1. 143Nd/144Nd
87Sr/86Sr
Sr vs Nd Plot. EG grey gneiss, Lewisian granulite and Miki gneiss are all inappropriate. Lewisian amphibolite okay (15%), Miki Granophyre okay (25-30%), EG granulite possible but high degrees of contamination (50%).

2. 206Pb/204Pb
Discuss last week: Simple mixing, some rheological problems in mixing components, involves mixing of liquids and ignore presence of crystals and possible crystal fractionation. (therefore isotopes are best) Mixing was used as a model for mixing of melts of contrastong composition and also as a model for crustal contamination
87Sr/86Sr
Sr vs Pb plot: Lewisian granulite and Miki gneiss still inappropriate so definitely no good. Although Miki granophyre was good in Sr vs. Nd it is obviously inappropriate for Pb. EG granulite again okay but again requires too much contamination (100%). EG grey gneiss is okay for Sr-Pb but not for Sr-Nd so cannot work. Lewisian amphibolite (15-20% contamination) is best contaminant but obviously not perfect (variation in composition of crustal end-member).

3. Lecture 4: Combined assimilation and fractional crystallization (AFC)
Modeling of trace element and radiogenic isotopic data in igneous petrology
AFC … more complex model for assimilation a.k.a. crustal contamination, involving effects of crystallisation. Basically combining simple mixing and fractional xaln.
On board draw magma chamber absorbing crust. Magma is hot, crust is cold, so there needs to be a transfer of heat to melt the crust and get it to assimilate into the magma.
This occurs through release of heat cause by crystallisation = latent heat of crystallisation, basically need to put heat into a system to change it from solid to liquid (melting) and that heat energy is released again on crystallisation of the magma, = system cooling down and freezing. Thermodynamics = change from relatively disordered system (liquid) to more ordered system = release of heat.
Phase diagrams = liquidus to solidus, system must cool, and that heat must go somewhere, into the country rocks.
This means …. By definition, when a hot magma assimilates a relatively cold country rock, the system will by deinition loose heat and therefore crystallise … therefore assimilation should almost always be accompanied by xaln.
Lecture 4:
Combined assimilation and fractional crystallization (AFC)

4. V. Commonly used to model assimilation.
To model AFC need to know (or guess) quite a few things.
Trace elements first … what we want to know is the elemental concentration in the contaminated magma, which by definition is also evolving through FX
Need to know Xo, original concentration of TE in parent magma (take from most primitive magma in suite?)
Xa concentration of TE in country rock, from exposures or from general geology
Elemental concentration in xalling assemblage, basically calculated from D … bulk partition coefficient calculate from petrographic observations on the crystallisaing assemblage and KD from literature.
We need to know the change in mass of the evolving magma, because not a closed system, adding material through assimilation, and removing material through crystallisation and this can be described by knowing the relative rates of xaln to assimilation (in reality we do not know this so we assume it, or try out different models
Model for assimilation and fractional crystallisation in a magma chamber (modified from DePaolo (1981))

5. ’r’
Term used to define relative rates of assimilation versus fractional crystallization.
Generally 1<r<0
r=1 (MA=MC) uncommon = zone refining
MC=0, no crystallization = simple mixing
r=0, MA=0. No assimilation = fractional crystallization
To describe the relative rate of assimilation versus crystallisation we define a value ’r’ = rate of assimilation/mass of crystallisation.
Generally r is between 1 and 0, can get values over 1, but only in a superheated magma chamber which is extremely vigorous so lots of movement promotes assimilation, but is detrimental to xaln
Zone refining r = 1, can use for models of magmas migrating up through crust/mantle by assimilating at top and same amount of xaln at bottom (unlikely)
Mc = 0 r breaks down = simple mixing (assimilation only)
FX etc

6. Trace elements F = fraction of melt remaining
D = bulk partition coefficient for fractionating assemblage
(note: I have used slightly different symbols than in the DePaolo paper, and a different version of this equation is given in Wilson (her eq. 1)… but gives the same results)
Xm = concentration of trace element in the magma following AFC
X0 = concentration of trace element in the original magma
Xa = concentration of trace element in the assimilant (country rock)
F = Degree of crystallization (same as used for fractional crystallisation) = Mm/M0, such that F = 1 completely crystallized and F = 0 uncrystallised.
r = Ma/Mc (less than 1)
Z as defined
D = bulk partition coefficient for crystallizing assemblage

7. Xm/Xo for bulk D of o.1 (incompatible) and assuming r = 0.2
Blue line = pure rayleigh xaln, concentration of TE increases with F
Black lines = AFC trends for different values of Xa/Xo i.e relative concentration of TE in assimilant to that in original magma.
If assimilant has same TE concentration as original magma (i.e. curve = 1), not far removed from FX (more so if less), but as as conc in assimilant increases then get increasing concentrations of TE because concentration is increasing due to a) FX and it being incompatibel, and assimilation of country rock with high concentrations of the TE.
Variations in relative concentrations of trace elements in a melt compared with the original melt composition with varying F and XA/X0, D = 0.1, r = 0.2.

8. Exactly the same graph, but now the trace element of interest is compatible, pure FX, concentrations fall.
But as concetration of TE in assimilant increases can see that effects of assimilation begin to swamp those of FX, such that even though TE is being removed in xalling assemblage, the amount added by assimilation is greater, such that TE content increases!
Variations in relative concentrations of trace elements in a melt compared with the original melt composition with varying F and XA/X0, D = 2, r = 0.2.

9. Of course these effects are also dependant on relative rates of assimiation to xaln
This is same as first graph, D = 0.1, Xa/X0 is constant at 10, but differing values of r
Can see with increasing relative assimilation to fx, effect s of assimilant are emphasized.
Variations in relative concentrations of trace elements in a melt compared with the original melt composition with varying F and r, XA/X0 = 10, D = 0.1.

10. Isotopic composition of evolved and contaminated magma ICM
Things are much more interesting w.r.t. isotopes, TE are in fact hard to interprete by themselves and AFC can really only be demonstrated when there are very large contrasts in TE concentration bw magma and assimilant.
Isotopes … often a large contrast bw magma and country rock.
So to model this we need to know some further information …. IC of magma originally and IC of assimilant.
Isotopic composition of magma
IC0
Isotopic composition of wallrock
ICA
Model for assimilation and fractional crystallisation in a magma chamber (modified from DePaolo (1981))

11. Radiogenic isotopes
ICM, ICA and IC0 = isotopic compositions of the evolving magma, assimilant and original magma, respectively.
Equation ….nastiest!

12. e.g. Sr isotopic composition
(Wilson gives a different formulation of this equation (eq. 2) gives the same results)
Obviously, from equation there are a lot of variables, and it would be a waste of time (and not very interesting) to see what they all do.

13. Sr concentration versus Sr isotopic composition for typical crust-mantle derived magma system where magma has 400ppm Sr and 87Sr/86Sr = and country rock with 87Sr/86Sr = and Sr = 150ppm .
Simple mixing only.
Sr concentration versus Sr isotopic composition in a typical crust mantle system of a magma with 400ppm Sr and 87Sr/86Sr = and country rock with 87Sr/86Sr = and Sr = 150ppm (basalt + metasedimentary bedrock).
Two models looking at D incompatible and D compatible
Blue line = simple mixing
Pure FX would result in changes in TE concentration, without changes in IC

14. Sr concentration versus Sr isotopic composition for typical crust-mantle derived magma system where magma has 400ppm Sr and 87Sr/86Sr = and country rock with 87Sr/86Sr = and Sr = 150ppm .
AFC with r = 0.1.
For r = 0.1 (system dominated by FX) can see that as expected TE increase in incompatible, and decrease in compatible, but IC also changes
IMPT difference from Simple Mix is that trends do not end up at the same IC as that of yr contaminant!

15. Sr concentration versus Sr isotopic composition for typical crust-mantle derived magma system where magma has 400ppm Sr and 87Sr/86Sr = and country rock with 87Sr/86Sr = and Sr = 150ppm .
AFC with variable r.
As the effects of assimilation are increased, then IC changes more, and the effects of pure FX are reduced.

16. Two isotope systems
Much more interesting (and complex) when compare two isotope systems (e.g. Sr and Nd).
Obviously now there are a huge number of variables we need to control, primarily isotopic compositions of end-members, relative TE concentrations, D and r., nearly and infinite range of possibilities!
At some point, we need to assume typical values, Sr is compatible, Nd incompatible etc etc etc.
R is low (0.1) …. Not far removed from simple mixing, but relatively large degrees of contamination result in much smaller shifts in IC, AND contaminaed magmas do not vector towards the actual composition of the assimilant!!!!!
Increasing r results in trends closer to simple mixing, but never makes it, and never gets down to the composition of the assimilant!

17. Same as previous example, but Sr now compatible
For example, if we use the same end-member compositions but now decide that plagioclase is incompatible (DSr = 0,7)
We get quite different results, influence of country rock composition is much greater.
And if we go back to the original example here, but now change the composition of the basaltic end-member so it is much more enriched in everything (kimberlite?)
We also see much different results.
So say now we envisage the same country rock, but this time it is being intruded with a very enriched basaltic magma (lamproite/kimberlite) with higher concentrations of Sr (2000 ppm) and Nd (200 ppm) perhaps produced by very small degrees of melting of an enriched mantle, such that Sr/Nd has actually decreased compared to the original basaltic magma.
Same type of graph and we can now see that the relative concentrations of the end-members are also important, so at low degrees of ‘r’ we get only small changes in isotopic composition.
Same as previous example, but magma is enriched in both Sr and Nd.

18. Exercises
Set-up spreadsheets for plotting trace elemental and isotopic variation during AFC.
Variation in Sr and Nd isotopes during AFC with ‘r’.
Determining possible contaminants in Taupo Volcanic Zone (NZ) basalts using AFC.
NEXT WEEK: Partial melting.