Phase rule
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Sunday, September 13, 2009
Gibbs Phase Rule
Goldschmidt mineralogical phase rule
implications for chemographic analysis
basis of phase rule
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minerals (phases) are reaction products!
therefore, they record the reactions that
occurred, as well as conditions
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why is phase rule useful?
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Sunday, September 13, 2009
helps to characterize state of the system
predict equilibrium relations of phases
helps to construct phase diagrams
F=C-P+2
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Sunday, September 13, 2009
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)
F=C-P+2
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what does Gibbs say?
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variance of the system is the minimum # of
intensive variables needed to define the
state of the system at equilibrium
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for each C we add, must specify 1 more
variable (more stuff)
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for each P we add, 1 less variable need be
specified (fewer boxes to put it in)
Sunday, September 13, 2009
F=C-P+2
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or, if you change 1 variable, how many other
things must you change to maintain the
system?
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if F = 2, can change either P or T
independently
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if F = 1, if change one thing, must change
the other (or, if know one, you know the
other)
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if F = 0, cannot change anything and still
keep system the same
Sunday, September 13, 2009
degrees of freedom
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Sunday, September 13, 2009
F = 0 invariant (no change in system)
F = 1 univariant (equilibrium line)
F = 2 divariant (stable phase region)
F=2
F=1
F=0
Sunday, September 13, 2009
selecting components
CaMg(CO3)2 + 2 SiO2 = CaMgSi2O6 + 2 CO2
dolomite + 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 subset of the whole system that still explains the
observed mineral assemblage, this is simpler
A
e.g., use B-C,
rather than A-B-C
A33B33C33
B100C0
B
Sunday, September 13, 2009
B0C100
B50C50
C
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
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need to know how many intensive (massindependent) variables govern the system
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if T & P are variables, F = C - P + 2
Sunday, September 13, 2009
if either one is fixed (constant), the “modified”
phase rule becomes F = C - P + 1
“modified” phase rule
for a T-X
diagram,
P = const.
A
so, only 1
intensive variable
B
Sunday, September 13, 2009
assumptions
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assumptions when applying Gibbs phase rule:
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EQUILIBRIUM!!! sufficient time & energy
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no kinetic effects
Sunday, September 13, 2009
minerals have uniform, simple structural
states (but allows for zoning, disorder, etc.)
Goldschmidt’s
mineralogical phase rule
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consider F = C - P + 2
normally:
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Sunday, September 13, 2009
as C increases, F increases
as P increases, F decreases ...
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as C increases, F increases
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as P increases, F decreases
C=2
P=1
P=2
Sunday, September 13, 2009
C=1
Goldschmidt’s
mineralogical phase rule
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consider F = C - P + 2; normally:
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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)
Sunday, September 13, 2009
Goldschmidt’s
mineralogical phase rule
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Goldschmidt observed that “common” mineral
assemblages occur over wide areas in rocks
of varying composition
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he reasoned, then, that this simpler
assemblage (low #P) is a consequence of
variable (P, T, X) and hence high #C
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it follows, then, that the common situation is to
have C > P, and more F
Sunday, September 13, 2009
Goldschmidt’s
mineralogical phase rule
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hence, GMPR rule says that for a rock in equilibrium
at fixed P & T, # phases ≤ # components
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in general, rock systems are divariant for P & T (i.e.,
F = 2), so P = C
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but because of natural variation in T-P-Xminerals, it is
also common that F ≥ 2
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if F ≥ 2 and F = C - P + 2, then P ≤ C!
let’s see how this works...
Sunday, September 13, 2009
if P = C
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this is the standard divariant condition, where
F=2
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you are probably within a mineral zone
Sunday, September 13, 2009
all is good
if P ≤ C
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how do we get higher F?
• either higher C or
variable P-T
if we simplify to easy-tounderstand 3-component
projection, then we can
still maximize C by
allowing for solid solution
so, consider the system
xyz...
Sunday, September 13, 2009
3-component projections
P, T = const.
Sunday, September 13, 2009
what do we
know?
3-component projections
P, T = const.
the
independent
variable is
composition
(not P or T)
what does the
phase rule say?
for rock (B)
for rock (f)
compositionally
degenerate
Sunday, September 13, 2009
for rock (xyz)
3-component compatibility diagrams
P, T = limited
C=3
P=1
phases:
• pure
• 2C ss
• 3C ss
P=2
P=3
Sunday, September 13, 2009
3-component compatibility diagrams
P, T = limited
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!!
Sunday, September 13, 2009
3-component compatibility diagrams
for (f):
F=3-2+2=
3
P, T = limited
C=3
P=2
(f)
Sunday, September 13, 2009
variance is in
P, T and phase
compositions
(ss)
phase
compositions
determined by
system
composition
recap 3-component compatibility diagrams
P, T = limited
C=3
F=
F=
F=
Sunday, September 13, 2009
more phases than components?
A
if C = 3,
P = 4?
???
B
Sunday, September 13, 2009
C
NO!
if P > C
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F < 2 (you are either on a univariant curve or
at an invariant point)
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as Winter points out, this has lower
probability so more common to be divariant
disequilibrium? (check phases and textures)
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Sunday, September 13, 2009
are your minerals in 1 “system”?
are some minerals retrograde?
is there evidence of incomplete reaction?
did not choose components carefully!