1. Introduction to Mineralogy Dr. Tark Hamilton Chapter 4: Lecture 11 The Chemical Basis of Minerals (Closest Packing & Valency) Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

2. 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)

3. Closest Packing of Uniform Spheres Basic Grid Cubic Plan View & Oblique Hexagonal AB Plan View B-voids Tetrahedral C-voids Octahedral

4. Coordination Polyhedra: 2,3,4,6,8 2 – Linear X variable, (UO 2 ) +2 3 – Triangular X = 0.155, (CO 3 ) -2, (NO 3 ) - 4 – Tetrahedral X = 0.225, (SiO 4 ) -4, (PO 4 ) -3 6 – Octahedral X = 0.414, (FeO 6 ) -5 8 – Cubic X = 0.732, (BaO 8 ) -14 Cation Z attraction & Madelung potential Permits larger cations

5. Pauling’s 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 don’t share 5: Principle of Parsimony (high symmetry, few geometries, common environments)

6. Pauling’s Rules 1: Coordination Principle: all ions in polyhedra 2: Electrostatic Valency Principle: Σ bonds = charge 3: Sharing of Polyhedral Elements decreases stability (e.g. edges rare or faces empty) 4: Hi valence & Low C.N. Cations don’t share 5: Principle of Parsimony (few geometries, common environments, high symmetry)

7. 1:Coordination 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

8. Atomic Packing Geometries Cation Size Increases +CN @ Higher Pressure

9. Other Geometries 5,7, 9, 10 All irregular, distorted Not Closest packing e.g. Andalusite Al 2 SiO 5 Non-ionic molecular – VSEPR shapes Valence Shell Electron Pair Repulsion e.g. Trigonal bipyramid, square, pyramidal

10. Fullerenes Soot Carbon: Industry, forest fire, firestorm C 60 – Hexagonal structure Hollow sphereules, lightweight, strong Leftovers from bolide airbursts High-tech properties for the future

11. Common Ions & Coordination No. Highly Oxidized Divalent +3, Big & Low Valence Cs +, Rb +, Ba +2

12. 2 Electrostatic Valency Principle Bond strength is ion charge divided by Coordination Number The valence charge on an ion is shared among all of it’s nearest neighbours Grossular Garnet Ca 3 Al 2 Si 3 O 12 – Ca +2, cubic, 2/8 = ¼ –Al +3, octahedral, 3/6 = ½ –Si +4, tetrahedral, 4/4 = 1 To neutralize O -2, each O belongs to 2 Ca +2 cubes, 1 Al +3 octahedron and 1 Si 4+ tetrahedron