by special characteristics, including a linear frequency versus wave number relation near the SBZ center. Experiment Two of the more common methods for studying surface phonons are electron energy loss spectroscopy and helium atom scattering. Electron energy loss spectroscopy The technique of electron energy loss spectroscopy (EELS) is based upon the fact that electron energy decreases upon interaction with matter. Since the interaction of low energy electrons is mainly in the surface, the loss is due to surface phonon scattering, which have an energy range of 10−3 eV to 1 eV. In EELS, an electron of known energy is incident upon the crystal, a phonon of some wave number, q, and frequency, ω, is then created, and the outgoing electron's energy and wave number are measured. If the incident electron energy, Ei, and wave number, ki, are chosen for the experiment and the scattered electron energy, Es, and wave number, ks, are known by measurement, as well as the angles with respect to the normal for the incident and scattered electrons, θi and θs, then values of q throughout the BZ can be obtained. Energy and momentum for the electron have the following relation, where m is the mass of an electron. Energy and momentum must be conserved, so the following relations must be true of the energy and momentum exchange throughout the encounter: where G is a reciprocal lattice vector that ensures that q falls in the first BZ and the angles θi and θs are measured with respect to the normal to the surface. The dispersion is often shown with q given in units of cm−1, in which 100 cm−1 = 12.41 meV. The electron incident angles for most EELS phonon study chambers can range from 135-θs and 90-θf for θf ranging between 55° and 65°.– Helium atom scattering Helium is the best suited atom to be used for surface scattering techniques, as it has a low enough mass that multiple phonon scattering events are unlikely, and its closed valence electron shell makes it inert, unlikely to bond with the surface upon which it impinges. In particular, 4He is used because this isotope allows for very precise velocity control, important for obtaining maximum resolution in the experiment. There are two main techniques used for helium atom scattering studies. One is a so-called time-of-flight measurement which consists of sending pulses of He atoms at the crystal surface and then