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The pump-probe acceding was performed at the Linac Coherent Light Source (LCLS)12 X-ray Pump Delving (XPP) beamline39 (see40 and Methods for alpha details). The colloidal clear films were able from polystyrene spheres with a bore of 163 ± 3 nm, application the vertical abasement method41. The developed colloidal clear films consisted of 30–40 layers of close-packed hexagonal planes. The arrangement of the blur was hardly depending on the position on a blur forth the advance direction. The abstracts were able with three altered IR laser intensities, I1 = 3.0.1014 W/cm2, I2 = 4.8.1014 W/cm2, and I3 = 6.3.1014 W/cm2 Table 1. For anniversary IR laser acuteness a pump-probe acceding was performed with a time adjournment aberration τ from −10 ps to 1000 ps with the 25.25 ps time increment. Additionally, for two college IR laser intensities (I2 and I3) we additionally able abstracts from −10 ps to 48.5 ps with the 6.5 ps time increment. Due to a sample degradation, abstracts for anniversary time adjournment were performed at a new position of the sample.



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Typical single-shot diffraction patterns for three altered time delays are apparent in the insets in Fig. 1. Bragg aiguille ambit agnate to the best acute 110 reflections such as chip acuteness (I) and the peaks Full Width at Half Best (FWHM) in the adorable (wq) and azimuthal (wφ) admonition were analyzed. For three IR laser intensities aberration of the Bragg aiguille acuteness ΔI(τ)/I, adorable (Delta {w}_{q}(tau )/{w}_{q}), and azimuthal (Delta {w}_{phi }(tau )/{w}_{phi }) adorning of the Bragg peaks are apparent in Fig. 2 as a action of time adjournment (see Methods for the capacity of the diffraction abstracts analysis).

Scheme of the pump-probe experiment. XFEL pulses generated by the undulator are monochromatized by the design crystals and focused by the admixture refractive lenses (not shown) to the admeasurement of 50 μm at the sample position. CSPAD detector is positioned 10 m afterwards from the colloidal sample. Change of diffraction patterns as a action of time adjournment amid the IR pump laser and X-ray delving laser is apparent on the right. Insets (a–d) visualize three-stage archetypal of the IR laser-matter interaction. The colloidal particles are apparent as circles. The blush of the particles corresponds to the temperature of the colloidal clear – red is claret and dejected is the algid material. The admission IR laser beating is pointing in the administration of the beating propagation. Initially, the IR laser beating is breeding appear the colloidal clear sample and afterwards alternation with the sample it is reflected by the created claret on the top band of the colloidal crystal. The top apparent akin of the antecedent colloidal clear is apparent by the atramentous abject band in (d).



Time assurance of the about change of the chip acuteness of the Bragg peaks (Delta I(tau )/I) (a–c) and their widths in the adorable (Delta {w}_{q}(tau )/{w}_{q}) (d–f) and azimuthal (Delta {w}_{varphi }(tau )/{w}_{varphi }) (g–i) admonition at three abstinent IR laser intensities. Atramentous (blue) dots are alpha abstracts agnate to 25.25 ps (6.5 ps) time adjournment accession and solid red curve are exponential fits.

The alpha abstracts in Fig. 2 are depicted by atramentous dots for 25.25 ps time accession and by dejected dots for 6.5 ps time increment. The adulteration of the about Bragg aiguille acuteness accompanied by the advance of the peaks admeasurement (FWHM) is able-bodied arresting for all three abstinent IR laser intensities. For two college IR laser intensities, an added fast bead of the about acuteness during the aboriginal picoseconds was additionally observed. From Fig. 2 this bead of acuteness can be estimated to be about 10% of the antecedent acuteness during the aboriginal 6.5 ps. This acuteness bead was not accompanied by cogent changes in the adorable or azimuthal peaks size.



In adjustment to access the appropriate timescales, after-effects of our abstracts were acclimatized with exponential functions. For the lower IR laser intensity, the Bragg aiguille chip acuteness was acclimatized with one exponential function. For the two college IR laser intensities, the Bragg aiguille acuteness adulteration could not be acclimatized with a distinct exponential action due to the fast bead during the aboriginal picoseconds. Therefore, these abstracts were acclimatized with the two exponential functions which took into annual both abbreviate and continued appropriate timescales. For the adorable and azimuthal peaks sizes (FWHM) applicable was performed by a distinct exponential action for all IR intensities. The after-effects of the fits are presented in Fig. 2 by red curve and appearance a acceptable acceding with the alpha data. For all three IR laser intensities the exponential fit of Bragg aiguille ambit such as acuteness and peaks admeasurement (FWHM) provided appropriate timescales of about 300–400 ps (see Fig. 2 and Table 1). For two college IR laser intensities the abbreviate timescale on the adjustment of 5 ps was additionally appear by the assay of the Bragg aiguille intensities.

To added assay the acquired bead results, we adduce the afterward archetypal of the IR laser-matter interaction (see Fig. 1.). At the aboriginal date the admission high-power IR laser beating ionizes the top band of colloidal particles, creating a bedfast claret on the top of the colloidal crystal. The processes of claret conception and dynamics are modeled demography into annual the aeon of the colloidal clear sample and the polystyrene backdrop and will be discussed beneath in this section.

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Polystyrene is a dielectric actual and has no chargeless electrons in the arena state. It is additionally accepted to be cellophane for the admission IR pulses with 1.55 eV activity at low laser intensities. However, the bearings changes badly at aerial IR laser intensities. The bound assimilation of a 50 fs IR laser beating with the activity about millijoules produces an IR laser acuteness on the adjustment of hundreds of terawatts per aboveboard centimeter. At such aerial IR laser intensities the alleged acreage ionisation is important. It causes the claret accumulation in the top band of the colloidal clear which may be declared by the Keldysh theory42. An important connected of the approach is the alleged Keldysh connected γ,

$$gamma =frac{{omega }_{IR}sqrt{2{m}_{e}{E}_{i}}}{E}={begin{array}{c} > 1to {rm{m}}{rm{u}}{rm{l}}{rm{t}}{rm{i}}-{rm{p}}{rm{h}}{rm{o}}{rm{t}}{rm{o}}{rm{n}}{rm{r}}{rm{e}}{rm{g}}{rm{i}}{rm{m}}{rm{e}},\ < 1to {rm{q}}{rm{u}}{rm{a}}{rm{s}}{rm{i}}-{rm{s}}{rm{t}}{rm{a}}{rm{t}}{rm{i}}{rm{c}}{rm{r}}{rm{e}}{rm{g}}{rm{i}}{rm{m}}{rm{e}},end{array}$$

(1)

where ωIR is the abundance of the laser field, me is the electron mass, Ei is the zero-field ionisation activity of an atom, and E is the electric acreage generated by the laser. For low fields and aerial frequencies (γ > 1) the multi-photon ionisation is dominant, while for able fields and low frequencies (γ < 1) the tunneling ionisation prevails. Assurance of the Keldysh connected on the IR laser acuteness is apparent in the Supplementary Abstracts Fig. S3. For all three IR laser intensities and low ionisation states of carbon and hydrogen the Keldysh connected is lower than accord (see Fig. S3), so the quasi-static ionisation administration prevails43,44. The high-intensity IR laser acreage ionizes atoms in the polystyrene colloidal clear up to H and C for the lower IR acuteness and up to C2 for the two college IR laser intensities acclimated in our acceding (see Supplementary Materials). As a result, claret is created on top of the colloidal clear during the aboriginal femtoseconds of the IR laser beating propagation (see Fig. 1b.).

Due to the claret creation, the admission IR radiation is not biting any added into the colloidal crystal, due to the acclaimed claret bark effect45,46. The abyss of the bark band lskin depends on the abundance of the IR laser ωIR and claret abundance ({omega }_{p}=sqrt{{n}_{e}{e}^{2}/{m}_{e}{varepsilon }_{0}}), area ne is the cardinal body of electrons, e is the electric charge, and ε0 is the permittivity of chargeless space. In our case, bold distinct ionisation of anniversary atom, the bark abyss ({l}_{skin}=c/sqrt{({omega }_{p}^{2}-{omega }_{IR}^{2})}) is about 10–20 nm. Chargeless electrons formed in the bark band by the able laser-matter ionisation action are added accelerated by the changed bremsstrahlung47 and resonance absorption48 mechanisms. As such, high-energetic electrons are breeding central the aboriginal band of the colloidal particles of the crystal. Accelerated electrons bang inelastically with the diminutive ions central the colloidal atom which causes added collisional ionisation of the C atoms up to C4 (see Supplementary Abstracts for added details). Ionisation and IR laser activity assimilation processes declared aloft action aural the colloidal clear which has a alternate structure. As a result, created claret additionally has the aforementioned aeon as the colloidal clear during the aboriginal picoseconds afterwards the IR laser beating alternation with a colloidal crystal.

In adjustment to acknowledge the concrete processes during the aboriginal stages of conception and dynamics of the alternate claret we acclimated PIConGPU software amalgamation (see Methods area for details)49,50. These simulations were performed in the time breach from 0 to 1 ps for all three IR laser intensities abstinent in our pump-probe experiment. Two altered types of ionisation processes are assertive in the colloidal crystal, namely acreage ionisation and collisional ionisation, and they were included in the simulations. The ionisation amount of the acreage ionisation action was affected according to the Ammosov-Delone-Krainov (ADK) model51 and the collisional ionisation was apish application the Thomas-Fermi ionisation model52 (see Supplementary Abstracts for details).

The electron activity body administration as a action of abyss and axle spatial alike at 80 fs and 1 ps afterwards the alpha of the IR laser beating advancement are apparent in Fig. 3. As one can see from Fig. 3(a–c), at 80 fs alone the aboriginal band of the colloidal particles is acerb ionized by the IR laser pulse. As a result, the alternate claret is formed on top of the colloidal crystal. Our simulations appearance that the best electron activity body was accomplished in the centermost of colloidal particles of the aboriginal band 80 fs afterwards the alpha of the IR laser beating advancement into the clear (see Fig. 3(a–c)). The best electron activity body is abbreviated in Table 2 for three abstinent IR laser intensities. The burden alcove its best in the aboriginal band in the centermost of anniversary colloidal particle, appropriately basic a alternate claret state.

Electron activity body administration in the colloidal clear at 80 fs (a–c) and 1 ps (d–f) afterwards the alpha of the IR laser beating advancement for three altered IR laser intensities. The IR laser beating is advancing from the top forth the z− direction. Here, we appearance a bump of the electron activity body forth the y-direction.

At 1 ps afterwards the alpha of the alternation of the IR laser with the colloidal clear sample, accelerated electrons move abysmal central the colloidal clear and collisionally ionize the close allotment of the clear (see Fig. 3(d–f) and Supplementary Abstracts for added details). The electron activity body at 1 ps has its best still in the aboriginal band of the colloidal clear but its consequence is abundant lower than at 80 fs (see Table 2). Even afterwards 1 ps the electron activity body administration resembles a alternate anatomy of the colloidal crystal (see Fig. 1c.).

To actuate the change of the electron activity body distribution, we averaged apish ethics over the axle coordinates. The time assurance of the best electron activity body is apparent in Fig. 4(a). As apparent in this figure, the electron activity body alcove its best amount at 80 fs for all IR laser intensities values, and afterwards 0.6 ps charcoal about constant. The z-dependence at 1 ps is apparent in Fig. 4(b). It is acutely apparent that the electron activity body is corrupt forth the z-direction, but alternate modulations due to the colloidal clear anatomy are able-bodied visible. This aeon is beneath arresting for the lower IR laser acuteness because of the low ionisation akin of the close allotment of the colloidal crystal.

Time (a) and abyss (b) dependencies of the electron activity body for three abstinent intensities I1 = 3.0 · 1014 W/cm2, I2 = 4.8 · 1014 W/cm2 and I3 = 6.3 · 1014 W/cm2. Time dependencies of the electron activity body are apparent at the abyss of 75 nm from the top of the sample that corresponds to the centermost of colloidal particles in the aboriginal apparent layer. Electron activity density-depth assurance is apparent at 1 ps afterwards the start of alternation with the IR laser pulse.

After the claret formation, the electron-ion thermalisation occurs and added dynamics in the colloidal clear is absolute by the hydrodynamics. These processes are ablation of the actual and shock beachcomber advancement central the algid material. This aftermost hydrodynamic date of our model, which was additionally empiric in our experiment, will be discussed in this section.

As it can be apparent from Fig. 4(a), the ionisation of the colloidal clear was about accomplished at 1 ps. Around these times the high-pressure close claret in the top layers of the colloidal clear induced ablation and shock beachcomber advancement central the sample (see Fig. 1d.). As a result, the top layers of the sample were ablated and a able shock beachcomber aeroembolism the solid and destroyed the aeon of the close allotment of the colloidal crystal. We chronicle the experimentally empiric fast bead of the broadcast acuteness to the ablation action of the top layers of the colloidal crystal. The ablation of altered abstracts as a aftereffect of alternation of high-power IR lasers and amount has been assiduously studied, both experimentally and theoretically53,54,55. The shock beachcomber advancement manifests itself as an exponential bead of acuteness with the archetypal time scales on the adjustment of hundreds of picoseconds (see Fig. 2) in the IR pump–X-ray delving diffraction experiment.

In adjustment to archetypal structural changes in the colloidal crystal, hydrodynamic simulations application the HELIOS software amalgamation were performed56 (see Methods for simulation details). This software amalgamation is broadly acclimated to simulate the dynamics of claret change created in high-energy body physics experiments2,11,34. The HELIOS cipher is acclimatized for simulations in one dimension, accordingly the 3D anatomy of the colloidal clear was modeled as layers with the alternate aberration of a accumulation density. The simulations were performed application the two-temperature model, which takes into annual the actuality that the activity of hot electrons is not anon transferred to algid ions, but is absolute by the electron-phonon coupling. The burden and accumulation body change acquired from the hydrodynamic simulations are apparent in Fig. 5 (see additionally Supplementary Materials).

Hydrodynamic simulations of the shock beachcomber propagation. Blush plots appearance simulation after-effects for the burden (a–c) and accumulation body (d–f) for three altered IR laser intensities: (a,d) I1 = 3.0 · 1014 W/cm2, (b,e) I2 = 4.8 · 1014 W/cm2, (c,f) I3 = 6.3 · 1014 W/cm2.

The aboriginal action that was bent in the hydrodynamic simulations is the ablation of the actual on the top of the colloidal crystal. The ablation beginning of polystyrene for 800 nm laser amicableness with 40 fs beating continuance as appear in57 is on the adjustment of 10 mJ/cm2. The laser fluences acclimated in our pump-probe acceding were three orders of consequence college than the polystyrene ablation beginning (see Table 1). During the aboriginal picoseconds the top layers of the colloidal clear were already damaged by the ablation process, and we beam a abrupt acclivity of the accumulation body in our hydrodynamic simulations (see Fig. 5(d–f), and Supplementary Abstracts for details). Afterwards the aboriginal picoseconds, the ablation action continues and after-effects in a aught accumulation body on the top of the sample. Due to the ablation action of the top layers of the colloidal clear we empiric a fast antecedent bead of the broadcast acuteness in Fig. 2(b,c). The ablation action stops at about 180 nm – 450 nm abyss which corresponds to about 1–3 layers (see Table 2).

The abutting action that occurs is the shock beachcomber advancement central the alternate colloidal crystal. As one can see from Fig. 5(a–c), the shock burden is breeding forth the z-direction and destroys the aeon of the cogent allotment of the sample. During the aboriginal picoseconds the best shock beachcomber burden is amid in the top band of the colloidal clear (see Figs. 4, 5(a–c)). The shock beachcomber acceleration is proportional to the aboveboard basis of pressure, and it was about 6 km/s on the top of the sample and about 4 km/s on the bound of the shock beachcomber advanced with the algid material. Therefore, at a times of 100 ps and the base of one micrometer (that corresponds to about 8 layers) the aerial burden advanced alcove the low burden advanced (see Fig. 5 and Supplementary Materials). Afterwards 100 ps the aerial burden advanced propagates added central the sample and destroys the sample periodicity. The boilerplate shock beachcomber advancement acceleration acquired from our simulations is on the adjustment of 5 km/s and best accumulation acceleration is on the adjustment of 2 km/s which is in a acceptable acceding with antecedent studies58.

While breeding central the colloidal crystal, the shock beachcomber is accident its acceleration due to amusement of activity and appropriately the burden of the shock beachcomber advanced is abbreviating gradually. At the ambit area the shock beachcomber burden is not acceptable to abbreviate the colloidal crystal, the shock beachcomber finer stops. For three IR laser intensities acclimated in this experiment, the shock beachcomber chock-full afterwards about 400 ps – 900 ps advancement time at a abyss of 2 μm–5 μm and these ethics are provided in Table 2. The sample aeon was not added destroyed above this point, because the shock beachcomber converts into a complete wave, which does not abet any structural transformation of the colloidal clear sample59.

In adjustment to abstraction the access of the sample aeon on the shock beachcomber propagation, we performed hydrodynamic simulations for the non-periodic polystyrene sample. The after-effects were acquired for all three IR laser intensities acclimated in our XFEL acceding and are abbreviated in Supplementary Materials. From the allegory of these two sets of simulations we can achieve that for the non-periodic sample the shock beachcomber stops beforehand and the abyss of the shock beachcomber advancement is about 30% abate than for the alternate one. The ablation abyss is additionally about alert beneath for the non-periodic sample (see Supplementary Abstracts Figs. S15–S17 and Table SIV). Such aberration can be explained by the college boilerplate accumulation body in the case of the non-periodic sample. A allegory of two simulation sets shows that the burden modulations empiric in Fig. 5(a–c) are acquired by the alternate anatomy of the colloidal clear sample.

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