Lecture 10: Mineral reactions and petrogenetic grids
Mineral reactions involve both continuous and discontinuous reactions. Continuous
reactions depend on XMg and are a field when plotted in P-T space. Discontinuous
reactions are a line in P-T space and make good field isograds.
1
Reading T versus XMg diagrams
from Philpotts & Ague 2009
at constant P and
projected from A,
ms, qtz and fluid
2
Continuous versus discontinuous reactions
Discontinuous reactions are reactions where one paragenesis changes to another:
these are lines in P-T-a(H2O) space
Continuous reactions are reactions where the paragenesis remains the same, but the
composition of the phases changes: they are fields in P-T space
Petrogenetic grids
A petrogenetic grid is a network of discontinuous reactions. It splits up P-T space into
domains of different mineral parageneses.
reaction positions depend
on a(H2O)
4
Constructing petrogenetic grids
To construct a petrogenetic grid, we need info on the slopes of the reactions and on
the arrangement of the reactions around their intersections: thermodynamics and
Schreinemaker’s rules
For a reaction A + B = C + D, the ∆Gr = ∆Hr - T∙∆Sr + P∙∆Vr
Using the cyclic rule for partial derivatives:
∂∆G
∂T
∂P
∂T
∂T
∂∆G
∂P
P
= -ΔS
P
∂∆G
∂P
∂∆G
= ΔV
T
∂P
∂T
=
= -1
ΔG
ΔSr
ΔVr
This is the Clapeyron
equation and its units
are Pa / K
5
T
Clapeyron reaction slopes
∂P
∂T
=
ΔSr
ΔVr
The Clapeyron equation is very useful to find the slope of the reaction, but it does not
tell you the position of the reaction in P-T space, nor what minerals reside on the high
P or the high T side of the reaction
ΔHr sill → ky = -7.2 kJ mol-1
ΔHr and → sill = +2.9 kJ mol-1
ΔHr and → ky = -4.3 kJ mol-1
ΔSr sill → ky = -12 J K-1 mol-1
dP/dT sill → ky = 20 bar K-1
ΔSr and → sill = +2.8 J K-1 mol-1
dP/dT and → sill = -17.5 bar K-1
ΔSr and → ky = -9.2 J K-1 mol-1
dP/dT and → ky = 12.4 bar K-1
ΔVr sill → ky = -0.58 J bar-1 mol-1
ΔVr and → sill = -0.16 J bar-1 mol-1
ΔVr and → ky = -0.74 J bar-1 mol-1
6
∂P
Clapeyron reaction slopes
∂T
=
ΔSr
ΔVr
Al-sil diagram
Reaction equations
written withto
the high
assemblage
of the
= sign
The Clapeyron equation
is veryareuseful
findT(K)the
slopeto the
ofright
the
reaction,
but it does not
tell you the position of the reaction in P-T space, nor what minerals reside on the high
P or the high T side of the reaction
8000
kyanite
ill
=s
ky
prl = H2O q ky
P(bar)
5200
∆H = -2593 kJ mol-1
V = 4.414 J bar-1
pyrophyllite
6600
sillimanite
3800
∆H = -2586 kJ mol-1
V = 4.986 J bar-1
(2)
d
ky
=
ll
si
∆H = -2589 kJ mol-1
V = 5.153 J bar-1
1
1000
andalusite
d
(1)
an
an
2400
=
673
773
873
973
7
1073
T(K)
A Schreinemaker example
absent phase
reaction
ΔV
ΔS
dP/dT
(An)
5 En + 5 Cor = Crd + 3 Sp
0.068
55.42
8.1
(En)
Crd + 5 Cor = 5 An + 2 Sp
-0.024
-36.37
15.2
(Cor)
2 Crd + Sp = 5 En + 5 An
-0.092
-91.79
10
(Crd)
An + Sp = En + 2 Cor
-0.009
-3.81
4.2
(Sp)
2 En + 3 An = Cor + Crd
0.042
43.99
10.5
8
P
An
+S
Crd
p
+C or
En
Cr + An
d+
Co
r
En
Cr + A
d
n
+
Sp
A Schreinemaker example
(En)
(Sp)
(Cor)
(An)
or
+C
p
En
+S
Crd
or
(Crd) : An + Sp = En + 2 Cor
+C p
n
E
+S
An
T
absent phase
ΔV
ΔS
dP/dT
(An)
0.068
55.42
8.1
15.2
(En)
-0.024
-36.37
(Cor)
-0.092
-91.79
10
(Crd)
-0.009
-3.81
4.2
(Sp)
0.042
43.99
10.5
9
A Schreinemaker example
invariant point:
degrees of freedom = 0
df = c - f + T + P + i
c: Al2O3 + SiO2 + MgO
f: En, Crd, Cor, An, Sp
T, P, but no i
10
Schreinemaker’s rules
The topology of reactions around an invariant point can be deduced using simple logic, but
Schreinemaker’s rules speed up the process and allow you to check the validity of your result:
The metastable extension of the (phase-absent) reaction must fall in the sector in
which that phase is stable in all possible parageneses
11
Schreinemaker’s rules
The topology of reactions around an invariant point can be deduced using simple logic, but
Schreinemaker’s rules speed up the process and allow you to check the validity of your result:
The metastable extension of the (phase-absent) reaction must fall in the sector in
which that phase is stable in all possible parageneses
1. No sector has a stability area greater than 180°
2. All reactants and products are stable in the field
where the reaction plots
3. Complex reactions (high number of participating
phases) usually lie within bounding, simple
reactions defining the phase stability region
4. The simplest divariant region usually contains
the most metastable extensions
12