Sulfur isotope biogeochemistry is the study of the distribution of sulfur isotopes in biological and geological materials. In addition to its common isotope, 32S, sulfur has three rare stable isotopes: 34S, 36S, and 33S. The distribution of these isotopes in the environment is controlled by many biochemical and physical processes, including biological metabolisms, mineral formation processes, and atmospheric chemistry. Measuring the abundance of sulfur stable isotopes in natural materials, like bacterial cultures, minerals, or seawater, can reveal information about these processes both in the modern environment and over Earth history.
Background
Natural abundance of sulfur isotopes
Sulfur has 24 known isotopes, 4 of which are stable (meaning that they do not undergo radioactive decay). 32S, the common isotope of sulfur, makes up 95.0% of the natural sulfur on Earth. In the atomic symbol of 32S, the number 32 refers to the mass of each sulfur atom in daltons, the result of the 16 protons and 16 neutrons of 1 dalton each that make up the sulfur nucleus. The three rare stable isotopes of sulfur are 34S (4.2% of natural sulfur), 33S (0.75%), and 36S (0.015%). These isotopes differ from 32S in the number of neutrons in each atom, but not the number of protons or electrons; as a result, each isotope has a slightly different mass, but has nearly identical chemical properties.
Physical chemistry Small differences in mass between stable isotopes of the same element can lead to a phenomenon called an "isotope effect," where heavier or lighter isotopes are preferentially incorporated into different natural materials depending on the materials' chemical composition or physical state. Isotope effects are divided into two main groups: kinetic isotope effects and equilibrium isotope effects. A kinetic isotope effect occurs when a reaction is irreversible, meaning that the reaction only proceeds in the direction from reactants to products. Kinetic isotope effects cause isotopic fractionation—meaning that they affect the isotopic composition of reactant and product compounds—because the mass differences between stable isotopes can affect the rate of chemical reactions. It takes more energy to reach the transition state of a reaction if the compound has bonds with a heavier isotope, which causes the compound with heavier isotopes to react more slowly. Normal kinetic isotope effects cause the lighter isotope (or isotopes) to be preferentially included in a reaction's product. The products are then said to be "depleted" in the heavy isotope relative to the reactant. Rarely, inverse kinetic isotope effects may occur, where the heavier isotope is preferentially included in a reaction's product.
Equilibrium isotope effects cause fractionation because it is more chemically favorable for heavy isotopes to take part in stronger bonds. An equilibrium isotope effect occurs when a reaction is at equilibrium, meaning that the reaction is able to occur in both directions simultaneously. When a reaction is at equilibrium, heavy isotopes will preferentially accumulate where they can form the strongest bonds. For example, when the water in a sealed, half-full bottle is in equilibrium with the vapor above it, the heavier isotopes 2H and 18O will accumulate in the liquid, where they form stronger bonds, while the lighter isotopes 1H and 16O will accumulate in the vapor.Craig, H. and Gordon, L. I. 1965. "Deuterium and oxygen 18 variations in the ocean and the marine atmosphere". In Stable Isotopes in Oceanographic Studies and Paleotemperatures, Edited by: Tongiorgi, E. 9–130. Pisa: Laboratorio di Geologia Nucleare. The liquid is then said to be "enriched" in the heavy isotope relative to the vapor.
Calculations
Delta notation Differences in the abundance of stable isotopes among natural materials are usually very small (natural differences in the ratio of rare to common isotope are almost always below 0.1%, and sometimes much smaller). Nevertheless, these very small differences can record meaningful biological and geological processes. To facilitate comparison of these small but meaningful differences, isotope abundances in natural materials are often reported relative to isotope abundances in designated standards. The convention for reporting the measured difference between a sample and a standard is called "delta notation." For example, imagine an element X for which we wish to compare the rare, heavy stable isotope with atomic mass A (AX) to the light, common isotope with atomic mass B (BX). The abundance of AX and BX in any given material is reported with the notation δAX. δAX for the sample material is calculated as follows:
AR = (total amount of AX)/(total amount of BX)
δAXsample = (ARsample − ARstandard)/ARstandard
δ values are most commonly reported in parts per thousand, commonly referred to in isotope chemistry as per mille and represented by the symbol ‰. To report δ values in per mille, the δ value as calculated above should be multiplied by 1000:
δAXsample (‰) = ((ARsample − ARstandard)/ARstandard) * 1000
Fractionation factors While an isotope effect is the physical tendency for stable isotopes to distribute in a particular way, the isotopic fractionation is the measurable result of this tendency. The isotopic fractionation of a natural process can be calculated from measured isotope abundances. The calculated value is called a "fractionation factor," and allows the effect of different processes on isotope distributions to be mathematically compared. For example, imagine a chemical reaction Reactant → Product. Reactant and Product are materials that both contain the element X, and X has two stable isotopes, AX (the heavy isotope, with a mass of A) and BX (the light isotope, with a mass of B). The fractionation factor for the element X in the reaction Reactant → Product is represented by the notation
AαProduct/Reactant. AαProduct/Reactant is calculated as follows:
AαProduct/Reactant = (δAXProduct + 1)/(δAXReactant + 1)
Fractionation factors can also be reported using the notation AεProduct/Reactant, which is sometimes called the "enrichment factor" and is calculated as follows:
AεProduct/Reactant = AαProduct/Reactant − 1
Like δ values, ε values can be reported in per mille by multiplying by 1000.
Δ33S and Δ36S notation All kinetic and equilibrium isotope effects result from differences in atomic mass. As a result, a reaction that fractionates 34S will also fractionate 33S and 36S, and the fractionation factor for each isotope will be mathematically proportional to its mass. Because of the mathematical relationships of their masses, the observed relationships between δ34S, δ33S, and δ36S in most natural materials are approximately δ33S = 0.515 × δ34S and δ36S = 1.90 × δ34S. Rarely, natural processes can create deviations from this relationship, and these deviations are reported as Δ33S and Δ36S values, usually pronounced as "cap delta." These values are typically calculated as follows:
Δ33S = 1000 × [(1 + δ33S/1000) − (1 + δ34S 1000)0.518 − 1]
Δ36S = 1000 × [(1 + δ36S/1000) − (1 + δ34S/1000)1.91 − 1]
However, the method for calculating Δ33S and Δ36S values is not standardized, and can differ among publications.
Reference materials Agreed-upon reference materials are required so that reported δ values are comparable among studies. For the sulfur isotope system, δ34S values are reported on the Vienna-Cañon Diablo Troilite (VCDT) scale. The original CDT scale was based on a sample of the mineral troilite recovered from the Canyon Diablo meteorite at Meteor Crater, Arizona, US. The Cañon Diablo Troilite was assigned a δ34S value of 0‰. However, troilite from the Canyon Diablo meteorite was later discovered to have variable sulfur isotope composition. As a result, VCDT was established as a hypothetical sulfur isotope reference with a 34R value of 0.044151 and δ34S of 0‰, but no physical sample of VCDT exists. Samples are now measured in comparison to International Atomic Energy Agency (IAEA) reference materials, which are well-characterized, lab-prepared compounds with known δ34S values. A commonly used IAEA reference material is IAEA-S-1, a silver sulfide reference material with a δ34S value of −0.30‰ VCDT. 33S and 36S abundance can also be measured relative to IAEA reference materials and reported on the VCDT scale. For these isotopes, too, VCDT is established as having δ33S and δ36S values of 0‰. The 33R value of VCDT is 0.007877 and the 36R value is 0.0002. IAEA-S-1 has a 33R value of 0.0007878 and a δ33S value of −0.05‰ VCDT; it has a δ36S value of −0.6‰ VCDT.
Analytical methods and instrumentation The sulfur isotopic composition of natural samples can be determined by Elemental Analysis-Isotope Ratio Mass Spectrometry (EA-IRMS), by Dual Inlet-Isotope Ratio Mass Spectrometry (DI-IRMS), by Multi-Collector-Inductively Coupled Plasma Mass Spectrometry (MC-ICPMS), by Secondary Ion Mass Spectrometry (SIMS), or by Nanoscale secondary ion mass spectrometry (NanoSIMS). MC-ICPMS can be paired with gas chromatography (GC-MC-ICPMS) to separate certain volatile compounds in a sample and measure the sulfur isotopic composition of individual compounds.
The sulfur isotopic compositions of minerals and porewater in sediment are subject to accumulation and diffusion after burial. Reactive transport models are often used to account for the effect of such physical processes and find out the isotopic effect of the process studied.
Natural variations in sulfur isotope abundance
Sulfur in natural materials
Sulfur is present in the environment in solids, gases, and aqueous species. Sulfur-containing solids on Earth include the common minerals pyrite (FeS2), galena (PbS), and gypsum (CaSO4•2H2O). Sulfur is also an important component of biological material, including in the essential amino acids cysteine and methionine, the B vitamins thiamine and biotin, and the ubiquitous substrate coenzyme A. In the ocean and other natural waters, sulfur is abundant as dissolved sulfate. Hydrogen sulfide is also present in some parts of the deep ocean where it is released from hydrothermal vents. Both sulfate and sulfide can be used by specialized microbes to obtain energy or to grow. Gases including sulfur dioxide and carbonyl sulfide make up the atmospheric component of the sulfur cycle. Any process that transports or chemically transforms sulfur between these many natural materials also has the potential to fractionate sulfur isotopes.
Sulfur isotopic abundance in natural materials
Sulfur in natural materials can vary widely in isotopic composition: compilations of the δ34S values of natural sulfur-containing materials include values ranging from −55‰ to 135‰ VCDT. The ranges of δ34S values vary across sulfur-containing materials: for example, the sulfur in animal tissue ranges from ~ −10 to +20‰ VCDT, while the sulfate in natural waters ranges from ~ −20 to +135‰ VCDT. The range of sulfur isotope abundances in different natural materials results from the isotope fractionation associated with natural processes like the formation and modification of those materials, discussed in the next section.
Processes that fractionate sulfur isotopes Numerous natural processes are capable of fractionating sulfur isotopes. Microbes are capable of a wide variety of sulfur metabolisms, including the oxidation, reduction, and disproportionation (or simultaneous oxidation and reduction) of sulfur compounds. The effect of these metabolisms on sulfur isotopic composition of the reactants and products is also highly variable, depending on the rate of relevant reactions, availability of nutrients, diagenesis, and other biological, physical and environmental parameters. As an example, the microbial reduction of sulfate to sulfide generally results in a 34S-depleted product, but the strength of this fractionation has been shown to range from 0 to 65.6‰ VCDT.