Introduction

Stable isotopes are those isotopes that do not undergo radioactive decay; thus, their nuclei are stable and their masses remain the same. However, they may themselves be the product of the decay of radioactive isotopes. (See "radiogenic" isotopes discussion on the Radioactive Isotopes page). The isotopic composition of stable isotoes is, however, subject to natural variation due to mass dependent fractionation. That is to say, mass differences between isotopes result in isotopic fractionation during chemical processes. In hydrological (as well as biological) studies, the stable isotopes of interest are generally H, C, N, O, S, B, and Li.

Isotopic fractionation

During isotopic fractionation, heavy and light isotopes partition differently between two compounds or phases. Isotope fractionation occurs because the bond energy of each isotope is slightly different, with heavier isotopes having stronger bonds and slower reaction rates. The difference in bonding energy and reaction rates are proportional to the mass difference between isotopes. Thus, light elements are more likely to exhibit isotopic fractionation than heavy isotopes. For example, the relatively light ¹²C and ¹³C isotopes have an 8% mass difference and undergo stable isotope fractionation. In contrast, the heavy isotopes ⁸⁷Sr and ⁸⁶Sr have a 1.1% mass difference and do not exhibit detectable mass fractionation. Isotopes especially susceptible to fractionation are of the elements that are among the most abundant on earth: H, C, N, O, and S.

Equilibrium fractionation describes isotopic exchange reactions that occur between two different phases of a compound at a rate that maintains equilibrium, as with the transformation of water vapor to liquid precipitation.Although the process is in equilibrium, the rate of these exchanges is different so that the result is an enrichment of one of the isotopes. Such an exchange can be expressed as:

where A and B are phases, and superscripts 1 and 2 are isotopes.

The equilibrium constant may be expressed by

This can also be expressed as a ratio of the isotopes in each phase:

and

where a_A-B is the fractionation factor, the ratio of the numbers of any two isotopes in one chemical compound A divided by the corresponding ratio for compound B.

Other factors come into play to influence equilibrium fractionation and isotope effects, chiefly vibrational energy, which is related to the zero-point energy difference and is dependent on temperature. Different isotopes have different zero point energies for the vibrational mode of a bond. Temperature is a measure of energy in a system, translated to the energy of the bond. The zero point of energy changes with temperature increases. The difference in zero point energy between two isotopes decreases. Typically, the heavier isotope has a lower zero point energy, thus it takes more energy to break the bond of a heavy isotope compared to the light isotope. One may expect greater isotopic fractionation at low temperatures, and no isotopic fractionation at very high temperatures.

Kinetic fractionation

Kinetic fractionation is fractionation that is unidirectional, where equilibrium is not attained. This type of fractionation applies to evaporation of surface waters and to most biogeochemical reactions, where the lighter isotope is faster reacting and becomes concentrated in the products. More information on kinetic fractionation is provided under the discussion of oxygen and hydrogen isotopes.