1. GOLDSCHMIDT’S RULES
1. The ions of one element can extensively replace those of another in ionic crystals if their radii differ by less than approximately 15%.
2. Ions whose charges differ by one unit substitute readily for one another provided electrical neutrality of the crystal is maintained. If the charges differ by more than one unit, substitution is generally slight.
3. When two different ions can occupy a particular position in a crystal lattice, the ion with the higher ionic potential forms a stronger bond with the anions surrounding the site.

2. RINGWOOD’S MODIFICATION OF GOLDSCHMIDT’S RULES
4. Substitutions may be limited, even when the size and charge criteria are satisfied, when the competing ions have different electronegativities and form bonds of different ionic character.
This rule was proposed in 1955 to explain discrepancies with respect to the first three Goldschmidt rules.
For example, Na+ and Cu+ have the same radius and charge, but do not substitute for one another.

3. INCOMPATIBLE VS. COMPATIBLE TRACE ELEMENTS
Incompatible elements: Elements that are too large and/or too highly charged to fit easily into common rock-forming minerals that crystallize from melts. These elements become concentrated in melts.
Large-ion lithophile elements (LIL’s): Incompatible owing to large size, e.g., Rb+, Cs+, Sr2+, Ba2+, (K+).
High-field strength elements (HFSE’s): Incompatible owing to high charge, e.g., Zr4+, Hf 4+, Ta4+, Nb5+, Th4+, U4+, Mo6+, W6+, etc.
Compatible elements: Elements that fit easily into rock-forming minerals, and may in fact be preferred, e.g., Cr, V, Ni, Co, Ti, etc.

4. Partition Coefficients
How can we quantify the distribution of trace elements into minerals/rocks?
Henry’s Law describes equilibrium distribution of a component (we usedit for thinking about gases dissolved in water recently):
aimin = kiminXimin
aimelt = kimeltXimelt
All simplifies to:
Often termed KD, values tabulated…

5. Changes in element concentration in the magma during crystal fractionation of the Skaergaard intrusion: Divalent cations

6. Changes in element concentration in the magma during crystal fractionation of the Skaergaard intrusion: Trivalent cations

7. THREE TYPES OF TRACE-ELEMENT SUBSTITUTION
1) CAMOUFLAGE
2) CAPTURE
3) ADMISSION

8. CAMOUFLAGE
Occurs when the minor element has the same charge and similar ionic radius as the major element (same ionic potential; no preference.
Zr4+ (0.80 Å); Hf4+ (0.79 Å)
Hf usually does not form its own mineral; it is camouflaged in zircon (ZrSiO4)

9. CAPTURE
Occurs when a minor element enters a crystal preferentially to the major element because it has a higher ionic potential than the major element.
For example, K-feldspar captures Ba2+ (1.44 Å; Z/r = 1.39) or Sr2+ (1.21 Å; Z/r = 1.65) in place of K+ (1.46 Å, Z/r = 0.68).
Requires coupled substitution to balance charge: K+ + Si4+  Sr2+ (Ba2+) + Al3+

10. ADMISSION
Involves entry of a foreign ion with an ionic potential less than that of the major ion.
Example Rb+ (1.57 Å; Z/r = 0.637) for K+ (1.46 Å, Z/r = 0.68) in K-feldspar.
The major ion is preferred.

11. Melt composition, evolution
Lots of different igneous rock types…
Where do all these different magma compositions come from?

12. Melts
Liquid composed of predominantly silica and oxygen. Like water, other ions impart greater conductivity to the solution
Si and O is polymerized in the liquid to differing degrees – how ‘rigid’ this network may be is uncertain…
Viscosity of the liquid  increases with increased silica content, i.e. it has less resistance to flow with more SiO2… related to polymerization??
There is H2O is magma  2-6% typically – H2O decreases the overall melting T of a magma, what does that mean for mineral crystallization?

14. Mg2+ Na+ Ca2+ Fe2+ Liquid hot rock MAGMA cooling O2- Si4+
Minerals which form are thus a function of melt composition and how fast it cools (re-equilibration?)  governed by the stability of those minerals and how quickly they may or may not react with the melt during crystallization
Liquid hot
MAGMA
Ca2+
Na+
Mg2+
Fe2+
Si4+
O2-
rock
Mg2+
Fe2+
cooling
Mg2+

15. Processes of chemical differentiation
Partial Melting: Melting of a different solid material into a hotter liquid
Fractional Crystallization: Separation of initial precipitates which selectively differentiate certain elements…
Equilibrium is KEY --? Hotter temperatures mean kinetics is fast…

16. Melting
First bit to melt from a solid rock is generally more silica-rich
At depth in the crust or mantle, melting/precipitation is a P-T process, governed by the Clausius-Clapeyron Equation – Slope is a function of entropy and volume changes!
But with water… when minerals precipitate they typically do not pull in the water, melt left is ‘diluted’  develop a negative P-T slope

17. Melting and Crystallization
Considering how trace elements incorporate the melt or solid:
Where KD(rock)=SKD(j minerals)Xj
For consideration of trace elements into a solid, use Rayleigh fractionation equation:
Where F is the fraction of melt remaining

18. Thermodynamic definitions
Gi(solid) = Gi(melt)
Ultimately the relationships between these is related to the entropy of fusion (DS0fus), which is the entropy change associated with the change in state from liquid to crystal
These entropies are the basis for the order associated with Bowen’s reaction series  greater bonding changes in networks, greater entropy change  lower T equilibrium

19. SOLID SOLUTION
Occurs when, in a crystalline solid, one element substitutes for another.
For example, a garnet may have the composition: (Mg1.7Fe0.9Mn0.2Ca0.2)Al2Si3O12.
The garnet is a solid solution of the following end member components:
Pyrope - Mg3Al2Si3O12; Spessartine - Mn3Al2Si3O12;
Almandine - Fe3Al2Si3O12; and Grossular - Ca3Al2Si3O12.

20. Melt-crystal equilibrium 1b
Precipitated crystals react with cooling liquid, eventually will re-equilibrate back, totally cooled magma xstals show same composition
UNLESS it cools so quickly the xstal becomes zoned or the early precipitates are segregated and removed from contact with the bulk of the melt

21. Why aren’t all feldspars zoned?
Kinetics, segregation
IF there is sufficient time, the crystals will re-equilibrate with the magma they are in – and reflect the total Na-Ca content of the magma
IF not, then different minerals of different composition will be present in zoned plagioclase or segregated from each other physically

22. What about minerals that do not coexist well – do not form a solid solution – are immiscible??

23. More than 1 crystal can precipitate from a melt – different crystals, different stabilities…
2+ minerals that do not share equilibrium in a melt are immiscible (opposite of a solid solution)
Liquidus  Line describing equilibrium between melt and one mineral at equilibrium
Solidus  Line describing equilibrium with melt and solid
Eutectic  point of composition where melt and solid can coexist at equilibrium
Diopside is a pyroxene
Anorthite is a feldspar
Solidus
Eutectic
Liquidus

24. Melt at composition X cools to point Y where anorthite (NOT diopside at all) crystallizes, the melt becomes more diopside rich to point C, precipitating more anorthite with the melt becoming more diopside-rich
This continues and the melt continues to cool and shift composition until it reaches the eutectic when diopside can start forming A B S1 Z C S2
At eutectic, diopside AND anorhtite crystals precipitate
Lever Rule  diopside/anorthite (42%/58%) crystallize until last of melt precipitates and the rock composition is Z

25. Melting  when heated to eutectic, the rock would melt such that all the heat goes towards heat of fusion of diopside and anorthite, melts so that 42% diopside / 58% anorthite…
When diopside gone, temperature can increase and rest of anorthite can melt (along liquidus)

26. Constructing immiscibility diagrams

27. Melt-crystal equilibrium 2 - miscibility
2 component mixing and separation  chicken soup analogy, cools and separates
Fat and liquid can crystallize separately if cooled slowly
Miscibility Gap – no single mineral is stable in a composition range for x temperature
Miscibility Gap
microcline
orthoclase
sanidine
anorthoclase
monalbite
high albite
low albite
intermediate albite
Orthoclase
KAlSi3O8
Albite
NaAlSi3O8
% NaAlSi3O8
Temperature (ºC)
300
900
700
500
1100 10 90 70 50 30
Need figure 5-11 or equivalent showing miscibility

28. Homework
Chapter 8
Problems 2, 6