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

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

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

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

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

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)

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

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

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.

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

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.

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.

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.

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

Order – Disorder Polymorphism Random vs. ordered atoms 1. Random 2. 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!

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

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

(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

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

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

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

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

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

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

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

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

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

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.

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

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

Staurolite

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 = 7.90 Å b = 16.65 Å x ⅓ = 5.55 Å c = 5.63 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.