Helium Atom Scattering - Elastic Measurements

Elastic Measurements

Under conditions for which elastic diffractive scattering dominates, the relative angular positions of the diffraction peaks reflect the geometric properties of the surface being examined. That is, the locations of the diffraction peaks reveal the symmetry of the two-dimensional space group that characterizes the observed surface of the crystal. The width of the diffraction peaks reflects the energy spread of the beam. The elastic scattering is governed by two kinematic conditions - conservation of energy and the of the momentum component parallel to the crystal:

E_f = E_i => k² = k_G² = k_Gz² + k_||G²

k_||G = k_||i + G

Here G is a reciprocal lattice vector, k_G and k_i are the final and initial (incident) wave vectors of the helium atom. The Ewald sphere construction will determine the diffracted beams to be seen and the scattering angles at which they will appear. A characteristic diffraction pattern will appear, determined by the periodicity of the surface, in a similar manner to that seen for Bragg scattering in electron and x-ray diffraction. Most helium atom scattering studies will scan the detector in a plane defined by the incoming atomic beam direction and the surface normal, reducing the Ewald sphere to a circle of radius R=k₀ intersecting only reciprocal lattice rods that lie in the scattering plane as shown here:

The intensities of the diffraction peaks provide information about the static gas-surface interaction potentials. Measuring the diffraction peak intensities under different incident beam conditions can reveal the surface corrugation (the surface electron density) of the outermost atoms on the surface.

Note that the detection of the helium atoms is much less efficient than for electrons, so the scattered intensity can only be determined for one point in k-space at a time. For an ideal surface, there should be no elastic scattering intensity between the observed diffraction peaks. If there is intensity seen here, it is due to a surface imperfection, such as steps or adatoms. From the angular position, width and intensity of the peaks, information is gained regarding the surface structure and symmetry, and the ordering of surface features.