• Ions represented as spheres – drawn to scale

• Stick and ball method

• Polyhedron method

• Hybrid: Sick and Ball, plus polyhdron

• Map view – unit cell dimensions
 

Isostructural Minerals

• Many minerals have identical structures, different compositions

 - example: Halite (NaCl) and Galena (PbS)
 - differ in many physical properties
 - identical symmetry, cleavage, and habit
 

• Isostructural group
 - Several isostructural minerals
 - Have common anion group
 - Much substitution between cations
 - E.g Calcite group

Polymorphism

• The ability for compounds to crystallize with more than one structure
 - Polymorphs
 - Polymorphic groups
 

• Caused by balance of conflicting requirements:
- attraction and repulsion of cations and anions
- fit of cations in coordination site (size)
- geometry of covalent bonds

• Polymorphs controlled by P and T conditions:
- High P favors tightly packed lattice, high density
- High T favors open lattice, low density, wide substitution

• Presence or absence of polymorphs provide information on P and T conditions

• Four types of polymorphism:
- reconstructive
- displacive
- order-disorder
- polytypism
 

Reconstructive Polymorphism

• Requires breaking of bonds – major reorganization
• May not have symmetry of structural elements in common, although may because of composition
• Example: C
 

• C: diamond and graphite
- Diamond: all covalent bonds
- Graphite: covalent bonds in sheets, van der Walls bonds between sheets

Graphite stable at earth surface T and P

• Diamond stable at high P and T
- Metastable: exists outside its stability field
- won’t spontaneously convert to graphite

• Metastable minerals occur because of energy required for conversion

- bonds must be broken to switch from one to another polymorph
- cooling removes energy required to break bonds
- rate of cooling often important for lack of conversion, e.g. fast cooling removes energy before reaction occurs
- quenchable
 

Displacive Polymorphism

• No bonds broken, only “bent”
• a and b quartz are good examples
- At 1 P and > 573ºC, SiO₂ has six fold axis, b (or high) quartz
- At 1 Pand < 573ºC, SiO₂ distorted to 3 fold axis, a (or low) quartz.

• Process is not quenchable, always occurs

• Crystal shape may be retained from conversion to low form

• Cause strain on internal lattice

• Strain may cause twinning

Order-disorder polymorphism

• The mineral structure remains same between polymorphs
• Difference is in the location of cations in structure.
• Good example is the K-feldspars

• KAlSi₃O₈ – one Al³⁺ substitution for a Si.
• K-feldspar has 4 tetrahedral sites, 2 T1 and 2 T2
- High Sanidine (high T) – Al can substitute for any Si, disorder
- Low Microcline – Al restricted to one site, ordered.
- There can be intermediate mixtures and locations of Al
 

• Degree of order depends on T
- high T favors disorder
- low T favors ordered

• Sanidine found in volcanic rocks, quenched at disordered state
• Microcline found in plutonic rocks, slow cooling allows for ordering to take place
 

Polytypism

• Staking differences
 - common example are micas and clays
 

Mineral Classifications

• Based on major anion or anionic group
- consistent with chemical organization of inorganic compounds
- families of mineral with common anions have similar structure and properties
- cation contents commonly quite variable

• Follows from Pauling’s rules
- 1, 3, and 4: anions define basic structure
- 2 separation of anionic groups
 

Compositional Variation

• Think of minerals as framework of anions
- form various sites where cations reside
- not all sites need to be filled
- some sites can accommodate more than one mineral

• Solid solution
- occurs when different cations can fit into a particular site
- three types: Substitution, omission, and interstitial
 

• substitution series or solid solution series: the complete range of composition of a mineral
• end members: the extremes in the range of compositions
• Continuous or complete solid solution series: all intermediate composition are possible
• Incomplete or discontinuous solid solution series: a restricted range of compositions.

Substitutional Solid Solution

• Two requirements for substitution:
 - size
 - charge: electrical neutrality must be maintained
 

• Size:
- comes from Pauling rule 1 – coordination
- in general size of ions must be < 15% different for substitution

- Tetrahedral sites: Si⁴⁺ an Al³⁺
- Octahedral sites: Mg²⁺, Fe²⁺, Fe³⁺, Al³⁺
- Larger sites: Na⁺ and Ca²⁺

• Temperature important

- example is K and Na substitution in feldspars
- Size difference ~25%
- Complete solid solution at high T, limited at low T

Simple substitution

• Occurs with cations of ~same size and same charge
• Example: Olivine (FeMg)₂SiO₄
 

Coupled substitution

• coupling one substitution that raises charge and another that decreases charge
• example: Plagioclase: Albite (NaAlSi₃O₈) and Anorthite (CaAl₂Si₂O₈)

- Ca and Na occupy distorted 8-fold sites
- Al and Si occupy tetrahedral sites
 

• Not always different sites
- Corundum: Fe and Ti substitute for 2Al in octahedral sites

• Can couple cations and anions
- Hornblende: Fe²⁺ and OH^- substitutes for Fe³⁺ and O^2-
 

Omission substitution

• Charge balance maintained by leaving site vacant
• Pyrrhotite: variable amounts of Fe²⁺ and Fe³⁺
 

Interstitial substitution

• type of omission substitution
• difference is that regular coordination sites are not location of substitution
- example: Beryl, a ring silicate
- large openings can have K⁺, Rb⁺ and Cs⁺

Mineral Formulas

• Rules:

- Cations first, then anions or anionic groups
- Charges must balance
- Cations of same sites grouped
- Cations listed in decreasing coordination
 

Examples:

• Diopside (a Pyroxene): CaMgSi₂O₆

- Charges balance
- Ca 8 fold coordination
- Mg 6 fold coordination
- Si 4 fold coordination

• substitution within sites indicated by parentheses:

Ca(Fe,Mg)Si₂O₆
 
 

• can explicitly describe substitution

e.g. Olivine: (Mg_2-x,Fe_x)SiO₄
 

• Alternatively: Can describe composition by relative amounts of end members:

- Forsterite = Fo
- Fayalite = Fa

example above:
Fo₇₈Fa₂₂, or Fo₇₈, or Fa₂₂

Graphic Representation