min lecture 4.06.ppt

8/10/2019 Min Lecture 4.06.ppt

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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.



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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



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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)



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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

min lecture 4.06.ppt

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