10. Appendix

Chapter 3 695
Inelastic x-ray Scattering (IXS)
As discussed in Chap. 7, laser Raman scattering yields very precise information
about the frequencies and line widths of phonons at or near the center of
the Brillouin zone. However, it cannot access phonons throughout the whole
Brillouin zone because the laser wavelength is much larger than the typical lattice
constants. The measured dispersion relations shown in this chapter were
obtained by inelastic neutron scattering (INS), taking advantage of the fact
that the wavelength of thermal neutrons is close to the lattice constants. This
technique, however, is slow, cumbersome, requires large samples and has poor
energy resolution. Within the past decade, these problems have been circumvented
(except for the poor resolution) by using IXS, with monochromatized
x-rays from a synchrotron radiation source. An example of these measurements
is given in Fig. 3.3. IXS allows the use of small samples ( 1mmin
size) and is thus suitable for measurements under pressure in diamond anvil
cells (DAC). A discussion can be found in the following articles:
M. Krisch: Status of Phonon Studies at High Pressure by inelastic X-ray scattering.
J. Raman Spectr. 34, 628–632 (2003).
M. Krisch and F. Sette: Inelastic X-ray Scattering from Phonons, in Light Scattering
in Solids IX, edited by M.Cardona and R. Merlin (Springer, Heidelberg,
2007) p. 317–369.
Effects of Hydrostatic Pressure on Phonons
The large samples required by INS limits the highest hydrostatic pressure that
can be reached to about 1 GPa. With IXS much smaller samples can be used
and, with the help of DACs pressures as high as a few hundred GPa can be
reached at the expense of the resolution. The pressure effects of main interest
are the shift in phonon frequencies (related to the mode Grüneisen parameters
discussed in Problem 3.17) and changes in phonon line widths. These “anharmonic”
effects are amenable to ab initio calculations. The phase transitions
which take place at high pressures are also evinced in the phonon spectra.
Recent advances in the field can be found in the following publications:
A. Debernardi: Anharmonic Èffects in the Phonons of III-V Semiconductors:
First Principles Calculations. Solid State Commun. 113, 1–10 (1999).
J. Camacho, K. Parlinski, A. Cantarero, and K. Syassen: Vibrational Properties
of the high pressure Cmcm phase of ZnTe. Phys. Rev. B70, 033205–033208
(2004).
J. Kulda, A. Debernardi, M. Cardona, F. de Geuser, and E. E. Haller: Self-
Energy of Zone- Boundary Phonons in Germanium: Ab initio Calculations
versus Neutron Spin-Echo Measurements. Phy. Rev. B69, 045209–045213
(2004).
J. Serrano, A. H. Romero, F. J. Manjon, R. Lauck, M. Cardona and A. Rubio:
Pressure Dependence of the Lattice Dynamics of ZnO, an ab initio approach.
Phys. Rev. B69, 094306–094319 (2004). (ABINIT)