分析材料科學(xué)3 chapter

CHAPTER3:

CRYSTAL

STRUCTURES&PROPERTIES

ISSUESTOADDRESS...

Howdoatomsassembleintosolidstructures?(fornow,focusonmetals)

Howdoesthedensityofamaterialdependonitsstructure?

Whendomaterialpropertiesvarywiththesample(i.e.,part)orientation?

1

EnergyandPacking

?

Nondense,randompacking

Energy

typicalneighborbondlength

typicalneighborbondenergy

r

?

Dense,orderedpacking

Energy

typicalneighborbondlength

r

typicalneighbor

bondenergy

2

Dense,orderedpackedstructurestendtohavelowerenergies.

MATERIALSANDPACKING

Crystallinematerials...Long-rangeOrder

atomspackinperiodic,3Darrays

typicalof:

-metals

-manyceramics

-somepolymers

crystallineSiO2

Si

Oxygen

Noncrystallinematerials...

atomshavenoperiodicpacking

occursfor:

-complexstructures

-rapidcooling

"Amorphous"=Noncrystalline

noncrystallineSiO2

3

Lattice+Basis=Crystal

Lattice點(diǎn)陣

Structure

Networkinwhichcrystalstructuresareembedded

Describedby

Specifyingtheatomspositionsinarepeatingunitcell

Referringtheatomstothepointsofintersectionoflines

Basis結(jié)構(gòu)基元

–“Groupofthings”locatedatthelatticepoint

UnitCell晶胞

–Smallestregionthatcompletelydescribesthepattern

Eachlatticepointhasidenticalsurroundingenvironment

CrystalSystems

Unitcell:

smallestrepetitivevolumewhich

containsthecompletelatticepatternofacrystal.

7

crystalsystems

theunitcellgeometry.

crystallattices

thegeometryandatomicarrangements

14

a,b,andcarethelatticeconstants

Fig.3.4,Callister&Rethwisch8e.

5

SevenDistinctsystems

6

Cubic立方

Tetragonal長(zhǎng)方

Hexagonal六方

orthorhombic正交

Rhombohedral斜方

Monoclinic單斜晶系

Triclinic三斜晶系

MetallicCrystalStructures

Mostelementalmetals(about90%)crystallizeintothreedenselypackedcrystalstructures:

?

Body-centeredcubic(BCC

Face-centeredcubic(FCC

體心立方)

面心立方)

–Hexagonalclose-packed(HCP密排六方)

7

BODYCENTEREDCUBICSTRUCTURE(BCC)

?Atomstouchalongbodydiagonal

--Note:Allatomsareidentical;thecenteratomisshadeddifferentlyonlyforeaseofviewing.

Ex:Fe,W,Mo,Nb,Ta,V,Cr

8

Coordination#=

Thenumberofthenearest–neighbouratoms

8

ATOMICPACKINGFACTOR:

BCC

Unitcellcontains:1+8x1/8

=2atoms/unitcellClose-packeddirections:

length=4R

=

3a

atoms

volume

Closepackeddirectionsarebodydiagonals.

unitcell

APF=

atom

volume

a3

unitcell

?

APFforabody-centeredcubicstructure=0.68

9

2

4(3a/4)3

3

APF=Volumeofatomsinunitcell*

Volumeofunitcell

*assumehardspheres

FACECENTEREDCUBICSTRUCTURE(FCC)

Atomstouchalongfacediagonal

Ex:Cu,Ag,Au,Al,Ni,Pt,Fe,Co…

?

Coordination#=12

Thenumberofthenearest

–neighbouratoms

4atoms/unitcell:6facex1/2+8cornersx1/8

10

FACECENTEREDCUBICSTRUCTURE(FCC)

AtomPackingFactor

#ofatoms/cell=8x(1/8)+6x(1/2)=4

=4/3R3

Vcell

=a3

;

Vatom

Relation:

4Ra

2

atoms

volume

unitcell

APF=

atom

volume

a3

unitcell

=0.74

11

4

4(2a/4)3

3

HEXAGONAL

CLOSE-PACKED

STRUCTURE(HCP)

Hexagonal

Ideal:c/a=1.633

a=b≠c

°

°

?

Ex:Mg,Zn,Be,Ti,Co

12

HEXAGONALCLOSE-PACKEDSTRUCTURE(HCP)

12

?

Coordination

#

=

Unitcellcontains:3+1/6X12+1/2X2

=6atoms/cell

APF=0.74

Thisisaclose

Packedstructure

13

FCCStackingSequence

ABCABC...StackingSequence2DProjection

?

?

B

B

C

B

A

B

B

Asites

Bsites

Csites

C

B

C

B

A

?

FCCUnitCell

BC

14

HexagonalClose-PackedStructure(HCP)

ABAB...StackingSequence

?

?

3DProjection

?

2DProjection

Asites

Top

layer

c

Middlelayer

Bsites

Asites

AdaptedfromFig.3.3(a),

Callister&Rethwisch8e.

Bottomlayer

a

15

TheoreticalDensity,

MassofAtomsinUnitCell

TotalVolumeofUnitCell

Density==

nAVCNA

=

where

n=numberofatoms/unitcell

A=atomicweight

VC=Volumeofunitcell=a3forcubic

NA=Avogadro’snumber

=6.022x1023atoms/mol

16

TheoreticalDensity,

?

Ex:Cr(BCC)

A=52.00g/mol

R=0.125nm

n=2atoms/unitcell

R

a=4R/3=0.2887nm

a

Adaptedfrom

Fig.3.2(a),Callister&Rethwisch8e.

atoms

g

unitcell

=volume

theoretical

=7.18g/cm3

=7.19g/cm3

mol

actual

atoms

mol

unitcell

17

a3

6.022x1023

2

52.00

DensitiesofMaterialClasses

Ingeneral

Graphite/Ceramics/Semicond

Metals/Alloys

Composites/fibers

metals>ceramics

>polymers

30

Polymers

Why?

Metalshave...

close-packing

BasedondatainTableB1,Callister

*GFRE,CFRE,&AFREareGlass,Carbon,&AramidFiber-ReinforcedEpoxycomposites(valuesbasedon60%volumefractionofalignedfibers

inanepoxymatrix).

20

10

(metallicbonding)

oftenlargeatomicmasses

Ceramicshave...

lessdensepacking

oftenlighterelements

Polymershave...

lowpackingdensity(oftenamorphous)

lighterelements(C,H,O)

Compositeshave...

intermediatevalues

5

4

3

2

1

0.5

0.4

0.3

DatafromTableB.1,Callister&Rethwisch,8e.

18

(g/cm3)

PlatinumGold,WTantalum

Silver,Mo

Cu,NiSteelsTin,Zinc

Titanium

AluminumMagnesium

Zirconia

AloxideDiamondSinitride

Glass-sodaConcreteSilicon

Graphite

GlassfibersGFRE*

CarbonfibersCFRE*

AramidfibersAFRE*

Wood

PTFE

SiliconePVCPETPC

HDPE,PSPP,LDPE

CrystalsasBuildingBlocks

Someengineeringapplicationsrequiresinglecrystals:

?

--turbineblades

Fig.8.33(c),Callister&Rethwisch8e.(Fig.8.33(c)courtesyofPrattandWhitney).

--diamondsinglecrystalsforabrasives

(CourtesyMartinDeakins,GESuperabrasives,Worthington,OH.Usedwithpermission.)

?

Propertiesofcrystallinematerialsoftenrelatedtocrystalstructure.

--Ex:

Quartzfracturesmoreeasily

alongsomecrystalplanesthanothers.

(CourtesyP.M.Anderson)

19

Polycrystals

Mostengineeringmaterialsarepolycrystals.

Anisotropic

?

AdaptedfromFig.K,colorinsetpagesofCallister5e.

(Fig.KiscourtesyofPaulE.Danielson,TeledyneWahChangAlbany)

1mm

Isotropic

?

?

?

Nb-Hf-Wplatewithanelectronbeamweld.Each"grain"isasinglecrystal.

Ifgrainsarerandomlyoriented,

overallcomponentpropertiesarenotdirectional.

Grainsizestypicallyrangefrom1nmto2cm

(i.e.,fromafewtomillionsofatomiclayers).

?

20

SINGLEVSPOLYCRYSTALS

?

SingleCrystals

-Propertiesvarywithdirection:anisotropic各向異性.

-Example:themodulus

ofelasticity(E)inBCCiron:

Polycrystals

-Propertiesmay/maynotvarywithdirection.

E(diagonal)=273GPa

atomsalongtheedgearemoreseparatedthanalongthefacediagonal.

E(edge)=125GPa

?

200m

-Ifgrainsarerandomlyoriented:isotropic.各向同性

(Epolyiron

=210GPa)

-Ifgrainsaretextured,anisotropic.

21

Polymorphism

Twoormoredistinctcrystalstructuresforthesamematerial(allotropy/polymorphism)

ironsystem

?

titanium

,-Ti

liquid

1538oC

-Fe1394oC

-Fe

912oC

-Fe

BCC

carbon

diamond,graphite

FCC

BCC

22

CrystalPositions,Directions,andPlanes

?Specifyaparticularpointwithinaunitcell,acrystallographicdirection,orsomecrystallographicplaneofatoms.

?Threenumbersorindicesareusedtodesignatepointlocations,directions,andplanes.

?Right-handedcoordinatesystemsituatedatoneofthe

cornersandcoincidingwiththeunitcelledges

23

Crystallographic

Algorithm

Directions

z

Vectorrepositioned(ifnecessary)topassthroughorigin.

Readoffprojectionsintermsofunitcelldimensionsa,b,andc

Adjusttosmallestintegervalues

Encloseinsquarebrackets,nocommas

[uvw]

y

x

ex:1,0,?

-1,1,1

=>

=>

2,0,1

[111]

=>

[201]

whereoverbarrepresentsanegativeindex

24

Crystallographic

directions

[001]

[111]

[011]

<100>cubeedges

[101]

<011>facediagonals

<111>cubediagonals

[010]

[110]

[100]

25

LinearDensity

Numberofatoms

LinearDensityofAtomsLD=

Unitlengthofdirectionvector

[110]

ex:

lineardensityofAlin[110]

direction

a=0.405nm

#atoms

LD

length

a

AdaptedfromFig.3.1(a),

Callister&Rethwisch8e.

26

2a

3.5nm1

2

Crystallographic

Planes

?

MillerIndices:

Reciprocalsofthe(three)axial

interceptsforaplane,clearedoffractions&commonmultiples.AllparallelplaneshavesameMillerindices.

Algorithm

?

1.

Readoffinterceptsofplanewithaxesin

termsofa,b,c

Takereciprocalsofintercepts

Reducetosmallestintegervalues

Encloseinparentheses,nocommasi.e.,(hkl)

27

Crystallographic

Planes

z

c

c

1/

0

0

example

a

1

1/1

1

1

(110)

b

1

1/1

1

1

1.

2.

Intercepts

Reciprocals

y

3.

4.

Reduction

MillerIndices

a

b

x

z

b

1/

0

0

c

1/

0

0

example

a

1/2

1/?

2

2

(100)

1.

2.

Intercepts

Reciprocals

c

3.

4.

Reduction

MillerIndices

y

a

b

x

28

Crystallographic

Planes

z

c

a

1/2

1/?

2

6

(634)

b

1

1/1

1

3

c

3/4

1/?

4/3

4

x

example

InterceptsReciprocals

1.

2.

b

y

a

3.

4.

Reduction

MillerIndices

FamilyofPlanes

{hkl}

Ex:

{100}=(100),(010),(001),(100),(010),(001)

29

FamiliesofPlanes

Z

?Groupsofplanesthatareequivalent

（110）

?Denotedby{hkl}

（101）

（011）

（011）

（101）

Y

（110）

X

{110}

PlanarDensity

PlanarDensityofAtomsPD

Atomscenteredontheplane

=

area

Examples:

Draw(100)and(111)crystallographicplanesforFe(BCC).

Calculatetheplanardensityforeachoftheseplanes.

31

PlanarDensityof(100)Iron

Solution:

AtT<912oCironhastheBCCstructure.

2Drepeatunit

a4 3R

3

(100)

RadiusofironR=0.1241nm

AdaptedfromFig.3.2(c),Callister&Re