Module 4 - How Dr is measured

The environmental dose rate comprises ionizing radiation from multiple sources including cosmic rays from outer space and the decay of naturally occurring radioisotopes in the burial environment. These isotopes include potassium-40 (⁴⁰K), rubidium-87 (⁸⁷Rb) and the decay series chains of uranium-238 (²³⁸U), uranium-235 (²³⁵U), and thorium-232 (²³²Th).

The decay of radioisotopes in the burial environment lead to the emission of alpha particles (U, Th), beta particles (U, Th, K, Rb), and gamma rays (U, Th, K), each of which can travel a different distance in a sediment matrix (Fig. 1). U, Th and K are the main contributors to sample dose rates, while the contribution from cosmic rays and Rb (in the form of beta radiation) is relatively minor (Aitken, 1998).

Sources of radiation

Potassium-40

Potassium-40 is a naturally occurring isotope that decays into Argon-40 (⁴⁰Ar), emitting gamma and beta radiation in the process. It has a long half-life of 1.25 billion years, which means that it takes 1.25 billion years for half of a sample of ⁴⁰K to decay. In sediments and rocks, ⁴⁰K is most concentrated in felsic rocks that contain potassium (K)-rich feldspar minerals. These include granites, granodiorites, some sandstones and siltstones as well as volcanic rocks such as rhyolite and andesite. When we date samples using feldspar minerals, we target K-rich feldspars because they tend to have the brightest luminescence signals. Because of their K content, K-rich feldspar grains tend to have high internal dose rates relative to quartz and other types of feldspar. This means that K-feldspar De distributions are less prone to scatter (OD) caused by beta microdosimetry effects, because a larger portion of their dose rate comes from inside the grains.

Uranium

Uranium can be found in accessory minerals in rocks and sediment, such as apatite, sphene, zircon, allanite, monazite, pyrochlore, uraninite, and xenotime. Because uranium is soluble in oxidizing aqueous solutions, it is quite mobile in surface and near surface geologic materials and can be found in rock, soil, water and air. Surface U concentrations, therefore, often exhibit greater variability than potassium or thorium (Cuney & Kyser, 2016).

There are three natural isotopes of uranium — uranium-234 (²³⁴U), uranium-235 (²³⁵U) and uranium-238 (²³⁸U). Uranium-238 makes up nearly all natural uranium. It's the most stable and longest-lived isotope of uranium with a half life of 4.5 billion years. Uranium-238 decays into a series of daughters (14) that emit alpha, beta, and gamma radiation before decaying into lead-206 (²⁰⁶Pb) which is stable (Fig. 2).

Uranium-234 is the third daughter down in the ²³⁸U decay chain after Protactinium and has a half-life of 245,500 years. It only comprises 0.005% of all natural U. While ²³⁴U is a small fraction of the total weight, it is responsible for up to half of the radioactivity because it has a shorter half-life.

Uranium-235 is much less prevalent than ²³⁸U, only comprising 0.72% of all natural U. It has a half-life of 700 million years and decays into a series of daughters ending in lead-207 (²⁰⁷Pb) (Fig. 2). ²³⁵U is the isotope used in nuclear power and weapons because it can sustain a fission chain reaction. Enriched uranium is made by removing ²³⁸U to increase the percentage of ²³⁵U.

Thorium

Thorium is enriched in acidic, pegmatitic, and alkaline rocks, leading to the formation of thorium-bearing phosphate minerals such as monazite. In the weathering crusts of granite, most thorium is adsorbed in clay minerals and it is relatively abundant in sandstone and shale and modern muddy sediments. Thorium salts are relatively insoluble and prone to mechanical weathering and will concentrate in residuum, alluvium, and coastal areas (Li et al., 2025).

Thorium has 6 natural isotopes, of which ²³²Th accounts for almost 100% of the natural isotope abundance. The half-life of ²³²Th, is 13.9 billion years (~3 times the age of Earth!), significantly surpassing those of ²³⁸U and ²³⁵U. The ²³²Th decay chain consists of 11 daughters ending in lead-208 (²⁰⁸Pb) (Fig. 2).

Rubidium

Rubidium is an alkali metal with two naturally occurring isotopes: stable ⁸⁵Rb and radioactive ⁸⁷Rb, the latter of which has a half-life of 48.8 billion years. Most naturally occurring rubidium is found as a rare substitute for potassium in the lattices of various potassium-containing minerals. Economic sources include cesium and lithium minerals in pegmatites (Butterman & Reese, 2003). It occurs naturally in potassium minerals in felsic rocks, sediments including alluvial, eolian, and glacial deposits, as well as clays and evaporites (Smith et al., 2017). Mejdahl (1987) measured Rb and K contents from 27 samples of feldspar and found a K:Rb ratio of 270:1. This allows Rb concentrations to be estimated based on K concentrations, in cases where Rb concentrations are not measured directly.

Rubidium-87 comprises 27.8% of all natural Rb and emits beta radiation as it decays to strontium-87 (⁸⁷Sr). It typically accounts for only a minor contribution to the beta and total dose rates of samples.

Secular equilibrium

In closed-system environments, daughter elements of U and Th decay chains exist in equilibrium relative to their parent radionuclides. This means that the quantity of each daughter remains constant and the rate of formation of daughter radionuclides is equal to the rate of decay of its precursors. Radionuclides with long half-lives are more abundant than those with short half-lives and may continue to exist once the shorter lived radionuclides have decayed away or, in open systems, are removed. When uranium-bearing minerals break down and dissolve, equilibrium is disrupted. This is because the elements present may behave differently, and daughters may be removed or added due to processes such as leaching (Ivonavich & Harmon, 1992; Olley et al., 1996). In this case, determining the dose rate by measuring the parent radionuclides in the U and Th decay chains (i.e., ²³⁸U and ²³²Th) would result in an inaccurate estimate of dose rate during the burial history of the sample (Degering & Degering, 2020).

The equilibrium in the U-series decay chain is commonly disrupted by the escape of the gaseous daughter, radon (²²²Rn, Fig. 2A). An example scenario illustrated by Aitken (1998) shows that an undetected loss of 50% radon gas can lead to 30, 28, and 47% underestimation of alpha, beta, and gamma dose rates, respectively, leading to a 6-8% underestimation of the total dose rate. Radon-220 (²²⁰Rn) is a daughter product of the ²³²Th decay chain (Fig. 2C), but because its half life is so short (55 s), there is no consequence to its escape.

The solubility of U makes it more mobile in surficial deposits than Th, making it more susceptible to disequilibrium as a result of leaching, remobilization, and/or adsorption to minerals (e.g., Ralston et al., 1986; Paradis et al., 2020). Given the relative stability of Th, and the short half-lives of the longer-lived daughters in the ²³²Th series (²²⁸Ra and ²²⁸Th have 5.75 and 1.91 year half lives, respectively; Fig. 2C), this decay chain is expected to be in secular equilibrium in most natural materials. This was found to be true in several hundred soil and sediment samples examined from south-eastern Australia (Olley et al., 1996), although it is often not true in materials in which active iron/manganese deposition is taking place (Murray, 1996). Disequilibrium in fluvial and lacustrine sediments has been shown to be common in Australia contributing 5-10% to luminescence age uncertainties (Olley et al., 1996).

Types of radiation and their measurement

Alpha particles

Alpha particles are highly ionizing, but their penetrating distance in mineral grains is only ~25 μm from the emitting nucleus. When sand-sized grains are considered, the external alpha contribution does not penetrate to the internal core of a grain. This can result in uncertainties in determining the external alpha dose rate because different regions of the same grain will have received different alpha contributions. To circumvent this problem, the outer rind of each grain is removed by HF acid etching during sample preparation in order to remove those parts of the grain that had been exposed to an external alpha contribution (Aitken, 1998). In situations where the alpha dose rate contribution is desired, it can be measured using an alpha counter or calculated from measurements of radioisotope concentrations.

Beta particles

Beta particles travel up to 3 mm in most sediments and rocks and can be measured directly using a low-level beta counter. This approach does not give information on whether the beta emissions originated from the uranium or thorium decay chains, or from 40K, but instead counts the total beta particle emissions from these sources. Because ~60% of the beta dose rate from the ²³⁸U decay series originates from decaying radioisotopes in the lower part of the decay chain (Fig. 2A), beta counting is more likely to yield accurate beta dose rate estimates than methods that measure the concentrations of parent radionuclides and assume secular equilibrium (e.g., ICP-MS or atomic absorption).

Gamma rays

Gamma dose rates can travel up to 30 cm in sediments and rock. They can be measured directly i) in the laboratory using high-resolution, lab-based gamma spectrometry with a high-purity germanium (HPGe) crystal detector, or ii) in the field using lower resolution portable gamma scintillation using sodium iodide (NaI) or lanthanum bromide (LaBr3) detectors (Table 1). Gamma spectrometry provides an estimate of the dose rate from gamma ray emitters in the uranium and thorium decay chains and from ⁴⁰K, and therefore is less sensitive to U-series disequilibria than methods that measure the concentration of parental nuclides, only.

Portable gamma ray spectrometers, although lower in resolution than HPGe detectors, are often preferred because they take into account spatial heterogeneity in the gamma radiation field within 30 cm of each luminescence sample. HPGe detectors are ideal for measuring relative concentrations of parent and daughter radionuclides in the U-series decay chain to check for disequilibrium that may have resulted in a non-static dose rate during the burial period of the sample.

Table 1. Energy resolution comparison between high-purity Ge (HPGe) detectors and various scintillators at a range of gamma ray energies.

¹NaI(Tl) – Thallium doped Sodium Iodide detector; LBC – Lanthanum BromoChloride detector; LaBr₃ – Lanthanum Bromide detector; SrI₂(Eu) – Europium doped Strontium Iodide detector. From Schotanus (2020).

Cosmic rays

Cosmic rays come from outer space, and, after penetrating the ground surface, are dominated by muons (Prescott & Hutton, 1994; Aitken, 1998). The cosmic-ray flux is calculated based on sample latitude and altitude, thickness and density of sediment and rock overburden, and sample water content. For samples collected at shallow depths, the less penetrating soft component of cosmic radiation is also taken into account (Durcan et al., 2015).

Approaches to measuring dose rates

Dose rates can be measured in two ways: i) by measurement of the concentrations of radionuclides U, Th, K, and Rb, and ii) by measurement of radiation (alpha, beta, or gamma) emissions. Radionuclide concentrations can be measured using neutron activation, atomic absorption, X-ray fluorescence, flame photometry (for K only), inductively coupled plasma–mass spectrometry (ICP-MS), and inductively coupled plasma-atomic emission spectrometry (ICP-AES). Because these approaches measure the parents of the U-series and Th-series decay chains only, they cannot detect disequilibrium.

Radionuclide concentrations are given in percent for K and parts per million (ppm) for U, Th, and Rb. These values are then converted to dose rates in Gray per thousand years (Gy/ka) using conversion factors (e.g., Guérin et al., 2011).

Radiation emissions can be measured using alpha/beta counters, high-resolution gamma spectrometers or portable gamma scintillators. Evidence for disequilibrium can be detected by using either high-resolution gamma spectrometry or alpha spectrometry as these techniques can measure the activities of daughter radionuclides as well as their parents (Murray et al., 1996). As previously mentioned, the advantage to portable gamma scintillators is that they can account for gamma dose rate heterogeneities at the sample site.

Correction factors and water attenuation

Corrections must be made to dose rates to account for various factors such as i) alpha efficiency (or rather its inefficiency relative to beta radiation), ii) grain size radiation attenuation effects, iii) shallow sampling depths (<0.3 m), iv) HF acid etching of grains during preparation, and v) radiation attenuation in water (Durcan et al., 2015).

One of the most important dose rate corrections are made to account for water attenuation as alpha, beta, and gamma dose rates are significantly attenuated by water. Figure 3 below shows how various water content values influence dose rates and calculated ages. Increasing water contents have the largest impact on alpha dose rates and ages calculated for quartz.

For this reason, an estimate of the water content of the sample during its burial history must be made. This can be challenging as sediment water content can vary significantly through time as a result of intense short-term precipitation events, seasonal moisture variations, inter-annual to decadal-scale drought, and centennial to millennial-scale fluctuations in groundwater levels related to changes in base level and shifts in climate regime.

Luminescence sample water contents are often taken as the modern day laboratory-measured water content, taking into consideration its hydrogeomorphic context. Modern day measured water contents, however, can be problematic if they are not representative of the time-averaged water content of the sample during burial. This can happen if: i) the excavated sedimentary exposure has dried significantly shortly after excavation, ii) collected water content samples have dried since collection due to poor sealing, iii) there has been significant sediment compaction, or iv) knowledge of past water table levels is inaccurate or missing. In these cases, a plausible range of water contents should be used based on available environmental and paleoclimate data to estimate the average water content over the lifetime of the sample (e.g., Nelson & Rittenour, 2015).