X-ray investigation of crystal structures / Laue method ... · 6 XR 4.0 X-ray Crystal holder for...

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Robert-.osch-.reite10 Tel:+49551604-0 [email protected]

D-37079Göttingen Fax:+49551604-107 www.phywe.com

Difficulty

Difficult

PreparationTime

1Hour

ExecutionTime

2Hours

RecommendedGroupSize

2Students

X-rayinvestigationofcrystalstructures/Laue

methodwithdigitalX-raydetector(XRIS)(ItemNo.:P2541602)

CurricularRelevance

AdditionalRequirements: ExperimentVariations:

Keywords:

CharacteristicX-radiation,.ravaislattices,reciprocallattices,Millerindices,atomicformfactor,structurefactor,.raggscattering

Overview

Shortdescription

RelatedTopics

CharacteristicX-radiation,.ravaislattices,reciprocallattices,Millerindices,atomicformfactor,structurefactor,and.ragg

scattering

Principle

LauediagramsareproducedwhenmonocrystalsareirradiatedwithpolychromaticX-rays.Thismethodisprimarilyusedforthe

determinationofcrystalsymmetriesandtheorientationofcrystals.WhenaLiFmonocrystalisirradiatedwithpolychromaticX-

rays,acharacteristicdiffractionpatternresults.Thispat-ternisphotographedandthenevaluated.AmonocrystalX-raystructure

analysiscanbeperformedliveduringalecturewiththeaidoftheXR4.0expertunitandthedirectdigitalx-rayimagesensor.If

aCuX-raytubeisused,thephotographyonlytakes1minute.

AreaofExpertise:

Physik

EducationLevel:

Hochschule

Topic:

ModernePhysik

Subtopic:

Röntgenphysik

Experiment:

X-rayinvestigationof

crystalstructures/

Lauemethodwith

digitalX-raydetector

(XRIS)

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Fig.1:P2541602

Note:ThisexperimentcanalsobeperformedwithacopperormolybdenumX-raytube.

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Equipment

PositionNo. Material OrderNo. Quantity

1 XRCT4.0X-rayComputedTomographyupgradeset 09180-88 1

2 XR4.0expertunit,X-rayunit,35kV 09057-99 1

3 XR4.0X-rayplug-inunitwithWtube 09057-80 1

4 XR4.0X-rayLiFcrystal,mounted 09056-05 1

5 XR4.0X-rayopticalbench 09057-18 1

6 XR4.0X-rayCrystalholderforLaue-pattern 09058-11 1

7 XR4.0X-rayDiaphragmtubed=1mm 09057-01 1

8 Verniercalliperstainlesssteel0-160mm,1/10 03010-00 1

Additional

material

PCwithUS.interface,WindowsXPorhigher

Tasks

1.TakeaphotographoftheLauepatternofaLiFmonocrystalperformingthefollowingsteps

a)Takeanoffset-Image.

b)TaketheImageoftheLauepattern.

c)ProcessImage.

2.AssigntheLauereflectionstothelatticeplanesofthecrystal.

Setupandprocedure

Setup

Installthe1mmcollimatorandplacetheCrystalholderforLauediffractiononthediaphragm(Fig.2).

Fig.2:Installationofdiaphragmandcrystalholder.

AttachtheXRIStoitsholder.

PlacetheDigitalX-raydetectorXRISontherailatposition9cm.ThebacksideoftheXRISstagecorrespondstoits

positionontherail(Fig.3).

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Fig.3:XRISsetup

ConnecttheX-rayunitviaUS.cabletotheUS.portofyourcomputer(thecorrectportoftheX-rayunitismarkedinFig.

4).

Fig.4:Commectionofthecomputer

ConnecttheUS.cableofthedetectortothecomputer

Startthe“measureCT”program.AvirtualX-rayunit,rotationstageanddetectorwillbedis-playedonthescreen.The

greenindicationLEDontheleftofeachcomponentsindicatesthatitspresencehasbeendetected(Fig.5)

YoucanchangetheHighVoltageandcurrentoftheX-raytubeinthecorrespondinginputwindowsormanuallyontheunit.

(Fig.5)

Whenclickingontheunitpictogramadditionalinformationconcerningtheunitcanberetrieved(Fig.5)

Thestatuspictogramindicatesthestatusoftheunitandcanalsobeusedtocontroltheunitsuchasswitchingonandoff

thelightortheX-rays(Fig.5)

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Fig.5:Partoftheuserinterfaceofthesoftware

ThesettingsoftheXRIScanbeadjustedusingtheinputwindows.

oTheexposuretimecontrolsthetimebetweentwoframesareretrievedfromthedetector

othenumberofframesdefineshowmanyframesareaveraged

oandwiththebinningmodethechargeofneighbouringpixelsisaveragedtoreducethetotalamountofpixelsinone

frame.

Procedure

Experimentexecution

1a)Takeanoffset-Image.

Startanewexperiment,giveitauniquenameandfillinyourdetails(Fig.6).Alternativelyitisalsopossibletoloadthis

experimentwithpre-recordedimages.Thecorrectconfigurationwillbeloadedautomaticallyaswell.

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Fig.6:Startanewexperimentandfillinyourdetails

AdjusttheXRISsettingsandX-rayunitsettingsaccordingtoFig.7orloadtheconfigurationfromthepredefinedCTOfile

'Experiment10'(seeFig.7).

Fig.7:Thesettingsforthisexperiment(leftpanel)andthemethodloadandadjustthesettings(rightpanel)

DonotcalibratetheXRIS!

Thedetectorisstillatapprox.9cmandthediaphragmandtheLauecrystalholderarealsoinstalled.

Activatethe'Liveview'(seeFig.8).WhentheLiveviewisactivated,everynewimagethatisretrievedfromtheX-ray

detectorisdisplayedandthesmallgreenlightnexttotheXRISliveindicationblinks.

Fig.8'LiveView'button(leftpanel)andblinkinggreenlight(rightpanel)

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Waituntilatleast3newimageshavebeenrenewedinordertoletthedarkcurrentofthedetectorstabilise(seetheoryfor

moreinformation).

Tosavetheresultingimage,stoptheliveview.Whenthenextfirstimageiscaptured,the'Imageprocessing'buttons

becomeavailable.Clickon'SaveImage'.Fourformatsofimagescanbesaved(tiff,png,jpgandbmp).Savethisimage

astiffandgiveisthename'DI1',whichstandsforDarkImagewith1frame.ThisisyourOffset-Image(Fig.

9).

Fig.9:InstructionshowtosavetheimageandresultingImage:Left:Tiff-ImageDI1.Right:thesameimagewithenhancedcontrastand

brightness.

1b)TaketheLauediffractionpattern.

NowplacetheLiF-crystalintheholder(Fig.10)andmovetheXRIStothesameposition(approx.9cm)asintask1a).

Fig.10:Placethecrystalintheholder

SwitchontheX-rays,activethe'LiveView'(doagainnotcalibratethesensor)andwaitagainuntilatleastthreeimages

havebeendisplayed.

StoptheLiveViewandsavetheimageasLaue1.YoucanalreadyseetheLauediffractionpattern.

1c)Processingoftheimage.

TofurtherprocessanimageyouneedtoopentheImageViewer(Fig.11).TheImageViewercanbeopenedintwoways,

eitherfromthetaskbarorusingtheshortcutbutton(moreinformationontheImageViewerinexperiment1).

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Fig.11:OpenImageViewerinstructions

Toprocessimagesthatyousavedintasks1a)andb),openthedestinationdirectory(Fig.12)bychoosing“Image”and

“SelectImagepath”(ifyoustartedanexperimentbeforeperformingsteps1a)andb)therightfolderopens

automatically).

Fig.12:Selecttheimagepath

Doubleclickon'DI1'fromthelist,setthisimageasoffsetbyclickingon“Setasoffset”andselectthenormalisation(Fig.

13).AnynewimagethatyouselectfromthelistwillfromnowbesubtractedwithDI1.

Fig.13:Correctforoffset

Selectthe'Laue1'imagefromthelist.Thedisplayedimageisnowthe'Laue1'subtractedwith'DI1'.

Autoscalethehistogramofthedisplayedimagebyclickingon“Autoscaleimagecolor”(Fig.14).

Fig.14:AutoscaleandadjusttheMiddlecolour

Adjusttheuppercontrasthandls(Fig.15)sothattheLauepatternsbecomevisible.Thecurrentimageiscomposedof

threeparts.

oThedirectbeamthathasbeencollimatedbythe1mmcollimator.Thispartoftheimageresultsinthebrightspotinthe

middleofthedetector.AsmanyX-rayphotonshaveinteractedwiththedetector,thisdirectbeamwillhavesaturatedthe

detector.

oTheLauepatternspotsthathavebeencausedbytheinteractionofthedirectbeamwiththecrystal.OnlyfewX-ray

photonsarediffractedandthus,thespotsarecomposedoffewdetectorcounts.

oThelargestpartofthedetectorhasnotdetectedanyX-rayphotons.

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Fig.15:Adjusttheuppercontrasthandletotheleftuntilthelauepatternsbecomevisible

Inordertofurtheroptimisethequalityoftheimagethecontrastoftheimagehastobeadjustedtothelauespots.With

theautoscaletool,theentirerangeofgrey-valuesofthesavedimagesaredis-played(0-30000)..yadjustingthecontrast

handles,youcanfocusonthespotsonly.Sinceveryfewcountsareregisteredinthesespotstheloweranduppercontrast

handleswillhavetobeonthefarleftorrightsideofthehistogram.Itispossibletomanuallychangetheupperlevelvalue

(Fig.16)ofthedisplayedhistogrambytypinginanewuppervalue(forexample2000).

Fig.16:Adjusttheuppercontrastleveltoasmallervalue

Savetheimagewithadjustedcontrastasabmp,jpgortif.

Note

Tooptimizetheimagequalityrepeatthisexperimentwithdifferentexposuretimesandnumberofframes.

Alternatively,itisalsopossibletovarythekVsettings.

ForeverychangeineithertheexposuretimeandthekVsettingsbothnewOffsetandLaueimageshavetobe

takenandsaved.

Theoryandevaluation

Theory

Detectorsaturation

WithdigitalX-rayimaging,X-rayphotonsthatinteractwiththedetectorareconvertedtoadigitalsignal.Suchadigitaldetector

iscomposedofarasterofpixels(pictureelements)andeachpixelcanbeconsideredasbucket.ForeachinteractionofanX-ray

photonwiththedetector,aseriesofelectronsareproducedinthepixelcorrespondingwiththelocationofthephoton

interaction.Theseelectronsarestoredinthepixel,graduallyfillingupthebucket.Afterasettimeinterval,"exposuretime",

theelectroncontentofthepixelismeasuredbyemptyingit.ForthesameintensityofX-ray's,alongerexposuretimewillresults

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inalargernumberofpixelsinthebucket.

Eachdigitaldetectorhasalimitedbucketsizewhichiscalledthe'fullwellcapacity'ofthedetector.Whenthislevelofffillis

reached,additionalelectronsarethrownawaybecausethedetectorissaturated.Asaturateddetectorwillcauseinconsistent

measurementsandhasthustobeavoided.

Detectorcalibration

Eachdigitaldetectorhasadifferentandvariableoffsetandpixel-specificoutput.Duringthecalibrationthesevariationswillbe

measuredandusedinthesubsequentimaging.

EvenwithouttheX-rayson,thedetectorwillgeneratearead-outvaluethatisdifferentfrom0,called'darkimage'or'affset'.

Thishasseveralreasonsfromwhichthemainreasonsareanelectronicoffsetandread-outnoise.Whendeterminingthebeam

intensity ,itisimportanttosubtractthisoffset( )fromthemeasuredread-out( ).

InterpretationofLauediffractionpatterns

LauediagramsareproducedwhenmonocrystalsareirradiatedwithpolychromaticX-rays.Thismethodisusedmainlyforthe

determinationofcrystalsymmetriesandtheorientationofcrystals.Acompleteanalysisofthediagramsisonlypossiblewith

simplecrystalstructures.

Anecessary,althoughinsufficient,conditionfortheconstructivereflectionatthevariouslatticeplanesisthe.raggcondition:

;(n=1,2,3,...)

( =interplanarspacing, =glancingangle, =wavelength,and =1,2,3,...)

Withthelatticeconstant ofacubiccrystal,thefollowingisvalidforthespacing betweentheindividuallattice

planes:

If isthedistancebetweenareflectionandthecentreoftheLauepattern,and thedistancebetweenthefilmandthe

sample(Fig.17),thentheglancingangle thatisdeterminedinanexperimentalmanneris:

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Fig.17:ScatteringgeometryofaLauepattern.They-axisisintheplaneofthefilmandisperpendiculartothex,zplane.

; (3)

and arethedistancesofthereflectioninasystemofrectangularcoordinateswithitsorigininthecentreofthepattern.

IftheX-raybeamcoincideswithacertaincrystallo-graphicdirection[h*,k*,l*](here,the[100]direction)andifitimpingesona

crystalplane( ),thentheangleofincidence (seeFig.18)isdeterminedbythescalarproductofthenormalvectorof

theplaneandtheincidentvector.

Then,thefollowingisvalidfortheglancingangle: .

Accordingtotheadditiontheoremandwith(h*,k*,l*)=(100),itfollowsfrom(4)that:

(5)

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Fig.18:Reflectiononalatticeplanewithrandomorientation.

Evaluation

Task1:TakeaphotographoftheLauepatternofaLiFmonocrystal.

Figure19showstheLauediagramofaLiF(100)monocrystalwithaface-centrecubiccrystallattice(fcc).Ifthediffraction

patternisrotatedby90°aroundthedirectionoftheprimarybeam,itisagainbroughttocoincidence.Sincetheprimarybeam

impingesperpendicularlyonthe(100)-planeoftheLiFcrystal,thecrystaldirection[100]isafourfoldaxisofsymmetry.The

intensityofthere-flectionsdependsonthereflectingcrystalsurfaceaswellasonthespectralintensitydistributionoftheX-

rays.

Fig.19:LauepatternoftheLiF(100)crystal.OperatingvaluesofthetungstenX-raytube:AcceleratingvoltageUA=35kV;anodecurrentIA

=1mA;exposuretime20s,1frameperimage,binningmode500x500.

Task2:AssigntheLauereflectionstothelatticeplanesofthecrystal.

Theglancingangle iscalculatedfrom(5)foralloftheplaneswithlow( )indices.Theangle isdetermined

using(3)basedonthediagram.Theassignmentofthereflectionstothelatticeplanesisfoundwhentheanglescoincide(

)andwhenthecondition isfulfilled,with and beingthecoordinatesofthereflections.

Afinalcontrolcanbeperformedasfollows.InaccordancewiththeDuane-Huntlawofdisplacement(seeexperimentP2540901),

thebeginningofthebremsspectrumisgivenbytheminimumwavelength .Foran

acceleratingvoltage ,thefollowingistrue: .Thismeansthatfortheassignmentofthe

reflectionstothelatticeplanes,onlyX-rayswithawavelengthof canplayarole.

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Figure20showsthelocationofthereflectionsinadifferentmanner.Forreasonsofsymmetry,theevaluationcanberestricted

to1/8ofthediagram.Theotherreflectionsareobtainedbypermutationoftheindicesandachangeofthesign.Reflectionnos.

4and8areonlyveryslightlyvisibleintheoriginalphotograph.Theycanonlybeseenclearlywhenalongerexposuretimeis

used.

Fig.20:SchematicrepresentationoftheLauereflections.

Table1showstheresultoftheevaluation.ItbecomesclearthatthereflectionsarevisibleonlyiftheMillerindicesareeitherall

oddoralleven.Thisisacharacteristicfeatureofaface-centredcubiccrystallattice(seeexperiment2541301).

Table1:EvaluationoftheLauediagram

Reflectionno.

1 4.0 12.5 13.25 17.29 113 17.55 0.33 0.32 121.4 72.2

2 0 25.5 25.5 26.66 204 26.75 0 0 100.7 90.4

3 9.75 19.0 21.25 24.17 224 24.09 0.5 0.51 82.2 67.3

4 6.75 6.75 9.50 13.34 133 13.26 1 1 92.4 42.6

5 10.75 10.75 15.50 19.33 244 19.47 1 1 90.1 59.6

6 38.25 38.25 54.50 53.30 111 35.26 1 1 232.6 268.8

7 7.0 34.0 35.50 30.75 315 30.47 0.2 0.2 68.1 69.6

8 0 45.75 45.75 33.72 406 33.69 0 0 55.8 62.0

Note

Inordertokeeptherelativeerrorassmallaspossiblewhendeterminingthedistancesbetweenthereflections,magnifyitonthe

computerandprintitinenlargedform.

ToshadowtheprimarybeamspotontheLaueImagewhichsometimesleadstoartefactsonthedigitalimageitcanbeusefulto

useambeamstop.Juststickasmallpieceofmetal(diameterapprox.3mm)toapieceoftapeandfixitinfrontofthesenor

rightinthemiddleoftheactivearea.Optimizethepositionbytakingimages(exposuretimearound1s)andcheckinginthelive

viewimageiftheprimarybeamiscompletelycoveredbythepeaceofmetal.

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Fig21:Lauediagramwith.eamstop.

X-ray investigation of crystal structures / Laue method ... · 6 XR 4.0 X-ray Crystal holder for...

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