Student'sSheet
Printed:30.03.201715:14:38|P2541602
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)
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Fig.1:P2541602
Note:ThisexperimentcanalsobeperformedwithacopperormolybdenumX-raytube.
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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).
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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)
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Fig.5:Partoftheuserinterfaceofthesoftware
ThesettingsoftheXRIScanbeadjustedusingtheinputwindows.
oTheexposuretimecontrolsthetimebetweentwoframesareretrievedfromthedetector
othenumberofframesdefineshowmanyframesareaveraged
oandwiththebinningmodethechargeofneighbouringpixelsisaveragedtoreducethetotalamountofpixelsinone
frame.
Procedure
Experimentexecution
1a)Takeanoffset-Image.
Startanewexperiment,giveitauniquenameandfillinyourdetails(Fig.6).Alternativelyitisalsopossibletoloadthis
experimentwithpre-recordedimages.Thecorrectconfigurationwillbeloadedautomaticallyaswell.
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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)
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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).
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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.
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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:
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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)
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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.
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
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.
Student'sSheet
Printed:30.03.201715:14:38|P2541602
Robert-.osch-.reite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Fig21:Lauediagramwith.eamstop.