As we have just seen, the different radioisotopes produced in activation are distinguished by their different g-ray energies and by their half-lives. Based on peak height or peak area (the number of pulses associated with a specific g-ray energy), the radioisotopes can also be analyzed quantitatively, permitting measurement of the concentration of the element(s) of interest. There are two primary approaches to quantifying elements based on their g-ray spectra: the parametric approach and the direct-comparison approach.
The ‘parametric approach’ (also called the absolute, standardless, or K-zero approach) holds that if all the parameters controlling the induced activity are known, then the quantity of the elements present can be calculated directly from the measured radioactivity (Box 3). The necessary irradiation parameters include the neutron flux and its energy spectrum, the isotopic neutron-capture cross-section (a measure of the probability of reaction with a neutron of a given energy), the duration of irradiation, and the half-life and/or decay constant of the isotope in question.
Measurement parameters include the length of decay prior to collecting a g-spectrum, the duration of the g-count, the detector efficiency (fraction of total gamma rays detected), possible interferences between g-peaks, and natural or background radiation in the
Figure 7 Exploded view of an HPGe gamma-ray detector. The ‘cold-finger’ connects the germanium crystal to a well of liquid nitrogen contained in an adjacent dewar, chilling the crystal so that it becomes a near-perfect semiconductor. Courtesy of AMETEK.
To electronics (amplifier, etc.)
Figure 8 Complex g-ray spectrum resulting from the irradiation of a ceramic vessel from Peru. Several of the isotopes are represented by multiple g-peaks.
Box 3 The Parametric Approach to INAA
The parametric approach holds that if all the parameters governing the generation and subsequent decay of radioactivity can be specified, then the amount of an element present in an irradiated sample can be determined from the area of the associated peak in the g-spectrum. Generically, to quantify a specific isotope, the necessary parameters are as follows:
The number of nuclei of a given isotope in the sample is based on sample weight, isotopic abundance, and Avogadro’s number, which expresses the fact that one gram-atomic weight of any element contains the same number of atoms.
During irradiation, the activity of a radioactive nuclide grows according to neutron flux (the number of available projectiles), the neutron capture cross-section (the probability of activation), and half-life of the isotope in question. Following irradiation, the activity of a radioactive nuclide decays according to the exponential law. During that decay interval, the sample is placed near a gamma detector, which detects a fraction of the total decays according to its relative efficiency.
Spectrum. A flux monitor (such as a small piece of high-purity gold wire) is included with each batch of samples in order to determine the flux for particular irradiation; other parameters are known through experimentation or system calibration.
The K-zero method has become the standard for INAA in Europe. It offers great flexibility, in that in theory, it is possible to quantify any element with enough activity to generate a peak in the g-spectrum.
An alternative approach, the ‘direct comparison’ or standard comparator method, is more common in the United States. The samples or unknowns are irradiated along with several replicates of standard reference materials or SRMs. These are materials for which elemental concentrations are known quite accurately through a variety of chemical analyses, and the ‘true’ composition is certified and published. In the United States, the National Institute of Standards and Technology (NIST) and the US Geological Survey (USGS) create, analyze, and certify SRMs, as do a number of nongovernment agencies. SRMs commonly used in the analysis of archaeological materials include NIST1633 (coal fly ash), NIST688 (basalt rock), NIST278 (obsidian), andNIST279 (brick clay).
Under the direct comparison method, the samples and standards are irradiated under the same conditions (frequently simultaneously); thus, all the parameters determining the induced activity for a given isotope are held constant for both unknowns and standards, and so cancel out. Elemental concentrations in the unknowns are then determined through simple weight-ratio comparisons with the reference materials of known composition (Box 4).
The direct comparison method is sometimes credited with being more precise than the parametric approach, as well as easier to implement, but the analysis is limited to quantifying those elements present in the SRM. Adherents of this approach must also specify the element library or ‘known’ values used for a given SRM, as the original certified values may be revised over time.
In either approach, is it common to include samples of a material of known composition to serve as a check on the accuracy and precision of results. These ‘check standards’ also serve as a basis for interlab calibration, ensuring that the results obtained by one INAA lab are comparable to those of other labs.
World History
