In an inelastic scattering experiment, an incident particle (electron, neutron, helium atom, X-ray) with an energy 1, and a wavevector k1, is scattered into 2 and k2 (Figure 11). The energy loss (2 - 1) corresponds to elementary excitations in condensed matter systems: phonons, magnons, electronic gaps, collective excitation (plasmon) ...
- Electrons and helium atoms probe the surface; neutrons and X-rays probe the bulk.
- Why use X-rays (compared to neutrons)?
- with X-rays, very small crystals (~ 200 µm) can be studied, in extreme thermodynamic conditions (high pressure, high/low temperature...)
- the Q resolution of X-rays is at least 10 times better,
- X-rays are applicable to liquids or amorphous systems where the velocity of sound is higher than the velocity of the incoming neutrons (> 2000 m / sec),
- the total energy resolution achieved at the ESRF is now 1.4 ± 0.1 meV at 21.748 keV. This corresponds to a relative energy resolution E/E = 6 x 10-8.
Transition from normal to fast sound in liquid water
A resolution of 1.4 meV has been reached this year in inelastic X-ray scattering experiments: this is opening tremendous new possibilities.
In the last year's «Highlights» we reported the observation of collective excitation in water, with a speed of sound of 3200 m/sec. However, with a resolution of 3 meV, it was not possible to see how the transition from normal sound to fast sound was happening.
Inelastic X-ray scattering (IXS) data from water at 5 °C show a variation of the velocity of sound from 2000 to 3200 m/s in the momentum transfer range 1-4 nm-1.
The transition occurs when, at 4 meV, the energy of the sound-excitations equals that of a second weakly dispersing mode. This is shown in Figure 12, where we report the dispersion of the IXS data of the longitudinal acoustic-like mode taken with different energy resolutions and the weakly dispersing mode, which can be observed only in the data taken with 1.5 meV energy resolution. This mode is reminiscent of a phonon branch in ice Ih crystals, which we showed to be of transverse character. The present work accounts for most of the highly debated difference between hydrodynamic (1500 m/s) and high-frequency ( 3200 m/s) velocities of sound in water.
 C. Masciovecchio (a), U. Bergmann (a), M. Krisch (a), G. Ruocco (b), F. Sette (a) R. Verbeni (a), Nucl. Instr. and Meth B-111, 181 (1996).
 C. Masciovecchio (a), U. Bergmann (a), M. Krisch (a), G. Ruocco (b), F. Sette (a), R. Verbeni (a), Nucl. Instr. and Meth., in print
 F. Sette (a), G. Ruocco (b), M. Krisch (a), C. Masciovecchio (a), R. Verbeni, (a), U. Bergmann (a), Phys. Rev. Lett. 77, 83 (1996)
(b) Università de L'Aquila/Istituto Nazionale di Fisica della Materia, L'Aquila (Italy)
The high frequency collective dynamics has been measured in solid (ice Ih) water by inelastic X-rays scattering. A comparison between the results in the liquid and crystalline phases shows that density fluctuations with wavelengths between 0.5 and 3 nm propagate with the same velocity. This result, summarised in the dispersion curves of Figure 13, demonstrates that, in spite of the fundamental structural and dynamic differences between liquid and solid water, a time-space domain exists where the dynamic interparticle correlations are strikingly similar in the two aggregation states.
Moreover, the linewidth of these collective acoustic-like modes in liquid and solid (ice Ih) water shows a large increase at the Q-value of ~7.5 nm-1. This, together with the results on both acoustic- and optic-like dynamics, emphasises the analogies in the whole high-frequency collective dynamics of liquid and crystalline H2O, and improves our understanding of these dynamical phenomena.
 F. Sette (a), G. Ruocco (b), M. Krisch (a), U. Bergmann (a), C. Masciovecchio (a), V. Mazzacurati (b), G.Signorelli (b), R. Verbeni (a), Phys. Rev. Lett. 75, 850 (1995).
 G. Ruocco (b), F. Sette (a), U. Bergmann (a), M. Krisch (a), C. Masciovecchio (a), V. Mazzacurati (b), G. Signorelli (b), R. Verbeni (a), Nature 379, 521 (1996).
 G. Ruocco (b), F. Sette (a), M. Krisch (a), U. Bergmann (a), C. Masciovecchio (a) and R. Verbeni (a), accepted by Physical Review B
(b) Università de L'Aquila/Istituto Nazionale di Fisica della Materia, L'Aquila (Italy)
An inelastic scattering experiment measures the momentum Q and energy that the probing particle (X-ray photon, neutron, etc.) transfers to the sample. The scattering rate peaks whenever equals the frequency (Q) of an elementary excitation, for example a phonon or sound wave, in the sample. By measuring these peak frequencies at different Q, one can determine phonon dispersion relations. The peaks also have a certain width, which originates from the experimental resolution and the limited lifetime of the excitations. They eventually decay into other degrees of freedom or are scattered by sample imperfections.
The Inelastic Scattering Group at the ESRF has studied phonons in ice and sound waves in water in a series of experiments. They found that the speed of sound is nearly the same in the two substances once the wave vector is larger than about 3 nm-1. Furthermore, the experiments showed that the lifetime of the phonons in ice and the sound waves in water decreases drastically when the wave vector becomes larger than ~ 7 nm-1, the measured peak widths are typically 7-8 meV (Figure 14).
A recent model calculation performed in the Theory Group studied two different mechanisms that may cause the shortening of the phonon lifetime in ice: anharmonicity and bond disorder. The first one, anharmonicity, is important because the intermolecular interaction in ice is the sum of two contributions of different character. There is (i) a so-called Lennard-Jones potential which becomes strongly repulsive at short distances, and (ii) a rather smooth, effectively attractive electrostatic interaction. Consequently, in contrast to the situation in a harmonic crystal, the restoring forces are larger when two molecules approach each other than when they are moved away from each other. As a result the phonons, which are stable elementary excitations of the harmonic crystal, now have a finite lifetime. The other decay mechanism is due to the inherent disorder present in an ordinary ice crystal; while the O atoms form a regular lattice, the H atoms are positioned around them in a partly random way. This leads to variations in the electrostatic interactions between the molecules, which in turn causes phonon scattering since the crystal is no longer perfectly periodic.
Detailed calculations show that bond disorder just gives a small broadening of the phonon peaks, about an order of magnitude smaller than what is observed. The widths due to anharmonicity are considerably larger. The figure shows some typical results of the calculation. The calculated Q dependence of the peak widths is qualitatively the same as in the experiment, namely there is a marked increase around Q ~ 8 nm-1. However, the contribution to the peak width from anharmonicity amounts to about 3 meV and is thus smaller than the experimental widths. The increased anharmonicity contribution to the peak width at Q ~ 8 nm-1 can be understood in the following way: as Q is increased beyond this value, it goes outside the first Brillouin zone and the scattered X-rays start to excite optical rather than acoustic phonons.The optical phonons involve relative motion of the H2O molecules parallel to the bond axis to a much larger extent than the acoustic ones and therefore the anharmonic part of the intermolecular potential becomes more important.
In summary, the results indicate that anharmonicity is an important mechanism in limiting the lifetime of short-wavelength phonons in ice. The inherent hydrogen disorder, on the other hand, gives only a small contribution to the peak width. Finally, in view of the very large experimental peak widths, it is not unlikely that some further broadening mechanism is present.
P. Johansson (a), Phys.Rev. B 54, 9. 2988 (1996).
Observation of large momentum phonon-like modes in glasses
The dynamic structure factor of glycerol and LiCl : 6H2O glasses, measured by inelastic X-ray scattering, shows modes dispersing linearly with momentum in the 2-8 nm-1 region.
This finding demonstrates that acoustic-like propagating modes can exist in glasses up to wavelengths comparable to interparticle separations. It also shows that the boson peak, a feature systematically observed in the same energy region spanned by these excitations, must have a contribution from this propagating collective dynamics and not only from possible localised modes.
C. Masciovecchio (a), G. Ruocco (b), F. Sette (a), M. Krisch (a), R. Verbeni (a), U. Bergmann (a), M. Soltwisch (c), Phys. Rev. Lett. 76, 3356 (1996)
(b) Università de L'Aquila/Instituto Nazionale di Fisica
della Materia, L'Aquila (Italy)
(c) Freie Universität Berlin, Institut für Experimentalphysik, Berlin (Germany)