Inelastic Measurements
The inelastic scattering of the helium atom beam reveals the surface phonon dispersion for a material. At scattering angles far away from the specular or diffraction angles, the scattering intensity of the ordered surface is dominated by inelastic collisions.
In order to study the inelastic scattering of the helium atom beam due only to single-phonon contributions, an energy analysis needs to be made of the scattered atoms. The most popular way to do this is through the use of time-of-flight (TOF) analysis. The TOF analysis requires the beam to be pulsed through the mechanical chopper, producing collimated beam 'packets' that have a 'time-of-flight' (TOF) to travel from the chopper to the detector. The beams that scatter inelastically will lose some energy in their encounter with the surface and therefore have a different velocity after scattering than they were incident with. The creation or annihilation of surface phonons can be measured, therefore, by the shifts in the energy of the scattered beam. By changing the scattering angles or incident beam energy, it is possible to sample inelastic scattering at different values of energy and momentum transfer, mapping out the dispersion relations for the surface modes. Analyzing the dispersion curves reveals sought-after information about the surface structure and bonding. A TOF analysis plot would show intensity peaks as a function of time. The main peak (with the highest intensity) is that for the unscattered helium beam 'packet'. A peak to the left is that for the annihilation of a phonon. If a phonon creation process occurred, it would appear as a peak to the right:
The qualitative sketch above shows what a time-of-flight plot might look like near a diffraction angle. However, as the crystal rotates away from the diffraction angle, the elastic (main) peak drops in intensity. The intensity never shrinks to zero even far from diffraction conditions, however, due to incoherent elastic scattering from surface defects. The intensity of the incoherent elastic peak and its dependence on scattering angle can therefore provide useful information about surface imperfections present on the crystal.
The kinematics of the phonon annihilation or creation process are extremely simple - conservation of energy and momentum can be combined to yield an equation for the energy exchange ΔE and momentum exchange q during the collision process. This inelastic scattering process is described as a phonon of energy ΔE=ћω and wavevector q. The vibrational modes of the lattice can then be described by the dispersion relations ω(q), which give the possible phonon frequencies ω as a function of the phonon wavevector q.
In addition to detecting surface phonons, because of the low energy of the helium beam, low-frequency vibrations of adsorbates can be detected as well, leading to the determination of their potential energy.
Read more about this topic: Helium Atom Scattering