Introduction to stable isotopes and IRMS theory

What are stable isotopes?

Isotopes are atoms with the same number of protons and electrons, but with differing numbers of neutrons. Some isotopes are known as stable (e.g. ¹²C and ¹³C), which as their name suggests are energetically stable over time and do not decay like their radioactive equivalents (e.g. ¹⁴C). The difference in mass, due to the variable neutron numbers can cause subtle chemical and physical differences between the isotopes of the same element.

Differences in chemical and physical properties arising from variations in the atomic mass of an element are known as ‘isotope effects’, while the partitioning of isotopes between two substances, or two phases of the same substance with different isotope ratios is known as ‘isotope fractionation’. The heavier isotope of an element forms stronger bonds (e.g. ¹³C-¹⁶O has a stronger bond than ¹²C-¹⁶O) and it is these slight differences in the bond energies that can cause isotopic fraction during physical processes or chemical reactions.

The natural variation in isotopic abundances in materials can be very small and require the use of an isotope ratio mass spectrometers (IRMS) to measure them.

Stable isotope nomenclature

The delta notation is traditionally used to express the variations in stable isotope ratios, where:

 

 

 

 

All samples must be reported relative to international scales which are defined by the original primary reference standards (Table 4-1)

 

There has been recent calls within the isotopic community to replace the delta notation with the ‘Urey’ unit (Ur); named after the Chemist Harold Urey who discovered deuterium (²H) and received the noble prize in 1934. Here, 1 mUr would equal 1 per mil.

The delta notation (and mUr) are used predominately for natural abundance work, however when samples are enriched with the minor isotope, e.g. for isotopically labeled tracer work, often atom percentage (Atm %) or atom percentage excess (Atm % excess) are used.

Measurement of stable isotope ratios

The measurement of stable isotope ratios is best obtained through an Isotope Ratio Mass Spectrometer (IRMS).

An Isotope Ratio Mass Spectrometer (IRMS) is a gas source magnet sector mass spectrometer comprising of an ion source, flight tube and collector array. To analyze a sample gas, the molecules must be ionized in the ion source, and the ions are then focused into a beam and accelerated by an electric field. The ions then pass from the ion source into the flight tube, where they are magnetically deflected, and finally they are detected by the collector array.

The ionization is achieved by passing a beam of electrons through the gas sample. Collision between, or close approach of, an electron and a sample molecule can cause one or more electrons either to adhere to the molecule and form a negative ion, or to detach from the molecule and generate a positive ion. Isotope analysis usually involves the singly charged positive ions (molecules that have lost one electron).

The positive ions are accelerated and formed into a well-defined beam by raising the ionization chamber to a positive potential and accelerating the ions out through a defining slit called the source slit. The ions are then passed towards a second defining slit at ground potential called the alpha slit, which eliminates unwanted ions.

The flight tube forms the arc of a circle that passes between the poles of the magnet. As the ions travel down the tube, they are separated into beams of different radii corresponding to different masses. The ion beam to be measured passes through a slit called the resolving slit into the collector. A particular radius and hence mass is selected by the combination of the alpha slit at the source end of the flight tube and the resolving slit at the collector end.

 

In the collector, ions of the chosen mass are transmitted through the resolving slit and detected by a Faraday cup. The ion current from the cup is proportional to the number of incident ions and hence to the partial pressure of the corresponding isotopic molecular species in the sample gas. Multiple Faraday cups are used to obtain simultaneous detection of different isotopes, e.g. for CO₂, ⁴⁴CO₂, ⁴⁵CO₂, ⁴⁶CO₂

A pronounced difference between a traditional scanning mass spectrometer and an IRMS instrument can be observed in the peak shapes when scanning the magnetic field. A traditional scanning instrument provides a spectrum of mass peaks that is characteristic of chemical composition, where very narrow peaks are used to distinguish closely spaced masses. In isotope ratio work the variation of the isotopes are more precisely measured by using broad peaks as these provide the most stable measurements; this is achieved by having the resolving slit wider than the ion beam. If one were to scan the ion beam across the resolving slit you would observe a flat-topped peak, this allows for any changes in the magnetic field and/or accelerating voltage to not alter the stability of the signal.

The Mass Spectrometer Equation

If an ion of mass M and charge Z is accelerated in a potential V and admitted into a uniform magnetic field B, then the ion experiences a force and moves in a circular orbit of radius R. The motion is defined by:

For singly charged ions, the radius is determined by the nature of the magnetic and electric field. The combination of fields selects ions of particular mass and forms a mass filter. This principle is the basis of all magnetic-sector mass spectrometers and the equation is frequently termed the mass spectrometer equation.