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Lecture 4 (9/18/2006) Crystal Chemistry Part 3: Coordination of Ions Pauling’s Rules Crystal Structures

Lecture 4 (9/18/2006) Crystal Chemistry Part 3: Coordination of Ions Pauling’s Rules Crystal Structures. Coordination of Ions. For minerals formed largely by ionic bonding, the ion geometry can be simply considered to be spherical

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Lecture 4 (9/18/2006) Crystal Chemistry Part 3: Coordination of Ions Pauling’s Rules Crystal Structures

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  1. Lecture 4 (9/18/2006)Crystal ChemistryPart 3: Coordination of IonsPauling’s RulesCrystal Structures

  2. Coordination of Ions • For minerals formed largely by ionic bonding, the ion geometry can be simply considered to be spherical • Spherical ions will geometrically pack (coordinate) oppositely charged ions around them as tightly as possible while maintaining charge neutrality • For a particular ion, the surrounding coordination ions define the apices of a polyhedron • The number of surrounding ions is the Coordination Number

  3. Coordination Number and Radius Ratio See Mineralogy CD: Crystal and Mineral Chemistry - Coordination of Ions

  4. Coordination with O-2 Anions

  5. When Ra(cation)/Rx(anion) ~1Closest Packed Array See Mineralogy CD: Crystal and Mineral Chemistry – Closest Packing

  6. Pauling’s Rules of Mineral Structure Rule 1: A coordination polyhedron of anions is formed around each cation, wherein: - the cation-anion distance is determined by the sum of the ionic radii, and - the coordination number of the polyhedron is determined by the cation/anion radius ratio (Ra:Rx) Linus Pauling

  7. Pauling’s Rules of Mineral Structure Rule 2: The electrostatic valency principle The strength of an ionic (electrostatic) bond (e.v.) between a cation and an anion is equal to the charge of the anion (z) divided by its coordination number (n): e.v. = z/n In a stable (neutral) structure, a charge balance results between the cation and its polyhedral anions with which it is bonded.

  8. Charge Balance of Ionic Bonds

  9. Formation of Anionic Groups Results from high valence cations with electrostatic valencies greater than half the valency of the polyhedral anions; other bonds with those anions will be relatively weaker. Carbonate Sulfate

  10. Pauling’s Rules of Mineral Structure • Rule 3: Anion polyhedra that share edges or faces decrease their stability due to bringing cations closer together; especially significant for high valency cations • Rule 4: In structures with different types of cations, those cations with high valency and small CN tend not to share polyhedra with each other; when they do, polyhedra are deformed to accommodate cation repulsion

  11. Pauling’s Rules of Mineral Structure • Rule 5: The principle of parsimony Because the number and types of different structural sites tends to be limited, even in complex minerals, different ionic elements are forced to occupy the same structural positions – leads to solid solution. See amphibole structure for example (See Mineralogy CD: Crystal and Mineral Chemistry – Pauling’s Rules - #5)

  12. Visualizing Crystal Structure Beryl - Be3Al2(Si6O18) Ball and Stick Model Polyhedra Model

  13. Portraying Crystal Structure in Two Dimensions

  14. Isostructural Types • AX Compounds – Halite (NaCl) structure Anions – in CCP packing Cations – in 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-2 Sulfides: +2 cations w/ S-2 (See Mineralogy CD: Crystal and Mineral Chemistry – Illustrations of Crystal Structures – Halite)

  15. Isostructural Types • AX Compounds – Sphalerite (ZnS) structure RZn/RS=0.60/1.84=0.32 (tetrahedral)

  16. Isostructural Types • AX2 Compounds – Flourite (CaF2) structure RCa/RF=1.12/1.31=0.75 (cubic) Examples: Halides (CaF2, BaCl2...); Oxides (ZrO2...)

  17. Isostructural Types • ABO4 Compounds – Spinel (MgAl2O4)structure - Oxygen anions in CCP array - Two different cations (or same cation with two different valences) in tetrahedral (A) sites (e.g. Mg2+, Fe2+, Mn2+, Zn2+) or octahedral (B) sites (e.g. Al3+, Cr3+, Fe3+)

  18. Nesosilicates Inosilicates (double chain) Sorosilicates Cyclosilicates Phyllosilicates Inosilicates (single chain) Tectosilicates

  19. Next Lecture • Crystal Chemistry IV Compositional Variation of Minerals Solid Solution Mineral Formula Calculations Graphical Representation of Mineral Compositions • Read p. 90 - 103

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