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Material Sciences and Engineering, MatE271 1
Material Sciences and Engineering MatE271 1
Crystal StructureMetals-Ceramics
Ashraf Bastawros
www.public.iastate.edu\~bastaw\courses\Mate271.html
Week 3
Material Sciences and Engineering MatE271 Week 3 2
- 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
Ceramic Crystal Structures
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o Still based on 14 Bravais latticeso Cation: Metal, positively charged, usually
smallero Anion: Usually O, C, or N, negative charge,
usually larger.
Ceramic Crystal Structure
Material Sciences and Engineering MatE271 Week 3 4
How do Cations and Anions arrange themselves in space???
� Structure is determined by two characteristics:1. Electrical charge
- Crystal (unit cell) must remain electricallyneutral
- Sum of cation and anion charges in cell is 0
2. Relative size of the ions
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- 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.
Ceramic Crystal Structures
Material Sciences and Engineering MatE271 Week 3 6
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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Material Sciences and Engineering MatE271 Week 3 7
Interstitial sites (Octahedral)
BCCFCC
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Interstitial sites (Tetrahedral)
BCC FCC
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-Any close packed array of N atoms contains
N octahedral interstitial sites
2N tetrahedral sites
- Octahedral sites are larger than tetrahedral sites
Interstitial sites
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Some common ceramic structures
FCCDiamond
M�M��X3SCPerovskite (CaTiO3)
hexagonalGraphite
M�M�� X4FCCSpinel (MgAlO4 )
M2X3hexagonalCorundum (Al2O3)
MX2FCCSilicates (complex) (SiO2)
MX2FCCFluorite (CaF2)
MXFCCRock salt (NaCl)
MXSCCesium Chloride (CsCl)
Ch. formulaLatticeStructure
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Note: What defines a lattice point
No of lattice (basis) points/unit cell
SC=1 BCC=2 FCC=4
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Cesium Chloride (CsCl)Lattice: SCChemical 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)
One/lattice pt. 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: (0,0,0)No lattice point/unit cell
Cr (BCC)CsCl (SC)
Cs
Cl
Cr
Material Sciences and Engineering MatE271 Week 3 14
Rock Salt Structure (NaCl)
Lattice: FCCChemical 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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Flourite Structure (CaF2 )
Ca2+
F _
Lattice: FCCChemical formula: MX2Ion/ Unit Cell: 4 Ca2++ 8 F
_= 12
Typical Ceramics: UO2 , ThO2 , and TeO2
¼ distance of body diagonal
Material Sciences and Engineering MatE271 Week 3 16
Corundum Structure (Al2O3)
Lattice: hexagonalChemical formula: M2X3Ion/ Unit Cell: 12 Al3++ 18 O2
_
= 30Typical Ceramics:Al2O3 , Cr2O3 , α Fe2O3
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Material Sciences and Engineering MatE271 Week 3 17
Perovskite Structure (BaTiO3 , Ca TiO3)
Lattice: SCChemical formula: M� M�� X3Atoms per lattice point = Ion/ Unit Cell =
FerroelectricPiezoelectric
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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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Material Sciences and Engineering MatE271 Week 3 19
Diamond Thin Film
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Carbon - Graphite
not
hcp
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Material Sciences and Engineering MatE271 Week 3 21
Fullerenes
BuckyballC60
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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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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)
Material Sciences and Engineering MatE271 Week 3 26
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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Material Sciences and Engineering MatE271 Week 3 27
Linear Densitiesfraction of line length in a particular direction that passes through atom centers
Planar Densitiesfraction of total crystallographic plane area that is occupied by atoms (plane must pass through center of atom)
Linear and Planar Densities
Material Sciences and Engineering MatE271 Week 3 28
Calculate the Linear Density
o Calculate the linear density of the (100) direction for the FCC crystal
LD = LC/LL linear densityLC = 2R circle lengthLL = a line length
For FCC a = 2R√2
LD = 2R/(2R√2) = 0.71
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Material Sciences and Engineering MatE271 Week 3 29
Calculate the Planar Density
o Calculate the planar density of the (110) plane for the FCC crystal
A B C
D E FA
BC
DE
F� Compute planar area� Compute total �circle� area
Material Sciences and Engineering MatE271 Week 3 30
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)