Chapter 3
Analytical techniques

Isotope geochemistry is based on the accurate and precise determination of elemental and isotopic compositions of rocks and minerals. Although some of the earliest geochronological methods (notably the ¹⁴C method, see Section 4.1) were based on the detection of radioactivity by means of Geiger-Müller counters and liquid scintillation detectors, nearly all modern isotope geochemistry is done by mass spectrometry.

3.1 Mass spectrometry

A mass spectrometer is a device that separates electrically charged atoms or molecules based on their mass, enabling precise measurement of the isotopic composition. A mass spectrometer consists of the following parts:

1. ion source: this can be either a filament (similar to that found in an incandescent light bulb), a plasma torch, a primary ion beam, or a spray chamber, among other possibilities.
2. mass analyser: this can be an electromagnet (possibly combined with an electrostatic field), or a rapidly fluctuating electric field.
3. ion detector: this is, essentially, a volt meter.

In the remainder of this section, we will assume the source to be a filament and the mass analyser to be an electromagnet.

After pumping the mass spectrometer down to (ultra-)high vacuum conditions (10^-6 to 10^-9 mbar), the sample enters the ion source as a gas, where it is bombarded with electrons. The resulting ions (with charge e) are accelerated in an electric field (with potential difference V ) and collimated to a narrow beam. This beam is sent through a magnetic field (with strength H) which deflects it into a circular trajectory with a radius proportional to the ion mass (m). This results in a physical separation of the incoming ion beam into various outgoing beams. The beams of interest are steered into the ion detector which, in its simplest design (the so-called ‘Faraday Cup’) consists of a long and narrow cup. The ion beam is neutralised in the cup by electrons flowing from ground through a resistor. The potential difference across this resistor is measured and registered on a computer for further processing.

The electric field transfers a certain amount of kinetic energy to the ions:

(3.1)

With e is the electrical charge (in multiples of 1.60219 ×10^-19C, which is the elementary charge of an electron. Because each type of ion has a different mass (m, in multiples of 1.660538 ×10^-27kg, the atomic mass unit), their terminal velocity (v) differs as well:

(3.2)

The mass analyser deflects the ions according to the following equation:

(3.3)

Substituting Equation 3.2 into 3.3 yields:

(3.4)

from which it follows that:

(3.5)

Equation 3.5 allows us to calculate the radius of the ion trajectory for any given mass-to-charge ratio m∕e. Note that light isotopes are more strongly deflected than equally charged heavy ones. Equation 3.5 can also be used to calculate the magnetic field strength required to deflect an ion beam with a given m∕e ratio into the collector. This is more practical because most mass spectrometers have a fixed radius so that the different ions must be collected by varying H. Some modern mass spectrometers are equipped with multiple ion collectors the enabling simultaneous analysis of several ionic masses.

Several types of mass spectrometers are used for geoscience applications:

1. Thermal Ionisation Mass Spectrometry (TIMS).
   The sample is dissolved and subjected to careful chemical separation procedures (liquid chromatography) in order to separate the parent and daughter elements to a high level of purity. The resulting solutions are spiked and deposited on a tungsten or tantalum filament, which is brought to a glow by an electric current and thus produces ions. These are separated by a large electromagnet and analysed in one or more Faraday cups. TIMS is very time consuming but produces extremely precise results (o-level precision on the ages).
2. Inductively Coupled Plasma Mass Spectrometry (ICP-MS).
   The sample is vapourised in one of two ways: either by introducing a liquid into a spray chamber, or by firing an ultraviolet laser at a solid sample and transporting the resulting aerosol into the ion source with a carrier gas (typically helium). The ion source itself consists of an argon flow which is heated to a temperature of approximately 10,000K by sending a radiofrequency current through a coil. This breaks up all the molecular bonds and produces a plasma (i.e. a ‘soup’ of ions and electrons) which enters the high vacuum chamber through a tiny opening. The mass analyser can either be a sector magnet or a quadrupole (which consists of four metal rods generating a rapidly fluctuating electrical field). ICP-MS offers a higher throughput than TIMS, especially in laser ablation mode, where hundreds of ages can be measured per day. However, this increased throughput comes at the expense of precision, which is on the percent level (better in solution mode).
3. Secondary ion mass spectrometry (SIMS)
   Prior to the development of laser ablation (LA-) ICP-MS, the only other method to produce spot measurements in solid samples was by firing a beam of negative (e.g. oxygen) or positive (e.g. caesium) ions at the target under high vacuum. This releases (‘sputters’) positive (or negative, in the case of a Cs beam) secondary ions from the sample surface, which are accelerated by an electrostatic field and sent to a sector field mass spectrometer. Although SIMS has been replaced by LA-ICP-MS in some applications, it remains an important instrument in the geochronological toolbox because (a) it offers higher spatial resolution than laser ablation (5-10μm vs. 25-50μm) and (b) can measure light ions (e.g, hydrogen) more reliably than LA-ICP-MS.
4. Accelerator Mass Spectrometer (AMS)
   The AMS combines two mass spectrometers with a (‘tandem’ type) particle accelerator. Ions are produced by a SIMS source and steered through a first mass analyser, which selects all ions of a desired mass (e.g., mass 14: ¹⁴C^-, ¹²CH₂^-, ). The resulting beam is accelerated in the first part of the tandem accelerator by a potential difference of several million eV, and sent through a thin chamber filled with a ‘stripper’ gas. Collisions of stripper gas atoms with the incoming ions destroys any molecular bonds and forms 3+ ions in the process. The beam now consists of purely atomic ions, which are accelerated in the second part of the accelerator and steered into a second mass analyser. The AMS has revolutionised the ¹⁴C method by enabling the analysis of extremely small (mg-sized) samples (see Section 4.1), and has enabled a whole new field of geochronology based on the analysis of terrestrial cosmogenic radionuclides (Chapter 8). The main limitation of AMS is its high cost. Currently only two AMS facilities are operating in the UK (in Oxford and Glasgow).

3.2 Isotope dilution

Besides determining isotopic compositions, the mass spectrometer can also be used to measure elemental concentrations, using a method called isotope dilution. This is done by mixing the sample solution (whose isotopic composition has already been determined) with a known quantity of a solution with a different (but known) isotopic composition and known elemental concentration. The latter solution is called the spike. The isotopic composition of the mixture is analysed by mass spectrometry. The measured isotopic ratio R_m for an element with two isotopes (^aX and ^bX) is given by:

(3.6)

with

N is the only unknown in Equation 3.6, which can therefore be rewritten as:

(3.7)

N can also be expressed as a function of the isotopic ratios in the sample R_N(= ^aX_N∕^bX_N) and in the spike R_S(= ^aX_S∕^bX_S). The atomic abundance of ^aX and ^bX in the sample are given by:

(3.8)

and in the spike:

(3.9)

Substituting Equations 3.9 and 3.8 into 3.7 yields:

(3.10)

Equations 3.7 and 3.10 give the atomic concentration of X (in atoms/g). Dividing N by Avogadro’s number N_A and multiplying with the atomic weights (g/mol) yields the corresponding weight percentages. Isotope dilution is a very powerful method because:

1. It does not require quantative separation of the elements of interest.
2. Chemical purification removes unwanted interferences from other species.
3. The method is very sensitive, so extremely low concentrations can be measured (ppb or less).

3.3 Sample-standard bracketing

Isotope dilution is the ‘gold standard’ for isotope geochemistry, recommended when the most accurate and precise results are desired. Unfortunately, isotope dilution is also very time consuming and cannot be readily applied to micro-analytical techniques such as LA-ICP-MS and SIMS. In those cases, and alternative method is used, which is less precise (%- rather than o- level precision) but quicker. The idea is to normalise the signal ratios recorded by the mass spectrometer to a standard of known age. As before, let P be a radioactive parent which decays to a radiogenic daughter D. Suppose that we can measure both nuclides on the same mass spectrometer, yielding two electronic signal intensities S_P and S_D. These signals may be recorded in units of V, A, or Hz. We cannot directly use the signal ratios as a proxy for the isotopic ratio:

because the parent and daughter are two different elements with different chemical properties and ionisation efficiencies. We can, however, assume that the isotopic ratio is proportional to the signal ratio:

(3.11)

Thus, if we double D (and thus D∕P), we would also expect to double S_D (and thus S_D∕S_P). To determine the constant of proportionality C, we analyse a standard of known age (t_s) and, hence (D∕P)-ratio (due to Equation 2.5):

(3.12)

where λ_P is the decay constant of the parent and S_P^s∕S_D^s is the (inverse) signal ratio of the standard.