Transcript Introduction to Petrology

Phase Equilibria in Silicate Systems
Intro. Petrol. EPSC-212, Francis-14
Winter, J.D.; 2001: An Introduction to Igneous and Metamorphic Petrology. Prentice Hall, Chapter 4, 2001.
Fundamentals: Units
Types of units commonly used:
Weight units: = gms species/ 100gms (X-Ray analytical techniques determine weight
fraction element)
• Molar Units: = gms species / (molecular wt. of species), normalized to 100 (most
chemical phenomena are proportional to molecular proportions)
• Atomic units: = (no. moles species) x (no. atoms per species), normalized to 100 atoms
• Cation units: = (no. moles species) x (no. cations per species), typically normalized to
some total number of cations (or anions).
• Oxygen units: = (no. moles species) x (no. oxygens per species), commonly normalized to
some total number of anions (closest to volume proportions)
Example:
Coordinates of Enstatite (MgSiO3) in: Mg2SiO4 - SiO2 space
Weight units:
70
30
Molecular units:
50
50
Cations units:
75
25
Oxygen units
66.7
33.3
Volatile have an importance beyond that predicted simply by their abundance
because:
- Volatiles have low molecular weights:
H2O = 18
CO2 = 44
SiO4 = 92
NaAlSi3O8 = 262
In a melt consisting of NaAlSi3O8 clusters and H2O molecules:
0.5 wt. % H20 ~ 45 mole % H2O
Small amounts of water produce large effects because of its low molecular wt.
compared to that of a silicate magma. This effect is enhanced by the fact that
at XH2O < 0.3, molecular water dissociates into 2 OH’s
fH20 ~ PH2O α XH2O.2
H2O + Obridging
2 × OH
The Rock Forming Minerals:
A mineral is defined as a naturally occurring crystalline phase or compound that is made up
of a 3-D ordered atomic arrangement or structure of different atoms.
The dominant rock forming minerals are silicates, compounds of Si and O, because Si is the
most abundant metal and oxygen the most abundant anion in the Earth's crust.
Minerals can be thought of as close packings of oxygens to a first approximation, because of
the large size of O, with the smaller Si and other metals occupying the interstices, or sites,
between the oxygens.
Mineral Name:
Olivine
Pyroxene
Feldspar
Structural Formula:
Y2TO4
XYT2O6
WT4O8
(Mg,Fe)2SiO4
Ca(Mg,Fe)Si2O6
(K,Na)AlSi3O8
Chemical Composition:
Rock Forming Minerals:
The ratio of Si to O determines the type and abundance of the silicate mineral(s) present, and the other
metals distribute themselves in sites between the oxygens according to the size and charge of their
cations. The amounts of different elements in any given mineral may vary somewhat, but the type and
proportion of occupied sites is fixed by the structure of the silicate mineral and can be expressed by a
formula of the type:
Ww Xx Yy Tt Aa
Where the capital letters stand for occupied sites of different co-ordination number and the small letters
are small whole numbers.
A
=
anion site
W
= 12 co-ordinated site
X
= 8 co-ordinated site
Y
= 6 co-ordinated site
T
= 4 co-ordinated site
K, Rb, Ba, Na
Ca, Mn, Na
Mg, Fe, Mn, Al, Ti
Si, Al
Rock Forming Minerals
Silicates (lithophile elements)
Olivine: Y2TO4
Mg2SiO4 - Fe2SiO4
Garnet: X3Y2(TO4)3
Mg3Al2(SiO4)3 - Fe3Al2(SiO4)3
Clinopyroxene: XYT2O6
CaMgSi2O6 - CaFeSi2O6
Orthopyroxene: Y2T2O6
Mg2Si2O6 - Fe2Si2O6
Amphibole: W01X2Y5T8O22(OH)2
Ca2Mg5Si8O22(OH)2 NaCa2Mg4Al(Al2Si6O22(OH)2
Feldspar: WT4O8
CaAl2Si2O8 - NaAlSi3O8 - KAlSi3O8
Quartz: TO2
SiO2
Micas: W Y2-3T4O10(OH)2
KAl2(AlSi3)O10(OH)2 - KMg3(AlSi3)O10(OH)2
Clays & Serpentine: Y3T2O5(OH)4
Mg3Si2O5(OH)4
Carbonates: (lithophile
elements)
Calcite - Dolomite: YCO3
CaCO3 - Ca(Mg,Fe)(CO3)2
Other Oxides: (lithophile
elements)
Spinel – Magnetite: Y3O4
MgAl2O4 - FeCr2O4 - Fe3O4
Hematite – Ilmenite: Y2O3
Fe2O3 - FeTiO3
Pyrite - Pyrrhotite
FeS2 - Fe1-xS
Sulfides: (chalcophile elements)
The Mineralogical Phase Rule
In any chemical system at equilibrium, the following relationship holds:
FDegrees of Freedom = Components - Phases + 2
F equals the minimum number of variables that must
be specified in order to completely define the state of
a system. F is thus the variance of the system, the
number of unknowns.
C
equals the number of independent chemical
components needed to define the composition of the
system.
P
equals the number of physical phases present in
the system, which include the number of solid
minerals, plus liquid and gas phases, if present.
2 represents the variables pressure and temperature.
Single Component Systems:
SiO2
When a solid consist of 2 coexisting minerals
(phases):
F = C–P+2 = 1 -2+2 = 1
Such a system is invariant at any given pressure,
and thus a single component solid phase will melt
at 1 unique temperature at any specified pressure.
The boundary between the 2 phases in P - T space
will be a univariant line with a slope approximated
by:
dG = - SdT + VdP = 0
dP/dT = S/ V
This is also true for solid - liquid phase boundaries
because, to a first approximation, Ho and So are
constant for small changes in temperature (true for
all reactions not involving a relatively
compressible vapour phase).
Two Component Systems:
Mg2SiO4 – SiO2
Pure forsterite melts at 2163oC at 1 atm. If extra SiO2 is added to the
system, SiO2 will be present only in the melt phase, while
forsterite will remain a pure phase. The temperature at which
forsterite crystallizes is now an inverse function of SiO2 content:
at equilibrium:
GFoOl
= GFoLiq
and
G
Fo
= 0
GoFo + R × T × Ln(aFoOl) = GoFoLiq + R × T × Ln(aFoLiq)
Go =
Fo
- R × T × Ln(aFoLiq/aFoOl)
or
Go
Fo
Go
Fo
= - R × T × Ln(1-XSiO2),
aFoOl = 1.0, assume activity (a) = mole fraction X)
and
= HoFo – T × SoFo = HoFo – T × HoFo / TFo
If Ho and So are insensitive to small changes in T & P, then:
Ho
Fo
– T × HoFo / TFo = - R × T × Ln(1-XSiO2)
or
Ln(1-XSiO2) = HoFo / R × (T - TFo) / (T×TFo)
van't Hoff equation for melting point depression
Two Component Systems:
Binary Phase Diagrams
If a system is comprised of 2
components, then where a solid
and liquid phase coexist:
F =2-2+2=2
Such a system is univariant at any
given pressure, and thus the
melting point of a solid will
depend on the proportions of the
two components. In the absence
of extensive solid solution, the
presence
of
an
additional
component will reduce the
melting temperature of single
component solid phases because
the
additional
component
typically dissolves preferentially
in the liquid phase.
e
No solid-solution
Between end-members
The Eutectic point “e” of a two component system is invariant (F =
0, if pressure fixed) and is defined by the intersection of two
univariant (F = 1) liquidus curves, originating from the melting
temperatures of the two pure end-member phases.
Peritectic versus Eutectic
Invariant points
e2
e1
p - oliv + liq
e -
liq
opx
e1 - liq
albite + qtz
opx + qtz
e2 - liq
neph + albite
The Lever Rule
X
For bulk
Composition X
T3 : Forst / liquid : b / a;
Forst / whole = b /(a+b)
T2 : Forst / liquid : c / a;
Forst / whole = c /(a+c)
T1 : Forst / Enst
Forst / whole = d /(a+d)
: d / a;
Cumulate Rocks versus Rocks
that represent liquids
Liquids
vs
Cumulates
Equilibrium
1557
vs
Fractional
Fractional Crystallization vs Partial Melting
Upon cooling to 1557oC, early crystallized olivine exhibits a reaction relationship with the residual
liquid of composition “p” to form orthopyroxene. Either olivine or melt must disappear before
cooling can continue. During partial melting, orthopyroxene begins to melt incongruently at 1557oC
to form olivine plus a liquid of composition “p”. Orthopyroxene must be consumed before the
temperature can increase.
The presence of other components in
solid solution at levels that are
insufficient to stabilize a separate phase
destroys the invariant nature of melting.
The temperature and composition of the
first melt are determined by the amount
of the additional component. During
partial melting, these additional
components are typically the first to be
refined
out
into
the
melt.
Bianary Systems with extensive
Solid Solution:
Olivine exhibits complete solid solution between the
forsterite (Mg2SiO4) and fayalite (Fe2SiO4) end-members.
In Fe and Mg bearing systems, neither the olivine solid
nor the olivine liquid are pure end-member components:
We now have two van't Hoff equations:
Ln(XFoLiq / XFoOl) = HoFo / R × (T - TFo) / (T × TFo)
Ln(XFaLiq / XFaOl) = HoFa /R × (T - TFa) /(T × TFa)
Because: XFaLig = 1-XFoLiq and XFaOl = 1-XFoOl
Then:
Ln(XFoLiq / XFoOl) = HoFo / R × (T - TFo) / (T × TFo)
Ln(1-XFoLiq / (1-XFoOl)) = HoFa /R × (T - TFa) / (T × TFa)
The choice of any T between TFo and TFa will enable the
calculation of the compositions of the coexisting olivine
and liquid for that T, and thus the solidus and liquidus at
any T. Exactly analogous solid solution relationships can
be developed for the plagioclase series feldspars:
anorthite CaAl2Si2O8
-
albite NaAlSi3O8
Ternary Systems: Forsterite – Diopside – Anorthite
Liquidus Projection
In order to portray the magmatic phase
relations of systems with more than two
chemical components, we need to
develop specialized projection schemes.
Three component systems can be
represented on a two dimensional sheet
of paper, if we project only those phase
relationships for which a magmatic liquid
is present.
P = 1 atm
Ternary Systems: Forsterite – Diopside - Anorthite
A Liquid of bulk composition X cools to the
olivine liquidus surface at 1600°C, at which
point Forsterite begins to crystalize
P = 1 atm
The liquid composition moves directly away
from Fo, producing a dunite cumulate, until
it reaches the cotectic, at which point
Diopside begins to crystallize with
Forsterite.
X
Forsterite – Diopside - Anorthite
P = 1 atm
Co-precipitation of Forsterite + Diopside
causes liquid composition to move down
cotectic curve, producing a wehrlite
cumulate.
X
Forsterite – Diopside - Anorthite
P = 1 atm
The liquid composition reaches the ternary
eutectic at 1270°C, at which point Anorthite
begins to crystallize with Diopside and
Forsterite, producing a gabbroic cumulate.
The composition of the liquid remains
at the eutectic point until all the liquid
is consumed.
X
Ternary Systems
The composition of the first melt of
an assemblage ABD is that of
invariant eutectic point eABD, while
the composition of the first melt of
assemblage DBC is that of invariant
eutectic point eDBC.
The intersection of a univariant
curve with the Alkemade line
joining the compositions of the
coexisting solid phases defines a
thermal maximum along the
univariant curve.
Ternary Systems
with
Solid Solution:
Oliv - Cpx - Qtz Liquidus Projection:
The invariant point “p”, at which olivine,
clinopyroxene and orthopyroxene coexist with a
liquid, is a peritectic point because it lies outside
of the compositional volume of the solid phases.
It represents the first melt of any assemblage
consisting of olivine, opx, and cpx (mantle
peridotite) at 1 atm., and is analogous in
composition to a quartz-normative basalt.
Similarly, the univariant curve along which
olivine and orthopyroxene coexist with a liquid is
a reaction curve because the tangent to the curve
at any point cuts the olivine - orthopyroxene
Alkemade line with a negative olivine intercept.
The invariant point “e” is a eutectic and
represents the composition of the first melt of an
assemblage of quartz-diopside-orthopyroxene.
The composition of “e” approximates that of the
Earth’s continental crust.
Mantle Ocean Continent
crust crust
SiO2
TiO2
Al2O3
MgO
FeO
CaO
Na2O
K2O
Total
45.2
0.7
3.5
37.5
8.5
3.1
0.6
0.1
99.2
49.4
1.4
15.4
7.6
10.1
12.5
2.6
0.3
99.3
60.3
1.0
15.6
3.9
7.2
5.8
3.2
2.5
99.5
Cations normalized to 100 cations
Si
Ti
Al
Mg
Fe
Ca
Na
K
O
38.5
0.5
3.6
47.6
6.0
2.8
0.9
0.1
140.2
46.1
1.0
16.9
10.6
7.9
12.5
4.7
0.5
153.0
56.4
0.7
17.2
5.4
5.6
5.8
5.8
3.0
161.3
Mineralogy (oxygen units, XFe3+ = 0.10)
Quartz
Feldspar
Clinopyroxene
Orthopyroxene
Olivine
Oxides
0.0
13.2
6.7
18.3
59.9
1.8
0.0
57.3
25.7
4.1
9.9
3.0
13.0
64.3
5.9
14.7
0.0
2.0
Oceanic crust - MORB basalt
p
Continental crust -
e
granite
Liquidus Projections for haplo-basalts
The Basalt Tetrahedron at 1 atm:
The olivine - clinopyroxene plagioclase plane is a thermal
divide in the haplo-basalt
system at low pressures and
separates natural magmas into
two fundamentally different
magmatic series. Sub-alkaline
basaltic
magmas
with
compositions to the Qtz-rich
side of the plane fractionate
towards Qtz-saturated residual
liquids, such as rhyolite.
Alkaline basaltic magmas with
compositions to the Qtz-poor
side of the plane fractionate
towards
residual
liquids
saturated in a feldspathoid,
such as nepheline phonolite.
Since the dominant mineral in the mantle source of basaltic magmas is olivine, we can achieve a
further simplification by projecting the liquidus of basaltic systems from the perspective of olivine:
Alkaline basalts fall to the Foid-side of the olivineclinopyroxene-plagioclase plane (1 atm thermal divide) and
fractionate to foid-saturated residual liquids. Sub-alkaline
basalts fall to the Quartz-side and fractionate towards
quartz-saturated residual liquids.
Alkaline basaltic lavas are volumetrically insignificant (~1%), but strongly enriched in highly
incompatible trace elements profiles compared to sub-alkaline lavas, and low in HREE, Y, & Sc.
These characteristics are generally ascribed to small degrees of partial melting at elevated
pressures, leaving garnet as a phase in the refractory residue.
The Effect of Pressure
1 atm
Increasing pressure shifts the olivcpx-opx peritectic point towards
less Si-rich compositions.
At
approximately 10 kbs this invariant
point moves into the oliv - cpx- opx
compositional volume, and the first
melt of the mantle has an olivine
basalt composition. The invariant
point is still a peritectic point,
however, because of the extensive
solid solution of cpx towards opx.
At pressures exceeding 15-20 kbs,
this invariant point moves outside
the simple olivine - cpx - qtz
system, into the Neph-normative
volume of the basalt tetrahedron.
The first melt of mantle peridotite
is an alkaline olivine basalt at these
high pressures.
Since the dominant mineral in the mantle source of basaltic magmas is olivine, we can achieve a
further simplification by projecting the liquidus of basaltic systems from the perspective of olivine:
Movement of the invariant point
determining the composition of the
first melt with increasing pressure.