1. 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

2. 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 is added (interstitial)
b. Interstitial (impurity) defect

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

4. Crystal Defects 2. Line Defects d) Edge dislocation
Migration aids ductile deformation

5. Crystal Defects 2. Line Defects
e) Screw dislocation (aids mineral growth)

6. 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)

7. Crystal Defects 3. Plane Defects
g) Domain structure (antiphase domains)
Also has short-range but not long-range order

8. Crystal Defects 3. Plane Defects h) Stacking faults
Common in sheet minerals and low-T disequilibrium
A - B - C layers may be various in sheet type
ABCABCABCABABCABC
AAAAAABAAAAAAA
ABABABABABCABABAB

9. Solid Solutions
A solid solution is formed when one element substitutes for another in a mineral structure. The substitution occurs completely randomly and is analogous to dissolution of a solute in water.

10. Mechanisms of solid solution formation
Simple substitution –
e.g. Fe2+ for Mg 2+ in forsterite forming the olivine solid solution (Mg,Fe)SiO4
Coupled substitution –
e.g. Ca2+ + Al3+ for Si4+ + Na+ in albite forming the plagioclase solid solution
Interstitial solid solution-
e.g. Fe3+ in a space in the structure of α-quartz, the precursor of amethyst formation
Omission solid solution –
e.g. Fe vacancies in pyrrhotite Fe1-xS

11. Solid solutions may be complete, forming a solid solution series, e. g
Solid solutions may be complete, forming a solid solution series, e.g. the olivine series formed between end-members forsterite Mg2SiO4 and fayalite Fe2SiO4.
Solid solutions may be partial, as in the case of Fe in ZnS.
Partial solid solutions are very common in minerals.

12. Pseudomorphism
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, but must be used with caution.

13. Polymorphism
A polymorph is a mineral with the same composition, but a different crystal structure as another mineral. The most familiar example is the case of diamond and graphite, polymorphic forms of carbon.

14. Isostructuralism is more or less the opposite of polymorphism
Isostructuralism is more or less the opposite of polymorphism. Minerals have the same crystal structure but are of different composition. For example,
galena PbS and halite NaCl are isostructures

15. Order – Disorder Polymorphism
Random vs. ordered atoms
1. Random Perfect Order
(higher Entropy) (lower Entropy)
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!

16. Reconstructive Polymorphism
Breaking of bonds between
Low temperature and high temperature phases
Low pressure and high pressure phases (Graphite/Diamond)
Reconstructive phase transformation
Large energy barrier for reverse reaction
Corresponding high temperature and high pressure phases
occur metastably at room temperature and atmospheric pressure

17. Displacive Polymorphism
Displacive phase transformation = slight displacement of atoms
or readjustment of bond angles between them.
Low temperature and high temperature phases
Low pressure and high pressure phases
Reversible transformation has low energy barrier .
Corresponding high temperature and high pressure phases
rarely occur at room temperature and atmospheric pressure
e.g. alpha-quartz /beta-quartz

18. (special form of polymorphism)
Polytypism
(special form of polymorphism)
Change of layer sequences
Minerals with close packing arrangement:
ABABABABAB ABCABCABCABC
e.g. wurtzite (α-ZnS)
e.g. sphalerite ( β-ZnS)
Sheet minerals: change of stacking sequences of layers
Two layers
Three layers

19. Packing in Ionic Crystals
Radius Ratio: RC/RA = 1.0 (commonly native elements)
Equal sized spheres
“Closest Packed”
Hexagonal array:
6 nearest neighbors in the plane
Note dimples in which next layer atoms will settle
Two dimple types:
Type 1
Type 2
They are equivalent since you could rotate the whole structure 60o and exchange them 2 1

20. Closest Packing Add next layer (red)
Red atoms can only settle in one dimple type
Both types are identical and red atoms could settle in either
Once first red atom settles in, one can only fill other dimples of that type
In this case filled all type 2 dimples 1

21. Closest Packing Third layer:
If occupy A-type site the layer ordering becomes A-B-A-B and creates a hexagonal closest packed structure (HCP)
6 coplanar
3 above the plane
3 below the plane

22. Closest Packing
Alternatively we could place the third layer in the C-type site (above voids in both A and B layers)

23. Closest Packing Third layer:
If occupy C-type site the layer ordering is A-B-C-A-B-C and creates a cubic closest packed structure (CCP)
Blue layer atoms are now in a unique position above voids between atoms in layers A and B

24. In fact, sphalerite, with a cubic structure, and wurtzite, with a
hexagonal structure are considered to be polymorphs rather
polytypes because of the difference in their crystal structures.
A large number of ordered (i.e. with a regular, repeated
stacking pattern) polytypes of wurtzite are known.
Wurtzite occurs with two space groups:
P63mc types: 2H, 4H, 6H, 8H, 10H
R3m types: 3R, 9R, 12R, 15R, 21R
For example the wurtzite-8H polytype has the stacking:
ABCABACB or ABACACAB
Sphalerite has only one type of stacking: ABC

25. Twinning
Rational symmetrically-related intergrowth of two or more crystals
Lattices of each orientation have definite crystallographic relation to each other

26. Twinning Aragonite twin
Note zone at twin plane which is common to each part
Although aragonite is orthorhombic, the twin looks hexagonal due to the 120o O-C-O angle in the CO3 group

27. In other words, the twin adds a symmetry element that is not present in the untwinned crystal.

28. Twinning
Twin Element is the symmetry element which relates the two (or more) parts (twin mirror, rotation axis)
Twin Law is a more exact description for a given type.
1) Reflection (twin plane) on (hkl)
Rotation about an axis common to both (twin axis): normal and parallel twins.
Parallel to [uvw]
3) Inversion (twin center)
The twin element cannot be a symmetry element of the individuals; e.g. a twin plane cannot be a mirror plane of the crystal.

29. Contact & Penetration twins
Both are simple twins; only two parts

30. Cyclic twins - successive planes not parallel Polysynthetic twins
Can also have multiple twins (> 2 orientations)
Cyclic twins - successive planes not parallel
Polysynthetic twins
Albite Law
in plagioclase

31. Staurolite

32. The twin creates an additional 2/m element.
Twinning can be understood by examination of the staurolite cross {031}. Staurolite is monoclinic C2/m with
β ≈ 90º
a = Å
b = Å x ⅓ = 5.55 Å
c = Å
But b/3 = 5.55 Å ≈ c
(031) → intercepts at ∞, ⅓, 1 m c
cross arm
b/3
45º
cross arm
2-fold axis
The twin creates an additional 2/m element.