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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 10 The Chemical Basis of Minerals (coordination polyhedra & lattice energy). Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300. Principles of Mineral Lattices. SPACE is used most efficiently

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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 10The Chemical Basis of Minerals(coordination polyhedra & lattice energy) Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

  2. Principles of Mineral Lattices • SPACE is used most efficiently • SYMMETRY is the greatest possible • CONNECTION is maximized (greatest CN)

  3. CsCl Formula unit 4 ZnS Formula unit 4 NaCl Formula unit

  4. Limiting Radius Ratios – Coordinating anions contact each other & cation (Pauling’s 1st rule)

  5. Goldschmidt’s Ionic Model • Ions are charged • Incompressible • Non-polarizable spheres • Modifications: • Most charge resides in a central hard core • Soft outer sphere has low electron density

  6. Pauling’s 1st Rule • Coordination Polyhedra • "A coordination polyhedron of anions is formed around every cation (and vice-versa) - it will only be stable if the cation is in contact with each of its neighbours. • Ionic crystals may thus be considered as sets of linked polyhedra. • The cation-anion distance is regarded as the sum of the ionic radii.

  7. Shape & Coordination No. • Molecular Materials Absolute coordination numbers are controlled by valency (VSEPR): H2O, (CO3)-2 , (SO4)-2 etc. • Non-Molecular Materials Valency has only an indirect bearing on coordination number e.g. NaICl, MgIIO, ScIIIN, TiIVC all have the Rock Salt (6:6) Structure despite change in valency and from predominantly ionic to covalent bonding • Ionic Size does influence coordination number • The Coordination Number of the Cation will be Maximized subject to maintaining Cation-Anion Contact, according to the ratio of the ionic radii, r+/r- & geometry.

  8. What is the Numerical Value of ionic radius?

  9. What's the Numerical Value of a specific Ionic Radius? • Ionic Radii in most scales do not generally meet at experimental electron density minima, because of polarization of the anion by the cation • The various scales are designed to be self-consistent in reproducing ro = r+ + r- • Ionic radii change with coordination number • r8 > r6 > r4 {use the appropriate one!} • Use the same scale for cation and anion

  10. Radius Ratio Test for Alkali Halides Test with Structures of Alkali Halides

  11. Do the Radius Ratio Rules Work? • Graph compares structures (CsCl / NaCl) with predictions by radius ratio rules from r+/r- {r-/r+ if cation is larger} • For Li+ and Na+ salts, ratios calculated from both r6 and r4 are indicated • Radius ratios suggest adoption of CsCl structure more than is observed in reality • NaCl structure is observed more than is predicted • Radius ratios are only correct ca. 50% of the time, not very good for a family of archetypal ionic solids - random choice might be just as successful as radius ratio rules and saying that all adopt the NaCl structure more so! • Is the Goldschmidt cation-anion Contact Criterion all there is to it? - No!

  12. Lattice Energy Qu.Why is highest possible Coordination adopted? Ans. Greater Madelung Potentials! u = (A q1 q2 )/r

  13. Plots of Coulombic Madelung Energy vs Radius Ratio Tetrahedral <0.414 Octahedral <0.732 Cubic

  14. Lattice Energy and Madelung Constants: • Madelung energy rises as r+/r- falls until the structure can no longer support cation-anion contact. • At the geometric limiting radius ratio, the Madelung energy remains constant as r+/r- falls, because ro ­ r+ + r- but instead is limited by "anion-anion contact". • Plot indicates structural transitions do not occur at limiting radius ratios • NaCl     CsCl transition at r+/r- Å 0.71 • ZnS     NaCl transition at r+/r- Å 0.32 • Taking into account that r8 > r6 indicates that the CsCl structure is never favourable (dotted line) • CsCl structure is only adopted where 8:8 coordination maximizes Dispersion Forces • NaCl structure is highly favoured by Covalencybest utilization of Cl- p3 orbitals

  15. Compression of ions under pressure:- Expect CsCl structure to be favoured at high pressures e.g. RbCl undergoes NaCl CsCl structural transition at 5~20 kbar

  16. Structure Maps Plots of rA versus rB with structure-type indicated Thenardite Mg2SiO4 Be2SiO4

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