Understanding X-rays: The electromagnetic spectrum
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1 Understanding X-rays: The electromagnetic spectrum 1 ULa kev 0.09 nm BeKa 0.11 kev nm E = hn = h c l where, E : energy, h : Planck's constant, n : frequency c : speed of light in vacuum, l : wavelength E (kev) = h c l = /l (nm) or, l (nm) = h c E = /E (kev) Examples: l BeKa = nm; Hence, E BeKa = /11.27 = 0.11 kev E ULa = kev; Hence, l ULa = /13.61 = 0.09 nm
2 X-ray spectrum 2 Ti Ka Characteristic X-rays Fe Ka Intensity Bremmstrahlung (continuum) X-rays Ti Kb Fe Kb Wavelength Energy
3 Characteristic X-ray generation 3 Overvoltage, U = E/E c, > 1 E : electron beam energy E c : critical excitation energy (or, ionization energy) of shell in target atom Inner shell ionization through inelastic scattering (Ka)
4 cross-section of ionization Condition for ionization: Overvoltage 4 Best analytical condition, U 5
5 X-ray energies 5 X-ray Electron transition Energy Ka L II+III to K I E Ka = E c(ki ) - E c(lii+iii ) Kb M III to K I E Kb = E c(ki ) - E c(miii ) La M IV+V to L III E La = E c(liii ) - E c(miv+v ) Ma N VII to M V E Ma = E c(mv ) - E c(nvii )
6 X-ray energy and critical excitation energy 6 What is the energy required to excite UKa? Critical excitation energy of the U K-shell, E c(k) E c(k) kev Required energy > kev E Ka = E c(k) - E c(l) Rearrange E c(k) = E Ka + E c(l) Substitute E c(l) = E La + E c(m) = E Ka + (E La + E c(m) ) Substitute E c(m) = E Ma + E c(n) = E Ka + E La + (E Ma + E c(n) ) Therefore, E c(k) E Ka + E La + E Ma
7 Maximum x-ray production depth (range) 7 (Castaing s formula) R X-ray = x-ray range (maximum depth) E = electron beam energy E c = critical excitation energy of target atomic shell A = atomic weight r = density Z = atomic number
8 Maximum x-ray production depth (range) 8
9 Electron range versus X-ray range 9 x-ray range electron range The characteristic x-ray range is always smaller than the electron range E = beam energy E c = critical excitation energy of sample atomic shell Z = atomic number A = atomic weight r = density
10 X-ray depth-distribution: the f(rz) function 10 f(drz) = intensity from a free standing layer of thickness z f(rz) at depth z = intensity from depth z divided by f(drz) where, r = density, and z = depth
11 Continuum X-ray generation 11 Electron beam Produced by deceleration of beam electrons in the electrostatic field of target atoms Energy lost by beam electrons is converted to x-ray (Maximum energy of continuum x-rays = electron beam energy)
12 Continuum X-rays: background intensity 12 Low-Z sample (Ca-Fe poor) Low background High-Z sample (Ca-Fe rich) High background Increases with sample atomic number
13 Wavelength Dispersive Spectrometer (WDS) 13 detector crystal
14 Wavelength Dispersive Spectrometer (WDS) 14 l q q for n=1, ABC = 1l A Bragg s Law: nl = 2d sin q B C d L-value : L = nl R d sin q = L 2R n: order of diffraction l: wavelength of x-ray d: lattice spacing in diffracting crystal q: angle of incidence or diffraction L: distance between sample and crystal R: radius of focusing (Rowland) circle
15 2d of x-ray diffractors 15 Crystal lattices l (nm) For n=1, ~ 0.5d < l < 2d Layered structures l of BeKa = nm. BeKa can be diffracted only by 2d > nm diffractors,e.g., LDEB, LDE3H, LDEBH
16 WDS operation: detecting a specific l 16 Radius of focusing circle (R) is fixed Different wavelengths (l 1, l 2 ) can be diffracted by changing the L-value (L 1, L 2 ) that effectively changes the incidence angle (q 1, q 2 )
17 L-value 17 Example 1. Example 2. Si Ka U Ma Energy, E = 1.74 kev Energy, E = 3.17 kev l (nm) = E (kev) l (nm) = E (kev) Wavelength, l = = nm Wavelength, l = = nm L (mm) = n l (nm) R (mm) d (nm) For R = 140, and n = 1, L TAP = 1 x x = mm L (mm) = n l (nm) R (mm) d (nm) For R = 140, and n = 1, L PET = 1 x x = mm
18 Theoretical and actual limits of spectrometer movement 18 2R L 0
19 Diffraction angle 19 l 1 (Element 1) Different elements l 2 (Element 2) q 1 q 2 nl 1 = 2d sinq 1 nl 2 = 2d sinq 2 Wavelength being diffracted changes with the incidence angle (for the same order of diffraction, n)
20 First and second order diffractions 20 Same element n=1 n=2 q 1 q 2 D F A C B 1l = 2d sinq 1 = ABC E 2l = 2d sinq 2 =DEF path DEF = 2* path ABC Same wavelength is being diffracted at different diffraction angles; sinq 2 = 2sinq 1
21 Spectral resolution 21 Full-Width Half-Maximum (FWHM)
22 Curved diffracting crystals 22 Johansson type bending radius: 2R polished and ground to R R Johan type only bent to 2R, not ground Peak resolution with fully focusing Johansson-type crystal: FWHM ~10 ev Some defocusing in Johan-type, but resolution is not compromised
23 WDS vs. EDS spectral resolution 23 Peak overlaps in EDS spectrum Peak resolution with WDS (FWHM ~10 ev) is an order of magnitude better than with EDS (FWHM ~150 ev)
24 X-ray focusing ellipsoid 24
25 WDS detector: Proportional counter 25 Tungsten collection wire at 1-3 kv voltage Voltage of the pulse generated in the wire is proportional to the applied voltage in the wire Flow counter: P-10 gas (90% Argon + 10% methane quenching agent) Polypropylene window Sealed counter: Xenon gas Beryllium window
26 (for pulse voltage) Signal amplification 26 (Voltage) Typical voltage range in the proportional counter region for a W wire: V Signal is amplified in the proportional counter region because of secondary ionizations in the gas
27 Counter gas efficiency 27 ArK absorption edge is at E c(ar K-shell) XeL absorption edge is at E c(xe L-shell) (E c : critical excitation energy) Heavier elements Lighter elements X-ray entering detector (E X-ray ) ionizes the Ar K-shell or Xe L-shell when overvoltage U = E X ray E c(ar K shell or Xe L shell) > 1 and fluoresces ArKa or XeLa Argon: long wavelength (low energy) detection Xenon: short wavelength (high energy) detection
28 Proportional counter setup 28 Proportional counter output: Voltage pulses from noise and x-ray signal de baseline window A Single Channel Analyzer (SCA) allows only pulses from x-rays to pass through the energy window DE SCA scan shows the variation in count rate as a small voltage window (de) is moved across the voltage range Baseline and window voltages (DE) are set to filter out noise DE is determined through Pulse Height Analysis (PHA)
29 Pulse voltage in SCA scan 29 Energy of SiKa (1.739 kev) is ~1.4 times the energy of If the pulse for MgKa is at 4 V, SCA scan the pulse for SiKa will be at 4 x 1.4 = ~5.6 V MgKa: (1.253 kev)
30 Escape peak in SCA scan 30 Escape peaks: P-10 counter: ArKa SCA scan Xenon counter: XeLa Energy difference between the x-ray of interest and ArKa or XeLa
31 Proportional counter window 31 Mylar has lower transmittance than polypropylene, especially for light element x-rays Thin windows are better for light elements 1 mm thick polypropylene window transmits ~60% of the F Ka 6 mm thick polypropylene window transmits only ~5% of the F Ka
32 Detector slit 32 Positioned at focal point of diffracted x-rays on the Rowland circle Cuts off stray x-rays and electrons Open: LDE P-10 flow counter Very light elements (very low E, very long l) mm: PET or LIF Xe sealed counter Heavy elements (high E, short l) 300 mm: TAP P-10 flow counter Light elements (low E, long l) 300 mm PET or LIF P-10 flow counter Heavy elements with Mylar film: (high E, short l)
33 Semi-quantitative analysis 33
34 Compositional imaging with x-rays: elemental mapping 34 Beam-rastered image: electron beam rasters over the area to be imaged Stage-rastered image: electron beam is stationary, stage moves
35 Background in x-ray spectra 35 Ti Ka Peak intensity Characteristic X-rays Intensity Fe Ka Peak minus Background Bremmstrahlung (continuum) X-rays Ti Kb Fe Kb Background intensity Wavelength Energy
36 Background in x-ray image 36 Zn-Sn composite Background image Zn-rich phase (low Z) Sn-rich phase (high Z)
37 X-ray defocusing in beam-rastered image 37
38 Image quality of x-ray maps 38 Two factors: Image resolution: number of points measured within the imaged area X-ray Signal: beam current and counting (dwell) time per point
39 Combined WDS and EDS X-ray mapping 39
40 Combined BSE, CL and X-ray mapping 40
Understanding X-rays: The electromagnetic spectrum
Understanding X-rays: The electromagnetic spectrum 1 ULa 13.61 kev 0.09 nm BeKa 0.11 kev 11.27 nm E = hn = h c l where, E : energy, h : Planck's constant, n : frequency c : speed of light in vacuum, l
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