Electron probe microanalysisWhat’s the point?OverviewElastic and inelastic scattering of HV electron by sampleSlide 5Scattering lexiconElastic and inelastic scatteringBackscattered ElectronsSecondary ElectronsSE imagesSE and BSE coefficientsInner-shell ionization: Production of X-ray or Auger e-X-ray Lines - K, L, MAll possible K, L, M X-ray LinesX-ray Lines with initial + final levelsNomenclature of X-raysAbsorption Edge EnergyOvervoltageFluorescence yieldContinuum X-raysContinuum and Atomic NumberX-ray units: A, keV, sin q, mmMoseley’s RelationCathodoluminesceCL ImagesElectron interaction volumesRanges and interaction volumesElectron and X-ray RangesRangesSlide 30Monte Carlo simulationsSpecimen Heating“Harper’s Index” of EPMASources of X-ray dataElectron probe microanalysis Electron - SpecimenInteractionRevised 9/10/2003UW- Madison Geology 777What’s the point?Electrons from a sourceinteract with electrons in specimenyielding a variety of photons and electronsvia elastic and inelastic scattering processes. These are the “signals” that we monitor and measure to characterize our specimens.UW- Madison Geology 777Overview•Elastic and inelastic processes•Characteristic and continuum X-rays•K,L,M etc: families of X-rays•Energy versus wavelength•Moseley’s relation•Absorption or critical excitation energy•Interaction volume and ranges•Monte Carlo models•Odds of X-ray productionUW- Madison Geology 777Elastic and inelastic scattering of HV electron by sampleElastic (a): incident electron’s direction altered by Coulombic field of nucleus (Rutherford scattering), screened by orbital electrons. Direction may be changed by 0-180° (ave 2-5°) but velocity remains virtually constant. <1 eV of beam energy transferred.Inelastic (b): incident electron transfers some energy (up to all, E0) to tightly bound inner-shell electrons and loosely bound outer-shell electrons. Direction barely changes (<0.1°)(Goldstein et al, 1992, p.72)E0 = accelerating voltage (of electrons emitted from gun); usually 15-20 keVUW- Madison Geology 777Elastic and inelastic scattering of HV electron by sample(Goldstein et al, 1992, p.72)This represents 1000 electron trajectories (idealized), in a cross-section--both elastic and inelastic scattering. UW- Madison Geology 777Scattering lexicon Cross section: a measure of the probability that an event of a certain kind will occur, e.g. K-shell cross section. Defined as Q = N/nint, where N=events of certain type/vol (sites/cm3), ni=number incident particles/unit area (particles/cm2), and nt=number target sites/vol (sites/cm3). Q has units of cm2 and is thought of as an effective ‘size’ which the atom presents as a target to incident particle. The Q for elastic scattering is ~10-17 cm2 and for K-shell ionization is ~10-20 cm2.Mean free path: average distance an electron travels within a specimen between events of a specific type. MFP=A/(NAQ) where A is atomic wt (g/mol), NA is Avogadro’s number,  is density (g/cm3).UW- Madison Geology 777Elastic and inelastic scattering Elastic : Backscattering of electrons (~high energy)Inelastic :Plasmon excitation (in metals, loosely bound outer-shell electrons are excited)Phonon excitation (lattice oscillations: heating)Secondary electron excitation Inner-shell ionization (Auger electrons, X-rays)Bremsstrahlung (continuum) X-ray generationCathodoluminescence radiation (non-metal valence shell phenomenon)UW- Madison Geology 777Backscattered ElectronsHigh energy beam electrons may suffer multiple elastic scattering events in the solid, with cumulative effect of escaping from the material.The fraction of beam electrons that scatter back () was found experimentally to vary directly as a function of composition (atomic number Z). This provides a valuable imaging tool: a rapid means to discriminate phases that have different mean Z values.Intensity (grey level) varies from black (voids/epoxy), to plagioclase, olivine, basaltic glass, with Ti-magnetitethe brightest phase.UW- Madison Geology 777Secondary ElectronsInelastic scattering of HV beam electron can promote loosely bound electrons from valence to conduction band in semiconductor or insulator with enough energy to move thru the solid (in metals, promotion from conduction-band directly). Backscattered electrons can also produce secondary electrons.a) Complete energy distribution of electrons emitted from target. Region I and II are BSE, Region III secondary. b) Secondary electron energy distribution, measured (points) and modeled (lines)By definition, these secondary electrons are <50 eV, with most <10 eV.(Goldstein et al, 1992, p. 107)UW- Madison Geology 777SE imagesSecondary electrons are generated throughout the interaction volume, but only secondary electrons produced near the surface are able to escape (~5 nm in metals, ~50 nm in insulators). For this reason, secondary electron imaging (SEI) yields high resolution images of surface features.These have grey-scales, though pseudo-coloring is sometimes done.Pollen, cat flea, and Si nanowires on alumina sphere.20 mUW- Madison Geology 777SE and BSE coefficients(Goldstein et al, 1992, p. 109)Coefficients for backscattered-electron () and secondary electron () as function of Z. Tilt of specimen from 90° beam incidence () is 0. E0=30 keV. Data from 1966; more recent views suggest the flat SE curve may be due to carbon contamination on specimen hindering SE escape.UW- Madison Geology 777Inner-shell ionization:Production of X-ray or Auger e-(Goldstein et al, 1992, p 120)HV electron knocks inner shell (K here) electron out of its orbit (time=1). This is an unstable configuration, and an electron from a higher energy orbital (L here) ‘falls in’ to fill the void (time=2). There is an excess of energy present and this is released internally as a photon. The photon has 2 ways to exit the atom (time=3), either by ejecting another outer shell electron as an Auger electron (L here, thus a KLL transition), or as X-ray (KL transition).K shellL shell(=photoelectron)Blue Lines indicate subsequent times: 1 to 2, then 3 where there are 2 alternate outcomesTime123UW- Madison Geology 777X-ray Lines - K, L, M(Goldstein et al, 1992, p 121)K X-ray is produced due to removal of K shell electron, with L shell electron taking its place. K occurs in the case where K shell electron is replaced by electron from the M shell.L X-ray is produced due to removal of L shell