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Chapter 6- Phase Relations and Binary Systems

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Title: Chapter 6- Phase Relations and Binary Systems


1
Phase Equilibria
2
Olivine and Clinopyroxene (Augite) follow Bowens
Reaction Series, Discontinuous Side. Olivine
appears first, then decreases as pyroxenes start.
Olivine becomes embayed. Note also that, in this
case, plagioclases start at cooler temperatures
than pyroxenes.
3
Mineral Stability
  • Phase Stability The stability of a phase is
    determined by the Gibbs free energy, G.
  • A Mineral of constant composition is considered a
    solid phase
  • Mineral stability is commonly portrayed on a
    Phase Diagram

4
Components and Phases
  • Components are the chemical entities necessary to
    define all the potential phases in a system of
    interest

Here one Component, Al2SiO5
Phases number of mineral species plus
fluids Here three Phases Kyanite, Sillimanite,
and Andalucite
And
5
Degrees of Freedom f by Examples
p f c 2
  • If T and P can change without changing the
    mineral assemblage, the system has two degrees of
    freedom f 2
  • If neither T or P can change without changing the
    mineral assemblage, the system has zero degrees
    of freedom f 0
  • If T and P must change together to maintain the
    same mineral, the system has one degree of
    freedom f 1

Sill.
Ky.
On a phase diagram f0 corresponds to a point,
f 1 to a reaction line, f 2 to a 1 phase
area.
And.
6
The Phase Rule
  • The number of minerals (phases) that may stably
    coexist is limited by the number of chemical
    components
  • p f c 2 OR f c p 2
  • where P is the number of mineral phases, c the
    number of chemical components, and f is the
    number of degrees of freedom.

7
Simple System H20
In a one component system, for example H2O, phase
changes occur at constant temperature until one
phase is used up. We can use this, for example,
to measure the true temperature of
crystallization, seen here as the level 2, where
liquid water turns to ice.
Note Temperature versus Time plot, Pressure
0.1 MPa (1 bar, atmospheric pressure)
8
Crystallization Behavior of Melts
1. Cooling melts crystallize from a liquid to a
solid over a range of temperatures (and
pressures) 2. Several minerals crystallize over
this T range, and the number of minerals
increases as T decreases 3. The minerals that
form do so sequentially, with considerable
overlap 4. Minerals that involve solid solution
change composition as cooling progresses 5. The
melt composition also changes during
crystallization 6. The minerals that crystallize
(as well as the sequence) depend on T and X of
the melt 7. Pressure can affect the types of
minerals that form and the sequence 8. The
nature and pressure of the volatiles can also
affect the minerals and their sequence
9
The Phase Rule
F C - f 2 F degrees of freedom The number
of intensive parameters that must be specified in
order to completely determine the system f
of phases phases are mechanically separable
constituents C minimum of components
(chemical constituents that must be specified
in order to define all phases) 2 2 intensive
parameters Usually temperature and pressure, or
temperature and composition, for geologists
10
Here is an internally heated pressure vessel at
the AMNH
With these you can study, for example 1. the
temperature and pressure conditions at which
polymorphs change from one form to another. 2.
The reactions of minerals with fluids (for
example salty or alkaline water) at high
temperatures and pressures. Dangerous, why? 3.
The conditions necessary to change one assemblage
of minerals to another
Called BOMBS
http//research.amnh.org/earthplan/research/Equipm
ent/Petrology
11
High Pressure Experimental Furnace
  • Cross section sample in red

the sample!
Fig. 6-5. After Boyd and England (1960), J.
Geophys. Res., 65, 741-748. AGU
12
1 - Component Systems
1. The system SiO2
Fig. 6-6. After Swamy and Saxena (1994), J.
Geophys. Res., 99, 11,787-11,794. AGU
13
1 - C Systems
2. The system H2O
Fig. 6-7. After Bridgman (1911) Proc. Amer. Acad.
Arts and Sci., 5, 441-513 (1936) J. Chem. Phys.,
3, 597-605 (1937) J. Chem. Phys., 5, 964-966.
14
2 - C Systems
A. Systems with Complete Solid Solution
  • 1. Plagioclase 2 components (Ab-An, i.e.
    NaSiAlSi2O8 - CaAlAlSi2O8)

A solid solution is a mixture of one or more
solutes in a solvent, where the crystal structure
of the solvent remains unchanged by addition of
the solutes. Typically the solutes are metal ions
of similar ionic radii and having the same charge.
Fig. 6-8. Isobaric T-X phase diagram at
atmospheric pressure. After Bowen (1913) Amer. J.
Sci., 35, 577-599.
T - X diagram at constant P 0.1 MPa F C -
phi 1 since Pressure is constant lose 1
degree of Freedom
15
  • Bulk composition a An60
  • 60 g An 40 g Ab
  • XAn 60/(6040) 0.60

Example of cooling with a specific bulk
composition Point a at 1560oC Phases 1
(liquid, X An60) 2 components An and Ab Fixed
pressure so Deg F C phases 1 F 2 - 1 1
2
16
When the temperature drops to b, about 1475C,
crystals of plagioclase form at composition c,
about 87An 2 Components An and Ab 2 phases
liquid and solid
a tie-line connects coexisting phases b and c
liquidus
solidus
17
At 1450oC, liquid d and plagioclase f coexist at
equilibrium
As the system cools, Xliq follows the liquidus
and Xsolid follows the solidus, in accordance
with F 1 At any T, X(An)Liq and X(An)Plag are
dependent upon T We can use the lever
principle to determine the proportions of liquid
and solid at any T
18
We can use the lever principle to determine the
proportions of liquid and solid at any T
The lever principle
The bulk composition is the pivot.
Amount of liquid
ef

Notice these are reversed Solid distance det.
Liq. amt.
Amount of solid
de
where d the liquid composition, f the solid
composition and e the bulk composition
d
f
e
D
liquidus
de
ef
solidus
19
When Xplag h, then Xplag Xbulk and, according
to the lever principle, the amount of liquid
0 Thus g is the composition of the last liquid
to crystallize at 1340oC for bulk X 0.60
20
Final plagioclase (solid) to form is i when
0.60 Now phases f 1 (all solid) so deg F
2 - 1 1 2
21
Note the following 1. The melt crystallized
over a T range of 135oC 4. The composition of
the liquid changed from b to g 5. The
composition of the solid changed from c to h
Numbers refer to the behavior of melts
observations
The actual temperatures and the range depend
on the bulk composition
22
  • Equilibrium melting is exactly the opposite
  • Heat An60 and the first melt is g at An20 and
    1340oC
  • Continue heating both melt and plagioclase
    change X
  • Last plagioclase to melt is c (An87) at 1475oC

23
Fractional crystallization Remove crystals
as they form so they cant undergo a
continuous reaction with the melt At any T Xbulk
Xliq due to the removal of the crystals
Thus liquid and solid continue to follow liquidus
and solidus toward low-T (Albite) end of the
system Get quite different final liquid (and
hence mineral) composition
24
Partial Melting Remove first melt as
forms Melt Xbulk 0.60 first liquid g remove
and cool bulk g final plagioclase i
Fractional crystallization and partial melting
are important processes in that they can cause
significant changes in the final rock that
crystallizes beginning with the same source.
25
Note the difference between the two types of
fields
The blue fields are one phase fields Any point
in these fields represents a true phase
composition The blank field is a two phase
field Any point in this field represents a bulk
composition composed of two phases at the edge of
the blue fields and connected by a horizontal
tie-line
26
2. The Olivine System
  • Fo - Fa (Mg2SiO4 - Fe2SiO4)
  • Is also a solid-solution series Mg2 to Fe2

Fig. 6-10. Isobaric T-X phase diagram at
atmospheric pressure After Bowen and Shairer
(1932), Amer. J. Sci. 5th Ser., 24, 177-213.
Are Mg2 and Fe2 about the same size? Early
Olivines react with the melt much more than early
Ca Plagioclases. Why?
27
2-Comp. Eutectic Systems
  • Example Diopside - Anorthite
  • No solid solution

Diopside is a pyroxene MgCaSi2O6
Fig. 6-11. Isobaric T-X phase diagram at
atmospheric pressure. After Bowen (1915), Amer.
J. Sci. 40, 161-185.
28
Cool composition a
bulk composition An70
At a phi phases 1 (all liquid) F C - phi
1 2 - 1 1 2 Good choice for axes is T and
X(An)Liq
29
Cool to 1455oC (point b)
What happens at b? Pure Anorthite forms (point
c) phi 2 liquid at b plus solid An at c F
2 - 2 1 1 composition of all phases
determined by T Xliq is really the only
compositional variable in this particular system
30
  • Continue cooling as Xliq varies along the
    liquidus
  • Continuous reaction liqa anorthite liqb

Lever rule shows less liquid and more Anorthite
as cooling progresses
31
  • At d, 1274oC f 3 Di, An, Liquid
  • so F 2 - 3 1 0 invariant
  • Pressure, Temp., and the composition of all
    phases is fixed
  • Must remain at 1274oC until a phase is lost

32
  • Discontinuous Reaction
  • at d all at a single T

d between g and h, so reaction must be Liquid
Diopside Anorthite must run right toward low
entropy of solids therefore first phase lost is
liquid Below 1274oC have pure Diopside pure
Anorthite phi 2 and F 2 - 2 1 1 Only
logical variable in this case is T (since the
composition of both solids is fixed)
33
Left of the eutectic get a similar situation
34
Note the following 1. The melt crystallizes
over a T range up to 280oC 2. A sequence of
minerals forms over this interval - And the
number of minerals increases as T drops 6. The
minerals that crystallize depend upon T - The
sequence changes with the bulk composition
s are listed points in text
35
Pyroxene forms before plagioclase
Gabbro of the Stillwater Complex, Montana
This forms on the left side of the eutectic
36
Plagioclase forms before Pyroxene
Ophitic texture
Diabase dike
This forms on the right side of the eutectic
37
  • Also note
  • The last melt to crystallize in any binary
    eutectic mixture is the eutectic composition
  • The final rock composition for no solid solution
    is the bulk composition

38
Equilibrium melting
  • is the opposite of equilibrium crystallization
  • Thus the first melt of any mixture of Di and An
    must be the eutectic composition as well

39
  • Fractional crystallization

If fractional crystallization is efficient, and
earlier xtals are removed, the last layer to
crystallize will be the eutectic composition,
because the last liquid composition is the
eutectic composition
Fig. 6-11. Isobaric T-X phase diagram at
atmospheric pressure. After Bowen (1915), Amer.
J. Sci. 40, 161-185.
40
Partial Melting
if remove liquid perfectly as soon as it forms
(must be rare) First melts of Di An would be
eutectic liquid composition d at 1274oC consume
either Di or An first depending on bulk X The
melting solid would be either pure Di or An dep
on bulk X After one solid consumed, the Temp
would rise, with no further melting,until the
melting point of the remainiing solid. New melt
temp and composition would jump from 1274oC f to
either 1392o for pure Diopside or to 1553 for
pure Anorthite. Thus heat 118oC or 279oC before
next melt
41
Binary Peritectic System
Crystallization of a mantle partial melt
It is possible to combine Forsterite, a Mg
Olivine, with Cristobalite SiO2 to get the
intermediate Mg-orthopyroxene Enstatite in the
Fo-SiO2 system.
Fo Cr En
Mg2SiO4 SiO2 2MgSiO3
Notice the is an extra inflection point, the
Peritectic P There are still only two
components, Fo and Cr, but an intermediate phase,
Enstatite, forms during cooling at and below
1557oC This is called a Peritectic System
42
Binary Partial Melt
Isopleth (the vertical blue line) a line of
constant composition
43
Binary Partial Melt
Isopleth (the vertical blue line) a line of
constant composition It shows the original bulk
composition
44
Fractional crystallization of a mantle partial
melt
Initially only Olivine freezes, settles, is
removed. Bulk composition in liquid becomes more
silica-rich. Melt composition (Liquidus)
approaches Enstatite as Magnesium ions are removed
45
Fractional crystallization of a mantle partial
melt
Peritectic - a low temperature inflection point
on the liquidus at which a liquid of specified
composition is in equilibrium with two or more
crystalline phases.
Melt changes composition past En , Temp lowers
to Peritectic P, then solids X changes
at constant T get Enstatite Fo L at the
Peritectic temperature
46
Fractional crystallization of a mantle partial
melt
Eutectic - the T on a T-X diagram where a mixture
of elements of a single chemical composition X
solidifies at a lower temperature than any other
composition made up of the same ingredients.
Between the Peritectic and Eutectic E, the
crystals forming are 100 Enstatite
47
Fractional crystallization of a mantle partial
melt
At Eutectic, Enstatite and SiO2 crystallize at
same time. New composition is much more silica
rich. Below Eutectic, solids are Enstatite and
Silica. At 100 MPa, the Silica mineral is
Cristobalite
Mantle Crust
48
Fractional crystallization of a mantle partial
melt
Notice what happened, Initially, a partial melt
of the mantle made of Forsterite olivine, and
below 1557C Forsterite plus the pyroxene
Enstatite. This is an upper mantle composition.
These early crystals are removed. From the
Peritectic 1557C to the Eutectic 1543C and
below, the composition shifts to Enstatite plus
silica, a crust composition
Mantle Crust
Fractionation of a Mantle partial melt yields a
silica rich crust composition
49
Fractional crystallization of a mantle partial
melt
Notice what happened, Initially, a partial melt
of the mantle made of Forsterite olivine, and
below 1557C Forsterite plus the pyroxene
Enstatite. This is an upper mantle composition.
These early crystals are removed. From the
Peritectic 1557C to the Eutectic 1543C and
below, the composition shifts to Enstatite plus
silica, a crust composition
Mantle Crust
Fractionation of a Mantle partial melt yields a
silica rich crust composition
50
Fractional crystallization of a mantle partial
melt
Original isopleth is mantle composition field.
For 100 MPa, as the partial melt is cooled, the
first Olivine crystals are formed at 1890C.
These crystals are 100 Forsterite and are
removed from the system, driving the bulk
composition to a more SiO2-rich or continental
nature. Forsterite continues to be the only
crystals formed until the temperature reaches
that of the Peritectic. At the Peritectic,
Enstatite begins to crystallize. Between the
Peritectic and the Eutectic the crystals forming
are 100 Enstatite. At the Eutectic the three
phases of Enstatite, melt, and Silica co-exist.
The melt continues to cool, resulting in two
solid phases, Enstatite and silica.
Mantle Crust
Fractionation of a Mantle partial melt yields a
silica rich crust composition
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