Chapter 13 Structures and Properties of Ceramics

Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Chapter Outline: Ceramics

Chapter 13: Structure and Properties of Ceramics
¾ Crystal Structures
¾ Silicate Ceramics
¾ Carbon
¾ Imperfections in Ceramics

Optional reading: 13.6 – 13.10

Chapter 14: Applications and Processing of Ceramics
¾ Short review of glass/ceramics applications and

processing (14.1 - 14.7)

Optional reading: 14.8 – 14.18

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Ceramics

¾ keramikos - burnt stuff in Greek - desirable properties
of ceramics are normally achieved through a high-
temperature heat treatment process (firing).

¾ Usually a compound between metallic and non-
metallic elements

¾ Always composed of more than one element (e.g.,
Al2O3, NaCl, SiC, SiO2)

¾ Bonds are partially or totally ionic, and can have
combination of ionic and covalent bonding

¾ Generally hard and brittle

¾ Generally electrical and thermal insulators

¾ Can be optically opaque, semi-transparent, or
transparent

¾ Traditional ceramics – based on clay (china, bricks,
tiles, porcelain), glasses.

¾ “New ceramics” for electronic, computer, aerospace
industries.

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Bonding in Ceramics (Review of Chapter 2)

Electronegativity - a measure of how willing atoms are to
accept electrons (subshells with one electron - low
electronegativity; subshells with one missing electron -
high electronegativity). Electronegativity increases from
left to right.

The atomic bonding in
ceramics is mixed, ionic and
covalent, the degree of ionic
character depends on the
difference of electronegativity
between the cations (+) and
anions (-).

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Crystal Structures in Ceramics
with predominantly ionic bonding

Crystal structure is defined by

¾ Magnitude of the electrical charge on each ion. Charge
balance dictates chemical formula (Ca2+ and F- form
CaF2).

¾ Relative sizes of the cations and anions. Cations wants
maximum possible number of anion nearest neighbors
and vice-versa.

Stable ceramic crystal structures: anions surrounding a
cation are all in contact with that cation. For a specific
coordination number there is a critical or minimum cation-
anion radius ratio rC/rA for which this contact can be
maintained.

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Coordination Number

The number of adjacent atoms (ions) surrounding
a reference
atom (ion) without overlap of electron orbitals.
• Also called ligancy
• Depends on ion size (close packed)
• Ideal: Like-sized atoms = 12
• Calculated by considering the greatest number
of larger ions
(radius R) that can be in contact with the smaller
one (radius r).

R=1.0

r =0.2

CN = 1 possible CN = 2 possible

30°

Cos 30°=0.866=R/(r+R)
→ r/R = 0.155

CN = 4 possible

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Coordination Number

CN numbers for CN r/R
ionic bonding 2 0<r/R<0.155
3 0.155≤r/R<0.225
4 0.225≤r/R<0.414
6 0.414≤r/R<0.732
8 0.732≤r/R<1
12 1

Example: KCl 6
K+ r=0.133nm, Cl- R=0.188nm,
r/R = 0.71, CN = 6

Example: CsCl
Cs+ r=0.165nm, Cl- R=0.188nm,
r/R = 0.91, CN = 8

Example: Al2O3
Al+3 r=0.057nm, O-2 R=0.132
nm, r/R = 0.43, CN = 6
However for O-2 CN= (2/3) (6)
=4
[(2/3) = (cation/ion) ratio]

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

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Introduction to Materials ScienCce.,NC.hapter 13r,CS/trruActure and PropGeretioesmofeCterryamics

• <0.155
The critical ratio can 0.155-0225

be determined by

simple geometrical

analysis •

• 0.225-0.414

30° • 0.414-0.732
• 0.732-1.0
Cos 30°= 0.866
= R/(r+R)
↓
r/R = 0.155

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Crystal Structures in Ceramics
Example: Rock Salt Structure

NaCl structure: rC = rNa = 0.102 nm, rA = rCl = 0.181 nm
⇒ rC/rA = 0.56
From the table for stable geometries we see that C.N. = 6

Two interpenetrating FCC lattices 9
NaCl, MgO, LiF, FeO have this crystal structure

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

More examples of crystal structures in ceramics
(not included on the test)

Cesium Chloride Structure: rC = rCs = 0.170 nm, rA = rCl =
0.181 nm
⇒ rC/rA = 0.94
From the table for stable geometries we see that C.N. = 8

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Semiconductor Structures

• Diamond cubic – Open Structure

– elemental semiconductors
– Interconnected tetrahedra
– Si, Ge, C

Interior atoms located at positions
¼ of the distance along the
body diagonal.

2 atoms per lattice point

Structure: diamond cubic 11
Bravais lattice: fcc
Ions/unit cell: 4 + 6 x ½ + 8 x ½ = 8
Typical ceramics: Si, Ge, and gray Sn

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

More examples of crystal structures in ceramics
(not included on the test)

Zinc Blende Structure: typical for compounds where
covalent bonding dominates. C.N. = 4

ZnS, ZnTe, SiC have this crystal structure

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

More examples of crystal structures in ceramics
(not included on the test)

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

FCC structure with 3 atoms per lattice point

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

• Crystal structure depends upon: (1) stacking
sequence (hcp or fcc) and (ii) interstitial sites
occupied by cations

• E.g. NaCl: Cl anions packed in fcc symmetry
(ABCABC…), Na cations on octahedral sites

• Spinel (MgAl2O4): O anions form fcc lattice, Mg
cations in tetrahedral sites, Al cations in octahedral
sites

How to Differentiate?

• Look at the formula

– perovskite = A’B”X3
– spinel = A’B2”X4
– fluorite = AX2
– calcite = AX

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Density computation
(similar to Chapter 3.5 for metals)

ρ = n’(ΣAC + ΣAA) / (VcNA)

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, 6.023×1023 (formula

units)/mol

Example: NaCl 15

n’ = 4 in FCC lattice
ΣAC = ANa = 22.99 g/mol
ΣAA = ACl = 35.45 g/mol
Vc = a3 = (2rNa+2rCl)3 =
= (2×0.102×10-7 + 2×0.181×10-7)3 cm3

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Silicate Ceramics

¾ Composed mainly of silicon and oxygen, the 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

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

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

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Window glasses

Most common window glasses are produced by adding
other oxides (e.g. CaO, Na2O) whose cations are
incorporated within SiO4 network. The cations break the
tetrahedral network and glasses melt at lower temperature
than pure amorphous SiO2 because. A lower melting point
makes it easy to form glass to make, for instance, bottles.
Some other oxides (TiO2, Al2O3 substitute for silicon and
become part of the network

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Carbon

Carbon is not a ceramic
Carbon exists in various polymorphic forms: sp3 diamond
and amorphous carbon, sp2 graphite and
fullerenes/nanotubes, one dimensional sp carbon…

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Carbon: Diamond

¾ Has diamond-cubic structure (like Si, Ge)
¾ One of the strongest/hardest material known
¾ High thermal conductivity (unlike ceramics)
¾ Transparent in the visible and infrared, with high index

of refraction, looks nice, costs $$$
¾ Semiconductor (can be doped to make electronic

devices)
¾ Metastable (transforms to carbon when heated)

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Diamond Thin Films

~ 100
microns

• Chemical vapor deposition (CVD)

• Thin films up to a few hundred microns

• Polycrystalline

• Applications: hard coatings (tool bits etc),
machine components, “heat sinks” for high
power semiconductor devices

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Carbon: Graphite

¾ Layered structure with strong bonding within the planar
layers and weak, van der Waals bonding between layers

¾ Easy interplanar cleavage, applications as a lubricant
and for writing (pencils)

¾ Good electrical conductor
¾ Chemically stable even at high temperatures
¾ Applications include furnaces, rocket nozzles, welding

electrodes

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

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).

Carbon nanotube T-junction Nanotubes as reinforcing
fibers in nanocomposites

Nano-gear Nanotube holepunching/etching

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Imperfections in Ceramics (I)

Point defects in ionic crystals are charged. The Coulombic
forces are very large and any charge imbalance has a strong
tendency to balance itself. To maintain charge neutrality
several point defects can be created:

Frenkel defect is a pair of cation (positive ion) vacancy
and a cation interstitial. (it may also be an anion (negative
ion) vacancy and anion interstitial. However anions are
larger than cations and it is not easy for an anion interstitial
to form)

Schottky defect is a pair of anion and cation vacancies

Schottky defect

Frenkel defect

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Imperfections in Ceramics (II)

• Frenkel and Schottky defects do not change ratio of
cations to anions → the 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+

• For example, 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

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

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 unlikely
¾ Solubilities higher if ion radii and charges match closely
¾ Incorporation of ion with different charge state requires

compensation by point defects

Interstitial impurity atom

Substitutional impurity ions

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Mechanical Properties of Ceramics

¾ Ceramics are brittle. For brittle fracture stress
concentrators are very important. (Chapter 8:
measured fracture strengths are significantly
smaller than theoretical predictions for perfect
materials, ~ E/10 due to the stress risers)

¾ Fracture strength of ceramic may be greatly
enhanced by creating compressive stresses at
surface (similar to shot peening, case hardening in
metals, chapter 8)

¾ The compressive strength is typically ten times the
tensile strength. This makes ceramics good structural
materials under compression (e.g., bricks in houses,
stone blocks in the pyramids).

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Mechanical Properties of Ceramics

Stress σ (MPa)
Stress σ (MPa)

(a) Tension (ε) (b) Compression (ε)

The brittle nature if fracture is illustrated by these stress-strain
curves, which show only linear, elastic behavior.

The bending test that generates a modulus of rupture, this 29
strength is similar to the tensile strength.

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Plastic Deformation in Ceramics

¾ Crystalline ceramics: Slip (dislocation motion)
is very difficult. This is because ions of like
charge has to be brought into close proximity of
each other → large barrier for dislocation motion.
In ceramics with covalent bonding slip is not easy
as well (covalent bonds are strong). ⇒ ceramics
are brittle.

¾ Non-crystalline ceramic: there is no regular
crystalline structure → no dislocations. Materials
deform by viscous flow, i.e. by breaking and
reforming of atomic bonds, allowing ions/atoms to
slide past each other (like in a liquid).

Viscosity is a measure of glassy material’s
resistance to deformation.

η = τ = F A
dv dy dv dy

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Summary

Make sure you understand language and concepts:

¾ Anion
¾ Cation
¾ Defect structure
¾ Frenkel defect
¾ Electroneutrality
¾ Schottky defect
¾ Stoichiometry
¾ Viscosity

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Introduction to Materials Science, Chapter 13, Structure and Properties of Ceramics

Reading for next class:

Chapter 14: Applications and Processing of Ceramics
¾ Short review of glass/ceramics applications and

processing (14.1 - 14.7)
Optional reading: 14.8 – 14.18

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