Training activity: Debye temperature of Ru(0001)

The determination of the Debye temperature θ_Dof solid surfaces, which is related to the vibrational motion of atoms, is of uttermost importance to understand how the physical properties of crystals are modified when the translational symmetry in three dimensions is broken.
The Debye temperature has been traditionally measured by diffraction techniques, in particular X-ray diffraction and Low Energy Electron Diffraction (LEED), which, thanks to their different surface sensitivity, have allowed to spot the differences between the Debye temperature of the bulk (i.e. the deep layers) and the surface of the crystals. In principle, each atomic layer is characterised by its own Debye temperature. Unfortunately, conventional experimental techniques are not sensitive enough to the differences among the individual layers, so that an alternative approach is required. This is the leading reason of the experimental work described in the following, where High Resolution X-ray Photoelectron Spectroscopy (XPS) was used to measure the Debye temperature of bulk, second layer and surface of a Ru(0001) crystal, and to study the thermal expansion of the latter.
This strategy exploits the fact that, the  photoemission  components originating from distinct atomic layers show distinct Binding Energies, and the energy separation of each component relative to the bulk, termed Core Level Shift (CLS), is deeply affected by the local electronic structure. Also the spectral line shape yields information on the local electronic and geometric structure; more specifically, the Gaussian  width of the peaks receives a substantial contribution from the vibrational motion of the atoms, which depends on the temperature.
The preliminary stage of the measurements was devoted to the investigation of the clean Ru(0001) surface. The analysis of the low temperature spectra (T=80 K) of the Ru 3d_5/2 core level highlighted the presence of three components, which were assigned to photoemission from bulk, first and second layer atoms, consistently with the interpretation proposed in an earlier study.
In a later stage, a set of temperature—resolved measurements was acquired by monitoring in real time the evolution of  the Ru 3d_5/2 core level while cooling the sample from 1000K to 80K. The experiments pointed out a distinct evolution of the three components as a function of the temperature: the Gaussian broadening of the surface at high temperature is significantly larger than that of the other components; in addition, a variation of the first and second layer  CLS is observed with respect to the low temperature values. An analysis  based on the Hedin-Rosengren model allowed to derive, in an harmonic approximation, a distinct estimate of the Debye temperature of bulk (668±5 K), surface (225±10 K) and second layer (445±10 K) of the crystal. At high temperature, however, a disagreement is observed between the trends of the first layer component (Gaussian width and SCLS) and the predictions of the Hedin-Rosengren theory, suggesting the onset of high-temperature anharmonic effects which are not adequately described by the model.