Howdodislocationsshuffletogrowcrystals?BraggCoherentDiffractionImaging(BCDI)isatechniquewhichbecameavailableforX-rayswiththeintroductionof3rdgeneration,undulator-basedstorageringsliketheDiamondLightSource.TheBCDImethodimagescrystalsinthreedimensions(3D)byphasing,andtheninverting,thediffractionpatternsurroundingoneoftheBraggpeaksdiffractedbythecrystalunderexamination.TheparticularadvantageofBCDIisphasecontrastimaging,wherethephaseofthe3Dimageofacrystalisattributedtothelocaldistortionsofthecrystalduetothepresenceoflatticestrains.TheworkofJohannesIhli,JesseClarkandcolleagues,publishedinNatureMaterialsandreportedhere,usedBCDItoobservescrewdislocationsbytheircharacteristicspiral-shapeddistortionseenwithingrowingcrystalsofcalcite.Thedislocationswereseentomoveaheadofthegrowing{104}facetsofacalcitecrystal,grownin-situfromsolutionatthebeamline.BeamlineI16ScientificHighlightThequestionofhowdislocationsmoveatthegrowingfacetsofacrystalwasaddressedbyJohannesIhli,JesseClarkandcolleaguesattheI16beamline.TheI16MaterialsandMagnetismbeamlinewasbuiltasoneoftheinauguralPhaseIbeamlinesofDiamondandhasoperatedreliablysince2007.Thebeamlinewasdesignedforpolarizationanalysisofmagneticstructuresatlowtemperatures,butwasbuiltinageneralenoughwaythatotherdiffractionexperimentswerepossible.IndeedthefirstcoherentdiffractionexperimentseverperformedintheUKtookplacethereduringitsfirstyearofoperation.Theonlymodificationneededtothebeamlinewasanextensionofthedetectorarmofthediffractometertocarryafine-pixeldetectortorecordthefinefringesduetoX-rayinterferencefromtheextremitiesofthemicron-sizedcrystalsunderinvestigation.In2007,theonlydetectorsavailablewerecharge-coupleddevices(CCDs),buttodaytheDiamond-developedMerlindetector,acountingdetectorbasedontheradiation-hardMediPix3technology,withits55-micronpixels,hasallowedmuchbetterBCDIexperiments.ThehighspatialcoherenceofthebeamisattributedtothelowemittanceoftheDiamondstorageringandisthesameatallitsbeamlines.However,whenI16wasfirstusedforBCDIexperiments,therewasconcernthatthebeamlineoptics,notablythefocussingmirrorat30m,wouldspoilthecoherencesothebeamlinewasreconfiguredtoremoveit.Butlater,itwasrealisedthatitisonlynecessarytonarrowtheslitsnearthemirrortoadjustthecoherencelengthtomatchthesizeofthesample[1].Sincethisisacontinuousadjustment,itmeansthebeamlinecanbeadaptedtoprovidefullcoherentflux(aslimitedbythehorizontalemittance)toausefulrangeofsamplesizes.IntheexperimentsofIhlietal,crystalsupto3micronsinsizeweremeasuredandimagedbyBCDI,usingsupport-basedphasingalgorithms[2]tosolvethephaseproblem.

Figure1.(Top)exampleofacalcitediffractionpatternmeasuredatoneofthe{104}Braggpeaks.Thefringesresultfromcoherentinterferencefromoppositesidesifthecrystalandthestrongasymmetryresultsfromthepresenceofstrain.(Bottom)BCDIimagesofacalcitecrystalattwotimesduringitsgrowthfromsolution.Notetheincreaseinsizeofthecrystalfrom1.5micronsto2.5micronsandthatthehighlighteddislocationsmigratewithitsgrowingoutersurface.TypicalBCDIdatacollectedwiththeMerlindetectorareshowninFig1.Aclassicalinterferencefringepatterncanbeseen,whichresultsfromthewellformedfacetsofthecrystal.Thedataareclearlyoversampledonthedetector,asrequiredforthephasingcalculation[2],sincethereareseveralpixelsvisiblewithineachfringe.Thefull3Ddatasetcontained101suchframesspanningtheentirewidthoftherockingcurveinanglestepsof0.003°.This3DvolumeofreciprocalspaceisthecompleteFouriertransformoftheimagedvolumeofthecrystal,followinganappropriatecoordinatetransformation.ThelowerpanelofFig1showsatranslucentblueisosurfaceviewofthecrystalshapeattwotimesduringthecrystalgrowth.Someofthecrystalfacetsareflatwhilethefacetpointingtowardsthetopofthepageisclearlyrougher.Betweenthetwotimes,thisroughfacetisfoundtogrowfasterthantheflatterones.Alsoshownsuperimposedonthepictureisanetworkofdislocations,identifiedbythenodallineoflowdensitypassingdowntheircore.Thedislocationshavebeenhighlightedasisosurfacetubesandcolouredaccordingtotheimagephase,whichisidentified

withtheprojectionofthelocallatticedisplacementalongthediffractionQ-vector.Thecolourscale,runningfrombluetored,correspondstoa2πphasechangeoradisplacementofonelatticespacing.Eventhoughtheoverallimageresolutionisonlyaround30nm,thephasemeasurementisverysensitivetodisplacements,i.e.strains,onthepicometrescale.Mostofthedislocationsarecongregatedontherapidlygrowingtopsurfaceofthecrystal,suggestingtheyplayaroleinthematerialtransportprocessesassociatedwithcrystalgrowth.

Figure2.(Left)cornerviewofacalcitecrystalwiththreescrewdislocationshighlightedbyisosurfacesdrawnsurroundingtheirnodallines.ThesurfacesofthesetubesarecolouredwiththeBCDIphase,whichvariesby2πaroundtheloop,correspondingtoanetdisplacementofonelatticeconstrant.Thephasescalerunsfrom–π(blue)to+π(red).(Right)comparisonoftheexperimentallyobserveddisplacementasafunctionofazimuthalanglearoundthreeexamplesofdislocationsincomparisonwiththetheoreticaldependence(black)oftheprojecteddisplacementforanidealscrewinanisotropicmedium[3].Fig2showsanenlargedviewofthreeofthesedislocationswherethephaseisseentorotateuniformlyaroundthesurfaceoftheillustrativetube.TherightsideofFig2showstypicalextractedvaluesofthedisplacementofthelatticemeasuredatthreelocations,areshownasafunctionofazimuthalangle,θ,measuredaroundthedislocationcore,identifiedbythenodallineintheimageamplitude.Thetrendisclearlylinear,inagreementwiththesimpleelastictheoryofthestructureofascrewdislocation[3],shownastheblackfittingcurveinFig2.Sourcepublication:Three-dimensionalimagingofdislocationpropagationduringcrystalgrowthanddissolution,J.N.Clark,J.Ihli,A.S.Schenk,Y-YKim,A.N.Kulak,J.M.Campbell,G.Nisbet,F.C.MeldrumandI.K.Robinson,NatureMaterials14780-784(2015)References:

1.Robinson,I.K.OptimisationofCoherentX-rayDiffractionImagingatUltrabrightSynchrotronSources,ZeitschriftfurKristallographieSuppl2727-35(2008)2.Fienup,J.R.Phaseretrievalalgorithms-acomparison.AppliedOptics21,2758-2769(1982).3.Hirth,J.P.andLothe,J.TheoryofDislocations(McGraw-Hill,1968).Fundingacknowledgements:ERCAdvancedGrant227711“Explorationofstrainsinsyntheticnanocrystals”,EPSRCLeadershipFellowshipandaVolkswagenFellowship.EPSRCProgrammeGrantEP/I001514/1,andEPSRCgrantsEP/I022562/1,EP/J018589/1andEP/K006304/1Correspondingauthor:ProfessorIanRobinson,UniversityCollegeLondon;ResearchComplexatHarwell;TongjiUniversity,i.robinson@ucl.ac.uk