1. No category

2
Thermodynamics deals with energy & equilibrium
Basics of thermodynamics & kinetics
Phase Relations,
Magma generation
Kinetics deals with rates and mechanisms
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4
System
Energy – the capability to do work
(ability to apply a force over a distance)
Surrounding
White Chapter 2
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6
Phase
Reaction
Feldspar
Quartz
1
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8
Ultimately, both heat and order are important in determining
whether a given reaction will occur.
Change of state
Gibbs free energy
G = H – TS
change in enthalpy (a
measure of the energy
gy
absorbed or released)
temperature
Energy
Energy barrier
change in entropy
(order/disorder, randomness)
White Chapter 2
9
Chemical Equilibrium
G and G


A system at equilibrium is:
• Dynamic (constantly in motion – reactions ongoing)
• Reversible (reactions can go either way; both directions are
equal)
A+B  C+D
A+B  C+D
or
A+BC+D
Figure 5.2. Schematic P-T phase diagram of a melting reaction.
Winter (2001) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.

G is a measure of relative chemical stability for a phase
We can determine G for any phase by measuring H and S for
the reaction creating the phase from the elements
We can then determine G at any T and P mathematically
• Most accurate if know how V and S vary with P and T
• dV/dP is the coefficient of isothermal compressibility
• dS/dT is the heat capacity (Cp)
Use?
If we know G for various phases, we can determine which is
most stable
 Why is melt more stable than solids at high T?
 Is diamond or graphite stable at 150 km depth?
 What will be the effect of increased P on melting?
Figure 5-2. Schematic P-T phase diagram of a melting reaction.
Winter (2001) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.
The phase assemblage with the lowest G under a specific set of conditions is the most stable
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14
Along this line,
Liquid  Solid
=
Liquid  Solid
and G = 0
G also gets larger with increasing distance from the equilibrium line.
http://serc.carleton.edu/files/research_educattion/equilibria/h20_phase_diagram.pdf
Equilibrium lines on the P-T phase diagram for water
Law of mass action
For the reaction:
A+BC+D
reactants
at equilibrium
K
products
cC cD
 constant
cA cB
products
reactants
K is the equilibrium constant for a specific set of conditions
CA to CD are the concentrations of the various phases
K varies with temperature
K is the ratio between product and reactant
concentrations at equilibrium
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The meaning of the equilibrium constant, K
For the reaction:
aA + bB  cC + dD
K
c
aA + bB  cC + dD
d
[cC ] [ cD ]
[c A ]a [ cB ]b
K
K is the equilibrium
q
constant for a specific
p
set of conditions
CA to CD are the concentrations of the various phases
a to d are the multiples in the equation (may also be
represented as XA, XB, etc.)
For example
2A + 1B  1C + 2D
K
[cC ]c [ cD ]d
[c A ]a [ cB ]b
products
reactants
What do the relative concentrations look like at equilibrium:
•
[cC ]1[ cD ]2
[c A ]2 [ cB ]1
if K is very large?
• if K is very small?
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Are we at equilibrium?
What if we have an open system
(or a secondary reation)?
aA + bB  cC + dD
Q
[cC ]c [ cD ]d
[c A ]a [ cB ]b
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products
aA + bB  cC + dD
reactants
Calculate the reaction quotient, Q, and compare it to K
K
[cC ]c [ cD ]d
[c A ]a [ cB ]b
products
reactants
We use our actual (measured) concentrations to calculate Q
What if Q = K?
What if Q > K?
What happens if we add or remove products or reactants?
What if Q < K?
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K and G
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Kinetics: Reaction mechanisms
Sequence of steps at the molecular level than controls the rate
and ultimate outcome of a reaction
 rG o   RT ln K
Where there are several steps in sequence, the slowest step is
Here we have the relationship between G and K.
This works for reactants & products in their standard states
( reference
(a
f
state,
t t often
ft chosen
h
as the
th solid
lid form
f
tto
minimize the influence of pressure).
rate-determining and limits the outcome
By knowing G, it is possible to determine K for a range of
temperatures
Step 1:
Step 2:
Step 3:
Br + O3 ---> BrO + O2
Cl + O3 ---> ClO + O2
BrO + ClO + light ---> Br + Cl + O2
Net result:
2 O3 ---> 3 O2
For a reaction to proceed, an energy barrier must be overcome.
Addition of a catalyst may lower this energy barrier by providing an
alternate reaction mechanism.
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Reaction rate
Reaction rate
Energy
Energy barrier
White Chapter 2
24
• Phase rule, components, and degrees of freedom
• Types of phase diagrams
• Single component – e.g. P vs. T
• Two components – e.g. T vs. X, P vs. X
• Etc.
• Special positions – e.g. invariant point, eutectic, peritectic
• Liquidus & solidus
• Lever rule
• Constructing phase diagrams – experimental & calculated
Recommended resource:
http://serc.carleton.edu/research_education/equilibria/index.html
Gibb’s Phase Rule
How many phases can coexist at equilibrium?
How many variables are necessary to define a system?
What variables can we change and still have equilibrium?
http://serc.carleton.edu/files/research_education/eq
quilibria/h20_phase_diagram.pdf
Phase Diagrams – Topics:
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Gibb’s Phase Rule
Gibb’s Phase Rule
Two kinds of variables:
f=c–p+2
• Intensive
• e.g. composition, mass
• relate to the amount of material
• i.e.
i e What is the system made of?
or
p+f=c+2
f = number of degrees of freedom – i.e. the number of variables
that may be changed independently and still maintain
equilibrium
p = number of phases
• Extensive
• e.g. P, T, density (relates to volume, pressure), fugacity,
activity
• independent of the amount of material
• i.e. What are the conditions the system is subject to?
c = minimum number of chemical components required to make all
the phases (often defined as simple oxides, e.g. FeO, Na2O)
2 = number of extensive variables (often P & T); In some cases the
number may be different (e.g. 3 for some water-rock reactions
with water flowing in pore space).
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Therefore f=1. This means we can change 1 variable.
Thus, this line is described as univariant.
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Gibb’s Phase Rule
f=c–p+2
f=c–p+2
What are c, p, and f here?
What does this say about the potential to change one or more
variables?
In this system, the triple point is an invariant point.
Gibb’s Phase Rule
http://serc.carleton.edu/files/research_education/eq
quilibria/h20_phase_diagram.pdf
Here c=1 and p=2.
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Gibb’s Phase Rule
f=c–p+2
http://serc.carleton.edu/files/research_education/eq
quilibria/h20_phase_diagram.pdf
Gibb’s Phase Rule
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f=c–p+2
In this area, the system is described as divariant.
A
two phases
B
two phases
What is c for this system?
What are p and f at locations A and B?
http://serc.carleton.edu/files/research_education/eq
quilibria/alcohol-ice.pdf
What are c, p, and f here? What does this mean?
http://serc.carleton.edu/files/research_education/eq
quilibria/h20_phase_diagram.pdf
one phase
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Goldschmidt's Mineralogical Phase Rule
Phase Diagrams
• Based on the observation that most rocks contain only a few
major phases (ignoring scarce accessory phases).
• Graphical/visual representation of the equilibrium relationships
between phases
• Show how phase relations change with P, T, composition, etc.
• For most rocks f = 2, so p = c. If f > 2, then p < c.
Feldspar
• Types of phase diagrams:
• IIn other
h words,
d for
f a
rock in equilibrium at
fixed P and T, the
number of phases is
less than or equal to
Quartz
the number of
components.
• Single component – e.g. P vs. T
• Two components (binary) – e.g. T vs. X, P vs. X,
P vs. T (at fixed composition)
X refers to the mol fraction of each component.
• Three components (ternary)
• Etc.
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Two components (binary)
with eutectic
Single component
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Proportions of liquid and
solid calculated by applying
the “Lever Rule” to this line
Liquidus
(line)
Solidus
(line)
eutectic (point)
http://serc.carleton.edu/files/research_education/equilibria/h20_phase_diagram.pdf
http://serc.carleton.edu/images/research_education/equilibria/sio2.jpg
http://serc.carleton.edu/files/research_education/equilibria/alcohol-ice.pdf
read liquid
composition here
Two components (binary) with eutectic
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The lever principle:
Amount of liquid
Amount of solid
ef
=
de
where d = the liquid composition, f = the solid composition
and e = the bulk composition
d
f
e

liquidus
de
ef
solidus
http://serc.carleton.edu/images/research_education/equilibria/leu-qza.jpg
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Two components with solid solution
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
Liquid
Plagioclase
The blank field is a two phase
field
plus
Liquid
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
Plagioclase
http://serc.carleton.edu/images/research_education/equilibria/aban3.jpg
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The Olivine System
http://serc.carleton.edu/images/research_education/eq
quilibria/abor_hypersolvus.jpg
Binary with
exosolution
Fo - Fa (Mg2SiO4 - Fe2SiO4)
also a solid-solution series
Fig. 6.10. Isobaric T-X phase
diagram at atmospheric
pressure After Bowen and
Shairer (1932), Amer. J. Sci.
5th Ser., 24, 177-213.
Effect of PH O on Ab-Or
2
Liquid imiscibility
Three phases enstatite = forsterite + SiO2
Figure 6.12.
6 12 Isobaric T
T-X
X
phase diagram of the system
Fo-Silica at 0.1 MPa. After
Bowen and Anderson (1914)
and Grieg (1927). Amer. J. Sci.
Figure 6.17. The Albite-K-feldspar system at various H2O pressures. (a) and (b) after Bowen and Tuttle (1950), J. Geol, (c) after Morse
(1970) J. Petrol.
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Three components
(ternary)
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Experimental determination of boundaries
REVERSED PHASE EQUILIBRIUM MEASUREMENTS
This one is contoured
with temperature and
represents the liquidus
as a surface, not a line.
Think of this like a
topographic map.
MgCO3
P
Usually f = c – p + 2.
Except here we have set a
fixed pressure so to stay
on this diagram, we
must use f = c – p + 1.
MgO + CO2
In this method, you start with
both reactants and products in
every run, and determine
whether reactants or products
are favored at each P and T.
With this method, the actual
equilibrium curve is not
directly obtained, but the
curve can be bracketed to
within the desired (or
possible) degree of accuracy.
T
Scott Wood, U Idaho
http://serc.carleton.edu/images/research_education/equilibria/di-fo-an_jpg.jpg
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Experimental determination of boundaries
High Pressure Experimental Furnace
ONE-WAY REACTIONS
Some reactions are too slow in
the reverse direction to be
experimentally observed. Such
experimental data only set
upper limits on the reaction
boundary. Runs to the left of
the
h curve which
hi h do
d not change
h
are meaningless because of
slow kinetics.
CaMg(CO3)2
P
Cross section: sample in red
the sample!
800 Ton Ram
Carbide
Pressure
Vessle
SAMPLE
Graphite Furnace
CaCO3 + MgO + CO2
1 cm
T
Scott Wood, U Idaho
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Furnace
Assembly
Fig. 6.5. After Boyd and England (1960), J. Geophys. Res., 65, 741-748. AGU
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Making magma
How to make rocks melt
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Deeeper
Note that water content varies
along the curved line – i.e. the
water content increases with
pressure along the curve. So,
this is not a simple P-T melting
diagram along the curved line.
Deeper
Effect of water content on
melting a rock of granitic
composition
For constant H2O (the straight
lines), the melting temperature
is be greater at higher pressure
as expected.
Brownlow’s Geochemistry
By adding water, the rock can
be made to melt at a lower
temperature. Or, the rock can
be made to melt to a greater
extent at the same temperature.
Igneous rocks and magmas are not pure substances,
but rather are complex mixtures of various components.
They do not change from liquid to solid or from solid to
liquid all at one temperature. When a rock melts, minerals
which have the lowest melting temperature melt first.
Brownlow's Geochemistry
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Pure substance
Melting of “dry” basalt
Dry means that no volatiles
like water or carbon dioxide are
present.
Mixed substance:
(Basalt)
Phase diagram for a simple two-component system
If water is added, the
boundaries change,
g , and
melting happens at lower
temperatures than illustrated.
“partial melt”
Felsic rocks also melt at lower
temperatures than mafic rocks
like basalt.
all
solid
all
liquid
Fig 5.1 from Francis, 1993
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Locations of magma formation
Where and how are magmas formed?
Mid-ocean ridges – decompression melting
mafic (basaltic) magma (primary mantle melt)
Continental rifts and other areas of extension – decompression melting
mostly mafic (basaltic) magma (primary mantle melt)
some intermediate and felsic magmas (crustal melts, derivative magmas)
Winter’s Prin. Ig. Met. Petrol.
Subduction zones – melting largely due to addition of fluids
mafic, intermediate, and felsic magmas - often water-rich
Mantle plumes (hot spots) – decompression melting
ocean basins: mafic magma (primary mantle melt)
continents: mostly mafic magma, (primary mantle melt)
some intermediate and felsic magmas (crustal melts, derivative magmas)
Fig 4.8 Understanding Earth
9
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Magma formation at subduction zones
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General Controls on Magma Compositions
During Melting
The addition of water to the mantle overlying the subducting plate
causes partial melting. When enough melting has occurred, the liquid
separates from the residual solid and rises buoyantly because it is less
dense than the solid.
Fig 4.19 Understanding Earth
57
Brownlow's Geochemistry
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