1. Lecture 5: Partial melting of the mantle
Modeling of trace element and radiogenic isotopic data in igneous petrology
Previous weeks we have talked a lot about what happens in magma chambers, during fractional crystallization, magma mixing and assimilation combined with fractional crystallization.
not addressed how the magmas actually form
Lecture 5:
Partial melting of the mantle

2. Mantle petrology Classification of Ultramafic rocks. After IUGS
Olivine
Clinopyroxene
Orthopyroxene
Lherzolite
Harzburgite
Wehrlite
Websterite
Orthopyroxenite
Clinopyroxenite
Olivine Websterite
Peridotites
Pyroxenites 90 40 10
Dunite
Partial melting of lherzolite leads to a reduction in fertility from lherzolite to harzburgite to dunite (reduction first in clinopyroxene, then orthopyroxene contents).
In addition to olivine, orthopyroxene and clinopyroxene are a few other important minerals, depending on depth (pressure), particularly the aluminium bearing phase
Classification of Ultramafic rocks.
After IUGS

3. Modal variation with depth
Aluminous phase varies with depth, plagioclase, spinel, garnet
Most basaltic melts come from shallower than 200km
Relatively deep (10kb+ (100km +)): GARNET.
Relatively shallow (less than 10kb km): Spinel ((Mg, Fe, Mn)(Al, Fe, Cr)204 (includes spinel MgAl2O4), hercynite FeAl2O4 (hercynite), chromite FeCr2O4 and magnetite (Fe3O4) (FIND a classification sheme)
Shallow (less than 3kb <30 km): Plagioclase.
BUT always the same composition chemically
Why do we care?
We come back to that later
Phase diagram for 4-phase aluminous lherzolite After Wyllie, P. J. (1981). Geol. Rundsch. 70,

4. Lherzolite → basalt?
Two questions?
How do we get the mantle to melt (below solidus with normal geoherm)
How do we get from a lherzolite (35-40% Si) to a basalt (45% Silica)
Spinel lherzolite xenoliths in basalt, Cerro Negro, New Mexico, U.S.A. Photo from Jane Selverstone

5. ... increasing temperature
Add heat somehow (radioactivity) It is heated up so it exceeds the solidus (may have been the case in the past when the earth was hotter)
GEOTHERM

6. .... addition of volatiles
The solidus is lowered by addition of fluids (important in subduction zones), fluids released from dehydration of downgoing slab (breakdown of amphiboles etc) ... impt under subduction zones, complex because addition of volatiles also results in metasomatism, addition of fluid mobile elements.

7. ... isothermal uplift
The mantle ascends relatively quickly so that it remains at the same T but drops to lower pressures (ascent of a mantle plume), ascent of mantle under MOR.

8. Melting experiments have shown that the major element characteristics of different basalt types can be produced from lherzolitic sources at differing degrees of partial melting at differing depths
(Figure 3.26 of Wilson)
Alkaline basalts are favoured over tholeiites by deeper melting and by low % PM
Such that tholeiitic basalts are produced by relatively small degrees of melting at relatively shallow depths, tholeiites at moderate degrees of melting and shallower depths, and picrites at moderate degrees of melting at greater depths, and alkali basalts produced by small degrees of melting of enriched-mantle at depth .
Major element compositions of melts generated by partial melting of mantle are largely insensitive to the type of melting, but we are really interested in trace elements (especially here we will focus again on the REE)

9. Trace elements
A simplistic model for melting is Batch melting which is essentially identical to Equilibrium crystallisation.
X0 = composition of solid source (lherzolite).
F = Fraction of melt produced. (75% melting => F = 0.75, system = 25% solid and 75% melt), i.e. small degrees of melting are the equivalent of large degrees of crystallisation.
During FX X0 = composition of melt prior to xaln (i.e. composition of 100% liquid)
In crystallisation F = fraction of melt remaining (25% crystallisation => F = 0.75)
(system consists of 25% solid and 75% melt)

10. Simplistically, melting is the opposite of fractional crystallisation
BATCH MELTING
EQUILIBRIUM
CRYSTALLISATION
What happens during large degrees of xaln to an incompatible element.
So if we draw a graph of Xm/X0 versus F on board and look at F = 0.1,
For fractional crystallisation this represents 90% crystallisation, 10% melt remaining
For partial melting this represents 10% melting
In both situations systems represents 10% liquid an 90% melt.
small amounts of melting are the same as large amounts of crystallisation.
What effect will this have on trace element composition
Small degree melting when trace element is incompatible?
(Trace element is strongly concentrated in melt)
Large degrees of melting when incompatible
(Trace element is less concentrated in melt, diluted by continued melting)
Simplistically, melting is the opposite of fractional crystallisation

11. Simplistic models
Equilibrium melting is simplistic because it assumes the melt that is formed reacts and equilibrates with the residual solid until segregation.
Rayleigh melting assumes the melt is removed as it forms. Requires very high porosity and permeability to remove small degree melts.
Both assume modal melting.
When we modeled fractional crystallization we used the parameter D to account for having a crystallizing assemblage which consists of more than one mineral
e.g. modal proportion of mineral A * Kd mineral A etc etc

12. Simple ternary phase diagram of the mantle
Olivine
Dunite 90
Harzburgite
Peridotites
Wehrlite
Lherzolite 40
Orthopyroxenite
Olivine Websterite
Pyroxenites 10
Websterite 10
Orthopyroxene
Clinopyroxenite
Clinopyroxene
Lherzolite = X, modal melting would melt minerals in these proportions, such that after e.g. 20% partial melting 20% of olivine, 20% of cpx and 20% of opx would have disappeared.
BUT phase diagram tells us that the first melt produced is Y (eutectic) and will continue to be so until all Di used up and have a source with composition Z (= enstatite (opx) and olivine only = Harzburgite). This will then start melting with a binary eutectic of composition ‘a’.
= lherzolite to harzburgite to dunite.
ALL SUGGEST NON-MODAl MELTINg
NON-MODAL MELTING MUST OCCUR!!

13. Aggregated non-modal melting
XL = composition of the generated melt
X0 = composition of source
F = amount of melt formed (0 = no melting, 1 = completely melted)
D = bulk partition coefficient (from modal assemblage)
P = Partition coefficient of the melt norm.
There are a number of different models for partial melting of mantle rocks including simplistic modal batch melting and rayleigh melting, and more complex non-modal batch melting and non-modal rayleigh melting. The latter is a good model, but is complicated by its extreme end-member nature of requiring melt to be removed instantaneously from the source, which in the case of the mantle basically requires very high permeability and porosity.Represents the aggregated melt formed by combining a large number of very small fractional melts (Shaw (1970) Trace element fractionation during anatexis. Geochimica et Cosmochimica Acta 34: )
Incorporates P a term to account for non-modal melting.
Go through terms and discuss what we need to know

14. P = partition coefficient of the melt norm
P can be calculated as the weight fraction of each mineral contributing to the melt (p) * its KD such that
P = pAKDA + pBKDB + pCKDC
Where the modal percents are their modal abundance in the lherzolitic source, something we can get directly from samples of lherzolite bought up as xenoliths in volcanoes.
ρ may seem a little arbitrary but ..
can you think about how we could estimate what proportions individual minerals contribute to a melt during non-modal melting?
can calculate this from phase diagram = composition of eutectic

15. Melting proportions ()
Calculation of P and D.
Modal proportions (X)
Melting proportions ()
KD Nd DO P
60% olivine
10%
0.01
0.6*0.01=0.0060
0.10*0.01=0.0010
25% opx
25%
0.02
0.25*0.02=0.0050
10% cpx
50%
0.50
0.10*0.5=0.0500
0.50*0.5=0.2500
5% spinel
15%
0.05*0.01=0.0005
0.15*0.01=0.0015
100
sum =
sum =

16. Things we need to know/assume.
Modal composition of mantle (xenoliths etc)
Trace element/REE composition of source lherzolite (measured or modeled)
Partition coefficients (measured)
Modal contributions to melts (phase diagrams, experiments)
(could measure, or as in this case based on a bulk earth model where original composition is that originally had the composition of a chondritic meteorite but has had a certain percentage of material removed to form the continental crust)
I have taken typical values from the literature for our exercises.

17. What is consequence of non-modal melting .....
At some point all Diopside is gone, only have Fo and En left so a) D changes, and b) P changes (need to recalculate), and bulk composition also changes!
If this value is 1 or greater then the mineral only disappears at 100% melting, less than 1 then will disappear before complete melting.
e.g. cpx will disappear at 20% melting
Spinel will disappear at 33% melting.
Can then recalculate how much of each phase was melted at that degree of melting by multiplying F by p
And if subtract that from original modal proportions, and recalculate to a modal proportion of 100% can recalculate a new mode, and therefore new ‘D’ and ‘P’.
Modal proportions (X)
Melting proportions ()
F for complete
removal of phase
Amount of phase melted at F = 0.2
Amount of phase left
recalc’d to 100%
60% olivine
10%
0.6/0.1=6
0.2*0.1 = 0.02
=0.58
0.58*1/0.8=0.725
25% opx
25%
0.25/0.25=1
0.2*0.25 = 0.05
=0.20
0.2*1/0.8=0.25
10% cpx
50%
0.1/0.5=0.20
0.2*0.5 = 0.1 =0
0*1/0.8=0
5% spinel
15%
0.05/0.15=0.33
0.2*0.15 = 0.03
=0.02
0.02*1/0.8=0.025
sum = 0.20
sum = 0.80
sum = 1

18. KD for mantle minerals
So if we make a small degree melt of mantle where garnet is present but remains as a residual phase (i.e. it doesn’t all melt) then what will happen to the HREE?
They will stay in the garnet.
So we will get very different REE patterns depending on if garnet is present or not.
Therefore we can use REE compositions of basaltic melts to get an idea of what the source mineralogy was and therefore the depth at which mantle melting occurred

19. Exercises
Calculate REE patterns for melts of spinel and garnet lherzolite.