been found in the bulk δ18O values of these reservoirs. For these reasons, it is likely that the bulk δ18O values of Earth and the Moon are identical and very close to +5.7 ± 0.2.

Isotope Hydrology

No substance exemplifies the principles of isotope distribution better than water. Water is practically ubiquitous at the Earth’s surface, where it undergoes phase transitions, interacts with minerals and the atmosphere, and participates in complex metabolic processes essential to life. The isotopes of hydrogen and oxygen undergo large fractionations during these processes, providing a multiple isotopic tracer record of diverse phenomena. In the hydrologic cycle, hydrogen and oxygen isotope ratios provide conservative tracers, uniquely intrinsic to the water molecule, that elucidate the origin, phase transitions, and transport of H2O. In particular, the isotope data associated with these processes are amenable to theoretical modeling using the laws of physical chemistry. The characteristics of the principal reservoirs of natural waters on Earth are provided in the following sections. The distinct characters of these different reservoirs are very clearly shown on graphs where the δD values are plotted against those of δ18O. The oceans constitute 97.25% of the hydrosphere, cover 70% of the Earth’s surface to a mean depth of 3.8 km, and have an enormous total volume of 1.37 × 109 km3. This large reservoir has strikingly uniform isotopic concentrations, with almost all samples having δ18O = 0 ± 1 and δD = 0 ± 5 per mil relative to SMOW (Craig and Gordon, 1965). Values outside these ranges are almost invariably confined to surface waters that have salinities that differ from the normal value of 3.5 wt. %. These varations are generally attributable to evaporation, formation of sea ice, or addition of meteoric precipitation that may occur by direct rainfall, by river inflow, or by melting of icebergs. The latter effect was clearly documented by Epstein and Mayeda (1953) in the surface waters of the North Atlantic, where the isotopic variations were strongly correlated with variations in salinity. In detail, the deep waters of different ocean basins have distinct values of δ18O and salinity. Thus, the δ18O values of deep waters from the North Atlantic (ca. +0.05‰), Pacific (-0.15‰), and Antarctic (-0.40‰) oceans are distinct, and careful measurements can be used to infer details of oceanic circulation patterns (Craig and Gordon, 1965).

Isotopic Exchange and Equilibrium Fractionation

Equilibrium isotopic fractionations are best understood in terms of reactions that involve the transfer of isotopes between two phases or molecular species that have a common element (M). These isotopic exchange reactions may be written in one of several standard forms, such as . . . aAM*b + cBMd = aAMb + cBM*d (2.1) . . . where AMb and BMd represent the chemical formulas of the phases or species, AM*b and BM*d represent the same phases or species in which the trace isotope has replaced some or all of the atoms of element M, and a, b, c, and d are stoichiometric coefficients. In the case where all of the molecules are homogeneous, that is, where AMb and BMd are composed solely of the common isotope of M, and where AM*b and BM*d are phases or species in which the trace isotope M* has replaced all atoms of element M, then the product a × b equals c × d and represents the total number of atoms exchanged in the reaction. The concept of the isotopic exchange reaction is best shown by an example. Consider the exchange of deuterium between water and hydrogen gas. This may be written as a reaction among isotopically homogeneous molecules; that is, . . . H2O + D2 = D2O + H2 (2.2a) . . . or, alternatively, as exchange between homogeneous and heterogeneous molecules: . . . H2O + HD = HDO + H2 (2.2b) . . . Much of the utility of isotopic exchange reactions is that they may be described by equilibrium constants, defined in the standard way as the quotient of the activities of the products and reactants. Thus, the equilibrium condition for equation 2.2b becomes . . . K = ([HDO][H2])/([H2O][HD]) (2.3) . . . where K is the equilibrium constant. In equation 2.3, K has a particularly high value of 3.7 at 25°C.

Nonequilibrium Fractionation and Isotopic Transport

At the Earth’s surface, isotopic disequilibrium is far more common than isotopic equilibrium. Although isotopic equilibrium is approached in certain instances, numerous constituents of the lithosphere, hydrosphere, atmosphere, and biosphere are simply not in mutual isotopic equilibrium. This condition is consistent with the complex and dynamic conditions typical of the Earth’s surface, particularly the large material fluxes, the rapid changes in temperature, and the biological mediation of chemical systems. Fortunately, several aspects of isotopic disequilibrium may be understood in terms of elementary physical laws. For homogeneous phases such as gases or well-stirred liquids, or for cases where spatial gradients in isotopic contents are not of primary interest, then the principles of elementary kinetics can be applied. For cases where isotopic gradients are important, the laws of diffusion are applicable. If two phases are out of isotopic equilibrium, they will progressively tend to approach the equilibrium state with the passage of time. This phenomenon occurs by the process of isotopic exchange, and its rate may be understood by examining isotopic exchange reactions from the viewpoint of elementary kinetic theory. In particular, consider the generalized exchange reaction where A and B are two phases that share a common major element, and A* and B* represent the same phases in which the trace isotope of that element is present. The present analysis is simplified if the exchange reaction is written so that only one atom is exchanged, in which case the stoichiometric coefficients are all unity. For reaction 4.1, kinetic principles assert that the forward and reverse reactions do not, in general, proceed at identical rates, but rather at the rates indicated by the quantities kα and k written by the arrows, multiplied by the appropriate concentrations terms. Assuming that the reaction is first order, then the reaction progress, represented by the quantity dA*/dt, may be expressed by the difference between these forward and reverse rates, as follows: . . . dA*/dt = kα(A)(B*) − k(A*)(B) (4.2) . . . In order to evaluate the exchange process more completely, is important to carefully chose a consistent set of concentrations for substitution equation 4.2.