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Metamorphic rocks One of the three major groups of rocks that make up the crust of the Earth. The other two groups are igneous rocks and sedimentary rocks. Metamorphic rocks are preexisting rock masses in which new minerals, or textures, or structures are formed at higher temperatures and greater pressures than those normally present at the Earth's surface. See also: Igneous rocks; Sedimentary rocks Two groups of metamorphic rocks may be distinguished; cataclastic rocks, formed by the operation of purely mechanical forces; and recrystallized rocks, or the metamorphic rocks properly so called, formed under the influence of metamorphic pressures and temperatures. Cataclastic rocks are mechanically sheared and crushed. They represent products of dynamometamorphism, or kinetic metamorphism. Chemical and mineralogical changes generally are negligible. The rocks are characterized by their minute mineral grain size. Each mineral grain is broken up along the edges and is surrounded by a corona of debris or strewn fragments (mortar structure, Fig. 1a). During the early stages of this alteration process the metamorphosed product is known as flaser rock (Fig. 1b). Eventually the original mineral grains are entirely gone, as in the mylonites. When seen through the microscope, the comminuted particles consist of a mixture of finely powdered quartz, feldspar, and other minerals with an incipient recrystallization of sericite or chlorite. Pseudotachylite is an extreme end product of this crushing process. See also: Metamorphism; Mylonite Fig. 1 Fabrics of metamorphic rocks under microscope. (a) Mortar fabric; (b) flaser or mylonitic fabric; © granoblastic fabric (after E. E. Wahlstrom, Petrographic Mineralogy, John Wiley and Sons, 1955). (d) Lepidoblastic fabric; (e) nematoblastic fabric; (f) porphyroblast with reaction rim (after T. F. W. Barth, Theoretical Petrology, John Wiley and Sons, 1952). Structural relations Metamorphic rocks, properly so called, are recrystallized rocks. The laws of recrystallization are not the same as those of simple crystallization from a liquid, because the crystals can develop freely in a liquid, but during recrystallization the new crystals are encumbered in their growth by the old minerals. Consequently, the structures which develop in metamorphic rocks are distinctive and of great importance, because they reflect the physiochemical environment of recrystallization and thereby the genesis and history of the metamorphic rock. Crystalloblastic structure A crystalloblast is a crystal that has grown during the metamorphism of a rock. The majority of minerals are frequently bounded by their own crystal faces (idioblasts). Larger crystals are often packed with small inclusions of other minerals exhibiting the so-called sieve structure (poikilitic or diablastic structure). Granoblastic refers to a nondirected rock fabric, with minerals forming grains without any preferred shape or dimensional orientation (Fig. 1c). Lepidoblastic (Fig. 1d), nematoblastic (Fig. 1e), and fibroblastic refer to rocks of scaly, rodlike, and fibrous minerals, respectively. The metamorphic minerals may be arranged in an idioblastic series (crystalloblastic series) in their order of decreasing force of crystallization as follows: (1) sphene, rutile, garnet, tourmaline, staurolite, kyanite; (2) epidote, zoisite; (3) pyroxene, hornblende; (4) ferromagnesite, dolomite, albite; (5) muscovite, biotite, chlorite; (6) calcite; (7) quartz, plagioclase; and (8) orthoclase, microcline. Crystals of any of the listed minerals tend to assume idioblastic outlines at surfaces of contact with simultaneously developed crystals of all minerals of lower position in the series. Preferred orientation Certain minerals have a tendency to assume parallel or partially parallel crystallographic orientation. The shape and spatial arrangement of minerals such as mica, hornblende, or augite show a definite relation to the foliation in the schist or gneiss; that is, both foliation and fissility of a metamorphic rock are directly related to the preferred position assumed by the so-called schist-forming minerals, such as mica, hornblende, and chlorite. See also: Gneiss; Schist Students of structural petrology distinguish between preferred orientation of inequidimensional grains according to their external crystal form, and preferred orientation of equidimensional grains according to their internal or atomic structure. See also: Petrofabric analysis; Structural petrology A special microscope technique (universal stage technique) is necessary in most cases to demonstrate in detail the preferred orientation of the mineral grains according to their atomic structure. See also: Petrography Relic structures Mineral relics often indicate the temperature and pressure that obtained in the preexisting rock. If a mineral, say quartz, is stable in the earlier rock and is also stable in the later rock, it will be preserved (unless stress action sets in) in its original form as a stable relic. However, when a mineral or a definite association of minerals becomes unstable, it may still escape alteration and appear as an unstable relic. These relics are proterogenic, that is, representative of an earlier, premetamorphic rock, or of an earlier stage of the metamorphism. Hysterogenic products are of later date, and are formed in consequence of changed conditions after the formation of the chief metamorphic minerals. A common phenomenon, fairly illustrative of the tendency toward equilibria, is the formation of armors or reaction rims around minerals (Fig. 1f) which have become unstable in their association but have not been brought beyond their fields of existence in general (the armored relics). Thereby the associations of minerals in actual contact with one another become stable. If, however, the constituent minerals of a rock containing armored relics are named without noting this phenomenon, it may be taken as an unstable association. See also: Porphyroblast Structure relics are perhaps of still more importance, directly indicating the nature of the preexisting rock and the mechanism of the metamorphic deformation. The interpretation of relics has been compared to the reading of palimpsests, parchments used for the second time after original writing was nearly erased. Every trace of original structure is important in attempting to reconstruct the history of the rock and in analyzing the causes of its metamorphism. In sedimentary rocks the most important structure is bedding (stratification or layering) which originally was approximately horizontal. In metamorphic rocks deformed by folding, faulting, or other dislocations, the sum of all deformations can be referred to the original horizontal plane, and the deformations can be analyzed. Fissility and schistosity One of the earliest secondary structures to develop in sediments of low metamorphic grade is that of slaty cleavage (also referred to as flow cleavage or fissility), which grades into schistosity which is different from fracture cleavage, or strain-slip cleavage. Slaty cleavage is developed normal to the direction of greatest shortening of the rock mass, and cuts the original bedding at various angles. Tectonic forces acting on a book of sediments of heterogeneous layers will throw them into a series of folds, and slaty cleavage develops in response to the stresses imposed on the rock system as a whole, because of the differential resistance of the several layers. Consequently, folding and slaty cleavage have a common parentage, as illustrated in Fig. 2. Fig. 2 Diagram showing the general relationship between deformation folding and slaty cleavage caused by pressure PP or the couple ScSc. Heavy black lines denote the original bedding deformed into folds. Thin lines indicate slaty cleavage which may grow into schistosity (false bedding). (After G. Wilson, Proceedings of the Geological Association, 1946) In the rock series slate-phyllite-schist the slaty cleavage will grade into schistosity. It is a chemical and recrystallization phenomenon, as well as a mechanical one, and the directions of the schistosity become the main avenues of chemical transport. See also: Rock cleavage; Slate Contact-metamorphic rocks Igneous magma at high temperature may penetrate into sedimentary rocks, it may reach the surface, or it may solidify in the form of intrusive bodies (plutons). Heat from such bodies spreads into the surrounding sediments, and because the mineral assemblages of the sediments are adjusted to low temperatures, the heating-up will result in a mineralogical and textural reconstruction known as contact metamorphism. See also: Pluton The width of the thermal aureole of contact metamorphism surrounding igneous bodies varies from almost complete absence in the case of small intrusions (basalt dikes or diabase sills) to several kilometers in the case of large bodies. See also: Contact aureole The effects produced do not depend only upon the size of the intrusive. Other factors are amount of cover and the closure of the system, composition and texture of the country rock, and the abundance of gaseous and hydrothermal magmatic emanations. The heat conductivity of rocks is so low that gases and vaporous emanations become chiefly responsible for the transportation and transfer of heat into the country rock. Alteration of stratified rocks Stratified rocks are altered in the contact zone to what is commonly called hornfels or hornstone. They are hardened, often flinty rocks, usable for road material, and so fine-grained that the mineral components can be discerned only with the microscope. Hornfels used to be regarded as “silicified” sediments. However, T. Kjerulf, in the later half of the nineteenth century, analyzed sedimentary shale and “silicified” shale of the Oslo region and found that, chemically, they were identical (except for water and carbon dioxide content). Then geologists realized that the “hardening” of the shale took place without appreciable change in the chemical composition. Kjerulf summarized his results by saying that the composition (the shale) was independent of the kind of adjacent igneous rock. Later H. Rosenbusch arrived at the same conclusion and pronounced that no chemical alterations accompany the formation of hornfelses except for the removal of fugitive constituents. The KjerulfRosenbusch rule is useful but needs modification, because chemical changes may ensue from hydrothermal and pneumatolytic action. The next problem then is to see how the mineral assemblages of the hornfelses depend upon the chemical composition of the original sediments. The chief types of sedimentary rocks are sandstone (sand), shale (clay), and limestone. Among the varieties of hornfelses which may develop from different mixtures of these components, the continuous series from shale to limestone is the most interesting. Most shales contain some iron- and magnesia-bearing constituents in addition to feldspar and clay minerals. Quartz, SiO2, is always admixed. Consequently, sufficient SiO2 is often present in the hornfelses to form highly silicified minerals. Other than SiO2, the four chief chemical constituents are Al2O3, CaO, FeO, and MgO. The last two constituents are grouped together to define a system of three components: alumina, lime, and ferromagnesia. By applying the mineralogical phase rule, which states that the number of stable minerals in a rock shall not be larger than the number of components, it follows that, except for quartz and some alkali-bearing minerals listed below, no more than three additional minerals should occur in any one (variety) of these hornfelses. Observations have verified this. Thus from alumina, lime, and ferromagnesia, seven minerals will form that are stable under the conditions of contact metamorphism: andalusite, Al2SiO5; cordierite, Mg2Al4Si5O18; anorthite, CaAl2Si2O8; hypersthene, (Mg,Fe)SiO3; diopside, Ca(Mg,Fe)Si2O6; grossularite, Ca3Al2Si3O12; and wollastonite, CaSiO3. Only three (or fewer) of these minerals can occur together. In this way different mineral combinations develop, each combination (plus quartz and an alkali-bearing mineral) representing a natural hornfels. There are 10 such combinations, corresponding to hornfelses of classes 1–10 of V. M. Goldschmidt's terminology. See also: Hornfels Variations from the above scheme are easily explained. Usually enough water and potash are present to produce mica; muscovite may form instead of, or together with, andalusite, and in the hornfelses of classes 4 and 5, biotite is usually present inducing a characteristic chocolate-brown color into the rocks. In hornfelses of class 10 some lime-rich hydrous silicates may develop, for example, vesuvianite (idocrase). The presence of ferric iron may produce andradite, Ca3Fe2Si3O12, a yellow to dark-green garnet which will form mixed crystals with grossularite. Pneumatolysis and metasomatism Other factors of importance in contact metamorphism are chemical changes that ensue from pneumatolytic and hydrothermal action. These changes are brought about by the magmatic gases and high temperatures that accompany igneous intrusions. The surrounding rocks are deeply penetrated not only by the heat but also by water and other volatile compounds. Because chemical alterations take place in this so-called pneumatolytic or hydrothermal contact zone, the Kjerulf-Rosenbusch rule is not applicable. The width of the affected zone varies from nil to thousands of feet. See also: Metasomatism; Pneumatolysis The primary magmatic gases are acid and in consequence show high reactivity. If the contact rock is basic, especially limestone, the acid gases will react effectively with it. Limestone acts as a filter, capturing the escaping gases. As a result, a great variety of reaction minerals is formed. The corresponding rocks are known as skarns. If the reaction rocks are limestones composed of lime silicates, the reaction minerals are mainly garnet and pyroxene, often accompanied by phlogopite and fluorite. Sulfides of iron, zinc, lead, or copper may be present, and in some occurrences magnetite is formed. See also: Skarn Summary Contact metamorphism caused by deep-seated magma intrusions is very common, and the products (disregarding the pneumatolytic action) vary regularly in accordance with the chemical compositions of the preexisting contact rock. Another factor of equal importance is the variation in temperature as influenced by the nature of the intruding rock and the distance from the contact. Thus it is possible to distinguish between an inner and an outer contact zone. The zones grade into each other by imperceptible transitions, but the mineral associations in the typical inner contact zone, the only zone considered so far, are markedly different from the associations in the outer contact zone. These problems involve a consideration of the general relationships between minerals and mineral associations, on the one hand, and the temperature and pressure, on the other. They are discussed further in connection with the facies principle and the general process of regional metamorphism. However, it is important to realize that contact metamorphism, although it appears to be well defined and seems to stand out as an isolated natural phenomenon, is complex and variegated and passes by gradual transitions into other kinds of metamorphism. Geologically, contact metamorphism should be considered in connection with, and as a part of, the general system of rock metamorphism and metasomatism. Regional metamorphic rocks Crystalline schists, gneisses, and magmatities are typical products of regional metamorphism and mountain building. If sediments accumulate in a slowly subsiding geosynclinal basin, they are subject to down-warping and deep burial, and thus to gradually increasing temperature and pressure. They become sheared and deformed, and a general recrystallization results. However, subsidence into deeper parts of the crust is not the only reason for increasing temperature. It is not known what happens at the deeper levels of a live geosyncline, but obviously heat from the interior of the Earth is introduced regionally and locally, partly associated with magmas, partly in the form of “emanations” following certain main avenues, determined by a variety of factors. From this milieu rose the lofty mountain ranges of the world, with their altered beds of thick sediments intercalated with tuffs, lava, and intrusives, all thrown into enormous series of folds and elevated to thousands of meters. Thus were born the crystalline schists with their variants of gneisses and migmatites. See also: Earth, heat flow in; Orogeny A. Michel-Lévy (1888) distinguished three main étages in the formation of the crystalline schists; F. Becke and U. Grubenmann (1910) demonstrated that the same original material may produce radically different metamorphic rocks according to the effective temperature and pressure during the metamorphism. Grubenmann distinguished three successive depth zones, epizone, mesozone, and katazone, corresponding to three consecutive steps of progressive metamorphism. In eroded mountain ranges, rocks of the katazone are, generally speaking, encountered in the central parts; toward the marginal parts are found rocks of the mesozone and epizone. It is of paramount importance to obtain better information about the temperature-pressure conditions of the recrystallization, and thus to show the relation between the chemical and mineralogical composition of all varieties of rocks. A large-scale attempt in this direction was the development of the facies classification of rocks. Mineral facies As defined by P. Eskola (1921), a mineral facies “comprises all the rocks that have originated under temperature and pressure conditions so similar that a definite chemical composition has resulted in the same set of minerals, quite regardless of their mode of crystallization, whether from magma or aqueous solution or gas, and whether by direct crystallization from solution … or by gradual change of earlier minerals.…” To learn which mineral associations were characteristic of high temperature or of low temperature, and to determine which associations combined with high pressure and with low pressure, Eskola studied the mineral associations in the rocks. It has long been known that in an area of progressive metamorphism each successive stage, or each new zone of metamorphism, is reflected in the appearance of characteristic rock types (G. Barrow, 1893). Rocks within the same zone may be called isofacial, or isograde as proposed by C. E. Tilley (1924) who, furthermore, proposed the term “isograd” for a line of similar degree of metamorphism. In going from an area of unmetamorphosed sedimentary rocks into an area of progressively more highly metamorphic rocks, new minerals appear in orderly succession. Thus, in a series of argillaceous rocks subjected to progressive metamorphism, the first index mineral to appear is usually chlorite, followed successively by biotite, garnet (almandite), and sillimanite. A line can be drawn on the map indicating where biotite first appears. This line is the biotite isograd. The less metamorphosed argillites on one side of this line lack bioite, whereas the more metamorphosed rocks on the other side contain biotite. An isograd can be drawn for each mineral. Actually the isograds are surfaces, and the lines drawn on the map are the intersections of these surfaces with the surface of the Earth. Further work along these lines resulted in the conclusion that it was possible to single out a well-defined series of mineral facies. Sedimentary rocks of the lowest metamorphic grade recrystallized to give rocks of the zeolite facies. At slightly higher temperatures the greenschist facies develops—chlorite, albite, and epidote being characteristic minerals. A higher degree of metamorphism produces the epidote-amphibolite facies, and a still higher degree the true amphibolite facies in which hornblende and plagioclase mainly take the place of chlorite and epidote. Representative of the highest regional metamorphic grade is the granulite facies, in which most of the stable minerals are water-free, such as pyroxenes and garnets. Any sedimentary unit will recrystallize according to the rules of the several mineral facies, the complete sequence of events being a progressive change of the sediment by deformation, recrystallization, and alteration in the successive stages: greenschist facies → epidote-amphibolite facies → amphibolite facies → granulite facies. The mineral associations of these rocks are summarized in the next section. During regional metamorphism a stationary temperature gradient is supposed to be established in the mountain masses. Usually, the outer parts of a geosynclinal region are less affected, and in the ideal case the marginal parts contain unmetamorphosed sediments, clay, sand, and limestone, which gradually change into metamorphic rocks of successively higher facies as they extend into the central and deeper parts. The table summarizes the metamorphic series of rocks that develop from the several types of common sediments and usually converge toward a granitic composition regardless of the nature of the original material. Basic igneous rocks (gabbros, basalts) show a composition related to that of marl and yield analogous metamorphic products. Not listed are ultrabasites (peridotites, and others) which by metamorphism become serpentine, chlorite or talc schist, soapstone, hornblende schist, pyroxene, or olivine masses. Original acid igneous rocks (granite, diorite, rhyolite) show a composition related to that of arkose and yield analogous products. Leptite is primarily fine-grained, usually showing tufaceous or blastoporphyric relic structures; or it is derived from argillaceous sediments. Hälleflintas are dense rocks of conchoidal fracture, genetically related to leptites. Kinzigites, characterized by containing aluminum silicates and usually also rich in magnesia, are metasomatic gneisses, but probably argillites also enter into their constitution. Granulite is a gneiss recrystallized in the high-temperature mineral facies group. See also: Granulite Chemical alterations The chemical changes in the progressive series are complicated. When a sediment is heated, it obviously loses water and other volatile components, carbon dioxide, halogens, and so forth. These vapors act as carriers of several of the nonvolatile elements, for example, Si, Fe, and Mn. As heat emanates from the central parts of a geosynclinal region, it is heralded by a cloud of these vapors migrating centrifugally through the surrounding sediments. Usually, however, no major chemical alterations take place. Petrographers used to believe that the vapors were rich in alkalis and that large quantities, particularly of sodium, gradually would be deposited and fixed in the sediments. The argument was that the sediments, concomitant with a progressive change by increasing metamorphism, seem to exhibit an increase in their sodium content. However, this is not a real increase, but due to an erroneous sampling of the sedimentary material. Normally the lower stages of metamorphism tend to conserve the original composition. Mineral associations of the facies Rocks of the greenschist facies recrystallized at low temperatures and often under high shearing stress. These include chlorite schists, epidote-albite schists, and actinolite schists, all of which are green, hence the name. Other common rocks in this group are serpentinites, talc schists, phyllites, and muscovite (sericite) schists. Plagioclase is not stable in greenschists but breaks up into epidote and albite. Glaucophane schists are rare and probably they represent greenschists formed under conditions of high stress. Rocks of the epidote-amphibolite facies recrystallized in a somewhat higher temperature range. Amphibolites with epidote and either albite or oligoclase are typical. Mica schists (garnet), biotite schists, staurolite schists, and kyanite schists are common. Cordierite-antophyllite (gedrite) schists and chloritoid schists also occur. Sodic plagioclase is stable in these rocks. Rocks of the amphibolite facies recrystallized at about 1100°F (600°C). Amphibolites of hornblende and plagioclase are typical and often carry quartz or biotite or both, or garnet. Sillimanite-muscovite schists (gneisses) are common. Andalusite and staurolite occur at low pressure; kyanite and staurolite at intermediate and high pressure. Rocks of the granulite facies have their greatest extension in old Precambrian areas, but are also found in younger deeply eroded mountain chains. Diagnostic association is ortho- and clinopyroxene; hence the alternative name, two-pyroxene facies group. Hypersthene and augite (garnet) plagioclase gneisses, usually with quartz but occasionally with olivine or spinel, are typical. Amphibolites with hypersthene or diopside or both, sillimanite gneisses, and at high pressure kyanite gneisses are found. The temperature range is probably around 1500°F (800°C). The experiments by H. S. Yoder (1952) in the system MgO–Al2O3–SiO2–H2O indicated that at approximately 1100°F (600°C) and 1200 atm (120 megapascals) it is possible to have different mineral assemblages suggestive of every one of the now accepted metamorphic facies in stable equilibrium. These different mineral assemblages (artificial facies) observed by Yoder are the result of differences in the water content, and are not related to variation in temperature and pressure. As an example, the mineral clinochlore, corresponding to one of the most common rock-making chlorites, shows an upper limit of stability, either alone or in association with talc, of 1300°F (680°C). This is, indeed, a high temperature for any kind of metamorphism, almost a magmatic temperature. But according to the tenets of the mineral facies, chlorite is strictly limited to the greenschist facies, about 390°F (200°C). Although Yoder has proved that there is no absolute relation between temperature and facies, it appears likely that, to the field geologist and to the laboratory worker as well, the facies will still remain the best system of classification of metamorphic rocks; and in a majority of cases the facies will indicate the temperature-pressure conditions under which the several rocks recrystallized. Generally speaking, there is a regular relation between the chemical activity of water and the facies of the metamorphic rock. Water content and mineral facies The role of water in metamorphism is determined by at least four variable, geologically related parameters: rock pressure, temperature, water pressure, and the amount of water present. During a normal progressive regional metamorphism, rock pressure and temperature are interdependent. The amount of water and the pressure of water are related to the encasing sediments and to the degree of metamorphism in such a way that, generally speaking, the low-grade metamorphic facies are characterized by the presence of an excess of water, the medium-grade by some deficiency in water, and the high-grade by virtual absence of water. In the usual diagrammatic illustration of the mineral facies of rocks, temperature and pressure (depth) are taken as coordinates; in regional-metamorphic rocks a third, dependent coordinate may be added, the activity of water running upward approximately along the geothermal gradient. Fig. 3 Mineral facies groups of regional metamorphic rocks showing the temperature and pressure of metamorphism. °F = (°C × 1.8) + 32.1 km = 0.6 mi. Facies series and groups Metamorphic facies may be divided into facies series depending mainly on pressure, and facies groups depending mainly on temperature. Three facies series have been proposed: low-pressure, intermediate-pressure, and high-pressure series. The low-pressure series dominates the Hercynian and Svecofennian of Europe, the Paleozoic of Australia, and part of the paired belts in Japan and New Zealand. The intermediate-pressure series (the original Barrowian zones) occurs in the European Caledonides, the Appalachians, the Precambrian Belt series of Idaho, the Himalayas, and parts of Africa. The high-pressure facies series is found in the Alps and the circum-Pacific region—Japan, New Zealand, Celebes, and the United States. Thus each intracontinental orogenic belt is characterized by one facies series which reflects the pressure that prevailed during metamorphism, whereas the circum-Pacific region with its paired metamorphic belts exhibits two facies series. Four facies groups are recognized from low to high temperature: laumontite and prehnite-pumpellyite; greenschist, including glaucophane schist; amphibolite, including epidote-amphibolite; and the two-pyroxene (granulite) facies group. This scheme is presented in Fig. 3. The “normal” geothermal gradient is in the range 45–70°F per mile (15–23°C per kilometer) depth. The intermediate-pressure facies series is found in areas with this gradient; the high-pressure series (the Alpine series) in areas with lower thermal gradients or with high over-pressure (orogenic pressure); and the low-pressure facies series in areas with steep thermal gradients. The phase boundaries of the polymorphic forms of Al2SiO5 (andalusite, sillimanite, kyanite) have a central position in this scheme, the triple point being located approximately at 840°F (450°C) and 6 kilobars (60 MPa). The “minimum” melting of granite under water pressure occurs approximately along the boundary between the amphibolite and the two-pyroxene facies group. A separate eclogite facies is not recognized by this scheme. See also: Eclogite Figure 3 illustrates the distributions and interrelations of the various metamorphic rocks. It also represents a schematic profile through the continental crust down to 40-mi (60-km) depth, that is, down to the Moho discontinuity. Thus the normal continental crust is entirely made up of metamorphic rocks; where thermal, mechanical, and geochemical equilibrium prevails, there are only metamorphic rocks. Border cases of this normal situation occur in the depths where ultrametamorphism brings about differential melting and local formation of magmas. When equilibrium is restored, these magmas congeal and recrystallize to (metamorphic) rocks. At the surface, weathering processes oxidize and disintegrate the rocks superficially and produce sediments as transient products. Thus the cycle is closed; petrology is without a break. All rocks that are found in the continental crust were once metamorphites. M. G. Best, Igneous and Metamorphic Petrology, 1982 K. Bucher and M. Frey, Petrogenesis of Metamorphic Rocks, 6th ed., 1994 R. Mason, Petrology of the Metamorphic Rocks, 2d ed., 1990 A. Miyashiro, Metamorphic Petrology, 1994 A. Nicolas and J. P. Poirier, Crystalline Plasticity and Solid-State Flow in Metamorphic Rocks, 1976 H. Ramberg, Gravity, Deformation and the Earth's Crust in Theory, Experiments and Geological Application, 2d ed., 1981