Characterization of Steels by Anomalous Small-Angle X-ray Scattering PeterRene´ Jemian June1990 ii (cid:13)c CopyrightbyPeterRene´ Jemian,1990 AllRightsReserved iii Abstract CharacterizationofSteelsbyAnomalousSmall-AngleX-rayScattering PeterRene´ Jemian ThesizedistributionandvolumefractionofCr C havebeenisolatedfromthedistributionsofallotherprecipi- 23 6 tatesinagedsamplesofaferriticalloy,ModifiedFe9Cr1Mosteel,bythetechniqueofanomaloussmall-angleX-ray scattering(ASAXS),inwhatisbelievedtobethefirstapplicationofthistechniquetoprecipitationinanengineering alloy. Thesteelhasbeenproposedforuseatelevatedtemperaturesforlongtimesinpowergenerationequipmentand the stability of the microstructure must be verified. Six samples were aged for 5000 hours at either room tempera- ture, 482, 538, 593, 649, or 704◦ C to simulate a typical in-service condition. Synchrotron radiation was used as a variable-wavelength source of X-rays. Three X-ray wavelengths near the Cr K absorption edge were used to vary the scattering contrast of Cr C while leaving that of the other precipitates fixed. A double-crystal diffractometer 23 6 and a silicon photodiode X-ray detector were specially designed for use atthe synchrotron to measure the scattered radiation. Thethreesmall-anglescatteringcurvesfromeachsamplewereanalyzedbyamaximumentropytechnique toobtainthreescatteringcontrast-weightedsizedistributionsofalltheprecipitatesthatgiverisetotheobservedscat- tering. AscatteringcontrastgradientanalysiscombinedthethreeexperimentstoisolatetheCr C volumefraction 23 6 distributions. The mean diameter of Cr C particles was found to increase with temperature for 5000 hour aging 23 6 between538and704◦C,consistentwithpriortransmissionelectronmicroscopyresults. Theultra-highstrengthsteelalloyAF1410,currentlyusedforarrestinghooksoncarrier-basedaircraft,derivesits desirablepropertiesbyadelicateheattreatmentthatcarefullybalancestheformationofonecarbidewiththedepletion ofanother. ThelackofASAXSneartheCrandFeK absorptionedgesindicatesthatthedistributionsofprecipitates observed(presumablyM Candaustenite)areiron-enrichedandchromium-deficient. 3 ApprovedbyProfessorJuliaR.Weertman iv v Preface ceiiinosssttuv-RobertHOOKE,1676 Chapter1providesinformationabouttheASAXSinvestigationsofotherworkersandalsosomebackgroundonthe twosteelalloysinvestigatedbytheASAXStechnique. InChapter2,thetheoryunderlyingsmall-anglescatteringand thespecificASAXSapplication, equationsthatdescribethedesignandoperationoftheDCDoptics, theprocessof resonantRamanscattering,andageneraldescriptionofthesiliconphotodiodedetectoraregiven. Theexperimental equipmentandprocedurearedescribedinChapter3. Chapter4describestheexperimentalcommissioningofthenew DCD and photodiode detector using the scattering of polystyrene spheres and bulk microporous silica. Also given there are the SAXS and ASAXS results for the two steels alloys being investigated. These data are summarized in Chapter 5 and suggestions for future investigations with the DCD are presented. In the first appendix, the results of SAXS experiments on other materials of interest in materials science are given. These materials are bulk micro- TM porous silica and porous Vycor glass. Other appendices contain the electrical schematics for the Si photodiode detector,thecomputerprogramsforcollimationcorrection,Lake.FOR,andinterpretationofsmall-anglescattering, MaxSAS.FOR,andtheexperimentalSAXSdataforthesteels. SI units are reported throughout with the exception of degrees Celsius, rather than Kelvins, and mass density in g·cm−3. The wavelength, λ, of X-ray photons is described in terms of their photon energy, E, where the relation Eλ = 1.239857804 nmkeV isused. Usageof nomenclaturewillbe keptconsistent withineach sectionofthe text orexplicitlynoted. Forstyle,thisworkfollowsguidelinessetforthbyMichaelson,98 butalsotakesadvicefromthe remarksofMermin.97 Argumentsoncomputerprogrammingstyle15,17,100werealsoconsidered. vi vii Acknowledgements uttensiosicvis-RobertHooke,1678 Iamgratefultomyadvisor,ProfessorJuliaR.Weertman,forherencouragement,guidance,andfinancialsupport throughout this study. I would like to express my great appreciation to Dr. Gabrielle G. Long of the National Insti- tuteofStandardsandTechnologyfornumerousilluminatingdiscussionsandmany∞ longhoursatthesynchrotron. Additionally, I would like to thank Dr. Joe Georgopoulos for materials, advice, and assistance in the early stages of this project and Dr. Greg Olson for samples and helpful advice. Special thanks go to Mr. Rich Matteson for ad- vising a change of career from jazz music. I think he would be proud. This research was supported by the United States Department of Energy under grant DE-FG02-86ER45229. Dean J. B. Cohen is to be acknowledged for his initial suggestion that anomalous dispersion might be used to separate the small-angle scattering from one type of scattererinamulti-componentalloy. FromtheOakRidgeNationalLaboratory,Dr.VinodSikkaisacknowledgedfor providing the Modified Fe9Cr1Mo steel, Dr. George Wignall and Dr. S. Spooner for conducting small-angle X-ray scatteringmeasurementsattheNationalCenterforSmall-AngleScatteringResearch,andDr.A.Habenschussforthe fPrime.FOR code which was obtained via Dean J. B. Cohen. The UKAEA-Harwell laboratory is acknowledged fortheMaxe.FORmaximumentropySASanalysiscode. Dr.RichardD.SpalofNISTistobeacknowledgedforhis supportoftheexperimentalphasebyprovidingassistanceatthesynchrotronbeamline. TothemembersoftheAll-NightScatteringCrewatthesynchrotronwhoengagedthemselvesinapracticalstudy ofthelong-termeffectsatambienttocryogenictemperaturesoflow-cyclefatigueofmaterialsscientists: Dr.Andrew Allen,Dr.DavidBlack,Dr.DidierGavillet,Dr.GabrielleLong,Dr.JuliaWeertman,Mr.JohnBarker,andMr.Kishio HidakaaretobecommendedfortheirabilitiestofighttheFourAMfatigue. SpecialthanksgotoMr.HaroldHalof theGoldenHandsBurdetteofNISTforassistanceindesign,mechanics,andconstructionoftheDCDSAXScamera. Appreciation is extended to my colleagues at Northwestern University, both past and present for their valuable discussion, friendly harangues, and general camaraderie. Particular thanks go to Mr. Mike Verrilli whose graphical machinationswithSASdataprovidedtherealizationofhowtoprocesstheSASdatamoreefficiently. Also,special thanks are extended to the personnel in the Chemistry Department Electronics Shop (especially the late Mr. Jim Baker),MaterialsScience“world’sfriendliest”MachineShop,MetallographyLab,TEMfacility,andX-raydiffraction facility.Lastbutnotleast,Iacknowledgetheguidanceofmyparentswhoatkeybifurcationpointsinmydevelopment providedagentlenudgeorevenastrongtuginwhattimehasproventobetherightdirection. viii Contents 1 Introduction 1 1.1 AnomalousDispersionSmall-AngleX-rayScattering(ASAXS) . . . . . . . . . . . . . . . . . . . . 1 1.1.1 MetallurgicalApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 OtherApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 SteelAlloyDescriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 ModifiedFe9Cr1MoSteel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 AF1410Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Theory 7 2.1 Small-AngleScattering(SAS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 BasicSASTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 ScatteringfromSphericalParticles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 InstrumentalCollimationCorrection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.4 SizeDistributionAnalysisbyMaximumEntropyTechnique . . . . . . . . . . . . . . . . . . 11 2.2 AnomalousDispersionSmall-AngleX-rayScattering(ASAXS) . . . . . . . . . . . . . . . . . . . . 14 2.2.1 AnomalousDispersionandtheDispersionCorrections . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 ScatteringLengthDensity,Contrast,andStrength . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.3 ExperimentRequirementsforASAXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.4 LimitsofDetectability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.5 IsolationofaSingleScattererbyASAXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 ResonantRamanScattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Double-CrystalDiffractometerCamera(DCD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 Bonse-HartDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.2 OptimizationoftheOpticsfortheSynchrotronSource . . . . . . . . . . . . . . . . . . . . . 24 2.4.3 RockingCurveCalculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4.4 AsymmetricReflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 SiliconPhotodiodeDetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.1 PrinciplesofOperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.2 AmplifierElectronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Experimental 31 3.1 SteelSamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1 HeatTreatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 SAXSSamplePreparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 ix x CONTENTS 3.3 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.1 X-raySource . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.2 Monochromator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.3 ExperimentalHutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.4 BeamTransportandIncidentBeamMonitor . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.5 Double-CrystalDiffractometerAnalyzerMonolith . . . . . . . . . . . . . . . . . . . . . . . 34 3.4 SiliconPhotodiodeX-rayDetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5 ComputerDataAcquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 DataReduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.7 RawData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8 AbsoluteIntensityConversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.9 Slit-LengthDesmearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.10 SizeDistributionAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 ResultsandDiscussion 41 4.1 ValidationofEquipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.1 PolystyreneSpheres: 255and460nmdiameters . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.2 SiliconPhotodiodeDetectorvs. ScintillationCounter . . . . . . . . . . . . . . . . . . . . . . 43 4.1.3 AbsoluteIntensityCorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.4 Slit-WidthCorrection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 ModifiedFe9Cr1MoSteel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.1 SampleThicknessMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.2 MeasurementofAnomalousDispersionCorrections . . . . . . . . . . . . . . . . . . . . . . 49 4.2.3 ScatteringStrength-WeightedSizeDistributionAnalyses . . . . . . . . . . . . . . . . . . . . 52 4.2.4 CalculationoftheScatteringContrasts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.5 Cr C VolumeFractionDistributionIsolatedbyASAXS . . . . . . . . . . . . . . . . . . . 60 23 6 4.2.6 SummaryofModifiedFe9Cr1MoSteelAnalyses . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3 AF1410Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3.1 ASAXSAnalyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3.2 Austenitizedat1000◦C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.3 Austenitizedat830◦C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.5 SummaryoftheAF1410SAXSanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5 Summary 77 5.1 SuggestionsforFutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Appendix: OtherSamples 81 A BulkMicroporousSilica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 B PorousVycorTMGlass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Appendix: SiliconPhotodiodeDetector 85 C ImplementationoftheSiliconPhotodiodeDetector . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 D CircuitDiagramsfortheModularDetector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87