Stuffing all the tetrahedral sites

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Stuffing all the tetrahedral sites

• The ionic radii of Na and Cl- ions are 91 and
  181 pm respectively. Calculate the radii ratio of
  cation to anions.
• Since the ratio of 0.5 is between 0.414 and
  0.732, the sodium ion prefers an octahedral
  coordination.
• The ionic radii of K and I- ions are 133 and 220
  pm respectively. What type of structure should KI
  have?
• The ratio is 0.605 and the NaCl structure type
  prevails.
• The ionic radii of Cs and Cl- ions are 167 and
  181 pm respectively. What type of coordination
  should Cs have?
• The ratio is 0.923. Cs ion has cubic
  coordination. The CsCl structure is an important
  type of structures.

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Examples of Structure Adoption

• NaCl (Halite)
• Very common (inc. 'ionics', 'covalents'
  'intermetallics' )
• Most alkali halides (CsCl, CsBr, CsI excepted)
• Most oxides / chalcogenides of alkaline earths
• Many nitrides, carbides, hydrides (e.g. ZrN, TiC,
  NaH)
• CaF2 (Fluorite)
• Fluorides of large divalent cations, chlorides of
  Sr, Ba
• Oxides of large quadrivalent cations (Zr, Hf, Ce,
  Th, U)
• Na2O (Anti-Fluorite)
• Oxides /chalcogenides of alkali metals
• ZnS (Zinc Blende/Sphalerite)
• Formed from Polarizing Cations (Cu, Ag, Cd2,
  Ga3...)
• and Polarizable Anions (I-, S2-, P3-, ...)
• e.g. Cu(F,Cl,Br,I), AgI, Zn(S,Se,Te), Ga(P,As),
  Hg(S,Se,Te)

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Packing of spheres with two different radii

• AB type compounds
• note that the CN's must relate to the overall
  stoichiometry, i.e. AB - type salt such as NaCl
  - the CN must be (n,n)
• it can be proven that the only geometric
  possibilities for coordination numbers
  are(cation CN, anion CN) (12,12), (8,8),
  (6,6), (4,4), (3,3) or (2,2)
• the packing efficiencies (and therefore Madelung
  energies - see Lattice Energy section) decreases
  with decreasing coordination numbers (CN), so
  higher coordination is favored if possible
• the maximum CN is limited by the radius ratio

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• Radius Ratio Coordination no. Binary
  (AB) Structure-type r/r- 1
  12 none known
• 1 gt r/r- gt 0.732 8 CsCl
• 0.732 gt r/r- gt 0.414 6 NaCl
• 0.414 gt r/r- gt 0.225 4 ZnS

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Zinc blende and diamond
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ZnS
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F.C.C. Unit cell - the basic structure of Diamond

• http//www.science.uwaterloo.ca/cchieh/cact/c123/
  tetrahed.html
• http//www.wou.edu/las/physci/ch412/lattice.html
  (Good notes)
• http//www.westsidevolleyball.com/gunther/lab24.ht
  ml (Crystal model making) http//www.molecules.org
  /VSEPR_table.html
• NaCl (FCC)
  Diamond (FCC)