CHAPTER
12
Structures and Properties
of Ceramics
1
Structures & Properties of Ceramics
ISSUES TO ADDRESS...
• How do the crystal structures of ceramic materials
differ from those for metals?
• How do point defects in ceramics differ from those
defects found in metals?
• How are impurities accommodated in the ceramic lattice?
• In what ways are ceramic phase diagrams different from
phase diagrams for metals?
• How are the mechanical properties of ceramics
measured, and how do they differ from those for metals?
2
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
3
Ceramics
SiO4-4
Cemented carbide (WC) inserts
Quartz, SiO2
Ceramics are inorganic,
nonmetallic materials that consist
of metallic and nonmetallic
elements bonded together
primarily by ionic and/or
covalent bonds.
4
Introduction
•
•
•
•
•
•
Ceramics are inorganic and nonmetallic.
Bounded by ionic or covalent bonds.
Good electrical and heat insulation property.
Brittle, and lesser ductility and toughness than metals.
High chemical stability and high melting temperature.
Traditional Ceramics: Basic components (Clay and
Silica).
• Engineering Ceramics: Pure compounds (Al2O3, SiC).
• Functional Ceramics:
5
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
6
Ionic and Covalent Bonding in Simple Ceramics
•
Mixture of Ionic and Covalent Types.
• Depends on electronegativity difference.
Table 12.1
Pauling equation for ionicity of AB compound:
% ionic character = (1- e (-1/4)(Xa-Xb)2)(100%)
7
Atomic Bonding in Ceramics
• Bonding:
-- Can be ionic and/or covalent in character.
-- % ionic character increases with difference in electronegativity of atoms
• Degree of ionic character may be large or small:
http://www.webelements.com/
CaF2: large
SiC: small
Adapted from Fig. 2.7, Callister & Rethwisch 8e. (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.)
8
Bond Hybridization
Bond Hybridization is possible when there is significant
covalent bonding
– hybrid electron orbitals form
– For example for 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, for SiC, Si atoms occupy tetrahedral sites
9
Simple Ionic Arrangements
•
Packing of Ions depends upon
 Relative size of ions.
 Need to balance electron charges.
•
If the anion does not touch the cation, then the
arrangement is unstable.
• Radius ratio = rcation/ranion
• Critical radius ratio for stability for coordination numbers
8, 6, 4 and 3 are >0.732, >0.414, >0.225 and > 0.155
10
Factors that Determine Crystal Structure
1. Relative sizes of ions – Formation of stable structures:
--maximize the # of oppositely charged ion neighbors.
-
+
-
-
-
unstable
2. Maintenance of
Charge Neutrality :
+
-
stable
--Net charge in ceramic
should be zero.
--Reflected in chemical
formula:
CaF 2 :
-
Adapted from Fig. 12.1,
Callister & Rethwisch 8e.
+
-
-
stable
Ca 2+ +
cation
Fanions
F-
Am Xp
m, p values to achieve charge neutrality
11
Coordination # and Ionic Radii
• Coordination # increases with
rcation
ranion
To form a stable structure, how many anions can
surround around a cation?
rcation
ranion
ZnS
(zinc blende)
< 0.155
Coord
#
2
linear
0.155 - 0.225
3
triangular
0.225 - 0.414
4
tetrahedral
0.414 - 0.732
6
octahedral
0.732 - 1.0
8
cubic
Adapted from Table 12.2,
Callister & Rethwisch 8e.
Adapted from Fig. 12.4,
Callister & Rethwisch 8e.
NaCl
(sodium
chloride)
Adapted from Fig. 12.2,
Callister & Rethwisch 8e.
CsCl
(cesium
chloride)
Adapted from Fig. 12.3,
Callister & Rethwisch 8e.
12
Computation of Minimum Cation-Anion Radius
Ratio
• Determine minimum rcation/ranion for an octahedral site
(C.N. = 6)
2ranion  2rcation  2a
a  2ranion
2ranion 2rcation  2 2ranion
ranion rcation  2ranion

rcation  ( 2 1)ranion
rcation
 2  1  0.414
ranion 
13
AX Crystal Structures
AX–Type Crystal Structures include NaCl, CsCl, and ZnS (zinc blende)
Cesium Chloride structure:
rCs 
rCl 

0.170
 0.939
0.181
 Since 0.732 < 0.939 < 1.0,
cubic sites preferred
Adapted from Fig. 12.3,
Callister & Rethwisch 8e.
So each Cs+ has 8 neighbor Cl-
14
Cesium Chloride Crystal Structure
•
CsCl is ionically bonded with radius ratio = 0.94 and
CN = 8.
• Eight chloride ion surround a central cesium cation
at the ( ½ , ½ , ½ ) position.
• CsBr, TlCl and TlBr have similar structure.
Figure 10.4
15
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 (Na+) prefer octahedral sites
Adapted from Fig. 12.2,
Callister & Rethwisch 8e.
16
Sodium Chloride Crystal Structure
•
Highly ionically bonded
with Na+ ions (0.102 nm)
occupying interstitial sites
between FCC and Cl- ions.
(0.181 nm)
•
Radius ratio = 0.56,
CN = 6.
•
MgO, CaO, NiO and FeO
have similar structures.
Figure 10.5
17
Ceramic Crystal Structures
Oxide structures
– oxygen anions larger than metal cations
– close packed oxygen in a lattice (usually FCC)
– cations fit into interstitial sites among oxygen ions
18
Example Problem: Predicting the Crystal
Structure of FeO
• On the basis of ionic radii, what crystal structure
would you predict for FeO?
Cation Ionic radius (nm)
• Answer:
Al3+
0.053
rcation 0.077

2
+
Fe
0.077
ranion 0.140
Fe 3+
0.069
 0.550
Ca 2+
0.100
Anion
O 2Cl F-
based on this ratio,
-- coord # = 6 because
0.140
0.181
0.133
0.414 < 0.550 < 0.732
-- crystal structure is NaCl
Data from Table 12.3,
Callister & Rethwisch 8e.
19
MgO and FeO
MgO and FeO also have the NaCl structure
O2-
rO = 0.140 nm
Mg2+
rMg = 0.072 nm
rMg/rO = 0.514
 cations prefer octahedral sites
Adapted from Fig. 12.2,
Callister & Rethwisch 8e.
So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms
20
AX2 Crystal Structures
Fluorite structure
• Calcium Fluorite (CaF2)
• Cations in cubic sites
• UO2, ThO2, ZrO2, CeO2
• Antifluorite structure –
positions of cations and
anions reversed
Adapted from Fig. 12.5,
Callister & Rethwisch 8e.
21
Calcium Fluorite (CaF2) Crystal Structure
•
Ca2+ ions occupy the FCC
lattice sites while the Fions are located at eight
tetrahedral sites.
• UO2, BaF2, PbMg2 have
similar structures.
Figure 10.10
• Large number of unoccupied octahedral sites in UO2
allow it to be used as nuclear fuel.
• Fission products are accommodated in these vacant
positions.
After W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976.
22
ABX3 Crystal Structures
• Perovskite structure
Ex: complex oxide
BaTiO3
Adapted from Fig. 12.6,
Callister & Rethwisch 8e.
23
VMSE: Ceramic Crystal Structures
24
Density Computations for Ceramics
Number of formula units/unit cell
n(AC  AA )

VC NA
Avogadro’s number
Volume of unit cell
AC = sum of atomic weights of all cations in formula unit
AA = sum of atomic weights of all anions in formula unit


25
Interstitial Sites in FCC and HCP Crystal Lattices
•
Octahedral interstitial
sites: Six nearest atoms or
ions equidistant from
central void.
• Tetrahedral Interstitial
Sites: Four nearest atoms
or ions equidistant from
central void.
• There are four octahedral
sites and eight tetrahedral
sites per unit cell of FCC.
– One octahedral and two
tetrahedral sides exist per
anion (FCC & HCP)
Figure 10.6
Figure 10.8
After W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976
.
26
Zinc Blende (ZnS) Crystal Structue
•
•
•
•
•
•
Four zinc and four sulfur atoms.
One type (Zn or S) occupies lattice points and another
occupies interstitial sites of FCC unit cell.
S Atoms
(0,0,0) ( ½ ,½ ,0) ( ½ , 0, ½ ) (0, ½ , ½ )
Zn Atoms
( ¾ ,¼ ,¼ ) ( ¼ ,¼ ,¾ )( ¼ ,¾ ,¼ ) ( ¾ ,¾ ,¾ )
Tetrahedrally covalently bonded
(87% covalent character) with
CN = 4
CdS, InAs, InSb and ZnSe have
similar structures.
Figure 10.9
After W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976
.
27
Other Crystal Structures
•
Antifluorite: Anions occupy lattice points and cations
occupy eight tetrahedral sites of FCC.
Examples: Li2O, Na2O
• Corundum: Oxygen ions in lattice
points of HCP unit cell.
 Two Al3+ ions in octahedral
sites for every three O- ions
distortion of structure.
Figure 10.11
• Spinel (MgAl2O4): Oxygen ions form FCC lattice and
Mg and Al ions occupy interstitial sites .
• These are nonmetallic magnetic materials.
28
29
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
30
Silicate Structures
•
•
•
•
•
Silicate (SiO44-) is building block of silicates.
50% Ionic and 50% covalent.
Many different silicate structures
can be produced.
Island structure: Positive ions
bond with the oxygen of SiO44tetrahedron. (Mg, Fe)2SiO4
Figure 10.16
Chain/ring structure: Two
corners of each SiO44- tetrahedron
bonds with corners of other
tetrahedron. MgSiO3
Figure 10.17a
After M. Eisenstadt, “Mechanical properties of Materials,” Macmillan, 1971, p.82.
31
Silicate Networks
Silica: All four corners of the SiO44- tetrahedra share
oxygen atoms. SiO2
• Basic structures: Quartz, tridynute and cristobarlite.
• Important compound
of many ceramic and glasses.
•
• Feldspars: Infinite 3D networks
• KAlSi3O8 – NaAlSi3O8 – CaAl2Si2O8
• Some Al3+ Ions replace Si4+ Ions
–
Net negative charge.
•
Alkali and alkaline fit into interstitial sites.
Figure 10.20
After W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976
.
32
Glass Structure
• Basic Unit:
-4
SiO4 tetrahedron
Si 4+
O2-
• Quartz is crystalline
SiO2:
Glass is noncrystalline (amorphous)
• Fused silica is SiO2 to which no
impurities have been added
• Other common glasses contain
impurity ions such as Na+, Ca2+,
Al3+, and B3+
Na +
Si 4+
O2 -
(soda glass)
Adapted from Fig. 12.11,
Callister & Rethwisch 8e.
33
Silicates
Bonding of adjacent SiO44- accomplished by the sharing
of common corners, edges, or faces
Mg2SiO4
Ca2MgSi2O7
Adapted from Fig.
12.12, Callister &
Rethwisch 8e.
Presence of cations such as Ca2+, Mg2+, & Al3+
1. maintain charge neutrality, and
2. ionically bond SiO44- to one another
34
Layered Silicates
• Layered silicates (e.g., clays, mica, talc)
– SiO4 tetrahedra connected
together to form 2-D plane
• A net negative charge is associated with
each (Si2O5)2- unit
• Negative charge balanced by
adjacent plane rich in positively charged
cations
Adapted from Fig.
12.13, Callister &
Rethwisch 8e.
35
Layered Silicates (cont.)
• Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)42+
layer
Adapted from Fig. 12.14,
Callister & Rethwisch 8e.
Note: Adjacent sheets of this type are loosely bound to one
another by van der Waal’s forces.
36
Sheet Structures of Silicates
•
Sheet structure: Three corners of same planes of silicate
tetrahedron bonded to the corners of three other silicate
tetrahedra. Mg3(OH)2(Si2O5)2
• Each tetrahedron has one
unbounded oxygen and hence
chains can bond with other
Figure 10.17b
type of sheets.
• If the bondings are weak,
sheets slide over each other
easily.
Figure 10.18
11-13
After M. Eisenstadt, “Mechanical properties of Materials,” Macmillan, 1971, p.83.
37
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
38
Carbon and Its Allotropes
39
0D: Buckyball
1D: Carbon nanotube
：
3D: Graphite
2D ： Graphene
 Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms
that are densely packed in a hexagonal crystal lattice.
 Graphene is a giant aromatic macromolecule that conducts both
electricity and heat well in two dimensions.
Graphene
Buckyball
Graphite
Carbon nanotube
Graphite and Graphene
Graphite
– layered structure – parallel hexagonal arrays of carbon
atoms
Adapted from Fig.
12.17, Callister &
Rethwisch 8e.
– weak van der Waal’s forces between layers
– planes slide easily over one another -- good lubricant
42
Fullerenes and Nanotubes
• Fullerenes – spherical cluster of 60 carbon atoms, C60
– Like a soccer ball
• Carbon nanotubes – sheet of graphite rolled into a tube
– Ends capped with fullerene hemispheres
Adapted from Figs. 12.18
& 12.19, Callister &
Rethwisch 8e.
43
Polymorphic Forms of Carbon
Diamond
– tetrahedral bonding of
carbon
• hardest material known
• very high thermal conductivity
– large single crystals – gem
stones
– small crystals – used to
grind/cut other materials
– diamond thin films
• hard surface coatings – used
for cutting tools, medical
devices, etc.
Adapted from Fig. 12.15,
Callister & Rethwisch 8e.
44
45
If diamond sheets could be made cheaply all objects that need to
be hard and indestructible would be made from diamond.
46
Microwave Plasma CVD Reactor
47
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
48
Point Defects in Ceramics (i)
• Vacancies
-- vacancies exist in ceramics for both cations and anions
• Interstitials
-- interstitials exist for cations
-- interstitials are not normally observed for anions because anions
are large relative to the interstitial sites
Cation
Interstitial
Cation
Vacancy
Adapted from Fig. 12.20, Callister &
Rethwisch 8e. (Fig. 12.20 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.)
Anion
Vacancy
49
Point Defects in Ceramics (ii)
• Frenkel Defect
-- a cation vacancy-cation interstitial pair.
• Shottky Defect
-- a paired set of cation and anion vacancies.
Shottky
Defect:
Adapted from Fig.12.21, Callister &
Rethwisch 8e. (Fig. 12.21 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.)
Frenkel
Defect
• Equilibrium concentration of defects
 e QD /kT
* Stoichiometry: exact composition predicted by the chemical formula
50
Point Defects (impurities) in Ceramics (iii)
51
Impurities in Ceramics
• Electroneutrality (charge balance) must be maintained
when impurities are present
Na +
Cl • Ex: NaCl
• Substitutional cation impurity
cation
vacancy
Ca 2+
Na +
Na +
without impurity
Ca 2+ impurity
• Substitutional anion impurity
O 2-
without impurity
Cl Cl O 2- impurity
Ca 2+
with impurity
an ion vacancy
with impurity
52
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
53
Diffusion in ionic materials
 More complicated than for metal
 Usually occurs by a vacancy mechanism
Ion vacancies occur in pairs
form in nonstoichiometry compounds
created by substitutional impurity ions
54
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
55
Ceramic Phase Diagrams (isomorphous)
fig_12_24
Ceramic Phase Diagrams
MgO-Al2O3 diagram:

Adapted from Fig.
12.25, Callister &
Rethwisch 8e.
57
fig_12_26
fig_12_27
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
60
Mechanical Properties
Ceramic materials are more brittle than metals.
Why is this so?
• Consider mechanism of deformation
– In crystalline, by dislocation motion
– In highly ionic solids, dislocation motion is difficult
• few slip systems
• resistance to motion of ions of like charge (e.g., anions) past one
another
• Plane strain fracture toughness for mode I crack
– KIc = Yσ (πa)1/2
61
fig_12_29
fig_12_30
fig_12_31
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
65
Flexural Tests – Measurement of 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
cross section
L/2
d
b
rect.
L/2
Adapted from Fig. 12.32,
Callister & Rethwisch 8e.
R
d = midpoint
circ.
deflection
• Determine elastic modulus according to:
F
x
slope =
F
d
d
linear-elastic behavior
F L3
E
d 4b d3
(rect. cross section)
F L3
(circ. cross section)
E
4
d 12R
66
Flexural Tests – Measurement of Flexural Strength
• 3-point bend test to measure room-T flexural strength.
cross section
d
b
rect.
L/2
F
L/2
Adapted from Fig. 12.32,
Callister & Rethwisch 8e.
R
d = midpoint
circ.
deflection
location of max tension
• Flexural strength:
sfs 
sfs 
3Ff L
2b d
2
Ff L
R
3
• Typical values:
sfs (MPa) E(GPa)
Si nitride
250-1000 304
Si carbide
100-820 345
Al oxide
275-700 393
glass (soda-lime) 69
69
Material
(rect. cross section)
(circ. cross section)
Data from Table 12.5, Callister & Rethwisch 8e.
67
fig_12_33
69
Content
 Introduction
 Crystal structures
 Silicate
 Carbon
 Imperfections in ceramics
 Diffusion in ionic materials
 Ceramic phase diagrams
 Brittle fracture of ceramics
 Stress-strain behavior
 Mechanisms of plastic deformation
 Miscellaneous mechanical considerations
70
Mechanisms of plastic deformation
• Crystalline ceramics
– A result of dislocation motion
– Brittleness: limited number of operable slip systems
• Noncrystalline ceramics (glass)
– By viscous flow
– Viscocity (Pa.s): materials resistance to deformation
– Very high at room temp.
71
Influence of porosity on modulus of elasticity for Al2O3
E = E0(1 – 1.9P + 0.9P2)
(= P)
fig_12_35
Influence of porosity on flexural strength for Al2O3
σfs = σ 0exp(-nP)
fig_12_36
74
SUMMARY
• Interatomic bonding in ceramics is ionic and/or covalent.
• Ceramic crystal structures are based on:
-- maintaining charge neutrality
-- cation-anion radii ratios.
• Imperfections
-- Atomic point: vacancy, interstitial (cation), Frenkel, Schottky
-- Impurities: substitutional, interstitial
-- Maintenance of charge neutrality
• Room-temperature mechanical behavior – flexural tests
-- linear-elastic; measurement of elastic modulus
-- brittle fracture; measurement of flexural modulus
75