1. Ceramic Their Properties and Material Behavior
Engr 2110
Dr. R. Lindeke

2. Ceramic Bonding • Bonding: • Large vs small ionic bond character:
-- Mostly ionic, some covalent.
-- % ionic character increases with difference in
electronegativity (remember!?!).
• Large vs small ionic bond character:
CaF2: large
SiC: small
Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by
Cornell University.

3. 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
The same ideas apply to all “ceramics”
Principles of Ceramic Architecture:
Size relationships Cation to Anion
Electrical Neutrality of the overall structure
Crystallographic Arrangements
Stoichiometry Must Match

4. Ionic Bonding & Structure
1. Size - Stable structures:
--maximize the # of nearest oppositely charged neighbors. - +
unstable - + - +
Adapted from Fig. 12.1, Callister 7e.
stable
stable
• Charge Neutrality:
--Net charge in the
structure should
be zero.
--General form:
CaF 2 : Ca 2+
cation F -
anions + A m X p
m, p determined by charge neutrality

5. Coordination # and Ionic Radii
cation
anion
• Coordination # increases with
Issue: How many anions can you arrange around a cation?
Adapted from Fig. 12.2, Callister 7e.
Adapted from Fig. 12.3, Callister 7e.
Adapted from Fig. 12.4, Callister 7e.
ZnS
(zincblende)
NaCl
(sodium
chloride)
CsCl
(cesium
Adapted from Table 12.2, Callister 7e. 2 r
cation
anion
Coord
__#__
< 0.155 3 4 6 8
linear
triangular TD OH
cubic

6. Cation Site Size: considering Tetrahedral, Octahedral or Cubic
Determine minimum rcation/ranion for OH site (Coor # is 6)
OH means Octahedral Site
Anion: 8*1/8 = 1
Cation: 1
Equal Stoichiometry!
a = 2ranion
We compute this one because its easy!

7. Site Selection II Stoichiometry
If all of one type of site is full the remainder have to go into other types of sites!
Ex: the 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 fill in OH
2 more are in TD (because they have to -- for electrical neutrality but the crystal is less stable)

8. Site Selection III
Bond Hybridization – considers 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
ca. 89% covalent bonding
we find that in SiC, TD sites are preferred due to covalence needs even though the radii ratio suggests otherwise

9. AX Crystal Structures  cubic sites preferred
AX–Type Crystal Structures include NaCl, CsCl, and zinc blende
Cesium Chloride structure:
 cubic sites preferred
So each Cs+ has 8 neighboring Cl- (cubic Sites)
Adapted from Fig. 12.3, Callister 7e.

10. AX Crystal Structures Why is Zn2+ in TD sites? Zinc Blende structure
Size arguments predict Zn in OH sites,
In observed structure Zn in TD sites
Why is Zn2+ in TD sites?
bonding hybridization of zinc favors TD sites
So each Zn2+ has 4 neighboring O2-
Adapted from Fig. 12.4, Callister 7e.
Ex: ZnO, ZnS, SiC

11. Example: Predicting Structure of FeO
• On the basis of ionic radii, what crystal structure
would you predict for FeO?
Cation
Anion Al 3+ Fe 2 + Ca 2+ O 2- Cl - F
Ionic radius (nm)
0.053
0.077
0.069
0.100
0.140
0.181
0.133
• Answer:
based on this ratio,
--coord # = 6
-- or structure is like NaCl (two interleaved FCC)
Data from Table 12.3, Callister 7e.

12. Rock Salt Structure
Same concepts can be applied to ionic solids in general.
Example: NaCl (rock salt) structure
rNa = nm
rCl = nm
rNa/rCl = 0.564
cations prefer OH sites in the Anion FCC lattice
Adapted from Fig. 12.2, Callister 7e.

13. MgO and FeO So each oxygen has 6 neighboring Mg2+ (octahedral sites)
MgO and FeO also have the NaCl structure (as we predicted for FeO earlier!)
O2- rO = nm
Mg2+ rMg = nm
rMg/rO = 0.514
cations prefer OH sites
Adapted from Fig. 12.2, Callister 7e.
So each oxygen has 6 neighboring Mg2+ (octahedral sites)

14. AX2 Crystal Structures Fluorite structure Calcium Fluorite (CaF2)
cations in cubic sites
same for UO2, ThO2, ZrO2, CeO2
what about an antifluorite structure? -- cations and anions reversed
see Concept Check 12.1 (K2O)
Both Cation and Anion is 8 so we should find CsCl structure, but
There needs to be twice as many K’s as O’s so K are at cube corners and O’s are alternating Centers of Cube – the opposite of Fluorite!
Adapted from Fig. 12.5, Callister 7e.

15. ABX3 Crystal Structures
Perovskite
Ex: complex oxide
BaTiO3
Adapted from Fig. 12.6, Callister 7e.

16. Silicate Ceramics Most common elements on earth are Si & O
SiO2 (silica) structures are quartz, crystobalite, & tridymite
The strong Si-O bond leads to a strong, high melting material (1710ºC)
Si4+
O2-
Adapted from Figs , Callister 7e.
crystobalite
Silicates make up most of the rock, etc.

17. Amorphous Silica Silica gels - amorphous SiO2
Si4+ and O2- not in well-ordered lattice
Charge balanced by H+ (to form OH-) at “dangling” bonds
very high surface area > 200 m2/g
SiO2 is quite stable, therefore unreactive
makes good catalyst support
Adapted from Fig , Callister 7e.

18. • Quartz sand is crystalline SiO2:
GLASS STRUCTURE
• Basic Unit:
• Glass is amorphous
• Amorphous structure
occurs by adding impurities
(Na+,Mg2+,Ca2+, Al3+)
• Impurities:
interfere with formation of
crystalline structure.
(soda glass)
Adapted from Fig , Callister, 6e.
• Quartz sand is crystalline
SiO2: 8

19. Silica Glass A “Dense form” of amorphous silica
Charge imbalance corrected with “counter cations” such as Na+
Borosilicate glass is the pyrex glass used in labs
better temperature stability & less brittle than sodium glass

20. GLASSES – transparent and easily shaped
Noncrystalline Silicates + oxides (CaO, Na2O, K2O, Al2O3)
E.g. Soda lime glass = 70wt% SiO2 + 30% [Na2O (soda) and CaO(lime)
Table 13.1

21. GLASS PROPERTIES • Specific volume (1/r) vs Temperature (T):
• Crystalline materials:
--crystallize at melting temp, Tm
--have abrupt change in spec.
vol. at Tm
• Glasses:
--do not crystallize
--spec. vol. varies smoothly with T
--Glass transition temp, Tg
Adapted from Fig. 13.5, Callister, 6e.
• Viscosity:
--relates shear stress &
velocity gradient:
--has units of (Pa-s) 9

22. GLASS VISCOSITY VS T AND IMPURITIES
• Viscosity decreases with T increase
• Impurities lower Tdeform
Adapted from Fig. 13.6, Callister, 6e.
(Fig is from E.B. Shand, Engineering Glass, Modern Materials, Vol. 6, Academic Press, New York, 1968, p. 262.) 10

23. Important Temperatures
Melting point = viscosity of 10 Pa.s
Working point= viscosity of 1000 Pa.s
Softening point= viscosity of 4x107Pa.s
Temperature above which glass cannot
be handled without altering dimensions)
Annealing point= viscosity of 1012 Pa.s.
Strain point = viscosity of 3x1013Pa.s
Fracture occurs before deformation
• Viscosity decreases with T
• Impurities lower Tdeform

24. Silicates
Combine SiO44- tetrahedra by having them share corners, edges, or faces
Cations such as Ca2+, Mg2+, & Al3+ act to neutralize & provide ionic bonding
Adapted from Fig , Callister 7e.
Mg2SiO4
Ca2MgSi2O7

25. Layered Silicates Layered silicates (clay silicates) =
SiO4 tetrahedra connected together to form 2-D plane
(Si2O5)2-
So need cations to balance charge =
Adapted from Fig , Callister 7e.

26. Layered Silicates
Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)42+ layer
Adapted from Fig , Callister 7e.
Note: these sheets loosely bound by van der Waal’s forces

27. Layered Silicates Can change the counterions Micas: KAl3Si3O10(OH)2
this changes layer spacing
the layers also allow absorption of water
Micas: KAl3Si3O10(OH)2
Bentonite
used to seal wells
packaged dry
swells 2-3 fold in H2O
pump in to seal up well so no polluted ground water seeps in to contaminate the water supply.
Used in bonding Foundry Sands and Taconite pellets

28. Carbon Forms Carbon black – amorphous – surface area ca. 1000 m2/g
Diamond
tetrahedral carbon
hard – no good slip planes
brittle – can cleave (cut) it
large diamonds – jewelry
small diamonds
often man made - used for cutting tools and polishing
diamond films
hard surface coat – cutting tools, medical devices, etc.
(C likes to have covalent bonds & tetravalent)
Adapted from Fig , Callister 7e.

29. Carbon Forms - Graphite
layer structure – aromatic layers
weak van der Waal’s forces between layers
planes slide easily, good lubricant
Adapted from Fig , Callister 7e.
Like connected benzene rings

30. Carbon Forms – Fullerenes and Nanotubes
Fullerenes or carbon nanotubes
wrap the graphite sheet by curving into ball or tube
Buckminister fullerenes
Like a soccer ball C60 - also C70 + others
Adapted from Figs & 12.19, Callister 7e.

31. Defects in Ceramic Structures
• Frenkel Defect
--a cation is out of place.
• Shottky Defect
--a paired set of cation and anion vacancies.
Shottky
Defect:
Frenkel
Defect
Adapted from Fig , Callister 7e. (Fig is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)
• Equilibrium concentration of defects

32. Lets take a look at 12.31
We must consider Schottky Defects formation energy for an “unknown” MO built in a NaCl structure: given Numbers of Defects and Density for various temperatures --
(a) find energy for defect formation (eV)
(b) find Ns at 1000 C
(c) Identify the Metal in the oxide

33. Solving Part (a) T (C)  (g/cc) Ns (m-3) 750 3.50 5.7x109 1000 3.45 ?
1500
3.40
5.8x1017
Now divide (2) by (1) and solve for Qs

34. Continuing:

35. Part B:

36. Part c: Using a modification to Density Models for Ceramics

37. Impurities
• Impurities must also satisfy charge balance leaving Electroneutrality Na + Cl -
• Ex: NaCl
initial geometry Ca 2+
impurity
resulting geometry Na +
cation
vacancy
• Substitutional cation impurity
• Substitutional anion impurity
initial geometry O 2-
impurity Cl - an
ion vacancy
resulting geometry

38. Ceramic Phase Diagrams
MgO-Al2O3 diagram: 
Adapted from Fig , Callister 7e.

39. Mechanical Properties
We know that ceramics are more brittle than metals. Why?
Consider method of deformation
slippage along slip planes
in ionic solids this slippage is very difficult
too much energy needed to move one anion past another anion (like charges repel)

40. Measuring Elastic Modulus
• Room T behavior is usually elastic, with brittle failure.
• 3-Point Bend Testing often used.
--tensile tests are difficult for brittle materials! F
L/2
d = midpoint
deflection
cross section R b d
rect.
circ.
Adapted from Fig , Callister 7e.
• Determine elastic modulus according to: F x
linear-elastic behavior d
slope = E = L 3 4 bd 12 p R
rect.
cross
section
circ.

41. Measuring Strength s = 1.5Ff L bd 2 Ff L pR3 x F F
• 3-point bend test to measure room T strength. F
L/2
d = midpoint
deflection
cross section R b d
rect.
circ.
location of max tension
Adapted from Fig , Callister 7e.
• Flexural strength:
• Typ. values:
Data from Table 12.5, Callister 7e.
rect. s fs =
1.5Ff L
bd 2
Ff L
pR3
Si nitride
Si carbide
Al oxide
glass (soda) 69
304
345
393
Material
(MPa) E(GPa) x F Ff d

42. Mechanical Issues:
Properties are significantly dependent on processing – and as it relates to the level of Porosity:
E = E0(1-1.9P+0.9P2) – P is fraction porosity
fs = 0e-nP -- 0 & n are empirical values
Because the very unpredictable nature of ceramic defects, we do not simply add a factor of safety for tensile loading
We may add compressive surface loads
We often choose to avoid tensile loading at all – most ceramic loading of any significance is compressive (consider buildings, dams, brigdes and roads!)