Chapter 3 –

Structures of Metals and Ceramics

•

Non dense, random

packing

• Dense, regular

packing

Dense, regularly-packed structures tend to havelower energy.

Energy

r

typical neighbor bond length

typical neighbor bond energy

Energy

r

typical neighbor bond length

typical neighbor bond energy

ENERGY AND PACKING

Order in solids -

definitions

•

Amorphous materials –

Short range order 

–

No long range order

–

Common examples: SiO2 glass,  

some polymers•

Crystalline materials–

Short and long range order

–

Common examples: metals, 

quartz (crystalline form of SiO2)

Diatomic gas 

molecule

Si04 tetrahedron4-

Si4+

O2-

(4 oxygen form a tetrahedron)

Examples of SRO

Concept visualization: Crystalline vs

Amorphous

Regular arrangement of building blocks: Long range order

Irregular arrangement of building blocks

Long Range Order: lattice

Crystal Lattice

Systems

•

tend to be densely packed-

Only one element, so all atomic radii are the same.

- Metallic bonding is not directional, electrons shared by all

- Cubic system- Hexagonal system

Simple Crystal Structures: Elemental Metals

Planes and directions identification – LATER

aLattice parameter

Cubic system3 lattice parametersare all the same, a

•

Rare due to poor packing

(only Po has this structure)

•

Close-packed directions

are cube edges.

•

Coordination #

= 6

(# nearest neighbors)

SIMPLE CUBIC STRUCTURE (SC)

Octahedral bonding!How many atoms in the unit cell?

APF = Volume of atoms in unit cell*

Volume of unit cell

*assume hard spheres

•

APF for a simple cubic structure = 0.52

APF = a3

4

3π (0.5a)31

atoms

unit cellatom

volume

unit cellvolume

close-packed directions

a

R=0.5a

contains 8 x 1/8 = 1 atom/unit cell

Adapted from Fig. 3.19,Callister 6e.

ATOMIC PACKING FACTOR

•

Coordination # = 8

Adapted from Fig. 3.2,Callister 6e.

(Courtesy P.M. Anderson)

•

Close packed directions are cube diagonals.

--Note: All atoms are identical; the center atom is shadeddifferently only for ease of viewing.

BODY CENTERED CUBIC STRUCTURE (BCC)

Click on image to animate

•

Coordination # = 12

Adapted from Fig. 3.1(a),Callister 6e.

(Courtesy P.M. Anderson)

•

Close packed directions are face diagonals.--Note: All atoms are identical; the face-centered atoms are shaded

differently only for ease of viewing.

FACE CENTERED CUBIC STRUCTURE (FCC)

Click on image to animate

APF = a3

4

3π ( 2a/4)34

atoms

unit cell atomvolume

unit cell

volume

Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell

a

•

APF for a body-centered cubic structure = 0.74

Close-packed directions: length = 4R

= 2 a

Adapted fromFig. 3.1(a),Callister 6e.

ATOMIC PACKING FACTOR: FCC

•

Coordination # = 12

•

ABAB... Stacking Sequence

• APF = 0.74

•

3D Projection •

2D Projection

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

Adapted from Fig. 3.3,Callister 6e.

HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

Translatable unit cell

Not centered in unit cell!

Lattice parameters a and c

HCP and FCC Both have close packed planes –

difference is stacking sequence of close packed planesCoordination = 12

FCC – Stacking ABC HCP – Stacking ABAB

•

ABCABC... Stacking Sequence

•

2D Projection

A sites

B sites

C sitesB B

B

BB

B BC C

CA

A

•

FCC Unit Cell

AB

C

FCC STACKING SEQUENCE

Example: Copper

ρ = n AVcNA

# atoms/unit cell Atomic weight (g/mol)

Volume/unit cell

(cm3/unit cell)Avogadro's number

(6.023 x 1023 atoms/mol)

Data from Table inside front cover of Callister (see next slide):•

crystal structure = FCC: 4 atoms/unit cell•

atomic weight = 63.55 g/mol

(1 amu = 1 g/mol)•

atomic radius R = 0.128 nm (1 nm = 10 cm)-7

Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3

Compare to actual: ρCu = 8.94 g/cm3Result: theoretical ρCu = 8.89 g/cm3

THEORETICAL DENSITY, ρ

Mass per unit cell (g/unit cell)

Ceramic Structures

•

Bonding:--

valence shell

--

net charge in thestructure shouldbe zero.

--

chemical formula:AmXp

m, p determined by charge neutrality•

Cation/Anion size :--maximize the # of contacting nearest oppositely

charged neighbors.

Coordination number

- -

- -+

unstable

- -

- -+

stable

- -

- -+

stable

CaF2: Ca2+

cationF-

F-

anions+

Ceramic Structure

•

Coordination # increases with

rcationranion

rcationranion

Coord #

< .155 .155-.225 .225-.414 .414-.732 .732-1.0

ZnS (zincblende)

NaCl (sodium chloride)

CsCl (cesium

chloride)

2 3 4 6 8

Cation

Coordination #

•

On the basis of ionic radii, what crystal structurewould you predict for FeO?

Cation

Al3+

Fe2+

Fe3+

Ca2+ Anion

O2-

Cl-

F-

Ionic radius (nm)

0.053

0.077

0.069

0.100

0.140

0.181

0.133

• Answer:

rcationranion

=0.0770.140

= 0.550

based on this ratio,--coord # = 6--structure = NaCl

Data from Table 12.3, Callister 6e.

EX: PREDICTING STRUCTURE OF FeO

Impact of Chemical formula

75.0133.0

1.0==

F

Ca

rr

92.0184.0170.0

==Cl

Cs

rr

Cs : +1Cl : -1

Ca : +2F : -1

Same coordination

•

Quartz is crystallineSiO2:

Si4+

Na+

O2-

•

Basic Unit:

Si04 tetrahedron4-

Si4+

O2-

•

Glass is amorphous

•

Amorphous structureoccurs by adding impurities(Na+,Mg2+,Ca2+, Al3+)

•

Impurities:interfere with formation ofcrystalline structure.

(soda glass)

Adapted from Fig. 12.11, Callister, 6e.

GLASS STRUCTURE

Chapter 3 – Structures of Metals and CeramicsENERGY AND PACKINGOrder in solids - definitionsConcept visualization: �Crystalline vs AmorphousLong Range Order: lattice Crystal Lattice SystemsSimple Crystal Structures: Elemental MetalsSIMPLE CUBIC STRUCTURE (SC)ATOMIC PACKING FACTORBODY CENTERED CUBIC STRUCTURE (BCC)FACE CENTERED CUBIC STRUCTURE (FCC)ATOMIC PACKING FACTOR: FCCHEXAGONAL CLOSE-PACKED STRUCTURE (HCP)HCP and FCC FCC STACKING SEQUENCETHEORETICAL DENSITY, rCeramic StructuresCeramic StructureCation Coordination # EX: PREDICTING STRUCTURE OF FeOImpact of Chemical formula GLASS STRUCTURE