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- Ionic Radii and Ionic Solid structures
- Point defects: How are they different from those in metals?
- Impurities: How are they accommodated in the lattice? How do they affect properties?
- Mechanical Properties: What special provisions/tests are made for ceramic materials?
Structures & Properties of Ionic Solids
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Textbooks: Solid State Chemistry
- Shriver, Atkins, Inorganic Chemistry (3rd ed, 1999) W.H. Freeman and Company (Chs. 2, 18 ...).
- A.R. West, Basic Solid State Chemistry (2nd ed. 1999) Wiley, New York, 1999.
- A. R. West, Structural Inorganic Chemistry , 5th^ ed., Oxford University Press, Oxford, 1984.
- U. Muller, Inorganic Structural Chemistry, 2 nd^ ed., Wiley, NY, 2006.
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The Ionic Model of Solids
The 'Ionic Model' (Goldschmidt')
Ions are essentially Charged, Incompressible, Non-Polarizable Spheres
More sophisticated model: a central hard, unperturbable core, where most electron density is concentrated a soft, polarizable outer sphere, which contains very little electron density
Pauling's Rules:
Goldschmidt's structural principles for ionic crystals were summarized by Pauling in a series of Rules.
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Pauling Rule 1: Coordination Polyhedra
A coordination polyhedron of anions is formed around every cation (and vice-versa): Only stable if cations are in contact with each neighbors. (i.e., “Tight packing”)
Ionic crystals may thus be considered as sets of linked polyhedra.
The cation-anion distance is regarded as the sum of the ionic radii.
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Pauling Rule 2: Local Electroneutrality
Stable ionic structures preserve Local Eletroneutrality.
Iions 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
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Pauling Rule 3: Polyhedral Linking
The stability of structures with different types of polyhedral:
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 center of each polyhedron closer together, hence increasing electrostatic repulsions.
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Pauling Rule 4: Cation Evasion
In a crystal containing different cations, those of high valency and small coordination number tend NOT to share polyhedron elements with each other.
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- Bonding: Mostly ionic, some covalent. % ionic character increases with difference in electronegativity.
- Large vs small ionic bond character:
Electronegativity& Bonding in Solids
SiC: small
CaF 2 : large
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Heyes-Ketelaar Triangle: Bonding in Solids
AB
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Different types of atomic radii
(!! atoms can be treated as hard spheres !!)
elements or alloys
element or compounds
Ionic compounds
Metals Atomic radius = d/2 in element (metallic radius) Covalent radius = d/2 in single bond
Non-metals Atomic radius = d/2 in element Covalent radius = d/2 in single bond
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Variation of atomic radii vs. Z
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Variation of ionic radii w/ CN
The radius of one ion has to be fixed to a reasonable value:
(r(O 2-) = 140 pm) Linus Pauling.
That value is then used to compile a set of self- consistent values for all other ions.
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Ceramic Crystal Structures
Oxide structures
oxygen anions much larger than metal cations close packed oxygen in a lattice (usually FCC) cations in the holes of the oxygen lattice
most
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Ionic Radii
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Principles of close packings of spheres
most important: hexagonal close packing (hcp) and cubic close packing (ccp)
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Holes in sphere packings
Calculation of the relative size of holes: r/r (^) h
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- Coordination # increases with
Coordination # and Ionic Radii
2
r cation r anion
**Coord
< 0.**
0.155 - 0.
0.225 - 0.
0.414 - 0.
0.732 - 1.
3
4
6
8
linear
triangular
T (^) D
OH
cubic
ZnS (zincblende)
NaCl (sodium chloride)
CsCl (cesium chloride)
r cation r anion
How many anions (bigger) can be arranged around a cation (smaller)?
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Cation Site Size
Determine minimum r cation /r anion for OH site (C.N. = 6)
a 2 r anion
2 r anion 2 r cation 2 2 r anion
r anion r cation 2 r anion r cation ( 2 1) r anion
2 r anion 2 r cation 2 a
anion
cation .
r
r
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- On the basis of ionic radii, what crystal structure would you predict for FeO? - Answer:
anion
cation
r
r
based on this ratio, coord # = 6 structure = NaCl
Example: Predicting Structure of FeO
Ionic radius (nm)
Cation
Anion
Al 3+ Fe2+ Fe3+ Ca2+
O2-
Cl- F-
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Predicting Ionic Solid Structures
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Site Selection II
2. Stoichiometry If all of one type of site is full, the remainder have to go into other types of sites.
Ex: FCC unit cell has 4 OH and 8 T (^) D sites.
If for a specific ceramic each unit cell has 6 cations and the catio
4 in OH 2 in T (^) D
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Site Selection III
- Bond Hybridization – significant covalent bonding
the hybrid orbitals can have impact if significant covalent bond character For example in SiC X Si = 1.8 and X C = 2.
% ionic character 100 {1-exp[-0.25( X Si X C )^2 ]} 11_._ 5 %
- ca. 89% covalent bonding
- both Si and C prefer sp^3 hybridization
- Therefore in SiC get TD sites
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Characteristic Structures of Solids I
The importance of the concepts of close packing of spheres in the crystal chemistry of elements and compounds: holes in sphere packings
Rock salt: NaCl LiCl, KBr, AgCl, MgO, TiO, FeO, SnAs, UC ... Fluorite: CaF 2 BaCl 2 , K 2 O, PbO 2 ...
Sphalerite: (zinc blende) ZnS CuCl, HgS, GaAs ...
Nickel arsenide: NiAs FeS, PtSn, CoS ... Wurtzite: ZnS ZnO, MnS, SiC
Further important structures of Solids
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Location and number of tetrahedral holes
in a fcc (ccp) unit cell
_- Z = 4 (number of atoms in the unit cell)
- N = 8 (number of tetrahedral holes in the unit cell)_
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Rock Salt Structure
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Rock salt structure (NaCl)
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MgO and FeO
MgO and FeO also have the NaCl structure
O 2-^ r O = 0.140 nm
Mg 2+^ r Mg = 0.072 nm
r Mg/ r O = 0.
cations prefer O (^) H sites
So each oxygen has 6 neighboring Mg2+
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AX Crystal Structures
AX–Type Crystal Structures include NaCl, CsCl, and zinc blende
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181
170 Cl
Cs (^)
r
r
Cesium Chloride structure:
cubic sites preferred
So each Cs+^ has 8 neighboring Cl-
