Lunds universitet, Fysiska institutionen, Avdelningen för synkrotronljusfysik. Spektroskopi och materiens kvantmekaniska beskrivning, vårterminen PDF

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Lunds universitet, Fysiska institutionen, Avdelningen för synkrotronljusfysik Spektroskopi och materiens kvantmekaniska beskrivning, vårterminen 2008 Discussion questions, meeting 4 th February ESCA Figure

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Lunds universitet, Fysiska institutionen, Avdelningen för synkrotronljusfysik Spektroskopi och materiens kvantmekaniska beskrivning, vårterminen 2008 Discussion questions, meeting 4 th February ESCA Figure 1 presents the core electron binding energies in the elements. Obviously the energies are relatively independent of the chemical environment in which they are found. What kind of analysis can the binding energies thus be used for? Now have a look at the spectra in Figure 2. They were measured on exactly the same sample, but using different photon energies. 1. Identify the two elements contained in the sample using the attached electron binding energy tables. Observe that the tabulated binding energies can deviate from the measured ones by up to a couple of ev. 2. Obviously some of the peaks in the spectra are not constant in binding energy. What characterises these peaks? Photoionisation cross sections Figure 3 displays the (partial) photoionisation cross sections for the electronic levels of silver. 1. The photoionisation cross section for a particular single electron level (orbital) x is proportional to f er x = d 3 rφ f (r) er φ x (r) (In the derivation we used the total states rather than the one electron states - why can we make the transition to single electron states? Think of the derivation of the Hartree and Hartree-Fock methods!). How does this matrix element explain the overall decreasing size of the photoionisation cross section with photon energy? 2. Some of the partial photoionisation cross section curves exhibit a more or less pronounced minimum, typically some ten evs and up to slightly more than 100 ev above threshold. These minima are the so-called Cooper minima. Read section III in J. W. Cooper, Phys. Rev. 128 (1962) 128 (you need not read the rest of the paper). Follow his argumentation and explain the occurrence of the minima. 1 3. Imagine you would like to study the gold valence band states of a single layer of gold on a silver surface. The valence states of Au are made up from the 5d and 6s levels, those of Ag from the 4d and 5s levels. The binding energies of the silver and gold valence bands are approximately the same. Which photon energy would you use? Use Figures 3 and 4 in your argumentation. Surface sensitivity Consider the attenuation lengths for photons in graphite and electrons in different materials shown in Figure Define the term attenuation length. 2. What gives rise to the feature at 300 ev photon energy in the photon attenuation length in graphite (consider the electronic structure of graphite)? 3. Compare the photon and electron attenuation lengths. Which of them is more relevant in photoelectron spectroscopy? How much more relevant? 4. Suggest methods for rendering a photoelectron spectroscopy experiment more surface- or more bulk-sensitive. 5. Identify the core level in Figure Which of the two peaks corresponds to photoemission from an element in the surface and which of them to photoemission from an element in the bulk? Koopmans theorem Koopmans theorem relates the observed binding energy E B,k of a particular electronic level to the one-electron energies derived using the Hartree-Fock or Density functional theory methods (or other variational methods). Read pages 16 and 17 up to equation (1.10) in Hüfners book and try to understand the argumentation. Now switch to Manne and Åberg s article on an extension of Koopmans theorem, which takes excited states of the final ionic state into account. 1. What do you expect to see in the spectra as a result of the physics described by Manne and Åberg? 2. Compare your expectations to the example in Figure The entire transition given rise to in the photoelectric effect is, as we know, governed by the dipole approximation. If ones writes the electronic states of the initial 2 and final states in terms of one-electron wave functions (see, e.g., Hüfner s text), it becomes obvious that a particular part of the transition has to obey the dipole selection rule. What does this imply for the remaining part of the transition? Chemical shifts The binding energies in photoemission spectroscopy and the transition energies in x-ray absorption spectroscopy are typical for the elements as discussed above. In addition, they exhibit small shifts, which depend on the chemical environment of the probed atoms. An illustration of this chemical shift can be found in Figure 8. Read the section on chemical shifts in Hüfners book and then reconsider the spectra in the figure. 1. Often (too often!) observed chemical shifts are interpreted in terms of a derivation of Hüfners equation (2.6): E B = KQ 1 + L 1 KQ 2 L 2 = K(Q 1 Q 2 ) since L 1 = L 2. Apply this interpretation to the case of ethyl trifluoroacetate in Figure Leaving the inaccurate Koopmans theorem behind us, the binding energy of a particular core level k can be rewritten as E B,k = ε k + E relaxation,k + E correlation,k, where the ε k are the Hartree-Fock (DFT,...) orbital energies. Obviously the first term corresponds to the original theorem of Koopman (prior to the extension of Manne and Åberg), while the second and third terms take further energy contributions into account. Which ones, if you just look at the names (remember that a photohole is created in the photoemission process!)? 3. One can thus write for a chemical shift: E B,k = ε k + E relaxation,k + E correlation,k. ε k is called the initial state contribution to the chemical shift (why?), while E relaxation,k is termed thefinal state contribution (why?). E correlation,k often cancels out. The final state contribution is very important; often it is more important than the initial state contribution. Consider a couple of different systems (for example gas phase carbon monoxide, ethane, ethene, a large organic molecule in a thick film of the molecule, carbon monoxide strongly bonded to a metal surface, a metallic atom in a metallic surface) and try to explain what processes could contribute to the final state effect. 3 From: Woodruff & Delchar, Modern Techniques of Surface Science, Second edition, Cambridge University Press, Cambridge, Figure 1: Electron binding energies in the elements. X-ray photoelectron spectroscopy Intensity hν = 650 ev hν = 675 ev Binding energy (ev) Figure 2: X-ray photoelectron spectra. The spectra were offseted for clarity. The peak positions are: upper spectrum: 532, 473, 466, 460, 295, 270, 236, 158, 138, 63, 39, and 24 ev, lower spectrum: 532, 473, 466, 460, 320, 295, 261, 183, 163, 63, 39, and 24 ev. 4 Cross sections compiled by J. J. Yeh and I. Lindau, Atomic Data and Nuclear Data Tables 32 (1985) 1 Figure 3: Partial photoionisation cross section for Ag. The x-axis displays the photon energy. Cross sections compiled by J. J. Yeh and I. Lindau, Atomic Data and Nuclear Data Tables 32 (1985) 1 Figure 4: Partial photoionisation cross section for the valence levels of Au. The x-axis displays the photon energy. 5 10-3 Graphite (compiled using data from Henke, Gullikson, and Davis, Atomic Data and Nuclear Data Tables 54 (1993) 181) Photon attenuation length (m) Photon energy (ev) From: Woodruff & Delchar, Modern Techniques of Surface Science, Second edition, Cambridge University Press, Cambridge, Figure 5: Attenuation length for photons in graphite (left) and for electrons in different materials (right). Figure 6: X-ray photoelectron spectrum measured on a film of isonicotinic acid. The photon energy was 500 ev. 0 emission corresponds to emission along the surface normal. 6 Spears, Fischbeck, and Carlson, Phys. Rev. A 9 (1973) 1603 Figure 7: Gas phase Ar 2s and 2p lines, which show a rich shake-up structure. From: S. Hüfner, Photoelectron Spectroscopy, 2nd Edition, Springer, Berlin, Heidelberg, 1996 Figure 8: Chemical shifts for the C 1s levels in some compounds. Observe that the binding energy axis is to higher binding energies to the right (in conflict with the convention of letting the kinetic energy axis point into this direction). 7
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