Assessment of Biotite-Based Thermobarometers in Porphyry Systems: A Case Study from the Julong Cu–Polymetallic District of Tibet, China

Abstract

In porphyry systems, the physicochemical properties of ore-related intrusions critically influence both metallogenic fertility and the resulting metal assemblages. Biotite is a widespread magmatic mineral capable of recording subtle changes in physicochemical parameters throughout the evolution of porphyry systems. Throughout the years, several biotite thermobarometers have been proposed; however, the most appropriate combination for application to porphyry systems remains uncertain. In the Julong Cu–polymetallic district, where magmatic biotite is pervasive in the ore-related intrusive suite, we integrate available temperature, pressure, and oxygen fugacity data to assess which combination of biotite-based thermobarometers best captures the physicochemical condition of the magma. Our results demonstrate that the structural formula recalculation method of Li et al. (2020), when combined with the thermometer of Li and Zhang (2022) and the barometer of Uchida et al. (2007), yields the most accurate reconstruction of magmatic conditions in porphyry systems. In the Julong district, this integrated approach reveals that the earliest granodiorite crystallized at depths of ~3.2–6.3 km, under strongly oxidizing conditions (~NNO+3 to HM) and in the presence of elevated volatile concentrations. A slightly younger monzogranite formed at ~4.4 km depth, recording lower oxygen fugacity conditions (~NNO+2 to NNO+4). Its elevated F concentration and lower oxygen fugacity suggest a genetic link to the fractional crystallization of magmatic phases, especially magnetite. On the other hand, the ore-related monzogranite porphyry (~NNO+3 to HM) shares the oxidized signature of the granodiorite and was emplaced at ~3.4 km depth. Its low log(f_H2O/f_HCl) value reflects elevated HCl activity, conducive to the efficient magmatic transport of Cu and Mo.

1. Introduction

Biotite, with the general formula X{Y₃[Z₄O₁₀](OH)₂}, is a ubiquitous rock-forming mineral broadly distributed in a wide range of geological environments [1,2,3,4]. Cation occupancy in the biotite structure is dominated by K at the X site, with subordinate Na, Ca, Ba, Rb, and Cs. The Y site is primarily occupied by Fe, Mg, and Al, with minor contributions from Ti, Mn, Li, Cr, and Zn. The Z site is composed mainly of Si and Al; in cases of Al deficiency, Fe³⁺ may act as a substitute. The hydroxyl group (OH⁻) at the interlayer site is variably replaced by F and Cl, either partially or completely. Owing to its complex crystal structure and broad compositional range, biotite serves as a sensitive proxy of magmatic and metamorphic conditions. Systematic variations in major and trace element chemistry, site occupancy, and halogen content allow for the quantitative reconstruction of temperature, pressure, oxygen fugacity, and fluid composition [5,6,7,8,9,10,11]. In ore deposit study, therefore, biotite composition is widely used to estimate the physicochemical conditions of ore-related magmas [12,13,14,15]. The most widely applied normalization scheme of biotite is the 22-positive-charge method [16]; however, it introduces significant uncertainties in the estimation of Fe³⁺ and OH⁻ concentrations. A principal component regression (PCR)-based algorithm has recently been proposed to significantly improve the estimation of Fe³⁺ and OH⁻ concentrations, as well as the Fe³⁺/ΣFe ratio, in biotite [10]. Based on such calculated structural formulas, the relative enrichment of F and Cl in melts or fluids in equilibrium with biotite can be inferred from its F, Cl, and OH⁻ concentrations [5,6]. Furthermore, Ti and Al concentrations in biotite are widely recognized as sensitive proxies for crystallization temperature and pressure, respectively, forming the basis for the development of the Ti-in-biotite thermometer and the Al-in-biotite barometer [7,8,9]. However, the Ti-in-biotite thermometers proposed by Luhr et al. (1984) [7] and Henry et al. (2005) [8] were calibrated specifically for volcanic and metapelitic biotite, respectively, while the Al-in-biotite barometer was developed primarily using granitic intrusions that host coexisting biotite and amphibole. Li and Zhang (2022) recently integrated experimental datasets with multiple machine learning algorithms to develop a new biotite thermobarometer, which they contend more accurately constrains the pressure–temperature conditions of andesitic to rhyolitic volcanic systems [11]. However, despite the diversity of structural formula normalization schemes and P–T estimation methods, the extent to which discrepancies among these approaches propagate into reconstructions of physicochemical conditions remains insufficiently evaluated.

Porphyry systems are one of the most important deposit types in the world, supplying ~80% Cu, ~95% Mo, and ~20% Au of the world’s total reserves [17,18]. They are intimately linked to magmatic–hydrothermal processes, and the physicochemical conditions prevailing during emplacement of the ore-related intrusive suite exercise a fundamental control on both deposit size and metal assemblage [19,20]. The Gangdese magmatic–tectonic belt of Tibet is an important Cu–polymetallic metallogenic belt in the world and includes considerable porphyry Cu(–Mo–Au), Cu–Au and Mo(–Cu), skarn Cu(–Mo–Au–W), Pb–Zn(–Ag), Fe(–Cu) and Mo–W, breccia-type and hydrothermal vein-type Pb–Zn(–Ag) deposits [21,22]. The Julong Cu–polymetallic district, located in the eastern part of the Gangdese magmatic–tectonic belt (Figure 1a), is the largest porphyry–skarn Cu–polymetallic system discovered in China [23]. The intrusive suite associated with porphyry formation comprises granodiorite, monzogranite, and monzogranite porphyry, all of which host abundant magmatic biotite. The physicochemical conditions governing the emplacement of the ore-related intrusive suite have been constrained through previous mineralogical studies [14,24,25,26,27]. This unique dataset offers a valuable opportunity to (1) evaluate discrepancies among existing biotite structural formula calculation methods; (2) quantify the extent to which these discrepancies propagate into derived physicochemical parameters; and (3) identify the combination of computational approaches that most reliably reconstruct magmatic conditions of porphyry systems.

In this study, the major element composition of magmatic biotite in various lithologies of the ore-related intrusive suite was determined using electron-probe microanalysis (EPMA). The EPMA data were subsequently used to calculate biotite structural formulas using two widely applied normalization schemes. Based on these calculations, we applied a suite of independent methods to estimate temperature, pressure, and volatile enrichment. The results were then compared with constraints derived from alternative approaches, including amphibole thermobarometer, whole-rock Zr-saturation thermometer, and fluid-inclusion microthermometry [24,26,27]. This integrated framework enables the identification of the most robust combination of biotite-based methods for recording physicochemical conditions in porphyry systems and provides precise constraints on the conditions prevailing during the formation of each lithology within the Julong ore-related intrusive suite.

2. Geological Background

2.1. Regional Geology

The Gangdese magmatic–tectonic belt is situated along the southern edge of the Lhasa terrane. It is located between the Bangong–Nujiang suture to the north and the Yarlung Zangbo suture to the south (Figure 1a). It is 150 to 300 km wide in a N–S direction and extends E–W for ~1500 km. The regional strata consist of a basement overlain by a series of sedimentary formations. The basement formed mainly during the Mesoproterozoic to early Cambrian, while the overlying sedimentary formations accumulated from the Ordovician onwards. These comprise pre-Ordovician tectono-stratigraphic units, Carboniferous–Paleogene sedimentary formations, and Neogene–Quaternary tectono-stratigraphic units. The Gangdese belt experienced a long and complex history of magmatism and deformation, which can be divided into three main tectono-magmatic stages. Stage 1 corresponds to the northward subduction of the Neotethyan oceanic plate (220–65 Ma) [29,30] and produced the Gangdese magmatic arc, characterized by widespread intermediate to felsic intrusions. Stage 2 marks the India–Asia continental collision (65–26 Ma) [31], the peak magmatic episode in the Gangdese belt, characterized by the Linzizong volcanic formation [32]. Stage 3 is the post-collisional stage (<26 Ma) [31], dominated by Oligocene–Miocene granitic porphyries that commonly display adakitic geochemical affinities [33] and are closely associated with porphyry-type mineralization. Regional structural trends are predominantly E–W; however, subsequent tectonic reactivation has generated numerous NE-trending and nearly N–S-trending extensional structures.

2.2. Deposit Geology

The Julong Cu–polymetallic district is located in Mozhugongka, ~50 km from Lhasa (Figure 1a). It mainly comprises the Qulong porphyry Cu–Mo deposit and the Zhibula skarn-type Cu–Pb–Zn deposit (Figure 1b). The exposed strata are dominated by Quaternary rocks and the Lower–Middle Jurassic Yeba Formation. The Yeba Formation outcrops extensively in an E–W direction across the southern and northern parts of the district and exhibits a temporal pattern whereby the central part is older than the flanks [34]. Lithologically, the Yeba Formation mainly consists of intermediate–felsic volcanic, volcaniclastic, and sedimentary rocks, primarily rhyolitic porphyry, crystalline tuff, and tuff, with minor carbonate interlayers. Published geochronology constrains its emplacement between 192.7 ± 1.3 Ma and 154.8 ± 6.8 Ma [26,35,36,37,38,39]. The Julong Cu–polymetallic district is structurally dominated by ductile shear zones and fracture networks. Two main ductile shear zones have been identified: (1) a NWW-striking zone in the central-southern part of the district, dipping at an angle of 60–80°, which separates the second and third groups of the Yeba Formation; and (2) an approximately E–W-trending zone in the central district, dipping 65–80°, which marks the boundary between the third and fourth groups of the Yeba Formation. Small-scale fractures are ubiquitous and exhibit highly variable orientations. They are closely associated with Cu–Mo mineralization within the Qulong porphyry Cu–Mo deposit [40].

Magmatic intrusions are extensively developed within the Julong Cu–polymetallic district, comprising Early Jurassic and Miocene intrusions. The Early Jurassic intrusions are dominated by granite porphyry, which is exposed in the central–western part of the district and intrudes the Yeba Formation. In the south, this unit is in contact with Miocene monzogranite and is pervasively foliated, commonly showing stretched K-feldspar phenocrysts. Zircon U–Pb geochronology indicates that the emplacement of the Early Jurassic granite porphyry occurred between 182.3 ± 1.5 Ma and 160.7 ± 2.0 Ma [26,39], suggesting that it is not genetically related to the formation of the Julong district. Miocene intrusions include (1) the Rongmucuola complex, composed of granodiorite (Figure 2a,b) and monzogranite (Figure 2c,d), which is temporally and spatially associated with skarn Cu mineralization [41]; (2) monzogranite porphyry (Figure 2e,f) and granodiorite porphyry, which are directly linked to porphyry Cu–Mo mineralization [39]; and (3) post-ore diorite porphyry dikes [25]. The Rongmucuola complex, monzogranite porphyry, and granodiorite porphyry constitute the ore-related intrusive suite genetically associated with the Julong district. The Rongmucuola complex occurs as a stock (Figure 1b), with granodiorite being largely exposed in the east of the district and monzogranite concentrated in the center and south. Field cross-cutting relationships and zircon U–Pb geochronology indicate that the granodiorite crystallized slightly earlier than the monzogranite, with respective ages of 19.5 ± 0.4 to 17.1 ± 0.5 Ma and 17.4 ± 0.4 to 16.4 ± 0.4 Ma, respectively [26,27,42,43,44]. Mafic enclaves are widespread within the Rongmucuola complex: their magmatic zircons record an age range of 22.2 ± 0.5 to 16.3 ± 0.7 Ma [27,43]. Monzogranite porphyry, also referred to as the P porphyry, intrudes the Rongmucuola complex as a NW-elongated elliptical stock and represents the largest porphyry by volume in the district (Figure 1b). With the exception of one older age (17.6 ± 0.7 Ma) [45], its emplacement is constrained between 17.0 ± 0.2 and 15.5 ± 0.4 Ma [26,27,37,46]. Granodiorite porphyry, also referred to as the X porphyry, occurs as narrow apophyses and small dikes of limited extent. It post-dates the P porphyry, which generated the main Cu–Mo mineralization [43]. Zircon U–Pb ages of 17.7 ± 0.3 Ma and 15.9 ± 0.3 Ma [27,43] suggest that the X porphyry is the result of continued crystallization within an underlying magma chamber [27]. The youngest magmatic activity in the district is represented by high-Mg diorite porphyry dikes, which were emplaced between 15.7 ± 0.2 and 14.7 ± 0.3 Ma [25,26,27]. These dikes cross-cut all earlier intrusions and mark the end of the magmatic evolution of the Julong district.

The Qulong porphyry Cu–Mo deposit exhibits classic porphyry-style alteration, characterized by an early assemblage of potassic alteration (dominated by K-feldspar, biotite, magnetite, and anhydrite) and propylitic alteration (dominated by chlorite and epidote), followed by a late-stage phyllic alteration (comprising sericite, chlorite, and clay minerals). Phyllic alteration extensively overprints the earlier potassic alteration. Copper and Mo mineralization are closely associated with potassic and phyllic alteration [23]. Re–Os dating of molybdenite constrains the mineralization event at Qulong to 16.4 ± 0.5 Ma and 15.877 ± 0.006 Ma [47,48,49]. The Zhibula skarn-type Cu–Pb–Zn deposit is similar to typical metasomatic skarn deposits that are related to magmatic-hydrothermal fluids, which develop through a prograde stage (stage I), to an early retrograde stage (stage II), and a late retrograde stage (stage III) [41]. Geochronological data from the genetically related granodiorite and monzogranite, together with garnet from the prograde skarn stage, indicate that the Zhibula skarn-style mineralization formed between 17.0 ± 0.4 and 16.9 ± 0.3 Ma [41,50].

3. Sampling and Methods

All samples examined in this study were collected from drill hole ZK001-1 in the Qulong deposit. Microscopic observation and back-scattered electron (BSE) imaging were used to confirm that magmatic biotite is devoid of hydrothermal alterations. From 25 relatively fresh samples, a set of two granodiorites, two monzogranites, and one monzogranite porphyry was selected for EPMA measurements.

The BSE images were phototed using the Zeiss Gemini 450 manufactured by Zeiss of Germany. Quantitative phase chemistry measurements were conducted using a JEOL JXA-8230 electron probe microanalyzer at Wuhan SampleSolution Analytical Technology Co., Ltd., Wuhan, China. Operating conditions included an accelerating voltage of 15 kV and a beam current of 10 nA. Peak counting times were set to 10 s for all elements, with background counting times of 5 s. Calibration was performed using a comprehensive suite of reference materials, including 53 mineral standards, 44 elemental standards, and 15 rare earth element standards provided by SPI Company. Data reduction was carried out using the ZAF correction method implemented by JEOL. Full EPMA datasets for biotite and amphibole are provided in the Supplementary Materials Tables S1–S3.

Biotite structural formulas were calculated using two independent approaches: (1) the conventional method based on normalization to 11 oxygen atoms and (2) a recently developed PCR-based method. Following structural recalculation, a suite of thermobarometers was applied to estimate the crystallization temperatures and pressures of the various lithologies within the intrusive suite:

• Titanium-in-biotite thermometer

  −

  Temperature (°C) = 838/(1.0337 − Ti/Fe²⁺) − 273.15 [7]

  −

  Temperature (°C) = {[ln(Ti) + 2.3594 + 1.7283 × (X_Mg)³]/(4.6482 × 10⁻⁹)}^0.333 [8], where X_Mg = Mg/(Mg + Fe);

• Aluminium-in-biotite barometer

  −

  Pressure (kbar) = 3.03 × Al_total − 6.53 (±0.33) [9];

• machine learning-based biotite thermobarometer [11].

In addition, the relative enrichments of F and Cl in biotite (represented by IV(F), IV(Cl), and IV(F/Cl)) and the halogen fugacities of the coexisting melt [i.e., log(f_H2O/f_HF), log(f_H2O/f_HCl), and log(f_HF/f_HCl)] were estimated following the procedures proposed by Muñoz (1984, 1992) [5,6]. All relevant equations are listed below:

• Enrichments of F and Cl in biotite [5]

IV(F) = 1.52 X_Phl + 0.42 X_Ann + 0.20 X_Sid − log(X_F/X_OH)

IV(Cl) = −5.01 − 1.93 X_Phl − log(X_Cl/X_OH)

IV(F/Cl) = IV(F) − IV(Cl);

• Halogen fugacities of the coexisting melt [6]

log(f_H2O/f_HF)^melt = (1000/T) × (2.37 + 1.1 X_Phl) + 0.43 − log(X_F/X_OH)^biotite

log(f_H2O/f_HCl)^melt = (1000/T) × (1.15 + 0.55 X_Phl) + 0.68 − log(X_Cl/X_OH)^biotite

log(f_HF/f_HCl)^melt = −(1000/T) × (1.22 + 1.65 X_Phl) + 0.25 + log(X_F/X_Cl)^biotite

where X_Phl = Mg/Σ(octahedral cations), X_Sid = [(3 − Si/Al)/1.75] × (1 − X_Phl), X_Ann = 1 − X_Phl − X_Sid.

Amphibole structural formulas were calculated using a 24-oxygen anion basis [51]. Crystallization temperatures and pressures were subsequently estimated using the amphibole thermobarometer [52,53]. Whole-rock Zr-saturation temperatures were determined using the model of Shao et al. (2020) [54]. These results were integrated with previously published estimates of temperature, pressure, and oxygen fugacity for the various lithologies [27], fluid-inclusion data [24,55], and the magmatic emplacement model established for the Qulong deposit [26], in order to evaluate the most appropriate biotite composition-based calculation method for application in porphyry systems.

4. Results

4.1. Biotite

Magmatic biotite in the granodiorite, monzogranite, and monzogranite porphyry underwent variable degrees of hydrothermal alteration, resulting in its partial to complete replacement by hydrothermal biotite and/or chlorite. In all three lithologies, magmatic biotite occurs as euhedral to subhedral phenocrysts, commonly enclosing early-crystallized magnetite and apatite. Chlorite preferentially replaces biotite along grain boundaries, cleavage planes, and fractures (Figure 3a). On the other hand, hydrothermal biotite is fine-grained and forms at the expense of mafic precursors such as biotite and amphibole (Figure 3b,c), occurring as disseminations, veinlets, or clustered aggregates. Localized hydrothermal overprint has also induced the formation of acicular rutile within some magmatic biotite grains (Figure 3d). Back-scattered electron imaging reveals no discernible difference between magmatic and hydrothermal biotite.

EPMA data indicate that the analyzed magmatic biotite plots along the boundary between “primary biotite” and “re-equilibrated primary biotite” (Figure 3e). In the Al–Mg–Fe diagram, all data fall within the domain of “calc-alkaline rock suite in orogenic belt” (Figure 3f). In granodiorite, magmatic biotite contains (average ±1 SD): SiO₂ 36.84 ± 0.43 wt.%, TiO₂ 3.66 ± 0.31 wt.%, Al₂O₃ 13.53 ± 0.16 wt.%, FeO 15.77 ± 0.45 wt.%, MnO 0.29 ± 0.04 wt.%, MgO 14.72 ± 0.42 wt.%, K₂O 9.53 ± 0.27 wt.%, F 0.55 ± 0.15 wt.%, and Cl 0.09 ± 0.02 wt.% (Supplementary Materials Tables S1 and S2). Magmatic biotite in monzogranite is comparatively enriched in SiO₂ (37.33 ± 0.88 wt.%), Al₂O₃ (14.27 ± 0.64 wt.%), and F (0.71 ± 0.17 wt.%), but depleted in FeO (13.96 ± 2.02 wt.%), MnO (0.21 ± 0.05 wt.%), MgO (15.35 ± 1.16 wt.%), and K₂O (9.35 ± 0.47 wt.%). The TiO₂ (3.64 ± 0.46 wt.%) and Cl (0.08 ± 0.02 wt.%) concentrations are similar to those in granodiorite (Supplementary Materials Tables S1 and S2). Biotite in monzogranite porphyry has the lowest concentrations of TiO₂ (3.57 ± 0.28 wt.%) and K₂O (9.30 ± 0.56 wt.%), but the highest concentrations of Cl (0.11 ± 0.02 wt.%). All other concentrations of major elements are intermediate between those of granodiorite and monzogranite (Supplementary Materials Tables S1 and S2).

4.2. Amphibole

The magmatic amphibole is restricted to granodiorite, where it forms euhedral prisms and columnar crystals (Figure 4a). Hydrothermal alteration commonly overprints amphibole, producing actinolite, biotite (Figure 3b), chlorite, and epidote. Altered domains appear dark green in plane-polarized light and exhibit increased brightness in BSE images (Figure 4a). Representative magmatic amphibole yields (average ±1 SD): SiO₂ 48.65 ± 0.73 wt.%, MgO 15.31 ± 0.56 wt.%, FeO 12.11 ± 0.43 wt.%, CaO 11.49 ± 0.16 wt.%, Al₂O₃ 5.73 ± 0.39 wt.%, TiO₂ 1.06 ± 0.09 wt.%, and Na₂O + K₂O 1.75 ± 0.14 wt.% (Supplementary Materials Table S3). The major element geochemistry of the analyzed amphibole classifies it as “Magnesiohornblende” (Figure 4b). The general amphibole formula is AB₂C₅T₈O₂₂W₂ [58]. Cation–cation plots reveal a positive correlation of ^TAl with ^A(Na + K) and ^CTi, whereas its relationships with ^CAl and ^BCa are weak to negative (Figure 4c–f). In contrast, the amphibole chemistry collected from altered domains plots within the “tremolite” field (Figure 4b) and exhibit higher contents of SiO₂ (52.34 ± 0.76 wt.%), MgO (18.23 ± 0.29 wt.%), and CaO (12.19 ± 0.31 wt.%), coupled with lower FeO (9.54 ± 0.36 wt.%), Al₂O₃ (2.55 ± 0.55 wt.%), TiO₂ (0.25 ± 0.14 wt.%), and Na₂O + K₂O (0.74 ± 0.19 wt.%) concentrations (Supplementary Materials Table S3).

5. Discussion

5.1. Comparison of Different Methods for Estimating the Structural Formula and Physicochemical Conditions of Magmatic Biotite

5.1.1. Classification of Biotite

Biotite comprises four principal end-members: annite (KFe₃²⁺AlSi₃O₁₀(OH)₂), phlogopite (KMg₃AlSi₃O₁₀(OH)₂), siderophyllite (KFe₂²⁺AlAl₂Si₂O₁₀(OH)₂), and eastonite (KMg₂AlAl₂Si₂O₁₀(OH)₂) [59]. Because Li concentration effectively tracks magmatic differentiation and provides key information for mineralization, a Li-bearing mica classification diagram has also been proposed [60]. Biotite structural formulas were calculated using the 11-oxygen-atom method and the PCR-based approach (Supplementary Materials Tables S1 and S2). When plotted according to both the Li-free traditional classification scheme and the Li-inclusive molecular classification, results from the two methods consistently classify the analyzed biotite as Mg-biotite. (Figure 5). However, because the PCR-based method reports the contents of ^TFe³⁺, ^MAl, ^MFe³⁺, and ^WO₂⁻ [10], its results for the same dataset deviate from those of the 11-oxygen-atom method. Specifically, the PCR-based approach yields higher ^TSi, ^MMg, and ^WF⁻ values, but lower ^TAl, ^MFe²⁺, ^MLi, and ^WOH⁻ values (Supplementary Materials Tables S1 and S2). Consequently, the results of PCR-based method are systematically shifted to the left in the (Fe²⁺ + Mn)–Mg–(Al^VI + Fe³⁺ + Ti) diagram, while displaced to the right in the (Mg–Li)–(Fe_total + Mn + Ti–Al^VI) diagram (Figure 5).

5.1.2. Estimation of Temperature and Pressure

The composition of biotite is commonly used to estimate the temperature and pressure conditions of the coexisting magma at the time of crystallization. Well-established approaches include the calibrations of Luhr et al. (1984) [7], Henry et al. (2005) [8], Uchida et al. (2007) [9], and Li and Zhang (2022) [11]. Figure 6 summarizes the calculated formation temperatures and pressures for the three lithologies, obtained from different normalization procedures and thermobarometers.

Magmatic crystallization temperatures are commonly derived from trace-element saturation thermometers and mineral thermometers [7,8,9,11,52,54]. In this study, the whole-rock Zr-saturation thermometer (T_{whole-rock Zr}) [54] and the amphibole thermometer (T_Amp) [52] were used to determine the most suitable biotite thermometer. This is because these two thermometers have been widely used to estimate magmatic crystallization temperatures and have demonstrated good reliability and accuracy [12,15,62,63]. The T_Amp constrains the crystallization temperature of granodiorite to 756–816 °C (average ±1 SD = 782 ± 20 °C), whereas the T_{whole-rock Zr} yields 713–791 °C (average ±1 SD = 742 ± 20 °C) for granodiorite, 678–754 °C (average ±1 SD = 712 ± 28 °C) for monzogranite, and 831–843 °C (average ±1 SD = 837 ± 8 °C) for monzogranite porphyry (Supplementary Materials Tables S3 and S4). It should be noted that (1) amphibole generally crystallized early in porphyry systems [64]; thus, its formation temperature records the thermal conditions during the early stage of magma evolution; (2) in granitic magmas, T_{whole-rock Zr} calculated from whole-rock compositions provide minimum temperature if the magma was undersaturated, but maxima if it was saturated [62,65]; whereas, if the magma contains inherited zircon, then the use of the whole-rock composition to represent the melt composition will inevitably result in a high crystallization temperature estimate based on Zr-saturation thermometer [54]. Previous cathodoluminescence spectroscopy studies of zircon texture for the three lithologies investigated herein indicate that inherited zircons are rare in monzogranite porphyry but common in granodiorite and monzogranite [27,49]. Accordingly, T_{whole-rock Zr} for granodiorite and monzogranite may define high crystallization temperatures. Comparisons of biotite crystallization temperatures obtained by different methods reveal that those calculated using the PCR-based method combined with the thermometer of Luhr et al. (1984) [7] and the thermometer of Li and Zhang (2022) [11] are higher than values yielded by the other three methods (Figure 6a–c). In granodiorite, biotite temperatures derived from the PCR-based method in conjunction with Luhr et al. (1984) [7] exceed the amphibole crystallization temperature (Figure 6a), which contradicts the expected crystallization sequence in porphyry systems [64]. In monzogranite porphyry, only the biotite temperatures from the PCR-based method combined with Luhr et al. (1984) [7] and from Li and Zhang (2022) [11] are equal to or slightly above T_{whole-rock Zr}, whereas all other methods yield significantly lower values (Figure 6c). Consequently, we propose that biotite temperatures obtained using the method proposed by Li and Zhang (2022) [11] are the most suitable. This conclusion is consistent with the findings of Xu and Wang (2024) [62], which, through a comparison of T_{whole-rock Zr} and biotite temperatures calculated by Li and Zhang (2022) [11] for representative granitic rocks, demonstrated that this thermometer provides reliable estimates of emplacement temperatures for both I- and S-type granites.

Estimates of magmatic emplacement pressure are commonly derived from mineral barometers and fluid-inclusion microthermometry. In this study, the reliability of the biotite barometer is assessed through comparison with previously reported emplacement depths obtained from fluid-inclusion microthermometry [24,55] and amphibole barometer [53]. This is because fluid-inclusion microthermometry provides the most reliable pressure estimates [66,67,68], and the amphibole barometer—despite its relatively large uncertainty [69,70]—has also been widely applied to estimate the emplacement depth of intrusions [15,33,71]. The relatively large uncertainty of amphibole barometers is likely due to the intrinsic sensitivity of amphibole to temperature and melt composition rather than pressure [63,69,70]. Amphibole barometer indicates an emplacement pressure of 1.69 ± 0.33 kbar for the granodiorite (Figure 6d). The poor correlation observed for the pressure-sensitive Al-Tschermak exchange in magmatic amphibole ((Mg, Fe)^C + Si^T = Al^IV + Al^VI; Figure 4c) further suggests that the amphibole barometer may be biased. Based on fluid-inclusion microthermometry, Xiao et al. (2012) estimated the vein formation depths of ~1.4–2.4 km [24]. Assuming a lithostatic gradient of 0.27 MPakm⁻¹, this corresponds to a formation pressure of ~0.38–0.65 kbar for the monzogranite porphyry, consistent with the ore-related intrusion emplacement pressure (~0.7 kbar) reported by Li et al. (2017) [55]. Comparisons among various biotite barometers reveal that pressures calculated using the barometer proposed by Li and Zhang (2022) [11] are significantly higher than those derived from fluid-inclusion and amphibole barometers (Figure 6d,f) and are further incompatible with the porphyritic texture of the monzogranite porphyry, indicating an overestimation of the formation pressure. Pressures calculated using the barometer of Uchida et al. (2007) [9] are consistent, within uncertainty, with estimates from fluid-inclusion and amphibole barometer, although application of the PCR-based structural formula calculation method in combination with this barometer yields values approximately 0.18 kbar higher than those obtained using the 11 oxygen atoms-based method (Figure 6d–f). Regardless of the structural formula calculation method used, the barometer proposed by Uchida et al. (2007) [9] is better suited for estimating emplacement depths in porphyry systems.

5.1.3. Estimation of Halogen and Oxygen Fugacity

Halogen concentrations and their fugacity in magma are critical for the formation of porphyry deposits [72,73]. Muñoz (1984) [5] defined biotite intercept values for F, Cl, and the F/Cl ratio to quantify the relative halogen enrichment in this mineral. Lower F and Cl intercept values indicate stronger enrichment of these elements in biotite, whereas the F/Cl intercept value is independent of both equilibrium temperature and OH⁻ content, thereby directly reflecting the HCl/HF fugacity ratio in the magmatic system [5]. Further on, Muñoz (1992) [6] derived expressions for estimating the halogen fugacity ratios of melts (or fluids) in equilibrium with biotite, based on experimentally determined F–Cl–OH partition coefficients between biotite and melt (or fluid) [74,75]. The parameters calculated using the different normalization procedures are compared in Figure 7 and Figure 8.

In the Julong district, the results of the formula calculation based on 11 oxygen atoms yield lower F intercepts but higher Cl and F/Cl intercepts than those of the PCR-based method (Figure 7a–c). Regardless of the normalization procedures, all halogen intercepts fall within the field of porphyry Cu deposits (Figure 7d,e). More importantly, the relative enrichment of volatiles among the three lithologies remains consistent regardless of the method used; monzogranite porphyry always exhibits the highest halogen enrichment (Figure 7a,b). The log(f_H2O/f_HF), log(f_H2O/f_HCl), and log(f_HF/f_HCl) ratios vary in step with the estimated biotite crystallization temperatures due to the temperature input in the calculations (Figure 6a–c). Specifically, the PCR-based method coupled with the thermometer proposed by Luhr et al. (1984) [7] and Li and Zhang (2022) [11] yields significantly lower log(f_H2O/f_HF) and log(f_H2O/f_HCl) but higher log(f_HF/f_HCl) relative to the other three approaches (Figure 8). Nevertheless, the relative magnitudes of these ratios among the lithologies remain method-independent (Figure 8): granodiorite and monzogranite show the highest and lowest log(f_H2O/f_HF), respectively; monzogranite and monzogranite porphyry exhibit the highest and lowest log(f_H2O/f_HCl), respectively; and monzogranite records the highest log(f_HF/f_HCl). Thus, the choice of normalization procedure does not affect the assessment of the relative halogen enrichment among the studied lithologies.

Oxygen fugacity is also critical for the formation and size of porphyry deposits [20,76]. The X_Mg value and the Fe³⁺/Fe_Total ratio of biotite are key indicators of the magmatic oxidation state; both increase with increasing oxygen fugacity [77]. However, the X_Mg value is also influenced by melt (or fluid) F concentrations and S fugacity [78,79]. Biotite X_Mg values calculated using the PCR-based method are slightly higher than those derived from the 11 oxygen atoms-based method, although the difference does not exceed 0.01 (Figure 9a). The PCR-based method also permits accurate estimation of the Fe³⁺/Fe_Total ratio in biotite [10]. The Fe³⁺/Fe_Total ratios of granodiorite, monzogranite, and monzogranite porphyry concentrates in 0.29–0.33 (average ±1 SD = 0.31 ± 0.03), 0.24–0.30 (average ±1 SD = 0.27 ± 0.05), and 0.28–0.33 (average ±1 SD = 0.31 ± 0.05), respectively (Figure 9b; Supplementary Materials Table S2). In the Mg–Fe³⁺–Fe²⁺ diagram, granodiorite and monzogranite porphyry plot closer to the HM buffer, whereas monzogranite and monzogranite porphyry exhibit wider compositional variations (Figure 9c). These characteristics are consistent with the previous conclusions based on zircon trace element data [27,80]: Eu/Eu*, Ce/Nd, Ce/Ce*, and Ce⁴⁺/Ce³⁺ ratios of zircon indicate that the granodiorite and monzogranitic porphyry crystallized under the highest oxygen fugacity, with the latter also showing a wider variation range.

In conclusion, the PCR-based structural formula calculation method proposed by Li et al. (2020) [10] has clear advantages over the 11 oxygen atom-based method in estimating the Fe³⁺/Fe_Total ratio. It yields no distinct differences in biotite classification or halogen enrichment estimation and is, therefore, recommended as the preferred method for calculating biotite formula. Regarding temperature and pressure constraints, the thermometer and barometer proposed by Li and Zhang (2022) [11] and Uchida et al. (2007) [9], respectively, are the most suitable for porphyry systems.

5.2. The Physicochemical Conditions During the Emplacement of the Ore-Related Intrusive Suite in the Julong Deposit

The above three methods (i.e., structural formula calculation method of Li et al. (2020) [10], thermometer of Li and Zhang (2022) [11], and barometer of Uchida et al. (2007) [9]) are applied together in the following to constrain the physicochemical conditions during the emplacement of the ore-related intrusive suite in the Julong district.

The granodiorite represents the earliest intrusion associated with mineralization, emplaced between 19.5 ± 0.4 and 17.1 ± 0.5 Ma [26,27,43,44]. Biotite- and amphibole-based thermometers indicate crystallization temperatures of ~782–819 °C (Figure 6a). Emplacement pressure estimated by biotite- and amphibole-based barometers ranges from ~0.87 MPa to ~1.69 MPa (Figure 6d). Assuming a lithostatic gradient of 0.27 MPakm⁻¹, the emplacement depths are ~3.2–6.3 km. The averages of biotite X_Mg values and Fe³⁺/Fe_Total ratios are ~0.63 and ~0.31, respectively (Figure 9a,b and Figure 10a), yielding an oxygen fugacity between ~NNO+3 and the HM buffer (Figure 9c), thereby indicating a highly oxidized magma. This conclusion is supported by amphibole compositions, which estimate the oxygen fugacity at NNO+1.5 to NNO+2.3 (average ±1 SD = NNO+1.9 ± 0.24) (Supplementary Materials, Table S3). Halogen fugacity ratios derived from biotite in the granodiorite yield IV(F), IV(Cl), IV(F/Cl), log(f_H2O/f_HF), log(f_H2O/f_HCl), and log(f_HF/f_HCl) values of 1.92–2.63 (average ±1 SD = 2.05 ± 0.13), –4.13 to –3.71 (average ±1 SD = –3.93 ± 0.09), 5.75–6.55 (average ±1 SD = 5.99 ± 0.15), 4.06–4.84 (average ±1 SD = 4.22 ± 0.15), 3.99–4.42 (average ±1 SD = 4.20 ± 0.08), and −1.22 to −0.35 (average ±1 SD = −0.59 ± 0.17), respectively (Supplementary Materials Table S2). These ratios are comparable to those of magmatic volatiles documented in world-class porphyry deposits (Figure 7). Despite its high oxidation state and elevated volatile concentrations, the granodiorite remained fluid-undersaturated upon emplacement, preventing large-scale hydrothermal alteration and mineralization [81]. Amphibole compositions indicate that the magmatic water contents are 3.52–4.57 wt.% (average ±1 SD = 3.99 ± 0.33 wt.%), which is below the maximum H₂O solubility (~5 wt.%) at the crystallization conditions (~782 °C, ~1.69 kbar) [15].

The emplacement age of monzogranite (17.4 ± 0.4 to 16.4 ± 0.4 Ma) [26,42,44] is slightly younger than that of granodiorite (Figure 11a). Biotite thermobarometer yields crystallization conditions of ~854 °C and ~1.18 MPa for monzogranite (Figure 6b,e), with X_Mg and Fe³⁺/Fe_Total values of ~0.66 and ~0.28, respectively (Figure 9a,b). Therefore, the emplacement depths are ~4.4 km, assuming a lithostatic gradient of 0.27 MPakm⁻¹. The calculated oxygen fugacity ranges from ~NNO+2 to NNO+4 (Figure 9c). In monzogranite, biotite X_Mg values exhibit a continuous positive correlation with F concentrations, whereas the Fe³⁺/Fe_Total ratios remain constant (Figure 10a,b). This indicates that the variation in X_Mg is linked to progressive F enrichment in the melt (or fluid) [79]. Biotite compositions yield log(f_H2O/f_HF), log(f_H2O/f_HCl), and log(f_HF/f_HCl) ratios of 3.85–4.66 (average ±1 SD = 4.07 ± 0.14), 3.95–4.50 (average ±1 SD = 4.24 ± 0.12), and −1.06 to −0.04 (average ±1 SD = −0.41 ± 0.17), respectively (Supplementary Materials, Table S2). Compared with granodiorite, monzogranite has lower log(f_H2O/f_HF) but higher log(f_HF/f_HCl) ratios (Figure 10c,d), confirming its higher F enrichment. This is likely related to continuous mineral fractional crystallization [39]. The monzogranite records lower oxygen fugacity than granodiorite, as indicated by lower biotite Fe³⁺/Fe_Total ratios and biotite-based fO₂ estimates. This decrease is probably caused by magnetite crystallization during magma evolution, which drives the residual melt towards more reduced conditions [76].

The monzogranite porphyry was emplaced between 17.0 ± 0.2 and 15.5 ± 0.4 Ma [26,27,37,46] (Figure 11b). Biotite thermobarometer constraints crystallization conditions of ~832 °C and ~0.91 MPa for this intrusion (Figure 6c,f), corresponding to an emplacement depth of ~3.4 km. The biotite X_Mg (~0.63) and Fe³⁺/Fe_Total (~0.30) values are comparable to those of granodiorite (Figure 9a,b), and the calculated oxygen fugacity likewise falls within the range of ~NNO+3 to the HM buffer (Figure 9c), indicating highly oxidized conditions. In contrast to granodiorite, however, monzogranite porphyry shows a wider spread in biotite X_Mg and Fe³⁺/Fe_Total values (Figure 10a). Although biotite X_Mg correlates positively with F concentrations, a conspicuous gap occurs at X_Mg of ~0.65–0.72 (Figure 10b). In addition, biotite grains with high X_Mg (0.66–0.77) do not show the highest crystallization temperatures (but always elevated: 835–914 °C, average ±1 SD = 868 ± 25 °C; Supplementary Materials Table S2), nor do they exhibit the highest F or the lowest Cl concentrations (Supplementary Materials Table S2), or the highest log(f_HF/f_HCl) ratios (Figure 10d). These features imply that the formation of monzogranite porphyry was accompanied by the involvement of a high-temperature, volatile-rich melt (or fluid) [79]. This likely reflects mafic magma injection in the Julong district, where the high temperature, oxygen fugacity, and volatile content of these magmas [25,27] elevated both parameters in the monzogranite porphyry. Biotite compositions yield log(f_H2O/f_HF), log(f_H2O/f_HCl), and log(f_HF/f_HCl) ratios of 3.93–4.53 (average ±1 SD = 4.12 ± 0.13), 3.95–4.40 (average ±1 SD = 4.12 ± 0.10), and −0.89 to −0.16 (average ±1 SD = −0.58 ± 0.14), respectively (Supplementary Materials, Table S2). The lowest log(f_H2O/f_HCl) ratio among the three lithologies indicates the highest HCl activity in the monzogranite porphyry. Elevated HCl activity facilitates the transport of Cu and Mo in the magma [82].

6. Conclusions

Comparison of the physicochemical conditions derived from amphibole thermobarometer, whole-rock Zr-saturation thermometer, and fluid-inclusion microthermometry with those obtained from biotite compositions for the ore-related intrusive suite of the Julong Cu–polymetallic district shows that the biotite composition-based method, using the structural formula calculation of Li et al. (2020) [10], together with the thermometer of Li and Zhang (2022) [11] and the barometer of Uchida et al. (2007) [9], yields the most reliable estimates of magmatic P–T–fO₂–volatile conditions. Based on magmatic biotite compositions and the above methods, the physicochemical parameters of the Julong ore-related intrusive suite have been well constrained. The earliest granodiorite was emplaced at depths of ~3.2–6.3 km under high oxygen fugacity (~NNO+3 to HM) and elevated volatile concentrations. The subsequent monzogranite crystallized at ~4.4 km from a less oxidized magma (~NNO+2 to NNO+4) but with higher F concentrations, reflecting progressive crystallization of magnetite and other magmatic minerals. The ore-related monzogranite porphyry, emplaced at ~3.4 km, is characterized by high oxygen fugacity (~NNO+3 to HM) and the lowest log(f_H2O/f_HCl) ratio, indicating the highest HCl activity among the three lithologies and enabling efficient transport of Cu and Mo.