1. Mineral Structures From definition of a mineral:
“…an ordered atomic arrangement…”
How do Pauling’s rules control “ordered atomic arrangement?”
How can crystal structure make one mineral different from another?
Can mineral structures be used to group minerals (e.g. classify them)?

2. Illustrations of mineral structures
2-D representation of 3-D materials
Ions represented as spheres – drawn to scale
Stick and ball method
Polyhedron method
Hybrid: Stick and Ball, plus polyhedron
Map view – unit cell dimensions

3. Olivine – view down a crystallographic axis
Unit cell outline
Olivine – view down a crystallographic axis
Fig. 4-10

4. Structures Isostructural minerals Polymorphism – polymorphic minerals
Same structure, different composition
Polymorphism – polymorphic minerals
Same composition, different structures

5. Isostructural Minerals
Many minerals have identical structures, different compositions
Example: halite (NaCl) and Galena (PbS)
Differ in many physical properties - composition
Identical symmetry, cleavage, and habit – elemental arrangement

6. Isostructural group Several isostructural minerals
Have common anion group
Much substitution between cations
Example: calcite group

8. Polymorphism
The ability for compounds with identical compositions to crystallize with more than one structure
Polymorphs
Polymorphic groups

9. P & T primary environmental variables
Caused by balance of conflicting requirements and environmental factors:
Attraction and repulsion of cations and anions (charge)
Fit of cations in coordination site (size)
Geometry of covalent bonds
P & T primary environmental variables

10. Composition of environment unimportant
P and T controls:
High P favors tightly packed lattice, high density
High T favors open lattice, low density, wide substitution
Composition of environment unimportant
All same elements in polymorphs
Presence or absence of polymorphs provide information on P and T conditions

11. Four types of mechanisms to create polymorphs:
Reconstructive – break bonds
Order-disorder – cation placement
Displacive – kink bonds
Polytypism – stacking arrangement

12. 1. Reconstructive polymorphism
Requires breaking bonds – major reorganization
Symmetry and/or structural elements may differ between polymorphs
Symmetry and/or structural elements may be similar because identical composition
Example: C

13. C = Diamond and Graphite
Diamond – all 100% covalent bonds
Graphite – covalent bonds within sheets, van der Waal bonds between sheets
What conditions cause one mineral or the other to form?

14. Graphite – stable at earth surface T and P
Diamond stable only at high P and T – but found on earth surface
Won’t spontaneously convert to graphite
Minerals that exists outside of their stability fields are metastable

15. What are temperatures at these depths?
Found on a Phase Diagram – e.g. for single component
Increasing
Depth (linear)
~200 km depth
~100 km depth
Where on (in) the earth would diamond form/be stable?
Single component = C
Increasing
Depth (non-linear)
Fig. 4-11

16. Diamond stability versus geothermal gradient
Kimberlite
Red line is geothermal gradient
Diamond window
Stability Boundary of Diamond and Graphite
Lithosphere
Asthenosphere
Phase diagram
Conceptual model of earth

17. Metastable minerals occur because of energy required for conversion
Bonds must be broken to switch between polymorphs
Cooling removes energy required to break bonds
Rate of cooling often important for lack of conversion – e.g. fast cooling removes energy before reactions occur
Quenching – “frozen”: e.g. K-feldspars
Example of Order-disorder polymorphism

18. 2. Order-disorder polymorphism
The mineral structure remains same between polymorphs
Difference is in the location of cations in structure
Good examples are the K-feldspars
One end-member of the alkali feldspars

19. Idealized feldspar structure
Si or Al
K (or Na, Ca)
Si or Al
K-feldspar has 4 tetrahedral sites called T1 and T2 (two each)
Fig. 12-6

20. “K-spars” KAlSi3O8 – one Al3+ substitutes for one Si4+
High Sanidine (high T) – Al can substitute for any Si – completely disordered
Low Microcline (low T) – Al restricted to one site – completely ordered
Orthoclase (Intermediate T) – Intermediate number of sites with Al

21. Order-disorder in the K-feldspars
High Sanidine – Al3+ equally likely to be in any one of the four T sites
Microcline – Al3+ is restricted to one T1 site. Si4+ fills other three sites
Fig. 4-13

22. Degree of order depends on T
High T favors disorder
Low T favors order
Sanidine formed in magmas found in volcanic rocks – quenched at disordered state: metastable
Microcline found in plutonic rocks – slow cooling allows for ordering to take place
Over time, sanidine will convert to microcline

23. 3. Displacive Polymorphism
No bonds broken
a and b quartz are good examples
b quartz (AKA high quartz)
1 atm P and > 573º C, SiO2 has 6-fold rotation axis.
a quartz (AKA low quartz)
1 atm P and < 573º C, SiO2 distorted to 3-fold axis

24. Conversion can not be quenched, always happens
View down c-axis
b quartz
a quartz
6-fold rotation axis
3-fold rotation axis
Conversion can not be quenched, always happens
Never find metastable b quartz
Fig. 4-12

25. External crystal shape may be retained from conversion to low form
Causes strain on internal lattice
Strain may cause twinning or undulatory extinction
Must have sufficient space for mineral to form
Undulatory extinction

26. (4) Polytypism
Stacking diffrences
Common examples are micas and clays

27. Common Sheet silicates – like clay minerals
Orthorhombic, two stacking vectors, not 90º
Monoclinic, single stacking vector, not 90º
Orthorhombic, single stacking vector, 90º
Fig. 4-14

28. Eventually will get to controls on compositional variations
First some “housekeeping” – necessary skills:
Scheme for mineral classification
Rules for chemical formulas
A graphing technique – ternary diagrams

29. Mineral Classification
Based on major anion or anionic group
Consistent with chemical organization of inorganic compounds
Families of minerals with common anions have similar structure and properties
Cation contents commonly quite variable

30. Follows from Pauling’s rules
1, 3, and 4 (coordination polyhedron & sharing of polyhedral elements) - anions define basic structure
2: (electrostatic valency principle) anionic group separate minerals

31. Mineral group
Anion or anion gp
Native elements
N/A
Oxides
O2-
Hydroxides
OH-
Halides
Cl-, Br-, F-
Sulfides
S2-
Sulfates
SO42-
Carbonates
CO32-
Phosphates
PO43-
Silicates
SiO44-

32. Mineral Formulas Rules Cations first, then anions or anionic group
Charges must balance
Cations of same sites grouped into parentheses
Cations listed in decreasing coordination number
Thus also decreasing ionic radius
Also increasing valence state

33. Examples Diopside – a pyroxene: CaMgSi2O6 Charges balance
Ca - 8 fold coordination: +2 valence
Mg - 6 fold coordination: +2 valence
Si – 4 fold coordination: +4 valence
Anionic group is Si2O6

34. Substitution within sites indicated by parentheses:
Ca(Fe,Mg)Si2O6
Intermediate of two end-members: Diopside CaMgSi2O6 – Hedenbergite CaFeSi2O6 complete solid solution series
(more on “solid solution” in a moment)

35. Can explicitly describe substitution
E.g. Olivine: (Mg2-x,Fex)SiO4 0 ≤ x ≤ 2
Alternatively: Can describe composition by relative amounts of end members:
Forsterite = Fo
Fayalite = Fa

36. General composition of olivine is (Mg,Fe)2SiO4
All of the following are the same exact composition:
(Mg0.78Fe0.22)2SiO4
Mg1.56Fe0.44SiO4
Fo78Fa22 (here numbers are percentages of amount of each mineral)
Fo78 (here implied that the remainder is Fa22)
Fa22

37. How to calculate chemical formulas for solid solutions
Eg. Plagioclase feldspars:
Albite, Ab – NaAlSi3O8
Anorthite, An – CaAl2Si2O8
What is chemical composition of say Ab25An75?

38. Graphic representation
Common to have three “end members”
Ca2+, Mg2+ and Fe2+ common substitutions between silicate minerals
Also K, Na, Ca – e.g. the Feldspars
Ternary diagrams
Used to describe distribution of each end member
Total amount is 100%

39. See page 84

40. Fig. 4-17 Ca2Si2O6 8% Fs 50% Wo 42% En Composition is: En42Fs8Wo50
(Mg0.42Fe0.08Ca0.5)2Si2O6
Pyroxenes:
(Mg,Fe,Ca)2Si2O6
Mg2Si2O6
Fe2Si2O6
Fig. 4-17

41. Compositional Variation
Think of minerals as framework of anions
Form various sites where cations reside
Principle of parsimony
Not all sites need to be filled
Some sites can accommodate more than one type of ion (e.g. polymorphism in feldspar, solid solution in olivine)

42. Anions can substitute for each other, but this is rare
Solid solution
Occurs when different cations can occur in a particular site
Three types: Substitution, omission, and interstitial
Anions can substitute for each other, but this is rare

43. Tourmaline – an example of extreme amount of substitution
Na(Mg,Fe,Li,Al)3Al6[Si6O18] (BO3)3(O,OH,F)4
W = 8-fold coordination, not cubic; usually Na, sometimes Ca or K
X = Regular octahedral; usually Mg and Fe, sometimes Mn, Li, and Al
Y = 6-fold coordination; usually Al, Less commonly Fe3+ or Mg, links columns
B = trigonal; Borate ions, B is small,
Fig. 15.9

44. Terms
Substitution series or solid solution series: the complete range of composition of a mineral
End members: the extremes in the range of compositions
E.g. olivine: Forsterite and Fayelite

45. Terms
Continuous or complete solid solution series: all intermediate compositions are possible
E.g. Olivine
Incomplete or discontinuous solid solution series: a restricted range of compositions
E.g Calcite - magnesite

46. Substitutional Solid Solution
Two requirements for substitution
Size – substituting ions must be close in size
Charge – electrical neutrality must be maintained

47. Size Comes from Pauling rule 1: coordination
In general size of ions must be < 15% different for substitution
Tetrahedral sites: Si4+ and Al3+
Octahedral sites: Mg2+, Fe2+, Fe3+, Al3+
Larger sites: Na+ and Ca2+

48. Temperature is important
Example is K and Na substitution in alkali feldspar (Sanidine and Albite)
Size difference is about 25%
Complete solid solution at high T
Limited solid solution at low T
Results in exsolution

49. Types of substitution Substitutional solid solution
Simple substitution
Coupled substitution
Omission substitution
Interstitial substitution
Different types have to do with where the substitution occurs in the crystal lattice

50. Simple Substitution
Occurs with cations of about same size and same charge
Example: Olivine

51. Olivine - (Fe.22Mg.78)2SiO4
View down a axis
22% Fe
78% Mg
Fig. 4-15

52. Coupled Substitution Coupling two substitutions
One that raises charge
Linked one that decreases charge
Example: Albite (NaAlSi3O8) and Anorthite (CaAl2Si2O8)
Ca and Na occupy distorted 8-fold site
Al and Si occupy tetrahedral sites

53. Coupled substitution:
Coupled substitution in different sites
Coupled substitution:
Na+ + Si4+ = Ca2+ + Al3+
Fig. 4-15

54. Coupled substitution
The substitution doesn’t always have to be different sites
Corundum (Al203)
Fe2+ and Ti4+ substitute for 2Al3+ (makes sapphire). Cr3+ makes Ruby
Both elements are in octahedral sites
Can couple cations and anions
Hornblende: Fe2+ and OH- substitutes for Fe3+ and O2-

55. Omission substitution
Charge balance maintained by leaving site vacant
Pyrrhotite: variable amounts of Fe2+ and Fe3+
Formula: Fe(1-x)S where 0<X<0.13
General substitution:
(n+1)Mn+ = nM(n+1)+ + □
where □ is vacant, n is the number of sites

56. 14Fe2+ = 8 Fe Fe3+ + 2□
28+ = 28+
Fig. 4-15
14 sites = 14 sites

57. Interstitial substitution
Type of omission substitution
Difference is that regular lattice framework site is not location of substitution
Example: Beryl, a ring silicate
Al3+ substitution for Si in tetrahedral sites
Balanced by K+, Rb+ and Cs+ substitution in open “channel” sites

58. Charge balance maintained by interstitial substitution
Al, Be substition for Si
Fig. 4-15

59. Structure of Beryl Be3Al2Si6O8 Silicate Rings
Substitution important: Cr substition makes emerald, other substitutions make Aquamarine – blue green variety of emerald
Al 6-fold coordination
Fig. 15-6
Be 4-fold coordination