9. Fabrics - Supplements
Contents
Crystallographic Fabrics (Textures)
SUPPORTING MATERIAL
Tectonic Fabric Terminology
Axial plane cleavage Cleavage that is parallel or subparallel to the axial plane of a fold; it is generally assumed that the cleavage formed roughly synchronous with folding and is subparallel to the XY-plane of the bulk finite strain ellipsoid.
Cleavage A secondary fabric element, formed under low-temperature conditions, that imparts to the rock a tendency to split along planes.
Cross-cutting cleavage Cleavage that is not parallel to the axial plane of a fold (also nonaxial plane cleavage); the term transecting cleavage is used when cleavage and folding are considered roughly synchronous in a transpressional regime.
Fabric The geometric arrangement of component features in a rock, seen on a scale large enough to include many samples of each feature.
Foliation The general term for any type of “planar” fabric in a rock (e.g., bedding, cleavage, schistosity).
Gneissosity Foliation in feldspar-rich metamorphic rock, formed at intermediate to high temperatures, which is defined by compositional banding; the prefixes “ortho” and “para” are used for igneous and sedimentary protoliths, respectively.
Lineation A fabric element that is best represented by a line, meaning that one of its dimensions is much longer than the other two.
Migmatite Semi-chaotic mixture of layers formed by partial melting and deformation.
Mylonitic foliation A foliation in ductile shear zones that is defined by the dimensional preferred orientation of flattened grains; the foliation tracks the XY flattening plane of the finite strain ellipsoid and is therefore at a low angle to the shear-zone boundary.
Phyllitic cleavage Foliation that is composed of strongly aligned fine-grained white mica and/or chlorite; the mineralogy and fabric of phyllites give the rock a distinctive silky appearance, called phyllitic luster.
Schistosity Foliation in metamorphic rock, formed at intermediate temperatures, that is defined by mica (primarily muscovite and biotite), which gives the rock a shiny appearance.
Texture The pattern of crystallographic axes in an aggregate of grains; also crystallographic fabric.
MORE EXPLORATION
Crystallographic Fabrics (Textures)
Crystal-plastic deformation mechanisms provide us with another tool for the interpretation of deformation. Recall that dislocation glide is the strain-producing crystal-plastic process that occurs on specific crystallographic planes in a crystal (Chapter 7). The properties of dislocation movement hold the key to interpreting the significance of textures or crystallographic-preferred fabrics in rocks. It turns out that the type of texture may be indicative of the dominant deformation mechanism and can provide valuable information on the rheologic conditions. You have earlier learned about shape (or dimensional-preferred) fabrics and now we add crystallographic fabrics to our vocabulary. Let’s first see how they differ.
Dimensional- and crystallographic-preferred fabrics describe different properties of rocks. A dimensional-preferred fabric is the quantification of grain shapes in a rock; it is, in essence, a geometric parameter. Aligned hornblende crystals provide an example of a dimensional-preferred fabric. A crystallographic-preferred fabric describes the collective crystallographic orientation of grains that make up the rock. In other words, crystallographic-preferred fabrics represent the degree of alignment of crystallographic axes. We start by looking at the principles governing the development of crystallographic-preferred orientation by intracrystalline slip.
|
|
|
FIGURE S9.1. The development of a crystallographic-preferred orientation by dislocation glide. The thin lines in grain ABCD are crystallographic glide planes, which here coincide with the basal plane (0001). The c-axis is indicated with the heavy line, labeled C, and the instantaneous shortening direction by heavy arrows. Strain arises from glide on the crystal planes; note that the length of individual planes remains the same, requiring that the glide planes rotate to accommodate the distortion. Various angular relationships are indicated: (α) angle of shear along the glide plane; (β) rotation angle of the c-axis with respect to an external reference system (e.g., shear-zone boundary); (ψ) rotation angle of material line BC with respect to an external reference system (angular shear); (φ′) angle of finite extension axis (subscript “f ”) with respect to an external reference system. Note that the instantaneous strain axes (subscript “i ”) define the external reference system, and that they do not change in orientation during the progressive history (i.e., there is no spin). [12.19] |
The square ABCD in Figure S9.1a marks the schematic cross section of a single crystal that is deformed by homogeneous shortening perpendicular to the top and bottom sides of the square. Stated more specifically, the infinitesimal shortening strain (Zi) is parallel to AD (heavy arrows). The grain only deforms by dislocation glide along specific crystallographic planes, which are shown by the thin lines (parallel to the diagonal BD). Let’s say that these planes coincide with the basal plane of the crystal with the indices (0001) for hexagonal minerals, so that the crystallographic c-axis is oriented perpendicular to these glide planes. We add one other restriction to the deformation: the faces AB and CD and the infinitesimal strain axes are held in a constant orientation relative to the external framework, which defines a non-spinning deformation. Because dislocation glide is a volume constant mechanism, the dimensions of the grain measured parallel to the glide plane do not change during deformation. At first glance this may not appear to be the case, but measure the length of the same glide plane in each step (a to c) to prove this to yourself. During deformation, shortening is accomplished by slip on the glide planes; this is accompanied by simultaneous extension, as shown by the finite strain axis (Xf) in Figure S9.1b. The critical ingredient is that if neither length nor spacing of the glide planes are to change, these planes have to rotate to accommodate the strain. As a consequence, the c-axis (perpendicular to the glide plane) rotates progressively toward the infinitesimal shortening direction. Meanwhile, the grain continues to elongate, with the long axis of the finite strain ellipsoid increasingly approaching AB (or CD). Thus, the finite strain axes and infinitesimal strain axes rotate relative to each other, which defines non-coaxial strain with simultaneous non-spinning deformation. In this generalized scenario, we recognize two important consequences: (1) the c-axes rotate toward the instantaneous shortening axis (Zi) and (b) the finite strain ellipsoid elongates toward the instantaneous shortening direction (Xi), which means that they are only parallel at very large strains. In Nature, matters may be more complex as we are dealing with three-dimensional space in which several glide planes may be active simultaneously. Computer modeling of the development of crystallographic fabrics in these more complex situations, however, shows overall behavior similar to that in our simple model. We can use the geometry and intensity of textures toward the characterization of strain and displacement, which requires an understanding of the Symmetry Principle.
The Symmetry Principle
Symmetry is a fascinating aspect of our world. Look in the mirror or at your neighbor and you see that a person’s face is symmetric (at least in general) around a single plane. This symmetry plane cuts between the eyes, and divides the nose and mouth in halves (bilateral or mirror symmetry). Most objects, living or inanimate, display some degree of symmetry, as do many of the geometric concepts basic to mathematics and physics. A cube has a higher symmetry than the human face, in that it contains three mutually perpendicular mirror planes. We say that a cube has a higher symmetry than a human face, because it contains more symmetry elements. In mineralogy, you learn about the symmetry of various types of crystals; for example, triclinic (only a center of symmetry or a two-fold axis), monoclinic (one mirror plane), and orthorhombic (three mutually perpendicular planes with intersections of unequal length).
|
|
|
FIGURE S9.2. The Symmetry Principle. A cube is distorted into a body with (a) orthorhombic and (b) monoclinic symmetry. (c) A random distribution of c-axis pattern reorganizes in response to these deformations into (d) a high-symmetry (orthorhombic) and (e) a low-symmetry (monoclinic) pattern. The symmetry of the c-axes patterns enables us to determine the strain condition. [12.20] |
Let’s explore the Symmetry Principle (or Curie principle[1]) with a simple example (Figure S9.2). Imagine that we apply strain to a cube such that the resulting shape is a rectangular block. The symmetry of the rectangular block is orthorhombic (three perpendicular symmetry planes or three perpendicular two-fold axes; Figure S9.2a). The symmetry of the simplest strain path causing this shape change is also orthorhombic, meaning that the incremental and finite strain ellipsoids differ only in shape, not in orientation (i.e., coaxial strain). We restate this by distinguishing the cause (the strain path) and the effect (the rectangular block): the effect has a symmetry that is equal to or greater than the cause. This is called the Symmetry Principle. Now we distort our cube, say by shear, such that it becomes a block with a lower symmetry (Figure S9.2b). In this case the resulting symmetry is monoclinic, because we can only recognize one mirror plane and one two-fold axis. Using the Symmetry Principle we therefore predict that the strain path (meaning, the cause) must have monoclinic or lower symmetry. Thus, the strain that caused the distortion must have been non-coaxial, as coaxial strain would have produced higher symmetry.
If the Symmetry Principle says that the effect is of equal or greater symmetry than the cause, is the reverse also true? No, the cause cannot have a symmetry that is higher than the effect. This is all fine and good, but what does it have to do with crystallographic-preferred fabrics? Figure S9.2c shows a random pattern of crystallographic c-axes in lower hemisphere projection, say from a statically recrystallized quartzite. In two separate deformation experiments we form characteristic c-axis patterns (Figure S9.2d and e). The symmetry of the two patterns is different; the pattern in Figure S9.2d has orthorhombic symmetry, whereas the pattern in Figure S9.2e is monoclinic. What can we say about the strain that produced these crystallographic patterns? Using the Symmetry Principle, the pattern in Figure S9.2d must have been caused by a strain path with a symmetry equal to or less than orthorhombic, whereas the symmetry of the strain path that produced the pattern in Figure S9.2e must have been monoclinic or lower. Thus, Figure S9.2e (“the effect”) can only have been formed by non-coaxial strain (“the cause”). Note that the pattern in Figure S9.2d, however, cannot be uniquely interpreted; it could have formed by either coaxial or non-coaxial strain according to the Symmetry Principle. With this information we can use crystallographic fabrics to determine whether the rocks were deformed in a non-coaxial or coaxial strain regime. A rich literature exists on this topic, including fabrics to determine strain quantities and displacement sense in shear zones.
READING
Barker, A. J., 1990. Introduction to metamorphic textures and microstructures. Blackie, Glasgow.
Borradaile, G. J., 1978. Transected folds: a study illustrated with examples from Canada and Scotland. Geological Society of America Bulletin, 89, 481–493.
Engelder, T. E., and Marshak, S., 1985. Disjunctive cleavage formation at shallow depths in sedimentary rocks. Journal of Structural Geology, 7, 327–343.
Etheridge, M. A., Wall, V. J., and Vernon, R. H., 1983. The role of the fluid phase during regional metamorphism and deformation. Journal of Metamorphic Geology, 1, 205–226. Gray, D. R., 1979. Microstructure of crenulation cleavages: an indicator of cleavage origin. American Journal of Science, 279, 97–128.
Hobbs, B. E., Means,W. D., and Williams, P. F., 1982. The relationship between foliation and strain: an experimental investigation. Journal of Structural Geology, 4, 411–428.
Housen, B. A., and van der Pluijm, B. A., 1991. Slaty cleavage development and magnetic anisotropy fabrics. Journal of Geophysical Research (B), 96, 9937–9946.
Knipe, R. J., 1981. The interaction of deformation and metamorphism in slates. Tectonophysics, 78, 249–272. Powell, C. M. A., 1979. A morphological classification of rock cleavage. Tectonophysics, 58, 21–34.
Passchier, C.W, and Trouw, R.A.J., 2005. Microtectonics. Springer-Verlag, Berlin, 366p.
van der Pluijm, B. A., Ho, N.-C., Peacor, D. R., and Merriman, R. J., 1998. Contradictions of slate formation resolved? Nature, 392, 348. Weber, K., 1981. Kinematic and metamorphic aspects of cleavage formation in very low-grade metamorphic slates. Tectonophysics, 78, 291–306.
Williams, P. F., 1972. Development of metamorphic layering and cleavage in low grade metamorphic rocks at Bermagui, Australia. American Journal of Science, 272, 1–47.
Wood, D. S., Oertel, G., Singh, J., and Bennett, H. F., 1976. Strain and anisotropy in rocks. Philosophical Transactions of the Royal Society of London, 283, 27–42.
Wright, T. O., and Platt, L. B., 1982. Pressure dissolution and cleavage in the Martinsburg shale. American Journal of Science, 282, 122–135.
Zwart, H. J., 1962. On the determination of polymetamorphic mineral associations, and its application to the Bosost area (central Pyrenees). Geologische Rundschau, 52, 38–65.