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

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- 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

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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 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

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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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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

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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

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Corundum Structure (Al2O3)

Lattice: hexagonalChemical formula: M2X3Ion/ Unit Cell: 12 Al3++ 18 O2

_

= 30Typical Ceramics:Al2O3 , Cr2O3 , α Fe2O3

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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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Diamond Thin Film

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Carbon - Graphite

not

hcp

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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)

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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 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

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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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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

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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 2