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


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)


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)


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


degrees of freedom

• F = 0 invariant (no change in system)

• F = 1 univariant (equilibrium line)

• F = 2 divariant (stable phase region)


F = 2

F = 1

F = 0


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?



suppose we have a pelitic rock containing 5 phases typical of lower amphibolite facies:

St + Grt + Bt + Ms + Qtz

how many components?



or suppose we have a mafic rock containing 5 phases typical of greenschist metavolcanics:

Act + Chl + Ep + Ab + Qtz

how many components?


“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



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)


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


“modified” phase rule

B

Afor a T-X diagram,

P = const.

so, only 1 intensive variable


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


Goldschmidt’smineralogical phase rule

• consider F = C - P + 2

• normally:

• as C increases, F increases

• as P increases, F decreases ...



• as P increases, F decreases

P = 1

P = 2

C = 1C = 2


• consider F = C - P + 2; normally:


• 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 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



• 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...



if P = C

• this is the standard divariant condition, where F = 2

• you are probably within a mineral zone

• all is good


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...


3-component projections

what do we know?P, T = const.


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)


C = 3

P = 3

P = 1

3-component compatibility diagrams

phases:• pure• 2C ss• 3C ss

P, T = limited

P = 2


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



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)



P, T = limitedC = 3 F =

F =

F =

recap 3-component compatibility diagrams


if C = 3,P = 4?

???

B C

A

more phases than components?

NO!


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!


gibbs phase rule goldschmidt mineralogical phase rule...

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