Chapter 26: Metamorphic Reactions
If we treat isograds as reactions, we can:
• Understand what physical variables might
affect the location of a particular isograd
• We may also be able to estimate the P-T-X
conditions that an isograd represents
From
Understanding
Earth, Press and
Siever. Freeman.
1. Phase Transformations
• Isochemical
• Polymorphs of SiO2 or Al2SiO5 or graphite-diamond or
calcite-aragonite
• Simplest: depend on temperature and pressure only
1. Phase Transformations
Figure 26.1. A portion of the
equilibrium boundary for the calcitearagonite phase transformation in the
CaCO3 system. After Johannes and
Puhan (1971), Contrib. Mineral. Petrol.,
31, 28-38. Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
1. Phase Transformations
Figure 26.15. The P-T phase diagram
for the system Al2SiO5 showing the
stability fields for the three
polymorphs andalusite, kyanite, and
sillimanite. Calculated using the
program TWQ (Berman, 1988, 1990,
1991). Winter (2010) An Introduction
to Igneous and Metamorphic
Petrology. Prentice Hall.
1. Phase Transformations
• Small DS for most polymorphic transformations
•  small DG between two alternative polymorphs, even
several tens of degrees from the equilibrium boundary
•  little driving force for the reaction to proceed 
common metastable relics in the stability field of other
• Coexisting polymorphs may therefore represent nonequilibrium states (overstepped equilibrium curves or
polymetamorphic overprints)
2. Exsolution
Figure 6.16. T-X phase
diagram of the system albiteorthoclase at 0.2 GPa H2O
pressure. After Bowen and
Tuttle (1950). J. Geology, 58,
489-511. Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology.
Prentice Hall.
3. Solid-Solid Net-Transfer Reactions
• Involve solids only
• Differ from polymorphic transformations: involve
solids of differing composition, and thus material
must diffuse from one site to another for the
reaction to proceed
3. Solid-Solid Net-Transfer Reactions
Examples:
NaAlSi2O6 + SiO2 = NaAlSi3O8
Jd
Qtz
Ab
MgSiO3 + CaAl2Si2O8 = CaMgSi2O6 + Al2SiO5
En
An
Di
And
4 (Mg,Fe)SiO3 + CaAl2Si2O8 =
Opx
Plag
(Mg,Fe)3Al2Si3O12 + Ca(Mg,Fe)Si2O6 + SiO2
Gnt
Cpx
Qtz
Figure 27-1. Temperature-pressure phase diagram for the reaction: Albite = Jadeite + Quartz calculated using the program TWQ
of Berman (1988, 1990, 1991). Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
3. Solid-Solid Net-Transfer Reactions
• If minerals contain volatiles, the volatiles must be
conserved in the reaction so that no fluid phase is
generated or consumed
• For example, the reaction:
Mg3Si4O10(OH)2 + 4 MgSiO3 = Mg7Si8O22(OH)2
Tlc
En
Ath
involves hydrous phases, but conserves H2O
It may therefore be treated as a solid-solid nettransfer reaction
3. Solid-Solid Net-Transfer Reactions
• When solid-solution is limited, solid-solid nettransfer reactions are discontinuous reactions
• Discontinuous reactions tend to run to completion
at a single temperature (at a particular pressure)
• There is thus an abrupt (discontinuous) change
from the reactant assemblage to the product
assemblage at the reaction isograd
Discontinuous reaction: f + 1 and XLiq fixed
4. Devolatilization Reactions
• Among the most common metamorphic reactions
• H2O-CO2 systems are most common, but the
principles same for any reaction involving volatiles
• Reactions dependent not only upon temperature
and pressure, but also upon the partial pressure of
the volatile species
4. Devolatilization Reactions
For example the location on a P-T phase diagram of the
dehydration reaction:
KAl2Si3AlO10(OH)2 + SiO2 = KAlSi3O8 + Al2SiO5 + H2O
Ms
Qtz
Kfs
Sill
depends upon the partial pressure of H2O (pH2O)
This dependence is easily demonstrated by applying Le
Châtelier’s principle to the reaction at equilibrium
W
4. Devolatilization Reactions
The equilibrium curve
represents equilibrium
between the reactants and
products under watersaturated conditions
(pH2O = PLithostatic)
Figure 26.2(a). P-T phase diagram for the
reaction Ms + Qtz = Kfs + Al2SiO5 + H2O
showing the shift in equilibrium conditions as
pH2O varies (assuming ideal H2O-CO2 mixing).
Calculated using the program TWQ by Berman
(1988, 1990, 1991). After Winter (2010) An
Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.
KAl2Si3AlO10(OH)2 + SiO2 = KAlSi3O8 + Al2SiO5 + H2O
Ms
Qtz
Kfs
Sill
W
Suppose H2O is withdrawn from the system at some point
on the water-saturated equilibrium curve: pH2O < Plithostatic
According to Le Châtelier’s Principle, removing water at
equilibrium will be compensated by the reaction running
to the right, thereby producing more water
This has the effect of stabilizing the right side of the
reaction at the expense of the left side
So as water is withdrawn the Kfs + Sill + H2O field
expands slightly at the expense of the Mu + Qtz field, and
the reaction curve shifts toward lower temperature
Figure 26.2. P-T phase diagram
for the reaction Ms + Qtz = Kfs
+ Al2SiO5 + H2O showing the
shift in equilibrium conditions
as pH2O varies (assuming ideal
H2O-CO2 mixing). Calculated
using the program TWQ by
Berman (1988, 1990, 1991).
Winter (2010) An Introduction
to Igneous and Metamorphic
Petrology. Prentice Hall.
4. Devolatilization Reactions
pH2O can become less than PLith by either of two ways
 Pfluid < PLith by drying out the rock and reducing the
fluid content
 Pfluid = PLith, but the water in the fluid can become
diluted by adding another fluid component, such as
CO2 or some other volatile phase
 In Fig. 26.2 I calculated the curves for the latter case
on the basis of ideal H2O-CO2 mixing
4. Devolatilization Reactions
• An important point arising from Fig. 26.2 is:
• The temperature of an isograd based on a
devolatilization reaction is sensitive to the partial
pressure of the volatile species involved
• An alternative: T-Xfluid phase diagram
 Because H2O and CO2 are by far the most common
metamorphic volatiles, the X in T-X diagrams is
usually the mole fraction of CO2 (or H2O) in H2OCO2 mixtures
 Because pressure is also a common variable, a T-Xfluid
diagram must be created for a specified pressure
4. Devolatilization Reactions
Figure 26.4. T-XH2O phase diagram
for the reaction Ms + Qtz = Kfs +
Sil + H2O at 0.5 GPa assuming
ideal H2O-CO2 mixing, calculated
using the program TWQ by
Berman (1988, 1990, 1991).
Winter (2010) An Introduction to
Igneous and Metamorphic
Petrology. Prentice Hall.
4. Devolatilization Reactions
Figure 26.4. Winter (2010) An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Figure 26.2. Winter (2010) An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
4. Devolatilization Reactions
Shape of ~ all dehydration curves on T-Xfluid
diagrams is similar to the curve in Fig. 26.2

Maximum temperature at the pure H2O end, and
slope gently at high XH2O, but steeper toward low
XH2O, becoming near vertical at very low XH2O
 Reaction temperature can thus be practically any
temperature below the maximum at pH2O = Plith
 Must constrain the fluid composition (if possible)
before using a dehydration reaction to indicate
metamorphic grade
A rare exception
Figure 26.3. Calculated P-T
equilibrium reaction curve for a
dehydration reaction illustrating
the full loop that is theoretically
possible. From Winter (2010). An
Introduction to Igneous and
Metamorphic Petrology, Prentice
Hall.
4. Devolatilization Reactions
• Decarbonation reactions may be treated in an
identical fashion
• For example, the reaction:
CaCO3 + SiO2 = CaSiO3 + CO2
Cal
Qtz
(26.6)
Wo
Can also be shown on a T-XCO2 diagram
Has the same form as reaction (26.5), only the
maximum thermal stability of the carbonate
mineral assemblage occurs at pure XCO2
4. Devolatilization Reactions
P-T phase diagram for the reaction Cal + Qtz = Wo + CO2
Figure 26.5. T-XCO2 phase diagram for the reaction Cal + Qtz =
Wo + CO2 at 0.5 GPa assuming ideal H2O-CO2 mixing,
calculated using the program TWQ by Berman (1988, 1990,
1991). Winter (2010) An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
• 5 types of devolatilization
reactions, each with a
unique general shape on a
T-X diagram
• Type 3: Tmax at XCO2
determined by the
stoichiometric ratio of
CO2/H2O produced
Ca2Mg5Si8O22(OH)2 + 3 CaCO3 + 2 SiO2
Tr
Cal
Qtz
= 5 CaMgSi2O6 + 3 CO2 + H2O
Di
Figure 26.6. Schematic T-XCO2 phase diagram illustrating the
general shapes of the five types of reactions involving CO2 and
H2O fluids. After Greenwood (1967). In P. H. Abelson (ed.),
Researches in Geochemistry. John Wiley. New York. V. 2, 542-567.
Winter (2010) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.
5. Continuous Reactions
Figure 26.8. Geologic map of a
hypothetical field area in which
metamorphosed pelitic sediments
strike directly up metamorphic
grade. From Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice
Hall.
5. Continuous Reactions
Two possible reasons:
1. Such contrasting composition that the garnet reaction is different
Example: garnet in some pelites may be created by the
(unbalanced) reaction:
Chl + Ms + Qtz  Grt + Bt + H2O
(26.11)
Whereas in more Fe-rich and K-poor pelites, garnet might be
generated by an (unbalanced) reaction involving chloritoid:
Chl + Cld + Qtz  Grt + H2O
(26.12)
5. Continuous Reactions
2. The reaction on which the isograd is based is the same in each
unit, but it is a continuous reaction, and its location is sensitive
to the composition of the solutions (either solid of fluid)
involved
The offsets this creates in an isograd are usually more subtle
than for reason #1, but in some cases they can be substantial
We will concentrate on this second reason here
5. Continuous Reactions
Fig. 6.10. Isobaric T-X
phase diagram at
atmospheric pressure
After Bowen and
Shairer (1932), Amer.
J. Sci. 5th Ser., 24, 177213. Winter (2010) An
Introduction to
Igneous and
Metamorphic
Petrology. Prentice
Hall.
“Melt-in”
isograd?
5. Continuous Reactions
Discontinuous reactions occur at a constant grade
Chl + Ms + Qtz  Grt + Bt + H2O
(26.11)
in KFASH
F=C–f+2=5–4+2=1
5. Continuous Reactions
If Chl + Ms + Qtz  Grt + Bt + H2O (26.11) in
KFMASH
were a continuous reaction, then we would find chlorite,
muscovite, quartz, biotite, and garnet all together in the
same rock over an interval of metamorphic grade above
the garnet-in isograd
• The composition of solid solution phases vary across the
interval, and the proportions of the minerals changes
until one of the reactants disappears with increasing
grade
Continuous reactions occur when F  1, and the reactants
and products coexist over a temperature (or grade)
interval
Fig. 26.9a. Schematic isobaric T-XMg
diagram representing the simplified
metamorphic reaction Chl + Qtz  Grt
+ H2O. From Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Pseudosections address (only) the reactions (continuous
or discontinuous) affecting a rock of specific Xbulk
Fig. 26.9b. Schematic P-T “pseudosection” for a specific bulk composition (in this case for Mg/(Mg + Fe) = 0.5 and quartz-excess)
showing the stability fields of Chl + Qtz, Chl + Grt + Qtz, and Grt + Qtz. Note the continuous nature of the reaction when all solid phases
are present (shaded area). Note also that one can contour the shaded divariant field in (b) for specific compositions of either garnet (as has
been done) or chlorite. The boundaries and contours would change for a different Xbulk (i.e. different XMg), and even the field assemblages
might change: for example the higher temperature garnet + quartz field would be garnet + chlorite if the SiO2 content were so low that
quartz were consumed before chlorite by the reaction. From Winter (2010) An Introduction to Igneous and Metamorphic Petrology.
6. Ion Exchange Reactions
• Reciprocal exchange of components between 2 or
more minerals
– MgSiO3 + CaFeSi2O6 = FeSiO3 + CaMgSi2O6
– Annite + Pyrope = Phlogopite + Almandine
• Expressed as pure end-members, but really
involves Mg-Fe (or other) exchange between
intermediate solutions
• Basis for many geothermobarometers
• Causes rotation of tie-lines on compatibility
diagrams
Figure 27.6. AFM projections showing the relative distribution of Fe and Mg in garnet vs. biotite at approximately 500oC
(a) and 800oC (b). From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc.
Amer. Monograph 1. MSA. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
6. Redox Reactions
• Involves a change in oxidation state of an element
 6 Fe2O3 = 4 Fe3O4 + O2
 2 Fe3O4 + 3 SiO2 = 3 Fe2SiO4 + O2
• At any particular pressure these become oxygen
buffers
Fig. 26.10. Isobaric T-fO2 diagram
showing the location of reactions
(26.13) - (26.15) used to buffer oxygen
in experimental systems. After Frost
(1991), Rev. in Mineralogy, 25, MSA,
pp. 469-488. Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
7. Reactions Involving Dissolved Species
• Minerals plus ions neutral molecules dissolved in a fluid
• One example is hydrolysis:
– 2 KAlSi3O8 + 2 H+ + H2O = Al2Si2O5 (OH)4 + SiO2 + 2 K+
Kfs
aq. species
kaolinite
aq. species
Can treat such reactions in terms of the phase rule and
the intensive variables: P, T, and concentrations of
the reactant species
 T-P diagrams for fixed or contoured Ci
 Isobaric T-Ci diagrams
 Isobaric and isothermal Ci - Cj diagrams
 Reaction above might be handled by a T vs.
CK+/CH+ diagram
Reactions and Chemographics
We can use chemographics to infer reactions
P
e
r
F
o
E
n
M
g
O
Q
t
z
S
i
O
2
• Any two phases in a binary system can react to
from a phase between them
•
•
•
•
Fo + Qtz = En
Mg2SiO4 + SiO2 = Mg2Si2O6
En + Per = Fo
Mg2Si2O6 + 2 MgO = 2 Mg2SiO4
Per + Qtz = Fo or En
If we know the chemographics we can determine that a
reaction is possible (and can dispense with balancing it)
Reactions and Chemographics
What reaction does this ternary system allow?
Fig. 26.12. From Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice
Hall.
Reactions and Chemographics
A+B+C=X
above x-in isograd
below x-in isograd
Reactions and Chemographics
What reaction does this system allow?
Fig. 26.13. From Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice
Hall.
Reactions and Chemographics
What reaction is possible between A-B-C-D?
A compatibility
diagram for some
metamorphic zone
Fig. 26.14a. From Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice
Hall.
Below the
isograd
Fig. 26.14. From Winter (2010) An
Introduction to Igneous and
Metamorphic Petrology. Prentice
Hall.
A+B=C+ D
At the isograd
Above the
isograd
This is called a tie-line flip, and
results in new groupings in the
next metamorphic zone
Petrogenetic Grids
P-T diagrams for multicomponent systems that show a set
of reactions, generally for a specific rock type
Petrogenetic grid
for mafic rocks
Fig. 26.19. Simplified petrogenetic grid for metamorphosed mafic rocks showing the location of several determined
univariant reactions in the CaO-MgO-Al2O3-SiO2-H2O-(Na2O) system (“C(N)MASH”). Winter (2010) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.
Text figures that I don’t have time to
cover in my 1-semester class
Fig. 26.7. T-XCO2 phase
diagram fro 2 reactions
in the CaO-MgO-SiO2H2O-CO2 system at 0.5
GPa, assuming ideal
mixing of non-ideal
gases, calculated using
the program TWQ by
Berman (1988, 1990,
1991). Winter (2010)
An Introduction to
Igneous and
Metamorphic
Petrology. Prentice
Hall.
Text figures that I don’t have time to
cover in my 1-semester class
Figure 26.15. The
Al2SiO5 T-P phase
diagram from Figure
21-9 (without H2O).
Winter (2010) An
Introduction to Igneous
and Metamorphic
Petrology. Prentice
Hall.
Text figures that I don’t have time to
cover in my 1-semester class
Figure 26.16. Schematic one-component T-P
phase diagram showing the topology of a fourphase multisystem in which all invariant points
are stable. Because only three phases (C+2)
coexist at an invariant point, a complete system
should have four invariant points, each with one
phase absent. Phases absent at invariant points
are in square brackets, phases absent for
univariant reactions are in parentheses. Winter
(2010) An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Text figures that I don’t have time to
cover in my 1-semester class
Figure 26.17. A portion of the P-T phase diagram
for SiO2 (Figure 6-6) showing two stable invariant
points [Trd] and [Liq] and two metastable ones. [bQtz] occurs at negative pressure, and [Crs] is truly
metastable in that it is the intersection of
metastable extensions. From Spear (1993)
Metamorphic Phase Equilibria and PressureTemperature-Time Paths. Mineral. Soc. Amer.
Monograph 1. MSA.
Text figures that I
don’t have time to
cover in my 1semester class
Figure 26.18. a. Hypothetical reaction D + E = F in a twocomponent phase diagram. Note that the D-absent and Eabsent curves must both lie on the side of the initial
univariant curve opposite to the field in which D + E is
stable. Likewise the F-absent curve must lie on the side
opposite to the field in which F is stable. b. A second
hypothetical univariant curve (D-absent) is added. c. The
complete topology of the invariant point can then be
derived from the two initial reactions in (b). The
chemographics may then be added to each divariant field.
Winter (2010) An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Figure 26.20. a. Sketch from a photomicrograph showing small crystals of kyanite (purple) and quartz (blue) in a larger
muscovite grain (green). Small crystals of fibrolitic sillimanite also occur in the muscovite. Glen Cova, Scotland. b. Sillimanite
needles in quartz (blue) embaying muscovite (green). Pink crystals are biotite. Donegal, Ireland. After Carmichael (1969).
Contrib. Mineral. Petrol., 20, 244-267.
Text figures that I don’t have time to
cover in my 1-semester class
Figure 26.21. A possible mechanism by which the Ky  Sil reaction can be accomplished while producing the textures
illustrated in Figure 26.20a and b. The exchange of ions shown between the two local zones is required if the reactions are to
occur. After Carmichael (1969). Contrib. Mineral. Petrol., 20, 244-267.
Text figures that I don’t have time to
cover in my 1-semester class
Figure 26.21. An alternative
mechanism by which the
reaction Ky  Sil reaction can
be accomplished while
producing sillimanite needles
associated with biotite with
plagioclase occupying
embayments in the biotite. The
exchange of ions shown between
the two local zones is required if
the reactions are to occur. After
Carmichael (1969). Contrib.
Mineral. Petrol., 20, 244-267.