3.2 Radiogenic isotopes

Fundamentals of radiogenic isotopes

Radiogenic isotopes are produced by radioactive decay, and they form the backbone of geochemical dating and tracing. By measuring how parent isotopes transform into daughter isotopes over time, geochemists can determine the age of rocks, identify magma sources, and reconstruct billions of years of Earth history.

Radioactive decay processes

Radioactive decay is a spontaneous nuclear transformation where an unstable nucleus emits particles or energy to reach a more stable configuration. Several types of decay are relevant in geochemistry:

• Alpha decay releases a helium nucleus ($^{4}_{2}\text{He}$), reducing the parent's atomic number by 2 and mass number by 4. This is the dominant decay mode for heavy isotopes like $^{238}\text{U}$ and $^{232}\text{Th}$.
• Beta decay converts a neutron into a proton ($\beta^{-}$) or a proton into a neutron ($\beta^{+}$), emitting an electron or positron respectively. The $^{87}\text{Rb} \rightarrow ^{87}\text{Sr}$ system is a classic $\beta^{-}$ example.
• Electron capture occurs when an inner-shell electron combines with a proton to form a neutron. The decay of $^{40}\text{K}$ to $^{40}\text{Ar}$ proceeds partly through this mechanism.
• Gamma decay releases high-energy photons without changing the element's identity or mass number. It often accompanies alpha or beta decay as the daughter nucleus sheds excess energy.

Parent-daughter isotope pairs

A parent-daughter pair consists of a radioactive parent isotope and the stable (or less radioactive) daughter isotope it decays into. The ratio of parent to daughter changes predictably with time according to the decay equation:

$D = D_0 + N(e^{\lambda t} - 1)$

where $D$ is the current number of daughter atoms, $D_0$ is the initial daughter abundance, $N$ is the current number of parent atoms, $\lambda$ is the decay constant, and $t$ is time.

The most widely used pairs in geochemistry:

Different pairs suit different timescales and rock types. Short-lived systems resolve young events; long-lived systems date the oldest rocks on Earth.

Half-life concept

The half-life ($t_{1/2}$) is the time required for half of the parent atoms in a system to decay. It relates to the decay constant by:

$t_{1/2} = \frac{\ln 2}{\lambda}$

Half-lives span an enormous range. $^{14}\text{C}$ has a half-life of ~5,730 years, useful for dating materials younger than ~50,000 years. $^{147}\text{Sm}$ has a half-life of 106 billion years, suitable for the oldest terrestrial and planetary samples.

A critical property: half-life is constant regardless of temperature, pressure, or chemical environment. This is what makes radioactive decay such a reliable geological clock.

Isotopic dating methods

Isotopic dating provides absolute ages for rocks and minerals, which is what allows geologists to assign numerical ages to the geologic timescale. Each method has strengths and limitations tied to the chemistry and half-life of its parent-daughter system.

K-Ar and Ar-Ar dating

The $^{40}\text{K} \rightarrow ^{40}\text{Ar}$ system (half-life 1.25 Ga) is widely used for volcanic and metamorphic rocks. Potassium is abundant in common minerals like micas, feldspars, and hornblende, making this system broadly applicable.

K-Ar dating measures the total $^{40}\text{Ar}$ accumulated in a sample and the $^{40}\text{K}$ content separately. A key assumption is that all argon was lost when the rock formed (or was last heated), so all measured $^{40}\text{Ar}$ is radiogenic.

Ar-Ar dating improves on this by irradiating the sample with neutrons to convert $^{39}\text{K}$ to $^{39}\text{Ar}$. Both argon isotopes are then measured in the same mass spectrometer run, and the age is calculated from the $^{40}\text{Ar}/^{39}\text{Ar}$ ratio. This approach offers several advantages:

• Only a single aliquot is needed (no separate K measurement)
• Step-heating experiments can reveal whether argon was partially lost or if excess argon is present
• Plateau ages from multiple heating steps increase confidence in the result

The main vulnerability of both methods is argon loss through diffusion, especially in low-retentivity minerals or rocks that experienced later thermal events.

Rb-Sr dating

The $^{87}\text{Rb} \rightarrow ^{87}\text{Sr}$ system (half-life 48.8 Ga) works well for rocks containing Rb-bearing minerals like biotite, muscovite, and K-feldspar.

Because you can't directly measure how much $^{87}\text{Sr}$ was present when the rock formed, this method uses an isochron approach:

1. Collect multiple cogenetic samples (or minerals from one rock) with different Rb/Sr ratios.
2. Plot $^{87}\text{Sr}/^{86}\text{Sr}$ (y-axis) against $^{87}\text{Rb}/^{86}\text{Sr}$ (x-axis).
3. If the system remained closed, the data points define a straight line. The slope gives the age, and the y-intercept gives the initial $^{87}\text{Sr}/^{86}\text{Sr}$ ratio.

The initial ratio is geochemically valuable on its own because it reflects the isotopic composition of the source at the time of formation. The very long half-life makes Rb-Sr especially useful for ancient rocks, though the system is susceptible to disturbance during metamorphism and fluid alteration.

U-Pb dating

U-Pb is the most precise geochronological method available, largely because it exploits two independent decay chains running in the same mineral:

• $^{238}\text{U} \rightarrow ^{206}\text{Pb}$ (half-life 4.47 Ga)
• $^{235}\text{U} \rightarrow ^{207}\text{Pb}$ (half-life 0.704 Ga)

Each chain gives an independent age. If both ages agree, the result is said to be concordant. On a concordia diagram ($^{206}\text{Pb}/^{238}\text{U}$ vs. $^{207}\text{Pb}/^{235}\text{U}$), concordant analyses plot on the concordia curve. Analyses that have experienced Pb loss or U gain plot below the curve (discordant), and a line through discordant points (a discordia) intersects the concordia at the crystallization age and the age of the disturbance.

Zircon ($\text{ZrSiO}_4$) is the mineral of choice because it incorporates U during crystallization but strongly excludes Pb, and it's extremely resistant to weathering and metamorphism. U-Pb zircon ages have dated the oldest known terrestrial material (Jack Hills zircons, ~4.4 Ga) and can also resolve ages of young volcanic eruptions with sub-million-year precision.

Sm-Nd dating

The $^{147}\text{Sm} \rightarrow ^{143}\text{Nd}$ system (half-life 106 Ga) is particularly useful for mafic and ultramafic rocks where Rb-Sr may not work well due to low Rb/Sr ratios.

Sm and Nd are both rare earth elements (REE) with similar geochemical behavior, so their ratio changes only modestly during most geological processes. This makes the Sm-Nd system more resistant to metamorphic disturbance than Rb-Sr, but it also means the spread in Sm/Nd ratios is small, requiring high analytical precision.

Like Rb-Sr, Sm-Nd dating uses an isochron approach. The system is especially valuable for studying mantle differentiation and the formation age of crustal material through model ages (see below).

Radiogenic isotope systems

Beyond dating, radiogenic isotope ratios serve as tracers that fingerprint different geological reservoirs. Because parent-daughter fractionation during melting and crystallization creates distinct isotopic signatures over time, you can use present-day ratios to infer the long-term chemical history of a rock's source.

Strontium isotope system

The $^{87}\text{Sr}/^{86}\text{Sr}$ ratio in a rock reflects the time-integrated Rb/Sr ratio of its source. Reservoirs with high Rb/Sr (like continental crust) develop high $^{87}\text{Sr}/^{86}\text{Sr}$ over time, while those with low Rb/Sr (like depleted mantle) remain low.

Typical present-day values:

• Depleted mantle (MORB source): ~0.7025
• Bulk silicate Earth: ~0.7045
• Old continental crust: 0.710–0.740+

This contrast makes Sr isotopes excellent for detecting crustal contamination in mantle-derived magmas. If a basalt has $^{87}\text{Sr}/^{86}\text{Sr}$ significantly above the mantle range, it likely assimilated crustal material.

Strontium isotope stratigraphy exploits the fact that seawater $^{87}\text{Sr}/^{86}\text{Sr}$ has varied through time (driven by the balance between mantle input at ridges and continental weathering input via rivers). Marine carbonates record the seawater ratio at the time of precipitation, providing a tool for dating and correlating sedimentary sequences.

Neodymium isotope system

The $^{143}\text{Nd}/^{144}\text{Nd}$ ratio reflects the time-integrated Sm/Nd ratio of the source. Because Nd is more incompatible than Sm during mantle melting, the melt (future crust) gets a lower Sm/Nd ratio than the residual mantle. Over time, the crust develops lower $^{143}\text{Nd}/^{144}\text{Nd}$ while the depleted mantle develops higher values.

Results are commonly expressed as epsilon Nd ($\varepsilon_{\text{Nd}}$):

$\varepsilon_{\text{Nd}} = \left(\frac{(^{143}\text{Nd}/^{144}\text{Nd})_{\text{sample}}}{(^{143}\text{Nd}/^{144}\text{Nd})_{\text{CHUR}}} - 1\right) \times 10^4$

where CHUR (Chondritic Uniform Reservoir) represents the bulk Earth composition. Positive $\varepsilon_{\text{Nd}}$ values indicate a depleted mantle source; negative values indicate long-term crustal residence or an enriched source.

Nd isotopes are widely used for determining sediment provenance, tracing ocean circulation (via dissolved Nd in seawater), and calculating model ages ($T_{\text{DM}}$) that estimate when crustal material was last extracted from the depleted mantle.

Lead isotope system

The Pb isotope system is uniquely complex because three radioactive parents ($^{238}\text{U}$, $^{235}\text{U}$, $^{232}\text{Th}$) produce three radiogenic Pb isotopes ($^{206}\text{Pb}$, $^{207}\text{Pb}$, $^{208}\text{Pb}$), all referenced to stable $^{204}\text{Pb}$.

Pb isotope ratios vary enormously across geological reservoirs because U and Th fractionate strongly from Pb during geological processes. The parameter $\mu$ (= $^{238}\text{U}/^{204}\text{Pb}$) describes the U/Pb ratio of a source; high-$\mu$ sources develop very radiogenic Pb over time.

Applications include:

• Identifying mantle source components (HIMU, EM1, EM2) in ocean island basalts
• Tracing ore-forming processes and the crustal history of ore leads
• Tracking anthropogenic Pb pollution, since industrial Pb has distinctive isotopic signatures that differ from natural background

Applications in geochemistry

Age determination of rocks

Radiometric dating provides the absolute time framework for geology. Igneous and metamorphic rocks are dated directly by analyzing minerals that crystallized from a melt or recrystallized during metamorphism.

Sedimentary rocks are harder to date directly because their minerals are typically detrital (inherited from older sources). Common workarounds include:

• Dating volcanic ash layers (tuffs) interbedded with sedimentary strata
• U-Pb dating of authigenic minerals like xenotime or monazite that grew in the sediment
• Using detrital zircon age populations to constrain maximum depositional ages

Applying multiple dating methods to the same sample provides cross-checks and can reveal complex thermal histories (for example, a zircon U-Pb age recording crystallization and a K-Ar biotite age recording later cooling through ~300°C).

Petrogenesis studies

Radiogenic isotopes are central to understanding how igneous rocks form because isotopic ratios are not changed by fractional crystallization (unlike trace element concentrations). This means the isotopic signature of a basalt directly reflects its source.

Key approaches:

• Plotting $^{87}\text{Sr}/^{86}\text{Sr}$ vs. $\varepsilon_{\text{Nd}}$ to distinguish mantle vs. crustal sources. Mantle-derived rocks plot in the upper-left (low Sr, high Nd); crustal rocks plot in the lower-right.
• Using mixing hyperbolae on isotope-isotope or isotope-concentration plots to quantify the proportions of two (or more) source components.
• Combining isotopic data with major and trace element data to distinguish assimilation-fractional crystallization (AFC) from simple source mixing.

Crustal evolution research

Radiogenic isotopes track how continental crust has grown and been recycled over Earth history. Nd model ages ($T_{\text{DM}}$) estimate when a sample's Nd was last in equilibrium with the depleted mantle, providing a "crustal formation age" even for rocks that have been reworked.

Maps of model ages across continents reveal isotopic provinces corresponding to major crust-forming events (for example, Archean cratons with $T_{\text{DM}}$ > 2.5 Ga vs. Phanerozoic accreted terranes with $T_{\text{DM}}$ < 1.0 Ga). Hf isotopes in zircon (the $^{176}\text{Lu} \rightarrow ^{176}\text{Hf}$ system) provide similar information and have become increasingly important because they can be measured on the same zircon grains dated by U-Pb.

Analytical techniques

Mass spectrometry basics

All radiogenic isotope measurements rely on mass spectrometry, which ionizes atoms and separates them by mass-to-charge ratio. The main instrument types used in isotope geochemistry:

• TIMS (Thermal Ionization Mass Spectrometry): Samples are loaded onto a metal filament and ionized by heating. Provides the highest precision for elements like Sr, Nd, and Pb (external reproducibility often better than ±0.001% for $^{87}\text{Sr}/^{86}\text{Sr}$).
• MC-ICP-MS (Multi-Collector Inductively Coupled Plasma Mass Spectrometry): Ionizes samples in an argon plasma. Faster throughput than TIMS and can handle elements that are difficult to ionize thermally (like Hf). Precision approaches TIMS levels with careful correction for mass bias.
• SIMS (Secondary Ion Mass Spectrometry): Fires a focused ion beam at a polished sample surface, sputtering secondary ions for analysis. Enables in-situ measurements at ~10–30 μm spatial resolution, critical for dating individual zircon growth zones.
• LA-ICP-MS (Laser Ablation ICP-MS): A laser ablates material from a polished sample into an ICP-MS. Lower precision than SIMS but much faster, making it the workhorse for detrital zircon studies where hundreds of grains need to be dated.

Sample preparation methods

Getting from a rock to a purified element solution for TIMS or MC-ICP-MS involves several steps:

1. Sample selection and cleaning: Choose fresh, unaltered material. Remove weathered surfaces.
2. Mineral separation: Crush the rock, then separate target minerals using magnetic separation (Frantz separator), heavy liquids (methylene iodide, sodium polytungstate), and hand-picking under a binocular microscope.
3. Dissolution: Dissolve minerals in strong acids. Silicates typically require HF + $\text{HNO}_3$; carbonates dissolve in dilute HCl.
4. Column chemistry: Pass the dissolved sample through ion exchange columns to isolate the element of interest (e.g., Sr, Nd, Pb) from the matrix. This removes isobaric interferences and improves ionization efficiency.
5. Spike addition (if needed): For isotope dilution measurements, a known amount of an enriched isotope tracer (spike) is added before dissolution to determine element concentrations precisely.

Contamination control is critical throughout. Blank levels must be monitored and kept far below sample levels, especially for Pb (which is a common lab contaminant).

Data reduction and interpretation

Raw mass spectrometer data require several corrections before they yield meaningful isotope ratios:

• Mass fractionation correction: Instruments preferentially transmit heavier or lighter isotopes. This bias is corrected using a known ratio of two non-radiogenic isotopes (e.g., $^{86}\text{Sr}/^{88}\text{Sr}$ = 0.1194 for Sr) or by standard-sample bracketing.
• Isobaric interference correction: Some isotopes have the same mass as isotopes of other elements (e.g., $^{87}\text{Rb}$ interferes with $^{87}\text{Sr}$). These are corrected mathematically using the measured abundance of a non-interfered isotope of the interfering element.
• Blank subtraction: The procedural blank contribution is subtracted, which matters most for low-concentration samples.

Ages are typically determined from isochron diagrams where the slope of a regression line through multiple cogenetic samples yields the age. Uncertainties are propagated through the regression using statistical methods (e.g., York regression, which accounts for errors in both x and y). Results are reported with 2σ uncertainties and often evaluated for their MSWD (Mean Square of Weighted Deviates) to assess whether scatter is consistent with analytical uncertainty alone.

Radiogenic isotopes in Earth systems

Mantle reservoirs

The mantle is not isotopically homogeneous. Decades of studying mid-ocean ridge basalts (MORB) and ocean island basalts (OIB) have revealed several distinct mantle components:

• DMM (Depleted MORB Mantle): The source of most mid-ocean ridge basalts. Low $^{87}\text{Sr}/^{86}\text{Sr}$, high $\varepsilon_{\text{Nd}}$, and moderate Pb isotope ratios. Depleted by billions of years of melt extraction.
• EM1 (Enriched Mantle 1): Low $\varepsilon_{\text{Nd}}$ and moderately low $^{87}\text{Sr}/^{86}\text{Sr}$. Possibly derived from recycled lower continental crust or ancient pelagic sediments.
• EM2 (Enriched Mantle 2): Low $\varepsilon_{\text{Nd}}$ with high $^{87}\text{Sr}/^{86}\text{Sr}$. Often attributed to recycled terrigenous sediments or upper continental crust.
• HIMU (High-μ): Extremely radiogenic Pb (high $^{206}\text{Pb}/^{204}\text{Pb}$) with moderate Sr and Nd. Best explained by recycled oceanic crust that lost Pb (low $\mu$) during subduction dehydration, then developed high $\mu$ over time.
• FOZO/C/PHEM: Various proposed "common" components that may represent the deep mantle or a primitive reservoir.

These components are identified on multi-isotope plots (Sr-Nd-Pb-Hf), and most OIB compositions can be explained as mixtures of two or more of them.

Crustal reservoirs

Continental crust is isotopically distinct from the mantle because of its high Rb/Sr, low Sm/Nd, and high U/Pb ratios accumulated over billions of years. Upper continental crust tends to be more radiogenic in Sr and less radiogenic in Nd than lower crust, reflecting greater enrichment in incompatible elements.

Sedimentary rocks preserve time-integrated crustal signatures and are useful for mapping isotopic provinces. For example, river sediment Nd isotopes reflect the average crustal age of the drainage basin.

Oceanic vs. continental crust

Oceanic crust forms continuously at mid-ocean ridges from depleted mantle, so its isotopic composition closely mirrors DMM. It's young (mostly < 200 Ma) and relatively homogeneous isotopically.

Continental crust, by contrast, spans ages from ~4.4 Ga to the present and shows enormous isotopic variability. Subduction transfers material between these reservoirs: oceanic crust and sediments are recycled into the mantle, while arc magmatism adds new material to the continents. Isotopic tracers are essential for quantifying these fluxes and understanding how continental crust has grown through time.

Isotopic fractionation processes

Fractionation refers to changes in isotope ratios caused by processes other than radioactive decay. While this topic overlaps with stable isotope geochemistry, it matters for radiogenic systems because fractionation can alter parent-daughter ratios or complicate mass spectrometric measurements.

Equilibrium fractionation

This occurs when isotopes partition between coexisting phases at thermodynamic equilibrium. Heavier isotopes tend to concentrate in phases with stronger, stiffer bonds. The magnitude of fractionation is temperature-dependent and decreases at higher temperatures.

For most heavy radiogenic isotope systems (Sr, Nd, Pb), equilibrium fractionation is small enough to be corrected during mass spectrometry using an internal normalization ratio. However, it can be significant for lighter systems and in low-temperature environments (e.g., Rb-Sr fractionation in evaporites).

Kinetic fractionation

Kinetic fractionation results from differences in reaction rates or diffusion speeds between isotopes. Lighter isotopes generally react and diffuse faster, so they're preferentially enriched in the product of a one-way process (evaporation, rapid precipitation, biological uptake).

Kinetic effects are usually more important for stable isotope systems (O, C, S) than for radiogenic systems. However, they can matter during sample preparation (e.g., incomplete dissolution or column chemistry yields) and must be controlled analytically.

Mass-independent fractionation

Most fractionation scales predictably with mass difference, but mass-independent fractionation (MIF) deviates from this pattern. MIF has been documented in oxygen (the famous $\Delta^{17}\text{O}$ anomaly in Archean sulfates), sulfur ($\Delta^{33}\text{S}$ in pre-2.4 Ga sediments, linked to the absence of an ozone layer), and mercury.

Mechanisms include nuclear volume (field shift) effects and magnetic isotope effects. MIF is rare in traditional radiogenic isotope systems but is relevant for some short-lived radionuclides and for understanding early Solar System processes recorded in meteorites.

Radiogenic heat production

Radioactive decay in Earth's interior converts nuclear binding energy into heat, and this heat is a primary driver of mantle convection, plate tectonics, and volcanism.

Decay energy release

Four isotopes dominate present-day radiogenic heat production:

Geothermal gradients

Continental crust is enriched in U, Th, and K relative to the mantle, so it produces disproportionately more radiogenic heat per unit volume. This is why continental geothermal gradients (typically 25–30°C/km in the upper crust) are often higher than oceanic ones, and why regions with thick, evolved crust (like granite-rich provinces) have elevated surface heat flow.

Variations in crustal heat production affect metamorphic conditions at depth and influence the thermal maturation of organic matter in sedimentary basins, which is directly relevant to hydrocarbon exploration.

Planetary thermal evolution

Early in Earth's history, heat production was much higher because short-lived isotopes like $^{26}\text{Al}$ (half-life 0.72 Ma) and $^{60}\text{Fe}$ (half-life 2.6 Ma) were still active, and the longer-lived isotopes were more abundant. Thermal models suggest that early Earth's radiogenic heat production was 3–4 times the present value.

This declining heat budget influences the vigor of mantle convection over time and may explain secular changes in tectonic style (e.g., the debate over when modern-style plate tectonics began). Smaller planetary bodies like Mars and the Moon cooled faster partly because of their lower total radiogenic element inventory, which is why they lack present-day plate tectonics.

Environmental applications

Groundwater tracing

Radiogenic isotopes are valuable for understanding water resources because different aquifer lithologies impart distinct isotopic signatures to groundwater:

• $^{87}\text{Sr}/^{86}\text{Sr}$ identifies water sources and flow paths because Sr isotope ratios reflect the rocks the water has interacted with.
• $^{234}\text{U}/^{238}\text{U}$ activity ratios in groundwater deviate from secular equilibrium due to alpha-recoil effects, providing information on water-rock interaction and residence time.
• Tritium ($^{3}\text{H}$) from atmospheric nuclear testing (peak in 1963) dates groundwater recharged within the last ~60 years.
• $^{14}\text{C}$ dates groundwater on timescales up to ~50,000 years, though corrections for carbonate dissolution are needed.
• $^{222}\text{Rn}$ (half-life 3.8 days) traces groundwater discharge into rivers, lakes, and coastal waters because radon concentrations are much higher in groundwater than surface water.

Sediment provenance studies

Nd and Sr isotopes in fine-grained sediments reflect the average isotopic composition of the source terrane, making them effective provenance tracers. For example, sediments derived from Archean cratons have very different $\varepsilon_{\text{Nd}}$ values than those from young volcanic arcs.

Detrital zircon U-Pb dating has become a standard tool: by dating hundreds of individual zircon grains from a sandstone, you build an age-probability distribution that can be matched to potential source regions. Pb isotopes in sediments also trace anthropogenic contamination, distinguishing between natural background and industrial sources (leaded gasoline, smelting, mining).

Paleoclimate reconstructions

• Seawater $^{87}\text{Sr}/^{86}\text{Sr}$ recorded in marine carbonates tracks the balance between continental weathering (high $^{87}\text{Sr}/^{86}\text{Sr}$) and hydrothermal exchange at mid-ocean ridges (low $^{87}\text{Sr}/^{86}\text{Sr}$). The well-calibrated Phanerozoic Sr isotope curve serves as both a dating tool and a weathering proxy.
• U-series dating of speleothems (cave carbonates) provides precise ages for oxygen isotope records that document past temperature and rainfall changes, with resolution down to decades.
• $\varepsilon_{\text{Nd}}$ in marine sediments and ferromanganese crusts traces past changes in ocean circulation, because different water masses carry distinct Nd isotopic signatures from their continental source regions.
• Pb isotopes in ice cores and peat bogs record atmospheric dust sources and the history of industrial pollution.

Limitations and challenges

Analytical uncertainties

Even with modern instruments, measurement precision has limits. TIMS and MC-ICP-MS can achieve internal precision of a few ppm for Sr and Nd ratios, but accuracy depends on how well mass fractionation, interferences, and blanks are corrected. Interlaboratory discrepancies for reference materials, though small, still exist and can matter when comparing datasets from different groups.

For isotopes present at very low abundances (e.g., $^{142}\text{Nd}$ anomalies from extinct $^{146}\text{Sm}$, or $^{182}\text{W}$ anomalies from extinct $^{182}\text{Hf}$), the signals of interest are only a few ppm deviations from normal, pushing instruments to their limits.

Closed system assumptions

Most dating methods assume the rock has been a closed system since formation, meaning no parent or daughter isotopes were added or removed. In reality, metamorphism, weathering, hydrothermal alteration, and fluid flow can all open the system.

When a system is partially reset, the resulting ages are geologically meaningless unless the disturbance can be recognized and accounted for. Strategies for dealing with open-system behavior include:

• Using minerals with high closure temperatures and chemical resistance (zircon > monazite > biotite > feldspar)
• Applying multiple isotope systems to the same sample to check for concordance
• Step-heating experiments (Ar-Ar) to identify partially degassed domains
• Recognizing disturbed isochrons through excess scatter (high MSWD)

Mixing and contamination effects

Natural rocks are often mixtures of components with different isotopic signatures. Crustal contamination of mantle-derived magmas,