Ceramics
Ceramics
keramikos - burnt stuff in Greek - desirable properties of
ceramics are normally achieved through a high temperature heat
treatment process (firing).
Usually a compound between metallic and nonmetallic elements
Always composed of more than one element (e.g., Al2O3, NaCl,
SiC, SiO2)
Bonds are partially or totally ionic, can have combination of ionic
and covalent bonding (electronegativity)
Generally hard, brittle and electrical and thermal insulators
Can be optically opaque, semi-transparent, or transparent
Traditional ceramics – based on clay (china, bricks, tiles,
porcelain), glasses.
“New ceramics” for electronic, computer, aerospace industries.
Types of Ceramics
Ceramics are divided into two general groups: Traditional (e.g. pottery, clays,
rocks) and engineering ceramics.
• Rocks and minerals
• Glasses
- SiO2 based
- attributes: transparent to light, easy to form
- applications: windows, containers, lenses, etc.
• Clays
- composed of Al2O3, SiO2 and chemically bound water
- attributes: easy to form with water addition
- applications: bricks, tiles, porcelain, pottery, etc.
• Cements
- consisting of CaO, SiO2 and AL2O3
- attributes: form paste with water and then harden
- applications: construction, roads, concrete
• Engineering Ceramics (advanced, high-performance)
- e.g. Al2O3, SiC, Si3N4, ZrO2
- attributes: excellent physical, chemical or mechanical properties
- applications: heat engines, cutting tools, die materials, superconductors
IONIC BONDING and STRUCTURE
The crystal structure of an ionically bonded material is determined by
the number of atoms of each element required for charge neutrality
and the optimum packing based on the relative sizes of the ions.
The building criteria for the ceramic crystal structure are:
- maintain neutrality (zero net electric charge)
- charge balance dictates chemical formula
- achieve closest packing (most stable structure)
The condition for minimum energy implies maximum attraction and
minimum repulsion of the atoms
This leads to atomic contact (hard sphere model), configurations
where anions (-) have the highest number of cation (+) neighbors and
vice versa.
Structure types: AX, AmXp, AmBnXp... based on chemistry and
charge balance.
(BCC, FCC and HCP structures involved only one type of atom)
Charge Neutrality:
--Net charge in the structure should be zero.
The structure maximizes the number of nearest oppositely charged
neighbors.
Since cations are usually smaller than anions, the crystal structure
is usually determined by the maximum number of anions that it is
possible to pack around the cations, which, for a given anion size
will increase as the size of the cation, increases.
To achieve the state of lowest energy, the cations and anions will
tend to maximize attractions and minimize repulsions. Attractions
are maximized when each cation surrounds itself with as many
anions as possible, but without touching.
Crystal Structures in Ceramics with
predominantly ionic bonding
Crystal structure is defined by
The electric charge: The crystal must remain electrically
neutral. Charge balance dictates chemical formula (Ca2+ and Fform CaF2).
Relative size of the cation and anion. The ratio of the atomic
radii (rcation/ranion) dictates the atomic arrangement. Stable
structures have cation/anion contact.
Coordination Number: the number of anions nearest neighbors for a
cation.
As the ratio gets larger (that is as rcation/ranion ~ 1) the coordination
number gets larger and larger.
Holes in sphere packing
Triangular
Tetrahedral
Octahedral
Calculating minimum radius ratio
for a triangle:
O
B
B
O
A
C
C
A
1
AB = ra
2
AO = ra + rc
1
AB = ra
2
AO = ra + rc
1 AB
2
= cosα (α = 30°)
AO
ra
3
= cos 30 =
ra + rc
2
1 AB
2
= cosα (α = 45°)
AO
ra
2
o
= cos 45 =
ra + rc
2
rc
= 0.155
ra
rc
= 0.414
ra
for an octahedral hole
C.N. = 2
rC/rA < 0.155
C.N. = 3
0.155 < rC/rA < 0.225
C.N. = 4
0.225 < rC/rA < 0.414
C.N. = 6
0.414 < rC/rA < 0.732
C.N. = 8
0.732 < rC/rA < 1.0
Ionic (and other) structures may be derived from the occupation of
interstitial sites in close-packed arrangements.
A2X
CRYSTAL STRUCTURE TYPES
AX-TYPE anion - cation charges are the same (equal + and -)
-Rock Salt Structure -NaCl, MgO, MnS, LiF, FeO
-Cesium Chloride Structure (CsCl)
-Zinc Blende Structure (ZnS, ZnTe, SiC)
AmXp -TYPE - cation charges are NOT the same
-AX2 (CaF2,UO2, PuO2 and ThO2)
AmBnXp -TYPE - more than one cation charges
-ABO3 (BaTiO3, CoTiO3, SrTiO3)
Comparison between structures with filled octahedral and tetrahedral holes
o/t
all oct.
all tetr.
o/t (all)
½t
(½ o
fcc(ccp)
NaCl
A2X
(Li3Bi)
sphalerite (ZnS)
CdCl2
hcp
NiAs
(ReB2)
(Na3As)
wurtzite (ZnS)
CdI2)
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)
AX-TYPE anion - cation charges are the same
-Rock Salt Structure -NaCl, MgO, MnS, LiF, FeO
-Cesium Chloride Structure (CsCl)
-Zinc Blende Structure (ZnS, ZnTe, SiC)
Note: Cesium chloride structure is NOT BCC as the structure has two
different atoms (if there was only one type of atom, it would be BCC)
Crystals having filled Interstitial Sites
Octahedral, Oh, Sites
Ionic Crystals prefer the NaCl
Structure:
NaCl structure has Na+ ions
at all 4 octahedral sites
Na+ ions
Cl- ions
• Large interatomic distance
• LiH, MgO, MnO, AgBr, PbS,
KCl, KBr
Crystals having filled Interstitial Sites
Tetrahedral, Th, Sites
Both the diamond cubic structure
And the Zinc sulfide structures
have 4 tetrahedral sites occupied
and 4 tetrahedral sited empty.
Zn atoms
S atoms
Covalently Bonded Crystals Prefer
this Structure
• Shorter Interatomic Distances
than ionic
• Group IV Crystals (C, Si, Ge, Sn)
• Group III--Group V Crystals
(AlP, GaP, GaAs, AlAs, InSb)
• Zn, Cd – Group VI Crystals
(ZnS, ZnSe, CdS)
• Cu, Ag – Group VII Crystals
(AgI, CuCl, CuF)
AX Type Crystal Structures
Rock Salt Structure (NaCl)
NaCl structure: rC = rNa = 0.102 nm,
rA = rCl = 0.181 nm rC/rA = 0.56
Coordination = 6
Cl
Na
NaCl, MgO, LiF, FeO, CoO
Cesium Chloride Structure (CsCl)
CsCl Structure: rC = rCs = 0.170 nm,
rA = rCl = 0.181 nm → rC/rA = 0.94
Coordination = 8
Cl
Cs
Is this a body centered cubic structure?
Zinc Blende Structure (ZnS)
radius ratio = 0.402
Coordination = 4
S
Zn
ZnS, ZnTe, SiC have this crystal structure
AmXp-Type Crystal Structures
If the charges on the cations and anions are not the same, a compound
can exist with the chemical formula AmXp , where m and/or p ≠ 1. An
example would be AX2 , for which a common crystal structure is
found in fluorite (CaF2).
AmXp -TYPE - cation charges are NOT the same
-AX2 (CaF2,UO2, PuO2 and ThO2)
Fluorite CaF2
Fluorite (CaF2): rC = rCa = 0.100 nm, rA
= rF = 0.133 nm ⇒ rC/rA = 0.75
From the table for stable geometries we
see that C.N. = 8
Other compounds that have this crystal
structure include UO2 , PuO2 , and ThO2.
AmBnXp-Type Crystal Structures
It is also possible for ceramic compounds to have more than one type
of cation; for two types of cations (represented by A and B), their
chemical formula may be designated as AmBnXp . Barium titanate
(BaTiO3), having both Ba2+ and Ti4+ cations, falls into this
classification. This material has a perovskite crystal structure and
rather interesting electromechanical properties.
AmBnXp -TYPE - more than one cation charges
-BaTiO3, CoTiO3, SrTiO3
Perovskite an Inorganic Chameleon
ABX3 - three compositional variables, A,
B and X
•
•
•
•
•
• (Y1/3Ba2/3)CuO3-x superconductor
• NaxWO3 - mixed conductor;
electrochromic
• SrCeO3 - H - protonic conductor
CaTiO3 - dielectric
• RECoO3-x - mixed conductor
BaTiO3 - ferroelectric
• (Li0.5-3xLa0.5+x)TiO3 - lithium ion
Pb(Mg1/3Nb2/3)O3 - relaxor
conductor
ferroelectric
Pb(Zr1-xTix)O3 - piezoelectric • LaMnO3-x - Giant magneto(Ba1-xLax)TiO3 – semiconductor resistance
The perovskite structure CaTiO3
- TiO6 – octahedra
- CaO12 – cuboctahedra
(Ca2+ and O2- form a cubic close
packing)
→ preferred basis structure of
piezoelectric, ferroelectric and
superconducting materials
Density Calculations in Ceramic Structures
ρ=
n'×( ∑ AC + ∑ AA )
Vc × N A
n’: number of formula units in unit cell (all ions that are included
in the chemical formula of the compound = formula unit)
ΣAC: sum of atomic weights of cations in the formula unit
ΣAA: sum of atomic weights of anions in the formula unit
Vc: volume of the unit cell
NA: Avogadro’s number, 6.023x1023 (formula units)/mol
Example: NaCl
n’ = 4 in FCC lattice
ΣAC = ANa = 22.99 g/mol
ΣAA = ACl = 35.45 g/mol
rCl=0.181x10-7 cm
rNa=0.102x10-7
Vc = a3 = (2rNa+2rCl)3
Vc = (2×0.102×10-7 + 2×0.181×10-7)3 cm3
ρ=
[2 × 0.102 ×10
4 × (22.99 + 35.45)
−7
+ 2 × 0.181× 10
] × 6.023 ×10
−7 3
23
= 2.14g.cm −3
Silicate Ceramics
¾ Composed mainly of silicon and oxygen, two most abundant
elements in earth’s crust (rocks, soils, clays, sand)
¾ Basic building block: SiO44- tetrahedron
¾ Si-O bonding is largely covalent, but overall SiO4 block has
charge of –4
¾ Various silicate structures – different ways to arrange SiO4-4
blocks
O
Si O
O
4-
O
Silica = silicon dioxide = SiO2
¾ Every oxygen atom is shared by adjacent tetrahedra
¾ Silica can be crystalline (e.g., quartz) or amorphous, as in glass
(fused or vitreous silica)
3D network of SiO4
tetrahedra in cristobalite
High melting temperature of
1710 °C
Window glasses
Most window glasses produced by
adding other oxides (e.g. CaO,
Na2O)
whose
cations
are
incorporated within SiO4 network.
The cations break the tetrahedral
network so glasses melt at lower
temperature than pure amorphous
SiO2. Lower melting point: easier
to mold (e.g., bottles).
Other
oxides (e.g., TiO2, Al2O3) substitute
for silicon and become
part of network
Carbon
Carbon is not a ceramic
Carbon exists in various polymorphic forms: sp3 diamond, and
amorphous carbon, sp2 graphite and fullerenes/nanotubes.
Carbon Diamond
Has diamond-cubic structure (like
Si, Ge)
One of the strongest/hardest
material known
High thermal conductivity
Transparent in the visible and
infrared, with high index of
refraction. Semiconductor (can be
doped to make electronic devices)
Metastable (transforms to carbon
when heated)
Carbon: Graphite
Layered structure with strong
bonding within the planar layers
and weak (van der Waals) between
layers
Easy interplanar cleavage (lubricant
and for writing pencils)
Good electrical conductor
Chemically stable even at high
temperatures
Applications include furnaces,
rocket nozzles, welding electrodes.
Carbon
Carbon: buckyballs and nanotubes
Buckminsterfullerenes (buckyballs) and carbon nanotubes are
expected to play an important role in future nanotechnology
applications (nanoscale materials, sensors, machines, and computers).
Nanotube
holepunching
/etching
Carbon nanotube T-junction
Nano-gear
Nanotubes as reinforcing
fibers in nano-composites
Figures from
http://www.nas.nasa.gov/Groups/SciTech/nano/
Made from tiny tubes of carbon standing
on end, this material is almost 30 times
darker than a carbon substance used by
the National Institute of Standards and
Technology as the current benchmark of
blackness. It is composed of carbon
nanotubes, standing on end. This
arrangement traps light in the tiny gaps
between the "blades.“ The substance
has a total reflective index of 0.045
percent - which is more than three times
darker than the nickel-phosphorus alloy
that now holds the record as the world's
darkest material
(0.16 to 0.18 percent reflectance).
Basic black paint, by comparison, has a
reflective index of 5 percent to 10
percent.
Examples
(A)Would you expect CsBr to have the sodium chloride, zinc
blende, fluorite or cesium chloride structure? Based on your
answer, determine (a) the lattice parameter, (b) the density
and (c) the packing factor of CsBr.
rCs = 0.167nm
ACs = 79.91 g.mol-1
rBr = 0.196nm
ABr = 132.91 g.mol-1
(B) For which set of crystallographic planes will a first-order
diffraction peak occur at a diffraction angle of 2θ = 44.53O
for FCC nickel (metallic atomic radius R=0.1246nm) when
monochromatic radiation having a wavelength of 0.1542nm
is used.
(A)
rCl
= 0.852
rBr
Lattice
Parameter
C.N.=8
3aO = 2rCl + 2rBr = 2(0.196 + 0.167) = 0.726nm
aO = 0.419nm
(79.909 + 132.905)g .mol −1
Density ρ =
(0.419nm ×10 −7 )3 × (6.023 × x10 23 atoms.mol −1 )
Packing
Factor
ρ = 4.8g .cm −3
( 4π )[(0.196)3 + (0.167)3 ]
PF =
3
(0.419)
3
= 0.693
(B)
The first step to solve this
(1)(0.1542 nm)
nl
= 0 .2035
problem is to compute the d hkl 2 sin θ =
44.53 ° ⎞
⎛
(2)
sin
⎜
interplanar spacing using
2
⎝
⎠
Bragg equation,
Now, employment of equations for cubic systems, and the
value of R for nickel leads to
h
2
+ k
2
+ l
2
=
This means that
a
d
=
2R
d
hkl
h
2
2
=
(2)(0.1246
(0.2035
hkl
+ k
2
+ l
2
nm)
2
nm)
= (1.732)
2
= 1.732
= 3.0
By trial and error, the only three integers which are all odd or
even, the sum of the squares of which equals 3.0 are 1, 1, and 1.
Therefore, the set of planes responsible for this diffraction peak is
the (111) set.
nm
Molybdenum Disulfide (MoS2)
Common high tech grease
Like graphite, MoS2 has weak van der Waals
forces between the basal planes. The bonds
between the sulfur layers are weaker than the
mbonds between the molybdenum layers. The
covalent bonds of both are strong in the basal
plane.
Crystalline lattice structure materials,such as
molybdenum disulfide, tungsten disulfide and
graphite, are widely used as lubricants.
Lamella lubricating powders have low shear
forces between their crystalline lattice layers that
minimize resistance between sliding surfaces.
MoS2 occurs naturally in the form of thin solid
veins within granite.
Imperfections in Ceramics
Point defects in ionic crystals are charged. Coulombic forces are large and any
charge imbalance wants to be balanced. Charge neutrality --> several point
defects created (Charge Neutrality Defects:
Frenkel defect: a cation vacancy and a cation interstitial or an anion (negative
ion) vacancy and anion interstitial. (Anions are larger so it is not easy for an
anion interstitial to form).
+
Schottky defect: pair of anion and cation vacancies
Schottky defect
Frenkel defect
Equilibrium concentration of defects
~e
−
QD
kT
These defects create the electrical
conductivity in ceramics.
An increasing number of defects
increases the conductivity.
Impurities must also satisfy
charge balance
Imperfections in Ceramics
• Frenkel or Schottky defects: no change in cation to anion ratio →
compound is stoichiometric
• Non-stoichiometry (composition deviates from the one predicted
by chemical formula) may occur when one ion type can exist in
two valence states, (e.g. Fe2+, Fe3+). In FeO, usual Fe valence state
is 2+. If two Fe ions are in 3+ state, then a Fe vacancy is
required to maintain charge neutrality → fewer Fe ions → nonstoichiometry
Impurities in Ceramics
¾ Impurity atoms can exist as either substitutional or interstitial
solid solutions
¾ Substitutional ions substitute for ions of like type
¾ Interstitial ions are small compared to host structure (anion
interstitials are unlikely).
¾Solubility high if
ion radii and charges
match
¾Incorporation of
ion with different
Interstitial impurity atom
charge state requires
compensation by
point defects.
Substitutional impurity ions