lecture 6 crystal chemistry part 5: rock suites applications of thermodynamics rock cart,...
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Lecture 6 Crystal Chemistry
Part 5:
Rock Suites Applications of Thermodynamics
Rock Cart, Kyanite. Andalusite, SillimaniteSerpentinite, Greenschist, AmphiboliteMica Schist with Staurolite, Microcline with Perthitic Texture
MARBLE DEMO
Basaltic Magma Cooling - Bowen’s Reaction Series
Molten- VERY HotNo solids
Molten- Not so hot
100% Solid
First mineral to crystallize out
Fine crystalsNeed a microscope
Course crystalsEasily seen
Low silica, HOT, fluid High silica, warm, viscousIntermediateFractionationminerals
Zoned feldspar (plagioclase) showing change in composition with time in magma chamber (calcium-rich in core to sodium-rich at rim)
If the first formed crystals of Calcium-rich (Ca) Plagioclase touch the melt they will react with it, and will become more sodium-rich on their outer rims
Crystals can react with the melt if they touch it
FRACTIONATION: if early crystals are removed, the melt becomes richer in Silica
A melt will crystallize its mafic components first, and the remaining melt may be granitic
Remove Fe, Mg, CaSome Si
Left withK and AlMost of Si
You can start with aMafic (silica-poor) magmaand end up with some Felsic (silica-rich)Granites. Marble Demo
Assimilation and magmatic differentiation
Show Samples
0 kmSedimentaryrock
Metamorphicrock
Igneousrock
50 km
10 km
~200ºC
~800ºC
Incr
easi
ng d
epth
and
tem
pera
ture
Melting
Metamorphism
Sedimentaryrock
Sediment
Most metamor-phism occurs between about 200 and 800o C
The rocks don’t melt
Metamorphism
Contact metamorphismProduced by contact with heat source
Hydrothermal Metamorphism
Basaltic Magma
MORs,Black Smokers, Cyprus & Bronze Age (Cu), Rome’s conquest of Britain (Sn), Sterling Zinc (and Manganese)
Circulation of hot water in cracks at mid-ocean ridge dissolves metals (Copper, Tin, Iron, Zinc, Lead, Barium) which are re-precipitated as sulfide ores. Hydrothermal waters are capable of metamorphism.
http://collections.ic.gc.ca/geoscience/images/detail/F92S0220.jpg
Copper plus Tin makes Bronze
Iron plus Carbon makes steel.
Dynamothermal Metamorphism, Before collision
Sediments are “unconsolidated”. They will fold if pushed.
Dynamothermal Metamorphism, in convergent margins (subduction, collision)
Index Minerals in metamorphic rocks
Note Quartz and Feldspar are not index minerals: Why?
Note Temperature gradient
Stable temperature ranges depend on Pressures
Thermometers and Pressure GaugesPolymorphs of Al2SiO5 Al2SiO5
Kyanite
Sillimanite
AndalusiteKyanite in Andalucite
solid - solid
Role of Volatiles - (H2O & CO2)
Catalyzes reactions Mobility during
metamorphism leads to non-isochemical reactions
Dehydration and decarbonation during prograde reactions
Lack of volatiles slows retrograde reactions
Prograde/
Prograde/
Dehydration
Dehydration
Retrograde
Retrograde
Example: Dehydration: Muscovite + Qtz = K-spar + Sill. + H2O
Metamorphic Facies near Subduction Zones and Arcs
We can note mineral facies in Metamorphic Rocks and determine where they formed.
More Basaltic Magmaformed by dehydration of ocean lithosphere and hydration of mantle
Greenschist Hand Sample
Greenschist Thin SectionChl-Ep
Blueschist glaucophanea sodic amphibole Amphibolite hornblende + Plag.
Pleochroism, cleavage in hornblende
Mineral Stability/Equilibrium 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
Stability and Gibbs Free Energy G
G(p,T) = E + PV − TS For a reaction or change of phase: System in equilibrium if no unbalanced forces
G = 0. If G<0, a phase can spontaneously transform
to another phase; e.g., solid to liquid If G > 0, a phase transformation will not
occur. Multiple phases can occur simultaneously.
A certain amount of energy goes to an increase in entropy of a system and a certain amount goes to a heat exchange for a reaction.
G = H –TS or G0R = H0
R – TS0R
Gibbs Free Energy (G) is measured in KJ/mol or Kcal/mol
)reactants()( 000i
iii
iiR GnproductsGnG
E + PV is Enthalpy H
G is a measure of driving force GR = HR – TSR
Again: For a reaction A B That is, for reactants products When GR is negative the forward reaction
has excess energy and will occur spontaneously A B
When GR is positive there is not enough energy in the forward direction, and the back reaction will occur B A
When GR is zero reaction is at equilibrium, both reactions occur equally.
Petrology Field Trip to Bemco Mining District
Supergene Enrichment, Bemco MineSupergene Enrichment, Bemco Mine
Oxidation of Ferrous Iron, Fe+2
Groundwater: iron in two oxidation states Reduced soluble ferrous iron (Fe+2) Oxidized insoluble ferric iron (Fe+3).
Modern atmosphere 21% oxygen, so most in shallow soils ferric state, (Fe+3). Initially Ferric hydroxide (Fe(OH)3) With time, mineralized. Decreasing solubility
amorphous hydrous ferric oxide (Fe2O3•xH2O),
Hematite (Fe2O3), and Goethite FeO(OH).
Gibbs Free Energy Example
G0R = H0
R – TS0R
H2O(l)=-63.32 kcal/mol = -63320 cal/mol (You look these up in these tables)
Fe2+ + ¼ O2 + H+ Fe3+ + ½ H2O=[-4120+(-63320*0.5)]-[-21870+(3954*0.25)]
=[-67440]-[-20887.5]=-46557.5 cal/molNegative, so forward (left to right) reaction will proceed
)reactants()( 000i
iii
iiR GnproductsGnG
Oxidation of ferrous ion to ferric ion
http://www.uwgb.edu/DutchS/PETROLGY/coordinationx.htm
Andalusite
Al2SiO5 polymorphsdiffer in coordinationof the Al+3In Andalusite, oneAluminum is in 5-foldcoordination, very unusual.
Stability of a phase (or mineral) is partly related to its internal energy (here “E”), which strives to be as low as possible under the external conditions.
Metastability exists in a phase when its energy is higher than P-T conditions indicate it should be. (1)
Activation Energy is the energy necessary to push a phase from its metastable state to its stable state. (2 minus 1)
Equilibrium exists when the phase is at its lowest energy level for the current P-T conditions. (3) (Two minerals that are reactive with one another, may be found to be in equilibrium at particular P-T conditions which on phase diagrams are recognized as phase boundaries)
Note: most metamorphic and igneous minerals at the earth’s surface are metastable.
Example: Exsolution of K-spar and Albite at low temperatures; they were in Solid Solution at higher temperatures.
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 fluidsHere three Phases: Ky, Sill, Andalucite
And
Degrees of Freedom f by Examples
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
Ky.
And.
Sill.
On a phase diagram f=0 corresponds to a point,
f = 1 to a reaction line,
f = 2 to a 1 phase area.
p + f = c + 2
The Phase Rule
The number of minerals (phases) that may stably coexist is limited by the number of chemical components
p + f = c + 2 where P is the number of mineral phases, c
the number of chemical components, and f is the number of degrees of freedom.
Basic Thermodynamics
The theoretical basis of phase equilibrium Three Laws of Thermodynamics
1. First Law: Change in Internal Energy (E)= dE = dQ – dWQ – heat energy
W – work = F * distance (notice distance is a length)
Pressure has units Force/Area = (F/dist2) so F* dist = P * area * dist = P * V
At constant pressure dW = PdV So if Pressure is constant: (1) dE = dQ – PdV where dV is thermal expansion or contraction
Second and Third Laws of Thermodynamics
2. All substances move to the greatest state of disorder (highest Entropy ”S”) for a particular T and P. (2) dQ/T = dS
“The state of greatest order [lowest S] is at the lowest temperature. With increasing temperature, disorder becomes more prevalent.”
Minerals with simple atomic structure and simple chemistry have lower entropy.
3. At absolute zero (0ºK), Entropy is zero
Does this suggest how to measure S?Can we measure changes in S by keeping track of temperature as we add heat to a system?“The entropy of a pure crystalline substance can therefore be obtained directly from heat-
capacity measurements by assuming that S0 (at 0o K) is zero” Wood and Fraser (1978) p38
ss
Gibbs Free Energy Define G – the energy of a system in excess of its internal energy E. This is
the energy necessary for a reaction to proceed
G = E + PV – TS
Differentiating dG = dE +PdV +VdP -TdS - SdTdE = dQ - PdV = TdS – PdV sodG = TdS – PdV + PdV + VdP -TdS – SdT = VdP –SdT
This is equation (3) dG = VdP –SdT
If T = constant dT = 0, then dG = VdP, if V decreases, P can increase without increasing G
(2) at constant T (dG/dP)T = V (dense (low V) phases are favored at high P) If P = constant dP = 0, then dG = -SdT, if T increases then S can increase without increasing G
(3) at constant P (dG/dT)P = -S (disordered phases (high S) are favored at high T)
Enthalpy
Earlier we saw G(T,p) = E + pV − TS
• But the Enthalpy H(S,p) = E + pV
• So G = H –TS
H can be measured in the laboratory with a calorimeter.
S can also be measured with heat capacity measurements.
Values are tabulated in books.
Clapeyron Equation
• Defines the state of equilibrium between reactants and products in terms of S and V
From Eqn.3, if dG =0, dP/dT = ΔS / ΔV (eqn.4)
The slope of the equilibrium curve will be positive if S and V both decrease or increase
with increased T and P
The function G can be represented graphically on P T diagrams
Constructing Phase DiagramsOne Component: H2O
Pressure-Temperature Phase Diagram
The Gibbs and Clapeyron Equations allow us to estimate phase diagrams with extrapolations from laboratory measurements.The lines show where equilibrium conditions (G = 0) occur. Clapeyron tells us the slope
The Payoff
• Our experiments and calculations allow us to construct the 3-D plot in (a), and to project the mineral with the lowest free energy at each PT onto the graph in (b).
Notice the points a,b and c at right.At c, G = 0 in the reaction Andalucite Sillimanite
Nesse fig 5.3
Of Nesse
The KSA Phase diagram allows us to assign PT conditions to various Plate Tectonic settings