Gibbs Phase Rule Goldschmidt mineralogical phase rule...
Transcript of Gibbs Phase Rule Goldschmidt mineralogical phase rule...
Phase rule
• Gibbs Phase Rule
• Goldschmidt mineralogical phase rule
• implications for chemographic analysis
Sunday, September 13, 2009
basis of phase rule
• minerals (phases) are reaction products! therefore, they record the reactions that occurred, as well as conditions
• why is phase rule useful?
• helps to characterize state of the system
• predict equilibrium relations of phases
• helps to construct phase diagrams
Sunday, September 13, 2009
F = C - P + 2
• F = degrees of freedom (variance)
• C = minimum # components in system
• P = # phases
• integers related to # intensive variables (scale independent; e.g., P, T, density, Xmineral)
Sunday, September 13, 2009
F = C - P + 2
• what does Gibbs say?
• variance of the system is the minimum # of intensive variables needed to define the state of the system at equilibrium
• for each C we add, must specify 1 more variable (more stuff)
• for each P we add, 1 less variable need be specified (fewer boxes to put it in)
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F = C - P + 2
• or, if you change 1 variable, how many other things must you change to maintain the system?
• if F = 2, can change either P or T independently
• if F = 1, if change one thing, must change the other (or, if know one, you know the other)
• if F = 0, cannot change anything and still keep system the same
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degrees of freedom
• F = 0 invariant (no change in system)
• F = 1 univariant (equilibrium line)
• F = 2 divariant (stable phase region)
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F = 2
F = 1
F = 0
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selecting components
CaMg(CO3)2 + 2 SiO2 = CaMgSi2O6 + 2 CO2dolomite + 2 quartz = diopside + 2 carbon dioxide
possible components CaO, MgO, SiO2, CO2
or
CaMgO2, SiO2, CO2
which is best? how do we choose?
Sunday, September 13, 2009
selecting components
suppose we have a pelitic rock containing 5 phases typical of lower amphibolite facies:
St + Grt + Bt + Ms + Qtz
how many components?
Sunday, September 13, 2009
selecting components
or suppose we have a mafic rock containing 5 phases typical of greenschist metavolcanics:
Act + Chl + Ep + Ab + Qtz
how many components?
Sunday, September 13, 2009
“degenerate” systems
if you can reduce the # components to a limited sub-set of the whole system that still explains the observed mineral assemblage, this is simpler
B C
Ae.g., use B-C,
rather than A-B-C
B100C0
B50C50
B0C100
A33B33C33
Sunday, September 13, 2009
selecting components
so for our greenschist:
Act + Chl + Ep + Ab + Qtz
how can we reduce the ACNFMS components?
• assume free substitution of Fe & Mg• assume plagioclase is pure Ab (and no Na in others)
• assume system is Si-H2O saturated
end up with 3 components (ACF);phase rule says F = 3 - 3 + 2 = 2 (not counting Ab & Qtz)
so the system is divariant, and might even have more freedom (will come back to this)
Sunday, September 13, 2009
intensive variables
• need to know how many intensive (mass-independent) variables govern the system
• if T & P are variables, F = C - P + 2
• if either one is fixed (constant), the “modified” phase rule becomes F = C - P + 1
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“modified” phase rule
B
Afor a T-X diagram,
P = const.
so, only 1 intensive variable
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assumptions
• assumptions when applying Gibbs phase rule:
• EQUILIBRIUM!!! sufficient time & energy
• minerals have uniform, simple structural states (but allows for zoning, disorder, etc.)
• no kinetic effects
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Goldschmidt’smineralogical phase rule
• consider F = C - P + 2
• normally:
• as C increases, F increases
• as P increases, F decreases ...
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• as C increases, F increases
• as P increases, F decreases
P = 1
P = 2
C = 1C = 2
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• consider F = C - P + 2; normally:
• as C increases, F increases
• as P increases, F decreases
• GMPR says that for a given rock in equilibrium at a fixed P & T, generally:
# phases ≤ # components (P ≤ C)
Goldschmidt’smineralogical phase rule
Sunday, September 13, 2009
• Goldschmidt observed that “common” mineral assemblages occur over wide areas in rocks of varying composition
• he reasoned, then, that this simpler assemblage (low #P) is a consequence of variable (P, T, X) and hence high #C
• it follows, then, that the common situation is to have C > P, and more F
Goldschmidt’smineralogical phase rule
Sunday, September 13, 2009
• hence, GMPR rule says that for a rock in equilibrium at fixed P & T, # phases ≤ # components
• in general, rock systems are divariant for P & T (i.e., F = 2), so P = C
• but because of natural variation in T-P-Xminerals, it is also common that F ≥ 2
• if F ≥ 2 and F = C - P + 2, then P ≤ C!
let’s see how this works...
Goldschmidt’smineralogical phase rule
Sunday, September 13, 2009
if P = C
• this is the standard divariant condition, where F = 2
• you are probably within a mineral zone
• all is good
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if P ≤ C
• how do we get higher F?• either higher C or
variable P-T• if we simplify to easy-to-
understand 3-component projection, then we can still maximize C by allowing for solid solution
• so, consider the system xyz...
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3-component projections
what do we know?P, T = const.
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3-component projections
for rock (B)
what does the phase rule say?
for rock (f)
for rock (xyz)
P, T = const.
compositionally degenerate
the independent variable is
composition (not P or T)
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C = 3
P = 3
P = 1
3-component compatibility diagrams
phases:• pure• 2C ss• 3C ss
P, T = limited
P = 2
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C = 3
P = 3
for (D), F = 3 - 3 + 2 = 2, but because solid solution
allows for small system variation in X,
variance F corresponds to
P & T
there is no compositional
freedom in phases!!
P, T = limited
3-component compatibility diagrams
Sunday, September 13, 2009
P, T = limitedC = 3
P = 2
for (f):F = 3 - 2 + 2 =
3
variance is in P, T and phase compositions
(ss)
phase compositions determined by
system composition
(f)
3-component compatibility diagrams
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P, T = limitedC = 3 F =
F =
F =
recap 3-component compatibility diagrams
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if C = 3,P = 4?
???
B C
A
more phases than components?
NO!
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if P > C
• F < 2 (you are either on a univariant curve or at an invariant point)
• as Winter points out, this has lower probability so more common to be divariant
• disequilibrium? (check phases and textures)
• are your minerals in 1 “system”?
• are some minerals retrograde?
• is there evidence of incomplete reaction?
• did not choose components carefully!
Sunday, September 13, 2009