crystal physics lect 1

8/18/2019 crystal physics lect 1

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IMPERFECTIONS INCRYSTALS

INTRODUCTION:


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What is Crystal?


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• Crystals are made up ofatoms, ions or moleculeswhich are periodically andre ularly arran ed in !

dimensions such thaten"ironment of each one ofthem is identical to e"eryother atoms, ions ormolecules in a lattice#


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• The e$amples areDiamond, %raphite, NaCl, &i, %eetc#

• 'll crystals are not totally or

completely perfect crystals#• There is always a de"iation fromperfect periodicity of atomicde"iation#

• De"iation from perfect periodicity

is (nown as imperfection#


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)erfect Crystal latticeassociated with atoms


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*attice Defect orImperfection

• 'n important feature of crystals is theirre ular atomic arran ement +ut no crystal isperfectly re ular#

• 'ny de"iation from this perfect atomicperiodicity is called an imperfection or latticedefect #

• A lattice defect is a state in which the

atomic arrangement in the small region(of a size of only a few lattice constants)of a crystal has departed from regularity.


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&tructure sensiti"e andinsensiti"e properties

On the +asis of perfect atomic periodicityof crystals

The properties li(e• density,• dielectric capacity,• speci c heats and• elastic properties of the lattice can +e

e$plained# &uch properties are calledstructure insensitive properties#


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&tructure sensiti"eproperties

*attice defects or atomic imperfectionsarisin due to irre ularities of atomicarrays in the crystals, a-ect reatlythe followin )hysical properties:

• The properties li(e color of thecrystal, di-usion in a crystal andcrystal rowth process


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.lectrical properties etsa-ected

• The electrical resistance of thecrystal is reatly a-ected#

• These defects scatter the conductionelectrons in a metal and thusincrease its electrical resistance#

• .specially in case of alloys thisincrease in electrical resistance isse"eral tens of percenta e#


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.lastic properties eta-ected

• The strength of crystals: • Certain (inds of defects e$ist "ery

rarely +ut they decrease the stren thof the crystal +y a factor of se"eralhundreds or thousands

• &uch properties that are reatlya-ected +y the defects are calleddefect or structure sensitive

properties.


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CLASSIFICATION OFIMPERFECTIONS

There are three types ofi perfections e!ist in "enera#.

$A% Crysta# I perfections orato ic i perfections%

$&% E#ectronic I perfections

$C% Transient I perfections


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/'0 Crystal Imperfections /oratomic imperfections0 :

Concerned with this types of imperfections# To list them they are: /20 Thermal "i+rations,

/30 )oint defects,

/i0 4acancies,/ii0 Interstitials,/iii0 Isolated impurities#

/!0*ine defects5 the dislocation: .d e and &crew dislocations,

/60 &urface defects,/i0 .$ternal surfaces of solids/ii0 Internal surfaces5 rain +oundaries and other internal+oundaries#


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$&% E#ectronicI perfections'

They are the defects in electronicstructure e# #,

• /i0 conduction electron• /ii0 hole,which are e$cited thermally from lled

+ands or impurity le"els# These defects are responsi+le for

important electrical and ma neticproperties,


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$C% TransientI perfections '

These defects are introduced into thecrystal from e$ternal sources and are, fore$ample

/i0 )hotons are +om+arded on crystals/ii0 7eam of char ed particles li(e

electrons, protons, and mesons etc#

/iii0 7eam of neutral particles e# #,neutrons and neutral atoms#

're +om+arded on crystals#


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Di-erent types of point defectsin crystals


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4acancy


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)oint defects in ioniccrystals


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CRYSTALLO(RAP)ICIMPERFECTIONS'

• To discuss the defects that arise due to

the departure from perfect periodicityof an atomic array in a crystal

• 8the so called lattice defects#• They can then +e classi ed accordin

as the periodic re ularity is interruptedin 9ero, one, two and three dimensions#


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(1) Point *efects'

• ' lattice defect which spreads out "erylittle in /9ero dimension0 is called a pointdefect#

• They are of followin types:/i0 Interstitial atoms/ii0 4acancy also (nown as &chott(y

defects/iii0Impurity atom/i"0 Interstitial ; 4acancy < =ren(el defects


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/i0 Interstitial atom:

• This is an e$tra atom inserted intothe "oids /called interstice of thelattice0 +etween the re ularlyoccupied sites#

• Thus such an atom does not occupyre ular lattice sites#

• This e$tra atom may +e an impurityatom or an atom of the same typesas on the re ular lattice sites#


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/ii0 4acancies :

• These are the lattice sites from which theatoms are missin #

• &uch a "acancy is also called &chott(y defect#

• 7ut if a "acancy is created +y transferrin anatom from a re ular lattice site to aninterstitial position then it is called =ren(eldefect#

• In this case, therefore, > two imperfections arecreated8"acancy as well as an interstitialatom#


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)oint defects in elementalsolids


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=ren(el defects in ioniccrystals


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Cation and 'nion "acancy


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/iii0 Impurity atom :

• This is a defect in which a forei natom occupies a re ular lattice site#

P i t d f t


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• Point defects• The simplest point defects are as follows:• Vacancy missin atom at a certain

crystal lattice position5• Interstitial impurity atom e$tra

impurity atom in an interstitial position5• elf!interstitial atom e$tra atom in an

interstitial position5• u"stitution impurity atom impurity

atom, su+stitutin an atom in crystallattice5

• #ren$el defect e$tra self>interstitialatom, responsi+le for the "acancy near+y#

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%ine defects

• *inear crystal defects are ed e andscrew dislocations#

• &dge dislocation is an e$tra halfplane of atoms inserted@ into thecrystal lattice#

• Due to the ed e dislocations metalspossess hi h plasticity characteristics:ductility and mallea+ility#


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&crew Dislocation

• crew dislocation forms when one partof crystal lattice is shifted /throu hshear0 relati"e to the other crystal part#

It is called screw as atomic planes form aspiral surface around the dislocation line#

• =or Auantitati"e characteri9ation of adi-erence +etween a crystal distorted +ya dislocation and the perfect crystal the'urgers "ector is used#

Th di l ti d it i t t l


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• The dislocation density is a totallen th of dislocations in a unit

crystal "olume#• The dislocation density ofannealed metals is a+out 2B 2B >

2B23

m #• 'fter wor( hardenin thedislocation density increases up to

2B 2E >2B2F m > #• =urther increase of dislocation

density causes crac(s formationand fracture#


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$+% Line *efects'

• When a lattice defect iscon ned to a small re ion in

one dimension, it is called aline defect# In this type ofdefect, called dislocation, partof the lattice under oes ashearin strain eAual to one

lattice "ector /called a Th f t t


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• They are of two types :• /20 .d e dislocation : This type

of dislocation is created +y amissin half plane of atoms#

• /ii0 &crew dislocation : It can +ethou ht of as created +y cuttinthe crystal part way andshearin down one part relati"eto other +y one atomic spacin #


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Planar defects

• )lanar defect is animperfection in the form ofa plane +etween uniformparts of the material# The

most important planardefect is a rain +oundary#


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• =ormation of a +oundary +etween two


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• =ormation of a +oundary +etween tworains may +e ima ined as a result of

rotation of crystal lattice of one of thema+out a speci c a$is# Dependin on therotation a$is direction, two ideal typesof a rain +oundary are possi+le:

• Tilt "oundary rotation a$is isparallel to the +oundary plane5

• Twist "oundary > rotation a$is is

perpendicular to the +oundary plane:• 'n actual +oundary is a mi$ture@ of

these two ideal types#

% i + d i ll d l !


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• %rain +oundaries are called large!angle "oundaries if misorientation oftwo nei h+orin rains e$ceeds 2BG>2EG#

• %rain +oundaries are called small!angle "oundaries if misorientation of

two nei h+orin rains is EG or less#• Tilt "oundary rotation a$is is parallel

to the +oundary plane5

• Twist "oundary > rotation a$is isperpendicular to the +oundary plane:• 'n actual +oundary is a mi$ture@ of

these two ideal types#

• %rains di"ided +y small>an le


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%rains, di ided +y small>an le+oundaries are also called su"grains #

• %rain +oundaries accumulate crystallattice defects /"acancies, dislocations0and other imperfections, therefore theye-ect on the metallur ical processes,occurrin in alloys and their properties#

• &ince the mechanism of metaldeformation is a motion of crystaldislocations throu h the lattice, rain+oundaries, enriched with dislocations,play an important role in thedeformation process#


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• Di-usion alon rain +oundaries ismuch faster, than throu hout the

rains#• &e re ation of impurities in form of

precipitatin phases in the +oundaryre ions causes a form of corrosion,associated with chemical attac( of

rain +oundaries# This corrosion iscalled Inter ranular corrosion#

$ f


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$,% P#ane *efects'

• When a lattice defect is con ned to asmall re ion only in two dimensions5it is called a plane defect#

• When line defects cluster to ether ina plane, they can form a plane whichis descri+ed as follows :

• /i0 *inea e 7oundary:


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/i0 inea e 7oundary:• It is +oundary +etween two adHacent perfect

re ions in the same crystal that are sli htlytilted with respect to each other#

• /ii0 %rain +oundary:• ' crystal is made up of a lar e num+er of

small rains or crystallites which are sin lecrystals, /i#e#, all molecules in a crystalliteare oriented in the same direction0#%enerally, these crystallites in# the crystal ofa solid remain oriented indiscriminately inrandom directions unless special precautionsare ta(en durin the crystal rowth# &uch

crystals are called polycrystalline# %rain


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/iii0 &tac(in fault:

• It is possi+le for mista(esJ to occur in thestac(in seAuence of he$a onal closepac(ed layers# The plane separatin the twoincorrectly Hu$taposed layers is called

stac(in fault#


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We take the blue atomsas the base plane for

what we are going tobuilt on it, we will call itthe " A - plane ".

The ne$t layer will ha"ethe center of the atomsri ht o"er the

depressions of the A >plane5 it could +e eitherthe ' > or >con uration# Kere thepin( layer is in the L ' L


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If you pic( the ' >con uration /and whate"eryou pic( at this sta e, wecan always call it the ' >con uration0, the thirdlayer can either +e directlyo"er the A > plane and then

is also an A > plane /shownfor one atom0, or in the >con uration#If you chose L L, you et the

face centered cu"ic lattice $fcc%

If you chose L AL5 you o+tain thehe agonal close pac$ed lattice / hcp 0,

The stac(in seAuences of the two

close>pac(ed lattices therefore are

fcc : A' A' A' A...

hcp : A'A'A'A...


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You can't have it both ways. Ifyou start in the C position

somewhere (in thepicture the green atoms an! onthe A position somewhere else(light blue , you will get a

problem as soon as the twolayers meet.

or varieties sake, an! to be able to!istinguish the layers better, the bottom A layer here is in !ark blue.

#ptical annealing of a


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#ptical annealing of alinear phase slip.(a $iagram of the

!efective region. %heregion correspon!ing tothe stacking fault&phaseslip is sha!e! in.(b %he same fiel! of view,after annealing. %hesha!e! region representsthe same region as the thesha!e! region in (a .

crystal physics lect 1

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