This convention so far considers mass-dependent fractionation, which can be expressed from the ratio of two isotopes of an element. This is sufficient for analysis and consideration of dD, d11B, d13C, and d18O. While oxygen has another minor isotope 17O, and its abundance is important in atmospheric chemistry, its use for ore studies has just begun (Peters et al. 2020), and multiple oxygen isotope analysis is not considered further here. However, for sulfur isotopes the abundances of the other minor isotopes are increasingly being used to examine potential processes affecting sulfide formation (one of the earliest examples of this is the study of Hulston and Thode 1965), and so some consideration of multiple isotope measurements is required.

Sulfur has four stable isotopes 32S, 33S, 34S, and 36S. As described above, the two-isotope ratio 34S/32S, and hence d34S, is generally used to consider an isotope fractionation related to mass dependent fractionation. Based on d34S, a prediction can therefore be made concerning the magnitude of d33S and d36S in any sample. This can be considered in terms of relative mass difference from the major isotope. If the isotope fractionation is 1.0‰ for d34S, then the prediction will be that d33S will be about 0.5‰ [0.5 being obtained from (33–32)/(34–32)], and d36S will be about 2.0‰ [2 being (36–32)/(34–32)]. This approximation can be refined using exact nuclidic masses, and also by changing the mass fractionation law that relates d33S and d36S to d34S (e.g. linear, power, exponential).

Another isotope parameter (D) can then be determined for the difference in isotope abundance measured, versus that predicted based on d34S. A common formalism for D33S and D36S can be expressed as2 :

$$
\Delta^{33}\mathbf{S} = \delta^{33}\mathbf{S}\_{\mathbf{X}} - 0.51\mathbf{S}\delta^{34}\mathbf{S}\_{\mathbf{X}} \tag{7}
$$

and

2 These definitions of D33S and D36S differ from that of D34S, which indicates the difference in isotopic composition between two minerals, that is D34SA-B = d34SA – d34SB.

$$
\Delta^{36}\text{S}^{\circ} = \delta^{36}\text{S}\_{\text{X}} - 1.90\delta^{36}\text{S}\_{\text{X}} \tag{8}
$$

where the values 0.515 and 1.90 represent the mass differences based on the exact nuclidic masses, and a linear mass-dependent relationship is assumed. For mass dependent fractionation, D33S and D36S will be 0 ‰; for non-massdependent fractionation, or, mass independent fractionation, D33S and D33S can be non-zero. It should be noted that the normalized abundances of D33S and D36S are based on the concurrent measurements of D34S, with D33S and D36S and so the precision of D33S and D36S is not a function of the external reproducibility of D34S in a sample suite.

#### 5 Analytical Methods

Since the first description of analytical techniques for carbon and oxygen isotope analyses of carbonate minerals by McCrea (1950), analytical methods have evolved to the point where for most stable isotope systems, procedures exist that allow the analysis of less than a few pictograms (pg: 10–12 g) of sample for micro-analytical methods. As the methods for stable isotope analysis is a wide field and a number of volumes have reviewed the analytical techniques (e.g. de Groot 2004, 2009; Foster et al. 2018), the description below is brief.

In a broad sense, analytical methods for stable isotopes can be grouped into bulk methods that generally produce a gas that is analysed by a gassource isotope ratio mass spectrometer, and microanalytical methods that generally extract material from the sample using either a laser or an ion beam followed by analysis using gassourced mass spectrometry, inductively coupled plasma mass spectrometry (ICP-MS) or secondary ion mass spectrometry (SIMS). Bulk methods, which were developed in the 1950s and 1960s, are still the mainstay for analyses in many laboratories. In contrast, microanalytical methods began to be developed in the 1980s and 1990s, and are only now becoming widespread as the number of instruments has increased and the relative costs of analyses have decreased.

#### 5.1 Bulk Analytical Methods

Most bulk stable isotope analytical methods involve the conversion of solid minerals into gases that can be analysed using gas-source mass spectrometry. Carbonate minerals are typically reacted with phosphoric acid at various temperatures (depending on the mineral) to produce CO2, which is then analysed for d13C and d18O (McCrea 1950). Typical external uncertainties (2r) 3 for this method are 0.10‰ for d13C and 0.16‰ for d18O.

Sulfide minerals are typically reacted with excess CuO at 800–1000 °C, with the sulfide converted to SO2 gas, which is analysed for d34S (Grinenko 1962; Robinson and Kusakabe 1975). Alternatively, sulfide minerals can be reacted with BrF5 or ClF3 to produce SF6 gas, which is then analysed (Puchelt et al. 1971). This latter method has an important advantage over the SO2 method in that fluorine has only one isotope (versus three for oxygen), removing uncertainties in analysis due to non-S isotope variations. As a consequence, the fluorination method is used in multiple sulfur isotope studies (Rumble et al. 1993). External uncertainties (2r) for the SO2 method are typically 0.2–0.3‰ for d34S, and uncertainties for the SF6 method are typically 0.2‰. For D33S and D36S, uncertainties of the order of 0.04 ‰ and 0.4 ‰ (2r) reflect the relative abundances of 33S and 36S (Farquhar et al. 2007).

As the reagents that have traditionally been used to fluorinate sulfide (and other) minerals (BrF5, ClF3 and F2) are hazardous and difficult to handle, Ueno et al. (2015) developed a rapid technique for fluorination of Ag2S using solid CoF3 as the fluorination agent. Following reaction at 590 °C using a Curie-point pyrolyzer, the resulting SF6 gas was purified using a combination of cryogenic cleaning and gas

3 To be consistent with radiogenic isotope systems, uncertainties cited here are external 2r values. ``External' refers to uncertainties determined from repeat analyses of individual samples or standards; internal uncertainties, which are usually less than external uncertainties, refer to uncertainties due to counting statistics on individual analyses.

chromoatogarphy. Details are provided by Ueno et al. (2015) and Caruso et al. (2022). External (2r) uncertainties are 0.7‰ for d34S, 0.01‰ for D33S and 0.2‰ for D36S.

Prior to analysis, sulfate minerals are typically converted to Ag2S using two methods. In the first method, described by Rafter (1957), the sulfate minerals are first dissolved, then precipitated as barite after the addition of BaCl2 to the solution. The barite is reduced with graphite at 900– 1050 °C to produce BaS and CO2, then the BaS is dissolved and AgCl added to precipitated Ag2S. Alternatively, the sulfate minerals are boiled either in an HI-H3PO2-HCl solution (Thode et al. 1961) or in Kiba reagent (Sasaki et al. 1979) to convert sulfur into H2S, which is then precipitated as Ag2S with the addition of AgCl. The Ag2S produced in both methods is analysed using either the CuO reaction or fluorination methods described above for sulfide analysis. The graphite-reduction method has the advantage that d18O can also be determined from the CO2 produced.

Oxygen is extracted from rocks and minerals by fluorination of the rock with either BrF5 or ClF3 at temperatures of 450–690 °C, depending on the mineral being analysed. The heating is done either with a heating element surrounding the reaction vessels or with lasers. This produces O2 gas, which, historically, has been converted to CO2 gas by Pt-calatysed reaction with graphite (Clayton and Mayeda 1963), although many laboratories currently use O2 directly. The CO2 or O2 gas is then analysed. This method typically produces external uncertainties (2r) in d18O of 0.2–0.4‰.

Hydrogen isotope analysis of whole rocks, minerals and fluid inclusions involves a fairly complicated procedure to produce H2 gas suitable for mass spectrometry. First the sample is heated to 150–200 °C under vacuum for several hours to remove adsorbed water. After the adsorbed water has been removed, whole rock and mineral samples are heated to a temperature of 900 °C using either a resistance furnace or an induction oven to release water, which is collected on a liquid N2 trap. To analyse fluid inclusions, after removal of adsorbed water, (generally) quartz chips are heated to 800 °C, which decrepitates the fluid inclusions, and water and other gases are collected using liquid N2. After cryogenic purification, the collected water is then reduced to form H2 gas using either heated uranium (Bigeleisen et al. 1952) or zinc (Vennemann and O'Neil 1993), with the H2 gas then being analysed. This method typically produces external uncertainties (2r) in dD of 4‰. It must be stressed that fluid inclusion decrepitation results in the collection of the mixing of all types of inclusions, which can introduce significant uncertainties in interpreting the resulting data.

Production of gases for bulk isotope analyses is always conducted on vacuum lines with all conversions in vacuo, and the resulting gases cleaned of impurities cryogenically. In most methods gas conversion is undertaken at high temperatures and involves the use of furnaces. In addition, preparation of SF6 and O2 by fluorination involves strong, and dangerous, oxidants. Hence, preparation of all gases for gas-sourced mass spectrometry has a degree of hazard, which some (though not all) micro-analytical methods eliminate.

In addition to the preparation methods described above, many laboratories use elemental analyzers to combust solids and produce gases such as CO2 and SO2, which are separated automatically using gas chromatography and analyzed by gas-source mass spectrometry (Pichlmayer and Blochberger 1988; Giesemann et al. 1994). With the removal of the need for cryogenic cleaning of the analyzed gases, this development has simplified analytical methods and made them much more rapid.

Bulk analytical methods for boron isotopes differ from those used for other light stable isotopes in that analysis is undertaken using either thermal ionization mass spectrometry (TIMS) or inductively-coupled plasma mass spectrometry (ICP-MS) rather than gas-source mass spectrometry. As a consequence, preparation for analysis involves solution chemistry and purification, whereby care is needed to avoid partial loss of volatile boron and resulting isotope fractionation. Details of sample preparation are described in detail by Sah and Brown (1997), Aggerwal and You (2016) and Foster et al. (2018). Historically, boron isotopes were generally analysed using TIMS, but the development of ICP-MS analysis in the late 1990s has enabled much easier and more rapid analysis. TIMS analyses are done using positive (PTIMS) or negative ions (NTIMS), the pros and cons of which are described in the specialized literature cited. TIMS analysis yields a typical uncertainty (2r) of 0.4–0.6‰, whereas ICP-MS analysis has an (2r) uncertainty of 0.2– 0.3‰ (c.f. Foster et al. 2013).

#### 5.2 Micro-analytical Methods

The development of micro-analytical tools for analyzing stable isotopes began in the late 1980s and continues today, with both the spatial resolution and precision of the analyses improving. Micro-analytical methods have used two different techniques to extract and analyse samples: laser ablation followed by gas-source isotope ratio mass spectrometry or inductively-coupledplasma mass spectrometry (ICP-MS, including triple quadrapole ICP-MS—ICP-QQQ-MS), and secondary-ion mass spectrometry (SIMS) utilising a focused ion beam of oxygen or cesium. The two techniques have both advantages and disadvantages. Laser-based systems tend to provide faster and less expensive analyses, but the analyses can have lower spatial and analytical precision and are relatively destructive. In contrast, secondary-ion mass spectrometry is slower and more expensive, but it can have better spatial and analytical precision, greater sensitivity, and is much less destructive, which can be important if multiple analyses are to be carried out of the same points.

#### 5.2.1 Laser Heating and Laser Ablation

Lasers can be used in two distinct ways for isotope analysis – either for heating a small and localized sample, or for direct ablation. Isotope analysis by laser heating gas source isotope ratio mass spectrometry involves laser heating of a sample with an oxidant (O2, or F2) in a reaction chamber prior to purification of the product gas (O2, SO2 or SF6: Elsenheimer and Valley 1992; Sharp 1990; Beaudoin and Taylor 1994) using cryogenic or chromatographic techniques, and measurement of the stable isotope composition by gas-source mass spectrometry. The advantage of the laser for heating is that localized heating of the sample can be effected without involving the container (crucible); hence blanks can be limited allowing smaller samples to be analysed. One of the first uses of laser heating for microanalysis was to determine d18O and d34S from silicate and sulfide minerals. Small crystals or small aliquots of powders are laser-heated using typically a Nd: YAG or CO2 laser in a F2 or BrF5 (or ClF3) atmosphere for oxygen analysis, or additionally with an O2 atmosphere for sulfur analysis (Crowe et al. 1990; Kelley and Fallick 1990; Sharp 1990; Elsenheimer and Valley 1992; Akagi et al. 1993; Beaudoin and Taylor 1994).

Laser ablation, which can occur in both reactive and inert atmospheres, typically produces a crater 50–200 µm in diameter, depending on the mineral being ablated and laser power and focus. The depth of the pit is typically of a similar dimension. Reaction of the ablated mineral with a reactive atmosphere produces SO2 (sulfide mineral in O2 atmosphere), SF6 (sulfide mineral in F2, BrF5 atmosphere) or O2 (silicate or oxide mineral in BrF5 atmosphere). In some systems the product gas is then cleaned offline and, in the case of oxygen, converted into CO2 before analysis. In other systems, the product gas is automatically cleaned cryogenically or by gas chromatography and then directly introduced into the mass spectrometer for analysis. Laser ablation and a reactive atmosphere produces a reproducible, but mineral- and laboratory-dependent, fractionation effect that has to be corrected to produce final results. The typical external (2r) errors associated with laser ablation are typically 0.2–0.4‰ for d34S and 0.2–0.6‰ for d18O.

Laser ablation in an inert atmosphere has supplanted that in a reactive atmosphere. In this method ablation products are introduced directly into a (multi-collector) inductively coupled plasma mass spectrometer with a carrier gas (commonly He and/or Ar) (Mason et al. 2006; Bendall et al. 2006). These methods typically produce external errors (2r) of 0.3–0.6‰.

Boron analysis using laser-ablation ICPMS has advantages of greater speed than SIMS and more flexibility in that it places lower demands on surface quality and is less strictly dependent on matrix-matched reference materials (but see Mikova et al., 2014). Studies report a similar level of external uncertainty as for SIMS (1‰ at 2r). The main disadvantage, however, is the larger spot size and deeper penetration depth of the laser compared to the ion beam. In many cases a larger spot size is required as a greater volume of material is required for analysis if the boron concentrations are low.

#### 5.2.2 Secondary Ion Mass Spectrometry

SIMS uses a focused ion beam, e.g. O− or Cs+ , to ablate the sample. The interaction of the primary ion beam (10–20 keV) with the target leads to secondary ionization. The probability of ionization is element specific, with metals producing positive secondary ions with O− primary ion beam, and non-metals being ionized to negative secondary ions with a Cs+ ion beam. The chemistry of the ion beam also aids in ionization with electronegative oxygen producing strong electropositive element secondary ion beams and electropositive cesium producing strong electronegative element secondary ion beams (Ireland 1995). As such, SIMS differs from LA in that an ion beam is produced directly from the target. This makes it a sensitive technique, but also strongly matrix dependent and so mineral standards of close composition to the target minerals are required.

SIMS was initially developed in geochemistry in an attempt to measure trace element abundances that were inaccessible by electron beam techniques in the 1960s. The capability to examine radiogenic isotope systems was not developed until the SHRIMP ion microprobes when the combined issues of transmission (sensitivity) and high mass resolution were addressed. While stable isotope analysis does not require high sensitivity or high mass resolution, the low transmission of early instruments led to variable measured isotope compositions simply because of differences in ion paths through the instruments (Shimizu and Hart 1982). SIMS has also been applied to measuring stable isotopes including those of hydrogen, boron, carbon, oxygen, and sulfur. As such, early analyses suffered from reproducibility at a level of greater than one permil for oxygen and sulfur isotope systems (Valley and Graham 1991; Eldridge et al. 1987). Subsequent developments have led to much higher reproducibility with external uncertainties (2r) of 0.3‰ for d18O analyses (e.g. Kita et al. 2009) and 0.3‰ for d34S analyses (e.g. Paterson et al. 1997; Kita et al. 2010). Moreover, recent developments have allowed analysis of all isotope ratios in both the oxygen (e.g. d17O and d18O) and sulfur (d34S, d33S and d36S) isotope systems with similar uncertainties (Ireland et al. 2014).

A key aspect in stable isotope analysis is the development of multiple collection whereby all isotopes are measured at the same time thereby cancelling the uncertainty associated with the primary ion beam noise. This is now the standard methodology for large sector ion microprobes. For d18O measurements, sufficient 18O− is produced for analysis of both 18O− and 16O− in Faraday cup multiple collection mode. Similarly, for sulfur, 32S, 33S, and 34S can be measured by Faraday cups. However, the low abundance 36S cannot be measured with the Faraday cups using high-ohmic resistors because of the Johnson noise associated with the circuitry. Measurements of 36S can use either an ion counter, or Faraday cup electrometers using charge mode (accumulation of charge across a capacitor). Precision for in situ analysis of D33S can be better than 0.1 ‰ while D36S measurements by electron multiplier are around 1 ‰ (2r) (Whitehouse 2013) and around 0.4 ‰ (2r) by charge mode (Ireland et al. 2014).

While the large sector ion microprobes are used to pursue highest precision stable isotope analyses, the nanoscale-SIMS offers high spatial resolution analysis. A typical "spot" for high precision stable isotope analysis is typically 10– 30 µm, which allows sufficient material to be sampled to give sufficient ions for the required counting precisions. However, the purpose of the nanoscale-SIMS is to analyse targets at the 100 nm scale. At this sampling scale, only major isotopes can be measured to high precision.

Boron analysis by magnet-sector SIMS is commonly done with instruments set for monocollection and mass-switching between 11 and 10B, but multi-collection SIMS is routinely used in some installations of the large-geometry instruments. The external uncertainty obtained by mono-collection SIMS is typically between 1 and 2‰ (2r), whereas multi-collection of the two isotopes can reduce this uncertainty by about half. Those values refer to "high-concentration" samples like tourmaline, which can contain percent levels of B. For low-concentration samples, often with less than 20 ppm B, the analytical precision may be limited by counting statistics. For example, large-geometry SIMS instruments have achieved precision of about 3‰ for samples with 1 ppm B (Foster et al. 2018).

An important, and for some applications limiting, issue for all SIMS analysis is the need for matrix-matched reference materials that are homogeneous on the micron scale or better. Such are available and internationally distributed for only a limited number of geologically relevant materials for stable isotope analysis. These include glass, tourmaline, carbonates, silicates/ oxides and sulfides; these are primarily standards for mass-dependent fractionation. Further development is required for minor isotope abundances (e.g. for D33S and D36S), boron isotope measurements at low levels, as well as a wider range of minerals relevant to ore deposits.

#### 6 Processes That Fractionate Light Stable Isotopes

Fundamentally, fractionation of light stable isotopes is the result of small differences in translational, rotational and vibrational motions of bonds within the respective phases. Although it is beyond the scope of this review (see Kieffer 1982 for more details), bonds involving heavier isotopes are marginally stronger than bonds involving lighter isotopes of the same element. This effect is strongly dependent upon the relative mass difference (RMD = (AMH - AML)/AML, where AMH = atomic mass of heavy isotope and AML = atomic mass of light isotope) between isotope pairs: the effect is much stronger between hydrogen (1 H) and deuterium (2 H) (RMD \* ((2– 1)/1) = 1) than between isotopes of heavier isotopes (e.g. 34S and 32S; RMD \* (34–32)/ 32 = 0.0625). Hence, isotope fractionation in the hydrogen system is much greater than that in the boron, carbon, oxygen and sulfur systems, in the absence of kinematic and biologic processes (C, S), and fractionations in light isotope systems are greater than fractionations in stable metal systems (e.g. Fe, Cu and Zn: Lobato et al. 2023; Mathur and Zhao 2023; Wilkinson 2023).

All geochemical processes involve some isotope fractionation, although for heavy elements (e.g. Pb, U), this effect is generally not measurable. The amount of fractionation depends not only on relative mass differences, but also on the type of geochemical reaction and the temperature at which the reaction occurs. For most stable isotope systems, the magnitude of isotope fractionation decreases with increasing temperature (Fig. 1), with mass dependent fractionation functions (except hydrogen) generally having the form:

$$\begin{aligned} 1000 \text{lnz}\_{\text{A}-\text{B}} (\text{ }\Delta\_{\text{A}-\text{B}}) &= \text{A}/\text{T}^2 \times 10^6 + \text{B}/\text{T} \\ &\times 10^3 + \text{C} \end{aligned} $$

ð9Þ where T is temperature in Kelvin and A, B and C are experimentally- or theoretically-determined constants. This temperature dependence of isotope fractionation between minerals can be used to estimate paleotemperatures of mineral deposition (see below).

Most geochemical reactions can be divided into two general groups: those reactions that do not involve electron exchange, and those that do (redox reactions). In general, redox reactions involve much larger isotope fractionations. For example, D34S at 300 °C for the reaction between sphalerite and aqueous H2S, which is not a redox reaction, is 1.5‰, whereas D34S at 300 °C for the reaction between anhydrite and aqueous H2S, which is a redox reaction, is 22.0‰ (calculated using Alpha-Delta (Beaudoin

Fig. 1 Temperature versus 1000 ln a diagrams for the (A) hydrogen (1000 ln amineral-H2O (l)), (B) carbon (1000 ln amineral-CO2 (aq)), (C) oxygen (1000 ln amineral-H2O (l)) and (D) sulfur (1000 ln amineral-H2S (aq)) isotope systems. For some systems, fractionation curves are also shown for dissolved species. Updated from Taylor (1979) and Ohmoto and Rye (1979). For hydrogen, isotope data of Taylor (1979: biotite and muscovite), Chacko et al. (1999: epidote curve a (300–600 °C)), Graham et al. (1980: epidote curve b (150–300 °C)), Gilg and Sheppard (1996: kaolinite) and Horita and Wesolowski (1994: H2O vapor) were used. For carbon, isotope data of Ohmoto and Rye

and Therrien 2009); most fractionation factors discussed below are calculated similarly). Moreover, redox reactions include some reactions, such as disproportionation, and photolytic and biogenic reactions, that are characterized by distinctive isotope effects, and at low temperatures (<250–300 °C), kinetic effects can strongly effect isotope fractionation.

(1979) were used. For oxygen, isotope data of Cole and Ripley (1998: chlorite), Sharp et al. (2016: quartz), Zheng (1993a: almandine, diopside and K-feldspar), Zheng (1993b: biotite, epidote, kaolinite and muscovite), Zheng (1999: anhydrite and calcite), and Zheng and Simon (1991: hematite and magnetite) were used. For sulfur, isotope data of Eldridge et al. (2016: SO2 (aq) and SO4 2− (aq)), Li and Liu (2006: bornite, chalcopyrite, galena, pyrrhotite andsphalerite), and Ohmoto and Rye (1979: sulfate minerals (anhydrite, gypsum, barite, strontianite and alunite) and pyrite), were used

#### 6.1 Reactions Not Involving Reduction or Oxidation

Reactions that do not involve electron exchange are many and varied, but the most important reactions in mineral systems (and geological systems in general) involve the transition between liquid and solid. In some systems (e.g. involving H and O) the transition between liquid and gas is also important.

The simplest reactions involve a physical phase change without a compositional change. Examples include boiling of pure water, condensation of steam or the recrystallization of aragonite to form calcite. Although these reactions involve changes in physical parameters such as density, the chemical composition of the reactants and products do not change. However, the isotope composition does change: D18Oliquidvapour for boiling or evaporation of pure H2O is 2.5‰ at 200 °C.

Although phase changes are important for some mineralising processes (e.g. boiling in some epithermal systems), by far the most important processes in mineral systems involve dissolution or melting in, or precipitation of minerals from, aqueous fluids or magmas. Processes whereby ore metals and other components are extracted from source rocks into a transporting media generally involve either melting of rocks to form a metal-bearing magma or water– rock reaction to form a metal-bearing aqueous fluid. In contrast, processes whereby metal is extracted from the melts or hydrothermal fluids to form mineral deposits generally involve precipitation or crystallization of ore and gangue minerals from these fluids. Isotope data can be very useful in tracing these processes. A third type of chemical reaction involves changing the speciation and complexing of components within hydrothermal fluids. This type of reaction may not be observable in rock chemistry, but in some cases, it can result in isotope fractionation. The last group of processes involves the formation of two immiscible fluids from an original fluid. Examples include the exsolution of an immiscible sulfide melt from a parent silicate magma or the exsolution of an aqueous magmatichydrothermal fluid during crystallization of a silicate magma.

As the exsolution of a magmatichydrothermal fluid from a crystallising magma occurs at magmatic temperature (700–1000 °C: Burnham 1979), and oxygen isotope fractionation at these temperatures is small, the inferred oxygen isotope composition of the magmatichydrothermal fluid (5.5–10.0‰: Taylor 1979) overlaps with that of igneous rocks (5.5–11.0‰: Taylor and Sheppard 1986).

The reaction of hydrothermal fluids with rocks causes significant changes to the mineralogy and chemical and isotope composition of the rock and of the fluid, as a function of temperature and atomic water/rock ratios. This process of hydrothermal alteration is dominated by hydrolysis. Many alteration minerals (e.g. sericite, chlorite, epidote and others), which are enriched in H2O or OH− relative to the rock-forming minerals they have replaced, are the product of hydrolytic reactions in which water has been added to the rock. Tourmaline is a special case in this regard because it is not only a hydrous mineral but it is commonly the only mineral sink for boron in alteration assemblages. If the fluid/rock ratio is high (as is generally the case for pervasive alteration assemblages), the isotope composition of the altered rock is determined by that of the altering fluid. In these cases, the isotope composition of the altering fluid can be estimated from the isotope composition of the altered rock, and, in some cases, the source of this fluid can be inferred.

The last non-redox process that affects isotope characteristics in geological systems is mixing between components with differing isotope compositions that does not involve redox reaction. Mixing can result in significant gradients in isotope ratios, which can be used to identify and map this process (see below). This process commonly is an important mechanism of ore deposition, with important applications for mineral exploration.

#### 6.2 Redox Reactions

Many elements involved in chemical reactions in geological systems exist in multiple valence states. In mineral systems the most important multivalent elements are Fe (Fe0 , Fe2+ and Fe3+), S (S2− , S0 , S4+ and S6+) and C (C4− , C0 , C4+). Many of the reaction types discussed above can involve changes in valency and if so, they are considered redox reactions. An important characteristic of most redox reactions is that while one element is reduced (i.e. gained electrons) during the reaction, another must be oxidized (i.e. lost electrons). Redox reactions generally involve strong isotope fractionation, because of the equilibrium between the reduced species forming lower bond energy compounds (e.g. H2S, CH4) with higher bond energy in oxidized compounds (e.g. SO4, CO2). Hence, large variations in isotope ratios can be an indicator of redox reactions, particularly those involving S, C and Fe (the importance of redox in Fe isotope fractionation is discussed by Lobato et al. 2023).

Figure 2a illustrates the variations in D34SH2Sfluid as a function of pH and fO2 (i.e. redox) at a temperature of 250 °C. Although current fractionation data indicate no significant gradients are present as a function of pH, there is a strong gradient in D34SH2S-fluid just below the boundary between the hematite and pyrite stability fields (c.f., Ohmoto 1972). This gradient reflects the relative abundance of reduced S (H2S and HS− ) and oxidized S (H2SO4, HSO4 − and SO4 2− ) species, which is a reflection of the oxidation state of the system (i.e. RSO4/RH2S, fO2 and fH2). Hence, if a large gradient in d34S exists either in space or time (i.e. paragenesis), this gradient could indicate the presence of redox reactions involving S species, particularly if accompanied by changes in Fe-S–O mineralogy.

Ohmoto (1972) indicated that carbon isotopes can experience shifts as a consequence of redox reactions involving graphite and carbonate minerals. Figure 2b shows variations in D13CH2CO3 fluid as a function of fO2 and pH at 250 °C. There is a strong gradient in D13CH2CO3-fluid that corresponds to the conversion of the C4− to C4+ in the lower part of the pyrite field. Hence gradients in d13C may indicate redox processes, although other geological processes (e.g. mixing) can also produce gradients.

Although Fig. 2 shows variations at 250 °C at specific conditions (details in caption), the

Fig. 2 Variations in (A) D34SH2S-fluid and (B) D13CH2CO3 fluid as a function of redox (fO2) and pH at 250 °C. These diagrams are updated from the original diagrams in Ohmoto (1972) using updated thermodynamic and isotope fractionation data (Ohmoto and Rye 1979; Eldridge

et al. 2016). The diagrams were calculated for a fluid with 5% dissolved NaCl, 10–2.5 m RS (\*320 ppm S) and 1 m RC (\*120 ppm C) taking into account activity coefficients and ion pairing

morphology of the diagram is retained for most hydrothermal conditions. For example, the gradient in D34SH2S-fluid near the upper margin of the pyrite field is retained at higher and lower temperature. Increasing the total sulfur content of the fluid expands the pyrite and, to a lesser extent, the pyrrhotite fields, but the sulfur isotope gradient is retained. Similarly, the gradient in D13CH2CO3-fluid also occurs near the bottom of the pyrite field and overlaps the graphite field under most hydrothermal temperatures.

Mixing of fluids with different redox characteristics can induce redox reactions and isotope fractionation. A good example of this is the mixing of relatively reduced H2S-rich vapor generated by boiling of epithermal fluids into oxidized groundwater. As the gaseous H2S is dissolved into groundwater, it is oxidized, producing sulfuric acid, which extensively alters rocks to aluminous assemblages (Simmons et al. 2005). In addition to the common hydrolytic, precipitation and mixing reactions, there are several special types of redox reactions that can have distinctive isotope effects, including disproportionation, photolytic and biologicallymediated reactions. In addition, many redox reactions are strongly affected by the speed, or kinetics, of reaction, which decreases as temperature decreases.

#### 6.2.1 Disproportionation Reactions

Disproportionation reactions involve a reactant with intermediate valency producing products of higher valency and lower valency together. Unlike other redox reactions, disproportionation reactions do not necessarily involve valency changes to other chemical components during the reaction. The best example of such a reaction in mineral systems is the disproportionation of SO2:

$$4\text{SO}\_2 + 4\text{H}\_2\text{O}^- = \text{H}\_2\text{S}^\cdot + 3\text{H}\_2\text{SO}\_4^\cdot \quad (10)$$

The most important role of SO2 disproportionation in mineral systems is during the evolution of magmatic-hydrothermal fluids from moderately oxidized magmas. This reaction, which causes aluminous alteration due to the production of sulfuric acid, can produce distinctive isotope effects: in many porphyry systems in which this process is important, D34Ssulfate-sulfide \* 5–20‰ (mostly 7–18‰: Rye 2005; Seal 2006). Hence, isotope fractionation can be indicative that this (and other) processes have occurred in a mineral system.

#### 6.2.2 Mass-Independent Fractionation and Photolytic SO2 Dissociation

For most reactions involving elements with three or more isotopes, fractionation between isotopes is ``mass-dependent', that is the fractionation between isotopes is dependent on relative mass differences. In most cases d17O = 0.525– 0.528 d18O (Young et al. 2002; Pack and Herwartz 2014; Sharp et al. 2016), and d33S = 0.515 d34S (Fig. 3a; Hulston and Thode 1965; Johnston 2011). Clayton et al. (1973, 1977), however, found that for O isotope fractionation within carbonaceous chondritic meteorites, the mass-dependent relationship did not hold. Subsequent studies have established this for anhydrous minerals from carbonaceous chondrites as well, where d17O = 0.941 d18O - 4.00 (Clayton 2003). Although it is beyond the scope of this contribution,4 these meteoritic effects identified "mass-independent" isotope fractionation (MIF) for the first time (Ireland 2012). Subsequent studies found that the formation of ozone (Heidenreich and Thiemens 1986; Mauersberger 1987) and the photolytic dissociation of gaseous SO2 (Farquhar et al. 2001) also involved MIF although it remains to be seen whether the MIF associated with ozone fractionation is related in any way to the 16O variability in meteorites.

Photolytic dissociation of SO2 and other Sbearing gases in the ancient (i.e. pre 2400 Ma) atmosphere was controlled by two factors, the abundance of the gas, and the shielding effects of other gas molecules (e.g. O2 and O3) present in the atmosphere (Farquhar et al. 2000; Lyons 2007; Ueno et al. 2009). The most important factor is likely shielding by O2 and O3, which

4 See Clayton 2003 for more details and processes that cause fractionation in meteorites.

Fig. 3 Diagrams (modified after Farquhar et al. 2000) showing mass-independent fractionation in the 34S-33S-32S isotope system. (A) d34S versus d33S diagram showing mass-dependent fractionation (heavy line with D33S value of 0.0‰), mass-independent fractionation reflected as light lines with variable D33S values, and analyses of syn-depositional sulfide and sulfate minerals from > 3.0 Ga sedimentary rocks. (B) Variations in D33S of syn-sedimentary sulfur-bearing minerals with

absorbs ultraviolet wavelengths of light thought to induce photolytic dissociation of SO2 (Farquhar et al. 2001). As the concentration of free O2 (and O3) gas in the atmosphere prior to the Great Oxidation Event at \* 2.42 Ga is thought to have been less than 1 ppm (Catling 2014), there would have been little shielding and photolytic dissociation of SO2 would have been pronounced (Farquhar et al. 2001). In contrast, the increased shielding of O2 (and O3) and/or a decreased concentration of SO2 in an oxygenated atmosphere after the Great Oxidation Event would have caused photolytic dissociation of atmospheric SO2, and the mass-independent effects of this reaction, to cease.

Mass-independent fractionation in the S isotope system is measured by the deviation from

geological time. For the purpose this diagram synsedimentary minerals includes both syn-depositional and early diagenetic minerals. The gray bar in B encompasses the mean ± one standard deviations of 73 younger (<2.09 Ga) samples. The diagrams shown are the first documenting mass independent fractionation of sulfur isotopes from syn-sedimentary minerals; the data available have expanded by orders of magnitude since the initial study of Farquhar et al. (2000)

mass-dependent fractionation. For 33S, this deviation is measured by D33S (Eq. 7). As the products (and isotope characteristics) of photolytic SO2 dissociations in the atmosphere can be "rained out" into the hydrosphere, sedimentary and diagenetic S-bearing minerals may inherit the photolytic isotope signature. As shown in Fig. 3b, prior to the Great Oxidation Event, D33S of syn-depositional or diagenetic Sbearing minerals is highly variable, with sulfide minerals (mostly pyrite) having mostly positive D33S values and sulfate minerals having negative D33S values (cf. Farquhar et al. 2000). This massindependent fractionation effect is powerful as it can be used to identify S that was present in the atmosphere and hydrosphere during the Archean and trace it through subsequent geological cycles including tectonic and mineral systems, because it is indelible in younger mass-fractionation processes (LaFlamme et al. 2018a). Examples of how this technique has been used to identify sulfur sources and infer tectonic processes related to ore formation are discussed below.

#### 6.2.3 Kinetic Effects, Thermochemical Sulfate Reduction and Biochemical Sulfate Reduction

Whereas most geochemical reactions occur very rapidly, redox reactions, involving the exchange of electrons, require significant time to occur, particularly at low temperatures (< 200 °C). Ohmoto and Lasaga (1982) were among the first to determine experimentally the rates of redox reactions between aqueous sulfate and aqueous sulfide. They found that at the pH conditions of most hydrothermal systems (4–7) thermochemical sulfate reduction to sulfide involved an intermediate thiosulfate species, and the rate at which thiosulfate formed was the rate-limiting step. Based upon this model they suggested that thermochemical sulfate reduction is an important hydrothermal process only at temperatures above 200 °C.

Subsequent studies have indicated that thermochemical sulfate reduction can be important at temperatures as low as 100–140 °C (Goldhaber and Orr 1995; Machel 2001; Thom and Anderson 2008), particularly when catalysed by the presence of H2S, certain reactive metals (e.g. Ni, Co, Mn, Cu, Fe, Mg) and organic molecules (Machel 2001; Meshoulan et al. 2016). The isotope effects of thermochemical sulfate reduction depend not only on temperature, but also upon the availability of sulfate. In systems with excess sulfate the kinetic D34Ssulfate-sulfide increases with decreasing temperature, from \* 10‰ at 200 °C to \* 20‰ at 100 °C (Machel et al. 1995; Meshoulan et al. 2016; and references therein). However, if the supply of sulfate is limited, or if the rate of sulfate supply is less than that of sulfate reduction, all sulfate is reduced to sulfide and d34S of the resulting sulfide (either as H2S in sour gas or as sulfide minerals) approximates the d34S value of the original sulfate (Machel et al. 1995). Hence, the absence of significant fractionation between reactant sulfate and product sulfide may indicate limited availability of sulfate in a mineral system.

At lower temperatures (< 100 °C), biochemical sulfate reduction can be an important process to produce H2S (Goldhaber and Orr 1995; Machel 2001). Due to its importance in a range of ecological and geological processes, including diagenesis, ore formation and sour gas formation, bacterial sulfate reduction has been extensively studied over the last three decades, and the geochemical and isotope effects of this process are well known. At present, sixty genera and over 220 species of sulfur-reducing bacteria are known (Barton and Fauque 2009), and kinetic sulfur isotope fractionation factors have been determined for 32 of these species, covering a large range of environments from freshwater and marine muds, salt lakes, arctic sediments, and hydrothermal environments. Detmers et al. (2001) reported experimental kinetic D34Ssulfatesulfide values of 2.0–42.0‰, and sulfate reduction rates of 0.9–434 fmole/cell/day.5 These workers noted no correlation between D34Ssulfate-sulfide and reduction rates, but found that the largest fractionations were associated with bacteria that completely oxidized electron-donor carbon to CO2, whereas bacteria that only partially oxidize the carbon (to acetate) produce lower fractionation factors. The four largest fractionation factors (28.5–42.0‰) were produced by bacteria isolated from marine muds (Detmers et al. 2001). When both thermochemical and biochemical sulfate reduction processes are considered, the most extreme fractionations are associated with biochemical sulfate reduction, which Machel et al. (1995) highlighted as one that can be used to distinguish thermochemical (10–20‰) from biochemical sulfate reduction (15–60‰).

In addition, biochemical sulfate reduction appears to have mass-independent fractionation effects, as shown in Fig. 4. This fractionation, which has D36S/D33S \* -7, was interpreted by Johnston (2011) to indicate biogenic sulfate reduction. This contrasts with the mass-

5 1 fmole (femtomole) = 10–15 mol.

Fig. 4 S isotopic fractionations as measured in situ on the ion microprobe SHRIMP SI. D33S and D36S are the residuals in 33S/32S and 36S/32S after correction for massdependent fractionation (as expressed by 34S/32S). Of particular significance is the resolution of the Biogeochemical Array (slope -7) from the Archean array (slope -

independent fractionation signal associated with Archean photolytic dissociation which has D36S/D33S \* -1. Moreover, biogenic massindependent fractionation is present in Phanerozoic rocks.

Biochemical (bacterial) reduction can also produce significant fractionation in the carbon isotope system. Reduction of acetate and CO2 to form CH4 produces significant, but variable fractionation (D13CCO2-CH4) of up to 95‰ (Whiticar 1999), with typical fractionation between 25‰ and 60‰ (Conrad 2005). Kennedy et al. (2010) found that carbon associated with bacteriogenic iron oxides was depleted in 13C by up to 22‰, with the greater depletion present in samples more highly enriched in organic carbon. Like biochemical sulfate reduction, the fractionation appears to be highly dependent upon the environment and it is likely to be also dependent upon the species of micro-organism involved.

1) which both can have subpermil anomalies in 33S. Previously, the presence of D33S anomalies alone has been used as a life signal, but in the Proterozoic with potential for Archean inheritance, a complete 4-isotope sulfur analysis is required to understand the origin of the sulfur

#### 6.3 Open- and Closed System Fractionation Between Isotope Reservoirs

Many geological processes, particularly devolatilization and degassing, involve the interaction of two distinct geochemical reservoirs. Isotope fractionation between these reservoirs can be modelled using two end-member processes: closed-system, or batch, fractionation, and open-system, or Rayleigh, fractionation. In closed-system fractionation, the two reservoirs are continuously in isotope equilibrium, whereas in open-system fractionation, aliquots of one reservoir are removed and isolated and do not interact with the other reservoir. Batch, or closedsystem fractionation (Nabalek et al. 1984) can be modelled according to the relation:

$$
\delta\_{\mathbf{B},\mathbf{f}} - \delta\_{\mathbf{B},\mathbf{i}} = -(1 - \mathbf{F})1000 \text{ ln } \mathbf{z}\_{\mathbf{A}-\mathbf{B}} \quad (11)
$$

Rayleigh, or open-system, fractionation (Broecker and Oversby 1971) can be modelled according to:

$$
\delta\_{\rm B,f} - \delta\_{\rm B,i} = 1000 \left( \mathcal{F}^{(\rm z\_{A-B}-1)} - 1 \right) \qquad (12)
$$

where dB,f is the final isotope composition of reservoir B, dB,i is the initial isotope composition of reservoir B, and F is the fraction of reservoir B remaining.

Taylor (1986a) provided a good illustration of the differences between closed- and open-system hydrogen isotope fractionation during the degassing of a magmatic vapor from a magma (Fig. 5). In closed systems (curves a and b) where the vapor remains in contact and in isotope equilibrium with the melt, dD of both reservoirs decrease uniformly as the vapor evolves from the melt. If all hydrogen is extracted into the vapor, the final dD of the vapor is identical to that of the original magma.

In contrast, open-system fractionation (curves c and d) involves continuous removal and isolation of aliqots of evolved vapor from the magma, with the aliquots equilibrating with the magma only prior to removal. As a consequence, the dD characteristics of the magma and evolved vapor decrease dramatically as the amount of H2O remaining in the magma (F) decreases (Taylor 1986a). Individual aliquots of vapor produced during open-system magma degassing can have dramatically lighter

Fig. 5 Hydrogen isotope shifts in magmatic vapor and magma in hypothetical models of closed-system (batch) degassing (curves a and b), and open-system (Rayleigh) degassing (curves c and d; curve e indicates the accumulated magmatic vapor). The solid lines indicate modelled composition of the residual magma, and the dashed lines indicated with modelled composition of the evolved vapor. The initial magma had dD = -50‰ and [H2O] = 1.9%; a value for 1000 ln avapor-melt of 20‰ was used. Reproduced with permission from Taylor (1986a); Copyright 1986 Mineralogical Society of America

Fig. 6 Rayleigh fractionation model to explain boron isotope zoning in tourmaline from the Teremkyn gold deposit, Darasun district, eastern Russia (modified after Baksheev et al. 2015). The initial boron (12‰) is

dD than fluids produced during closed-system degassing, particularly as degassing proceeds towards completion. However, the accumulated vapor produced by open-system degassing has a much more moderate evolution (curve e), not dissimilar to that produced by closed-system degassing.

Open- vs. closed-system fractionation has also been demonstrated for the boron isotope system. In this case, the fluid-vapor fractionation is generally insignificant (only about 1 ‰ at 400° C: Kowalski and Wunder 2018) but fluid-mineral fractionation is strong owing to the contrasting coordination environment of the boron ion in aqueous fluid versus solid phases. Furthermore, in the case of tourmaline or other B-rich minerals, crystallization can strongly deplete the fluid reservoir in boron, so that Rayleigh fractionation is a common process. This was demonstrated in controlled experiments by Marschall et al. (2009) and Rayleigh fractionation has been invoked to explain systematic core-rim isotope variations in zoned tourmaline from hydrothermal ore deposits in several studies (e.g., Baksheev et al. 2015, Fig. 6).

interpreted to be granite-derived (i.e., stage I core) while the composition of later tourmaline (stage I rim and stages II to IV) reflects Rayleigh fractionation driven by tourmaline crystallization (Baksheev et al. 2015)

#### 7 Light Stable Isotope Characteristics of Major Geological Reservoirs

Ore fluids in mineral systems have a number of different sources and they carry metals, sulfur, carbon, boron, chlorine and other components that have been sourced from many different geochemical reservoirs. Stable isotope studies are one of very few tools to determine these sources as the reservoirs commonly (although not always) have distinctive stable isotope signatures. Figure 7 and Table 2 summarizes the isotope characteristics of a range of natural reservoirs. Figure 8a illustrates the characteristics of different crustal fluids on a d18O versus dD diagram, and Fig. 8b shows a similar plot of d11B versus dD used by Adlakha et al. (2017) to distinguish fluid sources of the McArthur River U deposit. Huston and Champion (2023), Lobato et al. (2023), Mathur and Zhao (2023) and Wilkinson (2023) discuss how radiogenic lead isotopes and heavy stable metal isotopes can be used to infer metal source.

Fig. 7 Isotope characteristics of major reservoirs for (A) sulfur and (B) carbon reservoirs (modified after Ohmoto and Rye 1979), and (C) boron (derived from Marschall and Jiang 2011, deHoog and Savov 2018, Trumbull and Slack 2018)

Seawater is one of the major Earth reservoirs and it plays a key role in metallogenetic models for a range of stratiform ore deposit types. Modern ocean water has H- and O-isotope compositions identical to V-SMOW, and it is thought to have been relatively uniform through time, with ranges in dD and d18O of -25‰ to 0‰ and -3‰ to 0‰, respectively, since the Archean (Sheppard 1986). Seawater also has a uniform and distinctly heavy boron isotope composition (d11B \* 40 ‰) compared to all other Earth reservoirs (Table 2), which allows to distinguish marine and terrestrial provenance of boron in ore fluids and the minerals derived from them (e.g., Xavier et al. 2008). The H- and O-isotope composition of seawater is also the fundamental basis of the meteoric water line, an important reference on plots of H- and O-isotope compositions (Fig. 8a). The meteoric water line (Craig 1961) is defined by:

$$
\delta \mathbf{D}\_{\cdot} = 8 \delta^{18} \mathbf{O}\_{\cdot} + 10 \tag{13}
$$

The isotope composition of meteoric water is governed by that of seawater and the temperatures of seawater evaporation and precipitation from clouds, both of which are related to latitude and altitude. Lower values of dD and d18O are characteristic of higher latitude and altitude (Sheppard 1986).

Traditionally, formation waters in sedimentary basins were thought to be seawater or brine entrained in sediments at the time of deposition (i.e. connate waters), but subsequent work has demonstrated that many (or most) formation waters are meteoric waters that infiltrated into

Table 2 Range in stable isotope values of the mantle and common upper-crustal sedimentary and igneous rocks

Data from Ohmoto and Rye (1979), Kyser (1986), Taylor and Sheppard (1986), Hoefs (1997) and Marschall and Foster (2018). In most cases metamorphosed rocks retain the isotope characteristics of their precursors (see text)

sedimentary basins subsequent to deposition and diagenesis (Kharaka and Hanor 2003). Evidence for this interpretation stems in part from isotope arrays in d18O versus dD plots that trend toward the meteoric water line and are consistent with the composition of meteoric fluids at likely recharge zones (see Kharaka and Hanor 2003 for discussion). On the other hand, some basins contain formation waters that are interpreted as true connate waters. As these connate waters were originally derived from seawater, their isotope signature should reflect that of seawater at the time of sedimentation (Sheppard 1986). Figure 8a indicates that connate waters, including evaporative brines, are characterized by dD and d18O values somewhat lower and higher, respectively, than modern seawater. These data from Gulf coast basins in the United States Fig. 8 Variations in stable isotope characteristics of fluids present at the Earth's surface or in upper crustal rocks. A. d18O-dD diagram showing isotope characteristics of common crutal fluids. Data from Taylor (1979) and Kharaka and Hanor (2003). B. Variations in d11B (modified after Adlakha et al. 2017)

(Kharaka and Hanor 2003, and references therein), indicate a slight shift from oceanic water, possibly due to equilibration with the host rocks. Although limited, the data suggest that connate fluids may have a distinctive dD - d18O signature relative to meteoric water and other crustal fluids. Marine-derived connate fluids should also have a distinctive d11B signature relative to crustal fluids because of the uniquely high d11B value of seawater. This was used with success in studies of B-isotopes in tourmaline from U-deposits of the Athabasca Basin by Mercadier et al. (2012) and Adlakha et al. (2017) as shown on Fig. 8b.

The stable isotope composition of the upper mantle and mafic igneous rocks derived from it are thought to be relatively homogeneous, with d13C \* -5‰, d18O \* 5.7 ± 0.3‰, d34S \* 0– 1‰ (with D33S, D36S 0) and d11B \* 7 ± 1 ‰ (Table 2). The exception to this is where such rocks are altered on the seafloor or, in the case of arc settings, where the upper mantle is hydrated from slab-released fluids. The homogeneity of mantle-derived rocks contrasts with crustallyderived rocks, which are more variable (Fig. 7) due to the wider range of source components involved and to the number of chemical processes (metamorphism, melting, alteration and weathering) which cause isotope fractionation, particularly in the upper crust, atmosphere and hydrosphere. For example, siliciclastic sedimentary rocks have higher d18O values than igneous rocks from which they were derived due to fractionation during low temperature erosion and chemical weathering. Sedimentary rocks also have a wide range in d13C and d34S values (Table 2) due to biological processes and low-temperature, disequilibrium fractionation as discussed above, and their d11B values depend on their marine or terrestrial provenance (Table 2). The O-isotope discrimination of sedimentary versus igneous (juvenile, arc-related) sources of granites is well established (Taylor and Sheppard, 1986). Trumbull and Slack (2018) showed that the d11B composition of granites and related volcanic rocks also reflects the S- and I- type source dichotomy (see Table 2). The relatively heavy boron in I-type, continental arc magmas (d11B from -10‰ to 12‰, average -2‰), relates ultimately to seawater alteration of the sub-arc magma source, whereas the lighter boron in S-types (d11B from -22‰ to 0‰, average \* -11‰) is due to continental (meta)sedimentary rocks in the source.

In cases where magmas were derived by partial melting of hydrothermally altered rocks (Muehlenbachs et al. 1974; Taylor 1986b), the d18O signature shifts, commonly to lower values as seen in igneous rocks from Iceland (Muehlenbachs et al. 1974) and the Yellowstone complex in Wyoming, USA (Friedman et al. 1974; Hildreth et al. 1984). Schmitt and Simon (2004) attributed the same effect of hydrothermal alteration of the magma source to explain d11B variations in volcanic rocks from the Long Valley caldera.

#### 7.1 The Effects of Metamorphism, Metasomatism and Devolatilization

Metamorphism of a rock can change its stable isotope characteristics through two broad processes, devolatilization or the influx of exogeneous fluids. Devolatilization is the generic process whereby volatile components of a rock are lost during prograde metamorphism and includes dehydration, decarbonation and desulfidation. In some mineral systems, orogenic gold systems, for example, metamorphic fluids produced by these processes are thought to be ore fluids (e.g. Phillips and Groves 1983).

The most important devolatilization reaction is dehydration. According to Wedepohl (1969a) and Engel and Engel (1958b), the average water content of pelitic rocks decreases up metamorphic grade from 5.0% in shales, to 2.96% in phyllites and slates, to 2.41% in mica schists, to 2.02% in sillimanite gneisses, and to 0.62% in transitional amphibolite-granulite facies semipelitic rocks. On an atomic basis, metamorphic dehydration will remove at most 10% of oxygen, but up to 100% of the hydrogen if the process goes to completion. As a consequence, the effect on isotope composition is minor for oxygen (at most an increase in d18O of 0.6‰: Valley 1986), but can be significant for hydrogen (decreases in dD of up to 16‰ or 40‰, depending upon the process of devolatilization assumed: Valley 1986). As the water content in sandstone and igneous rocks is much lower than in pelitic rocks (Wedepohl 1969a,b), the effect of metamorphism on oxygen and hydrogen isotope characteristics of these rocks is much less. Hence, for most siliciclastic and igneous rocks, d18O of the metamorphosed rock is similar that of the protolith, but dD can significantly different.

Boron in clastic sedimentary rocks is hosted mainly in clays and micas (Trumbull and Slack 2018) and the breakdown of these hydrous minerals during metamorphism generally releases boron to the metamorphic fluid (Moran et al., 1992). At the same time, the B-isotope fractionation between sheet silicates and hydrous fluid causes a progressive lowering of d11B values in the higher-grade rocks and the opposite effect for the fluid phase. The situation changes if tourmaline forms during metamorphism because it has a high thermal stability and preserves the boron content in the rock, and its B-isotope composition, during prograde metamorphism (Trumbull and Slack 2018).

Decarbonation reactions can cause significant changes in both d13C and d18O. Metamorphism and devolatilization of marly carbonate rocks commonly produces calc-silicate rocks containing wollastonite (after marly limestone) or diopside (after marly dolostone). Both of these reactions produce CO2 as a product, which then escapes. Valley (1986) summarized the isotope effects of contact metamorphism on carbonate rocks, indicating isotope shifts of up to 14‰ in d13C and 22‰ in d18O, although these shifts were spatially restricted to within 3 km of the causative granite. These shifts in skarns and marbles related to igneous intrusion require that the magmatic-hydrothermal fluids present also experienced significant isotope shifts during decarbonation reactions.

During regional metamorphism, shifts in d13C and d18O are likely to be restricted. Valley (1986) showed that steep isotope gradients are present at the contacts between compositionally and isotopically distinct units, whereas within these units the isotope signature is uniform. Based on this he suggested that regional metamorphism does not affect the isotope characteristics of the protolith unless significant, channelized fluid flow occurred. However, under situations involving the influx of isotopically distinct exogeneous fluids, isotope shifts in dD, d13C and d18O can occur. In contrast to the C, O and H isotope systems, the variation of rock d11B values during prograde metamorphism can vary strongly depending on the specific mineral assemblage and reactions involved (Trumbull and Slack 2018 and references therein).

Studies by Ferry (1981), Pitcairn et al. (2010), Zhong et al. (2015) and Finch and Tomkins (2017) have indicated that as temperatures increase during regional and contact metamorphism, pre-existing pyrite converts to pyrrhotite according to one or more of the following (or similar) reactions:

$$\text{\textquotedblleft 2FeS}\_2 \rightarrow \text{\textquotedblleft 2FeS} + \text{\textquotedblright} \qquad \qquad (14)$$

2FeS2 þ 2H2O þ C ! 2FeS þ 2H2S þ CO2 ð15Þ

Or

$$\text{2FeS}\_2 + \text{2FeO}\_{\text{rock}} \rightarrow \text{4FeS} + \text{O}\_2 \qquad (16)$$

The first two reactions are desulfidation reactions in that sulfur is lost from the rock, but the last reaction does not involve sulfur loss. The above studies indicate that the metamorphic conversion of pyrite to pyrrhotite occurs over a temperature range of 200 °C to 550 °C. Graphical analysis of whole rock geochemical data by Ferry (1981) suggested that reactions similar to (15) are the most likely reactions for pyrite to pyrrhotite conversion and require fluid influx from metamorphic dehydration reactions or from external sources.

The isotope effects of pyrite breakdown during prograde metamorphism are not well studied, with the best example being a laser ablation study by Alirezaei and Cameron (2001) who found no statistically significant fractionation between pyrite and pyrrhotite or between metamorphic zones. They interpreted these results to indicate that the conversion of pyrite to pyrrhotite involved uptake of iron from wall rocks (i.e. reaction 16) rather than sulfur loss. However, at temperatures of 300–450 °C, conditions where the conversion of pyrite to pyrrhotite is greatest (Ferry 1981), D34Spyrite-H2S, D34Spyrrhotite-H2S and D34Spyrite-pyrrhotite are 0.8–1.2‰, 0.2–0.3‰ and 0.6–0.9‰, respectively. This suggests that d34S variations caused by metamorphic desulfidation are likely to be small, probably not recognizable given the large variations in d34S that characterize sedimentary pyrite. Moreover, the isotope composition of sulfur in metamorphic fluids is likely to be similar to that of the rocks that evolve the fluid.

Because primary metamorphic fluids cannot be sampled at or near the Earth's surface, their isotope composition has been inferred using the isotope, mineralogical and chemical composition of metamorphic rocks with estimates of fractionation factors at the temperature range characteristic of metamorphism. Due to the large range in the isotope composition of the protoliths and the range of metamorphic temperatures, the inferred isotope field of metamorphic fluids is large (Fig. 8). Despite this, metamorphic fluids have distinctive isotope characteristics relative to meteoric water, seawater and connate brines, although they overlap with the field of magmatic fluids.

The isotope composition of magmatic fluids also has been estimated from the isotope and chemical composition of igneous rocks and minerals, combined with crystallization temperatures and isotope fractionation factors (e.g. Taylor 1979; Sheppard 1986). The resulting field is large, although not as large as the metamorphic fluid field, with which it largely overlaps. Unlike metamorphic fluids, magmatic fluids have a distinctive isotope signature relative to other fluids such as seawater, basinal brines and meteoric waters present in the upper part of Earth's crust. It must be stressed that the isotope fields shown in Fig. 8 are for primary fluids. Reaction of these fluids with rock has the potential to shift the isotope composition of the fluid, particularly under rock-dominated conditions.

#### 8 Applications of Light Stable Isotopes to Ore Genesis Studies and Exploration

As discussed above, light stable isotopes fractionate during a range of geological processes, hence variations in stable isotope ratios can be used to track these processes. Moreover, isotope data can provide information as to the temperatures and pressures at which mineral systems evolve, and the sources of fluids. The following section discusses how stable isotope data can be used to constrain these processes and conditions of ore formation. More importantly, it also discusses the limitations and ambiguities of some of these constraints.

#### 8.1 Geothermometry and Geobarometry

Temperature, redox state, salinity and pH of the ore fluid largely determine what metals can be transported and how these metals can be deposited. These parameters can be determined from mineral assemblages, but also from fluid inclusion and stable isotope data. Due to temperaturedependent fractionation of stable isotopes between minerals (Fig. 1), the temperature of deposition can be estimated from D34S, D18O and D13C data. However, use of these parameters for geothermometry makes several implicit assumptions: (1) the minerals precipitated at the same time from an isotopically homogeneous fluid, (2) the fractionation between minerals has not been affected by later geological events, and (3) isotope fractionation between minerals occurred under equilibrium conditions. The first two assumptions can be largely (but not entirely) assessed by paragenetic studies, and at higher temperatures (>300 °C), disequilibrium becomes less important in most systems (see below).

Another factor that must be considered in assessing isotope thermometers is the purity of mineral separates analysed. Cross-contamination of mineral separates results in temperature estimates that are too high. For example, a hypothetical fluid with d18O of 8.0‰ will precipitate quartz and magnetite with d18O values of 17.4‰ and -1.5‰ at 250 °C, respectively, giving a D18Oquartz-magnetite = 18.9‰. If the two separates are cross-contaminated by 10% (based on atomic oxygen), the impure quartz and magnetite separates will have with d18O values of 15.5‰ and 0.4‰, respectively, giving a D18Oquartz-magnetite = 15.1‰, which corresponds to a temperature of 265 °C, which is 15 °C higher than the hypothetical conditions. This effect becomes stronger at higher temperature and with greater cross contamination. Hence, care must be taken to ensure sample purity, and temperatures estimated from isotope mineral pairs should be considered maximum temperatures. In-situ techniques like SIMS can solve many of the impurity issues, but at the cost of a larger analytical uncertainty, which equates to a larger temperature error.

If three or more minerals have been deposited concurrently from an isotopically homogeneous fluid, determining DX values for mineral pairs can be used to assess the reliability of the isotope thermometry. Determining dX of three coexisting minerals yields three separate DX and temperature estimates, and if all three temperature estimates are within error, greater confidence can be placed in the overall temperature estimate. If the temperatures differ, the mineral assemblage may not have formed concurrently under equilibrium conditions, or one or more minerals have been affected by post-depositional disturbance, or the mineral separates are not pure.

The uncertainties in stable isotope geothermometry depend on the relative uncertainties in determining dX. If the (2r) uncertainties associated with dX for each mineral pair are similar, the (2r) uncertainty in DX is √2 2rdX; if the uncertainties in dX are dissimilar, the uncertainty is DX is estimated by adding the individual uncertainties in dX in quadrature. This uncertainty in DX is then used to estimate the uncertainty in temperature. Note that the temperature uncertainty is asymmetric, with the lowertemperature uncertainty smaller than the highertemperature uncertainty. This is because the intensity of fractionation in most stable isotope systems decreases with increasing temperature.

Once a temperature estimate has been made, it can be used to constrain other characteristics of the mineral system. Possibly the most important of these is the isotope characteristics of the ore fluid, which is calculated from temperaturedependent fluid-mineral fractionation factors. If sufficient data are available, estimates of dDfluid, d11Bfluid, d13Cfluid, d18Ofluid and d34Sfluid can be made, which is very useful information for determining fluid sources. Furthermore, isotope temperature determinations can be combined with fluid inclusion data to estimate the pressure and, thereby, crustal depth at which mineralization occurred. The pressure can be estimated using the following equation:

$$\mathbf{P\_{l}} = \mathbf{P\_{h}} + (\mathbf{T\_{l}} - \mathbf{T\_{h}})(\Delta \mathbf{P}/\Delta \mathbf{T}) \tag{17}$$

where Pt is the trapping (geological) pressure of the fluid inclusion, Ph is the homogenization pressure (determined from fluid composition and Th), Tt is the trapping (geological) temperature of the fluids (determined from isotopic data as described above or from another independent geothermometer), Th is the fluid inclusion homogenization temperature, and DP/DT is the slope of the isochore. Examples where this methodology has been applied include Huston et al. (1993) Honlet et al. (2018), and many others.

#### 8.2 Tracking Fluid Sources

Stable isotopes are a powerful tool to determine the source of water in ore fluids, and, to a lesser extent the sources of boron, sulfur and carbon within them. As discussed earlier, many fluids present in the upper crust have quite distinctive isotope characteristics, which enables inference of the type of fluid from which the ore fluids were derived (see Fig. 8). An example is the strong contrast between the d11B values of seawater, marine carbonates and evaporitic rocks of marine origin on the one hand, and their equivalents from terrestrial, continental settings on the other (see Fig. 7). Thus the values of d11B, d34S and d13C can be indicative of source (Fig. 7, Table 2), but because there is considerable overlap between potential reservoirs, in many (most) cases, the isotope signature of the ore and gangue minerals is not definitive of a particular source.

An important exception to this generalization for the sulfur isotope system is the use of multiple sulfur isotope ratios to identify massindependent fractionation. The recognition of photolytic mass-independent fractionation of sulfur isotopes prior to the Great Oxidation Event (Farquhar et al. 2000, 2001) has opened a totally new method to identify the relative importance of sulfur that has or has not interacted with the atmosphere or hydrosphere, particularly in Archean and earliest Paleoproterozoic mineral systems. This tool is particularly useful for systems in which the source of sulfur is contested, for example volcanic-hosted massive sulfide mineral systems (Huston et al. 2023), orogenic gold deposits (LaFlamme et al. 2018b) and orthomagmatic Ni-Cu-PGE deposits. In the latter, one mechanism that has been proposed to produce an immiscible Ni-Cu-PGE sulfide melt from the parental mafic/ultramafic magmas is sulfur saturation of the magma by ingestion of sulfide-rich wall rocks (Lesher and Campbell 1993). As many of these deposits formed in the Neoarchean, the distinctive signature of massindependent sulfur isotope fractionation can distinguish between mantle and crustal and mantle sulfur.6 Bekker et al. (2009), Ding et al. (2012) and Fiorentini et al. (2012) used D33S, which indicates the presence (|D33S| > 0.0‰) or absence (D33S \* 0.0‰) of crustal sulfur, to indicate that sulfur contamination from the crust was an important process in some, but not all, orthomagmatic Ni-Cu-PGE deposits, and that the presence of mass-independent fractionation may be a signature of the larger deposits (Fiorentini et al. 2012).

#### 8.3 Tracking Geochemical Processes

One of the more powerful uses of stable isotopes in mineral systems studies is identifying and then tracking geochemical processes like redox reactions and phase separation (boiling, magma degassing). As discussed above, many geochemical processes cause significant, and, in some cases, diagnostic, isotope shifts in rocks and/or minerals, or cause spatial or temporal isotope gradients. These effects are most easily observed where there are strong isotope contrasts between the reactants and the products of the geochemical reaction. For example, in volcanichosted massive sulfide systems, evolved seawater, the main ore fluid, has hydrogen and oxygen isotope characteristics that contrast with the rocks and other potential fluids that it interacts with. As a consequence, hydrolytic alteration zones developed in these systems can be easily mapped using whole-rock d18O data, and the involvement of other fluids (e.g. magmatichydrothermal) can be assessed (Huston et al. 2011, 2023; and references therein).

One of the earliest uses of oxygen and hydrogen isotopes in alteration studies was determining the interaction of magmatichydrothermal ore fluids and meteroic water with host rocks in porphyry copper mineral systems. Sheppard et al. (1969, 1971) showed that hydrothermal minerals from core potassic alteration zones in these deposits formed from magmatic-hydrothermal fluids, whereas clay minerals in peripheral argillic alteration zones formed from heated, overprinting meteoric water. These isotope data were one of the key datasets in establishing the porphyry copper genetic model in the 1960s and 1970s, and the results of Sheppard et al. (1969, 1971) have been confirmed by studies of porphyry systems of different ages around the world.

Boron isotope studies of ore systems have focussed on tourmaline because this mineral is common, resists alteration, preserves zoning and contains percent levels of boron, but other minerals may become important (e.g. white mica, see "future directions"). One of the first uses of Bisotopes to understand ore fluid sources was the study of massive sulfide deposits associated with tourmalinite by Palmer and Slack (1989) and the method grew rapidly since the advent of in-situ studies using SIMS or LA-ICPMS (see Slack and Trumbull 2011; Trumbull et al. 2020). Common applications have been to constrain the fluid source or to define mixing of multiple sources and their temporal relationships. For example, Xavier et al. (2008) found distinctly high d11Btourmaline values (> 10‰) that indicate a marine origin for high-salinity ore fluids in Brazilian IOCG deposits. Zoning and replacement textures combined with in-situ B-isotope ratios tracked fluid evolution and mixing (Pal et al. 2010; Baksheev et al. 2015; Lambert-Smith et al. 2016). In granite-related Sn-W deposits and pegmatites, tourmaline B-isotope studies have been used to recognize the magmatichydrothermal transition by its effect on Bisotope partitioning (e.g. Drivenes et al. 2015; Siegel et al. 2016).

Rotherham et al. (1998) interpreted large variations in d34Ssulfide to be indicative that reduction of an originally highly oxidized ore fluid by interaction with ironstone was the depositional mechanism for the Starra (now known as Selwyn) copper–gold deposit in northwest Queensland, Australia. Large (1975) and Huston et al. (1993) interpreted zonation in d34Ssulfide data from ironstone-hosted deposits in the Tennant Creek district in a similar manner. Large variations in d34S data can be indicative of

6 In this case, defined as sulfur that has (crustal) and has not (mantle) interacted with the atmosphere prior to the Great Oxidation Event at \* 2420 Ma.

redox reactions and spatial and temporal gradients can be used to track and map the progression of these reactions.

Pyrite- and sulfate-bearing advanced argillic alteration assemblages form by two processes in the porphyry-epithermal mineral system: (1) disproportionation of magmatic SO2 to form aqueous H2S and sulfate, and (2) condensation of hydrothermal H2S into oxidized groundwater followed by oxidation of the H2S to form sulfate. Both of these processes produce sulfuric acid, which reacts with rock to produce pyrophyllite and/or kandite (a complex mixture of members of the kaolinite-nacrite-dickite family), which characterize advanced argillic assemblages. These two processes, which occur in different parts of the porphyry-epithermal system, can produce mineralogically similar alteration assemblages that are difficult to distinguish. Comparison of sulfur isotope data from sulfide and sulfate minerals is one method of distinguishing between them (Rye et al. 1992). Rye (2005) found that because SO2 disproportionation is a high temperature process, it produces equilibrium isotope fractionation, whereas oxidation of H2S in groundwater, a low temperature process, generally produces disequilibrium isotope fractionation between sulfide and sulfate minerals. These characteristics, combined with other mineralogical data can be used as criteria to distinguish between SO2 disproportionation and the oxidation of aqueous H2S in groundwater as mechanisms to form advanced argillic alteration assemblages.

In summary, variations in stable isotope ratios can be used to identify and track geochemical processes in mineral systems. It must be stressed, however, that stable-isotope signatures can be affected by many geochemical processes, and these signatures are rarely diagnostic of one process alone. As an example, the presence of a d34Ssulfide \* 0‰ is commonly taken to indicate that the sulfur was derived (directly) from a magma. However, this signature can be produced by the fortuitous mixing of two non-magmatic sources, or by leaching of volcanic rocks, which would have a similar signature. Hence, when interpreting isotope data (and geochemical data in general) all processes that produce an isotope signature must be considered valid, and not just the favoured process the signature "proves". It is rare that an isotope signature is sufficiently unique to eliminate all but one process as its cause. The non-uniqueness of isotope signatures can, in some cases, be overcome by the use of multiple isotope systems, including both stable and radiogenic isotopes (see future directions).

#### 8.4 Exploration and Discovery

Although stable isotopes have proved to be extremely useful in understanding fluid sources and processes that form ore deposits, discoveries of deposits using isotope data are uncommon. Two examples that we are aware of are the discovery of a new skarn lens in the Kamioka district in Japan using d18O data of carbonate minerals (Naito et al. 1995), and the discovery of the West 45 lens at the Thalanga volcanic-hosted massive sulfide deposit in Queensland, Australia using whole-rock d18O data (Miller et al. 2001). Despite well-documented and consistent zonation of isotope values for a number of deposit types (see above and later papers in this volume), isotope methods for exploration have not been taken up by industry to any significant extent. Barker et al. (2013) attribute the lack of uptake by industry to: (1) the costs of analyses, (2) the requirement of specialist analytical labs, and (3) the slow turnaround time for analyses. They noted that for isotopes to be taken up by industry, the quantity of analyses on a project would need to increase from the tens or hundreds typical for ore genesis studies to thousands for exploration. Barker et al. (2013) reported a study in the Carlin district, Nevada, USA in which they used large numbers of analyses to show decrease in d18O of carbonate minerals towards the Screamer gold deposit. Because of the large variability of the data at the drill hole scale, the statistical robustness of large data sets was required to document this zonation. Hence, uptake of stable isotope variations as an exploration tool will require a reduction in the costs and time required for analyses, and a greater number of laboratories able to provide them.

#### 9 Future Directions

As with other science fields, the techniques and interpretations of stable isotopes in metallogenic studies evolve over time. Techniques being developed at present could strongly influence the future direction of stable isotope research in metallogenic studies. These include the development of new techniques (e.g. clumped isotopes), the ability to integrate data from different isotope systems (both stable and radiogenic) on the same rock, mineral or spot, and the increasing capability for inexpensive and rapid analyses.

Like the discovery of significant massindependent sulfur isotope fractionation in the Archean, the development of analytical techniques to measure fractionation of clumped isotopes has the potential to provide a new tool to understand ore genesis. Rather than considering variations in the isotope abundance of an individual element, clumped isotopes measurements identify isotope variations in molecules. For example the CO2 molecule can vary in atomic mass from 44 to 49, with mass number 44 ( 12C16O2) being the most abundant (98.40%) and mass number 49 (13C18O2) the least (44.5 ppb) (Eiler 2007). Just like isotopes, these ``isotopologues' also fractionate with temperature (Ghosh et al. 2006). At present, clumped isotope geochemistry has been extensively used in paleoenvironmental, paleobiological and related studies (Huntington et al. 2011; Eagle et al. 2011), but the application to fluid flow and metamorphism (Swanson et al. 2012; Lloyd et al. 2017) suggest that they might also be useful in ore genesis studies where they can determine the temperature and isotope (i.e. d18O) composition of ore fluids (Mering et al. 2018). Clumped isotopes may be particularly useful in low temperature systems, such as those hosted in basins, where estimating temperature and determining the origin of fluids are problematic. Interpretation of these data does not require knowledge of other information such as salinity and the isotopic signature is less susceptible to later alteration.

To date, the application of B-isotope studies of ore deposits has been almost exclusively based on tourmaline (Trumbull et al. 2020). White mica has been targeted before in studies of metamorphism (Konrad-Schmolke and Halama 2014), but it is virtually unexplored in ore deposit studies even though mica, particularly white mica, contains the highest concentrations of boron of all common rock-forming minerals (Harder 1974). White mica is even more common than tourmaline in alteration zones, and in cases where both minerals coexist, the difference in fluid-mineral B-isotope fractionation between them can be used for geothermometry. A case study of the Panasqueira Sn-W deposit by Codeço et al. (2019) showed that mineralization temperatures derived from D11B in coexisting mica and tourmaline are consistent with other geothermometers and can be used to track cooling of the mineralizing system.

The development of microanalytical methods of isotope analysis has allowed for the first time determination of a large suite of isotope ratios, both stable and radiogenic, from essentially the same spot or the same mineral. Integration of such information can lead to conclusions that are more robust and far reaching than conclusions from each isotope system individually. A good example of this is the microanalytical collection of U–Pb, Lu– Hf and oxygen isotope data from zircon. The ability to collect such data individually has been around for 10–30 years, but only recently have these data been collected from the same spots, allowing synergy of interpretation. As an example, for magmatic zircons from an ore-related granite, the U–Pb system allows age determination (Chelle-Michou and Schaltegger 2023), the Lu–Hf system provides information about source of the magma (e.g. crustal versus mantle: Waltenberg 2023), and the oxygen system provides information about modifications of the source (e.g. metasomatism prior to magma generation: Valley 2003). Collectively, these data can provide information about the mineral system not available individually from the separate isotope information. For example, the data could indicate if a magma originated from the mantle and if the mantle had been metasomatized, potentially important information in determining magma fertility.

Another area with growth potential is the combination of isotope systems including the light stable isotopes described above (B, O, H, C, and S; also Li though not discussed herein), as well as heavier stable metal isotopes (e.g. Cu) and radiogenic isotopes. Many of these can be analysed in situ and with good precision by SIMS and/or LA-ICP-MS, which opens the door to detailed, petrographically-controlled analyses of zoning and overprinting relationships in ore and gangue minerals. Multiple-isotope analyses would remove much of the current ambiguity in identifying fluid and metals origin by isotope fingerprinting. However, a prerequisite for expanding the scope of in-situ analysis is the availability of homogeneous and matrix-matched reference materials for a wide range of mineral groups (oxides, sulfides, silicates, carbonates etc.). There needs to be heightened awareness of the importance for development and distribution of quality reference materials.

As discussed above and by Barker et al. (2013), the development of rapid, inexpensive methods of stable isotope data acquisition would enhance the utility of stable isotope data in mineral exploration. Although stable isotope data can provide vectors toward ore, the time required for analysis and the cost has generally restricted stable isotope (and other isotope) data to academic studies and not exploration. Continued development of rapid methods of analysis would increase the update by the exploration industry.

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Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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## Light Stable Isotopes in Volcanic-Hosted Massive Sulfide Ore Systems

David L. Huston, Crystal Laflamme, Georges Beaudoin, and Stephen Piercey

#### Abstract

Volcanic-hosted massive sulfide (VHMS) deposits, the ancient analogues of "black smoker" deposits that currently form on the seafloor, are the products of complex mineral systems involving the interaction of seawater with the underlying volcanic pile and associated magmatic intrusions. Light stable isotopes, particularly those of oxygen, hydrogen and sulfur, have had a strong influence in determining sources of ore fluids and sulfur as well as elucidating geological processes important in

Supplementary Information The online version contains supplementary material available at https://doi. org/10.1007/978-3-031-27897-6\_9.

D. L. Huston (&) Geoscience Australia, GPO Box 378, Canberra, ACT 2601, Australia e-mail<EMAIL_ADDRESS>
C. Laflamme G. Beaudoin Département de Géologie Et de Génie Géologique, Centre de Recherche Sur La Géologie Et L'ingénierie Des Ressources Minérales (E4m), Université Laval, 1065, Avenue de La Médecine, Québec, QC G1V 0A6, Canada

the VHMS mineral systems. Oxygen and hydrogen isotope data indicate that evolved seawater was the dominant ore-forming fluid in VHMS mineral systems through geological time, although a small proportion of deposits, including high sulfidation and tin-rich deposits, may have a significant, or dominant, magmatichydrothermal fluid component. Highertemperature (> 200 °C) interaction of evolved seawater alters the rock pile below the seafloor, producing d18O depletion anomalies at the deposit and district scales that can be used as a vector to ore. In contrast, lower-temperature hydrothermal alteration results in d18O-enriched zones that commonly cap mineralized positions. An apparent decrease in the degree of high temperature 18O depletion with time may relate to the increasing importance of felsicdominated host successions in younger deposits. d18O anomalies have potential as an exploration tool, and have contributed directly to discovery. The other important contribution of stable isotopes to understanding the VHMS mineral system is quantification of the contribution of sulfur sources. Conventional d34S data, when combined with D33S data acquired using recently developed technologies, indicate that the dominant sulfur source is igneous sulfur, either leached from the volcanic pile or introduced as a magmatic volatile (these sources are not distinguishable). The thermochemical reduction of seawater sulfate is also an important, but subordinate, sulfur source.

S. Piercey

Department of Earth Sciences, Memorial University of Newfoundland, Room 4063, Alexander Murray Building, 9 Arctic Avenue, St. John's, NL 1B 3X5, Canada

© The Author(s) 2023

D. Huston and J. Gutzmer (eds.), Isotopes in Economic Geology, Metallogenesis and Exploration, Mineral Resource Reviews, https://doi.org/10.1007/978-3-031-27897-6\_9

Estimation of the proportion of seawater sulfate with geological age indicate that, on average, it has increased from 5–10% in the Archean to 20–25% in the Phanerozoic. This most likely reflects the increase in seawater sulfate contents through geological time. Although untested as an exploration tool, variations in sulfur isotope data may have utility is discriminating fertile from barren sulfide accumulations or providing vectors to ores at the deposits scale. As exploration tools, light stable isotopes suffer from a relatively high cost and slow turn-around time. If these limitations can be overcome, and new analytical methods can be developed, light stable isotopes may emerge as another tool for exploration, particularly as discoveries are made at greater depth and under cover.

#### 1 Introduction

As discussed elsewhere in this volume, light stable isotope data has proven key to understanding the genesis of a range of mineral systems (Hagemann et al. 2023; Huston et al. 2023; Quesnel et al. 2023; Williams 2023). Although these data have been particularly useful in understanding the sources of ore fluids and sulfur, the data also have proven useful in exploration (Miller et al. 2001). This chapter presents an overview of variations in stable isotope geochemistry in the volcanic-hosted massive sulfide (VHMS) mineral system and how this data has been used to understand this system and where it may be practical for exploration vectoring. It follows and builds on previous syntheses of stable isotopes in VHMS systems by Huston (1999), Shanks (2014) and Leybourne et al. (2022) and of active seafloor systems by Zierenberg and Shanks (1988) and Shanks (2001). Studies of active systems provide information such as direct isotopic measurements of venting fluids and the effect of changes during the timespan of the mineral system not available from studies of ancient systems.

#### 2 The Volcanic-hosted Massive Sulfide Mineral System

The VHMS mineral system is arguably one of the best documented and understood mineral system. As VHMS deposits are preserved in many different parts of the world and formed through much of Earth's history, they provide, collectively, information on geological processes through time, including changes in hydrothermal and environmental processes. Despite these changes, VHMS deposits through time share many characteristics, both at the deposit- and district- to province-scale.

The understanding of the VHMS mineral system has come about not only from ancient deposits (Franklin et al. 1981, 2005; Huston et al. 2006) but also the discovery of "black smoker" deposits in modern oceanic basins (e.g., Hannington et al. 2005), which are thought to be modern analogues of VHMS deposits. Currently, hydrothermal fluids circulate extensively through the upper crust, particularly in submarine extensional zones associated with mid-oceanic ridges on divergent margins, or back-arc basins/rifted arcs along convergent margins. This circulation not only cools the oceanic upper crust, controlling the Earth's surficial heat budget (Stein 1995), but the fluids leach metals from the underlying rock and transfer these metals into the hydrosphere, having a major impact on the seawater metal budget. Although most metal is lost to the seawater column when these fluids vent (Converse et al. 1984), some of the metal is trapped in massive sulfide deposits that form at or just below the seafloor at venting sites (Herzig and Hannington 1995); the vents are also sites of abundant biological activity (Hannington et al. 2011). The growth of seafloor massive sulfide deposits involves dissolution, alteration and replacement of rock and massive sulfide within and below the mounds, forming complex mixtures of sulfide and altered host rock known as stockworks (Petersen et al. 2018).

Studies indicate that geologically ancient VHMS deposits formed mostly in back-arc basins and rifted arcs along convergent margins (e.g., Franklin et al. 2005). This differs from modern black smokers, which are known to form along both mid-oceanic ridges as well as backarc basins and rifted arcs (Hannington et al. 2005). This difference arises due the low likelihood of preserving oceanic crust in the ancient record—most of this crust is lost to subduction. Figure 1 illustrates an idealized asymmetric, VHMS-bearing back-arc basin that has rifted preexisting continental crust to the left and an arc that developed on this crust to the right. Geochemical analyses of volcanic successions that host VHMS deposits (Lesher et al., 1986; Kerrich and Wyman 1997; Hart et al. 2004; Piercey 2011) indicate that both back-arc and arc signatures are present in VHMS districts.

Volcanism and the associated magmatism are integral components of the VHMS mineral system, providing heat, fluids, metals and/or sulfur. The left-hand side of Fig. 1 illustrates a VHMS system associated with a semi-conformable, subvolcanic intrusion that has provided heat to drive fluid flow. The associated volcanic pile provided metals and sulfur to the mineralizing fluids. The right-hand side illustrates a situation in which a cross-cutting intrusion, possibly arcrelated, has provided heat, metals, sulfur and fluids to the evolving VHMS system. These two systems should be considered end-member variants of the VHMS mineral system.

The other major source of system components in VHMS systems is the overlying seawater column. Based mostly on stable isotope evidence seawater is thought to be the dominant fluid source in most VHMS systems and an important source of sulfur in many, particularly younger, systems. The left-hand inset in Fig. 1 illustrates a mineral system in which emplacement of a semiconformable, subvolcanic intrusion (c.f. Galley 2003) at a depth of 3–5 km drives convection of seawater in the volcanic pile. This produces semi-conformable alteration zones above the intrusion that become cross-cutting along synvolcanic structures to become the proximal alteration zones associated with most VHMS deposits. This alteration pattern records the convection of evolving seawater that interacts with

Fig. 1 Volcanic-hosted massive sulfide mineral system. Reproduced with permission from Huston et al. (2011); Copyright 2011 Geoscience Australia

the volcanic pile to extract metal and sulfur then moves upwards through the pile and deposits sulfur and metals to form a VHMS deposit. If the seawater was sulfate-bearing, reduction to sulfide by high temperature water–rock interaction was a second source of sulfur in the system.

Volcanic-hosted massive sulfide deposits form at and just below the seafloor and comprise three types of mineralized rock, stockwork, massive sulfide and exhalite (Fig. 2; Franklin et al. 1981, 2005; Huston et al. 2006). The stockwork zone consists of anastomosing veins, or "stockworks", of sulfide-bearing veins that also commonly contain quartz, carbonate, chlorite, sericite and, in some deposits, sulfate minerals. The stockworks typically vein strongly altered volcanic rocks. This "proximal" alteration typically is dominated by chlorite, sericite, quartz and iron sulfide minerals. In some cases, proximal alteration can contain advanced argillic assemblages (e.g., pyrophyllite, kaolinite) although such zones are much less common than the typical quartz-chlorite-sericite assemblage. Stockwork and proximal alteration zones generally grade outwards over a distance of 10–200 m to lower temperature "distal" alteration zones by either a decrease in alteration intensity or mineralogical changes.

Stockwork zones commonly grade upwards into massive sulfide zones, defined as rock that contains more than 60% sulfide minerals (Sangster and Scott 1976). Although early models interpreted that massive sulfide zones formed at the seafloor (e.g., Hutchinson 1973; Ohmoto 1986; Lydon 1988), more recent work has indicated that massive sulfide zones can also form by replacement of host rocks (Doyle and Allen 2003) or by increasing intensity of stockwork (Fig. 2). Massive sulfide zones are commonly zoned mineralogically and compositionally, typically from Cu-rich at the base to Zn-rich at the top; many Phanerozoic deposits have sulfate-rich zones at the very top. In some cases, massive sulfide zones are flanked by exhalite, chemical sediments formed from hydrothermal fluids that have interacted with seawater. Exhalites can be siliceous and/or iron-rich, can be enriched in many hydrothermal elements, including base metals, and can be deposited hundreds of meters to even kilometers away from massive sulfide deposits (Peter 2003 and references therein). In many, though not all, districts, exhalites mark

Fig. 2 Idealized cross-section of volcanic-hosted massive sulfide deposits showing different ore and alteration zones

stratigraphic positions prospective for VHMS mineralization.

The right hand inset in Fig. 1 shows a scenario in which the magmatic chamber that drove circulation in the VHMS system also concentrated magmatic-hydrothermal fluids and these were introduced into the circulating VHMS fluid system. In this case both seawater and magmatic volatiles would be fluid sources, and magmatichydrothermal sulfur and metals could form a significant component of ore fluid, with the rest derived either from convecting seawater or leaching of the volcanic pile. A mixed fluid with seawater and magmatic-hydrothermal components would then rise to the seafloor, where rapid cooling upon mixing with ambient seawater would cause metal deposition at or just below the seafloor.

#### 3 Stable Isotope Terminology

In this chapter conventional isotopic results are reported relative to internationally recognized standards using standard d notation: V-SMOW (Vienna-standard mean oceanic water: Werner and Brand 2001) for oxygen and hydrogen and V-CDT (Vienna- Canyon Diablo troillite: Ding et al 2001). Typical 1r uncertainties in measurements are 0.2‰ for d18O, 3‰ for dD and 0.2‰ for d34S. Details of analytical techniques, standards and uncertainties are summarized by Huston et al. (2023).

#### 4 Stable Isotopes and the Genesis of Volcanic-hosted Massive Sulfide Systems

Stable isotope data have played a key role in constraining and understanding fluid and sulfur sources in VHMS mineral systems. Because the oxygen and hydrogen isotope composition of seawater is thought to have been relatively constant over geological time (d18O \* −3 to 0‰ and dD \* −30 to 0‰: Sheppard 1986), and this value is significantly different to magmatichydrothermal fluids (d18O \* 5.5 to 10‰ and dD \* −50 to −35‰: Taylor 1987), these data can be used to assess the relative importance of evolved seawater and magmatic-hydrothermal fluids in individual VHMS ore systems at the deposit and district scales. Similarly, as the d34S composition of seawater sulfate (d34S + 10 to + 35‰; Crockford et al. 2019) differs to that of sulfur derived from volcanic or magmatichydrothermal sources (d34S −5 to + 8‰; Chaussidon et al. 1989), sulfur isotope data have been used to infer the importance of seawaterderived sulfur to the VHMS mineral system through geological time.

#### 4.1 Oxygen and Hydrogen Isotopes

As seawater has oxygen and hydrogen isotope compositions that are significantly different to the rocks that underlie and host VHMS deposits, alteration of these rocks by (evolved) seawater can significantly affect the isotopic composition of the altered rocks. This interaction occurs not only in proximity to the ore zones, but also more regionally. In both cases, oxygen isotope variations have been used to map hydrothermal alteration zones.

#### 4.1.1 Ore-proximal Patterns in Oxygen and Hydrogen Isotopes

Over the last five decades numerous studies (Table E1: updated from Huston 1999) have documented variations in d18O and dD in the immediate vicinity of VHMS deposits. These studies have indicated systematic patterns, such as a decrease in d18O toward ore (Fig. 3a), that can be used for exploration (e.g., Miller et al. 2001). There are fewer studies documenting variations in dD, and these studies do not show as consistent of a pattern and are likely to be affected by metamorphism. However, despite this, most of the deposits shown in Fig. 3b are characterized by an increase in dD proximal to ore.

Beaty and Taylor (1982) first illustrated these relationships in a diagram schematically illustrating variations in d18O away from proximal alteration zones for a range of deposits. Figure 3 is an update of this original diagram that includes many historic studies as well as more recent

Fig. 3 Schematic diagrams showing variations in wholerock d18O and dD values around VHMS deposits (updated from original diagrams in Beaty and Taylor 1982, using data from Table E1). Because of the large number of studies, this diagram mostly shows deposits with large number of analyses, but also includes some of the classic deposits (e.g., Beaty and Taylor 1982) where the relationship was first demonstrated. The width of the most intense isotopically-altered zone ranges from a few tens to a few hundreds of meters. The scale of the isotopic zonation is up to 1000 m, but more typically a few hundreds of meters

studies that are based on a large number of analyses (most deposits with a small dataset have been excluded, but are summarised in Table E1). At most deposits, there is a consistent pattern of decreasing whole rock d18O toward the core of the proximal alteration zone (Fig. 3a). In detail, however, the magnitude and variation between distal and proximal d18O varies between deposits and, possibly, through time. Deposits associated with advanced argillic alteration assemblages (red lines in Fig. 3a), however, are characterized by proximal d18O values that are similar to or even higher than distal d18O values.

To assess possible reasons for this variability, Fig. 4 plots the variation of (a) average distal whole-rock d18O, (b) average proximal wholerock d18O and (c) the isotopic contrast (i.e. d18Odistal – d18Oproximal) with geological time. The figure also shows the variations in (d) d18Odistal versus the isotopic contrast, and (e) d18Odistal and (f) d18Oproximal versus 100Cu/ (Cu + Zn) of the deposit. No correlation is evident between d18Oproximal and isotopic contrast, so this diagram is not shown. Although the certainty is limited due to a small sample size, there appears to be a broad decrease in d18O values from distal zones and, possibly, proximal zones, with age. Variations in d18O in altered rocks are controlled by the temperature of the isotopic exchange, the water/rock (W/R) ratio, d18O of the altering fluid and d18O and chemical and mineralogical composition of the altered rock.

Figure 4e and 4f indicate that although there is not a relationship between d18Odistal and 100Cu/ (Cu + Zn), low d18Oproximal alteration zones tend to be associated with Cu-rich deposits. As 100Cu/ (Cu + Zn) is a proxy for the overall temperature of the hydrothermal system (e.g., Large 1977; Lydon 1988), this suggests that d18Oproximal reflects, to a large degree, the overall temperature of the hydrothermal system, particularly in hydrothermal upflow zones with very high W/R. Overall, this temperature has decreased over geological time. The observation that d18Odistal is unrelated to 100Cu/(Cu + Zn) suggests, however a different control for the isotopic composition of the outer, lower temperature and lower W/R portions of the VHMS mineral system.

A possible reason for the disconnect between d18Odistal and the overall temperature of the hydrothermal system is that d18Odistal records a different type of fluid-rock interaction to the high temperature ore fluid. Under conditions of low W/R, the isotopic composition of fluids is largely controlled by the isotopic composition of the rocks with which they interact, in this case the bulk isotopic composition of the rock pile underlying the VHMS deposit. Figure 4a shows that rock pile in which felsic volcanic rocks

Fig. 4 Plots showing the variation of (a) average distal whole-rock d18O, (b) average proximal whole-rock d18O and (c) the isotopic contrast (i.e. d18Odistal – d18Oproximal) with geological time, (d) distal d18O versus isotopic

contrast, and (e) and (f) d18Odistal and d18Oproximal versus 100Cu/Cu + Zn) of the associated deposit. Data are from Table E1

dominate have higher d18Odistal those in which mafic volcanic rocks dominate. As unaltered felsic volcanic rocks (dacite and rhyolite) on average have higher d18O (6–9‰) than mafic rocks (basalt: 5–7‰) (Taylor and Sheppard 1986), low temperature, ambient fluids in equilibrium with felsic dominated rock piles under low W/R conditions would have higher d18O than fluids equilibrated with mafic-dominated piles. Interaction of such fluids in altered zones distal to the main hydrothermal channelway may account for the observed differences between d18Odiistal in felsic-dominated and maficdominated VHMS systems.

These mechanisms, however, do not directly account for the apparent correlations of d18Odistal and d18Oproximal with time (Figs. 4a and 4b); these correlations may be indirect. As shown by Barrie and Hannington (1999) and Huston et al. (2010), deposits in felsic-dominated succession are much more common in the Phanerozoic than in the Paleoproterozoic or Archean; conversely, deposits hosted by mafic-dominated successions are more common in the Paleoprotoerozoic and Archean. Hence, the correlation of d18Odistal and d18Oproximal with geological time may relate to the changing relative abundance of mafic- and felsic-dominated volcanic successions as VHMS hosts through time. A possible corollary to this inference is that, on average, older VHMS deposits formed at higher temperatures than younger deposits. Hence, it is important to consider the lithology of the altered host succession when interpreting whole rock d18O patterns in the context of genesis and exploration, an issue highlighted by many authors (e.g., Taylor et al. 2015). It also must be stressed that distal values are not those of pristine, unaltered volcanic rocks, but those of rocks that have experienced low temperature, pervasive alteration.

Metamorphic grade also does not seem to affect d18O patterns, since regional metamorphism most commonly did not involve significant water advection, and is considered isochemical (Riverin and Hodgson 1980); thus, variations in d18O see through regional metamorphism and reflect original fluid-rock interaction patterns and pathways.

As discussed below the difference in the isotopic patterns associated with deposits associated with advanced argillic alteration zones to those deposits associated with the typical chlorite and/or sericite dominated alteration assemblages could be caused by interaction of lower temperature hydrothermal fluids or by ore fluids with higher d18O, such as magmatic-hydrothermal fluids (e.g., Beaudoin et al. 2014). In high sulfidation epithermal deposits, which are typically associated with advanced argillic alteration assemblages, the advanced argillic assemblages are typically interpreted to be the consequence of acidic fluids formed by the dissociation of SO2 at high temperature (> 350 °C) in magmatichydrothermal fluids (Ohmoto and Rye 1979; Rye et al. 1992). Similar processes are envisioned to have occurred in VHMS deposits that have been influenced by magmatic-hydrothermal fluids, leading to hydrothermally altered rocks with elevated d18O (e.g., Sillitoe et al. 1996; Huston et al. 2011).

In general, oxygen and, to a lesser extent, hydrogen isotopes are zoned about VHMS deposits due to hydrothermal alteration associated with the ore-forming fluids. In detail, however, the patterns can be complicated and can be affected by the protolith lithological variability of the altered rocks. To illustrate this we summarize the results of some of the more detailed oxygen and hydrogen isotope studies to illustrate the similarities, and differences, in the isotopic patterns.

Hokuroku district, Japan. In the Miocene Hokuroku district of Japan, Hattori and Muehlenbachs (1980), Green et al. (1983) and Urabe et al. (1983) documented variations around bimodal felsic VHMS deposits of this district. Of the deposits described, the most information is available from the Fukazawa deposit (Green et al. 1983: Fig. 5a). Green et al. (1983) documented a zone with d18O below 8‰, which corresponds almost directly to the sericitechlorite alteration zone that cuts stratigraphy and forms a pipe that extends below and above the orebody. This zone is surrounded by a 500– 1500-m-wide, montmorillonite-altered halo that is characterized by d18O values between 8‰ and 14‰. Lateral to the montmorillonite zone, the rocks have been quartz- and zeolite-altered with d18O values above 14‰ (Date et al. 1983; Green et al. 1983).

Noranda district, Québec, Canada. Beaty and Taylor (1982) documented variations in whole rock d18O data along a traverse across the alteration pipe (in a similar position to stockwork zones in other VHMS deposits) at the Amulet deposit in the Noranda district, Québec (Fig. 5b), showing a pattern about the alteration pipe, with the central, most intensely, chlorite-altered part

Fig. 5 Sections and plans showing proximal whole-rock d18O variations around VHMS deposits: (a) Fukazawa deposit, Hokuroku district, Japan (modified after Green et al. 1983), (b) Amulet deposit, Quebec, Canada (modified after Beaty and Taylor 1983) and (c) Kidd Creek deposit, Ontario, Canada (modified after Huston and Taylor 1999). "Dalmationite" in (b) refers to a metamorphosed, intensely altered zone consisting of coarse-grained cordierite porphyroblasts set in a finegrained chlorite-quartzanthophyllite matrix. "Gridfractured" refers to a biotiterich rock with a grid-like network of quartz-filled fractures

of the pipe having a d18O values of 3.6–4.0‰ that increased over a distance of 150 m outward to 6.0–6.7‰ in least altered volcanic rocks. Beaty and Taylor (1982) also demonstrated that, with the exception of the Kidd Creek deposit (see below), this pattern was consistent through most deposits that had been studied at that time.

In the New Vauze-Norbec area in the central part of the Noranda volcanic complex, Paradis et al. (1993) showed an up stratigraphy increase in d18O, from values near 2‰ at the bottom of the stratigraphic section, to values near 14‰ at the top. This stratigraphic variation was interpreted to have formed under an increasing thermal gradient and increasing water/rock exchange during the cooling of the Flavrian syn-volcanic intrusion. Paradis et al. (1993) proposed that the hydrothermal fluid was Archean seawater with d18O near 0‰ that evolved through water–rock isotope exchange to a heavier composition.

The variations in d18O described above are one-dimensional transects or drill holes or two dimensional plans or sections. Taylor et al. (2014) determined three-dimensional variations in whole rock d18O at the Horne and Quemont deposits within the Noranda district, which combined have produced over 10 Moz of gold. The surface expression of the Horne deposit is associated with a zone of low d18O (< 6‰), as seen in other deposits discussed above. Zones of high (> 9‰) d18O distal to the deposits may indicate low temperature alteration peripheral to the higher temperature alteration. These data, data from elsewhere in the Noranda district (see below) and from Kidd Creek indicate that persistent zones of relatively high d18O may indicate the lack of significant high temperature fluid flow and downgrade exploration potential of these zones, although it must be stated that deposits associated with advanced argillic alteration zones may not be associated with proximal d18O depletion zones.

Kidd Creek deposit, Ontario, Canada. The \* 2714 Ma Kidd Creek deposit (147.88 Mt grading 2.31% Cu, 6.18% Zn, 0.22% Pb, 87 g/t Ag and 0.01 g/t Au) is the only significant deposit in the Kidd-Munro assemblage in eastern Ontario, Canada. It consists of several steeplyplunging orebodies that are hosted by a mainly rhyolitic volcaniclastic unit within a succession dominated by mafic volcanic rocks (Huston and Taylor 1999: Fig. 5c). The orebodies occur along the southeastern limb of a tight, steeply-plunging anticline.

The first oxygen isotope study by Beaty et al. (1988) at Kidd Creek demonstrated that d18O values in proximal quartz-rich alteration assemblages, at 10–12‰, were much higher than the d18O values of other VHMS deposits, and that these values increased stratigraphically below the ore zone to values of 13–16‰ in felsic rocks. Beaty et al. (1988) interpreted these results as indicative of a two-stage hydrothermal system, with the main stage fluids having values of 6– 9‰.

Huston and Taylor (1999) followed these initial studies with a more detailed study. They found that the d18O values are influenced by the original lithology of altered rocks; Fig. 4c shows variations in d18O only of samples with rhyolitic protoliths as determined by lithological observations (e.g., the presences of quartz phenocrysts) or the geochemistry of immobile elements. The lowest d18O values (<11‰) at Kidd Creek are associated with the "cherty breccia" alteration facies that is closely associated with the ore lenses, a result consistent with Beaty et al. (1988). Huston and Taylor (1999) also found that d18O values increase both laterally away from and stratigraphically above the ore zones to values that exceed 14‰. The host succession includes both fragmental and coherent rhyolitic rocks. Coherent units stratigraphically below or at the same position as the ore lenses are characterised by high dO values (> 13‰) that are interpreted to be the consequence of low temperature alteration that silicified these units. These rocks then became impermeable to later, higher temperature fluid flow, preserving the 18O-enriched signature and focussing fluid flow into fragmental rocks. These fragmental rocks were strongly affected by these later hightemperature fluids, which produced the cherty breccia and the 18O-depleted zone associated with the ore lenses (Fig. 5c: Huston and Taylor 1999). This may have produced the isotopic disequilibria that Beaty et al. (1988) interpreted to indicate two hydrothermal stages.

Stratigraphically above the ore position, d18O data define an 18O-enriched (d18O > 13‰) zone that forms a carapace that has been folded by the later anticline. This zone is interpreted to have formed as the result of lower temperature alteration associated with the cooling of the Kidd Creek hydrothermal system. This carapace is only breached above the southwest ore lens (Huston and Taylor 1999), and may indicate limited high-temperature fluid flow after the Kidd Creek deposit was covered by later volcanic rocks. d18O patterns around the Kidd Creek deposit not only provide vectors toward ore, but they also provide constraints on ore fluid hydrology before, during and after ore formation.

LaRonde deposit, Québec, Canada. The LaRonde deposit (58.76 Mt grading 0.33% Cu, 2.17% Z, 45 g/t Ag and 4.31 g/t Au) is hosted by dacitic to rhyolitic rocks of the Bousquet Formation, Blake River Group (2699–2697 Ma, Mercier-Langevin et al. 2007). The deposit consists of four stacked semi- to massive sulfide lenses within complexly zoned alteration assemblages that has been metamorphosed at lower amphibolite facies to assemblages of mostly quartz, biotite, chlorite, garnet, muscovite, staurolite, rutile and pyrite. An unusual characteristic of the deposit is the presence of an aluminous alteration zone consisting of quartz, kyanite, andalusite, muscovite and pyrite (Dubé et al. 2007). d18O values of the altered host rocks range between 9.0 and 14.2 ‰ for all but 2 analyses, with average d18O values of different alteration facies between 9.8 and 12.9‰ and the aluminous facies having the highest d18O (Beaudoin et al. 2014).

Fluid-rock modelling indicates that the high d18O values at LaRonde can be explained by reaction of volcanic rocks with an initial d18O value of 7–9‰ with a fluid with initial d18O close to 5‰, at temperatures of 100–200ºC, under W/R ratios up to 50:1 (Beaudoin et al. 2014). These W/R ratios are typical of proximal alteration zones, which are fluid dominated, as shown by Green et al. (1983), Shanks (2014) and many others. As these proximal alteration zones define fluid conduits, they have much higher W/R ratios than the VHMS system as a whole.

The initial fluid composition of 5‰ was interpreted to have been evolved seawater perhaps mixed with a magmatic water component exsolved from dacitic to rhyolitic magma, consistent with the aluminous alteration interpreted to be metamorphosed advanced argillic alteration analogous to subaerial high-sulfidation epithermal environments (Dubé et al. 2007).

#### 4.1.2 District-scale Patterns in Oxygen Isotopes

Although most d18O patterns have been established in the immediate vicinity of VHMS deposits, there are several more regional studies, including studies of the \* 400 Ma West Shasta district in California, USA (Taylor and South 1985), the \* 2698 Ma Noranda district in Quebec, Canada (Cathles 1993), the \* 2714 Ma Kidd-Munro district in Ontario, Canada (Taylor and Huston 1999), the \* 3240 Ma Panorama district in Western Australia (Brauhart et al. 2000), the \* 2745 Ma Sturgeon Lake district in Ontario, Canada (Holk et al. 2008) and the \* 2681 Ma Izok Lake district in Nunavut, Canada (Taylor et al. 2015). Of these the two best documented districts, Noranda and Panorama, are described below.

Noranda, Québec, Canada. The Noranda district in the Superior Province, Québec, is a classical VHMS district that rests undeformed since its formation (\*2700 Ma), with only a shallow tilt to the east. The district is hosted by a sequence of bimodal mafic-felsic volcanic rocks of the Blake River Group. The Noranda Volcanic Complex hosts 18 VHMS deposits that have yielded 48.5 Mt of ore, in addition to the Horne deposit (54.3 Mt) and its undeveloped Horne 5 zone (\*150 Mt; Kerr and Gibson 1993). A seminal study by Cathles (1993) documented the plan view of the VHMS system from 588 oxygen isotope analyses (Fig. 6) and was augmented by 599 analyses by Taylor and Timbal (2002). These studies show that the syn-volcanic Flavrian pluton is surrounded by an annular zone with d18O values < 6‰ that extend up section as six fingers that point toward most of the VHMS

Fig. 6 Whole-rock d18O variations in the Noranda district, Quebec, Canada (modified after Cathles 1993, to incorporate geological data from Kerr and Gibson 1993)

deposits of the district (Fig. 6: Cathles 1993). Stratigraphically above the low d18O fingers and most VHMS deposits, the volcanic rocks have d18O values > 9‰, interpreted to represent the reaction of the volcanic rocks above the deposits with cooled hydrothermal fluids, thus forming a cap rock indicative of underlying higher temperature hydrothermal fluid activity (Cathles 1993; Taylor and Holk 2002).

Panorama, Western Australia. The \* 3238 Ma (Buick et al. 2002) Panorama district in the East Pilbara Terrane of Western Australia is the oldest significant VHMS district known, and also one of the best preserved. The district contains two economically significant deposits including Sulphur Springs (13.8 Mt grading 3.8% Zn, 0.2% Pb, 1.5% Cu and 17.0 g/t Au) and Kangaroo Caves (3.8 Mt grading 6.0% Zn, 0.3% Pb, 0.8% Cu and 15.0 g/t Au) among several smaller deposits and prospects hosted at or near the top of the bimodal volcanic Kangaroo Caves Formation. Although the district has seen only sub-greenschist metamorphism, the host succession has been structurally tipped on its side, providing an oblique cross-section of the underlying sub-volcanic Strelley Granite, through the host Kangaroo Caves Formation, and into the overlying turbidites of the Soanesville Group (Fig. 7a). This volcanic succession was extensively altered, with systematic zonation in alteration assemblages at the district scale. Brauhart et al. (1998) found that the lower part of the volcanic succession is dominated by a semi-conformable chlorite-quartz alteration zone that becomes transgressive, forming crosscutting pipes below major deposits such as Sulphur Springs and Kangaroo Caves. This chloriterich zone grades upward from the semiconformable zone and outward from the crosscutting pipes into semi-conformable sericitequartz and feldspar-sericite-quartz zones.

As part of a district-scale alteration study, Brauhart et al. (2000) analyzed 188 volcanic and granite samples for both oxygen isotopes and whole rock geochemistry. Figure 7b shows the

Fig. 7 Maps of the Panorama VHMS district showing (a) geology and alteration zonation, (b) whole-rock d18O variations, and (c) variations in estimated hydrothermal temperatures calculated from whole-rock d18O and geochemical data (modified after Brauhart et al. 2000). The

distribution of d18Owhole rock from these data. The zone with the lowest d18O (< 6‰) corresponds closely with the semi-conformable chloritequartz alteration zone in the lower part of the volcanic pile. d18O increases upwards through the volcanic pile to values of 12–14‰ at the top. The higher d18O values correspond to the sericite-quartz and feldspar-sericite-quartz alteration zones. Like the chlorite-quartz alteration zones, pipes of low d18O values extend from the basal zone below the locations of known VHMS deposits. The pipe that extends below Sulphur Springs has d18O values of < 6‰, whereas the pipe that extends below Kangaroo Caves has values of 6–8‰. This observation is consistent with deposit-scale patterns in which Cu-rich

"background" alteration assemblage refers to spilitic assemblages in basalt or keratophyric assemblges in felsic rocks and typified by the presence albite-, Kfeldspar-chlorite- and/or ankerite-quartz-pyrite-dominant assemblages (Brauhart et al. 1998)

deposits are associated with stronger d18O anomalies than Zn-rich deposits.

Following the method of Miller et al. (2001) and using mineral abundances calculated from the whole rock geochemical data, Brauhart et al. (2000) estimated the fractionation function between the altered rock and altering fluid (D18Owhole rock-fluid). They then calculated the temperature of alteration using the D18Owhole rockfluid functions and assuming d18Ofluid (Fig. 7c). Using a d18Ofluid of 2‰ suggested that alteration temperatures locally exceeded 400 °C in the high temperature, semi-conformable chlorite-rich part of the alteration system, within and just above the Strelley Granite. The alteration temperature decreased, in general, upward to the contact with the overlying Soanesville Group, where the temperature was generally below 200 °C. Immediately below the Sulphur Springs and Kangaroo deposits, the chlorite-rich alteration zones become transgressive, connecting the semi-conformable zone at the base of the volcanic pile with individual deposits. The d18Owhole rock and calculated temperature also reflect this alteration pattern, with these data also defining transgressive zones connecting the high temperature semi-conformable alteration zone with the proximal alteration zones associated with the deposits. Although a d18Ofluid value of 2‰was assumed in Fig. 6c, changing this assumed value does not change the relative temperature patterns even though the absolute temperatures estimated do change.

#### 4.1.3 Implications of d18O-dD Data to Determining Fluid Sources

Oxygen and hydrogen isotope data were a key piece of evidence that was used to argue that ore fluids that formed VHMS deposits were evolved seawater (Ohmoto et al. 1983). Since then, the gathering of new data has indicated a more complicated picture, although evolved seawater still appears to be the most important ore fluid. Table 1 (updated from Huston 1999; this table excludes deposits metamorphosed at grades of amphibolite or higher and some deposits (e.g., Raul, Peru) for which a VHMS origin has been questioned) and Fig. 8 summarize the d18O and dD characteristics of VHMS ore fluids as deduced from deposits that have not undergone high-grade metamorphism (amphibolite or greater) that may disturb the original isotopic characteristics.

Most VHMS deposits have fluid d18O-dD signatures similar to seawater. In general, d18O values are within 2‰ and dD values are within 20‰ of standard mean oceanic water (SMOW). These values are consistent with evolved seawater being the dominant ore fluid (Fig. 8b).

As discussed above, currently active seafloor systems provide information, such as direct measurements of the isotopic composition of mineralizing fluids and the isotopic response (and geochemical response in general) of these

Fig. 8 d18O-dD diagrams showing (a) the fields of selected VHMS ore-forming fluids (from Table 1) and the fields of seawater and magmatic water (Sheppard, 1986; Taylor, 1992), and (b) paths showing the evolution of seawater undergoing evaporation (Knauth and Beeunus, 1986), open-system water–rock interaction (e.g., Taylor 1987), adiabatic boiling (using data of Friedman and O'Neil (1977) and Keenan et al. (1969)), and mixing with magmatic water (updated from Huston 1999)