Crystal Structure
Metals-Ceramics
Ashraf Bastawros
www.public.iastate.edu\~bastaw\courses\Mate271.html
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Week 3
1
Ceramic Crystal Structures
- Broader range of chemical composition than metals
with more complicated structures
- Contains at least 2 and often 3 or more atoms.
- Usually compounds between metallic ions (e.g. Fe,
Ni, Al) - called cations - and non-metallic ions (e.g.
O, N, Cl) - called anions
- Bonding will usually have some covalent character but
is usually mostly ionic
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1
Ceramic Crystal Structure
o Still based on 14 Bravais lattices
o Cation: Metal, positively charged, usually
smaller
o Anion: Usually O, C, or N, negative charge,
usually larger.
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How do Cations and Anions arrange
themselves in space???
• Structure is determined by two characteristics:
1. Electrical charge
- Crystal (unit cell) must remain electrically
neutral
- Sum of cation and anion charges in cell is 0
2. Relative size of the ions
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2
Ceramic Crystal Structures
- The ratio of ionic radii (rcation /r anion ) dictates
the coordination number of anions around each
cation.
- As the ratio gets larger (i.e. as rcation /r anion
1)
the coordination number gets larger and larger.
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Where do Cations and Anions fit ?
CN
Radius Ratio
Geometry
3
0.155 - 0.225
Triangular
4
0.255 - 0.414
Tetrahedron
6
0.414-0.732
Octahedron
8
0.732 - 1
Cube Center
rcation /r anion
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3
Interstitial sites (Octahedral)
FCC
BCC
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Interstitial sites (Tetrahedral)
BCC
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FCC
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Interstitial sites
-Any close packed array of N atoms contains
N octahedral interstitial sites
2N tetrahedral sites
- Octahedral sites are larger than tetrahedral sites
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Week 3
Some common ceramic structures
Structure
Lattice
Ch. formula
Cesium Chloride (CsCl)
SC
MX
Rock salt (NaCl)
FCC
MX
Fluorite (CaF2)
FCC
MX2
Silicates (complex) (SiO2)
FCC
MX2
Corundum (Al2O3)
hexagonal
M2X3
Perovskite (CaTiO3)
SC
M’M’’X3
Spinel (MgAlO4 )
FCC
M’M’’ X4
Diamond
FCC
Graphite
hexagonal
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Note: What defines a lattice point
No of lattice (basis) points/unit cell
SC=1
BCC=2
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FCC=4
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Cesium Chloride (CsCl)
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Lattice: SC
Chemical formula: MX
- Atoms per lattice point =
- Formula units/unit cell =
Cs located on cube center
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Differences between CsCl (SC) and Cr (BCC)
Cs
Cr
Cl
CsCl (SC)
Cr (BCC)
No lattice point/unit cell
one: (0,0,0)
two: (0,0,0),
(0.5,0.5,0.5)
No atoms/lattice point
two: (0,0,0),
(0.5,0.5,0.5)
One/lattice pt.
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Rock Salt Structure (NaCl)
Lattice: FCC
Chemical formula: MX
- Atoms per lattice point =
- Formula units/unit cell =
MgO, FeO, NiO, CaO also
have rock salt structure
Na located on octahedral sites
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7
Flourite Structure (CaF2 )
¼ distance of body diagonal
Ca2+
F
_
Lattice: FCC
Chemical formula: MX2
_
Ion/ Unit Cell: 4 Ca2++ 8 F = 12
Typical Ceramics: UO2 , ThO2 , and TeO2
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Corundum Structure (Al2O3)
Lattice: hexagonal
Chemical formula: M2X3
_
Ion/ Unit Cell: 12 Al3++ 18 O2
= 30
Typical Ceramics:
Al2O3 , Cr2O3 , α Fe2O3
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Perovskite Structure (BaTiO3 , Ca TiO3)
Lattice: SC
Chemical formula: M’ M’’ X3
Atoms per lattice point =
Ion/ Unit Cell =
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Ferroelectric
Piezoelectric
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Diamond Cubic Structure
¬
All atoms are C
¬
4 interior C atoms
(tetrahedrally coordinated with
corner and face-centered C
atoms)
¬ Covalent bonds (extremely strong)
¬ HARD
¬ Low electrical conductivity
¬ Optically transparent
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Diamond Thin Film
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Carbon - Graphite
not
hcp
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Fullerenes
Buckyball
C60
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Glass Structure
¬
The basic structural unit of a silicate glass is
the SiO4 tetrahedron
¬
Link together sharing corners to form a 3-D
network
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Glass Structure
¬
Beyond the short range order the structure is random
¬
Other ions may also be present
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Polymorphism and Allotropy
¬ Some materials may have more than one crystal
structure depending on temperature and pressure - called
POLYMORPHISM
¬
Carbon (diamond, graphite, fullerenes)
¬
Silica (quartz, tridymite, cristobalite, etc.)
¬
Iron (ferrite, austenite)
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12
Polymer Structures
¬ Chainlike structures of long polymeric molecules
(usually involving C, H, and O + other elements)
¬
Usually mostly noncrystalline
– Extremely complex and elongated molecules do not
readily “line up” on cooling to crystallize
¬
Structure is very dependent on thermal history
(so are properties)
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Atomic Densities
- Why do we care?
- Properties, in general, depend on linear and planar
density.
- Examples:
- Speed of sound along directions
- Slip (deformation in metals) depends on linear & planar
density
- Slip occurs on planes that have the greatest density
of atoms in direction with highest density
(we would say along closest packed directions on the closest packed
planes)
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Linear and Planar Densities
Linear Densities
fraction of line length in a particular direction
that passes through atom centers
Planar Densities
fraction of total crystallographic plane area that
is occupied by atoms (plane must pass
through center of atom)
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Calculate the Linear Density
o Calculate the linear density of the (100)
direction for the FCC crystal
LD = LC/LL
density
LC = 2R
LL = a
linear
circle length
line length
For FCC a = 2R√2
LD = 2R/(2R√2) = 0.71
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14
Calculate the Planar Density
o Calculate the planar density of the (110)
plane for the FCC crystal
C
A B C
B
A
D E F
F
•
•
E
D
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Compute planar area
Compute total “circle” area
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Semiconductor Structures
¬
Technologically, single crystals are very important
¬
More “perfect” than any other class of materials
(purer, fewer dislocations)
¬
Elemental semiconductors (Si and Ge) are of the
diamond cubic structure
¬
Compound semiconductors (GaAs, CdS) have
zincblende (similar to diamond cubic)
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Reading Assignment
Shackelford 2001(5th Ed)
– Read Chapter 3, pp 59-64
Read ahead to page 88, 101-110
Check class web site:
www.public.iastate.edu\~bastaw\courses\Mate271.html
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