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