the theory: characteristic x-ray...
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The theory:The theory:Characteristic XCharacteristic X--ray generationray generation
(Inelastic scattering)(Inelastic scattering)
InnerInner--shell shell ionizationionization
KKαα L to KL to K--shell transitionshell transitionKKββ M to KM to K--shell transitionshell transitionLLαα M to LM to L--shell transitionshell transitionLLββ N to LN to L--shell transitionshell transitionMMαα N to MN to M--shell transitionshell transition
OvervoltageOvervoltageU = E/Ec
where, E is the beam energyEc : critical excitation energy
or absorption edge of the shell
Condition forCondition for
inner shell ionizationinner shell ionization ::
U U > 1> 1
XX--ray energy and wavelengthray energy and wavelengthE=E=hhνν
h h : Planck's constant: Planck's constant((6.626x106.626x10--3434 Joule.secJoule.secor, 6.626x10or, 6.626x10--3434/1.6021x10/1.6021x10--1616 keV.seckeV.sec))
ν ν :: frequencyfrequency (= (= c/c/λλ))((c c : speed of light in vacuum: speed of light in vacuum== 2.99793x102.99793x101818 ÅÅ/sec/secλ λ : wavelength): wavelength)
λλ ((ÅÅ)) = = hchc/E/E = 12.398/= 12.398/E E ((keVkeV))
The electromagnetic spectrumThe electromagnetic spectrum
InnerInner--shell ionizationshell ionization
QQ=6.51x10=6.51x10--2020[([(nnssbbss)/()/(UEUEcc22)]ln()]ln(ccssU U ))
Q Q :: Cross sectionCross sectionnnss : # : # electrons in the shellelectrons in the shellbbss,,ccss : : constantsconstants
InnerInner--shell ionizationshell ionization
XX--ray production rangeray production range
An analogous expression to the electron range An analogous expression to the electron range ( R = KE( R = KE00
nn//ρ ρ ))
XX--ray Rangeray Range:: RR = = K(EK(E00nn -- EEcc
nn)/)/ρρwhere,where, KK = 0.064, = 0.064, nn = 1.68= 1.68
Always smaller than electron rangeAlways smaller than electron range
BremsstrahlungBremsstrahlung or Continuum or Continuum XX--raysrays
Generated by deceleration Generated by deceleration of beam electrons in of beam electrons in the the CoulombicCoulombic field of field of outer shells of target outer shells of target atoms.atoms.
Energy: any value in the Energy: any value in the 00--EE00 range forming a range forming a continuous spectrum.continuous spectrum.
crystalcrystal
detectordetector
WDSWDS WDSWDS
Wavelength Dispersive Spectrometer Wavelength Dispersive Spectrometer (WDS)(WDS)
BraggBragg’’s Laws Law
nnλλ = 2= 2dd sinsin θθ
WDS: Focusing geometryWDS: Focusing geometry
LL = = nnλλ .R/d.R/d
WDS: SetupWDS: Setup
WDS: Analyzing crystalsWDS: Analyzing crystals
NNaammee 22dd((ÅÅ))
TTyyppee RReessoolluuttiioonn RReefflleeccttiivviittyy EElleemmeennttss uussuuaallllyyaannaallyyzzeedd
LLDDEECC 9988 NNii//CC LLaayyeerreeddSSyynntthheettiiccMMiiccrroossttrruuccttuurree
LLooww HHiigghh BB--OO ((KKαα)),, ooppttiimmiizzeeddffoorr CC aannaallyyssiiss
SSTTEE 110000..44 PPbb sstteeaarraattee MMeeddiiuumm MMeeddiiuumm BB--OO ((KKαα)),, ooppttiimmiizzeeddffoorr CC aannaallyyssiiss
LLDDEE11 5599..88 WW//SSii LLaayyeerreeddSSyynntthheettiiccMMiiccrroossttrruuccttuurree
LLooww HHiigghh CC--FF ((KKαα)),, ooppttiimmiizzeeddffoorr OO aannaallyyssiiss
TTAAPP 2255..88 TThhaalllliiuumm aacciiddpphhtthhaallaattee
MMeeddiiuumm MMeeddiiuumm NNaa--PP ((KKαα));; CCuu--ZZrr((LLαα));; SSmm--AAuu ((MMαα))
PPEETT 88..774422 PPeennttaaeerryytthhrriittooll LLooww HHiigghh SS--MMnn ((KKαα));; NNbb--PPmm((LLαα));; HHgg--UU ((MMαα))
LLIIFF 44..002288 LLiitthhiiuumm fflluuoorriiddee HHiigghh HHiigghh TTii--RRbb ((KKαα));; BBaa--UU((LLαα))
WDS: Analyzing crystalsWDS: Analyzing crystals
WDS: XWDS: X--ray detectorray detector(proportional counter)(proportional counter)
Flow proportional counter
WDS: Proportional counterWDS: Proportional counter
Tungsten collection wireTungsten collection wireFlow counter: 90% Flow counter: 90% ArAr +10% CH+10% CH44 (P(P--10); 10); FormvarFormvar or cellulose nitrate windowor cellulose nitrate windowSealed counter: Sealed counter: XeXe or Kr; Be windowor Kr; Be window
Dynamic range: 0Dynamic range: 0--50,000 counts/second 50,000 counts/second Collection wire bias range: 1Collection wire bias range: 1--3 kV3 kV
Bias is set so that gas amplification is Bias is set so that gas amplification is in the proportional regionin the proportional region
Amplification in proportional Amplification in proportional countercounter
Gases in proportional counterGases in proportional counter
Gas used for long wavelengthsGas used for long wavelengths: : 90% 90% ArAr +10% CH+10% CH44 (P(P--10)10)Gas used for short wavelengthsGas used for short wavelengths: : XeXe or Kror Kr
WDS: Pulse Height Analysis (PHA)WDS: Pulse Height Analysis (PHA)
WDS: PHA setupWDS: PHA setup
Single Channel Analyzer (SCA) scanSingle Channel Analyzer (SCA) scan
Imaging with XImaging with X--rays: rays: compositional mappingcompositional mapping
BeamBeam--rasteredrastered image: image: electron beam electron beam rastersrastersover the area to be imagedover the area to be imagedStageStage--rasteredrastered image:image: electron beam is electron beam is stationary, stage movesstationary, stage moves
Uses of compositional mapsUses of compositional mapsMg Ca
Na Ti
A set of XA set of X--ray elemental maps can be used inray elemental maps can be used inestimating phase (mineral) proportionsestimating phase (mineral) proportions
estimating bulk chemical compositionestimating bulk chemical composition
textural analysistextural analysis
XX--ray image artifact: backgroundray image artifact: background
ZnZn--SnSn compositecomposite
Higher XHigher X--ray ray background for background for SnSnresults in spurious Ca results in spurious Ca imageimage
XX--ray image artifact: backgroundray image artifact: background
•• Phase with Elem #2 generates a higher XPhase with Elem #2 generates a higher X--ray ray background than phase with Elem #1background than phase with Elem #1•• At wavelength of interest, higher XAt wavelength of interest, higher X--ray intensity ray intensity results (on phase with Elem #2) even if element is results (on phase with Elem #2) even if element is absentabsent
Defocusing in beamDefocusing in beam--rasteredrasteredWDS XWDS X--ray mapsray maps
No defocusing in stageNo defocusing in stage--rasteredrastered maps: recommended maps: recommended for large area mappingfor large area mapping
StageStage--rasteredrastered XX--ray mapping ray mapping parametersparameters
ResolutionResolution# pixels (step size)# pixels (step size)
SignalSignalDwell time per pointDwell time per pointBeam currentBeam currentConcentrationConcentration
ContrastContrastInterInter--phase concentration phase concentration differencedifference
StageStage--rasteredrastered XX--ray map: ray map: acquisition time acquisition time
Stage speedStage speed
Decreases as resolution (#steps) Decreases as resolution (#steps) increasesincreases
Decreases as dwell time per point Decreases as dwell time per point increasesincreases
Limited by hardware (stageLimited by hardware (stage--motor) motor) settingsetting
StageStage--rasteredrastered XX--ray map example: ray map example: Hawaiian LavaHawaiian Lava
Scale bar: 4 mmScale bar: 4 mm
BEBE OO MgMg CaCa
•• Olivine (Mg,Fe)Olivine (Mg,Fe)22SiOSiO4 4 -- light in O and Mg mapslight in O and Mg maps
•• AugiteAugite Ca(Mg,Fe)SiCa(Mg,Fe)Si22OO6 6 -- light in Ca maplight in Ca map
•• Crystallized fineCrystallized fine--grained matrixgrained matrix
StageStage--rasteredrastered XX--ray map parameters: ray map parameters: Hawaiian Lava exampleHawaiian Lava example
Resolution: Resolution: 20 20 µµm/stepm/step# pixels (steps):# pixels (steps): 1500x7501500x750 (image (image size: size: 30mm x 15mm30mm x 15mm))
SignalSignalDwell time per point: Dwell time per point: 30 30 msecmsec/point/pointBeam current: Beam current: 30 30 nAnA (voltage: (voltage: 15 kV15 kV))
Hardware settingHardware settingAverage stage speed: Average stage speed: 0.71 mm/sec0.71 mm/sec(maximum allowed: (maximum allowed: 2 mm/sec2 mm/sec))
Acquisition time: Acquisition time: 14 hrs 18 min14 hrs 18 min
Matrix compositionMatrix compositionH
awai
ian
Lav
aH
awai
ian
Lav
abulk olivine augite matrix error
Area% 100% 19.9% 19.6% 60.4%Weight%
measured calculated SiO2 43.04 38.57 46.85 43.35 0.15TiO2 2.61 0.03 2.23 3.58 0.04Al2O3 11.43 0.05 7.42 16.50 0.39Cr2O3 0.05 0.02 0.08 0.06 0.01FeO 13.95 19.21 7.82 14.23 0.10MnO 0.19 0.25 0.10 0.20 0.01MgO 13.98 41.61 12.90 5.25 0.09CaO 11.62 0.33 22.11 11.96 0.25Na2O 2.11 0.55 3.32 0.07K2O 0.71 1.17P2O5 0.29 0.49Total 100 100.20 100.04 100.08
wwbulkbulkSiOSiO22bulkbulk = w= wolivolivSiOSiO22
olivoliv + w+ waugaugSiOSiO22augaug + w+ wmatrixmatrixSiOSiO22
matrixmatrix
where, where, wwii = (= (area%)area%)ii . . ρρii
Note: Bulk and mineral compositions determined by ICP Note: Bulk and mineral compositions determined by ICP and EPMA, respectivelyand EPMA, respectively