Introduction

Anatectic migmatites record signatures of partial melting events in mid- to deep-crustal levels at the roots of orogenic belts (Ashworth 1985; Brown 2001; Whitney et al. 2004; Beaumont et al. 2006). The restitic parts preserved in many migmatites are archives of the geological history that pre-dates the melting event (Guernina and Sawyer 2003; Sawyer 2008). Both experimental and theoretical works demonstrate that the dynamic viscosity of partially molten rocks is reduced by several orders of magnitude depending on the volume fraction of melt (Arzi 1978; Vigneresse et al. 1996; Berger and Kalt 1999; Takeda and Obata 2003). Therefore, in situations, where the production, segregation and emplacement of melts are synchronous with active deformation, strain is likely to be complexly partitioned into low-viscosity melt-dominated layers within the deforming matrix of the bulk rock. However, in such experiments strain rates and temperatures are unrealistic thus experimental results may not be directly applied to study deformation patterns in migmatites (Paterson 1987; Rutter and Neumann 1995). Consequently, detailed studies of natural migmatites are crucial.

Deformation microstructures in minerals in anatectic migmatites in melt-dominated and melt-absent domains can be determined from quantitative orientation analysis including internal deformation features (e.g., subgrains) and their CPOs using electron backscatter diffraction (EBSD) studies (Venables and Harland 1973; Prior et al. 1999; Kleinschrodt and Duyster 2002; Ji et al. 2003; Mainprice et al. 2004; Storey and Prior 2005; Hasalová et al. 2008; Menegon et al. 2011; Cavalcante et al. 2013). The results of such EBSD studies may be combined with quantitative phase equilibrium modeling of melting reactions in migmatites to understand how naturally occurring minerals respond to far-field stress before, at and after supra-solidus conditions. In this study, we integrate the results of phase equilibrium modeling of anatectic migmatites using P–T pseudosection modeling and EBSD studies in a garnet–biotite–mullite migmatite of the Bhilwara Supergroup (Fig. 1a) from a Grenvillian-age, Northern Indian shear zone to demonstrate the complex interplay between deformation strain, mineralogical reactions and crystallization microstructures developed in quartz, mullite and garnet at subsolidus and supra-solidus condition.

Fig. 1
figure 1

a Generalized tectonic map of India showing the Archean cratons and Proterozoic mobile belts. ADFB Aravalli Delhi Fold Belt, AC Aravalli Craton, BuC Bundelkhand Craton, SC Singhbhum Craton, BC Bastar Craton, EDC Eastern Dharwar Craton, WDC Western Dharwar Craton, CITZ Central Indian Tectonic Zone, CGC Chotanagpur Gneissic Complex, SPGC Shillong Plateau Gneissic Complex, EGMB Eastern Ghats Mobile Belt, SIG South Indian Granulite terrain, HOB Himalayan Orogenic Belt, DV Deccan Volcanics; 1 Mahanadi Rift, 2 Godavari Rift, 3 Closepet Granite. Gray regions show the Grenvillian orogenic belt. The study area (ADFB) is shown in the box. b Map showing different lithological and tectonic components of Aravalli Craton and Aravalli Delhi Fold Belt (modified after Heron 1953; Roy and Jakhar 2002). GF: Grenvillian Font after Ojha et al. (2016). Box indicates location of the study area. c Geological map of Bhilwara Supergroup from Rampura–Agucha area (modified after Roy 2000). Boxes show locations from which detailed structural analyses have been conducted and location (Rampura–Agucha mine pit) from which sample RAM-1 has been collected

Geological background and field relationships

The chosen field area lies in the Bhilwara Supergroup of Northern India (Fig. 1a). The Bhilwara Supergroup rocks are exposed along the central and eastern parts of Aravalli–Delhi Fold Belt (Raja Rao 1976; Gupta et al. 1980, 1997, Fig. 1b). Two distinct NNE–SSW trending belts constitute the Bhilwara Supergroup: (1) the western Meso- to Neoproterozoic amphibolite facies schist belt that extends from Rajpura–Dariba in the southwest to Pur-Banera in the northeast and the (2) eastern migmatite belt that extends up to the volcano-sedimentary successions of the Hindoli Group and Jahazpur Belt in the east, the granitoids and metasedimentary units of the North Delhi Fold Belt in the north (Fig. 1b; Gupta et al. 1997). The western schist belt consists of an interlayered sequence of garnet–staurolite–kyanite mica schists, calc-silicate gneisses and quartzites (Hazarika et al. 2013; Ojha et al. 2016). The garnet–sillimanite–biotite gneiss from which the sample studied stems forms the dominant lithology of the eastern anatectic migmatite belt and is associated with porphyritic granitoid plutons (Hazarika et al. 2013). The Archaean (~ 2.5 Ga) Berach granite (also called Banded Gneissic Complex, BGC-I; Heron 1953) and the ~ Palaeoproterozoic greenschist facies metasedimentary units of the Aravalli Supergroup defines the southern margin of Bhilwara Supergroup. Along their western margin, the migmatites of Bhilwara Supergroup share a NNE-trending tectonic contact (marked by ductile shear zones) with the polycyclic Meso- to Neoproterozoic granulites of the Mangalwar Complex and Sandmata Complex (together forming BGC-II, Heron 1953). Raja Rao (1976) and Gupta et al. (1980, 1997) propose the BGC-I to represent the basement for the Bhilwara Supergroup.

Geochronological data from the Bhilwara Supergroup are sparse. A single zircon age of ~ 1.45 Ga is reported from the mylonitized porphyritic granitoid in Rampura–Agucha (Roy and Jakhar 2002). A Pb–Pb model age of ~ 1.8 Ga is obtained by Deb and Thorpe (2004) and Deb et al. (1989) for the anatectic metapelites in Rampura–Agucha. Based on U–Th–Pb (total) age determinations, Hazarika et al. (2013) obtained a single age population of ~ 1.0 Ga in monazites in the pelitic migmatites of the area. However, multiple monazite age populations have been obtained from the garnet–staurolite–kyanite mica schists of the Rajpura–Dariba interpreted to date peak and retrograde metamorphic events (1.87 and 1.62 Ga; Hazarika et al. 2013) and Pur-Banera (1.37 and 1.05 Ga; Ojha et al. 2016).

The field area at Rampura–Agucha lies close to the northwestern margin of the migmatite belt (Fig. 1b). It is characterized by an ensemble of calc-silicate gneisses, amphibolites and anatectic garnet–biotite–sillimanite gneisses and mylonitized porphyritic granitoids (Fig. 1c). Three fabric-forming events are recognized in the garnet–biotite–sillimanite migmatites (Fig. 2a). We use a numbering system in accordance with relative age established in the field. The S1 fabric is noted exclusively as inclusion trails within garnet porphyroblasts (Table 1; Fig. 3a). The first set of mesoscopic fabric (S2) is defined by garnet-bearing leucosomes in a mesocratic matrix dominated by biotite intergrown with sillimanite, and coarse-grained quartz lenticles. The metatexite S2 layers are co-axially refolded (hook-shaped fold superposition structures are common) by isoclinal D3 folds and locally developed NNE-trending tight-to-open D4 folds that plunge towards NNE (Fig. 2a). The axial planar fabric (S3) is mutually indistinguishable from S2, except at D3 fold hinges (Fig. 2b, c). In contrast, D4 folding does not result in a recognizable fabric.

Fig. 2
figure 2

a Field photograph of anatectic garnet–biotite–sillimanite gneiss showing different stages of deformation (for detailed description see text). b, c Photographs showing the neosome parts of anatectic garnet–biotite–sillimanite-bearing migmatite (RAM-1). Mineral abbreviations in the figures and tables are after Kretz (1983). See text for description of structural elements in the rock

Table 1 Characteristics of microstructures and mineral assemblages
Fig. 3
figure 3

Optical microphotographs (a, b, df, hk), SEM image (c) and BSE image (g) displaying textures from RAM-1. a Photograph showing D1 crenulation hinges (defined by sillimanite and mullite) within garnet and pervasive S3 (defined by biotite, sillimanite, mullite), warping around garnet porphyroblast. Quartz–feldspar-bearing melt layers (S2) occur within the interfolial domains of S3. Relict rootless D1 crenulation hinges occur in the interfolial domains of S3; yellow arrowheads point to fracture filled with biotite and sillimanite/mullite. b Garnet porphyroblast preserving D1 crenulation hinges and quartz inclusion trails axial planar to the crenulation. c An elongated garnet porphyroblast in contact with S3. d A coarse potash feldspar grain (at contact of S3 biotites), containing rounded quartz inclusions and biotite inclusions. e Quartzo-feldspathic layer at contact of garnet porphyroblast showing melt-related microstructures like randomly oriented sillimanite and mullite and biotite grains in coarse potash feldspar, globular inclusions of quartz in potash feldspar and thin melt film (now represented by plagioclase) in between potash feldspar grains. f Thin films of plagioclase along the margins of coarser plagioclase indicate sites of melt crystallization. g Intergrowth of garnet with globular quartz grains indicates crystallization in presence of melt. h, i Coarse quartz grains in the D1 crenulation hinges are strained, show undulose extinction (yellow arrow) and presence of subgrains (red arrows). j Presence of euhedral plagioclase grain at the contact of coarse quartz grains crystallized from melt trapped melt in D2 garnet. Note presence of relict sillimanite

We selected a representative sample of the neosome part of the metatexite migmatite from a limb of a D3 fold, with typical garnet-bearing leucosome and restitic fine-grained layers warping around the leucosome layers (Fig. 2b, c). No D4 deformation features are seen at the sample location.

Analytical methods

Mineral chemistry and bulk chemistry

Mineral–chemical analyses of an anatectic garnet–biotite–sillimanite gneiss (RAM-1; Fig. 2b, c) were carried out with a CAMECA SX (EPMA) at Indian School of Mines, Dhanbad. Operating conditions for feldspar analyses were acceleration voltage 15 kV with 15 nA beam current, and 15 kV, 20 nA were used for biotite, garnet, sillimanite and ilmenite. In-built ZAF corrections were applied.

For pseudosection modeling, the bulk composition of the sample RAM-1 was determined by X-ray fluorescence at the National Geophysical Research Institute, Hyderabad. The analysis was done using a Phillips MagiX PRO Model 2440 XRF spectrometer.

Quantitative microstructural analysis and representation

Electron back-scatter diffraction (EBSD) analyses were done at Macquarie University on thin sections (sample RAM–1) cut perpendicular to S2 foliation (YX plane) and parallel to the fold axis lineation of F3 (X direction). Thin sections were carbon coated (~ 3 nm thick) following mechano-chemical polishing using colloidal silica. Full crystallographic orientation data were collected using automatically indexed EBSD patterns, acquired with an HKL Nordlys Nano high-sensitivity EBSD detector and indexed using the Aztec analysis software (Oxford Instruments). The SEM was run at a high vacuum, with an accelerating voltage of 20 kV, beam current of 8.2 nA, and with an aperture of 70 µm at a working distance of 9.5–10.5 mm. Data were collected on rectangular grids with step size of 5–25 µm (depending on the required spatial resolution of the crystallographic information) using a beam scan. Noise reduction on the raw data was performed following the procedure tested by Piazolo et al. (2006), Bestmann and Prior (2003) and Prior et al. (2002). In pole figures, data are represented as one point per grain, where a grain is defined as an area completely surrounded by high-angle (> 10°) boundaries. Grains which have a mean internal misorientation < 1° are considered to be strain free (Piazolo et al. 2006).

Monazite analyses

Th–U–Pb (total) age determinations in monazites were computed from analytical data obtained using the Cameca SX electron microprobe analyzer at the Indian School of Mines, Dhanbad following the “age calibration” (Petrík and Konecný 2009). These age data are then corrected against an age standard dated by SIMS method (Tomascak et al. 1998). Analytical settings were set as follows: counting times for Pb 150 s, Th 45 s, U 75 s, Y 45 s, and for all other elements 25–35 s; sample current 100–130 nA; beam diameter ~ 3 µm. Standards used were the following: P—Apatite, Ca—Wollastonite, La—La Glass, Ce—Ce Glass, Eu—Eu Glass, Si—Albite, Y—YAG, Al—Kyanite, Pb—Crocoite, Th—Thorium Glass, U—Uranium Glass, Pr—Pr Glass, Nd—Nd Glass, Sm—Sm Glass, Gd—Gd Glass, Dy—Dy Glass, Lu—Lu Glass. All errors are given as 2σ. Deconvolution histograms were calculated using Isoplot 4.15 (Ludwig 2001).

Results

General microstructure phase relationships and mineral chemistry

S2 foliation is defined by alternate melanocratic bands consisting of garnet porphyroblasts, biotite (Bt2), quartz (Qtz2) and leucocratic bands consisting of quartz (Qtz2), plagioclase (Pl2), and potash feldspar (Kfs2; Fig. 3a). Mineralogically similar leucocratic domains are also recognized in the pressure shadows of the garnet porphyroblasts (Table 1; Fig. 3a). Garnet porphyroblasts in the melanocratic bands of the penetrative S2 metatexite layers are often elongated with aspect ratios of 1.75–3.1 (Figs. 3c, 4). Often bulbous and lobate coarse, strain-free quartz (Qtz2) grains are intergrown with garnets. Fractures within garnet porphyroblasts are oriented perpendicular to porphyroblast elongation (Table 1; Fig. 3c). These fractures in garnet are filled with biotite (Fig. 3c) or biotite–mullite–sillimanite (Fig. 3a). In garnet porphyroblasts D1 crenulation hinges are mainly defined by mullite (Mul1) and sillimanite (Sil1) (Figs. 3a, b, 4). Inclusion trails of quartz (Qtz1) ribbons and resititic biotite (Bt1) grains are axial planar to these crenulations. Qtz1 from the relict D1 hinges in the matrix exhibit undulose extinction and distinct subgrains (Fig. 3h, i). Rootless crenulation hinges (defined by Bt1 + Sil1 + Mul1) that formed during D1 with orientation similar to those within garnet porphyroblasts also occur in the interfolial domains of S3 (Fig. 3a). Coarse potash feldspar (Kfs2) grains in the leucocratic layers of S2 contain sillimanite (Sil1), biotite (Bt1) and quartz (Qtz1) grains (Table 1; Fig. 3d, e). Quartz (Qtz1) inclusions in these potash feldspar (Kfs2) grains are often rounded and form rims around biotite (Bt1) inclusions (Fig. 3e). In leucocratic domains, plagioclase (Pl2) with low dihedral angles occurs at the margins of coarse potash feldspar grains (Fig. 3f). The pervasive foliation in the sample is S3 which is axial planar to the D3 folds and transposes S2. S3 is defined by the shape-preferred aggregates of biotite (Bt3), sillimanite (Sil3) and mullite (Mul3) that warp around garnet porphyroblasts in the melanocratic bands of S2 (Figs. 3a, b, 4; Table 1). In these S3 domains, quartz is fine grained. The interfolial domains of S3 consist of the quartz–feldspar-dominated S2 leucosomes (Figs. 3a, 4), with modally subordinate biotite, Bt2 (Fig. 3a). To distinguish between the Bt + Sil + Mul assemblages in the S3 foliation from those seen in garnet fractures, we label the latter as Bt4 + Sil4 + Mul4 (Fig. 3a, c, g).

Fig. 4
figure 4

Schematic sketch showing deformation microstructures, i.e., a D1 deformation; b D2 deformation; c D3 deformation

XMg in the cores of garnet porphyroblasts are tightly constrained between 0.19 and 0.20 (Table 2). In contrast, the corresponding values at the rims of the garnet grains (~ 0.15–0.17) against S3 biotite (Bt3) and biotites in the fractures are variable, but against quartz grains, the values are identical. Biotite inclusions in garnet (Bt1) and matrix biotite (Bt2) in the S2 foliation show near-identical XMg (0.54 for one Bt1 analyses and 0.55–0.56 for Bt2) and TiO2 contents (2.11 pfu for Bt1 and 1.74–1.99 pfu for Bt2; Table 2). XMg and TiO2 values of coarse biotite grains (Bt3) from the S3 foliation range from 0.55 to 0.58 and 1.21–2.13 pfu, respectively. The XMg values of Bt3 are similar to that of the Bt1 and Bt2, although their TiO2 contents show significant variations. Biotites filling the fractures in garnets (Bt4) are richer in Mg than Bt1, Bt2 and Bt3. TiO2 content of biotites in garnet fractures (Bt4) is in the range 0.1–0.89 pfu (Table 2).

Table 2 Representative mineral chemical analyses (EPMA) from RAM-1

Mineral paragenetic relationships: their interpretation in terms of succession of geological events

The succession of mineral assemblages that is stable with quartz and plagioclase is shown schematically in Fig. 4. The warping of Bt3 + Sil3 + Mul3 aggregates around garnet porphyroblasts and S3 continuity indicates pre-D3 garnet (Fig. 3a) growth and fracturing. Coarse K-feldspar (Kfs2) grains in the leucosomes rimming the garnet porphyroblasts, and those occurring in S3 interfolial domains, host biotite (Bt1), sillimanite (Sil1), and quartz (Qtz1) inclusions, indicating K-feldspar and garnet crystallized from melt (Fig. 3d, e). Bt2 at the contacts of garnets with globular quartz (Qtz2) grains and with the leucocratic layers of S2 is also observed (Fig. 3a, g). The occurrence of garnet within leucocratic domains indicates garnet formation was syn-D2. Relict sillimanite (Sil1)–mullite (Mul1)–biotite (Bt1)-bearing crenulation hinges within garnet porphyroblasts, and in the S3 interfolial domains indicate that these are D1 deformation features overgrown by D2 garnet porphyroblasts. The presence of thin films of plagioclase (Pl2) around coarse K-feldspar (Kfs2) and plagioclase (Pl1/2) in the leucosome and the coarse quartz (Qtz2) grains intergrown with garnet corroborate anatexis synchronous with D2 (Fig. 3e, f). Coarse quartz (Qtz2) and plagioclase (Pl2) within garnet grains in Fig. 3j are interpreted to have crystallized from trapped melt.

Bt4 + Sil4 + Mul4 assemblages present in garnet fractures or Bt4 at the contact with garnet margins and at the contacts of garnet and Qtz2 are interpreted to represent the retrograde assemblage generated by back-reactions of melt in garnet fractures and boundaries. Similar TiO2 content (1.77 pfu) noted in one such biotite grains (Table 2) with some of the biotite grains (Bt3; 1.74–1.88 pfu) from the S3 layers indicates that they crystallized at comparable temperatures. Hence, we conclude that retrogression along garnet fractures is at the veining stages of D2. The lower TiO2 (0.1–0.59 pfu) and higher XMg (0.63–0.67) contents in most of the biotite grains seen in garnet fractures compared to the Bt3 suggest that biotite crystallization continued to lower temperatures after the melt had largely crystallized and solid-state deformation occurred in S3 fabric.

Constraints on P–T conditions of melting

A key factor in pseudosection analyses is to determine the ‘effective bulk composition’, which represents the equilibration volume of the rock (Spear 1993; Stüwe 1997). This equilibration volume varies from grain scale, e.g., zoned minerals and reaction coronae (Nasipuri et al. 2009) to larger scales, i.e., in hand specimen scale (Stüwe 2007; Kelsey et al. 2005; Nasipuri et al. 2009). In the studied migmatite sample RAM-1, garnet, biotite, and plagioclase in different layers show strong compositional homogeneity (Table 2). This suggests that the length scale of mineral equilibration attained during metamorphism was larger than the scale of the layers of mineralogical segregations (Fig. 2b, c); the equilibration was possibly aided by element transfer across neosomes of varying width (couple of mm to cm) which are seen to be commonly inter-layered and dispersed in biotire + sillimanite segregations. Consequently, for pseudosection analyses we use the bulk rock composition derived from a handspecimen to define the effective bulk composition (results given in Table 3).

Table 3 XRF data of RAM-1

P–T pseudosections were constructed (Table 3) in the NCKFMASH system using the PERPLE_X (Connolly 2005) software built on the thermodynamic database of Holland and Powell (1998) modified in 2004. Manganese was excluded from the system as the spessartine contents in garnet is extremely low, and manganese is absent in other Fe–Mg phases (Table 2). The TiO2 content in the rock is low and, therefore, also excluded in the computation. Solution models for phases used in P–T pseudosection modeling are: (1) garnet: hybrid model of Holland and Powell (1998), Engi and Wersin (1987); (2) biotite: White et al. (2007); (3) muscovite: hybrid model of Coggon and Holland (2002) and Auzanneau et al. (2010); (4) feldspar: Benisek et al. (2004); (5) melt: hybrid model of Holland and Powell (2001) and White et al. (2001).

Melt volume percentages depend on the availability of free H2O during initiation and progress of partial melting reactions (Webb et al. 2015). H2O influencing partial melting reactions is primarily produced by dehydration reactions in surrounding rocks that may eventually get trapped in the rocks or added to the rock along shear zones (Brown 2002; White and Powell 2002, 2010; Webb et al. 2015). To estimate the H2O available in the rock during partial melting under both H2O-fluxed and H2O-absent conditions, we constructed isobaric T–MH2O pseudosections (“Appendix” Fig. 11a, b; MH2O representing mol% of water in the bulk). We chose reference pressures of 6 and 8 kbar based on the 6–8 kbar pressure reported for the Grenvillian-age peak metamorphic condition obtained in mica schists of the Bhilwara Supergroup rocks from the Pur-Banera area (Ojha et al. 2016). The T–MH2O pseudosections indicate stability of garnet–sillimanite–feldspar (ternary)–quartz–biotite–melt assemblage during H2O-deficient melting at temperature ranges of 690–840 °C, and during H2O-fluxed melting at 690–750 °C. H2O contents for H2O–undersaturated and water-fluxed conditions partial melting, as estimated from the T–MH2O pseudosections have been considered for construction of the PT pseudosections in Fig. 5a–d.

Fig. 5
figure 5figure 5

Pseudosections in NCKFMASH system from bulk composition of RAM-1. Molar proportions under H2O-fluxed conditions are SiO2:Al2O3:FeO:MgO:CaO:Na2O:K2O: H2O = 48.33:9.63:5.22:8.48:1.15:1.15:2.90:23.14. a PT pseudosection under H2O-fluxed melting condition, showing stability field of garnet–sillimanite–feldspar–biotite–quartz–melt-bearing assemblage noted in the sample, at PT ranges of 5–8 kbar, 725–780 °C. b Compositional isopleths of garnet, biotite and feldspar in the PT pseudosection of C and star sign indicates highest PT for melting reaction. c, d Modal isopleths of different phases in the PT pseudosection of (a). e PT pseudosection under H2O-absent melting condition. Oxide molar proportions of the bulk are SiO2:Al2O3:FeO:MgO:CaO:Na2O:K2O:H2O = 58.09:11.57:6.27:10.19:1.38:1.38:3.49:7.62. f Compositional isopleths of garnet, biotite and feldspar in the PT pseudosection of (e). The yellow-, gray- and pink-shaded fields, respectively, show stability of biotite ± garnet, orthopyroxene and cordierite with melt. MMC, MSC and MPB show peak PT conditions for the Grenvillian anatexis in the Mangalwar Complex (after Bhowmik et al. 2010), Sandmata Complex (after Saha et al. 2008) and Pur-Banera supracrustals (after Ojha et al. 2016)

The P–T pseudosections show stability of the garnet–sillimanite–feldspar–quartz–biotite–melt peak metamorphic assemblage in PT ranges of 5–8 kbar, 720–740 °C during H2O-fluxed melting and ~ 780–850 °C, 5–10 kbar at H2O-absent melting (Fig. 5a, e). In both cases, garnet modal isopleths increase with temperature and increasing melt modes and decreasing biotite and sillimanite modes thus indicating formation of garnet as a peritectic phase (Fig. 5c, d). Within the field of the peak assemblage in the PT pseudosections in Fig. 5b, f, (marked as yellow), the XMg isopleth of 0.2 for peritectic garnet (corresponding to the measured core composition of garnet porphyroblasts, Table 2) is bracketed between 730 °C and 780–800 °C. The computed volume % of melt in equilibrium with garnet compositional isopleth of XMg = 0.2, in case of H2O-fluxed melting is higher than the melt percolation threshold limit (~ 10–12 vol%) and lower for H2O-absent melting (Fig. 5d, e). Since the sample studied here is a migmatite where melt-rich layers form distinct bands supporting melt migration during formation of peritectic garnet porphyroblasts (Fig. 2a–c), we propose that the partial melting of the rock occurred under H2O-fluxed conditions when the mechanical conditions for melt segregation and migration was imparted. Peak pressure for stability of the assemblage garnet–biotite–sillimanite–melt is estimated to be ~ 8 kbar where the XMg isopleth (0.2) for garnet intersects the muscovite-in line (yellow field) in Fig. 5a, b (for water-fluxed melting). Based on isopleth thermometry from garnet composition, the peak PT estimated is ~ 8 kbar, 730 °C (Fig. 5b) for the following melting reaction (1):

$${\text{Biotite }}\left( {{\text{B}}{{\text{t}}_{\text{1}}}} \right){\text{ }}+{\text{ sillimanite }}\left( {{\text{Si}}{{\text{l}}_{\text{1}}}} \right){\text{ }}+{\text{ quartz }}\left( {{\text{Qt}}{{\text{z}}_{\text{1}}}} \right){\text{ }}+{\text{ plagioclase }}+{\text{ }}{{\text{H}}_{\text{2}}}{\text{O }} \to {\text{ garnet }}+{\text{ melt}}$$
(1)

The reaction is also supported by the textural observations like occurrences of inclusion trails of biotite (Bt1) and sillimanite (Sil1) in garnet porphyroblasts (Fig. 3a, b). The XAn isopleth of ~ 0.3 is the same as that measured in the plagioclase grains (in the leucocratic domains) in textural equilibrium with garnet. This isopleth intersects the garnet compositional isopleth of XMg = 0.2 at the peak PT conditions of ~ 8 kbar, 730 °C (Fig. 5b). For conventional thermometry, we have chosen the near-peak pressure of 8 kbar obtained from isopleths thermobarometry as a reference pressure for calculating temperatures from garnet cores, rims and biotites (Bt2) crystallized in melt-rich domains. Average temperature obtained for these pairs is ~ 680 °C (maximum and minimum values ranging from 670 to 690 °C; Table 4). This temperature is within the temperature range obtained from the garnet core and biotite inclusion data (690 °C). Any prograde path that may be proposed for reaction in Eq. 1 for the studied sample will cross the wet-solidus in the pseudosection, with increase in pressure and temperature (Fig. 5a).

Table 4 Results of geothermometry

Fractures in garnet porphyroblasts are filled with biotite and/or biotite + sillimanite + mullite (Fig. 3a, c, g). High XMg values of biotites in these fractures indicate metamorphic origin rather than crystallization from any melt. So it is proposed that these biotites were formed by back reaction between melt trapped in fractures and garnets during melt-present reaction:

$${\text{garnet }}+{\text{ melt }}={\text{ biotite }} \pm {\text{ sillimanite }} \pm {\text{ mullite}}$$
(2)

Because of variable equilibration volumes for such reactions which are smaller than even a thin-section scale, their bulk composition cannot be determined and hence the reaction in Eq. 2 could not be modeled by any pseudosection analyses. Nevertheless, it may be predicted that the retrograde segment of any clockwise PT path for such orogenic metamorphism will cross the H2O-saturated solidus for biotite melting at ~ 6 kbar (Fig. 10). Hence, we infer that the retrograde section of the clockwise PT path corroborates the back reaction between garnet and residual melt, which was H2O rich, leading to the formation of the retrograde Bt4 ± Sil4 ± Mul4 assemblage. For calculating the retrograde temperature range we have chosen the reference pressure at 6 kbar, which is the minimum pressure obtained for the retrograde section of PT path in Fig. 10. At this reference pressure, rims of garnet against the adjoining biotites (Bt3) in the S3 fabric yield average temperature of ~ 570 °C (maximum and minimum temperatures being 550–580 °C, Table 4); this estimate is somewhat higher than what is inferred from the compositions of garnet and biotite (Bt4) lodged in the garnet fracture (~ 540 °C). Hence, we infer that on the retrograde section of the clockwise PT path a back-reaction between garnet and residual melt occurs.

Crystallographic and microstructural characterization

To constrain deformation mechanisms of the phases in the presence of melt detailed crystallographic and microstructural analyses were carried out on garnet, quartz and mullite occurring within the different microstructural domains of the migmatite (Fig. 3a).

General orientation characteristics of mullite, quartz and garnet

Mullite Mullite (Mul1) occurring along the two limbs of D1 micro-folds hosted within D2 garnet porphyroblasts shows contrasting orientations (Fig. 6a, b). Elongate mullite mats (Mul3) defining the S3 foliation in the matrix show a strong CPO, with the c axes parallel to the stretching lineation (X direction) and (010) plane perpendicular to the foliation plane (Fig. 6c, d).

Fig. 6
figure 6

Orientation characteristics of different mullite types a Mul1; orientation map of garnet grain (lilac) and mullite as inclusions in the grain; note hinge trace (dashed white lines); b 3D representation of mullite crystal orientation grains present as inclusion in garnet forming crenulation hinges shown in (a). c Orientation map of mullite Mul3 intergrown with fine-grained biotite (khaki) and fine-grained quartz (red), for mullite coloring signifies crystal orientations as shown in inset. d Pole figures showing the orientation of Mul3 mullite grains shown in (c); one point per grain

Quartz Quartz occurs in different textural domains (Table 1; Fig. 4). Quartz grains at the hinges of D1 rootless fold in the matrix (Qtz1; Fig. 7a, b) exhibit a high number of subgrains and dauphine twins (60° rotation around c-axis) and a distinct CPO with clustering of (0001) poles to plane (Fig. 7c). In contrast, quartz grains within leucocratic layers and intergrown with garnet (Qtz2; Fig. 7b, d) show very weak to random CPO (Fig. 7e). The orientation map of the coarse quartz grains (Qtz2) within S2 leucosomes in the interfolial domains of S3 is shown in Fig. 7 f. Here, quartz grains exhibit lattice distortions, few continuous subgrain boundaries and a near-random CPO (Fig. 7g). In contrast, a weak, but distinct CPO (Fig. 7i) is documented in fine-grained quartz (Qtz3) in the biotite–mullite–sillimanite (Bt3–Mul3–Sil3)-dominated S3 foliation (Figs. 3a, 7 h, 10).

Fig. 7
figure 7figure 7

Orientation characteristics of different quartz types. a Petrographic image of microfold made up by Qtz1. b Orientation map of microfold limb shown in (a). c Pole figures of Qtz1 corresponding to orientation map of microfold shown in (a, b). d Orientation map of Qtz2 (quartz intergrown with garnet porphyroblast); note the presence of Dauphine twins (red lines) but the absence of subgrain boundaries (yellow lines). e Pole figures and contour maps of quartz corresponding to orientation map (d). f Orientation map of Qtz2 coarse-grained quartz from the leucocratic layers of S2. g Pole figures and contour maps of coarse-grained quartz corresponding to orientation map (f). h Orientation map of fine-grained quartz, Qtz3 intergrown with mullite (Mul3) in the S3 foliation planes. i Pole figures and contour maps of fine-grained quartz corresponding to orientation map (h)

Garnet All analyzed garnet grains exhibit an elongate shape (e.g., Fig. 8a, b, d). All grains have very similar crystallographic orientations (Fig. 8e) even if these grains do not appear to be physically continuous in the plane of observation (Fig. 3a). The crystallographic orientation map of a representative elongate garnet grain from the S2 melanocratic band shows an absence of distinct subgrain boundaries and/or systematic crystal lattice bending. However, distinct changes in orientation are seen associated with fractures filled or not filled by quartz, biotite and mullite (Mul3–Bt3) (Fig. 8b, c, d). Analysis of other garnet grains shows the same absence of systematic crystal lattice distortion or subgrain boundaries.

Fig. 8
figure 8

Orientation characteristics of garnet grains. a Map of elongate garnet grain with surrounding minerals; different phases are shown in different colors; b Map of orientation variations within garnet grain shown in (a), color variations indicate the progressive internal misorientation 0°–2°. pp′ outline misorientation profile shown in (c); note in (a) and (b) location of fractures is shown as stippled lines (c). Misorientation profile within grain along line pp′ shown in (b). d Photomicrograph of fracture within elongate garnet porphyroblast; e pole figures showing the orientation of all garnet grains by plotting data from 15 different garnet grains; note the similarity in orientation

Monazite dating

Monazites in the sample occur as inclusions in garnet, quartz (Qtz2) and potash feldspar (Kfs2) in the S2 layer, and overgrowing D1 crenulation hinges (Fig. 9a–d). Monazite grains are often anhedral and vary in size from 40 to 100 µm (Fig. 9c–o). BSE images show that the monazite grains are mostly homogeneous in composition with some grains having yttrium-rich cores. Monazites included in garnet and potash feldspar (Kfs2) yield 1028 Ma and 920–912 Ma, respectively (Fig. 9a, d, g, k). Cores of monazites occurring within S2 melt-bearing layer yield ages ranging from 1037 to 930 Ma and ages recorded from their rims vary from 887 to 840 Ma (Fig. 9e, f, h, n; Table 5). Monazites from the S3 foliations yield 965–889 Ma from the cores and 887–850 Ma from their rims (Fig. 9i, l-m, o; Table 5). The 33 monazite spot ages obtained from 15 grains yield two unmixed populations: 914 ± 11 Ma and 1285 ± 64 Ma (Fig. 9r). The older age population (~ 1285 Ma) is obtained from the core of one monazite included in a garnet porphyroblast.

Fig. 9
figure 9

Microstructural relationships (BSE images) of the monazites (ad), BSE images of monazite grains with spot ages (eo), X-Ray Th and Y images of monazite grains (pq) and probability density plot of monazite grains from the sample RAM-1

Table 5 Analytical data (EPMA) for the dated monazites of sample RAM-1

Discussion

Conditions of migmatization and synchronous deformation

Field and microscopic observations indicate that melting in the garnet–sillimanite migmatites of Rampura–Agucha initiated post-D1, and was pronounced during the D2 deformation stage resulting in melt segregation and formation of S2 layering including coarse-grained leucocratic, garnet-bearing bands and fine-grained, restitic layers dominated by biotite, mullite and some quartz. The absence of melts cross-cutting D3 fabrics precludes anatexis during or after the D3 deformation.

Microstructural observations (Fig. 3a, b) and pseudosection analyses indicate that the D2 peritectic garnet was formed during a H2O-fluxed partial melting event at the expense of D1 biotite–sillimanite aggregates at ~ 725 °C and at pressure ~ 8 kbar under granulite facies conditions indicated by isopleth thermometry involving garnet compositions (Figs. 5b, 10). The temperature recorded is thus close to the biotite melting reaction temperatures determined from pseudosection modeling using average metapelite bulk composition (White et al. 2001; Saha et al. 2008). A tight-loop clockwise PT path constructed for the metamorphic event (Fig. 10) indicates rapid burial and exhumation. Since the garnet porphyroblasts are chemically homogeneous, it is suggested that high degree of chemical equilibrium was attained at the anatectic conditions as ubiquitous melt allowed rapid elemental exchange. Biotite and/or sillimanite in the fractures of garnet porphyroblasts were formed by back-reactions with the melts trapped in the fractures during late stages of partial melt crystallization which marks the onset of retrogression (Figs. 3c, 10).

Fig. 10
figure 10

Summary of the PT path inferred for the migmatite of Bilwara Supergroup from the study area. Also shown are the calculated wet solidus (WSS) from Fig. 5a, granite wet solidus (GWS), granite dry solidus (GDS) curves (after Brown 2002). Schematic drawings show typical microstructures developed at the different segments of PT path. Labeling of deformation D1 to D3 according to discussion in text, in italic deformation mechanisms for noted minerals. Thin section photograph shows presence of polygonal fine-grained quartz from S3 layers (marked with the box). See text for details. Abbreviations used for metamorphic facies fields are: BS blueschist, AmEc amphibole eclogite, EpAm epidote amphibole, GrtAm garnet amphibolite, Gr granulite

The Aravalli–Delhi Fold Belt represents part of the Grenvillian-age orogeny in Northern India

Enclaves of polycyclic granulite facies migmatites from the Sandmata Complex of BGC-II (Fig. 1b) occur within charnockitic gneisses (Saha et al. 2008; Bhowmik et al. 2010). These migmatite enclaves record two partial melting events, namely M1 at ~ 1.7–1.6 Ga in the sillimanite stability field, at 6–7 kbar and 850 °C, followed by a second event (M2) at ~ 1.0 Ga in kyanite stability field, at ~ 14 kbar, 850 °C (Fig. 5a, e; Saha et al. 2008). The high-pressure Grenvillian-age M2 partial melting event recorded in the enclaves has also been recorded from the host felsic gneisses. Based on zircon and monazite ages from the gneisses of the Sandmata Complex and Mangalwar Complex (Fig. 1b), Buick et al. (2006, 2010) proposed recycling of Paleo-Mesoproterozoic (~ 1.7–1.4 Ga) crustal components during the Grenvillian Delhi orogeny. Bhowmik et al. (2010) reported partial melting of gneisses from the Mangalwar Complex at ~ 12 kbar, 800 °C during the Grenvillian orogeny (Fig. 5a, e). In contrast, for the Grenvillian metamorphism from the Pur-Banera supracrustal sequence (Fig. 1b), Ojha et al. (2016) recorded peak PT conditions of ~ 8 kbar, 600 °C (Fig. 5a, e).

In our sample, monazite aligned parallel to the S2 and S3 fabrics yield ages ranging between 1000 and 900 Ma (Fig. 9). Similar ages were also recorded by monazite grains sequestered within D2 garnets suggesting an anataxis event at that time. Rims of monazites in the melt-rich layers yield spot ages of ~ 870–850 Ma, which may be interpreted as minimum age of melting and/or the age range of melt crystallization. Monazite yielding older ages of ~ 1286 Ma (Fig. 9) may be detrital.

In summary, the Rampura–Agucha metapelite migmatites underwent Grenvillian-age anatexis at ~ 8 kbar and 730 °C. Peak PT condition was thus at substantially lower pressures than those recorded westwards in the Sandmata Complex.

Evolution of deformation microstructures in the Rampura–Agucha migmatite: characteristics and rheological implications

The correlation of microstructural development with the PT path vector is given in Fig. 10. Contrasting orientations of mullite (Mul1) grains in the limbs of the micro-folds hosted within garnet porphyroblast are consistent with systematic re-orientation (by rigid body rotation) of initially highly aligned mullite grains that inherited strong crystallographic preferred orientation during growth syn-tectonic with D1 prior to melting. Solid-state, prograde high strain is manifested by coarse quartz grains (Qtz1) with undulose extinction and subgrains (Fig. 3h, i). EBSD analyses of these quartz grains (Qtz1) in the relict D1 crenulation hinge in the matrix show a distinct CPO (Fig. 7a–c). The orientation of the c-axis relative to the reference frame along with the presence of undulatory extinction and distinct subgrains with continuous systematic subgrain boundaries suggests solid-state deformation via dislocation creep. The patterns observed in the pole figure is consistent with a dominance of < c > slip suggesting high-T (650–700 °C) deformation during D1 (Blumenfeld et al. 1986, Passchier and Trouw 2005; Law 2014; Fig. 7b) .

Quartz grains in the leucocratic S2 domains in the migmatite are coarser than 200 µm and exhibit a very weak to random CPO. Interestingly, despite near absence of a CPO, internally the grains show weak undulatory extinction, and few, discontinuous subgrain boundaries (Fig. 7f, g). We interpret these features to originate from the local stresses that occur when a melt cools and quartz crystallizes and grows as one of the last phases. During this phase, minor solid-state crystal plastic deformation can be induced, resulting in the observed internal deformation features, but since deformation is not due to regional differential stress, no distinct CPO develops. Similar features have been described by Hasalová et al. (2011) in frozen-in partial melts. We suggest that the newly crystallized coarse quartz grains escaped deformation post-anatexis because as the melt pool solidified, strain was partitioned first into adjacent melt-bearing rheologically weak domains; hence, the solidified melt pool deformed only to a minor extent. Once, all melt had solidified these coarse-grained domains were not subjected to the significant solid-state deformation. This lack of crystal plastic deformation imposed during later retrograde deformation is similar to conclusions for similar migmatitic rocks (Hasalová et al. 2011; Menegon et al. 2011).

In contrast, in the S3 realms the polygonised, finer grained quartz aggregate (10–50 µm; Figs. 7h, 10) shows a weak CPO (Fig. 7i). These aggregates are interleaved with relict prograde biotite, sillimanite and mullite layers that anastomose around the coarser grained domains. The relict nature of the latter phases is inferred from the chemistry of the biotites and is, therefore, also interpreted to represent the restitic parts of a migmatite. Based on to the geometric warping around the coarse-grained garnet-bearing leucosome, these fine-grained, phase-mixed layers must have deformed post-migmatzsation accommodating strain during the retrograde path. We suggest that deformation occurred during solid state where most of the strain was taken up by the basal slip of biotite along with rigid body rotation of biotite and mullite. Quartz is mostly “passive” as the rheologically weaker biotite and mullite concentrate strain. Therefore, quartz exhibits only minor internal lattice distortions and a weak CPO (Fig. 7i). We prefer this interpretation to the possibility of dislocation glide accommodated grain boundary sliding at high temperature (> 700 °C), aided by small grain sizes and possibly melt presence at grain boundaries (Schmid 1982; Behrmann and Mainprice 1987; Brodie and Rutter 2000; Song and Ree 2007; Kilian et al. 2011; Svahnberg and Piazolo 2010). Our preference is based on the fact, that biotite is known to be weak and in mixed, multiphase layers a weak CPO is possible to develop in the “harder” mineral phase. This is due to pronounced strain partitioning between easily deformed phases, e.g., graphite or biotite and a phase requiring higher critical resolved shear stress for activation of slip systems, e.g., ice or quartz (Cyprych et al. 2016). Furthermore, microstructurally there are no indications for melt film presence during D3 deformation. A consequence of our interpretation is that at the time of the last deformation event, the rock was relatively weak, not due to the presence of melt, but due to the presence of fine-grained phase-mixed layers that developed during the transient migmatization event. These fine-grained, biotite- and mullite-rich layers deform at relatively low stresses as suggested by experiments (e.g., of an analogous system of ice and graphite; Cyprych et al. 2016), hence are weak.

In summary, we interpret that high-strain deformation prevailed postdating anatexis. Strain was accommodated by solid-state deformation (D3) within the fine-grained quartz aggregates interleaved with biotite aggregates forming rheologically weak layers, and not by the coarse-grained leucosome domains similar to strain partitioning seen in other layered metamorphic rocks (e.g., Smith et al. 2015).

Large elongate garnet porphyroblasts described here seem at first sight to be similar to those noted by several researchers in metamorphic rocks formed under granulite facies to eclogite facies conditions (Ji and Martignole 1994; Prior et al. 2000; Kleinschrodt and McGrew 2000; Ji et al. 2003; Mainprice et al. 2004; Storey and Prior 2005). These studies conclude that under both subsolidus and supra-solidus conditions at different crustal depths coarse garnet crystals may achieve their elongated shape due to crystal–plastic deformation manifested by clear subgrain boundaries and systematic lattice bending. In contrast, the elongate garnet in our sample is characterized by the absence of subgrain boundaries and/or crystal lattice bending (Fig. 8a, b). The occurrence of vermicular quartz intergrown with garnet (Fig. 3b), melt films at feldspar–garnet interfacess (Fig. 3e, f), and melt-bearing domains trapped within garnets (Figs. 8d, 10), unmistakably point to the presence of melt during garnet growth. Furthermore, small plagioclase grains with low dihedral angles possibly represent melt pseudomorphs (Fig. 3j, e.g., Sawyer 2001). Hence, garnet is peritectic growing in response to incongruent melting of biotite–sillimanite aggregates. The extensional Mode I fractures in the elongate garnet porphyroblasts may have been induced by a combination of high fluid/melt pressure exerted by partial melt crystallization (Abe and Urai 2012; Komoróczi et al. 2013; Rimsa et al. 2007; Tretiakova et al. 2016) as well as tectonic forces (Abe and Urai 2012; Komoróczi et al. 2013). Subsequent to garnet fracturing, growth of biotite and mullite (Bt4–Mul4) along fractures and along garnet margins (Fig. 3a, g) indicate that melt-rich domains remained in contact with the garnet-bearing layers to promote their growth during cooling and back-reaction. However, these domains remained shielded during subsequent solid-state deformation as garnet and surrounding coarse-grained quartz and orthoclase remained rigid at the D3 event.

We attribute the elongate shape of garnet to its growth via partial melting (reaction 1) pseudomorphing a pre-existing three-dimensional network of biotite–sillimanite/mullite clusters. Such a biotite–sillimanite network intergrowth explains the uniform crystallographic orientation of garnet as one large garnet grew within the three-dimensional network. We, however, concede that the statistics for making the inference is low (number of grains exposed at the surface of the thin section analyzed = 15).

Mullite stable in the S3 foliation domains shows no substructure but strong CPOs (Fig. 6c, d), indicating either rigid body rotation in the presence of high shear stress under solid state (see Piazolo and Jaconelli 2013) or possibly by epitaxial replacements of Kfs2 in the presence of differential stress-inducing oriented growth during the same late-stage solid-state deformation.

Conclusions

Our analyses of microstructural development in the garnet–sillimanite–mullite–quartz–feldspar–biotite migmatite in the high-grade Aravalli–Delhi Fold Belt help to identify the supra-solidus to subsolidus deformation mechanisms in a migmatite-preserving signature of its prograde, peak and retrograde pressure–temperature-deformation path experienced by the migmatite. The following conclusions can be drawn.

During the Grenvillian Delhi Orogeny (spanning from 1000–870 Ma), garnet–biotite–sillimanite–mullite–quartz–feldspar-bearing migmatite from the shear zone in the Rampura–Agucha area of Aravalli–Delhi Fold Belt underwent crustal anatexis at ~ 8–9 kbar, 730 °C which is at much lower depth (~ 30 km) compared to the high-pressure crustal anatexis of the migmatites from the SC and MC (~ 14 kbar, > 40 km) in the west (Fig. 1). Three main stages of fabric development (S1–S3) occurred in the rock during the orogeny, where the S2 metatexite layers were formed on its prograde path which underwent folding leading to formation of biotite–sillimanite–mullite–quartz-bearing axial planar foliations (S3). During peak conditions, anatectic incongruent melting reaction involved breakdown of biotite, sillimanite and formation of garnet-bearing peritectic assemblage along a tight loop clockwise PT path. The preservation of sillimanite–mullite–biotite–quartz-bearing inclusion trails in the Grenvillian-age garnet porphyroblasts and strong CPOs, undulose extinction and subgrain boundaries in quartz grains in the relict crenulation hinges in matrix and within garnets imply that the rock was subjected to a pre-Grenvillian solid-state, high-temperature-deformation event (> 650–700 °C).

Peritectic garnet porphyroblasts are elongated with aspect ratios varying from 3.1 to 1.7 with Mode I fractures perpendicular to the elongation. Presence of biotite–sillimanite–mullite in these fractures indicate their crystallization during back-reaction of garnet and trapped hydrous melt during cooling. Absence of subgrain boundaries and systematic crystal lattice bending in the garnet porphyroblasts indicate that their elongated nature is not a result of ductile deformation. We suggest that the garnet grains attained elongated shape as a result of their growth over a 3-D network of pre-existing (prograde) biotite–sillimanite–mullite foliations. Post-garnet growth, extensional Mode I fractures formed due to local high melt pressure during veining stages of anataxis in combination with tectonic stresses. Microstructural analyses of garnet from the study hence imply that elongated shapes of peritectic garnets especially those crystallized in equilibrium with melts need not necessarily be due to ductile, crystal–plastic deformation and that under such conditions garnets may exhibit brittle behavior.

Near-random two weak CPOs of coarse-grained quartz in the matrix S2 indicate that crystallization of melt outlasted high-temperature (> 700 °C) D2 deformation in these areas. Post-migmatization solid-state deformation was instead accommodated in the fine-grained quartz-rich domains interleaved with biotite, sillimanite, mullite in the S3 layers. These layers represent restitic layers formed during partial melting. During post-migmatization deformation these phase-mixed, fine-grained layers act as rheological weak zones as they deform mainly by basal slip in biotite and rigid body rotation of both biotite and mullite and minor dislocation creep in quartz.

Our study suggests that the inferred rheological weakness of migmatites may outlast the actually melt-present time period, as biotite-*rich layers developed during partial melting facilitates late-stage, solid-state deformation with low rheological strength.