1. Pyroxene Mineral Formula

2. Pauling’s Rules for Ionic Crystals
Deal with the energy state of the crystal structure
1st Rule
The cation-anion distance =  radii
Can use RC/RA to determine the coordination number of the cation
This is our previous discussion on coordination polyhedra

3. Pauling’s Rules for Ionic Crystals
2nd Rule
First note that the strength of an electrostatic bond
= valence / CN
Na+ in NaCl is in VI coordination
For Na+ the strength =
+1 divided by 6 = + 1/6 Cl Cl Cl Cl Na

4. Pauling’s Rules for Ionic Crystals
2nd Rule: “the electrostatic valence principle”
An ionic structure will be stable to the extent that the sum of the strengths of electrostatic bonds that reach an anion from adjacent cations = the charge of that anion
6 ( + 1/6 ) = (sum from Na’s)
charge of Cl = -1
These charges are equal in magnitude so the structure is stable
+ 1/6 Na
+ 1/6 Na Na
Cl-
+ 1/6
+ 1/6 Na

5. Pauling’s Rules 3rd Rule:
The sharing of edges, and particularly of faces, of adjacent polyhedra tend to decrease the stability of an ionic structure
Fig of Bloss, Crystallography and Crystal Chemistry. © MSA

6. Pauling’s Rules 4th Rule:
In a crystal with different cations, those of high valence and small CN tend not to share polyhedral elements
An extension of Rule 3
Si4+ in IV coordination is very unlikely to share edges or faces

7. Pauling’s Rules 5th Rule:
The number of different kinds of constituents in a crystal tends to be small
Using the analogy of CP oxygens this rule states that the number of types of interstitial sites that are filled in a regular and periodic array tends to be small
4 common types of cation sites in such an array:
XII (large cations replace O positions)
VI VIII is not CP IV
III (small and uncommon cations)

8. Pauling’s Rules 5th Rule: HCP
VI and IV sites in HCP array of oxygen anions
(not all will be occupied due to charge balance)
HCP
Can’t fill both
(share face)
IV sites
VI sites

9. Pauling’s Rules 5th Rule: CCP
VI and IV sites in CCP array of oxygen anions
(not all will be occupied due to charge balance)
CCP
IV sites
VI sites

10. Pauling’s Rules ( ) A B O 5th Rule:IV VI + 2+ 3 2 4
The spinel structure at various angles
Note
CCP abcabc layers of Oxygens
White VI sites
Blue IV sites

11. Pauling’s Rules ( ) A B O 5th Rule:IV VI + 2+ 3 2 4
The spinel structure at various angles
Polyhedral model
White VI sites
Blue IV sites

12. Pauling’s Rules ( ) A B O 5th Rule:IV VI + 2+ 3 2 4
The spinel structure at various angles
Now see lines of VI and IV sites
Not all are occupied
1/8 of IV sites
1/2 of VI sites

13. Pauling’s Rules ( ) A B O 5th Rule:IV VI + 2+ 3 2 4
The spinel structure at various angles
Rotating to where cation sites almost line up

14. Pauling’s Rules ( ) A B O 5th Rule:IV VI + 2+ 3 2 4
The spinel structure at various angles
This orientation is looking down (010)
It makes an excellent projection, since atoms all stack up on top of one another toward you
The order becomes apparent
But you lose the third dimension

15. Two miscellaneous structural concepts
Isostructuralism
Minerals with the same structure, but different compositions
CaF2 - BaCl2
Antistructuralism
Minerals with the same struture, but one has cations where the other has anions and vice-versa
CaF2 - Na2O

16. Polymorphism
Different structural forms for compounds of the same composition  different minerals
The compound SiO2 has several different structural forms, or polymorphs
The common form is - or low- quartz, but there are others that become stable under different conditions, including - or high-quartz, tridymite, cristobalite, coesite, and stishovite
The SiO2 phase diagram 
After Swamy and Saxena (1994) J. Geophys. Res., 99, 11,787-11,794.

17. Polymorphism 1. Displacive polymorphism
   quartz at 573oC at atmospheric pressure
1000 2 4
High-Quartz
Low-Quartz
500
Temperature
Coesite
Pressure (GPa)

18. Polymorphism 1. Displacive polymorphism
High
1. Displacive polymorphism
Note: higher T  higher symmetry due to more thermal energy (may twin as lower T)
Transition involves small adjustments and no breaking of bonds
Easily reversed and non- quenchable (low E barrier)
P6222
Low
P3221

19. Polymorphism 2. Reconstructive polymorphs
More common: other quartz polymorphs, graphite-diamond, calcite-aragonite, sillimanite-kyanite-andalusite
Transition involves extensive adjustments, including breaking and reformation of bonds
High E barrier, so quenchable and not easily reversed (still find Precambrian tridymite)
Stable
Unstable
Metastable

20. Pseudorphism May be confused with polymorphs
A completely different thing
Complete replacement of one mineral by one or more other minerals such that the new minerals retain the external shape of the original one
Limonite after pyrite
Chlorite after garnet
etc.
Can use the shape to infer the original mineral
Very useful in petrogenetic interpretations

21. Solid Solutions
Substitution (mixing, solution) of ions on specific sites
Forsterite: Mg2SiO4
Mg occupies the VI sites in the olivine structure
Can substitute Fe for Mg and create Fayalite: Fe2SiO4
In olivine the substitution is very readily accomplished and any intermediate composition is possible
Olivine: (Mg, Fe)2SiO4
This means that olivine is a solid-solution series in which any ratio of Mg/Fe is possible as long as they sum to two ions per formula unit (required for electric neutrality)

22. Solid Solutions Intermediate compositions can be expressed as:
1. A chemical analysis (in weight % oxides)
SiO
FeO 22.9
MgO 38.6
Total
Such an analysis is very difficult to interpret in terms of the mineral that it represents

23. Solid Solutions Intermediate compositions can be expressed as:
1. A chemical analysis (in weight % oxides)
SiO
FeO 22.9
MgO 38.6
Total
2. This can be converted to a mineral formula
Mg1.5 Fe0.5 SiO4
Such an analysis is very difficult to interpret in terms of the mineral that it represents

24. Solid Solutions Intermediate compositions can be expressed as:
1. A chemical analysis (in weight % oxides)
SiO
FeO 22.9
MgO 38.6
Total
2. This can be converted to a mineral formula
Mg1.5 Fe0.5 SiO4
3. This can then be expressed in terms of end-members
XMg = Mg / (Mg + Fe) on an atomic basis = 1.5 / 2 = 0.75 or
Fo75 where the sum of the end-members = 1
(Fo75 implies Fa25)
Such an analysis is very difficult to interpret in terms of the mineral that it represents

25. Solid Solutions
Solid solutions are most extensive if the valence and radius of the substituting ions are similar
Good if radii differ by < 15%
Fe 2+ = 0.80 A Mg 2+ = 0.74 A (7.5%)
Mn 2+ = 0.91 A (14% - Fe and 21% - Mg)
Limited or rare if differ by %
Never if > 30 %

26. Solid Solutions
Solid solutions are most extensive if the valence and radius of the substituting ions are similar
If valence differs will not substitute or requires coupled substitution
NaAlSi3O8 - CaAl2Si2O8 in plagioclase
Na+ + Si4+ exchange for Ca2+ + Al3+ to maintain 5+ total
Jadeite NaAlSi2O6 - diopside CaMgSi2O6

27. Exsolution Lower T Limits impurity Structure may reject excess
Oriented lamellae, or
Entirely rejected from the crystal
Non-coherent masses
As temperature drops, the decreasing thermal energy in the lattice, the tolerance of one end-member for the complementary ion becomes less
In some solid solutions this may result in only limited admittance for the smaller (or larger) ion
As a result the structure may reject the excess that it tolerated at higher temperatures
The process is exsolution and the product may be oriented lamellae of the lesser complementary phase in the greater host
Alternatively the exsolved material may be entirely rejected from the crystal, or form as non-coherent masses

28. Exsolution
The process is exsolution and the product may be oriented lamellae of the lesser complementary phase in the greater host
Alternatively the exsolved material may be entirely rejected from the crystal, or form as non-coherent masses
Blebby cpx exsolved from opx host, Skaergaard Intrusion
Opx with 2 lamellae of exsolved cpx, Bushveld Intrusion
From Deer et al Rock-Forming Minerals vol 1A. WIley
whispy perthite lamellae as albite is exsolved from orthoclase
Opx with lamellae of exsolved plagioclase, Nain anorthosite

29. Random vs. ordered atoms
Order - Disorder
Random vs. ordered atoms
1. Random Perfect Order
At 0 K entropy drops to zero and all solutions become perfectly ordered at equilibrium
At higher temperatures solutions (even in solids) become progressively disordered until they eventually become completely disordered
The degree of disorder is a function of temperature, such that there is some equilibrium degree of disorder for a given solution at a given temperature
Each atom is statistically identical (chance of being A is the same for each position) Higher T
Alternating A and B- Lower T
Note larger unit cell!

30. Order - Disorder potential mirror
This is not a trivial concept that merely concerns sub-microscopic properties
The triclinic  monoclinic transition in feldspar KAlSi3O8 requires that there is mirror symmetry
If Al and Si are ordered on the IV sites (Al is grey in this picture, while Si is blue), then no mirror is possible
Must disorder at high temperature before can become monoclinic
Some feldspars, if they are heated rather slowly, may remain partially ordered, and thus will not invert to the monoclinic form at the temperature predicted (based on disordered feldspars)!
Triclinic  monoclinic in KAlSi3O8 requires mirror symmetry
Must disorder at high temperature before
® monoclinic
potential mirror

31. Crystal Defects Defects can affect Strength Conductivity
Deformation style
Color
All of our previous discussion is based on perfect crystals
New techniques of XRD and HRTEM have shown that defects are common in crystalline substances

32. Crystal Defects Steel spheres:
a) Regular packed array with 3 point defects
b) Point and line defects
c) Mosaic (or domains) separated by defect boundaries
These are not twins!
Fig of Klein and Hurlbut, Manual of Mineralogy, © John Wiley and Sons

33. Crystal Defects 1. Point Defects
a. Schottky defect
1. Point Defects
a) Schottky (vacancy) - seen with steel balls in last frame
b) Impurity
Foreign ion replaces normal one (solid solution)
Not considered a defect
Foreign ion is added (interstitial)
Both combined
b. Interstitial (impurity) defect

34. Crystal Defects 1. Point Defects
c) Frenkel (cation hops from lattice site to interstitial)
= a + b combination
b. Frenkel defect

35. Crystal Defects 2. Line Defects d) Edge dislocation
Migration aids ductile deformation
Fig of Bloss, Crystallography and Crystal Chemistry.© MSA

36. Crystal Defects 2. Line Defects
e) Screw dislocation (aids mineral growth)
Fig of Bloss, Crystallography and Crystal Chemistry. © MSA

37. Crystal Defects 3. Plane Defects
f) Lineage structure or mosaic crystal
Boundary of slightly mis-oriented volumes within a single crystal
Lattices are close enough to provide continuity (so not separate crystals)
Has short-range order, but not long-range (V4)
Fig of Bloss, Crystallography and Crystal Chemistry. © MSA

38. Crystal Defects 3. Plane Defects
g) Domain structure (antiphase domains)
Also has short-range but not long-range order
Fig of Bloss, Crystallography and Crystal Chemistry. © MSA

39. Crystal Defects 3. Plane Defects h) Stacking faults
Common in clays and low-T disequilibrium
A - B - C layers may be various clay types (illite, smectite, etc.)
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