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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15506–15515
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The rotating-crystal method in femtosecond X-ray diffraction

B. Freyer, J. Stingl, F. Zamponi, M. Woerner, and T. Elsaesser  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 15506-15515 (2011)
http://dx.doi.org/10.1364/OE.19.015506


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Abstract

We report the first implementation of the rotating-crystal method in femtosecond X-ray diffraction. Applying a pump-probe scheme with 100 fs hard X-ray probe pulses from a laser-driven plasma source, the novel technique is demonstrated by mapping structural dynamics of a photoexcited bismuth crystal via changes of the diffracted intensity on a multitude of Bragg reflections. The method is compared to femtosecond powder diffraction and to Bragg diffraction from a crystal with stationary orientation.

© 2011 OSA

1. Introduction

Mapping structural changes of condensed matter on the length scale of a chemical bond and the femtosecond time scale of atomic motions has developed into an important area of ultrafast science [1

1. E. Colleted., “Dynamical structural science,” Acta Crystallogr., Sect. A 66, 133–280 (2010). [CrossRef] [PubMed]

]. Among other methods, femtosecond X-ray diffraction stands out as a direct probe of both atomic motions and changes of the electronic charge distribution induced by optical excitation [2

2. A. Rousse, C. Rischel, and J. C. Gauthier, “Colloquium: femtosecond x-ray crystallography,” Rev. Mod. Phys. 73, 17–31 (2001). [CrossRef]

, 3

3. T. Elsaesser and M. Woerner, “Photoinduced structural dynamics of polar solids studied by femtosecond x-ray diffraction,” Acta Crystallogr., Sect. A 66, 168–178 (2010). [CrossRef] [PubMed]

].

So far, most femtosecond X-ray diffraction experiments have made use of a pump-probe scheme where a femtosecond optical pulse induces structural dynamics in a single crystal and an ultrashort hard X-ray pulse is diffracted from the excited sample. Changes of the angular position and intensity of individual Bragg peaks [4

4. W. L. Bragg, “The structure of some crystals as indicated by their diffraction of x-rays,” Proc. R. Soc. London, Ser. A 89, 248–277 (1913). [CrossRef]

] were measured as a function of pump-probe delay [5

5. C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, “Femtosecond time-resolved X-ray diffraction from laser-heated organic films,” Nature 390, 490–492 (1997). [CrossRef]

12

12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

]. While this method has provided important new insight into ultrafast structural dynamics and its sensitivity has been improved substantially, e.g., by implementing X-ray sources working at a kilohertz repetition rate, a measurement of individual Bragg peaks gives limited structural information. Moreover, a sequential recording of many Bragg peaks is very time-consuming and may fail in experiments with samples of limited photo- or X-ray stability. Such issues led to a quest for femtosecond X-ray diffraction techniques allowing for a simultaneous measurement of a larger number of transient diffraction peaks.

Recently, we have introduced ultrafast X-ray powder diffraction as a versatile tool for observing structural dynamics via up to 30 transient X-ray reflections [13

13. F. Zamponi, Z. Ansari, M. Woerner, and T. Elsaesser, “Femtosecond powder diffraction with a laser-driven hard x-ray source,” Opt. Express 18, 947–961 (2010). [CrossRef] [PubMed]

, 14

14. M. Woerner, F. Zamponi, Z. Ansari, J. Dreyer, B. Freyer, M. Premont-Schwarz, and T. Elsaesser, “Concerted electron and proton transfer in ionic crystals mapped by femtosecond x-ray powder diffraction,” J. Chem. Phys. 133, 064509 (2010). [CrossRef] [PubMed]

]. X-ray diffraction from a powder of crystallites with random orientation gives a series of diffraction rings, the so-called Debye-Scherrer pattern. Experiments with different molecular crystals containing comparably light elements demonstrated a time resolution of 100 fs and measured changes of diffracted intensity ΔI/I 0 as small as 5 × 10−3. From the X-ray data sets, we derived transient charge density maps of the photoexcited materials, i.e., the time dependent distribution of electronic charge in a unit cell.

A powerful technique of steady-state X-ray diffraction is the so-called rotation method [15

15. B. E. Warren, X-ray Diffraction (Dover Publications, 1990).

]. Here, a monochromatic beam of hard X-rays illuminates a single crystal which is rotated at a constant angular velocity. In this way, the Bragg condition for different diffraction peaks is fulfilled for different rotation angles and a set of diffraction peaks can be recorded. Changing the rotation axis with respect to the crystal’s orientation allows for recording a large set of diffraction peaks.

In this article, we report the first implementation of the X-ray rotation method in the femtosecond time domain. We present diffraction patterns and their time evolution for a single crystal of bismuth and compare the data measured with the rotating crystal to a measurement with the crystal at rest. The paper is organized as follows. In section 2, the rotation method is introduced and compared to the powder diffraction method. The experimental setup is described in section 3, followed by the results for bismuth and a discussion in section 4. Conclusions are presented in section 5.

2. Rotating-crystal diffraction

The rotation method is the most common method to determine steady state crystal structures. The orientation of the rotation axis and the rotation range can be chosen to select a subset of diffraction peaks fulfilling the Bragg condition Δk = k′k = H hkl(, ϕ). Here, k′ and k are the k-vectors of the scattered and incoming X-ray waves and H hkl(, ϕ) is the reciprocal lattice vector of the set of lattice planes (hkl), in the laboratory frame depending on the direction of the rotation axis (the hat on top of a vector indicates the unit vector in the same direction) and the rotation angle ϕ. The k-vectors k′ and k enclose an angle 2θ where θ is the diffraction angle. In the early days of X-ray crystallography cylindrical film cameras (e.g., the Weisenberg camera) or the precession camera were used to record diffraction patterns and determine crystal structures. The photographs of these cameras give an undistorted picture of the reciprocal lattice [16

16. C. Giacovazzo, Fundamentals of Crystallography (Oxford University Press, 2002). [PubMed]

]. These pictures make the indexing process very easy, but only show two dimensions, e.g. (h0l), of the reciprocal lattice. The Arndt-Wanacott camera, the most used today, was introduced in the 1970s [16

16. C. Giacovazzo, Fundamentals of Crystallography (Oxford University Press, 2002). [PubMed]

, 17

17. U. W. Arndt, J. N. Champness, R. P. Phizackerley, and A. J. Wonacott, “A single-crystal oscillation camera for large unit cells,” J. Appl. Cryst. 6, 457–463 (1973). [CrossRef]

]. The crystal is rotated perpendicular to the X-ray beam. All three dimensions of the reciprocal lattice are simultaneously measured, but in a distorted manner. In this way, the measurement time is optimized but indexing is not straightforward.

The power diffracted from a rotating crystal, which is small compared to the incoming beam and the extinction length, is given by [18

18. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenann, 1984).

]
Prot=I0Δφre2λ3VFhkl2v21+cos22θhkl4sinθhklH^hkl(r^×k^)
(1)
where I 0 is the incoming X-ray intensity, Δϕ the rotation interval, re the electron radius, λ the X-ray wavelength, V the illuminated crystal volume, Fhkl and θhkl the structure factor and the Bragg angle of the reflecting lattice planes and v the volume of the unit cell. The scalar triple product in the denominator indicates that the intensity of equivalent reflections is not isotropic, but increases towards the poles. In the special case of the rotation axis being perpendicular to the incoming beam this product reduces to Ĥ hkl ( × ) = cosθ [15

15. B. E. Warren, X-ray Diffraction (Dover Publications, 1990).

]. For the case of a stationary single crystal the rotation interval must be replaced by the beam convergence (or the crystal mosaicity, if it is larger). Thus, the data collection efficiency in an experiment with a continuously rotated crystal divided by the data collection efficiency in the case of a crystal at rest is equal to the ratio of the beam divergence and the rotation interval.

Equation (1) can be compared to the case of powder diffraction where the sample contains crystallites in all possible orientations. Using Δϕ = 2π the fraction between the power from a rotated and a powdered (Ppow [15

15. B. E. Warren, X-ray Diffraction (Dover Publications, 1990).

]) sample is
ProtPpow=1π1cosθ13
(2)

The connection between the rotation method and the powder method is obvious from a comparison of the two diffraction patterns. In Fig. 1, a powder pattern from an ammonium sulfate [(NH4)2SO4] powder sample is compared to the corresponding single crystal rotation pattern. In the powder pattern some rings overlap into a single one, whereas in the rotation pattern all reflections are separable. Even equivalent reflections originating from the sets of lattice planes whose reciprocal lattice vectors have the same length can be distinguished. This is important when the relative orientation between the crystal and the pump laser polarization has an influence on the induced structural changes. The diffracted photons in the powder pattern are scattered in rings whose width is defined by the size of the projection of the illuminated volume onto the detector and the convergence angle of the incoming beam. In the rotation pattern, the photons are concentrated in spots instead, whereas their size is determined by the illumination volume, the convergence of the incoming beam and the mosaicity of the sample. Since the photons are more concentrated in the rotation pattern the signal to noise ratio is better than in the powder pattern. Also it is easier to subtract the background, because the vicinity can be sampled in two dimensions, instead of one in the powder pattern.

Fig. 1 Comparison between the (a) powder diffraction and (b) rotating-crystal method. The samples were (a) an ammonium sulfate [AS, (NH4)2SO4] powder sample, and (b) a single crystal of AS. The patterns were taken in the femtosecond X-ray setup with an integration time of 300 s each.

3. Femtosecond rotation method

The femtosecond experiments are based on a pump-probe scheme with an optical pump and a synchronized hard X-ray probe pulse. The pump pulse induces structural dynamics in the sample from which the X-ray pulse is diffracted. The time evolution of the structural change is reconstructed from a sequence of diffraction patterns recorded for different time delays between pump and probe. The time resolution is determined by the pulse durations and by the interaction geometry in the sample and has a value of the order of 100 fs.

A schematic of our experimental setup is presented in Fig. 2. Both optical pump and X-ray probe pulses are derived from the output of a Ti:sapphire laser system, providing sub-50 fs pulses centered at 800 nm with an energy of up to 5 mJ per pulse at a 1 kHz repetition rate. The major fraction of the laser output (95 percent) drives a hard X-ray (Cu Kα 8.05 keV) plasma source to generate 100 fs pulses with a total X-ray photon flux of several 1010 per second [19

19. N. Zhavoronkov, Y. Gritsai, M. Bargheer, M. Woerner, Th. Elsaesser, F. Zamponi, I. Uschmann, and E. Förster, “Microfocus Cu Kα source for femtosecond x-ray science,” Opt. Lett. 30, 1737–1739 (2005). [CrossRef] [PubMed]

]. The X-ray pulses are focused onto the sample by an X-ray multilayer optic [20

20. M. Bargheer, N. Zhavoronkov, R. Bruch, H. Legall, H. Stiel, M. Woerner, and T. Elsaesser, “Comparison of focusing optics for femtosecond X-ray diffraction,” Appl. Phys. B 80, 715–719 (2005). [CrossRef]

], resulting in an incoming X-ray flux on the sample of approximately 5 × 106 photons per second, and an angular divergence of 0.7° × 0.7°. The optical pump pulses are derived from a small part (5 percent) of the output of the Ti:sapphire laser. A broad spectrum of pumping wavelengths from 266 nm to 20 μm is covered by nonlinear frequency conversion. The diffracted X-rays are recorded with a large area CCD detector (Princeton Instrument PI-LCX: 1300, 1340 × 1300 pixel, pixel size 20 μm × 20 μm, quantum efficiency ≈ 50 %).

Fig. 2 (a) Schematic of the experimental set-up for femtosecond X-ray diffraction including typical diffraction patterns. (b) Set-up for femtosecond powder diffraction. (c) Set-up for femtosecond rotating-crystal diffraction.

Different X-ray diffraction schemes are readily implemented in the setup. Figure 2(a) shows a Bragg diffraction experiment with a single crystal under a fixed orientation where the intensity and angular position of individual Bragg peaks is measured as a function of pump-probe delay. Figure 2(b) shows the setup for a sample consisting of a powder of randomly oriented crystallites. From the powder, diffraction cones emerge, giving rise to a ring-like pattern (Debye Scherrer rings) on the X-ray CCD detector. Two different rotating-crystal diffraction geometries are presented, in Fig. 2(c) (transmission) and Fig. 3 (reflection), which give a set of individual diffraction spots on the detector.

Fig. 3 Femtosecond grazing-incidence rotating-crystal diffraction setup showing the 800 nm pump, X-ray probe and diffracted beams. The diamond beam splitter is a diamond single crystal, which is cut parallel to the (111) lattice plane and aligned for the (111) reflection. The CCD screen shows the four reflections which were measured in the femtosecond experiment.

The sample geometry applied in the rotation experiment on AS is shown in Fig. 2(c). The rotation axis and the incoming X-ray beam enclose an angle close to 90°, in analogy to the Arndt-Wanacot method. The angular speed of rotation is 180°/s. Measurements are performed both with full 360° and with limited ≈ 10° rotations of the sample. For complex structures, smaller angle steps are necessary to avoid overlapping of different diffraction spots.

A rotation pattern recorded with an unexcited AS crystal in the femtosecond setup is presented in Fig. 1(b). A large number of diffraction peaks is clearly distinguishable, including sets of equivalent peaks. For an integration time of the detector of 900 s, the added number of photons from all equivalent peaks, e.g., for the eight (031) reflections, has a value of approximately N=50000. This number translates into a relative shot noise originating from photon statistics of 1/N=4.4×103. The shot noise represents a fundamental limit of the sensitivity of a pump-probe experiment, i.e., it determines the smallest relative intensity change ΔI/I0=(II0)/I0=1/N (I, I0: diffracted intensity with and without excitation, respectively) that can be measured [13

13. F. Zamponi, Z. Ansari, M. Woerner, and T. Elsaesser, “Femtosecond powder diffraction with a laser-driven hard x-ray source,” Opt. Express 18, 947–961 (2010). [CrossRef] [PubMed]

].

Femtosecond powder diffraction experiments with AS gave insight into a novel type of structure change, a concerted electron and proton transfer, and allowed for deriving transient charge density maps of the material [14

14. M. Woerner, F. Zamponi, Z. Ansari, J. Dreyer, B. Freyer, M. Premont-Schwarz, and T. Elsaesser, “Concerted electron and proton transfer in ionic crystals mapped by femtosecond x-ray powder diffraction,” J. Chem. Phys. 133, 064509 (2010). [CrossRef] [PubMed]

]. An equivalent experiment using the rotation method failed because the required pump flux at 400 nm was above the damage threshold of the AS single crystal [21

21. It is important to note that the experimentally observed damage does not change the X-ray diffraction pattern, i.e., the crystal structure, but the surface quality of the single crystal and, thus, the coupling of the optical pump beam into the crystal.

]. We, thus, decided to demonstrate the femtosecond rotation method with bismuth, another reference material for time-resolved X-ray diffraction.

4. Femtosecond rotating-crystal diffraction on bismuth

In the last decade, bismuth has been studied extensively by femtosecond X-ray diffraction [8

8. K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-von-Hoegen, and D. von der Linde, “Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit,” Nature 422, 287–289 (2003). [CrossRef] [PubMed]

, 10

10. D. M. Fritz, D. A. Reis, B. Adams, R. A. Akre, J. Arthur, C. Blome, P. H. Bucksbaum, A. L. Cavalieri, S. Engemann, S. Fahy, R. W. Falcone, P. H. Fuoss, K. J. Gaffney, M. J. George, J. Hajdu, M. P. Hertlein, P. B. Hillyard, M. Horn-von Hoegen, M. Kammler, J. Kaspar, R. Kienberger, P. Krejcik, S. H. Lee, A. M. Lindenberg, B. McFarland, D. Meyer, T. Montagne, A. D. Murray, A. J. Nelson, M. Nicoul, R. Pahl, J. Rudati, H. Schlarb, D. P. Siddons, K. Sokolowski-Tinten, T. Tschentscher, D. von der Linde, and J. B. Hastings, “Ultrafast bond softening in bismuth: mapping a solid’s interatomic potential with x-rays,” Science 315, 633–636 (2007). [CrossRef] [PubMed]

, 12

12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

, 22

22. S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, E. D. Murray, S. Fahy, and G. Ingold, “Directly observing squeezed phonon states with femtosecond x-ray diffraction,” Phys. Rev. Lett. 102, 175503 (2009). [CrossRef] [PubMed]

24

24. W. Lu, M. Nicoul, U. Shymanovich, A. Tarasevitch, M. Kammler, M. Horn von Hoegen, D. von der Linde, and K. Sokolowski-Tinten, “Transient reversal of a Peierls-transition: Extreme phonon softening in laser-excited Bismuth,” in Ultrafast Phenomena XVII, M. Chergui, D. Jonas, E. Riedle, R. Schoenlein, and A. Taylor, eds. (Oxford University Press, 2011).

]. Particular sets of lattice planes hkl show transient changes of diffracted X-ray intensity upon optical excitation of ΔI/I 0 = 5 – 30%, depending on the pump fluence and matching of the volumes excited by the optical pump and probed by the X-ray pulse [12

12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

]. Matching the pump and probe volumes is not trivial, since the penetration depth of the 800 nm pump beam (≈ 10 nm [8

8. K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-von-Hoegen, and D. von der Linde, “Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit,” Nature 422, 287–289 (2003). [CrossRef] [PubMed]

]) is distinctly smaller than the X-ray attenuation length which has a value of ≈ 4 μm for Cu Kα radiation [25

25. J. B. Woodhouse, A. L. A. Fields, and I. A. Bucklow, “X-ray mass absorption coefficients for gold, lead and bismuth in the range 1–10 Å,” J. Phys. D: Appl. Phys, 7, 483–489 (1974). [CrossRef]

]. Two methods have been used to improve the matching of the volumes. The grazing incidence scheme (Fig. 3) allows for tuning the penetration depth of the probe by changing its angle of incidence [12

12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

]. In Ref. [8

8. K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-von-Hoegen, and D. von der Linde, “Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit,” Nature 422, 287–289 (2003). [CrossRef] [PubMed]

] the authors instead used thin films of bismuth which were 50 nm thick, so approximately half of the detected X-ray beam is diffracted from the excited part of the crystal. The diffraction efficiency of a 50 nm film of bismuth is, however, too small to allow for a rotation experiment and, thus, we applied a grazing-incidence geometry in our measurements.

In our experiments, we study bulk single crystals of bismuth which are polished parallel to the (110) lattice plane (all orientations are given in rhombohedral coordinates). The samples have a cylindrical shape with a diameter of D =8 mm and a surface roughness of 30 nm, according to the specification of the sample manufacturer. In Fig. 3, a schematic of the grazing-incidence geometry is shown. The bismuth sample is mounted in the X-ray focus (200 μm FWHM) under a grazing-angle of incidence of α X-ray = 1.5° ± 0.2°. We carefully aligned the rotation axis to be perpendicular to the sample surface. This ensures that the angle of incidence remains constant while rotating the sample. The eccentricity and angular tilt of the rotation axis vs. the cylinder axis are less than 300 μm and 0.2°, respectively. The sample is optically excited by the 800 nm pump pulse which is focused to a elliptical spot size of 400 × 1200 μm2 under an angle of incidence of α Laser = 7°. The pump pulse is π-polarized and the area density of absorbed energy has a value of 1 mJ/cm2 (note that the penetration depth of the pump is almost independent of the angle of incidence and the polarization). Due to the non-collinearity between the pump and the probe beam there is a temporal walk off between the two pulses Δt walkoff = D(cosα X-ray – cosα Laser)/c = 200 fs, where c is the speed of light. Since the eccentricity and the angular tilt of the rotation axis vs. cylinder axis are negligibly small, a change of the walk off geometry for different X-ray reflections is much smaller than Δt walkoff itself.

In order to get a reference for the X-ray source fluctuations we used a thin (60 μm) diamond plate, which is cut parallel to the (111) lattice plane and oriented to reflect a small part [(111)-reflection] of the incoming beam. Approximately 4 × 104 photons per second are reflected by the diamond beam splitter. The count rate for an individual bismuth diffraction spot is of the order of 103 per second.

We first performed an experiment with a static sample under similar experimental conditions as Johnson et al. [12

12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

]. Since we only measured one reflection at a time we replaced the CCD detector by a CdTe diode X-ray detector, which allows us to measure the signal from each pulse separately, and to chop our pump beam to eliminate the influence of slow fluctuations of the X-ray source on the signal. The result of the measurement is shown in Fig. 4. This result agrees nicely with the result shown in Fig. 1 of Ref. [12

12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

] for an angle of incidence of α X-ray = 2.0°. Our signal (Fig. 4) displays pronounced coherent phonon oscillations which are due to coherent wavepacket motions along the A1 g phonon mode of bismuth. Due to the comparably large angle of incidence, the signal amplitude is ≤ 7 %. In Ref. [23

23. S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, É. D. Murray, S. Fahy, and G. Ingold, “Non-equilibrium phonon dynamics studied by grazing-incidence femtosecond X-ray crystallography,” Acta Crystallogr., Sect. A 66, 157–167 (2010). [CrossRef] [PubMed]

], larger amplitudes have been observed for an angle of incidence of 0.45°.

Fig. 4 Time resolved reflectivity change of the (111) reflection of Bismuth, measured under comparable experimental conditions as in [12]. The solid line is plotted to guide the eye.

After measuring the transient reflectivity of the static sample, we replaced the X-ray diode by the CCD detector and rotated the sample around the [110] direction. By reflecting a laser beam at the sample surface we verified that the surface orientation is perpendicular to the axis of rotation, i.e., the angle of incidence is unchanged when the crystal is rotated.

The number of reflections from bismuth occurring in a full revolution is substantially smaller than for ammonium sulfate, the latter having a larger unit cell. However, the number of diffuse scattered X-ray photons is higher than for ammonium sulfate because this number scales quadratically with the atomic number. To avoid wasting measuring time and to improve the ratio of coherent to diffuse scattered intensity we decided to oscillate the sample within a 15° range and slow down the rotation speed at angles where lattice planes are Bragg matched, resulting in 3 oscillations per minute. In this way we measured the transient reflectivity of 4 reflections (111), (222), (322), and (323) quasi-simultaneously.

The transients shown in Fig. 5 demonstrate a high signal-to-noise ratio and a high femtosecond time resolution of the experiment. Many scans were made to verify reproducibility and these were then averaged together to improve the signal to noise ratio. The data were taken within six days and 25 neighboring data points were averaged together in order to get the data points and error bars shown in Fig. 5. The total integration time at each time delay was approximately 30 min. For the (111) reflection, the result agrees with measurements at the static sample. In the literature, there are no comparable measurements for the (222) reflection under an angle of incidence of 1.5°. Measurements at 0.45° [23

23. S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, É. D. Murray, S. Fahy, and G. Ingold, “Non-equilibrium phonon dynamics studied by grazing-incidence femtosecond X-ray crystallography,” Acta Crystallogr., Sect. A 66, 157–167 (2010). [CrossRef] [PubMed]

], however, suggest that the amplitude is smaller by a factor of 3 and of opposite sign compared to the reflectivity change on the (111) peak. This qualitative picture is in line with our result for the (222) reflection which displays weak oscillatory features on top of a step-like intensity change. The result for the (322) reflection looks similar to the (111) peak, but the amplitude of the phonon oscillations is somewhat smaller. The reflectivity of the (323) lattice planes show only a small change, after photo excitation, similar to the reflectivity change of the (222) reflection. A step-like reflectivity increase can be found at time delay zero, reflecting the high time resolution of our setup of ≈ 200 fs [3

3. T. Elsaesser and M. Woerner, “Photoinduced structural dynamics of polar solids studied by femtosecond x-ray diffraction,” Acta Crystallogr., Sect. A 66, 168–178 (2010). [CrossRef] [PubMed]

]. A detailed analysis of the time-dependent reflectivity changes is beyond the scope of this article, which focuses on the new method, but will be presented elsewhere.

Fig. 5 Reflectivity change of particular reflections measured with the rotating-crystal experiment. The solid lines are guides to the eye.

It is important to note that the four transients shown in Fig. 5 were measured under identical excitation conditions. In the case of a predominant one photon absorption process in a non-dichroic crystal, this leads to a transient structure change independent of the crystal orientation relative to the pump laser polarization. In a dichroic crystal like bismuth one has to rotate the laser polarization of the pump beam synchronized to the crystal orientation, in order to get a transient structure change independent of the rotation angle.

Since the rotation axis is perpendicular to the crystal surface the spatial and temporal pump-probe overlap is identical for all reflections measured quasi-simultaneously. Thus, the relative femtosecond timing and amplitudes of the transients of different reflections are known with very high precision. This fact represents a major advantage over sequential measurements of different individual reflections, in particular when long data acquisition times are required.

5. Conclusions

In conclusion, we have introduced ultrafast X-ray diffraction on rotating crystals. We have chosen bulk crystals of bismuth, a well studied structure in femtosecond X-ray science, to give a exemplary experiment with femtosecond time resolution. The results are in good agreement with experiments already published.

As the powder diffraction method the rotation method is able to measure several reflections in one experiment, which guarantees that all reflections are measured under the same conditions (temporal and spatial pump-probe overlap, pulse shape, etc.). The main advantage compared to the powder experiment is the possibility to separate reflections which have the same diffraction angle and to control the direction and range of the rotation. The diffraction efficiency is approximately a factor of three smaller than in the powder method, according to the kinematic diffraction theory for small crystallites, and our measurements. The preparation, mounting and alignment of the sample is more difficult for the rotation method.

We have also shown that more complex structures like ammonium sulfate are possible candidates for a rotating-crystal experiment. By increasing the brilliance of femtosecond hard X-ray light sources more and more complex structure can be investigated.

Acknowledgments

We thank Steven Lee Johnson (Paul Scherrer Institut) for valuable discussions on femtosecond diffraction experiments on bismuth. This work was supported by the Deutsche Forschungsgemeinschaft (Grant No. WO 558/13-1) and the European Research Council under the European Unionś Seventh Framework Programme (FP7/2007-2013)/ERC grant Agreement no. 247051.

References and links

1.

E. Colleted., “Dynamical structural science,” Acta Crystallogr., Sect. A 66, 133–280 (2010). [CrossRef] [PubMed]

2.

A. Rousse, C. Rischel, and J. C. Gauthier, “Colloquium: femtosecond x-ray crystallography,” Rev. Mod. Phys. 73, 17–31 (2001). [CrossRef]

3.

T. Elsaesser and M. Woerner, “Photoinduced structural dynamics of polar solids studied by femtosecond x-ray diffraction,” Acta Crystallogr., Sect. A 66, 168–178 (2010). [CrossRef] [PubMed]

4.

W. L. Bragg, “The structure of some crystals as indicated by their diffraction of x-rays,” Proc. R. Soc. London, Ser. A 89, 248–277 (1913). [CrossRef]

5.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, “Femtosecond time-resolved X-ray diffraction from laser-heated organic films,” Nature 390, 490–492 (1997). [CrossRef]

6.

C. Rose-Petruck, R. Jiminez, T. Guo, A. Cavalleri, C. Siders, J. A. Squier, B. C. Walker, and K. R. Wilson, “Picosecond millianstrom lattice dynamics measured by ultrafast x-ray diffraction,” Nature 398, 310–312 (1999). [CrossRef]

7.

E. Collet, M.-H. Leme-Cailleau, M. Buron-Le Cointe, H. Cailleau, M. Wulff, T. Luty, S.-Y. Koshihara, M. Meyer, L. Toupet, P. Rabiller, and S. Techert, “Laser-induced ferroelectric structural order in an organic charge-transfer crystal,” Science 300, 612–615 (2003). [CrossRef] [PubMed]

8.

K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-von-Hoegen, and D. von der Linde, “Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit,” Nature 422, 287–289 (2003). [CrossRef] [PubMed]

9.

M. Bargheer, N. Zhavoronkov, Y. Gritsai, J. C. Woo, D. S. Kim, M. Woerner, and T. Elsaesser, “Coherent atomic motions in a nanostructure studied by femtosecond x-ray diffraction,” Science 306, 1771–1773 (2004). [CrossRef] [PubMed]

10.

D. M. Fritz, D. A. Reis, B. Adams, R. A. Akre, J. Arthur, C. Blome, P. H. Bucksbaum, A. L. Cavalieri, S. Engemann, S. Fahy, R. W. Falcone, P. H. Fuoss, K. J. Gaffney, M. J. George, J. Hajdu, M. P. Hertlein, P. B. Hillyard, M. Horn-von Hoegen, M. Kammler, J. Kaspar, R. Kienberger, P. Krejcik, S. H. Lee, A. M. Lindenberg, B. McFarland, D. Meyer, T. Montagne, A. D. Murray, A. J. Nelson, M. Nicoul, R. Pahl, J. Rudati, H. Schlarb, D. P. Siddons, K. Sokolowski-Tinten, T. Tschentscher, D. von der Linde, and J. B. Hastings, “Ultrafast bond softening in bismuth: mapping a solid’s interatomic potential with x-rays,” Science 315, 633–636 (2007). [CrossRef] [PubMed]

11.

C. v. Korff Schmising, M. Bargheer, M. Kiel, N. Zhavoronkov, M. Woerner, T. Elsaesser, I. Vrejoiu, D. Hesse, and M. Alexe, “Coupled ultrafast lattice and polarization dynamics in ferroelectric nanolayers,” Phys. Rev. Lett. 98, 257601 (2007). [CrossRef]

12.

S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]

13.

F. Zamponi, Z. Ansari, M. Woerner, and T. Elsaesser, “Femtosecond powder diffraction with a laser-driven hard x-ray source,” Opt. Express 18, 947–961 (2010). [CrossRef] [PubMed]

14.

M. Woerner, F. Zamponi, Z. Ansari, J. Dreyer, B. Freyer, M. Premont-Schwarz, and T. Elsaesser, “Concerted electron and proton transfer in ionic crystals mapped by femtosecond x-ray powder diffraction,” J. Chem. Phys. 133, 064509 (2010). [CrossRef] [PubMed]

15.

B. E. Warren, X-ray Diffraction (Dover Publications, 1990).

16.

C. Giacovazzo, Fundamentals of Crystallography (Oxford University Press, 2002). [PubMed]

17.

U. W. Arndt, J. N. Champness, R. P. Phizackerley, and A. J. Wonacott, “A single-crystal oscillation camera for large unit cells,” J. Appl. Cryst. 6, 457–463 (1973). [CrossRef]

18.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenann, 1984).

19.

N. Zhavoronkov, Y. Gritsai, M. Bargheer, M. Woerner, Th. Elsaesser, F. Zamponi, I. Uschmann, and E. Förster, “Microfocus Cu Kα source for femtosecond x-ray science,” Opt. Lett. 30, 1737–1739 (2005). [CrossRef] [PubMed]

20.

M. Bargheer, N. Zhavoronkov, R. Bruch, H. Legall, H. Stiel, M. Woerner, and T. Elsaesser, “Comparison of focusing optics for femtosecond X-ray diffraction,” Appl. Phys. B 80, 715–719 (2005). [CrossRef]

21.

It is important to note that the experimentally observed damage does not change the X-ray diffraction pattern, i.e., the crystal structure, but the surface quality of the single crystal and, thus, the coupling of the optical pump beam into the crystal.

22.

S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, E. D. Murray, S. Fahy, and G. Ingold, “Directly observing squeezed phonon states with femtosecond x-ray diffraction,” Phys. Rev. Lett. 102, 175503 (2009). [CrossRef] [PubMed]

23.

S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, É. D. Murray, S. Fahy, and G. Ingold, “Non-equilibrium phonon dynamics studied by grazing-incidence femtosecond X-ray crystallography,” Acta Crystallogr., Sect. A 66, 157–167 (2010). [CrossRef] [PubMed]

24.

W. Lu, M. Nicoul, U. Shymanovich, A. Tarasevitch, M. Kammler, M. Horn von Hoegen, D. von der Linde, and K. Sokolowski-Tinten, “Transient reversal of a Peierls-transition: Extreme phonon softening in laser-excited Bismuth,” in Ultrafast Phenomena XVII, M. Chergui, D. Jonas, E. Riedle, R. Schoenlein, and A. Taylor, eds. (Oxford University Press, 2011).

25.

J. B. Woodhouse, A. L. A. Fields, and I. A. Bucklow, “X-ray mass absorption coefficients for gold, lead and bismuth in the range 1–10 Å,” J. Phys. D: Appl. Phys, 7, 483–489 (1974). [CrossRef]

OCIS Codes
(000.2170) General : Equipment and techniques
(320.2250) Ultrafast optics : Femtosecond phenomena
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)

ToC Category:
X-ray Optics

History
Original Manuscript: May 23, 2011
Revised Manuscript: June 23, 2011
Manuscript Accepted: July 5, 2011
Published: July 28, 2011

Citation
B. Freyer, J. Stingl, F. Zamponi, M. Woerner, and T. Elsaesser, "The rotating-crystal method in femtosecond X-ray diffraction," Opt. Express 19, 15506-15515 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15506


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References

  1. E. Colleted., “Dynamical structural science,” Acta Crystallogr., Sect. A 66, 133–280 (2010). [CrossRef] [PubMed]
  2. A. Rousse, C. Rischel, and J. C. Gauthier, “Colloquium: femtosecond x-ray crystallography,” Rev. Mod. Phys. 73, 17–31 (2001). [CrossRef]
  3. T. Elsaesser and M. Woerner, “Photoinduced structural dynamics of polar solids studied by femtosecond x-ray diffraction,” Acta Crystallogr., Sect. A 66, 168–178 (2010). [CrossRef] [PubMed]
  4. W. L. Bragg, “The structure of some crystals as indicated by their diffraction of x-rays,” Proc. R. Soc. London, Ser. A 89, 248–277 (1913). [CrossRef]
  5. C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, “Femtosecond time-resolved X-ray diffraction from laser-heated organic films,” Nature 390, 490–492 (1997). [CrossRef]
  6. C. Rose-Petruck, R. Jiminez, T. Guo, A. Cavalleri, C. Siders, J. A. Squier, B. C. Walker, and K. R. Wilson, “Picosecond millianstrom lattice dynamics measured by ultrafast x-ray diffraction,” Nature 398, 310–312 (1999). [CrossRef]
  7. E. Collet, M.-H. Leme-Cailleau, M. Buron-Le Cointe, H. Cailleau, M. Wulff, T. Luty, S.-Y. Koshihara, M. Meyer, L. Toupet, P. Rabiller, and S. Techert, “Laser-induced ferroelectric structural order in an organic charge-transfer crystal,” Science 300, 612–615 (2003). [CrossRef] [PubMed]
  8. K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-von-Hoegen, and D. von der Linde, “Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit,” Nature 422, 287–289 (2003). [CrossRef] [PubMed]
  9. M. Bargheer, N. Zhavoronkov, Y. Gritsai, J. C. Woo, D. S. Kim, M. Woerner, and T. Elsaesser, “Coherent atomic motions in a nanostructure studied by femtosecond x-ray diffraction,” Science 306, 1771–1773 (2004). [CrossRef] [PubMed]
  10. D. M. Fritz, D. A. Reis, B. Adams, R. A. Akre, J. Arthur, C. Blome, P. H. Bucksbaum, A. L. Cavalieri, S. Engemann, S. Fahy, R. W. Falcone, P. H. Fuoss, K. J. Gaffney, M. J. George, J. Hajdu, M. P. Hertlein, P. B. Hillyard, M. Horn-von Hoegen, M. Kammler, J. Kaspar, R. Kienberger, P. Krejcik, S. H. Lee, A. M. Lindenberg, B. McFarland, D. Meyer, T. Montagne, A. D. Murray, A. J. Nelson, M. Nicoul, R. Pahl, J. Rudati, H. Schlarb, D. P. Siddons, K. Sokolowski-Tinten, T. Tschentscher, D. von der Linde, and J. B. Hastings, “Ultrafast bond softening in bismuth: mapping a solid’s interatomic potential with x-rays,” Science 315, 633–636 (2007). [CrossRef] [PubMed]
  11. C. v. Korff Schmising, M. Bargheer, M. Kiel, N. Zhavoronkov, M. Woerner, T. Elsaesser, I. Vrejoiu, D. Hesse, and M. Alexe, “Coupled ultrafast lattice and polarization dynamics in ferroelectric nanolayers,” Phys. Rev. Lett. 98, 257601 (2007). [CrossRef]
  12. S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi, E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund, R. Abela, and G. Ingold, “Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth,” Phys. Rev. Lett. 100, 155501 (2008). [CrossRef] [PubMed]
  13. F. Zamponi, Z. Ansari, M. Woerner, and T. Elsaesser, “Femtosecond powder diffraction with a laser-driven hard x-ray source,” Opt. Express 18, 947–961 (2010). [CrossRef] [PubMed]
  14. M. Woerner, F. Zamponi, Z. Ansari, J. Dreyer, B. Freyer, M. Premont-Schwarz, and T. Elsaesser, “Concerted electron and proton transfer in ionic crystals mapped by femtosecond x-ray powder diffraction,” J. Chem. Phys. 133, 064509 (2010). [CrossRef] [PubMed]
  15. B. E. Warren, X-ray Diffraction (Dover Publications, 1990).
  16. C. Giacovazzo, Fundamentals of Crystallography (Oxford University Press, 2002). [PubMed]
  17. U. W. Arndt, J. N. Champness, R. P. Phizackerley, and A. J. Wonacott, “A single-crystal oscillation camera for large unit cells,” J. Appl. Cryst. 6, 457–463 (1973). [CrossRef]
  18. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media , 2nd ed. (Butterworth-Heinenann, 1984).
  19. N. Zhavoronkov, Y. Gritsai, M. Bargheer, M. Woerner, Th. Elsaesser, F. Zamponi, I. Uschmann, and E. Förster, “Microfocus Cu Kα source for femtosecond x-ray science,” Opt. Lett. 30, 1737–1739 (2005). [CrossRef] [PubMed]
  20. M. Bargheer, N. Zhavoronkov, R. Bruch, H. Legall, H. Stiel, M. Woerner, and T. Elsaesser, “Comparison of focusing optics for femtosecond X-ray diffraction,” Appl. Phys. B 80, 715–719 (2005). [CrossRef]
  21. It is important to note that the experimentally observed damage does not change the X-ray diffraction pattern, i.e., the crystal structure, but the surface quality of the single crystal and, thus, the coupling of the optical pump beam into the crystal.
  22. S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, E. D. Murray, S. Fahy, and G. Ingold, “Directly observing squeezed phonon states with femtosecond x-ray diffraction,” Phys. Rev. Lett. 102, 175503 (2009). [CrossRef] [PubMed]
  23. S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, É. D. Murray, S. Fahy, and G. Ingold, “Non-equilibrium phonon dynamics studied by grazing-incidence femtosecond X-ray crystallography,” Acta Crystallogr., Sect. A 66, 157–167 (2010). [CrossRef] [PubMed]
  24. W. Lu, M. Nicoul, U. Shymanovich, A. Tarasevitch, M. Kammler, M. Horn von Hoegen, D. von der Linde, and K. Sokolowski-Tinten, “Transient reversal of a Peierls-transition: Extreme phonon softening in laser-excited Bismuth,” in Ultrafast Phenomena XVII , M. Chergui, D. Jonas, E. Riedle, R. Schoenlein, and A. Taylor, eds. (Oxford University Press, 2011).
  25. J. B. Woodhouse, A. L. A. Fields, and I. A. Bucklow, “X-ray mass absorption coefficients for gold, lead and bismuth in the range 1–10 Å,” J. Phys. D: Appl. Phys, 7, 483–489 (1974). [CrossRef]

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