MME 467
Ceramics for Advanced Applications
Lecture 05
Structure of Ceramics 2
Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000.
Prof. A. K. M. Bazlur Rashid
Department of MME, BUET, Dhaka
Topics to discuss....
1.
2.
3.
3.
AmXn - type ionic structures
Complex AmBnXp - type ionic structures
Covalent structures
Ceramic Density Calculations
1 Corundum Structures
q  Structure named after compound Al2O3
(alumina and sapphire are the polycrystalline and single crystal forms, respectively).
q  Based on the 2:3 cation:anion stoichiometry, two-third of the
available OH sites are filled by cation. The OH sites form a hexagonal
array with the same spacing of the oxygen layer.
u  Acording to Pauling’s second rule, the bond strength of Al3+ in the OH site is 3/6. Since,
oxygen ion has 6 OH sites around it (3 above and 3 below), to satisfy the local
neutrality, the Al3+ around oxygen ion must be 4. This is why Al3+ only fill two-third of
available octahedral sites.
q  Examples of corundum structure: Fe2O3 and Cr2O3 .
Filling of 2/3 of the octahedral sites in the basal plane of
corundum. Only one close- packed anion plane is shown.
Plane shown by dashed line in the left figure.
Two-third occupancy of the columns of
octahedral sites is shown.
2 Ilmenite and Lithium Niobate Structures
(Derivatives of corundum structure)
In ilmenite (FeTiO3), two-third of
octahedral sites are filled with
alternating cation layers occupied by
Fe and Ti alone.
This gives a vertical stacking
arrangement, which requires a six
cation layer sequence before the
structure is repeated.
The bond strength of Fe2+ is 2/6 and
that of Ti4+ is 4/6, because of oxygen
ion having cooridnation with two Fe2+
and two Ti4+.
Basal plane of LiNbO3 structure,
showing mixed Li, Nb occupancy
Ilmenite structure
Lithium niobate (LiNbO3 ) is different from
Ilmenite in case of cation arrangement.
Two-third of occupied octahedral sites are
filled with equal number of Li+ and Nb5+.
In every pair of adjacent occupied sites,
there is one Li+ and one Nb5+.
The bond strength of the Li+ and Nb5+ are
1/6 and 5/6, respectively, thus the oxygen
ion require to coordinate with two Li+ and
two Nb5+.
The orientation of the Li-Nb pairs is in the
same direction (unlike Fe-Ti in Ilmenite
that alternate direction), creating a net
dipole for each of the pair, yielding
ferroelectric crystal.
Cation arrangement in LiNbO3, showing
orientation of dipole between Li+ and Nb5+
3 Perovskite Structure
q  Many ternary compounds of formula ABO3 (A and B cations differ
considerably in size) crystallize in the perovskite (mineral CaTiO3)
structure.
q  An FCC-derivative structure in which the larger A (Ca) cation and
oxygen anion together form the FCC lattice.
q  The smaller B (Ti) cation occupies the octahedral sites and has
only oxygen as its nearest neighbours.
q  The perovskite family includes:
1. titanate compounds (CaTiO3, BaTiO3, SrTiO3 and PbTiO3),
2. zirconate compounds (PbZrO3 and BaZrO3), and
3. other compounds such as LaGaO3 , LaAlO3 and KNbO3 .
Many of these compounds
crystallize in several
polymorphous modifications
having slightly distorted
perovskite structures.
For example, BaTiO3
compound can transform to
tetragonal, orthorhombic, or
rhombohedral modifications
as temperature decreases.
!
Perovskite (CaTiO3) structure
In each case, the displacive
transformation is
accomplished by a shift in the
titanium atom positions.
4 Structure of Barium Titanate
In BaTiO3 unit cell, Ti4+
and Ba2+ are shielded
form one another.
The bond strength of
Ti4+ and Ba2+ are 4/6
and 2/12, respectively,
thus oxygen ion need
to coordinate with four
Ba2+ and two Ti4+.
Ion position in high temperature cubic form of BaTiO3.
For BaTiO3, the oxygen octahedron coordinating Ti is larger than necessary,
being expanded by the large Ba nearest neighbours. This is causing Ti to be
unstable and displace from body centered position.
Ti atoms can shift in its position relative to O atoms surrounding it, and O
atoms can shift relative to Ba atoms at the centre of the cube.
The consequence is change of crystal symmetry, yielding
noncentrosymmetric crystal and creating net electric dipole along the c-axis.
In the room-temperature tetragonal distortion of BaTiO3, it turns out that Ti
moves towards an O atom, while the O atoms move in the opposite direction by
about the same amount, causing a total displacement of Ti4+ is about 0.15 Å.
A more drastic displacement of ions occurs in the tetragonal modification of
PbTiO3, where both O and Ti ions are placed in the same direction relative to Pb
atoms.
The axial ratio c/a is 1.04 in BaTiO3 and 1.06 in PbTiO3, and both crystals
contains electric dipoles parallel to [001].
These crystals are, therefore, said to be polarized along the c axis, and possess
ferroelectric properties.
5 !
Ion positions on (100) planes for (A) tetragonal BaTiO3 , and (B) PbTiO3.
Below room temperature, a further shifting of atoms occurs and dipoles are
produced along [110] directions. This produced orthorhombic structure of
BiTiO3.
Finally at 193 K, another shift occurs so that polarization direction is parallel
to [111] direction and a rhombohedral structure results.
All of these polymorphs of BiTiO3 possess ferroelectric properties.
Typical examples of application:
speakers,
microphone,
sonar transducers,
ultrasonic cleaner,
actuators for high- precession positioning.
6 Spinel and Inverse Spinel Structures
The spinel (MgAl2O4) structure is based on FCC close-packed oxygen
sublattice, containing 32 oxygen atoms per unit cell. The metal atoms are
distributed among the fraction of 64 available tetrahedral (A+2 atoms) and
32 available octahedral (B+3 atoms) sites.
Compounds of stoichiometry AB2O4 in which A and B are divalent and
trivalent, respectively, often form as spinel.
Compounds of stoichiometry B(AB)O4 in which A and B are both divalent
often form as inverse spinel (example Fe(MgFe)O4).
Anion form an FCC sublattice,
with the unit cell contains 32
oxygen ions, 32 octahedral
holes (1/2 filled by B ions) and
64 tetrahedral holes (1/8 filled
by A ions).
Spinel (MgAl2O3) structure
The bond strength is therefore 2/4 for A2+ and 3/6 for B3+. In order to
sastify Pauling’s second rule, each oxygen must be coordinated by
three A2+ and one B3+.
The most commercially important spinel structure ceramics by far are
soft magnetic ferrite, which is used as inductors, transformer cores,
and read/write heads for magnetic storage media.
7 Covalent Ceramic Structures
Si-based:
SiO2 , Si3N4 and SiC
In all cases building block is SiX4 tetrahedron.
SiO4 for all silicates, SiN4 for Si3N4 and SiC4 for SiC.
Why?
sp3 rules !!!
SiX4
SiO2: Every Si bonded to 4 O, every O bonded to 2 Si
But SiO4 is still building block. How?
Answer: It is all in the sharing.
For the most part, SiX4 is corner-shared
8 Diamond
Silicon Carbide
Cubic unit cell
Each atom is at the corner of a
tetrahedron, with 4 bonds directed
at the corner atoms
CN=4 (for close-packing, CN=12),
resulting low density
Diamond cubic structure,
with half C atoms replaced
by Si atoms, forming SiC4
tetrahedron at the corner
Cubic Silica
Diamond cubic structure,
with a SiO4 tetrahedron on
each Si atom site
9 Ceramic Density Computation
ρ=
n’ ( ΣAC + ΣAA )
VC NA
ρ = theoretical density of ceramic
n’ = number of formula unit within the unit cell
ΣAC = sum of atomic weights of all cations in the formula unit
ΣAA = sum of atomic weights of all anions in the formula unit
VC = the unit cell volume
NA = Avogrado’s number = 6.023x1023 formula units/mol
Example Problem 13.3/Callister/P-391
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
Σ AC = ANa = 22.99 g/mol
Σ AA = ACl = 35.45 g/mol
VC = a3 = (2 rNa+ 2 rCl )3
= cm3
rNa
ρ
=
n’ ( ΣAC + ΣAA )
VC NA
= 2.14 g/cm3
rCl
a
10 Next Class
Lecture 06
Effect of Chemical Force on
Structure and Physical Properties
Ref: Barsoum, Fundamentals of Ceramics, Ch04, McGraw-Hill, 2000.
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