X射线特征谱线

Diffractioncanbeeasilydemonstratedusingacommonlaserpointerandacommonfactory-madecompactdigitalaudiodisk(CD).ScanningelectronmicroscopephotosofaCD,

polycarbonateremovedtoshowbumps.ScanningtunnelingmicroscopephotoofCDstamper.Heightofbumpis¼thewavelengthoflightusedtoreadthem,7800Ang.Trackpitchis1.6μm.(unitsarenm)RowsofbumpsontheCDcanact

asadiffractiongrating.

Usingaredlaser…1storderdiffractionvisibletotheleftandrightoftheprimaryspot(transmittedbeam).2ndorder&1storderdiffractionbothvisibleForconstructiveinterference,toformabrightspotatpointP,thepathlengthdifference,

betweentheraysr1andr2mustequalanintegernumberofwavelengthsoflight,nλ.D...or

=nλInthelimitD>>d,thelargerighttrianglewithsidesy&Dissimilartothesmalleronewithsidesd&

inwhichsinθ=opp/hyp≈

/dso

≈dsinθ,nλ≈dsinθFinally,forsmallangles,θ≈sinθ=y/D,soinsimplestformnλ≈dy/D.Measurethisyourselfwitharulerandcalculatethespacingdbetweentracks!Insteadofredlight,λ=6500Å,usex-rays,λ=1.5ÅforCuKα.Asthewavelengthisreducedbyafactorof4000,wecanexamineobjectssmallerbyafactorof4000.InsteadofmeasuringspacingbetweenrowsofpitsonCD,measurespacingbetweenplanesofatomsinacrystallinesolid!Therearemanydiversepracticalreasonswhywestudycrystallography.Wewillnowdiscussseveralofthese.(Dieter,MechanicalMetallurgy,p.61)(Elastic)(ASM,MetalsHandbook,vol.8p.230)TerminologyCrystal:1)Greek:kryos-cold,frost2)Greek:krystallos-iceorsomethingfrozen3)heavyclearglass,asin"crystalball"-NOTourinterestinthisclass4)Asolidcomposedofatomsormoleculesinafixedrepeatingpatternandhavinganexternalshapeboundedbyplanefacesinasymmetricalarrangement.5)Anymaterialhavingadiscretediffractionpattern.Crystallography:*Thestudyofcrystals.*Rene-JustHauyisconsideredthefounderofthemodernscienceofcrystallography,c.1800.*AugusteBravaiscorrectlydescribedthe14fundamentallatticesin1848.Diffraction:1)Latin:diffractus-tobreakintopieces2)Thebreakingupofawavecausedbyinterferenceofonepartofthewavefrontwithanotherattheedgeofanopaqueobjectorslit.Instructorwillsketchthelatterontheboard.NobelPrizesrelatingtocrystallographyanddiffraction

X-Rays

1901WilhelmRoentgeninPhysicsforthediscoveryofx-rays.(in1895)1914MaxvonLaueinPhysicsforx-raydiffractionfromcrystals.1915W.H.BraggandW.L.BragginPhysicsforcrystalstructurederivedfromx-raydiffraction.1917CharlesBarklainPhysicsforcharacteristicradiationofelements.1924K.M.G.SiegbahninPhysicsforx-rayspectroscopy.1927ArthurComptoninPhysicsforscatteringofx-raysbyelectrons.(Comptoneffect,inelastic)1936PeterDebyeinChemistryfordiffractionofx-raysandelectronsingases.1946HermannMullerinMedicineforthediscoveryoftheproductionofmutationsbymeansofX-rayirradiation.1954LinusPaulinginChemistryforresearchintothenatureofthechemicalbondanditsapplicationtotheelucidationofthestructureofcomplexsubstances.(x-raystudiesofaminoacids)X-Rayscontinued1962M.PerutzandJ.KendrewinChemistryforthestructureofhemoglobin(byx-raydiffraction)1962J.Watson,M.Wilkins,andF.CrickinMedicineforthestructureofDNA.Thekeyx-raydiffractionworkwasdonebyRosalindFranklinbetween1951and1953.Seelink

DorothyHodgkininBiologyfordeterminationsbyx-raytechniquesofthestructuresofimportantbiochemicalsubstancesincludingpenicillin.A.McLeodCormack&G.NewboldHounsfieldinMedicineforcomputedaxialtomography.H.HauptmanandJ.KarleinChemistryfordirectmethodstodeterminecrystalstructures.J.Deisenhofer,R.Huber,andH.MichelinChemistryforthestructuresofproteinsthatarecrucialtophotosynthesis.(byx-raydiffraction)ElectronsandNeutronsPhilippLenardinPhysicsforimportantworkoncathoderays.(discoveredaround1869byHittorf)J.J.ThomsoninPhysicsforresearchesintothedischargeofelectricityingases(discoveryoftheelectron,in1897)C.DavissonandG.ThomsoninPhysicsfortheirexperimentaldiscoveryofthediffractionofelectronsbycrystals.1981K.M.SiegbahninPhysicsforhighresolutionelectronspectroscopy.AaronKluginChemistryfordevelopmentofcrystallographicelectronmicroscopyandstructuralelucidationofbiologicallyimportantnucleiacid-proteincomplexes.1994B.BrockhouseandC.ShullinPhysicsforneutrondiffractionandspectroscopyforstudiesofcondensedmatter.MicroscopyErnstRuskainPhysicsforhisfundamentalworkinelectronoptics,andforthedesignofthefirstelectronmicroscope(aTEM,inBerlin,1933)andG.BinnigandH.RohrerinPhysicsfortheirdesignofthescanningtunnelingmicroscope(atIBM,1981)

Inonemodeofoperation,theTEMisusedforelectrondiffractionstructuredeterminationusingBraggs’Lawandinadifferentmodeofoperationitproducesimagesinnormalspace.Inthoseimages,diffractionisoneofthemainmechanismswhichproducescontrast.Bibliography:nobel.se,nobelprizes,/vol-56/iss-3/p42.htmlOntoCullityChapter1…Theproduction,absorption,detectionandvariouspropertiesofx-rays.Wheredox-rayscomefrom?Radioactivedecayofnumerousisotopes.Forexample40Kundergoeselectroncapture,decaysto40ArandemitsacharacteristicArKax-ray(andaneutrino).Thisisamanifestationoftheweaknuclearforce.Cosmicraysubatomicparticlesfromoutsideourgalaxywithenergiesashighas1020eV/particleimpactEarth’satmosphereandcreateshowersofsecondaryparticles.Thoseshowersincludesomex-rays.BlackbodyradiationfromtheSun’scorona(outeratmosphere)whichhasatemperatureofafewmilliondeg.C.AccordingtoWien’slawtheelectromagneticspectrumhasanintensitypeakatλpeak=.0029m°K/T.Cathoderaytubes(CRT)SynchrotronparticleacceleratorsAlthoughx-raysoccurinnature,thatisnotwheretheywerediscovered.Instead,RoentgenusedaCRT.Wedotoo.(Rigaku)Inthex-raylabCRTvoltageisusually≤40kV.Generally,ifvoltageis<100kVspecialrelativityisnotneededandtheelectronvelocityandenergyarerelatedbyE=e*V≈mv2/2whereVisvoltage,visvelocity,eistheelectronchargeandmisitsmass.Thisapproximationisgoodaslongaselectronvelocityismuchlessthanthespeedoflight,v2/c2<<1Seealso:RiceisamemberoftheGCPCCsowecouldgettimeonthemachineatLSUifneeded.Synchrotronradiationispolarized.AccordingtoSynchrotronRadiationBasicPropertiesbyL.Rivkin“Synchrotronradiationobservedintheplaneoftheparticleorbitishorizontallypolarized”and“Observedoutofthehorizontalplane,theradiationisellipticallypolarized.”InCullityChapter4wewillseethatpolarization(orlackofit)affectstheintensityofdiffractedx-raybeams.X-raysfromaCRTarenotpolarized.Propertiesofx-raysBythelate1800'sitwasapparentthatx-rays:CarrynochargeArenotdeflectedbymagnetHavevaryingabilitytopenetratematter(hardness)ArenotrefractedorfocusedbypassingthroughglasslensesPropertiesofx-raysLateritbecameapparentthatx-raysareelectromagneticradiation,soE=h

=hc/

IfEisineVand

inÅthenE=12398.4eVÅ/

.Inthisclasswedonotusenmorergsorjoules.Therearetwocomponentstox-rayemissionsfromaCRT:continuous“Bremsstrahlung”backgroundand“characteristic”radiationatdiscreteenergies(wavelengths).(Cullity)At20kVorlowervoltage,noK-shellx-raysareexcited.TheshortwavelengthlimitSWL=12398.4/kVisduetoconservationofenergy.Thewavelength(andenergy)ofKαandKβareconstant,characteristicofthechemicalelement.Moseley’sLaw(Cullity)Foragivenemissionline,Z=σ+√υ/Cor√υ=C(Z–σ).FortheBohrsingle-electronatom(orion)σ=0andC≈1/slopeoftheplottedKα1line.Notation:Thisx-raylinenomenclatureusingGreeklettersisknownasSiegbahnnotation.Anothersystemisshownonthenextslide.Ifone’stexteditordoesnotallowGreeklettersorthetypistisinahurryKαbecomesKa.Opticalcharacterrecognitionsoftwaremayconvertαintoa.IntensityofKaisthesumoftheintensitiesofKa1andKa2,aftersubtractingofftheBremsstrahlungbackground.Ka1andKa2areclosetoeachotherinenergyandoftenunresolved.WavelengthofKaistheweightedaverageofKa1andKa2.Ka1istwiceasintenseasKa2soit’sweightedtwiceasmuchinthataverage.Tobeentirelyproper,subscriptsshouldbeused.Forexample:Ka1shouldbeKα1.Goldsteinetal,ScanningElectronMicroscopyandX-rayMicroanalysisX-raysandtheircorrespondingelectronictransitionsarenamedoneoftwoways:SiegbahnnotationusingGreeklettersorequivalentenergylevelnotationperIUPAC:Kα1,Kβ3,Lβ1etc.KLIII,KMII,LIIMIV(Dickerson,ChemicalPrinciples)ShellQuantumnumbersn,l,m,scorrespondingtoshellsK,L,M,NCertaintransitionsare“forbidden”byquantummechanicsrules,becausethex-rayphotonhasangularmomentum1andbecauseangularmomentummustbeconservedduringthetransition.Forexample,thetransitionfrom(nlm)equal(200)to(100)isforbidden.ShellBasedontheformulaintheprecedingslide,EKa=hν=En=1–En=2=constant*Z2(1-¼)or√ν=4.97x107Z/sec-1/2

whichisrathersimilartoMoseley’sLawfromthreeslidesearlier

√ν≈5x107(Z-1)/sec-1/2Notallelectronictransitionsarepossible.Permissibleonesarespecifiedbythequantumselectionrulesbelow.Magneticquantumnumbermhasnoeffect,exceptinamagneticfield.Thechangein

n

mustbe≥1(Δn≠0)Thechangein

l

canonlybe±1Thechangein

j

canonlybe

±1or0Examplesofforbiddentransitions:(n,l,m,s)=(2,0,m,±½)→(1,0,m,±½)isforbiddenbyrule2.(n,l,m,s)=(2,1,m,+½)→(2,1,m,-½)isforbiddenbyrule2.References::///cefns/labs/electron-microprobe/glg-510-class-notes/signals/andand:///~kb12/1311/Electronic_spectra_revised.pdf.Cullityappendicesarenumberedabitdifferentin2nd&3rdeditions.MostofthedataarewavelengthsinAngstroms.OnlyonecolumnisinKeVenergy.Convertfromonetotheotherusing

=12,398.4eV

Ang/ELet’szoominonthetableinthelowerportionofthepage.(Cullity)Notes:*TheKedgewavelengthforanyelementisalwayslessthanitsKαandKβwavelengths.

Kedge<

Kβ1<

Kα1<

Kα2<

LIIIedge<

Lα1.*CuKαweightedaveragewavelengthis

Kα=(2

Kα1+

Kα2)/3=1.541838Ang.(Cullity)WhiletheabovetableinCullitygivescharacteristicwavelengths,sometimesweneedcharacteristicenergies.Inthatcaseuse

whichismuchmorecompletethanCullity.Let’stakealookatthat.Besidesthecharacteristicenergiesofemissionlines,thoselineshavesomenaturallinewidth>0andtheintensitiesofthelineshavesomefairlysystematicbehavior.Thesex-raypropertiesareoutlinedinthenextfewslides.Naturalwidthsofcharacteristicemissionlines(peaks)aresmall,butx-raydetectorsallbroadenthelinestovaryingextents.Afewslidesearlierwasaplotofx-rayintensityvs.wavelengthforaMotube.ThemeanenergyoftheMoKα1emissionlineis17,480eVascomparedwithitswidthtabulatedhereof6.82eVandaspacingbetweenMoKα1andMoKα2emissionlinesof105eV.Asanotherexample,anddoingabitofinterpolationfromthatprecedingtable,forCuKa1thenaturallinewidthisabout3.2eVwhichisabout0.04%oftheline’senergy.AndforCuKa2thefigureiscloserto0.05%.InlabourthreeRigakumachineshavex-raydetectorswhichbroadenthosenaturallinewidthstoabout50.%.Ifweweredoingspectroscopy,thatwouldbebad.Butformostdiffractionworkwefilterthex-raysemittedfromthesourcetubesoalmostallhavethesameenergy(CuKa).Weknowtheenergy,don’tneedtomeasureit.Insteadwecountx-raysasafunctionoftheirangleofdiffraction.Intensitiesofthevariousx-rayslinesproducedinthesourcetubearenotawell-behavedfunctionoftheindependentvariables:chemicalelement,voltage,etc.Forpureelements,iftheintensityofthestrongestlinefromashell(K,L,M)isarbitrarilynormalizedto100%,thenalltheotheremissionlinesfromthatshell(forthesameelementandvoltage)haveintensity<100%.Approximatevaluesofthoserelativeintensitiesaregivenby

FromthesumsofintensitiesKα=Kα1+Kα2andKβ=Kβ1+Kβ2+Kβ3onecancalculatetheintensityratioKβ/Kαwhichisplottedhereforthevariouselements:

Duetocomplicatedeffectsofatomicnumber,absorptionandfluorescenceinrealmaterials,theintensityofalinefromoneshellisnotcloselyrelatedtotheintensityofalinefromadifferentshell.IntensityofacharacteristicKline(peak)isapproximatedusing:

IK-line=const.i(V-VKedge)nwhereiiselectronbeamcurrent(emissioncurrent)intheCRTVKedgeisvoltageoftheKabsorptionedgeand(V-VKedge)is“overvoltage”n=1.5±0.5orsoconst.dependsonchoiceofKa1,Ka2,orKaaswellasmassdensityoftheemittingelementandofalltheotherelementsintheemittingmaterialwhichcanabsorbthoseKx-rays.IK-lineisintegratedintensityfromλ=0toλ=

ofIK-line(λ)dλandhastheunitsofpower.IntensityofthecontinuousBremsstrahlungbackgroundis

IBrem.=const.iZVmwhereZisatomicnumber,VisCRThighvoltagem≈2IBrem.isanintegratedintensityfromλ=0toλ=

notincludingcharacteristicemissionlinesandhastheunitsofpower.Soathighvoltage,thepeaktobackgroundratiodecreases.Notgood.Thefollowingiscrucialtoatleastonehomeworkproblem:InordertogenerateanyKx-raysinaCRT,itisnecessarytofirstknockoutelectronsfromthatinnerKshell.Thisrequiresacertainminimumamountofenergy(voltage)perincidentelectron,theK-shellabsorptionedgeenergy.Usingλ=12398.4Ang.eV/EthatabsorptionedgeenergycorrespondstoanabsorptionedgewavelengthwhichistabulatedinanappendixofCullity.OnceaninnerKshellelectronisknockedout,therearecertainprobabilities(intensities)ofKα1andKα2andKβx-raysandAugerelectronsbeingproduced.Ifanyofthoseareproduced,thentheywillallbeproducedinvariousamounts.AbsorptionofX-raysinthesamplematerialX-rayAbsorptionMechanismsfromSchwartz&Cohen,DiffractionfromMaterialsLefttoright,fourspectroscopies:XAS,XRF,XPS,AESInthepreviousslide,upperfigure:“Heat”isgeneratedinthesample,notavectorleavingthesample.“Diffractedbeam”and“incoherentscattering”aretwodifferentthings.Thediffractedbeamhasthesamewavelengthastheincidentbeam,buttheincoherentlyscatteredx-rayshavealongerwavelengthandarejustnoisewhichisuselessforXRDwork.Andinthelowerfigure:Theabsorbingmaterialhasahalf-filledvalenceband,soit’sametal.Intherightmostdiagram,AugerElectronEmission,theeventsshownmustcomeAFTERaninitialstepinwhichaKshellelectronisejected.Alsointhatsamerightmostdiagram,ifthex-raywerenotabsorbedwithintheatom,wewouldhaveXRF.Inaparticularatomataparticularinstant,ifoneprocessoccurs,thentheotherdidnotoccur.Ifaninnershellelectronisejectedfromanatom,leavingitinanunstablestate,andanoutershellelectronfallsintofillthevacantorbital,thenacharacteristicx-rayisgenerated.Inthiscasetherearetwopossibleoutcomes:XRF:Thecharacteristicx-rayescapesfromtheatomandcanbedetected.AE:Thecharacteristicx-rayisabsorbedwithinthesameatomandcausesanAugerelectrontobeejectedfromtheatom.So,wesaythatcharacteristicx-rayfluorescence(XRF)andAugerelectronemission(AE)arecomplementaryprocesses.Probabilityω:Ifaninner-shellvacancyiscreated,thenω(XRF)+ω(AE