Time resolved X-ray diffraction

Time-resolved X-ray diffraction (TRXRD), illustrated in Fig. 3.1, provides a powerful technique to probe directly the structural dynamics of crystals far from the equilibrium. It employs visible pump pulses from a laser, and laser-or accelerator-based X-ray probe pulses [1, 3]. As X-ray diffraction can in principle probe k 0 phonons, TRXRD has the potential to reveal the energy transfer dynamics, for example, from the zone-center to the zone-boundary phonons. 

TRXRD detects the propagation of coherent acoustic phonons as a transient change in the diffraction angles. In contrast, the atomic motions associated with coherent optical phonons modify only the Bragg peak intensity, because they do not change the barycentric positions of the crystal lattice. The Bragg peak intensity is proportional to the squared modulus of the structure factor [1,3,4]  

One of the applications of TRXRD is to study complex systems where electric fields couple to multiple degrees of freedom. Though femtosecond laser pulses can generate THz radiation from ferroelectric LiTa03, the corresponding lattice motion remained undetected by optical measurements. Cavalleri and coworkers demonstrated the coherent modulation of the X-ray intensity at 1.5 THz [10], and assigned it as phonon-polariton mode of A symmetry (Fig. 3.3). Nakamura and coworkers detected the coherent LO phonon of CdTe 

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Time-resolved x-ray diffraction of frog muscle confirmed movement of the cross-bridges... 

The purpose of this chapter is to review ultrafast, time-resolved X-ray diffraction from liquids. Both experimental and theoretical problems will be treated. The stmcture of the chapter is as follows. Section II describes the principles of a time-resolved X-ray experiment and details some of its characteristics. Basic elements of the theory are discussed briefly in Sections III-V. Finally, Section VI presents recent achievements in this domain. The related field of time-resolved X-ray spectroscopy, although very promising, wiU not be discussed. 

Figure 1. Time-resolved X-ray diffraction experiment (schematic). The liquid sample is excited by a laser pulse, and its temporal evolution is monitored by a time-delayed X-ray pulse. The diffracted radiation is measured by a charge-coupled detector (CCD). In practice, the laser and X-ray beams are not perpendicular to each other, but nearly parallel.

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

The purpose of this section is to describe recent achievements in time-resolved X-ray diffraction from liquids. Keeping the scope of the present chapter in mind, neither X-ray diffraction from solids nor X-ray absorption will be discussed. The majority of experiments realized up to now were performed using optical excitation, although some recent attempts using infrared excitation were also reported. The main topics that have been studied are (1) visualization of atomic motions during a chemical reaction, (2) structure of reaction intermediates in a complex reaction sequence, (3) heat propagation in impulsively heated liquids, and (4) chemical hydrodynamics of nanoparticle suspensions. We hope that the actual state-of-the-art will be illustrated in this way. 

A first study refers to liquid water [77]. The signals AS q,x) and A5[r, x] were measured using time-resolved X-ray diffraction techniques with 100 ps resolution. Laser pulses at 266 nm and 400 nm were employed. Only short times X were considered where thermal expansion was assumed to be negligible, and... 

However, time-resolved X-ray diffraction remains a young science. It is still impossible, or is at least very difficult, to attain time scales below to a picosecond. General characteristics of subpicosecond X-ray diffraction and absorption are hardly understood. To progress in this direction, free electron laser X-ray sources are actually under construction subject to heavy financial constraints. Nevertheless, this field is exceptionally promising. Working therein is a challenge for everybody ... 

S. Bratos, P. Mirloup, R. Vuilleumier, and M. Wulff, Time-resolved X-ray diffraction statistical theory and its application to the photo-physics of molecular iodine. J. Chem. Phys. 116(24), 10615-10625 (2002). 

M. Wulff, S. Bratos, A. Plech, R. Vuilleumier, F. Mirloup, M. Eorenc, Q. Kong, and H. Ihee,. Recombination of photodissociated iodine a time-resolved X-ray diffraction study. J. Chem. Phys. 124(3), 034501 (2006). 

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, Ultrafast structural dynamics in InSb probed by time-resolved X-ray diffraction. Phys. Rev. Lett. 83, 336-339 (1999). 

C. Rischel, A. Rousse, 1. Uschmann, P. A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Froster, J.-L. Martin, and A. Antonetti, Femtosecond time-resolved X-ray diffraction from laser-heated organic films. Nature 390, 490 92 (1997). 

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