Ele lectron and ele lectromagnetic radiation Generation and interactions with matter Interaction with sample Response Stimuli
Stimuli Waves and energy The energy is propotional to 1/ λ and 1/ λ 2 λ 1 λ λ 1 > λ 2 Electromagnetic waves : E= hc /λ = hf = hcν h: Plancks constant, f: frequency, ν: wave number E 1 <E 2 Electron waves :E= eV o , E=½ mv 2 = ½ m(h/ λ ) 2 Matter waves are referred to as de Broglie waves λ 2 where λ =h/p and p=mv.
Stimuli Electron radiation Relationship between acceleration voltage, wavevector, wavelength, mass and velocity k = λ -1 (nm -1 ) U (Volt) λ (nm) m/mo v/c 1 0.815 1.226 1.0000020 0.0020 10 2.579 0.3878 1.0000196 0.0063 10 2 8.154 0.1226 1.0001957 0.0198 10 4 81.94 0.01220 1.01957 0.1950 10 5 270.2 0.00370 1.1957 0.5482 2*10 5 398.7 0.00251 1.3914 0.6953 10 7 8468 0.00012 20.5690 0.9988 The speed of the electron is approaching the speed of light.
Stimuli Electromagnetic radiation Gamma Hard X-rays Soft X-rays Visible light F= Far E = Extreme N= Near HF = high freq. MF= medium freq. LF= low freq.
Energy conserv rvation «Bremsstrahung» When an electron is slowed down (accelerated) and the energy of the electron drops (speed is reduced), the energy can be transformed into electromagnetic radiation. How can an electron be slowed down? Why is the target cooled down?
Energy conserv rvation The wavelength of X-ray radiation ( λ ) is related to the acceleration voltage of electrons ( V ) as shown in the equation: 2.1 How can this equation be derrived? Electromagnetic waves : E= hc/ λ Electron waves :E= eV o What is the peak energy of the bremsstrahung in fig. 2.2 (Mo) from 10 and 20 keV electrons?
Interaction with sample In Interaction and penetration depth Coulombic interaction with e- (Much stronger interaction compared to the interaction with X-rays and neutrons) The Coulombic force F is defined as: F = Q 1 Q 2 / 4 πε o r 2 r : distance between the charges Q 1 and Q 2 ; ε o : dielectric constant. http://www.microscopy.ethz.ch/downloads/Interactions. pdf
Interaction with sample Interaction and penetration depth In E 0 =20 keV : Typical energy of electrons used for analytical TEM ~200keV scanning electron microscopy studies . t: up to a few X-ray penetration depth: hundred nm. The depth at which the intensity of the radiation inside t of interest the material falls to 1/e (about much less. 37%) of its original value at just beneath the surface. wiki
Interaction with sample Energy conserv rvation - Interaction with sample Response Stimuli E 1 E 2 Z+ Elastic scattering event If E 1 = E 2 If E 1 > E 2 Inelastic scattering event ~Elastic example: Back scattered electrons.
Interaction with sample Non, sin ingel or r plu lural/ multiple scattering of of ele lectrons Interaction cross-section ( σ , Q) and mean free path ( λ mfp ) represents the probability of a scattering event. t * * t t: thickness of the specimen Illustration based on figure in: http://www.microscopy.ethz.ch/ downloads/Interactions.pdf
Interaction with sample In Inelastic scattering
Interaction with sample Inelastic scattering Energy transfered to the specimen Electromagnetic waves tranfere all their energy. i.e. The initial electromagnetic wave is absorbed. Electrons can transfere parts of their energy. i.e. The electron continues with less speed/energy Interaction with sample Response Stimuli E 1 E 2 How can the sample absorb the energy E 1 -E 2 ?
Interaction with sample Inelastic scattering Energy transferred to matter • Oscillations/vibrations of Quantified energy states • Molecules and lattice (phonon) Phonon electron energy losses ~ 0.1 - 0.5 eV, Electromagnetic absorption (Molecules: 200-4000 cm -1 ) (Lattice: 20-300 cm -1 ) (Lattice vibrations are more temperature dependent than molecule vibrations) Ref. Ch. 9.0 - 9.1.3. • Free electron gas density (plasmon) Energy: E p =(h/2 π ) ω ~10-30 eV Plasmon frequency: ω =((ne 2 / ε o m)) 1/2 n: free electron density, ε o : dielectric constant
Example: Analysis of f molecule vib ibrations by IR IR Stimuli Responce Which energy do 1000 cm -1 correspond to? ν =100000 m -1 : λ =0.00001 m 1 J= 6.2415 e18 eV Electromagnetic waves : E= hc /λ = hf = hcν h: Plancks constant, f: frequency, ν: wave number
Responce Inelastic scattering Example: Ele lectron energy lo loss spectroscopy; pla lasmon peaks (a (and core lo loss edges). Thin specimen Wiki magnunor Similar to the absorption spectra of the electromagnetic radiation.
Responce Inelastic scattering Effect of of tecnic ical im improvments (T (TEM and STEM) ) EELS can now be use sed to detect energy lo loss sses due to la lattic ice vib vibratio ions (phonon) ) The progress has taken place on three principal fronts: (1) the energy resolution of EELS carried out in the electron microscope has been improved to around 10 meV; (2) the EELS – STEM instrument has been optimized so that the electron probe incident on the sample contains a current sufficient to perform EELS experiments Why? even when the energy width of the probe is ∼ 10 meV and its size <1 nm; and (3) the tail of the intense zero loss peak (ZLP) in the EELS spectrum has been reduced so that it does not obscure the vibrational features of interest.
Responce Inelastic scattering Measurement of f bandgap. . Spatial resolution!
Interaction with sample Inelastic scattering Energy transferred to matter • Oscillations/vibrations of Quantified energy states • Molecules (200-4000 cm -1 ) and lattice (20-300 cm -1 ) (phonon) Energy losses ~ 0.1 eV (Lattice vibrations are more temperature dependent than molecule vibrations) Ref. Ch. 9.0 - 9.1.3. • Free electron gas density (plasmon) Energy: E p =(h/2 π ) ω ~10-30 eV Plasmon frequency: ω =((ne 2 / ε o m)) 1/2 n: free electron density, ε o : dielectric constant • Exitation/ionisation • Electrons goes from a ground energy state to a higher energy state above the fermi level. - Ionization - Excitation (Above 50 eV and typically more than thousand eV for the ionization of inner electron shells (core electrons).)
Interaction with sample Inelastic scattering Ionization of Io of in inner shells x-ray Electron M M 3d 6 3p 4 L 3d 4 L 3s 2 2p 4 3p 2 K 2s 2 K 2p 2 1s 2 Secondary electron Photo electron EELS X-ray photo electron spectroscopy and X-ray absorption spectroscopy 1st. responce
X-ray absorption and photo ele lectron spectroscopy When the energy of the photons increases, More on XPS later the absorption coefficient μ(ω) decreases. in the semester! https://xpssimplified.com/whatisxps.php http://www.fis.unical.it/files/fl178/9232XASChap6.pdf Can also probe occupied and unoccupied valence states Singe wavelength X-ray Synchrotron radiation Commonly: Al K α https://xpssimplified.com/elements/germanium.php
X-ray energy fi filtering http://pd.chem.ucl.ac.uk/pdnn/inst1/filters.htm The absorption edge of nickel metal at 1.488 Å lies between the Kα (λ = 1.542 Å) and Kβ (λ = 1.392 Å) X-ray spectral lines Anode Cu Co Fe Cr Mo of copper. Hence nickel foil of an appropriate thickness can Filter Ni Fe Mn V Zr be used to reduce the intensity of the Cu Kβ X-rays
Relaxsation Responce Auger electron The probability to emit an Auger electron or X-ray M Characteristic x-ray L K Siegbahn notation Ex.: K α 1 Intensity: α > β > γ > and 1>2>3 Fluorescence: electromagnetic radiation generate new electromagnetic radiation
Fluorecent yield The relative effectiveness of X-ray generation
Example: Detection of f continuous and characteristic x-rays E K >E L >E M Characteristic X-ray energies. The cut-off energy for ? continous x-rays. Continous X-ray energies http://www.emeraldinsight.com/journals.htm?articleid=1454931&show=html
Example: Detection of f continuous and characteristic x-rays E K >E L >E M Characteristic X-ray energies. Two peaks Limited resolution of the detection method (EDS) http://www.emeraldinsight.com/journals.htm?articleid=1454931&show=html
Overlapping peaks Improved resolution with wavelength dispersive spectroscopy
A A very ry short summary ry: : Stimuli Interaction with sample Inelastic Elastic E 1 > E 2 E 1 = E 2 Excitations: phonon, plasmon, ionization Zero, single, multiple scatteing events Dynamic conditions Kinematic condition
Recommend
More recommend
