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Observation of femtosecond X-ray interactions withmatter using an X-ray–X-ray pump–probe schemeIchiro Inouea,b,1, Yuichi Inubushib,c, Takahiro Satob,2, Kensuke Tonob,c, Tetsuo Katayamab,c, Takashi Kameshimab,c,Kanade Ogawab,3, Tadashi Togashib,c, Shigeki Owadab, Yoshiyuki Amemiyaa, Takashi Tanakab, Toru Harab,and Makina Yabashib,c,1
aDepartment of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561,Japan; bRIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan; and cJapan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo,Hyogo 679-5198, Japan
Edited by Philip H. Bucksbaum, Stanford University, Menlo Park, CA, and approved December 14, 2015 (received for review August 18, 2015)
Resolution in the X-ray structure determination of noncrystallinesamples has been limited to several tens of nanometers, becausedeep X-ray irradiation required for enhanced resolution causesradiation damage to samples. However, theoretical studies predictthat the femtosecond (fs) durations of X-ray free-electron laser(XFEL) pulses make it possible to record scattering signals beforethe initiation of X-ray damage processes; thus, an ultraintenseX-ray beam can be used beyond the conventional limit of radiationdose. Here, we verify this scenario by directly observing femto-second X-ray damage processes in diamond irradiated withextraordinarily intense (∼1019 W/cm2) XFEL pulses. An X-raypump–probe diffraction scheme was developed in this study;tightly focused double–5-fs XFEL pulses with time separationsranging from sub-fs to 80 fs were used to excite (i.e., pump) thediamond and characterize (i.e., probe) the temporal changes of thecrystalline structures through Bragg reflection. It was found thatthe pump and probe diffraction intensities remain almost constantfor shorter time separations of the double pulse, whereas theprobe diffraction intensities decreased after 20 fs following pumppulse irradiation due to the X-ray–induced atomic displacement.This result indicates that sub-10-fs XFEL pulses enable conductionsof damageless structural determinations and supports the validityof the theoretical predictions of ultraintense X-ray–matter interac-tions. The X-ray pump–probe scheme demonstrated here would beeffective for understanding ultraintense X-ray–matter interac-tions, which will greatly stimulate advanced XFEL applications,such as atomic structure determination of a single molecule andgeneration of exotic matters with high energy densities.
X-ray free-electron laser | pump–probe | femtosecond X-ray damage
Since W. C. Röntgen discovered X-rays emitted from vacuumtube equipment in 1895, scientists have continuously endeav-
ored to develop brighter X-ray sources throughout the 20th century.One of the most remarkable breakthroughs was the emergence ofsynchrotron light sources, which were much more brilliant than theearly lab-based X-ray sources. Such dramatic increase in X-raybrilliance provided a pathway to obtain high-quality X-ray scat-tering data. This, in turn, enabled one to solve the structures ofcomplex systems such as proteins, functional units of living or-ganisms, and viruses. However, the increase in the brilliance is alsoaccompanied by a severe problem of X-ray radiation damage tothe samples being examined (1). X-rays ionize atoms and generatehighly activated radicals that break chemical bonds and causechanges in the structures of the samples. To achieve structuredetermination precisely, a sufficient scattering signal should berecorded before the samples are severely damaged. Radiationdamage was considered to be an intrinsic problem associated withX-ray scattering experiments, which imposed a fundamental limiton the resolution in X-ray structure determination (2).The recent advent of X-ray free-electron lasers (XFELs) (3–5),
which emit ultraintense X-ray pulses with durations of severalfemtoseconds, may totally avoid the problem of radiation damage.
The irradiation of intense XFEL pulses generates highly ionizedatoms, and the strong Coulomb repulsive force leads to evapora-tion of the samples. Meanwhile, it has been predicted theoretically(6) that atoms do not change their positions before the terminationof the femtosecond X-ray pulse owing to inertia, thus enabling theuse of X-ray radiations beyond the conventional X-ray dose limit.This innovative concept, called a “diffraction-before-destruction”scheme (6, 7), has paved a clear way to high-resolution structuredeterminations of weak scattering objects, including nano-meter-sized protein crystals (8), noncrystalline biological par-ticles (9), and damage-sensitive protein crystals (10).Despite the potential impact of XFELs, detailed understanding
of the ultrafast XFEL damage processes has been missing. As apioneering work, Barty et al. (11) measured the diffraction in-tensities of protein nanocrystals by changing the XFEL pulse du-rations from 70 to 300 fs at intensities of ∼1017 W/cm2. They foundthat the diffraction intensities greatly decrease for longer durations,clearly indicating sign of structural damage, i.e., X-ray–inducedatomic displacements within the XFEL pulse durations. For fur-ther understanding of ultraintense X-ray interactions with matter,we need to directly measure the temporal changes of the structuraldamage. In particular, measuring the ignition time of the atomicdisplacements is crucial for realizing advanced applications withgreatly intense XFELs. Although improving our knowledge of theX-ray damage processes is essential for all aspects of XFEL
Significance
Understanding ultraintense light–matter interactions is an in-triguing subject from viewpoints of basic science and practicalapplications. For the X-ray region, such research fields haveopened up with the emergence of X-ray free-electron lasers(XFELs). By using an X-ray–X-ray pump–probe scheme, wefirstly measured atomic response to XFEL light with femto-second–ångstrom time–space resolutions. It was found that theatomic position is freezing until 20 fs after the XFEL irradiation,which supports the feasibility of damageless structural deter-minations with ultraintense XFEL pulses. The pump–probescheme demonstrated here is an effective way to captureX-ray–matter interactions, and would contribute to verify andimprove theory of X-ray interactions with matter, and stimu-late advanced XFEL applications.
Author contributions: I.I., T.S., Y.A., and M.Y. designed research; I.I., Y.I., K.T., T. Katayama,T. Kameshima, K.O., T. Togashi, S.O., T.H., and M.Y. performed research; I.I. and T. Tanakaanalyzed data; and I.I., Y.A., and M.Y. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.1To whom correspondence may be addressed. Email: [email protected] [email protected].
2Present address: Department of Chemistry, School of Science, The University of Tokyo,7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
3Present address: Japan Atomic Energy Agency, 8-1-7 Umemidai, Kizugawa, Kyoto 619-0215, Japan.
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science, the experimental verifications have been missing because ofthe extreme difficulty in observation with ultrahigh resolutions inspace (ångstrom) and time (femtosecond).As a new approach to investigate the femtosecond X-ray
damage processes, we here propose an X-ray–X-ray pump–probeexperiment using double X-ray pulses; a pump X-ray pulse ex-cites a sample and a probe X-ray pulse with a well-controlledtime delay characterizes the change in the sample. In this ap-proach, it is highly useful to exploit two-color double pulses withtunable temporal separations (12–15), which have been de-veloped at SPring-8 Angstrom Compact free-electron LAser(SACLA) (4) and Linac Coherent Light Source (3). In thisarticle, we measured the X-ray damage processes of diamondby using an X-ray–X-ray pump–probe diffraction experimentat SACLA. As the carbon–carbon bond is one of the mostfundamental bonds in biomolecules, our results should pro-vide a benchmark for XFEL-induced damage to practicalsamples.
ResultsX-Ray–X-Ray Pump–Probe Experiment at SACLA. The experimentwas performed at SACLA BL3 (4, 16), as schematically shown inFig. 1 (Materials and Methods). We operated the XFEL source inthe two-color double-pulse mode (12). Here, the eight upstreamundulators were tuned to generate pump X-ray pulses with awavelength of 2.03 Å. The remaining downstream undulatorsgenerated probe X-ray pulses with a wavelength of 2.10 Å. Thetime interval was controlled by a magnetic chicane locateddownstream of the eighth undulator. The temporal durations ofthe two pulses were estimated to be ∼5 fs by autocorrelationmeasurements (17), which was consistent with the estimationbased on spectral spike width measurement (18). The X-ray in-tensities of the two pulses were increased up to ∼1019 W/cm2 byusing a two-stage focusing system (19), and the pulse energieswere determined shot-by-shot by an inline spectrometer. Typicalphoton numbers in the pump and the probe X-ray pulses at thefocus point were 9 × 109 and 2 × 1010, respectively. The X-rayfluences of the pump and probe pulses were ∼3 × 104 J cm−2 and∼7 × 104 J cm−2, respectively. We set a thin film of diamondnanocrystals at the focal point, and measured the DebyeScherrer rings of the 111- and 220 reflections, which correspondto the lattice plane distances of d111 = 2.06 Å and d220 = 1.26 Å,in the horizontal direction with two multiport charge-coupleddevice (MPCCD) detectors (20). To avoid the influence of theX-ray–induced damage, we scanned a fresh part of the diamondfilm surface to every XFEL shot. We performed the X-ray–X-raypump–probe experiment by changing the relative time delay be-tween the pump and the probe pulses from 0.3 to 80 fs.
Analysis of Pump and Probe Diffraction Intensities. Fig. 2 A and Cshows MPCCD images of the 111- and 220 reflections, re-spectively, at different time delays, which are averaged formultiple shots with the specific fluences of the pump and theprobe pulses. In this condition, the pump fluence correspondsto an X-ray dose of 320 MGy to carbon atoms, which is muchhigher than the conventional tolerable dose limit for proteincrystals of 30 MGy at cryogenic temperatures (1). In both dif-fraction patterns of the 111- and 220 reflections, we can observetwo well-separated diffraction peaks, reflecting the differences inBragg angles for the pump and the probe pulses. Fig. 2 B and Dshows the line profiles corresponding to Fig. 2 A and C, re-spectively. In these figures, we corrected the effect of XFELpolarization on the diffraction intensity (Materials and Methods).For both 111- and 220 reflections, the probe diffraction intensitiesgradually decrease as the time delay increases. We can considerthese changes indicative of the femtosecond X-ray–induced dam-age in diamond. In addition, we found that the diffuse scatteringintensity around the 111 reflection increases with the time delay
(Fig. 2B, Inset). The increase in the diffuse scattering intensity isalso considered indicative of the X-ray–induced damage in thefemtosecond time scale. For more quantitative analyses of theX-ray damage processes, we calculated the averaged line profilesof the 111- and 220 reflections at the respective fluences of thepump and the probe pulses. Then, we fitted each profile to thesummation of two Lorentzian functions and a baseline:
LðiÞ= Ipump
πγpump
"1+
i− ipump
γpump
!2#+ Iprobe
πγprobe
"1+
i− iprobeγprobe
!2#+B.
Here, i, γ, I, and B represent the index of pixels, the widths andintegrated diffraction intensities of Bragg reflections, and thebaseline, respectively. We analyzed the dependence of the in-tegrated probe diffraction intensities of the 111- and 220 reflec-tions (I111 and I220) on the time delay after correcting theinhomogeneity of the sample and the differences in the probepulse energies (Materials and Methods). Fig. 3 A–C shows thedependence of I111 and I220 on the time delay for three differentfluences of the pump pulses. In these figures, I111 and I220 arenormalized by the averaged values of those at the four shortesttime delays (0.3, 0.5, 0.7, and 1.5 fs), Iave111 and Iave220. Here wenote that I111 and I220 in the case of the shortest time delays werealmost the same as those when the diamond film was moved to a
A
B
Fig. 1. Schematic illustration of the X-ray–X-ray pump–probe experiment atSACLA. (A) XFEL pulses were generated at a repetition rate of 30 Hz in thetwo-color double-pulse operation mode of SACLA. The eight upstreamundulators generated pump X-ray pulses with a wavelength of 2.03 Å, andthe downstream undulators generated probe X-ray pulses with a wave-length of 2.10 Å. The time interval between the pump and the probe pulseswas tuned by a magnetic chicane located just after the eighth undulator,which controlled an additional path length of the electron beam with re-spect to the straight trajectory. (B) Two-color double pulses with time in-tervals, which were focused to 130 nm (horizontal) × 200 nm (vertical),irradiated a thin film of diamond nanocrystals. Debye Scherrer rings of thediamond 111- and 220 reflections in the horizontal direction weremeasured using two MPCCD detectors. The pulse energies of the incidentpump and probe pulses were determined in a shot-by-shot manner usingan inline spectrometer that combined a diamond foil and an MPCCDdetector.
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defocused position [10 mm apart from the focus along the beamaxis. The beam size at the position was 250 μm (H) and 400 μm(V)]. This result indicates that X-ray damage during irradiations ofthe pump or the probe pulses was negligibly small in the conditionsof the present pump–probe experiment. Interestingly, I220 decaysfaster than I111, as shown in Fig. 3 D and E, which represent thetime delays at which I111/Iave111 and I220/Iave220 decrease to 0.9 (Fig.3D) and 0.85 (Fig. 3E), respectively.
Evaluation of Temporal Changes of X-Ray-Induced Damage inDiamond. The decreases in I111 and I220 could be explained bytwo factors: electronic damage (21) and structural damage (11).The former is attributed to the increase in the number of ionizedcarbon atoms with longer time delays. As the atomic form factorof carbon that corresponds to the 111- and 220 reflections ofdiamond is almost proportional to the number of electrons oc-cupying the core shell (K shell) (22), the generation of core holesby pump X-ray irradiation and subsequent excitation processes,such as electron impact ionization, leads to decreases in I111 andI220. However, in our experimental conditions, such electronicdamage is negligible because the percentage of core hole atomsgenerated by the entire excitation processes is evaluated to be∼1% at most, which corresponds to a decrease in diffractionintensities much less than 1% (Materials and Methods). There-fore, we can assume that the latter, the atomic displacementcaused by strong Coulomb interactions between ionized atoms, isthe main mechanism that explains our observation. In this case,the diffraction intensities from smaller lattice spacing shoulddecrease faster because the atomic displacement leads to a largerphase mismatch between scattered X-rays from each atom. Infact, this tendency agrees with our observation (Fig. 3 D and E).To quantitatively verify the assumption, we evaluated the
temporal development of the atomic displacement using Barty
et al.’s simple model (11). We assume that the displacements ofcarbon atoms in diamond are independent and random with amean of zero. A change in the diffraction intensity with such ran-dom displacements is mathematically equivalent to the Debye–Waller factor in crystallography, which represents the effect ofthermal motion on the diffraction intensity. The diffraction in-tensity of Bragg reflection is reduced by a factor of expð−q2σ2Þ,where q is a scattering vector given by q= 4π sinθ=λ for wavelengthλ and scattering angle 2θ, and σ is the root-mean-square (rms)displacement perpendicular to the lattice plane. In our experiment,the diffraction intensities of the 111- and 220 reflections are almostconstant for time delays shorter than 1.5 fs (Fig. 3 A–C). This resultindicates that the atomic displacement does not increase in thistime scale, and the rms displacement is considered the same as thatof undamaged diamond at room temperature. Then, I111/I111aveand I220/I220ave can be expressed as expð−q2σ2111Þ=expð−q2σ20Þ andexpð−q2σ2220Þ=expð−q2σ20Þ, respectively. Here, σ0 = 0.043 Å are therms displacements of carbon atoms perpendicular to the (111)- and(220) planes in the undamaged state (23), and σ111 and σ220 arethose of atoms interacting with intense X-rays. Based on the aboverepresentations of the diffraction intensities, the temporal changesof σ111 and σ220 were evaluated for three different pump pulseenergies (Fig. 4). σ111 and σ220 rapidly increase from 20 fs afterirradiation of the pump pulse, indicating that the critical time forthe ignition of the X-ray–induced structure change is 20 fs for thepresent pump pulse fluences. Interestingly, σ111 is larger than σ220after the ignition of the atomic movement. Although it is difficultto conclusively explain the mechanism using only the presentlyavailable data, it may be caused by higher-order atomic dis-placement beyond the simple Debye–Waller model. The ratesof σ111 and σ220 are of the order of 10−3 Å/fs, which is comparable tothe unidirectional velocity of isolated carbon atom at room tem-perature (v=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikBT=M
p= 4 × 10−3 Å/fs, where kB is the Boltzmann
A
C
B
D
Fig. 2. Images and line profiles of the diffraction from diamond. (A and C) MPCCD images of the 111- and 220 reflections at time intervals between thepump and the probe pulses of 0.3, 0.6, 50, and 80 fs, which are averaged over multiple shots with specific fluences of the pump [(3.1 ± 0.2) × 104 J cm−2] andthe probe [(6.9 ± 1.1) × 104 J cm−2] pulses. (B and D) Line profiles of A and C after compensating for the effect of XFEL polarization on the diffraction intensity(Materials and Methods). (B, Inset) An enlarged figure that represents diffuse scattering around the 111 reflection.
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constant, T = 300 K, and M is the mass of carbon atom). Thissimilarity of the rate of rms atomic displacement and the velocity ofisolated atoms is a general feature in the nonthermal melting pro-cesses of semiconductors pumped by optical lasers (24, 25), whereinteratomic potential changes by excitation of valence electrons leadinertial dynamics. Such interatomic potential changes might becaused by the electronic damage processes in the present experiment.
DiscussionFinally, we discuss the maximum X-ray intensity that is accept-able for X-ray structure determination. We compare the degreeof X-ray damage induced by the pump 5-fs XFEL pulse used inthe present experiment (fluence of 3 × 104 J cm−2, which cor-responds to a photon density of 3 × 103 photons Å−2, an in-tensity of ∼1019 W cm−2, and a radiation dose of 320 MGy tocarbon atoms) and an XFEL pulse with duration of 20 fs at thesame fluence. Although the total number of photoelectrons atthe termination of the XFEL pulse is the same for both cases, the5-fs XFEL pulse generates more photoelectrons than the 20-fsXFEL pulse at any time within 20 fs after beginning of the XFELirradiation. As each photoelectron takes some time to ionizesurrounding atoms, the X-ray damage induced by the 5-fs XFELshould obviously become faster. In our experiment, structuralchanges were not prominent within 20 fs after pump pulse irra-diation. Thus, we can consider that structural determination isfeasible with 20-fs XFEL pulses at the same fluence of 3 × 104
J cm−2 as in our experiment. According to molecular dynamicssimulations of protein crystals, which predict that the rms dis-placement of atoms at the termination of the XFEL pulse isproportional to F1=2T for X-ray fluence of F and pulse duration ofT (7, 11), our results indicate that the atomic displacements are also
expected to be negligible for 2-fs XFEL pulses with fluenceof F = 3× 104 J cm−2 × ð20 fs=2 fsÞ2 = 3× 106 J cm−2. This con-dition of XFEL pulses, a pulse duration of 2 fs and a fluence of3× 106 J cm−2 (i.e., a photon density of 3 ×105 photons Å−2, anintensity of ∼1021 W cm−2, and a radiation dose of 32 GGy tocarbon atoms), would allow us to collect sufficient scattering signalsfrom single protein molecules for determination of molecular ori-entation (26), which enables structural determination with atomicscale from multiple scattering images. As sub-10-fs XFEL pulses areroutinely used in the current XFEL facilities (18, 27), increasing thephoton density by two orders higher than the value currently achievedwould enable the X-ray scattering experiment of single protein mol-ecules. Precisely shaped X-ray mirrors (28) producing an X-ray spotcomparable to the size of protein molecules (although the spot sizesets an upper limit of the molecule size to be analyzed) and increasesin the number of emitted photons from XFELs by optimizing ac-celerator parameters for production of high-current and low-emittanceelectron beams, would provide a platform for scattering experimentsof single molecule without X-ray–induced structural damage.The experimental results presented here support the feasibility
of molecular imaging with sub-10-fs XFEL pulses with fluence of106∼107 J cm−2, which has long been desired by scientists. To re-alize this ultimate measurement, we need further understanding ofthe interaction of high-intensity X-rays with matter. Simulationstudies predict (29, 30) that the effect of electronic damage for sub-10-fs hard XFEL pulses becomes prominent above the photondensity of 106∼107 photons Å-2, which corresponds to fluence of107∼108 J cm−2 and intensity of 1021∼1022 W cm−2. Although thisthreshold value of fluence is slightly larger than that required formolecular imaging, the margin is small. Thus, one may need toconsider modification of the conventional scattering theory, which
Fig. 3. Temporal changes of the probe diffraction intensities of the diamond 111- and 220 reflections after irradiation of the pump pulse. (A–C) Dependenceof the probe diffraction intensities of the 111- and 220 reflections on the time delay at specific fluences of the pump [(A) (2.3 ± 0.2) × 104 J cm−2, (B) (2.7 ±0.2) × 104 J cm−2, and (C) (3.1 ± 0.2) × 104 J cm−2] and the probe [(6.9 ± 0.5) × 104 J cm−2)] pulses. (D and E) Time delays for I111 (red) and I220 (blue) decreasing tobe, respectively, 90% and 85% of Iave111 and Iave220 for different fluence conditions of the pump [(2.3 ± 0.2) × 104 J cm−2, (2.7 ± 0.2) × 104 J cm−2, and (3.1 ±0.2) × 104 J cm−2] and the probe [(5.9 ± 0.5) × 104 J cm−2, (6.9 ± 0.5) × 104 J cm−2, and (7.9 ± 0.5) × 104 J cm−2] pulses. After evaluating I111 and I220 for therespective conditions, we performed the linear interpolation of I111 and I220 between the measured conditions of time delays and determined the values ofthe time delays shown in D and E.
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assumes all atoms being ground state, for analyzing scattering frommolecules with intense XFEL pulses. To achieve accurate analysis,new scattering theory that incorporates the effect of electronicdamage (31) would become a promising way. Understanding andmodeling of the X-ray–induced electronic damage and matter inextreme conditions with high energy densities (32, 33) would behelpful for constructing this new framework of scattering theorywith ultraintense X-rays. The experimental investigations of theXFEL-induced electronic damage are the next intriguing subjectsfor the X-ray–X-ray pump–probe experiment.
Materials and MethodsX-Ray–X-Ray Pump–Probe Experiment at SACLA. The experimentwas performedin EH5 at SACLA BL3. Double XFEL pulses were generated at a repetition rate of30 Hz in the two-color double-pulse operation mode of SACLA. By tuning theundulator gaps, we generated pump X-ray pulses with a wavelength of 2.03 Å(i.e., a photon energy of 6.1 keV) and probe X-ray pulses with a wavelength of2.10 Å (i.e., a photon energy of 5.9 keV). The time interval between the pumpand the probe pulses was controlled with ultrahigh accuracy of less than 0.1 fsusing a magnetic chicane located just after the eighth undulator. The spectralbandwidths of the pump and the probe pulses were ∼50 eV. The intensity profileof the double pulse measured at the optical hutch was almost identical andround-shaped for the different delay times and shots.
The XFEL pulses were focused using a two-stage reflective focusing system(19). The focused spot size of the pump and the probe pulses measured by aknife-edge scan method was 130 nm (horizontal) × 200 nm (vertical). We alsomeasured the focus size of the double pulses after transmission of a 25-μmchromium film. Because the absorption K edge of chromium is 5.99 keV andonly the probe pulse selectively transmitted the film, we were able to measurethe focus size of the probe pulse. The focus size of the probe pulse was thesame as that of the double XFEL pulses, which indicates that the pump and theprobe pulses perfectly overlapped in space.
We used a nanocrystal diamond film prepared by plasma-enhancedchemical vapor deposition as a sample for the X-ray–X-ray pump–probeexperiment. This diamond film is the same as that used for monitoring theposition and intensity of XFEL beam (34). The film thickness was 15 μm andthe crystal grain size was ∼30 nm. The X-ray transmittances at the wave-lengths of the pump and the probe pulses were above 95%. We set thediamond film at the focal point and measured the diffraction patterns of the
111- and 220 reflections in the horizontal direction with two MPCCD de-tectors at 30 Hz. The distances between the sample and the MPCCD detec-tors were 205 mm for the 111 reflection and 260 mm for the 220 reflection.The pulse energies of the pump and the probe pulses were determined usinga calibrated intensity monitor (34) installed at SACLA and a spectrometerlocated 5.5 m downstream of the focal point, consisting of the same di-amond foil as the sample and an MPCCD detector to measure the diffractionintensities of the 111 reflection.
We performed the experiment for the condition of time delays of 0.3, 0.5,0.7, 1.5, 3, 6, 10, 20, 30, 50, and 80 fs. For each condition, we measured∼12,000 shots by scanning the sample so as to use a fresh surface for everyshot to avoid the influence of XFEL-irradiation-induced damage.
Procedure for Calculating Line Profiles of Diffraction Intensities. To calculatethe line profiles of the diffraction intensities as shown in Fig. 2 B and D, wefirst extracted MPCCD images for specific fluences of the pump and theprobe pulses. For each image, we converted the digital signals at respectivepixels into the number of detected X-ray photons in a photon-countingmanner (20). Then, we averaged the number of detected photons over allextracted images for each pixel. Next, to compensate for the effect of theX-ray polarization on the diffraction intensity, the averaged number ofdetected photon at each pixel was divided by the polarization factor, whichwas determined under the assumption of the XFEL pulse having completelyhorizontal polarization. Finally, by integrating the compensated diffractionintensities along the shorter directions of the MPCCD images, we calculatedthe line profiles of the diffraction intensities.
Evaluation of Integrated Diffraction Intensities of Probe Pulses. To comparethe probe diffraction intensities for different time delays, we calculated thenormalized probe diffraction intensities of the 111- and 220 reflections, I111and I220, defined as
I111 =Iprobeð111Þ
�I0ðprobeÞ
Ipumpð111Þ�I0ðpumpÞ , [1]
I220 =Iprobeð220Þ
�I0ðprobeÞ
Ipumpð220Þ�I0ðpumpÞ , [2]
where Ipump and Iprobe represent the integrated diffraction intensities de-termined by the fitting of the line profiles for specific fluences of the pumpand the probe pulses, and I0ðprobeÞ and I0ðpumpÞ are the pulse energies ofthe incident pump and probe pulses, which are averaged over the XFEL shotsextracted for the calculation of the line profiles. The denominators of Eqs. 1and 2 are considered proportional to the number of crystals contributing tothe 111- and 220 reflections of the pump pulses, respectively. As the Braggdiffraction angles are almost the same for the pump and the probe pulses,the denominators should compensate for the effect of the inhomogeneityof the sample on the probe diffraction intensity. In addition, Iprobeð111Þ andIprobeð220Þ are divided by I0ðprobeÞ in Eqs. 1 and 2 to compensate for thedifferences of the incident probe pulse energies for different time delays.
Effect of Ionization of Carbon Atoms on Diffraction Intensity. During the ir-radiation of a pump X-ray pulse with a fluence of ∼3×104 J cm−2, ∼0.7% of allirradiated carbon atoms are photoionized (35), and the same number ofphotoelectrons with energies almost the same as the pump X-ray photonenergy (∼6 keV) are emitted mostly from the inner shell. Each photoelectroncollides with the bound electrons in the surrounding carbon atoms, leadingto the emission of electrons from the outer and inner shells of the carbonatoms, which is called the electron-impact ionization process. The ejectedelectrons also collide with the bound electrons, leading to the cascade ion-ization of carbon atoms. In such electronic damage processes, the inner shellionization terminates at ∼1 fs after the generation of photoelectrons, atwhich time the energies of the cascade electrons become lower than thebinding energy of the inner shell electron of carbon (273 eV) (21). By thetime of the termination, ∼30 bounded electrons are emitted per 6-keVphotoelectron (21). For electron energies ranging from 273 eV to 6 keV, thecross-section of the electron-impact inner shell ionization of carbon is almost thesame as or less than 1% of that of the total electron-impact ionization (36),indicating that the number of emitted electrons from the inner shell via impactionization is less than 0.3 per single 6-keV photoelectron. Therefore, the per-centage of core hole atoms generated by the irradiation of the pump pulse overall carbon atoms is ∼1% at most. As this value corresponds to a decrease indiffraction intensity of much less than 1%, the electronic damage is considerednegligible for the accuracy of our experiment.
Fig. 4. Temporal changes of the atomic displacements of carbon atomsperpendicular to the (111)- and (220) planes in diamond (σ111, σ220) afterirradiation of the probe pulses. We assumed that the atomic displacementsdid not depend on the fluence of the probe pulse, and estimated the atomicdisplacements for different fluence conditions of the pump [(2.3 ± 0.2) × 104
J cm−2, (2.7 ± 0.2) × 104 J cm−2, and (3.1 ± 0.2) × 104 J cm−2] pulses to be theaverage values of those for fluences of the probe pulses being (5.9 ± 0.5) ×104 J cm−2, (6.9 ± 0.5) × 104 J cm−2, and (7.9 ± 0.5) × 104 J cm−2. Here, data forcertain conditions of time delays and fluences are missing because theoverestimation of the diffraction intensities of the probe pulses owingto artifacts made it impossible to evaluate the atomic displacement [i.e.,I111=Iave111 > expðq2
111σ20Þ or I220=Iave220 > expðq2
220σ20Þ]. The atomic displace-
ment of carbon atoms in diamond in the undamaged state (σ0 = 0.043 Å) isalso shown for comparison.
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ACKNOWLEDGMENTS. We greatly thank H. Tanaka for his continuousencouragement and support for this project. We acknowledge the fruitfuldiscussions with Y. Shinohara, K. Tamasaku, E. Nishibori, and T. Arima. This
study was partially supported by the Japan Society for the Promotion ofScience (JSPS) Research Fellowship for Young Scientists and the SACLAGraduate-Course Student Program.
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