Melting the mantle
Using petrology/geochemistry of
magmas to study thermal boundary
layers
Cin-Ty Lee
Rice University
How melting happens
Temp ( oC)
500
0
1000
1500
2000
Decompression melting
5
200
10
300
Depth (km)
P (GPa)
100
Depression of solidus
Isobaric heating
Temperature (K)
1000
0
2000
3000
4000
Thermal boundary layer
Upper mantle
410
14
Transition zone
670
Depth (km)
Pressure (Gpa)
24
Lower Mantle
ULVZ?
3000
138
Ocean
Plume
Midocean
Ridge
Continental
Crust
Base of
lithosphere
Melting occurs near boundary
layers
Melts advect heat
Melts lead to chemical
differentiation
Mantle
Core
We are interested in determining the T, P, and F of melts
T
Thermal state of the mantle
Thickness of continental
lithosphere
P
The presence of
volatiles
1.What is melting
2.Decompression Melting
3.Hydrous melting
4. Constraining the thermal state
of the mantle (observables)
1. What is melting?
Solid = long-range (crystalline)
order
Liquid = short-range order
characterized by molecular
clusters having local ordered
structure
H2 O
UNARY SYSTEM - Constant P
solid
Liq
Solid + Liq
Melt fraction
F
Cumulative
Heat added
into system
H  mcp T
 dH 
H fus  
t fusion
 dt 
(or taken out of
the environment)
T
solidus
time
liquidus
H  mcp T
Temperature is buffered at the phase change because the heat being added
is involved in making a phase change: HEAT OF FUSION
If a phase change is not occurring, heat goes directly into causing the atoms
to vibrate more, resulting in an increase in temperature
In both cases, entropy increases
dq
dS 
T
Entropy change associated with melting is:
S 
H f
Tf
T 
dq
dT
 

S


mc

mc
ln
p
Entropy change associated with heating is:
T  p T
 To 
solid
solid+ Liq
Melt fraction
F
Entropy of
system
T 
S  mcp  
 To 
S 
T
time
H f
Tf
Liq
Same concepts hold in multi-component systems
1600
1 atm = 0.1 MPa
Temperature (oC)
1500
LIQUID
1400
T3
L3
L2
L1
T2
1300
x3
S3
X-specific
liquidus
x2
S2
x1
T1 S1
S1
solidus
Eutectic
1200
1100
Diopside
CaMgSi2O6
Anorthite
+ Diopside
X0
X (Wt. %)
Anorthite
CaAl2Si2O8
2. Decompression melting
Mid-ocean Ridge
T
P
Decompression melting
Stolper & Asimow 2007
What controls the slope of the solidus in P-T space?
Clapeyron slope
S f
 dP 

 
 dT  2 V f
S f  0
V f  0
 dP 

 0
 dT 2
Presnall et al. (1978). Contr. Min. Pet., 66, 203-220.
Isentropic decompression (“adiabatic” decompression)
•Assume buoyancy-driven advection rates >> thermal diffusion
no heat loss
q=0
•Assume process is reversible, dS = 0
dE = dq + dw = TdS – pdV = -pdV
Cp
 dP 

 
 dT  s TV
Solid isentrope (“adiabat”)
Temperature drops slightly during decompression because system
expands and does work on the environment, decreasing internal
energy (hence T)
CAUTION: there are many adiabatic processes that are not
isentropic
Melting the mantle
Potential temperature TP
  V 
Tp (0)  T ( P) exp 
P 
 CP 
  g
Tp (0)  T ( z ) exp 
 cP

z 

Let’s look at constant entropy processes
dE  dq  dW  dq  PdV
H  E  PV
dH  dq  VdP
dq  TdS
dH  TdS  VdP
H ( S , P)
 H 
 H 
dH  
 dS  
 dP
 S  P
 P  S
 H 

 T
 S  P
 H 

 V
 P S
For simplicity, let’s assume a one-component mantle
Constant P
Constant P
(S2, H2)
T
 
H
  S  P
 
pe 
H
(S1, H1)
1
H
slo
A
S
B
A+B
S
Stolper & Asimow 2007
Stolper & Asimow 2007
Unary system, melting solidus and liquidus coincide
melting is constrained to the solidus/liquidus
Partial melting occurs
Stolper & Asimow 2007
And now back to a multi-component mantle
liquidus does not coincide with solidus
partial melting occurs across the interval btwn solidus and liquidus
Melting isentrope is steeper
than that of solid isentrope
because energy is being
absorbed to cause a phase
change
3. Multicomponent melting
Example - Hydrous melting
Temp (oC)
500
0
1000
1500
2000
5
200
10
300
Depth (km)
P (GPa)
100
Ex: Water dissolves in liquid
T,P
GT , P   X i i
GT , P
i  io  RT ln X i
GT , P   X i io  RT  X i ln X i
S   R X i ln X i
Xi
Molar Gibbs Free Energy
Freezing point depression
Freezing point
depression
Tmelting
Tmelting
temperature
Why does wet solidus curve back
to dry solidus at low P
At low P, solubility of water in melt is
very small, so no significant increase
of melt entropy when water is added
to the system
Berndt et al. 2005
4. Constrain the physical
conditions of melting
F = melt fraction
T = temperature
P = pressure
T
Thermal state of the mantle
High F = High T
P
Solid residue
1-F
Original solid
=
o
sol
C M
o
sol
+
Melt
F
 Csol M sol  Cmelt M melt
F = Mmelt/Mosol
CONSTRAINING F (melt fraction)
Trace elements as a tool
melt
Partition coefficient
Csolid
D=
Cmelt
Cmelt
1

o
Csol DB  F (1  DB )
Solid residue
D>1
compatible in solid
D<1
incompatible in solid
Equilibrium Melting
100
Melts
Cmelt/Co
10
D<1
incompatible
D=0.01
0.1
0.5
1
1
D>1
compatible
5
10
0.1
0
0.2
0.4
0.6
0.8
1
F
When D = 0 (perfectly incompatible element)
(e.g., Na, Cs, Nb, Ba)
C melt
o
C sol
1
~
F
Primitive magma
MORBs
Klein and Langmuir 1987
F increases
Cmelt /Co ~ 1/F
Increasing F
Regionally averaged MORB compositions
plotted against axial depth of ridge
Klein and Langmuir 1987
Does crustal thickness vary with axial depth?
Forsyth, 1992
Temperature and Pressure
thermobarometry
Thermometers
Mg2SiO4 (olivine) + Fe2SiO4 (melt) = Mg2SiO4 (melt) + Fe2SiO4 (olivine)
Mg2SiO4 (olivine) = Mg2SiO4 (melt)
S f
 dP 

 
 dT  2 V f
Fe / Mg ol

Fe / Mg melt
small
P
1900
1 atm = 0.1 MPa
1800
Temperature (oC)
K
Fe / Mg
D
T
1700
“forbidden
zone”
1600 T3
1500
1400
LIQUID
T2
T1
S3
L3
X3
S2
X2
S1
L2
X1
L1
1300
OLIVINE
1200
1100
Mg2SiO4
X0
Wt. % Fayalite
Fe2SiO4
Roeder-type
45Plot of Magma Compositions
Using Putirka calibrations
0.93 0.92 0.91 0.90 0.89
40
Fo=0.88
35
1700
30
1600
25
mole % Mg
1500
20
1400
15
1300
10
1200 C
5
0
0
5
10
mole % Fe
15
20
Barometers
Mg2SiO4(olivine) + SiO2(melt) = Mg2Si2O6(pyroxene)
K (T , P) ~
K~
px
a Mg
2 Si 2 O 6
ol
melt
a Mg
2 SiO4 a SiO2
large
S f
 dP 



dT

 2 V f
1
a
melt
SiO 2
1 atm = 0.1 MPa
1700
T1
Liquid
+ Forsterite
T
B
LIQUID
L + Si-poly
1600
T (oC)
P
Pe
TPe
TE
L + En
E
1500
Enstatite
+ Si-polymorph
Forsterite
+ Enstatite
Xo
1400
Forsterite
Mg2SiO4
X1
Enstatite
MgSiO3
SiO2
Wt. %
65
1
0.9
55
0.8
0.7
0.6
0.5
0.4
0.3
50
45
40
35
30
25
0.2
A
0.1
B
20
1000 oC
15
0
35
40
45
50
55
60
65
0
1
2
3
4
5
6
7
P (GPa)
SiO2 (wt. %)
5.0
0.30
C
D
this study
Haase
Albarede
3.0
0.20
(TCalc-Texp)/Texp
4.0
PCalc - PExp
Mol % Si4O8 anhydrous
Mol % Si4O8 (hydrous)
Wt % SiO2 (anhydrous)
Wt % SiO2 (hydrous)
Experimental Melts
60
% silica index
Mg# = Mg/(Mg+Fe)
Anhydrous
Hydrous
Experimental Melts
2.0
1.0
0.0
-1.0
-2.0
-3.0
0.10
0.00
-0.10
-0.20
-4.0
This study
Putirka A (2005)
Putirka C (2005)
Sugawara (2000)
-0.30
-5.0
0
1
2
3
4
5
6
Experimental P (GPa)
7
8
1000
1200
1400
1600
Experimental T (oC)
1800
8
Classification of magma compositions – not just random classification!
16
15
14
phonolite
13
Nephelinite
12
Tephri-phonolite
trachyte
K2O + Na2O
11
rhyolite
10
Phono-tephrite
9
trachyandesite
Hi P
8
7
Basaltic
trachy-andesite
Tephrite or
basanite
6
Trachy-basalt
5
4
3
Basalt
2
Basaltic
andesite
Lo PAndesite
Dacite
Picrobasalt
1
0
40
45
50
55
60
SiO2
65
70
75
How hot is the mantle?
7.0
1600
1700
0
20
40
Spinel/garnet
transition
60
80
100
120
140
160
180
200
220
P (GPa)
1500
1200
1300
1400
0.0
20 30
0.5
F=10
1.0
1.5
2.0
2.5
.
3.0
3.5 LAB
plate
4.0
4.5
5.0
Hawaiian Hotspot
5.5
Post-shield
6.0
Shield stage
6.5
7.0
1500
1600
1700
0
TP
20
40
LABeroded
60
80
100
120
140
160
180
200
220
Depth (km)
1200
1300
1400
0.0
TP
0.5
1.0
1.5
2.0
2.5
.
3.0
3.5
4.0
4.5
Mid-ocean ridge
5.0
basalts
5.5
East Pacific Rise
6.0
Mid-Atlantic Ridge
6.5
T (oC)
Depth (km)
P (GPa)
T (oC)
CONTINENTAL LITHOSPHERE
T (oC)
western Basin and Range
Basin and
Range
A’
A
Colorado
Plateau
1200
1300
1400
1500
0.0
TP
0.5
1.0
1.5
2.0 LABBR
2.5
3.0 LABCP
3.5
4.0
4.5
5.0
5.5
Western North
6.0
America
6.5
7.0
1600
1700
0
20
40
60
80
100
120
140
160
180
200
220
Depth (km)
<1 Ma (Coso,
CA) Plateau
Colorado
<1 Ma (Amboy,
<1 CA)
Ma (San Francisco, AZ)
<1 Ma (Pisgah, CA)
Snake
River
Snake
Plain
River
Plain
P (GPa)
Rio Grande Rift
Cenozoic western
<1 MaNorth
(Big Pine,
CA)
<1 America
Ma
(Zuni Bandera, NM)
ARCS
T (oC)
1100
1200
F=10%
1300
20%
1400
1500
0
30%
0.5
Moho
P (GPa)
60
2.0
80
2.5
Depth to slab
3.0
Fo 90 anhydrous
Fo 90 3 % H2O
Fo 90 7 % H2O
4.0
100
120
1100
1200
F=10%
1300
30%
1500
0
20
Moho
1.0
40
1.5
60
2.0
80
2.5
3.0
3.5
Anhydrous (Fo90)
Hydrous (7 wt. % H2O)
Fo90 residue hydrous
Fo92 residue hydrous
4.0
Cascades Arc
1400
Izu-Bonin Arc
100
120
Depth (km)
.
Depth (km)
40
1.5
1000
0.0
0.5
20
1.0
3.5
B
P (GPa)
A
1000
0.0
T (oC)
T (oC)
T (oC)
1600 1700
0
100
1.0
200
1.5
300
2.0
400
2.5
500
3.0
3.5
4.0
4.5
600
MOON
700
Apollo 17
Apollo 14B
800
900
5.0
B
1100 1200
-0.5
1300 1400 1500
1600 1700
D
1.0
1.5
2.0
Cumulate
Eucrites
B-EUCRITES
Eucrites (Warren)
NWA 011
(Yamaguchi et al.)
P (GPa)
P (GPa)
0.5
1400
1500
1100 1200 1300
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Venera 13
6.0
Venera 14
6.5
Vega 2
7.0
1400 1500
1600
1700
0
100
200
300
400
MARS
500
1600 1700
0
50
100
150
VENUS
200
Venusian Depth (km)
0.0
1100 1200 1300
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Gusev crater
6.5
Yamato
7.0
Martian Depth (km)
0.5
C
P (GPa)
1300 1400 1500
Lunar Depth (km)
P (GPa)
A
1100 1200
0.0
Komatiites – deep melting
T (oC)
1200
1300
1400
1500
1600
1700
0.0
1800
1900
0
TP
0.5
TP
20
1.0
40
1.5
60
2.0
P (GPa)
Hawaii
80
.
3.0
100
3.5
120
4.0
140
4.5
5.0
5.5
6.0
6.5
7.0
Komatiites
Carribean-Colombia-Gorgona
Kaapvaal, South Africa
west Australia
Superior Prov., Canada
160
180
200
220
Depth (km)
2.5
At high pressure, dP/dT becomes very large
S f
 dP 

 
 dT  2 V f
S f  0
V f  0
Stolper & Asimow 2007
Deep Melting?
Could deep melts have been
negatively buoyant?
Could they have generated an
enriched and Fe-rich lower
mantle?
S f
 dP 
0

 
 dT  2 V f
S f  0
V f  0
Miller et al. 1991
?
Nature of thermal boundary
layers can be assessed by the
geochemistry and petrology of
magmas
Temp ( oC)
500
0
1000
1500
2000
5
200
10
300
Depth (km)
P (GPa)
100
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Grove, T. L. and S. W. Parman (2004). "Thermal evolution of the Earth as
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Klein, E. M. and C. H. Langmuir (1987). "Global correlations of ocean ridge
basalt chemistry with axial depth and crustal thickness." Journal of
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ridge basalts: constraints on melt generation beneath ocean ridges. Geophys.
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thermometry, and active vs. passive upwelling." Chem. Geol. 241: 177-206.
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regions: the importance of melt density and source region size." J. Geophys. Res.
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