Enhanced tunable X-rays from bulk crystals driven by table-top free electron energies

Domain: physics
Published: 2025-12-11
Editorial outcome: minor_revision

Abstract
Free-electron-driven crystalline materials have emerged as a promising platform for tunable, table-top X-ray generation in industrial, medical imaging applications, and fundamental research. It is commonly believed, however, that the use of bulk crystals is not feasible under the weakly relativistic energies necessitated by table-top electron sources. This belief is fueled by the perception that electron scattering inside bulk crystals produces substantial bremsstrahlung background which overwhelms the tunable, narrowband X-ray peaks. In this study, we overturn this belief by introducing a parameter that distinguishes a regime where tunable X-rays substantially dominate bremsstrahlung in bulk materials. We show that this regime is most readily accessible with van der Waals crystals, revealing an unprecedented property of van der Waals crystals in the X-ray regime. We experimentally demonstrate a tenfold intensity enhancement through the use of bulk van der Waals crystals, in good agreement with our theoretical predictions. The use of bulk crystals is also advantageous in requiring less labor-intensive material preparation and being less vulnerable to damage compared to thin films. Our findings pave the way to more efficient and more accessible table-top, tunable, narrowband X-ray sources for safer and more sustainable X-ray imaging in industries including semiconductors and healthcare.

Introduction
Van der Waals (vdW) materials consist of two-dimensional (2D) atomic planes held together by strong intralayer covalent bonds and weak interlayer vdW forces. Since the first isolation of graphene using adhesive tape in 20041, vdW materials have garnered significant research attention due to their intriguing properties and novel phenomena, including the anomalous quantum Hall effect2, massless Dirac particles3,4, superconductivity5, ultrahigh carrier mobility6,7, ferromagnetism8,9, strongly bound exciton states10,11, heterostructures12,13 and strong spin-orbit coupling14. In particular, free-electron-driven vdW crystals have emerged as a promising table-top platform for generating tunable X-rays. Such a platform marries the compactness of conventional X-ray tubes with advantages like tunability of larger, less accessible X-ray facilities, ushering in advanced X-ray imaging modalities on a compact scale for applications including semiconductor failure analysis, medical imaging15–19, security and fundamental research20–22.

Free-electron-based light sources have been studied across various platforms23, including plasmonic single-atom layers24, metasurfaces25–27, metamaterials28, nanostructures29–32, vdW materials33 and other mechanisms34–40, spanning a broad spectral range from terahertz radiation to X-rays41–45. Among these, the use of free-electron-driven vdW crystals as a platform for tunable X-ray generation has distinguished itself through features including continuous, real-time photon energy tunability46,47, multicolor X-ray generation48, water-window X-ray production49, X-ray caustics50, quantum recoil51–53, radiation shaping54 and heterostructure-enabled X-ray focusing55. Free-electron-driven vdW crystals overcome the challenge of current commercial X-ray sources in achieving compactness and photon energy tunability simultaneously46,48,49. Conventional X-ray tubes are compact but produce high-intensity characteristic peaks only at fixed photon energies determined by material composition, thus lacking continuous, real-time photon energy tunability. On the other hand, tunable X-ray sources such as synchrotrons and X-ray free-electron lasers56–60 feature a high degree of tunability but require significant space and high energy consumption61, making them less accessible for laboratory-scale applications.

The promise of free-electron-driven vdW crystals as a table-top X-ray platform, however, has been undermined by an implied dependence on thin films. Indeed, all studies of free-electron-driven vdW crystals have been confined to vdW thin films with thicknesses typically below 200 nm46–49,51, which are relatively challenging to produce due to labor-intensive preparation processes62. The resulting X-ray flux is thus fundamentally limited by the restricted crystal thickness. The common notion is that bulk crystals would cause so much electron scattering that the tunable X-ray peaks would be obscured by the bremsstrahlung background63. As such, the use of bulk crystals has been limited to X-ray sources with kinetic energies above 30 MeV64–67 or even hundreds of MeV68–76. The use of relativistic electrons, however, is an obstacle to the miniaturization of these sources. As such, the combination of table-top free electron energies and bulk crystals has remained unexplored, with a prevailing notion that it would be an unfeasible platform for producing tunable X-ray peaks.

Here, we overturn this notion by showing that the use of free-electron-driven bulk crystals as a platform for producing tunable X-ray peaks is not only feasible but highly advantageous. Specifically, we show that tunable, narrowband X-ray peaks can not only be observed in vdW bulk crystals driven by table-top free electron energies, but even exhibit tenfold intensity enhancement over the use of thin films. Starting from first-principles electromagnetism and electron scattering theory, we derive a parameter that quantitatively defines the regime where tunable X-rays can surpass bremsstrahlung significantly. Compared with conventional bulk crystals, vdW crystals are much more likely to attain large values of this parameter to access said regime, revealing an intriguing and unprecedented property of vdW crystals in the X-ray regime, and explaining the historical inability to observe tunable X-rays in conventional crystalline bulk materials. These findings are most welcome not only as a way to scale up tunable X-ray intensities, but especially in allowing for the use of bulk target materials, which involve less labor-intensive material preparation and are less vulnerable to damage compared to thin films. Our experimental results are in good agreement with the predictions of our theoretical framework – which fully accounts for electron scattering inside the crystal – in both the spectral bandwidth and the absolute intensity of the emitted X-rays. Our findings open up a new avenue in the optimization of tunable X-ray sources based on free-electron-driven crystalline materials, allowing bulk crystals to be employed toward the enhancement of X-ray intensities, leading to reduced costs, greater efficiency and smaller carbon footprint of the resulting X-ray imaging system.

Results
The mechanisms responsible for the generation of tunable, narrowband X-ray peaks from free-electron-driven crystals are parametric X-ray radiation and coherent bremsstrahlung. Parametric X-ray radiation is an atomic-scale version of Smith-Purcell radiation; the emission comes from free electrons passing through or in the vicinity of periodic structures. Parametric X-ray radiation thus arises from the diffraction of the incident electron’s Coulomb field by the crystal’s periodic atomic structure – acting as a nanometer-scale diffraction grating on the atomic scale. A higher-order radiation mechanism known as coherent bremsstrahlung63,71,77–83 can sometimes contribute significantly to the tunable X-ray emission as well. Coherent bremsstrahlung is generated by the periodic undulation of incident electrons due to the periodic potential as it traverses the crystal. In our regime of study, the output X-ray photon energies of the two forms of radiation, namely parametric X-ray radiation and coherent bremsstrahlung, are identical and the peak photon energies are given by47,77

E_p = \hbar v \cdot g / (1 - (v \cdot \hat{n} / c))

where \hbar is the reduced Planck constant, v is the electron velocity, g is the reciprocal lattice vector of a certain plane of the crystal, \hat{n} is the unit vector along the observation direction, c is the speed of light in vacuum. In our theoretical framework, the formula employed to calculate tunable X-ray intensity is derived by combining the Monte Carlo simulations of electron scattering and Maxwell’s equations, given by46,48,49,51

d^2N / d\Omega d\omega = (e^4 / 4\pi^2 \omega c^2) | \sum_j \int_0^{t_L} v_j(t) \cdot E_k^s(r_j(t), \omega) e^{i\omega t} dt |^2

where N is the number of emitted photons, \omega is the angular frequency of the emitted photon, \Omega is the solid angle, N_e is the number of electrons incident on the crystal, \alpha is the fine-structure constant, t_L is the electron interaction time with the crystal of the ith electron trajectory segment, v_i(t) is the velocity of the ith electron trajectory segment of the jth electron at time t, E_k^s represents the eigenmode of the crystal, which is a function of position of the electron r_i(t) and the angular frequency of the emitted photon \omega. More details are available in Supplementary Information (SI) Section S1. As electrons travel through a material, the electron scattering with atoms alters both their kinetic energy and traveling direction, which affects the emitted tunable X-ray spectrum. The electron scattering is simulated by using Monte Carlo method in the CASINO software84–88. The electron velocity v_i and position r_i for each scattered trajectory segment – defined by the electron path between consecutive collisions – are incorporated into Equation (1) and (2) to obtain the resulting tunable X-ray intensity spectrum.

Figure 1a, b illustrate the Monte Carlo simulations of electron scattering in bulk and thin graphite crystals, respectively. In Fig. 1a, a 20 keV electron beam is incident on a bulk graphite crystal. Owing to the long interaction length with the crystal, the electrons gradually lose all their kinetic energy and eventually come to a complete stop. In contrast, Fig. 1b shows electron scattering in a 29 nm-thick graphite thin film, where most electrons pass through the material with minimal energy loss, less than 0.5% and a slight directional deviation of approximately 3°. In bulk materials, the extended interaction lengths – defined as the total distance an electron travels within the crystal while emitting tunable X-rays – enhance electron-crystal interactions, resulting in higher tunable X-ray emission intensity. Figure 1c shows X-ray spectra generated from a 1 mm-thick highly oriented pyrolytic graphite (HOPG) bulk crystal, with electron energies of 17.5, 20, 22.5, and 25 keV, respectively. In our study, a bulk crystal refers to a crystal that is sufficiently thick to prevent all incident electrons from penetrating through it. In this case, further increasing the crystal’s thickness does not affect the tunable X-ray spectrum. Figure 1d presents the X-ray spectra from a 29 nm-thick graphite thin film, measured under the same electron energies as in Fig. 1c. Figure 1c, d reveal a tenfold intensity enhancement with bulk vdW crystals. This finding aligns well with our theoretical predictions, confirming not only that tunable X-ray peaks from bulk crystals are well observable over the bremsstrahlung but also that bulk crystals are more effective than thin films for tunable X-ray generation.

Experimental attempts to measure tunable X-ray radiation using bulk crystals and table-top electron sources remain unexplored due to the prevailing notion that relatively high electron scattering in bulk crystals would obscure tunable X-ray peaks beneath the bremsstrahlung background63. As we show in Fig. 2a, a regime exists where tunable X-ray peaks substantially dominate bremsstrahlung even in bulk materials. Each point in the figure corresponds to simulation results for different materials (including vdW and conventional materials), crystal planes, and electron energies. The color scale indicates the ratio of tunable X-ray to bremsstrahlung flux within a 10 eV bandwidth around the tunable X-ray peak energy: red denotes ratios \gtrsim 1 (tunable X-ray dominates), blue denotes ratios \lesssim 1 (bremsstrahlung dominates), and white denotes ratios \approx 1. The dotted purple line marks the boundary where the two fluxes are approximately equal. This boundary was obtained through numerical fitting from the data in the figure. Above this boundary lies the regime in which tunable X-ray emission tends to dominate, while below this boundary, bremsstrahlung tends to dominate.

As detailed in SI Section S14, we use first-principles electromagnetism and electron scattering theory to obtain the following ratio of the tunable X-ray flux \Phi_{tunx} to the bremsstrahlung flux \Phi_{brem}, for a given free electron mean free path in the material, as

\Phi_{tunx} / \Phi_{brem} \propto (E_p [eV] \cdot |\chi_g|^2) / (Z_{eff} \cdot E_p [eV] \cdot T_{accum})

In Equation (3), the numerator E_p [eV] \cdot |\chi_g|^2 originates from the tunable X-ray radiation process. E_p [eV] = E_p / (1 eV) is the value of the photon energy normalized to 1 eV, and \chi_g is the electric susceptibility, which depends on both the crystal plane and photon energy. \chi_g quantifies the diffraction strength of the incident electron’s Coulomb field by the crystal’s periodic lattice. The denominator Z_{eff} = E_p \cdot T_{accum} originates from the bremsstrahlung contribution, where Z_{eff} is the effective atomic number per unit volume and E_p is the bremsstrahlung photon energy. The factor Z_{eff} / E_p reflects the relative strength of the bremsstrahlung cross-section per unit volume. The factor T_{accum} accounts for the electron distribution after scattering inside the crystal, as well as the resulting X-ray self-absorption, which depends on the electron distribution. As we see in Fig. 2a, plotting Eq. (3) against mean free path separates the data points into two relatively distinct regimes for bulk materials: one where tunable X-ray dominates, and one where bremsstrahlung dominates. The trend of larger mean free paths favoring the dominance of tunable X-rays seen in Fig. 2a is not surprising: this trend can also be inferred from Eq. (2), where we see tunable X-ray emission originating from electron trajectories inside the crystal. A longer electron mean free path increases the interaction time t_L, leading to stronger tunable X-ray emission.

Figure 2b repeats the simulation points in Fig. 2a, but shows the category of material being used instead of the flux ratio. Note that vdW materials occupy the tunable X-ray dominated regime. Our results reveal an intriguing and unprecedented property of vdW materials in the X-ray regime: namely, their ability to feature a much larger \Phi_{tunx} / \Phi_{brem} ratio compared to conventional materials, allowing a higher chance of vdW materials emitting tunable X-ray peaks that dominate bremsstrahlung even when the vdW materials are in bulk form and electron scattering of free electrons is significant. The full list of materials and crystal planes used in the simulations is provided in SI Section S14, Supplementary Table 5.

An overview of earlier experimental studies on free-electron radiation using various materials and electron kinetic energies46–48,51,63–76,89–94 is shown in Fig. 2c. The theoretical regimes of these studies are represented by shaded regions, with pentagrams marking the corresponding material thickness and electron energy for each experiment. Experimental studies in the upper-right corner of Fig. 2c are conducted in the relatively low scattering regime, characterized by large crystal thicknesses and high electron energies. In this regime, electron kinetic energies ranging from a few MeV to over 1 GeV allow electrons to traverse millimeter-scale crystals with minimal energy loss less than 5% and only slight changes in direction, which is less than 10°.

Conversely, recent experimental studies in the lower-left corner of Fig. 2c focus on another relatively low scattering regime, characterized by low crystal thicknesses and low electron energies. Advances in nanoscale thin crystal fabrication have facilitated investigations in this regime using table-top electron sources, such as scanning electron microscopes (SEMs) and transmission electron microscopes (TEMs). Operating at electron energies below 300 keV, these sources enable electrons to traverse nanometer-thick crystals with relatively low electron scattering. Our study reports tunable X-ray emission in the relatively high electron scattering regime, characterized by large crystal thicknesses and low electron energies, as highlighted in the red box in Fig. 2c. Supported by theoretical predictions and experimental data, our work opens up a new avenue for tunable X-ray research under previously unexplored conditions.

Figure 3a illustrates the variation in tunable X-ray intensity with material thickness. Four tunable X-ray spectra collected at different graphite thicknesses under a 25 keV electron energy are shown. As the graphite thickness increases from 29 nm to 1 mm, the tunable X-ray intensity increases significantly, achieving up to a tenfold enhancement experimentally, consistent with our theoretical predictions. The inset in Fig. 3a shows the relationship between tunable X-ray intensity and graphite thickness. Each dot represents the tunable X-ray peak intensity predicted by our theory, which has been validated by experimental data. This relationship can be described by the equation

I(l) = I_s (1 - e^{-l / L})

where I is the tunable X-ray intensity, l is the crystal thickness, I_s is the saturation tunable X-ray intensity, and L is the fitting parameter. The values of I_s and L depend on the material properties and electron energy (details provided in the SI Section S10). Equation (4) accurately characterizes the increase in tunable X-ray intensity with material thickness and its saturation under specific electron energy conditions.

In Fig. 3a, the bremsstrahlung background is subtracted from the experimental data, and the tunable X-ray linewidth is broadened by the energy resolution of the energy-dispersive X-ray spectroscopy (EDS) detector. In Fig. 3b, we address the challenge identified in the previous experimental investigation, where tunable X-rays could not be distinguished from the bremsstrahlung background when using table-top electron sources and crystals thicker than 500 nm63. Our measurements (Fig. 3b) from graphite crystals of varying thicknesses clearly reveal tunable X-ray peaks (solid lines) above the bremsstrahlung background (dashed lines), despite broadening effects from the EDS detector. This demonstrates a significant enhancement in tunable X-ray intensity when using vdW materials. In the absence of detector resolution limits, the intrinsic tunable X-ray peaks (dotted lines) exhibit even greater intensity enhancement relative to the bremsstrahlung background. Employing an X-ray detector with higher resolution than EDS would enable direct observation of this stronger enhancement. Further details on the experimental setup limitations and EDS detector resolution are provided in SI Section S4.

Figure 3c compares the intensity of tunable X-ray and bremsstrahlung. Specifically, for a 2 mm-thick graphite sample under electron energies ranging from 10 keV to 300 keV, achievable with table-top electron sources. The tunable X-ray intensity can exceed the bremsstrahlung by up to a factor of 20. Figure 3d shows the dependence of tunable X-ray and bremsstrahlung intensity on graphite thickness at a fixed electron energy of 300 keV. Across all thicknesses, the tunable X-ray intensity consistently surpasses the bremsstrahlung. Notably, compared to emissions from nanometer-thick crystals, bulk graphite crystal exhibits significantly enhanced tunable X-ray intensity, achieving more than a 300-fold increase. Such order-of-magnitude enhancement can be further scaled by increasing the kinetic energy of the incident electrons. Nevertheless, even within the table-top electron energy range considered here, the tunable X-ray flux is sufficient to support X-ray applications such as imaging and spectroscopy at practical current densities. The applicability of the tunable X-rays and the maximum current density sustainable by the graphite sample are further detailed in SI Section S11.

The enhancement of tunable X-ray intensity by using bulk materials, as well as the superiority of vdW-based materials in achieving higher tunable X-ray intensity over bremsstrahlung, is not unique to HOPG but extends to a broad range of vdW materials, as demonstrated experimentally in SI Section S7, Supplementary Fig. 5. HOPG was employed here primarily because it is a readily available form of graphite crystal with millimeter-scale thickness. Figure 4 presents simulation results for tunable X-ray and bremsstrahlung background from three different vdW materials: h-BN, MoSe2, and WSe2. Since photon flux is more commonly referenced in X-ray applications such as X-ray imaging and spectroscopy, the results are expressed in terms of flux rather than intensity. The flux values are calculated by integrating the tunable X-ray and bremsstrahlung intensity spectra within a 10 eV spectral bandwidth centered at the tunable X-ray peak.

The left panels of Fig. 4 illustrate the dependence of tunable X-ray flux on incident electron energy. Specifically, we compare the tunable X-ray flux and bremsstrahlung flux emitted from 2 mm-thick bulk crystals under electron energies ranging from 10 keV to 300 keV, achievable with table-top electron sources. The right panels show the dependence of tunable X-ray flux on material thickness, with the electron energy fixed at 300 keV, where we compare the tunable X-ray and bremsstrahlung flux and examine the tunable X-ray flux emitted from nanometer-thick films versus bulk crystals. At an electron energy of 300 keV and a crystal thickness of 2 mm, tunable X-rays from all three materials exhibit approximately a tenfold enhancement in flux compared to the bremsstrahlung background. Our simulation results reveal that the degree of tunable X-ray enhancement with increasing crystal thickness depends on the material composition. Materials composed of lighter elements, such as h-BN, show greater enhancement due to extended total interaction lengths between electrons and the crystal lattice, and reduced X-ray self-absorption. However, materials composed of heavier elements, such as MoSe2 and WSe2, exhibit higher absolute tunable X-ray flux values as shown in Fig. 4b, c. A detailed comparison between the tunable X-rays, bremsstrahlung radiation and characteristic X-ray peaks is provided in SI Sections S8 and S9.

Methods
Theory and simulations
The theoretical framework for tunable, narrowband X-ray generation from free-electron-driven crystals is presented in Supplementary Information (SI) Section S1, with detailed explanations and derivations. The geometrical relationship is further illustrated by Supplementary Fig. 1. The Monte Carlo simulations of electron scattering in solids were performed using the CASINO software, with further details provided in SI Section S2.

X-ray measurements
The experimental X-ray spectra containing tunable X-ray peaks were collected using the JEOL 7800 field emission scanning electron microscope (FESEM) equipped with the Oxford Ultim Max 170 energy-dispersive X-ray spectroscopy (EDS) detector. Crystalline thin films were mounted on gold transmission electron microscopy grids, while bulk crystals were affixed directly to a nickel scanning electron microscope holder using aluminum stubs and secured with a carbon disc and carbon tapes. The performance of the Oxford Ultim Max 170 EDS detector is given in Supplementary Tables 1, 2. More detailed information can be found in SI Section S3.

Sample synthesis and preparation
Graphite nanoflakes were mechanically exfoliated onto silicon substrates coated with a 285 nm SiO2 layer. The flakes were subsequently transferred onto gold transmission electron microscopy grids via a conventional wet-transfer process. In this procedure, a PMMA layer was spin-coated onto the substrate and baked at 120 °C for 2 min. The underlying SiO2 was then etched away using a 20 wt% KOH solution, thereby releasing the PMMA film containing the graphite nanoflakes, which was carefully transferred onto the gold transmission electron microscopy grids. To expose the thin graphite layers, the PMMA support was removed by immersion in acetone, followed by thorough drying of the samples on the Au TEM grids.

Sample thickness measurements
The crystal thicknesses were measured using different techniques depending on the thickness range. For crystals thicker than 1 μm, the thickness was directly determined from cross-sectional images obtained via scanning electron microscopy (SEM). For crystals with thicknesses between 300 nm and 1 μm, atomic force microscopy (AFM) was used. For thinner crystals (<300 nm), thickness measurements were conducted using convergent beam electron diffraction (CBED) patterns shown in Supplementary Fig. 3. Crystal thickness values are given in the Supplementary Tables 3a, b. More detailed information can be found in SI Section S6.

Data availability
The raw data that support the plots of this study are openly available in NTU research data repository DR-NTU (Data) at https://doi.org/10.21979/N9/WZAMZ095.

Code availability
Simulation codes are available from the corresponding authors upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors report on observation of an enhancement of coherent X-ray generation yield by electrons propagating through crystalline materials (graphite) with extended thickness. Up to now, this type of generation was investigated only in materials with thickness of below few hundreds of nanometers, while here the comparison of different thicknesses up to a bulk material is studied. The authors also give comprehensive theoretical description of the observed phenomena.\nThe main novelty of the manuscript lies in the observation of approx. 10x enhancement of X-ray generation yield when the thickness of the generating material increases. However, the method is not really scalable because after a certain thickness, the electrons lose their energy via inelastic scattering with the sample and cannot generate X-rays by this method any more. The methodology used is not different from the one applied in previous publications, so the X-rays are detected using a standard EDS detector, which suffers from two limitations. First it only allows to collect the X-rays in a given emission angle and second, its spectral resolution is quite poor. For these reasons I do not think the novelty and significance of the presented results warrant publication in Nature Communications and the manuscript may be better suited for a more specialized journal. Here are few comments/questions for the authors:\n1) The authors show the comparison of the detected X-ray spectra with theory in absolute units of photons/(s.eV.nA). It is shown that the coherent radiation is stronger than the background caused by Brehmstrahlung. However, applicability of this generation method for X-ray spectroscopy, diffraction or imaging requires much higher photon fluxes. Can the authors compare the coherent emission yield with emission in characteristic peaks (e.g. the peak of C at 277 eV)?\n2) The maximum X-ray emission yield is limited by the electron current, which can be only few hundreds of nA in the FESEM. Could the authors comment in the manuscript what is the maximum theoretical current density which can be applied to the graphite sample? This is an important parameter since it limits the applicability of the method as a source of X-ray radiation.", "reviewer_2": "The authors observe tunable X-rays in a previously unreachable regime with high electron scattering, characterized by both slow electron energies and large sample sizes. The findings of this paper are exciting, as they challenge the common belief that X-ray signals might be drowned out by the bremsstrahlung background in highly scattering regimes. I would be happy to support the publication of this paper if the following comments are addressed:\n1. To emphasize the notion that X-ray signals might be drowned out by the bremsstrahlung background in highly scattering regimes, the authors might consider providing more theoretical work or experimental evidence to support this claim. Are there additional studies on this topic beyond the authors' own previous work?\n2. The critical points of electron energies where bremsstrahlung radiation and X-ray signals intersect could be worthwhile to research. For example, it is suggested to study (e.g. in theory) the relationship between these critical electron energies and sample thickness.\n3. Based on the inset in Fig. 1a, there appears to be an optimal minimal thickness that yields maximal intensity. For practical applications, it is also suggested to study (e.g. in theory) the dependence of this optimal thickness on electron energy.\n4. In the right panels of Fig. 3b&c, the ratio of the flux between bremsstrahlung and X-rays does not always increase as the thickness increases—for example, from 10^-7 m to 10^-5 m. This behavior is unusual in this context, and the authors may need to provide an explanation for this observation.\n5. To enhance the novelty and significance of this work, it is suggested to include more recent advances in free-electron radiation and van der Waals (vdW) or twisted structures. For example, consider referencing works such as PNAS 122, e2413336122 (2025), PRL 131, 113002 (2023), and Physical Review Applied 21, 064034 (2024).", "reviewer_3": "This manuscript „Enhanced tunable X-rays from bulk crystals driven by table-top free electron energies,” presents a study on generation of tunable x-ray sources by virtue on electron beam in SEMs interacting with thick bulk crystals. The results claim to be a significant improvement over previous studies where the role of Characteristic xray dominates over background radiation.\nThe study is an interesting and rather systematic presentation of the role of electron velocity and current on tunable x-ray sources. However at this present form, I cannot recommend it for publication in Nature Communications, due to the lack of several important clarifications. The work is also not properly inserted in the context of previous works and several important citations are missing here. See my comments below.\n1. The authors demonstrate a surprisingly excellent agreement between their theories and the experimental results in Figure 1 and part of Figure 2, and thereafter the explorations go purely theoretical. This is a surprise, as for example other electron sources in TEMs could be used as well to test the theory, or even simpler, bulk WSe2, hBN, … crystals are easily obtained now adays and are commercially available. Rather counting on theory, the authors would need to test the theory for other crystals with experiments.\n2. The excellent agreement with theory and experiment is kind of questionable. First and least, I would expect a comparison of the theory with various crystal thicknesses starting from thin to thick and compare them for experiments. See for example here: Fatemeh Chahshouri et al 2022 J. Phys. D: Appl. Phys. 55 145101.\n3. How is the assumption made in the supplementary meaning that “fluctuations in electron trajectories are small” are compared to the monte carlo simulation of figure 1a? From this figure, I see quite large fluctuations.\n4. Equation (2) of the paper does not seem to be entirely correct. The term named E_ks (eigenmode of the crystal) is just a function of frequency and comes out of the integral. The remaining integrand is just the Fourier transform of the electron velocity. It is not also clear how time factor is inhered from monte-carlo simulations. Should not the Eigenmode functions appear time-dependent?\n5. In the introduction under the claim of all tuneable electron-driven light sources, a class of important recent reports on not only designing visible-range light sources (Nature communications 10 (1), 599 (2019)), but also using them for spectroscopy inside SEMS (Nature Communications volume 16, Article number: 2326 (2025); Nature Physics 19 (6), 869-876 (2023)) have been ignored. This is not a good signal given the fact that this technology has gone far more advanced than just controlling the spectral shape, but also to control the spatial and coherence state of light.\n6. Why the authors have use for their experiments HOPG? This is a highly diamagnetic material and it is not clear if this has an effect.\n7. In overall the manuscript, I encounter in several parts the claim that tuneable x-ray sources from bulk crystal is observed here for the first time. But it is not explained why this is the fact and what has been improved here? I also find this paper rather technology relevant than explaining the physics behind the observations. For example, how does the modal eigen function affect the results?\n8. How do the authors measure the thickness?", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nThe manuscript titled “Enhanced tunable X-rays from bulk crystals driven by table-top free electron energies” presents a study on the generation of tunable X-ray sources via electron beams from scanning electron microscopes (SEMs) interacting with bulk crystals. The authors claim a significant enhancement over previous studies, emphasizing the dominance of characteristic X-ray emission over background radiation.\nThe topic is intriguing and the study offers a relatively systematic analysis of the role of electron velocity and current in the generation of tunable X-rays. However, in its current form, I cannot recommend the manuscript for publication in Nature Communications. Several critical clarifications are missing, and the work lacks proper contextualization with respect to prior literature. Below, I outline my specific concerns:\n1. The authors report excellent agreement between theoretical predictions and experimental results in Figure 1 and parts of Figure 2. However, beyond this point, the manuscript becomes predominantly theoretical. This is surprising, given that additional experimental validation could be readily performed using other electron sources (e.g., TEMs), or even with other bulk crystals such as WSe₂ or hBN, which are commercially available and widely studied. Rather than relying heavily on theory, the authors should support their claims with broader experimental validation across different material systems.\n2. The claimed agreement between theory and experiment warrants deeper scrutiny. In particular, I would expect to see a comparison of theoretical predictions across a range of crystal thicknesses—from thin to thick—and corresponding experimental data. For reference, see: Fatemeh Chahshouri et al., J. Phys. D: Appl. Phys. 55, 145101 (2022).\n3. The supplementary material states that \"fluctuations in electron trajectories are small,\" but this does not appear consistent with the Monte Carlo simulation shown in Figure 1a. On the contrary, the figure indicates significant trajectory fluctuations. The authors should address this apparent contradiction and clarify the assumptions involved.\n4. Equation (2) appears to contain inconsistencies. Specifically, the term E_ks, identified as the crystal eigenmode, is only frequency-dependent and should factor out of the integral. The remaining integrand seems to represent the Fourier transform of the electron velocity. Additionally, it is unclear how time-dependence is inherited from the Monte Carlo simulations. Shouldn't the eigenmodes themselves also be time-dependent? This point requires clarification.\n5. In the introduction, the authors reference tunable electron-driven light sources but fail to cite several recent and important developments—particularly those extending beyond mere spectral tuning to include control over spatial emission and coherence. Examples include:\n• Nature Communications 10, 599 (2019)\n• Nature Communications 16, 2326 (2025)\n• Nature Physics 19, 869–876 (2023)\nThese omissions weaken the contextual grounding of the manuscript and overlook key progress in the field.\n6. The use of highly oriented pyrolytic graphite (HOPG), a strongly diamagnetic material, is not justified in the manuscript. The authors should clarify why HOPG was chosen and whether its magnetic properties influence the observed results.\n7. Repetitive and Unsubstantiated Claims of Novelty: Throughout the manuscript, the authors repeatedly claim that tunable X-ray generation from bulk crystals is demonstrated \"for the first time.\" However, this claim is not adequately substantiated. The authors should clearly articulate what distinguishes this work from prior studies and what exactly is novel in terms of mechanism, performance, or conceptual advance. As it stands, the work appears more technology-oriented than aimed at revealing new physical insights. For instance, how do the modal eigenfunctions of the crystal affect the observed results?\n8. The methodology for measuring the crystal thickness is not described. This is an important parameter that can strongly affect the emission properties and should be explicitly discussed."}, "author_response": "Response to Reviewers\nWe thank the editors and reviewers for their comments and feedback. We have\nincorporated the suggestions of the reviewers into our revised manuscript, and fully\naddressed all comments in a point-by-point form below. For clarity, the reviewers’\ncomments are blue in color, whereas our replies are black in color.\nReviewer #1 (Remarks to the Author):\nThe authors report on observation of an enhancement of coherent X-ray generation\nyield by electrons propagating through crystalline materials (graphite) with extended\nthickness. Up to now, this type of generation was investigated only in materials with\nthickness of below few hundreds of nanometers, while here the comparison of different\nthicknesses up to a bulk material is studied. The authors also give comprehensive\ntheoretical description of the observed phenomena.\nThe main novelty of the manuscript lies in the observation of approx. 10x enhancement\nof X-ray generation yield when the thickness of the generating material increases.\nReply: We thank the reviewer for acknowledging the novelty of our work and the\ncomprehensiveness of our treatment. However, an even more important novelty of our\nwork is fundamental in nature: Our findings overturn the common notion that coherent\nX-rays will be overwhelmed by bremsstrahlung in bulk materials. To ensure this is clear,\nwe have now introduced a parameter that distinguishes a regime where tunable X-rays\nsubstantially dominate bremsstrahlung in bulk materials. This has now been clarified\nin our abstract, and presented in Figs. 1e,f and associated discussion.\nHowever, the method is not really scalable because after a certain thickness, the\nelectrons lose their energy via inelastic scattering with the sample and cannot generate\nX-rays by this method any more.\nReply: We thank the reviewer for this comment. This method of enhancement can in\nfact continue to be scaled indefinitely by increasing the kinetic energy of the incident\nelectron, thereby increasing the interaction length before they lose their energy\nsubstantially. For a fixed kinetic energy, this method is not indefinitely scalable, but\nstill does manage to introduce a substantial order-of-magnitude enhancement that was\nnot available or observed before, as we show in our work. We clarify this now in the\nparagraph eleven of the Results and Analysis section in the main text and newly added\nSupplementary Information Section 11.\nThe observation of coherent X-rays that dominate over the bremsstrahlung background\nis also fundamentally significant as it overturns the prevailing notion that this is\nimpossible in bulk materials. In Figs. 1e,f and its associated discussion in the main text,\nwe introduce a new parameter that quantitatively defines the new regime we have\nbroken into, and explains why others have not discovered or observed it before (i.e.,\ncompared with conventional materials, van der Waals materials are much more likely\nto exhibit sufficiently large values of this parameter to break into the new regime).\nWe also note that our resulting tunable X-ray flux is sufficient to meet the requirements\nfor X-ray spectroscopy at a current of and for X-ray imaging at . This has\n0.4 μA 6.4 μA\nbeen clarified in paragraph eleven of the Results and Analysis section in the main text\nand newly added Supplementary Information Section 11.\nThe methodology used is not different from the one applied in previous publications,\nso the X-rays are detected using a standard EDS detector, which suffers from two\nlimitations. First it only allows to collect the X-rays in a given emission angle and\nsecond, its spectral resolution is quite poor.\nReply: We thank the reviewer for this comment. The focus of our current study on bulk\nmaterials is unique and unprecedented. Our use of a standard EDS detector, with all its\nlimitations, has nevertheless allowed us to demonstrate an unprecedented regime of\ncoherent X-ray generation (coherent X-ray > bremsstrahlung in bulk), as well as order-\nof-magnitude enhancement of the coherent X-ray intensities. Note that the limitations\nof the standard EDS detector do not affect the prospective applications of our\ntechnology, since the standard EDS detector is used here only as a measurement device\nfor our X-rays and not part of any technology.\nIt is indeed possible to achieve better spectral resolution and more versatile detector\nangles using different equipment – but do note the use of better/different equipment\nwould not in itself constitute scientific novelties. This comment has motivated us to\ninclude a passage (paragraph ten) in the Results and Analysis section on alternative\nequipment that can be employed to overcome the limitations of the standard EDS\ndetector.\nFor these reasons I do not think the novelty and significance of the presented results\nwarrant publication in Nature Communications and the manuscript may be better suited\nfor a more specialized journal.\nReply: With the above clarifications and revisions, we hope that the reviewer may now\nconsider our manuscript in a positive light.\nHere are few comments/questions for the authors:\n1. The authors show the comparison of the detected X-ray spectra with theory in\nabsolute units of photons/(s.eV.nA). It is shown that the coherent radiation is\nstronger than the background caused by Brehmstrahlung. However, applicability of\nthis generation method for X-ray spectroscopy, diffraction or imaging requires\nmuch higher photon fluxes.\nReply: We thank the reviewer for asking this question. The tunable X-rays\ngenerated in our work are sufficient for X-ray absorption near edge structure\n(XANES) and X-ray emission spectroscopy (XES). As demonstrated by Review of\nScientific Instruments 85 (2014) 113906, an intensity of\nis adequate for XANES and XES. Under the same current (4 ), the\ntunable X-ray intensity produced across the full parameter0 s.2p a−ce 8in× ou1r0 st updhyo, tuosninsg/\nsb/uslkr/ vedVW materials, ranges from , wh0ic.4h μeAxceeds\nthe needed intensity. 4\n1 −10×10 photons/s/sr/eV\nThe tunable X-rays generated in our work are also sufficient for X-ray imaging.\nNuclear Instruments and Methods in Physics Research A 560 (2006) 589–597\nreports a required flux of for biological and\nintegrated circuit imaging within 30 seconds4. Under an equival2ent current ( ),\nour tunable X-ray source a0c.2hi e−ve0s. 4a ×flu1x0 o pf hotons/s/mm ,\nsubstantially exceeding the reported requirement. 4 6.4 μA 2\n0.9 −12×10 photons/s/mm\nCan the authors compare the coherent emission yield with emission in characteristic\npeaks (e.g. the peak of C at 277 eV)?\nReply: We thank the reviewer for asking this question. We have now added a\ndetailed comparison between the tunable X-ray flux and the characteristic X-ray\nflux in Supplementary Information Section S9.\nAs can be seen, the ratio between tunable X-rays and characteristic peaks varies\nsignificantly depending on the position of the characteristic peak. For example, at\n300 keV electron energy and 2 mm graphite thickness, the flux of the C peak at\n277 eV is 59 times higher than the tunable X-ray. Conversely, under the same\nelectron energy and a 2 mm WSe thickness, the tunable X-ray flux can 𝐾𝐾ex 𝛼𝛼 ceed the\n2. The𝐿𝐿 maximum X-ray emission yield is limited by the electron current, which can\nbe only few hundreds of nA in the FESEM. Could the authors comment in the\nmanuscript what is the maximum theoretical current density which can be applied\nto the graphite sample? This is an important parameter since it limits the\napplicability of the method as a source of X-ray radiation.\nReply: We thank the reviewer for asking this question. The maximum theoretical\ncurrent density which can be applied to the graphite sample is which\nis limited by the temperature rise induced by high-current electron beams.2 For an\nelectron beam with a 1 mm diameter spot size, this corresponds4 t4o ma Ato/taml mcurrent of\n. At this current level, our source can achieve an intensity of\n, approximately times higher than the intensity\nr3e4q umirAe8d for X-ray spectroscopy ( ) – suggesting\nt8h×e w1i0de pahpopltiocnasb/ilsit/ys ro/fe oVur method as a so1u0rc,0e 0 4o0f X-ray radiation.\n0.2 −8×10 photons/s/sr/eV\nThe maximum current density and current were determined through thermal\nanalysis of the temperature rise induced by high-current electron beams, ensuring\nthe crystal remains below its melting point. Structural damage from high-energy\nelectron irradiation occurs at a much higher current density of\n(Journal of Nuclear Materials 412 (2011) 321–326), as the current density is much2\nhigher than the thermal limit, it is therefore not considered a limitin4g0 f0a cmtoAr /inm omur\nanalysis. We first calculated the heat input from the electron beam using Monte\nCarlo simulations and then considered two mechanisms for heat dissipation:\nthermal conduction and thermal radiation. Full details of the thermal simulation\nmethodology are provided in the newly added Supplementary Information Section\n11.\nReviewer #2 (Remarks to the Author):\nThe authors observe tunable X-rays in a previously unreachable regime with high\nelectron scattering, characterized by both slow electron energies and large sample sizes.\nThe findings of this paper are exciting, as they challenge the common belief that X-ray\nsignals might be drowned out by the bremsstrahlung background in highly scattering\nregimes. I would be happy to support the publication of this paper if the following\ncomments are addressed:\nReply: We thank the reviewer for the positive comments and support for the publication\nof our paper. We are glad that our findings were found exciting, particularly in\nchallenging the common belief regarding X-ray signals in highly scattering regimes.\nWe have carefully addressed all the reviewer’s comments in the revised manuscript and\nprovide a detailed point-by-point response below.\n1. To emphasize the notion that X-ray signals might be drowned out by the\nbremsstrahlung background in highly scattering regimes, the authors might consider\nproviding more theoretical work or experimental evidence to support this claim. Are\nthere additional studies on this topic beyond the authors' own previous work?\nReply: We thank the reviewer for asking this question. The tunable X-ray signal\ncan be drowned out by the background when the tunable X-ray intensity is lower\nthan the bremsstrahlung. To emphasize this notion, we have now added suggested\nanalysis using our established theoretical framework in Supplementary Information\nSection S12.\nWe compare the tunable X-ray intensity with bremsstrahlung for two materials:\ngraphite, which is used in our current work, and silicon, which was used in the\nprevious study (Technical Physics Letters 32 (2006) 392–395) that failed to detect\ntunable X-rays from bulk silicon materials. Our simulation results show that the\nratio of tunable X-ray to bremsstrahlung for bulk silicon is only 0.3, whereas for\nbulk graphite the ratio is 5.2 under the identical condition. These findings provide\na theoretical explanation of why detecting tunable X-rays from bulk silicon has been\nexperimentally challenging and was previously considered unfeasible. The detailed\nsimulation results are shown in the newly added Supplementary Fig. S11.\nAt the same time, we have now introduced a novel parameter that quantitatively\ndefines the new regime that we have broken into and explains why others have not\ndiscovered or observed it before in the newly added Figs. 1e,f and its associated\ndiscussion in the main text and Supplementary Information S14.\n2. The critical points of electron energies where bremsstrahlung radiation and X-ray\nsignals intersect could be worthwhile to research. For example, it is suggested to\nstudy (e.g. in theory) the relationship between these critical electron energies and\nsample thickness.\nReply: We thank the reviewer for raising this point. We have included the suggested\nstudy with additional simulations using our theoretical framework in the revised\nSupplementary Information Section S8. For graphite and h-BN, the critical points\nas a function of both electron energy and sample thickness are highlighted in\nSupplementary Fig. S6. These critical points typically occur at low electron energies\nand large crystal thicknesses.\n3. Based on the inset in Fig. 1a, there appears to be an optimal minimal thickness that\nyields maximal intensity. For practical applications, it is also suggested to study (e.g.\nin theory) the dependence of this optimal thickness on electron energy.\nReply: We thank the reviewer for raising this point. We have now included the\nsuggested analysis with additional simulations using our theoretical framework in\nthe revised Supplementary Information Section S10. The dependence of the optimal\ncrystal thickness on electron energy is presented in Supplementary Fig. S10.\n4. In the right panels of Fig. 3b&c, the ratio of the flux between bremsstrahlung and\nX-rays does not always increase as the thickness increases—for example, from 10^-\n7 m to 10^-5 m. This behavior is unusual in this context, and the authors may need\nto provide an explanation for this observation.\nReply: We thank the reviewer for asking this question. The non-monotonic behavior\nof the tunable X-ray to bremsstrahlung flux ratio arises from the non-monotonic\nvariation of bremsstrahlung flux with increasing crystal thickness. This effect arises\nfrom the combined influence of two effects: the electron scattering and the X-ray\nself-absorption, both of which vary with crystal thickness. A detailed explanation\nof this phenomenon is provided in the newly added Supplementary Information\nSection S13.\n5. To enhance the novelty and significance of this work, it is suggested to include more\nrecent advances in free-electron radiation and van der Waals (vdW) or twisted\nstructures. For example, consider referencing works such as PNAS 122,\ne2413336122 (2025), PRL 131, 113002 (2023), and Physical Review Applied 21,\n064034 (2024).\nReply: We thank the reviewer for highlighting these important studies. We have\nnow revised the Introduction section to include these recent advances in free-\nelectron radiation research.\nReviewer #3 (Remarks to the Author):\nThis manuscript „Enhanced tunable X-rays from bulk crystals driven by table-top free\nelectron energies,” presents a study on generation of tunable x-ray sources by virtue on\nelectron beam in SEMs interacting with thick bulk crystals. The results claim to be a\nsignificant improvement over previous studies where the role of Characteristic xray\ndominates over background radiation.\nThe study is an interesting and rather systematic presentation of the role of electron\nvelocity and current on tunable x-ray sources. However at this present form, I cannot\nrecommend it for publication in Nature Communications, due to the lack of several\nimportant clarifications. The work is also not properly inserted in the context of\nprevious works and several important citations are missing here. See my comments\nbelow.\nReply: We thank the reviewer for their praise of our presentation. In the following, we\npresent a detailed, point-by-point response that fully addresses the reviewer’s remaining\nconcerns. In particular, we have ensured that the work is properly inserted in the context\nof previous works, and that important citations have been included. We hope that the\nreviewer may now recommend it for publication in Nature Communications.\n1. The authors demonstrate a surprisingly excellent agreement between their theories\nand the experimental results in Figure 1 and part of Figure 2, and thereafter the\nexplorations go purely theoretical. This is a surprise, as for example other electron\nsources in TEMs could be used as well to test the theory, or even simpler, bulk\nWSe2, hBN, … crystals are easily obtained now adays and are commercially\navailable. Rather counting on theory, the authors would need to test the theory for\nother crystals with experiments.\nReply: We thank the reviewer for raising this point. In accordance with the\nreviewer’s recommendation, we have now included additional experimental data\nalongside theoretical predictions in the revised Supplementary Information Section\nS7. Which includes results obtained using different electron sources (SEM and\nTEM), various crystals (graphite, h-BN, MoSe , and WSe ), and a wide range of\n2 2\nthicknesses (from nanometers to millimeters).\n2. The excellent agreement with theory and experiment is kind of questionable. First\nand least, I would expect a comparison of the theory with various crystal thicknesses\nstarting from thin to thick and compare them for experiments. See for example here:\nFatemeh Chahshouri et al 2022 J. Phys. D: Appl. Phys. 55 145101.\nReply: We thank the reviewer for raising this point. In accordance with the\nreviewer’s recommendation, we have now included a comparison between\ntheoretical predictions and experimental results across a wide range of crystal\nthicknesses, from thin to thick, in Supplementary Information Section S7. Moreover,\nwe cover an even broader thickness range (29 nm to 1 mm) than that explored in\nthe referenced work (656 nm, 1.544 μm, and 2.3 μm).\n3. How is the assumption made in the supplementary meaning that “fluctuations in\nelectron trajectories are small” are compared to the monte carlo simulation of figure\n1a? From this figure, I see quite large fluctuations.\nReply: We thank the reviewer for raising this point. The assumption of small\nfluctuations, as stated in the Supplementary Information Section 1, refers to the\nsmall fluctuations in electron trajectories within one segment between two\nconsecutive collisions. Fig. 1a in the main text presents the cumulative outcome of\nelectron scattering over many such collisions, typically involving hundreds of\nevents. These repeated interactions result in significant overall changes in electron\nvelocity and direction, leading to the appearance of “large fluctuations” mentioned\nby the reviewer. To clarify this, we have now changed the statement to “fluctuations\nin electron trajectory segment between two consecutive collisions are small”.\n4. Equation (2) of the paper does not seem to be entirely correct. The term named E_ks\n(eigenmode of the crystal) is just a function of frequency and comes out of the\nintegral. The remaining integrand is just the Fourier transform of the electron\nvelocity. It is not also clear how time factor is inhered from monte-carlo simulations.\nShould not the Eigenmode functions appear time-dependent?\nReply: We thank the reviewer for this question. The eigenmode of the crystal\nis indeed time-dependent, as it is a function of both photon angular frequency\nand electron position . Since the electron position varies with tim𝑬𝑬e 𝒌𝒌 𝑠𝑠\nduring a trajectory segment – i.e., the free path between two consecutive electro𝜔𝜔n\natom collisions – the te𝒓𝒓r 𝑖𝑖 m(𝑡𝑡 ) cannot be treated 𝒓𝒓a 𝑖𝑖 s( 𝑡𝑡a) constant and pulled𝑡𝑡\nout of the integral. To clarify this to readers, we have now rewritten as in\nall equations.\n𝑬𝑬𝒌𝒌𝑠𝑠[𝒓𝒓𝑖𝑖(𝑡𝑡),𝜔𝜔]\n𝒓𝒓𝑖𝑖 𝒓𝒓𝑖𝑖(𝑡𝑡)\nThe time variable is defined within each electron free path segment, beginning at\n(immediately after the previous collision) and ending at the (the next\ncollision occurs). T𝑡𝑡he interaction time , is determined from the electron velocity\n𝑡𝑡an=d 0the free path length, both of which are obtained from th𝑡𝑡e =M𝑡𝑡o 𝐿𝐿 nte Carlo\nsimulations.\n𝑡𝑡𝐿𝐿\n5. In the introduction under the claim of all tuneable electron-driven light sources, a\nclass of important recent reports on not only designing visible-range light sources\n(Nature communications 10 (1), 599 (2019)), but also using them for spectroscopy\ninside SEMS (Nature Communications volume 16, Article number: 2326 (2025);\nNature Physics 19 (6), 869-876 (2023)) have been ignored. This is not a good signal\ngiven the fact that this technology has gone far more advanced than just controlling\nthe spectral shape, but also to control the spatial and coherence state of light.\nReply: We thank the reviewer for highlighting these important studies. We have\nnow included these references in our introduction of free-electron-driven visible\nlight sources. At the same time, we would also like to emphasize that compared to\nthese works, our work focuses on a very different part of the electromagnetic\nspectrum – the X-ray regime. Beyond controlling X-ray spectra, our study\ninvestigates a regime which was previously considered impractical. This\nbreakthrough enables us to fully leverage the potential of vdW materials and paves\nthe way for the development of tunable, compact, and efficient X-ray sources with\nbroad applications in both fundamental research and industry.\n6. Why the authors have use for their experiments HOPG? This is a highly\ndiamagnetic material and it is not clear if this has an effect.\nReply: We thank the reviewer for this question. We used highly oriented pyrolytic\ngraphite (HOPG) because it is a readily available form of graphite crystal with\nmillimeter-scale thickness. However, HOPG is not essential for tunable X-ray\ngeneration. The experimental results of thin films shown in Fig. 1d, Fig. 2a, and Fig.\n2b of the main text were obtained using exfoliated natural graphite flakes rather\nthan HOPG. To demonstrate the broader applicability of our method, we have now\nincluded additional experimental results in the Supplementary Information Section\nS7 using other van der Waals crystals – h-BN, MoSe and WSe – further\n2 2\nconfirming the generality of our approach.\nAs a diamagnetic material, HOPG possesses no intrinsic magnetic moment and\ntherefore does not influence the interaction between free electrons and the crystal\nlattice, which is the mechanism of tunable X-ray generation. In fact, previous\nstudies on relativistic electron scattering in solids have shown that internal magnetic\nfields have a negligible effect on electron scattering, even in strongly ferromagnetic\nmaterials such as α-Fe (Ultramicroscopy 109 (2009) 154–160).\n7. In overall the manuscript, I encounter in several parts the claim that tuneable x-ray\nsources from bulk crystal is observed here for the first time. But it is not explained\nwhy this is the fact and what has been improved here? I also find this paper rather\ntechnology relevant than explaining the physics behind the observations. For\nexample, how does the modal eigen function affect the results?\nReply: We thank the reviewer for raising these points. An important fundamental\nbreakthrough in our paper is the fact that we have identified and leveraged an\nunprecedented regime where tunable X-rays surpass bremsstrahlung even for bulk\nmedia, overturning the conventional notion that this is impossible for bulk media.\nTo ensure that the above message is clear and that the underlying fundamental\nphysics is emphasized, we have now derived a parameter that quantitatively defines\nthe regime where tunable X-rays can surpass bremsstrahlung significantly – see\nEquation (3) of our revised main text and its surrounding description. We show that\nthis regime is most readily accessible with van der Waals crystals, revealing an\nunprecedented property of van der Waals crystals in the X-ray regime. Our results\nalso explain the historical inability to observe tunable X-rays in conventional\ncrystalline bulk materials, since compared to vdW crystals the parameter is typically\nsmall for these materials. Further details are presented in the main text Figs. 1e, 1f\nand Supplementary Information Section 14.\n8. How do the authors measure the thickness?\nReply: We thank the reviewer for asking this point. The crystal thicknesses were\nmeasured using different techniques depending on the thickness range. For crystals\nthicker than 1 μm, the thickness was directly determined from cross-sectional\nimages obtained via scanning electron microscopy (SEM). For crystals with\nthicknesses between 300 nm and 1 μm, atomic force microscopy (AFM) was used.\nFor thinner crystals (< 300 nm), thickness measurements were conducted using\nconvergent beam electron diffraction (CBED) patterns. To clarify this, we have now\nadded more thickness measurement details for different samples in the\nSupplementary Information Section S6.\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nThe manuscript titled “Enhanced tunable X-rays from bulk crystals driven by table-top\nfree electron energies” presents a study on the generation of tunable X-ray sources via\nelectron beams from scanning electron microscopes (SEMs) interacting with bulk\ncrystals. The authors claim a significant enhancement over previous studies,\nemphasizing the dominance of characteristic X-ray emission over background radiation.\nThe topic is intriguing and the study offers a relatively systematic analysis of the role\nof electron velocity and current in the generation of tunable X-rays. However, in its\ncurrent form, I cannot recommend the manuscript for publication in Nature\nCommunications. Several critical clarifications are missing, and the work lacks proper\ncontextualization with respect to prior literature. Below, I outline my specific concerns:\n1. The authors report excellent agreement between theoretical predictions and\nexperimental results in Figure 1 and parts of Figure 2. However, beyond this point,\nthe manuscript becomes predominantly theoretical. This is surprising, given that\nadditional experimental validation could be readily performed using other electron\nsources (e.g., TEMs), or even with other bulk crystals such as WSe₂ or hBN, which\nare commercially available and widely studied. Rather than relying heavily on\ntheory, the authors should support their claims with broader experimental validation\nacross different material systems.\nReply: We thank the reviewer for raising this point. In accordance with the\nreviewer’s recommendation, we have now included broader experimental\nvalidations in the revised Supplementary Information Section S7. Which includes\nresults obtained using different electron sources (SEM and TEM), various crystals\n(graphite, h-BN, MoSe , and WSe ), and a wide range of thicknesses (from\n2 2\nnanometers to millimeters).\n2. The claimed agreement between theory and experiment warrants deeper scrutiny.\nIn particular, I would expect to see a comparison of theoretical predictions across a\nrange of crystal thicknesses—from thin to thick—and corresponding experimental\ndata. For reference, see: Fatemeh Chahshouri et al., J. Phys. D: Appl. Phys. 55,\n145101 (2022).\nReply: We thank the reviewer for raising this point. In accordance with the\nreviewer’s recommendation, we have now included a comparison between\ntheoretical predictions and experimental results across a wide range of crystal\nthicknesses, from thin to thick, in Supplementary Information Section S7. Moreover,\nwe cover an even broader thickness range (29 nm to 1 mm) than that explored in\nthe referenced work (656 nm, 1.544 μm, and 2.3 μm).\n3. The supplementary material states that \"fluctuations in electron trajectories are\nsmall,\" but this does not appear consistent with the Monte Carlo simulation shown\nin Figure 1a. On the contrary, the figure indicates significant trajectory fluctuations.\nThe authors should address this apparent contradiction and clarify the assumptions\ninvolved.\nReply: We thank the reviewer for raising this point. The assumption of small\nfluctuations, as stated in the Supplementary Information Section 1, refers to the\nsmall fluctuations in electron trajectories within one segment between two\nconsecutive collisions. Fig. 1a in the main text presents the cumulative outcome of\nelectron scattering over many such collisions, typically involving hundreds of\nevents. These repeated interactions result in significant overall changes in electron\nvelocity and direction, leading to the appearance of “large fluctuations” mentioned\nby the reviewer. To clarify this, we have now changed the statement to “fluctuations\nin electron trajectory segment between two consecutive collisions are small”.\n4. Equation (2) appears to contain inconsistencies. Specifically, the term E_ks,\nidentified as the crystal eigenmode, is only frequency-dependent and should factor\nout of the integral. The remaining integrand seems to represent the Fourier\ntransform of the electron velocity. Additionally, it is unclear how time-dependence\nis inherited from the Monte Carlo simulations. Shouldn't the eigenmodes\nthemselves also be time-dependent? This point requires clarification.\nReply: We thank the reviewer for this question. The eigenmode of the crystal\nis indeed time-dependent, as it is a function of both photon angular frequency\nand electron position . Since the electron position varies with tim𝑬𝑬e 𝒌𝒌 𝑠𝑠\nduring a trajectory segment – i.e., the free path between two consecutive electro𝜔𝜔n\natom collisions – the te𝒓𝒓r 𝑖𝑖 m(𝑡𝑡 ) cannot be treated 𝒓𝒓a 𝑖𝑖 s( 𝑡𝑡a) constant and pulled𝑡𝑡\nout of the integral. To clarify this to readers, we have now rewritten as in\nall equations.\n𝑬𝑬𝒌𝒌𝑠𝑠[𝒓𝒓𝑖𝑖(𝑡𝑡),𝜔𝜔]\n𝒓𝒓𝑖𝑖 𝒓𝒓𝑖𝑖(𝑡𝑡)\nThe time variable is defined within each electron free path segment, beginning at\n(immediately after the previous collision) and ending at the (the next\ncollision occurs). T𝑡𝑡he interaction time , is determined from the electron velocity\n𝑡𝑡an=d 0the free path length, both of which are obtained from th𝑡𝑡e =M𝑡𝑡o 𝐿𝐿 nte Carlo\nsimulations.\n𝑡𝑡𝐿𝐿\n5. In the introduction, the authors reference tunable electron-driven light sources but\nfail to cite several recent and important developments—particularly those extending\nbeyond mere spectral tuning to include control over spatial emission and coherence.\nExamples include:\n• Nature Communications 10, 599 (2019)\n• Nature Communications 16, 2326 (2025)\n• Nature Physics 19, 869–876 (2023)\nThese omissions weaken the contextual grounding of the manuscript and overlook\nkey progress in the field.\nReply: We thank the reviewer for highlighting these important studies. We have\nnow included them in our introduction of free-electron-driven visible light sources.\nAt the same time, we would also like to emphasize that our work explores a different\npart of the electromagnetic spectrum – the X-ray regime. Beyond controlling X-ray\nspectra, our study investigates a regime which was previously considered\nimpossible to achieve, namely the regime where tunable coherent X-rays exceed\nbremsstrahlung. This breakthrough enables us to fully leverage the potential of vdW\nmaterials and paves the way for the development of tunable, compact, and efficient\nX-ray sources with broad applications in both fundamental research and industry.\nWe have ensured this is give due emphasis in our abstract, introduction, and the\nresults section of our main text.\n6. The use of highly oriented pyrolytic graphite (HOPG), a strongly diamagnetic\nmaterial, is not justified in the manuscript. The authors should clarify why HOPG\nwas chosen and whether its magnetic properties influence the observed results.\nReply: We thank the reviewer for asking this question. We used highly oriented\npyrolytic graphite (HOPG) because it is a readily available form of graphite crystal\nwith millimeter-scale thickness. However, HOPG is not essential for tunable X-ray\ngeneration. The experimental results of thin films shown in Fig. 1d, Fig. 2a, and Fig.\n2b of the main text were obtained using exfoliated natural graphite flakes rather\nthan HOPG. To demonstrate the broader applicability of our method, we have now\nincluded additional experimental results in the Supplementary Information Section\nS7 using other van der Waals crystals – h-BN, MoSe and WSe – further\n2 2\nconfirming the generality of our approach.\nAs a diamagnetic material, HOPG possesses no intrinsic magnetic moment and\ntherefore does not influence the interaction between free electrons and the crystal\nlattice, which is the mechanism of tunable X-ray generation. In fact, previous\nstudies on relativistic electron scattering in solids have shown that internal magnetic\nfields have a negligible effect on electron scattering, even in strongly ferromagnetic\nmaterials such as α-Fe (Ultramicroscopy 109 (2009) 154–160).\n7. Repetitive and Unsubstantiated Claims of Novelty: Throughout the manuscript, the\nauthors repeatedly claim that tunable X-ray generation from bulk crystals is\ndemonstrated \"for the first time.\" However, this claim is not adequately\nsubstantiated. The authors should clearly articulate what distinguishes this work\nfrom prior studies and what exactly is novel in terms of mechanism, performance,\nor conceptual advance. As it stands, the work appears more technology-oriented\nthan aimed at revealing new physical insights. For instance, how do the modal\neigenfunctions of the crystal affect the observed results?\nReply: We thank the reviewer for this feedback, as it has assisted us to clarify our\nnovelty as well as its underlying physics. A key fundamental breakthrough in our\npaper is the fact that we have identified and leveraged an unprecedented regime\nwhere tunable X-rays surpass bremsstrahlung even for bulk media, overturning the\nconventional notion that this is impossible for bulk media.\nTo ensure that the above message is clear and that the underlying fundamental\nphysics is emphasized, we have now derived a parameter that quantitatively defines\nthe regime where tunable X-rays can surpass bremsstrahlung significantly – see\nEquation (3) of our revised main text and its surrounding description. We show that\nthis regime is most readily accessible with van der Waals crystals, revealing an\nunprecedented property of van der Waals crystals in the X-ray regime. Our results\nalso explain the historical inability to observe tunable X-rays in conventional\ncrystalline bulk materials, since compared to vdW crystals the parameter is typically\nsmall for these materials. Further details are presented in the main text Figs. 1e, 1f\nand Supplementary Information Section 14.\n8. The methodology for measuring the crystal thickness is not described. This is an\nimportant parameter that can strongly affect the emission properties and should be\nexplicitly discussed.\nReply: We thank the reviewer for asking this point. The crystal thicknesses were\nmeasured using different techniques depending on the thickness range. For crystals\nthicker than 1 μm, the thickness was directly determined from cross-sectional\nimages obtained via scanning electron microscopy (SEM). For crystals with\nthicknesses between 300 nm and 1 μm, atomic force microscopy (AFM) was used.\nFor thinner crystals (< 300 nm), thickness measurements were conducted using\nconvergent beam electron diffraction (CBED) patterns. To clarify this, we have now\nadded more thickness measurement details for different samples in the\nSupplementary Information Section S6.\nConclusion\nIn summary, while the manuscript addresses an interesting topic with potential\ntechnological relevance, it requires substantial revisions to clarify key assumptions,\nprovide additional experimental support, and place the findings in proper context with\nrespect to existing literature. I encourage the authors to revise the manuscript\naccordingly and to strengthen both the theoretical and experimental foundations of their\nclaims.\nReply: We thank the reviewer for their valuable feedback. Following the above\nclarifications and revisions in accordance with the reviewer’s recommendations, we\nhope that the reviewer may now recommend our manuscript for publication in Nature\nCommunications."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors replied to all the comments raised during the first round of review satisfactorily. They added a comprehensive sets of data that were requested and improved the explanation of the novelty of the manuscript, including its relation to the state-of-the-art and previous literature. The explanation of the results was improved and is now supported by additional data, which helped to improve clarity of the text. For these reasons I am happy to recommend acceptance of the manuscript for publication in Nature Communications.", "reviewer_2": "I am satisfied with the authors' revision and fully support its publication in Nature Communications as is.", "reviewer_3": "I carefully read the new version of the manuscript. I am impressed by the effort inserted in addressing the comments and particularly the new experiments with different materials. The manuscript is improved significantly and can be published in its present form in Nature Communications.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

Decision letter