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Strain analysis of a shear zone in a granodiorite
~ectonoF~ysjcs, 47 (1978) 15-42 0 Elsevier Scientific Publishing Company, Amsterdam -Printed
15 in The Netherlands
STRAIN ANALYSIS OF A SHEAR ZONE IN A GRANODIORITE
J.P. BURG and Ph. LAURENT Laboratoire de G&lo&
St~uc~r~~e, 34060 ~un~~e~~~er,Cedeg ~~r~~~e~
(Received September, 29’76; revised version accepted September 6,1977)
ABSTRACT Burg, J-P_ and Laurent, Ph., 1978. Strain analysis of a shear zone in a granodiorite. Teetonophisics, 47: 1542. A ductile shear zone in a late Precambrian granodiorite, from the Rouergue (southwest part af the French Massif Central) has been studied. A single episode of deformation is responsible for the formation of a foliation and a well-defined lineation which are localized into an elongated zone, a few decimeters wide. The strain features can be attributed to a simple-shear mechanism (Ramsay and Graham, 1970), so that the main parameters of the deformation are defined, At stages of increasing deformation, the quartz isotropic sub-fabric of the undeformed host rock is progressively transformed into an anisotropic fabric composed of a single oblique girdle while the subgrain size progressively decrease and the dislocation density remains constant. It is suggested that the gliding planes of quartz are the ba.4 plane (0001) and a predominant prismatic plane {lOiO); the slip directions may be (a> for botb glide-planes. The results obtained in this investigation provide a basis for a high voltage electron microscope (H.V.E.M.) study which shows that the fabrics development may be related to dislocation processes. The difference of strain rates in the host rock and in the shear zone is calculated from the dislocation microstructures.
During the last decade, several publications have dealt with shear zones on various scales. Shear zones are generally localized planar features in which rocks are highly strained, and their thickness can vary from one millimeter to more than ten kilometers (e.g., Bak et al., 1975). Generally the deformatiun forming the shear zones is s~-rne~rnor~h~~ (~een~h~t to gram&e facie4 and produces. a typical welldefined lineation. Ductile shear zones may be divided into two classes: continuous and discontinuous. Continuous shear zones have been described by several geologists (e.g.? Ramsay and Graham, 1970; Hara et al., 1973). Their thickness varies from one centimeter to a few meters. They are characterized by a continuous increase of the shear strain 7 from the shear zone boundary to the center of the shear zone where the most highly strained rocks are localized. The shear
zone boundary is more or less well defined and the angle 8 between the foliation at this boundary and the shear plane (which is considered to be parallel to the shear boundary) is theoretically 45”. Due to the well defined foliation the values of y can be established withaut difficulty across the shear zone. From this geometric characteristic, one can infer the sense and amount of displacement without strain markers. The second type are ~h~~ter~zed by a d~~ont~nuo~s increase of y, The shear zone boundaries are generally welldefined, close in orientation to the foliation and look like faults. Determination of y is difficult without strain
I? 483
83
\ -
Fig. 1. a. Schematic representation of the deformed specimen. The black spherical and elliptical bodies are xenoliths; B is the shear boundary pfane. b. Schematic representation af deformation. 81 is the foliation plane; B is the shear boundary plane; 8 is the angle between S and B; X, Y, 2 are the principal directions of the finite strain ellipsoid (X B k* > 2); AsB3 is the studied cross-section; a---f are locations of thin sections studied (Figs. 7-9). c. Schema of the foliation in the (X2) plane of deform&an. A@z--A~B~ are cross-sections drawn in Fig. 4: b---f are positions of studied thin sections; Iso-8 lines are drawn (15*, 2@‘, W, 30*, 135~).
markers so the sense and amount of displacement are generally unknown. Discontinuous shear zones have been described by Eisbacher (1970) and Laurent (1974); their thickness varies from one hectometer to a few kilometers. This contribution is the study of a continuous ductile shear zone on every scale, which is important for the comprehension of deformation mechanisms and fur the quantification of strain. Moreover, referring to the work of Ramsay and Graham (1970), one can presume that simple shear m~hanism is responsible for the deformation of rocks in mountain chains hke the Himalaya (Mattauer, 1975; Bouchez and Pecher, 1976) or the Alps (Mattauer and Proust, 1975; Laurent and Etchecopar, 1976; Mattauer et al., in press). The purpose of this study is to get new evidence of relationships between the evolution of microstructural data, the strain and fabric data in a continuous shear zone. Sampling was restricted to half of the shear zone, that is to say the deformed part included between the shear zone boldly and the plane situated at the center of the shear zone since this plane is a symmetry plane for the deformation (Fig, la). The sample size was 60 cm parallel to the Iineation in the most deformed part of the shear zone, 45 cm perpendicular to the foliation, 26 cm in the plane of foliation, perpendicular to the lineation, The importance of transmission electron microscopy studies of naturally and expe~ment~ly deformed minerals is now well established for the determination of the slip system and the Bow law. The results of an exudation of minerals across the shear zone are pxesented. GEOLOGICAL
SETTING AND DESCRIPTION OF THE SAMPLE
The specimen has been sampled in the Rouergue (French Massif Central), where a granodiorite is cut by several shear-zones, one of which is studied in this paper. This grauodiurite has been deformed probably late in the variscan orogenesis, in the greenschist metamorphic facies (2’ = 350°C f 50°C and P = 2.5 kbar (Matte and Nicollet, 1976)). The shear zones functioned essentially as normal faults. The microstructure of the undeformed granodiorite is isotropic and homogeneous, comprising a coarse-grained matrix of quartz, piagioclase and biotite, enclosing some unoriented and equidimensional eentimetric melanocratic xenohths. Gram boundaries of qumtz are fobate (0.5-l mm) and the extortion is generally slightly undulose. The feldspars comprise plagioclase showing albitecarlsbad twins and some large euhedral crystals of microdine (5 mm) which are more or less sericitized. Micas are either large crystals of porphyroelastic biotite (2.5 mm) or crystals of neoblastic muscovite and chlorite (0.3 mm). The large crystals of biotite show undulose extinction. Accessory minerals are apatite and zircon.
Description of the def~rrnut~~n structures In the studied sample, the deformation structures are: (1) a well defined line&ion which is marked principally by elongated polycrystalline aggregates of quartz and plagioclase, and deformed xenoliths. (2) a foliation which is defined by the orientation of neoblastic micas (muscovite and ehlorite) and by a new orientation of porphyro~las~~ biotite. Evolution of microstructures with increasing strain A complete sequence of microstructures from the undeformed host rock to the center of the shear zone is observed. In quartz this evolution is very similar to that described in mylonites (Wilson, 1975) or in thrust zones (Christie, 1963). Referring to the work of Bouchez and Fecher f1976f, three types ‘of mierostrn~t~es are recognized: (a) ~orp~yr~clastic relics micrustr~ct~res present in the less deformed part of the ductile shear zone. Old polycrystalline aggregates of quartz are slightly deformed. Their X/Z ratio (X > Y > 2) is less than 3. Quartz grains are recrystallized and the extinction is slightly undulose. Porphyroclasts of biotite are deformed and show single or conjugate kinks. (b) ~~u~gated mosaics m~crustructure which is intermediate between a and c, is important because it has an anisotropic c-axis fabric of quartz. Pulycrystalline aggregates are elongated and are only composed of quartz. Some porphyroclasts of biotite show a particular structure which seams to lead to the definition of’the sense of shear (Eisbacher, 1970, p. 2016). The matrix is composed of small grains of plagioclase and neoblasts of micas, (c) ribbon microstructure appears in the most deformed part of the shear zone. Ribbons are essentially polycrystalline aggregates quartz. They represent the ultimate state in the evolution of initial poly~~st~line aggregates, Relic minerals are uncommon. The width of the three zones which show these types of microstructure is, respectively : 7 cm, 16 cm and 6 cm. STRAIN ANALYSIS
: STRUCTURES,
MICROSTRUCTURES,
FABRIC
Geometry The geometrical features of continuous ductile shear zones have been described by Ramsay and Graham, 1970 (p. 302-812) and by Ifara et al., 1973 (p. 2 and 3); three types of structures may be directly observed: (1) the foliation which is typically curved to a sigmoi’dal shape; (2) the shear boundary plane which is considered to be parallel to the shear plane; (3) the axial ratio X/Z (and Y/Z) of strain markers (grains, polycrystalline aggregates, xenoliths . . .), The initial shape of these strain markers is considered to be a sphere.
The definition of these three features allows an a&y&s of the deformation. The first two lead to the definition of the angle 6 between the foliation and the shear plane. If we make the assumption that the mechanism of deformation is simple shear with no change in volume, it is easy to show that from 8 the strain parameters: y, X/Z, Y/Z and the displacement can be calculated, (In the next section, we will discuss the validity of this assumption.) The angle B decreases from the boundary to the center of the shear zone (Fig. lc) the extreme values are 41” and 14”. This is accompanied by a progressive increase of the (X/Z) ratio of the polycrystalline aggregates (Fig. 2). The mean value of X/Z in the most deformed part of the shear zone is 15. But in this zone, values between 8 and 36 have been noted; most of them (77% of the measurements) are between 11.2 and 18.3. These values are quite similar (see below) to those predicted by a simple shear mechanism {see Fig. 2). Me~urement of the Y/Z ratio is difficult because the f YZ) plane of deformation is a curved plane. Moreover, the lengths along Y and 2 are small and quite similar. C~ns~uently the Y/Z ratio is not known precisely. In the most deformed part of the shear zone the Y/z values range between 1.4 and 3.7 with a mean value near 2. Xenoliths are more deformed than the polycrystalline aggregates of quartz
01,7
037 0
I I
$1
b
I
I
C
Fig. 2. Comparison of calculated values of (X/Z) ratio (continuous line) with the measured values (dashed line) for the A& crossaection. Vertical lines are intervals of variation of measured values; D is the domain of porphyroelastic relics texture; b is the domain of elongated mosaic texture; c is the domain of ribbon texture.
and plagiodase. For example, where the X/Z ratio of the aggregates is 6.5, the same ratio, for the xenoliths is 15. Interpretation
of strain
by a simple shear mechanism
Referring to previous works (Ramsay and Graham, 19’70; E&n-aet al, 1973), strain in this continuous ductile shear zone has been interpreted by a simple shear mechanism (Y invariant). This implies that: (1) the shear boundary is parallel to the shear plane, (2) the foliation is formed perpendicular to the principal finite shortening (Le., perpendicular to the short axis (z) of the finite strain ellipsoid). Variations in the orientation of foliation plane (sigmoi’dal shape) represent variations in the finite strain trajectories of the (XY) plane of deformation. Consequently the development of foliation is directly correlated with the increase of finite principal strain values (Fig. 3). In the continuous ductile shear zones, the value of B decreases progressively from the shear boundary to the center of the shear zone with the implication (eq. 1) that the shear angle rp increases progressively. The shear zone results from inhomogeneous simple shear. Various strain parameters have been defined by measuring B and the X/Z and Y/Z ratios, using the following relationships: tan 28 = 2/y and y = tan cp {Ramsay and Graham, 1970;P.799,eq.361 (1) XfZ = y
2+2+yt/~ 2
and Y/Z = X/Y(Ramsay,
1967; p. 85, eq. 3.67) (2)
For y 2 3 eq. 2 may be reduced to X/Z = y* f 2: x S=
f
y dsc (Ramsay and Graham, 1970; p_ 799, eq. 39)
(3)
0
in which cpis the angular shear; y is the shear strain; S is the displacement; x is the length along an (Ox)-axis perpendicular to the shear boundary. The origin 0 is a point on this shear boundary. Six cross-sections parallel to (Ox)-axis (A&-A&,) have been drawn (Fig. lc and Fig. 4); 7 = f@) for each of these cross sections have been calculated; the maximum value is 3.64 which lead to an angular shear ‘p = 74.6* and a (X/Z) ratio = 15.2. The integration of the area situated under the A&& ewve (Fig. 4 and eq. 3) gives a displacement S = 30.3 cm. This value represents the displacement of the shear zone center relative to the shear boundary, By symmetry the total displacement between the two shear boundary planes is near 60 cm. The results of the strain analysis have been summarized schematically in Fig, 51
=o
a
z.8
to 1
= 1 to 2.3
==7.1
Fig. 3. Summary
x/z
$ b2.3
X/Z = 2.6 to 7.4
f
f
d+e
d
a
Section
ribbon
mosaics
elongated
mosaics
elongated
relics
porphyroc
undeformec
macro&.
undeformec
Texture
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I..,
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-
1.5 mm
0.7 mm
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plagioclase
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and fabric in the shear zone.
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biotite
Deformation
.: ,a quartz
of relationships amongst strain parameters,
= 1.4 to 2.2
= .3.to
X/Z = 2.2 to 2.6
i
x/z
x
x/z,
1 to 1.4
= 1
‘d C.3
x/z
i
Strain parameters
Fig. 4. Comparison of 7 with distance from the shear boundary plane B for cross-se&ions to A&. y is calculated from the measure of 8 (7 = @an %?). u to fare locations of studied sections,
A$1
Discussion of the rymdts Without displaced strained markers such as dykes, the only available markers are polycrystalline aggregates. The interpretation of their deformatiop must be done carefully because: (1) the aggregates may not be spherical
Fig. 5. Schema of deformation of the studied granodiorite. The initial cube is deformed by inhomogeneous simple shear. cp is the angular shear; S1 is the foliation; f? is the angle between foiiation and shear plane. For this representation, discontinuous vahaes of 0 have been used. The interval of variation is the same as for the iso-ff curves in Fig. 1 (i.e. 5”).
23
before the deformations (2) deformation of aggregates may not represent the deformation of the whole rock. Nevertheless, a comparison of (X/Z) values calculated by eq. (2) with the directly measurable values (Fig. 2) shows consistent results; this suggests that the interpretation of strain by an inhomogeneous simple shear mechanism is reasonable. In the light of this model two points need discussion: (1) The maximum value of the angle 8 is 41” (which corresponds to an angular shear cp = 15.7” and an X/Z ratio = 1.3 in simple shear). This value is lower than the theoretical value 45” and it seems to be the general case (e.g,, Hara et al., 1973; p. 3). Three hypotheses may explain this discrepancy. (a) The shear boundary is not the shear plane. This is improbable. (b) The deformation mechanism is not simple shear so for low values of up, the angle 8 will also be lower. This hypothesis has been tested by calculation, A model of deformation has been established (Fig. 6) which can be described as a succession of two episodes of pure strain, comprising a simple shear followed by a pure shear with the direction of compression z perpendicular to the shear plane. Curve 0’ = f(q) has been drawn for different values of flattening: 5%, lo%, 15% and 20%. For 5% of flattening, the maximum value of the angle 0 ’ (that is to say the angle between the foliation and the shear plane) calculated with this
/q+y7y t” ‘------7
+
n
0 0
IO"
30”
50”
70”
90”
Pig. 6, Effect of flattening on magnitude of 8, The deformation is compared of (1) simple shear (2) pure shear with ~3 perpendicular to the shear plane; curves 8’ = f(q) have been drawn for different values of flattening (5%, IO%, IS%, 20%).
24
model is 32.3”, and the ~o~es~~ndi~g angular shear 9 equals 24”. These values are not compatible with the observed features. Consequently flattening, as described here, does not explain the lower value of 8, and it can be higher than 1 or 2% which is negligible. (c) The most probable hypothesis is to postulate a significant minimal value of the angular shear tp for the appearance of a foliation. Here this minimal value is tp = 15.7” which corresponds to a shear strain y = 0.28. This corroborates the observation of Hara et al_ (1973) who have described the shear boundary as the “apparent boundary of the shear belt”. (2) Measurements of the (Y/Z) ratio always gave values slightly lower than theoretical values. In the most deformed part of the shear zone, the maximum measured value is 3.7 and calculation gives 3.9. This is due either to a deformation with volume change ox by a complex mechanism of deformation which implies a slight flattening parallel to Y.
Fabrics of quartz and micas have been measured in the (X2) plane of deformation along the A& cross section (Fig. lc). Verification of the results has been provided by the study of corresponding sections in the (ZY) plane of deformation and by a study along the A& cross-section (Fig. lc), About 7000 c-axes were measured in grains showing the same habit. Every diagram has the same orientation relative to the axes of defo~ation. Foliation is East-West and X is horizontal. Sense of shear is indicated by arrows. It is sinistral. Description of fabric
The fabric of the undeformed host rock is isotropic (Fig. 7a). The section shown in Fig. 7b is situated near the shear boundary in the macroscopically undeformed host rock. It has been studied to test the hypothesis that the shear is an “apparent bonds of the shear zone” The c-axis sub-fabric of quartz is still isotropic (Fig. 7b) but the biotite sub-fabric becomes prugressively anisotropic. The measured crystals are slightly deformed (undulose exctinction) and the (001) axis have maxima within a (X2) girdle. This type of fabric is interpreted as transitional between the isotropic fabric characteristic of the undeformed host rock and the anisotropic fabric of the shear zone. The section shown in Fig. 7c is situated within the shear zone near the shear boundary. The rock is slightly schistosed and the texture presents po~hyro~~astic relics. The (001) axes of biotite form a well-defined maximum perpendicular to the foliation (Fig. 7~). The c-axis fabric of quartz is more or less isotropic but there is a tendency for a concentration of axes at a high angle from X. This is a prefiguration of the two-girdle fabric which will be obtained later. Sections d and e are from rock with elongated mosaics texture. The fabric uf quartz and biotite are elearly anisotropic (Fig. 8). The pattern of
25
Quartz
Biotite
Pig. 7. Fabric of quartz and micas in the less deformed part of the shear zone. For each diagram the same conventions are used: Projection into the lower hemisphere *. Equal area diagram; Sr is the foliation (line SW.); X is the direction of elongation (maximum principal axis of the finite strain eflipsoid); B is the shear-zone boundary plane; 8 is the angle between S1 and 3; a is the angle between the quartz girdle and the normal to the foliation. Sense of shear is indicated by arrows. a. Isotropic fabric of undeformed granodiorite (section a) 200 points, contours for 5;/2; 1; 0.5% per 1% area. b, Fabric of quartz and biotite in the macroscopically undeformed granodiorite (section b). Quartz and biotite: 120 points, contours for 5; 2; 1% per 1% area. e. Fabric of quartz and biotite in the section (e) (porphyroclastic relics texture). Quartz and biotite: 120 points, contours for: 10; 5; 2; 1% per 1% area. * For quartz: (0001) axis is measured (c axis); for biotite: (001) axis is measured (c axis).
.32”
Quartz
Quartz
Fig. 8. FaXlric of quartz nnd biatite in sections d and e (elongated mosaics texture); same conventions as in Fig, ‘7, d. Quartz and biotite: 120 points, contours far 10; 5; 2; 1% pttt 1% area. e. Quartz: 120 points, contcrurs for Xi; 5; 2; 1% per 1% area; Bilotite: 60 points, contours fer 15; 10; 6; 2; 1% per 1% area.
the former is foliation (Fig. is characteristic defined and a fabric (ce&d
either two girdles symmetrically situated with regard to the 8, section d) or one girdle (Fig. 8, section d) whose obliquity of the sense and amount of shear. These girdles may be illmaximum on Y may be the most important feature of the maximum Fig. 8, section d). The evolution from a two-girdle
fabric to a single-girdle fabric is observed in section d, for an angle 0 = 32” (Fig. 8). This corresponds theoretically to an angular shear cp = 44.3” 9 (X&q ratio = 2.66 and a shear strain +-y= 0.97, The fab~c*p~tte~ of biotite is a ma.ximum perpendictiar t;o foliation. It is better defined with j~c~e~~g strain.
28
Section f is situated in the most deformed part of the shear zone where one observes a ribban texture. The c-axis fabric of quartz is a single girdle, with or without a sharp maximum close to Y (Fig. 9). The oblique angle (Yof this girdle with the normal to the foliation is about equal to the measured angle 8 (214”). Fabric of micas is a sharp maximum perpendicular to foliation.
Experimental
techniques
Specimen preparation method is essentially that described by Barber (2970) and Champness and Lorimer (1971). Representative areas of the deformed grains were selected from normal petrological thin sections. These foils were then thinned by ion etching for electron microscopy. They were examined in a AEI EM7 ~~.V_E,M.~ electron microscope operating at 1000 kV at Imperial College in London. Electron microscopy
The most common mineral in the granodiorite is quartz. The behaviour of this mineral during natural deformation has been extensively studied (White, 1971-1977). Care was taken in the present study to get as much information as possible from its defect structures. Some observations on feldspar (albites) and micas are also presented. Quartz
As described by McLaren and Hobbs (1972), White (1973, 1975, 1976), quartz grains always contain unbound dislocations within well developed subgrains. The density of unbound dislocations (Fig. 1Ob) and dislocation loops were measured by the intersection method. The density varies significantly from grain to grain, and the dislocations may be heterogeneously distributed within one grain (from 8 . lo6 crne2 in the undeformed granite (section a) as well as in the most deformed part of the shear zone (section fl. Therefore it appears that there is no relationship between dislocation density and the shear strain (Fig. 11). The bound dislocations form walls sometimes slightly bowed (Fig. lOa), These are a~~roxima~ly parallel to the prism (Frond& 1962; Blacic, 1975) with a minor development of basal walls {OOOl) in the less deformed granite. The width of the prismatic subgrains (elongated in the (0001) direction and probably formed by a edge dislocations) is the only obvious element which varies from the undeformed granite to the center of the shear zone. More than one hundred subgrains were measured from montages of low mag-
29
Fig. 10, a. Elongated prismatic sub-grain in quartz. Sport within the subgrain are electron beam damage, Probable a-edge dislocations constitute the sub-boundary which is slightly bowed. b. Unbound dislocations in quartz (old grain in the underormed granodiorite). A fluid inclusion (arrowed) is undeformed.
nification micrograph or in the electron microscope itself. The width ranges from 8 to 15 pm with a mean value of 10 pm in the granite to an average of 4 pm in the shear zone (between 2 and 6 pm). This is a common diameter in mylonites (McLaren and Hobbs, 1972; White, 1974; 1975d). The recrystallization and grain-size refinement processes have not been studied in detail. Undoubtedly these were syntectonic and the microstructures are the consequence of a dynamic recovery (Cahn, 1970). White
30
b
f 29?5b, e; 1976) has demonstrated that if recovery dominates subgrains continually rotate while the strain increases. This phenomenon has also been recently described by Bell and Etheridge (1976). If the misorientation reaches 10” the subgrains occur as individual grains in optical microscopy (White, 19’73b; 1975b). The new grains are then deformed and normally contain dislocation densities similar to the host grains. As suggested by Singh, Rao and Taplin (1973) for metals and recently by White (1976b) for Myloni~s~ grain and subgrain boundaries are paraDeI to the direction of maximum resolved shear stress (Fig. lOa). Albite
Albite is the main feldspar in the granite, fortunately with a simple structure (McLaren and Marshall, 19741, The deformed grains also have a constant dislocation density (Fig. 12af of about 9 - lo7 lines emm2. This is clearly less than the mean dislocation density of the quartz. The dislocations are straight, generally parallel to (010) which is a slip plane in plagiocfaaes (Seifert, 1965; Borg and Heard, 1969; 1970). Most subboundaries were on {OlO} and (100). Subgrains generally have a larger size than those of quartz but can be smaller in the very strained areas. Nucleation of strain-free new grains takes place along subgrain boundaries (Fig. 12b). The nucleation along high stress boundaries seems to be the predominant grain refinement process and perhaps the r~~~s~~ation process during deformation. No twins were detected in the H.V.E.M. or in the optical microscope, This seems to be typical of the recrystallized albite and is surprising because slip processes are regarded as being of minor importance when compared with twinning (Borg and Handin, 1966; Borg and Heard, 1969, 1970; Lawrence, 1970; Carter, 1971). Absence of twins in this case might have facilitated dislocation movement. It has been suggested that recovery may be possible in albite which does not form a super~tti~e (White, 1975~). The dislocation structures in the albite though deformed during a low temperat~e green schist facies met~o~hism is evidence for recovery (see also Lorimer et al,, 1972). Inclusions of chlorite (Figs. 12a, 13) are common. These could also be seen in optical micrograph with a random orientation. However, some flakes are parallel to features (Fig. 13~) (marked by extinction fringes and which could be stacking faults, twins or exsolution boundaries).
Fig. 11. a. Relationship between quartz Q and biotite B. This montage has been made in the most deformed part of the shear zane (section f). Note the narrow elongated subgrains parallel to the prism (1010) (line RS-SB) in the quartz. Opening up of planes in biotite (arrowed) suggests that it is mainly by cataclastic fracture along this basal plane plane that the slip system (001) is activated. The c-axis tends to be normal to the foliation. b. Boundary between quartz Q and biotite B. Note the partings along planes of cleavage in the Mica, which is bent, kinked and fractured.
32
33
Micas The most deformed mica is biotite. No difference in microstructures was noticed between biotites in the granite and those in the shear zone. Throughout there are parting planes that are slip parallel to (001) (Fig. lla, b), which is a well known slip plane in phyllosilicates (Etheridge and Hobbs, 1974). Deformation features include curved cleavage and kinks of variable size and o~entation, often due to the rotation of the gram as the slip system (001) is activated (Fig. 11). Opening up of cleavage planes suggests that the slip was mainly by cataclastic failure along the basal plane (Fig. lla). Occasionally small crystals of what is regarded as chlorite have been found along boundaries of fractures (Fig. llb) or along areas when curvature induced by deformation is sharp. The distribution is compatible with localized crystallization associated with lattice bending, which is common in phyllosilicates (Knipe and White, 1975). Chlorite (?) is also often present as inclusions in feldspar. These inclusions may or may not be deformed (Figs. 13a, d) and this suggests that crystal growth took place during the deformation and perhaps lasted a little longer. On account of small grain-size it was not possible to obtain X-ray diffraction data to confirm the optical identification of chlorite. III. INTERPRETATION
OF FABRIC
AvC Lallemant and Carter (1971) and Tullis et al. (1973) have shown that the dominant slip systems in quartz are dependent on temperature, stress and strain rate. At low temperature and for a weak deformation (or for a high strain rate) the slip system is (0001) (a>. At higher temperature (or lower strain rate) prismatic slip becomes predominant on {lOiO} parallel to [c ] or on { 1010) parallel to (a> or on { lOi0) parallel to (c + a> (see also Blacic, 1975). The ch~c~~stics of the fabric described here can be interpreted in the light of these experimental data and with reference of the work of Nicolas et al. (1973), Etchecopar (1974), Bouchez (1977), Bouchez and Pecher (1976) and Laurent and Etchecopar (1976). The fabric data are interpreted as the result of simple shear on crystals which contain one, or more, preferential gliding planes. The H.V.E.M. study confirms that the c-axis fabric of quartz developed with increasing strain by dislocation process and therefore, in this case, there is a connection between fabric and deformation. The sequence shows that the c-axes progressively become concentrated in orientation with increase in shear strain across the shear zone. Fig. 12. a. Straight dislocations d in albite. The longest ones are parallel to (010). Note very small inclusions (i) and probably alteration (a) in deformed areas. b. New grain (rag) nucleated along a subgrain boundary (w) in albite where short straight dislocations are a constant feature. Note the absence of twins in both the old and new grains.
Fig. 13. a. Parallel inclusions of chlorite (North-South orientation) in albite. b. Strain free new grain of albite where no dislocations can be seen. This grain is rich in inclusions of chlorite with a random orientation. c. Chlorite parallel to fringe features in albite. The fringed features may appear to be stacking-faults. d. Chlorite crystal bent and spiit apart at one end.
The maximum concentration of c axes on or near Y (Fig. 9) indicates that basal planes are perp~~di~ul~ to foliation and parallel to X. This suggests (Wilson, 1975; Bouchez, 1977) that basal slip would be unimportant in these grains. Gliding must have operated on one, or more, prismatic planes parallel to the c-axis, with the slip direction nearly perpendicular to the c-axis. This result is also expected from the electron microscopy observations that the bound dislocations lie parallel to the prisms. This suggests that the prismatic glide was predomi~~t (maybe because of a high lattice water ~on~nt of quartz). The (10x0] slip concentrates the c-axes in the plane of the foliation, parailel to Y because slip in a dominating adirection is active. Petrofabric data have indicated the operation of basal slip, but only as a minor component during the deformation” We emphasize the importance of this (0001) slip plane in determining the shear-sense. The single girdle of caxes oblique to the foliation means that the basal planes of quartz contain the projection of X in the shear plane (Fig. 14). Basal planes (000~) are well oriented for gliding to operate on them with an unknown direction of slip (probably (a>). The sense of obliquity and the value of e indicate the same sense of shear and the amount of strain as it has been found in peridotites
Fig. 14. Schema of deformation by intracrystalline basal slip in a quartz grain with a favourabfe orientation. c-axis of quartz is perpendicular to basal plane (0001). The sense of shear in this plane is indicated by the arrows. ~a~r~~o~j~ foliation is Sr and the wefldefined Iineation is X. When strain increases, the angle between the foliation and the shear plane decreases. The ellipse represents schematicahy the section (2X) of finite strain ellipsoid in the quartz grain. Fig. 15. Schema of intracrystalline glide on the reverse sense (compared to the general sense of shear). This mechanism is active only in the grains which have a particular orientation and for a weak deformation (Etchecopar, 1974). (a) Initial solid: gliding planes (vertical lines) are perpendicular to the general direction of shear (arrows). (6) Final solid: the sense of shear on gliding pfane is indicated by dashed arrows.
36
(Nicolas et al., 1972, 1973). This method has been used by Laurent et al. (1976) in tectonites in the Dora-MaYra massif (Italian Alps), Double girdle pattern has been described by several authors. After the work of Etchecopar (1974), we interprete the second girdle by intracrystalline basal glide in the reverse sense referring to the general sense of shear, like a pile of books which falls on to the side (Fig. 15). This mechanism is possible only for particular initial orien~tions of b&al planes and for a weak deformation. Thus one can deduce that a symmetric fabric does not necessarily reflect flattening but may be due to simple shear. In conclusion, the fabric characteristics are interpreted as resulting from intracrystalline gliding on (1) dominant prismatic planes and (2) on basal planes. STRAIN PARAMETERS
Several attempts have been made recently by geologists to qu~tify strain parameters (Goetze and Kohlstedt, 1973; Heard, 1975; White, 1975-1977). They used different relationships between dislocation structures and the strain parameters formulated by metallurgists (Weertman, 1970; Orlova’ and Cadek, 1973). Most of these equations are based on variation of the subgrain size, so this is applicable to the shear-zone under investigation for stress and strain rates determination. The constants required (g, L and A) have been calculated from the experimental work of Tullis, Christie and Griggs (1973), different publications of White (1975d, e) and the synthesis of Heard (1975) giving the data on a wet quartzite from Canyon Creek studied by Parrish et al. (1975). The first equation shows that dislocation density p is stress ((T) dependent (Weertman, 1970): p=K;
0
n
Orlova’ et al. (1972) and Orlova’ and Cadek (1973) discussed this relationship where K and n are constants (n - l), p the temperature compensated shear modulus (~3,3 . 1011 dyne cmm2), If we apply this equation to the quartz in the shear zone we get a stress of about 500 bars which remains constant through the shear-zone because the dislocation density is constant. However, it has been suggested that some dislocation generation may occur during uplift (White, 1976a) so the density of unbound dislocations may not reflect past deformation conditions. The second equation relates the subgrain size d to the stress u (Holt, 1970; Orlova’ and Cadek, 1973). White (1975d, e) has shown that this formula could be applied to quartz:
up
d=L0 1
(1)
where L is a constant and p has a value of -i_ From this equation, we get in
37
the less deformed granite a stress of 250 bars, and in the most deformed part of the shear zone a stress of 1.5 kbar which is probably of too great a magnitude since these values apply to locations 50 cm apart (but it is assumed that the final grain and subgrain size is dependent upon the applied stress and is independent of the initial grain-size @ah et al., 1974). The variation in size may be due to differences in strain rate which can be calculated from: @=A
exp -& (
1
on
for steady state flow, where A is a constant for a particular material and deformation mechanism; Q the activation energy; R the gas constant; T temperature in degrees absolute; IZa constant with a value of 2 to 4. The first term is the ratio of the strain rates. If coy and & are, respectively, the strain rates in the granite and in the shear zone, from (2): (3) but from equation ( 1) : -l/2
we may write: (4) Ifn=4: e*y _ 6.5 * 1O-4 Z-sz Ifn-2:
e”7 -& cv 2.5
* 10-Z
Summarizing, the magnitude of this ratio is about 10s3. In the above equation the calculation of the strain rate is dependent on several constants, the values of which are not well established. For example Q has been estimated as 15 kcal mole-’ by Griggs (1974) and White (1975) or 45 kcal mole-’ by Goetze (1973), and 90 kcal mole-’ by Heard and Carter (1968). So determination of the deformation rate is debatable. However, using the different values, the ranging strain rates (from 2) were: lo-l3 set-’ < e*y < lo-l4 see-’ lO-‘O set-’ < ex, < lo-l1 set-l which seem to be reasonable values for natural deformation.
Gliding on basal planes may be responsible for the formation of the single oblique girdle * when gliding on prismatic planes give the c-axes concentration on Y: in the quartz sub-fabric the obliquity 01permits us to determine the sense and mount of shear, which is an impo~~t method for analysis of strain when strain markers are lacking. This kind of fabric has been described by ~isba~her {1970~, Laurent and Etcheeopar (1976) and Bouchez and Pecher (1976). For each of these studies a mechanism of simple shear had been proposed for field evidence (Mattauer, 1975). But quartz sub-fabric of shear zones is not always an oblique girdle. Ramsay and Graham (1970, p. 807) describe an (X2) girdle in the most deformed part of a metagabbro. Hara et al. (19733 described a complex fabric in a shear zone very similar to that we studied here: one may interpret the geometry of this fabric by two oblique girdles symmet~c~~y situated to the foliation; the two maxima situated in the (YZ) plane of finite strain at 30” to Y may be due to a flattening parallel to Y, These descriptions may also be due to differences in conditions of deformation. It is well-known (Tullis et al., 1973; Wilson, 1975; White, 1975d) that the main parameters which infhrence the slip systems are temperatures pressure, deviatoric stress and strain rate; and the knowledge of these slip systems is f~nd~ent~ for the interpretation of fabric. This study has indicated that prismatic slip and to a lesser extent, basal slip, in a probable
39
to calculate the strain rates. Therefore, there is difficulty in reconciling data from dislocation density and subgrain size. Poirier (1972) has shown that subgrains are low energy and therefore stable structures. We have to assume that what is measured is representative of the studied deformation; therefore the ratio of the strain rates with a magnitude of about 10e3 is certainly valuable. A late applied stress may be responsible for the constant dislocation density. ACKNOWLEDGEMENTS
We gratefully acknowledge Dr. M. Mattauer and A. Etchecopar for their constant helpfullness during this work and for their valuable criticism of the manuscript. J.P. Burg was supported by a grant from the Britsh Council. He is indebted to Dr. S. White for welcoming and assisting him in many aspects of electron microscopy and for helpful discussions. Dr. P.R. Swann who made available the H.V.E.M. facilities is gratefully thanked. REFERENCES Ave Lallemant, H.G. and Carter, N.L., 1971. Pressure dependance of quartz deformation lamellae orientations. Am. J. Sci., 270: 218-235. Bak, J., S$rensen, K., Grocott, J., Korstgard, J.A., Nash, D. and Watterson, J., 1975. Tectonic implications of Precambrian shear belts in western Greenland. Nature, 254: 566-569. Barber, D.J., 1970. Thin foils of non-metals made for electron microscopy by sputteretching. J. Mater. Sci., 5: 1-S. Bell, T.H. and Etheridge, M.A., 1976. The deformation and recrystallization of quartz in a mylonite zone, Central Australia. Tectonophysics, 32: 235-267. Blacic, J.D., 1975. Plastic deformation mechanisms in quartz. The effect of water. Tectonophysics, 27: 271-294. Borg, I.Y. and Handin, J., 1966. Experimental deformation of crystalline rocks. Tectonophysics, 3: 251-367. Borg, I.Y. and Heard, H.C., 1969. Mechanical twinning and slip in experimentally deformed plagioclases. Contrib. Mineral. Petrol., 23: 128-135. Borg, I.Y. and Heard, H.C., 1970. Experimental deformation of plagioclases. In: P. Paulitsch (Editor), Experimental and Natural Rock Deformation. Springer, Berlin, pp. 375403. Bouchez, J.L., 1977. Plastic deformation of quartzites at low temperature in an area of natural strain gradient. In: G.S. Lister, P.F. Williams, H.J. Zwart and R.J. Lisle (Editors), Fabrics, Microstructures and Microtectonics. Tectonophysics, 39 : 25-50. Bouchez, J.L. and Pecher, A., 1976. Textures et orientations preferentielles du quartz en relation avec le cisaillement du grand chevauchement central himalayen. 4ime Reunion Ann. Sci. Terre, Paris, p. 67. Cahn, R.W., 1970. Recovery and recrystallization. In: R.W. Cahn (Editor), Physical Metallurgy. North-Holland, Amsterdam, pp. 1129-1197. Carter, N.L., 1971. Static deformation of silica and silicates. J. Geophys. Res., 76-23: 5514-5540. Champness, P.E. and Lorimer, G.W., 1971. An electron microscopic study of a lunar pyroxene. Contrib. Mineral. Petrol., 33: 171-183. Christie, J.M., 1963. The Moine thrust zone in the Assynt region, Northwest Scotland. Calif. Univ. Publ. Geol. Sci., p. 345439.
40 Christie, J.M., Griggs, D.T. and Carters, N.L., 1964. Experimental evidence of basal slip in quartz. J. Geol. 72: 734-756. Eisbacher, G.H., 1970. Deformation mechanics of mylonitic rocks and fractured granites in Cobequid Mountains, Nova Scotia, Canada. Geol. Sot. Am. Bull., 81: 2009-2020. Etchecopar, A., 1974. Simulation par Ordinateur de la Deformation progressive d’un Aggregat polycristallin. Etude du Developpement de Structures orientees par Ecrasement et Cisaillement. Thesis, Univ. Nantes, 135 pp. Etchecopar, A., 1977. Kinematic model of progressive deformation in polycrystalline aggregate. In: G.S. Lister, P.F. W~lli~s, H.J. Zwart and R.J. Lisle (Editors), Fabrics, Microstructures, and Microtectonics, Tectonophysics; 39: 121-139. Etheridge, M.A. and Hobbs, B.E., 1974. Chemical and deformational controls on recrystallization of mica. Contriblb. Mineral. Petrol., 43: 111-124. Frondel, C., 1962. Dana’s System of Mineralogy. III. The Silica Minerals. Willey, New York, N.Y., 334 p. Goetze, C., 1973. A paleostress scale based on the dislocation microstructure of plastically deformed quartz and olivine (unpublished). Goetze, C. and Koblstedt, D.L., 1973. Laboratory study of dislocation climb and diffusion in olivine. J. Geophys. Res., 78-26: 5961-5971. Griggs, D.T., 1974. A model of hydrolytic weakening in quartz. J. Geophys. Res., 79: 1653-1661. Hara, I., Takada, K. and Kimura, T., 1973. Preferred lattice orientation of quartz in shear deformation. Hiroshima Univ. J. Sci., 7c: l-10. Heard, H.C., 1976. Comparison of the flow properties of rocks at crustal conditions. Phil. Trans. R. Sot. London, Ser. A, 283: 3-25. Heard, H.C. and Carter, N,L., 1968. Experimentally induced “natural” flow in quartz and quartzite. Am. J. Sci., 266: l-42. Holt, D.L., 1970. Dislocation cell formation in metals. J. Appl. Phys. 41: 3197-3201. Knipe, R.J. and White, S.H., 1975. Microstructural development of slaty cleavage, in development in electron microscopy and analysis. In: J. Venable (Editor), Proceedings of E.M.A.G. 75. Academic Press, New York, N.Y., p. 521-524. Laurent, P., 1974. Structure et petrologic de la bande blastomylonitique de BadajozCordoba (Chafne hercynienne sub-iberique) ri 1’Est d’Azuaga (Espagne). Description et Interpretation de la Deformation dans les Blastomylonites. Thesis, Univ. Montpellier, 105 pp. Laurent, P. and Etchecopar, A., 1976. Mise en evidence & l’aide de la fabrique du quartz d’un cisaillement simple a d&rersement ouest dans le Massif de Dora Maira (Alpes Occidentales). Bull. Sot. GBol. Fr., XVIII, 6: 1387-1393. Lawrence, R.D., 1970. Stress analysis based on albite twinning of plagioclase feldspars. Geol. Sot. Am. Bull., 81: 2507-2512. Lorimer, G.W., Champness, P.E. and Spooner, E.T., 1972. Dislocation distributions in naturally deformed onphacite and albite. Nature (London), Phys. Sci., 239: 108. Mattauer, M., 1975. Sur le mecanisme de formation de la schistosite dans 1’HimaIaya. Earth Planet. Sci, Lett., 28: 144-154. Mattauer, M. and Proust, F., 1975. Donnees nouvelies sur I’&olution structurale de la Gorse alpine. C.R. Acad. Sci. Paris, Ser. D, 281: 1681-1684. Mattauer, M., Proust, F. and Etchecopar, A., in press. Cisaillement simple et lineation “a” lies a la subduction continentale et au m&amorphisme haute pression dans la Come alpine. Matte, P. and Nicollet, C., 1976. Succession et style des deformations hercyniennes dans le substratum ante-permien du versant Sud du dome du Levezon (Sud du Massif Central francais). 48me Reunion Ann. Sci. Terre, Paris, p. 290. McLaren, A.C. and Hobbs, B.E., 1972. Transmission electron microscope investigation of some naturally deformed quartzites. In : Flow and Fracture of Rocks. The Griggs Volume, 16. Am. Geophys. Union, Byrd W. Press, pp. 55-66.
41 McLaren, A.C. and Marshall, D.B., 1974. Transmission electron microscope study of the domain structures associated with the b,c,d,e, and f reflections in plagioclase feldspars. Contrib. Mineral. and Petrol., 44: 237-249. Nicolas, A., Bouchez, J.L. and Boudier, F, 1972. Interpretation cinematique des deformations plastiques dans le massif de lhergolite de lanzo (Alpes Piemontaises). Comparison avec d’autres massifs. Tectonophysics, 14: 143-171. Nicolas, A., Boudier, F. and Boullier, A.M., 1973. Mechanisms of flow in naturally and experimentally deformed peridotites. Am. J. Sci., 273: 853-876. Orlova’, A. and Cadek, J., 1973. Some substructural aspects of high temperature creep in metals. Philos. Mag,, 28: 891-899. Orlova’, A., Tobolova’, Z. and Cadek, J., 1972. Internal stress and dislocation structure in Aluminium in high temperature creep. Phil. Mag., 26: 1263-1274. Parrish, D.K., Kriva, A. and Carter, N.L,, 1975. Geol. Sot. Am. Bull,, in press. Poirier, J.P., 1972. High temperature creep of simple crystaUine sodium chloride. II. Investigation of the creep substructure, Philos. Mag., 26: 713-725. Ramsay, J.G., 1967. Folding and Fracturing of Rocks. Mac Graw-Hill, New York, N.Y., 568 pp. Ramsay, J.G. and Graham, R.H., 1970. Strain variation in shear belts. Can. J. Earth Sci., 7: 786-813. Sah, J.P., Richardson, G.J. and Sellars, C.M., 1974. Grain size effects during dynamic recrystallization of nickel. Met. Sci. J., 8: 325-331. Seifert, K.E., 1965. Deformation bands in albite. Am. Mineral., 50: 1469-1472. Singh, V., Rao, R. and Taplin, D.M., 1973. On the role of grain-boundary migration during the creep of zinc. J. Mater. Sci., 8: 373-381. Streb, G. and Reppich, B., 1973. Steady state deformation and dislocation structure of pure and Mg-doped LiF simple crystals. II. Etchpit studies of dislocation structure. Phys. Status. Solidi. (a), 16: 493-505. Tullis, J., Christie, J.M. and Griggs, D.T., 1973. Microstructures and preferred orientations of experimentally deformed quartzites. Geol. Sot. Am. Bull., 84: 297-314. Weertman, J., 1970. The creep strength of the earth’s mantle. Rev. Geophys., 8: 145169. White, S.H., 1971. Natural creep deformation of quartzites. Nature (London), Phys. Sci., 234: 175-177. White, S.H., 1973a. The dislocation structures responsible for the optical effects in some naturally deformed quartzes. J. Mater. Sci., 8: 490-499. White, S.H., 1973b. Syntectonic recrystallization and texture development in quartz. Nature, 244: 276-278. White, S.H., 1974. Application of H.V.E.M. to metamorphic and structural Geology in High Voltage Electron Microscopy. In: Swann, Humphrey and Goringe (Editors) High-Voltage Electron Microscopy. Academic Press, New York, N-Y., pp. 317-322. White, S.H., 1975a. The effects of polyphase deformation in the intracrystalline defect structures of quartz. Neues Jahrb. Mineral., Abh., 123-3: 237-252. White, S-H., 1975b. The role of dislocation processes during tectonic deformations with particular reference to quartz. In: J. Strens (Editor), Chemistry and Physics of Rocks in Minerals. Wiley, New York (N.Y.), pp. 75-91. White, S.H., 1975~. Tectonic deformation and recrystallization of Oligoclase. Contrib. Mineral. Petrol., 50: 287-304. White, S.H., 1975d. Estimation of strain from microstructures. J. Geol. Sot., London, 131: 577-583. White, S.H., 1975e. The determination of deformation parameters from dislocation substructures in naturally deformed quartz. In: J. Venables (Editor), Development in Electron Microscopy and Analysis. Proceeding of EMAG 75. Academic Press, New York, N.Y., pp. 505-508.
42 White, S.H., 1976. Recrystailization and texture development in quartz. Proc. 4th European Texture Conf., in press. White, S.H., 1977. Geological significance of recovery and recrystallization processes in quartz. In: G.S. Lister, P.F. Williams, H.J. Zwart and R.J. Lisle (Editors), Fabrics, Microstructures, and Microtectonics. Tectonophysics, 39: 143-170. Wilson, C.J.L., 1975. Preferred orientation in quartz ribbon mylonites. Geol. Sot. Am. Bull., 86: 968-974.
15 in The Netherlands
STRAIN ANALYSIS OF A SHEAR ZONE IN A GRANODIORITE
J.P. BURG and Ph. LAURENT Laboratoire de G&lo&
St~uc~r~~e, 34060 ~un~~e~~~er,Cedeg ~~r~~~e~
(Received September, 29’76; revised version accepted September 6,1977)
ABSTRACT Burg, J-P_ and Laurent, Ph., 1978. Strain analysis of a shear zone in a granodiorite. Teetonophisics, 47: 1542. A ductile shear zone in a late Precambrian granodiorite, from the Rouergue (southwest part af the French Massif Central) has been studied. A single episode of deformation is responsible for the formation of a foliation and a well-defined lineation which are localized into an elongated zone, a few decimeters wide. The strain features can be attributed to a simple-shear mechanism (Ramsay and Graham, 1970), so that the main parameters of the deformation are defined, At stages of increasing deformation, the quartz isotropic sub-fabric of the undeformed host rock is progressively transformed into an anisotropic fabric composed of a single oblique girdle while the subgrain size progressively decrease and the dislocation density remains constant. It is suggested that the gliding planes of quartz are the ba.4 plane (0001) and a predominant prismatic plane {lOiO); the slip directions may be (a> for botb glide-planes. The results obtained in this investigation provide a basis for a high voltage electron microscope (H.V.E.M.) study which shows that the fabrics development may be related to dislocation processes. The difference of strain rates in the host rock and in the shear zone is calculated from the dislocation microstructures.
During the last decade, several publications have dealt with shear zones on various scales. Shear zones are generally localized planar features in which rocks are highly strained, and their thickness can vary from one millimeter to more than ten kilometers (e.g., Bak et al., 1975). Generally the deformatiun forming the shear zones is s~-rne~rnor~h~~ (~een~h~t to gram&e facie4 and produces. a typical welldefined lineation. Ductile shear zones may be divided into two classes: continuous and discontinuous. Continuous shear zones have been described by several geologists (e.g.? Ramsay and Graham, 1970; Hara et al., 1973). Their thickness varies from one centimeter to a few meters. They are characterized by a continuous increase of the shear strain 7 from the shear zone boundary to the center of the shear zone where the most highly strained rocks are localized. The shear
zone boundary is more or less well defined and the angle 8 between the foliation at this boundary and the shear plane (which is considered to be parallel to the shear boundary) is theoretically 45”. Due to the well defined foliation the values of y can be established withaut difficulty across the shear zone. From this geometric characteristic, one can infer the sense and amount of displacement without strain markers. The second type are ~h~~ter~zed by a d~~ont~nuo~s increase of y, The shear zone boundaries are generally welldefined, close in orientation to the foliation and look like faults. Determination of y is difficult without strain
I? 483
83
\ -
Fig. 1. a. Schematic representation of the deformed specimen. The black spherical and elliptical bodies are xenoliths; B is the shear boundary pfane. b. Schematic representation af deformation. 81 is the foliation plane; B is the shear boundary plane; 8 is the angle between S and B; X, Y, 2 are the principal directions of the finite strain ellipsoid (X B k* > 2); AsB3 is the studied cross-section; a---f are locations of thin sections studied (Figs. 7-9). c. Schema of the foliation in the (X2) plane of deform&an. A@z--A~B~ are cross-sections drawn in Fig. 4: b---f are positions of studied thin sections; Iso-8 lines are drawn (15*, 2@‘, W, 30*, 135~).
markers so the sense and amount of displacement are generally unknown. Discontinuous shear zones have been described by Eisbacher (1970) and Laurent (1974); their thickness varies from one hectometer to a few kilometers. This contribution is the study of a continuous ductile shear zone on every scale, which is important for the comprehension of deformation mechanisms and fur the quantification of strain. Moreover, referring to the work of Ramsay and Graham (1970), one can presume that simple shear m~hanism is responsible for the deformation of rocks in mountain chains hke the Himalaya (Mattauer, 1975; Bouchez and Pecher, 1976) or the Alps (Mattauer and Proust, 1975; Laurent and Etchecopar, 1976; Mattauer et al., in press). The purpose of this study is to get new evidence of relationships between the evolution of microstructural data, the strain and fabric data in a continuous shear zone. Sampling was restricted to half of the shear zone, that is to say the deformed part included between the shear zone boldly and the plane situated at the center of the shear zone since this plane is a symmetry plane for the deformation (Fig, la). The sample size was 60 cm parallel to the Iineation in the most deformed part of the shear zone, 45 cm perpendicular to the foliation, 26 cm in the plane of foliation, perpendicular to the lineation, The importance of transmission electron microscopy studies of naturally and expe~ment~ly deformed minerals is now well established for the determination of the slip system and the Bow law. The results of an exudation of minerals across the shear zone are pxesented. GEOLOGICAL
SETTING AND DESCRIPTION OF THE SAMPLE
The specimen has been sampled in the Rouergue (French Massif Central), where a granodiorite is cut by several shear-zones, one of which is studied in this paper. This grauodiurite has been deformed probably late in the variscan orogenesis, in the greenschist metamorphic facies (2’ = 350°C f 50°C and P = 2.5 kbar (Matte and Nicollet, 1976)). The shear zones functioned essentially as normal faults. The microstructure of the undeformed granodiorite is isotropic and homogeneous, comprising a coarse-grained matrix of quartz, piagioclase and biotite, enclosing some unoriented and equidimensional eentimetric melanocratic xenohths. Gram boundaries of qumtz are fobate (0.5-l mm) and the extortion is generally slightly undulose. The feldspars comprise plagioclase showing albitecarlsbad twins and some large euhedral crystals of microdine (5 mm) which are more or less sericitized. Micas are either large crystals of porphyroelastic biotite (2.5 mm) or crystals of neoblastic muscovite and chlorite (0.3 mm). The large crystals of biotite show undulose extinction. Accessory minerals are apatite and zircon.
Description of the def~rrnut~~n structures In the studied sample, the deformation structures are: (1) a well defined line&ion which is marked principally by elongated polycrystalline aggregates of quartz and plagioclase, and deformed xenoliths. (2) a foliation which is defined by the orientation of neoblastic micas (muscovite and ehlorite) and by a new orientation of porphyro~las~~ biotite. Evolution of microstructures with increasing strain A complete sequence of microstructures from the undeformed host rock to the center of the shear zone is observed. In quartz this evolution is very similar to that described in mylonites (Wilson, 1975) or in thrust zones (Christie, 1963). Referring to the work of Bouchez and Fecher f1976f, three types ‘of mierostrn~t~es are recognized: (a) ~orp~yr~clastic relics micrustr~ct~res present in the less deformed part of the ductile shear zone. Old polycrystalline aggregates of quartz are slightly deformed. Their X/Z ratio (X > Y > 2) is less than 3. Quartz grains are recrystallized and the extinction is slightly undulose. Porphyroclasts of biotite are deformed and show single or conjugate kinks. (b) ~~u~gated mosaics m~crustructure which is intermediate between a and c, is important because it has an anisotropic c-axis fabric of quartz. Pulycrystalline aggregates are elongated and are only composed of quartz. Some porphyroclasts of biotite show a particular structure which seams to lead to the definition of’the sense of shear (Eisbacher, 1970, p. 2016). The matrix is composed of small grains of plagioclase and neoblasts of micas, (c) ribbon microstructure appears in the most deformed part of the shear zone. Ribbons are essentially polycrystalline aggregates quartz. They represent the ultimate state in the evolution of initial poly~~st~line aggregates, Relic minerals are uncommon. The width of the three zones which show these types of microstructure is, respectively : 7 cm, 16 cm and 6 cm. STRAIN ANALYSIS
: STRUCTURES,
MICROSTRUCTURES,
FABRIC
Geometry The geometrical features of continuous ductile shear zones have been described by Ramsay and Graham, 1970 (p. 302-812) and by Ifara et al., 1973 (p. 2 and 3); three types of structures may be directly observed: (1) the foliation which is typically curved to a sigmoi’dal shape; (2) the shear boundary plane which is considered to be parallel to the shear plane; (3) the axial ratio X/Z (and Y/Z) of strain markers (grains, polycrystalline aggregates, xenoliths . . .), The initial shape of these strain markers is considered to be a sphere.
The definition of these three features allows an a&y&s of the deformation. The first two lead to the definition of the angle 6 between the foliation and the shear plane. If we make the assumption that the mechanism of deformation is simple shear with no change in volume, it is easy to show that from 8 the strain parameters: y, X/Z, Y/Z and the displacement can be calculated, (In the next section, we will discuss the validity of this assumption.) The angle B decreases from the boundary to the center of the shear zone (Fig. lc) the extreme values are 41” and 14”. This is accompanied by a progressive increase of the (X/Z) ratio of the polycrystalline aggregates (Fig. 2). The mean value of X/Z in the most deformed part of the shear zone is 15. But in this zone, values between 8 and 36 have been noted; most of them (77% of the measurements) are between 11.2 and 18.3. These values are quite similar (see below) to those predicted by a simple shear mechanism {see Fig. 2). Me~urement of the Y/Z ratio is difficult because the f YZ) plane of deformation is a curved plane. Moreover, the lengths along Y and 2 are small and quite similar. C~ns~uently the Y/Z ratio is not known precisely. In the most deformed part of the shear zone the Y/z values range between 1.4 and 3.7 with a mean value near 2. Xenoliths are more deformed than the polycrystalline aggregates of quartz
01,7
037 0
I I
$1
b
I
I
C
Fig. 2. Comparison of calculated values of (X/Z) ratio (continuous line) with the measured values (dashed line) for the A& crossaection. Vertical lines are intervals of variation of measured values; D is the domain of porphyroelastic relics texture; b is the domain of elongated mosaic texture; c is the domain of ribbon texture.
and plagiodase. For example, where the X/Z ratio of the aggregates is 6.5, the same ratio, for the xenoliths is 15. Interpretation
of strain
by a simple shear mechanism
Referring to previous works (Ramsay and Graham, 19’70; E&n-aet al, 1973), strain in this continuous ductile shear zone has been interpreted by a simple shear mechanism (Y invariant). This implies that: (1) the shear boundary is parallel to the shear plane, (2) the foliation is formed perpendicular to the principal finite shortening (Le., perpendicular to the short axis (z) of the finite strain ellipsoid). Variations in the orientation of foliation plane (sigmoi’dal shape) represent variations in the finite strain trajectories of the (XY) plane of deformation. Consequently the development of foliation is directly correlated with the increase of finite principal strain values (Fig. 3). In the continuous ductile shear zones, the value of B decreases progressively from the shear boundary to the center of the shear zone with the implication (eq. 1) that the shear angle rp increases progressively. The shear zone results from inhomogeneous simple shear. Various strain parameters have been defined by measuring B and the X/Z and Y/Z ratios, using the following relationships: tan 28 = 2/y and y = tan cp {Ramsay and Graham, 1970;P.799,eq.361 (1) XfZ = y
2+2+yt/~ 2
and Y/Z = X/Y(Ramsay,
1967; p. 85, eq. 3.67) (2)
For y 2 3 eq. 2 may be reduced to X/Z = y* f 2: x S=
f
y dsc (Ramsay and Graham, 1970; p_ 799, eq. 39)
(3)
0
in which cpis the angular shear; y is the shear strain; S is the displacement; x is the length along an (Ox)-axis perpendicular to the shear boundary. The origin 0 is a point on this shear boundary. Six cross-sections parallel to (Ox)-axis (A&-A&,) have been drawn (Fig. lc and Fig. 4); 7 = f@) for each of these cross sections have been calculated; the maximum value is 3.64 which lead to an angular shear ‘p = 74.6* and a (X/Z) ratio = 15.2. The integration of the area situated under the A&& ewve (Fig. 4 and eq. 3) gives a displacement S = 30.3 cm. This value represents the displacement of the shear zone center relative to the shear boundary, By symmetry the total displacement between the two shear boundary planes is near 60 cm. The results of the strain analysis have been summarized schematically in Fig, 51
=o
a
z.8
to 1
= 1 to 2.3
==7.1
Fig. 3. Summary
x/z
$ b2.3
X/Z = 2.6 to 7.4
f
f
d+e
d
a
Section
ribbon
mosaics
elongated
mosaics
elongated
relics
porphyroc
undeformec
macro&.
undeformec
Texture
I
I..,
-\
-
1.5 mm
0.7 mm
:..:. .,.I<. . ..__. .:‘:..
::; _.‘.T.
‘,.:.:‘.’
.;..‘,..
: :,,.:
C
-
C
aggregates
--\
I
;I ,
t
*
texture
I
, ..‘,
..
1
@
.:.
@
.::
. : .
_.’
.
. .
,..::. .
. .
,.
.
.:’
.
. .
.
*
..
.
....I: :.
plagioclase
.
@-
,
-
Y.
e-C
X
B
T isotropic
isotropic
2
1
20”
.30” \
-35”
?
CD
v)
0
cn
0 3 -.
cn
3
c
0
.42”
t
Ep _-
$
Y
+ isotropic
isotropic
biotite
Fa brie quartz
and fabric in the shear zone.
:
_..
biotite
Deformation
.: ,a quartz
of relationships amongst strain parameters,
= 1.4 to 2.2
= .3.to
X/Z = 2.2 to 2.6
i
x/z
x
x/z,
1 to 1.4
= 1
‘d C.3
x/z
i
Strain parameters
Fig. 4. Comparison of 7 with distance from the shear boundary plane B for cross-se&ions to A&. y is calculated from the measure of 8 (7 = @an %?). u to fare locations of studied sections,
A$1
Discussion of the rymdts Without displaced strained markers such as dykes, the only available markers are polycrystalline aggregates. The interpretation of their deformatiop must be done carefully because: (1) the aggregates may not be spherical
Fig. 5. Schema of deformation of the studied granodiorite. The initial cube is deformed by inhomogeneous simple shear. cp is the angular shear; S1 is the foliation; f? is the angle between foiiation and shear plane. For this representation, discontinuous vahaes of 0 have been used. The interval of variation is the same as for the iso-ff curves in Fig. 1 (i.e. 5”).
23
before the deformations (2) deformation of aggregates may not represent the deformation of the whole rock. Nevertheless, a comparison of (X/Z) values calculated by eq. (2) with the directly measurable values (Fig. 2) shows consistent results; this suggests that the interpretation of strain by an inhomogeneous simple shear mechanism is reasonable. In the light of this model two points need discussion: (1) The maximum value of the angle 8 is 41” (which corresponds to an angular shear cp = 15.7” and an X/Z ratio = 1.3 in simple shear). This value is lower than the theoretical value 45” and it seems to be the general case (e.g,, Hara et al., 1973; p. 3). Three hypotheses may explain this discrepancy. (a) The shear boundary is not the shear plane. This is improbable. (b) The deformation mechanism is not simple shear so for low values of up, the angle 8 will also be lower. This hypothesis has been tested by calculation, A model of deformation has been established (Fig. 6) which can be described as a succession of two episodes of pure strain, comprising a simple shear followed by a pure shear with the direction of compression z perpendicular to the shear plane. Curve 0’ = f(q) has been drawn for different values of flattening: 5%, lo%, 15% and 20%. For 5% of flattening, the maximum value of the angle 0 ’ (that is to say the angle between the foliation and the shear plane) calculated with this
/q+y7y t” ‘------7
+
n
0 0
IO"
30”
50”
70”
90”
Pig. 6, Effect of flattening on magnitude of 8, The deformation is compared of (1) simple shear (2) pure shear with ~3 perpendicular to the shear plane; curves 8’ = f(q) have been drawn for different values of flattening (5%, IO%, IS%, 20%).
24
model is 32.3”, and the ~o~es~~ndi~g angular shear 9 equals 24”. These values are not compatible with the observed features. Consequently flattening, as described here, does not explain the lower value of 8, and it can be higher than 1 or 2% which is negligible. (c) The most probable hypothesis is to postulate a significant minimal value of the angular shear tp for the appearance of a foliation. Here this minimal value is tp = 15.7” which corresponds to a shear strain y = 0.28. This corroborates the observation of Hara et al_ (1973) who have described the shear boundary as the “apparent boundary of the shear belt”. (2) Measurements of the (Y/Z) ratio always gave values slightly lower than theoretical values. In the most deformed part of the shear zone, the maximum measured value is 3.7 and calculation gives 3.9. This is due either to a deformation with volume change ox by a complex mechanism of deformation which implies a slight flattening parallel to Y.
Fabrics of quartz and micas have been measured in the (X2) plane of deformation along the A& cross section (Fig. lc). Verification of the results has been provided by the study of corresponding sections in the (ZY) plane of deformation and by a study along the A& cross-section (Fig. lc), About 7000 c-axes were measured in grains showing the same habit. Every diagram has the same orientation relative to the axes of defo~ation. Foliation is East-West and X is horizontal. Sense of shear is indicated by arrows. It is sinistral. Description of fabric
The fabric of the undeformed host rock is isotropic (Fig. 7a). The section shown in Fig. 7b is situated near the shear boundary in the macroscopically undeformed host rock. It has been studied to test the hypothesis that the shear is an “apparent bonds of the shear zone” The c-axis sub-fabric of quartz is still isotropic (Fig. 7b) but the biotite sub-fabric becomes prugressively anisotropic. The measured crystals are slightly deformed (undulose exctinction) and the (001) axis have maxima within a (X2) girdle. This type of fabric is interpreted as transitional between the isotropic fabric characteristic of the undeformed host rock and the anisotropic fabric of the shear zone. The section shown in Fig. 7c is situated within the shear zone near the shear boundary. The rock is slightly schistosed and the texture presents po~hyro~~astic relics. The (001) axes of biotite form a well-defined maximum perpendicular to the foliation (Fig. 7~). The c-axis fabric of quartz is more or less isotropic but there is a tendency for a concentration of axes at a high angle from X. This is a prefiguration of the two-girdle fabric which will be obtained later. Sections d and e are from rock with elongated mosaics texture. The fabric uf quartz and biotite are elearly anisotropic (Fig. 8). The pattern of
25
Quartz
Biotite
Pig. 7. Fabric of quartz and micas in the less deformed part of the shear zone. For each diagram the same conventions are used: Projection into the lower hemisphere *. Equal area diagram; Sr is the foliation (line SW.); X is the direction of elongation (maximum principal axis of the finite strain eflipsoid); B is the shear-zone boundary plane; 8 is the angle between S1 and 3; a is the angle between the quartz girdle and the normal to the foliation. Sense of shear is indicated by arrows. a. Isotropic fabric of undeformed granodiorite (section a) 200 points, contours for 5;/2; 1; 0.5% per 1% area. b, Fabric of quartz and biotite in the macroscopically undeformed granodiorite (section b). Quartz and biotite: 120 points, contours for 5; 2; 1% per 1% area. e. Fabric of quartz and biotite in the section (e) (porphyroclastic relics texture). Quartz and biotite: 120 points, contours for: 10; 5; 2; 1% per 1% area. * For quartz: (0001) axis is measured (c axis); for biotite: (001) axis is measured (c axis).
.32”
Quartz
Quartz
Fig. 8. FaXlric of quartz nnd biatite in sections d and e (elongated mosaics texture); same conventions as in Fig, ‘7, d. Quartz and biotite: 120 points, contours far 10; 5; 2; 1% pttt 1% area. e. Quartz: 120 points, contcrurs for Xi; 5; 2; 1% per 1% area; Bilotite: 60 points, contours fer 15; 10; 6; 2; 1% per 1% area.
the former is foliation (Fig. is characteristic defined and a fabric (ce&d
either two girdles symmetrically situated with regard to the 8, section d) or one girdle (Fig. 8, section d) whose obliquity of the sense and amount of shear. These girdles may be illmaximum on Y may be the most important feature of the maximum Fig. 8, section d). The evolution from a two-girdle
fabric to a single-girdle fabric is observed in section d, for an angle 0 = 32” (Fig. 8). This corresponds theoretically to an angular shear cp = 44.3” 9 (X&q ratio = 2.66 and a shear strain +-y= 0.97, The fab~c*p~tte~ of biotite is a ma.ximum perpendictiar t;o foliation. It is better defined with j~c~e~~g strain.
28
Section f is situated in the most deformed part of the shear zone where one observes a ribban texture. The c-axis fabric of quartz is a single girdle, with or without a sharp maximum close to Y (Fig. 9). The oblique angle (Yof this girdle with the normal to the foliation is about equal to the measured angle 8 (214”). Fabric of micas is a sharp maximum perpendicular to foliation.
Experimental
techniques
Specimen preparation method is essentially that described by Barber (2970) and Champness and Lorimer (1971). Representative areas of the deformed grains were selected from normal petrological thin sections. These foils were then thinned by ion etching for electron microscopy. They were examined in a AEI EM7 ~~.V_E,M.~ electron microscope operating at 1000 kV at Imperial College in London. Electron microscopy
The most common mineral in the granodiorite is quartz. The behaviour of this mineral during natural deformation has been extensively studied (White, 1971-1977). Care was taken in the present study to get as much information as possible from its defect structures. Some observations on feldspar (albites) and micas are also presented. Quartz
As described by McLaren and Hobbs (1972), White (1973, 1975, 1976), quartz grains always contain unbound dislocations within well developed subgrains. The density of unbound dislocations (Fig. 1Ob) and dislocation loops were measured by the intersection method. The density varies significantly from grain to grain, and the dislocations may be heterogeneously distributed within one grain (from 8 . lo6 crne2 in the undeformed granite (section a) as well as in the most deformed part of the shear zone (section fl. Therefore it appears that there is no relationship between dislocation density and the shear strain (Fig. 11). The bound dislocations form walls sometimes slightly bowed (Fig. lOa), These are a~~roxima~ly parallel to the prism (Frond& 1962; Blacic, 1975) with a minor development of basal walls {OOOl) in the less deformed granite. The width of the prismatic subgrains (elongated in the (0001) direction and probably formed by a edge dislocations) is the only obvious element which varies from the undeformed granite to the center of the shear zone. More than one hundred subgrains were measured from montages of low mag-
29
Fig. 10, a. Elongated prismatic sub-grain in quartz. Sport within the subgrain are electron beam damage, Probable a-edge dislocations constitute the sub-boundary which is slightly bowed. b. Unbound dislocations in quartz (old grain in the underormed granodiorite). A fluid inclusion (arrowed) is undeformed.
nification micrograph or in the electron microscope itself. The width ranges from 8 to 15 pm with a mean value of 10 pm in the granite to an average of 4 pm in the shear zone (between 2 and 6 pm). This is a common diameter in mylonites (McLaren and Hobbs, 1972; White, 1974; 1975d). The recrystallization and grain-size refinement processes have not been studied in detail. Undoubtedly these were syntectonic and the microstructures are the consequence of a dynamic recovery (Cahn, 1970). White
30
b
f 29?5b, e; 1976) has demonstrated that if recovery dominates subgrains continually rotate while the strain increases. This phenomenon has also been recently described by Bell and Etheridge (1976). If the misorientation reaches 10” the subgrains occur as individual grains in optical microscopy (White, 19’73b; 1975b). The new grains are then deformed and normally contain dislocation densities similar to the host grains. As suggested by Singh, Rao and Taplin (1973) for metals and recently by White (1976b) for Myloni~s~ grain and subgrain boundaries are paraDeI to the direction of maximum resolved shear stress (Fig. lOa). Albite
Albite is the main feldspar in the granite, fortunately with a simple structure (McLaren and Marshall, 19741, The deformed grains also have a constant dislocation density (Fig. 12af of about 9 - lo7 lines emm2. This is clearly less than the mean dislocation density of the quartz. The dislocations are straight, generally parallel to (010) which is a slip plane in plagiocfaaes (Seifert, 1965; Borg and Heard, 1969; 1970). Most subboundaries were on {OlO} and (100). Subgrains generally have a larger size than those of quartz but can be smaller in the very strained areas. Nucleation of strain-free new grains takes place along subgrain boundaries (Fig. 12b). The nucleation along high stress boundaries seems to be the predominant grain refinement process and perhaps the r~~~s~~ation process during deformation. No twins were detected in the H.V.E.M. or in the optical microscope, This seems to be typical of the recrystallized albite and is surprising because slip processes are regarded as being of minor importance when compared with twinning (Borg and Handin, 1966; Borg and Heard, 1969, 1970; Lawrence, 1970; Carter, 1971). Absence of twins in this case might have facilitated dislocation movement. It has been suggested that recovery may be possible in albite which does not form a super~tti~e (White, 1975~). The dislocation structures in the albite though deformed during a low temperat~e green schist facies met~o~hism is evidence for recovery (see also Lorimer et al,, 1972). Inclusions of chlorite (Figs. 12a, 13) are common. These could also be seen in optical micrograph with a random orientation. However, some flakes are parallel to features (Fig. 13~) (marked by extinction fringes and which could be stacking faults, twins or exsolution boundaries).
Fig. 11. a. Relationship between quartz Q and biotite B. This montage has been made in the most deformed part of the shear zane (section f). Note the narrow elongated subgrains parallel to the prism (1010) (line RS-SB) in the quartz. Opening up of planes in biotite (arrowed) suggests that it is mainly by cataclastic fracture along this basal plane plane that the slip system (001) is activated. The c-axis tends to be normal to the foliation. b. Boundary between quartz Q and biotite B. Note the partings along planes of cleavage in the Mica, which is bent, kinked and fractured.
32
33
Micas The most deformed mica is biotite. No difference in microstructures was noticed between biotites in the granite and those in the shear zone. Throughout there are parting planes that are slip parallel to (001) (Fig. lla, b), which is a well known slip plane in phyllosilicates (Etheridge and Hobbs, 1974). Deformation features include curved cleavage and kinks of variable size and o~entation, often due to the rotation of the gram as the slip system (001) is activated (Fig. 11). Opening up of cleavage planes suggests that the slip was mainly by cataclastic failure along the basal plane (Fig. lla). Occasionally small crystals of what is regarded as chlorite have been found along boundaries of fractures (Fig. llb) or along areas when curvature induced by deformation is sharp. The distribution is compatible with localized crystallization associated with lattice bending, which is common in phyllosilicates (Knipe and White, 1975). Chlorite (?) is also often present as inclusions in feldspar. These inclusions may or may not be deformed (Figs. 13a, d) and this suggests that crystal growth took place during the deformation and perhaps lasted a little longer. On account of small grain-size it was not possible to obtain X-ray diffraction data to confirm the optical identification of chlorite. III. INTERPRETATION
OF FABRIC
AvC Lallemant and Carter (1971) and Tullis et al. (1973) have shown that the dominant slip systems in quartz are dependent on temperature, stress and strain rate. At low temperature and for a weak deformation (or for a high strain rate) the slip system is (0001) (a>. At higher temperature (or lower strain rate) prismatic slip becomes predominant on {lOiO} parallel to [c ] or on { 1010) parallel to (a> or on { lOi0) parallel to (c + a> (see also Blacic, 1975). The ch~c~~stics of the fabric described here can be interpreted in the light of these experimental data and with reference of the work of Nicolas et al. (1973), Etchecopar (1974), Bouchez (1977), Bouchez and Pecher (1976) and Laurent and Etchecopar (1976). The fabric data are interpreted as the result of simple shear on crystals which contain one, or more, preferential gliding planes. The H.V.E.M. study confirms that the c-axis fabric of quartz developed with increasing strain by dislocation process and therefore, in this case, there is a connection between fabric and deformation. The sequence shows that the c-axes progressively become concentrated in orientation with increase in shear strain across the shear zone. Fig. 12. a. Straight dislocations d in albite. The longest ones are parallel to (010). Note very small inclusions (i) and probably alteration (a) in deformed areas. b. New grain (rag) nucleated along a subgrain boundary (w) in albite where short straight dislocations are a constant feature. Note the absence of twins in both the old and new grains.
Fig. 13. a. Parallel inclusions of chlorite (North-South orientation) in albite. b. Strain free new grain of albite where no dislocations can be seen. This grain is rich in inclusions of chlorite with a random orientation. c. Chlorite parallel to fringe features in albite. The fringed features may appear to be stacking-faults. d. Chlorite crystal bent and spiit apart at one end.
The maximum concentration of c axes on or near Y (Fig. 9) indicates that basal planes are perp~~di~ul~ to foliation and parallel to X. This suggests (Wilson, 1975; Bouchez, 1977) that basal slip would be unimportant in these grains. Gliding must have operated on one, or more, prismatic planes parallel to the c-axis, with the slip direction nearly perpendicular to the c-axis. This result is also expected from the electron microscopy observations that the bound dislocations lie parallel to the prisms. This suggests that the prismatic glide was predomi~~t (maybe because of a high lattice water ~on~nt of quartz). The (10x0] slip concentrates the c-axes in the plane of the foliation, parailel to Y because slip in a dominating adirection is active. Petrofabric data have indicated the operation of basal slip, but only as a minor component during the deformation” We emphasize the importance of this (0001) slip plane in determining the shear-sense. The single girdle of caxes oblique to the foliation means that the basal planes of quartz contain the projection of X in the shear plane (Fig. 14). Basal planes (000~) are well oriented for gliding to operate on them with an unknown direction of slip (probably (a>). The sense of obliquity and the value of e indicate the same sense of shear and the amount of strain as it has been found in peridotites
Fig. 14. Schema of deformation by intracrystalline basal slip in a quartz grain with a favourabfe orientation. c-axis of quartz is perpendicular to basal plane (0001). The sense of shear in this plane is indicated by the arrows. ~a~r~~o~j~ foliation is Sr and the wefldefined Iineation is X. When strain increases, the angle between the foliation and the shear plane decreases. The ellipse represents schematicahy the section (2X) of finite strain ellipsoid in the quartz grain. Fig. 15. Schema of intracrystalline glide on the reverse sense (compared to the general sense of shear). This mechanism is active only in the grains which have a particular orientation and for a weak deformation (Etchecopar, 1974). (a) Initial solid: gliding planes (vertical lines) are perpendicular to the general direction of shear (arrows). (6) Final solid: the sense of shear on gliding pfane is indicated by dashed arrows.
36
(Nicolas et al., 1972, 1973). This method has been used by Laurent et al. (1976) in tectonites in the Dora-MaYra massif (Italian Alps), Double girdle pattern has been described by several authors. After the work of Etchecopar (1974), we interprete the second girdle by intracrystalline basal glide in the reverse sense referring to the general sense of shear, like a pile of books which falls on to the side (Fig. 15). This mechanism is possible only for particular initial orien~tions of b&al planes and for a weak deformation. Thus one can deduce that a symmetric fabric does not necessarily reflect flattening but may be due to simple shear. In conclusion, the fabric characteristics are interpreted as resulting from intracrystalline gliding on (1) dominant prismatic planes and (2) on basal planes. STRAIN PARAMETERS
Several attempts have been made recently by geologists to qu~tify strain parameters (Goetze and Kohlstedt, 1973; Heard, 1975; White, 1975-1977). They used different relationships between dislocation structures and the strain parameters formulated by metallurgists (Weertman, 1970; Orlova’ and Cadek, 1973). Most of these equations are based on variation of the subgrain size, so this is applicable to the shear-zone under investigation for stress and strain rates determination. The constants required (g, L and A) have been calculated from the experimental work of Tullis, Christie and Griggs (1973), different publications of White (1975d, e) and the synthesis of Heard (1975) giving the data on a wet quartzite from Canyon Creek studied by Parrish et al. (1975). The first equation shows that dislocation density p is stress ((T) dependent (Weertman, 1970): p=K;
0
n
Orlova’ et al. (1972) and Orlova’ and Cadek (1973) discussed this relationship where K and n are constants (n - l), p the temperature compensated shear modulus (~3,3 . 1011 dyne cmm2), If we apply this equation to the quartz in the shear zone we get a stress of about 500 bars which remains constant through the shear-zone because the dislocation density is constant. However, it has been suggested that some dislocation generation may occur during uplift (White, 1976a) so the density of unbound dislocations may not reflect past deformation conditions. The second equation relates the subgrain size d to the stress u (Holt, 1970; Orlova’ and Cadek, 1973). White (1975d, e) has shown that this formula could be applied to quartz:
up
d=L0 1
(1)
where L is a constant and p has a value of -i_ From this equation, we get in
37
the less deformed granite a stress of 250 bars, and in the most deformed part of the shear zone a stress of 1.5 kbar which is probably of too great a magnitude since these values apply to locations 50 cm apart (but it is assumed that the final grain and subgrain size is dependent upon the applied stress and is independent of the initial grain-size @ah et al., 1974). The variation in size may be due to differences in strain rate which can be calculated from: @=A
exp -& (
1
on
for steady state flow, where A is a constant for a particular material and deformation mechanism; Q the activation energy; R the gas constant; T temperature in degrees absolute; IZa constant with a value of 2 to 4. The first term is the ratio of the strain rates. If coy and & are, respectively, the strain rates in the granite and in the shear zone, from (2): (3) but from equation ( 1) : -l/2
we may write: (4) Ifn=4: e*y _ 6.5 * 1O-4 Z-sz Ifn-2:
e”7 -& cv 2.5
* 10-Z
Summarizing, the magnitude of this ratio is about 10s3. In the above equation the calculation of the strain rate is dependent on several constants, the values of which are not well established. For example Q has been estimated as 15 kcal mole-’ by Griggs (1974) and White (1975) or 45 kcal mole-’ by Goetze (1973), and 90 kcal mole-’ by Heard and Carter (1968). So determination of the deformation rate is debatable. However, using the different values, the ranging strain rates (from 2) were: lo-l3 set-’ < e*y < lo-l4 see-’ lO-‘O set-’ < ex, < lo-l1 set-l which seem to be reasonable values for natural deformation.
Gliding on basal planes may be responsible for the formation of the single oblique girdle * when gliding on prismatic planes give the c-axes concentration on Y: in the quartz sub-fabric the obliquity 01permits us to determine the sense and mount of shear, which is an impo~~t method for analysis of strain when strain markers are lacking. This kind of fabric has been described by ~isba~her {1970~, Laurent and Etcheeopar (1976) and Bouchez and Pecher (1976). For each of these studies a mechanism of simple shear had been proposed for field evidence (Mattauer, 1975). But quartz sub-fabric of shear zones is not always an oblique girdle. Ramsay and Graham (1970, p. 807) describe an (X2) girdle in the most deformed part of a metagabbro. Hara et al. (19733 described a complex fabric in a shear zone very similar to that we studied here: one may interpret the geometry of this fabric by two oblique girdles symmet~c~~y situated to the foliation; the two maxima situated in the (YZ) plane of finite strain at 30” to Y may be due to a flattening parallel to Y, These descriptions may also be due to differences in conditions of deformation. It is well-known (Tullis et al., 1973; Wilson, 1975; White, 1975d) that the main parameters which infhrence the slip systems are temperatures pressure, deviatoric stress and strain rate; and the knowledge of these slip systems is f~nd~ent~ for the interpretation of fabric. This study has indicated that prismatic slip and to a lesser extent, basal slip, in a probable
39
to calculate the strain rates. Therefore, there is difficulty in reconciling data from dislocation density and subgrain size. Poirier (1972) has shown that subgrains are low energy and therefore stable structures. We have to assume that what is measured is representative of the studied deformation; therefore the ratio of the strain rates with a magnitude of about 10e3 is certainly valuable. A late applied stress may be responsible for the constant dislocation density. ACKNOWLEDGEMENTS
We gratefully acknowledge Dr. M. Mattauer and A. Etchecopar for their constant helpfullness during this work and for their valuable criticism of the manuscript. J.P. Burg was supported by a grant from the Britsh Council. He is indebted to Dr. S. White for welcoming and assisting him in many aspects of electron microscopy and for helpful discussions. Dr. P.R. Swann who made available the H.V.E.M. facilities is gratefully thanked. REFERENCES Ave Lallemant, H.G. and Carter, N.L., 1971. Pressure dependance of quartz deformation lamellae orientations. Am. J. Sci., 270: 218-235. Bak, J., S$rensen, K., Grocott, J., Korstgard, J.A., Nash, D. and Watterson, J., 1975. Tectonic implications of Precambrian shear belts in western Greenland. Nature, 254: 566-569. Barber, D.J., 1970. Thin foils of non-metals made for electron microscopy by sputteretching. J. Mater. Sci., 5: 1-S. Bell, T.H. and Etheridge, M.A., 1976. The deformation and recrystallization of quartz in a mylonite zone, Central Australia. Tectonophysics, 32: 235-267. Blacic, J.D., 1975. Plastic deformation mechanisms in quartz. The effect of water. Tectonophysics, 27: 271-294. Borg, I.Y. and Handin, J., 1966. Experimental deformation of crystalline rocks. Tectonophysics, 3: 251-367. Borg, I.Y. and Heard, H.C., 1969. Mechanical twinning and slip in experimentally deformed plagioclases. Contrib. Mineral. Petrol., 23: 128-135. Borg, I.Y. and Heard, H.C., 1970. Experimental deformation of plagioclases. In: P. Paulitsch (Editor), Experimental and Natural Rock Deformation. Springer, Berlin, pp. 375403. Bouchez, J.L., 1977. Plastic deformation of quartzites at low temperature in an area of natural strain gradient. In: G.S. Lister, P.F. Williams, H.J. Zwart and R.J. Lisle (Editors), Fabrics, Microstructures and Microtectonics. Tectonophysics, 39 : 25-50. Bouchez, J.L. and Pecher, A., 1976. Textures et orientations preferentielles du quartz en relation avec le cisaillement du grand chevauchement central himalayen. 4ime Reunion Ann. Sci. Terre, Paris, p. 67. Cahn, R.W., 1970. Recovery and recrystallization. In: R.W. Cahn (Editor), Physical Metallurgy. North-Holland, Amsterdam, pp. 1129-1197. Carter, N.L., 1971. Static deformation of silica and silicates. J. Geophys. Res., 76-23: 5514-5540. Champness, P.E. and Lorimer, G.W., 1971. An electron microscopic study of a lunar pyroxene. Contrib. Mineral. Petrol., 33: 171-183. Christie, J.M., 1963. The Moine thrust zone in the Assynt region, Northwest Scotland. Calif. Univ. Publ. Geol. Sci., p. 345439.
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