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Week 4: Feb. 6 and 8

(Pauling's Rules Continued ...)
    • Rule 4: In a crystal containing polyhedrons centered by different cations, the polyhedra occupied by small, highly charged cations tend not to share polyhedral edges and faces (see rule 3), but if they do the edges contract to put more negative charge between the cations
    • Rule 5: The Principle of Parsimony - In crystals with several cations, the number of distinct cation sites is equal to, or often less than, the number of different cations because some distinct cations may share the same sites (because of similar cation size)
  • Bonding forces in crystals
    • Ionic bond - "electrostatic bond" the bond formed by the attraction between oppositely charged ions
      • Typical physical properties of ionically bonded crystals are: moderate H and G; fairly high melting point (> 500 C); poor conductors of electricity; usually have high symmetry because the bonds are 'non-directional'
      • The strength of ionic bonds are a function of (1) charge, and (2) interionic distance--to a certain point. (Note effect of these factors on melting points and hardnesses of minerals.)
    • Covalent Bond - "electron sharing bond"; electrons are shared so that atoms can achieve a noble gas electron configuration
      • Properties of covalently bonded crystals: generally insoluble; very stable; very high melting points; poor-conductors; lower crystal symmetry because bonds are directional
    • Metallic bonds - the bond between cations and a "matrix" of free electrons.
      • Properties: high plasticity; high conductivitiy (because the electrons are not sequestered by any one atom); low H.
    • Note: most bonds are transitional between ionic and covalent or covalent and metallic. What controls the character of the bond?
      • Electronegativity: a measure of an atoms ability to attract electrons to itself
      • ionic bonds are favored when the two atoms have very different electronegativities (one wants to "give" the other wants to "take")
      • covalent bonds are favored between atoms of similar and high electronegativity (both have a strong affinity for and end up "sharing" the electrons)
      • metallic bonds are favored between atoms of similar and low electronegativity (the atoms want to lose the electron(s) and so the electrons end up "free" in a matrix around the cations
    • Van der Waals bond - "residual" bond; the bond between electrically neutral molecules/ structures with a slightly uneven distribution of charge; a very weak bond
      • ex. The bond that allows neutral gas molecules to solidify at low T
      • ex. The bond between electrically neutral sheets of C in graphite (leading to the perfect cleavage and low H of graphite--used as a lubricant!)
    • Hydrogen bond - a special type of ionic bond; the bond between the small, "naked" hydrogen nucleus and an anion. Because the H ion is so small, the surrounding anions are close to each other and repel each other making the bond weak.
    • Note: For similar charge, the bond strengths are, in order of decreasing strength: covalent > ionic > metallic > hydrogen > van der waals
  • Isomorphism (or isostructuralism) - the phenomenon of two or more substances of different composition having the same crystal structure; this is possible if the cation-anion radius ratios are similar.
    • ex., NaCl (halite), KCl (sylvite), MgO (periclase), and PbS (galena) are isomorphic--they all have a cubic structure with identical symmetry 
    • ex. UO2 (uraninite) and CaF2 (fluorite) are isomorphic
  • Polymorphism - the phenomenon of a single substance (fixed composition) exhibiting different crystalline structures.
    • The varieties of the substance are called "polymorphs"
    • Examples from crustal rocks (with phase diagrams):
      • Al2SiO5 has three polymorphs: kyanite, sillimanite and andalusite
      • CaCO3 has two polymorphs: calcite and aragonite
      • C has two polymorphs: diamond and graphite
      • SiO2 has several: high quartz, low quartz, coesite, stishovite, tridymite, cristobalite
      • FeS2 has two: pyrite and marcasite
    • Types of polymorphism:
      • reconstructive polymorphism - involves extensive re-arrangment of polyhedral elements; breaking and re-making of bonds; requires high activation energy; sluggish - leads to metastable survival of polymorphs under different P-T conditions (examples: diamond = graphite; quartz = coesite = stishovite = tridymite = cristobalite)
      • displacive polymorphism - small structural adjustments; requires little energy; no bonds broken; occurs rapidly (example: alpha quartz = beta quartz)
      • order-disorder polymorphism (to be continued ...)


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