Imaging material yielding and phase transitions in shock-compressed matter.

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Silvia Pandolfi, Eric Galtier, Hae Ja Lee, Daniel Hodge, Mikako Makita, and 11 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4384466/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Decades of research have investigated the mechanical properties of matter under extreme conditions, exploring how materials deform, yield, and fail when subjected to high strain rates. While plasticity codes and computational methods can provide atomic-scale precision, reliable experimental benchmarks are needed to validate these models. However, for decades only bulk and surface measurements (e.g., velocimetry and reflectivity) were available to the community, and data interpretation was mainly done relying on conventional plasticity models and drawing parallels with results obtained under quasi-hydrostatic conditions. In recent years the advent of X-ray free electron lasers has provided insight into the microscopic structure of shock-compressed matter, revealing substantial differences with static compression experiments. Information at the mesoscale was, however, still missing, and the onset and propagation of the deformation at this length-scale was only accessible using computational methods; in this paper we fill that void, providing experimental data at the relevant time- and length-scales. Here, we combine imaging and structural characterization in situ using a nanosecond pump laser coupled with a femtosecond X-ray probe in a novel experimental configuration at the LCLS. Our data provides a comprehensive characterization of the deformation of silicon, a simple, yet highly debated, model system for high-strength materials. Information spanning the macroscopic and mesoscopic scale down to the lattice level allows us to resolve and directly visualize the nucleation and growth of the high-pressure phase for the first time, providing a temporal constraint on its kinetics. These novel insights are crucial to unambiguously determine how silicon yields under shock-compression, as they are able to connect the structural evolution at the atomic level with the complex multi-wave dynamic observed at the macroscopic scale, reliably benchmarking decade-old theoretical predictions. Physical sciences/Materials science/Techniques and instrumentation/Imaging techniques Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Understanding the deformation of solids under high strain rates poses a significant challenge in the field of material science, with far-reaching implications spanning ballistics, planetary modeling, and the design of advanced materials 1–5 . When subjected to shock loading, solids undergo lattice-level rearrangements, exhibiting elastic behavior up to a yielding point, beyond which irreversible deformation and phase transitions occur 6–10 . While state-of-the-art computational methods offer atomic-scale precision in describing material responses under dynamic loading, their predictive capabilities are contingent on accurate experimental benchmarks 11 . Experimentally, gaining the detailed insights needed to validate deformation models proves to be challenging given the transient nature of the high-pressure (HP) and high-temperature states generated via laser ablation, which persist for only a few nanoseconds (ns). In recent years, the advent of X-ray Free Electron Lasers (XFELs) has provided the ultrabright and ultrafast (~fs) X-ray probe needed to collect data in situ , enabling measurements with unprecedented level of detail 12–21 and advancing our comprehension of materials’ response and phase transition mechanisms at extreme conditions 9,22–26 . Despite significant advancements from XFEL sources, precisely determining the mechanisms behind deformation and phase changes in solids at the atomic level remains challenging, even for simple single-element metals, e.g., Ag, Cu, Zr 25–29 . Here, for the first time we use the Linac Coherent Light Source (LCLS) for simultaneous collection of in situ ultrahigh-resolution imaging and X-ray diffraction (XRD) . Compared to previous studies ( e.g. , on diamond 24 ), the combination of X-ray imaging and XRD provides a comprehensive picture, allowing us to relate the structural evolution at the lattice level with the shock-wave propagation at the macroscopic scale and the sample’s morphology at the mesoscale, which is key for accurate data interpretation. Utilizing this technique, we study the response of silicon (Si) to ablation-driven shock compression over ns timescales. Over the years, the complex behavior of shock-compressed Si had raised numerous questions and prompted a lively debate 9,22,30–36 . For this reason and for the availability of effectively defect-free samples that allow analysis of the pristine crystalline evolution, Si is an excellent archetypical system to test novel characterization capabilities and their ability to validate the proposed deformation models. Computational studies had suggested a peculiar banding structure for the growth of the HP phase 35,37 ; however, information on this length scale was thus far non-existing. Almost a decade after molecular dynamic (MD) studies 35 , here we present data with the appropriate, combined temporal and spatial resolution to benchmark those models. Using a multi-scale approach, we have resolved and directly visualized the nucleation and growth of the HP phase domains, confirming earlier theoretical predictions. This study demonstrates a valuable method to unravel complex material dynamics at extreme conditions. Experiments were conducted at the Matter in Extreme Conditions (MEC) instrument at the LCLS 38,39 . We performed experiments in the so-called transverse geometry, i.e. , driving a compressive wave perpendicularly to the XFEL beam and measuring the propagation of the shock front through the sample (Figure 1a). The setup allowed for simultaneous collection of XRD and X-ray imaging 40 . A stack of Be lenses images the sample onto an X-ray detector (Figure 1a) allowing radiography of the sample with a spatial resolution of approximately 300nm 40 . This technique provides a straightforward tool to visualize the structural evolution upon shock compression and/or phase changes. Visibility was enhanced using a flat-field correction procedure already demonstrated in this experimental geometry 41 . The samples consisted of 20 µm Polymethyl methacrylate (PMMA) ablator and a 325 µm single-crystal Si oriented as to compress along the [001] crystal axis; using a high-power laser depositing intensities of ~10 12 W/cm 2 , peak pressures up to 70 GPa were reached (see also Method section). Si exhibits a complex behavior upon compression, with multiple phase transitions occurring at HP, as well as numerous metastable phases that have been observed 1,42–47 . Si’s yield mechanism under dynamic loading has been long debated, and previous studies reported a complex multi-wave behavior that exhibits a strong orientation and strain-rate dependence 34 . Our recent work at LCLS used XRD to confirm MD predictions of so-called inelastic deformation, i.e. , release of the shear stress through a solid-solid phase transition and change of the global crystalline symmetry, rather than generation and motion of crystalline defect 22 . However, insight from XRD alone is not sufficient to provide a direct comparison with the spatially resolved atomistic models, as they struggle to relate the deformation at the lattice level with a specific morphology at the macroscopic scale or with the shock-wave dynamics. Thanks to combined XRD and imaging data, here we provide new insight on this relationship at the meso- to nano-scale. At pressures below the phase transition onset, we observe propagation of the first, elastic deformation wave, E (Figure 1b), and in the XRD data only the signature of the uncompressed Si is visible (Figure 1c) As the pressure overcomes the threshold for the structural transition, both the hexagonal Si-V phase and the compressed cubic Si-I phase are identified in the XRD (Figure 1e). The orientation relationship between the low- and high-pressure phase is consistent with our previous XRD study and with the proposed inelastic shear release 22,35,37 . It is worth noting that the intensity around 55° is due to the superposition of multiple reflections; we identified the peaks belonging to each phase based on their position and intensity, with Si-I’s peaks being sensibly more intense than Si-V’s ones. Furthermore, the Si-I (311) diffused intensity coming from the plastically deformed material is localized around the well-defined spot coming from the uncompressed Si through which the X-rays propagate (Figure 1e, inset). Interestingly, as the phase transition takes place, the imaging data shows the appearance of a second wave, the inelastic wave I (Figure 1d). Behind this wavefront, the image displays features of varying contrast, linked to changes in the refractive index that correspond to density fluctuations. These include linear features, which may be related to the banding structure predicted by MD. However, in this data XRD coming from all features in the image is present, and it is thus not possible to deconvolve the signature of the different regions. We collected data at increasing time delays at 30 GPa, which enabled us to individuate the XRD signatures of the different regions (Figure 2a-b). At early times (2.5 ns), only the portion behind the E shock front is visible, and the XRD signal corresponds to the starting phase’s (311) reflection, in agreement with data from elastically compressed Si at low pressures (Figure 1c). At 5 ns time-delay, XRD data exhibits reflections from both Si-V and compressed Si-I, while both the second shock front and the linear features appear. The linear features are thus part of a mixed Si-I/Si-V region. At later times, the leading features appear to elongate, broaden, and become less numerous, while a solid, darker region forms behind them (Figure 2 c-e). Concurrently, in the XRD data we observe all peaks growing in intensity, with additional Si-I’s reflections becoming visible, e.g. , (220) and (111). It is worth noting that, despite previous studies reporting shock melting around 30 GPa 48 and even at pressures as low as 14 GPa 36 , here no liquid signal is visible in the data; however, since the XRD is collected from the whole imaged area, small fractions of molten Si would likely not be detectable in this configuration (for more details on XRD analysis, see Supplementary Information). The linear structures observed in the X-ray images appear upon phase transition and are part of a mixed Si-I/Si-V region. As in our experimental configuration the contrast in the images is directly linked with changes of the material’s refractive index, we conclude that the linear, dark bands are the crystalline domain of the HP Si-V phase, which has a sensibly higher (~20%) density than Si-I (see also Supplementary Information). Thus, for the first-time we are able to spatially resolve the appearance of localized and highly oriented high-density regions, which allows us to visualize the formation and evolution of the HP phase domains under shock compression. The crystallization along a preferred orientation and the formation of a banding structure are in good agreement with MD simulations; it should be stressed, however, that the orientation of these crystalline domains does not coincide with the {111} planes of Si-I as expected from earlier MD studies 35 . The linear bands are first observed with ~35° orientation, which is closer to that of the {112} planes; with time, the orientation changes, and the bands tend to align at ~45°, along the direction of maximum shear stress, in agreement with amorphous bands measured in ex situ studies 49 (see also Supplementary Information). Contrarily to similar linear features that have been recently observed in shock-compressed diamond 24 , we notice that here the bands do not appear directly behind the shock front as expected for defects during plastic deformation 10 : the second wave propagates ahead of the banding structures, and their distance increases with time. Over the decades, the nature of the second wave emerging in shock-compressed Si, the so-called “anomalous elastic” wave, has been highly debated 9,30,32,36,37 . Here, we can observe the formation and evolution of this feature, clarifying its origin. The second shock front is formed ahead of the mixed Si-V/Si-I region upon phase transition, and it propagates through the sample faster than the transformed region. To assess the velocity of each wave, we have performed additional experiments using ultrafast multi-frame imaging. This approach (details described elsewhere 41,50 ) allows us to minimize the time uncertainty when calculating shock speed from X-ray images, as all frames are acquired in a single XFEL pulse of known temporal structure (see also Method section). Data show that both the elastic and inelastic waves travel, at (10.00.4) km/s (Figure 3a), a value consistent with the elastic wave speed previously measured 9 . Interestingly, as both waves travel at the same speed, their distance does not vary over time at a given pressure; however, we observe a reduction in their relative distance with increasing pressure (Figure 3b). This trend is clearly visible when analyzing a wider pressure range, up to 70 GPa (Figure 4a). According to previous calculations by Higginbotham et al. 37 , the volume collapse during the phase transition (~20%) is expected to generate an internal release wave ( i. e., the inelastic wave) that forward propagates through the sample, modulating the stress back to the Hugoniot elastic limit. Our data directly confirm this theory, showing the second wave being generated next to the mixed region as the HP phase is nucleating, and then propagating ahead of it. In this scenario, the distance between the two waves can be linked with the kinetics of the phase transition itself. Indeed, as the inelastic wave is generated upon phase transformation, the E-I distance is determined by the delay between the initial, elastic over-compression and the phase transition. While the time scale estimated in this way measures the formation of the inelastic shock front rather than the nucleation at the nanometric scale, it still provides a temporal constraint on the phase transition kinetics and its evolution with pressure. As expected, we see that overshooting the transition, i.e. , compressing the sample to a stress value much higher than the transition onset, can help promote the transformation, ultimately accelerating the crystallization of the HP phase and reducing the delay between the two waves (Figure 4b). Thus, with this experimental approach, we have been able to connect the evolution at the lattice level to the multi-wave dynamics at the macroscopic scale. In conclusion, we have used a novel experimental geometry at the LCLS to provide new and detailed information on the deformation and yielding mechanisms of silicon under laser-driven shock-compression. By simultaneously collecting high-resolution (<400 nm) X-ray Imaging and XRD with the appropriate (<ns) time resolution, we have been able to characterize matter’s response over different length-scales and resolve for the first time the appearance and evolution of the HP phase domains. Our results allow us to connect the changes in the crystalline structure at the lattice level with the generation and propagation of shockwaves at the macroscopic level, providing a temporal constraint on the kinetics of the phase transition. Crucially, we provide a direct confirmation of previously proposed deformation models, demonstrating a new methodology to unravel complex material dynamics and resolving a decades-long debate surrounding silicon’s deformation. Methods Experimental and laser configuration. The experiment was performed in the so-called transverse pump-probe geometry in which the shock drive laser and the XFEL beam are perpendicular. The samples consisted of 20 µm PMMA ablator and a 325 µm single-crystal Si commercially available from Scitech. The single crystals were oriented as to compress along the (001) crystal axis and collect data in transmission along the (110) crystal axis. The MEC frequency-doubles Nd:glass long-pulse laser (=527 nm) was focused on the ablator surface and deposited up to 5 TW/cm 2 intensity, launching an ablation-driven compression wave. For this experiment, a 150 µm focal spot was achieved with the use of phase plates, and we used a 20 ns flat-top temporal profile to compress the samples. The setup allowed for simultaneous collection of XRD and X-ray imaging. The ablation pressure as a function of laser energy was determined using the MEC VISAR system (operating at 532 nm) in dedicated measurements; the peak pressure in silicon was subsequently estimated using impedance matching method. It is worth noting that, despite in situ VISAR measurements are technically possible in this experimental configuration, the samples’ thickness (325 µm) would have prevented collection of reliable data. X-ray Diffraction. The LCLS delivered 60-fs duration quasi-monochromatic X-ray pulses of energy 8.2 keV (ΔE = 15-40 eV, ΔE/E = 0.2−0.5%). The XRD signal was recorded on an ePix 10 k detector. The data were calibrated and integrated using the Dioptas 51 software and a high-purity CeO 2 standard. A reference measurement was collected before every compression run and allowed us to assess eventual misorientations of the samples by comparing the position of the Si-I (311) reflection of the uncompressed material. The peaks corresponding to each phase in the data were identified based on position and texture, as the HP phase has a markedly different texture than the plastically deformed, single-crystal starting material. In order to measure the density of each crystalline phase, the cell parameters have been fitted to the experimental data filtering the peaks from other to avoid uncertainties due to intensity overlap. For more information, see also the Supplemental Information file. X-ray Imaging. The X-ray imaging configuration is shown in Fig. 1a. A stack of 25 Be lenses with a curvature of 50µm at their apex is positioned approximately 215mm behind the sample. At 8.2keV, this lens set has a focal length of 206mm, and images the sample on a scintillator based X-ray camera, which sits approximately 4.6m downstream of the sample. Spatial resolution of 300nm can be achieved over a field of view of 250um.The imaging setup providing a straightforward way to visualize the variations in density due to shock compression and/or crystal structure changes. This method is particularly useful in cases in where full phase retrieval is challenging. The X-ray imaging setup is described in detail elsewhere 40 . Multi-frame X-ray Imaging. To capture the evolution of a single sample as the different shock fronts propagate, as well as the appearance and evolution of the linear band, we have performed multi-frame X-ray imaging. This experimental approach combines the XFEL four-pulse mode available at the LCLS with the Icarus V2 ultrafast x-ray imager (UXI) camera 52,53 . The UXI allows us to obtain multiple images from a single shock-compressed sample, and it has already been tested both in the PCI 50 and direct imaging 41 configuration at MEC. For this experiment, the XFEL probe consisted of a series of four pulses of 40-80 fs separated of 2.4 and 3.85 ns. The precise and reproducible temporal structure of the XFEL multi-pulse beam allowed us to accurately estimate the shock velocity and their evolution without being affected by the temporal jitter of the XFEL beam. Flat-field Correction. During the imaging process, spatial variations in the X-ray free electron laser and lens artifacts accumulated along the X-ray beam degrade the visibility of the captured intensity images and complicates the extraction of quantitative information. To enhance the visibility of features in these images, we implemented a flat-field correction scheme similar to the one used in our previous work 41 . This scheme involves image alignment to normalize against lens defects and the stochastic nature of the X-ray free electron laser. Initially, we improved our images by applying a median filter, with specified settings like neighborhood size and threshold, to remove pixels with extreme values, enhancing image quality by filtering out anomalies. Following this, we performed dark-field subtraction to eliminate detector noise. We utilized the ANTs image registration algorithm with a gradient descent optimizer and the ANTsNeighborhoodCorrelation metric from the Python SimpleITK library, aiming to maximize local similarities between the source (white fields) and target (dynamic) images. Upon achieving maximum similarity, the source image is warped towards the target image, ensuring a one-to-one correspondence between pixels in both images. Finally, we divided the dynamic image against the average of the warped white fields to produce a normalized, flat-field corrected dynamic image, significantly improving image clarity and interpretability. Some representative images are shown in the Supplementary Information file. Declarations Acknowledgments. This work was performed at the Matter at Extreme Conditions(MEC)instrument of LCLS, supported by the US DOE Office of Science, Fusion Energy Science under contract No. SF00515, and was supported by LCLS, a National User Facility operated by Stanford University on behalf of DOE-BES. S.P. and A.E.G. acknowledge support from the 2019 DOE FES ECA and the RISE Hub IFE-STAR Funded FWP 101126. We thank A. Vailionis for assisting with sample characterization at the Stanford Nano Shared Facilities (SNSF) supported by the National Science Foundation under award ECCS-2026822. References Kim, D. Y., Stefanoski, S., Kurakevych, O. O. & Strobel, T. A. Synthesis of an open-framework allotrope of silicon. Nat. Mater. 14 , 169–173 (2015). Shiell, T. B. et al. Bulk Crystalline 4H-Silicon through a Metastable Allotropic Transition. Phys. Rev. Lett. 126 , 215701 (2021). Smith, R. F. et al. Equation of state of iron under core conditions of large rocky exoplanets. Nat. Astron. 2 , 452–458 (2018). 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DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration. High Press. Res. 35 , 223–230 (2015). Hart, P. A. et al. First x-ray test of the Icarus nanosecond-gated camera. X-Ray Free-Electron Lasers: Adv. Source Dev. Instrum. V 11038 , 110380Q-110380Q–9 (2019). Looker, Q., Colombo, A. P., Kimmel, M. & Porter, J. L. X-ray characterization of the Icarus ultrafast x-ray imager. Rev. Sci. Instrum. 91 , 043502 (2020). Additional Declarations There is NO Competing Interest. Supplementary Files PandolfiSupplementaryInformation.pdf Supplementary Information File Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4384466","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":312650760,"identity":"86550912-7eba-4cb2-895e-56b590b84530","order_by":0,"name":"Silvia 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Galtier","email":"","orcid":"https://orcid.org/0000-0002-0396-285X","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Eric","middleName":"","lastName":"Galtier","suffix":""},{"id":312650762,"identity":"c9c53b07-af8d-440c-b244-54124dfe0c3a","order_by":2,"name":"Hae Ja Lee","email":"","orcid":"https://orcid.org/0000-0002-4035-5637","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Hae","middleName":"Ja","lastName":"Lee","suffix":""},{"id":312650763,"identity":"d7ea5f9f-9b4b-404a-8815-41016dd7088e","order_by":3,"name":"Daniel Hodge","email":"","orcid":"","institution":"Brigham Young University","correspondingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Hodge","suffix":""},{"id":312650764,"identity":"9ae56b58-7f76-4409-a334-ec3751c2b746","order_by":4,"name":"Mikako Makita","email":"","orcid":"","institution":"European XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany","correspondingAuthor":false,"prefix":"","firstName":"Mikako","middleName":"","lastName":"Makita","suffix":""},{"id":312650765,"identity":"9e6b8610-bac8-45a0-aeba-711f0ca44dd5","order_by":5,"name":"Dimitri Khaghani","email":"","orcid":"","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Dimitri","middleName":"","lastName":"Khaghani","suffix":""},{"id":312650766,"identity":"d94c78d0-65d0-4883-87a3-6812bf2b1238","order_by":6,"name":"Eric Cunningham","email":"","orcid":"","institution":"University of Central Florida","correspondingAuthor":false,"prefix":"","firstName":"Eric","middleName":"","lastName":"Cunningham","suffix":""},{"id":312650767,"identity":"4293b4e4-5cc3-43fc-a858-df2474cc0a8b","order_by":7,"name":"Phiip Hart","email":"","orcid":"","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Phiip","middleName":"","lastName":"Hart","suffix":""},{"id":312650768,"identity":"bd67cdfb-cb8f-4ca4-af9b-f6120c39df59","order_by":8,"name":"Matthew Ricks","email":"","orcid":"","institution":"Brigham Young University","correspondingAuthor":false,"prefix":"","firstName":"Matthew","middleName":"","lastName":"Ricks","suffix":""},{"id":312650769,"identity":"76630fe4-97b6-4a71-ab4e-e4b01635fa2d","order_by":9,"name":"Thomas Hatcher","email":"","orcid":"","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Hatcher","suffix":""},{"id":312650770,"identity":"944a40e8-2f8e-4242-8f15-37c00ad8f4d2","order_by":10,"name":"Sameen Yunus","email":"","orcid":"","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Sameen","middleName":"","lastName":"Yunus","suffix":""},{"id":312650771,"identity":"ef2471a6-6c31-4f35-a293-bc71e804683e","order_by":11,"name":"Phillip Heimann","email":"","orcid":"","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Phillip","middleName":"","lastName":"Heimann","suffix":""},{"id":312650772,"identity":"1c42baad-094f-46d3-9d70-20689445f3e2","order_by":12,"name":"Gilliss Dyer","email":"","orcid":"https://orcid.org/0000-0001-9755-9780","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Gilliss","middleName":"","lastName":"Dyer","suffix":""},{"id":312650773,"identity":"5a7aee30-6e8d-47a7-8327-db93446f8381","order_by":13,"name":"Richard Sandberg","email":"","orcid":"","institution":"Brigham Young University","correspondingAuthor":false,"prefix":"","firstName":"Richard","middleName":"","lastName":"Sandberg","suffix":""},{"id":312650774,"identity":"70ea86ea-ce88-45d4-b4be-01875b92cdd2","order_by":14,"name":"Arianna Gleason","email":"","orcid":"https://orcid.org/0000-0002-7736-5118","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Arianna","middleName":"","lastName":"Gleason","suffix":""},{"id":312650775,"identity":"59ba8ccd-698d-4419-95e6-83564e1932c2","order_by":15,"name":"Bob Nagler","email":"","orcid":"https://orcid.org/0009-0002-5736-7842","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Bob","middleName":"","lastName":"Nagler","suffix":""}],"badges":[],"createdAt":"2024-05-07 16:59:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4384466/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4384466/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58153385,"identity":"a434c67f-5b15-4b7f-9472-386b2a5ce2f5","added_by":"auto","created_at":"2024-06-11 20:27:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":476018,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea.\u003c/strong\u003e Experimental setup (not to scale); the orientation of the starting Si-I material with respect to the drive laser and the crystallographic axis in our X-ray view are shown on the top left side of the image. \u003cstrong\u003eb\u003c/strong\u003e, \u003cstrong\u003ed\u003c/strong\u003e: X-ray images collected at 10 ns time delay below (~10 GPa) and above (~18 GPa) phase transition. The elastic and inelastic waves are indicated in the figure. Inset: zoomed-in view of the area highlighted in \u003cstrong\u003ec\u003c/strong\u003e, in which linear features are visible. \u003cstrong\u003ec,e\u003c/strong\u003e: XRD data; the bi-dimensional data are overlaid with the integrated pattern and the zoomed-in panel shows the shape of the Si-I(311) reflection.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4384466/v1/8aaaa9e5c72ba4a7a2b174bb.png"},{"id":58153384,"identity":"484d264e-6ded-408f-b060-c1a539ec8e37","added_by":"auto","created_at":"2024-06-11 20:27:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":782037,"visible":true,"origin":"","legend":"\u003cp\u003eX-ray imaging and XRD data acquired at ~30 GPa peak pressure at varying time delays. \u003cstrong\u003ea\u003c/strong\u003e: X-ray images acquired between 2.5 \u0026nbsp;\u0026nbsp;\u0026nbsp;and 20 ns time delays; as the FOV had been moved at later time delays, the \u0026nbsp;\u0026nbsp;\u0026nbsp;images have been offset to align the ablator-sample interface in the \u0026nbsp;\u0026nbsp;\u0026nbsp;reference images. \u003cstrong\u003eb\u003c/strong\u003e: selected XRD \u0026nbsp;\u0026nbsp;\u0026nbsp;integrated patterns; the peaks corresponding to the Si-V and Si-I phase are indexed. \u003cstrong\u003ec\u003c/strong\u003e-\u003cstrong\u003ee\u003c/strong\u003e: zoomed-in view corresponding to the area highlighted by the green squares in \u003cstrong\u003ea\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4384466/v1/964901d5e2a75033798496af.png"},{"id":58153383,"identity":"ef2b2251-dd4f-4f9b-8664-e72852378807","added_by":"auto","created_at":"2024-06-11 20:27:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":87780,"visible":true,"origin":"","legend":"\u003cp\u003eEvolution of the waves’ velocity (\u003cstrong\u003ea\u003c/strong\u003e) and distance (\u003cstrong\u003eb\u003c/strong\u003e) measured by multi-frame X-ray imaging. In the upper panel, the symbols correspond to different experimental pressures, while the color indicates the elastic and inelastic waves’ position, respectively. In the lower panel, pink data was acquired at 24 GPa, while the blue points are collected at 31 GPa. The shaded areas indicate the average value (± standard deviation) of each data series.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4384466/v1/ae366782f612b48772a1a839.png"},{"id":58153386,"identity":"08be2ef4-5335-443d-bb33-17e1d20f2c9f","added_by":"auto","created_at":"2024-06-11 20:27:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":715559,"visible":true,"origin":"","legend":"\u003cp\u003eData acquired up to 70 GPa. \u003cstrong\u003eA\u003c/strong\u003e: cropped X-ray images acquired at 10 ns time delay. \u003cstrong\u003eB\u003c/strong\u003e: time delay between the generation of the elastic and inelastic wave as a function of pressure; the time delay was obtained by dividing the distance between the waves for the average speed.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4384466/v1/e866e96aba9bb7495d51959d.png"},{"id":59853721,"identity":"0d2e96f2-13d5-4398-b569-123bcc31c1bd","added_by":"auto","created_at":"2024-07-08 12:48:46","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2379318,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4384466/v1/02d68ca3-7fb7-4a88-922c-c5fa9d41abb8.pdf"},{"id":58153387,"identity":"984ce289-679b-4e07-bd2f-b5cebac4add5","added_by":"auto","created_at":"2024-06-11 20:27:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":5747476,"visible":true,"origin":"","legend":"Supplementary Information File","description":"","filename":"PandolfiSupplementaryInformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4384466/v1/a14e546ac21eae2951b71edd.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Imaging material yielding and phase transitions in shock-compressed matter.","fulltext":[{"header":"Introduction","content":"\u003cp\u003eUnderstanding the deformation of solids under high strain rates poses a significant challenge in the field of material science, with far-reaching implications spanning ballistics, planetary modeling, and the design of advanced materials\u003csup\u003e1\u0026ndash;5\u003c/sup\u003e. When subjected to shock loading, solids undergo lattice-level rearrangements, exhibiting elastic behavior up to a yielding point, beyond which irreversible deformation and phase transitions occur\u003csup\u003e6\u0026ndash;10\u003c/sup\u003e. While state-of-the-art computational methods offer atomic-scale precision in describing material responses under dynamic loading, their predictive capabilities are contingent on accurate experimental benchmarks\u003csup\u003e11\u003c/sup\u003e. Experimentally, gaining the detailed insights needed to validate deformation models proves to be challenging given the transient nature of the high-pressure (HP) and high-temperature states generated via laser ablation, which persist for only a few nanoseconds (ns). In recent years, the advent of X-ray Free Electron Lasers (XFELs) has provided the ultrabright and ultrafast (~fs) X-ray probe needed to collect data \u003cem\u003ein situ\u003c/em\u003e, enabling measurements with unprecedented level of detail\u003csup\u003e12\u0026ndash;21\u003c/sup\u003e and advancing our comprehension of materials\u0026rsquo; response and phase transition mechanisms at extreme conditions\u003csup\u003e9,22\u0026ndash;26\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eDespite significant advancements from XFEL sources, precisely determining the mechanisms behind deformation and phase changes in solids at the atomic level remains challenging, even for simple single-element metals, e.g., Ag, Cu, Zr\u003csup\u003e25\u0026ndash;29\u003c/sup\u003e. Here, for the first time we use the Linac Coherent Light Source (LCLS) for simultaneous collection of \u003cem\u003ein situ\u003c/em\u003e ultrahigh-resolution imaging and X-ray diffraction (XRD)\u003cem\u003e.\u003c/em\u003e Compared to previous studies (\u003cem\u003ee.g.\u003c/em\u003e, on diamond\u003csup\u003e24\u003c/sup\u003e),\u0026nbsp;the combination of X-ray imaging and XRD provides a comprehensive picture, allowing\u0026nbsp;us to\u0026nbsp;relate\u0026nbsp;the structural evolution at the lattice level with the shock-wave propagation at the macroscopic scale\u0026nbsp;and the\u0026nbsp;sample\u0026rsquo;s morphology at the mesoscale, which is key for accurate data interpretation. Utilizing this technique, we study the response of silicon (Si) to ablation-driven shock compression over ns timescales. Over the years, the complex behavior of shock-compressed Si had raised numerous questions and prompted a lively debate\u003csup\u003e9,22,30\u0026ndash;36\u003c/sup\u003e.\u0026nbsp;For\u0026nbsp;this reason and for the availability of effectively defect-free samples that allow analysis of\u0026nbsp;the pristine crystalline evolution, Si is an excellent archetypical system to test novel characterization capabilities and their ability to validate the proposed deformation models. Computational studies had suggested a peculiar banding structure for the growth of the HP phase\u003csup\u003e35,37\u003c/sup\u003e; however, information on this length scale was thus far non-existing. \u0026nbsp; Almost a decade after molecular dynamic (MD) studies\u003csup\u003e35\u003c/sup\u003e, here we present data with the appropriate, combined temporal and spatial resolution to benchmark those models. Using a multi-scale approach, we have resolved and directly visualized the nucleation and growth of the HP phase domains, confirming earlier theoretical predictions. This study demonstrates a valuable method to unravel complex material dynamics at extreme conditions.\u003c/p\u003e\n\u003cp\u003eExperiments were conducted at the Matter in Extreme Conditions (MEC) instrument at the \u0026nbsp; \u0026nbsp; \u0026nbsp;LCLS\u003csup\u003e38,39\u003c/sup\u003e. We performed experiments in the so-called transverse geometry, \u003cem\u003ei.e.\u003c/em\u003e, driving a compressive wave perpendicularly to the XFEL beam and measuring the propagation of the shock front through the sample (Figure\u0026nbsp;1a).\u0026nbsp;The setup allowed for simultaneous collection of XRD and X-ray imaging\u003csup\u003e40\u003c/sup\u003e. A stack of Be lenses images the sample onto an X-ray detector (Figure 1a) allowing radiography of the sample with a spatial resolution of approximately 300nm\u003csup\u003e40\u003c/sup\u003e.\u0026nbsp;This technique provides a straightforward tool to visualize the structural evolution upon shock compression and/or phase changes. Visibility was enhanced using a flat-field correction procedure already demonstrated in this experimental geometry\u003csup\u003e41\u003c/sup\u003e. The samples consisted of 20 \u0026micro;m Polymethyl methacrylate (PMMA)\u0026nbsp;ablator and a 325 \u0026micro;m single-crystal Si oriented as to compress along the [001]\u0026nbsp;crystal\u0026nbsp;axis; using a high-power laser depositing intensities of ~10\u003csup\u003e12\u003c/sup\u003e W/cm\u003csup\u003e2\u003c/sup\u003e, peak pressures up to 70 GPa were reached (see also Method section).\u003c/p\u003e\n\u003cp\u003eSi exhibits a complex behavior upon compression, with multiple phase transitions occurring at HP, as well as numerous metastable phases that have been observed\u003csup\u003e1,42\u0026ndash;47\u003c/sup\u003e. Si\u0026rsquo;s yield mechanism under dynamic loading has been long debated, and previous studies reported a complex multi-wave behavior that exhibits a strong orientation and strain-rate dependence\u003csup\u003e34\u003c/sup\u003e. Our recent work at LCLS used XRD to confirm MD predictions of so-called \u003cem\u003einelastic\u0026nbsp;\u003c/em\u003edeformation, \u003cem\u003ei.e.\u003c/em\u003e, release of the shear stress through a solid-solid phase transition and change of the global crystalline symmetry,\u0026nbsp;rather than generation and motion of crystalline defect\u003csup\u003e22\u003c/sup\u003e. However, insight \u0026nbsp; \u0026nbsp; \u0026nbsp;from XRD alone is not sufficient to provide a direct comparison with the spatially resolved atomistic models, as they struggle to relate the deformation at the lattice level with a specific morphology at the macroscopic scale or with the shock-wave dynamics. Thanks to combined XRD and imaging data, here we provide new insight on this relationship at the meso- to nano-scale.\u003c/p\u003e\n\u003cp\u003eAt pressures below the phase transition onset, we observe propagation of the first, elastic deformation wave, \u003cem\u003eE\u0026nbsp;\u003c/em\u003e(Figure 1b), and in the XRD data only the signature of the uncompressed Si is visible (Figure 1c) As the pressure overcomes the threshold for the structural transition, both the hexagonal Si-V phase and the compressed cubic Si-I phase are identified in the XRD (Figure 1e). The orientation relationship between the low- and high-pressure phase is consistent with our previous XRD study and with the proposed \u003cem\u003einelastic\u003c/em\u003e shear release\u003csup\u003e22,35,37\u003c/sup\u003e. It is worth noting that the intensity around 55\u0026deg; is due to the superposition of multiple reflections; we identified the peaks belonging to each phase based on their position and intensity, with Si-I\u0026rsquo;s peaks being sensibly more intense than Si-V\u0026rsquo;s ones. Furthermore, the Si-I (311) diffused intensity coming from the plastically deformed material is localized around the well-defined spot coming from the uncompressed Si through which the X-rays propagate (Figure 1e, inset). Interestingly, as the phase transition takes place, the imaging data shows the appearance of a second wave, the inelastic wave \u003cem\u003eI\u003c/em\u003e (Figure 1d). Behind this wavefront, the image displays features of varying contrast, linked to changes in the refractive index that correspond to density fluctuations. These include linear features, which may be related to the banding structure predicted by MD. However, in this data XRD coming from all features in the image is present, and it is thus not possible to deconvolve the signature of the different regions.\u003c/p\u003e\n\u003cp\u003eWe collected data at increasing time delays at 30 GPa, which enabled us to individuate the XRD signatures of the different regions (Figure 2a-b). At early times (2.5 ns), only the portion behind the \u003cem\u003eE\u003c/em\u003e shock front is visible, and the XRD signal corresponds to the starting phase\u0026rsquo;s (311) reflection, in agreement with data from elastically compressed Si at low pressures (Figure 1c). At 5 ns time-delay, XRD data exhibits reflections from both Si-V and compressed Si-I, while both the second shock front and the linear features appear. The linear features are thus part of a mixed Si-I/Si-V region. At later times, the leading features appear to elongate, broaden, and become less numerous, while a solid, darker region forms behind them (Figure 2 c-e). Concurrently, in the XRD data we observe all peaks growing in intensity, with additional Si-I\u0026rsquo;s reflections becoming visible, \u003cem\u003ee.g.\u003c/em\u003e, (220) and (111). It is worth noting that, despite previous studies reporting shock melting around 30 GPa\u003csup\u003e48\u003c/sup\u003e and even at pressures as low as 14 GPa\u003csup\u003e36\u003c/sup\u003e, here no liquid signal is visible in the data; however, since the XRD is collected from the whole imaged area, small fractions of molten Si would likely not be detectable in this configuration (for more details on XRD analysis, see Supplementary Information).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe linear structures observed in the X-ray images appear upon phase transition and are part of a mixed Si-I/Si-V region. As in our experimental configuration the contrast in the images is directly linked with changes of the material\u0026rsquo;s refractive index, we conclude that the linear, dark bands are the crystalline domain of the HP Si-V phase, which has a sensibly higher (~20%) density than Si-I (see also Supplementary Information). Thus, for the first-time we are able to spatially resolve the appearance of localized and highly oriented high-density regions, which allows us to visualize the formation and evolution of the HP phase domains under shock compression. The crystallization along a preferred orientation and the formation of a banding structure \u0026nbsp; \u0026nbsp; \u0026nbsp;are in good agreement with MD simulations; it should be stressed, however, that the orientation of these crystalline domains does not coincide with the {111} planes of Si-I as expected from earlier MD studies\u003csup\u003e35\u003c/sup\u003e. The linear bands are first observed with ~35\u0026deg; orientation, which is closer to that of the {112} planes; with time, the orientation changes, and the bands tend to align at ~45\u0026deg;, along the direction of maximum shear stress, in agreement with amorphous bands measured in \u003cem\u003eex situ\u003c/em\u003e studies\u003csup\u003e49\u003c/sup\u003e (see also Supplementary Information). Contrarily to similar linear features that have been recently observed in shock-compressed diamond\u003csup\u003e24\u003c/sup\u003e, we notice that here the bands do not appear directly behind the shock front as expected for defects during plastic deformation\u003csup\u003e10\u003c/sup\u003e: the second wave propagates ahead of the banding structures, and their distance increases with time.\u003c/p\u003e\n\u003cp\u003eOver the decades, the nature of the second wave emerging in shock-compressed Si, the so-called \u0026ldquo;anomalous elastic\u0026rdquo; wave, has been highly debated\u003csup\u003e9,30,32,36,37\u003c/sup\u003e. Here, we can observe the formation and evolution of this feature, clarifying its origin. The second shock front is formed ahead of the mixed Si-V/Si-I region upon phase transition, and it propagates through the sample faster than the transformed region. To assess the velocity of each wave, we have performed additional experiments using ultrafast multi-frame imaging. This approach (details described elsewhere\u003csup\u003e41,50\u003c/sup\u003e) allows us to minimize the time uncertainty when calculating shock speed from X-ray images, as all frames are acquired in a single XFEL pulse of known temporal structure (see also Method section). Data show that both the elastic and inelastic waves travel, at (10.00.4) km/s (Figure 3a), a value consistent with the elastic wave speed previously measured\u003csup\u003e9\u003c/sup\u003e. Interestingly, as both waves travel at the same speed, their distance does not vary over time at a given pressure; however, we observe a reduction in their relative distance with increasing pressure (Figure 3b). This trend is clearly visible when analyzing a wider pressure range, up to 70 GPa (Figure 4a). According to previous calculations by Higginbotham \u003cem\u003eet al.\u003c/em\u003e\u003csup\u003e37\u003c/sup\u003e, the volume collapse during the phase transition (~20%) is expected to generate an \u003cem\u003einternal\u003c/em\u003e release wave (\u003cem\u003ei.\u003c/em\u003ee., the \u003cem\u003einelastic\u003c/em\u003e wave) that forward propagates through the sample, modulating the stress back to the Hugoniot elastic limit. Our data directly confirm this theory, showing the second wave being generated next to the mixed region as the HP phase is nucleating, and then propagating ahead of it. In this scenario, the distance between the two waves can be linked with the kinetics of the phase transition itself. Indeed, as the inelastic wave is generated upon phase transformation, the \u003cem\u003eE-I\u0026nbsp;\u003c/em\u003edistance is determined by the delay between the initial, elastic over-compression and the phase transition. While the time scale estimated in this way measures the formation of the inelastic shock front rather than the nucleation at the nanometric scale, it still provides a temporal constraint on the phase transition kinetics and its evolution with pressure. As expected, we see that overshooting the transition, \u003cem\u003ei.e.\u003c/em\u003e, compressing the sample to a stress value much higher than the transition onset, can help promote the transformation, ultimately accelerating the crystallization of the HP phase and reducing the delay between the two waves (Figure 4b). Thus, with this experimental approach, we have been able to connect the evolution at the lattice level to the multi-wave dynamics at the macroscopic scale.\u003c/p\u003e\n\u003cp\u003eIn conclusion, we have used a novel experimental geometry at the LCLS to provide new and detailed information on the deformation and yielding mechanisms of silicon under laser-driven shock-compression. By simultaneously collecting high-resolution (\u0026lt;400 nm) X-ray Imaging and XRD with the appropriate (\u0026lt;ns) time resolution, we have been able to characterize matter\u0026rsquo;s response over different length-scales and resolve for the first time the appearance and evolution of the HP phase domains. Our results allow us to connect the changes in the crystalline structure at the lattice level with the generation and propagation of shockwaves at the macroscopic level, providing a temporal constraint on the kinetics of the phase transition. Crucially, we provide a direct confirmation of previously proposed deformation models, demonstrating a new methodology to unravel complex material dynamics and resolving a decades-long debate surrounding silicon\u0026rsquo;s deformation.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eExperimental and laser configuration.\u0026nbsp;\u003c/strong\u003eThe experiment was performed in the so-called transverse pump-probe geometry in which the shock drive laser and the XFEL beam are perpendicular. The samples consisted of 20 \u0026micro;m PMMA ablator and a 325 \u0026micro;m single-crystal Si commercially available from Scitech. The single crystals were oriented as to compress along the (001) crystal axis and collect data in transmission along the (110) crystal axis. The MEC frequency-doubles Nd:glass long-pulse laser (=527 nm)\u0026nbsp;was focused on the ablator surface and deposited up to 5 TW/cm\u003csup\u003e2\u003c/sup\u003e intensity, launching an ablation-driven compression wave. For this experiment, a 150 \u0026micro;m focal spot was achieved with the use of phase plates, and we used a 20 ns flat-top temporal profile to compress the samples. The setup allowed for simultaneous collection of XRD and X-ray imaging. The ablation pressure as a function of laser energy was determined using the MEC VISAR system (operating at 532 nm) in dedicated measurements; the peak pressure in silicon was subsequently estimated using impedance matching method. It is worth noting that, despite \u003cem\u003ein situ\u003c/em\u003e VISAR measurements are technically possible in this experimental configuration, the samples\u0026rsquo; thickness (325 \u0026micro;m) would have prevented collection of reliable data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eX-ray Diffraction.\u0026nbsp;\u003c/strong\u003eThe LCLS delivered 60-fs duration quasi-monochromatic X-ray pulses of energy 8.2 keV (\u0026Delta;E = 15-40 eV, \u0026Delta;E/E = 0.2\u0026minus;0.5%). The XRD signal was recorded on an ePix 10 k detector. The data were calibrated and integrated using the Dioptas\u003csup\u003e51\u003c/sup\u003e software and a high-purity CeO\u003csub\u003e2\u003c/sub\u003e standard. A reference measurement was collected before every compression run and allowed us to assess eventual misorientations of the samples by comparing the position of the Si-I (311) reflection of the uncompressed material. The peaks corresponding to each phase in the data were identified based on position and texture, as the HP phase has a markedly different texture than the plastically deformed, single-crystal starting material. In order to measure the density of each crystalline phase, the cell parameters have been fitted to the experimental data filtering the peaks from other to avoid uncertainties due to intensity overlap. For more information, see also the Supplemental Information file.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eX-ray Imaging.\u0026nbsp;\u003c/strong\u003eThe X-ray imaging configuration is shown in Fig. 1a. A stack of 25 Be lenses with a curvature of 50\u0026micro;m at their apex is positioned approximately 215mm behind the sample. At 8.2keV, this lens set has a focal length of 206mm, and images the sample on a scintillator based X-ray camera, which sits approximately 4.6m downstream of the sample. Spatial resolution of 300nm can be achieved over a field of view of 250um.The imaging setup providing a straightforward way to visualize the variations in density due to shock compression and/or crystal structure changes. This method is particularly useful in cases in where full phase retrieval is challenging. The X-ray imaging setup is described in detail elsewhere\u003csup\u003e40\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMulti-frame X-ray Imaging.\u003c/strong\u003e To capture the evolution of a single sample as the different shock fronts propagate, as well as the appearance and evolution of the linear band, we have performed multi-frame X-ray imaging. This experimental approach combines the XFEL four-pulse mode available at the LCLS with the Icarus V2 ultrafast x-ray imager (UXI) camera\u003csup\u003e52,53\u003c/sup\u003e. The UXI allows us to obtain multiple images from a single shock-compressed sample, and it has already been tested both in the PCI\u003csup\u003e50\u003c/sup\u003e and direct imaging\u003csup\u003e41\u003c/sup\u003e configuration at MEC. For this experiment, the XFEL probe consisted of a series of four pulses of 40-80 fs separated of 2.4 and 3.85 ns. The precise and reproducible temporal structure of the XFEL multi-pulse beam allowed us to accurately estimate the shock velocity and their evolution without being affected by the temporal jitter of the XFEL beam.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFlat-field Correction.\u0026nbsp;\u003c/strong\u003eDuring the imaging process, spatial variations in the X-ray free electron laser and lens artifacts accumulated along the X-ray beam degrade the visibility of the captured intensity images and complicates the extraction of quantitative information. To enhance the visibility of features in these images, we implemented a flat-field correction scheme similar to the one used in our previous work\u003csup\u003e41\u003c/sup\u003e. This scheme involves image alignment to normalize against lens defects and the stochastic nature of the X-ray free electron laser. Initially, we improved our images by applying a median filter, with specified settings like neighborhood size and threshold, to remove pixels with extreme values, enhancing image quality by filtering out anomalies. Following this, we performed dark-field subtraction to eliminate detector noise. We utilized the ANTs image registration algorithm with a gradient descent optimizer and the ANTsNeighborhoodCorrelation metric from the Python SimpleITK library, aiming to maximize local similarities between the source (white fields) and target (dynamic) images. Upon achieving maximum similarity, the source image is warped towards the target image, ensuring a one-to-one correspondence between pixels in both images. Finally, we divided the dynamic image against the average of the warped white fields to produce a normalized, flat-field corrected dynamic image, significantly improving image clarity and interpretability. Some representative images are shown in the Supplementary Information file.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was performed at the Matter at Extreme Conditions(MEC)instrument of LCLS, supported by the US DOE Office of Science, Fusion Energy Science under contract No. SF00515, and was supported by LCLS, a National User Facility operated by Stanford University on behalf of DOE-BES.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eS.P. and A.E.G. acknowledge support from the 2019 DOE FES ECA and the RISE Hub IFE-STAR Funded FWP 101126. We thank A. Vailionis for assisting with sample characterization at the Stanford Nano Shared Facilities (SNSF) supported by the National Science Foundation under award ECCS-2026822.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKim, D. Y., Stefanoski, S., Kurakevych, O. O. \u0026amp; Strobel, T. A. 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A. \u003cem\u003eet al.\u003c/em\u003e First x-ray test of the Icarus nanosecond-gated camera. \u003cem\u003eX-Ray Free-Electron Lasers: Adv. Source Dev. Instrum. V\u003c/em\u003e \u003cstrong\u003e11038\u003c/strong\u003e, 110380Q-110380Q\u0026ndash;9 (2019).\u003c/li\u003e\n\u003cli\u003eLooker, Q., Colombo, A. P., Kimmel, M. \u0026amp; Porter, J. L. X-ray characterization of the Icarus ultrafast x-ray imager. \u003cem\u003eRev. Sci. Instrum.\u003c/em\u003e\u003cstrong\u003e91\u003c/strong\u003e, 043502 (2020).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4384466/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4384466/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eDecades of research have investigated the mechanical properties of matter under extreme conditions, exploring how materials deform, yield, and fail when subjected to high strain rates. While plasticity codes and computational methods can provide atomic-scale precision, reliable experimental benchmarks are needed to validate these models. However, for decades only bulk and surface measurements (e.g., velocimetry and reflectivity) were available to the community, and data interpretation was mainly done relying on conventional plasticity models and drawing parallels with results obtained under quasi-hydrostatic conditions. In recent years the advent of X-ray free electron lasers has provided insight into the microscopic structure of shock-compressed matter, revealing substantial differences with static compression experiments. Information at the mesoscale was, however, still missing, and the onset and propagation of the deformation at this length-scale was only accessible using computational methods; in this paper we fill that void, providing experimental data at the relevant time- and length-scales.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eHere, we combine imaging and structural characterization in situ using a nanosecond pump laser coupled with a femtosecond X-ray probe in a novel experimental configuration at the LCLS. Our data provides a comprehensive characterization of the deformation of silicon, a simple, yet highly debated, model system for high-strength materials. Information spanning the macroscopic and mesoscopic scale down to the lattice level allows us to resolve and directly visualize the nucleation and growth of the high-pressure phase for the first time, providing a temporal constraint on its kinetics. These novel insights are crucial to unambiguously determine how silicon yields under shock-compression, as they are able to connect the structural evolution at the atomic level with the complex multi-wave dynamic observed at the macroscopic scale, reliably benchmarking decade-old theoretical predictions.\u003c/em\u003e\u003c/p\u003e","manuscriptTitle":"Imaging material yielding and phase transitions in shock-compressed matter.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-11 20:27:37","doi":"10.21203/rs.3.rs-4384466/v1","editorialEvents":[],"status":"published","journal":{"display":false,"email":"[email protected]","identity":"nature","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"nature","sideBox":"Learn more about [Nature](http://www.nature.com/nature/)","snPcode":"","submissionUrl":"","title":"Nature","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"e1e01038-b578-4df3-a18b-68950a7866c7","owner":[],"postedDate":"June 11th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":33048291,"name":"Physical sciences/Materials science/Techniques and instrumentation/Imaging techniques"},{"id":33048292,"name":"Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2026-02-09T17:11:38+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-11 20:27:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4384466","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4384466","identity":"rs-4384466","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}