03 crystal structure

8/8/2019 03 Crystal Structure

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CHAPTERCHAPTER 33::STRUCTURE OFSTRUCTURE OF

CRYSTALLINE SOLIDSCRYSTALLINE SOLIDS


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MOSFETMOSFET


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SiO2 (amorphous)

Si (crystalline)


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Materials and packing:

atoms pac in perio ic, D arrays

typical of: -metals--some polymers

crystalline SiOcrystalline SiO22

Si Oxygen

occurs for: -complex structures

-ra id coolin

"Amorphous" = Noncrystalline

noncrystalline SiOnoncrystalline SiO22


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Hard sphere model and lattice:

Atomic hard sphere model is used to describe thearrangement of atoms.

Lattice:A 3D array ofpoints in spacecoinciding w ith

(or sphere centers).


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Unit cell:

(Lattice cell)Smallest structuralunit that describes

the symmetrycrystal structure.Small repeat entities.


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cubes or similar geometrical tools to represent a unit cell.


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Metallic CrystalsMetallic Crystals

tend to be densely packed.

have several reasons for dense packing:

-Typically, only one element is present, so all atomicradii are the same.

-Metallic bonding is not directional.-

order to lower bond energy.

.

We will look at three such structures...


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SSimpleimple CCubic (SC)ubic (SC)

Rare for metals due to poor packing (only PoPoloniom has this structure)

Close-packed directions are cube edges.

=

(# nearest neighbors)Examples: CsCl, brass


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FF -- n rn rCCubic (FCC)ubic (FCC)

Examples: Cu, Al, Ag, Au


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BBodyody--CCenteredentered CCubic (BCC)ubic (BCC)

Examples: Fe(), Cr, Mo


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HHexagonalexagonal CCloselose--PPacked (HCP)acked (HCP)

Examples: Mg, Ti, Zn,


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6


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Characteristics of Selected Elements at 20CElementAluminum

SymbolAl

.(amu)26.98

(nm)0.143------

(g/cm3)2.71------

StructureFCC------

BariumBerylliumBoron

BaBeB

.137.339.01210.81

0.2170.114------

3.51.852.34

BCCHCPRhomb Adapted from

BromineCadmiumCalcium

BrCdCa

79.90112.4140.08

------0.1490.197

------8.651.55

------HCPFCC

a e, arac-teristics ofSelectedElements",inside front

CarbonCesiumChlorine

CCsCl

12.011132.9135.45

0.0710.265------

2.251.87------

HexBCC------

cover,

Callister 6e.

rom umCobaltCopper

rCoCu

.58.9363.55

.0.1250.128

.8.98.94------

HCPFCC

GalliumGermaniumGold

GaGeAu

.69.7272.59

0.1220.1220.144

5.905.3219.32

Ortho.Dia. cubicFCC

15

HeliumHydrogen

HeH

4.0031.008

------------

------------

------------


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DENSITIES OF MATERIAL CLASSES

Graphite/Ceramics/Semicond

Metals/Alloys

Composites/fibers

Polymersmetals> ceramics> polymers

20Based on data in Table B1, Callister

*GFRE, CFRE, & AFRE are Glass,Carbon, & Aramid Fiber-ReinforcedEpoxy composites (values based onTantalum

Gold, WPlatinumMetals have...

close-packing

3)

vo ume rac on o a gne ersin an epoxy matrix).10

SteelsCu,Ni

Tin, Zinc

Silver, Mo

Zirconia

(metallic bonding) large atomic mass

Ceramics have...

(g/c 3

4

Aluminum

Titanium

Glass-sodaConcrete

Si nitrideDiamondAl oxide

*

Glass fibers

less dense packing(covalent bonding)

1

Magnesium Graphite

HDPE, PSPCPETPVCSilicone

AFRE*

CFRE*Carbon fibers

Aramid fibersPolymers have...

poor packing

0.4

0.5

,

Wood

lighter elements (C,H,O)

Composites have...0.3 intermediate values

Data from Table B1, Callister 6e.


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Polymorphism,

polymorphism.If the material is an elemental solid, it is called allotropy. e.g. carbon, can exist as

But they all havedifferent

MacroscopicProperties


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Hybridization of Carbon atom

sp3 - Diamond

4 -electrons sp2 - Graphite

1 - and 3 -electrons

C

C ' C

120 C CC

C

C

sp1 (No pure C solids)

2 - and 2 -electrons

180

1CCC C

2


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Parameters defining a unit cell:

Different variations for unit cellsare possi e. Parameters escri ing

the unit cells are.2. Translation factors (Dimensions)

Lattice Parameters

mos o etime)


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of this coursecourse

Total of SEVENCRYSTAL STRUCTURES


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Plane A: (243)


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Planes that are crystallographicallyPlanes that are crystallographically

equivalent, which have the sameequivalent, which have the sameatomic packing.atomic packing.


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Atomic P lanar Density =Area occupied by the atoms on the plane

FCC (110 plane)

BCC 110 p ane


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((FCCFCC)) STACKING SEQUENCESTACKING SEQUENCE

ABCABC... Stack ing Sequence 2D Projection

BB

CA

A

s es

B sites B B

C C

C sites

FCC Unit CellA

B

C

11


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(HCP) STACKING SEQUENCESTACKING SEQUENCE

... ac ng equence

3D Projection 2D Projection

A sites Top layer

B sites

Middle layer


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HCP FCC

Blue shaded planes correspond to the highest planar packing.


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Types of CTypes of Crystal linerystal line sol idssolids

Single crystal: atoms are in a repeating or periodic array

Polycrystalline material:

ra ns:Orderely arrangementw ithin each grain,or en a on c anges n

The neighbouring grain


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Amorphous/CrystallineAmorphous/Crystalline

(c) 2003 Brooks/Cole Publishing / Thomson

Learning

tom c arrangements n crysta ne s con an amorp ous s con. aAmorphous silicon. (b) Crystalline silicon. Note the variation in the inter-atomic distance for amorphous silicon.


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SingleSingle CrystallineCrystal line Si Grow thSi Grow th

(a) Czochralski growth technique for growing single crystals of

. , , .VanZant, Fig. 3-7. Copyright 1997 The McGraw-Hill Companies.Reprinted with permission The McGraw-Hill Companies.) (b) Overall

.FromFundamentals of Modern Manufacturing, by M.P. Groover, p.849, Fig. 34-3. Copyright 1996 Prentice Hall.)


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Todays processor

Smart cards,displays

E-paper


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MonocrystallineSilicon Panel

PolycrystallineSilicon Panel

AmorphousSilicon Panel

SINGLE VS POLYCRYSTALS


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SINGLE VS POLYCRYSTALS

Single Crystals

-Pro erties var with

E (diagonal) = 273 GPaData from Table 3.3,Callister 6e.

direction: anisotropic.

-Example: the modulus

(Source of data isR.W. Hertzberg,Deformation and

Fracture Mechanics of

o e as c y n ron:

Pol cr stalsE (edge) = 125 GPa

,3rd ed., John Wileyand Sons, 1989.)

-Properties may/may notvar with direction.

200 m Adapted from Fig.4.12(b), Callister 6e.(Fig. 4.12(b) is

-If grains are randomlyoriented: isotropic.

courtesy of L.C. Smithand C. Brady, theNational Bureau ofStandards,

poly iron = a

-If grains are textured:anisotro ic.

,the National Instituteof Standards andTechnology,Gaithersburg, MD].)

19


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ANISOTROPY

-

The directional properties are related with the variance in

The de ree of anisotro increases

atomic an ionic spacing.

with decreasing structural symmetry.


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Diffraction - The constructive interference, or reinforcement, of a- .

diffracted beam provides useful information concerning thestructure of the material.

Braggs law - The relationship describing the angle at which a

beam of x-rays of a particular wavelength diffracts fromcrystallographic planes of a given interplanar spacing.

In a diffractometer a moving x-ray detector records the 2y anglesat which the beam is diffracted, giving a characteristic diffraction


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XRD

(a) Destructive andre n orc ng n erac onsbetween x-rays and thecrystalline material.

angles that satisfy Braggslaw.

c)2003Brooks/C

ole

earning

Publishing/Thomsn


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XRD

(c)2003Brooks/Cole

homsonLearni

ng

Diagram of a diffractometer,

showing powder sample, incidentPublishing/

and diffracted beams.


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Example:

For BCC iron, compute (a) the interplanar spacing, and (b) the diffraction angle forthe (220) set of planes. The lattice parameter for Fe is 0.2866 nm. Also, assume

. ,order of reflection is 1.


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amorphous structures.

,provided we know the atomic weight, atomicradius, and crystal geometry (e.g., FCC,

, .

Material properties generally vary with singlecrystal orientation (i.e., they are anisotropic),but properties are generally non-directional

(i.e., they are isotropic) in polycrystals withrandomly oriented grains.


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Readin Assi nment:

CHAPTER 3: The Structure of Crystalline Solidsof Callister

Crystal Structures Crystallographic Directions and Planes Crystalline and Non crystalline Materials

03 crystal structure

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