Ceramics - UPRM

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 F-
form 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 O
for a triangle:
B
B
O

AC C

A for an octahedral hole

1 AB = ra 1 AB = ra
2 2

AO = ra + rc AO = ra + rc

12 AB = cosα (α = 30°) 12 AB = cosα (α = 45°)
AO AO

ra = cos30 = 3 ra = cos 45o = 2
ra + rc 2 ra + rc 2

rc = 0.155 rc = 0.414
ra ra

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 fcc(ccp) hcp

all oct. NaCl NiAs

all tetr. A2X (ReB2)
o/t (all) (Li3Bi) (Na3As)
½t sphalerite (ZnS) wurtzite (ZnS)

(½ o CdCl2 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

NaCl structure has Na+ ions Ionic Crystals prefer the NaCl
at all 4 octahedral sites Structure:

• Large interatomic distance
• LiH, MgO, MnO, AgBr, PbS,
KCl, KBr

Na+ ions
Cl- ions

Crystals having filled Interstitial Sites

Tetrahedral, Th, Sites

Both the diamond cubic structure Covalently Bonded Crystals Prefer
And the Zinc sulfide structures this Structure
have 4 tetrahedral sites occupied • Shorter Interatomic Distances
and 4 tetrahedral sited empty. than ionic
• Group IV Crystals (C, Si, Ge, Sn)
Zn atoms • 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)

S atoms

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

• CaTiO3 - dielectric • SrCeO3 - H - protonic conductor
• BaTiO3 - ferroelectric • RECoO3-x - mixed conductor
• Pb(Mg1/3Nb2/3)O3 - relaxor • (Li0.5-3xLa0.5+x)TiO3 - lithium ion
ferroelectric conductor
• 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

∑ ∑n'×(

ρ=
AC + AA )
Vc × NA

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

rNa=0.102x10-7 rCl=0.181x10-7 cm

Vc = a3 = (2rNa+2rCl)3

Vc = (2×0.102×10-7 + 2×0.181×10-7)3 cm3

4× (22.99 + 35.45) = 2.14g.cm−3

2 × 0.102 ×10−7 + 2 × 0.181×10−7 3 × 6.023×1023
[ ]ρ =

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 4-
Si O
O 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 Carbon: Graphite
Has diamond-cubic structure (like Layered structure with strong
Si, Ge) bonding within the planar layers
One of the strongest/hardest and weak (van der Waals) between
material known layers
High thermal conductivity Easy interplanar cleavage (lubricant
Transparent in the visible and and for writing pencils)
infrared, with high index of Good electrical conductor
refraction. Semiconductor (can be Chemically stable even at high
doped to make electronic devices) temperatures
Metastable (transforms to carbon Applications include furnaces,
when heated) 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 C.N.=8
rBr

PLaarttaimceeteraO3a=O0=.421r9Cln+m2rBr = 2(0.196 + 0.167) = 0.726nm

Density ρ = (0.419nm (79.909 +132.905)g.mol −1 −1 )
×10−7 )3 × (6.023× x1023atoms.mol

ρ = 4.8g.cm−3

[ ]Packing (4π

Factor
PF = 3) (0.196)3 + (0.167)3 = 0.693
(0.419)3

(B)

The first step to solve this nl = (1)(0.1542 nm) = 0 .2035 nm
problem is to compute the d hkl 2 sin θ
interplanar spacing using (2) ⎛ sin 44.53 °⎞
Bragg equation, ⎜ 2 ⎠
⎝

Now, employment of equations for cubic systems, and the

value of R for nickel leads to

h 2 + k 2 + l2 = a 2R 2 = (2)(0.1246 nm) 2
= (0.2035 = 1.732
dhkl dhkl
nm)

This means that h 2 + k 2 + l 2 = (1.732) 2 = 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.

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

~ − QD

e 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 → non-
stoichiometry