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Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit


The study of phase-transition dynamics in solids beyond a time-averaged kinetic description requires direct measurement of the changes in the atomic configuration along the physical pathways leading to the new phase. The timescale of interest is in the range 10-14 to 10-12 s. Until recently, only optical techniques were capable of providing adequate time resolution1, albeit with indirect sensitivity to structural arrangement. Ultrafast laser-induced changes of long-range order have recently been directly established for some materials using time-resolved X-ray diffraction2,3,4,5,6,7,8. However, the measurement of the atomic displacements within the unit cell, as well as their relationship with the stability limit of a structural phase9,10,11, has to date remained obscure. Here we report time-resolved X-ray diffraction measurements of the coherent atomic displacement of the lattice atoms in photoexcited bismuth close to a phase transition. Excitation of large-amplitude coherent optical phonons gives rise to a periodic modulation of the X-ray diffraction efficiency. Stronger excitation corresponding to atomic displacements exceeding 10 per cent of the nearest-neighbour distance—near the Lindemann limit—leads to a subsequent loss of long-range order, which is most probably due to melting of the material.

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Figure 1: Geometrical structure factor |S(h, k, l)|2 of bismuth as a function of the distance d of the two basis atoms for diffraction from (111) and (222) lattice planes.
Figure 2: X-ray diffraction efficiency of the (222) reflection as a function of time delay between the optical pump pulse (fluence 6 mJ cm-2) and the X-ray probe pulse.
Figure 3: X-ray diffraction efficiency of the (111) reflection as a function of time delay between the optical pump pulse (fluence 6 mJ cm-2) and the X-ray probe pulse.
Figure 4


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Financial support by the Deutsche Forschungsgemeinschaft, the European Community (Research and Training Network XPOSE) and the German Academic Exchange Service (DAAD) is acknowledged.

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Sokolowski-Tinten, K., Blome, C., Blums, J. et al. Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit. Nature 422, 287–289 (2003).

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