Effectiveness of Ti-in-amphibole thermometry and performance of different thermometers across lower continental crust up to UHT metamorphism

Abstract

Metabasites are important constituents of deep crustal sections and are the favored rock type for studying lower crustal amphibolite to granulite transitions. However, metapelites may develop a larger number of temperature-sensitive mineral assemblages and are particular useful when extreme ultrahigh temperature (UHT) conditions are envisaged. A recent calibration of the Ti-in-amphibole thermometer by Liao et al. (2021) was supposed to make thermometry on metabasites quick and easy to apply. However, their calibration is based on experiments which were not originally designed to investigate in detail the temperature dependence of Ti in amphibole. In addition, a possible effect of a_TiO2 and/or pressure on the Ti content of amphibole was not fully taken into account. This resulted in a calibration uncertainty of ± 70 °C (2σ), much higher than that of other single-mineral thermometers. In this study we firstly test the newly calibrated Ti-in-amphibole thermometer across the mid to lower crustal section of the Ivrea–Verbano Zone (IVZ; NW Italy) and compare the performance of different thermometric techniques across the sequence. Ti-in-amphibole thermometry records increasing peak temperatures from amphibolite (600–700 °C), transition (750–800 °C) and granulite (850–950 °C) zones. Titanium content of amphibole may be modified by retrograde fluid influx returning temperatures c. 200–300 °C lower than in non-altered domains. The comparison reveals that Zr-in-rutile thermometer in pelitic granulites seems to be more prone to post-peak resetting than the Ti-in-amphibole thermometry in nearby mafic rocks. This behavior is also confirmed by amphibole analyses from other UHT localities, where the performance of Ti-in-amphibole thermometry is comparable with that of Al-in-orthopyroxene in pelitic granulites. However, Ti-in-amphibole temperatures are underestimated in rutile-bearing samples and this limitation is not solely restricted to rocks containing high H₂O contents as previously thought. Derived constraints on the diffusivity of Ti through amphibole demonstrate the robustness of the Ti-in-amphibole thermometer to later thermal disturbances. However, ad-hoc experiments are still necessary to improve the accuracy and precision of calibration and to extend its applicability. This advance will make mafic granulites routine targets for studies devoted to understanding the regional extent of UHT metamorphism.

Introduction

One of the main goals of metamorphic petrology is to unravel the pressure and temperature evolution of metamorphic terranes, often adding these important pieces of information to temporal and microstructural constraints to recover complete P–T–D–t paths. In the high- to ultrahigh temperature realm, getting robust constraints on maximum temperatures is crucial to gain a better understanding on the heat source and tectonic settings where extremely high crustal temperatures (> 900–950 °C) are achieved, a topic stirring a considerable debate (Clark et al. 2011; Harley 2021; Jiao et al. 2023). Moreover, knowing the thermal evolution of metamorphic terranes is crucial for interpreting the significance of geochronological data (Yakymchuk and Brown 2014). Limitations of conventional element exchange thermometry for granulites (Frost and Chacko 1989; Spear 1991) were circumvented (1) correcting for the effects of late Fe–Mg exchange (Pattison et al. 2003, 2019), (2) calculating P–T pseudosections with the most up-to-date activity-composition (a–x) models for key minerals in residual granulites (Wheller and Powell 2014), (3) applying single-mineral thermometers, such as Zr-in-rutile, Al-in-orthopyroxene and ternary feldspar thermometry, among the others (e.g., Harley and Green 1982; Tomkins et al. 2007), or (4) by applying a hybrid approach of phase equilibria modelling and quadrivalent (4+) cation trace element thermometry (e.g., Korhonen et al. 2015; Dharmapriya et al. 2021).

Metabasic rocks are considered a key rock type to investigate lower crustal metamorphism (e.g., Bohlen and Essene 1979; Clough and Field 1980; Raase et al. 1986; Raith and Raase 1986; Waters 1988; Sawyer 1991). Recent improvements of a–x models for complex solutions such as amphibole and clinopyroxene, along with the development of a model for melt of broadly trondhjemitic–tonalitic composition (Green et al. 2016), has allowed high temperature (HT) to ultrahigh temperature (UHT) equilibria in metabasic systems to be properly calculated (Palin et al. 2016; Kunz and White 2019). Despite this important step forward for interpreting the petrological evolution of mafic migmatites and granulites, consistent discrepancies have been reported in the literature between observed compositions and modal abundances of amphibole and clinopyroxene and those calculated applying the most recent a–x models (Forshaw et al. 2019; Santos et al. 2019). Indeed, a–x formulations of these complex phases suffer from the large uncertainties of thermodynamic mixing properties, which inevitably affect the reliability and accuracy of phase equilibria calculations (Lanari and Duesterhoeft 2019). This, in turn, may lead to a knock-on effect on the predicted stability of other phases (Forshaw et al. 2019; Schorn and Diener 2019). For these reasons, single-mineral thermometers, whose associated uncertainties are generally quantified (e.g., Tomkins et al. 2007; Kohn 2020), are fundamental tools for metamorphic petrologists, being often preferred to phase equilibria modeling (Qi et al. 2022).

Regarding metabasic systems, Liao et al. (2021) recently calibrated a new Ti-in-amphibole thermometer to recover crystallization temperature in igneous and high-grade metamorphic rocks in the presence of Ti-phases (ilmenite, rutile, or titanite). Its alleged independence from pressure and the low diffusivity of Ti in silicates (up to 1–3 orders of magnitude slower than those of Mg and Fe; Cherniak and Liang 2012) are considered to be the main strengths of Ti-in-amphibole thermometer. Moreover, amphibole may survive up to 950–1000 °C during prograde metamorphism and melting of basic rocks (Fig. 1a), independently from the prograde P–T path and the closed- vs. open-system behavior of the rock (Rushmer 1991; Wolf and Wyllie 1993; Rapp and Watson 1995; Kunz and White 2019; Huang et al. 2021). These characteristics make this thermometer a potentially powerful tool in recovering thermal history of mafic migmatitic and granulitic terranes (e.g., Aidoo et al. 2022; Corvò et al. 2022; Duan et al. 2023; Li et al. 2022).

Fig. 1

(a) Petrological diagram constructed from a P–T pseudosection calculated for a tholeiitic bulk composition. (redrawn from Palin et al. 2016). Green line marks the limit of amphibole stability. Colored dots reflect the P–T conditions of experimental datasets used by Liao et al. (2021) to calibrate the Ti-in-amphibole thermometer; color coding identifies the Ti-phase present in the experimental run. Dashed white line reflects the P–T window of Fig. 5b. (b) Predicted isopleths (black thin lines) for Ti content of amphibole for the tholeiitic bulk composition reported in (a). Calculations were performed using Perple_X software (Connolly 2009) using solution models reported in Palin et al. (2016). The stability fields of rutile, ilmenite and titanite are also shown by light blue, red and grey areas and lines. Green line as in (a). The dashed white line at 8 kbar marks the P and T conditions at which the diagram of Fig. 2 was calculated

Here, we delve deeply into the calibration of Ti-in-amphibole thermometer proposed by Liao et al. (2021) and apply this thermometric technique to the mid amphibolite- to granulite-facies mafic rocks of the archetypal continental crustal section of the Ivrea–Verbano Zone (IVZ; NW Italy). Peak temperatures attained across this sequence are well constrained by a combination of different thermometric techniques (P–T pseudosections, classical and quadrivalent (4+) cation trace element thermometry) applied to these rocks over the last > 50 years (e.g., Reinsch 1973; Hunziker and Zingg 1980; Sills 1984; Henk et al. 1997; Luvizotto and Zack 2009; Redler et al. 2012; Ewing et al. 2013; Kunz and White 2019). After interpreting the variability of Ti-in-amphibole temperatures among samples and within the same thin section, the performance of different thermometers across the IVZ crustal section is compared. We then combine amphibole data collected in this study with those from other renowned UHT localities to obtain a more comprehensive overview of the effectiveness of Ti-in-amphibole thermometry up to extreme crustal conditions. Lastly, on the basis of what is known about the cooling history of the IVZ, we speculate on the diffusivity of Ti in amphibole.

Ti-in-amphibole thermometry: a critical assessment

Taking advantage of previous studies which show a relationship between temperature and the Ti content of amphibole (e.g., Leake 1965; Raase 1974; Otten 1984; Ernst and Liu 1998), Liao et al. (2021) proposed a new calibration for the thermometer based on Ti content of calcium amphibole. These authors used both crystallization and melting experiments from the literature, with pressure and temperature in the range 2–20 kbar and 700–1000 °C, respectively (Fig. 1a). Following their recommendations, this thermometer should be applied to subalkaline systems when amphibole is in equilibrium with Ti-phases (ilmenite, rutile or titanite) at ΔNNO ≤ 2. Liao et al. (2021) state that Ti-in-amphibole thermometry is likely (i) to overestimate temperature when applied to subsolidus H₂O-undersaturated rocks with low (< 1.5 wt%) H₂O content, or (ii) to underestimate temperature for rocks equilibrated at > 850 °C, in the rutile stability field and containing high (> 3.5 wt%) H₂O content. The standard error (1σ) of calibration was quantified to be ± 35 °C.

Despite the few potential limitations reported above, the general applicability of Ti-in-amphibole thermometry to high-grade metamorphic terrains remains uncertain. Only 15% of experiments used for the calibration were run at > 900 °C (Fig. 1a) and the R² value of 0.84 obtained from the nonlinear fitting of the experimental dataset is worse than R² reported for other single-mineral thermometers. For instance, the regression for the Zr-in-rutile calibration has a R² value of 0.99 (see Kohn 2020). This discrepancy is also evident considering the calibration error: Liao et al. (2021) reported a 1σ value of ± 35 °C, i.e., ± 70 °C (2σ), much higher than 20–30 and 10–15 °C (2σ) documented by Kohn (2020) for different calibrations of the Zr-in-rutile thermometer.

Regarding Ti-in-amphibole thermometry, one important unresolved issue is whether a_TiO2 and pressure may affect the Ti content of amphibole or not. Models predict a marked change of the slope of isopleths for Ti content in amphibole from ilmenite- to titanite and rutile-bearing mineral assemblages (Fig. 1b). The possible a_TiO2 dependence of Ti-in-amphibole thermometry would open the door to another potential source of uncertainty. Indeed, the activity of titania has to be considered a dynamic parameter in rutile-absent systems, even though other Ti-phases (ilmenite and/or titanite) are present (Fig. 2). Different reaction sequences impact on the amount of ilmenite/titanite whose modal variations impose different values for bulk rock a_TiO2 (Fig. 2). Also the TiO₂ of melt may impact on a_TiO2 (Fonseca Texeira et al. 2023). However, this aspect cannot be explored with the melt model proposed by Green et al. (2016) for metabasites, because it does not consider TiO₂. The melt model released later by Holland et al. (2018) has a TiO₂ end member, but it seems to overestimate the TiO₂ content of melt when compared to experimental runs (García-Arias 2020).

Fig. 2

T-a_TiO2 diagram calculated at 8 kbar (see Fig. 1b). The stability fields for rutile, titanite and ilmenite are shown

The experimental dataset constructed by Liao et al. (2021) implicitly assumes that pressure does not play a role in controlling the Ti content of amphibole (Fig. 3a, b), even though no experimental studies have been conducted to specifically explore this aspect. Only 18% of experimental runs (i.e., 13 over 72 among those considered by Liao et al. 2021) generated a product in which amphibole is present together with rutile (Figs. 1a and 3a) and Liao et al. (2021) did not consider separately the two datasets (rutile-bearing vs. -absent) when they calibrated this thermometer. However, two different second-order polynomial least squares regression curves can be fitted for the two datasets, suggesting that the equation proposed by Liao et al. (2021) could underestimate temperature when amphibole is in equilibrium with rutile (Fig. 3c), whatever the bulk H₂O content is. For instance, the two empirical equations reported in Fig. 3c for rutile- and ilmenite-bearing systems provide temperature estimates of 960 and 900 °C, respectively, for the same Ti content in amphibole of 0.30 apfu. Instead, Liao’s equation yields 902 °C, in agreement with their calibration being more appropriate for ilmenite-bearing metabasites.

Fig. 3

Diagrams showing T, P and Ti content of amphibole from the experimental dataset used by Liao et al. (2021) to calibrate the Ti-in-amphibole thermometer. Colored symbols in (a) and (c) refer to the different Ti-phases present in experimental runs (symbols as in Fig. 1a). (b) Arrhenius plot of Ti-in-amphibole contents considering experimental runs at 5, 10 and 16 kbar, where ilmenite, titanite or rutile were present. In (c), regression curves and related equations are shown for both ilmenite- and rutile- bearing datasets. The nonlinearl fitting of Liao et al. (2021) is reported for comparison

Further issues that should be tackled are: models presented by Liao et al. (2021) exclude a dependence of Ti content of amphibole from bulk rock composition; however, this aspect has not been evaluated in natural samples. In addition, is Ti content of amphibole susceptible to post-peak resetting? If yes, to what extent and through what processes? For instance, other single-mineral thermometers based on the temperature-dependent incorporation of Ti have been demonstrated to be potentially susceptible to diffusive modification of Ti when applied to slowly cooled rocks with peak temperature > 800 °C – e.g., Ti-in-garnet (Ague and Eckert 2012) and Ti-in-zircon (Bloch et al. 2022). Therefore, it is essential to assess the utility and effectiveness of the Ti-in-amphibole thermometer in high-grade metamorphic terranes up to UHT conditions.

Geological background and sampling

The IVZ (NW Italy) is a well-preserved section of the Carboniferous-Permian continental crust (e.g. Zingg et al. 1990; Quick et al. 1995) that was attenuated during the Mesozoic rifting of the Adriatic microcontinent (e.g. Henk et al. 1997; Handy et al. 1999; Smye and Stockli 2014; Ewing et al. 2015) and tilted during the Alpine collision (Handy et al. 1999; Rutter et al. 2007; Siegesmund et al. 2008; Wolff et al. 2012). The IVZ belongs to the South Alpine domain and it is juxtaposed against the Sesia Zone by the Cenozoic Insubric Line to the NW (Fig. 5). Towards the SE, the IVZ is separated from the upper crust of the Strona-Ceneri Zone by the late-Variscan Cossato-Mergozzo-Brissago Line (CMB) and, in places, the Triassic-Jurassic Pogallo Line (PL) (Schmid et al. 1987; Boriani et al. 1990; Zingg et al. 1990).

The IVZ is composed of ultramafic rocks (Balmuccia and Finero peridotites), the Mafic Complex and the Kinzigite Formation (Fig. 4; see Schmid and Wood 1976; Zingg 1983; Schmid 1993; Quick et al. 2003). The Mafic Complex consists of gabbros, diorites and norites (Rivalenti et al. 1975; Voshage et al. 1990; Mazzuchelli et al. 1992; Sinigoi et al. 1991, 1994) which underplated the lower crustal rocks of the Kinzigite Formation during the Permian (c. 282–286 Ma), coevally with the granitic magmatism and acid volcanism in the upper crust (Peressini et al. 2007; Karakas et al. 2019). Within the Mafic Complex, Sinigoi et al. (1996) identified the “paragneiss-bearing belt”, consisting of metapelitic slivers (septa) derived from the Kinzigite Formation and incorporated into the Mafic Complex.

Fig. 4

Geological overview map of the Ivrea-Verbano Zone (redrawn after Kunz and White 2019)

The Kinzigite Formation consists of interlayered metapelites and metabasites with subordinate metapsammites, calcsilicates and marbles (Bertolani 1968; Schmidt 1993) and is best exposed in Val Strona di Omegna (Fig. 4). Here, the Kinzigite Formation has been subdivided from SE to NW into three sections on the basis of the metamorphic grade (Fig. 5a): an amphibolite facies zone, a transition zone and a granulite facies zone (Bea and Montero 1999; Redler et al. 2012). The upper and lower boundary of the transition zone is marked by Opx-in and Ms-out isograds in metabasite and metapelite, respectively (mineral abbreviations after Whitney and Evans 2010). The appearance of clinopyroxene in metabasic rocks (Cpx-in) occurs close to the Ms-out isograd in metapelites (Fig. 5a). The sequence displays a continuous metamorphic field gradient (Fig. 5b) perpendicular to the dominant planar fabric, with metamorphic conditions ranging from mid-amphibolite facies (≈ 650 °C, ≈ 5 kbar) in the SE to granulite facies (> 900 °C, ≈ 10 kbar) in the NW, adjacent to the Insubric Line (e.g., Schmid and Wood 1976; Sills 1984; Henk et al. 1997; Luvizotto and Zack 2009; Redler et al. 2012, 2013; Ewing et al. 2013; Kunz and White 2019). The highest temperatures (> 1000 °C) for IVZ crustal rocks have been recorded by rutile of metapelitic septa (Ewing et al. 2013; Pape et al. 2016).

Fig. 5

(a) Schematic map of Val Strona di Omegna, redrawn after Redler et al. (2012). Colored stars mark the position of rock samples for which temperature estimates were calculated (literature data from: Henk et al. 1997; Bea and Montero 1999; Luvizotto and Zack 2009; Redler et al. 2012; Ewing et al. 2013; Kunz et al. 2018; Kunz and White 2019; Wyatt et al. 2022). FRSZ: Forno-Rosarolo shear zone (from Simonetti et al. 2023) (b) Metamorphic field gradient for Val Strona di Omegna (KW19) based on peak mineral assemblage fields from metabasic and metapelitic rocks (redrawn from Kunz and White 2019)

Regional amphibolite to granulite facies metamorphism likely started at c. 310–320 Ma (Ewing et al. 2013; Williams et al. 2022; Wyatt et al. 2022) and was followed by an extended period (> 40 Ma) of HT conditions (Vavra et al. 1999; Ewing et al. 2013; Kunz et al. 2018). The HT to UHT metamorphism was accompanied by widespread anatexis and formation of metatexite to diatexite migmatites (e.g., Schnetger 1994; Barboza and Bergantz 2000; Barboza et al. 1999; Redler et al. 2012, 2013; Kunz et al. 2014; Carvalho et al. 2019, 2020; Bartoli and Carvalho 2021; Kunz and White 2019).

After the post-orogenic extension during the Permian, the IVZ experienced multiple episodes of rifting during the Triassic-Jurassic (e.g., Henk et al. 1997; Rutter et al. 2007; Smye et al. 2019). Crustal thinning was accommodated by several shear zones (e.g., Brodie et al. 1987; Siegesmund et al. 2008; Corvò et al. 2022; Simonetti et al. 2023).

Field and petrographic features of metapelitic, metapsammitic and metabasic rocks from Val Strona di Omegna have been extensively described in several papers –among the others Bertolani (1964a, b, c) Bertolani (1968); Bertolani and Rivalenti (1966); Zingg (1980); Redler et al. (2012, 2013); Kunz et al. (2014); Kunz and White (2019); Carvalho et al. (2019, 2020, 2023a); Simonetti et al. (2023), to which the interested reader is referred. In this study, seven metabasic rocks were collected for the application of Ti-in-amphibole thermometer (STR105 and STR133 from amphibolite facies zone, STR82, STR86 and STR116 from transition zone, STR130 and STR120 from granulite facies zone; Fig. 5a) and are briefly described below. Metabasites from Val Strona di Omegna were interpreted as former basalt injections into an accretionary sedimentary wedge (Sills and Tarney 1984; Mazzuchelli and Siena 1986) and were geochemically classified as N-MORB and E-MORB.

Field relationships and petrography

Samples STR105 and STR133 were collected in the amphibolite facies zone; they are fine-grained, weakly foliated rocks (Fig. 6a), where the foliation is mostly defined by amphibole and, to a lesser extent, by intergrowths of biotite and amphibole. The mineral assemblage is composed of green hornblende, plagioclase, quartz and biotite (Fig. 7a, b). Rock STR133 also contains garnet crystals with mineral inclusions of amphibole, plagioclase and quartz. Accessory minerals include titanite, ilmenite, zircon, apatite and pyrite. These samples lack field evidence and microstructures indicative of partial melting.

Fig. 6

Field aspect of metabasic rocks from the Kinzigite Formation, Val Strona di Omegna. (a) Fine-grained metabasic rock STR105 from the amphibolite facies zone. (b) Partially-melted amphibolite STR82 from the transition zone showing segregation of patchy leucosomes. Mafic selvedges of amphibole can be present at the contact between the leucosome and the matrix (yellow arrows). (c) Close-up of (b), showing a patchy leucosome made of pale green clinopyroxene (yellow arrow), quartz and plagioclase. (d) Close-up of (b), showing amphibole-rich mafic selvedges (yellow arrows) around leucosome segregation. The size of amphibole clearly decreases from the selvedge to the matrix. (e-f) Granulite facies metabasic rocks STR130 and STR120, respectively, ranging from metatexite (e) to diatexite (f)

Fig. 7

Photomicrographs of metabasic rocks from the Kinzigite Formation, Val Strona di Omegna. (a,b) Amphibolite facies samples STR105 and STR133 containing lepidoblastic amphibole. (c) Sample STR116 from the transition zone with the mineral assemblage amphibole, biotite, quartz, plagioclase and ilmenite. (d) Sample STR82 from the transition zone where mafic selvedges composed of coarse-grained amphibole were developed at the contact between leucosome and the rock matrix (area bounded by dashed light blue lines). The leucosome is composed of coarse-grained quartz, plagioclase and clinopyroxene. Red area: figure (e). (e) Close-up of (d) showing the transition from brown to green amphibole at the contact with leucosome; plagioclase is strongly altered. Plane polarized light (upper portion) and crossed polars (lower portion). Red square: area of Fig. 11. (f) Brown to green amphibole in a mafic selvedge of STR82; plagioclase and clinopyroxene from leucosome are strongly altered. Dashed light blue line: boundary between mafic seldvedge and leucosome (g, h) Mafic granulites STR130 and STR120 with the mineral assemblage amphibole, garnet, clinopyroxene, orthopyroxene, quartz and ilmenite; yellow arrows: inclusion of amphibole in garnet; white arrow: triple junction between two clinopyroxene crystals and amphibole. (i) Biotite overgrowths replacing amphibole rim; sample STR130

In the field, rocks from the transition zone (STR116, STR82 and STR86) are characterized by the appearance of elongated (few centimeters long) patches of leucosome, subparallel to the foliation, containing quartz, plagioclase and pale green peritectic clinopyroxene (Fig. 6b, c). The latter often shows rational crystal faces against the leucocratic matrix (Fig. 6c), suggesting its formation in the presence of melt (Sawyer 2008). The mineral assemblage is composed of hornblende (mostly green and brown in STR116 and STR86, respectively), clinopyroxene, plagioclase and quartz with rare biotite (Fig. 7c, d). Accessory minerals are ilmenite, zircon and apatite. In places, mafic selvedges composed of coarse-grained amphibole develop around leucocratic patches (Fig. 6b, d, and 7d-f). In sample STR82, plagioclase, and clinopyroxene in leucosome are often partially altered and replaced by fine-grained mineral aggregates (Fig. 7d-f), whereas the selvedge-forming amphibole shows a change in color from brown to green towards the contact with leucosome (Fig. 7e, f).

Rocks from granulite facies zone (STR130 and STR120) are granoblastic with evident millimeter- to centimeter-sized porphyroblasts of garnet, clinopyroxene and orthopyroxene (Fig. 6e, f). The mineral assemblage also contains hornblende, plagioclase, quartz, minor biotite and accessory ilmenite, apatite and pyrite. Last remnants of hornblende occur included in garnet along with quartz or are scattered in the matrix (Fig. 7g, h); in the latter textural setting, amphibole rim is often overgrown by tiny (0.1–0.2 mm) biotite crystals (Fig. 7i).

Methods

Major element compositions of amphibole were analysed using a JEOL JXA 8200 Superprobe at the Dipartimento di Scienze della Terra, Università di Milano, Italy. The operating conditions for WDS were 5 nA beam current, 15 kV accelerating voltage, counting time of 30s on peak and 10s on background. Natural minerals and synthetic oxides used for calibration are: omphacite (Na), grossular (Al, Si, Ca), fayalite (Fe), rodonite (Mn), K-feldspar (K), olivine (Mg), ilmenite (Ti), scapolite (Cl), Cr2O3 (Cr). Detection limits (1s) were ca. 0.01 wt% for Al, K and Ca, 0.02 wt% for Mg, Si, Na and Cl, 0.03 wt% for Cr, Fe, Ti, Mn. Ti measurements have a precision between ± 8–16% (2σ). Backscattered electron imaging (BSE) and X-ray elemental maps were obtained with a TESCAN SOLARIS dual beam FIB-FE-SEM available at the Dipartimento di Geoscienze, Università di Padova, Italy. Chemical maps were obtained with the Ultim max 65 Oxford Instrument silicon drift EDS, at working conditions of: 10 nA beam current, 15 kV acceleration voltage and 1 μm beam diameter. The amphibole formulas were calculated using the spreadsheets available in Ridolfi et al. (2018), on the basis of 23 oxygens.

Rock samples were crushed and then powdered in a tungsten ring mill. The major element composition of the samples was obtained by X-ray fluorescence (XRF) with a Panalytical Zetium spectrometer at the Dipartimento di Geoscienze, Università di Padova, using international rock standards (Govindaraju 1994). Absolute uncertainties in XRF analyses are in the range of 0.5 wt% (2σ) for major elements such as SiO₂ to < 0.01 wt% for minor elements.

Results

Bulk rock composition

Investigated rocks show SiO₂ contents ranging between 44 and 51 wt% and Na₂O + K₂O between 1.3 and 3.8 wt%, belonging to the subalkaline series, with Mg# between 0.3 and 0.5 (Table S1). In the ACF compatibility diagram, they plot in the field of common mafic rocks (Fig. S1). Bulk rock compositions are variable and no systematic trends were observed in major elements across the Kinzigite Formation, except for SiO₂ which decreases with increasing metamorphic grade (Fig. S2). TiO₂ varies between 1.00 and 3.31 wt%, with sample STR82 showing the lowest TiO₂ content (1.00 wt%), while other samples from the transition zone have TiO₂ between 2.5 and 2.8 wt%. In terms of trace elements, sample STR82 is strongly depleted in Zr (56 ppm) compared to other metabasites (150–289 ppm). Ni and Cr contents are much higher in STR116 and STR82 (217–256 ppm and 490–578 ppm, respectively) than the other samples (24–65 ppm and 17–74 ppm, respectively).

Amphibole composition

A total of 358 analyses of amphibole were obtained from the seven selected samples and they are listed in supplementary Table S2. All analyzed grains are classified as calcium amphibole, with Si = 6.1–7.8 apfu, Ca = 0.9–2.0 apfu and Mg# = 0.41–0.76 and are plotted in Fig. 8. A compositional variation is observed across the crustal sequence, with magnesio-hornblende typical in amphibolite facies rocks, magnesio-hornblende to pargasite in the transition zone and pargasite to sadanagaite in granulite facies zone (Fig. 8a). Analyses from each sample are clustered together, with the exception of rock STR82 where the composition of amphibole spreads out over a wide range, pointing toward the tremolite-hornblende boundary (Fig. 8a). Importantly, amphiboles from amphibolite facies rocks have a lower occupancy of the A-site compared to those from other samples. Consequently, they define a different trajectory in the compositional space of Fig. 8a.

Fig. 8

(a) Classification of calcium amphibole from the investigated rocks, based on Hawthorne et al. (2012). (b) Si vs. Ti diagram of studied amphiboles with the boundaries for high amphibolite facies (HAM), high-temperature granulite facies (HT-GR) and ultrahigh temperature granulite facies (UHT) proposed by Liao et al. (2021). The temperatures inferred for HAM, HT-GR and UHT fields are 680–800, 800–900 and > 900 °C, respectively (more details in Liao et al. 2021). Analytical uncertainties (2σ) related to the counting statistics were propagated through the mineral recalculation following De Angelis et al. (2013) and are reported for some representative analyses (black bars). The uncertainty is smaller than the symbol for the lowest Ti contents

In the dataset, the TiO₂ content ranges from 0.14 to 3.76 wt% (Ti = 0.015–0.426 apfu) and increases with increasing metamorphic grade (Figs. 8b and 9). The highest Ti values in each sample increases from amphibolite (0.125–0.147 apfu), to transition (0.152–0.210 apfu), up to granulite facies (0.393–0.426 apfu) (Fig. 9). The lowest Ti contents are found in samples STR133 and STR82 from amphibolite facies and transition zones, respectively. The lowest Ti values found in granulites overlap with the highest ones in transition zone rocks (Figs. 8b and 9). Liao et al. (2021) proposed to utilize the diagram Si vs. Ti to roughly discriminate metamorphic facies on the basis of amphibole composition. Adopting their compositional fields for the high amphibolite facies (HAM) and the granulite to ultrahigh granulite facies (HT-GR and UHT), respectively, amphiboles from STR105, STR133 and STR82 plot within the HAM field, the majority of those from STR120 and STR130 in the UHT field, whereas those from STR86 within the overlapping area between HAM and HT-GR (Fig. 8b). The analyzed grains from rock STR116, instead, straddle the boundaries between HT-GR and HAM amphiboles.

Fig. 9

Box and whisker plots of the Ti content of amphibole and calculated temperatures for metabasites across the Val Strona di Omegna. Data were grouped on the basis of their textural setting; Rim(Bt): amphibole rim characterized by the presence of biotite overgrowths; selv./leucos.: rim of selvedge-forming amphibole at the contact with leucosome. Black vertical bars show the error (2σ) inherent in the calibration at 600 and 900 °C, respectively

All the analyzed amphiboles display a distinct positive correlation between Na and K content on the A-site [(Na + K)^A] and tetrahedral Al, indicating edenite substitution (Fig. 10a). Overall, the Ti concentrations increase with increasing Al^IV, which could indicate the operation of the Ti–Tschermak substitution (Fig. 10b). However, an exception to this general behavior is represented by the amphiboles from granulites, where the Ti content varies between 0.2 and 0.4 apfu at constant values of Al^IV (ca. 1.75 apfu). Additionally, in this plot STR82 clearly defines a separate trend with respect to other rocks. In the Al^IV-Al^VI plot of Fig. 10c, amphiboles from rocks STR82 and STR105 define a positive linear trend, which indicates Al–Tschermak substitution in these samples.

Fig. 10

Compositional variation in amphiboles. (a) A-site occupancy vs. tetrahedral aluminum (Al^IV). (b) titanium vs. Al^IV. (c) octahedral aluminum (Al^VI) vs. Al^IV. Symbols as in Fig. 8

The internal variability of Ti in amphibole from individual rock samples varies from small (ΔTi = 0.045 apfu; STR86) to large (ΔTi = 0.082 and 0.142 apfu; STR133 and STR82) (Fig. 9). In granulite samples, the Ti concentrations varies with the textural position, with amphibole rims that generally show lower Ti values when overgrown by Ti-rich biotite (TiO₂ = 4.7–5.2 wt%) (Fig. 9). In sample STR82, Ti systematically decreases from core of matrix grains to selvedge-forming amphiboles, with the lowest values found approaching the selvedge-leucosome boundary (Fig. 9). This is evident in the X-ray elemental maps reported in Fig. 11, documenting a sharp compositional variation between amphibole interior and rim. The latter is depleted in Ti, Al, K and Na, and enriched in Mg and Si when in contact with altered leucosome.

Fig. 11

BSE image and elemental EDS X-ray maps of amphibole from a mafic selvedge of sample STR82. The investigated area is represented by a red square in Fig. 7e. The portion of amphibole in contact with the leucosome is depleted in Ti, K, Al and Na (not shown), and enriched in Mg and Si (not shown). Similar compositional variations occur also in the grain interior and are associated to the presence of fractures (white arrows). A quantitative EMP concentration profile of Ti is reported on the BSE image together with the Ti-in-amphibole temperatures calculated for the highest and lowest Ti contents, respectively

Ti-in-amphibole temperatures

The temperature recorded by amphibole in each sample has been calculated applying the equation proposed by Liao et al. (2021) and the estimates are reported in Table S2. In all the investigated rocks, amphibole coexists with a Ti-phase (titanite and/or ilmenite) randomly distributed across the sample, whose presence is critical to obtain reliable temperature using this thermometer. Titanium measurements have a precision of ± 8–16% (2σ), which contributes an additional uncertainty of ± 5–30 °C over the compositional range investigated in this study.

The average temperatures in each sample range from 632 to 706 °C (amphibolite facies), 655 to 773 °C (transition) and 885 to 890 °C (granulite-facies) (Fig. 9). The widest temperature variability is observed in rock STR82 from the transition zone.

When the textural setting of the amphibole is considered for this sample, three temperature peaks are observed: ≈770 °C (average temperature) for amphibole in the matrix, ≈ 710 °C for amphibole forming mafic selvedges and ≈ 525 °C for portions of amphibole in mafic selvedges at the very contact with leucosome (Fig. 9). In the latter textural setting, the lowest Ti content of 0.015 apfu corresponds to a temperature of ≈ 450 °C (Figs. 9 and 11). In granulites, similar average temperatures of ≈ 900 °C are obtained from the two investigated samples; when amphibole rim is overgrown by biotite, the calculated temperatures decrease to ≈ 830 °C (the lowest temperature value is 785 °C) (Fig. 9).

Discussion

Conventional thermobarometry, phase equilibria modelling and quadrivalent (4+) cation thermometry have been all applied along the continuous metamorphic field gradient exposed in Val Strona di Omegna over the last 40 years (e.g., Henk et al. 1997; Bea and Montero 1999; Redler et al. 2012; Ewing et al. 2013; Kunz et al. 2018; Luvizotto and Zack 2009; Kunz and White 2019). In this study, we firstly focus on the significance (i) of the Ti contents measured in amphibole from IVZ metabasic rocks and (ii) of the temperatures obtained by Ti-in-amphibole thermometry. Secondly, we use all the thermometric constraints available from the Val Strona di Omegna to compare how the different thermometers perform across this crustal section, focusing in particular on granulite facies rocks. We then focus on other UHT terranes to better understand the fidelity of Ti-in-amphibole thermometry under extreme crustal conditions. Lastly, potential implications for Ti diffusivity in amphibole are discussed.

Significance of Ti content of amphibole and calculated temperatures

The positive correlation observed for amphibole composition in Ti vs. Al^IV and (Na + K)^Avs. Al^IV plots and the increase of these compositional values with increasing metamorphic grade (Fig. 10a, b) are consistent with the well-known effect of temperature on the Ti-Tschermak and edenite exchange vectors (e.g., Spear 1981; Holland and Blundy 1994). Additional substitution occurs in samples STR82 and STR105 via Al-Tschermak exchange vector (Fig. 10c), which is pressure-dependent (Hollister et al. 1987; Thomas and Ernst 1990; Schmidt 1992). However, another substitution mechanism appears to play a role in the HT amphiboles. This is the Ti-oxy substitution, in which the dehydrogenation is accompanied by substitution of one divalent cation in the M (1) site by Ti⁴⁺ (King et al. 1999). This exchange mechanism would explain the lack of a clear correlation between Ti and Al^IV in amphibole from granulites (Fig. 10b). However, a more precise assessment of the importance of the Ti-Tschermak and Ti-oxy substitutions requires direct measurements of H and Fe³⁺ contents in amphibole.

Composition of calcic amphibole is sensitive to temperature, pressure, fO₂ and bulk composition. To evaluate the control exerted by the composition of the bulk system, amphibole compositions are compared with the composition of host rocks (Fig. 12). Notably, the composition of amphibole from rock STR82 is markedly different from that of amphiboles from the other rocks in the transition zone (i.e. STR116 and STR86), with the former showing the highest Mg# and the lowest Al₂O₃ and Na₂O + K₂O values (Fig. 12). These chemical features are partially controlled by the composition of the bulk rocks. In fact, sample STR82 shows the highest Mg# and CaO content of the dataset, but its Al₂O₃ content is similar to the values exhibited by the other rocks. Regarding TiO₂, rock STR82 shows the lowest content, a feature that is reflected by the composition of some of their amphiboles having TiO₂ < 0.5 wt%. (Fig. 12). However, no systematic trends between rock and amphibole compositions are recognizable for Ti in all the other samples. For instance, amphiboles from granulites STR130 and STR120 show similar TiO₂ contents, despite a markedly different bulk rock composition (3.3 vs. 1.6 wt% TiO₂, respectively) (Fig. 12). The Ti content of amphibole seems to be mainly buffered by the presence of a Ti-phase (ilmenite, rutile, titanite), even though a control of the bulk rock TiO₂ content cannot be excluded for amphibole grains from rock STR82 (Fig. 12).

Fig. 12

Compositional variations of amphiboles and bulk rocks. Small symbols as in Fig. 8b

The application of the Ti-in-amphibole thermometry in this study shows increasing temperatures matching the increasing metamorphic grade (Fig. 9). The highest temperatures (850–980 °C; average ≈ 900 °C) for granulites are those calculated for amphibole from the rock matrix and for grains included in garnet (Fig. 7). Much lower temperatures (average ≈ 830 °C, but up to 785 °C) are instead recorded by amphibole rims overgrown by small Ti-rich (TiO₂ = 4.7–5.2 wt%) biotite crystals (Fig. 9). Since these microstructures are the result of retrograde reactions, the temperature range of ≈ 785–850 °C suggests that resetting of the Ti-in-amphibole thermometer likely occurred in the presence of melt, as supported by field and petrographic observations (see above). Therefore, the newly formed biotite can be interpreted as product of retrograde reactions between residual amphibole and anatectic melt, where the former provided Fe, Mg and Ti and the latter K. Although leucosomes in metabasites are dominated by quartz, plagioclase and clinopyroxene, reflecting a K-poor tonalitic composition, the injection of K-bearing leucosomes from the adjacent metapelites has been well documented in IVZ metabasites (Harlov and Förster 2002; Kunz et al. 2014).

The three samples from the transition zone mostly yielded temperatures between ≈ 740 and ≈ 800 °C (Fig. 9), even though the widest temperature range (≈ 300 °C) of the dataset presented in this study was found in sample STR82. This sample also records the lowest temperature of this crustal section (≈ 450 °C). Temperatures from amphibole core in the matrix of STR82 (≈ 760–810 °C) are likely to be related to the prograde to peak evolution, being similar to those documented in the nearby sample STR86 (Fig. 9).

Amphibole-rich selvedges in mafic migmatites are interpreted to form by reaction between a leucosome and its wallrocks during melt crystallization, similar to the biotite-rich ones in metapelitic migmatites (Sawyer 2008). Temperatures of 680–750 °C provided by amphibole in the selvedge (Fig. 9) would be consistent with such a process occurring in the presence of melt. However, the portions of amphibole grains directly in contact with leucosome are commonly depleted in Ti and provide much lower temperatures (≈ 450–600 °C; Figs. 9 and 11), which are not consistent with suprasolidus conditions. It should be noted that (i) these temperatures are lower than those for which the Ti-in-amphibole thermometer was calibrated (≥ 700 °C) and (ii) we do not know if this portion of amphibole was in equilibrium with a Ti-saturating phase during its formation/modification. Although caution should be used when interpreting these temperature values, the detailed microstructural and microchemical characterization clearly indicates that amphibole composition has been modified (Figs. 7d-f, 9 and 11).

Leucosome in sample STR82 shows clear evidence of hydration after crystallization, with retrograde fine-grained sericite and chlorite replacing plagioclase and clinopyroxene, respectively (Figs. 7d-f and 11). Several lines of evidence testify for retrograde fluid influx across IVZ crustal section (e.g., Boriani and Villa 1997; Vavra et al. 1999; Franz and Harlov 1998; Luvizotto and Zack 2009; Ewing et al. 2013; Smye et al. 2019) and the origin of these fluids has been ascribed to the Permian post-magmatic exsolution following the crystallization of the Mafic Complex (e.g., Ewing et al. 2013) and/or to the Triassic to Jurassic lithospheric thinning and rifting (e.g., Ewing et al. 2015; Langone et al. 2017; Smye et al. 2019). Interestingly, Smye et al. (2019) argued that IVZ underwent local fluid infiltration when temperature was ≈ 500 °C during Tethyan extension. Such subsolidus temperatures are consistent with the ones reported by sample STR82 in this study.

The compositional change toward the rim of amphibole in the selvedge is quite sharp and did not occur steadily (Fig. 11). Moreover, a similar depletion in Ti, K and Al is also present in amphibole interior in the form of crosscutting veins (white arrows in Fig. 11). These textures exclude the possibility of Ti diffusion out of amphibole during cooling. Rather, we interpret the composition of amphibole rim in contact with altered leucosome of rock STR82 to have been modified by fluid-rock interaction. Fluid percolation was mostly confined within near-leucosome portions probably due to the larger grain size compared to the surrounding matrix (Figs. 6c and 7d), which enhances porosity. Moreover, self-generated transient fluid pathways are likely to form in feldspar-rich portions of rocks undergoing fluid-mediated alteration, enhancing mineral transformation reactions (Plumper et al. 2017).

Textures associated to rutile replacement in IVZ metapelites are considered to support that Ti and Zr, frequently interpreted to be immobile elements, can be significantly mobilized by hot fluids (Luvizotto and Zack 2009; and discussion therein). Our results indicate that Ti mobilization was not solely confined to metapelites, but it likely involved other lithologies. Noteworthy, Harlov et al. (2006) documented newly-formed titanite rims in metabasites of Val Strona di Omegna, interpreted as result of fluid-assisted mass transport. Bulk rock analyses support this view, as rock STR82 shows much lower contents of TiO₂ and Zr compared to other metabasites (Table S1).

Performance of different thermometers across the central Ivrea–Verbano Zone

Figure 13a shows a comparison between published thermometric constraints from metapelites, metagreywackes and metabasites across the section of Val Strona di Omegna with Ti-in-amphibole temperatures presented in this study. Temperatures provided by each sample are plotted as a function of metamorphic grade, against distance from the Insubric Line. Rutile temperatures have been recalculated using the equation recently proposed by Kohn (2020) and the Zr contents reported by Luvizotto and Zack (2009) and Ewing et al. (2013). To avoid the strong resetting of the Zr content, Luvizotto and Zack (2009) suggested to select exclusively values above the 90th percentile in each sample. We followed this suggestion and considered lower values as reset temperatures (dashed portion of red bars in Fig. 13a). Similarly, temperature values provided by Ti-in-amphibole thermometry for selvedge-forming amphibole in sample STR82 and for amphibole rims in contact with retrograde biotite in granulites STR130 and STR120 are not considered.

Fig. 13

(a) Temperature constraints obtained from different thermometers across the IVZ crustal sequence. Location of samples was projected onto a linear transect of Val Strona di Omegna. Conventional thermometry is from Henk et al. (1997) and Bea and Montero (1999). P–T pseudosection constraints are from Redler et al. (2012), Kunz and White (2019) and Wyatt et al. (2022). Rutile data are from Luvizotto and Zack (2009) and Ewing et al. (2013), recalculated considering the equation proposed by Kohn (2020); a pressure of 8 kbar was commonly used, with the exception of the highest-grade sample (9 kbar). Ti-in-zircon temperatures are from Ewing et al. (2013) and Kunz et al. (2018). FRSZ: Forno-Rosarolo shear zone (temperature estimates from Simonetti et al. 2023). Amphibole thermometry is from this study. Dashed lines correspond to the in-field location of the extrapolated mineral isograds (from Redler et al. 2012). The hatched area in colored bars reflects cooling or reset temperatures recorded in rutile and amphibole grains. Hatch lines below some vertical bars reflect extension to lower temperatures due to the mismatch between textural observations and phase equilibria modeling. (b) Histograms showing frequencies of temperature estimates obtained by Ti-in-amphibole (green) and Zr-in-rutile (red) thermometers on mafic and pelitic IVZ granulites, respectively. Green and red curves reflect Kernel Density Estimation (KDE) of calculated temperatures. The grey area marks the temperature estimates obtained for metapelitic septa within the Mafic Complex (data from Ewing et al. 2013; Pape et al. 2016)

In comparing all temperature ranges reported in Fig. 13a, it is worth recalling that diverse thermometric techniques suffer from different uncertainties. The calibration uncertainties (2σ) for quadrivalent (4+) cation thermometry are usually < ± 30 °C, with the exception of Ti-in-amphibole thermometer (± 70 °C; Table 1). Regarding the error associated to analytical uncertainties, Ewing et al. (2013) reported values of ± 15–25 and ± 10–20 °C for Zr-in-rutile and Ti-in-zircon thermometers, respectively, applied to IVZ rocks. These uncertainties are similar to those calculated in this study considering the analytical error in the determination of Ti content in amphibole (± 5–30 °C; Table 1). Values of ± 50 °C are commonly reported as uncertainties associated to conventional thermometry and P–T pseudosections (Powell and Holland 2008; Green et al. 2016). For the latter, however, it should be noted that quantifying uncertainties is still a challenge due to the absence of reliable calculations dealing with error propagation through thermodynamic databases and models.

Table 1 Examples of uncertainties reported for single-mineral thermometers

For IVZ granulites, Ti-in-amphibole thermometry yields peak temperatures from 850 to 980 °C (≈ 900 °C on the average), matching those obtained from P–T pseudosections as well as the highest values provided by Zr-in-rutile thermometer (Fig. 13a). Temperatures > 1000 °C reported for a single mafic granulite on the basis of phase equilibria modelling (Kunz and White 2019) are not supported by other thermometric techniques (Fig. 13a).

Rutile in IVZ metapelites is expected to form at > 850 °C (see detailed modelling and discussion in Luvizotto and Zack 2009; Carvalho et al. 2023a). However, temperatures obtained by Zr-in-rutile thermometer across the entire granulite zone are in the range of 600 to 975 °C, significantly lower than temperatures provided by Ti-in-amphibole thermometry and phase equilibria modeling for granulite rocks (Fig. 13a). All the studies on IVZ rutile have reported microstructural evidence suggesting post-peak resetting of Zr concentrations (Luvizotto and Zack 2009; Ewing et al. 2013; Pape et al. 2016). Ewing et al. (2013) discussed in detail all the possible ways of modifying Zr concentrations of rutile and concluded that recrystallization (i.e., dissolution-reprecipitation) under retrograde conditions was the most likely process to explain resetting of the thermometer at ≈ 700–800 °C. These values match most of the temperatures of zircon crystallization from anatectic melt in pelitic granulite (Fig. 13a; see below), reinforcing the view that rutile partly recrystallized in the presence of melt at ≈ 700–800 °C (Fig. 13b). On the other hand, Luvizotto and Zack (2009) also documented rutile veinlets associated with textures suggesting post-peak influx of fluid in IVZ granulites. Therefore, the lowest (< 700 °C) Zr-in-rutile temperatures likely reflect late resetting of Zr content in rutile in the presence of a fluid phase rather than melt (Fig. 13b).

The lowest temperatures documented by Zr-in-rutile thermometry for IVZ granulites (650–750 °C) are also recorded by Ti-in-zircon thermometer (Fig. 13a). In the detailed study of Kunz et al. (2018) on IVZ zircons, these authors argued that CL-textures are in most cases not disturbed by fluid alteration and that the scatter observed in the Ti-in-zircon temperatures is likely to reflect different growth periods. This interpretation is reinforced by the Ti distribution within analyzed zircons in granulite with only a single datapoint indicating a temperature < 670 °C (see Fig. 7b in Kunz et al. 2018). The absence of Ti-in-zircon temperatures which are as high as those recorded by Ti-in-amphibole and Zr-in-rutile thermometers (≈ 900–980 °C) are most probably due to the fact that zircon only starts crystallizing at lower temperatures (≈ 650–850 °C; Ewing et al. 2013; Klötzli et al. 2014). However, the lowest Ti-in-zircon temperatures from the amphibolite facies and transition zones (≈ 550–650 °C) are incompatible with crystallization from a melt. Excluding a dissolution-reprecipitation process in the presence of a fluid phase on the basis of textures of investigated zircons, Kunz et al. (2018) consider these low temperature values as an artifact resulting from erroneously considering a_TiO2=1 in the calculation of Ti-in-zircon temperatures in a sample containing no rutile.

In amphibolite and transition zones, Ti-in-amphibole thermometry yields temperature estimates that are consistent with those obtained by phase equilibria modelling (Fig. 13a). On the contrary, conventional thermometry based on Fe–Mg exchange thermometers (Bt-Grt and Grt-Opx pairs; Henk et al. 1997; Bea and Montero 1999) provided significantly lower temperatures than those yielded by other techniques for near peak conditions across the entire crustal sequence (Fig. 13a), as result of the retrograde resetting of mineral compositions during slow cooling (Frost and Chacko 1989; Pattison et al. 2003).

Effectiveness of Ti-in-amphibole thermometry in UHT rocks

Since thermometry is a crucial tool to identify the mechanisms which generate UHT metamorphism, the validation of any new thermometric technique at these extreme crustal conditions is of paramount importance. Clark et al. (2019) reported a comparative study among different thermometers applied to a single UHT metapelitic sample from the Rauer Group, East Antarctica. These authors concluded that the most reliable estimates of peak UHT temperature are provided by Al-in-orthopyroxene thermometry.

The present work is mostly focused on ilmenite-bearing metabasites and an important finding is that Ti-in-amphibole thermometer seems to be more robust in recording peak near-UHT conditions, compared to Zr-in-rutile thermometry applied to coexisting pelitic granulites (Fig. 13). Despite the fact that some mafic and pelitic samples were collected from the same outcrop (Fig. 5a), Zr-in-rutile thermometer in metapelite records lower temperatures and thus resulted to be more prone to post-peak resetting compared to Ti-in-amphibole thermometry in metabasite (Fig. 13a). This is evident from Fig. 13b, where Ti-in-amphibole temperatures collectively show a single peak at ≈ 900 °C, whereas Zr-in-rutile thermometer is characterized by a bimodal distribution of temperatures, with two well-defined peaks at ≈ 860 and ≈ 730 °C. Temperatures of 850–900 °C for IVZ granulites are consistent with the geological and petrological scenario of the crustal section of Val Strona di Omegna where these rocks are not in direct contact with the Mafic Complex (Figs. 4 and 5). When metapelite slices are instead intermingled with gabbro of the Mafic Complex (i.e., the metapelitic septa of Val Mastallone and Valsesia; Fig. 4), the recorded temperatures are higher (950–1150 °C; Fig. 13b).

The bimodality of Zr-in-rutile temperatures reported for IVZ rocks with a well-defined temperature mode around 700–800 °C (Fig. 13b; see also Ewing et al. 2013) has been documented in many UHT terranes worldwide (see compilation in Kelsey and Hand 2015; Harley 2021), suggesting that dissolution-reprecipitation of rutile in the presence of residual melt may be a common process in granulite. For instance, in rocks from the Lützow-Holm Complex (East Antarctica) Carvalho et al. (2023b) reported lower temperatures for rutile grains trapped and re-equilibrated within former melt inclusions; instead, UHT conditions are better recorded by rutile within garnet and in the rock matrix. Mitchell and Harley (2017) documented a complete resetting of Zr-in-rutile temperatures in UHT granulites from Napier Complex (Antarctica) to ≈ 600–750 °C. In this case, the dissolution of rutile and mobility of Zr were attributed to saline fluid infiltration. This reinforces the importance of having alternative techniques (such as Ti-in-amphibole thermometer) to validate the achievement of extremely hot crustal conditions.

To better evaluate the effectiveness of Ti-in-amphibole thermometry at UHT, we compiled a dataset of amphibole analyses from four localities where UHT conditions were documented (Fig. 14): the Rauer Group in East Antarctica, the Madurai Block in southern India, the Highland Complex of Sri Lanka and the lower continental arc crust beneath the Northern Volcanic Zone in Colombia. The calculated temperatures for amphibole grains interpreted as part of peak mineral assemblage in metabasites were compared (i) with those recorded by Zr-in-rutile and/or Al-in-orthopyroxene thermometry in nearby UHT metapelites (Fig. 14a-c) or (ii) with results of elastic geothermobarometry and phase equilibria modelling from the same sample (Fig. 14d). This comparison supports what is already shown by the IVZ data: Ti-in-amphibole technique seems to be a more faithful recorder of UHT conditions compared to Zr-in-rutile thermometry from coexisting pelitic granulites. The latter may return significantly lower temperature estimates, up to ≈ 650 °C in granulites from Rauer Group, East Antarctica (Fig. 14a) and it is fundamental to use the least reset rutile Zr concentrations in order to constrain peak UHT conditions (Fig. 14a, b).

Fig. 14

Compilation of thermometric estimates from Rauer Group, East Antarctica (a), Madurai Block, southern India (b), Highland Complex, Sri Lanka (c) and Northern Volcanic Zone, Colombia (d). Ti-in-amphibole temperatures were obtained applying the calibration of Liao et al. (2021) and using amphibole compositions from the literature. Zr-in-rutile temperatures were recalculated considering the equation proposed by Kohn (2020) and Zr content of rutile and pressure values reported in the literature. The grey area marks the temperature field of UHT metamorphism. Average temperatures are reported for Ti-in-amphibole (Ti-Amph) and Zr-in-rutile (Zr-Ru) thermometers; for the latter, also average temperatures considering only values between the 90th percentile and the maximum are reported. Data from: Sajeev and Osanai (2004); Tamashiro et al. (2004); Sajeev et al. (2009); Prakash et al. (2010); Osanai et al. (2016); Hart et al. (2018); Clark et al. (2019); Dharmapriya et al. (2021); Dev et al. (2021); He et al. (2021); Ray et al. (2021); Shimizu and Tsunogae (2021); Chen et al. (2023); Gianola et al. (2023); Liu et al. (2023)

Whereas the good match between Al-in-orthopyroxene (in pelitic granulite) and Ti-in-amphibole temperatures is a further evidence of the robustness of the amphibole-based thermometric technique when applied to ilmenite-bearing metabasites, (Fig. 14a-c), the rutile-bearing HP granulite from the Northern Volcanic Zone in Colombia tells a different story (Fig. 14d). The sample 18XC10 from Gianola et al. (2023) represents the residuum after partial melting of mafic rocks and displays a well-equilibrated texture made of pargasitic amphibole, garnet and rutile. Peak temperature, constrained by phase equilibria modelling and elastic geothermobarometry of quartz and zircon inclusions in garnet, ranges between 950 and 1150 °C. However, Ti-in-amphibole thermometry yields systematically lower values (800–900 °C; Fig. 14d). When equation reported in Fig. 3c for rutile-bearing rocks is applied, temperatures increase up to 960 °C. This finding reinforces the view that the calibration of Liao et al. (2021) underestimates temperature for rocks equilibrated in the rutile stability field, whatever their H₂O content is (< 0.1 wt% for sample discussed in Fig. 14d).

Ti diffusion in amphibole: a matter for further investigations

The preservation of peak temperatures ≥ 900 °C in amphibole from slowly cooled rocks suggests that Ti content of amphibole may be resistant to post-peak diffusive re-equilibration. However, experimentally-derived Arrhenian parameters for the diffusion of Ti through amphibole are still missing. Many recent studies focused on Ti diffusion in quartz and zircon due to the interest in applying Ti-in-quartz and Ti-in-zircon thermometers (e.g., Jollands et al. 2020; Bloch et al. 2022; Audétat et al. 2023). Some Ti diffusion data were also reported for pyroxene, feldspar and olivine (e.g. Cherniak and Liang 2012; Jollands et al. 2016; Cherniak and Watson 2020). Diffusivity values of Ti differ by more than three orders of magnitude (Fig. 15a). Jollands at al. (2020) highlighted the fact that a single element in a single mineral may have multiple diffusion mechanisms as a function of element concentration, and used this argument to explain the discrepancy of the Ti diffusivities in quartz reported in different studies.

Fig. 15

(a) Arrhenius plot comparing the Ti-in-amphibole diffusivities inferred in this study (dashed grey area) against experimentally derived diffusivities of Ti in other minerals and Zr in rutile. Data from: Sasaki et al. (1985); Cherniak et al. (2007a, b); Cherniak and Watson (2020); Cherniak and Liang (2012, 2014); Jollands et al. (2016, 2020); Dohmen et al. (2019); Bloch et al. (2022); Audétat et al. (2021, 2023). Also, the Al diffusivities in orthopyroxene are reported (Smye et al. 2017). (b) Diffusivity (D) dependent diffusion distance (x), calculated for different durations. Red area refers to diffusion distances hypothesized for amphiboles from IVZ granulites

We assume a simple model in which an amphibole grain with a radius x and a certain initial concentration is placed in a medium with a different concentration, driving diffusive loss from amphibole interior. Diffusion is considered to take place only in one dimension, perpendicular to the interface. Figure 15b reports the relation between diffusivity (D) and diffusion distance (x), calculated for different values of time (t), assuming the time-distance-diffusivity approximation x ≈ (Dt)^1/2 (e.g., Watson 1982; Watson and Jurewicz 1984; Backer 1992; Acosta-Vigil et al. 2006). Considering that the high Ti contents measured in this study come from amphibole grains with a variable size from 200 μm to 1 mm, we assume a diffusion distance of 100 to 500 μm. After the thermal peak of 900 °C dated at ≈ 300–290 Ma, the IVZ experienced a protracted period of 20–30 Myr between 800 and 650 °C (Ewing et al. 2013, 2015). In order to preserve high Ti concentrations in the amphibole interior at these conditions, we calculated that the diffusivity (D) for Ti in amphibole must be slower than 10^− 21.5 and 10^− 23 m²sec^− 1 for diffusion distances of 100 and 500 μm, respectively (Fig. 15b).

From this simplified model, it results that the diffusivity of Ti in amphibole at 650–800 °C might be similar to that in quartz (data from Jollands et al. 2020; Audétat et al. 2023), olivine and pyroxenes (data of Cherniak and Liang (2012, 2014) extrapolated at lower temperature). In contrast, diffusivity of Ti in amphibole appears to be at least one-order of magnitude slower than diffusivity of Zr in rutile (Cherniak et al. 2007; Fig. 15a). When Zr-in-rutile diffusivities from Sasaki et al. (1985) and Dohmen et al. (2019) are considered, this difference is greater. Assuming Zr diffusivities in rutile of 10^− 23 m²sec^− 1 at 750 °C (data from Cherniak et al. 2007), Zr-in-rutile temperatures should be reset in rutile crystals of ≈ 200 μm in size (x = 100 μm) which experienced ≈ 30 Myr of slow cooling between 800 and 700 °C (Fig. 15b). Regarding the IVZ, it is important to recall that the resetting of Zr-in-rutile thermometer was mostly explained by recrystallization, rather than diffusive re-equilibration (see above).

Despite the importance of Al content in orthopyroxene for thermometry of granulites (Harley and Green 1982; Clark et al. 2019), no experimental data are available for Al diffusion in orthopyroxene. Smye et al. (2017) derived some estimations on Al diffusivities based on REE-in-pyroxene speedometry. Although their calculations suffer from severe uncertainties, the potential overlap between diffusivities of Ti in amphibole and Al in orthopyroxene (Fig. 15a) is consistent with the fact that both Ti-in-amphibole and Al-in-orthopyroxene thermometers record UHT conditions (Fig. 14).

To our knowledge, this is the first study trying to infer some Arrhenian parameters for Ti diffusion in amphibole. However, the empirically constrained diffusivities reported above (> 10^− 23 m²sec^− 1 at 650–800 °C) have to be considered with caution. Their sound quantification demands experimental studies, which should also consider the possible effect of composition and anisotropy on diffusion. Modeling diffusive mass transport in amphibole will also require more complex solutions and simulations.

Conclusions

We applied the Ti-in-amphibole thermometer to ilmenite-bearing metabasites from the Ivrea–Verbano Zone (NW Italy) and the following conclusions can be drawn:

• The Ti content of amphibole is buffered by the presence of a Ti-phase (ilmenite, rutile, titanite), whereas the bulk rock TiO₂ content may have a second-order effect.

• Ti-in-amphibole thermometry returns progressively higher temperatures across the IVZ, compatible with the observed increase in metamorphic grade seen in the field.

• The Ti-in-amphibole thermometer, Zr-in-rutile thermometer, and phase equilibria modelling record peak conditions across the IVZ.

• The Zr-in-rutile thermometer is more prone to post-peak resetting when compared to Ti-in-amphibole thermometry in the IVZ granulites.

• The peak metamorphic Ti content of amphibole can be reset locally, in portions of rock significantly affected by retrograde fluid influx.

The robustness of the Ti-in-amphibole thermometer in recording UHT conditions is confirmed by other case studies and its performance is comparable with that of Al-in-orthopyroxene in pelitic granulites. However, Ti-in-amphibole thermometry underestimates temperature for rocks equilibrated in the rutile stability field, whatever their H₂O content is. The empirically constrained Ti diffusivity in amphibole (> 10^− 23 m²sec^− 1 at 650–800 °C) indicates that Ti concentrations in amphibole will be less affected by later thermal disturbance than Zr concentrations in rutile, as indicated by natural occurrences. Future experimental studies are, however, necessary to develop a more robust calibration for the Ti-in-amphibole thermometer, in order to take into account the possible effect of a_TiO2 and pressure and to extend its applicability.