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