Daniela Rupp
email: daniela.rupp@phys.ethz.ch

Leonie Flückiger

Marcus Adolph

Alessandro Colombo

Taisia Gorkhover

Marion Harmand

Maria Krikunova

Jan Philippe Müller

Tim Oelze

Yevheniy Ovcharenko

Maria Richter

Mario Sauppe

Sebastian Schorb

Rolf Treusch

David Wolter

Christoph Bostedt
email: christoph.bostedt@psi.ch

Thomas Möller

Imaging plasma formation in isolated nanoparticles with ultrafast resonant scattering

Keywords: numbers: 36.40.-c Keywords: X-ray scattering, single particle imaging, rare-gas clusters

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Intense femtosecond short-wavelength pulses from freeelectron lasers (FELs) open new avenues to investigate transient states and ultrafast processes with unprecedented spatial and temporal resolution [START_REF] Feldhaus | Amo science at the flash and european xfel free-electron laser facilities[END_REF][2][START_REF] Bencivenga | Coherent and transient states studied with extreme ultraviolet and x-ray free electron lasers: present and future prospects[END_REF][START_REF] Yabashi | Compact xfel and amo sciences: Sacla and scss[END_REF] . One prominent example are ultrafast X-ray diffraction methods like femtosecond Coherent Diffraction Imaging (CDI) which have enabled the structure determination of individual nonperiodic nanoscale objects [START_REF] Chapman | Femtosecond diffractive imaging with a soft-x-ray freeelectron laser[END_REF] . The elastically scattered photons of a single-shot exposure form an interference pattern containing a snapshot of the object before it is quickly destroyed due to the large amount of deposited energy [START_REF] Neutze | Potential for biomolecular imaging with femtosecond X-ray pulses[END_REF][START_REF] Chapman | Diffraction before destruction[END_REF] . The encoded structural information can be retrieved via phase retrieval methods [START_REF] Fienup | Phase retrieval algorithms: a comparison[END_REF] or forward simulations 9 , which allowed for the structural characterization of such fragile objects as single viruses [START_REF] Seibert | Single mimivirus particles intercepted and imaged with an X-ray laser[END_REF][START_REF] Ekeberg | Three-dimensional reconstruction of the giant mimivirus particle with an x-ray free-electron laser[END_REF] , aerosols [START_REF] Bogan | Aerosol Imaging with a Soft X-Ray Free Electron Laser[END_REF][START_REF] Loh | Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight[END_REF] , Imaging nanoplasma formation 2 and the electronic structure of the target [START_REF] Ho | The role of transient resonances for ultra-fast imaging of single sucrose nanoclusters[END_REF][START_REF] Bostedt | Ultrafast x-ray scattering of xenon nanoparticles: Imaging transient states of matter[END_REF][START_REF] Son | Multiwavelength anomalous diffraction at high x-ray intensity[END_REF][START_REF] Song | Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy[END_REF] .

In this work we demonstrate how ultrafast resonant scattering can be used to visualize the spatial distribution of transient charge states in an evolving nanoplasma. As samples we use submicron-sized xenon clusters that are transformed to a highly excited nanoplasma during irradiation, and imaged with the same intense femtosecond FEL pulse. On the timescale of the pulse the position of the clusters is frozen in space and the measured ion kinetic energies show that ionic motion in the generated nanoplasma can be neglected. Nevertheless, in the radial intensity profiles of single-shot single-cluster scattering patterns, we find an intensity dependent lobe structure corresponding to the appearance of an additional characteristic length in the otherwise homogeneous particle. At the FEL wavelength used in our study, neutral xenon and also its low charge state ions (Xe ≤4+ ) are strongly absorbing while higher charge states are almost transparent. The choice of a resonant wavelength allows us to discriminate between areas of different charge states. We carried out a one-dimensional Monte-Carlo simulation of the photoionization process suggesting the formation of a highly charged outer shell in the evolving nanoplasma with strongly altered optical properties. By grouping and averaging the experimental patterns obtained at similar FEL intensities, we suppress individual cluster effects e.g. from a rough surface while enhancing the relevant dynamic signature. The radial profiles of the grouped patterns are fitted with Mie-calculations for a concentric core-shell model to extract tendencies of the evolution as a function of illumination intensity. The fitting yields a sequence of core-shell structures with strongly altered refractive indices and increasing shell thickness. The experiments demonstrate the possibility to extract spatial information on transient plasma formation in isolated nanoparticles with resonant ultrafast x-ray scattering. The method provides the potential for imaging ultrafast excitation, ionization, and charge transfer dynamics in complex samples with femtosecond time and nanometer spatial resolution.

II. EXPERIMENT

The experiments were performed at beamline BL2 at the soft X-ray free-electron laser FLASH 31,32 . Intense extreme ultraviolet (XUV) pulses at 91 eV photon energy were produced with an electron bunch charge of 0.5 nC, yielding a pulse energy of 150 µJ as measured with the gas monitor detector 32 . An estimate for the pulse duration of 100 fs is derived for these parameters from measurements [START_REF] Behrens | Constraints on photon pulse duration from longitudinal electron beam diagnostics at a soft x-ray free-electron laser[END_REF] carried out with the electron bunch length diagnostics LOLA [START_REF] Düsterer | Development of experimental techniques for the characterization of ultrashort photon pulses of extreme ultraviolet free-electron lasers[END_REF] . Considering a beamline transmission of 64% and a focal spot size of 20 µm (FWHM) at the beamline BL2 32 , a power density of up to 3×10 14 W/cm 2 was reached. The pulses intersected a highly diluted jet of very large xenon clusters [START_REF] Rupp | Generation and structure of extremely large clusters in pulsed jets[END_REF] . An adjustable piezo skimmer slit ensured that only one single cluster was present in the focus volume per FEL shot [START_REF] Rupp | Identifica-tion of twinned gas phase clusters by single-shot scattering with intense soft x-ray pulses[END_REF] . The scattering patterns were measured with a previously described [START_REF] Bostedt | Clusters in intense flash pulses: ultrafast ionization dynamics and electron emission studied with spectroscopic and scattering techniques[END_REF][START_REF] Bostedt | Ultrafast x-ray scattering of xenon nanoparticles: Imaging transient states of matter[END_REF] large area scattering detector consisting of an MCPphosphor stack with a center hole and an out-of-vacuum CCD camera. In addition to the diffraction images, coincident single-shot ion time-of-flight (tof) spectra were recorded [START_REF] Gorkhover | Nanoplasma dynamics of single large xenon clusters irradiated with superintense x-ray pulses from the linac coherent light source free-electron laser[END_REF][START_REF] Rupp | Recombination-enhanced surface expansion of clusters in intense soft x-ray laser pulses[END_REF] . In the polarization plane of the FEL, the setup allowed to measure diffraction patterns between 3 • and 30 • scattering angle. In the perpendicular direction, the detection angle was limited to 10 • due to a shadow of the spectrometer's electrodes. Prior to further analysis, the measured scattering intensities were corrected for a nonlinear detector response 9 by taking each pixel's intensity to the power of 2.5 and for the flat detector geometry [START_REF] Bostedt | Ultrafast x-ray scattering of xenon nanoparticles: Imaging transient states of matter[END_REF] by multiplying with a factor of cos(θ) -3 .

III. RESULTS

Two representative examples of the single-shot singleparticle diffraction patterns are shown in Fig. 1a) and 1b). The difference in brightness results from different irradiation intensities of the FEL due to the varying positions of the xenon clusters within the focal plane [START_REF] Gorkhover | Nanoplasma dynamics of single large xenon clusters irradiated with superintense x-ray pulses from the linac coherent light source free-electron laser[END_REF] . As known from previous work, the basic structure of the diffraction images, with concentric but intermittend rings, indicates nearly spherical shapes with rough surfaces resulting from the coagulation-dominated growth process [START_REF] Rupp | Generation and structure of extremely large clusters in pulsed jets[END_REF] . The size of each single cluster (average radius) could be determined from comparing the spacing of the extrema in the diffraction patterns with Mie calculations [START_REF] Rupp | Generation and structure of extremely large clusters in pulsed jets[END_REF] . A total of 32 patterns within the size regime of R = (400 ± 50) nm were selected (the raw data of all patterns was uploaded to the CXIDB [START_REF] Maia | The coherent x-ray imaging data bank[END_REF]40 ). Then the patterns were radially averaged and plotted on a logarithmic scale vs. scattering angle in Fig. 1c).

A. Intensity dependent evolution

A number of observations can already be made when following the profiles' evolution in Fig. 1c) from lowest to highest intensity: First, a high-frequency modulation can be observed in all profiles, originating from the ring structures in the patterns (see Fig. 1a) and b)) and reflecting the cluster size information. In the case of the least intense profile (yellow curve), the envelope agrees rather well with the expected curve for a homogeneous spherical xenon cluster, dropping linearly on a logarithmic scale. In the absence of light induced changes in the particle, all other profiles from the clusters irradiated with higher FEL intensity would follow a similar curve, just with a proportionally higher scattering signal. Instead, the envelopes of the more intense profiles show an additional large-scale structure.

In order to analyze only the intensity dependent signature in the patterns and to reduce effects from irregular shapes and slightly different sizes, the events were sorted for increasing detector brightness and binned into four different categories A to D (the bins are indicated by the color coding in Fig. 1c). The diffraction patterns within each of the four bins A to D were averaged and radial profiles were extracted from the averaged patterns. These averaged profiles are plotted in Fig. 1d).

When following the averaged profiles of categories A to D, the evolution of the profile envelopes can be seen even more clearly. A lobe structure appears with a minimum roughly at 15 • scattering angle that becomes more pronounced with increasing irradiation intensity. In general, a modulation in any diffracted intensity distribution corresponds to a characteristic length scale in the scattering object. We thus conclude that the evolving superstructure corresponds to the development of an additional scattering structure in the sample, an area with different optical properties. It is notable that the modulation structure appears to be a general feature because it survives the averaging over many single-cluster patters which themselves incorporate the average scattering signal over the FEL pulse duration. This raises the question of the origin of the transient refractive structure with a spatial extension on the order of a few tens of nanometers, as estimated from an Airy pattern with a minimum at 15 • .

Results from theoretical [START_REF] Siedschlag | Small rare-gas clusters in soft x-ray pulses[END_REF][START_REF] Saalmann | Mechanisms of cluster ionization in strong laser pulses[END_REF][START_REF] Islam | Kinetic energy of ions after coulomb explosion of clusters induced by an intense laser pulse[END_REF][START_REF] Ziaja | Atomic clusters of various sizes irradiated with short intense pulses of vuv radiation[END_REF][START_REF] Ziaja | Emission of electrons from rare gas clusters after irradiation with intense vuv pulses of wavelength 100 nm and 32 nm[END_REF][START_REF] Fennel | Laser-driven nonlinear cluster dynamics[END_REF][START_REF] Arbeiter | Ionization heating in rare-gas clusters under intense xuv laser pulses[END_REF][START_REF] Arbeiter | Rare-gas clusters in intense VUV, XUV and soft x-ray pulses: signatures of the transition from nanoplasma-driven cluster expansion to Coulomb explosion in ion and electron spectra[END_REF][START_REF] Ackad | Clusters in intense xuv pulses: effects of cluster size on expansion dynamics and ionization[END_REF][START_REF] Ackad | Recombination effects in soft-x-ray cluster interactions at the xenon giant resonance[END_REF][START_REF] Arbeiter | Electron-relocalization dynamics in xenon clusters in intense soft-x-ray fields[END_REF][START_REF] Last | Electron-ion impact energy transfer in nanoplasmas of coulomb exploding clusters[END_REF][START_REF] Last | Microscopic and hydrodynamic impact energy transfer from nanoplasma electrons to ions in exploding clusters[END_REF] and experimental [START_REF] Flückiger | Time-resolved x-ray imaging of a laser-induced nanoplasma and its neutral residuals[END_REF][START_REF] Gorkhover | Nanoplasma dynamics of single large xenon clusters irradiated with superintense x-ray pulses from the linac coherent light source free-electron laser[END_REF][START_REF] Rupp | Recombination-enhanced surface expansion of clusters in intense soft x-ray laser pulses[END_REF][54][START_REF] Hoener | Charge recombination in soft x-ray laser produced nanoplasmas[END_REF][START_REF] Bostedt | Multistep ionization of argon clusters in intense femtosecond extreme ultraviolet pulses[END_REF][57][START_REF] Bostedt | Clusters in intense flash pulses: ultrafast ionization dynamics and electron emission studied with spectroscopic and scattering techniques[END_REF][START_REF] Bostedt | Fast electrons from multi-electron dynamics in xenon clusters induced by inner-shell ionization[END_REF][START_REF] Nagaya | Investigation of the interaction of xenon cluster with intense EUV-FEL pulses using pulsed cluster beam source and momentum imaging spectrometer[END_REF][START_REF] Iwayama | Inhomogeneous charge redistribution in xe clusters exposed to an intense extreme ultraviolet free electron laser[END_REF][62][START_REF] Krikunova | Ionization dynamics in expanding clusters studied by xuv pump-probe spectroscopy[END_REF][START_REF] Iwayama | Frustration of photoionization of ar nanoplasma produced by extreme ultraviolet fel pulses[END_REF][65][START_REF] Schütte | Rare-gas clusters in intense extreme-ultraviolet pulses from a high-order harmonic source[END_REF][START_REF] Schütte | Tracing electron-ion recombination in nanoplasmas produced by extreme-ultraviolet irradiation of rare-gas clusters[END_REF][START_REF] Schütte | Ionization avalanching in clusters ignited by extreme-ultraviolet driven seed electrons[END_REF] studies on clusters in intense XUV pulses provide a basic knowledge about the interaction between an intense short wavelength pulse and a rare gas cluster. From this body of work we can exclude ionic motion as the origin of the observed modulation feature. A general picture divides the dynamics in three phases [START_REF] Arbeiter | Rare-gas clusters in intense VUV, XUV and soft x-ray pulses: signatures of the transition from nanoplasma-driven cluster expansion to Coulomb explosion in ion and electron spectra[END_REF]54,[START_REF] Last | Dynamics of the coulomb explosion of large clusters in a strong laser field[END_REF][START_REF] Saalmann | Mechanisms of cluster ionization in strong laser pulses[END_REF] . In the first phase, photo ionization and Auger decay lead to the emission of electrons with residual kinetic energy from the cluster and therefore result in a charge-up of the cluster as a whole [START_REF] Arbeiter | Rare-gas clusters in intense VUV, XUV and soft x-ray pulses: signatures of the transition from nanoplasma-driven cluster expansion to Coulomb explosion in ion and electron spectra[END_REF][START_REF] Last | Quasiresonance ionization of large multicharged clusters in a strong laser field[END_REF] . As soon as the Coulomb attraction between positively charged cluster and photoelectrons (or Auger electrons) exceeds their kinetic energy, the second phase starts and subsequently released electrons become trapped in the cluster potential [START_REF] Siedschlag | Small rare-gas clusters in soft x-ray pulses[END_REF][START_REF] Bostedt | Multistep ionization of argon clusters in intense femtosecond extreme ultraviolet pulses[END_REF] . A nanoplasma is formed in which further electrons are released from the single atoms or ions, but they reside within the cluster. Within the following pico-to nanoseconds, in the third phase of the cluster dynamics, the electrons transfer their kinetic energy to the ions, expelling one surface layer after the other in a hydrodynamic expansion [START_REF] Gorkhover | Nanoplasma dynamics of single large xenon clusters irradiated with superintense x-ray pulses from the linac coherent light source free-electron laser[END_REF][START_REF] Rupp | Recombination-enhanced surface expansion of clusters in intense soft x-ray laser pulses[END_REF][START_REF] Arbeiter | Rare-gas clusters in intense VUV, XUV and soft x-ray pulses: signatures of the transition from nanoplasma-driven cluster expansion to Coulomb explosion in ion and electron spectra[END_REF][START_REF] Flückiger | Time-resolved x-ray imaging of a laser-induced nanoplasma and its neutral residuals[END_REF] . Also the net charge on the cluster leads to ion repulsion of the unshielded surface, referred to as Coulomb explosion [START_REF] Ziaja | Emission of electrons from rare gas clusters after irradiation with intense vuv pulses of wavelength 100 nm and 32 nm[END_REF]57,[START_REF] Iwayama | Inhomogeneous charge redistribution in xe clusters exposed to an intense extreme ultraviolet free electron laser[END_REF][START_REF] Peltz | Time-resolved x-ray imaging of anisotropic nanoplasma expansion[END_REF] . A theoretical study [START_REF] Arbeiter | Rare-gas clusters in intense VUV, XUV and soft x-ray pulses: signatures of the transition from nanoplasma-driven cluster expansion to Coulomb explosion in ion and electron spectra[END_REF] modeling argon clusters irradiated with 90 eV radiation predicts a motion of the outermost cluster shell of about 1.5 Å within the first 100 fs of the interaction for conditions comparable to the current experiment (the argon ions being a factor of 3 lighter, the intensity being a factor of 6 smaller) [START_REF] Arbeiter | Rare-gas clusters in intense VUV, XUV and soft x-ray pulses: signatures of the transition from nanoplasma-driven cluster expansion to Coulomb explosion in ion and electron spectra[END_REF] . Furthermore, we can get a first-order estimate for the maximum motion of ions from the ion time-of-flight spectra measured in our experiment.

An estimate for the acceleration at the surface can be derived from the final kinetic energies of the cluster ions of up to 600 eV per charge [START_REF] Rupp | Recombination-enhanced surface expansion of clusters in intense soft x-ray laser pulses[END_REF] . Assuming a 400 nm sphere that accelerates a Xe 5+ ion to its final kinetic energy of 3000 eV yields an effective charge of that sphere of 10 5 e. Such a sphere drives the Xe 5+ , starting at the sphere's surface from rest, less than 1 Å within the first 100 fs.

Having excluded ionic motion, we attribute the observed modulations to light-induced electronic structure changes (i) resulting from the ionization and plasma formation within the FEL-irradiated particle and (ii) visualized by the use of a wavelength of the FEL resonant with neutral xenon and low charge states while being non-resonant with higher charge states. In the next section, based on a first-order model of the cluster ionization process, we develop a physical picture of the plasma formation and discuss the generation of an outer shell in the cluster with strongly altered optical properties. Subsequently, using a classical concentric core-shell Mie model, we fit the modulation features observed in Fig. 1 in order to extract tendencies for the evolution of shell thickness and optical constants of the shell with increasing irradiation intensity (section III C).

B. Simulation of the charge state distributions

The appearance of the dynamic scattering features can be connected to the peculiar electronic properties of xenon atoms and ions in the vicinity of the photon energy of 91 eV. Absorption cross-sections for gas-phase xenon atoms and atomic ions have been measured [START_REF] Ederer | Photoionization of the 4 d electrons in xenon[END_REF][START_REF] Itoh | Absolute photoionization cross section measurements of Xe + ions in the 4d threshold energy region[END_REF][START_REF] Andersen | Absolute cross sections for the photoionization of 4d electrons in Xe + and Xe 2+ ions[END_REF][START_REF] Emmons | Photoionization and electronimpact ionization of Xe 3+[END_REF][START_REF] Aguilar | Absolute photoionization cross sections for Xe 4+ , Xe 5+ , and Xe 6+ near 13.5 nm: Experiment and theory[END_REF][START_REF] Bizau | Photoionization of highly charged ions using an ECR ion source and undulator radiation[END_REF] and are summarized in Fig. 2. A clear step from high to low absorption between Xe 4+ and Xe 5+ can be observed, with extremely high values for the charge state 4+ which exhibits a large ionic resonance at 91 eV. Correspondingly, the penetration depth, i.e. the depth into the material for the intensity to decay to 1/e, increases from about 30 to 300 nm.

To gain a first-order model of the radial distributions of different charge states in an irradiated cluster, we investigate the photoionization of a one-dimensional chain of atoms using an atomistic Monte-Carlo approach. The results are presented in Fig. 3. For the simulation, each photon is "propagated" along the chain, starting at x = 0 from the first atom, by probing at every atomic position whether an absorption is taking place. If the random drawing dictates an absorption process, the photon is annihilated and the charge state of the corresponding atom is increased by 1 (or 2 in case of an Auger process), followed by the start of the propagation of the next photon, again at x = 0. According to the number density of solid xenon [START_REF] Sears | Density and Expansivity of Solid Xenon[END_REF] of n a = 1.67 • 10 28 particles per m 3 , we consider 824 atoms for a chain length of 400 nm. The charge state dependent absorption probabilities for each atom are derived from the absorption cross sections of the different xenon charge states [START_REF] Ederer | Photoionization of the 4 d electrons in xenon[END_REF][START_REF] Itoh | Absolute photoionization cross section measurements of Xe + ions in the 4d threshold energy region[END_REF][START_REF] Andersen | Absolute cross sections for the photoionization of 4d electrons in Xe + and Xe 2+ ions[END_REF][START_REF] Emmons | Photoionization and electronimpact ionization of Xe 3+[END_REF][START_REF] Aguilar | Absolute photoionization cross sections for Xe 4+ , Xe 5+ , and Xe 6+ near 13.5 nm: Experiment and theory[END_REF][START_REF] Bizau | Photoionization of highly charged ions using an ECR ion source and undulator radiation[END_REF] . Only linear photo-absorption and subsequent Auger processes are taken into account, while nonlinear effects, light scattering and plasma processes such as collisional ionization are neglected. The derivation of the absorption probabilities and the number of photons impinging on the one-dimensional chain of atoms as well as a benchmarking of the model by simulating the penetration depth for individual charge states are given in the Supplementary Material.

In Fig. 3a), the simulated distributions of the relative charge state abundances ρ q (x) with q = 0 to 8+ are presented for an irradiation intensity of 10 14 W/cm 2 , corresponding to 870 photons falling on the respective area of a single xenon atom (calculated via π • r 2

Xe with the atomic radius of xenon r Xe being determined from the solid density value [START_REF] Sears | Density and Expansivity of Solid Xenon[END_REF] given above). From the relative charge state abundances the distribution of the average charge state q(x) as well as an effective imaginary part of the refractive index β(x) along the chain are calculated [START_REF] Attwood | Soft x-ray and extreme ultraviolet radiation[END_REF] , as given in Fig. 3b). Note that the complex refractive index n = 1 -δ + iβ is a dimensionless quantity with the absorption index β and the so called refractive index decrement δ, which is related to the phase shift of light traveling through matter. The effective absorption index along the chain is derived as

β(x) = 8 q=0 ρ q (r) • β q with β q = 1 4π λ • n a • σ abs,q ,
using the atomic/ionic cross sections given in Fig. 2 and the wavelength λ. Both curves given in Fig. 3b) indicate that after irradiation, an outer shell exists up to a propagation depth of about 120 nm. In this depth, the average charge state q(r) drastically drops in a transition region of about 80 nm thickness from about six to zero while the effective absorption index β(r) jumps from 0.004 to 0.05, revealing an even more pronounced kink.

Our basic one-dimensional Monte-Carlo simulation therefore indicates the formation an outer shell in the cluster with only highly charged ions, that is rather transparent as compared to the opaque core. As mentioned above, the simulation omits nonlinear effects, the light scattering process itself, and all plasma related processes such as collisional ionization. While it yields simulated values of the imaginary part of the refractive index β, it does not allow for a prediction of possible changes in the refraction (δ) of the shell. Nevertheless, it provides a first-order explanation for the dynamic diffraction feature arising from the resonant interaction of 91 eV radiation with the xenon clusters.

C. Core-shell Mie fitting

The ionization model described above indicates the formation of an outer part in the cluster with altered optical properties, but it is important to note that the geometrical nanoplasma structure may considerably deviate from a concentric core-shell system. Instead the model suggests a distribution that is asymmetric in the direction of the incident light, with a transparent part at the irradiated side of the cluster, while the back of the cluster remains neutral. However, assuming a concentric core-shell model has the advantage that the patterns can be further analyzed using classical core-shell Mie theory [START_REF] Mie | Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen[END_REF][START_REF] Bohren | Absorption and scattering of light by small particles[END_REF] , i.e. the analytic solution of the Maxwell equations for the case of a concentric core-shell system. The input values and parameters of the Mie simulation -the size of particle and shell, the complex refractive index in both areas, the wavelength and intensity of the incoming light -provide important handles to capture main tendencies of the nanoplasma formation. While the influence of the expected asymmetry needs to be tested with advanced theoretical models [START_REF] Peltz | Time-resolved x-ray imaging of anisotropic nanoplasma expansion[END_REF] , we note that the contribution from the back of the cluster to the diffraction should be also small in a concentric Mie-model with a highly absorbing core, shadowing the back of the cluster from irradiation.

For the Mie analysis, not the averaged patterns A to D obtained at similar irradiation intensities (radial profiles are shown in Fig. 1d) are considered, but their difference signal. This approach is conceptually similar to resonant X-ray imaging, e.g. of the ultrafast switching of magnetic domains [START_REF] Von Korff | Imaging ultrafast demagnetization dynamics after a spatially localized optical excitation[END_REF] , where the difference signal between patterns obtained at different helicity of circularly polarized light is analyzed, or of buried structures [START_REF] Song | Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy[END_REF] , where diffraction patterns just above and below an absorption edge are subtracted from each other to enhance in the difference signal the location of a certain element.

Using a difference signal approach in combination with Mie fitting is based on the following considerations: The measured patterns (and also averaged data) do not correspond to a single, intermediate plasma state that can be approximated by a single nanoplasma structure such as a single core-shell system. Always, the onset of the FEL pulse intercepts a cluster that is neutral and unchanged and the last photons of the pulse interact with an evolved nanoplasma. By analyzing the difference spectra with Mie core-shell fits, we discretize this evolution and link the intensity-resolved information in different profiles with the idea of a common plasma dynamics (see also mathematical derivation in the Supplementary Material).

This includes the simplifying assumption that the patterns belonging to the groups A to D, obtained at different irradiation intensities, all result in principle from the same continuous evolution of nanoparticle ionization and plasma formation, but up to different stages. In other words, profile A corresponds to an only weakly irradiated cluster, profile B contains the response of this initial phase and additionally the response of a more advanced nanoplasma, and so on. This perspective is equivalent with the statement that the number of impinged photons is the decisive factor for the plasma state reached. This assumption allows us to replace the variable of time by the variable of energy, but it can only be a rough approximation. Implicitly this means that all nonlinear processes such as multiphoton absorption are neglected (for the instantaneous absorption of two photons, the in-This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/4.0000006 tensity, i.e. the number of photons per time interval is relevant, not only the number of photons in total). Now, instead of a gradually evolving and changing system, we may approximate the nanoplasma formation process by a sequence of a few discrete steps. The profiles of the difference signals D-C, C-B, and so on, are fitted with a concentric core-shell Mie model (note that profile A can be seen as the difference between A and 0). In Fig. 4a) the radial profiles from the difference signal of the averaged patterns A-0, B -A, C -B, and D -C are given. The difference profiles reveal even more distinct features in the superstructure: With increasing irradiation intensity a broad lobe appears that becomes more and more pronounced, narrows, and shifts towards higher scattering angles.

With a Mie code which was extended for spheres with a core-shell structure [START_REF] Mie | Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen[END_REF][START_REF] Bohren | Absorption and scattering of light by small particles[END_REF]85 , profiles were simulated and fitted to the experimental curves, see Fig. 4b). A global optimization was carried out using a differential genetic algorithm [START_REF] Storn | Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[END_REF] . This approach, even if it is among the slowest optimization methods, has the advantage of being flexible and it doesn't require an initial guess for the solution. A range between 10 • and 30 • scattering angle was selected for the fitting because smaller angles are prone to detector saturation effects (see single profiles in Fig. 1c). The optimization target was set to the L2-norm of the logarithm of the profiles (i.e. least-squares minimization in logarithmic scale). The shell thickness d, the refraction decrement δ shell , and the absorption index β shell were varied within the parameter bounds given in table I. For the core, the values of neutral xenon at 91 eV photon energy [START_REF] Henke | X-ray interactions: photoabsorption, scattering, transmission and reflection e=[END_REF] were used, see table I. It is noted that the fitting results were rather insensitive to the choice of the core's refractive index, as long as the core's absorption was considerably higher than the shell's. Instead of using a single particle size, the average profiles from several spheres with different sizes, following a distribution given by the scaling parameter σ, were fitted to the experimental profiles. This allows to make the fitting insensitive to influences from the high-frequency oscillations of the profiles corresponding to the cluster size by taking into account the individual particles' deviation from spherical shape as well as the difference in sizes. For further details and observations on the fitting procedure, see the Supplementary Material.

The parameters of the shell resulting from the global optimization are given in Fig. 4c). They reveal (i) a compared to the core low value of β around 0.02, which indicates a transparent shell, (ii) an increasing shell thickness of 20 to 55 nm, and (iii) a refractive index decrement δ increasing with intensity with positive values up to 0.08. The same fitting results are obtained for a broad range of starting values (cf. table I). Systematic Mie simulations, in which the three parameters are varied separately, are shown in the supplementary material. They support the assumption of a single optimal parameter set, as they show that the three parameters d, β and δ have a separable influence on different characteristics of the core-shell signature. The fitting results also provide a scaling factor for the incoming number of photons and thus enable an estimate of the incoming intensities for the average profiles A to D in Fig. 1d). Assigning the maximum irradiation intensity, I D = 3 • 10 14 W/cm 2 to group D, the values for the other average profiles can be determined accordingly to I A = 6 • 10 13 W/cm 2 , I B = 1 • 10 14 W/cm 2 , and I C = 2 • 10 14 W/cm 2 .

IV. DISCUSSION

Our one-dimensional first-order ionization model indicates that the transient characteristic length, revealed by the observed modulations, is connected to the formation and evolution of a highly charged outer shell with dramatically changed optical properties. The fact that we are able to fit the experimental profiles well with a sequence of concentric core-shell Mie models further supports the general physical picture, even though both models are clearly limited. For gaining a clearer picture, a full description of the light propagation via sophisticated many-particle simulations will be needed that includes also other processes such as impact ionization, charge transfer, plasma shifts of the energy levels, and further nanoplasma dynamics [START_REF] Saalmann | Cluster nanoplasmas in strong flash pulses: formation, excitation and relaxation[END_REF][START_REF] Peltz | Fully microscopic analysis of laser-driven finite plasmas using the example of clusters[END_REF][START_REF] Ho | Large-scale atomistic calculations of clusters in intense x-ray pulses[END_REF] . Nevertheless, our general considerations provide a first step towards understanding the observed results.

The results from the Mie-calculations are in good qualitative agreement with the atomistic ionization model. They show the same general trend of a rather transparent outer shell which is increasing in thickness with the irradiation level. From the Mie-fitting we further extract a tendency for the real part of the refractive index, indicating a strong change in the refraction between core and shell, which is growing with the incoming intensity. This general agreement in combination with the robustness of the fitting results indicates that key trends are captured in the analysis.

On the other hand, the large differences in the absolute values of shell thickness and absorption index demonstrate the limitations of our modeling approaches. In addition, while the Mie approach assumes a discontinuous transition between core and shell, the ionization model indicates a transition range on the order of 50 nm thickness. This may partly explain the higher absorption values in the Mie fits, since a higher absorption can in principle take over the effect of a gradual transition (see variation of beta in Supplementary Materials). Nevertheless, a transition region of such broadness cannot actually explain the formation of an observable scattering feature. We have tested with a simple scattering simulation (see Supplementary Material) that the modulation in the scattering profiles disappears already for a transition region of half that thickness. The required sharp transition is puzzling and cannot be explained by our simple models.

The following considerations may allow to hypothesize on the origin of a narrow reflective layer tens of nanometers deep in the nanoplasma. In general, a high reflectivity is connected to a strong change in the real part of the refractive index. The above discussed first-order ionization simulation only describes the absorption of the nanoplasma, i.e. the imaginary part β, and a model of its radial dependence. For the optical response of the cluster both, the real and imaginary part of the refractive index, 1 -δ and β are relevant, which are interrelated through the Kramers-Kronig dispersions relations. In this context, the optical properties of the charge state Xe 3+ are worth a closer look. Plasma calculations of the atomic scattering factors of Xe 3+ indicate that between 90 eV and 98 eV the real part of the atomic scattering factor f 1 (proportional to the refractive index decrement δ) rapidly changes from strongly positive to negative values and back several times [START_REF] Nilsen | Searching for plasmas with anomalous dispersion in the soft X-ray regime[END_REF] . Now we have to take into account that in the environment of the nanoplasma the Xe 3+ ions are not isolated (as in the gas-phase measurements carried out to determine the atomic absorption cross-sections [START_REF] Emmons | Photoionization and electronimpact ionization of Xe 3+[END_REF] ) but instead surrounded by other ionic species and quasi-free electrons in the nanoplasma. By comparing the Xe 3+ -distribution (orange curve in Fig. 3a), peaking between 150 and 200 nm depth) with the average charge state at the same x-positions (magenta curve in Fig. 3b), we find that the neighbourhood of the Xe 3+ ions drastically changes. In a plasma environment, atomic or ionic resonances can be shifted in energy up to several eV [START_REF] Gets | The ionization potentials of atomic ions in laser-irradiated Ar, Kr and Xe clusters[END_REF] . It is to be expected, that the change in environment as a function of the propagation depth translates into an energy shift, possibly from just below a sharp resonance to just above the resonance. This would result in a drastic change of the real part of the refractive index within a short distance, acting like a transient plasma mirror. A similar argument could be made for other xenon charge states Xe 4+ to Xe 6+ , which also exhibit narrow and very strong absorption resonances in the vicinity of 91 eV [START_REF] Emmons | Photoionization and electronimpact ionization of Xe 3+[END_REF][START_REF] Aguilar | Absolute photoionization cross sections for Xe 4+ , Xe 5+ , and Xe 6+ near 13.5 nm: Experiment and theory[END_REF] . For testing this hypothesis, more sophisticated theoretical approaches will be required.

V. CONCLUSION

In summary, we have presented scattering patterns of single large xenon clusters resonantly excited with intense XUV pulses. The patterns reveal strong intensity dependent modulations in the radial distribution of the diffracted light, indicating the formation of an additional characteristic scattering length scale in an otherwise homogeneous nanoscale particle. Using a first-order modelling of the ionization in combination with Mie-based simulations we assigned the transient diffraction signal to light induced electronic core-shell structures with an increasingly thick outer shell of low absorption and high refraction. An abrupt change in refraction, needed to explain the prominent diffraction feature observed, may be correlated to the radially changing plasma environment of higher charge states, translating into a radially changing shift of the electronic resonances. Our work shows that ultrafast resonant light scattering can map the transient spatial charge distributions in laser-excited nanoscale matter. The method can be employed to develop a deeper understanding of nanoplasma formation and charge transfer dynamics which play a key role in many areas ranging from single-shot X-ray imaging to fusion and warm dense matter research as well as condensed matter physics. In the future, the approach provides an avenue to resolve ultrafast electron dynamics in extended systems on their natural time scale with intense attosecond pulses currently under development at FELs and lab-based sources [START_REF] Zholents | Obtaining attosecond x-ray pulses using a self-amplified spontaneous emission free electron laser[END_REF][START_REF] Saldin | Selfamplified spontaneous emission fel with energy-chirped electron beam and its application for generation of attosecond x-ray pulses[END_REF][START_REF] Coffee | Development of ultrafast capabilities for x-ray freeelectron lasers at the linac coherent light source[END_REF][START_REF] Duris | Tunable isolated attosecond x-ray pulses with gigawatt peak power from a free-electron laser[END_REF][START_REF] Tzallas | Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics[END_REF][START_REF] Takahashi | Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses[END_REF] .

SUPPLEMENTARY MATERIAL AND DATA AVAILABILITY

See the supplementary material for a mathematical expression of the discretization approach, further details on the fitting procedure, a systematic investigation of the influence of each input parameter on the modulation features, simulations for sharp and smooth interfaces, and for the derivation of the radial absorption index. The data that support the findings of this study are openly available at the CXI data bank at http://cxidb.org/id-146.html, reference number 146.

ACKNOWLEDGEMENT

The authors thank Thomas Fennel and Christian Peltz for enlightening and helpful discussions. Excellent support from IOAP and DESY machine shops is acknowledged. The experiments have received funding from BMBF (grants 05K13KT2/05K16KT2) and DFG (grants MO 719/13-1, /14-1 and /14-2). The color coding indicates the binning of events with similar intensities (the least intense category only contains a single pattern). d) Radial profiles of averaged patterns from bins A to D. For increasing scattered intensity, an upward shift of the profiles (linear response) and an additional modulation of the profiles (corresponding to the ionization and plasma formation) can be observed. FIG. 2. Absorption of neutral xenon atoms and atomic ions at 91 eV. Total absorption cross-sections σabs in Mbarn of neutral Xe 74 , Xe + 75 , Xe 2+ 76 , Xe 3+ 77 , Xe 4+ 78 , Xe 5,6,7+ 79 (colored points). Note that the value of 2 Mbarn for 5 to 7+ constitutes an upper bound. Corresponding penetration depth in nm (black crosses), calculated via labs = 1 na•σ abs , na being the atomic density of solid xenon [START_REF] Sears | Density and Expansivity of Solid Xenon[END_REF][START_REF] Attwood | Soft x-ray and extreme ultraviolet radiation[END_REF] . FIG. 3. a) Simulation of the distributions of the relative charge state abundances ρq(x) for a one dimensional chain of 824 atoms, i.e. 400 nm length. 870 photons (corresponding to 10 14 W/cm 2 ) fall on the geometric cross-section of one xenon atom and are propagated along the chain. Absorption cross-sections of atomic xenon and its ions from Fig. 2 are used for calculating absorption probabilities. b) The average charge state q(x) drops from around 6+ to neutral within 80 nm. The relative charge states abundances further allow to determine an effective absorption index β(x) revealing a transition within 50 nm by an order of magnitude. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS

  σshell (0, 50) [nm]TABLE I. Fixed values and parameter bounds of the input parameters for the fitting routine. The literature values of neutral solid xenon at 91 eV are taken from Henke tables 87 .

FIG. 1 .

 1 FIG.1. Isolated xenon clusters were irradiated with intense XUV pulses (91 eV photon energy, 3 × 10 14 W/cm 2 peak intensity in the center of the focal spot). A total of 32 events with single clusters of (400 ± 50) nm radius were selected for analysis by the characteristic spacing of the diffraction rings. a) and b) Representative diffraction images (2nd brightest darkest image of 32 events). c) Radial profiles of the 32 single-shot images (corrected for flat detector and nonlinear response, averaged over the scattering angle φ, see text). The color coding indicates the binning of events with similar intensities (the least intense category only contains a single pattern). d) Radial profiles of averaged patterns from bins A to D. For increasing scattered intensity, an upward shift of the profiles (linear response) and an additional modulation of the profiles (corresponding to the ionization and plasma formation) can be observed.

  FIG.4. a) Difference profiles from the averaged profiles shown in Fig.1d). For better visibility the upper curves were shifted by multiplication with a factor. b) Fitted core-shell Mie profiles using the code from Shen 85 . The refractive index of the core was kept constant to n = 1.004+i•0.045 (values of neutral xenon at 91 eV 87 ). See text for details. Analog to a), the profiles II -IV were shifted by a multiplicative factor for better visibility. Dashed lines in a) and b) show the profiles below an angle of 10 • , where the experimental data was excluded from the fitting process. c) Parameters of the shell obtained from the fitting, i.e. shell thickness d (in nm), absorption index β, and refractive index decrement δ. d) Visualization of the sequence of core-shell structures derived from the fitting with changing parameters of the shell (for exact values of the refractive indices compare with 2D color map or with the graphs for β and δ given in Fig.4c).


E E Mcbride
email: emcbride@slac.stanford.edu

A Krygier

A Ehnes

E Galtier

M Harmand

Z Konôpková

H J Lee

H.-P Liermann

B Nagler

A Pelka

M Rödel

A Schropp

R F Smith

C Spindloe

D Swift

F Tavella

S Toleikis

T Tschentscher

J S Wark

A Higginbotham

Phase Transition Lowering in Dynamically-Compressed Silicon

Silicon, being one of the most abundant elements in nature, attracts wide-ranging scientific and technological interest. Specifically, in its elemental form, crystals of remarkable purity can be produced. One may assume that this would lead to Si being well understood, and indeed, this is the case for many ambient properties, as well as for higher pressure behaviour under quasi-static loading.

However, despite many decades of study, a detailed understanding of the response of silicon to rapid compression such as that experienced under shock impact -remains elusive. Here, we combine a novel Free Electron Laser (FEL) based X-ray diffraction geometry with laser-driven compression to elucidate the importance of shear generated during shock compression on the occurrence of phase transitions. We observe the lowering of the hydrostatic phase boundary in elemental silicon, an ideal model system for investigating high-strength materials, analogous to planetary constituents. Moreover, we unambiguously determine the onset of melting above 14 GPa, previously ascribed to a solid-solid phase transition, undetectable in the now conventional shocked diffraction geometry; transitions to the liquid state are expected to be ubiquitous in all systems at sufficiently high pressures and temperatures.

Since Bancroft [START_REF] Bancroft | Polymorphism of iron at high pressure[END_REF] first reported shock-induced polymorphism over fifty years ago, solid-solid and solid-liquid phase transitions have been the focus of innumerable shock-compression studies. Velocimetry techniques have been key diagnostic tools in the inference of such phase transitions, with plateaus in density interpreted as plastic deformation or phase transitions. However, such methods are not able to shed light on the crystallographic phase of material, especially since effects, such as kinetics, have the potential to cause significant differences between statically and dynamically determined sample response. In this work we focus on the behaviour of elemental silicon (Si), which despite being well-understood under hydrostatic conditions, remains a subject of vigorous debate following dynamic loading [START_REF] Colburn | Electrical measurements in silicon under shock-wave compression[END_REF][START_REF] Smith | Orientation and rate dependence in high strain-rate compression of single-crystal silicon[END_REF][START_REF] Gust | Axial yield strengths and two successive phase transition stresses for crystalline silicon[END_REF][START_REF] Goto | Reduction of shear strength and phase-transition in shock-loaded silicon[END_REF][START_REF] Turneaure | Inelastic deformation and phase transformation of shock compressed silicon single crystals[END_REF]. Under uniaxial compression conditions, significant shear is generated as the material resists compression, a direct consequence of the material strength, yet the nature of the shear-relieving mechanism plasticity or via a phase transformation), and the structure(s) of the proposed high pressure phases remain largely unknown.

More generally, previous works suggest that phase boundaries in rapidly-compressed solids depend strongly on the strain-rate of the compression, with a higher strain-rate drive (i.e. shock compression) leading to a higher transition pressure [START_REF] Smith | Ultrafast dynamic compression technique to study the kinetics of phase transformations in bismuth[END_REF][START_REF] Smith | Time-dependence of the alpha to epsilon phase transformation in iron[END_REF]. However, it is also suggested that the anisotropic nature of planar shock compression may lead to significant shear stresses in samples, which can lead to lowering of phase transition boundaries from hydrostatically determined values [START_REF] Higginbotham | Inelastic response of silicon to shock compression[END_REF]. This points to the danger in the typical method of assigning phase transitions under shock loading to those observed under hydrostatic conditions at similar pressure conditions. Moreover, it means that phase transition pressures determined from dynamic compression experiments must be interpreted with care before application to hydrostatic systems, such as planetary interiors.

As one of the most abundant elements in nature, Si attracts wide-ranging scientific and technological interest, and hence many of its properties at ambient conditions, and at higher pressure under quasi-static loading, are well understood. Static compression experiments reveal a complex phase diagram, where thirteen different polymorphs have been observed to date [START_REF] Jamieson | Crystal structures at high pressures of metallic modifications of silicon and germanium[END_REF][START_REF] Mcmahon | New high-pressure phase of Si[END_REF][START_REF] Mcmahon | Pressure dependence of the Imma phase of silicon[END_REF][START_REF] Olijnyk | Structural phase transitions in Si and Ge under pressures up to 50 GPa[END_REF][START_REF] Duclos | hcp-to-fcc transition in silicon at 78 GPa and studies to 100 GPa[END_REF][START_REF] Hanfland | Crystal Structure of the High-Pressure Phase Silicon VI[END_REF][START_REF] Wentorf | Two new forms of silicon[END_REF][START_REF] Piltz | Structure and properties of silicon XII: A complex tetrahedrally bonded phase[END_REF]. Of particular relevance to this work is the highly reconstructive phase transformation from the ambient pressure semi-conducting cubic diamond (CD) structure to the metallic β-tin structure at ∼12 GPa, with an associated 20% volume collapse [START_REF] Jamieson | Crystal structures at high pressures of metallic modifications of silicon and germanium[END_REF]. On further increase of pressure, the closely related orthorhombic phase Imma is formed, which in turn transforms to a simple hexagonal (SH) crystal structure at 16 GPa [START_REF] Mcmahon | New high-pressure phase of Si[END_REF][START_REF] Olijnyk | Structural phase transitions in Si and Ge under pressures up to 50 GPa[END_REF].

However, among dynamic-loading experiments, a clear consensus in the data is yet to emerge. Such studies using velocimitery measurements report the observation of three distinct waves traversing the sample [START_REF] Smith | Orientation and rate dependence in high strain-rate compression of single-crystal silicon[END_REF][START_REF] Gust | Axial yield strengths and two successive phase transition stresses for crystalline silicon[END_REF][START_REF] Goto | Reduction of shear strength and phase-transition in shock-loaded silicon[END_REF][START_REF] Turneaure | Inelastic deformation and phase transformation of shock compressed silicon single crystals[END_REF]. For example, early work by Gust & Royce find waves at 5.4 GPa, 10.1 GPa and 13.7 GPa for compression along the [111] crystal direction. Such waves are often interpreted as occurring at the onset pressure of shear dissipation mechanisms, such as plasticity i.e. by the generation and motion of defects, or via a phase transformation. These velocimetry data are therefore often taken to suggest that the first phase transition occurs at 10 GPa, in broad agreement with the hydrostatically determined value of 12 GPa. The second wave emerging at 5.4 GPa is then assigned to plasticity within the compressed CD phase. However, positive identification of the mechanisms associated with these waves in silicon is still outstanding.

Numerous laser-driven compression experiments coupled with traditional laser-plasma X-ray sources have failed to find evidence for higher pressure phases in compressed single crystal samples. Molecular dynamics (MD) simulations have suggested that this may be due to any new phases forming small (sub-micron), potentially misaligned grains, which would lead to highly diffuse diffraction features, difficult to detect in experiments using these conventional laser-plasma X-ray sources [START_REF] Mogni | Molecular dynamics simulations of shock-compressed single-crystal silicon[END_REF]. The structure of the high pressure phase(s) adopted by Si on the Hugoniot, and the nature of the two waves which emerge following the elastic wave, remains unknown, leaving the dynamic behaviour of Si a matter of ongoing debate.

Here, we present a systematic study of the behaviour of Si following laser-driven shock-compression. Specifically, we employ polycrystalline Si samples, and exploit the high brightness X-rays offered by Free Electron Lasers to study diffuse reciprocal space features. In doing so, we are able to identify the structural response of the sample from its ambient CD phase, through to shock-induced melting at 14 GPa, coinciding with the emergence of the third wave. Crucially, we observe a lowering of two solid-solid phase boundaries from their hydrostatically determined values, suggesting the significant role that shear stress plays in modifying the phase diagram of Si.

Experiments were conducted at the Matter in Extreme Conditions (MEC) endstation at the Linear Coherent Light Source (LCLS) [START_REF] Nagler | The Matter in Extreme Conditions instrument at the Linac Coherent Light Source[END_REF]. Polycrystalline silicon samples, with 50 µm polyimide ablators, were shock compressed via irradiation with the nanosecond pulsed Nd:glass laser system. During shock transit through the Si sample, the high brightness LCLS X-ray beam was used to determine the structure of the material via X-ray diffraction in a Debye-Scherrer geometry. Two distinct experimental geometries were employed in this work. The first is a 'collinear' geometry, where the X-ray beam is incident at around 11 • to the target normal, and thus to the direction of shock compression. This is a common geometry at LCLS [START_REF] Fletcher | Ultrabright X-ray laser scattering for dynamic warm dense matter physics[END_REF][START_REF] Gorman | Direct observation of melting in shock-compressed bismuth with femtosecond X-ray diffraction[END_REF][START_REF] Gleason | Ultrafast visualization of crystallization and grain growth in shock-compressed SiO2[END_REF][START_REF] Harmand | X-ray absorption spectroscopy of iron at multimegabar pressures in laser shock experiments[END_REF][START_REF] Kraus | Nanosecond formation of diamond and ionsdaleite by shock compression of graphite[END_REF], and other laser-plasma based experiments [START_REF] Rygg | Powder diffraction from solids in the terapascal regime[END_REF][START_REF] Coppari | Experimental evidence for a phase transition in magnesium oxide at exoplanet pressures[END_REF][START_REF] Lazicki | X-ray diffraction of solid tin to 1.2 TPa[END_REF][START_REF] Wang | X-ray diffraction of molybdenum under shock compression to 450 GPa[END_REF]. It is described in Supp. Info. Sec. I. However, this configuration has the distinct disadvantage of providing a signal that integrates through all states within the sample. This greatly complicates both the detection and the analysis of low-symmetry complex phases on the Hugoniot, including melting, where multiple high-pressure phases may be present in successive compression waves.

The second 'transverse' geometry aims to resolve this shortcoming by driving the shockwave perpendicular to the LCLS beam direction (Fig. 1 (a)). In this configuration, by taking advantage of the highly collimated and microfocussed beam available at the LCLS we ensure that, predominantly, a single wave in the multi-wave compression response is probed, greatly aiding interpretation and phase identification. Further details of the experimental configurations and target designs employed are confined to the Methods section and Supp. Info. Secs. I-III. A detailed comparison of the collinear and transverse configurations is found in the Supp. Info. Sec. VI.

Utilising optical velocimetry (VISAR) combined with X-ray diffraction in the collinear configuration, the wave profile as a function of laser intensity was investigated, and the sample pressure was inferred from the free surface velocity, U F S (Supp. Info. Sec. IV). An example of typical velocimetry traces may be seen in Fig. 1 (b). The wave profiles observed were in good agreement with previous laser and gas-gun based shock experiments [START_REF] Smith | Orientation and rate dependence in high strain-rate compression of single-crystal silicon[END_REF][START_REF] Turneaure | Inelastic deformation and phase transformation of shock compressed silicon single crystals[END_REF]. Here, consistent with previous studies, we observe the significant elastic response, followed by a pullback and a second wave, often ascribed to plastic deformation. Above 14 GPa (U F S ∼1.3 km/s), we observe a plateau in the velocity-time data indicating a change in sound speed in the sample. Following the plateau we observe the emergence of a third wave, again consistent with previous studies. The plateau is described as the onset of a structural phase transition. As these polycrystalline samples have large grains (∼100 µm) with different orientations, we observe that the magnitude of the elastic response differs from shot to shot depending on the starting orientation of the sample -varying from 6.6(5) GPa to 7.9(5) GPa (Supp. Info. Fig. 6). This is consistent with the previously-reported orientational dependence of the elastic response of single-crystal [START_REF] Gust | Axial yield strengths and two successive phase transition stresses for crystalline silicon[END_REF]. We also note that the plateau observed is independent of the starting orientation, consistent with previous studies [START_REF] Turneaure | Inelastic deformation and phase transformation of shock compressed silicon single crystals[END_REF].

Figure 1 (c) shows azimuthally integrated 1D diffraction patterns as a function of increasing laser intensity, and hence increasing pressure, in both geometries (see caption). As the initial grain size of the sample is large compared to the X-ray beam diameter (10-40 µm), prior to the shock, we are unlikely to satisfy the Bragg condition due to preferred orientation. Therefore the diffraction profile is flat (Fig. 1 (c i)). As laser intensity is increased we observe the emergence of sharp peaks, consistent with the formation of a new phase (Fig. 1 (c ii)). Note, in some diffraction patterns we also observe reflections belonging to the compressed CD phase ( * symbols), suggesting the generation of smaller grains of CD material between domains of the newly formed high pressure phase. An example of the 2D diffraction images may be seen in Fig. 1 (a), and in Supp. Info. Fig. 7. Here, the smooth Debye-Scherrer rings belong to the high pressure phase, and indicate that the large grains of the initial CD phase have broken up into nanometer-sized grains, inferred from the smooth powder rings observed in the 2D diffraction patterns.

In the collinear configuration, at a pressure of 7.4(5) GPa, just above the elastic limit, we observe an increase in scattering intensity of diffraction features at Q ∼ 2.7 and Q ∼ 3.8 Å-1 (Fig. 2 (ii)), but here the structure cannot be fully resolved. By using the same laser-drive conditions, in the transverse geometry we can clearly assign these features to the β-tin structure, with a c/a ratio of 0.550, as shown by the diffraction pattern Fig. 2 (iii). A Le Bail fit is shown by the dotted black line, and is in excellent agreement with the data [START_REF] Bail | Whole powder pattern decomposition methods and applications: A retrospection[END_REF]. A distinguishing feature used to identify the high pressure phases is the evolution of the c/a ratio as a function of pressure. The β-tin structure has a c/a value of 0.550, and the SH a value of 0.533; the c/a ratio of the Imma structure evolves from 0.550 to 0.533 with increasing pressure [START_REF] Mcmahon | Pressure dependence of the Imma phase of silicon[END_REF] (See Methods). As laser intensity, and hence pressure is increased to 9.0(5) GPa, we observe what can be best described as a mixed phase (Fig. 1 (c iii)), consisting of both the β-tin and Imma structures. At 9.4(5) GPa, the high-pressure phase transforms completely to the Imma structure (Fig. 1 (c iv), with no evidence of co-existence with β-tin. The Imma structure also co-exists with the compressed CD phase. This phase co-existence has previously been observed in quasi-hydrostatic diamond anvil cell studies [START_REF] Mcmahon | Pressure dependence of the Imma phase of silicon[END_REF][START_REF] Olijnyk | Structural phase transitions in Si and Ge under pressures up to 50 GPa[END_REF].

Hence, we observe that, for laser-driven compression, rather than through plastic deformation, the significant shear stress at the Hugoniot elastic limit (HEL) is consistent with being relieved via a phase transformation to a mixed phase of CD and a high-pressure structure i.e. the dominant shear dissipation mechanism as the material is compressed beyond the HEL is a phase transformation. As suggested by Mogni et al. [START_REF] Mogni | Molecular dynamics simulations of shock-compressed single-crystal silicon[END_REF] in their MD simulations, we observe that the second wave is concurrent with transformation to a body-centred tetragonal structure, yet we identify it as the βtin phase, rather than Imma as they suggest. Moreover, we note a considerable lowering of the onset of the β-tin phase transformation as compared with hydrostatic diamond anvil cell experiments -from 12 GPa in ref. [START_REF] Mcmahon | Pressure dependence of the Imma phase of silicon[END_REF] down to as low as 5.4(5) GPa in this work. Such an effect has been observed in ab initio simulations where it was suggested that the transition pressure decreases from 11.4 GPa under hydrostatic conditions to 3.9 GPa under uniaxial compression [START_REF] Cheng | Thermodynamics of uniaxial phase transition: Ab initio study of the diamond-to-β-tin transition in Si and Ge[END_REF].

Additionally, in experimental studies combining resistivity measurements with nanoindentation techniques, Gupta & Ruoff [START_REF] Gupta | Static compression of silicon in the[END_REF] note that the onset of the metallic phase, interpreted as the onset of the β-tin phase, lowers from 12 GPa in under static loading, to 8 GPa under a compression rate of 1 kbar/sec, for compression along the [100] axis. This work, therefore, highlights the failure of the long-standing approach of understanding the nature of shock-induced phase transformation through comparison with hydrostatic phase transformations occurring at similar pressures.

As the Imma structure is further compressed, we observe an evolution of the c/a ratio as a function of normalised volume (V/V 0 ), (Fig. 3 (a)) away from the ideal experimental and theoretical β-tin values (0.550 and 0.549) towards the ideal SH values (0.535 and 0.533), with the same trend observed in both the collinear and transverse experimental configurations [START_REF] Mcmahon | Pressure dependence of the Imma phase of silicon[END_REF][START_REF] Lewis | Theoretical study of high-pressure orthorhombic silicon[END_REF]. At a c/a ratio of 0.537, and a corresponding V/V 0 of 0.681, we note a distinct change in the gradient of the c/a ratio, indicating a change in compressibility of the structure. This change occurs at a pressure inferred via VISAR of 13.8(5) GPa, coinciding with the emergence of the third wave discussed above. One should note that in our data obtained in the collinear configuration, we do not observe any additional scattering in the diffraction patterns, that would be indicative of the formation of a second new phase, and hence account for such a change in compressibility (Fig. 3 (b)).

Owing to the unique ability that we are afforded by the transverse configuration, we are able to isolate each of the different waves as they traverse the sample following shock compression. We are therefore able to determine that the 1 (c v)). Moreover, we note that both the shape and position of the broad diffuse peak are in good agreement with that of liquid silicon at 14 GPa (Fig. 3 (c)), as determined through static compression techniques combined with synchrotron X-ray diffraction [START_REF] Funamori | Pressure-induced structural changes of liquid silicon[END_REF]. Notably, we do not observe the second strong broad diffraction peak at Q∼3.6 Å-1 characteristic of the high-density amorphous polymorph at P∼13 GPa, and therefore conclude that the diffuse scattering is most consistent with the liquid state (Supp. Info. Fig. 9). [START_REF] Daisenberger | High-pressure x-ray scattering and computer simulation studies of density-induced polyamorphism in silicon[END_REF] The third wave, rather than being due to a solid-solid phase transition as previously reported, is therefore attributed to shock-induced melting along the Hugoniot.

In comparing diffraction from both configurations, we note that in the collinear configuration we are overwhelmed by the solid Bragg diffraction and insensitive to the presence of liquid diffraction until we have incubated a significant fraction of the liquid phase (Supp. Info. Fig. 13). Moreover, in the collinear configuration, the amount of volumetric compression as determined from the diffraction patterns is directly related to the timing of the X-rays with respect to the supported shock (Supp. Info Fig. 12). It is clear from Fig. 3 (b) that, in the collinear geometry, depending on the timing of the X-rays, we are sensitive to different parts of the wave profile, i.e. to different volumes (and hence pressures), and insensitive to the onset of melting on the Hugoniot.

As pressure is increased, the solid Imma phase transforms to the SH phase, and the diffuse feature grows more intense, as a larger volume fraction of the sample is now in the liquid state (Fig. 1 (c vi)). Due to the significant latent heat of fusion of Si, the second highest of the elements, we observe that the Hugoniot follows the melting curve over a considerable pressure range, as indicated by solid-liquid co-existence up to at least a V/V 0 of 0.632 (P∼ 27 GPa) as shown in Fig. 1 (c vii). Above 27 GPa, the sample is able to overcome the latent heat of fusion and melts entirely (Fig. 1 (c viii & ix). Such a plateau of the Hugoniot along the melting line, and two-phase coexistence, has been previously reported in laser-driven shock compression studies of diamond [START_REF] Eggert | Melting temperature of diamond at ultrahigh pressure[END_REF]. In contrast to recent shock-recovery and MD studies on Si, at similar maximum pressures of 30 GPa, which suggest the formation of localised amorphous banding [START_REF] Hahn | Supersonic dislocation bursts in silicon[END_REF][START_REF] Zhao | Pressure and shear-induced amorphization of silicon[END_REF], we observe the occurrence of bulk, or complete, melting of the sample. Hence, we conclude that the formation of bands of amorphous and CD Si is formed on release to ambient pressure following shock compression, demonstrating the importance of in situ measurements.

In their recent work combining a gas-gun pressure driver and synchrotron X-ray diffraction, Turneaure et al. [START_REF] Turneaure | Real-time examination of atomistic mechanisms during shock-induced structural transformation in silicon[END_REF] report that at P∼19 GPa, above the onset of the third wave, Si adopts the SH structure. However, unlike our work, they find no evidence of melting in their diffraction data. In their study, the sample was initially shock-compressed to a peak pressure of 26 GPa, and only conclusively identified transforming to the SH structure after at least one reflection of the phase transformation wave had passed back through the silicon, releasing pressure. Hence they were probing an off-Hugoniot, and rather complex, hydrodynamic state. Moreover, the lack of liquid signal in their diffraction data is likely due to the transmission (collinear configuration) geometry employed in their experiment. As we have demonstrated, in the oft used collinear geometry one is unable to resolve the various components of a complex, multi-wave shock structure, and specifically one is insensitive to the incubation of melting along the Hugoniot, particularly where there are regions of solid-liquid coexistence. By using the novel transverse approach, collecting diffraction patterns perpendicular to the shock propagation direction, we have much greater sensitivity to the onset of low-symmetry phase transitions and melting along the Hugoniot, expected in all systems at sufficiently high pressures and temperatures.

The stress-volume plot shown in Fig. 4 compares the relative volume (V/V 0 ) of the high-pressure phases from this work with recent density functional theory calculations [START_REF] Strickson | Ab initio calculation of the shock Hugoniot of bulk silicon[END_REF], and with static diamond anvil cell work. [START_REF] Mcmahon | Pressure dependence of the Imma phase of silicon[END_REF] We clearly observe the occurrence of a shear-relieving solid-solid transition concurrent with the HEL, and the observation of the high-pressure phases at considerably lower pressures than previously reported, below the stability field of the static phases. It should also be noted that the additional reflections marked with the † symbol in diffraction profiles Fig. 1 (c vii) cannot be accounted for by any of the candidate structures observed statically up to 30 GPa -the CD, β-tin, Imma or SH structure described in this manuscript. These diffraction peaks suggest that prior to melting entirely, we may reach a mixed phase region between the liquid, the SH phase, and an additional solid phase. A likely candidate is the Cmca structure, which has been reported to co-exist with the SH phase at room temperature at close to 30 GPa [START_REF] Hanfland | Crystal Structure of the High-Pressure Phase Silicon VI[END_REF]. However, with the observation of only a few weak reflections it is impossible to provide a full structural solution to conclusively determine from which structure these additional peaks arise.

In conclusion, we have determined the nature of the multiple waves that traverse silicon samples following shock compression. We show that the second wave is concurrent with a phase transition to a β-tin structure, rather than due to plasticity. We further determine that the third wave observed above P∼14 GPa is due to the onset of melting along the Hugoniot, rather than due to a solid-solid transition as was previously reported. We observe that the solid and liquid co-exist over a significant pressure range of ∆P∼10 GPa, before enough energy is supplied to overcome the significant latent heat of fusion of silicon where the sample melts entirely, as indicated by the observation of only the broad diffuse scattering at the highest pressure achieved, 30 GPa. We demonstrate that the now conventional X-ray diffraction geometry for probing shock-compressed matter is insensitive to the onset of melting, expected in all systems at extreme conditions. Crucially, we demonstrate a shock-induced lowering of the onset of phase transitions, and thus modification of the phase diagram away from that which would be determined utilising a diamond anvil cell-based (quasi-hydrostatic) approach. Here, we find the lowering of two subsequent solid-solid phase transitions: CD→ β-tin→ Imma, illustrating that shock-compression experiments can have a profound impact on hydrostatic phase boundaries. Previous shockcompression studies suggest that high strain-rates may cause phase transition boundaries to be shifted upwards in pressure, relative to their static boundaries [START_REF] Smith | Ultrafast dynamic compression technique to study the kinetics of phase transformations in bismuth[END_REF][START_REF] Smith | Time-dependence of the alpha to epsilon phase transformation in iron[END_REF]. Clearly, the influence of shock-induced shear and strain-rate on the occurrence of phase transitions is non-trivial, and will have a significant impact when employing dynamic compression techniques to explore high pressure phases of materials found in planetary interiors, where conditions are largely hydrostatic and strain-rates are very low. In particular, careful attention will need to be paid when investigating non-metallic systems, the dominant constituents of planetary interiors, which typically exhibit higher strength, and may thus be more susceptible to the effects of shear-induced phase boundary modification. Fletcher for a critical review of the manuscript.

FIG. 1 .

 1 FIG. 1. Experimental configuration and data examples: a the transverse configuration whereby the compression laser was perpendicular to the X-ray beam. b Velocimetry data (VISAR) lineouts showing free surface velocity (UF S ). Laser intensity increases to the right. Dashed lines indicate the onset of the 2nd and 3rd wave. c Azimuthally integrated 1D diffraction patterns as a function of increasing laser intensity and hence increasing pressure in both the transverse: (i), (ii), (iv), (v), (ix) and collinear (iii), (vi), (vii), (viii) configurations. Peaks marked with the * symbol belong to the compressed cubic diamond phase. Peaks marked with the † symbol cannot be described by the cubic diamond, β-tin, Imma, or simple hexagonal phases.

FIG. 2 .

 2 FIG. 2. The greater sensitivity of the transverse configuration 1D diffraction profiles in the collinear (ii) and transverse (iii) configurations. Profile (i) shows X-ray only pre-shot. The dotted black line under profile (iii) is a Le Bail fit to the β-tin structure. The tick marks underneath diffraction profiles (ii) and (iii) indicate the position of the first four β-tin reflections. The * symbol indicates reflections belonging to the compressed cubic diamond phase.

FIG. 3 .

 3 FIG. 3. Evidence of the onset of melting: a Evolution of the c/a ratio as a function of volumetric change (V/V0) in the collinear (blue circles) and transverse (red triangles) configurations. Open symbols are from a hydrostatic diamond anvil cell study Ref. 12: β-tin (triangles), Imma (squares), simple hexagonal (circles). Theoretical ideal c/a ratios from Ref. 32 are shown for β-tin (dashed line) and the simple hexagonal (dot-dashed line). b Comparison of azimuthally integrated 1D diffraction patterns in the collinear and transverse configurations. In the transverse configuration we are more sensitive to the onset of melting, as indicated by the emergence of a broad diffuse peak characteristic of a liquid phase. c 1D diffraction patterns in the transverse configuration showing a significant region of solid-liquid co-existence on the Hugoniot. The emergence of the broad diffuse peak at ∼14 GPa is in good agreement with both the position and shape of the liquid peak as determined by static compression experiments, Ref. 33.

FIG. 4 .

 4 FIG. 4. Dynamic shear-lowering of phase transition boundaries: Stress-Volume plot of data obtained in this study, compared with density functional theory calculations (Ref. 39) and static diamond anvil cell experiments (Refs. 10-12). Hugoniot Elastic Limits for the [100] and [111] directions are from Ref. 4. Horizontal dot-dashed lines indicate phase transition boundaries from this study.

  .M and A.S. acknowledge funding from the Volkswagen Foundation. J.S.W. is grateful for support from EPSRC under grant EP/J017256/1. This work is supported by the French Agence Nationale de la Recherche (ANR) with the ANR IRONFEL 12-PDOC-0011 Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. The MEC instrument is supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under contract No. SF00515. The authors thank J. B. Hastings and L. B.

Data Availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request

II. AUTHOR CONTRIBUTIONS

E.E.M., A.H., and A.N. designed the experiment, and E.E.M., A.H., D.S. and C.S. designed the targets, and C.S. manufactured the targets. E.E.M., A.K., M.H., E.G., Z.K., H-.J.L., B.N., A.P., M.R., A.S., C.S., F.T., S.T., T.T. and A.H. contributed to the setup of the experiment and data collection. E.E.M. analysed the data, with assistance from A.K., M.H., R.F.S. and A.H.. E.E.M. and A.H. interpreted the data. E.E.M., A.H. and J.S.W. wrote the manuscript.

All authors commented critically on the manuscript.

Experimental Configuration

Experiments were conducted at the Matter in Extreme Conditions (MEC) end station at the Linear Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory. Polycrystalline silicon samples were shock compressed via irradiation with both arms of the nanosecond pulsed Nd:glass laser system. The incident laser light was frequency doubled to 527 nm, and a 20 ns temporally square pulse was combined with phase plate optics producing a spatiallysmoothed 250 µm spot size on target, [START_REF] Dixit | Kinoform phase plates for focal plane irradiance profile control[END_REF] to achieve laser intensities on target in the range 2×10 10 -2×10 11 W/cm 2 . Two experimental geometries were employed in this work: (1) A 'collinear' geometry (Supp. Info. Sec I), where the X-ray beam is incident at 11 • to the target normal, and thus along the direction of shock compression, and, (2) A transverse geometry, whereby the laser beam, and hence direction of shock compression was perpendicular to the X-ray direction (Fig. 1 (a)). In both configurations, the X-ray pulse length was approximately 80 fs, and the jitter between the optical drive laser and the X-ray beam was no more than 20 ps [START_REF] Nagler | The Matter in Extreme Conditions instrument at the Linac Coherent Light Source[END_REF].

(

1) Collinear Configuration

In this configuration, velocimetry from the sample rear surface was recorded via optical velocimetry (VISAR) simultaneous with X-ray diffraction. The X-ray wavelength was 1.3051(2) Å. The beam was focussed to 40 µm, and centred on the 250 µm laser drive spot. In this configuration, X-rays were timed at 18 ns, 2 ns before the 20 ns laser pulse was turned off. This was to probe the maximum amount of material during a pressure-supported shock wave, before the falling edge of the laser pulse caused pressure to reduce. The rising edge of the pulse was measured to be 0.9 ns, and the falling edge was measured to be 2.1 ns. The same laser pulse shape was used in the transverse configuration.

(2) Transverse Configuration The X-ray wavelength was 1.3007(5) Å and X-ray beam was focussed to 10 µm, and placed a distance of 50 µm into the silicon sample i.e. 50 µm from the ablator-silicon interface. This ensured that that the waves within the sample had separated out sufficiently to discriminate each individual wave, yet was close enough to the origin of the shock wave to ensure that wave reverberations and release from the target edges did not play a significant role. For the lowest pressures reported here, the Si targets were ablated directly. The X-ray beam was then placed 50 µm from the drive surface. The phase plates were defocussed by 2 mm to a spot size of 380 µm so that the entire target package is shock-compressed, maximising the amount of material in the shocked state. However, to reach the highest pressures, the 250 µm spot at best focus was used. Images of the laser spot, and VISAR planarity shots are found in the Supp.

Info. Here, the position of the X-ray beam was placed at the same position -50 µm -and the timing of the X-rays relative to the drive laser was varied between 14 ns and 18 ns to capture the different multiple waves traversing the target.

Target Design

Where specified, the polyimide ablators had a 100 nm coating of aluminium on both the drive surface to prevent tamped ablation. The polycrystalline silicon was quasi-single crystal in nature with grain sizes of order 100 µm.

Hence, it was significantly larger than the X-ray beam in both configurations.

In the collinear configuration, targets consisted of the polyimide ablator, bonded to polycrystalline silicon, 125 µm thick in the X-ray and shock direction. Perpendicular to the shock/X-ray direction, the samples were 3×3 mm squares, significantly larger than the laser drive spot, hence limiting edge rarefaction effects at the silicon-vacuum interface.

In the transverse configuration, 125 µm of polycrystalline silicon was sandwiched between two 100 µm thick silicon single crystals ([001] orientation), to provide good impedance matching and hence reduce complex wave interactions between the silicon-vacuum interface at the target edge (perpendicular to the shock direction). The polyimide ablator was bonded across all three layers of the target. Additional target information may be found in Supp. Info. Sec. II.

The transverse targets were characterised during laser-only beamtime with the VISAR diagnostic. Supp. Info. Fig. 10 a shows VISAR traces from the collinear and transverse configuration targets under identical laser conditions.

For a thickness of 100 µm, there is no evidence of complex wave reverberations, and similar pressure conditions were achieved with both targets, demonstrating that at a thickness of 50 µm where we probed with the X-ray beam, one would not expect reverberations to be significant. Similarly, Supp. Info. Fig. 10 b compares diffraction from the collinear and transverse configurations, with no evidence of peak broadening, and hence pressure gradients, in the sample.

Diffraction Analysis and Interpretation

In our assignment of the high-pressure phases observed we consider that the β-tin, Imma, and simple hexagonal phases may all be described through a common orthorhombic cell, in which the β-tin and simple hexagonal phases