MME365 Glass and Ceramics Engineering: Bonding in Ceramic Materials

MME365 Glass and Ceramics
Engineering
Lecture 03
Bonding in Ceramic Materials
Introduction
• Atomic scale structure:
– crystalline
– Amorphous
• Larger scale structure:
– shape and arrangement of grains or phases
– the size and volume fraction of pores
• Ceramic structures differ from those of metals.
– much wider variety
– Complex
• Named after the mineral for which the structure was first decoded.
– rock salt structure, corundum structure,
• Common ceramic structures
– AX-type
– AX2-type
– AmBnXp-type
Importance of Crystallography
• Diffusion. Often depends on the size and number of interstitial sites, both
functions of the crystal structure.
• Deformation by slip or twinning. In ceramics there are both
crystallographic and electrostatic considerations.
• Piezoelectricity. Crystals must be noncentrosymmetric.
• Thermal conductivity. Phonon conductivity is most efficient in simple
crystal structures formed by small atoms.
• Fracture. Often crystallographic, but not always (e.g., glass and cubic
zirconia).
• Cleavage. Always crystallographic. Cleavage planes have high atomic
density, but we also need to consider charge.
• Ferrimagnetism. In ferrimagnets the coordination number of the magnetic
cation (usually an Fe ion) determines its behavior in an applied magnetic
field
AX-type crystal structure
Cesium chloride structure Zinc Blende structure

• CN=8, 8 anions at cube • CN=4, FCC structure of
corners and 1 cation at S with Zn at interior
center of cube, tetrahedral positions
simple cubic (not BCC)
AmXp type crystal structures
A unit cell of CaF2

(AX2)
• Rc/Ra=0.8, CNCa=8, CNF=4

•†Ca ions in a face centered cubic array with F ions in all (8) of
the tetrahedral holes.
•†Unit cell consists of 8 cubes
AmBnXp type crystal structures
 Ba at cubic corner, O at center of 6
faces, Ti at body center
†CNO=12, CNBa=6, and CN Ti=6
†Large A cation and oxygen form an

FCC lattice
†Cubic--tetragonal at 130C (Curie

points)
†Cubic -- orthrhombic and

rhombohedral at low T
A unit cell of perovskite
crystal structure (ABX3)
Simple ionic ceramics
Rock salt structure
• Sodium chloride (NaCl) is the
most common
• Rc/Ra =0.564
• CN=6 for both cations and anions
• Unit cell: FCC arrangement of anions with one cation
at center of each of 12 cube edges
• Two interpenetrating FCC lattices
Rock salt structure _Cont.
Anions ccp (fcc). Radius Na+ =

1.02Å, radius Cl- = 1.81Å; radius ratio
= 0.563.
Therefore Na octahedral.
1 octahedral / anion
therefore 100% octahedral sites are
filled.
Coordination # Na = 6;
coordination # Cl = 6.
Simple ionic ceramics_ Cont.
•Magnesia, MgO is an engineering ceramics.
•Structure is exactly the same as that of rock
salt.
•The atoms pack to maximise the density, with
the constraint that like ions are not nearest
neighbours.
•oxygen ions form an f.c.c. packing.
•f.c.c. structure contains two interstitial holes:
the larger octahedral holes, (one for each
oxygen atom)
the smaller tetrahedral holes, (two for
each oxygen atom)
A face-centred cubic packing of
oxygen with an Mg ion squeezed
into each octahedral hole.
Simple ionic ceramics _Cont.
Structure of cubic zirconia, ZrO2
An f.c.c. packing of Zr with the O2- ions in the tetrahedral

holes. Since there are two tetrahedral holes for each atom
of the f.c.c. structure, the formula works out at ZrO2.
Simple ionic ceramics _Cont.
Structure of cubic alumina, Al2O3
oxygen ions in close-packed,
c.p.h. arrangement
one octahedral hole and two
tetrahedral holes per atom
Al3+ ions into the octahedral
interstices, each is surrounded by
six O2- ions.
to balance charges (as they
must), there are only enough Al
ions to fill two-thirds of the sites.
One-third of the sites, in an ordered pattern, remain empty.
This introduces a small distortion of the original hexagon,
but from our point of view this is unimportant.
Simple covalent ceramics
Diamond-cubic structure
• each atom is at the centre of a tetrahedron with its four bonds
directed to the four corners of the tetrahedron
• not a close-packed structure - density is low.
Silicon carbide
•diamond cubic structure with half the atoms replaced by Si.
Cubic silica
•diamond cubic structure with an SiO4 tetrahedron on each atom site.
Diamond Silicon carbide Cubic silica

Anion-cation Coordination Configuration
stable Critically stable unstable
For a specific CN, there is a critical or minimum radius ratio

Coordination # and Ionic Radii
r
cation
• Coordination # increases with
r anion
To form a stable structure, how many anions can

surround around a cation?
r cation Coord ZnS
r anion # (zinc blende)
Adapted from Fig. 12.4,
< 0.155 2 linear Callister & Rethwisch 8e.
0.155 - 0.225 3 triangular NaCl

(sodium
0.225 - 0.414 4 tetrahedral chloride)
Adapted from Fig. 12.2,
Callister & Rethwisch 8e.
0.414 - 0.732 6 octahedral CsCl

(cesium
chloride)
0.732 - 1.0 8 cubic Adapted from Fig. 12.3,
Adapted from Table 12.2, Callister & Rethwisch 8e.
Callister & Rethwisch 8e.
14
Common Ceramic Crystal Structures
Structure Structure Atomic CN CN Example

Type Name Packing Cation Anion of Structure
AX Rock salt FCC 6 6 NaCl, MgO, FeO

AX Cesium chloride Simple cubic 8 8 CsCl
AX Zinc blende FCC 4 4 ZnS, SiC
AmXp Fluorite (AX2) Simple cubic 8 4 CaF2, UO2, ThO2

AmXp Corundum HCP Al2O3, Fe2O3
AmBnXp Perovskite (ABX3) FCC 12(A), 6(B) 6 BaTiO3, SrZrO3

AmBnXp Spinel (AB2X4) FCC 4(A), 6(B) 4 MgAl2O4, FeAl2O4
Common Ceramic Crystal _Cont.
Common Ceramic Crystal _Cont.
Example Problem
On the basis of crystal structure, compute the theoretical density
of sodium chloride. Atomic radius: rNa = 0.102 nm, rCl = 0.181
nm
2 (rNa+ rCl)
n’ = 4 in FCC lattice
 AC = ANa = 22.99 g/mol
 AA = ACl = 35.45 g/mol
VC = a3 = (2 rNa+ 2 rCl )3
= cm3 rNa
rCl
n’ ( AC + AA )
r= = 2.14 g/cm3 a
VC NA
Try Yourself
#On the basis of ionic charge and ionic radii given in Table 12.3, predict
crystal structures for the following materials: (a) CaO, (b) MnS, (c) KBr,
and (d) CsBr. Justify your selections.
#Using the ionic radii in Table 12.3, compute the theoretical density of CsCl.
#From the data in Table 12.3, compute the theoretical density of CaF2 which
has the fluorite structure.
#Calculate the theoretical density of NiO, given that it has the

rock salt crystal structure.
Silicate structure
• Crystals Solids: • Amorphous solids:
– Short-range Order – ~Short-range Order
– Long-range Order – No Long-range Order
Silicate structure: The SiO4 Tetrahedron
 Each silicon atom bonds strongly

with 4 oxygen atoms to give SiO4
tetrahedron.
 This stable SiO4 tetrahedron is the
basic building block of all silicates,
including pure silica.
 Treated as a negatively charged entity; each SiO4 unit

carries with it a net 4 negative charge (SiO44-).
Silicate Structure: The SiO4 Tetrahedron
 Silicates are not considered to be ionic, due to strong

covalent character of Si-O bond
 Bonds are directional and relatively strong.
Various silicate structures form due to the ways in which

SiO4 units can be linked together to form 1-, 2-, and 3-D
arrangements.
 The SiO4 units link to each other either directly by the

bridging oxygen (BO), or via a metal ion (M) link.
Silicate Structures _ Cont.
 When silica combines with a metal oxide such that the
ratio MO/SiO2 ≥ 2
 the resultant silicates are made up of separated SiO4
tetrahedron (island silicates or, in polymer terms,
monomers) ), ionically linked by MO molecules.
(BO = 0, NBO = 4)
 this group of silicates is called orthosilicates AX(SiO4)
 example: olivine Mg2SiO4,
garnet Mg3Al2(SiO4)3
Silicate Structures _ Cont.
 When ratio MO/SiO2 < 2

 two tetrahedra are shared by one bridging oxygen atom
(BO = 1, NBO = 3)
 the resulted ion Si2O76- is known as silica dimer.
 example: Akermanite (Ca2MgSi2O7), where two Ca2+
and one Mg2+ ions are bonded to each Si2O76- unit.
This is the first step of the so called “polymerisation” of SiO4 monomer to give
chain, sheet and network silicates.
Silicate Structures
Chain/Ring Silicates
 With decreasing MO, degree of polymerisation increases.
 Chains of linked tetrahedra forms (-Si-O-Si-O-Si-).
 For single chain, O/Si = 3 (BO = 2, NBO = 2)

 For double chain, O/Si = 2.75 (BO = 2.5, NBO = 1.5)
 The NBO bonds between chains, joined by MO;

these bonds are weaker than Si-O bond.
 Thus, chain silicates are fibrous in nature.
 Example: Double chain - Enstatite (MgSiO3)
Silicate Structures
Sheet/Layered Silicates
 O/Si = 2.5; BO = 3, NBO = 1
 the two bridging oxygen form 2-D sheets by joining repeating
units of (Si2O5)2-
 the unbonded oxygen projected outwards of the sheet and
combined with positively charged M ions.
 the sheet becomes polarised; can be hydroplastic.
 example: kaolinite clay Al2(Si2O5)(OH)2
talc Mg3(Si2O5)2(OH)2
Silicate Structures
Ceramic Alloys
• Ceramics form alloys with each other, just as metals do.
• Metals alloyed to increase the yield strength, fatigue strength or
corrosion resistance.
• Ceramics alloyed to have full density, or to improve fracture
toughness.
• One deals with ceramic alloys just as one did with metallic alloys.
• Just as for metals, the constitution of a ceramic alloy is described by
the appropriate phase diagram.
SiO2 with Al2O3

phase diagram
The Microstructure of Ceramics
• Crystalline ceramics form polycrystalline microstructures,
just like those of metals.
• Microstructural features of a crystalline ceramic:
– grains, grain boundaries
– pores, microcracks and second phases.
• Porosities, as high as 20 %, are a common feature
– weaken the structure.
•More damaging are cracks, nucleated by

differences in thermal expansion between
grains or phases.
•ultimately determine the strength of the
material.
Vitreous Ceramics
• Bricks, tiles and whiteware - all are made from clays, sheet silicates
such as the hydrated aluminosilicate kaolin, Al2(Si2O5)(OH)4.
• When wet, the clay draws water between the silicate sheets
(because of its polar layers), making it plastic and easily worked.
• When dried to the green state, loses plasticity and acquire enough
strength for handling.
• The firing (800 and 1200°C) drives off the remaining water, and
causes silica to combine with impurities like CaO to form a liquid
glass which wets the remaining solids.
• On cooling, the glass solidifies (but is still a glass), giving strength to
the final composite of crystalline silicates bonded by vitreous
bonds.
• The amount of glass needs careful controlling
• As fired, vitreous ceramics are usually porous. To seal the surface, a
glaze is applied.
• The glaze melts completely, flows over the surface and wets the
underlying ceramic.
Stone or Rock
Igneous rocks (like granite)
• More like SiO2-Al2O3 alloys
• Structure can be read from the
appropriate phase diagram
• Formed by melting
• Fully dense (still contain cracks)
Sedimentary rocks (like sandstone)

• Microstructure rather like that of
a vitreous ceramic.
• Made of particles of silica,
bonded together either by more
silica or by calcium carbonate
• Porous
• Precipitated from solution in
ground water, rather than
formed by melting.
Ceramic Composites
• stiffness and hardness of a ceramic (like glass,
carbon, or tungsten carbide)
• ductility and toughness of a polymer (like epoxy) or
a metal (like cobalt).
unidirectional alumina fiber/glass Phosphate glass fibre/polymer composite

matrix composite cross section

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MME365 Glass and Ceramics

Cesium chloride structure Zinc Blende structure

A unit cell of CaF2

• Rc/Ra=0.8, CNCa=8, CNF=4

†CNO=12, CNBa=6, and CN Ti=6

†Large A cation and oxygen form an

†Cubic--tetragonal at 130C (Curie

†Cubic -- orthrhombic and

Anions ccp (fcc). Radius Na+ =

An f.c.c. packing of Zr with the O2- ions in the tetrahedral

Diamond Silicon carbide Cubic silica

stable Critically stable unstable

For a specific CN, there is a critical or minimum radius ratio

To form a stable structure, how many anions can

0.155 - 0.225 3 triangular NaCl

0.414 - 0.732 6 octahedral CsCl

Structure Structure Atomic CN CN Example

AX Rock salt FCC 6 6 NaCl, MgO, FeO

AmXp Fluorite (AX2) Simple cubic 8 4 CaF2, UO2, ThO2

AmBnXp Perovskite (ABX3) FCC 12(A), 6(B) 6 BaTiO3, SrZrO3

#Calculate the theoretical density of NiO, given that it has the

 Each silicon atom bonds strongly

 Treated as a negatively charged entity; each SiO4 unit

 Silicates are not considered to be ionic, due to strong

Various silicate structures form due to the ways in which

 The SiO4 units link to each other either directly by the

 When ratio MO/SiO2 < 2

 For single chain, O/Si = 3 (BO = 2, NBO = 2)

 The NBO bonds between chains, joined by MO;

SiO2 with Al2O3

•More damaging are cracks, nucleated by

Sedimentary rocks (like sandstone)

unidirectional alumina fiber/glass Phosphate glass fibre/polymer composite

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