Lutetium–hafnium dating

Lutetium–hafnium dating is a geochronological dating method utilizing the radioactive decay system of lutetium–176 to hafnium–176. With a commonly accepted half-life of 37.1 billion years, the long-living Lu–Hf decay pair survives through geological time scales, thus is useful in geological studies. Due to chemical properties of the two elements, namely their valences and ionic radii, Lu is usually found in trace amount in rare-earth element loving minerals, such as garnet and phosphates, while Hf is usually found in trace amount in zirconium-rich minerals, such as zircon, baddeleyite and zirkelite. The trace concentration of the Lu and Hf in earth materials posed some technological difficulties in using Lu–Hf dating extensively in the 1980s. With the use of inductively coupled plasma mass spectrometry (ICP–MS) with multi-collector (also known as MC–ICP–MS) in later years, the dating method is made applicable to date diverse earth materials. The Lu–Hf system is now a common tool in geological studies such as igneous and metamorphic rock petrogenesis, early earth mantle-crust differentiation, and provenance.

Radiometric dating

Lutetium is a rare-earth element, with one naturally occurring stable isotope 175Lu and one naturally occurring radioactive isotope 176Lu. When 176Lu atoms are incorporated into earth materials, such as rocks and minerals, they began to be "trapped" while starting to decay. Through radioactive decay, an unstable nucleus decays into another relatively stable one. Radiometric dating makes use of the decay relationship to calculate how long the atoms have been "trapped", i.e. the time since the earth material was formed.

Decay of 176Lu

The only natural occurring radioactive isotope of lutetium Lu 71 176 {\displaystyle {\ce {^{176}_{71}Lu}}} decays in the following two ways:

Lu 71 176 ⟶ Hf 72 176 + e − {\displaystyle {\ce {^{176}_{71}Lu->{^{176}_{72}Hf}+e^{-}}}}

Lu 71 176 + e − ⟶ Yb 70 176 {\displaystyle {\ce {{^{176}_{71}Lu}+e^{-}->{^{176}_{70}Yb}}}}

Lutetium, Lu 71 176 {\displaystyle {\ce {^{176}_{71}Lu}}} can decay into Hf 72 176 {\displaystyle {\ce {^{176}_{72}Hf}}} , a heavier element, or ytterbium, Yb 70 176 {\displaystyle {\ce {^{176}_{70}Yb}}} , a lighter element. However, as the major mode of decay is by β− emission, i.e. release of electron (e−), as in the case for Lu 71 176 {\displaystyle {\ce {^{176}_{71}Lu}}} decaying to Hf 72 176 {\displaystyle {\ce {^{176}_{72}Hf}}} , the presence of Yb 70 176 {\displaystyle {\ce {^{176}_{70}Yb}}} is of negligible effect to Lu–Hf age determination.

Decay constant determination

The decay constant of Lu 176 {\displaystyle {\ce {^{176}Lu}}} can be obtained through direct counting experiments and by comparing Lu–Hf ages with other isotope system ages of samples whose ages are determined. The commonly accepted decay constant has the value of 1.867 (± 0.007) × 10−11 yr−1. However, there remain discrepancies on the value of decay constant.

Age determination An age equation is set up for every radiometric dating technique to describe the mathematical relationship of the number of parent and daughter nuclide. In Lu–Hf system, the parent would be Lu (the radioactive isotope) and Hf as the daughter nuclide (the product after radioactive decay). The age equation to Lu–Hf system is as follows:

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