1. Mantle rocks Figure 2.2 C After IUGS Olivine Peridotites Lherzolite
Dunite 90
Peridotites
Wehrlite
Harzburgite
Lherzolite 40
Olivine Websterite
Pyroxenites
Orthopyroxenite 10
Websterite 10
Clinopyroxenite
Orthopyroxene
Clinopyroxene
Figure 2.2 C After IUGS

2. Phase diagram for aluminous 4-phase lherzolite:
Al-phase =
Plagioclase
shallow (< 50 km)
Spinel
50-80 km
Garnet km
Si ® VI coord.
> 400 km
Note: the mantle will not melt under normal ocean geotherm!
Figure Phase diagram of aluminous lherzolite with melting interval (gray), sub-solidus reactions, and geothermal gradient. After Wyllie, P. J. (1981). Geol. Rundsch. 70,

3. Lherzolite is probably fertile unaltered mantle
Dunite and harzburgite are refractory residuum after basalt has been extracted by partial melting 15
Tholeiitic basalt 10
Partial Melting
Wt.% Al2O3 5
Figure 10-1 Brown and Mussett, A. E. (1993), The Inaccessible Earth: An Integrated View of Its Structure and Composition. Chapman & Hall/Kluwer.
Lherzolite
Harzburgite
Residuum
Dunite
0.0
0.2
0.4
0.6
0.8
Wt.% TiO2

4. Generation of tholeiitic and alkaline basalts from a chemically uniform mantle
Variables (other than X)
Temperature
Pressure
Variables (other than X)
Temperature
= % partial melting
Pressure
Fig indicates that, although the chemistry may be the same, the mineralogy varies
Pressure effects on eutectic shift
Figure Phase diagram of aluminous lherzolite with melting interval (gray), sub-solidus reactions, and geothermal gradient. After Wyllie, P. J. (1981). Geol. Rundsch. 70,

5. Temperature: % of partial melting
No realistic mechanism for the general case
Local hot spots OK
very limited area
Figure Melting by raising the temperature.

6. Pressure effects:
Increased pressure moves the ternary eutectic minimum from the oversaturated tholeiite field to the under-saturated alkaline basalt field
Alkaline basalts are thus favored by greater depth of melting In
Figure 10.8 Change in the eutectic (first melt) composition with increasing pressure from 1 to 3 GPa projected onto the base of the basalt tetrahedron. After Kushiro (1968), J. Geophys. Res., 73,

7. Fractional Crystallization
Dominant mechanism by which most magmas, once formed, differentiate
Bowen reaction series
Stoke’s law for mineral settling
Late stage fractional crystallization
Chapters 6 and 7: effects of removing crystals as they formed (compared to equilibrium crystallization) on the liquid line of descent

8. The Soret Effect and Thermogravitational Diffusion
Thermal diffusion, or the Soret effect
Heavy elements/molecules migrate toward the colder end and lighter ones to the hotter end of the gradient
Soret Effect:
A stagnant homogeneous binary solution, when subject to a strong temperature gradient, spontaneously develop a concentration gradient in the two components

9. Samples reached a steady state in a few days
Walker and DeLong (1982) subjected two basalts to thermal gradients of nearly 50oC/mm (!)
Found that:
Samples reached a steady state in a few days
Heavier elements ® cooler end and the lighter ® hot end
The chemical concentration is similar to that expected from fractional crystallization
Due to the extreme thermal gradients, it is unlikely that thermal diffusion is effective in natural systems
Natural thermal gradients are much smaller
Components must diffuse over greater distances
Diffusion is quite slow in silicate magmas so crystal settling and/or convection may stir up the delicate Soret gradients
Figure 7.4. After Walker, D. C. and S. E. DeLong (1982). Contrib. Mineral. Petrol., 79,

10. Richter et al (2008, 2009) show that Soret effect can significantly fractionate isotopes while fractional crystallization generally does not
Due to the extreme thermal gradients, it is unlikely that thermal diffusion is effective in natural systems
Natural thermal gradients are much smaller
Components must diffuse over greater distances
Diffusion is quite slow in silicate magmas so crystal settling and/or convection may stir up the delicate Soret gradients

11. Thermogravitational diffusion
Stable and persistent stagnant boundary layers have been shown to occur near the top and sides of magma chambers

12. Hildreth (1979) 0.7 Ma Bishop Tuff at Long Valley, California
Vertical compositional variation in the stratified tuff
Thermal gradient in chamber
Vertical compositional variation in the stratified tuff
Correlates with variations in a compositionally stratified upper magma chamber that was progressively emptied from the top downward. Compositional gradient in chamber
Thermal gradient in chamber
Using mineral geothermometry Hildreth was able to demonstrate that the earliest eruptive materials, now at the base of the flow (but representing the top of the chamber) erupted at 720oC, while the latest material (lower in the chamber) erupted at 780oC

13. Model
The magma near the vertical contact becomes enriched in water from the wall rocks
Water-enriched boundary layer, although cooler, is less dense than the interior magma, and rises to concentrate near the top of the chamber
This is compositional convection
 A growing density-stabilized boundary layer cap, which inhibits convection in that portion
 Gradients in the cap rock, initially reflecting the water content, which, due to density differences, increases upward
So far it is quite likely
Hildreth then went on to propose Thermogravitational Diffusion
Volatile gradient affects structure of the melt and the degree of polymerization (Section 7.4.1), and thus O/(Si+Al) in the liquid
T, volatile, and O/(Si + Al) gradients  diffusion in the cap  vertical compositional gradients in the other components
Hildreth’s stratigraphic enrichments do not correlate well with the thermal Soret gradients
Thermogravitational diffusion no longer in vogue, but a number of in situ processes are possible, including the first parts of Hildreth’s scheme
Figure Schematic section through a rhyolitic magma chamber undergoing convection-aided in-situ differentiation. After Hildreth (1979). Geol. Soc. Amer. Special Paper, 180,

14. Langmuir Model
Thermal gradient at wall and cap  variation in % crystallized
Compositional convection ® evolved magmas from boundary layer to cap (or mix into interior)
Thermal gradient at wall and cap  variation in % crystallized from ~100% at margin to ~0% in the interior
Compositional convection can introduce evolved magmas from boundary layer to cap (or mix into interior)
This is a lot like Hildreth’s model, but does not involve volatiles
Figure Formation of boundary layers along the walls and top of a magma chamber. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall

15. Large and small scales Solar system The Earth Water column
A bit like liquid immiscibility in reverse
Early notion that basalt and rhyolite were the two main primitive magmas
The intermediate magmas were created by mixing these two in various proportions
But the variety of natural magmas is much broader than can be attained by the mixing of two end members
End-member mixing:
Variation in each element or oxide on Harker-type diagrams should lie on a straight line between the values representing the two most extreme compositions (presumably representing the two parental magmas)
Nearly all volcanic suites have a number of curved lines that we can explain by multiphase fractional crystallization, but not as easily by binary end member mixing

16. Comingled basalt-Rhyolite Mt. McLoughlin, Oregon
Magma Mixing
End member mixing for a suite of rocks
Comingled basalt-Rhyolite Mt. McLoughlin, Oregon
Figure 11.8 From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall
A bit like liquid immiscibility in reverse
Early notion that basalt and rhyolite were the two main primitive magmas
The intermediate magmas were created by mixing these two in various proportions
But the variety of natural magmas is much broader than can be attained by the mixing of two end members
End-member mixing:
Variation in each element or oxide on Harker-type diagrams should lie on a straight line between the values representing the two most extreme compositions (presumably representing the two parental magmas)
Nearly all volcanic suites have a number of curved lines that we can explain by multiphase fractional crystallization, but not as easily by binary end member mixing

17. Assimilation Incorporation of wall rocks (diffusion, xenoliths)
Assimilation by melting is limited by the heat available in the magma
Assimilation by melting is limited by the heat available in the magma
Wall rock must first be heated to the melting point, and then at least partially melted in order to be assimilated, and this heat must be supplied by the magma itself
Theoretically possible for a magma to assimilate 40% of its weight in country rock
But the crystallized portion of the magma at the cool walls will form a barrier to inhibit further exchange
Assimilated components must then diffuse through the barrier
Diffusion of heat is much faster that diffusion of mass, so the magma will probably solidify before appreciable assimilation has occurred

18. Mixed Processes
May be more than coincidence: two processes may operate in conjunction (cooperation?)
AFC: FX supplies the necessary heat for assimilation
Fractional crystallization + recharge of more primitive magma
Two or more processes may work simultaneously or in sequence during the generation, migration, and solidification of magmatic systems
Thus a number of magmas (and the resulting rocks) may be complex hybrids reflecting the combined effects of the various processes
May be more than coincidence: two processes may operate in conjunction (cooperation?)
AFC:
Combination of assimilation and fractional crystallization required
FX supplies the necessary heat for assimilation as proposed earlier
Fractional crystallization + recharge of more primitive magma
One approach: devise mathematical models for the behavior of certain trace elements and isotopes (or ratios) that are based on a combination of processes

19. Summary on magmatic differentiation
Different degree of partial melting
Different degree of crystallization
Magma mixing
Magma assimilation
Assimilation and fractional crystallization
Thermal diffusion
Two or more processes may work simultaneously or in sequence during the generation, migration, and solidification of magmatic systems
Thus a number of magmas (and the resulting rocks) may be complex hybrids reflecting the combined effects of the various processes
May be more than coincidence: two processes may operate in conjunction (cooperation?)
AFC:
Combination of assimilation and fractional crystallization required
FX supplies the necessary heat for assimilation as proposed earlier
Fractional crystallization + recharge of more primitive magma
One approach: devise mathematical models for the behavior of certain trace elements and isotopes (or ratios) that are based on a combination of processes

20. Chemical Petrology Major and trace elements
Stable and radiogenic isotopes
Analytical Methods
Chapters 8 and 9

21. What are you going to do with a rock sample?

22. Bivariate diagrams for major element
Harker
diagram
for
Crater
Lake
Propose a hypothesis
Test the hypothesis against the trends shown
Can do qualitatively at first, but quantitatively if have a proposed bulk solid extract
Figure 8.2. Harker variation diagram for 310 analyzed volcanic rocks from Crater Lake (Mt. Mazama), Oregon Cascades. Data compiled by Rick Conrey (personal communication).

23. Trace Elements Now note magnitude of trace element changes
TE often vary by > 103 very useful since so sensitive to distr. & fractionation
Figure 9.1. Harker Diagram for Crater Lake. From data compiled by Rick Conrey. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

24. Element Distribution Goldschmidt’s rules (simplistic, but useful)
2 ions with the same valence and radius should exchange easily and enter a solid solution in amounts equal to their overall proportions
Major cations in the mantle: Fe and Mg
R (Li+)
R (Mg2+)
Coordinate type
4-fold
0.73 Å
8-fold
6-fold
0.71 Å
0.90 Å
0.86 Å
1.03 Å
1.06 Å
R (Fe2+)
0.77 Å
0.92 Å
therefore some TE's will follow similar major E
Periodic Table is next slide

25. incompatible elements are concentrated in the melt
(KD or D) « 1
compatible elements are concentrated in the solid
KD or D » 1

26. Incompatible elements commonly  two subgroups
Smaller, highly charged high field strength (HFS) elements (REE, Th, U, Ce, Pb4+, Zr, Hf, Ti, Nb, Ta)
Low field strength large ion lithophile (LIL) elements (K, Rb, Cs, Ba, Pb2+, Sr, Eu2+) are more mobile, particularly if a fluid phase is involved
Depends on the minerals involved!
Sr -> melt as ol & px separate -> plag (Ca) & not melt if plag is phenocryst phase
Commonly standardized to mantle compositions (olivine, pyroxenes, and perhaps garnet)
Thus the major elements Mg and Fe would usually be referred to as compatible, while K and Na as incompatible

27. Models of Magma Evolution
Batch Melting
eq. 9-5
CL = trace element concentration in the liquid
CO = trace element concentration in the original rock before melting began
F = wt fraction of melt produced = melt/(melt + rock) C 1 Di (1 F) F L O = - +

28. A plot of CL/CO vs. F for various values of Di using eq. 9-5
Batch Melting
A plot of CL/CO vs. F for various values of Di using eq. 9-5
Di = 1.0
D = No fractionation so CL/CO = 1 for all values of F
Figure 9.2. Variation in the relative concentration of a trace element in a liquid vs. source rock as a fiunction of D and the fraction melted, using equation (9-5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

29. Di » 1.0 (compatible element) Very low concentration in melt
Especially for low % melting (low F)
Values of F > 0.4 unlikely for batch melting since greater amounts should separate and rise
Figure 9.2. Variation in the relative concentration of a trace element in a liquid vs. source rock as a fiunction of D and the fraction melted, using equation (9-5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

30. Highly incompatible elements
Greatly concentrated in the initial small fraction of melt produced by partial melting
Subsequently diluted as F increases
Highly incompatible elements are greatly concentrated in the initial small fraction of melt that is produced by partial melting, and subsequently get diluted as F increases
Figure 9.2. Variation in the relative concentration of a trace element in a liquid vs. source rock as a fiunction of D and the fraction melted, using equation (9-5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

31. As F  1 the concentration of every trace element in the liquid = the source rock (CL/CO  1)Di (1 F) F L O = - +
All -> 1.0 because all of the source is melted
Figure 9.2. Variation in the relative concentration of a trace element in a liquid vs. source rock as a fiunction of D and the fraction melted, using equation (9-5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

32. C 1 Di (1 F) F L O = - +
As F  0 CL/CO  1/Di
If we know CL of a magma derived by a small degree of batch melting, and we know Di we can estimate the concentration of that element in the source region (CO)
If know (CL) for magma derived by a small degree of batch melting, and we know D, we can estimate the concentration of that element in the source region (CO).
This can provide very valuable information in constraining and characterizing the source region.
Figure 9.2. Variation in the relative concentration of a trace element in a liquid vs. source rock as a fiunction of D and the fraction melted, using equation (9-5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

33. For very incompatible elements as Di  0 equation 9-5 reduces to:1 Di (1 F) F L O = - + C 1 F L O =
If we know the concentration of a very incompatible element in both a magma and the source rock, we can determine the fraction of partial melt produced

34. Stable isotopes useful in assessing relative contribution of various reservoirs, each with a distinctive isotopic signature
O and H isotopes - juvenile vs. meteoric vs. brine water
d18O for mantle rocks  surface-reworked sediments: evaluate contamination of mantle-derived magmas by crustal sediments
O and H isotopes used to evaluate juvenile vs. meteoric vs. brine characteristics of water and the type of water responsible for rock alteration
d18O is quite different for mantle rocks and surface-reworked sediments, so it may be used to evaluate the extent to which mantle-derived magmas are contaminated by crustal sediments
Thermometry of minerals?
Beware of re-equilibration and alteration!

35. Isotopes are generally the best
Continental crust becomes progressively enriched in 87Sr/86Sr and depleted in 143Nd/144Nd
Figure Estimated Rb and Sr isotopic evolution of the Earth’s upper mantle, assuming a large-scale melting event producing granitic-type continental rocks at 3.0 Ga b.p After Wilson (1989). Igneous Petrogenesis. Unwin Hyman/Kluwer.
The addition of a trace element simply adds to the overall trace element content of the melt and minerals in the magmatic system
Some trace elements are much more abundant in the continental crust than in mantle-derived magmas, and the assimilation of a modest amount of crustal material rich in that element may have a considerable effect on a magma that initially contained very little of it
Trace element models are discussed in the text
Fly in - Isotopes:
Thus primitive magmas with unusually high values of 87Sr/86Sr and low values of 143Nd/144Nd are probably contaminated by ancient continental material
87Sr/86Sr values below would be appropriate for relatively unmodified mantle melts, while ratios above that value are probably contaminated by old continental components

36. Detecting and assessing assimilation
238U  234U  206Pb (l = x a-1)
235U  207Pb (l = x a-1)
232Th  208Pb (l = x a-1)
U-Th-Pb system as an indicator of continental contamination is particularly useful
All are incompatible LIL elements, so they concentrate strongly into the continental crust
the continental crust becomes enriched in 207Pb and 206Pb by the breakdown of U in the crust with time
207Pb/204Pb and 206Pb/204Pb ratios are considerably higher in the older continental crust than in the mantle or in mantle-derived melts (204Pb is non-radiogenic)
Because the amount of Pb in the basalts is relatively small, it is very susceptible to contamination by crustal Pb