Myron G. Best. Igneous and metamorphic 2003 Blackwell Science

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Metamorphic Mineral Reactions and Equilibria

507

Relict chert nodule

Qtz  Tr

Tremolite

 Cal  Dol

02cm

16.28 Diffusion-controlled metamorphism of a chert nodule in dolo-

stone host, Alta contact aureole, Utah. Sample collected about

1 km inside the tremolite zone. Outline of relict nodule may be

marked by (inert?) particles of black Fe-oxides inside the zone

of ﬁne-grained quartz  tremolite. Outside this zone is a thick

rind of calcite and dolomite with coarse tremolite columns

oriented perpendicular to the rind boundary. Beyond this rind

(not in sample) is the metamorphosed siliceous dolostone host

rock now made of calcite  dolomite  tremolite.

Jasperoid

100

0 40 80 120 160 200

Dolomitic shale protolith

MASS

LOST

CONSTANT MASS

ISO CON

ADDED

800Na

10 Ag

10Fe

1000MnO

15MgO

300TiO

15CaO

100S

10Al

1000P

30K

SiO

16.29 Comparison of whole-rock chemical compositions of dolomitic shale protolith and metasomatic jasperoid, Golden Butte ore deposit,

east-central Nevada. Concentrations of major elements are plotted as oxide wt. percentages and trace elements in ppm. Several concen-

trations have been adjusted by a multiplication factor so as to avoid overlaps and spread the plotted points farther apart from one

another; thus, the concentration of TiO

in the protolith and jasperoid have both been multiplied by 300, Sb multiplied by 1/50, and

so on. The scatter of points for relatively immobile constituents (Nb, MnO, Fe

, V, Al

, Zr, and TiO

) along the isocon reﬂects

analytical errors and the fact that they are averages of several analyzed samples. Data from Wilson (1991).

what frame of reference can be used to tell which com-

ponents were added and which ones were lost during

metasomatism?

Comparison of tabulated bulk chemical composi-

tions of the metasomatic rock and its putative protolith

is generally misleading because of the way in which

analyses are presented—as wt.% in a 100 g sample

with all oxides totaling 100%. Suppose, for example,

that CaO, MgO, Na

O, and FeO all have greater weight

percentages in the altered rock than the protolith. It

might be concluded that these constituents were added

during the metamsomatism with compensating losses

in other oxides (SiO

, Al

, K

O, and so on). How-

ever, this is only one possibility. CaO, MgO, Na

and FeO might have simply remained immobile in the

protolith during alteration while other oxides (SiO

and K

O) were leached out of the rock, resulting in

an overall loss of rock mass but an apparent increase in

the weight percentages of the immobile constituents.

There are several other possible scenarios; all result

from the “closure problem” inherent in dealing with

the percentages of things that sum to 100%.

One way to get around this closure obstacle is with

the isocon diagram conceived by Grant (1986) and

based on equations of R. L. Gresens. Figure 16.29 is

such a diagram in which concentrations of constitu-

tents in a metasomatic jasperoid (Section 15.2.8) are

plotted versus those in the probable dolomitic shale

protolith. A straight “isocon line” is drawn from the

origin in a best-ﬁt manner through data points for

constituents that are normally immobile in ﬂuid-rich

systems, including TiO

, Al

, MnO, and Zr. In

other words, it is a line of “equal geochemical con-

centration” that connects points of constituents whose

concentrations relative to one another remained

unchanged during the alteration process. But these

immobile elements were diluted during the process

because they lie below a line of constant mass whose

slope is 1. This constant mass line is the locus of points

for which constituents remained unchanged during a

hypothetical isochemical metamorphism where the

ﬁnal and initial rocks are identical in composition.

Points plotting above the constant mass line represent

constituents that were added during alteration. Silica

was added so its concentration increased from 60.5

wt.% in the protolith to 94.6 wt.% in the jasperoid.

The greatest relative increase is in Sb, from 0.1 to 42.8

ppm. Au went from 0.025 to 1.5 ppm and Ag from 1.13

to 12.4 ppm in this low-grade ore deposit. These

increases were compensated by a loss in CaO plus

MgO from about 18 wt.% to 0.4 wt.% as relatively

soluble dolomite in the protolith was leached out by

the silica-bearing hydrothermal solutions.

16.9 REDOX MINERAL EQUILIBRIA

Oxygen is the most abundant element in the crust and

mantle of the Earth and plays an important role in min-

eral equilibria, even though the amount of free O

can

be minute. For example, its effective partial pressure,

or fugacity, f (Section 3.5.1), in a system of pure

water at 2 kbar ranges from about 10

11

bars at 300°C

to 10

5

bars at 700°C and 10

3

bars at 1000°C. Even

smaller oxygen fugacities–down to about 10

40

bars

at 300–400°C—govern redox equilibria in Fe-bearing

minerals and mineral assemblages in which there are

variable amounts of Fe

2

and Fe

3

. These minute fu-

gacities correspond to only a few free molecules of O

per cm

of rock; this fact, together with the slow rates

of diffusion of O

through crystalline solids (Figure 6.4),

readily accounts for the alternation of layers 1 cm

thick of hematite and magnetite in metamorphosed

Precambrian iron formations (Section 14.2.1). Since

some oxidation-reduction equilibria were discussed in

Sections 3.5.4 and 5.7.2 and shown in Figures 3.14 and

5.30 (see also Spear, 1993, Chapter 18), only the major

features pertinent to metamorphic systems are con-

sidered here.

In rock systems in the crust of the Earth, most

oxygen fugacities are near the NNO and QFM buffers

where magnetite is stable. In more oxidized systems

at the surface hematite is stable. Provided a buffer

assemblage exists in a rock, such as quartz  fayalite 

magnetite, the oxygen fugacity is constrained to lie at

speciﬁc values dependent on T along the univariant

QFM curve in Figure 3.14. Stabilities of Fe-bearing mi-

cas, amphiboles, and other solid-solution hydrous min-

erals are likewise constrained by f , T, and, to a lesser

extent, P in buffer assemblages with other minerals.

The generalized redox reaction

16.32 Fe

2

-rich hydrous silicate  O

 Mg-rich hydrous silicate  Fe

3

-oxides

shows that more Mg-rich solid solutions are more sta-

ble at higher f and T (see biotite in Figure 5.30). The

coexisting Fe–Ti oxides can be ilmenite  magnetite

under relatively reducing conditions and hematite

under more oxidizing.

Although less widespread than Fe, rocks that contain

C can be important in constraining and buffering oxi-

dation conditions. Redox reactions can yield, with pro-

gressively more reduced C, carbonate minerals with C

4

in CO

, graphite with C

, and methane (CH

) ﬂuid with

4

that may be preserved in ﬂuid inclusions. These

phases are involved in equilibria with H

O, O

, and H

A few metamorphic rocks contain Fe-sulﬁdes that

equilibrate with volatile ﬂuids such as H

S, SO

, and

. The mole fractions of these volatile species in meta-

morphic ﬂuids are very small, generally 0.01. Stabil-

ities of the dominant sulﬁdes pyrite and pyrrhotite as a

function of f and f are shown in Figure 16.30, along

with hematite, magnetite, and graphite with which they

locally coexist.

In regional metamorphic terranes, intergranular

ﬂuids are generally internally buffered with respect to

oxygen fugacities by redox reactions and rocks tend to

retain the oxidation state of their protolith. Thus,

metamorphosed magmatic rocks are relatively reduced

whereas weathered and hydrothermally altered rocks

are more oxidized. Nonetheless, both pelitic and maﬁc

rocks reveal an increasing FeO/Fe

ratio with in-

creasing grade (Miyashiro, 1994, p. 155). The mineral

508 Igneous and Metamorphic Petrology

log f

(bar)

–5

–10

–15

–20

–25

–15 –10

Graphite

Magnetite

Hematite

Pyrite

Pyrrhotite

–50 5

log f

(bar)

Iron

16.30 Stability ﬁeld of graphite compared with those of Fe-oxides

and Fe-sulﬁdes at P  2 kbar, P  1 kbar, and 700°C.

Redrawn from Froese (1981).

reactions responsible for this progressive reduction of

Fe are undoubtedly complex. One possibility (modeled

by end-members) is

16.33 C  2Fe

2

3

 KAl

AlSi

(OH)

graphite magnetite muscovite

 3SiO

 KAlFe

2

(OH)

quartz annite

 Fe

2

 CO

almandine

Buffering by large volumes of inﬁltrating ﬂuids can

occur locally in open systems.

16.10 KINETICS AND MINERAL

REACTIONS: WHAT ACTUALLY

HAPPENS IN METAMORPHIC

ROCKS

Except for comments regarding polymorphic transitions,

discussions of mineral equilibria in this chapter have

essentially ignored the role of kinetics. However, chang-

ing rock systems do not ignore this time-dependent

factor. Whether changes in P, T, and compositional para-

meters are actually effective in driving mineralogical

changes and controlling equilibria in natural systems

depends on kinetics. No system spontaneously equili-

brates to new P–T–X conditions inﬁnitely fast; rather,

all metamorphic mineral reactions have ﬁnite rates that

require some ﬁnite interval of time. In this section,

using concepts from Section 3.6, some aspects of the

kinetics of metamorphic mineral reactions are brieﬂy

reviewed, including overstepping, nucleation of tran-

sient metastable phases, and the roles of ﬂuids and

reactive surfaces in catalyzing reactions.

A general principle of the kinetics of reactions is

that they cannot proceed until the equilibrium P–T

conditions are exceeded by a ﬁnite amount (Ridley and

Thompson, 1986). The amount of this overstepping

that is required depends on the type of reaction, as can

be seen in the expression for the reaction afﬁnity 

S(T  T

), where S is the entropy change in the

reaction and (T  T

) is the overstepping. S for

solid–solid reactions, such as a polymorphic transition,

may be on the order of 25 J/K mole but more than 80

J/K mole for a dehydration reaction. Consequently, the

latter require a smaller overstepping to accomplish the

same afﬁnity or rate as a solid–solid reaction. Prograde

dehydration reactions are accomplished at small over-

steppings of perhaps a few degrees, whereas solid–solid

reaction in a dry system might require an overstepping

of tens of degrees. From another perspective, activation

energies, E

(Section 3.6) of metamorphic reactions

range from 150–300 kJ/mole for dehydration reactions

and diffusion of Si and Al to 400–800 kJ/mole for

breakup of Si–O bonds in solid–solid reactions.

Some mineral reactions appear to proceed faster by

a path involving an intermediate transient phase, rather

than going directly from unstable reactant to stable

product phases. In an example from the laboratory,

Greenwood (1963) showed that at 1 kbar and 820°C

talc decomposes initially to anthophyllite but eventu-

ally in long-term experiments the metastable anthophy-

llite breaks down to stable enstatite  quartz  water.

Three sequential processes are involved in the

progress of most reactions. These are breakdown of

unstable reactant minerals, transport of ions released

from the surface of the decomposing grains, and

growth of new product mineral grains following their

nucleation. The process with the slowest rate deter-

mines the overall rate of the reaction. Clearly, rates of

the ﬁrst two processes are considerably greater where a

ﬂuid is present in the system, relative to a ﬂuid-free

one. For example, in their seminal discussion of the

kinetics of metamorphic reactions, Fyfe et al. (1958)

cited experimental work of H. R. Shaw, who found that

in the reaction SiO

 2MgO → Mg

SiO

under “dry”

conditions at 1000°C about 26% of the MgO was

converted to forsterite in four days. On the other hand,

in the presence of water the reaction was complete in

minutes at 450°C.

As a general rule, then, we may expect that prograde

dehydration reactions will closely approach thermo-

dynamic equilibrium, a conclusion drawn almost a cen-

tury ago by V. M. Goldschmidt. On the other hand,

states of disequilibrium can be expected during meta-

morphism of dry rocks, where reactions are essentially

of the solid–solid type, such as impermeable phaneritic

magmatic rocks and high-grade granulite-facies rocks

made of anhydrous assemblages.

Lasaga (1998, pp. 104–6, 597) emphasizes that the

amount of reactive surface area is critical in reaction

kinetics. This factor depends on the surface area of

each participating phase and on an intrinsic surface

property speciﬁc to each. For example, in the devo-

latilization reactions tremolite  3 calcite  2 quartz

→ 5 diopside  3 CO

 H

O and dolomite  2

quartz → diopside  2 CO

experiments have shown

that diopside nucleates exclusively on the Mg-bearing

reactant phase, either tremolite or dolomite. Con-

sequently, the greater the amount of this favorable

substrate phase in the rock the greater is the rate of the

reaction.

16.10.1 Role of Fluids in the Mechanism of

Metamorphic Reactions

This concept of reactive surface area may play a role in

the long-standing paradox of why Al

SiO

polymorphs

commonly do not directly replace one another. Al-

though there are exceptions (see, for example, Yardley

Metamorphic Mineral Reactions and Equilibria

509

et al., 1990, pp. 110–12), in most pelitic rocks anda-

lusite and sillimanite occur in different domains in

the same thin section and are not necessarily in direct

contact with one another (Figure 14.25d). Apparently,

kinetic barriers usually inhibit direct conversion of a

grain of one polymorph directly into another because

solid–solid reactions are very sluggish. A common

texture consists of ﬁbrolitic sillimanite intimately inter-

grown with micas (Figure 16.2), as if these phyllosilic-

ates provided a favorable substrate for nucleation of

sillimanite (Section 16.3.1). Not only might a favorable

or reactive surface be provided in micas but some sort

of ﬂuid reaction involving them might “catalyze” the

solid–solid polymorphic transition.

Carmichael (1969) has suggested that the kyanite →

sillimanite transition takes place via an intergranular

aqueous ﬂuid by simultaneous coupled reactions and

ion transfer in two different grain-scale domains within

pelitic rocks. Mica serves as an intermediary agent in

the coupled reactions. In the ﬁrst domain, reaction

16.29 described above may take place, readily yielding

sillimanite at the expense of muscovite

16.29 2KAl

AlSi

(OH)

 2H





muscovite in ﬂuid

3Al

SiO

 3SiO

 3H

O  2K



sillimanite quartz in ﬂuid solution

In the second domain, unstable kyanite reacts with the

byproducts of the ﬁrst-domain reaction transported

in an intergranular ﬂuid, yielding compensating mus-

covite according to

16.34 3Al

SiO

 3SiO

 2K



 3H

kyanite quartz in ﬂuid

 2KAl

AlSi

(OH)

 2H



muscovite in ﬂuid

Exchange of H



and K



ions via an aqueous ﬂuid pro-

duces muscovite grains from kyanite in one local do-

mainal system and sillimanite grains from muscovite in

another (Figure 16.31). The net balanced polymorphic

reaction kyanite → sillimanite is achieved by adding

these two local reactions together. Relatively insoluble,

more slowly diffusing Al

3

and Si

ions are immobile

and these ions (plus oxygens), which make up the ﬁnal

sillimanite grains, are likely not the same ones in the

original kyanite. In such linked reactions, an interme-

diate transient phase, muscovite in this case, may not

leave evidence of its existence but it must be stable

at P–T conditions above and below the kyanite →

sillimanite transition (Figure 14.31). Muscovite grains

destroyed in reaction 16.29 are compensated by pro-

duction of others in 16.34. Micas may be utilized for

heterogeneous nucleation of sillimanite.

Carmichael (1969, p. 255) concludes: “Given a

choice between a number of possible reaction paths, a

natural metamorphic reaction will proceed to comple-

tion by means of that path for which the activation

energy is lowest, provided that the overstepping of

the equilibrium T is too small to activate other paths as

well. This condition is likely to be met in regional meta-

morphic rocks because of their necessarily slow rate of

heating. It is safe to conclude that the activation energy

for the reaction kyanite → sillimanite, by the reaction

path (via intermediate transient muscovite)...is sig-

niﬁcantly lower than that for nucleation and growth of

sillimanite directly from kyanite...all of the chemical

species that participate in the various subreactions, with-

out appearing in the balanced reaction that expresses

the net change taking place in the system, are catalysts,

in that they accelerate the reaction without changing its

equilibrium conditions.”

Another example of reaction paths that is more

complex than implied by a simple written reaction or a

simple reaction texture lies in corona textures (Figures

510 Igneous and Metamorphic Petrology

DOMAIN I

DOMAIN II



 FLUID 2K



 3H

O

2Ms 3Sil  3Qtz 

2Ms 3Ky  3Qtz

16.31 Possible mechanism for the reaction kyanite → sillimanite via transfer of ions in an intergranular aqueous phase between neighboring

domains in a pelitic rock. In the schematic thin section views on the right, in domain I a muscovite grain has partially broken down

to quartz and needlelike sillimanite plus water and K



ions while in domain II a new muscovite has crystallized from reactant K



 kyan-

ite  quartz, the latter occurring as residual anhedra. The net reaction is kyanite → sillimanite. Redrawn from Carmichael (1969).

16.6 and 16.8); these are reminiscent of the layered

mineral assemblages that result from local equilibrium

during diffusion-controlled reactions in metasomatic

systems (Figure 16.27). Carlson and Johnson (1991,

p. 756) conclude that corona-forming reactions must

take place “in an open system in which the local prod-

uct assemblages may change with time in response to

the progress of reactions taking place beyond the con-

ﬁnes of any individual coronal reaction band” (emphasis

added). The spatial mineral organization in the corona

textures reﬂects diffusion-controlled reactions in chem-

ical potential gradients but the seeming simplicity of

coronas belies a complex open-system behavior. It is

impossible to write an accurate stoichiometric reaction

for almost any corona because the exact position of the

original interface, the changes in volume, and gains

and losses of mass (chemical components) cannot be

unequivocally ascertained (compare Figure 16.28).

The conclusion to be drawn here is that even the

simplest of reaction textures and interpreted mineral

reactions can belie open-system complexities. To cir-

cumvent kinetic obstacles, the actual reactions in meta-

morphosing rocks may utilize intermediary “catalytic”

phases and intergranular ﬂuids through which mobile

ions can move in places beyond the conﬁnes of the

product grains and observed reaction textures.

16.11 PUTTING MINERAL EQUILIBRIA

TO WORK: BROADER

PETROLOGIC IMPLICATIONS

In metamorphic petrology, mineral equilibria have an

importance beyond that of their intrinsic interest. For

example, they tell us about ﬂuid transfer in the con-

tinental crust. In this section, two additional applica-

tions of mineral equilibria merit further consideration,

namely, the meaning of isograds and how they develop

and, secondly, geothermobarometry. A byproduct of

the ﬂourishing of quantitative petrology in the late

decades of the twentieth century has been the con-

struction of detailed P–T–t paths by geothermobar-

ometry. Because of their importance in constraining

tectonic models of metamorphism, these paths will be

discussed in Chapter 18.

16.11.1 Isograds

Graphic representations of multivariant stability ﬁelds

and their bounding univariant equilibrium lines serve

as models of mappable zones and isograds in meta-

morphic terranes. Zoned regional terranes furnish

valuable insights into the character and evolution of

orogens. Consideration of zones and isograds provides

a convenient vehicle to summarize reactions and their

link to changing mineral assemblages.

The simplest type of isograd that is unaffected by

compositional variations in the system results from a

polymorphic transition. Although the usefulness of

polymorphs of Al

SiO

can be compromised by

metastability problems (Section 16.3), the ﬁrst appear-

ance of ﬁbrolitic sillimanite in kyanite-bearing rocks is

generally taken as a suitable marker for the sillimanite

isograd and lower boundary of the sillimanite zone.

Other isograds, discussed next, that mark Barrovian

zones (Figure 14.30) result from continuous and dis-

continuous heterogeneous reactions in systems that

contain solid solutions, the general situation in rocks.

Isograd Resulting from Continuous Mineral Reaction.

The upper left of Figure 16.32 (see also Figures 16.12

and 16.13) depicts the result of increasing T in the con-

tinuous reaction 16.18, namely, chlorite  muscovite 

quartz  garnet  biotite  water. As garnet of in-

creasing Mg content is stabilized at the expense of

Fe-rich chlorite during prograde metamorphism, the

three-phase triangle representing coexisting garnet 

biotite  chlorite sweeps toward more magnesian com-

positions. As the three-phase triangle eclipses a particu-

lar pelitic rock composition, garnet appears, marking

the garnet isograd. Thus, at a lower T, garnet has al-

ready been stabilized in rock B because it lies within

the triangle, whereas garnet has just appeared in rock C

but not in the more magnesian, less aluminous rock D.

At a higher T, the sweep of the three-phase triangle

has caused the appearance of garnet in rock D. In the

geologic map of the metamorphic terrane in Figure

16.32, where zones resulted from a thermal gradient,

the garnet isograd in these three rocks is positioned

differently because of their differing proportions of the

AFM components. The isograd in rock B that has the

most Fe-rich bulk chemical composition is displaced

toward the lower T part of the terrane (biotite zone),

whereas the isograd in the more magnesian compositions

—rocks C and D—is shifted toward the part of the

terrane that was subjected to higher temperatures.

Isograds produced by the ﬁrst appearance of a solid-

solution by a continuous reaction that are stepped at

lithologic boundaries probably reﬂect their dependence

on bulk rock composition rather than, for example,

post-metamorphic faulting.

Changes in the modal proportions of phases or their

chemical compositions at isograds created by continu-

ous reactions are typically inconspicuous.

Isograds Resulting from Discontinuous Heterogeneous

Mineral Reactions. In typical Barrovian terranes, the

garnet zone is succeeded up-T by the staurolite zone.

The staurolite isograd can result from the discontinu-

ous reaction

16.35 garnet  chlorite  muscovite

 staurolite  biotite  quartz  water

This reaction is manifest by a distinct change in the

conﬁguration of tie-lines in the AFM projection. This is

Metamorphic Mineral Reactions and Equilibria

511

a tie-line switching reaction where a compatibility tie-

line between coexisting garnet and chlorite disappears

as a new compatibility of staurolite  biotite appears

(lower left of Figure 16.32). These phases are all solid

solutions, but the reaction is not a continuous one that

takes place over a range of metamorphic conditions.

Discontinuous reactions like 16.35 are less dependent

on the bulk chemical composition of the rocks and, in

fact, are manifest in a range of pelitic compositions,

including rocks B, C, and D in lower left diagram of

Figure 16.32. For this reason, such reactions tend to be

readily observed and are less inﬂuenced by variations

in bulk chemical composition, and their products serve

admirably as isograds.

Other isograds and zones produced by discontin-

uous reactions can be seen in Figure 16.32. Higher

grade zones in this hypothetical pelitic terrane are

shown on the right side of the map and their mineral

assemblages are represented in terms of the com-

ponents Al

, SiO

, and KAlSi

( H

O) in the

three diagrams on the right side of the diagram. In the

lowest-grade zone I of the terrane, rocks B, C, and D

contain stably coexisting muscovite  quartz. Rocks

B and D also contain K-feldspar whereas C contains

SiO

. (Rock A contains corundum rather than

quartz and so does not deﬁne this zone.) With increas-

ing T in rocks B, C, and D, muscovite and quartz react

to form K-feldspar  Al

SiO

so that tie-line compat-

ibilites switch. In these initially quartz-bearing rocks,

there is an isograd marked by the appearance of both

K-feldspar  Al

SiO

; this compatibility deﬁnes a K-

feldspar  Al

SiO

zone II. (The K-feldspar  sillimanite

512 Igneous and Metamorphic Petrology

Qtz

SiO

KAlSi

ZONE IIZONE I

Kfs

Crn

SiO

Qtz

SiO

KAlSiO

 Ms  Qtz  H

Increasing T

GARNET ZONE

ISOGRADS

Garnet

Staurolite

Crn

SiO

Qtz

SiO

KAlSi

STAUROLITE ZONE ZONE III

Kfs

Crn

SiO

B C B C

FMFM

ZONE

BIOTITE

ZONE

GARNET

ZONE

STAUROLITE

ZONE

III

ZONE

B C

First prograde

appearance of

K-feldspar  Al

SiO

First prograde

appearance of

K-feldspar  corundum

ZONES

I Muscovite  quartz

 Al

SiO

 Kfs

II K-feldspar  Al

SiO

 Ms  Qtz

III K-feldspar  corundum

 Al

SiO

 H

16.32 Hypothetical pelitic terrane made up of four rock layers, each of uniform composition, whose bulk compositions A, B, C, and D are

depicted in the compatibility diagrams. Hypothetical metamorphic isograds and zones are described in text.

isograd in zoned Barrovian terranes is sometimes re-

ferred to as the “second sillimanite” isograd because it

commonly occurs at higher temperatures than the

polymorphic transition from kyanite to sillimanite that

marks the “ﬁrst sillimanite” isograd.) Because silica

undersaturated rock A has no quartz, it preserves no

record of this prograde reaction. Muscovite in quartz-

free rocks (A, B, and C) in zone II breaks down at still

higher T to K-feldspar  corundum (Figure 14.31) in

zone III. Thus, two prograde isograds appear in this

hypothetical pelitic terrane—the ﬁrst appearance of K-

feldspar  Al

SiO

at the second sillimanite isograd

and the ﬁrst appearance of K-feldspar  corundum.

Signiﬁcantly, their deﬁnition depends on the modal

amount of quartz in the protolith.

It may be noted that the ﬁrst appearance of K-

feldspar  corundum coincides with the terminal

disappearance of muscovite. This disappearance and

the tie-line switch are the two types of discontinuous

reactions that occur in metamorphic systems.

As an example of isograds based on mineral equi-

libria in mixed-volatile ﬂuids those delineated around

Whetstone Lake, Ontario (Figure 16.33) can be cited.

Isograds in pelitic rocks are intersected obliquely by

another isograd related to the combined decarbonation

–dehydration reaction in carbonate-bearing rocks

16.36 biotite  calcite  quartz  amphibole

 K-feldspar  CO

 H

Carmichael (1970) believes the intersecting pattern of

isograds was caused by the compounding effect of a re-

gional geothermal gradient, with higher temperatures

to the northwest, combined with a gradient in X ,

possibly related to H

O expelled from a granitic intru-

sion in the northern part of the terrane.

16.11.2 Evaluation of Intensive Variables during

Metamorphism

Since the infancy of metamorphic petrology, investig-

ators have tried to infer something of the P–T conditions

of mineral formation. Early attempts were essentially

relative and qualitative, using ﬁeld criteria, such as

proximity to magmatic intrusions, for elucidation of

temperatures, and mineral properties, such as density,

to infer that Mg–Fe garnet typically forms at higher

pressures than cordierite. Quantitative determinations

of the intensive variables that prevailed during equili-

bration of mineral assemblages has become an im-

portant objective of modern metamorphic petrology.

Realization of this objective depends on an accurate as-

sessment of the stable equilibrium mineral assemblage

in the rock (Section 16.1), not overlooking potential ki-

netic problems in so doing. If it cannot be decided

what minerals in a rock constitute an equilibrium as-

semblage then there is no sense in applying sophisticated

petrogenetic grids and thermobarometers to a rock.

(Garbage in, garbage out!)

One way of inferring P, T, and ﬂuid composition

from mineral assemblages is to relate equilibria to pet-

rogenetic grids of univariant reaction lines in P–T–X

space, such as in Figure 16.24 for the Ubehebe Peak

contact aureole discussed above. Obviously, there is a

need for accurate, composition-speciﬁc grids. Until the

latter part of the twentieth century, the positions of

univariant lines in P–T–X space were established by

laborious experiments but many of these lines were

ﬂawed to varying degrees because of kinetic difﬁculties

(e.g. Figure 16.3) and other problems. Since then, in-

ternally consistent thermodynamic datasets based on a

variety of experimental measurements have become

available, three of which are Chatterjee et al. (1998),

Gordon (1998), and Powell et al. (1998). Spear (1993)

provides an extensive review of petrogenetic grids for

several compositional systems. Continued reﬁnement

of thermodynamic data in the future will bring about

improved accuracy and reliability.

Metamorphic Mineral Reactions and Equilibria

513

(a)

(b)

0.0 0.2

Near intrusion

Farther from

intrusion

Sil

Chl



Grt



Qtz

0.4 0.6 0.8

03km

02miles

1.0

 0 63

Granitic rocks

0.24



16.33 Metamorphic reactions and isograds in pelitic rocks near

Whetstone Lake, Ontario. (a) Map of isograds, keyed to dis-

cussion in text. (b) T– X plot for univariant reactions with

corresponding line symbols as on map. Dotted lines show how

regional thermal gradient at different ﬂuid compositions

intersects the sequence of univariant reaction curves to give

the sequence of isograds on the map in (a). More hydrous

ﬂuid X  0.24 prevailed near granitic intrusion, more

carbonate-rich ﬂuid X  0.63 farther from intrusion.

Redrawn from Carmichael (1970).

16.11.3 Mineral Thermobarometers

Quantiﬁcation of P–T conditions of metamorphic

equilibration can also be made by mineral thermo-

barometry, sometimes called geothermobarometry.

Numerous mineral assemblages are available for such

measurements; three previously introduced include:

1. Fe–Ti oxides (Section 3.5.5). Compositions of

stably coexisting cubic and rhombohedral phases

(basically magnetite and ilmenite) provide values of

oxygen fugacity and T in metamorphic as well as

magmatic systems.

2. Ternary feldspars (Section 5.5.4) and pyroxene

solid solutions (Section 5.6). Both are thermome-

ters in providing a T of equilibration if P can be in-

dependently evaluated. Although chieﬂy applicable

to magmatic rocks there is potential use in high-

grade metamorphic rocks as well.

3. Jadeite end-member concentration in clinopyrox-

ene coexisting with plagioclase and quartz (Section

16.5.1) provides a barometer if T can be indepen-

dently evaluated.

Spear (1993, Chapter 15) and Winter (2001,

pp. 543–59) review numerous thermobarometers spe-

ciﬁcally applicable to metamorphic rocks and include

example calculations.

The most useful mineral thermobarometers involve

pairs of equilibria in which there is a strong depen-

dence on P and T. Two such equilibria are applicable

to widespread amphibolite-facies pelitic schists that

contain stably coexisting garnet  biotite  plagioclase

 Al

SiO

 quartz. Written for the pure end-mem-

bers, these are

16.19 Fe

 KMg

AlSi

(OH)

almandine phlogopite

 Mg

 KFe

AlSi

(OH)

pyrope annite

16.37 3CaAl

 Ca

anorthite grossular

 2Al

SiO

 SiO

quartz

The ﬁrst equilibria (16.19) is the basis of the garnet

–biotite Fe–Mg exchange thermometer. Exchange

equilibria like this typically have small Vs because

the reactants and products are the same phases and

are, therefore, relatively insensitive to P but they are

strongly dependent on T, making them useful ther-

mometers. In a P–T diagram, the dP/dT (S/V)

slope of an equilibrium line for any particular garnet–

biotite reaction is large. Different composition pairs

have similar slopes but different positions in P–T

space. On an AFM diagram there is an obvious differ-

ence in the partitioning of Fe and Mg between biotite

and garnet at different temperatures as expressed in

different tie-line orientations (Figure 16.11).

The second equilibrium (16.37), shown in Figure

16.4, is a net transfer reaction that is the basis of the

GASP barometer, so-called because it involves Garnet,

Aluminosilicate, Silica, and Plagioclase. Heterogeneous

net-transfer reactions, consuming and producing dif-

ferent types of phases, can have relatively large Vs, and

are therefore sensitive to changing pressures, and their

dP/dT (S/V ) is correspondingly small. The inter-

section of a steep thermometer equilibrium line for garnet

–biotite and a shallow GASP barometer line provides a

unique value of T and P at which minerals equilibrated.

Thermodynamic Evaluation. This section follows closely

after Spear (1993, Chapter 15). The general thermody-

namic expression for garnet–biotite, GASP, and many

other equilibria that is the basis for mineral thermo-

barometry can be written as

16.38 RT ln K

(H  TS) V(P  P

ref

)

where K

is the equilibrium constant (Section 3.5.2).

For the pure end-member reaction 16.19, the equilib-

rium constant written in terms of activities is

16.39 K



Making the assumption of ideal solution behavior in

both biotite and garnet, activities may be cast in terms

of mole fractions. For example

Grt



where the mole fraction expression is raised to the

third power because Mg and other substituting cations

mix at three octahedral lattice sites. The equilibrium

constant can now be rewritten as

16.40 K



and in terms of the distribution coefﬁcient

16.41

Ferry and Spear (1978) experimentally determined dis-

tribution coefﬁcients for garnet–biotite equilibria be-

tween 550 and 800°C at 2070 bars. On a ln K

versus

1/T diagram with T in Kelvins the data conform to a

straight line, consistent with an ideal solution model.

From this experimental data plot, H and S can be

determined and V evaluated from Robie and Hem-

ingway (1995). Substituting values in equation 16.38

gives

Grt–Bt



(Mg/Fe)

Grt

(Mg/Fe)

 K

1/3

Grt

≤

Grt

)

 ¢

Mg  Fe  Mn  Ca

≤

Prp

Ann

Alm

Phl

514 Igneous and Metamorphic Petrology

16.42 52 112  19.51T  0.238P  3RT ln K

 0

where T is in Kelvins and P is in bars.

For application to rocks, analyses of mineral com-

positions by electron microprobe are converted into

mole fractions. In a still ongoing reﬁnement of this

geothermometer, Holdaway et al. (1997) took into

account the effects of Mn and Ca in garnet and Ti

and Al in biotite as well as Fe–Mg nonideality and the

presence of Fe

3

in both phases.

For the GASP equilibria (equation 16.37), the equi-

librium constant (for a kyanite-bearing assemblage) is

16.43 K



where the activities of kyanite and quartz are made

equal to 1 because they are essentially pure phases.

For this equilibrium, an ideal solution model for the

garnet and plagioclase has proven to give poor results

and several different activity-composition models have

been proposed instead.

Based on experiments in the pure end-member

system between 650 and 1250°C at 19–28 kbar (Fig-

ure 16.4), the equation for the P–T dependence of K

for the GASP equilibrium is

16.44 48 357  150.66 T  (P  1)(6.608)

 RT ln K

Simultaneous solution of Equations 16.42 and 16.44

provides values of T and P.

Case Study: Thermobarometry in Zoned Garnet

Poikiloblasts, Wopmay Orogen. As an example of the

application of the garnet–biotite thermometer and

the GASP barometer we show data from amphibolite-

facies pelitic schists in the Proterozoic Wopmay Oro-

gen, Canada. Only the details of the thermobarometry

of these informative poikiloblasts will be presented

here, drawing from the classic work of St-Onge (1987).

Implications for P–T paths and the tectonothermal

evolution of the regional metamorphic terrane in this

orogen will be considered in Section 18.3.2.

The 5–7 mm diameter garnet poikiloblasts contain

abundant inclusions of biotite, plagioclase, quartz, and

less common sillimanite in their outer parts and rare

kyanite in the inner cores. These same phases, except

kyanite, also occur in the ﬁner grained matrix. Garnets

are compositionally zoned in a continuous concentric

manner (Figure 16.34); cores are markedly enriched

in Mn (spessartine end-member) and less so in Ca

(grossular) relative to outer zones, whereas Fe (alman-

dine) and Mg (pyrope) are opposite. Mg/(Mg  Fe) in-

creases outward. This overall zoning is not perturbed

immediately adjacent to any inclusion, indicating a lack

of reaction between them and the host garnet. During

garnet growth, there was a continuous change in the

Grs

Grt

)

Qtz

)



Grs

Grt

)

composition (e.g. Figure 16.12) of the material sup-

plied to the expanding outer surface as small matrix

grains were engulfed. Slow diffusion within the garnet

precluded any further reaction with the matrix phases,

effectively freezing-in local mineral equilibria between

inclusion phases and immediately neighboring host

garnet. Only the very outermost rim (0.2–0.3 mm wide)

of the garnets apparently experienced post-thermal

peak re-equilibration manifest in reversal of the ele-

mental zoning. St-Onge notes that muscovite and stau-

rolite occur down grade from the garnetiferous rocks,

suggesting garnet formed by the reaction muscovite 

staurolite  quartz  Al

SiO

 biotite  garnet 

Anhedral porphyroblasts of plagioclase 4–5 mm

in diameter reveal a continuous compositional zoning

essentially matching the compositions of small homo-

geneous plagioclase inclusions in the garnet poikilo-

blasts as they occur from core to rim (Figure 16.34).

Using an electron microprobe analyzer, St-Onge

(1987) determined the composition of nearby plagio-

clase and biotite inclusions and host garnet at as many

as 17 sites from core to rim of the garnet poikiloblasts.

He then used these analytical data from these local

states of equilibrium to ﬁnd simultaneous solutions to

equations 16.42 and 16.44, determining a P and T for

each state and their range over which the garnet grew

(Figure 16.35). Transgression of the P–T conditions

from the stability ﬁeld of kyanite into the sillimanite

ﬁeld is consistent with the character of the Al

SiO

inclusions in the poikiloblasts—sparse kyanite in inner

parts and sillimanite in outer.

Uncertainties and Pitfalls in Thermobarometry. As with

any numerical determinations, there are sources of

error in thermobarometry that diminish the reliabil-

ity and accuracy of the calculated P and T. Merely

“crunching” numbers in ignorance of how they were

obtained, of the assumptions in thermodynamic equa-

tions, and of possible errors in experimental calibra-

tions can seriously compromise the validity of the ﬁnal

results. Thermobarometry assumes a state of equilib-

rium is represented in the mineral assemblage and

chemical compositions of minerals. While the criteria

discussed in Section 16.1 serve as guidelines, one can

never be totally certain that measured compositions

reﬂect equilibrium. Caution must be exercised in

using compositionally zoned grains and in interpreting

Fe concentrations measured by the electron micro-

probe that does not discriminate between Fe

3

and

2

. The conditions under which calibrating experi-

mental measurements of component partitioning were

made should not be far removed from those condi-

tions under which the mineral assemblage equilibrated

unless accurate activity-composition models can be

employed.

Metamorphic Mineral Reactions and Equilibria

515

Altogether, a single P–T determination of about

6 kbar and 600°C in a pelitic rock using the garnet–

biotite thermometer and the GASP barometer can

have uncertainties as much as 3 kbar and 80°C,

respectively (Spear, 1993, p. 539). Although the uncer-

tainty of one absolute value such as this can be consid-

erable, relative differences between determinations of

the same kind among several cogenetic samples, or in-

tracrystalline sites within zoned garnet poikiloblasts as

just described, can be more reliable because of smaller

516 Igneous and Metamorphic Petrology

0.190

0.070

MgO

FeO

MnO

Alm

0mm2

Prp

Sps

Grs

38.1

35.7

34.2

31.7

29.1

27.4

30.0

31.3

34.1

36.7

38.5

Grt

16.35 (left) Mineral thermobarometry of a compositionally zoned

poikiloblastic garnet, Wopmay Orogen, Canada. Sample 3.

Filled circles are values of P and T at 17 sites within the garnet

shown in Figure 16.34 from core outward to rim, deﬁning an

essentially decompressing P–T path during metamorphism

and garnet growth. Two lines intersecting at the highest P

value show that each P–T point represents the simultaneous

solution of Equations 16.42 (garnet–biotite thermometer) and

16.44 (GASP barometer). Shaded box indicates the estimated

uncertainties in the individual P–T determinations. Data from

St-Onge (1987).

16.34 Compositionally zoned poikiloblastic garnet, Wopmay Orogen, Canada. Sample 3. Top is a drawing of the poikiloblast showing plagio-

clase inclusions and their anorthite contents; positions of corresponding anorthite contents are indicated in a nearby zoned plagioclase

on the right. Note that plagioclase became more calcic during growth. Bottom diagrams indicate compositional zoning in garnet as

revealed by electron microprobe “spot” analyses (in wt.%) in a traverse across the poikiloblast from rim to rim. The garnet in this pelitic

schist is mostly almandine but the core has large amounts of the spessartine and grossular end-members, whereas the rim is rich in

pyrope. In bottom left diagram, X

 Mg/(Mg  Fe  Mn  Ca). Redrawn from St-Onge (1987).

P (kbar)

500 600 700

T (°C)

RIM

CORE

Kyanite

sillimanite

GASP

barometer

Equation 16.44

Garnet-biotite thermometer

Equation

16 42