Interaction of Radiation with Matter « Element of modern x-ray physics »Element of modern x-ray physics J. Als-Nielsen et D. McMorrow « Processus d’interaction.

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Interaction of Radiation with Matter Element of modern x-ray physics Element of modern x-ray physics J. Als-Nielsen et D. McMorrow Processus dinteraction entre photons et atomes C. Cohen-Tannoudji, Particles: probes Two process of interaction Absorption and scattering dd kiki kdkd I0I0 I l dz Slide 2 Characteristics of particles Three types of particles Are used in condensed matter physics Tender and hard X-ray photons: 3-100 keV Low or high energy electrons: 150 eV-100 keV Hot, thermal or cold neutrons: 120-25-10 meV Interference effects: Wave length of particle must be smaller than interatomic distances Slide 3 Characteristics of particles X Photons Electromagnetic field E=h =hc/ =12398/E(eV) , E=12.4 keV =3.10 18 Hz (EHz) p=hk=h /c 3.10 -6 X-ray absorption Photoelectric effect Photon is absorbed if h > E I ( E I binding energy of e - ) Excitation: Photoelectron is emitted ( E=h - E I - ) : work function ~1 eV De-excitation: fluorescence photon ( h = E I - E II ) Auger electron ( E= E I - E II - E III ) h K (1s) 2 (2p 3/2 ) 4 L (2p 1/2 ) 2 (2s) 2 M Excitation For E < 1000 keV photoelectric effect is dominant De-excitation Photoelectron Auger electron Fluorescence photon Core levels Fermi level Continuum KK KK -E I -E II -E F Absorption of photons Emission of photons and electrons Slide 15 Order of magnitude Li 5,7 B 36 Gd 78300 Ni 4760 Pb 79800 aa X-rays: = 1.542 6 Li 520 10 B 2100 Gd 74000 Ni 4.6 Pb 0.17 aa Neutrons: 1.8 Slide 16 Electrons mean free paths From A. Zangwill, Physics at Surfaces, Cambridge Univ. Press. Distance between two inelastic collisions with Plasmons Valence electrons After this distance (attenuation length), electrons loose their coherence. Low energy electron diffraction (LEED) is a surface technique Only surface photoelectrons and Auger electrons escape from the sample Importance in X-Ray Absorption (XAS) Slide 17 Scattering Slide 18 Scattering: atome-particle system changes of state Elastic scattering: Initial state, i Final state, f Does not change the nature or the internal state of the particles and the target Slide 19 Rayleigh scattering: Low energy elastic scattering hE I ; i = f ; X-ray scattering Compton scattering: High energy inelastic scattering h >> E I ; i f ; X-ray scattering Slide 20 Photons scattering E p EOEO Free electron (e- mass m) Compton scattering E p EOEO Bound electron (atom, crystal mass Mm) Thomson scattering Compton scattering E O -E L (p i,E i ) (p f,E f ) Slide 21 Refraction A consequence of scattering Slide 22 Refraction n ktkt kiki krkr Refraction index For X-rays and neutrons Snells law Existence of a critical angle above which total reflection Stationnary wave kiki krkr cc Phase shift and absorption Measure of the sign of b (holography) Slide 23 Experimental techniques DIFFUSION : Rayons X Diffraction (Etude des structures) Diffusion diffuse (Etude du dsordre dans les cristaux, liquides, cristaux liquides) DiffusionCompton (Structure lectronique) Diffusion aux petits angles (Polymres, cristaux liquides, agrgats, grandes mailles) Diffusion magntique, inlastique, cohrente (synchrotrons) Neutrons Diffraction, Diffusion diffuse (Structures, Hydrogne, contraste diffrent) Inlastique (Excitations lmentaires, phonons, dynamique) Magntique (Structures magntique, magnons) Electrons Diffraction, LEED, RHEED (Etude des surfaces) EMISSION (par rayons X) : Rayons X Fluorescence (Analyse chimique) Electrons Photo-lectrons, lectrons Auger (Spectromtrie, analyse) Diffraction de photo-lectrons (structure locale) Photo-mission (Structure de bande, surface de Fermi ) WAVES/PARTICLES X-Rays Neutrons Electrons EMISSION : X-ray Fluorescence (Chemical analysis) Electron Spectroscopy Photoelectrons, Auger electrons (analysis) Photoelectron diffraction (local structure) Photoemission (band structure) REFRACTION : X-ray, neutrons Reflectrometry (surfaces, interfaces) Stationnary waves (surfaces) ABSORPTION : X-ray XAS, EXAFS, XANES (local order) Dichroism (Magnetism, surfaces) SCATTERING X-rays Diffraction (Structures); Diffuse scattering (Disorder, liquids, soft matter) Compton scattering (electronic structure) Small angle scattering (Polymer, liquid crystal, nano-particles, proteins) Magnetic, inelastic, surface, coherent diffraction (synchrotrons) Neutrons Diffraction, Diffuse scattering (Structures, Hydrogen, contrast) Inelastic scattering (phonons, dynamics, excitations) Magnetic (magnetism, magnons) Electrons Low- or high-energy electron diffraction (surfaces, thin samples) Crystal Liquid, liquid crystal Polymer Surface