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Crystallographyisbecomingasciencedrivenbyprobabilities&statistics.@tsinghua.edu.cn3DataCollection•Thethreebasicquestionsincollectingdiffractiondata:–Whethertocollect?–How&whattocollect?–Analyzethedata?2011-11-21JiaweiWangjwwang@tsinghua.edu.cn4DataCollection–whethertocollect?•Collecttwosingleoscillationimagesatrightanglestooneanother.•Checkreflectionprofiles,diffractionlimit,mosaicityetal.DiffractioncartographyofasinglecrystalofbovinemitochondrialF1-ATPaseBowleretal.(2010)ActaCryst.D66,855-864.Locatingandevaluating10umcrystalsinanopaquesolution.2011-11-21JiaweiWangjwwang@tsinghua.edu.cn7Howtocollect?-OscillationRangeUnitCellΔφ=180d/πa-ηa=b=56.022.76–ηc=287.430.54-ηResolution:2.7(drICE)Toavoidtheoverlapoflunesatmaximumresolution,therotationrangecannotbewiderthanthespacingbetweenplanes,leadingtotheconditionΔφ180d/πa-η,ifthemosaicityηisalsotakenintoaccount.2011-11-21JiaweiWangjwwang@tsinghua.edu.cn8LuneOverlap2011-11-21JiaweiWangjwwang@tsinghua.edu.cn9Howtocollect?-OscillationStartPosition(-1529)(-1629)(-15210)c*-a*2011-11-21JiaweiWangjwwang@tsinghua.edu.cn10TotalRotationRange2011-11-21JiaweiWangjwwang@tsinghua.edu.cn14TotalRotationRange2011-11-21JiaweiWangjwwang@tsinghua.edu.cn15Howtocollect?–Overloads•Eachdetectorhasacertaincountlevelwhichsaturatesitspixels,resultingmainlyfromthelimitationsofitselectronics.2011-11-21JiaweiWangjwwang@tsinghua.edu.cn16DataCollection-whattocollect?2011-11-21JiaweiWangjwwang@tsinghua.edu.cn17ProcessingDiffractionData•StartingPoint:Aseriesofdiffractionimages,eachrecordedona2Dareadetectorwhilerotatingthecrystalthroughasmallangle(typically0.2-1.0degreesperimages)aboutafixedaxis(ietheRotationMethod).•Outcome:Adatasetconsistingoftheindices(h,k,l)ofallreflectionsrecordedontheimageswithanestimateoftheirintensitiesandthestandarduncertaintiesoftheintensities:h,k,l,I(hkl),σ(I).2011-11-21JiaweiWangjwwang@tsinghua.edu.cn18DataAnalysisSteps①Visualinspectionofthediffractionimages②(Auto)-indexing③Diffractiongeometryrefinement④Integrationofthediffractionpeaks⑤Conversionofthedatatoacommonscale⑥Symmetrydeterminationandmergingofthesymmetryrelatedreflections⑦Statisticalsymmaryandestimationoferrors2011-11-21JiaweiWangjwwang@tsinghua.edu.cn19ProcessingDiffractionDatawithHKL2000•HKL2000–XdisplayF–denzo_3d–scalepack2011-11-21JiaweiWangjwwang@tsinghua.edu.cn20BeamStopRegion2011-11-21JiaweiWangjwwang@tsinghua.edu.cn21Autoindexing-PeakSearchThespotpositionsinadiffractionimageareadistortedprojectionofthereciprocallattice.Autoindexingstartswithapeaksearch,whichresultsinthesetof{p,q,i}triplets,whereiisthenumberoftheimageinwhichpeakwithposition{p,q}wasfound.Fordatacollectedinthewideoscillationmode,theangleatwhichdiffractionoccursisnotknowapriorihowever,itcanbeapproximatedbythemiddleoftheoscillationrangeoftheimage.2011-11-21JiaweiWangjwwang@tsinghua.edu.cn22Autoindexing•Autoindexingissensitivetoinaccuracyinthedescriptionofdetectorgeometry.•AutoindexingwillshifttheoriginofthelatticetothenearestBraglatticepoint.Objective:Todeterminetheunitcell,probableLauegroupsymmetryandcrystalorientation.(Notethatintensitiesarerequiredtofindthetruesymmetry).[]()0RSah•=[]()()0cos2iiRSaπ•∑2011-11-21JiaweiWangjwwang@tsinghua.edu.cn23Autoindexing–NigglireducedcellHavingidentifiedalattice,the“reducedcell”mustbefound.Inthe2Dexampleshown,theblackcellcorrespondstothereducedcell,whiletheredorbluecellsmayhavebeenfoundintheautoindexing.《FundamentalsofCrystallography》,Page85-86.2011-11-21JiaweiWangjwwang@tsinghua.edu.cn24•[A]=[M][P]•[U]=[A][A’]-1•[U]T-[U]-1=0LatticeSymmetry[][]()216TijijPenaltyIndexUU−=−∑∑Apenaltyindexisassociatedwitheachlattice,whichreflectshowwellthedeterminedcellobeystheconstraintsforthatlatticetype.Thesolutionwiththehighestsymmetrywithlowpenaltiesisusuallychosenasthecorrectsolution.2011-11-21JiaweiWangjwwang@tsinghua.edu.cn25DiffractionGeometryRefinement()222predcentxhklxxxχσ−=∑()222predcentyhklyyyχσ−=∑()12222oophklPPPϕϕχσ−=∑Ifthecrystalrotyhappenstofallbetween45and135degrees,thishasahighercorrelationthanotherzonesandmakestherefinementofthecrystalorientationmoredifficult(althoughitwillstillwork).Choosinganequivalentzonefromthelistisaneasywaytoovercomethis.RockingCurve2011-11-21JiaweiWangjwwang@tsinghua.edu.cn26Integration-ProfileFitting•Twomajorassumptions–Reflectionshavethesameprofile:•Sameshape•Samedistribution–ReflectionsarepredictedaccuratelyIntegrate–Profilefitting•Twomajorassumptions–Reflectionshavethesameprofile:•Sameshape•Samedistribution–ReflectionsarepredictedaccuratelyDiamond(1969)ActaCrystA25,43-55.Ford(1974)JApplCryst7,555-564.Rossmann(1979)JApplCryst12,225-238.Kabsch(1988)JApplCryst21,916-924.Integrate–ProfilefittingIntegrate–ProfilefittingIntegrate–ProfilefittingIntegrate–ProfilefittingBadpredictions=Badreferenceprofile2011-11-21JiaweiWangjwwang@tsinghua.edu.cn32Integration–spotshape2011-11-21JiaweiWangjwwang@tsinghua.edu.cn33Integr