Ceramics
• Term ceramics comes from the greek word keramikos –
“burnt stuff”
• Ceramics are typically formed during high temperature heat
treating – “Firing”
• Traditionally ceramics included:
• China
• Porcelain
• Bricks (both construction and refractory)
• Tiles
• Glasses
• Over the last 60 years or so…there has been an explosion
in new technologies similar to other areas of material
science
Ceramic Bonding
• Bonding:
-- Mostly ionic, some covalent.
-- % ionic character increases with difference in
electronegativity.
• Amount of ionic bond character:
CaF2: large
SiC: small
Eq 2.10: % ionic character = {1 – exp[-(0.25)(XA – XB)2]} x 100
XA, XB are electronegativities of components A and B
Ionic Ceramics
• Crystal structure are composed of electrically charged
ions
– Cations (Fe3+) – Positive Charge Typically metals
– Anions (O2-) – Negatively Charged Typically non-metals
• Two characteristics influence crystal structure:
– The magnitude of charge on the component ions
• Stoichiometry must balance
• Overall charge neutrality is required
rcation
– Relative sizes of the component ions
ranion
small
large
Note that size of ion is affected by charge:
For iron: r(Fe2+) = 0.077 nm, r(Fe3+) = 0.069 nm, r(Fe) = 0.124 nm
Criteria of Site Selection
Which sites will cations occupy to form stable crystal structure?
1. Size of sites
–
does the cation fit in the site
2. Stoichiometry
–
if all of one type of site is full the remainder have to go
into other types of sites.
3. Covalent Bond Hybridization
Ionic Bonding & Structure
1. Size - Stable structures:
--maximize the # of nearest oppositely charged neighbors.
-
+
-
-
-
-
unstable
• Charge Neutrality:
-
stable
--Net charge in the
structure should
be zero.
--General form:
+
-
CaF 2 :
-
-
+
-
-
stable
Ca 2+ +
cation
Fanions
F-
A m Xp
m, p determined by charge neutrality
Coordination # and Ionic Radii
r cation
• Coordination # increases with
r anion
How many anions can you arrange around the cation?
r cation
r anion
< 0.155
Coord
#
linear
2
0.155 - 0.225
3
triangular
0.225 - 0.414
4
TD
0.414 - 0.732
6
OH
0.732 - 1.0
8
ZnS
(zincblende)
cubic
Purely geometrical argument
NaCl
(sodium
chloride)
CsCl
(cesium
chloride)
Geometrical Derivation of Site Size
Determine minimum rcation/ranion for OH site (C.N. = 6)
2ranion  2rcation = 2a

a = 2ranion
2ranion  2rcation = 2 2ranion
ranion  rcation = 2ranion

rcation = ( 2 1)ranion
rcation
= 0.414
ranion
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: We know that an FCC unit cell has 4 OH and 8 TD sites.
If for a specific ceramic each unit cell has 6 cations and the
cations prefer OH sites, then
4 in OH
2 in TD
Site Selection III
3. Bond Hybridization – significant covalent bonding
–
–
the hybrid orbitals can have impact if significant covalent bond
character present
For example in SiC
XSi = 1.8 and XC = 2.5
% ionic character = 100 {1 - exp[-0.25( X Si  X C )2 ]} = 11.5%
• 89% covalent bonding
• both Si and C prefer sp3 hybridization
• Therefore in SiC get TD sites
Example: Predicting Structure of FeO
• On the basis of ionic radii, what crystal structure
would you predict for FeO?
Cation Ionic radius (nm)
Al 3+
0.053
Fe 2+
0.077
Fe 3+
0.069
Ca 2+
0.100
Anion
O2Cl F-
• Answer:
rcation 0.077
=
ranion 0.140
= 0.550
based on this ratio,
--coord # = 6
--structure = NaCl
0.140
0.181
0.133
Rock Salt Structure
Same concepts can be applied to ionic solids in general
Example: NaCl (rock salt) structure
rNa = 0.102 nm
rCl = 0.181 nm
rNa/rCl = 0.564
 cations prefer OH sites
AX Crystal Structure: equal number of Anion and Cation locations
MgO and FeO
MgO and FeO also have the Rock Salt structure
O2-
rO = 0.140 nm
Mg2+
rMg = 0.072 nm
rMg/rO = 0.514
 cations prefer OH sites
So each oxygen has 6 neighboring Mg2+
2nd Type of AX Crystal Structure
Cesium Chloride structure:
rCs 
rCl 
=
0.170
= 0.939
0.181
 cubic sites preferred
So each Cs+ has 8 neighboring Cl-
3rd Type of AX Crystal Structures
Zinc Blende structure
rZn 2
rO 2
=
0.074
= 0.529  OH ??
0.140
• Size arguments predict Zn2+ in OH sites,
• In observed structure Zn2+ in TD sites
• Why is Zn2+ in TD sites?
– bonding hybridization of
zinc favors TD sites
So each Zn2+ has 4 neighboring S2Ex: ZnO, ZnS, SiC
AX2 Crystal Structures
Fluorite structure
• Calcium Fluorite (CaF2)
• Cations in cubic sites
• UO2, ThO2, ZrO2, CeO2
antifluorite structure –
cations and anions reversed
rC/rA for CaF2 is about 0.8 – coordination number of 8  cubic structure
But, stoichiometry calls for ½ as many Ca2+ as F- ions 8 cubes in unit cell
ABX3 Crystal Structures
Perovskite crystal structure
Ex: Barium Titanate – BaTiO3
Temperatures above 120oF –
cubic crystal structure
Summary of Common Structures
Close Packing of Anions
Coordination = 4
Coordination = 6
Since Anions are commonly packed in FCC structure – we can talk about close
packed planes of anions
Can have both:
FCC Stacking – ABCABC
HCP Stacking – ABABAB
Cl- form FCC Lattice
Close packed planes are {111}
Mechanical Properties
Why are ceramics more brittle than metals?
• Consider method of deformation
– In metals we have dislocation motion along slip
planes
– Slip planes are the close packed planes
• In ionic solids dislocation motion is very difficult
– Why? Too much energy needed to move one anion
past another anion