GEOL 2312
IGNEOUS AND METAMORPHIC
PETROLOGY
Lecture 18
Stable Mineral Assemblages in Metamorphic Rocks
March 30, 2016
EQUILIBRIUM MINERAL
ASSEMBLAGES
Evidence of Chemical Equilibrium
- Lack of disequilibrium textures (replacement textures,
corona, compositional zoning, ....)
- Each mineral type shares contacts with every other
mineral phase in the rock
- Layers are rare or textures are homogeneous within
the layers
- Rocks are in textural equilibrium
- Rocks conform to Gibbs Phase Rule
- Minerals lack chemical zoning
PHASE RULE IN METAMORPHIC ROCKS
Phase rule, as applied to systems at equilibrium:
F=C-f+2
f = the number of phases in the system
C = the number of components: the minimum number of chemical
constituents required to specify every phase in the system
F = the number of degrees of freedom: the number of independently
variable intensive parameters of state (such as temperature, pressure,
the composition of each phase, etc.)
In natural systems, there are multiple compositional variables in
addition to independent changes in P & T. If F  2 is the most
common situation, then the phase rule may be adjusted
accordingly:
F = C - f + 2  2, or
f C
Goldschmidt’s mineralogical phase rule,
or simply the mineralogical phase rule
PHASE RULE IN METAMORPHIC ROCKS
Suppose we have determined C for a rock
Consider the following three scenarios:
1) f = C
The standard divariant situation of the Phase Rule
The rock probably represents an equilibrium mineral
assemblage from within a metamorphic zone
2) f < C
Common with minerals that exhibit solid solution
(e.g., Plagioclase - single mineral, but two
components)
PHASE RULE IN METAMORPHIC ROCKS
3) f > C
A more interesting situation and at least one of three
situations must be responsible:
A) F < 2

The sample is collected from a location right on a
univariant reaction curve (isograd) or invariant point
B) Equilibrium has not been attained
C) The number of components were
not properly chosen
PHASE RULE IN METAMORPHIC ROCKS
Choosing Components to define Metamorphic Systems
As with igneous rocks, it is not reasonable to choose every
chemical constituent of a rock as a component.
Stick to:
- Essential Components that generate a new phase with a
limited P&T range (garnet – yes; plagioclase – no)
- Three Components (or component combinations) that
can be graphically portrayed in 2D
Avoid:
- Components that are major constituents of single phases
(e.g., P2O5 – apatite, TiO2 – ilmenite)
- Components that substitute for other components
(e.g. Ab-An, Fa-Fo, Mn for Fe, Al for Si, Na for K)
- “Perfectly mobile” components (H2O, CO2, ...)
PHASE RULE IN METAMORPHIC ROCKS
“Perfectly Mobile” H2O or Not
Implies that fluid may come
and go based on external
conditions not controlled by
mineral reactions. It is
typically not considered a
component. It is added as
needed and leaves when in
excess.
Prograde reaction will go
regardless if H2O fluid is
present
Retrograde reaction requires
H2O to be present to go, but it
is not a component of this
system (one comp – MgO)
Mg(OH)2
MgO
Winter (2001)Figure 24-1. P-T diagram for the
reaction brucite = periclase + water. From Winter
(2001). An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
PHASE RULE IN METAMORPHIC ROCKS
How do you know if you have chosen the proper components?
The rocks should tell you
 The phase rule is an interpretive tool, not a predictive
tool, and does not tell the rocks how to behave
 If you only see low-f assemblages (e.g. Per or Bru in
the MgO-H2O system), then some components may be
mobile
 If assemblages have many phases in an area it is
unlikely that so much of the area is right on a
univariant curve, and may require the number of
components to include otherwise mobile phases, such
as H2O or CO2, in order to apply the phase rule
correctly
CHEMOGRAPHIC DIAGRAMS
Chemographics refers to the graphical representation of the
chemistry of mineral assemblages
Mineral compositions possible in a 3component system are plotted on a
triangular chemographic diagram
COMPONENTS = x, y, and z
PHASES = x, y, z, xz, xyz, and yz2
A simple example: the plagioclase
system as a linear 2-component plot:
CHEMOGRAPHIC DIAGRAMS
Compatibility Diagrams
determines the
equilibrium mineral
assemblage that should
develop for a particular
whole rock composition
defined by three
components
Divariant Equilibrium
Mineral Assemblages
(A) x-xy-x2z
(B) xy-xyz-x2z
(C) xy-xyz-y
(D) xyz-z-x2z
(E) y-z-xyz
CHEMOGRAPHIC DIAGRAMS
Valid compatibility diagram must be referenced to a
specific range of P-T conditions, such as a zone in some
metamorphic terrane, because the stability of the minerals
and their groupings vary as P and T vary
 Previous diagram refers to a P-T range in which the fictitious
minerals x, y, z, xy, xyz, and x2z are all stable and occur in the
groups shown
 At different grades the diagrams change

Other minerals become stable

Different arrangements of the same minerals (different tielines connect different coexisting phases)
CHEMOGRAPHIC DIAGRAMS
W/
SOLID SOLUTION
Phases with SS
between Y and Z
Phases with SS
between Y, X. and Z
CHEMOGRAPHIC DIAGRAMS
W/
SOLID SOLUTION
Tie lines link
coexisting
compositions
CHEMOGRAPHIC DIAGRAMS
ACF DIAGRAM
The three pseudo-components are
all calculated on an atomic basis:
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO - 3.3 P2O5
F = FeO + MgO + MnO
Best Suited to Mafic
Igneous Rocks and
Sedimentary Rocks
(Graywackes)
Figure 24-4. After Ehlers and Blatt (1982). Petrology. Freeman. And
Miyashiro (1994) Metamorphic Petrology. Oxford.
CHEMOGRAPHIC DIAGRAMS
ACF DIAGRAM
By creating these three pseudocomponents, Eskola reduced the number of
components in mafic rocks from 8 to 3
Water is omitted under the
assumption that it is
perfectly mobile
Note that SiO2 is simply
ignored. We shall see
that this is equivalent to
projecting from quartz
In order for a projected
phase diagram to be
truly valid, the phase
from which it is
projected must be
present in the mineral
assemblages
represented
e.g. Alkali Feldspar
CHEMOGRAPHIC DIAGRAMS
AKF DIAGRAM
A = Al2O3 + Fe2O3 - Na2O K2O - CaO
K = K2O
F = FeO + MgO + MnO
Best Suited to
Pelitic (clay-rich)
Sedimentary Rocks
Projected From
Quartz &
Plagioclase
CHEMOGRAPHIC DIAGRAMS
APICAL PHASE PROJECTIONS
Mathematically, the
same as ignoring CaO
in the Di formula and
normalizing MgO and
SiO2 to 100%
Only valid if
phase projecting
from is present
with all phases
MgO
Per
Fo
En
Di'
SiO2
Q
CHEMOGRAPHIC DIAGRAMS
APICAL PHASE PROJECTIONS
Mathematically the
same as ignoring SiO2
in the X & Y formulas
and normalizing A, B,
and C to 100%
Possible Phase
assemblages
(q)-b-x-c
(q)-a-x-y
(q)-b-x-y
(q)-a-b-y
(q)-a-x-c
x = ABCQ
y = A2B2CQ
Fig. 24-13