Otto Stern, O.R. Frisch, I. Estermann (Hamburg, 1929-1933) He a NaCl(001)
“These experiments are of interest not only because of their confirmation of the predictions of quantum mechanics, but also because they introduce the possibility of applying atom diffraction to investigations of the atomic constitution of surfaces.” (T. M. Johnson, Phys. Rev. 37 (1931) 847).
Bound-state resonances Frisch-Stern (1933) I00 J. E. Lennard-Jones and A. F. Devonshire, Nature 137 (1936) 1069.
Gas – Surface Interactions: - energy transfer - sticking (adsorption) INELASTIC SCATTERING INELASTIC RESONANCES Lattice vibrations (phonons) J.M. Jackson and N.F. Mott, Proc. Roy. Soc. A 137 (1932) 703: Quantum DWBA
L.D. Landau, Phys. Z. Sowjet. 8 (1935) 489. B.L. Bonch-Bruevich, Usp. Fiz. Nauka 40 (1950) 369 Classical Rarified Gas Dynamics Supersonic Molecular Beams
High-resolution diffraction Supersonic He-atom beam sources Time-of-flight spectroscopy
Angular distributions Diffraction • Inelastic processes: • inelastic bound state resonances - kinematical focussing • - surfing
Time of Flight (TOF) Inelastic scattering Phonons via the mechanical action (Pauli repulsion) on the electron density Phonon dispersion curves Forces between atoms Forces between ions and electrons (electron-phonon interaction) & electronic susceptibility
inelastic He atom scattering excites phonons phonon excitations probe interatomic forces
Surface waves Lord Rayleigh (1887) Irpinia 1980 (Polo Sismico Alberto Gabriele, FCCSEM Erice)
interatomic potential force constant matrix harmonic eq. of motion rl r(l1 l2 l3,) = l1a1 +l2a2 +l3a3+ d() 3D rl r(l1 l2 l3,) = l1a1 +l2a2 + d(l3,) 2D slab Bloch waves secular equation
…to a slab of Nz layers Surface phonons 2: from one monolayer…
TOF spectrum Energy-transfer spectrum scan curves for 90° geometry
HAS versus theory NaF(001) LiF(001) theory: Green Function surface dynamics + DWBA scattering theory end of lecture 3
Longitudinal resonance Rayleigh wave Metals: Skin & Bones I Cu(111) HAS
Anomalous longitudinal resonance Cu(111) HAS data C. Kaden et al. PRB (1992)
Cu(001) a giant resonance G. Benedek et al. PRB 1993
There is something fundamental in the anomalous longitudinal resonance A feature common to all metal surfaces A strong amplitude in HAS but weak in EELS Unphysical fitting with force-constant models
The Multipole Expansion (ME) Method Equilibrium:
Adiabatic condition Secular equation Dynamic electron density oscillations Non-local dielectric response (susceptibility)
Density-functional Hellmann-Feynman vs. Multipole expansion ynk Kohn-Sham wavefunctions:
Ion-core displacements Electron density oscillations ME DFPT
HAS hole-electron pairs! 1D conductor electron-hole excitations Peierls instability
The Helium-3 Spin-Echo Spectroscopy P. Fouquet, A.P. Jardine, S. Dworski, G. Alexandrowicz, W. Allison and J. Ellis "Thermal energy 3He spin-echo spectrometer for ultrahigh resolution surface dynamics measurements“ Rev. Sci. Inst. 76, 053109 (2005).
First tests for He3 Spin-Echo: • Bound states of He3 on LiF(001) • Surface Transport Measurements using Quasi-elastic Helium Atom Scattering (QHAS) back to Frisch & Stern! A.P. Jardine, S. Dworski, P. Fouquet, G. Alexandrowicz, G.Y.H. Lee, D.J. Riley, J. Ellis, W. Allison, "Ultrahigh resolution spin-echo measurement of surface potential energy landscapes", Science 304, 1790-1793 (2004).
atom microscope 4He gas jets atom interferometry cluster, droplets at 0.37 K 4He liquid jets nano-scale superfluididity targets for high-energy physics targets for laser accelerators (e.g., for hadrotherapy) superfluid 4He (p-H2) clusters inside 3He droplets jets from expansion of solid 4He: the geyser effect
cluster beam cluster assembled film Grenoble - 9 SUPERSONIC CLUSTER BEAM DEPOSITION at the Department of Physics, University of Milano TOF-MS CHAMBER DEPOSITION CHAMBER SOURCE CHAMBER quartz MB sample manipulator He line PMCS substrate time of flight mass spectrometer to pulsed power supply target 2000 l/s diff. pump 700 l/s diff. pump 500 l/s turbo pump
something more on inelastic atom scattering: Giorgio Benedek J. Peter Toennies Helium Atom Scattering Spectroscopy of Surface Phonons Springer-Verlag Berlin Heidelberg New York 2007 end of lecture 4
Bibi Bortolani JPT