2. Phonons in single crystals 

2.1 Phonons in diamond
 
Phonons in diamond Besides beryllium (Burkel et al 1986, Dorner et al 1987), diamond was the first crystal which was used to demonstrate the capabilities of inelastic X-ray scattering. Diamond has an fcc Bravais lattice with two atoms per primitive unit cell. The dynamics of diamond or of other group IV elements allow important tests for ab initio calculations, since the band structure and the lattice properties of the crystals can be calculated from first principles. Figure 5 shows an energy scan at (0 0 4.2) with both phonon signals, for energy gain and energy loss obtained at that time. The ratio of the peak intensities is in excellent agreement with the ratio determined by the Bose occupation factor.
 
Figure 5.  
The energy scan at Q = (0 0 4.2) in diamond shows the energy gain and energy loss signal of the longitudinal phonon clearly separated. hni is the Bose occupation factor 
 
The complete dispersions of the longitudinal 1,2 and transverse 3 modes along the [0 0 ] direction (- X) were obtained. They are shown in figure 6 with the  symbols. The overall good agreement of the X-ray data with a shell-model fit (dotted line) from  Warren et al (1967) allowed the conclusion that both methods, X-ray and neutron scattering, lead to the same frequencies of the phonons. Therefore, the validity of the adiabatic approximation is a good assumption. However, there was some deviation visible in the optical part of the longitudinal mode (2 ). Since the energy resolution at that time was only 19 meV, further experiments were done with improved resolution of 11.5 meV by Röll and Burkel (1993). The result ( in figure 6) confirmed this deviation, yet, to be less pronounced.
 
Meanwhile, an experiment on diamond was performed by Schwoerer-Böhning et al (1998) with an energy resolution of 9 meV at the inelastic spectrometer at the APS. Figure 6 shows the data of the longitudinal ,  and  and the transverse  phonon branches, as obtained by inelastic scattering up to the present time.
 
Figure 6.  
Phonon dispersion curves for the longitudinal  ,  and  and the transverse  modes in diamond as obtained with X-ray scattering by Burkel ()(1991), by Röll and Burkel () (1993) and Schwoerer-Böhning et al (o)(1998). The results are shown together with a shell-model t from the literature (Warren, Yarnell, Dolling and Cowley 1967). 
The unusual behaviour of the longitudinal 2(- X) branch with the energy maximum for the optical part of this branch within the Brillouin zone rather than at the -point (origin) is confirmed in all data. There was indication for such phenomena found as a sharp peak in the second order Raman spectra more than 50 years ago. One of the explanations discussed by Uchinokura et al (1974) and by Musgrave and Pople (1962) is a maximum of the longitudinal optic mode within the Brillouin zone as visible in the X-ray data, for the first time.
 
Due to the very high frequencies of the optical phonon modes, conventional neutron scattering at a reactor source is tedious and thus, there are still not many neutron data available for the optic modes of diamond. Recent neutron data by Kulda et al (1996) reported also a slight overbending of this mode. The observed experimental value is about half the value resulting from ab initio calculations (Windl et al 1993). This example proves that inelastic X-ray scattering results can deliver data which help to improve theoretical approaches.