Synchrotron radiation

Transcription

1 Synchrotron radiation Bremsstrahlung is the electromagnetic radiation produced by the acceleration of a charged particle, such as an electron The electromagnetic field generated by a particle of charge q subjected to an acceleration a is described (at large distance R) by: E = q/(4πε 0 c 2 R) 1/(1-n v/c) 3 n [(n v/c) a] B = (n E)/c Poynting s vector: Σ = 1/μ 0 E B Σ n [(n v/c) a] 2 1/(1-n v/c) 6 v c The larger is a the larger the intensity of the emitted radiation B α = 1/γ = (1 β 2 ) 1/2 e - e - hν The synchrotron light is linearly polarized in the electron plane perpendicularly to the electrons trajectory

2 ESRF in Grenoble Electrons emitted by an electron gun are first accelerated in a linear accelerator (linac) and then transmitted to a circular accelerator (booster synchrotron) where they are accelerated to reach an energy level of 6 GeV. European Synchrotron Radiation Facility, Grenoble E = mc β β = These high-energy electrons are then injected into a large storage ring (844 meters in circumference) where they circulate in a vacuum environment, at a constant energy, for many hours.

3 Beamline Beamlines at ESRF The synchrotron beams emitted by the electrons are directed towards the "beamlines" which surround the storage ring in the experimental hall. Each beamline is designed for use with a specific technique or for a specific type of research. Experiments run throughout the day and night.

4 Undulator: The elliptical undulator is a devices for the production of circularly polarized synchrotron radiation. In an EPU, the magnetic field vector rotates as a particle passes through the device, causing the particle to spiral about a central axis. EPUs consist of four banks of magnets two on top and two below. The peak energy of the undulator output is changed by varying the vertical separation between the magnet assemblies, a so-called gap scan, while the polarization is varied by changing the relative positions (phases) of adjacent rows of magnets a row scan. Magnets and particle path in an EPU. Monochromator: an optics consisting of mirror and gratings select the photon energy -> ΔE/E <10-3 Intensity: photons/second For comparison a Mg K α XPS laboratory source produces an intensity of 10 7 photons/second Acquisition time: 1 second vs 30 hours for comparable signal to noise ratio

5 Synchrotron light spectrum SLS: Swiss Light Source Photons/sec/mr 2 /0.1%BW Electron energy: 2Gev Bending magnetic field:1t BW = band width = Δλ/λ Photons energy (ev) You can chose the photon energy you want Convention: Soft X-rays -> energy < 1keV Hard X-rays -> energy > 1keV

6 Photon - electron interaction Electron in the electric field generate by the photons H = H part + H int = p 2 /2m + V coulomb + H int Example: the electron in a H atom with H int = 0 V coulomb = -e 2 /4πε 0 r In terms of the spherical coordinates r, θ, and φ the wave function takes the form Ψ(r, θ, φ) = R(r) Θ(θ) Φ(φ) which gives three equations. The equation for each of the three variables gives rise to a quantum number and the quantized energy states of the atom can be specified in terms of these quantum numbers. A fourth quantum number arises from electron spin. Two electrons can not have an identical set of quantum numbers according to the Pauli exclusion principle. R(r) -> principal quantum number n = 1, 2, 3,.. (K, L, M,..) Θ(θ) -> orbital quantum number L = 0, 1, 2,, n-1 Φ(φ) -> magnetic quantum number m l = -L, -(L-1),. L-1, L -> spin quantum number m S = ± 1/2

7 Interaction of the electron with the electromagnetic field H int = Σ i (-q i /m i p A + q i2 /2m i A 2 + b i S i B) A(r,t) = Σ k α k ε k [a k exp(-iω k t+ik r)+ a k+ exp(iω k t-ik r)] ε is a unit vector defining the light polarization 1) Single photon process: destruction (a k term) or creation (a k+ term) of a photon conserving the energy 2) Two photons process: elastic diffusion with the destruction and the creation of a photon with the same energy 3) Zeeman effect: electron interaction with the magnetic field of the electromagnetic radiation On a first approximation only the first term is taken into account. Moreover, if the photon wavelength is large compared to the electronic shell dimension the electrical field can be considered position independent (A(r,t) = A(0,t) -> dipole approximation). It can also be shown that: e/m p A(0,t) = e r E(0,t) H int (0,t) r ε [a k exp(-iω k t) + c.c.]

8 The probability of the electronic transition between an initial state i and a final exited state f is described by the time dependent perturbation theory: W i f = 2π/ħ 2 f H int i 2 δ(ω fi ) with ω fi = (E f E i )/ħ For example in the case of the Hydrogen atom (central potential) i is described by n i, l i, m i where n, l, m are the quantum numbers In the dipole approximation W i f = 2π/ħ 2 f r ε i 2 [ a k 2 δ(ω fi - ω k ) + a k + 2 δ(ω fi + ω k ) ] σ= W i f /I 0 -> cross section of the photon-electron interaction (I 0 photon intensity) Energy conservation: term a k : annihilation of a photon with energy ħω k = (E f E i ) term a k + : creation of a photon with energy ħω k = (E i E f ) Dipole selection rule: ΔL = ± 1, Δm = 0, ± 1 ΔL = ± 1, Δm = + 1, ΔL = ± 1, Δm = 1, ΔS = 0 (linear polarization) ΔS = 0 (circular right polarization) ΔS = 0 (circular left polarization) Note: in a solid the quantum number L is replaced by J Any electron transition which involves the emission of a photon must involve a change of 1 in the angular momentum. The photon is said to have an intrinsic angular momentum or "spin" of 1, so that conservation of angular momentum in photon emission requires a change of 1 in the atom's angular momentum.

9 XAS: X-rays absorption spectroscopy Z = 79 Gold Measure of the x-rays intensity absorbed by the sample as a function of the in-coming photon energy A narrow beam of mono energetic photons with an incident intensity I o, penetrating a layer of material with mass thickness x and density ρ, emerges with intensity I given by the exponential attenuation law: I/I 0 = exp[-(μ/ρ)x] The mass thickness is defined as the mass per unit area, and is obtained by multiplying the thickness t by the density ρ, i.e., x = ρt. Usually the ratio μ/ρ is tabulated where: μ/ρ = x -1 ln(i 0 /I) The ratio μ/ρ is a measure of the probability of a given interaction process of photons with matter In particular we have μ/ρ = σ tot /ua where u = g is the atomic mass unit, A is the relative atomic mass of the target element, and σ tot is the total cross section for an interaction by the photon, frequently given in units of b/atom (barns/atom), where b = cm 2.

10 The total cross section can be written as the sum over contributions from the principal photon interactions The sharp edges correspond to the photon-electron interaction, while the intensity reduction in between is due to the other interaction processes σ tot = σ pe + σ coh + σ incoh + σ pair + σ trip + σ ph.n where σ pe is the atomic photon-electron cross section, σ coh and σ incoh are the coherent (Rayleigh) and the incoherent (Compton) scattering cross sections, respectively, σ pair and σ trip are the cross sections for electronpositron production in the fields of the nucleus and of the atomic electrons, respectively, and σ ph.n is the photonuclear cross section. M I edge E = 3425 ev M II edge E = 3148 ev M III edge E = 2743 ev M IV edge E = 2291 ev M V edge E = 2206 ev L I edge E = ev L II edge E = ev L III edge E = ev K edge E = ev

11 Some examples Z = 13 Aluminum Z = 29 copper Z = 79 Gold Z = 82 Lead For a fixed photon energy, absorption is highest in heavy material like Au or Pb Ex: for E = 2 kev Pb > μ/ρ = cm 2 /g and ρ = 11 g/cm 3 > I/I 0 = e -1 for t = cm Al > μ/ρ = cm 2 /g and ρ = 2.7 g/cm 3 > I/I 0 = e -1 for t = cm for E = 400 kev Pb > μ/ρ = cm 2 /g and ρ = 11 g/cm 3 > I/I 0 = e -1 for t = 0.4 cm Al > μ/ρ = cm 2 /g and ρ = 2.7 g/cm 3 > I/I 0 = e -1 for t = 3.9 cm

12 Several ways to measure the X-rays absorption: 1) Transmission: measure of the photon intensity after the beam traveled across the sample -> the more clean technique but for soft X-rays you need a thin sample (< 100 nm) 2) Total electron yield: measure of the current flowing from ground to the sample to counterbalance the emitted electrons -> surface sensibility because only the electrons coming from the surface layers can escape the sample 3) Emitted electrons: measure of the emitted electrons like in the Auger and XPS technique -> you need a complicate and expensive analyzer but you can have surface sensibility 4) Fluorescence: measure of the photons emitted during the relaxation process -> you have bulk sensibility but you need to separate the contribution of the in-coming and out-coming photons Photons + electrons X-rays Transmitted X-rays A

13 Actually the detection mode depends on the experiment you want to perform Ex.: detection of the emitted electrons K. Amemiya et al., J. Phys.: Condens. Matter 15, S561 (2003) The Cu signal increases increasing the detection angle (measured respect to the surface plane) -> you are loosing surface sensibility due to the increased electron escape depth Electron mean free path Only electrons generated at a surface distance not exciding the red line can escape in a direction parallel to the surface

14 Oscillations in absorption due to interference between outgoing and scattered photoelectrons by neighbors at r - Higher coordination higher amplitude - Shorter r increased period Convention: EXAFS -> about 100 ev above absorption edge XANES -> around the absorption edge

15 XPS Two well-separated N 1s peaks are observed with a chemical shift of 1.3 ev. The peak with the lowest binding energy (399.4 ev) corresponds to ionization of the outer N atom, whereas the high binding energy peak at ev is due to ionization of the inner N atom XAS In X-ray Absorption spectroscopy, a core electron is excited into unocupied atomic/molecular orbitals above the Fermi level. The XAS records the absorption intensity as a function of the incoming photon energy. In the soft x-ray regime electronic transitions are governed by dipole selection rules and consequently the absorption cross-sections show a polarization dependent angular anisotropy. By means of polarization dependent XAS measurements it is therefore possible to determine the orientation of molecular adsorbates.

16 Chemical shift H = H + H atom crystal field p Ze e H = + + ( r) l s; H = eφ ( r) i atom ξ i i i crystal field 2m ri rij XAS XPS Spin-orbit coupling of the 2p core levels Spin-orbit coupling of the 3d valence states Ti 2 O 3 Modification of the electronic cloud produces a perturbation of the entire Hamiltonian (included the core levels) Appl. Phys. A 78, (2004); J. Phys. Soc. Jpn., Vol. 75, (2006)

17 XANES: X-ray Absorption Near Edge Structure The absorption edge shape is representative of the film thickness and chemical composition Co/Pt(111) J. Thiele et al. Surf. Sci.. 384, 120 (1997) SiO 2 /Ni 81 Fe 19 (80 Å)/Co(20 Å)/ Al(20 Å+plasma oxidation for x seconds)/ Ni 18 Fe 19 (100 Å)/Cu(30 Å) Satellite peak due to the CoO N.D. Telling et al. Appl. Phys. Lett. 85, 3803 (2004)

18 Catalysis and catalysts A catalyst is a substance that increases the rate of a reaction Gold particles as a catalyst: CO + O 2 -> 2CO 2 A. T. Bell, Science, 299, 1688 (2003); M. Valden et al., Science, 281, 1647 (1998); C. Zhang et al., J. Am. Chem. Soc., 129, 2228 (2007); A. Cho, Science, 299, 1684 (2003) CO2 formation. (a-c) Au20 island with coadsorbed O 2 and CO (C atom in gray online): (a) the initial configuration; (b) the transition state (c) formation and desorption of CO 2 ; (d) the total energy profile along the C-O(2) reaction coordinate.

19 XANES spectra Angew. Chem. Int. Ed., 45, 4651 (2006) Pure Au Au + O 2 Au + CO Exposing the Au + O 2 to CO Produces first the CO + O 2 -> CO 2 And then the Au + CO.bonding formation

20 Diffraction Structure of chocolate unraveled at the ESRF Think about a piece of chocolate. Imagine it melting in your mouth. The sensation is delicious. Now think of the same image, but this time the chocolate is covered by a white film on its surface. This white film is produced when chocolate is poorly crystallized or when it is stored under the wrong conditions. We 'eat' also with our eyes and such badlooking chocolate seems less nice to the palate. Researchers from The Netherlands, working at the ESRF, are trying to avoid this white layer, called fat bloom, by studying the structure of chocolate. They studied the structure of a component of cocoa butter and also the crystal structure of the most common form of cocoa butter in chocolate

21 Band structure Schematic ray diagrams for the interference paths corresponding to quantum well states of the first kind (top panel) and the second kind (bottom panel). The first kind involves two S reflections, one each at the surface and the interface, while the second kind involves two S reflections at the surface and a pair of conjugate U (umklapp) reflections at the interface. While a S reflection preserves k //, a U reflection changes k // to k // -G (with G the surface reciprocal lattice vector of Ge) Angle-resolved photoemission data taken from a 13 ML Ag film on Ge(111) (top panel) and the same overlaid with labels and results from a model calculation (bottom panel). The set of approximately parabolic bands centered about the M point of Ge are quantum well states of the second kind. The quantum numbers n are indicated. Q1, Q2, and Q3 are quantum well states of the first kind. SS is a Shockley surface state. Phys. Rev. Lett., 96, (2006) Phys. Rev. Lett. 97, (2006)