Femtosecond X-ray Diffraction Research Articles

Reciprocal space slicing: A time-efficient approach to femtosecond x-ray diffraction.

An experimental technique that allows faster assessment of out-of-plane strain dynamics of thin film heterostructures via x-ray diffraction is presented. In contrast to conventional high-speed reciprocal space-mapping setups, our approach reduces the measurement time drastically due to a fixed measurement geometry with a position-sensitive detector. This means that neither the incident (ω) nor the exit () diffraction angle is scanned during the strain assessment via x-ray diffraction. Shifts of diffraction peaks on the fixed x-ray area detector originate from an out-of-plane strain within the sample. Quantitative strain assessment requires the determination of a factor relating the observed shift to the change in the reciprocal lattice vector. The factor depends only on the widths of the peak along certain directions in reciprocal space, the diffraction angle of the studied reflection, and the resolution of the instrumental setup. We provide a full theoretical explanation and exemplify the concept with picosecond strain dynamics of a thin layer of NbO2.

Spin stress contribution to the lattice dynamics of FePt.

Invar-behavior occurring in many magnetic materials has long been of interest to materials science. Here, we show not only invar behavior of a continuous film of FePt but also even negative thermal expansion of FePt nanograins upon equilibrium heating. Yet, both samples exhibit pronounced transient expansion upon laser heating in femtosecond x-ray diffraction experiments. We show that the granular microstructure is essential to support the contractive out-of-plane stresses originating from in-plane expansion via the Poisson effect that add to the uniaxial contractive stress driven by spin disorder. We prove the spin contribution by saturating the magnetic excitations with a first laser pulse and then detecting the purely expansive response to a second pulse. The contractive spin stress is reestablished on the same 100-ps time scale that we observe for the recovery of the ferromagnetic order. Finite-element modeling of the mechanical response of FePt nanosystems confirms the morphology dependence of the dynamics.

Enhanced X-ray diffraction of in vivo-grown μNS crystals by viscous jets at XFELs.

μNS is a 70 kDa major nonstructural protein of avian reoviruses, which cause significant economic losses in the poultry industry. They replicate inside viral factories in host cells, and the μNS protein has been suggested to be the minimal viral factor required for factory formation. Thus, determining the structure of μNS is of great importance for understanding its role in viral infection. In the study presented here, a fragment consisting of residues 448-605 of μNS was expressed as an EGFP fusion protein in Sf9 insect cells. EGFP-μNS(448-605) crystallization in Sf9 cells was monitored and verified by several imaging techniques. Cells infected with the EGFP-μNS(448-605) baculovirus formed rod-shaped microcrystals (5-15 µm in length) which were reconstituted in high-viscosity media (LCP and agarose) and investigated by serial femtosecond X-ray diffraction using viscous jets at an X-ray free-electron laser (XFEL). The crystals diffracted to 4.5 Å resolution. A total of 4227 diffraction snapshots were successfully indexed into a hexagonal lattice with unit-cell parameters a=109.29, b = 110.29, c = 324.97 Å. The final data set was merged and refined to 7.0 Å resolution. Preliminary electron-density maps were obtained. While more diffraction data are required to solve the structure of μNS(448-605), the current experimental strategy, which couples high-viscosity crystal delivery at an XFEL with in cellulo crystallization, paves the way towards structure determination of the μNS protein.

Decoupling spin-orbital correlations in a layered manganite amidst ultrafast hybridized charge-transfer band excitation

In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods -- both femtosecond resonant x-ray diffraction and optical reflectivity -- to demonstrate that the orbital response in the layered manganite Nd$_{1-x}$Sr$_{1+x}$MnO$_{4}$ ($\it{x}$ = 2/3) does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the transient state. Instead of the typical $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ transition, a near-infrared pump in this compound promotes a fundamentally distinct mechanism of charge transfer, the $d^{0}$ $ \xrightarrow{}$ $d^{1}L$, where $\it{L}$ denotes a hole in the oxygen band. This novel finding may pave a new avenue for selectively manipulating specific types of order in complex materials of this class.

Measurement of diamond nucleation rates from hydrocarbons at conditions comparable to the interiors of icy giant planets

We present measurements of the nucleation rate into a diamond lattice in dynamically compressed polystyrene obtained in a pump-probe experiment using a high-energy laser system and in situ femtosecond x-ray diffraction. Different temperature-pressure conditions that occur in planetary interiors were probed. For a single shock reaching 70 GPa and 3000 K no diamond formation was observed, while with a double shock driving polystyrene to pressures around 150 GPa and temperatures around 5000 K nucleation rates between ${10}^{29}$ and ${10}^{34}\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}$ ${\mathrm{s}}^{\ensuremath{-}1}$ were recorded. These nucleation rates do not agree with predictions of the state-of-the-art theoretical models for carbon-hydrogen mixtures by many orders of magnitude. Our data suggest that there is significant diamond formation to be expected inside icy giant planets like Neptune and Uranus.

Coordination changes in liquid tin under shock compression determined using in situ femtosecond x-ray diffraction

Little is known regarding the liquid structure of materials compressed to extreme conditions, and even less is known about liquid structures undergoing rapid compression on nanosecond timescales. Here, we report on liquid structure factor and radial distribution function measurements of tin shock compressed to 84(19) GPa. High-quality, femtosecond x-ray diffraction measurements at the Linac Coherent Light Source were used to extract the liquid diffuse scattering signal. From the radial distribution function, we find that the structural evolution of the liquid with increasing pressure mimics the evolution of the solid phase. With increasing pressure, we find that the liquid structure evolves from a complex structure, with a low coordination number, to a simple liquid structure with a coordination number of ∼12. We provide a pathway for future experiments to study liquids at elevated pressures using high-energy lasers to shock compress materials beyond the reach of static diamond anvil cell techniques.

In depth characterization of Ge-Si core-shell nanowires using X-ray coherent diffraction and time resolved pump-probe spectroscopy

We report on the ultrafast vibrational response of single Ge-Si core-shell nanowires obtained by epitaxial growth and investigated by femtosecond transient reflectivity and coherent x-ray diffraction measurements. The oscillations of the sample reflectivity are correlated with the fundamental breathing mode for wires with a diameter ranging from 150 to 350 nm and compared with solutions of the Navier equation. Taking advantage of a free standing geometry, we are able to get a mechanical quality factor of higher than 80. Coupling electron microscopy and pump and probe investigations with a very high spectral resolution performed on the same wire, we demonstrate that both shell and core diameter fluctuations are revealed and quantified. X-ray coherent diffraction measurements on individual nanowires evidence changes in the Ge-core diameter and different strain states along a single structure.

Ultrafast transient increase of oxygen octahedral rotations in a perovskite

The ability to control the structure of a crystalline solid on ultrafast timescales bears enormous potential for information storage and manipulation or generating new functional states of matter [1]. In many materials where the ultrafast control of crystalline structures has been explored, optical excitation pushes materials towards their less ordered high temperature phase [2{9] as electronically driven ordered phases melt and possible concomitant structural modifications relax. Nonetheless, for a few select materials it has been shown that photoexcitation can slightly enhance the amplitude of an electronic ordering phenomenon (i.e. its electronic order parameter) [9{13]. Here we show via femtosecond hard X-ray diffraction that photodoping of the perovskite EuTiO3 transiently increases the order parameter associated with a purely structural [14] phase transition represented by the antiferrodistortive rotation of the oxygen octahedra. This can be understood from an ultrafast charge-transfer induced reduction of the Goldschmidt tolerance factor [15], which is a fundamental control parameter for the properties of perovskites

Fine microstructure formation in steel under ultrafast heating

In this study, phase transformation kinetics was directly evaluated using a femtosecond X-ray diffraction technique for operand measurements of the dislocation densities and carbon concentrations in Fe-0.1mass%C martensitic steel. To identify the reverse transformation mechanism from α′ to γ, we used an X-ray free-electron laser and ultrafast heating. A maximum heating rate of 104 °C/s, which is sufficient to avoid diffusive reversion, was achieved, and the reverse transformation during ultrafast heating was successfully observed. Our results demonstrated that a fine microstructure formed because of a phase transformation in which the dislocation density and carbon concentrations remained high owing to ultrafast heating. Fe–C martensitic steels were also found to undergo a massive reverse transformation during ultrafast heating. The formation of a fine microstructure by a simple manufacturing process, without rare elements such as Ti, Nb, or Mo, can be expected. This study will help further the development of functional steels.

Femtosecond x-ray diffraction reveals a liquid-liquid phase transition in phase-change materials.

In phase-change memory devices, a material is cycled between glassy and crystalline states. The highly temperature-dependent kinetics of its crystallization process enables application in memory technology, but the transition has not been resolved on an atomic scale. Using femtosecond x-ray diffraction and ab initio computer simulations, we determined the time-dependent pair-correlation function of phase-change materials throughout the melt-quenching and crystallization process. We found a liquid-liquid phase transition in the phase-change materials Ag4In3Sb67Te26 and Ge15Sb85 at 660 and 610 kelvin, respectively. The transition is predominantly caused by the onset of Peierls distortions, the amplitude of which correlates with an increase of the apparent activation energy of diffusivity. This reveals a relationship between atomic structure and kinetics, enabling a systematic optimization of the memory-switching kinetics.

Disentangling transient charge order from structural dynamics contributions during coherent atomic motion studied by ultrafast resonant x-ray diffraction

We report on the ultrafast dynamics of charge order and structural response during the photoinduced suppression of charge and orbital order in a mixed-valence manganite. Employing femtosecond time-resolved resonant x-ray diffraction below and at the Mn K absorption edge, we present a method to disentangle the transient charge order and structural dynamics in thin films of Pr0.5Ca0.5MnO3. Based on the static resonant scattering spectra, we extract the dispersion correction of charge ordered Mn3+ and Mn4+ ions, allowing us to separate the transient contributions of purely charge order from structural contributions to the scattering amplitude after optical excitation. Our finding of a coherent structural mode at around 2.3 THz, which primarily modulates the lattice, but does not strongly affect the charge order, confirms the picture of the charge order being the driving force of the combined charge, orbital and structural transition.

Measuring non-equilibrium dynamics in complex solids with ultrashort X-ray pulses.

Strong interactions between electrons give rise to the complexity of quantum materials, which exhibit exotic functional properties and extreme susceptibility to external perturbations. A growing research trend involves the study of these materials away from equilibrium, especially in cases in which the stimulation with optical pulses can coherently enhance cooperative orders. Time-resolved X-ray probes are integral to this type of research, as they can be used to track atomic and electronic structures as they evolve on ultrafast timescales. Here, we review a series of recent experiments where femtosecond X-ray diffraction was used to measure dynamics of complex solids. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Anisotropic structural dynamics of monolayer crystals revealed by femtosecond surface X-ray scattering

Ultrafast X-ray scattering is one of the primary tools to track intrinsic crystallographic evolution with atomic accuracy in real time. However, its application to study nonequilibrium structural properties at the two-dimensional limit remains a long-standing challenge due to a significant reduction of diffraction volume and complexity of data analysis. Here, we report femtosecond surface X-ray diffraction in combination with crystallographic model-refinement calculations to quantify the ultrafast structural dynamics of monolayer WSe2 crystals supported on a substrate. We found the absorbed optical photon energy is preferably coupled to the in-plane lattice vibrations within one picosecond whereas the out-of-plane lattice vibration amplitude remains unchanged during the first ten picoseconds. The model-assisted fitting suggests an asymmetric intralayer spacing change upon excitation. The observed nonequilibrium anisotropic structural dynamics agrees with first-principles modelling in both real and momentum space, marking the distinct structural dynamics of monolayer crystals from their bulk counterparts. Electron–phonon coupling in a monolayer WSe2 on a substrate is investigated by femtosecond surface X-ray scattering. Counterintuitively, the absorbed optical photon energy is dominantly coupled to the in-plane lattice vibrations within 1 ps.

The ultrafast Einstein-de Haas effect.

The Einstein-de Haas effect was originally observed in a landmark experiment1 demonstratingthat the angular momentum associated with aligned electron spins in a ferromagnet can be converted to mechanical angular momentum by reversing the direction of magnetization using an external magnetic field. A related problem concerns the timescale of this angular momentum transfer. Experiments have established that intense photoexcitation in several metallic ferromagnets leads to a drop in magnetization on a timescale shorter than 100 femtoseconds-a phenomenon called ultrafast demagnetization2-4. Although the microscopic mechanism for this process has been hotly debated, the key question of where the angular momentum goes on these femtosecond timescales remains unanswered. Here we use femtosecond time-resolved X-ray diffraction to show that most of the angular momentum lost from the spin system upon laser-induced demagnetization of ferromagnetic iron is transferred to the lattice on sub-picosecond timescales, launching a transverse strain wave that propagates from the surface into the bulk. By fitting a simple model of the X-ray data to simulations and optical data, we estimate that the angular momentum transfer occurs on a timescale of 200 femtoseconds and corresponds to 80 per cent of the angular momentum that is lost from the spin system. Our results show that interaction with the lattice has an essential role in the process of ultrafast demagnetization in this system.

Femtosecond diffraction studies of solid and liquid phase changes in shock-compressed bismuth

Bismuth has long been a prototypical system for investigating phase transformations and melting at high pressure. Despite decades of experimental study, however, the lattice-level response of Bi to rapid (shock) compression and the relationship between structures occurring dynamically and those observed during slow (static) compression, are still not clearly understood. We have determined the structural response of shock-compressed Bi to 68 GPa using femtosecond X-ray diffraction, thereby revealing the phase transition sequence and equation-of-state in unprecedented detail for the first time. We show that shocked-Bi exhibits a marked departure from equilibrium behavior - the incommensurate Bi-III phase is not observed, but rather a new metastable phase, and the Bi-V phase is formed at significantly lower pressures compared to static compression studies. We also directly measure structural changes in a shocked liquid for the first time. These observations reveal new behaviour in the solid and liquid phases of a shocked material and give important insights into the validity of comparing static and dynamic datasets.

Macroscopic electric polarization and microscopic electron dynamics: Quantitative insight from femtosecond x-ray diffraction

Phenomena in the macroscopic world are described by classical physics while processes at the microscopic atomic scale are governed by the laws of quantum mechanics. The connection between microscopic and macroscopic physical quantities is far from being trivial and remains partly unexplained. This study presents a novel theoretical approach for calculating macroscopic polarizations from transient microscopic charge densities that are derived from ultrafast time-resolved x-ray diffraction experiments. This is important for understanding the properties of polar and ionic materials and, in particular, those of ferroelectrics with widespread technical applications.

Layer specific observation of slow thermal equilibration in ultrathin metallic nanostructures by femtosecond X-ray diffraction

Ultrafast heat transport in nanoscale metal multilayers is of great interest in the context of optically induced demagnetization, remagnetization and switching. If the penetration depth of light exceeds the bilayer thickness, layer-specific information is unavailable from optical probes. Femtosecond diffraction experiments provide unique experimental access to heat transport over single digit nanometer distances. Here, we investigate the structural response and the energy flow in the ultrathin double-layer system: gold on ferromagnetic nickel. Even though the excitation pulse is incident from the Au side, we observe a very rapid heating of the Ni lattice, whereas the Au lattice initially remains cold. The subsequent heat transfer from Ni to the Au lattice is found to be two orders of magnitude slower than predicted by the conventional heat equation and much slower than electron–phonon coupling times in Au. We present a simplified model calculation highlighting the relevant thermophysical quantities.

Femtosecond X-Ray Diffraction Studies of the Reversal of the Microstructural Effects of Plastic Deformation during Shock Release of Tantalum

We have used femtosecond x-ray diffraction to study laser-shocked fiber-textured polycrystalline tantalum targets as the 37-253GPa shock waves break out from the free surface. We extract the time and depth-dependent strain profiles within the Ta target as the rarefaction wave travels back into the bulk of the sample. In agreement with molecular dynamics simulations, the lattice rotation and the twins that are formed under shock compression are observed to be almost fully eliminated by the rarefaction process.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

Multistep transition of diamond to warm dense matter state revealed by femtosecond X-ray diffraction

Diamond bulk irradiated with a free-electron laser pulse of 6100 eV photon energy, 5 fs duration, at the ~19–25 eV/atom absorbed doses, is studied theoretically on its way to warm dense matter state. Simulations with our hybrid code XTANT show disordering on sub-100 fs timescale, with the diffraction peak (220) vanishing faster than the peak (111). The warm dense matter formation proceeds as a nonthermal damage of diamond with the band gap collapse triggering atomic disordering. Short-living graphite-like state is identified during a few femtoseconds between the disappearance of (220) peak and the disappearance of (111) peak. The results obtained are compared with the data from the recent experiment at SACLA, showing qualitative agreement. Challenges remaining for the accurate modeling of the transition of solids to warm dense matter state and proposals for supplementary measurements are discussed in detail.