INTRODUCTION

The reconstruction of δ18О values of melts based on the oxygen isotope composition of proxy mineral (this term refers to the mineral–indicator of nature of parental melts) is required in solving many petrological problems (see overviews, e.g., Bindeman, 2008; Valley, 2003; Valley et al., 2005). The proxy mineral for mafic and ultramafic melts is olivine phenocrysts (e.g., Eiler et al., 2011, 1996; Gurenko and Chaussidon, 2002), which record the earliest isotope composition of parental melt due to the low diffusion rate of oxygen in it. Further processes related to the emplacement of magmatic body could lead to a change of δ18О in the melt, but olivine records the early stages of the evolution of magmatic system.

During crystallization of felsic melts, for instance, rhyolite or granite porphyry, rock-forming minerals with low diffusion rate are not formed. Zircon having the minimum diffusion rates for many components, including oxygen, can be regarded as the suitable proxy mineral for estimating the nature of protolith or parental melt (Watson and Cherniak, 1997; Farver, 2010). However, this mineral occurs in accessory amounts and frequently has a more complex nature than the host rock. In addition, it is difficult to analyze a large amount of matter and estimate reliably isotope homogeneity of zircon, as well as to determine the affiliation of all analyzed grains to the studied magmatic process. Nevertheless, zircon has been increasingly applied as mineral reflecting the evolution of sources of felsic rocks (e.g., Colón et al., 2018; Pietranik et al., 2013; Kitajiama et al., 2012). Quartz can be conditionally regarded as the second proxy-mineral for oxygen isotope composition of felsic melts, although it is characterized by the high oxygen diffusion rates (Farver, 2010; Dennis, 1984a, 1984b). At the same time, it has the lowest diffusion rates among minerals of granite association and can be conditionally considered as stable mineral compared to other minerals of felsic rocks. It should be taken into account that the oxygen diffusion rates in quartz are significant and the δ18О(Qz) value can be modified, for instance, by interaction with external fluid or by contamination (e.g., Dubinina et al., 2010). However, the main process responsible for a change of δ18О(Qz) value in felsic rocks is a retrograde isotope exchange (Giletti, 1986; Harris et al., 1997; Jenkin et al., 1994; Kohn and Valley, 1998), which proceeds from the onset of mineral crystallization to the closure temperature of its oxygen isotope system (Тq). This process is the least expressed in phenocrysts of rapidly cooling felsic lavas and is very common in minerals of the holocrystalline rocks. The retrograde exchange could be ignored only in the first case, unless the δ18О(Qz) value was not modified during later process. For instance, the direct evidence for the late fluid impact is the lowered δ18О value in other less “stable” minerals of the rock: Pl or Kfs. Evidence for reactive contamination could be disequilibrium relations between phenocryst minerals and groundmass (Dubinina et al., 2010). However, these observations require the measurement of not only quartz, but also other minerals, while reconstruction performed using δ18О(Qz) value alone, even with correction, could be erroneous.

In order to reconstruct δ18О value of felsic melts using quartz and (or) zircon as proxy minerals, the values of Δ(Qz–R) and Δ(R–Zrn) representing the equilibrium oxygen isotope shift between minerals and rock are required. In this paper, we attempted to estimate these parameters.

There are two variants of Δ(Qz–R) correction. In the first variant, the correction is constant (1‰ for quartz porphyry and 2‰ for coarse-grained granites) and proposed in (Harris et al., 1997). This correction takes into account only “cooling effect” of granitoid rocks. It is applied to calculate the oxygen isotope composition of initial felsic rock at the moment of its crystallization using known δ18О(Qz) value, assuming that the oxygen isotope system of quartz was not disturbed after closure. This correction is empirical and does not involve the mineral composition of rock and the closure temperature of minerals, which depends not only on grain size but also on the cooling environment.

The second variant of correction Δ(Qz–R) was proposed for rapidly cooling felsic lavas (Bindeman et al., 2004; Bindeman, 2008). It represents an oxygen isotope shift between quartz and melt (rock) at crystallization temperature of phenocrysts, which is estimated based on the SiO2 and alkali contents in the rock. The rock is approximated by a set of normative minerals, for which the weighted average fractionation coefficient relative to quartz is calculated. This correction Δ(Qz–R) does not imply the subsolidus isotope exchange at cooling. In addition, this correction is insignificant at high temperatures of formation of quartz phenocrysts. For instance, it was constant (0.45‰, Akinin and Bindeman, 2021) for rhyolites of the Okhotsk–Chukotka volcanic belt. Of great importance in this approach is the problem of oxygen isotope equilibrium between quartz and groundmass (Bindeman et al., 2008; Dubinina et al., 2020).

Only one variant of reconstruction was proposed for zircon based on the dependence of Δ(R–Zrn) correction on the SiO2 content in the rock (Lackey et al., 2008). This dependence was established empirically, although it is obvious that the isotope fractionation in the system Zrn–melt (rock) is controlled not only by SiO2 content in the melt or rock.

We carried out the theoretical evaluation of Δ(Qz–R) and Δ(R–Zrn) and considered factors that determined these values. The efficiency of these corrections compared to those available in the literature was tested using definite examples in order to understand the strategy of application of quartz and zircon as proxy minerals for the reconstruction of δ18О value of felsic melts.

EVALUATION OF OXYGEN ISOTOPE FRACTIONATION BETWEEN QUARTZ AND OTHER MINERALS OF GRANITIC ROCKS

The oxygen system of quartz is the first to close (at Тq) among rock-forming minerals of a cooling rock. Up to this moment, the δ18О(Qz) value is controlled by the oxygen isotope composition of all other minerals of the rock (Giletti, 1986; Kohn and Valley, 1998; Farquhar et al., 1993), and the lower the Тq the stronger is this influence. Assume that Тq is known, while the oxygen isotope system of rock was not disturbed by later events. In this case, we can apply approach based on the thermometric equations and mass-balance conditions for definite domain of the rock (e.g., Jenkin et al., 1994; Farquhar et al., 1993). A simplified order of closure of the oxygen isotope system of the granitic rock is assumed: Qz → Bt → (P), where Р is the K-feldspar and plagioclase, which are considered as a single mineral phase. Combining Kfs and Pl into a single phase for most felsic rocks is quite justified, as at the plagioclase composition close to albite (An10–20), the isotope fractionation between Kfs and Pl is negligible and comparable with analytical error (within 400–800°С, it is ≈0.3‰ for Pl(An20) and ≈0.2‰ for Pl(An10), Chacko et al., 2001; Vho et al., 2020). In addition, Kfs and Pl are characterized by the similar oxygen diffusion rates, i.e., their closure temperature also should be close at similar crystal sizes. A simplified temperature dependence of fractionation coefficient (\(\Delta \approx {{10}^{3}}{\text{Ln}}\alpha \left( {a - b} \right) = {{A}_{{a - b}}} \times {{10}^{6}}{{T}^{{ - 2}}}\)) is taken, which is usually used for the description of magmatic processes (Valley, 2001; Chacko et al., 2001). It was also suggested that the transitional zone in the closure temperature region of the oxygen isotope system of minerals is minimum or absent (Valley, 2001), i.e., the values of Тq, Tb, and Tp (closure temperature of quartz, biotite, and feldspar, respectively) are the minimum boundary temperatures at which mineral is in isotope equilibrium with other isotopically open minerals. Up to approaching temperature Тq, all minerals of the rock are in isotope equilibrium with each other. Therefore, isotope shifts between feldspars and biotite, as well as between quartz and feldspar at Тq can be written as follows:

$${{\Delta }}_{{{\text{p}} - {\text{b}}}}^{{\text{q}}} = {{A}_{{{\text{p}} - {\text{b}}}}} \times {{10}^{6}}T_{{\text{q}}}^{{ - 2}}$$

and

$${{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}} = {{A}_{{{\text{q}} - {\text{p}}}}} \times {{10}^{6}}T_{{\text{q}}}^{{ - 2}},$$
(2)

where indices q, b, and p designate quartz, biotite, and feldspars, while \({{A}_{{{\text{p}} - {\text{b}}}}}\) and \({{A}_{{{\text{q}} - {\text{p}}}}}\) values are coefficients in the corresponding thermometric equations (\({{10}^{3}}{\text{Ln}}\alpha \left( {a - b} \right) = {{A}_{{a - b}}} \times {{10}^{6}}{{T}^{{ - 2}}}\)). Equilibria (2) can be combined, omitting Тq:

$$\frac{{{{\Delta }}_{{{\text{p}} - {\text{b}}}}^{{\text{q}}}}}{{{{A}_{{{\text{p}} - {\text{b}}}}}}} = \frac{{{{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}}}}{{{{A}_{{{\text{q}} - {\text{p}}}}}}}\,\,\,\,{\text{and}}\,\,\,\,{{\Delta }}_{{{\text{p}} - {\text{b}}}}^{{\text{q}}} = {{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}}\frac{{{{A}_{{{\text{p}} - {\text{b}}}}}}}{{{{A}_{{{\text{q}} - {\text{p}}}}}}}.$$
(3)

Oxygen mass balance for rock consisting of three minerals (q – Qz, b – Bt and p – (Kfs + Pl)) has the following form:

$${{{{\delta }}}_{{\text{R}}}} = {{X}_{{\text{q}}}}{{\delta }_{{\text{q}}}} + {{X}_{{\text{b}}}}{{{{\delta }}}_{{\text{b}}}} + {{X}_{{\text{p}}}}{{{{\delta }}}_{{\text{p}}}},$$
(4)

where Xq, Xb, and Xp are the oxygen fractions of rock in the corresponing mineral (\({{X}_{{\text{q}}}} + {{X}_{{\text{b}}}} + ~{{X}_{{\text{p}}}} = 1\)). The stoichiometric coefficient k(i) (mass fraction of oxygen in mineral formula) should be taken into account in calculation. For instance, the oxygen content in quartz (k(q) = 0.53) with mass fraction of x(q) can be written as follows:

$${{X}_{{\text{q}}}} = {{k\left( {\text{q}} \right)X\left( {\text{q}} \right)} \mathord{\left/ {\vphantom {{k\left( {\text{q}} \right)X\left( {\text{q}} \right)} {[(k\left( {\text{q}} \right)X\left( {\text{q}} \right) + k\left( {\text{b}} \right)X\left( {\text{b}} \right) + k\left( {\text{p}} \right)X\left( {\text{p}} \right)]}}} \right. \kern-0em} {[(k\left( {\text{q}} \right)X\left( {\text{q}} \right) + k\left( {\text{b}} \right)X\left( {\text{b}} \right) + k\left( {\text{p}} \right)X\left( {\text{p}} \right)]}}.$$

δq in equation (4) corresponds to the measured δ18О(Qz) value. The oxygen isotope composition of other minerals at Тq is:

$$\begin{gathered} {{\delta }_{{\text{b}}}} = {{{{\delta }}}_{{\text{p}}}} - {{\left( {{{\Delta }}_{{{\text{p}} - {\text{b}}}}^{{\text{q}}}} \right)}_{{T{\text{q}}}}} = {{{{\delta }}}_{{\text{q}}}} - {{({{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}})}_{{T{\text{q}}}}} - {{\left( {{{\Delta }}_{{{\text{p}} - {\text{b}}}}^{{\text{q}}}} \right)}_{{T{\text{q}}}}} \\ {\text{and}}\,\,\,\,{{{{\delta }}}_{{\text{p}}}} = {{{{\delta }}}_{{\text{q}}}} - {{\left( {{{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}}} \right)}_{{T{\text{q}}}}}. \\ \end{gathered} $$
(5)

Substituting (2), (4), and (5) in equation (3) yields the following equation for whole-rock oxygen isotope composition:

$${{{{\delta }}}_{{\text{R}}}} = {{{{\delta }}}_{{\text{q}}}} - {{({{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}})}_{{T{\text{q}}}}}\left( {{{X}_{{\text{p}}}} + {{X}_{{\text{b}}}}\left( {1 + \frac{{{{A}_{{{\text{p}} - {\text{b}}}}}}}{{{{A}_{{{\text{q}} - {\text{p}}}}}}}} \right)} \right),$$
(6)

From this equation, we obtain Δ(Qz–R):

$$\begin{gathered} {{\Delta }}\left( {Qz{\text{ - R}}} \right) = {{{{\delta }}}_{{\text{q}}}} - {{{{\delta }}}_{{\text{R}}}} \\ = {{({{\Delta }}_{{{\text{q}} - {\text{p}}}}^{{\text{q}}})}_{{T{\text{q}}}}}\left( {{{X}_{{\text{p}}}} + {{X}_{{\text{b}}}}\left( {1 + \frac{{{{A}_{{{\text{p}} - {\text{b}}}}}}}{{{{A}_{{{\text{q}} - {\text{p}}}}}}}} \right)} \right). \\ \end{gathered} $$
(7)

Equation (7) shows that Δ(Qz–R) is not a constant value, but depends on two factors: closure temperature of the oxygen isotope system of quartz, Тq, and proportions of other rock-forming minerals, biotite and feldspars. The role of the last factor is illustrated by the calculation presented in Figs. 1a–1d. The calculation was carried out at varying fraction of quartz in the rock (Хq from 0.05 to 0.5) for two variants of feldspars and biotite proportions: fixed Xb at variable Xp (Figs. 1a, 1b) and fixed Xp : Xb ratio (Figs. 1c, 1d). Two temperatures were given for calculations: 900°С and 600°С, which corresponded, respectively, to conditions close to quenching of igneous felsic melt (at 900°С, Figs. 1a, 1c) and conditions of retrograde cooling of granitic intrusion up to Тq = 600°С (Figs. 1b, 1d). It should be noted that Тq in many cases can decrease up to 400°С and lower depending on the quartz grain size and cooling rate of the rock (Dodson, 1973). Values of corrections for quartz porphyry (Δ(Qz-R) ≈ 1‰, Harris et al., 1997) and felsic lavas (Δ(Qz-R) ≈ 0.45‰, Bindeman et al., 2004; Akinin and Bindeman, 2021) are plotted in Fig. 1 for comparison.

Fig. 1.
figure 1

Values of isotope shift between quartz and granitoid rock Δ(Qz-R) at Tq = 900°С (a, c) and retrograde cooling up to Tq = 600°С (b, d). Dashes 1 and 2 are values of constant corrections for felsic lavas (Bindeman et al., 2004) and quartz porphyry (Harris et al., 1997), respectively. Proportions of biotite and feldspars taken in calculations: (a, b) biotite content was taken to be constant (Хb = 0.05, 0.1 and 0.2—numbers near curves), the value of Хр decreases with the growth of Хq; (c, d) the proportions of feldspars and biotite were taken to be constant (Хр : Хb = 1.5, 5, 10—numbers near curves).

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The calculated value Δ(Qz–R) for Тq = 900°С (i.e., at quenching of felsic melt) could be close both to the correction for quartz porphyry and for felsic lavas, depending on the quartz content in the rock. An increase of biotite content in the rock also leads to the increase of Δ(Qz–R). At lower temperature, the value always exceeds the correction for felsic lavas and varies between the cooling rate corrections for coarse-grained granites and quartz porphyries (1–2‰, Harris et al., 1997). Thus, the mineral composition of rocks should be taken into account at evaluating Δ(Qz–R). For instance, rock with high biotite and low quartz contents requires the higher correction than typical leucogranites and rocks with high quartz content.

Indeed, the value of Δ(Qz–R) is also controlled by the closure temperature of the oxygen isotope system of quartz. To illustrate the Тq influence, the coefficient was calculated for several fixed compositions of felsic rock (at Xq = 0.3, Xb = 0.05, 0.1, and 0.2) at Тq varied from 1000 to 400°С Тq (Fig. 2). This calculation demonstrates that Δ(Qz–R) at high Тq values (≈900°С and higher) is close to the correction for felsic lavas (Bindeman et al., 2004), while within the range of Тq ≈ 500–600°С it is close to values for quartz porphyries (Harris et al., 1997) and approaches that for coarse-grained granites (2‰) at even lower closure temperature of the oxygen isotope system of quartz. In general, Δ(Qz–R) increases with decreasing Тq, which means that Тq is required to reconstruct the compositions of slowly cooling granitic melts.

Fig. 2.
figure 2

Values of isotope shift between quartz and granitoid rock at change of the closure temperature of quartz (Tq). Dashes 1 and 2 are values of constant corrections for felsic lavas (Bindeman et al., 2004) and for quartz porphyries (Harris et al., 1997), respectively. In all calculations, quartz content was taken to be constant (Xq = 0.3), whereas other minerals varied at Xb = 0.05, 0.1, and 0.2; Хр = 0.65, 0.6, and 0.5, respectively. Numerals near calculated curves mean the fraction of biotite in rock (Xb).

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It is obvious that the application of constant correction Δ(Qz–R) based on the rock petrography (e.g., rhyolite or porphyritic granite) is not correct, even if isotope system of the rock was not disturbed. Nevertheless, Δ(Qz–R) in real rocks can weakly vary, and can be taken to be constant within conditional accuracy of its estimates. This is related to two factors: (1) proportions of rock-forming minerals in similar felsic rocks show limited variations and (2) oxygen isotope fractionation coefficients between quartz and feldspar, which determine Δ(Qz-R), weakly depend on temperature. Thus, the effects of both these factors could be not critical, and empirical approach can be justified. However, any corrections (constant or no) are valid only if the oxygen isotope system of quartz was not disturbed after closure. The absence of such disturbances is illustrated by the example of the Eocene leucogranite porphyry of the Raumid massif.

Example 1: Leucogranite Porphyry of the Raumid Massif

These rocks form a multiphase (eight intrusive phases) massif of Eocene age (35.5 ± 0.9 Ma, Kostitsyn et al., 2007a; Volkov et al., 2016) located in the South Pamirs. The geological description of the massif is reported in (Volkov and Negrei, 1974; Kostitsyn et al., 2007b; Volkov et al., 2016). We studied petrological, geochemical, and oxygen isotope characterisics of the rocks of the Raumid massif (Dubinina et al., 2023a). Based on our data and works by other authors, the rocks of the Raumid massif did not experience any external influence, besides sufficiently complex cooling scheme caused by the multiphase emplacement of the massif. The δ18О values of quartz and rock simultaneously changes from one phase to another (Fig. 3a), with Δ(Qz–R) variations from 0.73 to 1.17‰ (Fig. 3b). These variations mainly reflect different closure temperatures of quartz, since the mineral composition of rocks of all phases is almost identical. On average, the estimated Δ(Qz–R) value is 0.98 ± 0.2‰, which is very close to the correction for cooling effect of leucogranites (1‰, Harris et al., 1997). Therefore, the δ18О(R) value reconstructed using a constant correction of 1‰ is very close to the measured δ18О of leucogranite porphyries of the Raumid massif (dashed line in Fig. 4). Unambiguously, such coincidence is caused by the absence of later external impact on the rocks of the Raumid massif and proximity of their mineral composition to typical leucogranites, correction for which was introduced in (Harris et al., 1997). In this case, quartz well operates as a proxy mineral.

Fig. 3.
figure 3

Oxygen isotope composition of quartz and whole-rock samples of leucogranite porphyry of the Raumid massif (a) and observed value of Δ(Qz-R) (b). Dashes in fig. (a) is the calculation of δ18О(R) using constant correction for quartz porphyry (Δ(Qz-R) = 1‰, Harris et al., 1997).

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Fig. 4.
figure 4

Oxygen isotope composition of zircon and whole-rock samples of Late Cretaceous leucogranite porphyry of the Omsukchan trough relative to the oxygen isotope composition of quartz. (1) whole-rock samples; (2) zircon; (3) initial composition of felsic melts reconstructed using δ18О(Zrn) and corrections calculated from Zr content in the rock (see text). Dashed curves 4, 5 are reconstructions of initial composition of felsic melts using δ18О(Qz) and constant corrections for felsic lavas (Bindeman et al., 2004) and quartz porphyry (Harris et al., 1997), respectively. Horizontal fields: (M) mantle melts, (K) average composition of continental crust (Simon and Lécuyer, 2005). Arrows show the direction of isotope shift in the whole-rock isotope composition due to the influence of isotopically light fluid.

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The second example illustrates the erroneous reconstruction of composition of initial rocks (or melts) using quartz due to the rock alteration by the isotopically light fluid.

Example 2: Leucogranites of the Omsukchan Trough

The Late Cretaceous leucogranite porphyries (nevadites) are developed within the Omsukchan trough (Northeast Russia), being confined to numerous ore deposits and occurrences. In particular, they surround the structure of the Dukat ore field (Konstantinov et al., 1998; Struzhkov and Konstantinov, 2005; Bannikova, 1990; Dubinina et al., 2019; Filimonova et al., 2014). Data obtained in (Dubinina et al., 2023b) confirmed intense influence of isotopically light fluid on these rocks (Fig. 4): the δ18О value for whole-rock samples of leucogranites decreases to the strong negative values (<–7‰). The isotope lightening mainly spanned feldspar, but fluid also affected the isotope systems of quartz and even zircon (Dubinina et al., 2023b). The values of δ18О (Qz) decrease from 10–10.5 to 4‰ with depletion of rocks in heavy oxygen isotope, while δ18О(Zrn) weakly varies within 5.2–3.9‰, systematically decreasing with isotope lightening of the rock. The initial oxygen isotope composition of the rocks reconstructed using δ18О(Qz) and any constant (and variable) corrections yields the wide range of δ18О(R) from 3 to 10‰, which indicates the contribution of different sources of felsic melts: 18О‑depleted and 18О-enriched ones. However, this conclusion is likely premature, because it is based only on δ18О values of quartz, the isotope system of which is clearly disturbed.

We attempted to reconstruct δ18О(R) using other proxy mineral, zircon, which is more resistant to the diffusion isotope exchange than quartz (Watson and Cherniak, 1997; Farver, 2010) and does not require correction for cooling rate. However, only euhedral zircon with no traces of hydrothermal alteration can be used as proxy mineral. In the leucogranites of the Omsukchan trough, zircon experienced insignificant hydrothermal alteration (maximum decrease of δ18О(Zrn) is no more than 1.3‰). This alteration was likely caused by fluid-assisted partial recrystallization of Zrn (Dubinina et al, 2023b). For this reason, our reconstruction with zircon is only approximate. However, the measured δ18О(Zrn) value even in partially altered zircon indicates a normal magma source, which was homogenous for all studied rocks (Valley, 2003; Fu et al., 2014). Below we consider the approach to reconstruction of δ18О(R) using zircon as proxy mineral. For this purpose, the isotope exchange Δ(R–Zrn) between zircon and granitic rock (or melt) was estimated.

ESTIMATION OF OXYGEN ISOTOPE FRACTIONATION BETWEEN ZIRCON AND OTHER MINERALS OF GRANITIC ROCK

Zircon is not a rock-forming mineral and its oxygen isotope system usually closes earlier than that of relatively stable quartz. Thus, both quartz and all other rock-forming minerals will affect the Δ(R–Zrn) (=δ18O(R) – δ18О(Zrn)). Unlike quartz, the fractionation coefficient between zircon and major minerals of felsic rocks is higher and shows more significant temperature dependence (Vho et al., 2019; Valley, 2003). Hence, variations in the content of rock-forming minerals should more significantly affect Δ(R–Zrn) than Δ(Qz–R). This calls into question the use of constant Δ(R–Zrn), unlike Δ(Qz–R), and highlights the need in the individual estimate of this parameter for each rock or rock group. For this purpose, the simplified empirical equation is proposed, in which correction between zircon and melt is determined by the SiO2 content in rock (Lackey et al., 2008).

It is proposed to calculate the value of Δ(R–Zrn) as weighted average fractionation coefficient between zircon and rock-forming minerals of granitic rock: Qz, Bt, Kfs, and Pl (Fig. 5). As an example, we calculated the temperature dependence of Δ(R–Zrn) for three variants of rocks with variable proportions of the indicated minerals (see captions to Fig. 5). The coefficients of thermometric equations for the quartz–mineral system, which were applied in calculations and summarized in Table 1, were taken from the internally consistent data base (Vho et al., 2019). In addition to the coefficients, the closure temperature of zircon is required to estimate Δ(R–Zrn). Available variant of Δ(R–Zrn) estimation according to (Lackey et al., 2008) indirectly implies temperature factor, because it is based on the degree of silica saturation of rock (Δ(R–Zrn) = 0.0612SiO2 – 2.50). Using this equation yields Δ(R–Zrn) = 2.1‰ for leucogranite porphyry of the Omsukchan trough (SiO2 ≈ 75 wt %). In order to compare this value with calculated weighted average fractionation coefficients, it is sufficient to calculate the SiO2 content in the rock from normative mineral composition (in Fig. 5, they are indicated for each variant of calculation). The mineral composition of leucogranite porphyry of the Omsukchan trough corresponds to the calculated curve 3 in Fig. 5, and correction of 2.1‰ in this line corresponds to the closure temperature of zircon Tz ≈ 650°С. It is unclear whether this temperature is valid, but it is seen in Fig. 5 that Tz values calculated for other variants of rocks (SiO2 ≈ 63 and 70 wt %) are also close to 650°С. It is hardly likely that the closure temperature remains the same in rocks that significantly differ in SiO2 and mineral composition.

Fig. 5.
figure 5

Weighted average oxygen fractionation coefficient between granitic rock and zircon depending on temperature. Curves 1–3 were calculated for the following rock compositions: (1) Xq = 0.1, XPl, An20 = 0.3, XKfs = 0.4, Xb = 0.2, SiO2 ≈ 63 wt %; (2) Xq = 0.35, XPl, An20 = 0.2, XKfs = 0.4, Xb = 0.05, SiO2 ≈ 70 wt %; (3) Xq = 0.2, XPl, An15 = 0.15, XKfs = 0.35, Xb = 0.1, SiO2 ≈ 76 wt %. Horizontal lines show zircon–rock isotope shift calculated from SiO2 content (Lackey et al., 2008). Temperatures estimated using zirconium thermometer are shown in curve 3 (calculated using equations Boehnke et al., 2013; Borisov and Aranovich, 2019) for the same leucogranite porphyry samples from the Omsukchan trough (see text).

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Table 1. Coefficients in thermometric equation 103Lnα(Qz–mineral) = А × 106Т–2 + В × 103Т–1, used for calculation*
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Thus, independent evaluation of the Tz is required, which is possible for zircon, unlike quartz. For instance, we can apply Zrn thermometer, which determines the melt saturation temperature in Zrn (Watson and Harrison, 1983; Boehnke et al., 2013; Borisov and Aranovich, 2019) and records the beginning of zircon crystallization from melt. At extremely low oxygen diffusion rate in zircon, the temperature estimated using zircon thermometer should be close to Tz. This approach was applied by us to estimate Tz for leucogranite porphyries of the Omsukchan trough. According to the Zr (120–300 ppm) and major oxides content in these rocks (Filimonova et al., 2014), the values of Tz vary from 780 to 930°С according to equation (Boehnke et al., 2013) or from 726 to 934°С according to equation (Borisov and Aranovich, 2019). Depending on the chosen thermometer, Δ(R–Zrn) calculated from curve 3 varies in the same samples from 1.36 to 1.71‰ or from 1.35 to 1.88‰, respectively. These estimates significantly differ from the constant correction calculated from SiO2 content in these rocks (≈2.1‰, Lackey et al., 2008), and this difference reaches 0.8‰ with the growth of temperature (Fig. 5).

Initial δ18О(R) estimates for the melt reconstructed using the above mentioned Δ(R–Zrn) values vary within a narrow range from 5.6 to 6.9‰ (Fig. 5), which is typical of normal melts and occupies position between δ18О of mantle (5.7 ± 0.3, Taylor and Sheppard, 1986) and average continental crust (8.9 ± 0.7‰, Simon and Lecuyer, 2005). It should be noted that the obtained δ18О(R) estimates for the leucogranite porphyry of the Omsukchan trough could be slightly underestimated (by no more than 1.3‰), because estimates of δ18О(Zrn) in these leucogranites could be hydrothermally modified during strong impact of meteoric fluid (Dubinina et al., 2023b). Nevertheless, the estimated δ18О(R) values indicate that the initial melts of leucogranite of the Omsukchan massif were derived through a simple interaction of mantle melts with continental crust, and do not require the contribution of some exotic high- or low-δ18О melt sources.

An example of leucogranites of the Omsukchan massif shows that an approach based on the study of a single “ubiquitous” mineral (for instance, quartz, Akinin and Bindeman, 2021) would lead us to erroneous conclusions concerning the nature of melt source. The application of zircon as proxy mineral could yield more reliable results, especially with allowance for the independent estimate of Tz. In addition to zircon thermometer, other approaches can be used. For instance, the Tz can be estimated from Ti content in zircon (Trail et al., 2007) or from zirconium–hafnium geothermometer (Aranovich and Bortnikov, 2018). Indeed, some errors can be caused by the choice of equation for Tz calculation. There are some other complicating factors for zircons. For instance, it is difficult to extract the sufficient amount of zircon for oxygen isotope analysis by laser heating fluorination (≈1 mg). In most cases, the value of δ18О(Zrn) is determined by local methods (for instance, by SIMS), which, however, require to exclude xenomorphic and inherited zircons (Bindeman, 2008). Unlike quartz, the application of constant corrections Δ(R-Zrn) is hardly possible, especially at significant variations of the mineral composition of rock. In addition, the value of δ18О(Zrn) can be disturbed, although with lower probability than δ18О of quartz during fluid-assisted hydrothermal recrystallization (e.g., Chen and Zhou, 2017). The zircon isotope system also could be disturbed by metamict breakdown. In spite of all these difficulties, zircon has a high promise for the reconstruction of oxygen isotope composition of felsic silicate melts (Lackey et al., 2008).

CONCLUSIONS

Calculations and presented examples show that the application of quartz as proxy mineral has several strong limitations. It can be used only if the isotope system of mineral was not disturbed by later events. For common granitoids and rocks cooling with a finite (not instant) rate, the accurate reconstruction requires the involvement of the mineral composition of rocks and closure temperature of the quartz isotope system. In this case, the value of isotope shift Δ(Qz–R) between quartz and a given rock can be calculated using equation (7). At weakly varying mineral composition of rocks with similar textures and cooling rates, the constant correction for cooling effect can be applied for porphyritic and coarse-grained granites (Harris et al., 1997). The value of this correction could be corrected for rocks whose mineral composition strongly differs from standard granite. Correction proposed for felsic lavas (Bindeman et al., 2004) can be applied only to phenocrysts that did not experience retrograde isotope exchange and show no disturbance of oxygen isotope system. This requirement is true for any minerals with significant diffusion rates (quartz, feldspars, micas).

Evidences for the disturbance of quartz isotope system in rock are not only the absence of equilibrium relations between δ18О values of its minerals (which could be caused by cooling), but also the correlation of δ18О values between altered minerals. Additional petrological, geochemical, and isotope studies should be carried out to reveal the possible disturbances. For instance, an indicator of fluid impact for granites is altered δ18О value for feldspars, because this group of minerals differs in the higher diffusion rates of oxygen (Farver, 2010) and ability to interact with fluid even at moderate temperatures (O’Neil and Taylor, 1967; Fiebig and Hoefs, 2002). Thus, quartz can be used as a proxy mineral for reconstruction of oxygen isotope composition of initial rocks or melts only under a number of conditions, for instance, the measurements of oxygen isotope composition not only in quartz (approach of “ubiquitous” mineral) but also in the whole rock, as well as in other rock-forming minerals, in order to estimate the preservation of oxygen isotope system of the whole rock and quartz.

An approach of “ubiquitous” mineral is also frequently applied to zircon, especially in studies performed by local methods (SIMS, SHRIMP), when δ18О(Zrn) value is analyzed, without determination of oxygen isotope composition in rock. In this case, it is required to estimate the possible disturbances of oxygen isotope system of mineral, as well as to ensure in primary magmatic origin of the zircon. In all other respects, zircon has a high promise as proxy mineral not only due to the extremely low oxygen diffusion rate, but also owing to the possibility of independent estimates of crystallization temperature of magmatic zircon (Zr thermometer, Ti-in-Zrn thermometer). It is reasonable to improve approaches to estimating the Δ(R–Zrn) values for rocks of different composition and different geodynamic settings.