Lecture-1-Principle-and-Application-of-X-Ray-Diffractometer.pdf

This is about information of x ray diffraction

1. Pre -Ph.D. Course Work 2021
Department of Physics
Topic: Experimental Tools and Techniques
Lecture1:PrincipleandApplicationsofPowderX-RayDiffractometer
Lecture by: Dr.AnjuDixit
ChhatrapatiShahuJiMaharajUniversity
(Formerly Kanpur University)

2. Outlines
1.Introduction to X-Rays
2.Principle of X-Ray Diffraction
3.Bragg’s Law
4.X-ray Diffractometer
5.Types of X-Ray radiation
6.X-Ray Diffraction Methods
7.Applications of Powder X-Ray Diffraction

3. Experimental tools and Techniques
S.No.Titleof the Lecture Lecture No.
1 Principle and Application of Powder X-Ray
Diffractometer
Lecture 1
2 SEM and Energy Dispersive X-Ray Analysis Lecture 2
3 TEM Lecture 3
4 AFM and STM Lecture 4
5 Spectrometer ( IR and UV Visible)
FT-IRSpectrometer
Lecture 5

4. Introduction
1.X-rayswerediscoveredin1895bytheGermanphysicist
WilhelmConradRöntgen.
2.Electromagneticradiationdescribedashavingpacketsof
energy,orphotons.Theenergyofthephotonisrelatedtoits
frequencybythefollowingformula:E=hν(E=hc/λ)
3.Electromagneticradiationcanbeexpressedintermsofenergy,
wavelength,orfrequency.

5. Type of Radiation Frequency Range (Hz) Wavelength Range
gamma-rays 10
20
–10
24
< 10
-12
m
x-rays 10
17
–10
20
1 nm –1 pm
ultraviolet 10
15
–10
17
400 nm –1 nm
visible 4 –7.5*10
14
750 nm –400 nm
near-infrared 1*10
14
–4*10
14
2.5 μm –750 nm
infrared 10
13
–10
14
25 μm –2.5 μm
microwaves 3*10
11
–10
13
1 mm –25 μm
radio waves < 3*10
11
> 1 mm
Theentirerange(electromagneticspectrum)isgivenbyradiowaves,
microwaves,infraredradiation,visiblelight,ultra-violetradiation,X-rays,
gammaraysintheincreasingorderoffrequencyanddecreasingorderof
wavelength.Thetypeofradiationandtheirfrequencyandwavelengthranges
areasfollows:

6. X-Ray Diffraction
X-raysareelectromagneticradiationwithwavelengthsbetween1
pmto1nm.ThewavelengthofX-raysisonanatomiclevelandis
muchsmallerthanthatofvisiblelight(400nmto750nm).
SinceX-rayshaveasmallerwavelengththanvisiblelight,they
havehigherenergyandaremorepenetrative.Itsabilityto
penetratematter,however,isdependentondensityofthematter.
Therefore,X-raysareusefulinexploringstructuresofatoms.
X-RayCrystallographyisatechniqueusedforidentifyingthe
atomicandmolecularstructureofacrystal,inwhichthe
crystallineatomscauseabeamofincidentX-raystodiffractinto
manyspecificdirections.Thisformsapattern,thistypeofpattern
iscalledtheX-raydiffractionpattern

7. Interference
X-raydiffraction,aphenomenoninwhichtheatomsofacrystal,byvirtueof
theiruniformspacing,causeaninterferencepatternofthewavespresentinan
incidentbeamofXrays.TheatomicplanesofthecrystalactontheXraysin
exactlythesamemannerasdoesauniformlyruledgratingonabeamoflight.
BecauseX-raysarebundlesofseparatewaves,eachwavecaninteractwithon
anothereitherconstructivelyordestructively.Theinteractionbetweenwavesis
calledinterference.Ifwavesareinphasemeaningthateachoftheircrestsand
troughsoccurexactlyatthesametime,thenthewaveswillstacktogetherto
producearesultantwavethathasahigheramplitudeandresultsinthe
constructiveinterference.
Iftheywavesareoutofphase,thendestructiveinterferenceoccursandthe
amplitudeoftheresultantwavewillbereduced. Ifwavesareexactlyoutof
phasebyamultipleofn/(2*lambda)thentherewillbecompletedestructive
interferenceandtheresultantwavehasnoamplitude,meaningthatitis
completeddestroyed.

8. Principle of X-Ray Diffraction
TheatomicplanesofacrystalcauseanincidentbeamofX-rays
tointerferewithoneanotherastheyleavethecrystal.The
phenomenoniscalledX-raydiffraction. AndscatteringofX-
raysbytheatomsofacrystalthatproducesaninterference
effectsothatthediffractionpatterngivesinformationonthe
structureofthecrystalortheidentityofacrystallinesubstance.
SoX-raydiffractionisbasedonconstructiveinterferenceof
monochromaticx-raysandacrystallinesample.OrX-rays
arerelativelyshort-wavelengthEMradiationandcanexhibit
wavecharacteristicssuchasinterferencewheninteracting
withcorrespondinglysmallobjects.

10. Bragg’s Law
Bragg'slawisaspecialcaseofdiffraction,whichdetermines
theanglesofcoherentandincoherentscatteringfromacrystal
lattice.WhenX-raysareincidentonaparticularatom,they
makeanelectroniccloudmovelikeanelectromagneticwave.
WhentheX-rayisincidentontoacrystalsurface,itsangleof
incidence,θ,willreflectwiththesameangleofscattering,θ.
And,whenthepathdifference,disequaltoawholenumber,
n,ofwavelength,constructiveinterferencewilloccur.

11. Bragg'sLawcaneasilybederivedbyconsideringtheconditions
necessarytomakethephasesofthebeamscoincidewhenthe
incidentangleequalstoreflectingangle.
Theraysoftheincidentbeamarealwaysinphaseandparallelupto
thepointatwhichthetopbeamstrikesthetoplayeratatomz.
Thesecondbeamcontinuestothenextlayerwhereitisscattered
byatomB.Thesecondbeammusttraveltheextradistance
AB+BCifthetwobeamsaretocontinuetravelingadjacentand
parallel.
Thisextradistancemustbeanintegral(n)multipleofthe
wavelength()forthephasesofthetwobeamstobethesame:
nλ=AB+BC----------------------------------------------(1)

12. Recognizingdasthehypotenuseofthe
righttriangleABZ,wecanuse
trigonometrytorelatedandtothe
distance(AB+BC).
The distance AB is opposite θSo,
AB = d sin θ----------------------------( 2)
Because AB = BC eq. (1) becomes,
nλ=2AB----------------------------( 3)
Substituting eq. (2) in eq. (3) we have,
nλ=2dsinθ------------------------(4)
SotheprincipleisthatwhenabeamofX-raysofwavelengthλentersacrystal,the
maximumintensityofthereflectedrayoccurswhensinθ=nλ/2d,whereθisthe
complementoftheangleofincidence,nisawholenumber,anddisthedistancebetween
layersofatoms.

14. X-ray Diffractometer

15. Working of X-ray Diffractometer
X-raydiffractometersconsistofthreebasicelements:anX-raytube,a
sampleholder,andanX-raydetector.X-Raysaregeneratedinacathode
raytubebyheatingafilamenttoproduceelectrons,acceleratingthe
electronstowardatarget(tungsten)byapplyingavoltage,and
bombardingthetargetmaterialwithelectrons.
Whenelectronshavesufficientenergytodislodgeinnershellelectrons
ofthetargetmaterial,characteristicX-rayspectraareproduced.
Thesespectraconsistofseveralcomponents,themostcommonbeing
K
α
andK
β
.K
α
consists,inpart,ofK
α1
andK
α2
.K
α1
hasaslightlyshorter
wavelengthandtwicetheintensityasK
α2
.Thespecificwavelengthsare
characteristicofthetargetmaterial(Cu,Fe,Mo,Cr).

16. Filtering,byfoilsorcrystalmonochrometers,isrequiredtoproducemonochromaticX-
raysneededfordiffraction. K
α1
andK
α2
aresufficientlycloseinwavelengthsuchthata
weightedaverageofthetwoisused.
Copperisthemostcommontargetmaterialforsingle-crystal diffraction,withCuK
α
radiation=1.5418Å .TheseX-raysarecollimatedanddirectedontothesample. Asthe
sampleanddetectorarerotated,theintensityofthereflectedX-raysisrecorded.
WhenthegeometryoftheincidentX-raysimpingingthesamplesatisfiestheBragg
Equation,constructiveinterferenceoccursandapeakinintensityoccurs.Adetector
recordsandprocessesthisX-raysignalandconvertsthesignaltoacountratewhichis
thenoutputtoadevicesuchasaprinterorcomputermonitor.
ThedominanteffectthatoccurswhenanincidentbeamofmonochromaticX-rays
interactswithatargetmaterialisscatteringofthoseX-raysfromatomswithinthe
targetmaterial.
Inmaterialswithregularstructure(i.e.crystalline),thescatteredX-raysundergo
constructiveanddestructiveinterference.Thisistheprocessofdiffraction. The
diffractionofX-raysbycrystalsisdescribedbyBragg’sLaw,
nλ=2dsinθ.

17. Thedirectionsofpossiblediffractionsdependonthesizeandshapeofthe
unitcellofthematerial.Theintensitiesofthediffractedwavesdependon
thekindandarrangementofatomsinthecrystalstructure.
However,mostmaterialsarenotsinglecrystals,butarecomposedofmany
tinycrystallitesinallpossibleorientationscalledapolycrystalline
aggregateorpowder.
WhenapowderwithrandomlyorientedcrystallitesisplacedinanX-ray
beam,thebeamwillseeallpossibleinteratomicplanes.Iftheexperimental
angleissystematicallychanged,allpossiblediffractionpeaksfromthe
powderwillbedetected.
X-raysaregeneratedviainteractionsoftheacceleratedelectronswith
electronsoftungstennucleiwithinthetubeanode.Therearetwotypesof
X-raygenerated:characteristicradiationandbremsstrahlungradiation.
Electronstravelingfromthefilament(cathode)tothetarget(anode)
convertasmallpercentage(1%)oftheirkineticenergyintox-rayphotons
bytheformationofbremsstrahlungandcharacteristicradiation.

18. BREMSSTRAHLUNG RADIATION
Bremsstrahlunginteractions,theprimarysourceofx-rayphotonsfromanx-ray
tube,areproducedbythesuddenstopping,breakingorslowingofhigh-speed
electronsatthetarget.Whentheelectronsfromthefilamentstrikethetungsten
target,x-rayphotonsarecreatediftheyeitherhitatargetnucleusdirectly(rare)
ortheirpathtakesthemclosetothenucleus.
Ifahighspeedelectronhitsthenucleusofatargetatom,allitskineticenergyis
transformedintoasinglex-rayphoton.(Totalabsorptionhasoccurred).Thus,
theenergyoftheresultantphoton(keV)isnumericallyequaltotheenergyof
theelectron.Thisinturnisequaltothekilovoltageappliedacrossthex-ray
tubeattheinstantofitspassage.

19. CHARACTERISTIC RADIATION
Characteristicradiationoccurswhenanelectronfromthefilamentdisplaces
anelectronfromaninner-shellofthetungstentargetatom,therebyionizing
theatom.
Whenthishappens,anotherelectroninanouter-shellofthetungstenatomis
quicklyattractedintothevoidinthedeficientinner-shell.
Whenthedisplacedelectronisreplacedbytheouter-shellelectron,aphoton
isemittedwithanenergyequivalenttothedifferenceinthetwoorbital
bindingenergies.

20. X-Ray Diffraction Methods
Therearethreediffractionmethodsbywhichwecanobtainthe
informationaboutcrystalstructures:

LaueDiffractionmethod
RotatingcrystalDiffractionmethod
PowderDiffractionmethod

21. Laue Diffraction method
TheLauemethodisasinglecrystaldiffractionmethod.The
discoveryofthephenomenonofcrystaldiffractionwasobtained
forthefirsttimebytheLauemethod.
Themethodrequiresapolychromaticbeam,i.e.thefullspectrum
ofx-raywavelengths.Thesinglecrystalplacedinthe
polychromaticbeamdiffractsinmanydifferentdirections.
TheresultingLauediffractionpatterndependsontheorientation
ofthecrystal.ThustheLauemethodisidealtodetectthe
orientationofasinglecrystal,i.e.tofindthedirectionsofthe
translationvectorsoftheunitcell.

22. Laue Diffraction method

23. Laue Diffraction method
Asinglecrystalismountedonarotatingtablewhichenablesthecrystaltobe
rotatedthroughcertainknownanglesandmaintainedstationarywithrespect
toabeamofX-raysofdifferentwavelengths.
Thecrystalselectsoutanddiffractsthosediscretevaluesofλ,forwhich
crystalplanesexist,ofspacingdandglancingangleθsatisfyingBragg’s
equation:
nλ=2dsin(θ)
Anarrow,parallelbeamiscollimatedonthecrystal.Photographicfilmsare
placedeithertoreceivethetransmittedorreflectedbeams.
Theresultantpatternconsistsofaseriesofsharpwelldefinedspots.Theseare
indicativeofaperfectcrystalstructure,whereasbroken,extendedspots
indicatelatticedistortionandimperfectionsinthecrystal.

24. Laue Diffraction method
Singlecrystalplacedonathree-axisgoniometerinfrontof
narrowbeamofx-rays
X-raysarenotmonochromatic
2θanddremainfixedforeachsetofplanes(onlyλisvaried)
EachsetdiffractsthatparticularλwhichsatisfiestheBragg
equationforit
Eachdiffractedbeamhasadifferentλ
Incidentbeampassesthroughphotographicfilm,hitsthe
crystal,andisback-reflectedtowardsthefilm

25. Rotating crystal Diffraction method
Intherotatingcrystalmethod,asinglecrystalismountedwithanaxis
normaltoamonochromaticx-raybeam.
Acylindricalfilmisplacedarounditandthecrystalisrotatedaboutthe
chosenaxis.Asthecrystalrotates,setsoflatticeplaneswillatsomepoint
makethecorrectBraggangleforthemonochromaticincidentbeam,andat
thatpointadiffractedbeamwillbeformed.
Latticeconstantofthecrystalcanbedeterminedbymeansofthismethod;
foragivenwavelengthiftheangleθatwhichareflectionoccursdhkl
known,iscanbedetermined.
Thereflectedbeamsarelocatedonthesurfaceofimaginarycones.By
recordingthediffractionpatterns(bothanglesandintensities)forvarious
crystalorientations; onecandeterminetheshapeandsizeofunitcellaswell
asarrangementofatomsinsidethecell.

26. Powder Diffraction method
ItisascientifictechniqueusingX-Ray,neutron,orelectrondiffractionon
powderormicrocrystallinesamplesforstructuralcharacterizationofmaterials.An
instrumentdedicatedtoperformingsuchpowdermeasurementsiscalledapowder
diffractometer.
Powderdiffractionstandsincontrasttosinglecrystaldiffractiontechniques,whichwork
bestwithasingle,well-orderedcrystal.Ifapowderedspecimenisused,insteadofasingle
crystal,thenthereisnoneedtorotatethespecimen,becausetherewillalwaysbesome
crystalsatanorientationforwhichdiffractionispermitted. HereamonochromaticX-ray
beamisincidentonapowderedorpolycrystallinesample. Thismethodisusefulforsamples
thataredifficulttoobtaininsinglecrystal.

Thepowdermethodisusedtodeterminethevalueofthelatticeparametersaccurately.
Latticeparametersarethemagnitudesoftheunitvectorsa,bandcwhichdefinetheunitcell
forthecrystal.Foreverysetofcrystalplanes,bychance,oneormorecrystalswillbeinthe
correctorientationtogivethecorrectBraggangletosatisfyBragg'sequation. Everycrystal
planeisthuscapableofdiffraction. Eachdiffractionlineismadeupofalargenumberof
smallspots,eachfromaseparatecrystal

27. Powder Diffraction method
Adiffractometerproduceswavesataknownfrequency,whichis
determinedbytheirsource.Thesourceisoftenx-rays,becausetheyare
theonlykindofenergywiththecorrectfrequencyforinter-atomic-
scalediffraction.However,electronsandneutronsarealsocommon
sources,withtheirfrequencydeterminedbytheirdeBroglie
wavelength.
Whenthesewavesreachthesample,theatomsofthesampleactjust
likeadiffractiongrating,producingbrightspotsatparticularangles.
Bymeasuringtheanglewherethesebrightspotsoccur,thespacingof
thediffractiongratingcanbedeterminedbyBragg'slawBecausethe
sampleitselfisthediffractiongrating,thisspacingistheatomic
spacing.

28. Powder Diffraction method
Thedistinctionbetweenpowderandsinglecrystaldiffractionisthe
degreeoftexturinginthesample.Singlecrystalshavemaximal
texturing,andaresaidtobeanisotropic
Incontrast,inpowderdiffraction,everypossiblecrystallineorientation
isrepresentedequallyinapowderedsample,theisotropiccase.PXRD
operatesundertheassumptionthatthesampleisrandomlyarranged.
Therefore,astatisticallysignificantnumberofeachplaneofthecrystal
structurewillbeintheproperorientationtodiffracttheX-rays.
Therefore,eachplanewillberepresentedinthesignal.Inpractice,itis
sometimesnecessarytorotatethesampleorientationtoeliminatethe
effectsoftexturingandachievetruerandomness.

29. Lauemethod RotatingcrystalmethodPowdermethod
Orientation
Singlecrystal
Latticeconstant
Singlecrystal
Latticeparameter
Polycrystal
Polychromaticbeam
Fixedangle
Monochromaticbeam
Variableangle
Monochromatic
beam
Variableangle

30. Applications of PXRD
Diffractionoccurswhenlightisscatteredbyaperiodicarraywithlong-
rangeorder,producingconstructiveinterferenceatspecificangles.
Theatomsinacrystalareperiodicallyarrangedthusdiffractlight. The
wavelengthofX-rayaresimilartothedistancebetweenatoms,PowderX-
rayDiffraction(PXRD)techniquesusesthisprincipletoelucidatethe
crystallinenatureofmaterials.
ThescatteringofX-raysfromatomsproduceadiffractionpatternthat
containsinformationabouttheatomicarrangementincrystal.
Amorphousmaterialslikeglassdonothaveperiodicarraywithlong-range
orderso;theydonotproduceanysignificantpeakindiffractionpattern

31. Crystal structure and Lattice parameters
using PXRD
X-raydiffractionprovidesampleinformationaboutthelattice
parameters.Thepositionofadiffractionpeakisdeterminedbythesize
andshapeofunitcellofthecrystallinephase.Peakrepresentsalattice
planeandthereforecanbecharacterizedbyMillerindex.
Ifthesymmetryishighasincaseofcubicorhexagonal,itisnot
difficulttoidentifythepeakindexforanunknownphase.Thisisvery
usefulinsolid-statechemistrytoidentifyingnewmaterials.Oncea
patterngetsindexed,itservesasreferencefornewentitie

32. XRD Graph

33. Polymorph study
PXRDishelpfulinidentificationandcharacterizationofpolymorph
(Polymorphismdescribestheexistenceofasolidmaterialinmorethanone
formorcrystalstructure).,monitoringthestability,methoddevelopmentand
validationforidentificationandquantificationofdrugsinPharmaceutical
Industries.
ThepartoftheX-raythatisnotscatteredsimplypassesthroughthenext
layerofatoms,whereagainpartoftheX-rayisscatteredandpartofit
passesthroughtothenextlayer.Thiscausesanoveralldiffractionpattern,
similartohowagratingdiffractsabeamoflight.InorderforanX-rayto
diffract,thesamplemustbecrystallineandthespacingbetweenatom
layersmustbeclosetotheradiationwavelength.

34. Polymorph study
Ifbeamsdiffractedbytwodifferentlayersareinphase,
constructiveinterferenceoccursandthediffractionpattern
showsapeak.However,iftheyareoutofphase,destructive
interferenceoccursappearandnopeakisobserved. Diffraction
peaksonlyoccurifitfollowsBragg’sLaw.
Since,ahighlyregularstructureisneededfordiffractionto
occur,onlycrystallinesolidsdiffract,thePXRDofamorphous
materialsdonotdepictanysignificantpeakindiffraction
pattern

35. Crystallinitystudy by PXRD
TheXRDanalysisofcrystallinecompoundsgivesadiffraction
patternconsistingofawell-defined,narrow,sharpand
significantpeakwhileamorphousmaterialsdonotgiveclear
peaksratherthepatternhasnoisesignals,smearedpeakoritcan
havesomeshortorderbumps.
Manypolymersdepictsemi-crystallinebehaviorandproduce
halopattern. PowderXRDcanbeusedtodetermine
thecrystallinityybycomparingtheintegratedintensityofthe
backgroundpatterntothatofthesharppeaks.

36. Particle Size and Crystallite Size
Thetermparticlesizeandcrystallitesizerefertotwodistinct
propertiesinamaterial.Particlescompriseofseveral
smallcrystallite.
Crystallitesizeisthefundamentalpropertyofmaterials.
Propertiesofnanomaterialsdependoncrystalssizeandnot
particlesize.
PXRDcanmeasuremillionsofcrystalsandaccurately
determinethesizedistributionofnanomaterials.

37. Phase Transition
SomecrystalsexhibitsseveralphasetransitionssuchasBaTiO
3.
Withtemperaturevariationthesedifferentphasesoccurs.Atthis
pointnewdiffractionpeakswillappearoroldonesdisappear
accordingtothesymmetryofthenewphase.
Thesephaseshavedifferentsymmetry.Sodiiferentphaseswith
correspondtodifferentcrystalstructurecanbeidentified. Insuch
casesthesymmetrymaychangebecausetheexistingstructureis
distortedratherthanreplacedbyacompletelydifferentone.

38. Summary
X-RayDiffractionisatechniqueusedforidentifyingtheatomicand
molecularstructureofacrystal,inwhichthecrystallineatomscause
abeamofincidentX-raystodiffractintomanyspecificdirections.This
formsapattern,thistypeofpatterniscalledtheX-raydiffractionpattern
WhentheX-rayisincidentontoacrystalsurface,itsangleofincidence,θ,
willreflectwiththesameangleofscattering,θ.And,whenthepath
difference,disequaltoawholenumber,n,ofwavelength,constructive
interferencewilloccur.
X-RaydiffractionmethodsalongwithSeveralApplicationsofPowderX-
RayDiffractionwereexplored.

39. References
1.ReviewArticle:PowderXRDTechniqueanditsApplicationsin
ScienceandTechnology,AshishChauhanandPriyanka
Chauhan,JournalofAnalytical&BioanalyticalTechniques,5,
2014.DOI:10.4172/ 2155-9872.1000212
2.ElementsofX-RayDiffraction,SecondEditionbyB.D.
Cullity.