Crystal Structure

Crystal Structure Metals-Ceramics

Ashraf Bastawros www.public.iastate.edu\~bastaw\courses\Mate271.html

Material Sciences and Engineering MatE271

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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 Material Sciences and Engineering

Material Sciences and Engineering, MatE271

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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.

Material Sciences and Engineering

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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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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

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0.155 - 0.225

Triangular

4

0.255 - 0.414

Tetrahedron

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0.414-0.732

Octahedron

8

0.732 - 1

Cube Center

rcation /r anion Material Sciences and Engineering


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Interstitial sites (Octahedral)

FCC

BCC


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Interstitial sites (Tetrahedral)

BCC



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


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 Material Sciences and Engineering


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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 Material Sciences and Engineering


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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 Material Sciences and Engineering

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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 =


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 Material Sciences and Engineering


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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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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) Material Sciences and Engineering


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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 Material Sciences and Engineering


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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 Material Sciences and Engineering

Compute planar area Compute total “circle” area

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Semiconductor Structures ¬

Technologically, single crystals are very important

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More “perfect” than any other class of materials (purer, fewer dislocations)

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Elemental semiconductors (Si and Ge) are of the diamond cubic structure

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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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