Ceramic Their Properties and
Material Behavior
Engr 2110
Dr. R. Lindeke
• Bonding:
Ceramic Bonding
-- 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.
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
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 :
-
Adapted from Fig. 12.1,
Callister 7e.
+
-
-
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
Issue: How many anions can you arrange around a 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
cubic
Adapted from Table 12.2,
Callister 7e.
ZnS
(zincblende)
Adapted from Fig.
12.4, Callister 7e.
NaCl
(sodium
chloride)
Adapted from Fig.
12.2, Callister 7e.
CsCl
(cesium
chloride)
Adapted from Fig.
12.3, Callister 7e.
Cation Site Size: considering Tetrahedral,
Octahedral or Cubic
• Determine minimum rcation/ranion for OH site (Coor # is 6)
2ranion  2rcation = 2a
OH means Octahedral
Site
Anion: 8*1/8 = 1

a = 2ranion
Cation: 1
Equal Stoichiometry!
2ranion  2rcation = 2 2 * ranion
ranion  rcation = 2ranion

rcation = ( 2 1)ranion
rcation
= 0.414
ranion
We compute this
one because its
easy!
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: 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)
Site Selection III
3. 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
% ionic character = 100 {1 - exp[-0.25( X Si  X C )2 ]} = 11.5%
•
•
ca. 89% covalent bonding
we find that in SiC, TD sites are preferred due to covalence needs even
though the radii ratio suggests otherwise
AX Crystal Structures
AX–Type Crystal Structures include NaCl, CsCl, and zinc blende
Cesium Chloride structure:
rCs 
rCl 
=
0.170
= 0.939
0.181
 cubic sites preferred
So each Cs+ has 8 neighboring Cl(cubic Sites)
Adapted from Fig.
12.3, Callister 7e.
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
Adapted from Fig.
12.4, Callister 7e.
Ex: ZnO, ZnS, SiC
So each Zn2+ has 4 neighboring
O2-
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-
0.140
0.181
0.133
• Answer:
rcation 0.077
=
ranion 0.140
= 0.550
based on this ratio,
--coord # = 6
-- or structure is like NaCl
(two interleaved FCC)
Data from Table 12.3,
Callister 7e.
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 in the
Anion FCC lattice
Adapted from Fig.
12.2, Callister 7e.
MgO and FeO
MgO and FeO also have the NaCl structure (as we predicted for
FeO earlier!)
O2-
rO = 0.140 nm
Mg2+
rMg = 0.072 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)
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)
rK 
rO2
Adapted from Fig.
12.5, Callister 7e.
=
0.138nm
= 0.986  coor. # for oxygen = is 8
0.140nm
• 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!
ABX3 Crystal Structures
• Perovskite
Ex: complex oxide
BaTiO3
Adapted from Fig.
12.6, Callister 7e.
Silicate Ceramics
Most common elements on earth are Si & O
Si4+
O2Adapted from Figs.
12.9-10, Callister 7e.
crystobalite
• SiO2 (silica) structures are quartz, crystobalite, &
tridymite
• The strong Si-O bond leads to a strong, high
melting material (1710ºC)
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.
12.11, Callister 7e.
• Basic Unit:
GLASS STRUCTURE
• Glass is amorphous
• Amorphous structure
4Si04 tetrahedron
Si4+
O2-
occurs by adding impurities
(Na+,Mg2+,Ca2+, Al3+)
• Impurities:
interfere with formation of
crystalline structure.
• Quartz sand is crystalline
SiO2:
(soda glass)
Adapted from Fig. 12.11,
Callister, 6e.
8
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
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
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:
Adapted from Fig. 13.5, Callister, 6e.
--do not crystallize
--spec. vol. varies smoothly with T
--Glass transition temp, Tg
• Viscosity:
--relates shear stress &
velocity gradient:
--has units of (Pa-s)
dv
=
dy
9
GLASS VISCOSITY VS T AND IMPURITIES
• Viscosity decreases with T increase
• Impurities lower Tdeform
Adapted from Fig. 13.6, Callister, 6e.
(Fig. 13.6 is from E.B. Shand, Engineering
Glass, Modern Materials, Vol. 6,
Academic Press, New York, 1968, p. 262.)
10
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
Silicates
– Combine SiO44- tetrahedra by having them
share corners, edges, or faces
Adapted from Fig.
12.12, Callister 7e.
Mg2SiO4
Ca2MgSi2O7
– Cations such as Ca2+, Mg2+, & Al3+ act to
neutralize & provide ionic bonding
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.
12.13, Callister 7e.
Layered Silicates
• Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)42+ layer
Adapted from Fig.
12.14, Callister 7e.
Note: these sheets loosely bound by van der Waal’s forces
Layered Silicates
• Can change the counterions
– 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
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.
Adapted from Fig.
12.15, Callister 7e.
Carbon Forms - Graphite
• layer structure – aromatic layers
Adapted from Fig.
12.17, Callister 7e.
– weak van der Waal’s forces between layers
– planes slide easily, good lubricant
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.
12.18 & 12.19,
Callister 7e.
Defects in Ceramic Structures
• Frenkel Defect
--a cation is out of place.
• Shottky Defect
--a paired set of cation and anion vacancies.
Shottky
Defect:
Adapted from Fig. 12.21, Callister
7e. (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
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
Solving Part (a)
T (C)
750
r
(g/cc)
3.50
Ns (m-3)
N s = Ne
5.7x109
 QS
2 kT
we need 2 eqns. because we have 2 unknowns
lets use T = 750 & T = 1500
 QS
1000
3.45
?
9
5.7 *10 = Ne
2*8.62*10
5
 QS
17
1500
3.40
5.8x1017
5.8 *10
= Ne
2*8.62*10
* 750 273
5
(1)
*1500 273
Now divide (2) by (1) and
solve for Qs
(2)
Continuing:
QS
1.018 x10
17 9 
=
2 * 8.62 *10
e
5
* 1500  273 
5
*  750  273 
QS
e
2 * 8.62 *10
QS
 11023 11773
5 *
1.018 x10 = e
take natural logs of both sides:
8
2*8.62*10
=e
2.398Qs
ln 1.018 x108  = 2.398QS
18.4385 = 2.398QS  QS = 7.69  7.7eV
Part B:
7.7
N = N
2 * 8.62 * 10
*e
5
*T
S
considering T at 750  C
7.7
9
N = 5.7 * 10  e
N = 5.214 * 10
2 * 8.63 * 10
5
* 1073
27
7.7
N
N
S , 1000 C
S , 1000 C
= 5.214 * 10
27
*e
2 * 8.62 * 10
5
* 1273
= 3.0183*1012 defects/m 3
Part c: Using a modification to Density
Models for Ceramics
N
A  A 
r=
Structure
M
O
NA
7.7
where : N Structure
= N
*e
2 * 8.62 * 10
5
*T
S
using 750C data and restructuring:
6
23
A A =
M
O
3.50 gm / cc * 6.023 * 10 ion / mole * 10 cc / m
27
5.214 * 10 ion / m
AM
3
 40.45  16.00 = 24.45 gm / mole
Cation with +2 (metal)  in Table (on inside cover) likely is Mg
3
Impurities
• Impurities must also satisfy charge balance leaving Electroneutrality
• Ex: NaCl
Na +
Cl -
• Substitutional cation impurity
cation
vacancy
Ca 2+
Na +
Na +
initial geometry
Ca 2+ impurity
• Substitutional anion impurity
Ca 2+
resulting geometry
anion vacancy
O2-
initial geometry
Cl Cl O2- impurity
resulting geometry
Ceramic Phase Diagrams
MgO-Al2O3 diagram:

Adapted from Fig.
12.25, Callister 7e.
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)
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
cross section
d
L/2
Adapted from Fig. 12.32,
Callister 7e.
L/2
R
b
rect.
d = midpoint
deflection
circ.
• Determine elastic modulus according to:
F
x
slope =
E=
F
L3
F
d 4bd 3
d
rect.
cross
section
d
linear-elastic behavior
=
F
L3
d 12 p R4
circ.
cross
section
Measuring Strength
• 3-point bend test to measure room T strength.
cross section
d
L/2
F
L/2
Adapted from Fig. 12.32,
Callister 7e.
R
b
rect.
circ.
location of max tension
• Typ. values:
• Flexural strength:
Ff
s fs =
1.5Ff L
F
rect.
x
bd 2
=
Ff L
pR3
sfs (MPa) E(GPa)
Si nitride
250-1000 304
Si carbide
100-820 345
Al oxide
275-700 393
glass (soda)
69
69
Material
Data from Table 12.5, Callister 7e.
dfs
d
d = midpoint
deflection
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
• sfs = s0e-nP -- s0 & 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!)