1 Introduction

Metallic ore deposits are anomalous accumulations of metal commodities within a few kilometres of the Earth’s surface, which have been concentrated significantly above their average crustal contents and in mineralogical forms that make them economically and metallurgically exploitable (e.g., Skinner 1997). Although various geological processes are implicated in concentrating metals in the Earth’s crust, metals in most ore deposits, except some types, like orthomagmatic deposits, are precipitated by aqueous solutions displaying a range of temperature and pH conditions (e.g., Seward and Barnes 1997). These aqueous solutions may derive directly from cooling and/or rising magmas or may be modified seawater, meteoric or connate water, or a mixture of all the above and other fluids, depending on the typology of the ore deposit formed (e.g.,Giggenbach 1997; Scott 1997; Mckibben and Hardie 1997). Precipitation of metals from these aqueous solutions is usually accompanied by an alteration process of the rocks adjacent to the fluid path (e.g., Reed 1997). This is due to chemical disequilibrium between the fluid and the rocks it interacts with. Therefore, a mineralization process results ultimately in the precipitation of metal-bearing ore minerals (usually sulfides and/or oxides) and metal-barren gangue minerals (e.g., carbonates, sulfates, silicates) directly from hydrothermal fluids or as replacement of pre-existing mineral phases by fluid-rock reactions.

Dating the time in the past when metals in the Earth’s crust have been concentrated is instrumental for a complete understanding of the geological processes that form mineral deposits. Determining the timing of mineralization allows us to associate it with magmatic, metamorphic, climatic, biologic, tectonic, and/or geodynamic events that are the drivers of the mineralization processes. Many researchers have studied the distribution of mineral deposit types through time highlighting their link with major events of the Earth’s history (e.g., supercontinent assembly, oxidation events, climatic changes) and their temporal recurrence or uniqueness (Watson 1978; Veizer et al. 1989; Barley and Groves 1992; Goldfarb et al. 2001; Frimmel 2005; Heinrich 2015). Geochronology of ore deposits is fundamental to pinpoint these relationships, to evaluate their repeatability through time, and eventually to offer a “predictive” tool for exploration of different mineral deposits within specific geochronological windows.

In addition, establishing the timescales of mineralizing events improves our understanding of the physico-chemical processes that lead to metal precipitation, especially the rate at which metal precipitation occurs, which is a function of the energy of the system and how this is distributed through time (Weis et al. 2012; Chiaradia et al. 2013, 2014; Chelle-Michou et al. 2017; Chiaradia and Caricchi 2017; Chiaradia 2020).

Dating of mineral deposits can be accomplished through “indirect” stratigraphic methods (e.g., paleomagnetism, fossil assemblages, isotope chemostratigraphy using C and Sr isotopes) or “direct” absolute radiometric dating methods (e.g., U–Pb, Re–Os, 40Ar/39Ar, K/Ar, Rb–Sr). It should be emphasized that ages obtained through “indirect” stratigraphic methods are ultimately determined by absolute radiometric dating that establish the geological time scale of the sedimentary sequences deposited on the surface of our planet (Gradstein et al. 2020). Such “indirect” stratigraphic methods can only be applied to deposits that are interpreted or inferred to be syn-diagenetic or syn-depositional, e.g., VHMS deposits, potentially, but not necessarily, sediment-hosted base metal deposits and carbonate-hosted Pb–Zn deposits (Symons and Sangster 1994; Leach et al. 2001). In the case of deposits that are not syn-sedimentary, these stratigraphic methods only allow us to establish upper and/or lower limits to the age of mineralization. The recognition of the syn-diagenetic or syn-depositional nature of a mineralization is a difficult task especially where deposits of older ages are overprinted by subsequent geological events that may mask primary textural relationships (e.g., see controversy on the age of the Zambia copper belt: Sillitoe et al. 2017a, b; Hitzman and Broughton 2017; Muchez et al. 2017).

The most accurate and precise way of determining the age of an ore deposit is radiometric dating, while recognizing that careful textural constraints on the minerals used for dating are essential in order to date ore or alteration minerals that are genetically associated with the mineralization (e.g., Chiaradia et al. 2013). Accuracy refers to how close a measurement of an age is to the “real” value, which is not trivial to assess because a priori we do not know what the “real” age is. Estimation of the accuracy can be done through measurement of standards with known, certified ages and evaluating how far our measure is from the certified value. However, such measurements do not guarantee that sample ages are accurate, if, for instance, unknown samples are affected by open system behavior. Several parameters may affect the accuracy of an age determination as it will be discussed below. Precision indicates the uncertainty that we can attach to an age that we have measured and usually depends on limitations of the analytical tools used.

The goal of this chapter is to provide basic information on minerals, techniques, accuracy and precision of radiometric methods used for dating metallic mineral deposits.

2 Principles of Radiometric Dating

2.1 Radioactive Decay

Isotopes are nuclides of the same element and as such are characterized by the same number of protons but different numbers of neutrons. Radioactivity is the process through which naturally unstable isotopes of elements emit sub-atomic particles and energy resulting in changes of the number of protons and neutrons which lead to the transformation of the initial isotope into an isotope of another element (Fig. 1) (Rutherford and Soddy 1902a, b). When a radioactive isotope is incorporated into a mineral at the time of its formation it becomes a natural clock that may allow the determination of the time in the past when such incorporation, or the mineral formation, occurred. Strutt (1905) was the first to use radioactivity as a geochronological tool. Although the formation of a mineral may not be instantaneous at the scale of human life it is so at the scale of most geological events. The way the radioactive isotope clock works is that in several specific minerals radioactive isotopes of some elements can be incorporated at levels sufficient to be measured with available analytical techniques and instruments (mass spectrometers). Through time these radioactive isotopes (called parents) decay, emitting various forms of energy and sub-atomic particles and transforming into isotopes of other elements (called radiogenic daughters) which may also be measurable if enough time has occurred since the formation of the mineral to allow sufficient decay of the radioactive isotope (Fig. 1). Several types of radioactive decay exist (e.g., α and β decay: Fig. 1) and apply to different parent radioactive isotopes (see specific literature for more details: e.g., Faure and Mensing 2005; Dickin 2005; Table 1). The products of radioactive decay may be stable (i.e., non-radioactive) daughter isotopes (a typical example is the decay of 187Re to stable 187Os by β− decay or the decay of 147Sm to 143Nd by α decay) or daughter isotopes that are themselves radioactive parents and decay to another daughter isotope a typical example of the latter is the decay chain of 238U to 206Pb, which occurs through a series of intermediate radioactive daughter/parent isotopes formed by α and β decay processes, e.g.,

$$^{238} {\text{U}}\to ^\alpha {}^{234}{\text{Th}}\to ^\beta {}^{234}{\text{Pa}}\to ^\beta {}^{234}{\text{U}}\to ^\alpha {}^{230}{\text{Th}}$$
(1)
Fig. 1
figure 1

Graphic examples of α and β decay processes and their expression in the pertinent portions of the nuclide table

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Table 1 Some radioactive system decay schemes and their applications to dating mineral deposits
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and so on until stable 206Pb.

The use of radioactivity as a geological clock is possible because the decay rate of a large population of a particular radioactive isotope is statistically constant (and for this reason it is called the decay constant, identified by the Greek letter λ), can be measured and quantified, and does not change with changes of physico-chemical parameters like temperature, pressure and composition of the phase hosting the radioactive isotopes (e.g., Faure and Mensing 2005). Different radioactive parent isotopes have widely differing rates of decay encompassing > 10 orders of magnitude (Table 1), which allows determination of events that range in age from billions of years ago to decades ago depending on the chosen isotopic decay system. Thus, by measuring the amounts of radioactive parent isotopes and daughter products present today in a mineral, and knowing the constant rate at which the parents have decayed into the daughters, we can determine the time elapsed over which the mineral has been accumulating the daughter isotope since its formation. Time, rate of disintegration and atomic abundances of parents and daughters are linked together through a simple exponential equation

$$D^* = N\left( {e^{\lambda t} - 1} \right)$$
(2)

where D* and N are the numbers of radiogenic daughter and radioactive parent isotopes, respectively, measured in the system today, λ is the decay rate (known as decay constant) and t is the time since the system (mineral in geological applications) has formed incorporating the radioactive parent isotope. This equation can be solved in order to obtain the time

$$t = \frac{1}{\lambda }\ln \left( {\frac{D^* }{N} + 1} \right).$$
(3)

2.2 Conditions

There are several conditions that must be met in order to use Eq. (3) to obtain a meaningful age. First of all, the mineral must behave as a closed system since its formation, not allowing any escape or any ingression of either parent or daughter isotope, which would modify the D*/N ratio produced by the radioactive decay.

This is a condition that is difficult to be realized because: (i) all elements occurring in minerals, including the radioactive isotopes, tend to diffuse in order to re-equilibrate with the surrounding environment under the drive of chemical and thermal gradients; (ii) radioactive decay creates damage to the crystalline lattice of minerals, which favors the escape or ingression of elements; (iii) the minerals hosting the radioactive parents may be subject to interactions with fluids during their geological life which will cause a release or an ingression of radiogenic and parent isotopes (the reader may refer to Mattinson 2005, to see how the problem of crystal lattice damage of zircons can be tackled in U–Pb geochronology). Among these three processes, thermally activated diffusion is a ubiquitous process, by which elements diffuse within crystals as a function of atomic size, crystal structure and size, and temperature. For a particular element in a particular crystal structure diffusion becomes increasingly fast with increasing temperature, through an exponential function known as the Arrhenius law.

All the points above bear on the fundamental question of what exactly are we dating when we apply a radiometric clock to a mineral? In ideal cases, where the mineral has remained a closed system since its formation, the answer is that we are dating the time elapsed since the mineral crystallised. In other cases, the radiometric age may reflect the time since the mineral cooled to a temperature below which diffusion of the parent and daughter isotopes becomes so slow that the mineral acts as a closed system. This temperature is known as closure temperature (Dodson 1973). Because the closure temperature depends on crystal structure, grain size of the crystal, and atomic size of the diffusing isotope, there is a wide range of closure temperatures (from > 900 to < 100 ℃) for the different radiometric dating systems applied to different minerals (Fig. 2).

Fig. 2
figure 2

Reproduced with permission from Chiaradia et al. (2013); Copyright 2013 Society of Economic Geologists

Range of closure temperatures for various geochronometers.

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In cases where a mineral has grown at temperatures below its closure temperature for the isotopic system of interest, an isotopic age from this system is likely to reflect the time of formation of that mineral. In contrast, where a mineral grows at temperatures above its closure temperature, the isotopic age will be younger than the timing of mineral formation. The time at which a mineral passes below its closure temperature can be variably younger than the time of its formation and reflects the thermal history of the rock that contains the mineral.

These considerations highlight the need to carefully assess the geological meaning of a radiometric age on a case by case basis, requiring as much knowledge as possible of the geological context of the sample.

2.3 Systems not Incorporating Initial Daughter or with Known Initial Daughter

A rock or mineral can be dated using Eq. (3) only if it does not incorporate any significant amount of daughter isotope from the surrounding environment during its formation or if the amount and isotopic composition of the incorporated daughter isotope are known. In such cases either all the daughter isotopes measured in the mineral can be attributed to in-situ radioactive decay or they can be corrected for the incorporation of the initial daughter isotopes. Daughter isotopes of any parent-daughter system are continuously produced everywhere on Earth and therefore the possibility to use Eq. (3) depends on the ability of a mineral to selectively incorporate a radioactive parent and exclude the radiogenic daughter at the time of mineral formation. Several commonly-dated mineral and isotopic pairs satisfy this requirement, for example, the U–Pb system in zircon, the Re–Os system in molybdenite, and, to some extent, the K–Ar system in micas and feldspars. In the latter case it is assumed that initial argon present in a mineral has the isotopic composition of atmospheric argon, which is known and is assumed to have not changed through time (see below): this allows the subtraction of the initial atmospheric Ar.

The K–Ar method of dating of K-bearing minerals is more complex than U–Pb dating of zircon and Re–Os dating of molybdenite for at least two additional physical and methodological issues. The first issue is that the relatively low closure temperatures of Ar diffusion in commonly dated K-bearing minerals (Fig. 2), due to the high diffusivity of Ar, implies that K–Ar dates record the time at which the minerals pass below their Ar closure temperatures. The latter, for most K-bearing minerals, fall in the lower range of hydrothermal temperatures (Fig. 2) and therefore may be lower than the dated mineral crystallization temperatures. In such a case, the K–Ar age recorded by the mineral will be younger than the mineral crystallization age. In other cases, the crystallization of the K-bearing minerals may occur at temperatures that are similar or lower than their closure temperature. In such a case the 40Ar/39Ar date will yield the crystallization age of the mineral. Careful petrographic studies should be carried out to evaluate the meaning of K–Ar ages of K-bearing minerals associated with ore deposits. This is especially true in multi-pulsed systems like porphyry deposits that are characterized by long-lived thermal anomalies above the closure temperature of commonly dated K-bearing minerals (e.g., Chiaradia et al. 2014). In contrast, the high closure temperatures of zircon (Cherniak and Watson 2001) and molybdenite (Stein et al. 2001) for the corresponding U–Pb and Re–Os systems, most of the time higher than crystallization temperatures of these minerals, imply that dates obtained on these minerals are crystallization ages. The second issue is that the K–Ar method requires independent measurements of K and Ar by distinct analytical methods on different sample aliquots, which poses a problem if the sample aliquots are not homogeneous.

The 40Ar/39Ar method of dating is a derivation of the K–Ar method, which has the advantage that a date can be obtained through a single measurement of the same sample aliquot on a noble gas mass spectrometer, thanks to the conversion of 39K of the sample to 39Ar by neutron irradiation in a nuclear reactor. Since 39K and 40K occur in a fixed ratio, 39Ar becomes a proxy of 40K measurement. This method requires the use of monitors with a known age for the quantification of the conversion of 39K to 39Ar in the reactor, and is therefore an indirect dating method relying on the accuracy of the monitors’ ages.

Another advantage of the 40Ar/39Ar method is that it allows the acquisition of a series of dates on the same sample by incrementally heating it, which causes the release of Ar aliquots at each different heating step. The dates so obtained correspond to the release of Ar from increasingly retentive (i.e., higher closure temperatures) parts or crystallographic domains of the mineral. This method allows us to draw an age spectrum diagram using the dates obtained for each step of argon released during the mineral heating process. In ideal cases, several steps (usually the higher temperature ones) provide statistically identical ages forming a so-called plateau age. Younger ages, usually pertaining to the lower temperature steps, correspond to parts and/or crystallographic domains of the mineral that have undergone variable Ar loss. Sometimes, steps with older ages than a plateau may also occur and can be associated with other problems of the 40Ar/39Ar method like Ar excess and Ar recoil. The reader is invited to consult the specific literature (e.g., Faure and Mensing 2005; Dickin 2005) for detailed information on the K–Ar and 40Ar/39Ar dating methods.

2.4 Systems with Initial Daughter—The Isochron Method

For other cases, where a significant and not constrainable amount of daughter isotope may be incorporated in the mineral at the time of its formation

$$D = D_i + D^*$$
(4)

where D is the total amount of daughter isotope resulting from the sum of the daughter isotope incorporated from the surrounding environment at the time of formation of the mineral (Di) plus the daughter isotope produced within the mineral after its formation by decay of the incorporated radioactive parent (D*).

Thus, Eq. (4) above becomes, by substituting Eq. (2) into it,

$$D = D_i + N\left( {e^{\lambda t} - 1} \right)$$
(5)

and Eq. (5) can be solved for t

$$t = \frac{1}{\lambda }\ln \left( {\frac{D - D_i }{N} + 1} \right)$$
(6)

This equation, to be solved for t, requires knowledge of Di, which cannot be known if t is not known, except in some cases like discussed above for the K–Ar system, in which all initial Ar (Di) is attributed to atmospheric Ar. However, a solution to Eq. (6) is given by the observation that

$$\frac{D - D_i }{N}$$
(7)

is the slope of a straight line in the space [D–Di] versus N, which corresponds to an isochron. All the terms of Eq. (7) are usually normalized to a common reference isotope, like a stable non-radiogenic isotope of the daughter element.

This solution allows us to solve the age Eq. (6) by determining the slope of a linear regression between daughter radiogenic and parent radioactive isotopes, which form as a consequence of the radioactive decay.

In order to obtain a linear regression at least two points should be obtained, but, in reality, two and three point regressions have very limited statistical significance (e.g., Ludwig 2001). Therefore, the reliability and precision of linear regressions lies in the number of points by which they are formed and in the statistical dispersion around the regression (Fig. 3).

Fig. 3
figure 3

Examples of different synthetic Rb–Sr isochrons with common natural ranges of 87Sr/86Sr and 87Rb/86Sr values and with a slope corresponding to an age of 701 Ma: a 4-point isochron with large internal uncertainties of single point analyses (up to 1.3% for 87Sr/86Sr) yielding a large uncertainty on the age (~80%); b same 4-point isochron with 10 times smaller internal uncertainties of single point analyses yielding a 10 time better precision on the age ~8%); c 4-point isochron with larger spread of 87Rb/86Sr values yielding a much smaller uncertainty on the age (~2%); d 7-point isochron with same spread of 87Rb/86Sr values yielding an even smaller uncertainty on the age (< 2%)

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Robustness and precision of the regression depend on: (i) the spread of the points along the isochron (the wider the spread the lower the uncertainty on the isochron age), (ii) the analytical uncertainty of the isotope ratios of each analysis (the lower this uncertainty the lower the uncertainty on the age), and (iii) the number of points defining the regression (Fig. 3). In many applications of isochron methods in geochronology, the different points of a linear regression are represented by different but cogenetic minerals. The use of different minerals ensures that they have a broad range of parent/daughter ratios which is a prerequisite to obtain a spread of points along the regression. In some cases (e.g., Pb–Pb isochrons) a single mineral isochron can be obtained by sequentially leaching the mineral and extracting different proportions of radiogenic lead from it (e.g., Frei and Kamber 1995).

The use of Eq. (6) requires that the minerals (or mineral leachate fractions) used for the regression have remained closed systems since their formation and that they have formed coevally incorporating the radiogenic isotope from the formation environment (fluid) in the same ratio to the non-radiogenic isotope, i.e., they must be formed by an isotopically homogeneous hydrothermal fluid, in the case of hydrothermal ore deposits. It should be noted that, for the reasons discussed above and summarized in Fig. 3, the precision of the isochron dating method is usually poorer than dating of minerals which incorporate very little initial daughter isotope, e.g., U–Pb dating of zircon, Re–Os dating of molybdenite, 40Ar/39Ar (K–Ar) dating of K-bearing minerals (under the reasonable assumption that all initial Ar is atmospheric).

3 Dating Methods

Table 1 reports the most used radiometric dating systems in ore geology. The usefulness of these methods depends on the occurrence of datable minerals in any particular ore system.

Each method has different ranges of applicability, but a first-level evaluation of the radiometric dating methods concerns what type of ore or ore-related minerals they can date. From this perspective we can distinguish three main classes:

  1. 1.

    Methods that may directly date ore minerals (e.g., sulphides, oxides);

  2. 2.

    Methods that may date hydrothermal minerals that are paragenetically associated with ore minerals as a result of fluid-rock interaction or co-precipitation from the ore fluid;

  3. 3.

    Methods that allow upper and lower age bracketing of the ore event.

3.1 Methods Directly Dating Ore Minerals

Re–Os is the most precise and accurate method for directly dating ore minerals (Stein et al. 2001; Norman 2023). Rhenium is a siderophile to chalcophile element, which is incorporated to variable extents into sulfide minerals. This method allows high precision dating of molybdenite (MoS2) through Eq. (3) and a variety of sulfides (pyrite, chalcopyrite, etc.; Morelli et al. 2007; Saintilan et al. 2018) through the isochron method (Eq. (6)). Because of the widespread occurrence of molybdenite and other sulfides datable by the Re–Os method in a great variety of geological environments this method is very versatile and allows dating of a broad range of ore deposits (e.g., porphyry systems, stratiform copper deposits, iron oxide copper–gold (IOCG), volcanic-hosted massive sulfide (VHMS), Mississippi Valley-type (MVT) deposits: Li et al. 2017; Saintilan et al. 2018; Liu et al. 2015; Requia et al. 2003; Nozaki et al. 2014).

Another method that has been used for dating directly an ore mineral (sphalerite) is the Rb–Sr isochron method. This method allows direct dating of sphalerite from MVT deposits (Nakai et al. 1993; Christensen et al. 1997). U–Pb dating of cassiterite is another method that allows direct dating of ores containing this mineral (e.g., Yuan et al. 2011).

Other methods that have been used in particular cases for directly dating ore minerals are Pb-Pb isochrons on sulfides and oxides (Frei and Kamber 1995; Requia et al. 2003), 40Ar/39Ar dating of pyrite (Smith et al. 2001), sphalerite (Qiu and Jiang 2007), and U-Th/He dating of Fe-oxides (Wernicke and Lippolt 1994). 40Ar/39Ar dating of hydrothermal quartz fluid inclusions (Kendrick et al. 2001) and Rb–Sr isochron dating of quartz-hosted fluid inclusions (Li et al. 2008) are methods that have been applied to date ore-related fluids. In addition, Sm–Nd isochron dating has been applied to date scheelite (CaWO4) as the main ore mineral (Eichhorn et al. 1997) or associated with gold mineralization of variable age and type (e.g., Anglin et al. 1996; Zhang et al. 2019). These methods may represent the only possibility to date the mineralization in some types of deposits and may return successful results.

3.2 Methods Dating Hydrothermal Alteration Associated with Mineralization

40Ar/39Ar dating of K-bearing phases is the most applied method for dating hydrothermal alteration associated with ore processes. This is due to the fact that 40Ar/39Ar dating yields high precision dates and age spectra that indicate the thermal history of the dated mineral (see above). K-bearing alteration minerals (ranging from amphibole to biotite, adularia, muscovite, illite, alunite and various clay minerals) are almost ubiquitously associated with porphyry system mineralization and with low sulfidation epithermal deposits, but also with other types of mineralization (orogenic gold, Carlin-type, VHMS) and therefore they have been widely used for dating hydrothermal activity associated with various types of mineralization (e.g., Henry et al. 1997; Marsh et al. 1997; Arehart et al. 2003). As discussed above, the 40Ar/39Ar system, due to its low closure temperature in the greatest majority of datable minerals (Fig. 2), records the time at which a certain mineral has passed below its closure temperature. Closure temperatures for the most commonly dated K-bearing minerals mentioned above range between 550° and 200 ℃ (Fig. 2), which is a range of temperatures for a wide variety of geological processes. Therefore, this method is sensitive to later geologic events during which temperatures may rise above the closure temperatures of these minerals, but even to sustained temperature in the lifetime of the same mineralization event which may be characterized by a protracted thermal anomaly induced by multiple subsequent magma intrusions (Chiaradia et al. 2013). In such a case the time recorded by the minerals will be the time at which the temperature drops below the closure temperatures of each mineral which may be variably later than its time of formation. In other cases, in contrast, the temperature of formation of the K-bearing mineral can be similar to its closure temperature and/or the cooling rate of the mineral can be sufficiently rapid that the cooling age virtually coincides with the crystallization age of the mineral.

Rb–Sr dating of hydrothermal minerals (biotite, muscovite) has the same problems of closure temperatures as 40Ar/39Ar (Fig. 2) and additionally it is less precise due to the fact that a date in such a case is obtained through the isochron method (see above).

U–Pb dating of hydrothermal titanite, zircon, rutile, monazite, xenotime, allanite, and U–Pb isochron dating of garnet have been applied in several studies and may allow dating of different mineralization types like skarns, VHMS, and orogenic gold-type deposits among others (e.g.,Vielreicher et al. 2003; Schaltegger 2007; Chiaradia et al. 2009; Fielding et al. 2017; Wafforn et al. 2018; Schirra and Laurent 2021). U–Pb isochrons have been applied to date hydrothermal carbonates associated with MVT mineralization (Grandia et al. 2000).

3.3 Bracketing

An alternative approach to direct dating of either ore or hydrothermal minerals associated with the mineralization is that of dating geological events bracketing the mineralization. The most common case is dating magmatic events that, through stratigraphic or cross-cutting relationships, are demonstrably pre- and post-mineralization.

For instance, U–Pb dating of zircon has been widely used to bracket age and duration of magmatic hydrothermal activity associated with porphyry-type mineralization by dating pre- to syn- and post-ore porphyry intrusions (e.g., von Quadt et al. 2011). Figure 4 shows an idealized example of such a situation in which the age of mineralized veins can be bracketed by U–Pb zircon ages of subsequently emplaced porphyritic intrusions. The same method, applied to dating volcanic rocks occurring in the stratigraphic footwall and hanging-wall of strata-bound VHMS mineralization, has also been used to bracket the age of VHMS mineralization (e.g., Barrie et al. 2002). Of course the closer in age the bracketing events the more useful the resulting age for constraining the timing of mineralization. Unfortunately, this cannot be known a priori, although both in the porphyry and in the VHMS environment genetic models suggest that magmatism used for bracketing is closely spaced in time (to a maximum of few 100 s of thousands of years in most cases). In the absence of alternative methods this remains a powerful method, principally when it is based on the presently most accurate and precise dating method, which is U–Pb dating of zircon.

Fig. 4
figure 4

Schematic crosscutting relationships between early porphyry (immediately premineral), intermineral, and late mineral porphyry phases in porphyry Cu stocks and wall rocks (modified from Sillitoe 2010 and Chiaradia et al. 2014). U–Pb zircon, Re–Os molybdenite, and 40Ar/39Ar dating can be applied to magmatic phases and hydrothermal veins. With younging ages, each magmatic unit may present an increasing range of zircon types inherited from protracted crystallization in the deeper parental magma chamber

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3.4 Other Methods Applicable to Dating of Ore Deposits and Associated Processes

Low-temperature thermochronological methods like the U-Th/He and fission track dating methods have been used in combination with geochronological methods (e.g., U–Pb zircon dating) to determine timing and duration of porphyry mineralization processes, rate of exhumation and erosion of intrusive-related ore deposits and comparative preservation potential (e.g., McInnes 2005).

4 Successful Dating of Ore Deposits

The possibility to date reliably and precisely ore-forming events depends on the occurrence of suitable minerals in the mineralization. Ore deposits intimately associated with intermediate-felsic magmatism (e.g., porphyry deposits, high-sulfidation epithermal deposits, skarn deposits) are probably the most reliably and precisely datable. This is so because these deposits can be dated by the three most accurate and precise dating methods available. U–Pb zircon ages provide a close-to-mineralization upper temporal limit or, in the case of multiple intrusive events showing cross-cutting relationships, also a tight temporal bracketing (Fig. 4). In addition, such deposits very often contain molybdenite, which allows direct Re–Os dating of the mineralization and its comparison with zircon U–Pb ages of the magmatic pulses associated with it (Fig. 4). Further constraints on these types of deposits come from the possibility of dating K-bearing alteration minerals by the 40Ar/39Ar method. There is a large amount of literature showing the successful combined use of U–Pb dating (zircon, titanite), Re–Os (molybdenite), and 40Ar/39Ar (various K-bearing alteration phases) in porphyry Cu-Au, high-sulfidation epithermal, and skarn deposits (e.g., Maksaev et al. 2004; Barra et al. 2013; Deckart et al. 2013; Burrows et al. 2020). Figure 5 shows an example of the gold skarn of Nambija (Ecuador), which has been dated using U–Pb in zircon of the causative porphyry intrusions, U–Pb dating of hydrothermal titanite from the prograde skarn, and Re–Os dating of molybdenite from veins of the retrograde skarn stage, cross-cutting the gold mineralization (Chiaradia et al. 2009). All three minerals returned undistinguishable ages, around 145 Ma, within uncertainty indicating that magma intrusion, skarn formation and gold deposition occurred in a short time that is not resolvable with the available precision of the most precise radiometric techniques. The occurrence of sericite in the same paragenetic association (Fig. 5) could also be used for 40Ar/39Ar dating of this mineral.

Fig. 5
figure 5

Skarn and associated ore and alteration mineral assemblages from the Nambija gold skarn (Ecuador) showing various minerals that have been dated with different techniques (modified from Chiaradia et al. 2009). a Photomicrograph of the endoskarn assemblage with hydrothermal titanite (ttn) that has been dated by the U–Pb method (transmitted light, crossed nicols). b Molybdenite (mol) dated by Re–Os method in a sulfide-rich vein cutting through garnet prograde skarn and post-dating retrograde skarn gold mineralization. c Photomicrograph of molybdenite in the sulfide-rich vein dated by Re–Os (reflected light). In the skarn assemblage there are also K-bearing minerals (e.g., K-feldspar, sericite) that could be eventually dated by the 40Ar/39Ar method. U–Pb titantite and Re–Os molybdenite dates have returned undistinguishable ages (~145 Ma) also with respect to U–Pb zircon dates of the causative porphyritic intrusions (see Chiaradia et al. 2009 for details). Other abbreviations: act = actinolite, ap = apatite, cp = chalcopyrite, kfs = K-feldspar, pl = plagioclase, px = pyroxene, py = pyrite, qtz = quartz, ser = sericite

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Ore deposits for which a genetic and spatial association with magmatic activity is more elusive rely on the occurrence of datable ore and/or gangue minerals. Examples of these deposits are low sulfidation epithermal deposits that have been dated by 40Ar/39Ar on K-bearing minerals (Love et al. 1998; Hames et al. 2009), IOCG deposits that have been dated using Re–Os ages on molybdenite (Requia et al. 2003), U–Pb ages on hematite and U–Th–Pb dating of monazite (Zhou et al. 2017; Courtney-Davies et al. 2019, 2020), and orogenic gold deposits that have been dated using a variety of methods (Re–Os isochrons on sulfides, U–Pb on hydrothermal monazite and xenotime, 40Ar/39Ar on white mica).

Low-temperature hydrothermal deposits hosted by sedimentary sequences, e.g., Carlin-type deposits, MVT deposits, sediment-hosted massive sulfides, stratiform copper deposits, are probably the most difficult to date due to the paucity of datable minerals with reliable and precise methods and the small size of the minerals which make them more prone to open-system behavior (e.g., Rb–Sr on galkhaite, Sm–Nd on fluorite and calcite, Re–Os on Cu–Co sulphides: Tretbar et al. 2000; Saintilan et al. 2017, 2018; Tan et al. 2019).

In summary, whenever possible, a multi-method approach carried out on minerals encompassing different stages of the mineralization process (magmatism, ore deposition, alteration) and coupling in situ dating of petrographically constrained grains with higher precision bulk grain or sub-grain methods on the same minerals should be viewed as the ideal approach for a successful dating of ore deposits.

5 Timing and Duration of Mineralization Processes

It has been highlighted in the Introduction that radiometric dating may provide two types of information: (i) the time in the past when the mineralization occurred and possibly (ii) how long the mineralizing process lasted.

Mineral deposit formation is invariably linked to specific triggering processes, which in turn depend on large-scale geodynamic, climatic, and biologic events that may have recurrent or cyclic occurrence (e.g.,Bekker et al. 2010; Richards 2013; Wilkinson 2013; Heinrich 2015). Determining the time in the past when a mineralization occurred allows us to place the mineralizing event in relationship with geological processes that have triggered and caused the mineralization. This is the case for instance of dating the metallogenic belts of the Andes, which has revealed an initial trenchward shift of the metallogenic porphyry belts and a later shift away from the trench towards the back-arc through time (Sillitoe 1988). Also dating of orogenic gold deposits has highlighted their links with major geodynamic changes through Earth’s history (Goldfarb et al. 2001). Such information may help us to understand the possibilities to find similar deposits in specific time intervals as a result of geodynamic events and/or of preservation and is therefore essential for mineral exploration strategies.

In recent years, ore geologists have also started to appreciate the importance of determining the duration of a mineralizing process. This can in fact provide valuable information on the rate at which metals are deposited and, therefore, a better understanding of the processes that govern metal deposition and the formation of a mineral deposit (e.g.,Chelle-Michou et al. 2017; Chiaradia and Caricchi 2017, 2022). Porphyry deposits have been the most investigated from this point of view because the most accurate and precise dating methods (U–Pb, Re–Os, 40Ar/39Ar) can all be applied to this type of mineralization. We have now acquired, also in combination with thermodynamic (Cathles et al. 1997) and numerical modelling (Weis et al. 2012), and element diffusion studies (Mercer et al. 2015), a quite good understanding of how long a single mineralizing pulse and the overall mineralizing event can last to form a porphyry deposit. The high precision dating obtained in these deposits (see summary in Chiaradia et al. 2013, 2014; Chiaradia and Caricchi 2017; Chiaradia 2020) agrees with the durations obtained through thermodynamic and numerical modelling (Cathles et al. 1997; Weis et al. 2012) or through mass balance calculations carried out using metal concentrations and fluid fluxes of active geothermal fields (e.g., Simmons and Brown 2006). According to these data, single magmatic pulses and associated hydrothermal-ore activity last for a maximum of a few 10 s of thousands of years. However, in order to form the largest deposits these single pulse events must be repeated several times through a process that leads to a progressive step-wise increment of the metal endowment of the deposit over time intervals that can span up to more than one million years (Ballard et al. 2001; Deckart et al. 2013; Chiaradia and Caricchi 2017; Chiaradia 2020).

6 Instrumentation

High-precision radiometric dating is carried out by mass spectrometry (the reader may consult Faure and Mensing 2005 and Dickin 2005 for more detailed introductions to mass spectrometry). Currently the following types of mass spectrometry techniques are the most used for radiometric dating of ore deposits:

  1. 1.

    Isotope Dilution Thermal Ionization Mass Spectrometry (ID-TIMS) (Chelle-Michou and Schaltegger 2023): This technique is routinely used for U–Pb, Re–Os, Rb–Sr and Sm–Nd dating of various minerals. Single or multiple grains, but even portions of single grains (Fig. 6), are dissolved in acids and the elements of interest are separated from each other through column chemistry, and then measured on a mass spectrometer.

  2. 2.

    Noble gas mass spectrometry: this is the technique used for 40Ar/39Ar dating. Previous irradiation of the sample to be analysed to convert 39K to 39Ar, the sample is outgassed under vacuum using a furnace or a laser, to liberate stepwise the Ar gas contained in it (see above). At each step Ar isotope ratios are obtained that can be converted into dates yielding an age spectrum (see above).

  3. 3.

    LA-(MC)-ICPMS (Chelle-Michou and Schaltegger 2023): Laser ablation coupled to a multi- or single collector mass spectrometer is used for dating zircons (mostly) but also other minerals (e.g., titanite, cassiterite, monazite, hematite, calcite). The material analysed is ablated by a laser inside an ablation cell and transferred to the mass spectrometer where it is ionized and isotope ratios are measured. The ablated material corresponds usually to circular pits of 30–60 µm in diameter and a few µm in depth for a total ablated volume in the order of 103–104 µm3 compared to ~105 µm3 for TIMS analyses (Sylvester 2008) (Fig. 6).

  4. 4.

    SIMS (Chelle-Michou and Schaltegger 2023): Secondary Ion Mass Spectrometry is a dating technique largely used for U–Pb dating of minerals that is conceptually similar to LA-ICPMS but differs in the way by which the analysed elements are extracted from the mineral. In SIMS an ion beam (usually of oxygen ions for U–Pb dating) hits the mineral surface and sputters it producing secondary ions that are accelerated and focused into the mass spectrometer. The beam size can be as small as 15 µm thus providing the highest spatial resolution of all dating techniques, but also resulting in smaller volumes of analysed material (~102 µm3; Sylvester 2008) (Fig. 6).

    Fig. 6
    figure 6

    Analytical techniques of high-precision U–Pb geochronology. a CA-ID-TIMS: Chemical-Abrasion, Isotope-Dilution Thermal Ionization Mass Spectrometry can be applied to bulk single grains or portions of them. LA-ICP-MS (Laser Ablation Inductively Coupled Plasma Mass Spectrometry) and SIMS (Secondary-Ion Mass Spectrometry) are in situ techniques allowing a much higher spatial resolution but a smaller volume of analyzed material. b Different precisions of the CA-ID-TIMS versus the in situ LA-ICPMS and SIMS methods resulting from the different volumes of zircon analysed by these methods. The 2SD error bars refer to single spot or single/fraction grain a zircon 100 Myr old assuming typical precisions associated with the 2 methods (i.e., 0.1% for CA-ID-TIMS and 3% for LA-ICPMS and SIMS). See text for further discussion

    Full size image

The major differences among these techniques in terms of precision and accuracy of the obtained ages are two: techniques 1 and 2 above, by virtue of the larger amounts of material analysed, yield higher-precision whereas in situ techniques (3 and 4 above) yield a spatial resolution that is not obtainable with bulk mineral techniques (Fig. 6). Also, in situ techniques have a much higher throughput and overall lower operational costs.

It should be highlighted that the “bulk” minerals (1 and 2) and in situ (3 and 4) methods should be viewed as complementary and that the choice of one or the other depends on the actual goals of the dating. High precision dating by ID-TIMS is the only technique to precisely and accurately constrain the timescales of hydrothermal events where minerals datable by high-precision U–Pb and Re–Os techniques are available, whereas in-situ techniques are the choice for regional studies and for dating minerals with complex textures indicating several growth episodes. High precision CA-ID-TIMS dating of zircon may also benefit from previous dating of the same zircons by in-situ methods in order to allow a selection of the most appropriate zircon grains to be subsequently dated by the more labor intensive CA-ID-TIMS technique (Chelle-Michou et al. 2014).

A limitation in all radiometric dating is the physical limitation of signal detectors in mass spectrometers to precisely and accurately measure very low signals. This places limits on precision and accuracy of ages in very young geological systems in which not enough time has elapsed to allow the formation of measurable signals of radiogenic daughter isotopes (Chiaradia et al., 2013). These limits are being progressively improved via technological advances in ion detection. Accuracy and precision of all dating methods are also dependent on minimization of ‘blanks’ and background signals within the measurement system, that is, the presence of interfering isotopic signals related to sample preparation and/or instrument cleanliness.

7 Intra-method Age Reproducibility, Inter-laboratory Comparison, Inter-method Comparisons and Other Caveats

From the above discussion, it is clear that radiometric dating of an ore deposit can be conducted through different methods. Various analytical techniques are available at different laboratories throughout the world. The quality of the data output of a laboratory is monitored by continuous analysis of standards (natural or synthetic) with known (ideally certified) isotopic compositions, intercalated with the measurement of the unknown samples. There are two main parameters associated with the age obtained at a laboratory that can be used to evaluate the quality of the measurement: (i) the uncertainty of the measured value (precision) and (ii) the accuracy of the obtained value. Uncertainty depends mostly on repeatability of procedural methods (including blanks), counting statistics of the measurements and on mass instrumental bias among the different isotopes. Counting statistics depend on the size of the sample analyzed (Chiaradia et al. 2013), which translates into higher or lower signals (counts) of the analyzed isotopes in the mass spectrometer. Mass instrumental bias may represent the largest amount of the uncertainty associated with an age (e.g., U–Pb: Schmitz and Schoene 2007) and can be overcome by using appropriate doping solutions (spikes) to the unknown samples. These solutions consist of mixtures of isotopes in known ratios which allow the determination of an instrumental fractionation factor associated with the measurement that can be used to correct isotope ratio measurements in the mass spectrometer of the radiometric systems (U–Pb, Re–Os: Markey et al., 2003; Schmitz and Schoene, 2007). Additional sources of uncertainties derive from uncertainties in the calibration of spikes, uncertainties of the decay constants, and also uncertainties in the ages of secondary standards in the 40Ar/39Ar method (e.g., Min et al. 2000; Kuiper et al. 2008; Renne et al. 2010).

The accuracy of a measurement is how close the value of such a measurement is to the “real” value. A way to assess the accuracy of measurements in a laboratory is by measuring certified standards in order to see if the measurements return the expected values of the certified standard. Accuracy depends on systematic uncertainties of various origins (Chiaradia et al. 2013; Schaltegger et al. 2015).

Age data obtained within the same laboratory using the same radiometric method can be compared confidently with each other using the “internal” reproducibility that is associated with the measurements at that laboratory. In such a case, uncertainties associated with spike calibration and decay constants can be disregarded because they apply in the same way to all sample analyses (since the same lab will use the same spike solution and for a given radiometric system the decay constant uncertainties are fixed). These “internal” uncertainties are very low (< 0.1–0.2%, 95% confidence level) for the main dating systems (i.e., ID-TIMS U/Pb dating of zircons, ID-NTIMS Re–Os dating of molybdenite, 40Ar/39Ar dating of K-rich minerals; Chiaradia et al. 2013). This means that the uncertainty on a mineral that is 10 Ma old is only 10,000 years! However, if one wants to compare ages obtained using the same radiometric method at two different laboratories, then “external” uncertainties in the spike calibration must be taken into account, if the two laboratories do not use the same calibrated spike solution. Uncertainty on the calibration of the spikes, which is an essential part of the high precision obtainable by ID-(N)TIMS dating techniques (Chiaradia et al. 2013), can be considerable (Chiaradia et al. 2013). For this reason, there is an increased awareness in the geochronological community to use common calibrated spike solutions which allow the achievement of reproducible ages of standard minerals from different laboratories at the same level of uncertainty obtained by dating within the same laboratory (e.g., Condon et al. 2015).

When we want to compare ages from different radiometric systems (e.g., U–Pb versus Re–Os and 40Ar/39Ar for instance), uncertainties in the decay constants must also be considered. Currently, the decay constants of 238U and 235U are known to a higher precision level than those of 40K and 187Re (see discussion in Chiaradia et al. 2013) and this is one of the main reasons why the U–Pb system is used as a reference system. Therefore, there is a progressive increase of the uncertainties of an age measurement when one wants to compare such a measurement with another measurement using the same radiometric system in the same laboratory (“internal” uncertainty associated mostly with counting statistics and instrumental bias), or with another measurement obtained with the same radiometric system but in another laboratory (“internal” uncertainty plus “external” uncertainty associated, with uncertainty in the spike calibration, if not using the same calibrated solution), or with a measurement carried out using another radiometric system (“internal” plus “external” uncertainties, plus uncertainties in decay constants).

Accuracy of the ages of standards in secondary dating methods (like 40Ar/39Ar) must be also considered and may result in significant discrepancies of the dates of the same geological event using different geochronometers (see discussions in Chiaradia et al. 2013, 2014).

7.1 Geological Factors

An important geological consideration about radiometric dating is that the older the mineral dated the more likely is the possibility that it has been affected by post-formation geological processes which might have variably disturbed its closed-system behavior, a fundamental requirement to be a reliable mineral for dating. Superimposed geological processes may also cause remobilization and formation of new ore minerals at a different time from that of the initial mineralization, complicating the interpretation of geochronologic data.

8 Conclusion

Radiometric systems provide the only quantitative tool for dating ore deposits. Dating ore deposits is an essential step in the formulation of metallogenetic models because it allows us to relate the formation of an ore deposit to a specific geological cause or trigger. In certain cases, like porphyry systems, it also allows us to determine the duration of the mineralizing event which provides essential information on the amount of energy, fluid and magma needed to form such deposits, and which can be used to model the magmatic system features needed to comply with such timescales.

Dating ore deposits using radiometric methods is nonetheless not an easy task and require specialized laboratories and trained personnel. One should keep in mind that dating minerals from an ore deposit should be the final step of a detailed geological and petrographic work that already provides us with an idea of the relative timing of the events we intend to date with absolute ages. Discordancy between a clear-cut geological and petrographic sequence of events and absolute radiometric dating should warn us that some issues may have affected radiometric dating.

Successful radiometric dating of ore deposits is best accomplished using a multi-method approach, through which minerals belonging to different stages of the ore deposit (e.g., causative magmatic intrusion, ore deposition, alteration) are dated with different methods. This, on the other hand, requires careful consideration and tackling of the issues that comparing dates obtained with different radiometric clocks implies, as discussed above. Also coupling in situ dating techniques with “bulk” (single grain or sub-grain) dating is a complementary approach that should be considered for an optimal use of the different advantages that these different methods offer.

Analytical and technological developments over the last 10–15 years and continuously ongoing have resulted in increased accuracy and precision of radiometric dating and this is opening new avenues for the application of geochronology to the understanding of how mineral deposits form.