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Lecture 4 (9/18/2006)
Crystal Chemistry
Part 3:Coordination of Ions
Paulings RulesCrystal Structures
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Coordination of Ions
For minerals formed largely by ionic bonding,the ion geometry can be simply considered to bespherical
Spherical ions will geometrically pack(coordinate) oppositely charged ions aroundthem as tightly as possible while maintainingcharge neutrality
For a particular ion, the surroundingcoordination ions define the apices of apolyhedron
The number of surrounding ions is theCoordination Number
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CoordinationNumber and
Radius Ratio
See Mineralogy CD: Crystal
and Mineral Chemistry -Coordination of Ions
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Coordination
with O-2
Anions
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WhenRa(cation)/Rx(anion)
~1ClosestPacked
Array
See MineralogyCD: Crystal andMineral Chemistry
Closest Packing
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Paulings Rules of Mineral Structure
Rule 1: A coordination polyhedronof anions is formed around each
cation, wherein:- the cation-anion distance is
determined by the sum of theionic radii, and
- the coordination number of thepolyhedron is determined by thecation/anion radius ratio (Ra:Rx)
Linus Pauling
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Rule 2:The electrostatic valency principle
The strength of an ionic (electrostatic)
bond (e.v.) between a cation and an anionis equal to the charge of the anion (z)divided by its coordination number (n):
e.v. = z/nIn a stable (neutral) structure, a chargebalance results between the cation and itspolyhedral anions with which it is bonded.
Paulings Rules of Mineral Structure
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Charge Balance
of Ionic Bonds
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Formation of Anionic Groups
Results from high valence cations with electrostaticvalencies greater than half the valency of thepolyhedral anions; other bonds with those anions willbe relatively weaker.
Carbonate Sulfate
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Rule 3:Anion polyhedra that share edges orfaces decrease their stability due to bringingcations closer together; especially significant forhigh valency cations
Rule 4:In structures with different types of
cations, those cations with high valency andsmall CN tend not to share polyhedra with eachother; when they do, polyhedra are deformed toaccommodate cation repulsion
Paulings Rules of Mineral Structure
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Rule 5:The principle of parsimony
Because the number and types of different structuralsites tends to be limited, even in complex minerals,different ionic elements are forced to occupy the samestructural positionsleads to solid solution.
See amphibole structure for example (See Mineralogy CD:Crystal and Mineral Chemistry Paulings Rules - #5)
Paulings Rules of Mineral Structure
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Visualizing Crystal Structure
Ball and Stick Model Polyhedra Model
Beryl - Be3Al2(Si6O18)
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Portraying Crystal Structure in TwoDimensions
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Isostructural Types
AX CompoundsHalite (NaCl) structure
Anionsin CCP packing
Cationsin octahedral sites
Ra/Rx=.73-.41
Examples:
Halides: +1 cations (Li, Na, K, Rb) w/ -1
anions (F, Cl, Br, I)
Oxides: +2 cations (Mg, Ca, Sr, Ba, Ni) w/ O-2Sulfides: +2 cations w/ S-2
(See Mineralogy CD: Crystal and Mineral Chemistry
Illustrations of Crystal Structures Halite)
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Isostructural Types
AX CompoundsSphalerite (ZnS) structure
RZn/RS=0.60/1.84=0.32 (tetrahedral)
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AX2CompoundsFlourite (CaF
2) structure
RCa/RF=1.12/1.31=0.75 (cubic)
Examples: Halides (CaF2, BaCl2...); Oxides (ZrO2...)
Isostructural Types
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ABO4CompoundsSpinel (MgAl
2O
4)structure
- Oxygen anions in CCP array
- Two different cations (or same cation with two different valences) intetrahedral (A) sites (e.g. Mg2+, Fe2+, Mn2+, Zn2+) or octahedral (B) sites(e.g. Al3+, Cr3+, Fe3+)
Isostructural Types
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Nesosilicates
Sorosilicates
Cyclosilicates
Inosilicates(single chain)
Inosilicates(double chain)
Phyllosilicates
Tectosilicates
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Next Lecture
Crystal Chemistry IV
Compositional Variation of Minerals
Solid SolutionMineral Formula Calculations
Graphical Representation of Mineral
Compositions
Read p. 90 - 103