Introduction to Mineralogy Dr. Tark Hamilton Chapter 4: Lecture 11 The Chemical Basis of Minerals (Closest Packing

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Introduction to MineralogyDr. Tark
HamiltonChapter 4 Lecture 11The Chemical Basis
of Minerals(Closest Packing Valency)

• Camosun College GEOS 250
• Lectures 930-1020 M T Th F300
• Lab 930-1220 W F300

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Halite Cubic unit cell p.393 F m3m, (4/m 3 2/m)
p.202
4 Na 1 center (¼ x 12 edge)
4 Cl- (1/8 x 8 corner) (½ x 6 face)
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Closest Packing of Uniform Spheres
B-voids Tetrahedral
Basic Grid
Hexagonal AB Plan View
C-voids Octahedral
Cubic Plan View Oblique
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4
m
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Coordination Polyhedra 2,3,4,6,8
2 Linear X variable, (UO2)2
6 Octahedral X 0.414, (FeO6)-5
3 Triangular X 0.155, (CO3)-2 , (NO3)-
8 Cubic X 0.732, (BaO8)-14
4 Tetrahedral X 0.225, (SiO4)-4 , (PO4)-3
Cation Z attraction Madelung potential Permits
larger cations
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Paulings Rules

• 1 Coordination Principle
• 2 Electrostatic Valency Principle
• 3 Sharing of Polyhedral Elements decreases
  stability (e.g. edges rare or faces empty)
• 4 Hi valence Low C.N. Cations dont share
• 5 Principle of Parsimony (high symmetry, few
  geometries, common environments)

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Paulings Rules

• 1 Coordination Principle all ions in polyhedra
• 2 Electrostatic Valency Principle S bonds
  charge
• 3 Sharing of Polyhedral Elements decreases
  stability (e.g. edges rare or faces empty)
• 4 Hi valence Low C.N. Cations dont share
• 5 Principle of Parsimony (few geometries, common
  environments, high symmetry)

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1Coordination Principle

• Cations coordinate with several anions
• Maximizing C.N. according to radius ratio
• As many as size permits
• Spreads electron attraction energy uniformly
• Bonds are equal in length strength
• Crystal is uniform and stable

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Atomic Packing Geometries
Cation Size Increases
B
Al
Mg
Cs
CN _at_ Higher Pressure
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Other Geometries

• 5,7, 9, 10
• All irregular, distorted
• Not Closest packing
• e.g. Andalusite Al2SiO5
• Non-ionic molecular VSEPR shapes
• Valence Shell Electron Pair Repulsion
• e.g. Trigonal bipyramid, square, pyramidal

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Fullerenes

• Soot Carbon Industry, forest fire, firestorm
• C60 Hexagonal structure
• Hollow sphereules, lightweight, strong
• Leftovers from bolide airbursts
• High-tech properties for the future

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Common Ions Coordination No.
Cs, Rb , Ba2
Big Low Valence
Divalent 3,
Highly Oxidized
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2 Electrostatic Valency Principle

• Bond strength is ion charge divided by
  Coordination Number
• The valence charge on an ion is shared among all
  of its nearest neighbours
• Grossular Garnet Ca3 Al2 Si3 O12
• Ca2 , cubic, 2/8 ¼
• Al3 , octahedral, 3/6 ½
• Si4 , tetrahedral, 4/4 1
• To neutralize O-2 , each O belongs to 2 Ca2
  cubes, 1 Al3 octahedron and 1 Si4 tetrahedron