#### Transcript Ch 24 Mineral Assemblages mod 9

```Chapter 24. Stable Mineral
Assemblages in Metamorphic
Rocks
 Equilibrium

Mineral Assemblages
At equilibrium, the mineralogy (and the
composition of each mineral) is determined
by T, P, and X . “Mineral paragenesis”
The Phase Rule in Metamorphic
Systems

at equilibrium:
F=C-f+2
f = #phases at a point
C = # components: the minimum
number of chemical constituents
required to specify every phase in
the system. Many poss. choices
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.)
the phase rule
(6-1)
Goldschmidt’s Rule
If F  2 (phase field)
then
F=C-f+2 2
So f  C
(24-1)
Useful in evaluating whether
or not a rock is at equilibrium
http://serc.carleton.edu/research_education/equilibria/phaserule.html
Picking the Components

C is the minimum number of chemical components
required to constitute all the phases. Consider the
reaction:
CaMg(CO3)2 + 2 SiO2 = CaMgSi2O6 + 2 CO2
Dolomite + 2 Quartz = Diopside + 2 Carbon Dioxide

Normally we would pick the 4 components: CaO, MgO,
SiO2, and CO2 based on the simple oxides. However,
because Ca and Mg are in a 1:1 ratio in both dolomite
and diopside (and not present in quartz or carbon
dioxide), we could choose a ternary system with
components: CaMgO2, SiO2, and CO2
Easier to plot
The Phase Rule in Metamorphic
Systems
Suppose we have determined C for a rock
Consider the following three scenarios:
Case 1 f = C
– The rock probably
represents an
equilibrium mineral
assemblage from
within a
metamorphic zone
b)
The Phase Rule in Metamorphic
Systems
f<C
– Common with mineral systems that exhibit
solid solution
•For example, in the
plagioclase or the olivine
system we can see that under
metamorphic conditions
(below the solidus) these 2-C
systems consist of a single
mineral phase
• F = 1 and C = 2 so F < C
Liquid
Plagioclase
plus
Liquid
Plagioclase
Case 3:
f>C
Consider the following three scenarios:
Subcase a: C = 1



f = 1 is common
common
f = 3 only at the
specific P-T
conditions of the
invariant point
(~ 0.37 GPa and
500oC)
Figure 21-9. The P-T phase diagram for the system Al2SiO5
calculated using the program TWQ (Berman, 1988, 1990,
1991). Winter (2001) An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Case 3
f>C
Subcase b: Equilibrium has not been attained
The phase rule applies only to systems at
equilibrium, and there could be any number of
minerals coexisting if equilibrium is not attained
Relict inclusions in garnet
http://serc.carleton.edu/research_education/equilibria/PTtPaths.html
Case 3 f > C
Subcase 3: We didn’t choose the # of
components correctly

Some guidelines for an appropriate choice of C
– Begin with a 1-component system such as CaAl2Si2O8
(anorthite), there are 3 common types of major/minor
Case a) Components that generate a new
phase
 Adding a component such as CaMgSi2O6
(diopside), results in an additional phase: in
the binary Di-An system diopside coexists with
anorthite below the solidus
Case 3 f > C
– Begin with a 1-component system, such as CaAl2Si2O8
(anorthite), there are 3 common types of major/minor
Case b) Components that substitute for other
components
 Adding a component such as NaAlSi3O8 (albite) to the
CaAl2Si2O8 anorthite system. Albite would dissolve in
the anorthite structure, resulting in a single solidsolution mineral (plagioclase) below the solidus
 Fe and Mn commonly substitute for Mg
 Al may substitute for Si
 Na may substitute for K
Case 3 f > C
Begin with a 1-component system, such as CaAl2Si2O8
(anorthite), there are 3 common types of major/minor
c) “Perfectly mobile” components, e.g. abundant
H2O with excellent permeability
 These are components are either a freely mobile fluid
or a component that dissolves readily in a fluid phase
and can be transported easily (e.g. LILs)
Perfectly Mobile Components
Consider the very simple metamorphic system, MgOH2O
– Possible natural phases in this system are periclase
(MgO), aqueous fluid (H2O), and brucite (Mg(OH)2)
F > C
– How we deal with H2O depends upon whether
water is perfectly mobile or not
– A reaction can occur between the potential phases
in this system:
MgO + H2O  Mg(OH)2 Per + Fluid = Bru
BTW this is a retrograde reaction as written
(occurs as the rock cools and hydrates)
If water is not abundant or perfectly mobile
it may become a limiting factor in the
reaction
•A reaction involving more than one reactant will proceed until any one of the
reactants is consumed
MgO + H2O  Mg(OH)2 Per + water = Bru
•The reaction will proceed until either periclase or water is
consumed
•Periclase can react only with the quantity of water that can
diffuse into the system
•If water is not perfectly mobile, and is limited in quantity, it
will be consumed first
Once the water is gone, the excess periclase remains stable as
conditions change into the brucite stability field
•The reaction line is not the absolute
stability boundary of periclase, or of
water, because either can be stable
across the boundary if the other reactant
is absent
Figure 24-1. P-T diagram for the reaction brucite = periclase +
water. From Winter (2001). An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Chemographic Diagrams
Chemographics refers to the graphical
representation of the chemistry of mineral
assemblages
A simple example: the plagioclase system as a
linear C = 2 plot:
Metamorphic components typically expressed as molar quantities, and not as weight %
Any intermediate composition is simply plotted an appropriate distance along the line
An50 would plot in the center, An25 would plot ¼ of the way from Ab to An, etc.
Chemographic Diagrams
Suppose you had a small area of a metamorphic terrane in
which the rocks correspond to a hypothetical 3-component
system with variable proportions of the components x-y-z
as shown in Fig. 24-2
The rocks in the area
are found to contain 6
minerals with the fixed
compositions x, y, z, xz,
xyz, and yz2
Example: components x,y and z
are MgO, FeO, and SiO2 respectively
Actual choices more complex
Suppose that the rocks in
our area are found to have
the following 5 assemblages:
–
–
–
–
–
x-xy-x2z
xy-xyz-x2z
xy-xyz-y
xyz-z-x2z
y-z-xyz
Figure 24-2 Phases that
coexist at equilibrium in a
rock are connected by tie-
lines
Compatibility
Diagram
MgO, FeO, and SiO2
x2z = Mg2SiO4 Forsterite
Note that this subdivides the chemographic diagram
into 5 sub-triangles, labeled (A)-(E)
–
–
–
–
–
A:x-xy-x2z
B:xy-xyz-x2z
C:xy-xyz-y
D:xyz-z-x2z
E:y-z-xyz
Any point within the diagram represents a
specific bulk rock composition
The diagram determines the corresponding
mineral assemblage that develops at
equilibrium
For example, a point within the sub-triangle
(E), the corresponding mineral assemblage
corresponds to the corners = y - z - xyz
Any rock with a bulk composition plotting
within triangle (E) will develop that same
mineral assemblage
What happens if you find a place that falls directly on a
tie-line, such as point (f)?
In this case the
mineral assemblage
consists of xyz and z
only (the ends of the
tie-line), since by
phases together in
the proper proportion
you can produce the
bulk composition (f)
In such a situation
F= C = 2, as
required at
equilibrium
In the unlikely event that the bulk
composition equals that of a
single mineral, such as xyz, then
f = 1, but C = 1 as well
“compositionally
degenerate” i.e
“requiring fewer
components than
normal
Chemographic Diagrams for
Metamorphic Rocks
Most common natural rocks contain the
major elements: SiO2, Al2O3, K2O, CaO, Na2O,
FeO, MgO, MnO and H2O such that C = 9
 Three components is the maximum number
that we can easily deal with in two
dimensions
 What is the “right” choice of components?
 Some simplifying choices:

The ACF Diagram
• Eskola (1915) proposed the ACF diagram as a way to
illustrate metamorphic mineral assemblages in mafic
rocks on a simplified 3-C triangular diagram
• He wanted to concentrate only on the minerals that
appeared or disappeared during metamorphism, thus
acting as indicators of metamorphic grade
Fig. 24-4 illustrates the positions of several common metamorphic
minerals on the ACF diagram. Note: this diagram is presented only
to show you where a number of important phases plot.
It is not specific to a P-T range and therefore is not a true
compatibility diagram, and has no petrological significance
Figure 24-4. After Ehlers and Blatt
(1982). Petrology. Freeman. And
Miyashiro (1994) Metamorphic
Petrology. Oxford.
The 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
For A we are here interested only in the Al
that occurs in excess of that combined
with K and Na to make any feldspar
The ACF Diagram
By creating these three pseudo-components, 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

WHERE DOES A MINERAL PLOT?
HOW DO SOLID SOLUTIONS OR MIXTURES PLOT?

The ACF Diagram
An example:
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO - 3.3 P2O5
F = FeO + MgO + MnO
Anorthite CaAl2Si2O8
 A = 1 + 0 - 0 - 0 = 1, C = 1 - 0 = 1, and F = 0
 Provisional values sum to 2, so we can normalize to
1.0 by multiplying each value by ½, resulting in
A = 0.5
C = 0.5
F=0

X
Anorthite thus plots half way
between A and C on the side of the
ACF triangle, as shown in Fig. 24-4
Example 1: Where does K-feldspar plot?
•For KAlSi3O8 A = 0.5 + 0 - 0.5 = 0, C = 0, and F = 0
•Kspar doesn’t plot on the ACF diagram
•Example 2: If you try this for albite NaAlSi3O8 you will
find that it doesn’t plot either
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO - 3.3 P2O5
Figure 24-4.
F = FeO + MgO + MnO
For albite NaAlSi3O8
A = 0.5 + 0 - 0.5 -0 = 0
C=0+0
F=0+0+0
A typical ACF compatibility diagram, referring to a
specific range of P and T (the kyanite zone in the
Scottish Highlands)
•Plot all phases and connect coexisting ones
with tie-lines
• Field R: Mafic rocks in the hb-plag –gt
(almandine) triangle, and thus most
metabasaltic rocks occur as amphibolites or
garnet amphibolites in this zone
•Field S: More aluminous rocks develop
kyanite and/or muscovite and not hornblende
• Field T: More calcic rocks lose Ca-free
garnet, and contain diopside, grossularite, or
even calcite (if CO2 is present)
S
•The diagram allows us to interpret the
relationship between the chemical
composition of a rock and the equilibrium
mineral assemblage
Figure 24-5. After Turner
(1981). Metamorphic Petrology.
McGraw Hill.
R
T
NEW for Pelitics:The AKF Diagram
Because pelitic sediments are high in Al2O3 and K2O,
and low in CaO, Eskola proposed a different diagram
that included K2O to depict the mineral assemblages
that develop in them
 In
the AKF diagram, the pseudocomponents are:
A = Al2O3 + Fe2O3 - Na2O - K2O - CaO
K = K2O
F = FeO + MgO + MnO
We are now interested only in the Al that occurs in excess of that
combined with K, Na, and Ca to make any feldspar
Another
figurative
AKF to
show where
metapelitic
minerals
plot
Figure 24-6. After Ehlers and
Blatt (1982). Petrology.
Freeman.
AKF compatibility diagram (Eskola, 1915) illustrating
paragenesis of pelitic hornfelses, Orijärvi region
Finland
Figure 24-7. After Eskola (1915) and Turner (1981) Metamorphic
Petrology. McGraw Hill.
• Region R:
•Al-poor rocks contain biotite
K(Mg,Fe)2(AlSi3O10)(F,OH)2, and
may contain an amphibole (e.g.
Anthophyllite
(Mg,
Fe)7Si8O22(OH)2 ) if sufficiently rich
in Mg and Fe, or microcline
KAlSi3O8 if not.
• Region S: Rocks richer in Al
contain andalusite Al2SiO5
,cordierite (Mg,Fe)2Al4Si5O18
and Muscovite
KAl2(AlSi3O10)(OH)2
S
R
Three of the most common minerals in metapelites:
andalusite, muscovite, and microcline, all plot as
distinct points in the AKF diagram
 And
& Ms plot as the
same point in the
ACF diagram, and
Micr doesn’t plot at
all, so the ACF
diagram is much less
useful for pelitic
rocks (rich in K and
Al)
Figure 24-7. After Ehlers and Blatt
(1982). Petrology. Freeman.
Projection from Apical Phases

ACF and AKF diagrams eliminate SiO2 by projecting
from quartz, so quartz MUST be present

The shortcoming is that these projections compress
the true relationships as a dimension is lost

Let’s examine projections on another diagram, the
A(K)FM of Thompson.
J.B. Thompson’s A(K)FM Diagram
An alternative to the AKF diagram for
metamorphosed pelitic rocks

Although the AKF is useful in this capacity, J.B.
Thompson (1957) noted that Fe and Mg do not
partition themselves equally between the various
mafic minerals in most rocks

Biotite is useful in assessing temperature
histories of metamorphic rocks, because the
partitioning of iron and magnesium between
biotite and garnet is sensitive to temperature
J.B. Thompson’s A(K)FM Diagram
A = Al2O3
K = K2O
F = FeO
M = MgO
In order to avoid dealing with a
three-dimensional tetrahedron,
Thompson projected the phases in
the system to the AFM face, thereby
eliminating K2O
He recognized that projecting from
K2O would not work, since no phase
corresponds to this apical point, and
projections would cross important
tie-lines
J.B.
Thompson’s
A(K)FM
Diagram
Since muscovite is
K-rich phase in
metapelites, he
decided to project
from muscovite (Mu)
to the AFM base as
shown
Biotite is outside this volume, and projecting it
from Mu causes it to plot as a band (of
variable Fe/Mg) outside the AFM triangle
J.B. Thompson’s A(K)FM Diagram


