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Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

Introduction to Mineralogy Dr. Tark Hamilton Chapter 4: Lecture 12 The Chemical Basis of Minerals (Pauling’s Rules). Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300. Pauling’s Rules. 1: Coordination Principle: all ions in polyhedra

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Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

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  1. Introduction to MineralogyDr. Tark HamiltonChapter 4: Lecture 12The Chemical Basis of Minerals(Pauling’s Rules) Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

  2. 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. corners OK, 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)

  3. Pauling Rule 2: Electrostatic Valency Principle ("Bond Strength") • "In a stable ionic structure the charge on an ion is balanced by the sum of electrostatic bond strengths to the ions in its coordination polyhedron" • i.e. A stable ionic structure must be arranged to preserve Local Electroneutrality • (Ions in a crystal are surrounded by ions of opposite charge so as not to produce large volumes of similar charge in the crystal - this maximizes Madelung potential!) • Ion-ion or ion-radical all the same or unstable

  4. 2: Bond Strength (e.v.) = Z+ / C.N. Na+ or F- in NaCl C.N. = 6, e.v. = 1 Octahedral e.b.s. = 1/6 Ca+2 in CaF2 C.N. = 8, e.v. = 2 Cubic e.b.s. = 2/8 = ¼ F- in CaF2 C.N. = 4, e.v. = 1 Tetrahedral e.b.s. = ¼

  5. Only 1 Bond Strength • Uniform Bond Strength – Isodesmic crystals • NaCl Chloride all bonds = 1 (ordinary ionic crystal implied, but preference for C.N.=6 due to Cl- ‘s 3 normal p-orbitals.) • MgAl2O4Aluminate, FeCr2O4Chromrate (mol. radicals?) • Spinels: AB2O4Radicals or Isodesmic? • Mg+2 or Fe2+ , tetrahedral, 2/4 = ½ • Al+3 or Cr+3 , octahedral, 3/6 = ½ • So isodesmic and no radicals! • Different I.R. & valence made up for by varying C.N. • 1 bond strength = 1 uniform energy level throughout

  6. Unequal Bond Strengths • Small highly charged cations form radicals with larger low valence anions, Anisodesmic • (CO3)-2 , (NO3)- , (PO4)-3 , (SO4)-2 , (WO4)-2 • C+4 in Carbonate is 3 C.N. so bond is 4/3 = 1.33 • N+5 in Nitrate is 3 C.N. so bond is 5/3 = 1.67 • S+6 in Sulphate is 4 C.N. so bond is 6/4 = 1.5 • These are more than half of O-2 valence, so O in these groups is more tightly bonded than to Cations • Oxygens much more tightly bonded to core atom (C,N,S,P, W, V, Cr…) than to surrounding cations • These molecular radicals usually persist through melting, decrepitation or mineral-chemical reactions • Carbonatite melts, Apatite-Magnetite melts

  7. Tightly Bonded Radicals (Viva Che!) 2 Lone Pairs 3 Isomers in solutions 1 radical in solid minerals O (-2) C O O 3 Lone Pairs 4 isomers in solutions 1 radical in solid minerals

  8. Pauling Rule 3: Polyhedral Linking • "The stability of structures with different types of polyhedral linking is vertex-sharing > edge-sharing > face-sharing" • effect is largest for cations with high charge and low coordination number • especially large when r+/r- approaches the lower limit of the polyhedral stability • Why? Sharing edges/faces brings ions at the centre of each polyhedron closer together, hence increasing electrostatic repulsions • i.e.disposition of ions of similar charge will be such as to minimize the Electrostatic Energy between them • Linked polyhedra act as a single ionic structural unit

  9. 2+- 4+: Sharing Polyhedral Elements Rare Empty +sites, too much cation repulsion Tetrahedra +4 cations not +3, 1.5 e.v. OK Edge contracts +2 cations Octahedra

  10. Pauling’s Rules 1-4 all: • Tend to maximize cation-anion interactions due to attraction • Tend to minimize cation-cation or anion-anion interactions due to repulsion

  11. #5 - Principle of Parsimony • # of contrasting elements are small because there are few anion or cation sites • Complex compositions tend toward several constituents (cations) in the same kind of site • This is termed solid solution: Fe for Mg, Si for Al, Ca for Na (definite not exact compositions) • Goldschmidt’s rules say ions have to be similar size +/-15% and +/- 1 charge unit

  12. Limited Types of Coordination Halite Octahedral – Na & Cl Cubic – Ca Tetrahedral – F Fluorite Sphalerite Octahedral – empty Tetrahedral - S

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