Lutetium–hafnium dating

Lutetium is a rare-earth element, with one naturally occurring stable isotope 175Lu and one naturally occurring radioactive isotope 176Lu. :^{176}_{71}Lu -> {^{176}_{72}Hf} + e^- :{^{176}_{71}Lu} + e^- -> {^{176}_{70}Yb} Lutetium, ^{176}_{71}Lu can decay into ^{176}_{72}Hf , a heavier element, or ytterbium, ^{176}_{70}Yb , a lighter element. Decay constant determination The decay constant of ^{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: : \left(\frac\ce{^{176}Hf}\ce{^{177}Hf}\right) = \left(\frac\ce{^{176}Hf}\ce{^{177}Hf}\right)_i + \left(\frac\ce{^{176}Lu}\ce{^{177}Hf}\right)(e^{\lambda t}-1) where: • (^{176}Hf/^{177}Hf) is the measured ratio of the two isotopes of the sample. • (^{176}Hf/^{177}Hf)_i is the initial ratio of the two isotopes when the sample is formed. • (^{176}Lu/^{177}Hf) is the measured ratio of the two isotopes of the sample. • is the decay constant of ^{176}Lu. • t is the time since the sample is formed. The two isotopes, 176Lu and 176Hf, in the system are measured as ratio to the reference stable isotope of 177Hf. The measured ratio can be obtained from mass spectrometry. A common practice for geochronological dating is to establish an isochron plot. Multiple set of data would be measured and plotted with 176Hf/177Hf on y-axis and 176Lu/177Hf on x-axis. A linear relationship would be obtained. The initial ratio can either be assumed to be natural isotopic abundance ratio or, for a better approach, obtained from the y-intercept of plotted isochron. The slope of the plotted isochron would represent (e^{\lambda t}-1). == Epsilon (ɛHf value) ==

ɛHf value is an expression of ^{176}Hf/^{177}Hf ratio of a sample with respect to ^{176}Hf/^{177}Hf ratio of chondritic uniform reservoir. ɛHf is expressed in the following equation: : \varepsilon_{\ce{Hf}(0)} = \left[\frac{\left(\frac\ce{^{176}Hf}\ce{^{177}Hf}\right)_{\ce{sample}(0)}}{\left(\frac\ce{^{176}Hf}\ce{^{177}Hf}\right)_{\ce{CHUR}(0)}} - 1\right] \times 10\,000 where: • "0" in the bracket denoting time = 0, meaning present day. Numbers in bracket can represent any time in the past up to the formation of Earth. • \left(\frac\ce{^{176}Hf}\ce{^{177}Hf}\right)_{\ce{sample}} is the Hf-176 to Hf-177 ratio in the sample. For t = 0, it represent the ratio at present. • \left(\frac\ce{^{176}Hf}\ce{^{177}Hf}\right)_{\ce{CHUR}} is the Hf-176 to Hf-177 ratio in the chondritic uniform reservoir. For t = 0, it represent the ratio at present. Geochemistry of lutetium and hafnium According to the Goldschmidt classification scheme, Lu and Hf are both lithophile (earth-loving) elements, meaning they are mainly found in the silicate fraction of Earth, i.e. the mantle and crust. An example of ɛHf plot. == CHUR model age ==

The chondritic uniform reservoir model age is the age at which the material, from which rock and mineral forms, leaves the chondritic uniform reservoir, i.e. the mantle, when assuming the silicate earth retained chemical signature of chondritic uniform reservoir. or even by 28%. The ^{176}Hf/^{177}Hf ratios yielded varies by 14 ɛHf units. One later study focused on chondrites of petrological types 1 to 3, which are unequilibrated, show variation of 3% in ^{176}Lu/^{177}Hf ratios, and 4 ɛHf units in ^{176}Hf/^{177}Hf ratios. == Analytical methods ==

In the earliest years, at around the 1980s, age acquisition based on Lu–Hf system make use of chemical dissolution of sample and thermal ionization mass spectrometry (TIMS). Different studies may use slightly different protocols and procedures, but all are trying to ensure complete dissolution of Lu and Hf bearing materials. == Applications ==

Igneous rock petrogenesis Lu–Hf isotope system can provide information on where and when a magmatic body originate. By applying Hf concentration determination to zircons from A-type granites in Laurentia, ɛHf values ranging from −31.9 to −21.9 were obtained, representing a crustal melt origin. Apatite has also promising Lu–Hf information, as apatite has high Lu content relative to Hf content. In cases where rocks are silica-poor, if more evolved rocks of the same magmatic origin can be identified, apatite could provide high Lu/Hf ratio data to produce accurate isochron, with an example from Smålands Taberg, southern Sweden, where apatite Lu/Hf age of 1204.3±1.8 million yr was identified as the lower boundary of a 1.2 billion yr magmatic event that caused the Fe–Ti mineralization at Smålands Taberg. Metamorphic rock petrogenesis and metamorphic events In understanding metamorphic rocks, Lu–Hf can still provide information of origin. In cases where zircon phase is absent or very low in abundance, such as eclogite with cumulate protolith, kyanite and orthopyroxene eclogites can be candidate for Hf analysis. Although the overall rare-earth element concentration is low is the two eclogites, Lu/Hf ratios is high, therefore enabling concentration determination of Lu and Hf. Garnets play an important role in Lu/Hf applications, as they are common metamorphic minerals while having high affinity to rare-earth element. With the help of garnet Lu/Hf ages, a study on Lago di Cignana, western Alps, Italy, an age of 48.8±2.1 million yr for lower boundary of garnet growth time was identified. From this, the burial rate of ultra-high-pressure rocks at Lago di Cignana was estimated to be 0.23–0.47 cm/yr, which suggest ocean floor rocks were carried down to subduction and reached ultra-high-pressure metamorphism conditions. Another low-temperature, high-pressure metamorphic index mineral, lawsonite was brought into use in recent years to understand subduction metamorphism using Lu/Hf dating. A study showed that lawsonite could be significant in dating low-temperature metamorphic rocks, typically in prograde metamorphism in a subduction zone settings, as garnets are formed after lawsonite is stabilized, so that lawsonite can be enriched in Lu for radiometric dating. Early Earth mantle-crust differentiation The crust formation process is supposedly chemically depleting the mantle, as crust forms from partial melts originating from the mantle. To further constrain the modelling of depleted mantle, Lu–Hf information from zircons are useful, as zircons are resistant to Lu–Hf re-equilibrating. Detrital zircon and provenance Hf ages determined from detrital zircon can help to identify major event of crustal growth. Hf ages from detrital zircon also help tracing sediment source. == References ==