Chapter 8: Major Elements

Chapter 8: Major Elements

Chapter 25. Metamorphic Facies and Metamorphosed Mafic Rocks V.M. Goldschmidt (1911, 1912a), contact metamorphosed pelitic, calcareous, and psammitic hornfelses in the Oslo region Relatively simple mineral assemblages of fewer than six major minerals in the inner zones of the aureoles around granitoid intrusives

Equilibrium mineral assemblage related to X bulk Metamorphic Facies Certain mineral pairs (e.g. anorthite + hypersthene) were consistently present in rocks of appropriate composition, whereas the compositionally equivalent pair (diopside + andalusite) was not If two alternative assemblages are X-equivalent,

we must be able to relate them by a reaction In this case the reaction is simple: MgSiO3 + CaAl2Si2O8 = CaMgSi2O6 + Al2SiO5 En An Di Als Metamorphic Facies

Pentii Eskola (1914, 1915) Orijrvi region of southern Finland Rocks with K-feldspar + cordierite at Oslo contained the compositionally equivalent pair biotite + muscovite at Orijrvi Eskola concluded that the difference must reflect differing physical conditions between the regions

Concluded that Finnish rocks (with a more hydrous nature and lower volume assemblage) equilibrated at lower temperatures and higher pressures than the Norwegian ones Metamorphic Facies Oslo: Ksp + Cord Orijrvi: Bi + Mu Reaction: 2 KMg3AlSi3O10(OH)2 + 6 KAl2AlSi3O10(OH)2 + 15 SiO2 Bt Ms

= 3 Mg2Al4Si5O18 + 8 KAlSi3O8 + 8 H2O Crd Kfs Qtz Metamorphic Facies Eskola (1915) developed the concept of metamorphic facies: In any rock or metamorphic formation which has

arrived at a chemical equilibrium through metamorphism at constant temperature and pressure conditions, the mineral composition is controlled only by the chemical composition. We are led to a general conception which the writer proposes to call metamorphic facies. Metamorphic Facies Dual basis for the facies concept Descriptive: the relationship between the composition of a rock and its mineralogy This descriptive aspect was a fundamental feature of Eskolas concept

A metamorphic facies is then a set of repeatedly associated metamorphic mineral assemblages If we find a specified assemblage (or better yet, a group of compatible assemblages covering a range of compositions) in the field, then a certain facies may be assigned to the area Metamorphic Facies Interpretive: the range of temperature and pressure conditions represented by each facies Eskola was aware of the temperature-pressure implications of the concept and correctly deduced the

relative temperatures and pressures represented by the different facies that he proposed We can now assign relatively accurate temperature and pressure limits to individual facies Metamorphic Facies Eskola (1920) proposed 5 original facies: Greenschist Amphibolite Hornfels Sanidinite Eclogite Each easily defined on the basis of mineral

assemblages that develop in mafic rocks Metamorphic Facies In his final account, Eskola (1939) added: Granulite Epidote-amphibolite Glaucophane-schist (now called Blueschist) ... and changed the name of the hornfels facies to the pyroxene hornfels facies His facies, and his estimate of their relative temperature-pressure relationships are shown in Fig. 25-1

Metamorphic Facies Temperature Sanadinite Facies Pressure Formation of Zeolites Greenschist Facies EpidoteAmphibolite

Facies Amphibolite Facies PyroxeneHornfels Facies Granulite Facies GlaucophaneSchist Facies Eclogite Facies

Fig. 25-1 The metamorphic facies proposed by Eskola and their relative temperature-pressure relationships. After Eskola (1939) Die Entstehung der Gesteine. Gesteine. Julius Springer. Berlin. Metamorphic Facies Several additional facies types have been proposed. Most notable are: Zeolite Prehnite-pumpellyite ...resulting from the work of Coombs in the burial metamorphic terranes of New Zealand Fyfe et al. (1958) also proposed:

Albite-epidote hornfels Hornblende hornfels Metamorphic Facies Fig. 25-2. Temperaturepressure diagram showing the generally accepted limits of the various facies used in this text. Boundaries are approximate and gradational. The typical or average continental geotherm is

from Brown and Mussett (1993). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Metamorphic Facies Table 25-1. The definitive mineral assemblages that characterize each facies (for mafic rocks). Table 25-1. Definitive Mineral Assemblages of Metamorphic Facies Facies

Definitive Mineral Assemblage in Mafic Rocks Zeolite zeolites: especially laumontite, wairakite, analcime Prehnite-Pumpellyite prehnite + pumpellyite (+ chlorite + albite) Greenschist chlorite + albite + epidote (or zoisite) + quartz actinolite

Amphibolite hornblende + plagioclase (oligoclase-andesine) garnet Granulite orthopyroxene (+ clinopyrixene + plagioclase garnet hornblende) Blueschist glaucophane + lawsonite or epidote (+albite chlorite) Eclogite

pyrope garnet + omphacitic pyroxene ( kyanite) Contact Facies After Spear (1993) Mineral assemblages in mafic rocks of the facies of contact metamorphism do not differ substantially from that of the corresponding regional facies at higher pressure. It is convenient to consider metamorphic facies in 4 groups: 1) Facies of high pressure

The blueschist and eclogite facies: low molar volume phases under conditions of high pressure The lower-temperature blueschist facies occurs in areas of low T/P gradients, characteristically developed in subduction zones Because eclogites are stable under normal geothermal conditions, they may develop wherever mafic magmas solidify in the deep crust or mantle (crustal chambers or dikes, sub-crustal magmatic underplates, subducted crust that is redistributed into the mantle)

Metamorphic Facies 2) Facies of medium pressure Most metamorphic rocks now exposed at the surface of the Earth belong to the greenschist, amphibolite, or granulite facies As you can see in Fig. 25-2, the greenschist and amphibolite facies conform to the typical geothermal gradient

Fig. 25-2. Temperaturepressure diagram showing the generally accepted limits of the various facies used in this text. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Metamorphic Facies 3) Facies of low pressure The albite-epidote hornfels, hornblende hornfels, and pyroxene hornfels facies: contact metamorphic terranes and regional terranes with very high geothermal gradients The sanidinite facies is rare and limited to xenoliths in basic magmas and the innermost portions of some contact aureoles adjacent to hot basic intrusives

Fig. 25-2. Temperaturepressure diagram showing the generally accepted limits of the various facies used in this text. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Metamorphic Facies 4) Facies of low grades Rocks often fail to recrystallize thoroughly at very low grades, and equilibrium is not always attained The zeolite and prehnite-pumpellyite facies are thus not always represented, and the greenschist facies is the lowest grade developed in many regional terranes Metamorphic Facies Combine the concepts of isograds, zones, and facies

Examples: chlorite zone of the greenschist facies, the staurolite zone of the amphibolite facies, or the cordierite zone of the hornblende hornfels facies, etc. Metamorphic maps typically include isograds that define zones and ones that define facies boundaries Determining a facies or zone is most reliably done when several rocks of varying composition and mineralogy are available Facies Series A traverse up grade through a metamorphic terrane should follow one of several possible metamorphic field gradients (Fig. 21-1), and, if extensive enough, cross through a sequence of facies

Figure 21-1. Metamorphic field gradients (estimated P-T conditions along surface traverses directly up metamorphic grade) for several metamorphic areas. After Turner (1981). Metamorphic Petrology: Mineralogical, Field, and Tectonic Aspects. McGrawHill. Facies Series Miyashiro (1961) initially proposed five facies series, most of them named for a specific representative type locality The series were: 1. Contact Facies Series (very low-P) 2. Buchan or Abukuma Facies Series (low-P regional) 3. Barrovian Facies Series (medium-P regional)

4. Sanbagawa Facies Series (high-P, moderate-T) 5. Franciscan Facies Series (high-P, low T) Fig. 25-3. Temperaturepressure diagram showing the three major types of metamorphic facies series proposed by Miyashiro (1973, 1994). Winter (2001) An Introduction to

Igneous and Metamorphic Petrology. Prentice Hall. Metamorphism of Mafic Rocks Mineral changes and associations along T-P gradients characteristic of the three facies series

Hydration of original mafic minerals required for the development of the metamorphic mineral assemblages of most facies If water is unavailable, mafic igneous rocks will remain largely unaffected in metamorphic terranes, even as associated sediments are completely re-equilibrated Coarse-grained intrusives are the least permeable, and thus most likely to resist metamorphic changes Tuffs and graywackes are the most susceptible Metamorphism of Mafic Rocks

Plagioclase: More Ca-rich plagioclases become progressively unstable as T lowered General correlation between temperature and the maximum An-content of the stable plagioclase

At low metamorphic grades only albite (An0-3) is stable In the upper-greenschist facies oligoclase becomes stable. The An-content of plagioclase thus jumps from An1-7 to An17-20 (across the peristerite solvus) as grade increases Andesine and more calcic plagioclases are stable in the upper amphibolite and granulite facies The excess Ca and Al calcite, an epidote mineral, sphene, or amphibole, etc., depending on P-T-X Metamorphism of Mafic Rocks

Clinopyroxene breaks down to a number of mafic minerals, depending on grade. These minerals include chlorite, actinolite, hornblende, epidote, a metamorphic pyroxene, etc. The mafic(s) that form are commonly diagnostic of the grade and facies Mafic Assemblages at Low Grades

Zeolite and prehnite-pumpellyite facies Do not always occur - typically require unstable protolith Boles and Coombs (1975) showed that metamorphism of tuffs in NZ accompanied by substantial chemical changes due to circulating fluids, and that these fluids played an important role in the metamorphic minerals that were stable The classic area of burial metamorphism thus has a strong component of hydrothermal metamorphism as well Mafic Assemblages of the Medium P/T

Series: Greenschist, Amphibolite, and Granulite Facies The greenschist, amphibolite and granulite facies constitute the most common facies series of regional metamorphism The classical Barrovian series of pelitic zones and the lower-pressure Buchan-Abukuma series are variations on this trend Greenschist, Amphibolite, Granulite Facies

The zeolite and prehnite-pumpellyite facies are not present in the Scottish Highlands Metamorphism of mafic rocks is first evident in the greenschist facies, which correlates with the chlorite and biotite zones of the associated pelitic rocks Typical minerals include chlorite, albite, actinolite, epidote, quartz, and possibly calcite, biotite, or stilpnomelane Chlorite, actinolite, and epidote impart the green color from which the mafic rocks and facies get their name

Greenschist, Amphibolite, Granulite Facies ACF diagram The most characteristic mineral assemblage of the greenschist facies is: chlorite + albite + epidote + actinolite quartz Fig. 25-6. ACF diagram illustrating representative mineral assemblages for

metabasites in the greenschist facies. The composition range of common mafic rocks is shaded. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Greenschist, Amphibolite, Granulite Facies Greenschist to amphibolite facies transition involves two major mineralogical changes 1. Transition from albite to oligoclase (increased Ca-content of stable plagioclase with temperature across the peristerite gap) 2. Transition from actinolite to hornblende (amphibole becomes able to accept increasing

amounts of aluminum and alkalis at higher temperatures) Both of these transitions occur at approximately the same grade, but have different P/T slopes Fig. 26-19. Simplified petrogenetic grid for metamorphosed mafic rocks showing the location of several determined univariant reactions in the CaO-MgO-Al 2O3-SiO2-H2O-(Na2O) system (C(N)MASH). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Greenschist, Amphibolite, Granulite Facies

ACF diagram Typically two-phase Hbl-Plag Amphibolites are typically black rocks with up to about 30% white plagioclase Garnet in more Al-Fe-rich and Ca-poor mafic rocks Clinopyroxene in Al-poor-Carich rocks

Fig. 25-7. ACF diagram illustrating representative mineral assemblages for metabasites in the amphibolite facies. The composition range of common mafic rocks is shaded. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Greenschist, Amphibolite, Granulite Facies

The transition from amphibolite to granulite facies occurs in the range 650-700oC If aqueous fluid, associated pelitic and quartzofeldspathic rocks (including granitoids) begin to melt in this range at low to medium pressures , so that migmatites may form and the melts may become mobilized Not all pelites and quartzo-feldspathic rocks reach the granulite facies as a result Greenschist, Amphibolite, Granulite Facies

Mafic rocks generally melt at somewhat higher temperatures If water is removed by the earlier melts the remaining mafic rocks may become depleted in water Hornblende decomposes and orthopyroxene + clinopyroxene appear This reaction occurs over a temperature interval of at least 50oC

Fig. 26-19. Simplified petrogenetic grid for metamorphosed mafic rocks showing the location of several determined univariant reactions in the CaO-MgO-Al 2O3-SiO2-H2O-(Na2O) system (C(N)MASH). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Greenschist, Amphibolite, Granulite Facies The granulite facies is characterized by the presence of a largely anhydrous mineral assemblage Metabasites critical mineral assemblage is orthopyroxene +

clinopyroxene + plagioclase + quartz Garnet, minor hornblende and/or biotite may be present Fig. 25-8. ACF diagram for the granulite facies. The composition range of common mafic rocks is shaded. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Greenschist, Amphibolite, Granulite Facies The origin of granulite facies rocks is complex and

controversial. There is general agreement, however, on two points 1) Granulites represent unusually hot conditions Temperatures > 700oC (geothermometry has yielded some very high temperatures, even in excess of 1000oC) Average geotherm temperatures for granulite facies depths should be in the vicinity of 500oC, suggesting that granulites are the products of crustal thickening and excess heating Greenschist, Amphibolite, Granulite Facies 2) Granulites are dry

Rocks dont melt due to lack of available water Granulite facies terranes represent deeply buried and dehydrated roots of the continental crust Fluid inclusions in granulite facies rocks of S. Norway are CO2rich, whereas those in the amphibolite facies rocks are H2O-rich Fig. 25-9. Typical mineral changes that take place in metabasic rocks during progressive metamorphism in the medium P/T facies series. The approximate location of the pelitic zones of Barrovian metamorphism are included for comparison. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Mafic Assemblages of the Low P/T Series: AlbiteEpidote Hornfels, Hornblende Hornfels, Pyroxene Hornfels, and Sanidinite Facies

Mineralogy of low-pressure metabasites not appreciably different from the med.-P facies series Albite-epidote hornfels facies correlates with the greenschist facies into which it grades with increasing pressure Similarly the hornblende hornfels facies correlates with the amphibolite facies, and the pyroxene hornfels and sanidinite facies correlate with the

granulite facies Fig. 25-2. Temperaturepressure diagram showing the generally accepted limits of the various facies used in this text. Winter (2001) An Introduction to Igneous and Metamorphic Petrology.

Prentice Hall. Mafic Assemblages of the Low P/T Series: AlbiteEpidote Hornfels, Hornblende Hornfels, Pyroxene Hornfels, and Sanidinite Facies The facies of contact metamorphism are readily distinguished from those of medium-pressure regional metamorphism on the basis of: Metapelites (e.g. andalusite and cordierite) Textures and field relationships Mineral thermobarometry Mafic Assemblages of the Low P/T Series: AlbiteEpidote Hornfels, Hornblende Hornfels, Pyroxene Hornfels, and Sanidinite Facies

The innermost zone of most aureoles rarely reaches the pyroxene hornfels facies If the intrusion is hot and dry enough, a narrow zone develops in which amphiboles break down to orthopyroxene + clinopyroxene + plagioclase + quartz (without garnet), characterizing this facies Sanidinite facies is not evident in basic rocks Mafic Assemblages of the High P/T Series: Blueschist and Eclogite Facies

The mafic rocks (not the pelites) develop conspicuous and definitive mineral assemblages under high P/T conditions High P/T geothermal gradients characterize subduction zones Mafic blueschists are easily recognizable by their color, and are useful indicators of ancient subduction zones The great density of eclogites: subducted basaltic oceanic crust becomes more dense than the surrounding mantle

Blueschist and Eclogite Facies Alternative paths to the blueschist facies Fig. 25-2. Temperaturepressure diagram showing the generally accepted limits of the various facies used in this text. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Blueschist and Eclogite Facies

The blueschist facies is characterized in metabasites by the presence of a sodic blue amphibole stable only at high pressures (notably glaucophane, but some solution of crossite or riebeckite is possible) The association of glaucophane + lawsonite is diagnostic. Crossite is stable to lower pressures, and may extend into transitional zones Albite breaks down at high pressure by reaction to jadeitic pyroxene + quartz: NaAlSi3O8 = NaAlSi2O6 + SiO2

(reaction 25-3) Ab Jd Qtz Blueschist and Eclogite Facies Fig. 25-10. ACF diagram illustrating representative mineral assemblages for metabasites in the blueschist facies. The composition range of common mafic rocks is shaded. Winter (2001) An Introduction to

Igneous and Metamorphic Petrology. Prentice Hall. Blueschist and Eclogite Facies Eclogite facies: mafic assemblage omphacitic pyroxene + pyrope-grossular garnet Fig. 25-11. ACF diagram illustrating representative mineral assemblages for metabasites in the eclogite facies. The composition range of common mafic rocks is shaded. Winter (2001) An Introduction to

Igneous and Metamorphic Petrology. Prentice Hall. Pressure-Temperature-Time (P-T-t) Paths The facies series concept suggests that a traverse up grade through a metamorphic terrane should follow a metamorphic field gradient, and may cross through a sequence of facies (spatial sequences)

Progressive metamorphism: rocks pass through a series of mineral assemblages as they continuously equilibrate to increasing metamorphic grade (temporal sequences) But does a rock in the upper amphibolite facies, for example, pass through the same sequence of mineral assemblages that are encountered via a traverse up grade to that rock through greenschist facies, etc.? Pressure-Temperature-Time (P-T-t) Paths The complete set of T-P conditions that a rock may experience during a metamorphic cycle from burial to metamorphism (and orogeny) to uplift and erosion is

called a pressure-temperature-time path, or P-T-t path Pressure-Temperature-Time (P-T-t) Paths Metamorphic P-T-t paths may be addressed by: 1) Observing partial overprints of one mineral assemblage upon another The relict minerals may indicate a portion of either the prograde or retrograde path (or both) depending upon when they were created Pressure-Temperature-Time (P-T-t) Paths Metamorphic P-T-t paths may be addressed by:

2) Apply geothermometers and geobarometers to the core vs. rim compositions of chemically zoned minerals to document the changing P-T conditions experienced by a rock during their growth Fig. 25-13a. Chemical zoning profiles across a garnet from the Tauern Window. After Spear (1989) Fig. 25-13a. Conventional P-T diagram (pressure increases upward) showing three modeled clockwise P-T-t paths computed from the profiles using the method of Selverstone et al. (1984) J. Petrol., 25, 501-531 and Spear (1989). After Spear (1989) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths . Mineral. Soc. Amer. Monograph 1. Pressure-Temperature-Time (P-T-t) Paths Metamorphic P-T-t paths may be addressed by:

Even under the best of circumstances (1) overprints and (2) geothermobarometry can usually document only a small portion of the full P-T-t path 3) We thus rely on forward heat-flow models for various tectonic regimes to compute more complete P-T-t paths, and evaluate them by comparison with the results of the backward methods Pressure-Temperature-Time (P-T-t) Paths

Classic view: regional metamorphism is a result of deep burial or intrusion of hot magmas Plate tectonics: regional metamorphism is a result of crustal thickening and heat input during orogeny at convergent plate boundaries (not simple burial) Heat-flow models have been developed for various regimes, including burial, progressive thrust stacking, crustal doubling by continental collision, and the effects of crustal anatexis and magma migration Higher than the normal heat flow is required for typical greenschist-amphibolite medium P/T facies series Uplift and erosion has a fundamental effect on the geotherm and

must be considered in any complete model of metamorphism Fig. 25-12. Schematic pressure-temperature-time paths based on heat-flow models. The Al 2SiO5 phase diagram and two hypothetical dehydration curves are included. Facies boundaries, and facies series from Figs. 25-2 and 25-3. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Fig. 25-12a. Schematic pressure-temperature-time paths based on a crustal thickening heat-flow model. The Al2SiO5 phase diagram and two hypothetical dehydration curves are included. Facies boundaries, and facies series from Figs. 25-2 and 25-3. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Pressure-Temperature-Time (P-T-t) Paths

Most examples of crustal thickening have the same general looping shape, whether the model assumes homogeneous thickening or thrusting of large masses, conductive heat transfer or additional magmatic rise Paths such as (a) are called clockwise P-T-t paths in the literature, and are considered to be the norm for regional metamorphism Fig. 25-12b. Schematic pressure-temperature-time paths based on a shallow magmatism heat-flow model. The Al2SiO5 phase diagram and two hypothetical dehydration curves are included. Facies boundaries, and facies series from Figs. 25-2 and 25-3. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Fig. 25-12c. Schematic pressure-temperature-time paths based on a heat-flow model for some types of granulite facies

metamorphism. Facies boundaries, and facies series from Figs. 25-2 and 25-3. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Pressure-Temperature-Time (P-T-t) Paths Broad agreement between the forward (model) and backward (geothermobarometry) techniques regarding PT-t paths The general form of a path such as (a) therefore probably represents a typical rock during orogeny and regional metamorphism

Pressure-Temperature-Time (P-T-t) Paths 1. Contrary to the classical treatment of metamorphism, temperature and pressure do not both increase in unison as a single unified metamorphic grade. Their relative magnitudes vary considerably during the process of metamorphism Pressure-Temperature-Time (P-T-t) Paths 2. Pmax and Tmax do not occur at the same time

In the usual clockwise P-T-t paths, Pmax occurs much earlier than Tmax. Tmax should represent the maximum grade at which chemical equilibrium is frozen in and the metamorphic mineral assemblage is developed This occurs at a pressure well below Pmax, which is uncertain because a mineral geobarometer should record the pressure of Tmax Metamorphic grade should refer to the temperature and pressure at Tmax, because the grade is determined

via reference to the equilibrium mineral assemblage Pressure-Temperature-Time (P-T-t) Paths 3. Some variations on the cooling-uplift portion of the clockwise path (a) indicate some surprising circumstances For example, the kyanite sillimanite transition is generally considered a prograde transition (as in path a1), but path a2 crosses the kyanite sillimanite transition as temperature is decreasing. This may result in only minor replacement of kyanite by sillimanite during such a retrograde process Fig. 25-12a. Schematic pressure-temperature-time paths based on a crustal thickening heat-flow model. The Al2SiO5

phase diagram and two hypothetical dehydration curves are included. Facies boundaries, and facies series from Figs. 25-2 and 25-3. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Pressure-Temperature-Time (P-T-t) Paths 3. Some variations on the cooling-uplift portion of the clockwise path (a) in Fig. 25-12 indicate some surprising circumstances If the P-T-t path is steeper than a dehydration reaction curve, it is also possible that a dehydration reaction can occur with decreasing temperature (although this is only likely at low pressures where the dehydration curve slope is low)

Fig. 25-14. A typical Barrovian-type metamorphic field gradient and a series of metamorphic P-T-t paths for rocks found along that gradient in the field. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Figures not used Fig. 25-4. ACF diagrams illustrating representative mineral assemblages for metabasites in the (a) zeolite and (b) prehnite-pumpellyite facies. Actinolite is stable only in the upper prehnite-pumpellyite facies. The composition range of common mafic rocks is shaded. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Figures not used Fig. 25-5. Typical mineral changes that take place in metabasic rocks during progressive metamorphism in the zeolite, prehnite-pumpellyite, and incipient greenschist facies. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

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