Myron G. Best. Igneous and metamorphic 2003 Blackwell Science

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The differential partitioning of Mg and Fe among

the maﬁc phases vary over a range of P–T conditions

according to two exchange reactions

16.19 Fe

 KMg

AlSi

(OH)

almandine phlogopite

 Mg

 KFe

AlSi

(OH)

pyrope annite

16.20 Fe

 Mg

AlSi

AlO

(OH)

almandine Mg-chlorite

 Mg

 Fe

AlSi

AlO

(OH)

pyrope Fe-chlorite

In an exchange reaction, there is only an exchange of

substituting cations, in this case Fe and Mg, between

two phases, garnet and biotite or garnet and chlorite,

without any modiﬁcation in the modal proportions of

the phases. Because the same phases are involved in

these two exchange reactions they are not very sensitive

to P but the distribution coefﬁcient, K

, is strongly de-

pendent on T (Figure 16.11). Hence, the partitioning

of Fe and Mg between garnet and biotite provides a

useful mineral thermometer that is explored near the

end of this chapter in Section 16.11.2.

The divariance of the continuous reaction 16.18 is

readily seen in a T–X diagram (Figure 16.12), where

the similarity to continuous reaction relations and

incongruent melting in the plagioclase system is obvi-

ous (Section 5.5.2). In this pseudo-binary diagram (so

designated because more than two components are rep-

resented), the univariant, pure Fe end-member reaction

16.17 occurs at a speciﬁc T that is lower than that of the

Mg end-member reaction. This behavior is typical of

maﬁc metamorphic mineral systems. As the T of an

assemblage of quartz  muscovite  chlorite (X

0.3)

is raised in Figure 16.12 it begins to react at T  T

forming an Fe-rich biotite and a more Fe-rich garnet

(plus some water). With increasing T, progressively

more biotite and garnet are created and these product

phases, together with the reacting chlorite, become

more enriched in the Mg end-member. As in the sys-

tem of plagioclase crystals and melt, to maintain a mass

balance, the modal proportions of reactant and prod-

uct phases change (according to the lever rule) as they

become more magnesian with increasing T. Also, as in

the plagioclase system, two contrasting paths of product

crystallization are possible.

1. In the equilibrium crystallization path, every phase

remains homogeneous and maintains its equilib-

rium composition at every T during heating. As-

suming there are sufﬁcient muscovite and quartz

reactants, the reaction is complete when all of the

chlorite is entirely consumed and the ﬁnal products

are a relatively magnesian biotite and a more Fe-

rich garnet at T

(plus possible excess muscovite

and quartz).

2. In the fractional crystallization path, because of the

slow rates of diffusion in garnet, even up to mid-

grade temperatures, divalent cations cannot main-

tain equilibrium concentrations and proportions.

Metamorphic Mineral Reactions and Equilibria

487

Alm  Ann  H

Fe-Chl  Qtz  Ms

KFASH

Mg  Fe

Garnet  biotite  H

Prp  Phl  H

Mg-Chl  Qtz  Ms

KMASH

Grt  Bt

 Qtz  Ms

 ChlH

Chlorite  quartz

 muscovite

0.3 1



16.12 Schematic pseudobinary T–X diagram for the K

O–FeO–MgO–Al

–SiO

–H

O (KFMASH) system at some ﬁxed P showing reaction

loops for garnet, biotite, and chlorite. These loops enclose the divariant region where the six-phase assemblage of garnet  biotite 

quartz  muscovite  chlorite  water is stable. Mg/(Mg  Fe)  X

in maﬁc phases in the divariant assemblage varies as a function

of T. The assemblage garnet  biotite  water is stable above the garnet loop and chlorite  quartz  muscovite is stable below the

chlorite loop. End-member reactions in the pure Fe (KFASH) and Mg (KMASH) systems indicated on the sides of the diagram. Redrawn

from Spear (1993).

Consequently, garnets in all but the highest grades

of metamorphic rocks are typically zoned, in like

manner as plagioclases in magmatic rocks (as a re-

sult of the very slow rates of coupled diffusion of

SiAl). Fractional crystallization of garnet produced

by reaction 16.18 can be predicted to yield a zoning

in which Mg/(Mg  Fe) increases outward from

core to rim. Other garnet-producing reactions can

also create this same type of zoning (see Figure

16.34). Diffusivities of components in biotite and

chlorite are sufﬁciently fast so that their composi-

tions adjust continuously to changing temperatures

and result in growth of essentially homogeneous

grains.

The continuous reaction 16.18 can also be repre-

sented in an AFM diagram (Figure 16.13; these pro-

jections are described in Section 15.3.3). At a lower T,

a reference pelitic rock (ﬁlled circle) consists of biotite

 chlorite ( quartz  muscovite). As T increases,

the continuous sweep of the three-phase compatibility

triangle for garnet  biotite  chlorite toward more

magnesian and more stable compositions eclipses the

rock, causing production of garnet. At still higher T,

stable garnets become more magnesian, as do coexist-

ing biotites and chlorites.

16.6 SOLID–FLUID MINERAL REACTIONS

H, C, O—mainly in the form of H

O and CO

—and

lesser amounts of Cl, F, and S are essential constituents

in the atomic structures of crystalline phases in all

kinds of metamorphic rocks (Table 14.1). Reactions

liberating and consuming volatiles are the most com-

mon in metamorphic systems.

16.6.1 Fluids in the Crust of the Earth

Before moving onto metamorphic mineral reactions

involving volatile ﬂuids, it is appropriate here to put

crustal volatile ﬂuids into a global perspective.

The role of ﬂuids in the crust of the Earth and how

they interact with the overlying hydrosphere are far

from trivial, as expounded in the classic work of Fyfe

et al. (1978). Ramiﬁcations are many and profound.

The 65,000-km long system of oceanic spreading ridges

focuses advective circulation of cold seawater through

hot basaltic rock, recycling the entire mass of the

world’s oceans once every 5 My (Special Interest Box

11.3). Devolatilization of subducting, ﬂuid-rich oceanic

crust leads to generation of arc magmas in the over-

lying mantle wedge, with further contributions from

dehydration melting reactions in the deep contin-

ental crust. Fluid ﬂow in the continental crust is now

acknowledged to play fundamental roles in all kinds of

transfers of matter and heat, in metamorphic mineral

reactions, in creating ore deposits and geothermal

resources (Section 4.3.3 and Figure 4.12), and in rock

deformation (Section 8.2.1; see also Section 17.2.5).

The amount of water in the crust is impressive (Fyfe

et al., 1978). Because the average amount of water is

about 4% of the mass of the crust, which is 2.3 

g, then the mass of water lodged in the crust is

0.92  10

g. But this is the same order of magnitude

as the mass of water in the oceans, 1.4  10

Crustal ﬂuids are of three types and sources:

488 Igneous and Metamorphic Petrology

Grt

Cld

Chl

Grt

Cld

Increasing T

 Ms  Qtz  H

Chl

16.13 AFM projections (Section 15.3.3) projected from muscovite showing shift of the three-phase triangle representing compatible garnet 

chlorite  biotite toward more magnesian compositions with increasing T as a result of the continuous reaction 16.18. A reference pelitic

rock (ﬁlled circle) in the biotite zone at low T is eclipsed by the sweeping triangle, causing the appearance of garnet at higher T.

1. Water from the hydrosphere of the Earth that is

held in openings in rocks. In the continental crust,

cracks in rocks such as granite and pore spaces

between sediment grains hold meteoric (ground)

water, while in oceanic regions saline seawater re-

sides in fractured maﬁc rocks at spreading ridges

and in seaﬂoor sediment.

2. Metamorphic ﬂuids produced by devolatilizing

metamorphic reactions.

3. Magmatic ﬂuids exsolved from evolving magmas

(Section 4.2.3). Common arc magmas of intermedi-

ate to silicic composition crystallizing biotite and

hornblende must have water concentrations of at

least 3–4 wt.% in order to stabilize these hydrous

phases. However, modal amounts of these hydrous

minerals are typically 30%; with 1–2 wt.% water

in hornblendes and 2–3 wt.% in biotites the excess

water in the magma system can be released into the

surroundings during crystallization.

Mixing from the three sources is likely in many crustal

ﬂuids. Oxygen isotope ratios (Section 2.6 and Figure

2.24) can indicate dominant contributions.

During burial and compaction of marine sediment-

ary deposits along continental margins and in subduc-

tion zones, enormous volumes of entrapped aqueous

ﬂuid are liberated. Sediments and loosely cemented

sedimentary rocks can have pore spaces occupying as

much as one-third the total rock volume to depths of

hundreds of feet but after burial to 5 km or so, 2

wt.% water remains in increasingly more isolated and

smaller pore spaces or perhaps as an intergranular ﬂuid

along grain edges. In addition to compaction, pore vol-

ume diminishes as a consequence of recrystallization,

including grain boundary adjustments during pressure

solution (see Section 17.2.1), and precipitation of ce-

menting minerals from pore solutions. In rock bodies

with interconnecting openings (permeability) extend-

ing all the way to the surface, buoyant water will ﬂow

upwards out of the body, commonly venting in springs.

After physical release of entrapped pore ﬂuid, mostly

water, 5–10 wt.% H

O bound structurally in protolith

minerals can be driven out of rocks with rising T during

prograde dehydration reactions. These aqueous meta-

morphic ﬂuids are released over virtually the whole

range of metamorphic conditions from widespread

hydrous solid solutions undergoing continuous break-

down (Figure 16.14; compare Table 14.2). In pelitic

rocks, for example, the generalized prograde reaction

sequence of clay minerals → chlorites → micas → an-

hydrous silicates consists entirely of solid solutions.

Walther and Orville (1982) calculated that the expelled

water (and smaller amounts of CO

) during devolatiliza-

tion of an average shale could instantaneously occupy

about 12% of the rock volume at 500°C and 5 kbar. To

put this in perspective, if all of the expelled water from

a 1000 km

block of dehydrated shale were to be col-

lected into a 100 km

lake it would be 1.25 km deep!

A similar situation prevails for metamorphism of

hydrous maﬁc rocks, where again, upwards of 5 wt.%

water can be liberated (Figure 16.14d). In the less

widespread calc–silicate rocks, decarbonation reactions

can potentially liberate vast amounts of CO

. On a

weight basis, there is 44 and 47% CO

in pure calcite

and dolomite, respectively. Most decarbonation reac-

tions are continuous over a range of P–T conditions

and the amount of liberated CO

depends on the ﬂuid

composition and proportions of silicate- and carbonate-

bearing phases, as will be appreciated later. At lowest

metamorphic grades, methane (CH

) may also be ex-

pelled by reactions involving carbonaceous material in

shale and carbonate rock protoliths (Special Interest

Box 16.2).

Clearly, the amount of ﬂuid in a metamorphic system

varies through time (Rubie, 1986). This is especially

true of polymetamorphic rocks. At a given depth and

P, the amount of ﬂuid and its associated ﬂuid pressure,

ﬂuid

, is likely to change during the course of metamor-

phism. This means that P

ﬂuid

does not always equal P,

as commonly assumed.

Virtually the only tangible, separate ﬂuid phase re-

maining from metamorphic reactions in rocks collected

at the surface occurs as minute volumes entrapped in

ﬂuid inclusions (Special Interest Box 16.3).

Metamorphic Mineral Reactions and Equilibria

489

Special Interest Box 16.2 Bleaching of

carbonate rocks around magmatic intrusions

In many contact metamorphic aureoles around

granitic intrusions, the most conspicuous change is

a bleaching of limestone or dolomite country rocks

whose original gray color is a result of very small

amounts of ﬁne carbonaceous matter. The progres-

sive whitening of the protolith toward the magmatic

contact is generally not regular and concentric, but

is strongly inﬂuenced by bedding. Some relict beds

are more bleached than adjacent ones at the same

distance from the contact, suggesting a control re-

lated to bedding characterisitics such as permeabil-

ity rather than simple conductive heating. For the

Notch Peak aureole in western Utah, Todd (1990)

concluded that the bleaching agent was inﬁltrated

water that reacted with carbonaceous matter (mod-

eled as graphite, C) producing methane and carbon

dioxide according to 2C  2H

O  CH

 CO

The water-rich ﬂuids cannot have come from

devolatilization reactions in the protolith because

they would have been CO

-rich. Isotopic data indic-

ate the inﬁltrating water that reacted with the rock

was of magmatic origin, not heated meteoric water.

Under most metamorphic conditions, above those

appropriate to the lower greenschist facies, mixtures

of CO

and H

O are completely miscible and form

a homogeneous supercritical ﬂuid (Section 4.2.1).

However, dissolved salts (NaCl, KCl, and so on) ex-

tend a miscibility gap prevailing at low temperatures

to higher metamorphic temperatures (Labotka, 1991).

Immiscibility complicates phase equilibria but will be

ignored in this chapter. At high T and low P, say,

600°C and 2 kbar, CO

and H

O mix almost

ideally so that the proportion of one volatile component

in a mixture of the two can generally be represented

by its mole fraction, X (Section 3.5.1). Thus, under

ideal conditions for H

O in a ﬂuid, X  P /P

ﬂuidH

490 Igneous and Metamorphic Petrology

P (kbar)

Depth (km)

(a)

0 400200 600 800 1000

T (°C)

Sil

30°C/km

Prl



Wt. % H

01020

Depth (km)

Rock Fluid

2Ky  6Qtz

2Sil  6Qtz

Kln  4Qtz

Prl

T (°C)

200

400

(b)



Wt. % H

(c)

01020

1000

Depth (km)

200 400 600

T (°C)

Pelitic

rock

Clays

Chlorite–mica

Mica–garnet

Staurolite–garnet-mica

Sillimanite–K-feldspar

Migmatite

Partial

melts

Fluid

Wt. % H

(d)

0 102030

1000

Depth (km)

200 400 600

T (°C)

Maﬁc

rock

Partial

melts

Fluid

Zeolites

Prehnite–pumpellyite

Chlorite–epidote–

actinolite–albite

Hornblende–plagioclase

Hornblende–plagioclase–

pyroxene

Pyroxene–plagioclase

16.14 Water-release curves for hydrous mineral assemblages subjected to prograde dehydration reactions. Redrawn from Fyfe et al. (1978).

(a) Stability ﬁelds and univariant breakdown curves for some low-grade hydrous aluminosilicates. Note the metastability of andalusite

and kyanite at temperatures below about 400°C where kaolinite and pyrophyllite are more stable in systems that contain sufﬁcient

water (a

water

 1). (b) Steplike ﬂuid-release line (heavy line) for a model pelitic rock that consists of kaolinite  4 quartz along a 30°C/km

geotherm from (a). This assemblage contains 9.5 wt.% water bound structurally in kaolinite. At a depth of about 12 km, T reaches

370°C where this assemblage reacts to produce pyrophyllite  2H

O. On a wt.% basis this liberated water is 4.5 wt.%; 5 wt.%

remains structurally bound in pyrophyllite. With increasing T, pyrophyllite breaks down at 425°C to 2 kyanite  6 quartz  4 H

All of the water has now been released from solid phases. At 550°C, kyanite should convert to sillimanite. Because kaolinite and

pyrophyllite are here considered to be pure phases with no solid solution, release of water occurs sharply at their univariant dehydration

curves. (c) Generalized ﬂuid-release curve for a shale along a 30°C/km geotherm. Water release is continuous with increasing P and T

because of the complex crystalline solid solutions constituting pelitic rocks that progressively break down by continuous reactions.

Changes in slope of the release curve are related to beginning and completion of dehydration of major hydrous silicates. Depending upon

the exact composition of the system, especially the remaining water concentration, partial melting may begin somewhere near 700°C to

form migmatite. (d) Generalized ﬂuid-release curve for maﬁc rock along a 30°C/km geotherm, assuming rock is initially dry and then hy-

drates to a zeolite facies assemblage with 5 wt.% water. (On the seaﬂoor palagonitization could produce a more hydrous rock at lower

T.) Note temperatures for partial melting and migmatite formation.

 P /(P  P ), where P and P are

partial pressures. At lower T and higher P, volatile

mixtures are nonideal. For thermodynamic calculations,

this nonideality requires use of ﬂuid activities or fugac-

ities (Spear, 1993, p. 228).

Among natural ﬂuids, water has unusually high

solvent capacity, especially for ionic compounds such

as NaCl, because of the strongly polar nature of its

molecule and lone-pair electrons (e.g. Brimhall and

Crerar, 1987).

The separate volatile phase in metamorphic systems

has been referred to as a vapor, gas, liquid, ﬂuid, and

supercritical ﬂuid. However, because of the low P and

T of the critical points of H

O and CO

, above which

there is no sharp distinction between gas (vapor) and

liquid, a separate phase of these volatiles can simply

be called a ﬂuid (Section 4.2.1). In most metamorphic

systems the density, or speciﬁc volume, of the ﬂuid

varies continuously as a function of T and P. But as

both increase with increasing depth, the ﬂuid expan-

sion resulting from increasing T is nearly compensated

by compression from increasing P. For example, along

a geothermal gradient of 15°C/km to a depth of 35 km

the speciﬁc volume of water deviates only slightly

from its familiar value at atmospheric conditions of

1.0 cm

/g (Figure 4.3). For carbon dioxide along the

same geotherm the speciﬁc volume ranges between

about 0.8 and 1.2 cm

/g (Spear, 1993, p. 229).

16.6.2 Fundamental Concepts of Solid–Fluid Reactions

The general form of a prograde, volatile-liberating re-

action is

16.21 Heat  volatile-bearing crystalline phase

→ volatile-poor (or -free) crystalline phase

 volatile ﬂuid

Hence, most devolatilization reactions are endothermic;

they consume heat, “dry out” mineral assemblages, and

moderate otherwise rising temperatures during meta-

morphic heating. In the reverse sense, hydration and

carbonation reactions are exothermic. Conversion of

volatile-free rocks, such as dry basalt, into volatile-

bearing greenschist or zeolite facies assemblages pro-

duces heat; temperatures can increase several tens of

degrees if all the heat in the rock is conserved. Provid-

ing CO

and H

O are continuously available, exother-

mic reactions might be thermally self-accelerating and

cause an initially volatile-free magmatic protolith to

move rapidly through the lowest metamorphic grades.

Entropy–Molar Volume Relations. Under most meta-

morphic conditions, a volatile phase has a large molar

entropy compared to the partial molar entropy of the

same volatile structurally bound in a hydrous silicate or

carbonate mineral. Consequently, the separate volatile

OCO

Metamorphic Mineral Reactions and Equilibria

491

Special Interest Box 16.3 Fluid inclusions

Metamorphic minerals, typically quartz, commonly

contain minute ﬂuid inclusions (Crawford and

Hollister, 1986). They originate as more or less

randomly distributed pockets of ﬂuid entrapped

during growth of the host grain (primary inclu-

sions) or as healed ﬂuid-ﬁlled microcracks formed

after the host grain crystallized (secondary inclu-

sions; Figure 16.25). Inclusions are generally

0.03–0.05 mm in diameter but larger ones can

be found in veins formed from ﬂuid precipitates

in rock fractures. Vein quartz in metamorphic

terranes is typically snow-white because of an

estimated 10

ﬂuid inclusions per cm

(Roedder,

1984, p. 2). Inclusions can provide important

insights into the composition of the ﬂuid present

when the host mineral grain formed and P–T con-

ditions of crystallization.

In addition to a homogeneous ﬂuid, or locally

two immiscible ﬂuids, inclusions also may contain

a bubble of low-density vapor and one or more

crystalline daughter phases (usually halite, but also

sylvite, calcite, and various ﬂuorides) that appar-

ently precipitated as the ﬂuid cooled from high

temperatures.

Laser-excited Raman microspectroscopy dis-

criminates among ﬂuids of SO

, CH

, CO

, and

O within inclusions. More indirect information

is provided by observations on a heating–freezing

stage. Pure H

O ﬂuid freezes at 0°C but dissolved

salts depress the freezing T, to as much as 23°C

at the NaCl–H

O eutectic. Identiﬁable daughter

crystal may help constrain the ﬂuid composition.

Pure CO

freezes at 56.6°C, but mixed with H

raises the freezing T towards 0°C while mixtures

with CH

(methane) lower it towards about

184°C.

Distinguishing inclusions formed during pro-

grade and particularly peak metamorphic condi-

tions from secondary inclusions formed during

cracking accompanying uplift and cooling of a

metamorphic terrane is not easy. Moreover, inclu-

sions can be perturbed in many ways after initial

entrapment, such as by leakage and reaction with

the host crystal. Caution must, therefore, be taken

in the interpretation of P–T–X data based on ﬂuid

inclusions.

Inclusion studies reveal that ﬂuids in low-grade

metamorphic rocks are dominantly methane, pre-

sumably derived from carbonaceous material,

those in lower greenschist- to middle amphibolite-

facies rocks ﬂuids are essentially aqueous, while in

granulite-facies rocks CO

dominates (Spear, 1993,

p. 669).

ﬂuid phase is almost always on the higher T side of the

reaction because for that assemblage to be stabilized

with lower free energy, there must be a positive T and

a positive S so that G (ST) is negative.

All mineral equilibria involving a volatile phase are

governed by the volatile partial pressure, P

volatile

, as

well as P and T. In systems where P

volatile

 P, the equi-

librium pressure increases with increasing T so that the

reaction line in P–T space has a positive slope (Figure

16.15; see also Figure 5.31). Unlike the straight or

nearly straight equilibrium line for solid-solid reactions

(Figure 16.4), the univariant equilibrium line in P–T

space for solid-ﬂuid net-transfer reactions (16.21) is

markedly curved. The changing slope is governed by

the relative magnitude of changes in molar volume and

entropy expressed in the Clapeyron equation, dP/dT 

S/V. In metamorphic systems where P  2–3 kbars

but T is high, as in contact aureoles around shallow

crustal magmatic intrusions, the univariant reaction

curve typically has a low positive slope. Relative to the

S of the reaction, V is large because molar volumes

of volatile phases are large (see Figure 4.3 for water).

But as V for reaction 16.21 diminishes with increas-

ing P because of the greater compressibility of ﬂuids

than solids (Section 8.3.1), the slope of the reaction

curve steepens. Steep devolatilization reaction curves

that typify many regional metamorphic systems indic-

ate a stronger dependency on T than on P. Ultimately,

increasing P may sufﬁciently compress the ﬂuid so that

V  0. As S is still positive, the reaction curve bends

back on itself with negative dP/dT slope. Depending

on the speciﬁc reaction, this bendback can occur in the

continental crust or the upper mantle.

Coupled Reactions. Like solid–solid reactions (Figure

16.4), the maximum thermal stability of a volatile-bearing

mineral is always that of the mineral alone. In the

presence of other reactable phases the stability ﬁeld

shrinks. An important example of this concept is found

in the stability of calcite. Pure calcite breaks down

according to the reaction

16.22 CaCO

 CaO  CO

calcite lime

at temperatures in excess of 1200°C, which is almost

invariably greater than that attained during meta-

morphism. Hence, calcite alone, as in pure marbles, is

stable throughout the realm of metamorphism and lime

does not occur naturally as a mineral. However, calcite

commonly coexists with quartz in sandy limestones,

allowing the coupled reaction (Figure 16.16)

16.23 CaCO

 SiO

 CaSiO

 CO

calcite quartz wollastonite

The free energy change at, say, 600°C and 1 atm for

this reaction is 54,000 J/mol in contrast to 33,000

J/mol for reaction 16.22, the breakdown of pure calcite

(Robie and Hemingway, 1995). Hence, wollastonite 

is stable at 600°C, whereas lime  CO

is not. The

coupled reaction with quartz substantially lowers the T

of the breakdown of calcite. In the presence of another

phase, such as rutile, in addition to quartz, calcite

breaks down at still lower T.

Similar depression of the T of a dehydration reac-

tion occurs in the presence of an additional phase in

silicate systems, such as where quartz can react in

coupled manner with muscovite (Figure 14.31).

Equilibria Where P

volatile

 P. In systems where the

volatile partial pressure is less than the conﬁning P the

equilibria can also be shifted to lower T. This follows

from Le Chatelier’s principle: A reduction, at some

ﬁxed P and T, in the amount of water in, for example,

the muscovite  quartz  K-feldspar  Al

SiO



O equilibrium causes a shift to the right to produce

492 Igneous and Metamorphic Petrology

Volatile-poor or

volatile-free

mineral assemblage



volatile ﬂuid

∆V  0

∆V  0

∆V  0

Volatile-bearing

mineral

assemblage

16.15 Idealized univariant devolatilization curve for reaction 16.21.

P  P

ﬂuid

 P

(kbar)

Calcite  quartz

 rutile 

titanite  CO

200 400 600 800 1000

T (°C)



16.16 Univariant decarbonation curves for calcite-bearing assem-

blages where the ﬂuid is pure CO

(X  1) and P

ﬂuid

 P.

Redrawn from Greenwood (1976).

more water ( K-feldspar  Al

SiO

) to compensate

for the reduction. Consequently, the univariant equilib-

rium line in P–T space shifts to lower temperatures

(Figure 14.31).

Situations where P

volatile

 P can arise in two ways.

First, there may be little or no separate water phase

in the rock—it is “dried out.” Second, the total ﬂuid

pressure may be the same as the conﬁning pressure

ﬂuid

 P) but because of the presence of an additional

volatile, such as CO

, the partial pressure of water,

P , is reduced. P

ﬂuid

 P  P . In terms of con-

centration, there is a dilution of water by the additional

volatile. In terms of the activity, a  1. This situation

might arise where CO

liberated from decarbonation

reactions in nearby calc–silicate rocks invades pelites

undergoing dehydration reactions. These mixed-volatile

ﬂuids are of paramount signiﬁcance in metamorphic

reactions, warranting the following section.

16.6.3 Equilibria with Mixed-Volatile Fluids

The fact that wollastonite is common in contact meta-

morphosed sandy limestones near magmatic intrusions

but is rare in similar protoliths in regional terranes

could be explained by the stabilization of wollastonite

at the lower pressures (Figure 16.16) that prevail in

many contact metamorphic aureoles. However, it turns

out that there is another explanation that also has a

bearing on paradoxes in devolatilization reactions

noted by early workers (Special Interest Box 16.4). It

turns out that the composition of the volatile ﬂuid is

an explicit governing variable in mineral equilibria, in

addition to P and T. Fundamental concepts regarding

the inﬂuence of ﬂuid composition in mixed-volatile

ﬂuid equilibria were established by H. J. Greenwood

(see 1976). Kerrick (1974) and Spear (1993) also review

the thermodynamics.

Although calc–silicate rocks are not as widespread

in metamorphic terranes as maﬁc and pelitic rocks,

mixed-ﬂuid mineral reactions in them provide signiﬁc-

ant insights into the advective ﬂow of volatile ﬂuids

during metamorphism and serve as monitors of the

volume of transported ﬂuid.

Calcite–Quartz–Wollastonite Equilibria. In a closed

CaO–SiO

–CO

system consisting of the univariant as-

semblage calcite  quartz  wollastonite the equilib-

rium CO

pressure increases as T increases, creating a

positively sloping reaction curve. If for any reason the

amount of CO

is perturbed to be less than this equi-

librium value at a particular T, in other words, P

 P

ﬂuid

or X  1, more calcite will tend to liberate

by reacting with quartz, shifting the equilibria in

favor of wollastonite. Accordingly, the univariant reac-

tion curve is shifted to lower temperatures in Figure

16.17a. Hence, as a general rule, where the partial pres-

sure or mole fraction of a particular volatile species is

 P

ﬂuid

or  1, respectively, in a mixed-volatile ﬂuid

phase the stability ﬁeld of a phase that contains the

volatile shrinks to lower T.

An alternative way of viewing such equilibria stems

from the concept of a perfectly mobile component.

This is an ideal ﬂuid, including possible dissolved ions,

such as Na



and Cl



, that can move freely into and out

of an open rock as a result of its high permeability. Any

reaction requiring the perfectly mobile components

can be freely accomplished. The thermodynamic prop-

erties of these mobile components, such as their chem-

ical potentials, , are determined in some unlimited

reservoir external to the rock. In the inventory of com-

ponents in the rock system, mobile components are

Metamorphic Mineral Reactions and Equilibria

493

Special Interest Box 16.4 N. L. Bowen,

pioneer metamorphic petrologist

Special Interest Box 5.1 indicated that N. L. Bowen

is generally considered to be the founder of modern

igneous petrology. Although his work in metamor-

phic petrology was much more limited, consisting

of essentially only two journal articles, in one of

these Bowen (1940) laid some of the groundwork

for modern metamorphic petrology. A product of

his brief tenure at the University of Chicago, this

one article was written “with the purpose of pre-

senting to students as a logical whole, with a con-

necting thread of fundamental law, a subject that

otherwise is bare” (p. 227). With typical thorough-

ness and clarity, Bowen not only described the

nature of mineral assemblages produced by pro-

grade metamorphism of calc–silicate rocks but in so

doing established the use of the now-standard (1)

graphical techniques for depiction of mineral assem-

blages and bulk rock compositions in triangular

diagrams and (2) petrogenetic grids wherein phase

assemblages are linked to intensive variables (P and

T). Bowen also recognized a conundrum in the

metamorphism of siliceous dolostones. In some

metamorphic terranes periclase appears at an appar-

ent lower grade than wollastonite, whereas in

others the appearances are reversed. He also noted

that dolomite  quartz in sandy dolomite rocks

should react to tremolite  calcite but subsequent

petrologists found that the products of this reaction

are talc  calcite or diopside (Ferry, 1994). These

inconsistencies were resolved in the late 1960s and

1970s as experimental work and thermodynamic

calculations (see Greenwood, 1976) revealed that

mineral equilibria are governed by the composition

of C–O–H ﬂuids, in addition to P and T that were

deemed the sole relevant intensive variables by

Bowen.

ignored. In a system of CaO and SiO

where CO

is a

perfectly mobile component, equilibria are dictated by

the univariant line labeled X  1 in Figure 16.17a.

However, if CO

is not perfectly mobile and its amount

in a rock is restricted then during a retrograde process

of decreasing T from, say, 800°C and 1 kbar, there may

be insufﬁcient CO

to react with all of the wollastonite

in the rock below this univariant line; that is, the excess

wollastonite remains stable at declining temperatures,

together with some calcite and quartz. As a general

rule, then, in a system where there is insufﬁcient of a

volatile to react with some volatile-free solid phase, the

unreacted excess of that solid remains stable into the

P–T ﬁeld where the volatile-bearing product assemblage

would otherwise be stable. Implications for widespread

anhydrous magmatic rock protoliths undergoing meta-

morphism under water-deﬁcient conditions should be

clear.

In systems involving a volatile ﬂuid phase, such as

, equation 16.3 takes the form

16.24 

where the V

term refers only to the solid phases in an

equilibria. f is the fugacity of CO

(Section 3.5.1)

and the last term in the expression takes into account

the contribution of the ﬂuid phase to changes in free

energy. Philpotts (1990, p. 335) discusses application of

this expression to calcite–quartz–wollastonite equilib-

ria and indicates how f can be related to the mole

fraction X in Figure 16.17a.

The dependence of the calcite–quartz–wollastonite

equilibria on ﬂuid composition (X or X ) and T

at ﬁxed P  1 kbar is shown in Figure 16.17b. The

maximum thermal stability of calcite ( quartz) occurs

in systems in which the ﬂuid is pure CO

, providing an

optimum condition where the volatile can be lodged in

calcite. At low X where the ﬂuid is practically pure

water, calcite is stable only at relatively low tempera-

tures. Because carbonates are not stable in systems

where X  0, the equilibrium curve never reaches

this value, only becomes asymptotic to it.

Other Mixed-Volatile Reactions. A generalized mixed-

volatile reaction can be written as

16.25 A  B 

where A and B are solid phases and n and n are

the amounts, or stoichiometric coefﬁcients, of H

and CO

. These coefﬁcients are positive if they are on

the right-hand side of the reaction as products or neg-

ative if they are on the left-hand side as reactants. n

and n can have opposite sign.

Six types of reactions based on reaction 16.25 are

listed below as prograde reactions with increasing T

and entropy. Corresponding univariant reaction curves

are shown in T–X

ﬂuid

space in Figure 16.18.

1. Solid–solid reaction, such as grossular  quartz 

wollastonite  anorthite (compare Figure 16.4).

Because none of the solid phases contain volatiles,

the equilibrium T is not governed by ﬂuid composi-

tion and the univariant reaction line is a straight

isotherm.

2. Decarbonation reaction, such as calcite  quartz 

wollastonite  CO

(reaction 16.23 and Figure

16.17). The equilibrium T for the reaction is high-

est where X  1 and decreases as the ﬂuid in the

system is diluted by increasing H

3. Dehydration reaction, such as muscovite  quartz

 alkali feldspar  Al

SiO

 H

O (reaction 14.1

and Figure 14.31). The equilibrium T for the reac-

tion is highest where X  1 and decreases as the

ﬂuid in the system is diluted by increasing CO

This is a mirror image of type 2.

4. Reaction liberates both H

O and CO

, such as

tremolite  3 calcite  2 quartz  5 diopside 

O  n

OCO

ref

V

 P

ref

)  RT ln

ref

494 Igneous and Metamorphic Petrology

1.0

0.8

0.6

0.4

0.2

0.0

(b)

(a)

0.0

0.2

0.4

0.6

0.8

1.0

400200 600 800

T (°C)

ﬂuid

(kbar)

Calcite

 quartz

 ﬂuid

Calcite

 quartz

 ﬂuid

ﬂuid

 1 kbar



1 atm)



1 0

~0 0

0 13

0 5

Wollastonite

 ﬂuid

Wollastonite

 ﬂuid

200 400 600 800 1000

T (°C)

16.17 Univariant decarbonation curves for reaction 16.23 as a func-

tion of composition of the ﬂuid. Compare Figure 16.16.

Dotted lines show correspondence between speciﬁc values

of T, P, and composition in the two diagrams. (a) P

ﬂuid



P  P and X  X  1. (b) Reaction curve in

T–X (X ) space at P

ﬂuid

 1 kbar. The four data points

deﬁning the curve are taken from (a). From experimental

work of H. J. Greenwood.

OCO

O  3CO

. The univariant reaction curve has a

maximum T at a ﬂuid composition equivalent to

that liberated in the reaction (one mole of H

for every 3 moles of CO

) and diminishes in T

for increasing concentrations of H

O and CO

The peak T lies at X  n /(n  n ) 

3/(1  3)  0.75. The curve cannot intersect either

the pure CO

axis or H

O axis because that would

mean that a hydrous mineral is stable in a pure CO

ﬂuid and vice versa, which is impossible.

OCO

5. Reaction consumes CO

and liberates H

O, such

as 2 zoisite  CO

 3 anorthite  calcite  H

6. Reaction consumes H

O and liberates CO

, such as

6 dolomite  8 quartz  2 H

O  talc  6 calcite

 6 CO

Reaction curves 5 and 6 are mirror images of one

another and both have substantially decreasing tem-

peratures as the concentration of the product volatile is

decreased and the reactant volatile increased. In another

sense, the T of reaction is decreased if the ambient ﬂuid

in the rock differs from that given off by the reaction.

16.6.4 Local versus External Control of Fluid

Composition during Devolatilization Reactions

The CO

O ratio in pore ﬂuids can vary in space

and time during the course of metamorphism depend-

ing upon the mobility and amount of the ﬂuid, rock

permeability, the nature of reactions, especially their kin-

etic rates, and the assemblage of reacting solid phases.

This variability introduces additional complexity into

mixed-volatile reactions as just described. Two ideal

end-member processes can be envisaged—closed ver-

sus open system behavior. These can also be described

as locally internally buffered versus externally controlled

inﬁltration reactions. These contrasting processes are

described using as a model the isobaric univariant re-

action curve in Figure 16.19 for tremolite  3 calcite 

2 quartz  5 diopside  H

O  3CO

. The three re-

actant phases are found in some low-grade calc–silicate

rocks.

Internally Buffered Devolatilization Reactions. In a

closed rock system suppose there is only a very small

amount of an ambient ﬂuid possibly entrapped in iso-

lated pore spaces and whose composition is X 

X  0.5. Because permeability is nil and essentially

no ﬂuid leaves or enters, the ﬂuid is not perfectly

mobile. As the rock is heated from, say, 400°C in Fig-

ure 16.19a nothing happens until the vertical isopleth

intersects the univariant curve at about 525°C. Here,

or actually overstepping this equilibrium value by some

amount to promote the reaction, diopside begins to

crystallize by reaction between tremolite, calcite and

quartz. As T continues to rise, the closed system is con-

strained to move along the univariant curve so long as

these four solids coexist and because the composition

of the liberated ﬂuid becomes more enriched in CO

;

three times as much of it is evolved from the reaction

as is H

O, easily changing the composition of the small

volume of initial ambient ﬂuid. In this isobaric univari-

ant equilibrium, the four stably coexisting solids in

concert with the one independent variable of T buffers

the ﬂuid composition. Should one or more of the reac-

tant phases—tremolite, calcite and quartz—be entirely

consumed at any T, the rock system will leave the

curve, lose its buffering capability, and resume a vertical

Metamorphic Mineral Reactions and Equilibria

495

T (°C)

800

700

600

500

400

0.0 0.2 0.4 0.6 0.8 1.0

1.0

(a)

P  2 kbar

(b)

0.8 0.6 0.4 0.2 0.0



2Wo  An

Grs  Qtz

16.18 Petrogenetic grid showing univariant curves for select mixed-

volatile ﬂuid reactions in T–X (X ) space. Note the

change in coordinate axes from Figure 16.17b so that here, by

convention, the T is represented on the y-axis and X on the

x-axis. The Cal  Qtz  Wo  CO

curve is common to both

and can be compared in the two ﬁgures. Each univariant

reaction curve is drawn for its own unique compositional

system. Fluid is pure water on the left-hand vertical axis and

pure CO

on the right-hand axis. Curves are schematic in (b).

Redrawn from Kerrick (1974) and Blatt and Tracy (1996).

OCO

trajectory. However, if none of the reactant phases is

completely consumed the prograding buffered system

produces more diopside and a changing ﬂuid composi-

tion that is ever richer in CO

via continuous reactions

that consume the reactants. Eventually the system may

reach the maximum T on the univariant curve at about

540°C where the ﬂuid composition is X  0.75,

the exact ratio of the ﬂuid liberated from the reaction

(3CO

: 1H

O). Additional input of heat into the sys-

tem cannot raise its T until one or more of the reactant

phases has been consumed. (This behavior is reminis-

cent of peritectic behavior in the Mg

SiO

–SiO

sys-

tem in Figure 5.8.) Once this happens, a heating system

can leave the curve and its T continue to rise.

Mixed-volatile reactions during metamorphism of

calc-silicate and impure carbonate rocks can be mon-

itored by a reaction progress variable, , that provides

quantitative information on changes in the modal and

bulk chemical composition of the rock and its volume

as well as the compositions and amounts of evolved

ﬂuids and thermal budget (Advanced Topic Box 16.5).

Even with large changes in T and ﬂuid composition

496 Igneous and Metamorphic Petrology

T (°C) T (°C)

525

400

500

(b) INFILTRATION

IN OPEN SYSTEM

INTERNALLY BUFFERED

CLOSED SYSTEM

540

710

0.0 0.2 0.3 0.4 0.6

0.8 1.0

 0.75(a)



16.19 Contrasting metamorphism of siliceous dolostone under

closed- and open-system conditions in the presence of a

mixed-volatile ﬂuid based on two reaction curves from Figure

16.18a. See text for discussion.

Advanced Topic Box 16.5 Evaluation of the

progress variable during metamorphism of

impure carbonate rocks

The progress variable, , quantiﬁes changes in modal

mineral and ﬂuid composition of a rock system during

mixed-volatile metamorphism (Ferry, 1983; Spear,

1993, pp. 459–66 and 678–81). There are two basic

equations based on mass balance considerations:

where 

is the stoichiometric coefﬁcient of species

in the reaction and n is the number of moles

of species i that is produced (positive 

) or con-

sumed (negative 

) and

Two examples show the use of the progress variable.

Consider internal buffering in the 5 kbar reac-

tion (Figure 16.24c)

5 dolomite  8 quartz  H

 tremolite  3 calcite  7CO

starting at 400°C with an initial ﬂuid composition

of X  0.4 and the ﬁnal ﬂuid composition at the

invariant point at 625°C of X  0.95. In this

5 kbar reaction, the stoichiometric coefﬁcients

of H

O and CO

are v 1 and v  7.

Hence, the second basic equation above becomes

To evaluate n it is set equal to (porosity 

volume of rock)/molar volume of ﬂuid. Assum-

ing a liberal porosity of 1% and molar volume

of the ﬂuid from Spear (1993, Figure 7.21) of

28.2 cm

/mol, n  0.0355/100 cm

of rock so

that 0.423  0.0355  0.015 moles (per 100 cm

of rock). The change in the molar abundances of

phases during the course of the reaction is

Cal

 33  0.015  0.045 moles per

100 cm

of rock

n  70.105 moles per 100 cm

of rock

n 10.015 moles per 100 cm

of rock

These molar abundances can be converted into

volumetric changes, as follows (using again Spear,

1993, Figure 7.21 for the volatiles):

V

Cal

 0.045 moles  36.934 cm

/mole

 1.66 cm

per 100 cm

of rock

total



total

(0.95  0.40)

0.95(–1)  0.057

 0.423n

total



total

 X

)



 X



)













 . . .

