crystal imperfection ch 4

8/18/2019 Crystal Imperfection CH 4

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Chapter 4

Crystal Defects andNoncrystalline Structure–

Imperfection

ME 2105 – Dr. Lindeke


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In our pervious Lecture when

discussing Crystals we

ASSUMED PERFEC !RDER

In real materials we find:

Crystalline Defects or lattice irregularity

Most real materials have one or more “errors in perfection”

with dimensions on the order of an atomic diameter to many

lattice sites

De"ects can #e classi"ication$%& according to geo'etry

(point) line or plane*

+& di'ensions o" the de"ect


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alcohol. Mixing occurs on the

molecular scale.

We can defne thismixture/s!utin na "ei#ht r $atmic%

&asis

' simi!ar discussincan app!( t$mixtures% ) meta!s– ca!!ed a!!(s


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* +acancies,

-acant atmic sites in a structure.

* e!)-nterstitia!s,-extra atms psitined &et"een atmic sites.

int De)ects – in the s!idstate are mre predicta&!e

+acanc(

distrtin) p!anes

se!)-interstitia!distrtin) p!anes


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P!I, DEFECS

• he si'plest o" the point de"ect is a vacancy) or vacant lattice site&

• All crystalline solids contain vacancies&

• Principles o" ther'odyna'ics is used e-plain the necessity o" the

e-istence o" vacancies in crystalline solids&

• he presence o" vacancies increases the entropy (rando'ness* o"the crystal&

• he e.uili#riu' nu'#er o" vacancies "or a given .uantity o"

'aterial depends on and increases with te'perature as "ollows$ (an

Arrhenius 'odel*

N v= N exp(-Qv/kT)

Equilibrium no of vacancies

!otal no of atomic sites Energy required to form vacancy

T = absolute temperature in °Kelvin

k = gas or Boltzmann’s constant


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3" utcmes i) impurit( 6 added t hst '6,

* !id s!utin ) in ' i.e.7 randm dist. ) pintde)ects6

* !id s!utin ) in ' p!us partic!es ) a new phase usua!!( )r a !ar#er amunt ) 6

89

u&stitutina! s!ids!n.

e.#.7 Cu in :i6

nterstitia! s!ids!n.

e.#.7 C in ;e6

ecnd phase partic!e--di


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Solid solution of nickel in copper shown

along a (100) plane. This is asu&stitutina! solid solution with nickelatoms sustituting for copper atomson fcc atom sites.


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mper)ectins in !ids

Cnditins )r su&stitutina! s!id s!utin..6

• =ume – 9ther( ru!es – 1. ∆r atmic radius6 > 15?

– 2. rximit( in peridic ta&!e• i.e.7 simi!ar e!ectrne#atiities

– @. ame cr(sta! structure )r pure meta!s

– 4. +a!enc( eAua!it(• '!! e!se &ein# eAua!7 a meta! "i!! hae a #reater

tendenc( t diss!e a meta! ) hi#her a!enc( thanne ) !"er a!enc( it prides mre e!ectrns t the$c!ud%6


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mper)ectins in !ids

'pp!icatin ) =ume–9ther( ru!es – !id!utins

1. Wu!d (u predict

mre '! r '#t diss!e in Bn

2. Mre Bn r '!

in Cu

3a&!e n p. 107 !allister "e.

#lement $tomic !r%stal #lectro& 'alenceadius Structure nega&

(nm) tiit%

Cu 0.12F ;CC 1.G H2

C 0.01= 0.048 0.00'# 0.1445 ;CC 1.G H1'! 0.14@1 ;CC 1.5 H@C 0.125@ =C 1.F H2Cr 0.124G CC 1. H@;e 0.1241 CC 1.F H2:i 0.124 ;CC 1.F H2d 0.1@ ;CC 2.2 H2Bn 0.1@@2 =C 1. H2

Mre '! &ecause siIe is c!ser anda!. s hi#her – &ut nt t much&ecause ) structura! di


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mper)ectins in !ids

• Specication of composition

– "ei#ht percent100x

21

11

mm

mC

+=

m1 J mass ) cmpnent 1

100x21

1'

1

mm

m

nn

nC

+=

nm1 J num&er ) m!es ) cmpnent 1

– atm percent


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Wt. ? and 't. ? -- 'n examp!e

T!picall! "e "ork "it# a basis "eig#t ($%%g or $ kg) or moles

given& allo! b! "eig#t -- '% u* +% ,i

'%%.++

'.00 /

+%%'.12

01.' /

.++.01$ or 01.$

.++ '.12'.12

.+$.++ '.12

Cu

Ni

Cu

Ni

g n m

g m

g n m

g m

C

C

= =

= =

= ≈+

= ≈+

or +$.


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Cnertin# et"een, Wt? and 't?6

$ 2$

$ 2 2 $

2 $2

$ 2 2 $

$ $$

$ $ 2 2

2 22

$ $ 2 2

$%%

$%%

$%%

$%%

C AC

C A C A

C AC C A C A

C AC

C A C AC A

C C A C A

∗= ×∗ + ∗

∗= ×∗ + ∗

∗= ×

∗ + ∗∗

= ×∗ + ∗

Cnerts )rm"t? t 't? 'i

is atmic"ei#ht6

Cnerts )rmat? t "t? 'iis atmic"ei#ht6


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nterstitia! s!id s!utin app!ies t car&n in K-irn. 3he car&n atm is sma!! enu#h t ft

"ith sme strain in the interstice r penin#6amn# adacent ;e atms in this imprtantstee! structure. 3his unit-ce!! structure can &ecmpared "ith that sh"n in ;i#ure @.4&.N

ut the interstitia! s!u&i!it( is Auite !" since the siIe mismatch ) the site tthe radius ) a car&n atm is n!( a&ut 1/4


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andom* sustitution solid solutioncan occur in +onic !r%stalline

materials as well. ,ere of -i inMg. The 2O arrangement isuna/ected. The sustitution occurs

among -i2H

and Mg2H

ions.


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$ sustitution solid solution of $l2@ in Mg

is not as simple as the case of -i in Mg.The requirement of charge neutralit% in theoerall compound permits onl% two $l@H ionsto ll eer% threeMg2H acant sites* leaing

oneMg2H

acanc%.


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+ron oxide* Fe1O x with x P 0.05* is an

example of a nonstoichiometric compound.Similar to the case of Figure .2* oth Fe2H and Fe@H ions occup% the cation sites* withone Fe2H acanc% occurring for eer% twoFe@H ions present.


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• Frenkel Defect

--a cation is out of place.

• Shottky Defect --a paired set of cation and anion vacancies.

• !uili"riu# concentration of defectskT / QDe~ −

fro# $.%. &offatt %.$. (earsall

and ). $ulff The Structure and

Properties of Materials *ol. 1

Structure )ohn $iley and Sons

+nc. p. ,.

De)ects in Ceramictructures

Shottky

Defect

Frenkel

Defect


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'nd,* s!ip &et"een cr(sta! p!anes resu!t "hen dis!catinsme7* this mtin prduces permanent p!astic6de)rmatin.

're ca!!ed Dis!catins,

chematic ) Binc =C6,

* &e)re de)rmatin * a)ter tensi!e e!n#atin

s!ip steps "hichare the ph(sica!

eidence ) !ar#enum&ers )dis!catinss!ippin# a!n#the c!se packedp!ane Q0001R

Line De)ects

'dapted )rm ;i#. .F7 !allister "e.


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Linear De)ects Dis!catins6

– 're ne-dimensina! de)ects arund "hich atms aremisa!i#ned

• Ed#e dis!catin, – extra ha!)-p!ane ) atms inserted in a cr(sta!

structure

– b (the berger’s vector is ⊥ perpendicu!ar6 tdis!catin !ine

• cre" dis!catin, – spira! p!anar ramp resu!tin# )rm shear de)rmatin

– b is || para!!e!6 t dis!catin !ine

!urger’s vector" b# is a measure of latticedistortion and is measured as a distance along theclose pac$ed directions in the lattice


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Ed#e Dis!catin

;i#. 4.@7 !allister "e.

Ed#e Dis!catin


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3enition of the 4urgers ector* b*relatie to an edge dislocation. (a) +nthe perfect cr%stal* an mS n atomicstep loop closes at the starting point.() +n the region of a dislocation* thesame loop does not close* and theclosure ector (b represents themagnitude of the structural defect.For the edge dislocation* the 4urgers

ector is perpendicu!ar to thedislocation line.


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Screw dislocation. The spiral stacking of cr%stal planes leads to the 4urgers ector eing parallel to

the dislocation line.


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Mixed dislocation. This dislocation has oth edge

and screw character with a single 4urgers ectorconsistent with the pure edge and pure screwregions.


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4urgers ector for thealuminum oxide structure.The large repeat distancein this relatiel% complex

structure causes the4urgers ector to eroken up into two (for2O ) or four (for $l@H )

partial dislocations* each

representing a smaller slip


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mper)ectins in !ids

Dis!catins are isi&!e in 36 e!ectrn micr#raphs

'dapted )rm ;i#. 4.7 !allister "e.


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Dis!catins T Cr(sta! tructures

* tructure, c!se-

packed p!anes T directins are pre)erred.

ie" nt t"

c!se-packedp!anes.

c!se-packed p!ane &ttm6c!se-packed p!ane tp6

c!se-packed directins

* Cmparisn amn# cr(sta! structures, ;CC, man( c!se-packed p!anes/directinsU =C, n!( ne p!ane7 @ directinsU CC, nne $super-c!se% man( $near c!se%

* pecimens that"ere tensi!e

tested.

M# =C6

'! ;CC6

tensi!e directin


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• 8ne case is a t"in &undar( p!ane6 – Essentia!!( a reVectin ) atm psitins acrss the

t"innin# p!ane.

• tackin# )au!ts – ;r ;CC meta!s an errr in 'C'C packin# seAuence – Ex, 'C''C

!anar De)ects in !ids

'dapted )rm ;i#. 4.G7 !allister "e.


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Simple iew of the surface of a cr%stallinematerial.


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$ more detailed model of the elaorate ledgelikestructure of the surface of a cr%stalline material.#ach cue represents a single atom. =From 9. >.

,irth and ?. M. >ound* . Chem. h(s. 2* 1812(1


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T%pical opticalmicrograph of a grain

structure* 100S. Thematerial is a low&caronsteel. The grainoundaries hae een

lightl% etched with achemical solution so thatthe% reBect lightdi/erentl% from the

polished grains* there%

giing a distinctiecontrast. (From Meta!s=and&k* Cth ed.* 'ol. "D't!as ) Micrstructures )

ndustria! '!!(s*


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Simple grain&oundar%structure. This is termed atilt oundar% ecause it is

formed when two adEacentcr%stalline grains are tiltedrelatie to each other % afew degrees (). The

resulting structure isequialent to isolated edgedislocations separated %the distance G* where isthe length of the 4urgersector* b. (From 5. T. ead*Dis!catins in Cr(sta!s*Mc?raw&,ill 4ook !ompan%*-ew ;ork* 1


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he ledge /rowth leads to structures with /rain

0oundries he shape and average si1e or

dia'eter o" the grains "or so'e polycrystalline

speci'ens are large enough to o#serve with the

unaided eye& (Macrosocipic e-a'ination*


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Specimen for the calculation of the grain&siIenumer* ? is dened at a magnication of 100S.This material is a low&caron steel similar to that

shown in Figure .1C. (From Meta!s =and&k* Cthed.* 'ol. "D 't!as ) Micrstructures ) ndustria!'!!(s* $merican Societ% for Metals* Metals >ark*,* 1


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* Xse)u! up t ∼2000Y ma#nifcatin 6.

* !ishin# remes sur)ace )eatures e.#.7scratches6* Etchin# chan#es reVectance7 dependin# ncr(sta! rientatin since di


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ince Zrain

&undaries...* are p!aner imper)ectins7* are mre suscepti&!e t etchin#7* ma( &e reea!ed as dark !ines7

* re!ate chan#e in cr(sta!rientatin acrss&undar(.

curtes( ) L.C. mithand C. rad(7 the:atina! ureau )tandards7 Washin#tn7

DC n" the :atina!nstitute ) tandardsand 3echn!#(7Zaithers&ur#7 MDN.6

8ptica! Micrscp(

'3M #rain

siIe num&er

- J 2? & 1

num&er ) #rains/in2 at 100x

ma#nifcatin

;e-Cr a!!(&6

#rain &undar(

sur)ace #re

p!ished sur)ace

a6


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ASM (A'erican Society "or testing and Materials*

2ISUAL C3ARS (3$%%x) eac# "it# a number

Quick an4 eas! 5 use4 6or steel

ASM has prepared several standard co'parison charts) all having di""erentaverage grain si1es& o each is assigned a nu'#er "ro' % to %4) which is ter'ed

the grain si1e nu'#er5 the larger this nu'#er) the s'aller the grains&

, 6 + " 7% ,o. o6 grains/s7uare inc#

8rain size no.

:83E, 3he '3M #rain siIe is re!ated rre!ates6 a #rain area $T 100x M$?-+F+!$T+-


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Determinin# Zrain iIe7 usin# a

micr#raph taken at @00x

• We cunt 14 #rainsin a 1 in2 area nthe @00x6 ima#e

• 3 reprt '3M#rain siIe "eneeded a measure) : at 100x nt@00x

• We need acnersin methd[

( ) ( )( ) ( ) ( )

( ) ( )

( )( ) ( )

2

$2$%%

9 is mag. o6 image

, is measure4 grain count at 9

no" solve 6or 8&

log( ) 2 log log $%% $ log 2

log 2log +$

log 2log $+ 2log %% +

$ :.1 1%.%$

G

M

M

M

m

M N

N M G

N M G

G

− = ÷

+ − = −

∴

+ −= +

+ −= + = ≅

;r this same materia! h" man(


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;r this same materia!7 h" man(Zrains "u!d expect /in2 at 100x 't

50x

$ 1 $ 2

2 2

1 $

2 2

(at $%%x)2 2 $21 grains/in

,o"* #o" man! grain "oul4 ; expect at 0%x<$%% $%%

, 2 $210%

, $212 0$2 grains/in

G

M

M

N

M

− −

−

= = ≅

= ∗ = ÷ ÷

= =


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>t $%%x

T di i l h ti i i f


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Two&dimensional schematics gie a comparison of(a) a cr%stalline oxide and () a non&cr%stallineoxide. The non&cr%stalline material retains short&range order (the triangularl% coordinated uildinglock)* ut loses long&range order (cr%stallinit%).This illustration was also used to dene glass in!hapter 1 (Figure 1.C).


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4ernal model of an amorphous metal structure. Theirregular stacking of atoms is represented as aconnected set of pol%hedra. #ach pol%hedron is

produced % drawing lines etween the centers ofadEacent atoms. Such pol%hedra are irregular inshape and the stacking is not repetitie.


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$ chemical impurit% suchas -aH is a glassmodier* reaking up therandom network and

leaing nonridgingox%gen ions. =From 4. #.5arren* . 'm. Ceram.c. 24* 8@2 (1


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Schematic illustration ofmedium&range ordering in a!aJSi2 glass. #dge&sharing

!a octahedra hae een

identied % neutron&di/ractionexperiments. =From >. ,.?askell et al.* :ature @50* 2"@(1


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ummar(

• int7 Line7 ur)ace and +!umetric de)ects exist ins!ids.

• 3he num&er and t(pe ) de)ects can &e aried andcntr!!ed – T cntr!s acanc( cnc.

– amunt ) p!astic de)rmatin cntr!s \ ) dis!catins

– Wei#ht ) char#e materia!s determine cncentratin )su&stitutina! r interstitia! pint ]de)ects^

• De)ects a

crystal imperfection ch 4

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