Crystal Structure of CeramicsCrystal Structure of Ceramics

Interstices in Crystal Structure  location ： center of the cube at  number ： one per unit cell Interstices ≡ Interstitial site ≡Interstitial position ≡ sublattice  Shape of interstic

I Introduction to Ceramics

 Chemical Composition

mostly are compounds composed of metallic

and nonmetallic elements, i.e., composed of

at

least two different elements,

usually considering metallic element as cation, and nonmetallic element as anion

example ： Al2O3, SiO2, TiO2, AlN, BN, ……

exceptions ： diamond, graphite,……

• % ionic character = ( 1-e –(0.25)(X

A-XB)2 ) 100

 Bonding

• mostly mixed ionic and covalent bonding

 Coordination number (CN) ： 4, 6, and 8.

• exception ： diamond, silicon, graphite, ……

cations and anions

• CN relative size of cation and anion

 Crystal Structure

• considering the ceramics to be made up of

cations and anions

T 12.1

II General Features of Ceramic Crystal Structures

 The crystal sturctures may be thought of as being

composed of cations , and anions

 Two characteristics influencing the crystal structure: ˙ magnitude of the electrical charge (electrically

neutral)

˙ relative sizes of the cations and anions ( CN)

 The chemical formula of a compound indicates the

ratio of cations to anions, for example: CaF2., Ca+2 :

F-1=1:2 (the crystal must be electrically neutral)

F 12.2 F 3.7-4

 Basis (group) or lattice point

˙ metals ： one basis usually represents one atom.

 all the atoms are located at the positions of

lattice points, i.e., there are atoms only at

the positions of lattice points (lattice sites).

˙ ceramics ： one basis usually represents at least one cation and one anion.

e.g., NaCl ： one Na + and one Cl

ZnO ： one Zn +2 and one O -2

CaF2： one Ca +2 and two F -1

 one lattice point represents at least one cation and one anion.

If the lattice point is assigned to the center of the anion, the cations will not be at the positions of lattice

points Where are the cations accommodated ：

 Interstices ： the space among lattice points

III Interstices in Crystal Structure

 location ： center of the cube at

 number ： one per unit cell

Interstices ≡ Interstitial site ≡Interstitial position ≡ sublattice

 Shape of interstices ： the geometric shape

by connecting straight lines through all the nearest surrounding atoms (or ions)

T 12.2

Interstices

 the largest hole in an FCC structure is at the center

of the unit cell and at the center of each edge

 It has eight sides, celled an octahedral site There are four octahedral sites per FCC unit cell.

 CN = 6  rcation / ranion = 0.414~0.732

 the size of the octahedral hole is defined as the

radius of the largest sphere that can be placed

An atom roughly 40% of the size of the host

atoms can “fit” into an octahedral interstitial

position in the FCC structure

 the FCC sturcture also contains tetrahedral sites,

in the l/4, m/4, n/4 positions, where l, m, and n

are 1 or 3 Each cell contains eight of these ¼,

¼,, ¼-type tetrahedral sites The k/r ratio for

 The BCC structure also contains both octahedral

and tetrahedral sites

 the octahedral sites are located in the center of each face and the center of each edge, giving a total of six sites per unit cell

C Interstices in the BCC

Structure

k r

a 2  2

 a BCC  4r / 3  k /  r 0 155

F 3.6-1

 The tetrahedral sites in BCC structures are located in the

¼, ½, 0- type positions, which are on the {100} faces, a total of 12 tetrahedral sites per unit cell, k/r =0.29

F 3.3-1

D interstices in the HCP Structure F 3.6-1

 Also contains both octahedral and tetrahedral

interstices

 6 octahedral sites per “big” cell or 2 sites per unit cell

 12 tetrahedral sites per big cell or 4 per unit cell

Each small unit cell contains 2, each edge contains

2×(1/3) and 2 are located at the center line.

 k/r = 0.225

 Since both FCC and HCP are close-packed crystal

structures, the relative sizes of the interstitial sites are the same in these two types of crystals.

F 11.15 T 3.6-1

IV Crystal Structures based on Number

of Atoms

(Ions) per Lattice Site

 One atom per lattice site

 A simple cubic lattice with two ions , one of each

type, per lattice position (i.e., the basis) anion ： lattice site

cation ： cubic site (center of the unit cell)

 The coordination number is eight , a0(CsCl) =

Atoms per Lattice Site

No of cubic site

No of lattice site ：

1 1

B The Sodium Chloride

Structure

 a 0 (NaCl)=2(r+R) Ions touch along the cube edge

 Other compounds with this sturcture: MgO, CaO, SrO, FeO, BaO,MnO, NiO and KCl

 NaCl has an FCC lattice with a basis of two different

atoms

anion ： lattice site

cation ： octahedral site

No of octahedral site

No of lattice site ：

4 4

2 2 ( ) / ( )

 a 0 (diamond cubic)=8r/ Other materials with this

structure: silicon and germanium.

one carbon ： lattice siteThe other carbon ： tetrahedral site

No of tetrahedral site

No of lattice site ：

8

4 ：

2 1

 Only half of the tetrahedral sites are occupied and the other half are empty.

3

 The zinc-blende structure is similar to the

diamond cubic structure but with two different elements: zinc and sulfur

 Other materials with this structure ： GaAs,

CdTe

 Why are only half of the tetrahedral sites filled

：

The answers are the stoichiometry of the

compound ： there are four FCC sites per cell

and eight tetrahedral sites per cell

 Coordination number ： four ：

 M2X , including Li2O, Na2O, and K2O, simple the inverse

of the fluorite structure with the X ions at the FCC positions and the M ions filling all of the tetrahedral positions.

 The cations are smaller than the anions as ordinary

 The cations are relatively large compared to

ordinary cases.

F 3.7-5

F 3.5

Sodium chloride (NaCl), or rock salt type, coordination

number: 6, cation-anion radius ratio: 0.414―0.732, unit cell : FCC

examples:NaCl, MgO, MnS, LiF, and FeO.

CsCl, coordination number: 8, crystal sturcture: SC (not a BCC )

(3) Zinc Blende Structure

Coordination number: 4; tetrahedrally coordinated

Zinc blende, or sphalerite, structure, e.g., zinc sulfide (ZnS): sach Zn atom is bonded to four S atoms, and vice versa Examples: ZnS, ZnTe, and SiC

VI Ceramic Crystal Structure based on Chemical

UO2, PU2, and ThO2

C A m B n X p – TYPE CRYSTAL STRUCTURES

A typical example ： barium titanate (BaTiO3), perovskite

Ba 2+ ions at all eight corners, single Ti 4+ at the cube

center, O 2- ions at the center of each of the six faces.

B AmXp— type Crystal

Structures

F 3.7-5 F 3.5 F 12.5

F 12.6 T 12-4

◎ Calcium titanate, CaTiO3

◎ Barium titanate, BaTiO3: simple tetraggonal, a=b=0.398nm, c=0.403nm

The central Ti4+ ion does not lie in the same plane as the four oxygen atoms in the side faces of the tetragonal unit cell

VII Ceramic Crystal Structures based on

building blocksimagine the structure to be made of the various

building blocks

F 12.6 F 3.9 F 3.8

F 3.7-8

An idealized version consisting of TiO6 octahedra , each oxygen

is shared by three octahedra Actual structure comprises

distorted octahedra rather than the regular ones.

 Important electrical properties arising from local electric dipoles : The strength of the dipole can be altered by either

as a transducer to convert electrical voltages into

mechanical energy and vice versa.

 Applications: telephone receivers, phonograph cartridges, and etc.

While SiO2 (silica) has three atoms per lattice site , it is much

easier to visualize the structure of crystobalite in a different

fashion: The basic building block for all Si-O compounds is the negatively charged (SiO4)4- tetrahedron The crystobalite crystal structure, can be envisioned as the diamond cubic structure with

an (SiO4)4- tetrahedron positioned on each lattice site Thus,

crystobalite has an FCC lattice with six atoms, or two tetrahedra, perlattice site.

The building block of silicon-based covalent ceramics (silicates, SiC and Si3N4): Si tetrahedron , e.g., SiO4 in silicates, SiC4 in

SiC , SiN4 in Si3N4.

E STRUCTURE OF COVALENT CERAMICS

F The Crystobalite Structure

F 12.9 F 3.11

F 12.10

F 12.9

F 3.4-6

 A number of ceramic crystal structures may

be considered in terms of close-packed planes

of ions, (the large anions), the cations may reside small interstitial sites

 Interstitial positions, two different types:

tetrahedral position and octahedral position, the coordination numbers for cations: 4and 6, respectively

 Two factors: (1) the stacking of the

close-packed anion layers: FCC or HCP (ABCABC……

or ABABAB…… ); (2) the interstitial sites: for example, the rock salt crystal structure

VIII Ceramic Crystal Structures From The Close Packing

of Anions

F 3.6-1

F 3.5-3 F 3.5-3

A Cubic close-Packed

 The structure in which the anions are in an FCC arrangement ： rock salt, rutile, zinc blende,

antifluorite, perovskite and spinel

 Rock salt structure ： cations on each of the

octahedral sites Zinc blende structure ： half the tetrahedral sites are filled

B Hexagonal close-packed

arsenide, cadmium odide, corundum, illmenite, and olivine

 For example, corundum (Al2O3): the oxygen ions are hexagonally close-packed, Al ions fill two-

thirds of octahedral sites Wurtzite: One-half the tetrahedral sites are filled

F 12.2 F 3.7-4

F 11.15

Other, but not all, ceramic crystal structures may

be treated in a similar manner, included are the zinc blende and perovskite sturctures

Spinel sturcture (AmBnXp): magnesium aluminate or

spinel (MgAl2O4): the O2 - ions form an FCC lattice, M2+

ions fill tetrahedral sites and Al3+ reside in octahedral

positions

Magnetic ceramics, or ferrites, have a crystal

structure that is a slight variant of this spinel

structure, and the magnetic characteristics are

affected by the occupancy of tetrahedral and

octahedral positions

C

N V

A A



n’ = the number of formula units’ within the unit cell

 AC = the sum of the atomic weights of all cations in the

formula unit

 AA = the sum of the atomic weights of all anions in the

formula unit

VC = the unit cell volume

NA = Avogadro’s number, 6.023  10 23 formula

units/mol

% theoretical density = measured density

theoretical density × 100%

Example

Problem

On the basis of crystal structure, compute the

theoretical density for sodium chloride How does

this compare with its measured density?

7 7

3

/ 14

.

2

10 023

6 10

181

0 2 10

102

0

2

45 35 99

22 4

2 2

cm g

NA r

r

A A

n

Cl Na

Cl Na

12.3 Silicate Ceramics

Silicates are materials composed primarily of silicon and

oxygen: soils, rocks, clays, and sand

Rather than unit cells, it is more convenient to use various arrangements of an SiO44- tetrahedron (Figure 12.9)

SILICA

Every corner oxygen atom in each tetrahedron is

shared by adjacent tetrahedra

Three primary polymorphic crystalline forms: quarttz,

cristobalite, and tridymite The atoms are not closely

packed to gether, silicas have relatively low densities

F12-9

F12-10

Silica Glasses

Noncrystalline solid or glass, called fused silica, or vitreous silica

Other oxides (e.g., B2O3 and GeO2) may also form glassy

structures these materials, as well as SiO2, are termed network

formers

Common inorganic glasses: silica glasses with added other oxides such as CaO and Na2O These oxides do not form polyhedral

networks, rather modify the SiO44- network: network modifiers

Other oxides, such as TiO2 and Al2O3, while not network

formers, substitute for silicon and become part of and stabilize the network; these are called intermediates

These modifiers and intermediates lowers the melting point and viscosity of a glass, and makes it easier to form at lower

temperatures

F12-11

THE SILICATES

One, two or three of the corner oxyge atoms of the SiO4-–4

thtrahedra are shared by other tetrahedra, examples: SiO44–,

Si2O76-and Si3O9–6, positively charged cations such as Ca2+,

Mg2+ , and Al3+ (1) compensate the negative charges from the SiO44- (2) ionically bond the SiO44- together

Simple Silicates

For example, forsterite (Mg2SiO4): every Mg 2+ ion has six

oxygen nearest neighbors

Akermanite (Ca2MgSi2O7) : Two Ca–2 and one Mg+2 bonded to eachSi2O7-6

F 12.12

Layered Silicates

Characteristic of the clays ( ：： ) and other minerals

Kaolinite ( ：：： ) clay has: Al2(Si2O5)(OH)4 , silica tetrahedral

layer (Si2O5)2- is made electrically neutral by an adjacent

Al2(OH)42+ layer, the bonding within this two layered sheet is

strong and intermediate ionic-covalent, adjacent sheets are only

loosely bound to one another by weak van der waals forces

A crystal of kaolinite is made of a series of these double

layers or sheets stacked parallel to each other, flat plates <1m

nearly hexagonal

Other minerals also in this group are talc ( ：： ) [Mg3(Si2O5)2(OH)2]

and the micas ( ：： )

[e.g., muscovite, KAl3Si3O10(OH)2]

DIAMOND

A metastable carbon polymorph at room temperature and

atmospheric pressure

Crystal structure: a variant of the zinc blende, carbon atoms

occupy all positions (both Zn and S) Each carbon bonds to four other carbons and totally covalent: diamond cubic crystal structure

[also: germanium, silicon, and gray tin, below 13℃ (55℉)]

F12-15

12.4 CARBON

Various polymorphic forms: graphite, diamond, fullerenes,

carbon nanotubes, as well as in the amorphous state

Potential applications: gears, optical recording heads and

disks, and as substrates for semiconductor devices

F12-16

Physical properties: extremely hard (the hardest known

material ), a very low electrical conductivity, an unusually high thermal conductivity, optically transparent in the visible and

infrared regions, high index of refraction

Industrial applications: to grind or cut other softer materials.Synthetic diamonds beginning in the mid-1950s, today a large proportion of the industrial-quality materials are man-made

interplanar bonds : excellent lubricative properties of graphite

Electrical conductivity is relatively high in crystallographic directions

parallel to the hexagonal sheets.

Other desirable properties: high strength, and good chemical stability at elevated temperatures and in nonoxidizing atmospheres, high thermal

conductivity, low coefficient of thermal expansion, high resistance to

thermal shock, high adsorption of gases , good machinability.

Applications: heating elements, electrodes for arc welding, metallurgical crucibles, insulations in rocket nozzles, chemical reactor vessels, electrical contacts, brushes and resistors, electrodes in batteries in air purification devices

F12-17

Today a large proportion of the industrial-quality materials are

man-made,diammond thin films

For example, the surfaces of drills, dies, bearings, knives, and

other tools have been coated with diamond films to increase surface hardness; some lenses and radomes.Potential applications: gears, to optical recording heads and disks, and as substrates for

GRAPHITE

Crystal structure more stable than diamond at ambient temperature and pressure.layers of hexagonally arranged carbon atoms; within the layers: strong covalent bonds Van der Waals type of bond between the layers

Weak interplanar bonds, excellent lubricative properties of graphite.Electrical conductivity is reatively high in crystallographic

directions parallel to the hexagonal sheets