The radiogenic isotope applications of the Lu-Hf system utilize variations in 176 Hf resulting from the radioactive decay of 176 Lu to 176 Hf and variations in the Lu/Hf ratios in rocks and minerals. It is used both in geochronology, primarily in rocks containing a high Lu/Hf phase, and in tracer isotopic applications, to track the chemical evolution of the Earth and other solar system materials and to constrain the sources of magmas and sediments.
The Lu-Hf isotope system, with applications to geo- and cosmochemistry, was first investigated in the early 1980s (Patchett 1983b ; Patchett and Tatsumoto 1980 a, b , c , 1981 ) following the successful implementation of the Rb-Sr and Sm-Nd isotope systems several years earlier.
There are some obvious similarities between the Lu-Hf and Sm-Nd isotope systems and, as a result, they have long been used in concert in a w >1993 ; Blichert-Toft and Albarède 1997 ; Johnson and Beard 1993 ; Patchett and Chauvel 1984 ; Patchett 1983b ; Salters and Hart 1991 ; Vervoort and Blichert-Toft 1999 ; Vervoort et al. 1999 ). In these two systems all elements are lithophile and refractory with high condensation temperatures. Because of these characteristics it has long been assumed that their abundances in the Earth can be approximated by chondritic meteorites (see discussion below). In addition, all elements in these systems behave incompatibly during melting and are concentrated in the melt over the residual solid. In both systems, the daughter element (e.g., Nd, Hf) is more incompatible than the parent, leading to lower Sm/Nd and Lu/Hf ratios in the melt than the residual solid. As a result, the 143 Nd/ 144 Nd and 176 Hf/ 177 Hf ratios in magmatic rocks are highly correlated (e.g., Chauvel et al. 2008 ; Johnson and Beard 1993 ; Patchett 1983a ; Salters and Hart 1991 ; Vervoort and Blichert-Toft 1999 ). Both Lu and Hf are highly immobile and insoluble and, as is the case with the Sm-Nd system, are thought to be resistant to perturbations and retain their isotopic information through significant degrees of alteration and metamorphism.
In the case of the Lu-Hf isotope system, the parent is the heaviest of the rare-earth elements (REEs) and has broad geochemical similarities with all other +3 valence REEs. The daughter element, however, is not an REE, but a high-field-strength element (HFSE) with a +4 valence and, as such, can behave much differently than the REEs. These differences can confer some advantages to the Lu-Hf isotope system for both geochronology and tracer isotopic work as will be discussed below.
Although the Lu/Hf ratio is fractionated during magmatic processes, the degree of this fractionation, as is the case for Sm-Nd, is not very large. This results in small variations in Lu/Hf ratios between not only rocks within a comagmatic suite but also for most mineral phases within individual rocks. This lack of parent/daughter variation severely limits the application of the Lu-Hf chronometer, much as it does for the Sm-Nd isotope system. Therefore, whole-rock Lu/Hf isochrons of truly comagmatic suites of rocks either have too limited variation in Lu/Hf ratios to provide precise ages or, if there is a significant Lu/Hf variation, chances are the suite of rocks used in creating the isochron was not truly comagmatic. There are a few phases, however, with high affinity for Lu, which make them highly useful in geochronology in both magmatic (e.g., apatite) and metamorphic (e.g., garnet, lawsonite) rocks. In addition, some other phases (particularly phases with Zr or Ti as stoichiometric constituents) have strong affinities for Hf (e.g., zircon, baddeleyite, rutile), which make them useful in tracer isotopic studies – especially when used in conjunction with the U-Pb geochronologic information from these mineral phases.
Although the Lu-Hf system was introduced to the geochemical and cosmochemical communities in the 1980s, analytical challenges limited the w >2003 ), which prevented easy and routine analysis of Hf isotopes using thermal ionization mass spectrometry (TIMS). As a result there were only a few practitioners using this system in the 1980s and much of the 1990s. These difficult analyses utilized specialized techniques and required cons >1997 ; Walder and Freedman 1992 ). This revolutionized the use of the Lu-Hf isotope system for geochronology and tracer isotope applications by allowing the routine analysis not only of Hf isotopes in general but also of much smaller amounts of Hf. This made several important things possible. First, it allowed for the more precise and accurate determination of the 176 Lu decay constant (Scherer et al. 2001 ; Söderlund et al. 2004 ). Second, the new MC-ICPMS instrumentation also facilitated the analysis of high Lu-Hf, but Hf-poor, phases like garnet or apatite, which made the use of these phases for geochronology possible. Third, it also made it possible to analyze Hf-poor rocks such as chondritic meteorites, which allowed more accurate constraints to be placed on the chondritic Lu-Hf value (e.g., Bouvier et al. 2008 ). Finally, MC-ICPMS technology has made it possible to determine the Lu-Hf isotope composition in very small, Hf-rich phases such as zircon. This latter application, particularly when done in conjunction with U-Pb geochronology, has enjoyed an explosion of use in recent years (e.g., Amelin et al. 2000 ; Fisher et al. 2014 ; Gerdes and Zeh 2009 ; Kemp et al. 2010 ; Woodhead et al. 2004 ; Xie et al. 2008 ; Yuan et al. 2008 ).
Isotopic composition of Lu and Hf
Ratio to 176 Lu
Atomic weight Lu
Ratio to 177 Hf
Atomic weight Hf
Hafnium is the next higher element from Lu on the periodic table (Z = 72) and is a high-field-strength element (HFSE) sharing geochemical similarities with other Group IVB elements, most notably Zr and Ti. It is relatively under-abundant in the Earth (0.28 ppm, McDonough and Sun 1995 ) but enriched in the continental crust (5.3 ppm, Rudnick and Gao 2003 ). It has six isotopes, five of which are stable (Table 1 ). One isotope, 176 Hf (5.20 %), is radiogenic and produced, in part, by beta decay of 176 Lu and, together with 176 Lu, provides the basis of the Lu-Hf chronometer. By convention the reference stable isotope for the Lu-Hf system is 177 Hf (18.60 %).
In order to determine accurate Lu and Hf concentrations and, most importantly, the precise 176 Lu/ 177 Hf ratios required for geochronology and calculating accurate initial ratios, the “isotopic dilution” technique is required. This technique involves the addition of measured amounts of tracers of known isotopic composition (highly enriched in 176 Lu and 180 Hf, typically, with some labs using 178 Hf). These tracers, or “spikes,” are generally mixed and precisely calibrated so that evaporative loss will not affect the precise determination of the parent/daughter ratios. These spikes are added to the sample solution following or during dissolution, equilibrated with the solution, and become part of the isotopic mixture of the sample. Ultimately the 176 Lu/ 177 Hf and 180 Hf/ 177 Hf ratios of the samples are measured to determine Lu and Hf concentrations and precise Lu/Hf ratios.
In order to correct for mass dependent fractionation during mass spectrometry (i.e., mass bias), the convention for the Hf isotope system is to normalize to 179 Hf/ 177 Hf = 0.7325 (Patchett and Tatsumoto 1980b ), the value that has been used since the early days of Hf isotope analyses. Mass bias for Lu isotopic analyses is complicated by virtue of the fact that Lu has only two isotopes, making internal normalization impossible. In the early TIMS era of Lu-Hf isotope measurements, the small degree of mass bias (
0.1 % per amu) was not as significant for the less stringent requirements of the Lu isotope dilution analysis. With the advent of the MC-ICPMS analyses, however, mass fractionation that is over an order of magnitude larger than TIMS necessitated an accurate mass bias correction. The current approach is to use a different element with at least one invariant isotope ratio and which has a similar mass bias response, such as Yb, to correct for mass bias in the Lu isotopic measurement. Because of the similarity of behavior of the REEs (particularly for adjacent REEs), it is often difficult to quantitatively remove Yb from Lu. The current practice employed in most labs is to remove the majority of the Yb (recall that Yb is an even element and so is much more abundant than the odd numbered Lu) and use the Yb isotope measurements to determine the mass bias and then apply this to the Lu measurement. This approach is somewhat complicated by the uncertain isotopic composition of Yb (e.g., Amelin and Davis 2005 ; Chu et al. 2002 ; Segal et al. 2003 ; Vervoort et al. 2004 ) and the fact that 176 Yb is a relatively abundant isotope (12.70 %) with the same mass as the 176 Lu spike. The interference of 176 Yb on the spike isotope, 176 Lu, requires that most of the Yb be removed from the sample. In detail there are probably small differences in the mass bias of Yb and Lu, and there are approaches to quantify these differences (e.g., White et al. 2000 ). Despite all of these challenges, 176 Lu/ 177 Hf ratios in rock samples can probably be determined to
0.2 % accuracy (Vervoort et al. 2004 ).
The Hf solution standard employed throughout the history of Hf isotope analysis has been JMC-475, a Hf metal obtained from Johnson Matthey Corporation (Patchett and Tatsumoto 1980b ) with a currently accepted 176 Hf/ 177 Hf value of 0.282160 (Vervoort and Blichert-Toft 1999 ). The JMC-475 Hf standard solution is available from the author on request.
1 %) of 176 Hf in rocks and minerals is radiogenic and produced in this way; the majority of 176 Hf is “common” Hf, produced primarily during nucleosynthesis. The radiogenic decay equation for the Lu-Hf isotope system describes how radiogenic 176 Hf in a rock or mineral will evolve over time:
Therefore, the material with high Lu/Hf ratios, such as garnet, will generate proportionally more 176 Hf over time and evolve to higher 176 Hf/ 177 Hf ratios. Conversely, the material with low Lu/Hf ratios, such as zircon, will produce proportionally little 176 Hf with time and so its 176 Hf/ 177 Hf ratios will increase only very slowly.
An important part of using these radiogenic equations for geochronology and for determining precise initial isotopic compositions is not only measuring the present-day ratios accurately but also knowing the decay constant precisely and accurately. The 176 Lu decay constant has been a source of uncertainty, however, and this has limited the full application of the Lu-Hf isotope system. The first determination of the 176 Lu decay constant for use in geochemistry and cosmochemistry was performed by Patchett and Tatsumoto ( 1980a ) who determined an isochron on a collection of basaltic and cumulate eucrite meteorites. Using a presumed age of 4.55 Ga for the differentiation event for the eucrites, they determined a value for λ 176 Lu of 1.962 ± 0.081 * 10 −11 year −1 with a corresponding half-life of 35.3 Ga. This value was later revised by Patchett ( 1983b ) to λ 176 Lu = 1.94 ± 0.07 * 10 − 11 year − 1 and a half-life of 35.7 ± 1.4 Ga. This revised value was similar to a decay constant value of 1.93 ± 0.03 * 10 −11 year −1 determined by physical counting experiments (Sguigna et al. 1982 ). The agreement between these results led, in part, to the use of the λ 176 Lu value of 1.94 ± 0.07 * 10 −11 year −1 throughout the 1980s and much of the 1990s, with later studies (e.g., Blichert-Toft and Albarède 1997 and subsequent papers) using the Sguigna et al.’s ( 1982 ) values. This early history of 176 Lu decay constant determinations is reviewed more thoroughly by Begemann et al. ( 2001 ).
The value determined for λ 176 Lu changed dramatically following age comparison studies by Scherer et al. ( 2001 ) and Söderlund et al. ( 2004 ). Scherer et al. ( 2001 ) suggested a λ 176 Lu value of 1.865 ± 0.015 * 10 −11 year −1 based on the age comparisons of 4 samples from diverse localities and with different ages. This included two pegmatites from Norway with ages
1.1 and 0.9 Ga, an apatite-xenotime bearing gneiss from New York State with an age of
1.0 Ga, and a carbonatite from South Africa with an age of
2.1 Ga. The U-Pb crystallization ages for these samples were based on the measurements of gadolinite, xenotime, baddeleyite, and apatite in these rocks; the Lu-Hf isochron was determined using the high Lu/Hf ratios of gadolinite, xenotime, and apatite combined with low Lu/Hf phases in the rock (baddeleyite, zircon, biotite) or the whole-rock compositions.
In a similar study, Söderlund et al. ( 2004 ) determined a λ 176 Lu value of 1.867 ± 0.008 * 10 −11 year −1 based on age comparisons using two Proterozoic dolerite dikes from Sweden. The ages of these rocks were determined using baddeleyite U-Pb geochronology; apatite was the high Lu/Hf phase prov >2003 ) agreed with the slightly faster decay of Söderlund et al.’s ( 2004 ) value. As a result of this agreement, the isotopic community is now using the λ 176 Lu value of 1.867 ± 0.008 * 10 −11 year −1 . The half-life corresponding to this value is 37.12 Ga. The revision in the value for the 176 Lu decay constant from the Patchett ( 1983b ) and Sguigna et al.’s ( 1982 ) values has two important consequences for Lu-Hf geochronology and isotope geochemistry. The first, and most obvious of these, is the change in calculated Lu-Hf ages. Using the Scherer/Söderlund decay constant results in ages that are 4 % older than ages determined with the Patchett/Sguigna value. The second consequence is that this lowers the calculated initial 176 Hf/ 177 Hf of rocks. The degree of this effect is a function of age but also of the 176 Lu/ 177 Hf ratios. For Archean and older samples, the lowering of the calculated initial 176 Hf/ 177 Hf for the Earth’s oldest rocks has very significant implications for the record of the Hf isotope evolution of the Earth (e.g., Scherer et al. 2001 , 2007 ).
Although the Söderlund/Scherer decay constant determinations, which used terrestrial samples in their age comparisons, have converged on a well constrained value of 1.867 ± 0.008 * 10 −11 year −1 , age comparison determinations based on meteorites continue to yield a faster 176 Lu decay rate. Blichert-Toft et al. ( 2002 ) reanalyzed a suite of basaltic and cumulate eucrites and concluded that their regression was consistent with the 1.93 ± 0.03 * 10 −11 year −1 value of Sguigna et al. ( 1982 ) and not the slower decay rates determined from terrestrial age comparisons. As was true with the earlier work of Patchett and Tatsumoto ( 1980a ), however, the basaltic and cumulate eucrites plot at opposite ends of the isochron with the basaltic eucrites at the low Lu-Hf end and the cumulate eucrites at the high Lu-Hf end, which may indicate these are not truly cogenetic. Further, these samples appear to have different formation ages with the cumulate eucrites arguably younger (Mittlefehldt et al. 1998 ). In another study using meteorite age comparison, Bizzarro et al. ( 2003 ) determined a λ 176 Lu value of 1.983 ± 0.033 * 10 −11 year −1 , even faster than the Patchett/Sguigna values. The Bizzarro et al. ( 2003 ) study included analyses of ordinary chondrites, carbonaceous chondrites, and basaltic eucrites and used a common age of 4.56 Ga. As was true with the eucrite-based determination, this study included a diverse suite of meteorites of potentially different ages and metamorphic histories, and therefore, the decay constant determination may be affected in some way by the use of samples that do not strictly meet the requirements for an isochron. These caveats notwithstanding, there are indications that meteorite isochrons yield a faster decay constant. One possible explanation for this apparent difference between the terrestrial and meteorite determinations is the presence of excess 176 Hf in meteorites. This may have been produced by excitation of the long-lived radioactive isotope 176 Lu to a short-lived 176 Lu isomer early in the history of the solar system that then decays quickly to 176 Hf, thereby producing the excess 176 Hf (Albarède et al. 2006 ; Thrane et al. 2010 ). The exact mechanism of how this might have occurred is still a matter of debate (Albarède et al. 2006 ; Thrane et al. 2010 ).
All Lu-Hf geochronology uses the “isochron” method to determine absolute ages. Unlike some chronometers such as U-Pb in zircon where there is little, if any, daughter isotope at the time of mineral growth, in the Lu-Hf system, there is invariably an abundance of daughter isotopes present (i.e., “common Hf”). For this reason, it is not possible to determine the age of a single mineral sample by measuring the accumulation of daughter isotopes in the sample. Thus all Lu-Hf geochronometry relies on the isochron approach, which utilizes coexisting rocks and minerals to determine an age. Important assumptions in this approach include the following: (1) All the minerals formed at the same time (i.e., have the same age); (2) all samples are cogenetic (have the same isotopic composition at the time of formation); and (3) the sample being dated has been a closed system since the time of mineral growth.
The isochron method applied to garnet Lu-Hf geochronology. ( 1) uniform Hf isotopic composition at time t = 0; ( 2) phases in rock acquire different Lu/Hf ratios (garnets with high Lu/Hf), but all with the same 176 Hf/ 177 Hf; ( 3) Hf isotopic compositions of the different components evolve with time as a function of their Lu/Hf ratios; ( 4) if the rock has remained a closed system with respect to Lu and Hf, all components will plot along a line (isochron) that is a function of time
In detail, many of the assumptions of the garnet isochron method are not strictly met. In most cases the rock is certainly not in perfect isotopic equilibrium (i.e., homogeneous 176 Hf/ 177 Hf) prior to metamorphism. In addition, the time different phases in the rock form may not be precisely the same, especially in the case of prolonged garnet growth (e.g., Kohn 2009 ). These can be serious obstacles if there is a small range of Lu/Hf and 176 Hf/ 177 Hf variations in samples but are often overcome in isochrons with high Lu/Hf phases and large amounts of radiogenic Hf ingrowth.
Because of the limited fractionation in Lu/Hf that occurs during magmatic processes, there is rarely a sufficiently large range in Lu/Hf ratios in suites of rocks that are truly cogenetic to generate an isochron with enough precision to be useful (Patchett 1983b ). If there is a large variation in Lu/Hf in a suite of samples, it is likely these samples are probably not strictly cogenetic. Examples of the former may be represented by the eucrite isochrons combining both basaltic and cumulate eucrites (Blichert-Toft et al. 2002 ; Patchett 1983b ) and in the collective chondrite-eucrite isochron of Bizzarro et al. ( 2003 ). In practice, therefore, Lu-Hf whole-rock isochrons are rarely employed for geochronology, especially for terrestrial samples.
There is potential in some magmatic rocks, however, to crystallize a high Lu/Hf phase (e.g., apatite, magmatic garnet) that can then be used in geochronology. The magmatic rocks that have the most promise for useful geochronometry are those that contain apatite as a crystallizing phase. As demonstrated by the decay constant work of Scherer et al. ( 2001 ) and Söderlund et al. ( 2004 ) and the pioneering work applying Lu-Hf geochronology to phosphates by Barfod et al. ( 2003 ), apatite generally has very high Lu/Hf ratios and can be used in generating meaningful isochrons. In addition, these phases are likely in isotopic equilibrium with the magma at the time of their formation and likely formed at the same time as the other phases in the rock. Furthermore, apatite can occur in mafic rocks that generally lack zircon and that may not contain baddeleyite. The potential of Lu-Hf apatite geochronology for providing important geochronologic information for some rocks that are notoriously difficult to date is high, and this should be a growth area in the future.
The most successful geochronologic application of the Lu-Hf system has been garnet geochronology. This technique shares the same principles as Sm-Nd garnet geochronology in that it utilizes garnet’s generally high affinity for HREEs which results in elevated Sm/Nd ratios and (generally higher) Lu/Hf ratios in the garnets as they grow. The potential of the garnet Lu-Hf technique was first demonstrated by a number of papers in the late 1990s (Blichert-Toft et al. 1999 ; Duchene et al. 1997 ; Scherer et al. 1997 ). Following this early proof-of-concept work, there have been a large number of studies in a w >2004 ; Bird et al. 2013 ; Cheng et al. 2008 ; Herwartz et al. 2011 ; Kelly et al. 2011 ; Scherer et al. 2000 ; Smit et al. 2013 ; Wells et al. 2012 ; Zirakparvar et al. 2010 ). Reliable garnet Lu-Hf ages have been reported for rocks as old as Archean (e.g., Smit et al. 2013 ) and as young as Miocene (e.g., Zirakparvar et al. 2011 ) and everything in between.
Although there are many parallels between Lu-Hf and Sm-Nd garnet geochronology, there are important differences between these two systems. First, the decay rate of the parent isotope in the Lu-Hf system, 176 Lu, is
3 times faster than 147 Sm in the Sm-Nd system. This results in a higher rate of ingrowth in the radiogenic daughter, 176 Hf, compared to 143 Nd. Second, owing to the different geochemical behavior between a REE and a HFSE, there is generally more fractionation in the Lu/Hf ratios compared to Sm/Nd, which is especially manifest in phases like garnet and apatite.
Melt-solid partition coefficients for Lu and Hf in various minerals
Hf datingLu-Hf Dating: The Lu-Hf Isotope System, SpringerLink, hf dating.