Transcript Document

Crust to Core workshop:
An introduction to Perple_X
Part 3: What data is Perple_X actually using?
Ins titut
e of Mi neral og
y and Petrology
Perple_X finds an optimum set of pseudocompounds for the P, T, X conditions of interest.
This is based on available information on the H, S,
V of end-members, combining these into solutionphases.
Perple_X finds an optimum set of pseudocompounds for the P, T, X conditions of interest.
This is based on available information on the H, S,
V of end-members, combining these into solutionphases.
Ignoring some complexity (e.g.X), we could write a
simple equilibria that we could solve by hand
Kyanite = Al2SiO5 = Sillimanite
TSKyanite  PVKyanite  TSSillimanite  PVSillimanite
It is univariant, so each P has one unique T at which
this occurs, we just need S and V for each phase…
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
S max
V max
4
0.035
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
S max
V max
4
0.035
But these are the values for V, S (and H) at 25 ˚C, atmospheric pressure!
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
CP  a  bT  cT
CP = J mol-1 K-1
CP of kyanite as a function of T, using
tabulated values of a, b, c, d
2
 dT
S max
V max
4
0.035
1/ 2
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
CP  a  bT  cT
CP = J mol-1 K-1
ST  S0  SMax / 1000 Q298 
2

T
298
CP
T
dT
2
 dT
S max
V max
4
0.035
1/ 2
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
CP  a  bT  cT
CP = J mol-1 K-1
ST  S0  SMax / 1000 Q298 
2

T
298
CP
T
dT
2
 dT
S max
V max
4
0.035
1/ 2
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
CP  a  bT  cT
CP = J mol-1 K-1
ST  S0  SMax / 1000 Q298 

T
ST  S0  SMax / 1000 Q298 

T
2
2
298
CP
4
0.035
1/ 2
dT
a  bT  cT
298


 dT
V max
T
ST  S0  SMax / 1000 Q298  a ln
2
2
S max
2
 dT
1/ 2
dT
T
 T    b T  298   c  1  1   2d  1  1 

  2


2
 298  
2 T
298 
T
298
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
V at 25 ˚C, 1 atm
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
Thermal expansivity, K-1
S max
V max
4
0.035
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
V at 25 ˚C, 1 atm


a
0.2794
0.2802
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
Thermal expansivity, K-1
V1,T  V0  VMaxQ298 1  a T  298   20a
2
b
-0.7124
-0.69
o
V at T of interest, 1 atm
o

T 

298 
S max
V max
4
0.035
Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite

H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5

V
4.414
4.986
a
0.2794
0.2802
V1,T  V0  VMaxQ298 1  a T  298   20a
2
o
o
b
-0.7124
-0.69

T 
c
-2055.6
-1375.7

298 
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
S max
V max
4
0.035
Bulk modulus (degree of
incompressibility)
V at T of interest, 1 atm

P
1
VdP 
V1, T T  
4P 
 1  
3 
T 
3/ 4

 1

Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite

H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5

V
4.414
4.986
a
0.2794
0.2802
V1,T  V0  VMaxQ298 1  a T  298   20a
2
o
o
b
-0.7124
-0.69

T 
c
-2055.6
-1375.7

298 
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
S max
V max
4
0.035
Bulk modulus (degree of
incompressibility)
V at T of interest, 1 atm
Volume at the P and T of interest
(based on the Murnaghan EoS)

P
1
VdP 
V1, T T  
4P 
 1  
3 
T 
3/ 4

 1

Extract of THERMOCALC molar thermodynamic properties, Table 5 of Holland & Powell, 1998
Ky anite
Sillimanite
H
sd(H) S
-2593.13 0.7 83.5
-2585.89 0.7 95.5
V
4.414
4.986
a
0.2794
0.2802
b
-0.7124
-0.69
c
-2055.6
-1375.7
d
-2.2894
-2.3994
aû

Tc
4.04 1590
2.21 1320 2200
We can thus use the tabulated data, with the correct set
of equations, to extrapolate the thermodynamic
properties (V, S & H) to the P and T of interest - this is
part of what THERMOCALC does.
This handling of data is explained more fully in:
HOLLAND, T. J. B. & POWELL, R. (1998), J.
Metamorphic Geology, v16, 309-343.
S max
V max
4
0.035