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Strain variation between quartz grains of different crystallographic orientation in a naturally deformed metasiltstone
Tectonophysics, 78 (1981) 73-84 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
73
STRAIN VARIATION BETWEEN QUARTZ GRAINS OF DIFFERENT CRYSTALLOGRAPHIC ORIENTATION IN A NATURALLY DEFORMED METASILTSTONE
NEIL S. MANCKTELOW Department (Australia)
*
of Geology and Mineralogy, University of Adelaide, Adelaide 5000, S.A.
(Received January 26,198l)
ABSTRACT Mancktelow, N.S., 1981. Strain variation between quartz grains of different crystallographic orientation in a naturally deformed metasiltstone. In: G.S. Lister, H.-J. Behr, K. Weber and H.J. Zwart (Editors), The Effect of Deformation on Rocks. Tectonophysics, 78: 73-84. The shapes of isolated quartz grains in a metasiltstone from the Fleurieu Peninsula, South Australia, vary markedly, the amount of strain undergone by individual grains being strongly influenced by crystallographic orientation relative to the finite strain axes. The least-deformed grains have c-axis orientations clustered about the principal strain directions; that is, they have orientations for which the resolved shear stress on the (0001) (a) and {lOiO} (c) slip systems would have been close to zero during coaxial deformation. A simple theoretical approach suggests that the geometry of the bulk strain should influence the observed c-axis fabric of these least-deformed grains. The fabrics should vary from (a) a pronounced maximum parallel to 2 with a subsiduary distribution in the XY-plane for pure flattening strain, through (b) fabrics with maxima parallel to X and 2 and a weak maximum parallel to Y, to (c) fabrics with a pronounced maximum parallel to X and a subsiduary distribution within the YZ-plane for pure constriction. The most elongate quartz grains in the metasiltstone show a strong maximum of c-axes parallel to the intermediate strain axis, Y. This suggests predominant prismatic slip in a direction at a large angle to the c-axis, probably on (lOi0) (a). The bulk strain undergone by the specimen is an integral of the variable strains in the component minerals, and the extremes (the least deformed or the most elongate grains) cannot be regarded as anomalous if a realistic strain estimate is to be obtained.
INTRODUCTION
The deformed shape of sedimentary quartz grains has often been used to obtain an estimate of bulk strain in low metamorphic grade quartz-rich rocks.
* Present address: Geologisches Institut, ETH-Zentrum, 0040-1951/81/0000-0000/$02.50
CH-8092 Zurich, Switzerland
@ 1981 Elsevier Scientific
Publishing Company
Allowance is usually made for an original sedimentary fabric, but the variation imposed by the crystallographic anisotropy of quartz has commonly been ignored. Recently, Marjoribanks (1976) and Bouchez (1977) have both noted that in deformed quartzites there are some grains which fall outside the general range of deformed grain shapes, being either much more equant or more elongate than the majority. They ascribed this variation to the crystallographic orientation of these particular grains. However, as outlined below, the more equant and more elongate grains are not unusual or anomalous but merely the extremes of a continuum, with the strain in each quartz grain being strongly influenced by the crystallographic orientation of the grain relative to the stress field effective on that grain. The sample of granule-bearing metasiltstone examined in this study was collected 3 km south of Rapid Bay, South Australia (138” 10’ E, 35” 33’ S), in an area of greenschist facies metamorphism (biotitechlorite-muscovite zone) within the Adelaide Fold Belt. The present mineralogy of the metasiltstone is quartz + muscovite + biotite + chlorite + plagioclase + K-feldspar + accessory tourmaline, apatite, zircon and opaques. A well-developed slaty cleavage is defined in thin section by the alignment of mica and by the dimensional fabric of the quartz grains. The metasiltstone was deformed during the major slaty cleavage-forming orogeny which affected the Adelaide Fold Belt in the early Ordovician. STRAIN
AND C-AXIS
FABRIC
DETERMINATIONS
The specimen was studied originally to obtain an estimate of the bulk strain. To this end, thin-sections were cut parallel to the principal strain planes, assuming the slaty cleavage is parallel to XY and the quartz elongation lineation is X, the direction of maximum elongation (see Wood, 1974). The length to width ratios and orientations of the quartz grains were measured and the results plotted on the Shape Factor Grid of Elliot (1970) (Fig. 1). It was obvious that some factor other than an original sedimentary fabric had influenced the resultant deformation shape fabric. The X2-plot of Fig. 1 shows considerable variation in the length to width ratio of the grains but little divergence in orientation of the long axis away from the cleavage trace. This relationship is quite striking in the thin-section itself (Fig. 2). Such a distribution is unlikely to be achieved by imposition of a homogeneous strain on an original sedimentary fabric. The alternative is that the strain from grain to grain, rather than being homogeneous, is markedly heterogeneous and that the variation in shape of individual grains reflects this heterogeneity. The work of Hobbs et al. (1972) and Baeta and Ashbee (1970) has shown that there is marked variation in the yield stress of individual quartz crystals with different crystallographic orientations relative to the applied stress. It follows that in a deforming aggregate of quartz grains there may often be marked variation in strain between grains of varying original orientation, particularly if the stress and strain remain
xz
I
E 0
,.,.,,,., 3.0
I AX IAL
RATIO
Fig. 1. Elliot plots of dimensional fabric of deformed quartz grains from the metasiltstone specimen studied. XY 115 points, YZ 99 points, X2 81 points. Contours for XY at 12.87,6.43,3.22%; YZ at 13.08, 6.54, 3.27%;XZ at 15.99, 7.99,4.00%.
approximately coaxial during deformation. To investigate this heterogeneity, the length to width ratios and c-axis orientations of individual grains were measured on an X&e&ion, using an optical microscope with graduated eyepiece and universal stage. The limited number of grains which had poorly defined grain boundaries, showed marked recrystallization or undulosity of extinction, or had suffered interference from other grains (e.g. wrapping around) were not measured. The orientation readings were grouped according to length/width ratio (taken as an indication of the strain undergone by each grain) and computer contoured on equal area projections using Program Orient (Bridges and Etheridge, 1974). Some of the limitations of this technique are: (1) Only the two-dimensional ratio can be obtained for each grain. It is not possible to obtain both the true three-dimensional shape of a grain and its c-axis orientation.
(2) The complete crystallographic orientation of each grain is indeterminate - only the c-axis can be measured optically. (3) The original sedimentary fabric is neglected. This is believed to be a valid first approximation in the specimen studied. However, note that because of variance from original sphericity, some length/width ratios will not represent the true two-dimensional strain ratios, and consequently some orientation values will be grouped with the wrong strain magnitude class. Provided sedimentary grainshape is itself independent of crystallographic orientation, this additional variable will only obscure trends in the change in c-axis orientation from low- to high-strain grains, but should not modify the actual trends observed. The results of this analysis are given in Fig. 3. Weakly deformed grains (L/ W < 2.0) show a clustering of c-axes around the principal strain directions X, Y, and 2, with the dominant maximum around the direction of maximum elongation, X. With greater elongation of individual grains the c-axes swing into a poorly defined crossed girdle through Y, and with further increases the range of c-axis orientations contracts towards the Y-axis. The most elongate grains show a marked maximum of c-axis orientations parallel to Y, though still with some variation of the distribution along the plane YZ. The
Fig. 2. A. Low magnification photomicrograph of an X2-section through the metasiltstone, showing the wide range of X to Z ratios for the larger quartz grains. X : Z varies from approximately 1 : 1 to more than 10 : 1. Feldspar grains (in this case plagioclase) are marked with a p. Field of view, 1 cm.
B. Photomicrograph showing the considerable difference in the degree of deformation adjacent quartz grains, with the more highly deformed grain tending to wrap around resistant neighbour. X2-section; field of view, 5 mm.
of its
patterns for the least and most deformed grains in this study are very similar to those for the “globular and tabular porphyroclasts” (L/W in X.5sections <2.0) and “ribbon grain (L/W > 8.0) found by Bouchez in deformed quartzites from Angers, France (see fig. 13, Bouchez, 1977). However, the pattern for the least-deformed grains differs from that found for similar grains by Tullis et al. (1973) in experimentally deformed quartzites, and by Marjoribanks (1976) in quartzites from central Australia. Both these workers found that the dominant c-axis maximum in the least deformed grains was parallel to 2. DISCUSSION
Two features of the grain shape and crystallographic fabric need to be considered. They are: (1) The marked heterogeneity of strain from grain to grain and, in particular, the family of very weakly deformed grains which have their c-axes clustered around the principal strain directions. (2) The rotation of the c-axis in individual grains towards Y, the intermediate strain axis, with increasing strain.
ALL
GRAINS
Fig. 3. Computer contoured stereoplots of c-axis orientations for class intervals of grains with particular X : 2 ratios. All grains: 165 points, contours 4.48, 2.24, 1.12% per 1% area. X : 2 1.0-2.0: 59 points, contours 2.74, 1.37% per 1% area. X : 2 2.0-3.0: 42 points, contours 2.75, 1.38% per 1% area. X : Z 3.0-5.0: 39 points, contours 6.52, 3.26, 1.63% per 1% area. X : 2 > 5.0: 35 points, contours 11.23, 5.62, 2.81, 1.40% per 1% area.
The weakly deformed
grains
It is now well established experimentally that the yield stress of individual quartz crystals (and therefore single quartz grams in a rock) varies markedly with crystallographic orientation. Baeta and Ashbee (1970) found that at atmospheric pressure the order of increasing yield stress for axial compression was O’, lr and IA, la and lm, and //c.Hobbs et al. (1972) determined a similar order at 3 kbar, the only significant difference being a softening of the 0’ orientation. In both sets of experiments the strongest orientation was that with the c-axis parallel to the axial loading direction. Deformation with u, perpendicular to either the first- or second-order prisms was also relatively
79
difficult. Therefore, if grains within a rock behave like single crystals, those grains with their c-axis parallel to u, (and to a lesser extent oz or 03) will be unfavourably oriented for deformation, if the stress-strain history remains coaxial. The behaviour of grain aggregates is obviously more complex than that of single crystals, owing to grain-grain interactions and the need to maintain grain boundary coherence. Maintenance of grain boundary coherence in a ~o~o~eneous~y deformed aggregate requires at least five independent slip systems (Von Mises, 1928), or the availability of alternative deformation mechanisms (diffusion, climb, grain boundary sliding etc., see Paterson, 1969). However, during deformation of polymineralic aggregates with a wide range of grainsizes (e.g. the metasiltstone considered in this study), the strain from grain to grain will certainly not be homogeneous, and the fabric developed by such rocks is more likely to be predictable by an isostress (or lower bound) model than by an isostrain (or upper bound) model (cf. for steels Semiatin et al., 1979). The deformation of individual large quartz grains within rocks which approach this isostress model will probably be controlled by the one or two glide systems which are both easy and subjected to high shear stress. This greatly simplifies the investigation. The usual tendency among geological workers in describing aggregates is to determine their behaviour in terms of what is happening to individual grains. Although this concept can be criticized on the grounds that it ignores the influence of surrounding grains (e.g. Taylor, 1938), it has already proved very useful in empirically predicting the fabric of deformed aggregates (e.g. Tullis et al., 1973; Wilson, 1975; Marjo~banks, 1976; Bouchez, 1977). Using this basic approach together with an isostress model, we can consider those quartz grains in particular orientations which have resisted deformation and maintained a near equant shape. The yield strength and flow characteristics of any such quartz grain will be a function of the resolved shear stress and relative ease of movement of the operative slip systems. Recent work (Tullis et al., 1973; Mo~ison-Smith et al., 1976; Burg and Laurent, 1978; Lister and Paterson, 1979; and many others) suggests that (0001) (a>, {lOiO} (a), and (lOi0) (c) (with or without {lOil} (a) and {Olil} (a)) are the most active slip systems in quartz during deformation under conditions of the greenschist facies. For coaxial deformation, the weakly deformed grains with c-axis clustered around the ol, cr2, and o3 directions would have very low resolved shear stress on (0001) (a> and (lOTO} (c). The resolved shear stress on {lOiO} (II) will be non-zero, but slip on this system may be inhibited without some additional component of basal slip (cf. Ave Ladlement and Carter, 1971; Tullis et al., 1973). Table I lists the reduced expressions for the magnitude of shear stress on {lOiO} (a> when the c-axis is parallel to one of the principal stress directions. This shear stress will vary with the geometry of the deformation. With increasingly constrictional defor-
80
TABLE
I
Reduced expressions for the magnitude of shear stress on the {lO?O} planes in quartz, when c is parallel to one of the principal directions. Derived from the general threedimensional equation of Jaeger (1969), where ([. m, n) are the direction cosines of the pole to the plane in question relative to the 01: 02 and ~3 principal stress directions (01 for the specific orientation with c parallel to a principal direction, the 02 >, u3). Note: shear stress on the prism plans acts entirely along direction (a). 1
m
n
T2
01
0
m
n
(u2 -u3)*m2n2
02
1
0
I1
(us - U1 )*n*l*
(J3
1
m
0
(al -u2)*12m2
Cl
to
Equivalent expressions for r’ using 1’ + m2 + 11’ = 1 (1) (u* -- U3)2(1 - n2)n2 (3) (u3 -u,)‘(l (5) (ul -u2)l(l
-n2)n2
(2) (u2 - ~7,)~(1 - m2)m2 (4) (u, -O,)Z(l -P)P (6)
-m2)m2
(nl -u2)2(1
--1*)1*
mation u2 -+ u1 and therefore, referring tothe equations of Table I, (3) + (l), (5) and (6) + 0. For purely constrictional deformation, quartz grains with c-axes parallel to u3 will have zero resolved shear stress on the slip systems {lOTO} (a), {lOiO} Cc), and (0001) (a). The dominant c-axis orientations for the weakly deformed grains should cluster around cr3. In pure constriction the distinction between axes u1 and u2 is lost. For quartz grains with c-axis orientations lying anywhere in the plane perpendicular to u3, the resolved shear stress on (0001) (a) and {lOiO} (c) is always zero, though the resolved shear stress on {lOiO} (a) may still be considerable. The predicted pole figure diagram for the least deformed grains in constriction has a point maximum around X (parallel to u3 for coaxial deformation) and a weaker YZ girdle. For increasingly axial deformation, u2 + u3, therefore, again referring to Table I(6) + (4), (1) and (2) + 0. Following arguments similar to those above, the c-axis maximum for the weakly deformed grains should parallel 2 (lo,), with a weaker girdle along XY. As (ul -us)’ is always greater than or equal to (a2 -us)2 and (al -u~)~, it follows from equations (1) to (6) (Table I) that the resolved shear stress on {lOiO} (a) is in general higher for orientations with c parallel to u2 than for c parallel to u, or us. Therefore, the c-axis maximum parallel to u2 (i.e. Y) for the weakly deformed grains should in general be the weakest. Using this generalization, the predicted end geometries for axial and constrictional deformation, and the observation that the resolved shear stress on (0001) (a) and { lOi0) (c) is zero when c parallels a principal stress direction, it is possible to interpolate the range of pole figures expected from the weakly deformed grain populations for the range of coaxial strain geometries (Fig. 4).
81
The results from the limited number of observations on such grains accord well with these predictions. Tullis et al. (1973) found that in axial shortening experiments on quartzites, the weakly deformed grains usually had their caxes parallel to the shortening axis 2, with a few c-axes in the perpendicular plane, XY. Marjoribanks (1976) obtained a similar pattern in a naturally deformed quartzite with h = 0.3 (see Flinn, 1962). Bouchez (1977) presented a composite diagram of c-axis measurements on “globular and tabular grains” from several specimens of varying h value. However, in all cases the strain was within the constriction field (h > 1). It is significant that his pattern of c-axis orientations is quite similar to that found in this study (where k N 1.7), but different from those of Tullis et al. (1973) and Marjoribanks (1976). The model outlined above is useful in predicting the overall pattern of clustering for the least-deformed grains, but it should be noted that this clustering is in general quite broad (Fig. 3; Bouchez, 1977; to a lesser extent, Marjoribanks, 1976). This broadening of the fabric diagram maxima may be due to intrinsic properties of individual detrital grains (water and other impurity content, previous U-E-P-T history, etc.) which are not directly related to crystallography, such that some grains will be relatively “hard” irrespective of their c-axis orientation. It is a basic assumption of the preceding discussion that the weakly deformed grains can survive only in an effectively coaxial, non-rotational deformation. This contention is supported by the work of Tullis et al. (1973) who found that the preservation of “augen” grains in unfavourable orientations for deformation rapidly diminished in the boundary regions of their specimens, where the component of shear became significant. Etchecopar
k-o
t
k-oo
P lg. 4. rrecllcted c-axls tabrrc of the least deformed grains for strain geometries ranging from oblate (k = 0) to prolate (h = 00).
(1977) has demonstrated that in a much simplified model involving twodimensional simple shear of grains with only one slip plane, certain grains may “lock up” as they rotate into an unfavourable orientation. However, it should be noted that: (a) This locked orientation is metastable. A slight bending or sympathetic rigid rotation of part or all of the grain just past the locked position will place the slip plane in an orientation suitable for continued and theoretically unlimited slip. This can lead to the “retort shaped” grains sometimes seen in shear zones (Etchecopar, 1977) but not observed in the siltstone described here (see Fig. 2). (b) The model does not allow for multiple slip planes, as would generally be the case for quartz. (c) The model does not predict the clustering of c-axis around the principal strain axes for the weakly deformed grains. The suggestion by Tullis et al. (1973) that the preservation of “augen” grains, as observed in their experiments, requires an effectively coaxial stress-strain history appears to be still valid. The fabric of the more deformed
grains
The development of crystallographic preferred orientation in a deformed aggregate of quartz grains can be directly related to the mechanics of intracrystalline slip (see Hobbs et al., 1976, pp. 122-135 for a brief review). During deformation by slip the shape of individual quartz grains changes but the internal crystallographic structure remains undeformed, with crystallographic planes and directions merely rotating relative to the applied stress axes. Addition of climb lowers the number of operative slip systems required for a general strain but makes no contribution to the crystallographic reorientation (Groves and Kelly, 1969). Crystallographic preferred orientation due to intracrystalline slip has been produced both experimentally (Tullis et al., 1973) and theoretically (Lister et al., 1978). The preferred orientation developed depends on the intracrystalline deformation mechanism (i.e. the operative slip systems and the relative importance of climb and cross-slip), and on the imposed geometry of the deformation. The elongate grains in this study have a weak type II crossed girdle pattern intersecting in Y (see Lister, 1974; Bouchez, 1977), which contracts further towards the Y axis for the most elongate “ribbon grains”. This basic pattern has often been reported for highly strained quartz grains, and is generally attributed to glide dominated by {lOiO} (a) (e.g. Wilson, 1975; Bouchez, 1977; Burg and Laurent, 1978). However, the orientation in which the c-axis is parallel to Y is not an initial orientation favoured for deformation, as is demonstrated by the preservation of weakly deformed, sub-equant grains with this orientation (Fig. 3). As discussed above, this may be due to the reluctance of quartz to deform by (lOi0) (a) alone (despite an appreciable shear stress on this system) without some associated activity on (0001) (a)
83
(see observations of Tullis et al., 1973 and Ave Lallement and Carter, 1971) or perhaps {lOiO} (c>, both of which are unfavourably oriented when c parallels a principal direction. There are, then, two possibilities for the most highly strained grains: (1) Their crystallographic lattice is rotating with increasing strain towards an orientation unfavourable for continued deformation. This would produce a “locking-up” effect as the c-axis approaches Y, and on a c-axis fabric diagram the area immediately surrounding Y should be less populated; i.e. the high strain fabric would tend towards a small circfe distribution around Y. (2) An unspecified strain softening mechanism allows continued deformation dominated by {lOiO} (a), without a need for (0001) (a) or {lOTO} cc), such that the c-axis continues rotating towards parallelism with Y. This would produce a c-axis maximum centred on Y. The observed fabric shows no depopulation of the immediate Y axis area, and therefore supports suggestion (2). CONCLUSION
As discussed by TulIis et al. (1973), the presence of relatively undeformed “augen” grains may be a good indicator of an effectively coaxial stress-strain history. For environments in which quartz deforms by intracrystalline slip on {lOiO} (a), (0001) (a), and {lOTO} (c), the c-axis orientation of such weakly deformed grams may be predicted for various geometries of the imposed bulk strain. Constrictional deformation should result in a dominant maximum of c-axes clustered about X, whereas more oblate strain may be indicated by a dominant maximum about 2. The variability in strain from grain to grain in a deformed aggregate may often be an important factor when using deformed quartz grains as indicators of bulk rock strain. The bulk strain will be an integral of the strain in each individual grain, and it is incorrect to ignore the extreme high and low strain grains as anomalous. This further emphasizes the need to use passive strain markers in detailed strain analysis studies. The use of active markers, such as quartz grains, introduces many additional variables, and the result obtained may not be acceptably accurate. ACKNOWLEDGEMENTS
This work was carried out while the author held an Australian Commonwealth Postgraduate Scholarship in the Geology Department of the University of Adelaide. Thanks are extended to G. Lister, J. Parker, T. Bell, P. James, R. Marjoribanks, S. Schmid and M. Casey for discussion and criticism. REFERENCES Av6 Lallement, H.G. and Carter, N.L., 1971. Pressure dependence of quartz deformation lamellae orientations. Am. J. Sci.. 270: 218-235.
Baeta, R.D. and Ashbee, K.H.G., 1970. Mechanical deformation of quartz I. Constant strain-rate compression experiments. Philos. Mag., 22: 601-623. Bouchez, J.L., 1977. Plastic deformation of quartzites of low temperature in an area of natural strain gradient. Tectonophysics, 39: 25-50. Bridges, M.C. and Etheridge, MA., 1974. A computer program to contour orientation densities. Internal Rep. Dept. Geol. and Mineral., Univ. Adelaide. Burg, J.P. and Laurent, Ph., 1978. Strain analysis of a shear zone in a granodiorite. Tectonophysics, -17: 15-42. Elliot, D., 1970. Determination of finite strain and initial shape from deformed elliptical objects. Geol. Sot. Am. Bull., 81: 2221-2236. Etchecopar, A., 1977. A plane kinematic mode1 of progressive deformation in a polycrystalline aggregate. Tectonophysics, 39: 121-139. Flinn, D., 1962. On folding during three-dimensional progressive deformation. J. Geol. Sot. London, 118: 385-428. Groves, G.W. and Kelly, A.. 1969. Change of shape due to dislocation climb. Philos. Mag., 19: 977-986. Hobbs, B.E., McLaren, A.C. and Paterson, MS., 1972. Plasticity of single crystals of synthetic quartz. In: H.C. Heard, I.Y. Borg, N.L. Carter and C.B. Raleigh (Editors), Flow and Fracture of Rocks. Geophys. Monogr. Ser., Am. Geophys. Union, 16: 29-53. Geology. Hobbs, B.E., Means, W.D. and Williams, P.F., 1976. An Outline of Structural John Wiley and Sons, New York, N.Y., 571 pp. Jaeger, J.C., 1969. Elasticity, Fracture and Flow with Engineering and Geological Applications. Methuen and Co., London, 268 pp. Lister, G.S., 1974. The Theory of Deformation Fabrics. Ph.D. thesis. Australian National University, 463 pp. Lister, G.S. and Paterson, M.S., 1979. The simulation of fabric development during plastic deformation and its application to quartzite: fabric transitions. J. Struct. Geol., 1: 99-115. Lister, G.S., Paterson, M.S. and Hobbs, B.E., 1978. The simulation of fabric development during plastic deformation and its application to quartzite: the model. Tectonophysics, 45: 107-158. Marjoribanks, R.W., 1976. The relation between microfabric and strain in a progressively deformed quartzite sequence from Central Australia. Tectonophysics, 32: 269-293. Morrison-Smith, D.J., Paterson, M.S. and Hobbs, B.E., 1976. An electron microscope study of plastic deformation in single crystals of synthetic quartz. Tectonophysics, 33: 43-50. Paterson, M.S., 1969. The ductility of rocks. In: A.S. Argon (Editor), Physics of Strength and Plasticity. The M.I.T. Press, London, pp. 377-392. Semiatin, S.L., Morris, P.R. and Piehler, H.R., 1979. Microplasticity predictions of r-values and yield loci of low carbon sheet steels deforming by (111) pencil glide. Texture Cryst. Sol., 3: 149-214. 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. Taylor, G.I., 1938. Plastic strain in metals. J. Inst. Metall., 62: 307-324. Von Mises, R., 1928. Mechanik der plastischen Formlnderung von Kristallen. Z. Angew. Math. Mech., 8: 161-185. Wilson, C.J.L., 1975. Preferred orientation in quartz ribbon mylonites. Geol. Sot. Am. Bull., 86: 968-974. Wood, D.S., 1974. Current views on the development of slaty cleavage. Annu. Rev. Earth Planet. Sci., 2: l-35.
73
STRAIN VARIATION BETWEEN QUARTZ GRAINS OF DIFFERENT CRYSTALLOGRAPHIC ORIENTATION IN A NATURALLY DEFORMED METASILTSTONE
NEIL S. MANCKTELOW Department (Australia)
*
of Geology and Mineralogy, University of Adelaide, Adelaide 5000, S.A.
(Received January 26,198l)
ABSTRACT Mancktelow, N.S., 1981. Strain variation between quartz grains of different crystallographic orientation in a naturally deformed metasiltstone. In: G.S. Lister, H.-J. Behr, K. Weber and H.J. Zwart (Editors), The Effect of Deformation on Rocks. Tectonophysics, 78: 73-84. The shapes of isolated quartz grains in a metasiltstone from the Fleurieu Peninsula, South Australia, vary markedly, the amount of strain undergone by individual grains being strongly influenced by crystallographic orientation relative to the finite strain axes. The least-deformed grains have c-axis orientations clustered about the principal strain directions; that is, they have orientations for which the resolved shear stress on the (0001) (a) and {lOiO} (c) slip systems would have been close to zero during coaxial deformation. A simple theoretical approach suggests that the geometry of the bulk strain should influence the observed c-axis fabric of these least-deformed grains. The fabrics should vary from (a) a pronounced maximum parallel to 2 with a subsiduary distribution in the XY-plane for pure flattening strain, through (b) fabrics with maxima parallel to X and 2 and a weak maximum parallel to Y, to (c) fabrics with a pronounced maximum parallel to X and a subsiduary distribution within the YZ-plane for pure constriction. The most elongate quartz grains in the metasiltstone show a strong maximum of c-axes parallel to the intermediate strain axis, Y. This suggests predominant prismatic slip in a direction at a large angle to the c-axis, probably on (lOi0) (a). The bulk strain undergone by the specimen is an integral of the variable strains in the component minerals, and the extremes (the least deformed or the most elongate grains) cannot be regarded as anomalous if a realistic strain estimate is to be obtained.
INTRODUCTION
The deformed shape of sedimentary quartz grains has often been used to obtain an estimate of bulk strain in low metamorphic grade quartz-rich rocks.
* Present address: Geologisches Institut, ETH-Zentrum, 0040-1951/81/0000-0000/$02.50
CH-8092 Zurich, Switzerland
@ 1981 Elsevier Scientific
Publishing Company
Allowance is usually made for an original sedimentary fabric, but the variation imposed by the crystallographic anisotropy of quartz has commonly been ignored. Recently, Marjoribanks (1976) and Bouchez (1977) have both noted that in deformed quartzites there are some grains which fall outside the general range of deformed grain shapes, being either much more equant or more elongate than the majority. They ascribed this variation to the crystallographic orientation of these particular grains. However, as outlined below, the more equant and more elongate grains are not unusual or anomalous but merely the extremes of a continuum, with the strain in each quartz grain being strongly influenced by the crystallographic orientation of the grain relative to the stress field effective on that grain. The sample of granule-bearing metasiltstone examined in this study was collected 3 km south of Rapid Bay, South Australia (138” 10’ E, 35” 33’ S), in an area of greenschist facies metamorphism (biotitechlorite-muscovite zone) within the Adelaide Fold Belt. The present mineralogy of the metasiltstone is quartz + muscovite + biotite + chlorite + plagioclase + K-feldspar + accessory tourmaline, apatite, zircon and opaques. A well-developed slaty cleavage is defined in thin section by the alignment of mica and by the dimensional fabric of the quartz grains. The metasiltstone was deformed during the major slaty cleavage-forming orogeny which affected the Adelaide Fold Belt in the early Ordovician. STRAIN
AND C-AXIS
FABRIC
DETERMINATIONS
The specimen was studied originally to obtain an estimate of the bulk strain. To this end, thin-sections were cut parallel to the principal strain planes, assuming the slaty cleavage is parallel to XY and the quartz elongation lineation is X, the direction of maximum elongation (see Wood, 1974). The length to width ratios and orientations of the quartz grains were measured and the results plotted on the Shape Factor Grid of Elliot (1970) (Fig. 1). It was obvious that some factor other than an original sedimentary fabric had influenced the resultant deformation shape fabric. The X2-plot of Fig. 1 shows considerable variation in the length to width ratio of the grains but little divergence in orientation of the long axis away from the cleavage trace. This relationship is quite striking in the thin-section itself (Fig. 2). Such a distribution is unlikely to be achieved by imposition of a homogeneous strain on an original sedimentary fabric. The alternative is that the strain from grain to grain, rather than being homogeneous, is markedly heterogeneous and that the variation in shape of individual grains reflects this heterogeneity. The work of Hobbs et al. (1972) and Baeta and Ashbee (1970) has shown that there is marked variation in the yield stress of individual quartz crystals with different crystallographic orientations relative to the applied stress. It follows that in a deforming aggregate of quartz grains there may often be marked variation in strain between grains of varying original orientation, particularly if the stress and strain remain
xz
I
E 0
,.,.,,,., 3.0
I AX IAL
RATIO
Fig. 1. Elliot plots of dimensional fabric of deformed quartz grains from the metasiltstone specimen studied. XY 115 points, YZ 99 points, X2 81 points. Contours for XY at 12.87,6.43,3.22%; YZ at 13.08, 6.54, 3.27%;XZ at 15.99, 7.99,4.00%.
approximately coaxial during deformation. To investigate this heterogeneity, the length to width ratios and c-axis orientations of individual grains were measured on an X&e&ion, using an optical microscope with graduated eyepiece and universal stage. The limited number of grains which had poorly defined grain boundaries, showed marked recrystallization or undulosity of extinction, or had suffered interference from other grains (e.g. wrapping around) were not measured. The orientation readings were grouped according to length/width ratio (taken as an indication of the strain undergone by each grain) and computer contoured on equal area projections using Program Orient (Bridges and Etheridge, 1974). Some of the limitations of this technique are: (1) Only the two-dimensional ratio can be obtained for each grain. It is not possible to obtain both the true three-dimensional shape of a grain and its c-axis orientation.
(2) The complete crystallographic orientation of each grain is indeterminate - only the c-axis can be measured optically. (3) The original sedimentary fabric is neglected. This is believed to be a valid first approximation in the specimen studied. However, note that because of variance from original sphericity, some length/width ratios will not represent the true two-dimensional strain ratios, and consequently some orientation values will be grouped with the wrong strain magnitude class. Provided sedimentary grainshape is itself independent of crystallographic orientation, this additional variable will only obscure trends in the change in c-axis orientation from low- to high-strain grains, but should not modify the actual trends observed. The results of this analysis are given in Fig. 3. Weakly deformed grains (L/ W < 2.0) show a clustering of c-axes around the principal strain directions X, Y, and 2, with the dominant maximum around the direction of maximum elongation, X. With greater elongation of individual grains the c-axes swing into a poorly defined crossed girdle through Y, and with further increases the range of c-axis orientations contracts towards the Y-axis. The most elongate grains show a marked maximum of c-axis orientations parallel to Y, though still with some variation of the distribution along the plane YZ. The
Fig. 2. A. Low magnification photomicrograph of an X2-section through the metasiltstone, showing the wide range of X to Z ratios for the larger quartz grains. X : Z varies from approximately 1 : 1 to more than 10 : 1. Feldspar grains (in this case plagioclase) are marked with a p. Field of view, 1 cm.
B. Photomicrograph showing the considerable difference in the degree of deformation adjacent quartz grains, with the more highly deformed grain tending to wrap around resistant neighbour. X2-section; field of view, 5 mm.
of its
patterns for the least and most deformed grains in this study are very similar to those for the “globular and tabular porphyroclasts” (L/W in X.5sections <2.0) and “ribbon grain (L/W > 8.0) found by Bouchez in deformed quartzites from Angers, France (see fig. 13, Bouchez, 1977). However, the pattern for the least-deformed grains differs from that found for similar grains by Tullis et al. (1973) in experimentally deformed quartzites, and by Marjoribanks (1976) in quartzites from central Australia. Both these workers found that the dominant c-axis maximum in the least deformed grains was parallel to 2. DISCUSSION
Two features of the grain shape and crystallographic fabric need to be considered. They are: (1) The marked heterogeneity of strain from grain to grain and, in particular, the family of very weakly deformed grains which have their c-axes clustered around the principal strain directions. (2) The rotation of the c-axis in individual grains towards Y, the intermediate strain axis, with increasing strain.
ALL
GRAINS
Fig. 3. Computer contoured stereoplots of c-axis orientations for class intervals of grains with particular X : 2 ratios. All grains: 165 points, contours 4.48, 2.24, 1.12% per 1% area. X : 2 1.0-2.0: 59 points, contours 2.74, 1.37% per 1% area. X : 2 2.0-3.0: 42 points, contours 2.75, 1.38% per 1% area. X : Z 3.0-5.0: 39 points, contours 6.52, 3.26, 1.63% per 1% area. X : 2 > 5.0: 35 points, contours 11.23, 5.62, 2.81, 1.40% per 1% area.
The weakly deformed
grains
It is now well established experimentally that the yield stress of individual quartz crystals (and therefore single quartz grams in a rock) varies markedly with crystallographic orientation. Baeta and Ashbee (1970) found that at atmospheric pressure the order of increasing yield stress for axial compression was O’, lr and IA, la and lm, and //c.Hobbs et al. (1972) determined a similar order at 3 kbar, the only significant difference being a softening of the 0’ orientation. In both sets of experiments the strongest orientation was that with the c-axis parallel to the axial loading direction. Deformation with u, perpendicular to either the first- or second-order prisms was also relatively
79
difficult. Therefore, if grains within a rock behave like single crystals, those grains with their c-axis parallel to u, (and to a lesser extent oz or 03) will be unfavourably oriented for deformation, if the stress-strain history remains coaxial. The behaviour of grain aggregates is obviously more complex than that of single crystals, owing to grain-grain interactions and the need to maintain grain boundary coherence. Maintenance of grain boundary coherence in a ~o~o~eneous~y deformed aggregate requires at least five independent slip systems (Von Mises, 1928), or the availability of alternative deformation mechanisms (diffusion, climb, grain boundary sliding etc., see Paterson, 1969). However, during deformation of polymineralic aggregates with a wide range of grainsizes (e.g. the metasiltstone considered in this study), the strain from grain to grain will certainly not be homogeneous, and the fabric developed by such rocks is more likely to be predictable by an isostress (or lower bound) model than by an isostrain (or upper bound) model (cf. for steels Semiatin et al., 1979). The deformation of individual large quartz grains within rocks which approach this isostress model will probably be controlled by the one or two glide systems which are both easy and subjected to high shear stress. This greatly simplifies the investigation. The usual tendency among geological workers in describing aggregates is to determine their behaviour in terms of what is happening to individual grains. Although this concept can be criticized on the grounds that it ignores the influence of surrounding grains (e.g. Taylor, 1938), it has already proved very useful in empirically predicting the fabric of deformed aggregates (e.g. Tullis et al., 1973; Wilson, 1975; Marjo~banks, 1976; Bouchez, 1977). Using this basic approach together with an isostress model, we can consider those quartz grains in particular orientations which have resisted deformation and maintained a near equant shape. The yield strength and flow characteristics of any such quartz grain will be a function of the resolved shear stress and relative ease of movement of the operative slip systems. Recent work (Tullis et al., 1973; Mo~ison-Smith et al., 1976; Burg and Laurent, 1978; Lister and Paterson, 1979; and many others) suggests that (0001) (a>, {lOiO} (a), and (lOi0) (c) (with or without {lOil} (a) and {Olil} (a)) are the most active slip systems in quartz during deformation under conditions of the greenschist facies. For coaxial deformation, the weakly deformed grains with c-axis clustered around the ol, cr2, and o3 directions would have very low resolved shear stress on (0001) (a> and (lOTO} (c). The resolved shear stress on {lOiO} (II) will be non-zero, but slip on this system may be inhibited without some additional component of basal slip (cf. Ave Ladlement and Carter, 1971; Tullis et al., 1973). Table I lists the reduced expressions for the magnitude of shear stress on {lOiO} (a> when the c-axis is parallel to one of the principal stress directions. This shear stress will vary with the geometry of the deformation. With increasingly constrictional defor-
80
TABLE
I
Reduced expressions for the magnitude of shear stress on the {lO?O} planes in quartz, when c is parallel to one of the principal directions. Derived from the general threedimensional equation of Jaeger (1969), where ([. m, n) are the direction cosines of the pole to the plane in question relative to the 01: 02 and ~3 principal stress directions (01 for the specific orientation with c parallel to a principal direction, the 02 >, u3). Note: shear stress on the prism plans acts entirely along direction (a). 1
m
n
T2
01
0
m
n
(u2 -u3)*m2n2
02
1
0
I1
(us - U1 )*n*l*
(J3
1
m
0
(al -u2)*12m2
Cl
to
Equivalent expressions for r’ using 1’ + m2 + 11’ = 1 (1) (u* -- U3)2(1 - n2)n2 (3) (u3 -u,)‘(l (5) (ul -u2)l(l
-n2)n2
(2) (u2 - ~7,)~(1 - m2)m2 (4) (u, -O,)Z(l -P)P (6)
-m2)m2
(nl -u2)2(1
--1*)1*
mation u2 -+ u1 and therefore, referring tothe equations of Table I, (3) + (l), (5) and (6) + 0. For purely constrictional deformation, quartz grains with c-axes parallel to u3 will have zero resolved shear stress on the slip systems {lOTO} (a), {lOiO} Cc), and (0001) (a). The dominant c-axis orientations for the weakly deformed grains should cluster around cr3. In pure constriction the distinction between axes u1 and u2 is lost. For quartz grains with c-axis orientations lying anywhere in the plane perpendicular to u3, the resolved shear stress on (0001) (a) and {lOiO} (c) is always zero, though the resolved shear stress on {lOiO} (a) may still be considerable. The predicted pole figure diagram for the least deformed grains in constriction has a point maximum around X (parallel to u3 for coaxial deformation) and a weaker YZ girdle. For increasingly axial deformation, u2 + u3, therefore, again referring to Table I(6) + (4), (1) and (2) + 0. Following arguments similar to those above, the c-axis maximum for the weakly deformed grains should parallel 2 (lo,), with a weaker girdle along XY. As (ul -us)’ is always greater than or equal to (a2 -us)2 and (al -u~)~, it follows from equations (1) to (6) (Table I) that the resolved shear stress on {lOiO} (a) is in general higher for orientations with c parallel to u2 than for c parallel to u, or us. Therefore, the c-axis maximum parallel to u2 (i.e. Y) for the weakly deformed grains should in general be the weakest. Using this generalization, the predicted end geometries for axial and constrictional deformation, and the observation that the resolved shear stress on (0001) (a) and { lOi0) (c) is zero when c parallels a principal stress direction, it is possible to interpolate the range of pole figures expected from the weakly deformed grain populations for the range of coaxial strain geometries (Fig. 4).
81
The results from the limited number of observations on such grains accord well with these predictions. Tullis et al. (1973) found that in axial shortening experiments on quartzites, the weakly deformed grains usually had their caxes parallel to the shortening axis 2, with a few c-axes in the perpendicular plane, XY. Marjoribanks (1976) obtained a similar pattern in a naturally deformed quartzite with h = 0.3 (see Flinn, 1962). Bouchez (1977) presented a composite diagram of c-axis measurements on “globular and tabular grains” from several specimens of varying h value. However, in all cases the strain was within the constriction field (h > 1). It is significant that his pattern of c-axis orientations is quite similar to that found in this study (where k N 1.7), but different from those of Tullis et al. (1973) and Marjoribanks (1976). The model outlined above is useful in predicting the overall pattern of clustering for the least-deformed grains, but it should be noted that this clustering is in general quite broad (Fig. 3; Bouchez, 1977; to a lesser extent, Marjoribanks, 1976). This broadening of the fabric diagram maxima may be due to intrinsic properties of individual detrital grains (water and other impurity content, previous U-E-P-T history, etc.) which are not directly related to crystallography, such that some grains will be relatively “hard” irrespective of their c-axis orientation. It is a basic assumption of the preceding discussion that the weakly deformed grains can survive only in an effectively coaxial, non-rotational deformation. This contention is supported by the work of Tullis et al. (1973) who found that the preservation of “augen” grains in unfavourable orientations for deformation rapidly diminished in the boundary regions of their specimens, where the component of shear became significant. Etchecopar
k-o
t
k-oo
P lg. 4. rrecllcted c-axls tabrrc of the least deformed grains for strain geometries ranging from oblate (k = 0) to prolate (h = 00).
(1977) has demonstrated that in a much simplified model involving twodimensional simple shear of grains with only one slip plane, certain grains may “lock up” as they rotate into an unfavourable orientation. However, it should be noted that: (a) This locked orientation is metastable. A slight bending or sympathetic rigid rotation of part or all of the grain just past the locked position will place the slip plane in an orientation suitable for continued and theoretically unlimited slip. This can lead to the “retort shaped” grains sometimes seen in shear zones (Etchecopar, 1977) but not observed in the siltstone described here (see Fig. 2). (b) The model does not allow for multiple slip planes, as would generally be the case for quartz. (c) The model does not predict the clustering of c-axis around the principal strain axes for the weakly deformed grains. The suggestion by Tullis et al. (1973) that the preservation of “augen” grains, as observed in their experiments, requires an effectively coaxial stress-strain history appears to be still valid. The fabric of the more deformed
grains
The development of crystallographic preferred orientation in a deformed aggregate of quartz grains can be directly related to the mechanics of intracrystalline slip (see Hobbs et al., 1976, pp. 122-135 for a brief review). During deformation by slip the shape of individual quartz grains changes but the internal crystallographic structure remains undeformed, with crystallographic planes and directions merely rotating relative to the applied stress axes. Addition of climb lowers the number of operative slip systems required for a general strain but makes no contribution to the crystallographic reorientation (Groves and Kelly, 1969). Crystallographic preferred orientation due to intracrystalline slip has been produced both experimentally (Tullis et al., 1973) and theoretically (Lister et al., 1978). The preferred orientation developed depends on the intracrystalline deformation mechanism (i.e. the operative slip systems and the relative importance of climb and cross-slip), and on the imposed geometry of the deformation. The elongate grains in this study have a weak type II crossed girdle pattern intersecting in Y (see Lister, 1974; Bouchez, 1977), which contracts further towards the Y axis for the most elongate “ribbon grains”. This basic pattern has often been reported for highly strained quartz grains, and is generally attributed to glide dominated by {lOiO} (a) (e.g. Wilson, 1975; Bouchez, 1977; Burg and Laurent, 1978). However, the orientation in which the c-axis is parallel to Y is not an initial orientation favoured for deformation, as is demonstrated by the preservation of weakly deformed, sub-equant grains with this orientation (Fig. 3). As discussed above, this may be due to the reluctance of quartz to deform by (lOi0) (a) alone (despite an appreciable shear stress on this system) without some associated activity on (0001) (a)
83
(see observations of Tullis et al., 1973 and Ave Lallement and Carter, 1971) or perhaps {lOiO} (c>, both of which are unfavourably oriented when c parallels a principal direction. There are, then, two possibilities for the most highly strained grains: (1) Their crystallographic lattice is rotating with increasing strain towards an orientation unfavourable for continued deformation. This would produce a “locking-up” effect as the c-axis approaches Y, and on a c-axis fabric diagram the area immediately surrounding Y should be less populated; i.e. the high strain fabric would tend towards a small circfe distribution around Y. (2) An unspecified strain softening mechanism allows continued deformation dominated by {lOiO} (a), without a need for (0001) (a) or {lOTO} cc), such that the c-axis continues rotating towards parallelism with Y. This would produce a c-axis maximum centred on Y. The observed fabric shows no depopulation of the immediate Y axis area, and therefore supports suggestion (2). CONCLUSION
As discussed by TulIis et al. (1973), the presence of relatively undeformed “augen” grains may be a good indicator of an effectively coaxial stress-strain history. For environments in which quartz deforms by intracrystalline slip on {lOiO} (a), (0001) (a), and {lOTO} (c), the c-axis orientation of such weakly deformed grams may be predicted for various geometries of the imposed bulk strain. Constrictional deformation should result in a dominant maximum of c-axes clustered about X, whereas more oblate strain may be indicated by a dominant maximum about 2. The variability in strain from grain to grain in a deformed aggregate may often be an important factor when using deformed quartz grains as indicators of bulk rock strain. The bulk strain will be an integral of the strain in each individual grain, and it is incorrect to ignore the extreme high and low strain grains as anomalous. This further emphasizes the need to use passive strain markers in detailed strain analysis studies. The use of active markers, such as quartz grains, introduces many additional variables, and the result obtained may not be acceptably accurate. ACKNOWLEDGEMENTS
This work was carried out while the author held an Australian Commonwealth Postgraduate Scholarship in the Geology Department of the University of Adelaide. Thanks are extended to G. Lister, J. Parker, T. Bell, P. James, R. Marjoribanks, S. Schmid and M. Casey for discussion and criticism. REFERENCES Av6 Lallement, H.G. and Carter, N.L., 1971. Pressure dependence of quartz deformation lamellae orientations. Am. J. Sci.. 270: 218-235.
Baeta, R.D. and Ashbee, K.H.G., 1970. Mechanical deformation of quartz I. Constant strain-rate compression experiments. Philos. Mag., 22: 601-623. Bouchez, J.L., 1977. Plastic deformation of quartzites of low temperature in an area of natural strain gradient. Tectonophysics, 39: 25-50. Bridges, M.C. and Etheridge, MA., 1974. A computer program to contour orientation densities. Internal Rep. Dept. Geol. and Mineral., Univ. Adelaide. Burg, J.P. and Laurent, Ph., 1978. Strain analysis of a shear zone in a granodiorite. Tectonophysics, -17: 15-42. Elliot, D., 1970. Determination of finite strain and initial shape from deformed elliptical objects. Geol. Sot. Am. Bull., 81: 2221-2236. Etchecopar, A., 1977. A plane kinematic mode1 of progressive deformation in a polycrystalline aggregate. Tectonophysics, 39: 121-139. Flinn, D., 1962. On folding during three-dimensional progressive deformation. J. Geol. Sot. London, 118: 385-428. Groves, G.W. and Kelly, A.. 1969. Change of shape due to dislocation climb. Philos. Mag., 19: 977-986. Hobbs, B.E., McLaren, A.C. and Paterson, MS., 1972. Plasticity of single crystals of synthetic quartz. In: H.C. Heard, I.Y. Borg, N.L. Carter and C.B. Raleigh (Editors), Flow and Fracture of Rocks. Geophys. Monogr. Ser., Am. Geophys. Union, 16: 29-53. Geology. Hobbs, B.E., Means, W.D. and Williams, P.F., 1976. An Outline of Structural John Wiley and Sons, New York, N.Y., 571 pp. Jaeger, J.C., 1969. Elasticity, Fracture and Flow with Engineering and Geological Applications. Methuen and Co., London, 268 pp. Lister, G.S., 1974. The Theory of Deformation Fabrics. Ph.D. thesis. Australian National University, 463 pp. Lister, G.S. and Paterson, M.S., 1979. The simulation of fabric development during plastic deformation and its application to quartzite: fabric transitions. J. Struct. Geol., 1: 99-115. Lister, G.S., Paterson, M.S. and Hobbs, B.E., 1978. The simulation of fabric development during plastic deformation and its application to quartzite: the model. Tectonophysics, 45: 107-158. Marjoribanks, R.W., 1976. The relation between microfabric and strain in a progressively deformed quartzite sequence from Central Australia. Tectonophysics, 32: 269-293. Morrison-Smith, D.J., Paterson, M.S. and Hobbs, B.E., 1976. An electron microscope study of plastic deformation in single crystals of synthetic quartz. Tectonophysics, 33: 43-50. Paterson, M.S., 1969. The ductility of rocks. In: A.S. Argon (Editor), Physics of Strength and Plasticity. The M.I.T. Press, London, pp. 377-392. Semiatin, S.L., Morris, P.R. and Piehler, H.R., 1979. Microplasticity predictions of r-values and yield loci of low carbon sheet steels deforming by (111) pencil glide. Texture Cryst. Sol., 3: 149-214. 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. Taylor, G.I., 1938. Plastic strain in metals. J. Inst. Metall., 62: 307-324. Von Mises, R., 1928. Mechanik der plastischen Formlnderung von Kristallen. Z. Angew. Math. Mech., 8: 161-185. Wilson, C.J.L., 1975. Preferred orientation in quartz ribbon mylonites. Geol. Sot. Am. Bull., 86: 968-974. Wood, D.S., 1974. Current views on the development of slaty cleavage. Annu. Rev. Earth Planet. Sci., 2: l-35.