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Quartz c-axis evidence for deformation characteristicsin the Sanandaj–Sirjan metamorphic belt, Iran

Babak SamaniFaculty of Earth Sciences, Shahid Chamran University, Ahvaz, Iran

a r t i c l e i n f o

Article history:Received 19 June 2012Received in revised form 22 December 2012Accepted 8 January 2013Available online 4 February 2013

Keywords:Quartz c-axisFinite strainVorticitySanandaj–Sirjan metamorphic beltZagrosIran

a b s t r a c t

Quartz c-axis fabric, finite strain, and kinematic vorticity analyses were carried out in well-exposedquartz mylonites to investigate the heterogeneous nature of ductile deformation within the Eghliddeformed area in the High Pressure–Low Temperature (HP–LT) Sanandaj–Sirjan metamorphic belt(Zagros Mountains, Iran). This belt belongs to a sequence of tectonometamorphic complexes with low-to high-grade metamorphic rocks affected by a polyphase deformation history. Asymmetric quartz c-axisfabrics (type I) confirm a localized top-to-the-southeast sense of shear. Quantitative finite strain analysisin the XZ, XY and YZ principal planes of the finite strain ellipsoid demonstrate that the strain ratioincreases towards the thrust planes of the Zagros Thrust System. Kinematic vorticity analysis of deformedquartz grains showed sequential variation in the kinematic vorticity number from �0.5 to �0.8 betweenthe thrust sheets. Such vorticity numbers show that both simple and pure shear components contributeto the deformation. Our results show that simple shear dominated deformation near the thrust faults, andpure shear dominated deformation far from them. Quartz c-axis opening angles suggest deformationtemperatures range between 450� ± 50 �C and 600� ± 50 �C, which yield greenschist to amphibolite faciesconditions during ductile deformation.

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1. Introduction

In many deformed rocks, the lattice orientation of crystals is notrandomly distributed, but arranged in a systematic way. Such rockshave a lattice preferred orientation (LPO) for a specific mineral. Inthe case of crystals with a planar or elongate shape in a particularcrystallographic direction, such as micas and amphiboles, an LPO iseasy to recognize as a foliation or lineation (Passchier and Trouw,2005). However, for minerals such as quartz and calcite this ismore difficult. In minerals with equate grain shapes, dislocationcreep is the most important mechanism for development of aLPO (Passchier and Trouw, 2005). The slip system or deformationtwinning that is active in a crystal depends on the critical resolvedshear stress (CRSS) and indirectly reveals the metamorphic anddeformation conditions. Usually, more than one slip system canoperate in a mineral and the CRSS of each slip system changes withtemperature and activity of certain chemical elements. Compari-son of natural LPO patterns with known temperature, strain geom-etry and vorticity of the progressive deformation can help todetermine the influence of these parameters on LPO development.

The analysis of lattice preferred orientation patterns is of con-siderable interest for investigating the kinematics and geometryof flow in natural shear zones (Bouchez and Pecher, 1981). Micro-

structural studies of quartz are of great significance especially inunderstanding the flow mechanisms and deformation patterns inthese zones. Fabric development in quartz is governed by the dom-inant slip systems (basal hai slip, rhomb hai slip and prism hai slip)and the strain path (Bhattacharya and Webber, 2004; Passchierand Trouw, 2005). This paper shows the results of fabric data, finitestrain, and kinematic vorticity from a natural shear zone within theHigh Pressure–Low Temperature (HP–LT) Sanandaj–Sirjan meta-morphic belt. This systematic study shows the sequential develop-ment of quartz fabrics between two thrust fault sheets in theZagros Thrust System.

2. Regional geological background

The Zagros Orogenic Belt is part of the Alpine–HimalayanMountain Range and extends for about 2000 km in a NW–SE direc-tion from the East Anatolian Fault of Eastern Turkey to the OmanLine in southern Iran (Alavi, 1994). The Zagros Belt is the resultof the closure of the Neo-Tethys by oceanic crust consumption ata NE-dipping subduction zone below the Iranian microcontinent,and subsequent Late Cretaceous continental collision betweenthe Afro-Arabian continent and Iranian microcontinent (Stocklin,1968; Dewey et al., 1973; Berberian and King, 1981; Alavi, 1994;Blanc et al., 2003; Sarkarinejad et al., 2008). Convergence betweenthe Afro-Arabian continent and the Iranian microcontinent

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accounts for thrusting and large-scale strike slip faulting associ-ated with crustal shortening. Postcollisional crustal shortening isstill active (Jackson and McKenzie, 1984; Allen et al., 2004) witha N–S oriented convergence rate of approximately 20 ± 2 mmyr�1

(Vernant et al., 2004).From northeast to southwest the Zagros consists of three

NW–SE trending parallel zones (Alavi, 1994) (Fig. 1): (1) TheUrumieh–Dokhtar Magmatic Assemblage (UDMA). (2) The Sana-ndaj–Sirjan Metamorphic Belt (SSMB). (3) The Zagros Fold andThrust Belt (ZFTB). The SSMB is 150–200 km wide and more than1500 km long from northwest (Sanandaj) to southeast (Sirjan).The borders of the SSMB are parallel to the main NW–SE regionalstructures. Widespread thrusting in the Sanandaj–Sirjan Zone is re-lated to the subduction and collision from Cretaceous to Tertiarytimes (Alavi, 1994). In addition to thrust faults, ductile structures,including tight-isoclinal folds and associated foliations and linea-tions abound in the metamorphic Late Palaeozoic and Mesozoicformations, and plutonic rocks outcrop in the central part of theSSMB (Sarkarinejad et al., 2010a, 2010b). The study area withinthe SSMB was located in the region of Eghlid, 130 km north of Shi-raz in southwest Iran (Fig. 2). The study area has been sandwichedbetween two major thrusts due to the Zagros Thrust System andshows the geometry of a transpressional shear zone (Sarkarinejadet al., 2010a, 2010b). The most abundant rocks are deformed meta-morphic rocks such as micaschists, greenschists and quartzites.

3. Quartz LPO patterns

Quartz c-axis were measured for seven oriented samples ofquartz-rich mylonites from a NE–SW transect in the study area(Fig. 2). The aim of these measurements was to estimate the finitestrain from the quartz porphyroclasts, and the vorticity numbersbetween the thrust faults bounding the shear zone. c-axis orienta-tion of 200 or more quartz grains from each sample were measuredon XZ sections (cut parallel to the lineation and perpendicular tothe foliation). In this reference frame, the foliation is assumed torepresent the XY-plane of the finite strain ellipsoid, and in thisplane, the lineation represents the direction of the maximum finiteelongation. All analyzed samples are strongly foliated and formquartz ribbons. The quartz grains in the quartz ribbons show evi-dence of extensive dynamic recrystallization associated with grainboundary migration and subgrain rotation (Fig. 3).

The c-axis measurements were carried out for each sample(Fig. 4a). Fabric skeletons were prepared by connecting the crestsand ridges of each fabric diagram (Fig. 4b) (Lister and Williams,1979; Lister and Hobbs, 1980). All diagrams record a well-pre-served shape and lattice fabrics form asymmetric crossed girdlsindicating non-coaxial shearing consistent with the dextral senseof shear of the SSMB (Law, 1990). The top-to-the-SE sense of shearis confirmed by quartz c-axis microtextures (Fig. 4a and b). Theobliquity of the central girdle segment with respect to the foliation

Fig. 1. The Sanandaj–Sirjan shear zone and the Zagros belt from northeast to southwest in western Iran.

B. Samani / Journal of African Earth Sciences 81 (2013) 28–34 29


(w), or the external asymmetry parameter, varies between 80� and85� (Fig. 4; Table 1). These fabrics also exhibit monoclinic periph-eral point-maxima asymmetry with respect to the foliation, which

is consistent with non-coaxial deformation (Wang et al., 2005). Theexternal fabric asymmetry may also be expressed by the relativemagnitudes of the angles c1 and c2 (Platt and Behrmann, 1986;Law, 1990), c2 being is consistently greater than c1 in each sample(Fig. 4 and Table 1).

3.1. Finite strain analysis

The seven samples were analyzed for their finite strain ratios(RXZ, RXY and RYZ) by applying the Rf /U method from the grainshapes, U being the angle between the X-axis and an arbitrary ref-erence direction. In order to measure the angles between the longaxes of the quartz grains in the XZ plane, the trace line obtainedfrom the intersection between the foliation and the stretching lin-eation was used as reference line. For each thin section, at least 40deformed quartz grains were measured. By using the Rf/U software(Chew, 2003) the Rf/U diagrams were constructed (Fig. 5). Finitestrain values (Rs) were estimated on XZ, XY and YZ planes of thestrain ellipsoid for each sample (Table 2).

3.2. Kinematic vorticity analysis

Kinematic vorticity (WK) is a dimensionless measure of rotationrelative to strain and characterizes the amount of shortening pro-portional to displacement. WK was originally defined as an instan-taneous rotation relative to the instantaneous stretching at a point

To E

ghlid

Meta tuff

Alluvium

Grey to dark thick-bedded limestone

Micaschist, greenschist and quartzite

L E G E N D

Eghlid fault

Thrust fault

Fault

Road

N

Sample location

E1

E2

E3

E4

E5

E6

E7

0 1 2 km

Fig. 2. Geological map of the study area and the sample locations.

Fig. 3. Photomicrograph of a quartz mylonite from the quartz-rich metamorphicrocks of the study area. The quartz grains record evidence of dynamic recrystal-lization by subgrain rotation and grain boundary migration.

30 B. Samani / Journal of African Earth Sciences 81 (2013) 28–34


(Truesdell, 1953; Means et al., 1980). Kinematic vorticity is mea-sured on a scale between 0 (pure shear) and 1 (simple shear). Gen-eral shear is the term used for flows between pure and simpleshear (1 > WK > 0) (Passchier and Trouw, 2005). Pure and simpleshearing components contribute equally to the instantaneous flowat WK = 0.71 (Law et al., 2004). In natural systems the vorticity offlow may vary with both position and time (Fossen and Tikoff,1998). This research uses the mean vorticity number, Wm (Passchi-er, 1988) which integrates the vorticity of the flow (WK) over timeand space. Determination of the vorticity helps to reconstruct thedegree of non-coaxiality of flow, i.e. the relative amounts of pureversus simple shear. It also helps to better define the kinematic ref-erence frame for the flow in ductile shear zones (Grasemann et al.,

1999; Law et al., 2004; Jessup et al., 2007; Forte and Bailey, 2007).The approximately plane-strain condition which is suggested fromthe cross-girdle pattern of the quartz c-axis fabrics (Law, 1990) sat-isfies the application of two-dimensional vorticity analysis (Tikoffand Fossen, 1995).

Wallis (1992, 1995) has proposed two techniques for quantify-ing the vorticity of flow in naturally deformed quartz grains: theoblique-grain-shape/quartz c-axis-fabric method (d/b-method),and the strain ratio/quartz c-axis-fabric method (RXZ/b-method).According to the d/b-method, if both angles are known then an

Fig. 4. (a) Equal area, lower hemisphere Schmidt projections of quartz c-axis fabrics (E1–E7 see Fig. 2 for locations). In all diagrams, the foliation is vertical (\Z) and thestretching lineation (X) is horizontal. (b) Fabric skeletons and angular relationships between c-axis external and internal fabric asymmetry used here. The observed fabricasymmetry indicates a significant component of non-coaxial, top-to-the-SE or dextral sense of shear.

Table 1Quartz c-axis external fabric asymmetry (w, c1 and c2) and internal fabric asymmetryparameters (x1, x2).

E1 (�) E2 (�) E3 (�) E4 (�) E5 (�) E6 (�) E7 (�)

w 80 83 85 83 83 80 82c1 29 28 36 28 28 30 23c2 44 42 42 45 46 42 36

Fig. 5. Estimation of Rs finite strain parameters from the Rf/U method for the same collection of specimens.

Table 2Finite strain ratios in the XZ, XY and YZ planes, b angle and kinematic vorticity numberdata for all stations in the study area.

E1 E2 E3 E4 E5 E6 E7

RXZ 5.2 4.5 4.8 3.2 4.5 4 6.3RXY 3.3 3.4 3.4 2.5 3.0 3.1 3.8RYZ 4.1 3.8 3.8 2.1 3.2 3.6 4.5b 10� 7� 5� 7� 7� 10� 8�Wm 0.78 0.65 0.47 0.48 0.6 0.7 0.75



estimate of the vorticity number can be obtained using the equa-tion (Wallis, 1995):

Wm ¼ sin 2g ¼ sin 2ðdþ bÞ

where g (Fig. 6a) defines the acute angle between the instantaneousstretching axis (ISA1) and the flow apophysis (A1), b is the angle be-tween maximum principal strain axis (X) and the flow apophysis(the angle between the perpendicular to the central girdle segmentof quartz c-axis fabric and the foliation (SA)), and d is the angle be-tween ISA1 and X (Fig. 6a and b). The RXZ/b-method is an improve-ment of the semi-quantitative technique proposed by Platt andBehrmann (1986), that incorporates strain data measured in theXZ-plane (RXZ) with the angle b between the flow plane (A1) andthe foliation (SA) as determined from quartz (Fig. 6a and b). Wallis(1992, 1995) demonstrated that for a given pair of values (RXZ, b),Wm can be estimated either by constructing the Mohr-circle for fi-nite deformation in stretch space, or by using the following analyt-ical solutions:

Wm ¼ sin tan�1 sinð2bÞ½ðRXZ þ 1Þ=ðRXZ � 1Þ� � cosð2bÞ

� �� ðRXZ þ 1ÞðRXZ � 1Þ

Note that the RXZ/b-method is equivalent to the RXZ/h0-method(Tikoff and Fossen, 1995; Bailey and Eyster, 2003) which uses theangle (h0) between the long axis of the finite strain ellipsoid andthe shear zone boundary to estimate Wm. Mathematical solutionsof the strain and fabric parameters show that it is possible to con-struct a nomogram that incorporates all the parameters (b, d, RXZ

and Wm) involved in the three vorticity analyses (Xypolias, 2009).As illustrated in Fig. 7, this nomogram is a planar graph of b versusd for different Wm and RXZ values. According to Xypolias (2009) theadvantage of such an approach are multi-fold: (1) it instantly pro-vides the vorticity number for all methods; (2) it allows for tests ofthe sensitivity of the estimated vorticity numbers by changing theinput parameters (b, d, RXZ); (3) it provides a rapid means of eval-uating the consistency of values issued from the various methods;and (4) it enables the rapid evaluation of the mean strain level for asuite of samples, where only b- and d-angles are available. Theinvestigated quartz c-axis girdles and grain shapes give b between5� and 10� and RXZ values between 3.2 and 6.3. Applying the (b, d,RXZ and Wm) nomogram of Xypolias (2009) for this research pro-vides mean vorticity numbers between 0.47 < Wm < 0.78 (Fig. 7and Table 2).

3.3. Deformation temperatures

Several techniques were used to estimate the temperature thatwas present during the development of deformation. Temperaturewas estimated based on (1) mineral assemblages preserved within

strain shadows of rotated porphyroclasts (Jessell, 1987), (2) quartzand feldspar deformation microstructures (Jessell, 1987; Lloyd andFreeman, 1994; Hirth et al., 2001), (3) quartz LPOs (Bouchez, 1977;Bouchez and Pecher, 1981; Mainprice et al., 1986), and (4) theopening angle of quartz fabrics (Kruhl, 1998; Law et al., 2004).Experiments (Tullis et al., 1973) and numerical simulations (Listerand Hobbs, 1980; Wenk et al., 1989) indicate that the opening an-gle of quartz c-axis fabrics increases with increasing deformationtemperature and hydrolytic weakening, and with decreasing strainrate. Other factors, such as strain path and strain geometry mayalso play a role. According to Kruhl (1998) the opening anglearound Z in the XZ plane between two point maxima can serveas a deformation-related thermometer. Therefore the opening an-gles were measured from the fabric skeleton and the temperaturesof deformation were defined. The samples show opening anglesranging from 59� to 78�, giving deformation temperatures rangingfrom 450� ± 50 �C to 600� ± 50 �C (Fig. 8).

3.4. Deformation path partitioning

Partitioning of deformation occurs in many natural deformedzones and results from the varying amounts of localization of thesimple shear and pure shear components. Accordingly, the simpleshear versus pure shear ratio also varies due to strain localization.The simple shear component tends to concentrate in the highstrain zone whereas the pure shear component tends to be morewidely distributed (Jones and Tanner, 1995; Lin et al., 1998).Hence, different areas across a high strain zone follow differentdeformation paths, a phenomenon called deformation path parti-tioning by Lin et al. (1999). The studied specimens show an

a b

Fig. 6. Simplified sketches showing the relative orientation of instantaneous flow elements and their angular relationships in real space for a dextral general shear flow (a). A1

and A2: flow apophyses; ISA1 and ISA3: instantaneous stretching axes; X and Z: principal strain axes. In (b) The angle, b, between the perpendicular to the central girdlesegment of quartz c-axis fabric and the main foliation (SA) is inferred to be equal to the angle between the flow apophysis A1 (flow plane) and the principal finite strain axis X.

Fig. 7. (b, d, RXZ and Wm) nomogram (after Xypolias, 2009). Plot of b versus RXZ forthe measured seven samples indicate Wm values between 0.47 and 0.78.



important deformation path partitioning throughout the studiedshear zone since vorticity numbers and the simple shear/pureshear ratio continuously increase toward the thrust planes (Fig. 9).

4. Discussion

The asymmetries displayed by the quartz fabrics are consistentwith a dextral sense of shear, similar to that proposed by others forthe northern (Mohajjel and Fergusson, 2000) and southern parts(Sarkarinejad et al., 2010a, 2010b) of the Sanandaj–Sirjan meta-morphic belt. The crossed-girdle pattern itself approximately indi-cates plane-strain conditions during dextral ductile shearing. Thequartz fabric also reflects deformation temperatures since the fab-ric pattern is controlled by the relative contributions of differentslip systems, which in turn are temperature sensitive (Passchierand Trouw, 2005). Slip in quartz occurs primarily in the hai crystal-lographic direction, predominantly on the basal, rhomb and prismplanes (Christie et al., 1964). Basal hai slip is dominant at lowertemperatures and at faster strain rates, causing a c-axis fabric max-imum near the Z-axis of the finite strain ellipsoid. With increasingtemperature, a rhombohedral hai slip system becomes activated,causing a fabric maximum at an intermediate orientation betweenthe Y- and Z-axes. Ultimately, at still higher temperature andslower strain rates, the prism hai slip system operates, causing afabric maximum near the Y-axis of the finite strain ellipsoid (Bou-chez and Pecher, 1981; Mainprice et al., 1986). Using a modifiedgeothermometer based on the opening angles of quartz girdles,

temperatures of 450� ± 50 �C to 600� ± 50 �C are strongly suggestedduring deformation of the study area. These fabric patterns thusindicate that the rocks were deformed under greenschist toamphibolite facies conditions. Strain values in the XZ, XY and YZ-principal planes of the strain ellipsoid were used to evaluate the fi-nite natural logarithmic strain e (Ramsay and Huber, 1983;Fig. 10):

e ¼ 13

� �1=2

½ðlnðRXZÞÞ2 þ ðlnðRYZÞÞ2 þ ðlnðRXYÞÞ2�1=2

Across the thrust planes it suggests that finite strain increases inan approximately linear fashion toward the thrust planes. Vitaleand Mazzoli (2008) discriminated mylonite types using strainintervals of e = 0–1 (protomylonites), e = 1–2.5 (mylonite) ande > 2.5 (ultramylonite). According to this classification, the samplesthat have strain values between 0.95 and 1.57 correspond to myl-onites. The different LPOs that are observed in the area are bestinterpreted in terms of locally contrasting finite strain with a gen-eral increase of strain towards the thrust planes. This is consistentwith the kinematic vorticity measurements that show a continu-ous increase toward the thrust planes. Finite strain and vorticitynumbers therefore reflect an increase of the simple shear compo-nent towards the thrust planes.

5. Conclusions

Microscopic kinematic indicators reveal an unequivocal dextralsense of shear within the metamorphic rocks of the Sanandaj–Sir-jan metamorphic belt. Quartz c-axis fabrics in this research displayType-I cross-girdles, which also indicates non-coaxial dextral sheardeformation with the basal hai slip system under approximatelyplane strain condition. Quantitative finite strain and vorticityanalyses demonstrate that both the strain ratio and the vorticitycomponents increase towards the boundary thrusts of the Sana-ndaj–Sirjan shear zone. An important deformation path partition-ing is demonstrated with changes from simple shear to pureshear components with distance from the thrust faults. The simpleshear component increases toward the thrust faults, with the pureshear component being at its maximum away from the borderfaults. Such an observation that strain and vorticity increase to-ward the fault planes is consistent with many similar observationselsewhere in the world. The similar studies in different parts of theSanandaj–Sirjan metamorphic belt (Sarkarinejad et al., 2010a,2010b; Faghih and Sarkarinejad, 2011) show continuous increaseof vorticity numbers and the simple shear/pure shear ratio towardthe Zagros thrust planes.

Z

XY

Opening Angle

0

30

60

90

120

0

Lineation

Foliation

200 400 600 800

Temperature C

Ope

ning

ang

le (

)

Fig. 8. Opening angles versus estimated temperatures of deformation for the sevenrock samples (solid-lined box). The other boxes are taken from the literature.

0% 10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.95

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.95

1.00

Kinematic Vorticity Number

Pure Shear Dominated

Simple Shear DominatedGeneral Shear Dominated

E1

E2

E3

E4

E5

E6E7

Fig. 9. Kinematic vorticity number versus pure shear–simple shear percentages forthe seven rock samples under study, showing their increase toward the thrustplanes.

0 1 2 km

1

0.8

1.2

1.4

1.6

E1 E2 E3 E4 E5 E6 E7

SW

thru

st p

lane

NE

thru

st p

lane

Nat

ural

loga

rith

mic

str

ain

Fig. 10. Finite natural logarithmic strain plotted against sample locations (E1–E7)from the thrust planes. Sample locations are shown in Fig. 2.



Acknowledgements

The author would like to thank the editor Professor P.G. Eriks-son and M. Fernandez for their editorial authority. I am gratefulto J.L. Bouchez and A. Faghih for helpful and valuable reviews ofthe manuscript. Also I would like to thank Professor Adrian Fosterfor final grammar review of the paper. The Research Council of theShahid Chamran University of Ahvaz has supported this study,which is gratefully acknowledged.

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