Diffusion and fluid interaction in Itrongay pegmatite (Madagascar): Evidence from in situ 40Ar/39Ar dating of gem-quality alkali feldspar and U Pb dating of protogenetic apatite inclusions

Alkali feldspar 40Ar/39Ar and apatite UPb geochronological studies have typically invoked two mechanisms to account for apparent loss of radiogenic 40Ar and 206-208Pb. Some studies have suggested that the radiogenic isotopes were lost by volume diffusion and used these dates to constrain temporal variations of rock temperatures; others have argued that the radiogenic isotopes were lost due to interaction with fluids and related these dates to chemical alteration. These two end-member interpretations have fundamentally different implications for tectonic models derived from geochronological data, and therefore it is important to reliably identify the principal mechanism for loss of radiogenic isotopes. Here, we revisit the mechanisms of 40Ar loss in the famous gem-quality alkali feldspar from the Itrongay pegmatite in Madagascar. Previous studies have suggested that volume diffusion is the dominant mechanism of 40Ar loss, providing key evidence to support the use of 40Ar/39Ar dating of alkali feldspar for thermochronology. We attempted to verify these results by obtaining time-temperature paths from petrologically characterised cogenetic feldspar and apatite from the Itrongay pegmatite and comparing them with each other. However, our results suggest that only a minor component in the variability of 40Ar/39Ar dates of Itrongay feldspar is related to the diffusive loss of 40Ar, and that this loss was not compatible with the majority of previously proposed models, which hinders quantitative interpretations. The crystal studied here grew in five episodes related to the influx initially of co-existing dense SiO2-rich solution and CO2-dominated fluid (the first and supposedly the following two episodes) and subsequently of H2O-rich fluid (supposedly the final two episodes). Much greater component in the variability of the acquired 40Ar/39Ar dates is interpreted to reflect the differences in the ages of these growth episodes, which we estimate to span from 477 Ma to 176 Ma (the first four episodes). Apatite inclusions in this crystal are interpreted to be xenocrysts derived from the country rocks of the Itrongay pegmatite. These yield older UPb dates than the estimated age of their host feldspar and have apparently experienced diffusive loss of 206,207Pb prior to entrapment. Our 40Ar/39Ar results indicate that there is a lack of unambiguous evidence for diffusive loss of 40Ar from alkali feldspar that can be readily interpreted for thermochronological purposes. However, in situ 40Ar/39Ar dating of alkali feldspar appears to be a promising tool for tracking fluid-flow events in the Earth's crust whose applicability is not restricted to sedimentary rocks. Our UPb results corroborate previous suggestions that UPb dating of apatite can be used for thermochronology.


Introduction
Many geological studies use isotopic dating of minerals for constraining the thermal histories of rocks. Time-temperature paths have been frequently inferred from 40 Ar/ 39 Ar data acquired by stepwise heating of alkali feldspar (e.g. Harrison and Lovera, 2014 and references therein) and increasingly more often using apatite UePb data (e.g. Paul et al., 2019 and references therein). Interpretations of these data assume that the loss of radiogenic 40 Ar from alkali feldspar and radiogenic [206][207][208] Pb from apatite occurs solely by volume diffusion before cooling below ~150-350 °C and ~ 350-550 °C, respectively. However, a growing number of studies suggest that the distributions of 40 Ar in alkali feldspar (Chafe et al., 2014;Parsons et al., 1999;Villa and Hanchar, 2013) and [206][207][208] Pb in apatite (Glorie et al., 2019;Kirkland et al., 2018) can be significantly altered by fluid-induced dissolutionreprecipitation at temperatures within or below the specified temperature windows. This can impair our ability to constrain the thermal histories of rocks using alkali feldspar 40 Ar/ 39 Ar and apatite UePb data. The aim of this study is to improve our understanding of whether and in which geologic settings we can find alkali feldspar and apatite that were not significantly affected by fluid-induced dissolution-reprecipitation and thus are suitable for thermochronology.
Here we focus on the mechanisms of 40 Ar loss from alkali feldspar, which have been intensively debated over the past 30 years. Some studies have used step-heating 40 Ar/ 39 Ar analysis of bulk grains to suggest that the dominant mechanism for 40 Ar redistribution is volume diffusion (Harrison and Lovera, 2014;Lovera et al., 2002Lovera et al., , 1989. However, other studies indicate that alkali feldspar is usually affected by fluid-induced recrystallisation and suggested that this process is more likely to account for the date variations in the 40 Ar/ 39 Ar age spectra (Chafe et al., 2014;Parsons et al., 1999;Villa and Hanchar, 2013). Furthermore, crystals that have partially lost 40 Ar by either volume diffusion or fluid-induced recrystallisation can yield indistinguishable step-heating 40 Ar/ 39 Ar data , while laboratory heating can significantly alter the inventory of fast diffusion pathways . These factors make it problematic to assess the role of volume diffusion in resetting 40 Ar concentrations solely by using step-heating 40 Ar/ 39 Ar analysis. Only a few studies have used in situ techniques to obtain Ar isotope data from alkali feldspar from non-sedimentary rocks, and only one of them documented 40 Ar concentration gradients consistent with diffusive loss. Flude et al. (2014) report that in situ 40 Ar/ 39 Ar dates of a gem-quality alkali feldspar crystal from the Itrongay pegmatite (Madagascar) gradually increase from the rim towards the core. They were able to reproduce the observed 40 Ar/ 39 Ar date variations by modelling diffusive loss of 40 Ar that occurred while this crystal cooled following a simplified version of the regional time-temperature path. Flude et al. (2014) applied diffusion parameters that were obtained by Wartho et al. (1999) for other crystals of Itrongay feldspar, which led them to suggest that accurate thermal histories of rocks can be recovered from in situ or step-heating 40 Ar/ 39 Ar data using sample-specific experimentally-derived diffusion parameters. Our work is an attempt to verify these results.
Gem-quality crystals of Itrongay feldspar are considered to behave largely as single grain-scale diffusion domains both over geological time and in laboratory experiments (Arnaud and Kelley, 1997;Cassata and Renne, 2013;Flude et al., 2014;Lovera et al., 2015;Wartho et al., 1999). Given that these crystals can reach several cm in the shortest dimension, this suggests that their closure temperature with respect to diffusive loss of 40 Ar should fall within the temperature range that is usually constrained using the apatite UePb thermochronometer (i.e. ~350-550 °C; Cherniak, 2010a;Chamberlain and Bowring, 2001;Cochrane et al., 2014;Paul et al., 2019). The equation of Dodson (1973) yields a closure temperature of 441 °C for a spherical alkali feldspar crystal with a diameter of 1 cm, a cooling a rate of 20 °C/Ma, and using the diffusion properties defined by the low-temperature Arrhenius relationship from Wartho et al. (1999). This potential overlap between the closure intervals for Ar in alkali feldspar and Pb in apatite thus provides an opportunity to directly compare thermochronological constraints obtained using these systems and thereby verify their accuracy. Therefore, our work was set out to (i) find and characterise cogenetic gem-quality alkali feldspar and apatite from the Itrongay pegmatite, (ii) date them using in situ 40 Ar/ 39 Ar and UePb methods, respectively, and (iii) derive an independent time-temperature path for each of them and compare these paths. However, while we were able to find a crystal of Itrongay feldspar that contains inclusions of apatite, they could not be used for thermal history reconstruction. Petrological and geochronological evidence suggests that the feldspar crystal records a protracted history of interaction with fluids with only minor diffusive loss of 40 Ar that could not be quantified, while the apatite inclusions are xenocrysts that predate this feldspar crystal by at least several tens of millions of years.

Previous studies of Itrongay feldspar
Itrongay feldspar is a vague term that is applied to gem-quality alkali feldspar crystals that are reportedly derived from several pegmatitic bodies scattered over a ~5 × 20 km area in southern Madagascar. Previous studies of Itrongay feldspar do not report sampling coordinates, probably because they used crystals that were bought from brokers and cannot be traced back to a specific location (e.g. Nägler and Villa, 2000). It is important to keep this in mind because different crystals may have experienced different geologic histories, and any observation made for one crystal is not necessarily valid for others. Typically, Itrongay feldspar is yellow transparent gem-quality orthoclase to low sanidine with high concentrations of K (K > 0.9 apfu, frequently > 0.94 apfu) and Fe (up to 0.11 apfu; Arnaud and Kelley, 1997;Nyfeler et al., 1998;Wartho et al., 1999;Simmons and Falster, 2002;Ackermann et al., 2004;Parsons and Lee, 2005). Transmission electron microscopy observations of Wartho et al. (1999) and Parsons and Lee (2005) showed that it has a nm-scale tweed texture and ~15-25 nm wide inclusions of an unidentified mineral. Parsons and Lee (2005) report exsolution lamellae of Na-rich feldspar with thicknesses of up to 10 nm and lengths of up to 500 nm, which could form at very low temperature (potentially below 200 °C). Experimental studies on Ar diffusion in Itrongay feldspar have obtained non-linear Arrhenius arrays using both step-heating of bulk grains and in situ analysis of partially outgassed grains (Arnaud and Kelley, 1997;Cassata and Renne, 2013;Wartho et al., 1999). Several phenomena have been invoked to explain these non-linear Arrhenius arrays, which include structural transitions (Cassata and Renne, 2013;Wartho et al., 1999), changes in vacancy-specific mechanisms of diffusion (Wartho et al., 1999), the presence of fast pathways for Ar diffusion (Arnaud and Kelley, 1997; see also Baxter, 2010) and the presence of variably-sized intra-grain diffusion domains (Lovera et al., 2015). Nevertheless, it is generally considered that the effective diffusion length of Itrongay feldspar grains is well approximated by their half-width (Arnaud and Kelley, 1997;Cassata and Renne, 2013;Wartho et al., 1999; consider also that the size of the largest domain in Lovera et al., 2015, is assumed to be equal to the size of the analysed grain). Previous step-heating 40 Ar/ 39 Ar analyses of Itrongay feldspar gave plateau dates of 435 ± 8 Ma (Arnaud and Kelley, 1997; 2σ errors are shown throughout) and 461 ± 6 Ma (Nägler and Villa, 2000), while previous in situ 40 Ar/ 39 Ar dates vary between 416 ± 3 Ma and 474 ± 5 Ma (Flude et al., 2014). Nägler and Villa (2000) obtained by bulk-grain analysis a KeCa isochron date of 477 ± 2 Ma. These variations in isotopic dates have been attributed to the diffusive loss of 40 Ar (Flude et al., 2014;Nägler and Villa, 2000).

Methods
Non-destructive characterisation of the studied Itrongay feldspar crystal and apatite inclusions within it was carried out using equipment housed at the University of Geneva. Backscattered electron (BSE) imaging and semiquantitative analyses via energy-dispersive X-ray spectroscopy (EDS) were acquired using a JEOL JSM7001F scanning electron microscope equipped with an EDS JED2300 analyser. Optical cathodoluminescence (CL) images were acquired using an ERI-MRTech stage. Raman spectra were acquired using a HORIBA LabRAM spectrometer and interpreted using the RRUFF database (Lafuente et al., 2015), which provided the reference spectra for pyroxene, carbonate, apatite and baddeleyite, along with the studies of Beyssac et al. (2002), Frezzotti et al. (2012), Cicconi and Neuville (2019) and Curtis et al. (2019), which provided the reference spectra for graphite, CO 2 , SiO 2rich glass and opal, respectively. Selected Raman spectra of opal are given in Supplementary Tables (sheet Raman spectra of opal).
In situ 40 Ar/ 39 Ar dates were obtained from a ~0.5 mm thick crystal slice going through the centre of the Itrongay feldspar crystal. The slice was irradiated along with Fish Canyon Tuff sanidine for 13 h without Cd shielding (ICIT) in the F12 position of the TRIGA reactor at the Oregon State University. The slice was fixed horizontally during the irradiation to minimise potential variations in the neutron flux across it, and four monitors were fixed around the slice to seek lateral variations in the neutron flux, although none were detectable. In situ 40 Ar/ 39 Ar data were obtained at the Institut des Sciences de la Terre d'Orléans with the use of a Teledyne Cetac LSX-213 G2 213 nm Nd:YAG laser ablation system. Each single analysis comprises gas released either from 12 spots with a diameter of 20 μm or 4 spots with a diameter of 50 μm. The spots defined a straight line that was orthogonal to the chosen general direction of analysis (usually parallel to the nearest crystal boundary). The released gas was purified for 6 min using a liquid N 2 cold trap and two hot SAES GP50 getters and two Ta filaments held at 1500 °C. 36,37,38,39,40 Ar along with 35 Cl were measured by peak jumping in 10 cycles of 70-second duration using an electron multiplier detector of a Thermo Fisher Helix SFT mass spectrometer. Peak intensity data were reduced following the procedures of Scaillet (2000). Fish Canyon Tuff sanidine monitors were analysed at the University of Geneva. Each monitor was degassed using a CO 2 infrared laser, and the released gas was purified for 6.5 min using a cold trap (−130 °C) and hot SAES AP10 and GP50 (ST101) getters. 36,37,38,39,40 Ar isotopes were measured  Roig et al., 2012). Ambalavao and Imorona-Itsindro suites are suites of largely metamorphosed intrusive rocks. The label "Itrongay" shows the location of the ~5 × 20 km field of "pegmatites dites d'Itrongay" from the maps of Savornin (1932Savornin ( , 1933. We sampled near the southwestern boundary of this field (see in Section 4.1 for details).
Semiquantitative trace element maps of apatite were obtained by laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) at Trinity College Dublin. We used a Photon Machines Analyte Excite 193 nm ArF excimer laser ablation system with a HelEx 2-volume ablation cell coupled to an Agilent 7900 quadrupole mass spectrometer to measure 44 Ca, 55 Mn, 57 Fe, 88 Sr, 89 Y, 90 Zr, 137 Ba, 139 La, 206 Pb, 232 Th, 238 U by peak jumping. Apatite was analysed by ablating lines with a 7 μm diameter circular spot at a scan speed of 15 μm/s. The acquired mass spectrometry data were reduced in Iolite 2.5 (Paton et al., 2011) using the data reduction scheme trace_element_image, option semi_quantitative. In situ UePb dating of apatite was done by laser ablation multiple collector inductively coupled plasma mass spectrometry (LA-MC-ICPMS) at the National Centre for Isotope Geochemistry at University College Dublin. We used a Teledyne Cetac Analyte G2 193 nm ArF excimer laser ablation system with a HelEx II 2-volume ablation cell coupled to a Thermo Fisher Neptune mass spectrometer to simultaneously measure 238 U, 207 Pb, 206 Pb on separate electron multiplier detectors (we also monitored 232 Th, 202 Hg, 204 Pb, 208 Pb and 235 U, but these were not used in the UePb date calculations). Apatite was analysed by ablating 20 × 20 μm square spots. The acquired data were reduced using in-house MS Excel-based software that closely reproduces LAMTRACE (Jackson, 2008) and utilises the ratio-of-themean-intensities method of correction for UePb fractionation (Ulianov et al., 2012). The initial functionality of LAMTRACE was extended by implementing the 207 Pb-based algorithm for UePb fractionation correction using standards with variable quantities of common Pb . McClure Mountain apatite Schoene and Bowring, 2006) was used as a primary standard, while Emerald Lake apatite and Durango apatite (Chew et al., 2011) were used as secondary standards. Common Pb correction was made using the 207 Pbcorrection method (Chew et al., 2011) assuming a common Pb composition predicted by the model of Stacey and Kramers (1975). UePb data are provided in Supplementary Tables (sheet UePb dates).

Sampling and field observations
The Itrongay feldspar crystal that we used in our study was picked from the ground in the vicinity of Beapombo II village (approximate sampling location is S 23°35′33" E 45°34'06"). Due to poor bedrock exposure, we only have fragmentary information on its geologic context, which is largely based on the observation of rock fragments scattered around abandoned pits. We observed the following seven rock types (1-7): (1-2) quartz-feldspar rocks that are sometimes interlayered with pyroxene-phlogopite rocks (Fig. 2B, C), (3) pyroxene-feldspar rock (Fig. 2D), (4) friable rock that consists of phlogopite and presumably kaolinite (Fig. 2E), (5) variably deformed and altered pegmatitic rocks that only consist of green feldspar (Fig. 2F, G), (6) sometimes brecciated pegmatitic rocks that consist of smoky quartz and green feldspar (Fig. 2H, I), and (7) very coarse-grained rocks that consist of pyroxene, feldspar, quartz and titanite (Fig. 2J, K). Some of the brecciated pegmatitic rocks are cemented with opal-CT (identified using Raman spectroscopy). One of the samples of brecciated quartz-feldspar pegmatitic rock contained a large brecciated amphibole crystal. We interpret the pyroxene-phlogopite, quartz-feldspar and pyroxene-feldspar rocks (types 1-3) to be host rocks that were intruded by one or several pegmatitic bodies, which have feldspathic flanks (type 5) and quartzofeldspathic cores (type 6). The friable rock with phlogopite (type 4) occurs at the contact between the pyroxene-feldspar country rock and the deformed pegmatitic rock that consists only of feldspar, suggesting that it is either an altered aplitic rim of a pegmatitic body or a hydrothermally reworked fault zone. The relationship between these rocks and the coarse-grained rocks consisting of pyroxene, feldspar, quartz and titanite (type 7) is unclear.
We observed a variety of gem-quality feldspar grains that ranged in colour from green to yellow. The green and greenish yellow grains never form euhedral crystals and represent fresh fragments of large feldspar crystals from the abovementioned pegmatitic rocks (greenish yellow grains tend to occur with smoky quartz in brecciated samples; Fig. 2G-I). In contrast, the yellow grains sometimes form euhedral crystals, which typically have etched surfaces and in some cases are overgrown by a thin layer of whitish turbid felspar (Fig. 3A, B). These grains fit the description of typical Itrongay feldspar provided in Section 2.1 and will be referred to by this term for the rest of this work. Most of these grains were picked from the ground. We have found only one rock sample containing yellow gem-quality felspar, which is a deformed feldspar-dominated pegmatitic rock that was collected at the contact with pyroxene-feldspar country rock. In this sample, two yellow feldspar fragments, which once were part of a larger crystal, are surrounded by a matrix of brecciated and altered green feldspar (Fig. 2F).

Feldspar characterisation and 40 Ar/ 39 Ar dating
We have studied one euhedral crystal of Itrongay feldspar, which appears turbid when viewed from the side but has a transparent and gem-quality interior (Fig. 3A, B). The apparent turbidity is related to natural etching and a thin overgrowth layer of turbid feldspar. This crystal contains a variety of inclusions, which are unevenly distributed. Three growth zones can be distinguished based on the assemblage and the morphology of the inclusions. In the core (zone 1) this crystal contains inclusions of liquid CO 2 , amorphous SiO 2 , carbonates, apatite, pyroxene and baddeleyite ( Fig. 3C-P). The majority of liquid CO 2 inclusions and amorphous SiO 2 inclusions have well-developed negative crystal shapes (Fig. 3C, D, F, H). Liquid CO 2 inclusions exsolve into liquid and gas after a few minutes in a regular refrigerator (Fig. 3L, M), suggesting that their homogenisation temperature is only slightly lower than room temperature (20-25 °C). Similar CO 2 inclusions were also reported from Itrongay feldspar by Touret (1974Touret ( , 1977, and the inclusion shown in Touret (1977) consists of liquid and gas at room temperature. Amorphous SiO 2 inclusions yield Raman spectra (Fig. 3E) that are typical of opal-CT (Curtis et al., 2019). These can be distinguished from Raman spectra of SiO 2 -rich glasses (Cicconi and Neuville, 2019) because the low-frequency band is shifted to < 400 cm −1 (specifically to ~350 cm −1 ) and the high-frequency band at ~900-1400 cm −1 is absent. Three types of carbonate inclusions are present. Two of these are opaque isometric inclusions with well-developed crystal shapes and characteristic peaks in Raman spectra at different positions (Carb1 in Fig. 3C, D, and Carb3 in Fig. 3O). Their opaqueness is probably related to natural etching prior to entrapment (note the rough surface of Carb1 in Fig. 3D). Carbonate inclusions of the third type are transparent and have irregular shapes, and they are usually co-trapped with pyroxene and/or liquid CO 2 (Carb 2 in Fig. 3F, L, M). Apatite inclusions are isometric and have no pronounced faceting ( Fig. 3F, H, J, O). Smaller apatite inclusions are transparent and are sometimes co-trapped with liquid CO 2 or amorphous SiO 2 (Ap1 in Fig. 3F, H, J). Larger apatite inclusions appear turbid when viewing from the side, perhaps due to natural etching prior to their entrapment, and they are occasionally co-trapped with opaque carbonate (Ap2 in Fig. 3O) or sub-isometric pyroxene. Pyroxene inclusions are sometimes well-faceted and generally have a needle-like or even hair-like morphology ( Fig. 3L, M), although platy and sub-isometric crystals were also observed. According to our semiquantitative EDS analyses, the needle-like crystals are inclusions of Fe-rich diopside with Fe/Mg ratios approaching 1 (in at. %). Very small baddeleyite crystals were cotrapped with an apatite crystal and amorphous SiO 2 (Fig. 3H). Zone 1 is followed by zone 2, which comprises the outer ≲ 1 mm of gem-quality feldspar and hosts very scarce and small inclusions. The inclusions are slightly elongated or more often isometric pyroxene crystals with irregular morphologies, which are generally co-trapped with other phases, including graphite, CO 2 , apatite and an unidentified phase that has strong luminescence (Figs. 3Q-T). Zone 2 is followed by zone 3, which comprises the outer ≲ 0.1 mm layer of turbid feldspar and contains abundant tiny inclusions that cause the turbidity ( Fig. 3U; nanopores with fluid?).
CL and BSE imaging also showed that the studied crystal has complex internal zoning, which partly correlates with the distribution of inclusions and the variation in turbidity. The same three major zones can be distinguished in the CL image of this crystal (Fig. 4A), which includes a deep blue core with very weak CL (zone 1), a light blue intermediate zone with bright CL (zone 2) and a deep blue outer rim with very weak CL (zone 3). The boundary between zones 1 and 2 is irregular, wavy and is marked by a change in the assemblage of inclusions, as described above. Feldspar remains optically coherent across this boundary, and zones 1 and 2 become simultaneously extinct in cross-polarised light. The boundary between zones 2 and 3 is irregular, wavy in some places and straight in others, and zone 3 is turbid and has a different extinction angle to zones 1 and 2. These three major zones can also be distinguished in the high-contrast BSE image (Fig. 4B), where the inner boundary of zone 2 is marked by a prominent dark wavy stripe, while zone 3 is considerably darker than the rest of the crystal. However, additional complexity is observed within zone 2, which is divided by a less prominent dark wavy stripe into two subzones, an inner subzone 2a and an outer subzone 2b. The two dark stripes sometimes merge, so that subzone 2a pinches out. Lastly, higher magnification BSE images (Fig. 4D) reveal that zone 3 also comprises two subzones, which are a thicker and darker inner subzone 3a and a thinner and brighter outer subzone 3b. The relationships between all of the (sub)zones are summarised in Fig. 4E. Our semiquantitative EDS analyses suggest that the composition of the studied crystal varies from zone to zone. Exceptionally high Fe concentrations (a few wt%) were only observed in zone 1. The Na/K ratio remains constant across zones 1 and 2, where the Na concentration is very low. No Na was detected in zone 3, and subzone 3b has a very high concentration of Ba (several wt %). Notably, despite the differences in the concentration of Fe, similar BSE signal intensities were obtained from zones 1 and 2. Lower BSE signal intensities were obtained from subzone 3a, despite the fact that it has a lower Na/K ratio than zones 1 and 2. This indicates that the variations of the BSE signal intensities across (sub)zones 1, 2 and 3a largely characterise the orientation or the defectiveness of the crystal structure rather than variations in the mean atomic number (Lloyd, 1987;Robinson, 1980).
We have obtained eight in situ 40 Ar/ 39 Ar date profiles from the studied crystal, which are shown in Fig. 5A to H and are referred to as profiles A to H throughout. Arrows in Fig. 5I show the location of the profiles. Profile A traverses zone 1 and starts in the place where zone 1 is exposed at the original surface of the crystal and zones 2 and 3 are discontinuous and very thin, so that they could only contribute to the first one or two spot analyses. This profile starts with a date of ~420 Ma, which then gradually increases to ~455 Ma over the first ~500 μm and remains at this value across the subsequent ~1600 μm.
Profile B was obtained from the central part of the crystal within zone 1 and only includes dates of ~455 Ma. Profiles C to F cross all three major zones, and each starts with a date of ~200 Ma, which corresponds to subzone 3a. The dates abruptly increase to ~385 Ma traversing towards the core of the crystal, which corresponds to subzone 2b, and then the dates gradually increase to ~405 Ma in profiles E and F, which corresponds to subzone 2a. Finally, an abrupt change to ~455 Ma occurs within zone 1 in all four profiles. Profile G only crosses subzones 3a and 2b and reproduces the corresponding part of the trend described for profiles C to F. Profile H only intersects subzone 2a and only includes dates of ~405 Ma. Overall, the obtained dates group into four clusters that correspond to (sub)zones 1, 2a, 2b and 3a, which can be easily recognised when they are plotted in descending order or used to plot histograms and probability density functions ( Fig. 6A and B).
The 40 Ar/ 39 Ar dates obtained from any given (sub)zone are significantly scattered, giving rise to high MSWD values for their weighted  40 Ar/ 39 Ar dating was obtained. C-U: optical microscope images of different types of inclusions and their Raman spectra. The same carbonate inclusion is visible in Fig. 3C and D, and the same SiO 2 and CO 2 inclusions are visible in Fig. 3D and F. Fig. 3L and M were taken before and after placing the mount into a fridge. Carb1, Carb2 and Carb3 are three types of carbonate. Ap1 and Ap2 are two types of apatite in zone 1, while Ap is apatite in zone 2. Di: diopside. Gr: graphite. See text for details. means (Fig. 6B). For example, with the exception of one date of ~434 Ma, all of the dates from zone 1 fall within the range of 440-466 Ma (average internal 2σ uncertainty is 5 Ma) with an MSWD value of 7.6 for their weighted mean (Fig. 6B). A comparable scatter within zone 1 is observed for the individual profiles. For example, all of the dates in profile B (zone 1 only) fall within the range of 447-463 Ma (average internal 2σ uncertainty is 6 Ma) with an MSWD of 2.9 for their weighted mean (Fig. 5B). These variations are unlikely to be related to analytical issues because in some cases the observed date variations along the profile have been reproduced by repeated measurements in the same area (Fig. 5B). While in some places the dates from any given (sub)zone consistently increase with increasing distance from the rim (e.g. first 500 μm in profile A, Fig. 5A), this is not always the case. For example, profile B has three segments of ~300 μm length where the dates in zone 1 consistently decrease with increasing distance from the upper tip of the crystal, each terminating with an abrupt increase of the dates (Fig. 5A). Another example is provided by profile F, where traversing towards the core of the crystal the dates in zone 2 consistently increase in the outer ~350 μm and then decrease in the subsequent ~150 μm (Fig. 5F). Nevertheless, the youngest dates from any given (sub)zone consistently decrease when traversing from the core towards the rim of the crystal, which is evident from the comparison of the weighted means of the second to fourth youngest dates shown in Fig. 6C (the first youngest dates were chosen to be excluded from the calculation of the weighted means to minimise the potential influence of outliers).

Apatite characterisation and UePb dating
Three apatite inclusions from zone 1 of the studied crystal were prepared for in situ UePb dating. Small pieces of feldspar with apatite inclusions were cut out, mounted separately in epoxy resin and ground to expose the inclusions at the surface. The largest of these inclusions was characterised by CL imaging and trace element mapping (Fig. 7), while the smaller inclusions were characterised using only CL imaging (Fig. 7G, H). All three inclusions are isometric, rounded and appear slightly turbid from the outside while being mostly clear inside (e.g. Fig. 7A). All of them are co-trapped with sub-isometric pyroxene crystals, which they partly surround in some places (e.g. Fig. 7B). The largest inclusion contains an inclusion of an unidentified phase (Fig. 7B). A small carbonate crystal is attached to the medium-sized inclusion (Fig. 7G). These apatite inclusions appear orange in CL images (Fig. 7B, G, H), although the CL signal is very weak and is weaker at the core than at the boundaries, where carbonate with bright orange luminescence occurs (Fig. 7G). This suggests that the orange colour of the apatite inclusions in the CL images can be related to the presence of a sub-microscopic layer of carbonate at their boundaries. The CL image of the largest inclusion revealed some irregular bright features (marked as alteration in Fig. 7B), which appear as slightly turbid volumes beneath the polished surface in transmitted light. Their appearance in the CL image is probably related to scattering of CL signal that comes from the side. Trace element mapping showed that this inclusion has higher concentrations of U, Th, La, Y, and Zr in the core than at the rim (see  This image was acquired for 16 min using a very high contrast setting, so that the observed differences in BSE signal intensity are not necessarily related to variations in composition. Note the presence of two dark stripes in the outer ~1 mm and a very dark outer rim. The most internal and more prominent stripe correlates with the beginning of zone 2 in Fig. 4A, while the second less prominent stripe splits zone 2 into two regions, which are designated 2a, from the beginning of the first stripe to the beginning of the second stripe, and 2b, from the beginning of the second stripe (or the first stripe where only one stripe is present) to the beginning of the very dark outer rim (zone 3). C-D: CL (C) and BSE (D) images of the outer ~300 μm of the crystal. The BSE image shows that zone 3 consists of two layers, which include a thicker and darker discontinuous layer adjacent to zone 2 (subzone 3a), and a thinner and brighter layer in the outermost part of the crystal (subzone 3b). E: schematic sketch (not to scale) showing the relationships between all the zones and subzones. Zone 1 corresponds to the core of the crystal with very weak CL. Zone 2 is the intermediate zone with light blue CL, and is divided into subzone 2a, which starts with the first dark stripe visible in the BSE image (shown with grey hatching), and subzone 2b, which starts with the second dark stripe visible in the BSE image (also shown with grey hatching). Zone 3 is the outer rim with very weak CL, which includes subzones 3a and 3b, corresponding to the dark and bright layers visible in the BSE images, respectively. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. within this apatite inclusion and at the apatite-feldspar boundary as in the bottom part of the Pb map could also affect our measurements. Therefore, we suggest that Pb is homogeneously distributed in this apatite inclusion. We observed no clear variations of trace element concentrations, including Pb, in feldspar around this inclusion (Supplementary Figures).
Three UePb dates were obtained from the largest apatite inclusion. A date of 569.2 ± 8.3 Ma was obtained from its U-rich core, while older and younger dates of 576.4 ± 8.5 Ma and 558.5 ± 8.5 Ma were obtained from its U-poor flanks (Fig. 7B, C, I). The location of the younger date is close to one of the irregular features that are visible in the CL image (Fig. 7B). Two overlapping UePb dates of 548.1 ± 7.7 Ma and 549.8 ± 7.9 Ma were obtained for the mediumsized inclusion (Fig. 7G, J). One UePb date of 530.0 ± 7.3 Ma was obtained from the smallest inclusion (Fig. 7H, K). There is an overall positive correlation between the UePb dates of these apatite inclusions and their half-widths (Fig. 7K).

Genesis of Itrongay feldspar
Previous geochronological studies assumed that Itrongay feldspar formed in a single event at a relatively high temperature (> 500 °C; e.g. Nägler and Villa, 2000;Flude et al., 2014), which exceeds the expected temperature of its closure with respect to diffusive loss of 40 Ar (~440 °C, see Section 1). This assumption followed from two considerations. First, Itrongay feldspar is derived from a pegmatite, and pegmatites are considered to be products of melt crystallisation (e.g. Simmons and Webber, 2008). Second, Itrongay feldspar has a disordered orthoclase to low sanidine structure and a nm-scale tweed texture (Parsons and Lee, 2005;Wartho et al., 1999), which is typical of K-rich feldspars from intrusive rocks (e.g. Parsons et al., 2015). However, these considerations do not provide unequivocal evidence for crystallisation at high temperatures. Pegmatites are generally considered to crystallise from very undercooled melts and/or melts that are very rich in fluxing components such as B, F, P, Li and H 2 O, and some estimates of their crystallisation temperatures (350-500 °C; Sirbescu and Nabelek, 2003a;Simmons and Webber, 2008;London et al., 2020) are close to the expected closure temperature of Itrongay feldspar. Furthermore, pegmatites frequently contain adularia (morphological variety of potassium feldspar; Černý and Chapman, 1984;Černý, 1994), which is typically formed in hydrothermal systems at ≲ 350 °C and is frequently characterised by high degrees of SieAl disorder (Akizuki and Sunagawa, 1978;Černý and Chapman, 1986;Dong and Morrison, 1995; Rauchenstein-Martinek, 2014; Rossi and Rolland, 2014; Takahashi  40 Ar/ 39 Ar dates along the profiles. Strip profiles above the date plots show the variations of BSE and CL signals. These were used to locate the boundaries between the zones, which are shown with grey dotted lines and are labelled above the plots. Blue markers in Fig. 5A show the composite in situ 40 Ar/ 39 Ar date profile from (Flude et al., 2014). Their dates were recalculated using the decay constants of (Steiger and Jäger, 1977), which changed these dates by < 0.1 Ma. Blue arrows in Fig. 5B and F indicate notable segments of the date profiles where the dates consistently increase or decrease with increasing distance from the rim of the crystal. The colour coded dates shown in Fig. 5B were obtained in a sequential order of light green, then orange, then deep blue, revealing their reproducibility. Weighted means and MSWD values shown in Fig. 5A-E were calculated for intervals that are indicated with double headed arrows, internal uncertainties were used in calculations. I: composite optical CL image with yellow arrows showing the location of the in situ 40 Ar/ 39 Ar date profiles. Arrowheads designate the righthand side of the plots in Fig. 5A-H. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. et al., 2008). Notably, nm-scale cross-hatched twinning, which is referred to as a tweed texture, was first observed in adularia derived from an alpine cleft (McConnell, 1965).
Our field observations indicate that Itrongay feldspar, i.e. yellow gem-quality feldspar, is a minor constituent of the Itrongay pegmatite, which is predominantly composed of variably altered green feldspar and, in some places, smoky quartz. While the dominant variety of green feldspar becomes more yellow in some brecciated samples with smoky quartz, it still preserves a green hue. The only crystal of purely yellow feldspar that we found within a rock is hosted by brecciated and altered feldspar-dominated pegmatitic rock that was sampled near the contact with the host rocks of the Itrongay pegmatite. This suggests that the occurrence of Itrongay feldspar is not restricted to the quartz core of the Itrongay pegmatite. At the same time, purely yellow feldspar sometimes forms crystals with well-faceted tips, indicating that it grew into free spaces from some substrate. Therefore, Itrongay feldspar is likely a late phase that postdates the main sequence of pegmatite crystallisation. This is reminiscent of adularia reported from other pegmatites (Černý, 1994;Černý and Chapman, 1984), where it occurs in late veins and fills cavities that formed by leaching after the development of all pegmatite zones. Our petrographic observations indicate that the formation of Itrongay feldspar was sometimes a multi-stage process. The crystal that was chosen for this study formed by five discrete growth episodes, corresponding to (sub)zones 1, 2a, 2b, 3a and 3b. Irregular, wavy boundaries between the (sub)zones indicate that these growth episodes alternated with dissolution episodes (this texture is analogous to resorption zones in plagioclase from magmatic systems; Pearce and Kolisnik, 1990;Shcherbakov et al., 2011;Tsuchiyama, 1985).
Zones 1 and 2 are optically continuous and gem-quality. Zone 1 has a very weak CL response, which is unusual for magmatic feldspars (Görz et al., 1970;Götze et al., 2000;Smith and Stenstrom, 1965), but is typical for authigenic feldspars (Götze et al., 2000;Kastner and Siever, 1979;Krainer and Spötl, 1989;Lee and Parsons, 2003) and has been observed in adularia (Takahashi et al., 2008). In contrast, zone 2 has bright blue CL response, which is common in magmatic feldspars (Görz et al., 1970;Götze et al., 2000;Smith and Stenstrom, 1965). Zone 1 contains inclusions of liquid CO 2 and amorphous SiO 2 . These have large sizes, well-developed negative crystal shapes and in one instance form a three-dimensional group, which indicates that they are primary inclusions of two co-existing substances from which zone 1 grew (Roedder, 1984). Amorphous SiO 2 inclusions yield Raman spectra that are typical of opal-CT (as opposed to silicate glass) and do not have shrinkage/fluid bubbles and daughter minerals, which are typically present in melt inclusions from pegmatites (Thomas et al., 2000(Thomas et al., , 2009Thomas and Davidson, 2012a). They resemble some of "gel-like" inclusions that were reported from pegmatites (Fig. 11 in Thomas and Davidson, 2012b) and from chalcedony veins and amygdales in volcanic rocks ( Fig. 3.1 in Khakimov, 1968). Liquid CO 2 is occasionally co-trapped with variably-sized carbonate, apatite and pyroxene crystals, while amorphous SiO 2 was co-trapped with apatite and baddeleyite crystals, suggesting that all these phases form an equilibrium assemblage with their host feldspar. Zone 2 has a different assemblage of inclusions, which comprises CO 2 , graphite, pyroxene, apatite and an unidentified luminescent phase. The mineral inclusions are very small and frequently occur as polyphase intergrowths with rounded shapes, suggesting that they could be in disequilibrium with their host feldspar and potentially represent xenocrysts. The difference in the inventory of CL activators and the inclusion assemblage between zones 1 and 2 indicates that the physicochemical conditions of their crystallisation were not the same. However, the inclusion assemblages are not contrasting, and therefore these conditions could be broadly similar.
We are not aware of any other reports of an equilibrium assemblage that includes liquid CO 2 , amorphous SiO 2 , pyroxene, carbonate, apatite and baddeleyite. To our knowledge, only secondary CO 2 inclusions have been documented from pegmatites (Sirbescu and Nabelek, 2003b). CO 2 inclusions of variable density are common in granulite-facies metamorphic rocks, where they are interpreted to be trapped either at peak metamorphic conditions (e.g. Tsunogae et al., 2002;Touret and Huizenga, 2011) or during retrogression (Lamb et al., 1991(Lamb et al., , 1987. We could not find any reports of proven amorphous SiO 2 (not glass) inclusions in natural samples, although several studies have documented visually similar inclusions that were interpreted as inclusions of SiO 2rich colloid solutions. The most visually similar inclusions have been described within cleavelandite from the Naipa pegmatite (Mozambique; Thomas and Davidson, 2012b) and within chalcedony from Cretaceous volcanic rocks near Ijevan (Armenia; Khakimov, 1968). Less similar inclusions that consist of quartz ± cristobalite ± FeOOH flakes in liquid ± gas have been reported from quartz and plagioclase from the Rønne pegmatite (Denmark; Thomas and Davidson, 2012b) and from achroite from the Malkhan pegmatite field (Russia; Thomas and A: all dates plotted in descending order along with a histogram and probability density function. B: dates from each (sub)zone plotted in descending order along with a histogram and probability density function. Weighted means were calculated for each of the (sub)zones. We have omitted dates that were obtained from the boundaries between the (sub)zones or proximal to these boundaries, as constrained using CL and BSE images, and these are also not included in the calculations of the weighted means. Brown and orange arrows show the youngest and the oldest dates in profiles A and B, respectively. C: the five youngest dates from each of the (sub)zones and weighted means calculated for the second to fourth youngest dates, internal uncertainties of which are shown in pink. All MSWD values were calculated using internal uncertainties. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. Davidson, 2008). Synthetic inclusions of SiO 2 -rich liquids have been obtained in K 2 O-CO 2 -SiO 2 -H 2 O (Wilkinson et al., 1996) and Na 2 O-CO 2 -SiO 2 -(Al 2 O 3 )-H 2 O (Kotel'nikova and Kotel'nikov, 2011) systems and some other systems containing F and B (e.g. Peretyazhko et al., 2010 and therein). The presence of colloidal SiO 2 has been advocated for some hydrothermal systems that crystallise adularia (Dong and Morrison, 1995;Saunders, 1994;Takahashi et al., 2008).
While we do not have precise thermometric data for the CO 2 inclusions, our observations combined with those of Touret (1977) suggest that their homogenisation temperature is very close to room temperature and thus likely lies in the range of 15-25 °C. Isochores calculated for feldspar-hosted CO 2 inclusions with homogenisation temperatures of 15-25 °C using the FLUIDS software (Bakker, 2003; equations of state after Duan et al., 1992Duan et al., , 1996 do not cross the pressure-temperature fields experienced by the rocks of the Androyan domain during peak metamorphism and retrogression ( Fig. 8; Markl et al., 2000;Tucker et al., 2014). Hence, we conclude that the Itrongay feldspar formed after the metamorphic events that are recorded in the rocks of southern Madagascar. Notably, post-metamorphic circulation of CO 2 -dominated fluids has been proposed for other granulite-facies terranes (Lamb et al., 1991(Lamb et al., , 1987. The isochores cross the pressuretemperature fields where SiO 2 -rich liquids have been experimentally synthetized by Wilkinson et al. (1996) andKotel'nikov (2011) (Fig. 8). Therefore, it is reasonable to assume that Itrongay feldspar formed in a similar system comprising dense SiO 2 -rich colloid solution and CO 2 -dominated fluid. Considering that the proposed crystallisation ages of zones 1 and 2 differ by ≳75 Ma (see Section 5.3), and zone 1 contains xenocrysts of apatite (see Section 5.2), it is also reasonable to assume that CO 2 -dominated fluid was derived from the surrounding metamorphic rocks rather than representing the residual of pegmatite melt crystallisation.  Fig. 7B and G designate the righthand side of the plots in Fig. 7I and J, respectively. Green asterisks in Fig. 7I, K indicate date that was presumably affected by alteration (see Section 5.2). Ap: apatite. Di: diopside. Carb: carbonate. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. Fig. 8. A comparison of the crystallisation pressure and temperature estimates for Itrongay feldspar and for the surrounding metamorphic rocks of the Androyan domain. The pressure-temperature field of Itrongay feldspar crystallisation that satisfies isochores of CO 2 inclusions is shown in green. Dark green isochores were calculated using FLUIDS (Bakker, 2003; equations of state after Duan et al., 1992Duan et al., , 1996 assuming homogenisation temperatures 15, 20 and 25 °C. Red and the orange rectangles depict the pressure-temperature conditions that were attained within the Androyan domain during peak metamorphism and retrogression, respectively (Markl et al., 2000;Tucker et al., 2014). Blue fields show the pressure-temperature conditions where SiO 2 -rich liquids were obtained in the experiments of (a) Wilkinson et al. (1996) and(b) Kotel'nikova andKotel'nikov (2011). For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.
Zone 3 is different from zones 1 and 2 because it has a very weak CL response, which is typical of authigenic feldspar (Götze et al., 2000;Kastner and Siever, 1979;Krainer and Spötl, 1989), and is also optically similar to authigenic feldspar (Lee and Parsons, 2003;Worden and Rushton, 1992). The optical similarities include (i) a turbid appearance due to the presence of very small inclusions, (ii) simultaneous extinction across the zone in cross-polarised light, rendering it optically continuous, and (iii) asynchronous extinction with zones 1 and 2 in cross-polarised light, revealing an optical discontinuity with the rest of the crystal. Therefore, we suggest that zone 3 is analogous to authigenic felspar from sedimentary rocks and thus likely formed from H 2 O-rich fluid (Kastner and Siever, 1979).
Unfortunately, quantitative estimates of the temperature at which any given zone of the studied crystal formed cannot be made with the available data. However, several lines of evidence suggest that Itrongay felspar could have formed and subsequently remained at lower temperatures than previously assumed. First, zones 1 and 3 have very weak luminescence, which has only been observed in authigenic feldspar and hydrothermal adularia that were estimated to have formed at temperatures below ~300 °C (Kastner and Siever, 1979;Lee and Parsons, 2003;Takahashi et al., 2008). Second, the estimated temperatures of adularia crystallisation in hydrothermal systems that were suggested to have had colloidal SiO 2 fall within the range of 150-285 °C (Dong and Morrison, 1995;Takahashi et al., 2008). Third, in sedimentary rocks opal-CT transforms to quartz at > 100 °C, albeit in the presence of H 2 Orich fluid (Behl, 2011;Keller and Isaacs, 1985). Therefore, it is conceivable that each subzone in the studied crystal rapidly crystallised at ≲300 °C and subsequently cooled to < 100 °C. While there are no experimental data that can be directly compared with our observations, data for apparently similar systems suggest that SiO 2 -rich liquids can form at temperatures as low as ~300 °C (Wilkinson et al., 1996) and remain liquid even at ~250 °C (Kotel'nikova and Kotel'nikov, 2011). Further petrological and/or experimental studies are required to estimate precisely the temperature (and pressure) of Itrongay feldspar crystallisation.

Apatite inclusions and their UePb dates
We have characterised and dated three apatite inclusions from zone 1 of the studied Itrongay feldspar crystal. These inclusions were isometric, rounded and appeared slightly turbid when viewing from the side due to surface roughness, which is probably related to natural etching before their entrapment. Trace element mapping of the largest inclusion revealed concentric zoning in U, Th, La, Y, and Zr, indicating that trace elements were evenly supplied from every side during its crystallisation. All of these characteristics suggest the apatite inclusions formed before being trapped within the feldspar, and thus they are protogenetic inclusions. The UePb dates of these inclusions (530.0 ± 7.3 to 576.4 ± 8.5 Ma) exceed the 40 Ar/ 39 Ar dates of their host feldspar (120 ± 70 Ma to 466 ± 8 Ma) by > 50-100 Ma (Fig. 9). They also exceed by the same amount all of the previous 40 Ar/ 39 Ar dates (416 ± 3 Ma to 474 ± 5 Ma; Arnaud and Kelley, 1997;Flude et al., 2014;Nägler and Villa, 2000) and the previous KeCa date (477 ± 2 Ma; Nägler and Villa, 2000) of Itrongay feldspar (Fig. 9). While the difference between the UePb dates and the 40 Ar/ 39 Ar dates can in principle be explained by assuming that the apatite inclusions and their host feldspar are of the same age and that the host feldspar has partially lost 40 Ar by diffusion, such explanation would contradict the observation that the UePb dates are much older than the KeCa date of Itrongay feldspar, albeit not of the same crystal. If this assumption was accurate, the KeCa date would be expected to exceed the UePb dates, since Ca diffusion in potassium feldspar (Cherniak and Watson, 2019) is slower than Pb diffusion both in potassium feldspar (Cherniak, 2010b) and apatite (Cherniak, 2010a). Another contradiction to this assumption is that there is no elevated 206,207 Pb concentrations in the feldspar adjacent to these inclusions, which would be expected considering that Pb diffusion in potassium feldspar (Cherniak, 2010b) is slower than in apatite (Cherniak, 2010a). Therefore, we suggest that the dated apatite inclusions are older than their host feldspar and represent xenocrysts. Considering that each of these apatite xenocrysts is contiguous with a pyroxene crystal, it seems reasonable to assume that they were derived from one of the pyroxene-bearing rocks that host the Itrongay pegmatite.
Different inclusions yielded different UePb dates (Fig. 7K). These variations could be explained by suggesting that the dated inclusions were derived from different rocks. However, considering the following two observations, it seems more likely that these inclusions were derived from the same rock. First, the mineralogical diversity of inclusions in zones 1 and 2 in the studied feldspar crystal is relatively narrow, while the assemblages of potential xenocrysts are different. For example, graphite is only present in zone 2. This suggests that the fluids from which any given zone grew carry xenocrysts from a limited amount of sources rather than from every rock in southern Madagascar (note that graphite is relatively common in them, e.g. de Wit et al., 2001). Second, all three dated inclusions have similar appearance in CL images and each of them is contiguous with a pyroxene crystal. This suggests that they could have been part of the same rock. If the dated inclusions are from the same rock, then what accounts for the variation in their UePb dates? Considering that they were carried and apparently even etched by fluids, the first guess would probably be the fluid-induced recrystallisation. The CL image of the largest inclusion has some irregular bright features that appear as slightly turbid volumes beneath the polished surface in transmitted light. By analogy with alkali feldspar, where turbidity usually develops by fluid-induced recrystallisation (e.g. Parsons et al., 2015;Parsons and Lee, 2005), we suggest that these turbid volumes represent altered apatite. However, this visible alteration has affected relatively small volumes within the inclusion and probably occurred simultaneously with the above-mentioned natural etching (there is no evidence of alteration in surrounding feldspar). Only in one of our UePb analyses we sampled from such altered volume (not intentionally), which gave the youngest UePb date from the largest inclusion (marked with asterisk in Fig. 7I). Other UePb analyses were obtained from pristine volumes, and there is no evidence to suggest that these volumes were affected by alteration (such as different U/ Th ratios in trace element maps). Therefore, we suggest that fluid-induced recrystallisation did not play a significant role in resetting UePb dates of these apatite inclusions. The remaining alternative is that the observed UePb date variations result from the diffusive loss of 206,207 Pb that occurred before the dated xenocrysts were entrained by the fluid from which their host feldspar grew. It may seem at a first glance that such interpretation is contradicted by the fact that Pb is homogeneously distributed in the largest inclusion (Fig. 7E) rather than showing a decrease in concentration towards the rim. However, two things need to be pointed out here. First, following previous application of apatite UePb thermochronometer (Chamberlain and Bowring, 2001;Cochrane et al., 2014;Paul et al., 2019Paul et al., , 2018Schoene and Bowring, 2007), only radiogenic 206,207 Pb is expected to show bell-shaped rim-core-rim concentration gradients, not total. Second, the very expectation of such gradients is based on the assumption that radiogenic 206,207 Pb is lost to an infinite reservoir as soon as it reaches the boundary of apatite crystal, which has not been systematically tested, and violation of which can result in homogeneously distributed 206,207 Pb in apatite (both total and radiogenic; Popov and Spikings, 2018). The only prediction of the diffusive loss of radiogenic 206,207 Pb that can be checked using our data is the presence of positive correlation between the UePb dates of the inclusions and their sizes (e.g. Dodson, 1973;Cochrane et al., 2014;Popov and Spikings, 2018), and there is such correlation (Fig. 7K). In the absence of significant alteration this correlation indicates that the obtained UePb dates likely were partially reset by diffusion.
While the dated apatite inclusions seem to have lost 206,207 Pb by diffusion, their xenocrystic origin and natural etching render them poorly suited for thermochronology. The size of the dated inclusions was apparently reduced to an unknown extent by etching, it is impossible to constrain how boundary conditions changed through time, and there still is a chance that these inclusions were derived from three different rocks with similar lithology but different histories. Any timetemperature path derived by inversion modelling of our UePb data would be of questionable reliability. The only point of such modelling would be to show that a time-temperature solution can be found, and that this solution is not completely unreasonable when compared with a priori knowledge of regional geology. A failure to show this would falsify our hypothesis that the dated apatite inclusions were derived from the same rock. Even without inversion modelling our results indicate that at the time when Itrongay feldspar formed, some rock adjacent to the Itrongay pegmatite contained apatite that apparently lost 206,207 Pb by diffusion. This rock would be a perfect target for any further attempt to constrain the thermal history of the host rocks of the Itrongay pegmatite using fully appropriate material. It is also important to note that some apatite inclusions in the studied crystal of Itrongay feldspar appear to be cogenetic with it. We were unable to successfully find and prepare for analysis sufficiently large inclusions of this kind, but it might be possible to find them in some other crystal of Itrongay feldspar.

40 Ar/ 39 Ar dates of Itrongay feldspar
We obtained eight in situ 40 Ar/ 39 Ar date profiles traversing (sub) zones 1, 2a, 2b and 3a of the studied Itrongay feldspar crystal. The 40 Ar/ 39 Ar dates range from 120 ± 70 Ma to 466 ± 8 Ma (2σ ext.), and overlap with previously reported 40 Ar/ 39 Ar dates of Itrongay feldspar, including plateau dates of 435 ± 8 Ma (Arnaud and Kelley, 1997) and 461 ± 6 Ma (Nägler and Villa, 2000) and in situ dates ranging from 416 ± 3 Ma to 474 ± 5 Ma (Flude et al., 2014;Fig. 9). Most of the 40 Ar/ 39 Ar dates are younger than the KeCa isochron date of 477 ± 2 Ma that was obtained for Itrongay feldspar (Nägler and Villa, 2000; Fig. 9). Previous studies suggested that the intra-grain variation of the 40 Ar/ 39 Ar dates (Flude et al., 2014) and the differences between the 40 Ar/ 39 Ar dates and the KeCa date (Flude et al., 2014;Nägler and Villa, 2000) solely result from the diffusive loss of 40 Ar. It was also argued that Itrongay feldspar crystals acted as grain-scale diffusion domains during their geologic histories (Flude et al., 2014). However, as we discuss below, our results are not consistent with these interpretations, as well as any other previously proposed model for the diffusive loss of 40 Ar.
An excess of the KeCa date reported by Nägler and Villa (2000) over the 40 Ar/ 39 Ar date of the same sample (Nägler and Villa, 2000) and the majority of 40 Ar/ 39 Ar dates of other samples (this work; Arnaud and Kelley, 1997;Flude et al., 2014) indicates that Itrongay feldspar may have partially lost 40 Ar by diffusion. However, two of our observations are incompatible with the diffusive loss of 40 Ar via a single mechanism from a grain-scale diffusion domain with homogeneously distributed 40 K (i.e. following the proposition of Flude et al., 2014), which is expected to produce smooth bell-shaped rim-core-rim 40 Ar/ 39 Ar date profiles with monotonically decreasing 40 Ar/ 39 Ar dates towards the crystal rims. First, many of the 40 Ar/ 39 Ar date profiles obtained here have a staircase topology (Fig. 5D-G). Second, while the obtained 40 Ar/ 39 Ar dates generally decrease with increasing distance from the crystal core, some deviations from this trend occur. Profile B shows that in some regions within zone 1 the 40 Ar/ 39 Ar dates steadily increase over a distance of ~300 μm when approaching the crystal rim, after which they abruptly decrease (Fig. 5B). Profile F shows an analogous relationship within zone 2 (Fig. 5F). The first observation can in principle be accounted for by invoking multi-path diffusion (e.g. Lee, 1995;Baxter, 2010) or diffusion via several mechanisms (by analogy with Li in olivine in Dohmen et al., 2010) from a grain-scale diffusion domain with homogeneously distributed 40 K. However, both these scenarios are expected to produce 40 Ar/ 39 Ar dates that steadily decrease when approaching the crystal rim, which conflicts with the second observation. This complication can in principle be accounted for by introducing unevenly distributed traps for 40 Ar, and as we discuss in the next paragraph there are potential candidates for this role. However, the resulting model would probably be excessively ad hoc, and there is no evidence to support any hypothetical distribution of short  40 Ar/ 39 Ar plateau date from Arnaud and Kelley (1997), (c) 40 Ar/ 39 Ar plateau date and KeCa isochron date from Nägler and Villa (2000). Our 40 Ar/ 39 Ar dates are grouped by (sub)zones and 40 Ar/ 39 Ar dates that were obtained from the boundaries between the (sub)zones are not shown. 2σ external uncertainties are shown in all cases except for crystal B from Flude et al. (2014), where the nature of 2σ uncertainty is unclear to us (not specified in the original work, potentially internal). Horizontal line of pale orange colour shows the KeCa date from Nägler and Villa (2000) with 2σ external uncertainty. circuits or the use of several diffusion mechanism. Finally, when combined with the results of Ar diffusion experiments on Itrongay feldspar (Arnaud and Kelley, 1997;Cassata and Renne, 2013;Wartho et al., 1999), our second observation is inconsistent with the diffusive loss of 40 Ar that would be compatible with multi-diffusion domain theory of Lovera et al. (1989). Abrupt changes in the 40 Ar/ 39 Ar dates along the profiles imply that the size of any intra-grain diffusion domain cannot significantly exceed the size of an ablation pit with 50 μm diameter, which is incompatible with the diffusion experiments, since they suggest that much larger Itrongay feldspar fragments generally behave as grain-scale diffusion domains during laboratory outgassing. Therefore, we suggest that while some diffusive loss of 40 Ar may have occurred, it does not represent the main factor accounting the observed variability in 40 Ar/ 39 Ar dates.
The most significant changes in dates along the 40 Ar/ 39 Ar date profiles obtained here correspond to the boundaries between different (sub)zones (Fig. 5A-H), and different (sub)zones yield distinguishable average 40 Ar/ 39 Ar dates that steadily decrease when approaching the crystal rim (Fig. 6B). This suggests that the major component in the observed 40 Ar/ 39 Ar date variations likely reflects the real crystallisation age differences between the described (sub)zones. However, several observations indicate that these variations cannot be entirely explained by the crystallisation age variations. First, in several places 40 Ar/ 39 Ar dates increase towards the rim, for example in zone 1 in profile B (5B) and in zone 2 in profile F (Fig. 5F). Second, any given (sub)zone yields significantly scattered 40 Ar/ 39 Ar dates, which is expressed in high MSWD values that are calculated for their weighted means (Figs. 5A-E, 6B). Third, a comparison of the 40 Ar/ 39 Ar dates obtained here and in Arnaud and Kelley (1997), Nägler and Villa (2000), and Flude et al. (2014) with the KeCa date from Nägler and Villa (2000) indicates that some diffusive loss of 40 Ar may have occurred (Fig. 9). The available evidence is yet not sufficient to reliably identify the cause(s) of these complications. Probably, some component in the observed variability of in situ 40 Ar/ 39 Ar dates is related to the presence of nm-scale inclusions of an unidentified mineral, which were previously reported from Itrongay feldspar (Parsons and Lee, 2005;Wartho et al., 1999). We envisage two end-member models (A and B), both of which assume that the inclusions are unevenly distributed within Itrongay feldspar (as was suggested by the cited studies), and have low Cl and Ca concentrations (to account for the absence of Cl-derived 38 Ar and Ca-derived 37 Ar in our analyses). Model A further assumes that the inclusions host excess or inherited 40 Ar within them or excess 40 Ar at their boundaries, so that the regions with abundant inclusions yield older 40 Ar/ 39 Ar dates (Fig. 10). Model B further assumes that some radiogenic 40 Ar diffused into the boundaries of these inclusions during the geologic past and escaped from them during sample preparation, for example due to microcracking. In this case, regions with higher concentrations of inclusions would yield younger 40 Ar/ 39 Ar dates (Fig. 10). An analogous model was proposed in Arnaud and Kelley (1997), who conducted several step-heating and in vacuo crushing experiments with Itrongay feldspar. Their step-heating 40 Ar/ 39 Ar data suggested partial loss of 40 Ar from the outer 5-10 μm of the analysed fragments irrespective of where these fragments were located in the original crystal. Their in vacuo crushing experiments suggested that a considerable amount of 40 Ar is stored in relatively Cl-free traps (almost no Cl-derived 38 Ar was detected). Their preferred interpretation is that some of 40 Ar diffused into the traps during geologic past and escaped the analysed fragments when the traps were opened by sample preparation.
While further studies are clearly required to verify the proposed models, we speculate that both come into play in the studied crystal of Itrongay feldspar. Model A provides a reasonable explanation for fact that the oldest 40 Ar/ 39 Ar dates obtained from zone 2 in profile F were obtained from the boundary between subzones 2a and 2b. This boundary appears as a dark wavy stripe in the BSE image of the studied crystal, indicating that it may contain an increased amount of some crystal structure defects, potentially inclusions with excess or inherited 40 Ar (consider that zone 2 is optically continuous). However, model A cannot readily explain why all of the 40 Ar/ 39 Ar dates that were obtained here and previously (Arnaud and Kelley, 1997;Flude et al., 2014;Nägler and Villa, 2000) are younger than the KeCa date of Itrongay feldspar (Nägler and Villa, 2000). Model B can account for the discrepancy between the 40 Ar/ 39 Ar and KeCa dates by relating it to the diffusive loss of 40 Ar (followed by the loss of 40 Ar induced by sample preparation). However, it is not trivial to invoke model B as an explanation for relatively old 40 Ar/ 39 Ar dates from the boundary between subzones 2a and 2b, as it would require that the inclusions are less abundant at the boundary than around it and thus contradict the results of BSE imaging. Therefore, we suggest that the 40 Ar/ 39 Ar date variations in zone 1 are explained by model B, while the 40 Ar/ 39 Ar date variations in zones 2 and 3 are explained by model A. Following model B, the previously reported KeCa date of 477 ± 2 Ma (Nägler and Villa, 2000) can be interpreted as the crystallisation age of zone 1, while the youngest 40 Ar/ 39 Ar dates obtained from this zone, which have a weighted mean of 440.9 ± 4.5 Ma, can be interpreted as the age of cooling through an unconstrained temperature. Following model A, the youngest 40 Ar/ 39 Ar dates that we obtained from subzones 2a, 2b and 3a, which have weighted means of 401.7 ± 4.8 Ma, 375.3 ± 4.5 Ma and 176 ± 19 Ma, respectively, are least affected by excess or inherited 40 Ar and thus can be interpreted as the crystallisation ages of these subzones. Notably, the composite 40 Ar/ 39 Ar date profile presented in Flude et al. (2014) is similar to our profile A (Fig. 5A). While we cannot rule out the possibility that the interpretation made in Flude et al. (2014) is accurate, this similarity suggests that it could have resulted from not recognising the presence of thin overgrowths of younger feldspar. Their crystal did not have noticeable overgrowths of turbid feldspar like ours, but it could have had overgrowths of gemquality feldspar similar to zone 2 in the crystal studied here.

Summary and implications
Collectively our petrological and geochronological interpretations suggest that the studied Itrongay feldspar crystal formed during five discrete growth episodes that were separated from each other by tens to hundreds of millions of years. Each growth episode postdates hightemperature metamorphism that is recorded regionally across the Androyan domain. Zone 1 precipitated from co-existing CO 2 -dominated fluid and dense SiO 2 -rich colloid solution, and its crystallisation age is estimated to be 477 ± 2 Ma (KeCa date reported by Nägler and Villa, 2000). The 40 Ar/ 39 Ar dates obtained from this zone are interpreted to be partly reset by the diffusive loss of 40 Ar. Subzones 2a and 2b probably formed in a similar environment, and their crystallisation ages are estimated to be 401.7 ± 4.8 Ma and 375.3 ± 4.5 Ma, respectively (weighted means of the second to fourth youngest 40 Ar/ 39 Ar dates). Subzones 3a and 3b appear analogous to authigenic feldspar from sedimentary rocks and thus may have precipitated from H 2 O-rich fluid. The crystallisation age of subzone 3a is estimated to be 176 ± 19 Ma (weighted mean of the second to fourth youngest 40 Ar/ 39 Ar dates), while subzone 3b is too thin to be dated. Some small apatite inclusions within zone 1 (the crystal core) are cogenetic with the host feldspar. However, the three large apatite inclusions that we used for UePb dating are xenocrysts that could have been derived from the pyroxenebearing rocks that host the Itrongay pegmatite. The UePb dates of these xenocrysts are interpreted to be partially reset by the diffusive loss of radiogenic 206,207 Pb that occurred before trapping by the feldspar crystal.
Our results have important implications for 40 Ar/ 39 Ar dating of alkali feldspar and UePb dating of apatite. The 40 Ar/ 39 Ar data acquired here are inconsistent with the suggestion of Flude et al. (2014) that Itrongay feldspar partially lost 40 Ar by volume diffusion through a continuous crystal structure without any complications related to the presence of crystal structure defects. In combination with the results of previous diffusion experiments on Itrongay feldspar (Arnaud and Kelley, 1997;Cassata and Renne, 2013;Wartho et al., 1999), these data are also inconsistent with the model of the diffusive 40 Ar loss offered by multi-diffusion domain theory (Lovera et al., 1989). Furthermore, while the studied Itrongay feldspar crystal probably experienced some diffusive loss of 40 Ar (via yet unconfirmed model B; Section 5.3), much greater component in the observed 40 Ar/ 39 Ar date variations is the result of fluid-induced dissolution and overgrowth. Clearly, there is a lack of unambiguous evidence for the diffusive loss of 40 Ar from alkali feldspar that can be quantitatively interpreted using existing models, and further research is needed to develop a framework for reconstructing the thermal histories of rocks using this mineral. Our results also show that in situ 40 Ar/ 39 Ar dating of alkali feldspar combined with petrological characterisation is a promising tool for tracking fluid flow events in the Earth's crust, which can seek applications beyond authigenic K-rich feldspars from sedimentary rocks (e.g. Hagen et al., 2001;Mark et al., 2007) and perhaps used in a way analogous to U-Th-Pb dating of texturally different domains within gem-quality monazite from alpine clefts (e.g. Bergemann et al., 2017;Ricchi et al., 2019). Our apatite UePb data suggest that in some cases 206,207 Pb can be lost from apatite by volume diffusion without significant contribution from chemical alteration, supporting previous suggestions that UePb dating of apatite can be used for thermochronology (Chamberlain and Bowring, 2001;Cochrane et al., 2014;Paul et al., 2019Paul et al., , 2018Schoene and Bowring, 2007).
The most important implication of our work for the geology of southern Madagascar is that it provides evidence for multiple episodes of fluid circulation which occurred after the Ediacaran to early Cambrian high-temperature metamorphism. This adds to several previous studies that invoked fluid-induced dissolution-reprecipitation to explain some U-(Th)-Pb dates of monazite (Fernandez et al., 2003;Grégoire et al., 2009;Martelat et al., 2000) and titanite (Holder and Hacker, 2019) and 40 Ar/ 39 Ar dates of micas (Fernandez et al., 2003) derived from Madagascan rocks. Collectively, these results show that resetting of isotopic dates by fluid-induced recrystallisation is a viable process that could have affected the geochronological record of Madagascar and therefore requires careful consideration in future studies. Our work also reveals the nature of the mineralising fluids that percolated Madagascan crust subsequent to the Ediacaran to early Cambrian metamorphism (CO 2 -dominated fluid + dense SiO 2 -rich colloid solution, later probably H 2 O-rich fluid), adding to several previous studies that constrain the origin of mineralisation in this region (e.g. Morteani et al., 2013;Martin et al., 2014;Montel et al., 2018).

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.