Orientation-dependent mutual crystalline and amorphous order in a single phase solid

Domain: physics
Published: 2026-02-12
Editorial outcome: major_revision

Abstract
Amorphous materials distinguish themselves from crystalline materials by lacking long-range order while retaining structural order at the local scale (2–5 Å). However, the complexity in topological and chemical order prevents current characterization tools from fully unveiling the structure in disordered materials. Consequently, the nature of medium-range order in amorphous materials has remained elusive. The Zachariasen and crystal competing models have been proposed to describe disordered phases and have both been verified through synthesis and characterization. The main difference between them is thought to be whether the amorphous phase shows medium-range order. Here we demonstrate a form of organized inorganic matter that is amorphous in two dimensions, while exhibiting long-range order and a high degree of crystallinity in the third. The structure consists of periodically stacked 2-dimensional amorphous Nb-W-O monolayers without long-range in-plane order. The unique periodic and therefore crystalline stacking along one principal axis enables direct imaging and revealed that the amorphous Nb-W-O monolayers formed in agreement with the Zachariasen model for 2 dimensions. Our findings show that the gap between crystalline and amorphous materials does not only depend on medium-range order but can also apply to principal dimensions within the same solid.

Introduction
Amorphous materials have received much interest due to their complexity and unique chemical structure and properties. In contrast to crystalline phases that show translation symmetry on nanometer to micrometer length scales, amorphous material lacks such long-range order while retaining local order at atomic distances 1–6. Despite efforts to decipher the structure of amorphous materials by electron diffraction, the direct imaging of amorphous phases remains a challenge 5,7–9. By taking advantage of the 2-dimensional nature of some materials, single-layer amorphous materials, since the first discovery by Huang 8,9 as the thinnest glass, have expanded greatly including 2D amorphous carbon 5,10. Nevertheless, efforts to elucidate the structure of 3-dimensional amorphous materials usually lead to the question of whether the particular amorphous phase shows medium-range order 6,11–15, a fundamental consideration in the long-lasting discussion on the gap between amorphous and crystalline materials. Here, we present a material that is amorphous in the x-y plane while being completely ordered, and therefore crystalline, along the z-axis (Fig. 1a–c). The periodicity along the third-dimensional axis enabled the direct imaging of the amorphous 2D Nb-W-O monolayers, which are found to follow Zachariasen’s model 7,16,17 rather than the crystal-competing model 18–20. The amorphous layers consist of MO6 (M=Nb/W) octahedral building blocks with short-range order, but without translational order on the medium- and long-range. In the third dimension, the amorphous layers stack regularly with correlation lengths of a few hundred nanometers. The finding of such unique structure enables advanced insight for the boundary between amorphous and crystalline phases beyond the debate of medium-range order.

Results
The amorphous-crystalline Nb-W-O phase was prepared by pulsed laser deposition of stoichiometric crystalline Nb18W16O93 (prepared from Nb2O5 and WO3) onto Nb-doped SrTiO3 substrates (details in Methods section). SrTiO3 substrates with different orientations, i.e., the (001), (011), and (111) terminal planes, were used and the morphologies of as-grown Nb-W-O on different substrates are shown in Fig. 1d–l. Scanning electron microscopy (SEM) results reveal 2, 1 and 3 orientational growth of Nb-W-O nanorods on Nb-doped SrTiO3 (001), (011) and (111) substrates, respectively. Considering the similar lattice constant of the c axis of stoichiometric Nb18W16O93 (3.951 Å) and the lattice constant of Nb-doped SrTiO3 (3.905 Å), epitaxial growth of a crystalline phase Nb-W-O was hypothesized. On SrTiO3 (001) substrates, the Nb-W-O nanorods grew parallel to the substrate surface in two orthogonal orientations (x’ and y’ directions), caused by the two available directions for epitaxial growth. On SrTiO3 (011) substrates, nanorod growth occurred in the x’ direction only, leading to a single orientation along the substrate surface. In contrast, for SrTiO3 (111) substrates Nb-W-O nanorods grew out-of-plane in 3 distinct directions at a certain fixed angle with respect to the substrate surface. The 3-fold point symmetry of the nanorod growth orientation matches the C3 rotational symmetry present on the SrTiO3 (111) plane (Supplementary Note 2 and Figures. S1-S2). The angle is determined to be 35.2°, in agreement with the x’, y’ and z’ growth directions.

The atomic arrangement of the as-grown Nb-W-O nanorod phase on the different SrTiO3 substrates was characterized by Scanning Transmission Electron Microscopy (STEM). For a nanorod on SrTiO3 (011) substrate, the transverse section of Nb-W-O nanorods in Fig. 2a shows a fairly regular distribution of atom columns over the two-dimensional plane, but without an observable long-range periodicity. The Fourier transform image of this transverse section of Nb-W-O nanorods (Fig. 2b) with its broad continuous halo confirm the absence of long-range order and, thus, indicates a planar distribution of atom columns that is amorphous in structure. The related longitudinal section of Nb-W-O nanorods (in Fig. 2c) shows clear translational periodicity in the stacking of the Nb-W-O layers. The Fourier transform indicates the periodic stacking of atom columns along the [001] growth direction of the nanorods (Fig. 2d), in close agreement with the assumption of epitaxial growth described above. The layer spacing (3.905 Å) was inherited from the lattice constant of the (001) plane of SrTiO3 (3.905 Å). However, the atomic arrangement of the atom columns in the [001] direction forms a straight line that results from the amorphous nature within the (001) plane. This unique structure is different from the typical Nb-based nanorods (nanocrystal) 21–23, and in niobium tungsten oxide materials synthesized by traditional calcination (tetragonal tungsten bronze structure with defects) 24–42.

The interface (zoomed in from Fig. 2e) between the SrTiO3 (001) substrate and the as-grown Nb-W-O nanorods in Fig. 2f consists of two atomic layers of a semi-perovskite structure formed by high Z contrast atomic columns, i.e., Nb and W, followed by densely packed layers with random in-plane atomic arrangements. The first semi-perovskite Nb-W-O layer on SrTiO3 (001) substrate seems to have grown epitaxially, although the A site cations from the ABO3 perovskite structure are mostly missing, as evidenced by the lower brightness of the A site. Furthermore, atomic resolution energy dispersive X-ray spectrometry (EDX) results show both Nb and W appearing at the B sites of the perovskite structure at the interface (Supplementary Note 3, Figs. S3–S5 and Table S1). A defect is formed at the step on the vicinal surface of the SrTiO3 (001) substrate, as indicated by the yellow circle in Fig. 2f, to lower the mechanical strain between the layers, as Nb-W-O is thermodynamically unable to form a relaxed perovskite structure 24. Despite the occurrence of initial epitaxial growth in the first layer exhibiting a clear lattice structure, the atomic arrangements gradually lose coherence in the subsequent layers, and no translational order is observed. The FIB cut schematics of the above STEM analysis are shown in Supplementary Note 4, Fig. S6.

To further identify the structural features in the as-grown nanorods, the short-range order was evaluated by synchrotron X-ray pair distribution function (PDF) analysis. In Fig. 2g, the PDFs of the Nb-W-O nanorods on all three SrTiO3 substrate orientations show similar peaks located at ~2.1 and ~2.8 Å, corresponding to the M-O and M-M (M=Nb/W) bond lengths, respectively. However, the peaks are broad, suggesting a high degree of disorder. The peaks at ~3.95 Å in all three samples represent the M-M distances of the layer spacing and this is observed up to distances of 15 Å (Fig. S7a), corresponding to 4 unit-cell layers. Signal from SrTiO3 substrate (peaks at ~3.5 Å presents Ti-Ti bond) also appears in the PDF results. The PDF results simulated from the STEM images are shown in Supplementary Note 5, Fig. S8–10 and only reveal the distance distribution between the metal ions. The conventional Nb18W16O93 crystal exhibits multiple peaks distributed over distance till 60 Å, while in strong contrast the Nb-W-O nanorods on SrTiO3 (001) and (011) substrates show relatively flat lines after 10 Å. These results confirm the 2D amorphous nature of the transverse section of Nb-W-O nanorods. In Fig. 2h, i, extended X-ray absorption fine structure (EXAFS) measurements are shown which corroborate the short-range order. The Nb and W spectra showed the typical features of NbO6 43 and WO6 44 octahedrons. The intermolecular Nb-O and W-O distances are smaller than values commonly reported in literature 43,44, which suggest that the M-O octahedrons are distorted. The X-ray absorption near edge structure (XANES) spectra of Nb and W shown in Figure. S7b, c reveals a higher oxidation state as compared to the metallic state, further supporting the M-O bond formation. Based on these results, it can be concluded that despite the loss of long-range order, short-range order was retained on the length scale of the MO6 octahedrons.

The medium-range order was compared for as-grown nanorods on SrTiO3 (001) (Fig. 3a) and SrTiO3 (011) substrates (Fig. 3b), as well as its crystalline counterpart 42 (Fig. 3c). The cation arrangements in tetragonal tungsten bronze NbxW1-xO6-½x usually consist of ring-like motifs with the number of atomic columns ranging from 3 to 5. Two distinct types of five-atom ring structures can be distinguished, depending on whether the pentagonal motif contains an additional atomic column at its center 24,45–47 (Supplementary Note 6 and Fig. S11). Based on this knowledge of NbxW1-xO6-½x, the frequency of occurrence of specific ring-like motifs was quantified, formed by MO6 octahedrons, depending on their size and their in-plane rotational angle. These motifs are denoted as (a, b), where a represents the number of atomic columns forming the ring, and b represents the number of atomic columns in the center of the ring (Supplementary Note 7, Fig. S12). In crystalline Nb18W16O93, the number ratio between the different ring motifs is fixed to the ratio 2: 1: 2 for (3,0): (4,0): (5,0)+(5,1), respectively. More detailed analysis is available in Figs. S13–S19. The frequency of occurrence of these rings was quantified for the as-grown Nb-W-O nanorod phase on two different SrTiO3 substrate orientations in Fig. 3d. A more detailed analysis is shown in Figs. S20–S33. The as-grown Nb-W-O samples exhibit different frequencies of occurrence of the (3,0), (4,0), (5,0), and (5,1) rings, also in comparison to crystalline bulk Nb18W16O93. Moreover, the as-grown Nb-W-O nanorods on SrTiO3 (001) and SrTiO3 (011) also exhibit (6,0), (6,1), (7,0), and (7,1) ring motifs, which have never been observed before in the Nb-W-O system 21. The assemblies of (3,0), (4,0), (5,0), and (5,1) rings are expected to show C4 rotational symmetries, respectively. This is similar to crystalline Nb18W16O93 in which (3,0), (4,0), (5,0), and (5,1) rings only show rotational angles of 90°, 45°, 90°, and 90°, respectively. In contrast, here, the rotational angles of the (3,0), (4,0), (5,0), and (5,1) ring-like motifs in Fig. 3e–h are randomly distributed in both samples. This is in sharp contrast with the crystalline starting material (Nb18W16O93) for PLD (Supplementary Note 8, Figs. S34–40 and Table S2). These results suggest the loss of long-range orders in the as-grown Nb-W-O phases. Furthermore, additional analysis on the order parameter 48 (Supplementary Note 9, Figs. S41–S44, Table S3) of the basic units (different rings) for Fig. 3a, b reveals that the order parameters of every different ring in the 2D amorphous plane of Nb-W-O nanorods on both SrTiO3 (001) and (011) substrates are quite small, which indicates high randomness of the amorphous plane of Nb-W-O nanorods on SrTiO3 (001) and (011) substrates. The results of this order parameter analysis underline the difference between the 2D amorphous plane of in Nb-W-O nanorods and the typical quasicrystals 49,50. Due to the inconsistency of the comparison for both cases and the low order parameters for every ring structure in these 2D amorphous plane of Nb-W-O nanorods, the future development of advanced models for analyzing degree of order along different orientations is required. After detailed analysis (Supplementary Note 10, Fig. S45) on the STEM images of 2D amorphous layers of Nb-W-O nanorods (Fig. 3a, b), we determine that only a few percent medium-range order exists in the 2D amorphous plane of Nb-W-O on SrTiO3 (011) and SrTiO3 (001) substrates. As the medium-range order area proportions are very small in combination with the small order parameters, we can conclude that the 2D plane of Nb-W-O nanorods is amorphous with continuous random network structure 5,8,9. This randomness of the plane would be similar when we use the same growth conditions even with differently oriented SrTiO3 substrates.

The atomic occupancy of Nb and W was further characterized by high-resolution energy dispersive X-ray spectrometry (HR-EDX) mapping, as shown in Fig. 3i. HR-EDX provides laterally local elemental abundances from atomic columns into the sample surface. The selected STEM area is shown in Fig. S46. In the mapped areas, no in-plane regular spatial ordering of atomic columns was found. The magnified image in Fig. 3j contains 10 metal occupation sites that form one (5,1) and two (4,0) ring motifs. The elemental Nb fractions at the positions of the outer atomic columns of the (5,1) ring vary from 0.27 to 0.45. In contrast, the Nb fraction at the location of the center atomic column is 0.57. Another (5,1) ring motif shown in Fig. S47 exhibits a different trend (Supplementary Note 11) because 2 outer ring locations are Nb-rich. Both these (5,1) rings differ strongly from their crystalline counterparts 51,52. Moreover, the existence of two neighboring (4,0) rings also illustrates the different assembly of ring motifs compared to that in its crystalline counterparts. The atomic positions show no long-range periodic order, and the atomic sites seem to be randomly occupied by Nb and W. In the as-prepared sample, even if a ring is formed similar to a Nb18W16O93 crystal, the site occupancy changes greatly with the loss of order in Nb/W. It can thus be concluded that the in-plane arrangement of metal atomic columns within the Nb-W-O layer is random and that the different rotational angles follow Zachariasen’s model (continuous random network) 7,16,17. Despite the long- and medium-range disorder, the as-grown Nb-W-O samples do show short-range order in the form of the NbO6 and WO6 octahedral building blocks.

Concerning the vertical stacking of these amorphous layers, Nb-W-O samples are studied in detail by STEM analysis in Fig. S48. The layer spacings from these three Nb-W-O samples grown on (001), (110), and (111) oriented surfaces show same layer spacings of 3.91 ± 0.05 Å (Supplementary Note 12 and Tables S4–S12). This spacing is similar to the d spacing of the [001] direction of SrTiO3 and therefore could be a sign of single-directional epitaxial growth. It is concluded that the as-grown samples show the unique combination of 2D amorphous structures, in combination with crystalline stacking at the atomic scale in the third dimension. The stability of the Nb-W-O samples under the electron beam (analysis condition of STEM) was investigated by video recording during STEM analysis, which demonstrated stability of the structures under electron beam beyond 120 seconds (Supplementary Note 13, Fig. S49, Video S1). To confirm the bonding between the Nb-W-O layers, integrated differential phase contrast (IDPC) STEM and XPS were performed on Nb-W-O nanorods on SrTiO3 (001) substrate sample (Supplementary Note 14, Figs. S50–S51). IDPC results suggest that M-O-M bonds do exist in between the disordered Nb-W-O layers. XPS results confirm that the oxidation state of niobium is Nb5+ and tungsten is W6+, which suggests MO6 octahedrons are forming the Nb-W-O disordered layers while M-O-M bonds are in between the Nb-W-O disordered layers.

Following characterization of the local structure by advanced electron microscopy, the global structure of this phase was further elucidated by 3-dimensional high-resolution X-ray reciprocal space mapping (3DRSM) analysis. 3DRSM is a common technique for thin film sample analysis to directly reflect the large area X-ray coherence of the thin film (Nb-W-O nanorods in our case) through its reciprocal space map (Supplementary Note 15, Fig. S52). Since current understanding of the reciprocal space of amorphous phase is limited, first a detailed reciprocal space simulation was carried out of the periodical stacking of the amorphous layers (Supplementary Note 16, Figs. S53–S55). The simulated 3D reciprocal space map of the as-constructed phase shows solid circle planes in parallel in 3D, a line structure in the qx-qz plane (2D) and a solid circle in qy-qz plane (2D) (Fig. 4a–c). In Fig. 5d, experimental 3D RSM results of the Nb-W-O nanorods on SrTiO3 (011) substrate show a line structure in the qx-qz plane and line structures in different qx-qy slices. Thus, the experimental 3DRSM results match with the simulated 3DRSM results and suggest that the Nb-W-O nanorods on SrTiO3 (011) substrate form a crystal stack of amorphous layers, in good agreement with the STEM results. To further confirm the structure of the Nb-W-O nanorods, a series of 3DRSM simulations of the Nb-W-O nanorods on (011), (001) and (111) substrates were compared in detail with the experimental 3DRSM results.

SEM analysis of the Nb-W-O nanorods on SrTiO3 (011) substrate (Fig. 1h) indicates that the nanorods preferentially grow in a single orientation with the long axis parallel to the [100]-direction of the SrTiO3 (011) substrate. Thus, the simulation of the 3DRSM of Nb-W-O nanorods on SrTiO3 (011) substrate is based on the single-direction crystal stacking of the amorphous layers. For easier comparison between the simulated 3D RSM’s and the experimental results, the simulated 3D RSM’s are rotated to the coordinate system to match both 3DRSM analyses. The 3DRSM’s of Nb-W-O nanorods on SrTiO3 (011) substrate are simulated according to the x*-y*-z* coordinate system, as shown in Fig. 4d. Thus, the simulated 3DRSM of Nb-W-O nanorods on SrTiO3 (011) substrate shows planes in parallel with qx-qz and qy-qz planes. However, only one plane in each direction was captured in the analysis range, as shown in Fig. 4g, j. For the experimental 3DRSM analysis of Nb-W-O nanorods on SrTiO3 (011) substrate, the area around the point of the SrTiO3 (011) plane in reciprocal space is measured, as shown in Fig. 5d1. The qx-qz view of the experimental 3DRSM shows a broad intensity distribution over a wider range of qz (2.3–3.6 Å−1), but with a finite qx around 0 Å−1. This indicates a well-defined d-spacing along the x-axis that is oriented parallel to the substrate in the [100] direction, and an absence of long-range order along the z-axis ([011]-direction of this substrate). In Fig. 5d2–d5, the qx-qy slices of experimental 3DRSMs of the Nb-W-O nanorods on SrTiO3 (011) substrate in 4 ranges of qz (0.25–0.26 Å−1, 0.29–0.30 Å−1, 0.32–0.33 Å−1, and 0.35–0.36 Å−1) exhibit the same pattern over a wider range of qy with a fixed finite qx around 0 Å−1, suggesting a crystal structure consisting of an amorphous yz layer and a fixed layer spacing along the x-axis. These findings agree well with the STEM observations and simulation comparison shown in Fig. 5a (qx-qz projection and qx-qy slices obtained from Fig. 4j). More details about the 3D RSM simulations and experiments are in Supplementary Note 16 and Figs. S56–S71.

As shown in Fig. 1e, the SEM image of Nb-W-O nanorods on SrTiO3 (001) substrate shows the nanorod growth along 2 orthogonal directions, i.e., parallel to substrate [100] and [010] directions. Thus, two crystal stacking of the amorphous layer with perpendicular placement was used as simulation model for 3DRSM (shown in Fig. 4e). The coordinate system of the 3DRSM analysis for Nb-W-O nanorods on SrTiO3 (001) substrate is the same x*-y*-z* coordinate system, as discussed above. Thus, the simulated 3DRSM of Nb-W-O nanorods on SrTiO3 (001) substrate shows planes in parallel with qx-qz and qy-qz planes. However, only one plane in each direction was captured in the analysis range, as shown in Fig. 4h, k. The qx-qz view of the 3DRSM (shown in Fig. 5e1) with the same intensity range in qz as the previous case including the point of the SrTiO3 (001) plane in the reciprocal space, indicating long-range disorder along that axis perpendicular to the substrate surface. In Fig. 5e2-e5, qx-qy slices of the 3DRSMs of the Nb-W-O nanorods on Nb-doped SrTiO3 (011) substrate in 4 different qz ranges (0.25–0.26 Å−1, 0.27–0.28 Å−1, 0.30–0.31 Å−1, 0.33–0.34 Å−1, respectively) show similar patterns with broad intensity distributions over wide ranges of qy (for qx=0) and qx (for qy=0). These intersecting line patterns confirm the absence of long-range order in either the xz or the yz plane, in close agreement with the visible microstructure of the alignment of Nb-W-O along one of two axes. This case can be thought of as two domains of the material shown in panel (a) rotated by 90 degrees. As shown in Fig. 5b, simulated qx-qz projection and qx-qy slices obtained from Fig. 4k match well with the experimental 3DRSM analysis results (Fig. 5e), which further validates directly the plane structure in 3D reciprocal space, which matches the simulated 3DRSM of the crystal stack of the amorphous layers.

Lastly, SEM analysis of the Nb-W-O nanorods on SrTiO3 (111) substrate is shown in Fig. 1k. It reveals three distinct growth directions for Nb-W-O, each under a certain tilt and rotation angle with respect to the substrate. As shown in Fig. 1j, the Nb-W-O nanorods are 35.2˚ rotated to the substrate and 90˚ to each other (in 3D). The simulation model was assembled by a combination of 3 crystal stackings of the amorphous layer with 3 directions as the x*, y* and z* axes, as shown in Fig. 4f. The simulated 3DRSM of Nb-W-O nanorods on SrTiO3 (111) substrate shows planes in parallel with qx-qz, qy-qz and qx-qy planes. However, only one plane in each direction was captured in the analysis range, as shown in Fig. 4i, l. In Fig. 5f, the experimental 3DRSM results were collected in skew geometry with the scattering vector rotating perpendicular to the (001) plane of the SrTiO3 (111) substrate. While the qx-qz view (Fig. 5f1) appears featureless apart from the strong substrate (001) reflection, in-plane RSM slices in the qx-qy plane (Fig. 5f2–f5) reveal information that qx-qz view cannot visualize: there are two orthogonal scattering features similar to the RSMs of Nb-W-O nanorods on SrTiO3 (001) as shown in Fig. 4e2–e5. This implies that the nanorods are epitaxially grown parallel to the [001] orientation of the (111)-terminated substrate. As shown in Fig. 5c, simulated qx-qz projection and qx-qy slices obtained from Fig. 4l match well with the 3D RSM analysis results (Fig. 5f). Thus, the observation of thin, sheet-like intensity distributions in reciprocal space points to a unique class of materials that is amorphous in two dimensions and crystalline in the third dimension.

To understand in detail the complex structure of the Nb-W-O nanorods on SrTiO3 (111) substrate, two extra 3DRSM analyses were performed, in which the scattering vector was directed perpendicular to the (111) plane (direction 1) and the (110) plane (direction 2) of the SrTiO3 (111) substrate (Figs. S65–S66). Based on the experimental 3D RSM results on Nb-W-O nanorods on SrTiO3 (111) substrate for the three different directions ([001], [110] and [111] directions of SrTiO3), it can be confirmed that the planes (1xx), (x1x), (xx1), (xx0), (0xx) and (x0x) all exist in the reciprocal space of the Nb-W-O nanorods on SrTiO3 (111) substrate. Thus, the parallel planes pattern of the multilayered 2D amorphous structure with a crystalline axis (Nb-W-O nanorods) can be proven only by the combined experimental results of the 3D RSM of the Nb-W-O nanorods on SrTiO3 (111) substrate in 3 different analysis directions. Moreover, the reflection high-energy electron diffraction (RHEED) data (Supplementary Note 18 and Figs. S72–S73) independently confirms this conclusion. Since 3DRSM and RHEED analyses are measuring the global information (analysis range shown in Fig. S74) of the structure, it can be confirmed that the Nb-W-O nanorods exhibit a homogeneous structure as the crystal stack of the amorphous layers. This unprecedented and unique structure of periodically stacked 2D amorphous layers is further confirmed by the STEM images and the corresponding FFT images in Figs. S75–S79 and Supplementary Note 19.

In summary, we report a unique phase consisting of periodically stacked amorphous Nb-W-O monolayers. The phase has 2 amorphous and 1 crystalline dimension and differs from the commonly known systems with medium-range order. The in-plane amorphous layer shows short-range order by forming MO6 octahedral building blocks, while a lack of atomic and elemental ordering occurs on the medium and long range. The amorphous layer is able to stack for several hundred nanometers, which yields the long-range order in the vertical direction. The formation of this unique metastable structure is defined by the choice of substrate and probably due to a non-equilibrium low-temperature reaction state and anisotropic ion diffusion pathways, leading to the formation of crystalline stackings of amorphous Nb-W-O monolayers. Our work sheds light on the intricate interplay between order and disorder in solid matter and contributes to the understanding of the structural properties of amorphous/crystalline systems beyond the debate of medium-range order.

Methods
Target Preparation
The Nb-W-O target for Nb-W-O samples (by pulsed laser deposition) was prepared by a two-step solid-state synthesis method. First, Nb2O5 (Sigma Aldrich, ~325 mesh, 99.9% trace metals basis) and WO3 (Sigma Aldrich, powder, 99.995% trace metals basis) were mixed in a 9:16 molar ratio, which is the stoichiometric ratio of Nb18W16O93 and calcined in air at 1000 °C for 2 h. The sintered Nb-W-O powder was then pressed into a pellet and calcined at 1200 °C for 12 h to obtain the Nb-W-O target with a 61% density relative to the theoretical density of 5.72 g cm-3.

Nanorod film growth
Nb-W-O thin films were grown by pulsed laser deposition (PLD) on conducting Nb-doped (0.5 wt%) single-crystalline SrTiO3 (001), (110), and (111) (CrysTec) substrates from the above target using a fluency of 2.3 J cm-2 and a repetition rate of 2 Hz. Before heating, the background gas was adjusted to 0.2 mbar O2. During growth, the temperature was kept at 650 °C for 3600 deposition pulses and afterward cooled down to room temperature with a cooling rate of 10 °C per minute. In this study, we compared thin films with similar volumes grown on Nb-doped SrTiO3 (001), (110), and (111) substrates.

Structural characterization
Electron diffraction analysis of the surface crystal structure was performed during the growth of the Nb-W-O films by reflection high-energy electron diffraction (RHEED) at an acceleration voltage of 30 kV. The morphology of the films was characterized by scanning electron microscopy (SEM, Zeiss Merlin HRSEM). A Bruker D8 Discover X-ray diffractometer with Cu-Kα1 radiation (wavelength: 1.5406 Å) and an Eiger 2R 500K hybrid photon counting area detector were used for reciprocal space mapping (RSM). On the incident beam side, this unique system used a rotating anode generator (TXS-HE), a hybrid (parallel-focusing) Montel multilayer mirror optic, and an asymmetric Ge(022) channel-cut monochromator, and a circular 1 mm diameter pinhole collimator to shape and condition the X-ray beam. The specular θ–2θ scans were performed with a step size of 0.01° and a counting time of 1 s per step. For those measurements, the detector was operated in 0D mode with a small region of interest (13×61 pixels, pixel size 75×75 µm2). A multilevel rotary absorber was used to automatically attenuate the intensity of the incident beam to optimize the effective dynamic range of each measurement and to avoid detector saturation. The RSMs were constructed from sets of omega rocking curves collected with a step size of 0.015° while the detector remained stationary and operated in 2D snapshot mode. The large field of view facilitated this at a sample-to-detector distance of 220 mm. Since the incident beam is highly collimated into a point-like focus at the sample location, it is possible to reconstruct a 3-dimensional (3D) reciprocal space map with this setup. The atomic resolution images of the crystal structures were obtained by scanning transmission electron microscopy (STEM, Titan Themis TEM with CEOS probe and image aberration corrector operated at 200 KeV). The Nb:W ratios in the films were measured by Energy dispersive X-ray spectrometry (EDX, Oxford Instruments; detector: X-Max 80 mm2 and large-area silicon drift detectors (SDDs); software: Aztec 3.3 SP1), and the valence state of Nb and W were confirmed by X-ray photoelectron spectroscopy (XPS, Omicron Nanotechnology GmbH surface analysis system with a photon energy of 1486.7 eV, Al Kα X-ray source). The TEM/STEM EDS atomic-resolution mapping images were collected using a CEOS probe-corrected FEI Themis TEM instrument (electron accelerating voltage of 300 kV). The probe convergence angle was 17.8 mrad, and the probe current was ~90 pA for STEM imaging and EDS acquisition.

All synchrotron-based measurements were performed at the Advanced Photon Source (APS) in Argonne National Laboratory. High-energy X-Ray diffraction (XRD) and pair distribution function (PDF) were measured at the Sector 11-ID-C beamline, utilizing a wavelength of 0.1173 Å. Additionally, X-Ray absorption spectroscopy (XAS) data was gathered at the 12-BM-B beamline, using a Si (111) double-crystal monochromator.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General comment: This paper deals with the elaboration and deep structural analysis of samples made of periodic stacking of niobium and tungsten oxide layers without in plane long range order. The authors describe this 1D ordering without in plane long range order as a new state of condensed matter, which they call “amorphous-crystalline”. Such ambition is of course very high and it corresponds to noteworthy results.\nSome experimental aspects support the author’s assumption. Nevertheless, the manuscript is too hard to read, and figures are often very difficult to understand. The writing of all the paper has to be reconsidered in order to be more readable. One of the aspects that makes reading difficult is the continuous transition, throughout the text, between the orientation of the columns of atoms and the crystallographic orientation of the nanorods. In addition, often the authors refer their scientific comments to supplementary data or notes. This increases the difficulty for the readers. This aspect must be carefully reconsidered case by case.\nA large part of the experimental results is strongly related to crystallography. As a result, a stronger full crystallographic notation and description must be used. Due to the fundamental influence of the crystallographic orientation of the substrate surface, all the crystallographic results (in the text and in the figures) have to be presented with respect to the crystallographic axis of these substrates instead of using the qx, qy and qz vector components. These components are related to the measurement conditions, and therefore their meaning often changes, sometimes even in the same figure.\nPoints to be improved or answered\n1- Page 4: according to page 4, the image reported fig2a, is a plane view and in this case (SrTiO3 (011) substrate) the Nb-W-O nanorods have grown in the plane, along the [100] direction (see Fig. 1g). It seems to mean that the atom columns are along the [011] direction. This must be described in an easier understanding way.\n2- On Fig. 2, the images reported in a, b, c and d are corresponding to observation of the columns that have grown on the SrTiO3(011) substrate. Please, separate this case from that one reported in fig. 2e, that is related to the interface with a SrTiO3(001) substrate. In the current state, Fig. 2 is really hard to understand. Moreover, the main crystallographic directions must be reported on the images.\n3- The contrast observed on Fig. 2c must be discussed. How can a 1D atomic ordering results on such contrast in the image in the TEM? Such image, that is fundamentally an interferences image, comes from a volume of matter. Please give some explanations of the observation in direct space (high resolution TEM image) of a periodic arrangement in transmission mode in such a case as only a 1D periodicity. Moreover, the Fourier transform (Fig. 2d) of this image seems to evidence the presence of regularly spaced points along the straight diffuse lines.\n4- Page 10 and 11, Fig.4: 3D RSM are recorded on the sample. According to the size of the x-ray beam, each RSM is due to a large number of columns. How the authors have separated the influence of both the intra-nanorods disorder from the rotational disorder coming to the fact that a large number of nanorods are simultaneously probed?\n5- Fig. 4 is very hard to read. As written above, the first improvement is to replace the qx, qy and qz vectors notation by the true crystallographic directions in the reciprocal space. The relationships between the Q-vector components and the crystallographic directions depend on the growth direction, that itself differs when the three types of substrate cutting are considered. In the present form, the notations reported in this figure are too confusing.", "reviewer_2": "The manuscript entitled “Crystalline or Amorphous? A Matter of Perspective” by Xia et al. demonstrates an interesting inorganic matter which is amorphous in two dimensions but crystalline in the third. The crystalline (including quasicrystal) and amorphous structures are two states for solid matters. They are commonly believed to be mutually exclusive that a state of matter cannot be both crystalline and amorphous at the same time. Usually, a partially crystalline or amorphous matter is just a composite of purely crystalline and amorphous parts. Hence, the matter demonstrated in this manuscript presents experimentally a novel state which is only ordered in certain dimensions.\nIn fact, such a state of matter has been theoretically proposed as paracrystalline. The term paracrystal refers to a state of matter with less than three-dimensional order, characteristic of a true crystal (Ref: https://www.merriam-webster.com/dictionary/paracrystal). Paracrystals are often used in materials science to understand the transition between crystalline and amorphous states. Although the paracrystalline matter has been demonstrated microscopically in many papers (Science 335, 950, (2012); Nature 599, 605 (2021); JAP 90, 4438 (2001)), a direct observation of such matter in bulk is still missing. In this manuscript, we can see the micrometer-scale formation of paracrystalline matter, and the structural characterizations provide compelling evidence in a degree of intermediate order between crystalline and amorphous materials. This manuscript contributes significantly to the existing knowledge on the state of solid matter.\nReviewer has carefully examined the manuscript and supports its publication in Nature Communications. However, it will be shown in the following comments why this matter should be considered as paracrystalline rather than amorphous in one direction.\n(1) In Fig. 1, Nb-W-O nanorod films were deposited on crystalline substrates of different orientations. It is a smart approach to demonstrate the difference in structures between different orientations of a matter by showing the various growth morphologies. However, why do these rods all have a diameter around 50 nanometers? If it is truly amorphous in the x-y plane, the diameters of these rods should be infinite or distributed randomly.\n(2) What would happen if the films were deposited on an amorphous substrate?\n(3) In Fig. 2a and b, the author tries to prove the amorphous structure of the x-y plane by showing its STEM image and the corresponding FFT pattern. However, when the review carefully checks them, some tiny crystalline features can be observed as shown in the following Figures 1R, 2R and 3R. Hence, the x-y plane cannot be understood as fully amorphous but paracrystalline phase.\nFig. 1R. (a) STEM image of Fig. 2a in manuscript and (b) its corresponding halo FFT pattern. If we tuned the intensity of the FFT pattern, some diffraction spots corresponding to crystalline phase can be observed.\nFig. 2R. If we zoom in Figure 2a, a lot of tiny crystals can be observed.\nFig. 3R. Another region where the tiny crystals can be observed. Such regions are distributed over the whole image.\n(4) The most important feature of amorphous matter differing from crystalline matter is the glass transition. Can the glass transition be observed in this matter by differential scanning calorimetry? It not, then this matter is paracrystalline rather than amorphous.\nBy the way, some typos can be seen in the manuscript. “F PDF of Nb-W-O nanorods”.\nIn summary, the state of matter in this manuscript is still unclear. The author needs to verify which kind of structure it is, amorphous or paracrystalline?", "reviewer_3": "This paper is interesting, though perhaps not as generally applicable as the authors imply in their abstract. The manuscript is well-written, and the characterization work seems solid. However, as I describe below, the authors need to update their knowledge of oxide structures beyond the year 1932 when Zachariasen published his seminal work on glass structures.\nMy primary issue with this paper is that it’s not as original as the author’s claims imply. While the atomic resolution characterization in the current work is excellent, I have seen very similar structures (seemingly ordered along one axis) in several previous manuscripts: (none of which are cited by the authors)\n- Miran MozeticÏ, Uros Cvelbar, Mahendra K. Sunkara, and Sreeram Vaddiraju, A Method for the Rapid Synthesis of Large Quantities of Metal Oxide Nanowires at Low Temperatures, Adv. Mater. 17, 2138 (2005).\n- Subhra Jana and Robert M. Rioux, Seeded growth induced amorphous to crystalline transformation of niobium oxide nanostructures, Nanoscale, 4, 1782 (2012).\n-Sophia B. Betzler, Ai Leen Koh, Bettina V. Lotsch, Robert Sinclair, Christina Scheu, Atomic Resolution Observation of the Oxidation of Niobium Oxide Nanowires: Implications for Renewable Energy Applications, ACS Appl. Nano Mater, 3, 9285 (2020).\nGiven that the current paper primarily focuses on structure, I expect to see a much deeper dive into other imaging studies on similar nanowires / materials.\nIn fact, I believe the most similar crystallographic system to the current study isn’t mentioned by the authors at all: 2D quasicrystals / (semi)rational approximates in ternary oxides. Figures 3a, b, and especially Figure 3c look like 2D decagonal quasicrystals to me. I suspect there may be additional disorder introduced by substrate and growth effects which may add some randomness to the quasicrystal lattice. For example, in Figure 2a, the (pseudo)coherent domain length appears to be only ~4 nm. Either way, the authors certaintly need to explain exactly how their proposed structural models are similar to and distinct from 2D stacked quasicrystals. Here are a few references to get them started (there are many possible references here)\n-https://link.springer.com/content/pdf/10.1007/978-3-642-58434-3_3 (textbook chapter)\n-Stefan Förster et al., Quasicrystals and their Approximants in 2D Ternary Oxides, physica status solidi (b) 257, 1900624 (2020).\n-Catalina Ruano-Merchan et al., Stoichiometry-Driven Formation of Two-Dimensional Ternary Oxides: From Quasicrystal Approximants to Honeycomb Lattice Structures, J. Phys. Chem. C 128, 8839 (2024).\nTherefore, I cannot accept this manuscript for publication in its current form. The authors need to identify precisely how their new observations and models extend the existing literature of semi-ordered ternary oxides.\nMinor comments\n“Scanning electron microscopy (SEM) results reveal 2, 1 and 3 orientational growth of Nb-W-O nanorods on Nb-doped SrTiO3 (001), (011) and (111) substrates, respectively.” This statement is very unclear – what does “2 orientational growth” etc. mean? While I think I see what the authors are getting at, they should clarify that they mean families of nanowire orientation.\nFigure 4 caption is way too long. All the captions are too long, but especially this one. Concisely describe your observations and move discussion to the main text.\n\"... defined by the choice of substrate, rather than that it is the result of an uncontrolled local phenomenon.\" Could be clarified.", "reviewer_4": "The authors have fabricated a unique three-dimensional structure composed of stacked two-dimensional amorphous layers in the Nb-W-O system. By taking advantage of the unidirectional periodicity of this structure, they performed direct imaging of the amorphous structure using state-of-the-art STEM techniques. This approach, combined with X-ray diffraction, EXAFS, and RSM analyses, enables a detailed structural characterization. A key strength of the study is that the electron beam was aligned parallel to the periodic axis, allowing unambiguous imaging of the amorphous structures. The experimental work is thorough, and the discovery of a 3D structure possessing 2D amorphous character is noteworthy. However, I have several concerns as listed below:\n1.The authors should address the relationship between their findings and previous work, particularly Ref. 8 (Huang et al., Nano Lett. 12, 1081 (2012)), where a two-dimensional amorphous SiO2 film was directly imaged using STEM and shown to reproduce the classic Zachariasen model. Although the current study focuses on a three-dimensional structure, the amorphous nature is still essentially two-dimensional. The authors should clearly articulate the scientific advancement beyond previous studies.\n2.In the introduction, the authors refer to the longstanding debate on whether three-dimensional amorphous materials exhibit medium-range order (MRO). However, the present structure is fundamentally a two-dimensional amorphous material, and thus may not directly address this question. The authors are encouraged to comment on this point and clarify their position.\n3.The manuscript claims that the amorphous layers exhibit only short-range order (SRO), without MRO. Is this conclusion fully justified? For example, the reduced pair distribution function G(r) shown in Fig. 2f extends only up to 5 angstrom, making it difficult to conclusively determine the absence of MRO. Furthermore, the peak near 4.8 angstrom might correspond to in-plane amorphous features and could be indicative of MRO, especially since it exceeds typical interatomic distances.\n4.In Figs. 3a and 3b, STEM images of samples grown on SrTiO3 (001) and (011) substrates are shown, respectively. Fig. 3b appears more ordered than Fig. 3a. Could this reflect a difference in the degree of medium-range order? The authors should address this observation and provide their interpretation.\n5.It is possible to extract atomic coordinates from the bright spots in the STEM images and calculate the reduced pair distribution function G(r). I recommend comparing this with the G(r) obtained from XRD measurements. This comparison would help disentangle the contributions from amorphous in-plane structure and periodicity along the stacking direction.\n6.It remains unclear what conceptual or structural insights this study offers beyond the compatibility with Zachariasen's model. The authors are encouraged to more clearly state the broader implications of their findings for the structural science of amorphous materials, particularly in the summary section."}, "author_response": "Response to Reviewer #1\nGeneral comment: This paper deals with the elaboration and deep structural analysis\nof samples made of periodic stacking of niobium and tungsten oxide layers without in\nplane long range order. The authors describe this 1D ordering without in plane long\nrange order as a new state of condensed matter, which they call “amorphous-\ncrystalline”. Such ambition is of course very high and it corresponds to noteworthy\nresults.\nSome experimental aspects support the author’s assumption. Nevertheless, the\nmanuscript is too hard to read, and figures are often very difficult to understand. The\nwriting of all the paper has to be reconsidered in order to be more readable. One of\nthe aspects that makes reading difficult is the continuous transition, throughout the text,\nbetween the orientation of the columns of atoms and the crystallographic orientation\nof the nanorods. In addition, often the authors refer their scientific comments to\nsupplementary data or notes. This increases the difficulty for the readers. This aspect\nmust be carefully reconsidered case by case.\nA large part of the experimental results is strongly related to crystallography. As a result,\na stronger full crystallographic notation and description must be used. Due to the\nfundamental influence of the crystallographic orientation of the substrate surface, all\nthe crystallographic results (in the text and in the figures) have to be presented with\nrespect to the crystallographic axis of these substrates instead of using the qx, qy and\nqz vector components. These components are related to the measurement conditions,\nand therefore their meaning often changes, sometimes even in the same figure.\nResponse to general comment: We sincerely thank Reviewer 1 for the positive\nevaluation. We fully agree that the different coordinate systems, and corresponding\ndescriptions, make it difficult for readers to understand. Following your insights, we\nunify the coordinate system in all the characterizations. Firstly, we introduced the main\ncoordinate system x*-y*-z* from Fig. 1. We defined the two main coordinate systems\nin Supplementary Note 1 for easier understanding.\nThe x*-y*-z* coordinate system is defined:\nx* is the [100] orientation of SrTiO ,\n3\ny* is the [010] orientation of SrTiO ,\n3\nz* is the [001] orientation of SrTiO .\nx y z\nq is defined as a certain crystallographic direction of SrTiO which is used as the\nz 3\n1\ncalibration peak for each High resolution XRD test (3D RSM test),\nq and q are defined as the simplest crystallographic directions of SrTiO which are in\nx y 3\nthe perpendicular plane to the defined q and allow the input X-ray to detect the\nz\nnanorods film.\nBased on those, we revised Fig. 2 and Fig. 4 by adding the coordinate system x*-y*-\nz* for coherent description on different characterization results. Furthermore, we gave\nthe definition on the 2 coordinate systems we used for descriptions in the captions of\nnew Fig. 1 and new Fig. 4 for better understanding.\nBased on those, we have revised Fig. 1, Fig. 2, and Fig. 4 and added more information\nto the main text (line 80 to 96) for easier understanding, as shown in Figure R1-2,5-6.\nThe modification of the supporting information related to this part can be seen in\nSupplementary Note 1.\nSupplementary note 1\nIn this work, two coordinate systems are defined for coherent description though\ndifferent characterization and simulation results.\nThe x*-y*-z* coordinate system is defined:\nx* is the [100] orientation of SrTiO ,\n3\ny* is the [010] orientation of SrTiO ,\n3\nz* is the [001] orientation of SrTiO .\n3D RSM simulation results.\nThe q - q - q coordinate system is defined:\nx y z\nq is defined as a certain crystallographic direction of SrTiO which is used as the\nz 3\ncalibration peak for each High resolution XRD test (3D RSM test),\nq and q are defined as the simplest crystallographic directions of SrTiO which are in\nx y 3\nthe perpendicular plane to the defined q and allow the input X-ray to detect the\nz\nnanorods film.\nThe q - q - q coordinate system is used in the description of 3D RSM test and the\nx y z\nmatched simulation results. Therefore, q - q - q coordinate systems are different in the\nx y z\nfive 3D RSM tests:\n2\n1. For the 3D RSM test of Nb-W-O nanorods on SrTiO (011) and its matched\n3\nsimulation, q is defined as [011] orientation of SrTiO . Then, q and q are aligned\nz 3 x y\nwith [100], [0-11] orientation of SrTiO , respectively.\n3\n2. For the 3D RSM test of Nb-W-O nanorods on SrTiO (001) and its matched\n3\nsimulation, q is defined as [001] orientation of SrTiO . Then, q and q are aligned\nz 3 x y\nwith [100], [010] orientation of SrTiO , respectively.\n3\n3. For the 3D RSM test of Nb-W-O nanorods on SrTiO (111) at testing direction 1\n3\n(SrTiO (111) peak as the calibration peak of the 3D RSM test) and its matched\n3\nsimulation, q is defined as [111] orientation of SrTiO . Then, q and q are aligned\nz 3 x y\nwith [1-10], [11-2] orientation of SrTiO , respectively.\n3\n4. For the 3D RSM test of Nb-W-O nanorods on SrTiO (111) at testing direction 2\n3\n(SrTiO (011) peak as the calibration peak of the 3D RSM test) and its matched\n3\nsimulation, q is defined as [011] orientation of SrTiO . Then, q and q are aligned\nz 3 x y\nwith [100], [0-11] orientation of SrTiO , respectively.\n3\n5. For the 3D RSM test of Nb-W-O nanorods on SrTiO (111) at testing direction 3\n3\n(SrTiO (001) peak as the calibration peak of the 3D RSM test) and its matched\n3\nsimulation, q is defined as [001] orientation of SrTiO . Then, q and q are aligned\nz 3 x y\nwith [1-10], [110] orientation of SrTiO , respectively.\n3\nnanorod films, a 3D Structure of Nb-W-O nanorods (z axis is the growth direction), b\nTransverse section of Nb-W-O nanorods, c Longitudinal section of Nb-W-O nanorods,\nd Schematic of the Nb-W-O nanorods on SrTiO (001) substrate, e-f Top and side view\n3\nthe Nb-W-O nanorods on SrTiO (011) substrate, j Schematic of the Nb-W-O nanorods\n3\non SrTiO (111) substrate, k-l Top and side view SEM images of the Nb-W-O nanorods\n3\non SrTiO (111) substrate. (In this work, x*, y*, z* are defined as the [100], [010], [001]\n3\ndirection of SrTiO , details are described in Supplementary Note 1.)\n3\nand in this case (SrTiO3 (011) substrate) the Nb-W-O nanorods have grown in the\nplane, along the [100] direction (see Fig. 1g). It seems to mean that the atom columns\nare along the [011] direction. This must be described in an easier understanding way.\nResponse to comment 1: We agree that “plane view” and “side view” are not very\nclear to the reader. Thus, we modified Fig.2, changed the terms for each STEM image\nand added schematic for the FIB cut direction in each STEM image. We also added\nsubstrate information in the new Fig. 2 for better reading. The FIB cutting direction is\nalso explained as a Supplementary Note 4.\nFig.2a is captured at “transverse section of Nb-W-O nanorods on SrTiO (011)\n3\nsubstrate” and “[100] projection of the SrTiO (011) substrate”. Fig.2c is captured at\n3\n“longitudinal section of Nb-W-O nanorods on SrTiO (011) substrate” and “[0-11]\n3\nprojection of the SrTiO (011) substrate”. Fig.2e is captured at “[100] projection of the\n3 3\n(011) substrate are along the [100] direction of SrTiO and the Nb-W-O nanorods on\n3 3\nThe modification of the manuscript related to this part can be seen in line 97 to 112\nand Fig.2. The modification of the support information related to this part can be seen\nin Supplementary Note 4.\nfilms, a STEM image of the transverse section of Nb-W-O nanorods on SrTiO (011)\n3\nsubstrate, b Fast Fourier transform image of a, c STEM image of the longitudinal\nsection of Nb-W-O nanorods on SrTiO (011) substrate, d Fast Fourier transform image\n3\nof c, e STEM image of Nb-W-O nanorods on SrTiO (001) substrate, f Zoomed in\ntwo directions in Nb-W-O. The blue box represents the first epitaxial Nb-W-O layer.\nThe yellow circle indicates the step of the substrate.), g PDF of Nb-W-O nanorods on\nSrTiO (001), SrTiO (011), and SrTiO (111) substrates, h-i EXAFS data of Nb (h) and\n3 3 3\nW (i) of Nb-W-O nanorods on SrTiO (001) substrate.\nSample in Fig.2a was cut along the SrTiO₃ (100) plane using FIB to expose this\ntransverse section of the nanorods (shown in Figure S6a). Therefore, in Fig. 2a, the\ntransverse section of Nb-W-O nanorods on the SrTiO₃ (011) substrate lies parallel to\nthe SrTiO₃ (100) plane.\nSample in Fig. 2c was cut along the SrTiO₃ (0-11) plane using FIB to expose this\nlongitudinal section of the nanorods (shown in Figure S6b). Therefore, in Fig. 2c, the\n6\nlongitudinal section of Nb-W-O nanorods on the SrTiO₃ (011) substrate lies parallel to\nthe SrTiO₃ (0-11) plane.\nSample in Fig. 2e was cut along the SrTiO₃ (100) plane using FIB to expose both the\ntransverse and longitudinal sections of the nanorods (shown in Figure S6c). Therefore,\nin Fig. 2e, the transverse and longitudinal sections of Nb-W-O nanorods on the SrTiO₃\n(001) substrate are both lies parallel to the (010) and (100) plane of the SrTiO₃ (001)\nsubstrate due to the orthogonal in plane growth of thw Nb-W-O nanorods on the SrTiO₃\n(001) substrate.\nFigure R3 (Figure S6) Focused ion beam (FIB) cut schematic for a sample 1 present\nin Fig.2 a, b sample 2 present in Fig.2 c, c sample 3 present in Fig.2 e.\nComment 2: On Fig. 2, the images reported in a, b, c and d are corresponding to\nobservation of the columns that have grown on the SrTiO3(011) substrate. Please,\nseparate this case from that one reported in fig. 2e, that is related to the interface with\na SrTiO3(001) substrate. In the current state, Fig. 2 is really hard to understand.\nMoreover, the main crystallographic directions must be reported on the images.\nshown in Figure R2. In the new Fig. 2, we added substrate information on each STEM\nimage. Also, we added the crystallographic orientation of the SrTiO to explain the\n3\nprojection of the STEM images for easier understanding.\nComment 3: The contrast observed on Fig. 2c must be discussed. How can a 1D\natomic ordering results on such contrast in the image in the TEM? Such image, that is\nfundamentally an interferences image, comes from a volume of matter. Please give\nsome explanations of the observation in direct space (high resolution TEM image) of\na periodic arrangement in transmission mode in such a case as only a 1D periodicity.\nMoreover, the Fourier transform (Fig. 2d) of this image seems to evidence the\npresence of regularly spaced points along the straight diffuse lines.\nResponse to comment 3: All TEM images are HAADF-STEM images, which is an\nincoherent imaging technique without interference. It directly reveals atomic columns\nand enables atom-by-atom analysis. FFT pattern is likely due to slight instrument\ninstability.\nComment 4: Page 10 and 11, Fig.4: 3D RSM are recorded on the sample. According\nto the size of the x-ray beam, each RSM is due to a large number of columns. How\nthe authors have separated the influence of both the intra-nanorods disorder from the\nrotational disorder coming to the fact that a large number of nanorods are\nsimultaneously probed?\nResponse to comment 4: We agree with reviewer 1 that a large number of nanorods\nare simultaneously probed. We roughly calculated the number of the nanorods\ndetected to be 104 (Figure S71) by the diameter of X-ray beam (2.92 mm) and\ndiameter of the nanorod (30 nm).\nThe observed disorder of the nanorods from RSM has two possible origins:\n1. the intra-nanorods disorder;\n2. the intrinsic disorder in the nanorod.\nFirst, we observe and confirm the disorder along the transverse section of the\nnanorods in the STEM images in Fig. 2.\nSecond, the nanorods in the detection range can be observed in the SEM images\n(Figure R4). All the nanorods are grown in a fixed direction:\n3 3\nalong SrTiO [100] orientation on SrTiO (011) substrate,\n3 3\nalong SrTiO [100], [010] and [001] orientations on SrTiO (111) substrate.\n3 3\nFor samples grown on SrTiO (001) and SrTiO (011) substrates, the intra-nanorod\n3 3\ndisorder due to rotational disorder is not possible, since the nanorods are grown\nparallel to the substrate.\nRotational disorder is only possible for samples grown on SrTiO (111) substrates,\n3\nalthough the nanorods in this sample are fixed in three directions (SrTiO [100], [010]\n3\nand [001] orientations) and no rotation is observed.\nFigure R4 a-c Low magnification SEM image of Nb-W-O nanorods on SrTiO (001),\n3\n(011) and (111) substrates.\nComment 5: Fig. 4 is very hard to read. As written above, the first improvement is to\nreplace the qx, qy and qz vectors notation by the true crystallographic directions in the\nreciprocal space. The relationships between the Q-vector components and the\ncrystallographic directions depend on the growth direction, that itself differs when the\nthree types of substrate cutting are considered. In the present form, the notations\nreported in this figure are too confusing.\nResponse to comment 5: We agree that the simulation and experimental analysis of\nthe reciprocal space structural information investigated by 3D RSM and RHEED\nanalyses of the Nb-W-O nanorods is an important section of our manuscript, and we\nneed to expand this section in detail in the main text. Thus, we revised this section into\ntwo separate Figures in the revised manuscript to emphasize the importance of this\nsection and to improve it’s readability.\nIn the new Fig.4 (Figure R5) we added the schematic of the 3D RSM analysis and the\n3D RSM simulation in 3D RSM analysis area. We transferred the 3D RSM analysis\nresults to the additional figure. The schematic of the 3D RSM analysis will help the\nreader to understand the relationships between x*, y*, z* and q , q , q coordinates.\nx y z\nx* is the [100] orientation of SrTiO ,\n3\ny* is the [010] orientation of SrTiO ,\n3\nz* is the [001] orientation of SrTiO .\nx y z\nq is defined as a certain crystallographic direction of SrTiO which is used as the\nz 3\ncalibration peak for each High resolution XRD test (3D RSM test),\nq and q are defined as the simplest crystallographic directions of SrTiO which are in\nx y 3\nthe perpendicular plane to the defined q and allow the input X-ray to detect the\nz\nnanorods film. The detailed explanation of the defined coordinate systems is in\nSupplementary Note 1.\nIn the new Fig.5 (Figure R6) we added the q -q projection and q -q slice at different\nx z x y\nq of the 3D RSM simulation results for direct comparison to the 3D RSM experimental\nz\nresults.\nO nanorod films, a 3D RSM simulation for the stack of single amorphous layers, b q -\nx\nq projection of a, c q -q projection of a, d-f Schematic of 3D RSM analysis of Nb-W-\nz y z\nO nanorods on SrTiO (011), (001) and (111) substrates respectively*, g-i 3D RSM\n3\nsimulation for Nb-W-O nanorods on SrTiO (011), (001) and (111) substrates\n3\nrespectively, j-l Results of g-i in 3D RSM analysis area respectively. (*In this work, q ,\nx\nq , q are defined by the calibration peak of SrTiO which is applied for each 3D RSM\ny z 3\nanalysis, as described in Supplementary Note 1.)\nfilms, a-c q -q projection and q -q slice at different q of the 3D RSM simulation\nx z x y z\nresults in the 3D RSM analysis area for Nb-W-O nanorods on SrTiO (011), (001) and\n3\n(111) substrates (Fig.4 j-l) respectively, d-f q -q projection and q -q slice at different\nx z x y\nq of the experimental 3D RSM of Nb-W-O nanorods on SrTiO (011), (001) and (111)\nz 3\nsubstrates respectively.\nWe still retain “q , q , q ” in the figure based on the standard convention for RSM\nx y z\nFigures as shown for example in different references (Nature Communications,\n2023, 14, 8496; Journal of Applied Crystallography, 2014, 47(2), 762–769). When we\nreport a RSM image, we usually observe the crystallographic information from the\nsubstrate as well as the film, and it is not clear to use only one of their crystallographic\norientations as the axis. Thus, we added the explanation of q , q , q coordinates for\nx y z\neach 3D RSM simulation and experimental analysis for easier understanding.\nThe modification of the manuscript related to this part can be seen in line 241 to 334\nand Fig.4-5.\nGeneral comment: The manuscript entitled “Crystalline or Amorphous? A Matter of\nPerspective” by Xia et al. demonstrates an interesting inorganic matter which is\namorphous in two dimensions but crystalline in the third. The crystalline (including\nquasicrystal) and amorphous structures are two states for solid matters. They are\ncommonly believed to be mutually exclusive that a state of matter cannot be both\ncrystalline and amorphous at the same time. Usually, a partially crystalline or\namorphous matter is just a composite of purely crystalline and amorphous parts.\nHence, the matter demonstrated in this manuscript presents experimentally a novel\nstate which is only ordered in certain dimensions.\nIn fact, such a state of matter has been theoretically proposed as paracrystalline. The\nterm paracrystal refers to a state of matter with less than three-dimensional order,\ncharacteristic of a true crystal (Ref: https://www.merriam-\nwebster.com/dictionary/paracrystal). Paracrystals are often used in materials science\nto understand the transition between crystalline and amorphous states. Although the\nparacrystalline matter has been demonstrated microscopically in many papers\n(Science 335, 950, (2012); Nature 599, 605 (2021); JAP 90, 4438 (2001)), a direct\nobservation of such matter in bulk is still missing. In this manuscript, we can see the\nmicrometer-scale formation of paracrystalline matter, and the structural\ncharacterizations provide compelling evidence in a degree of intermediate order\nbetween crystalline and amorphous materials. This manuscript contributes significantly\nto the existing knowledge on the state of solid matter.\nResponse to the general comment: We agree with reviewer 2 that the structure of\nNb-W-O nanorods falls under the definition of paracrystal. The definition of paracrystal\nis “a solid body with less than three-dimensional order characteristic of a true crystal”.\n(Ref: https://www.merriam-webster.com/dictionary/paracrystal) Basically, everything\nbetween pure amorphous phase and crystal phase fits this definition. Thus, it does not\nconflict with our structural description (amorphous in two dimensions but crystalline in\nthe third). Furthermore, a 2D continuous random network amorphous structure also\nallows small proportion of medium-range order inside of its structure, as confirmed by\nVoyles et al. (Journal of Applied Physics, 2001, 90 (9), 4437.): “…is a signature of\nstructures with little or no medium-range order, such as a continuous random network”.\nTherefore, we believe that our study provides new insight to distinguish the boundary\nbetween amorphous and crystalline cases, for which the direction matters. This is\nbeyond current understanding in the debate how medium range disorder determines\nthe boundary between amorphous and crystalline materials.\nhas been described in the new supplementary notes 8 and 9, and Figures S38-S42.\nSupplementary note 8\nOrder parameter calculation for 2D amorphous plane of the Nb-W-O nanorods\nThe scalar order parameter described by Tsvetkov quantifies the ordering of nematic\nmolecules behaving as rod-like ellipsoids or rigid rods (Molecular Crystals and Liquid\nCrystals, 2002, 381(1), 1–19.) :\n1\n𝑆 = (3𝑐𝑜𝑠!𝜃−1) 𝑆𝑁8.1\n2\nwhere 𝜃 is the angle between the long molecular axis and the optic axis, shown in\nFigure R7.\nFigure R7 (Figure S38) Schematic of angle 𝜃 between the long molecular axis and\nthe optic axis.\nFor a uniaxial rod-like ellipsoids or rigid rods, the order parameter of the liquid crystal\nsystem can be described by a function with only one variable (𝜃) which presents the\nangle between the long molecular axis and the optic axis. Because of the inversion\nsymmetry of the rod-like ellipsoids or rigid rods, 𝜃 and 𝜋−𝜃 are indistinguishable.\nThus, second order Legendre polynomial can be used to describe the order parameter\nof rod-like ellipsoids or rigid rods.\nBased on the above definition, the order parameter of different rings in Nb-W-O 2D\namorphous plane can also be described.\nused as the most ordered direction to easily calculate the order parameter by using\nthe angle between the long molecular axis and the optic axis. However, in the 2D\namorphous plane of the Nb-W-O nanorods, multiple ring like structures are the basic\nunit, which does not have a certain axis that can be used as the most ordered direction.\nThus, we need to assume any direction can be the most ordered direction. Thus, we\ndefine the angle 𝛼 as an angle between the ordered direction and the normal direction.\nAnd we define the angle 𝜃 as the angel between the direction of every ring and the\n\"\nnormal direction (𝑖 ∈ [1,𝑚] & 𝑖 ∈ ℤ,𝑚 is the total number of the rings), as shown in\nFigure R8.\nFigure R8 (Figure S39) Schematic of the order parameter definition for the (3,0)\nrings in the 2D amorphous plane of the Nb-W-O nanorods.\nOrder parameter for (3,0) rings\nAs shown in Figure R9, (3,0) ring is a regular triangle and has c4 symmetry in the\nNb W O crystal. Thus, in principle, we need to use the twelfth order Legendre\n18 16 93\npolynomial to describe the order parameter, which is a complex equation. In this case,\nwe can process the obtained 𝜃 by the following equation:\n($,&)\"\n𝑛𝜋 𝜋\n𝜃( = 𝜃 − >𝑛 ∈ ℤ,0 ≤ 𝜃( ≤ A 𝑆𝑁8.2\n($,&)\" ($,&)\" 6 ($,&)\" 6\nAfter processing the obtained 𝜃 , we can use the first order Legendre polynomial\n($,&)\"\nto write the function between order parameter and 𝛼:\n∑) 𝑐𝑜𝑠 (12(𝜃( −𝛼) 𝜋\n𝑆 (𝛼)=B\n\"*( ($,&)\"\nB 𝛼 ∈ D0, A 𝑆𝑁8.3\n($,&)\n𝑚 6\nAnd we can describe the order parameter:\n∑) 𝑐𝑜𝑠 (12(𝜃( −𝛼) 𝜋\n𝑆 = max>𝑆 (𝛼)A = maxHB\n)*( ($,&))\nBI 𝛼 ∈ D0, A 𝑆𝑁8.4\n($,&) ($,&)\n𝑚 6\nTo verify the above equation, we calculated the maximum and minimum of the equation\nSNx.4.\nWhen the distribution of 𝜃( are a concentrated distribution into one angle 𝜃,\n($,&))\n𝑆 (𝛼) has its maximum when 𝛼 = 𝜃 :\n($,&)\n∑) 𝑐𝑜𝑠 (12(𝜃−𝛼) ∑) 1\n𝑆 (𝛼)=B )*( B = B )*( B= 1 𝑆𝑁8.5\n($,&)\n𝑚 𝑚\nWhen the distribution of 𝜃( are an even distribution in the range of 𝜃( ,\n($,&)) ($,&))\n𝑆 (𝛼) has its maximum and α can be any value in its’ range:\n($,&)\n+\n∑) cos (12(𝜃−𝛼) ∫, -. cosQ12𝜃( R𝑑𝜃(\n𝑆 (𝛼)=B )*( B=O &-. ($,&)) ($,&)) O\n($,&)\n𝑚 𝑚\n1\n(sin(2𝜋−12𝛼)+sin(12𝛼))\n12\n=O O = 0 𝑆𝑁8.6\n𝑚\nThus, when the distribution of 𝜃( are a concentrated distribution, 𝑆 is 1.\n($,&)) ($,&)\nWhen the distribution of 𝜃( are an even distribution, 𝑆 is 0. The above results\n($,&)) ($,&)\nshow that the equation of 𝑆 can describe the order parameter of (3,0) rings nicely.\n($,&)\n18 16 93\ncrystal.\nOrder parameter for (4,0) and (5,0/1) rings\nOrder parameters for the other rings are described similar to the (3,0) rings.\nAs shown in Figure R9, (4,0) ring is a square and has c8 symmetry in the Nb W O\n18 16 93\ncrystal. Thus, in principle, we need to use the eighth order Legendre polynomial to\ndescribe the order parameter, which is a complex equation. In this case, we can\nprocess the obtained 𝜃 by the following equation:\n(/,&)\"\n𝑛𝜋 𝜋\n𝜃( = 𝜃 − >𝑛 ∈ ℤ,0 ≤ 𝜃( ≤ A 𝑆𝑁8.7\n(/,&)\" (/,&)\" 4 (/,&)\" 4\nAfter processing the obtained 𝜃 , we can use the first order Legendre polynomial\n(/,&)\"\nto write the function between order parameter and 𝛼:\n∑) 𝑐𝑜𝑠 (8(𝜃( −𝛼) 𝜋\n𝑆 (𝛼) = B\n\"*( (/,&)\"\nB 𝛼 ∈ D0, A 𝑆𝑁8.8\n(/,&)\n𝑚 4\nAnd we can describe the order parameter:\n∑) 𝑐𝑜𝑠 (8(𝜃( −𝛼) 𝜋\n𝑆 = max>𝑆 (𝛼)A = maxHB\n\"*( (/,&)\"\nBI 𝛼 ∈D0, A 𝑆𝑁8.9\n(/,&) (/,&)\n𝑚 4\nAs shown in Figure R9, the direction of (5,0) rings and (5,1) rings are the same. Thus,\nwe consider using one order parameter to describe the 5 side rings ((5,0/1) rings). As\n16\nshown in Figure R9, (5,0/1) ring is a regular pentagon and has c4 symmetry in the\nNb W O crystal. Thus, in principle, we need to use the twentieth order Legendre\n18 16 93\npolynomial to describe the order parameter, which is a complex equation. In this case,\nwe can process the obtained 𝜃 by the following equation:\n(0,&/()\"\n𝑛𝜋 𝜋\n𝜃( = 𝜃 − >𝑛 ∈ ℤ,0 ≤ 𝜃( ≤ A 𝑆𝑁8.10\n(0,&/()\" (0,&/()\" 10 (0,&/()\" 10\nAfter processing the obtained 𝜃 , we can use the first order Legendre polynomial\n(0,&/()\"\nto write the function between order parameter and 𝛼:\n∑) 𝑐𝑜𝑠 (20(𝜃( −𝛼) 𝜋\n\"*( (0,&/()\"\n𝑆 (𝛼) = B B 𝛼 ∈ D0, A 𝑆𝑁8.11\n(0,&/() 𝑚 10\nAnd we can describe the order parameter:\n∑) 𝑐𝑜𝑠 (20(𝜃( −𝛼) 𝜋\n\"*( (0,&/()\"\n𝑆 = max>𝑆 (𝛼)A= maxHB BI 𝛼 ∈ D0, A 𝑆𝑁8.12\n(0,&/() (0,&/() 𝑚 10\nResults for order parameter calculation\nIn Fig.3, we collected the direction of (3,0), (4,0) and (5,0/1) rings (angle 𝜃 in Figure\nR2). Thus, we can use them for the calculation of the order parameter.\nFigure R10 a-c (Figure S41) Order parameter curve with altered α for (3,0), (4,0) and\n(5,0/1) rings respectively in 2D amorphous plane of Nb-W-O nanorods on SrTiO\n3\n(001) and (011) substrate.\nAs shown in Figure R10, each curve has two maximum points, the angle 𝛼 at 𝑆\n)23\nmeans the actual ordered direction for its matched rings. Thus, the order parameter of\n(3,0), (4,0) and (5,0/1) rings in 2D amorphous plane of Nb-W-O nanorods on SrTiO\n3\n(001) and (011) substrates (Fig.3 a-b) are listed in Table 1.\nNb-W-O nanorods on SrTiO (001) and (011) substrates\n3\n𝑺 𝑺 𝑺\n(𝟑,𝟎) (𝟒,𝟎) (𝟓,𝟎/𝟏)\nNb-W-O on SrTiO (001) 0.031 0.139 0.077\nplane of Nb-W-O nanorods on both SrTiO (001) and (011) substrates are quite small,\n3\nwhich shows high randomness of the amorphous plane of Nb-W-O nanorods on SrTiO\n3\n(001) and (011) substrates. Higher order parameters are revealed in (3,0) ring on\nSrTiO (011) substrate and (4,0) ring on SrTiO (001) substrate and the order\n3 3\nparameter for (5,0/1) ring is similar in both cases. Due to the inconsistency of the\ncomparison of the order parameters in both cases and the low order parameters for\nevery ring structure in the 2D amorphous plane of Nb-W-O nanorods, the randomness\nof 2D amorphous plane of Nb-W-O nanorods can be similar and high for both cases.\nSupplementary note 9\nmedium-range order area analysis\nFigure R11 a-b (Figure S42) medium-range order analysis for Fig.3 a-b respectively.\nBased on the examples shown by reviewer 2, we find the medium-range order area in\nFig.3 a-b. As shown in Figure R11a, in the STEM image of the 2D amorphous plane\nof Nb-W-O nanorods on SrTiO (001), the medium-range order area proportion of the\n3\ntotal STEM image is 1.1%. As shown in Figure R11b, in the STEM image of the 2D\n18\namorphous plane of Nb-W-O nanorods on SrTiO (011), the medium-range order area\n3\nproportion of the total STEM image is 3.9%. Comparing the medium-range order area\nproportion, we can conclude that the randomness of the 2D amorphous plane on\nSrTiO (011) is less than the one on SrTiO (001). However, both medium-range order\n3 3\narea proportions are small and considering the small order parameters, we can\nconclude that the 2D plane of Nb-W-O nanorods is amorphous with continuous random\nnetwork (continuous random network) structure (Nano Letter, 2012, 12, 1081-1086;\nNature, 2020, 577, 199–203). This randomness of the plane would be similar when we\nuse the same growth conditions even with differently oriented SrTiO substrates.\ncommon existence of medium-range order in 2D continuous random network\namorphous materials. Also the appearance of a crystalline pattern in the FFT of the\nmedium-range order area is a common phenomenon.\n[Figure Redacted]\nFigure R12 medium-range order in 2D continuous random network amorphous plane.\n(case 1, Nano Letter, 2012, 12, 1081-1086)\n19\n[Figure Redacted]\nFigure R13 medium-range order in 2D continuous random network amorphous plane.\n(case 2, Nature, 2020, 577, 199–203)\n[Figure Redacted]\nFigure R14 a certain medium-range order area in 2D continuous random network\namorphous plane, b FFT of the medium-range order area 2D continuous random\nnetwork amorphous plane. (case 3, Nano Letter, 2012, 12, 1081-1086)\nCommunications. However, it will be shown in the following comments why this matter\nshould be considered as paracrystalline rather than amorphous in one direction.\nComment 1:\nIn Fig. 1, Nb-W-O nanorod films were deposited on crystalline substrates of different\norientations. It is a smart approach to demonstrate the difference in structures between\ndifferent orientations of a matter by showing the various growth morphologies.\nHowever, why do these rods all have a diameter around 50 nanometers? If it is truly\namorphous in the x-y plane, the diameters of these rods should be infinite or distributed\nrandomly.\nResponse to comment 1: The amorphous plane is the transverse section of the Nb-\nW-O nanorods. It is not always the x-y plane. In Figure R15, low magnification SEM\nimages of Nb-W-O nanorods on SrTiO (001), (011) and (111) substrates were used\n3\nfor diameter analysis. As shown in Figure R15 a-c, numerous nanorods are merged\nand nanorods with different widths are visible in the images. As shown in Figure R15d,\nthe diameter widths of Nb-W-O nanorods on different substrates are all distributed in\na large range (10-100 nm, 30-100 nm and 10-60 nm respectively).\nFigure R15 a-c SEM images of Nb-W-O nanorods on SrTiO3 (001), (011) and (111)\nsubstrates respectively, d diameter distribution of Nb-W-O nanorods on SrTiO (001),\n3\n(011) and (111) substrates.\nsubstrate?\nResponse to comment 2: The d-spacing of our Nb-W-O nanorods matches with the\nd-spacing of [001], [010] and [100] directions of SrTiO substrate crystal, which forces\n3\nthe nanorods to grow along these directions (crystal axis are along these directions).\nThus, if Nb-W-O are grown on amorphous substrates, we expect no nanorods structure\nwill appear on the substrate for the growth conditions used.\nComment 3: In Fig. 2a and b, the author tries to prove the amorphous structure of the\nx-y plane by showing its STEM image and the corresponding FFT pattern. However,\nwhen the review carefully checks them, some tiny crystalline features can be observed\nas shown in the following Figures 1R, 2R and 3R. Hence, the x-y plane cannot be\nunderstood as fully amorphous but paracrystalline phase.\nFig. 1R. (a) STEM image of Fig. 2a in manuscript and (b) its corresponding halo FFT\npattern. If we tuned the intensity of the FFT pattern, some diffraction spots\ncorresponding to crystalline phase can be observed.\nFig. 2R. If we zoom in Figure 2a, a lot of tiny crystals can be observed.\nFig. 3R. Another region where the tiny crystals can be observed. Such regions are\ndistributed over the whole image.\nResponse to comment 3: As we discussed above, everything between pure\namorphous phase and crystal phase fits under this definition of a paracrystal and we\nagree with reviewer 2. However, we insist that the Nb-W-O nanorods exhibit a structure\nwith 2D continuous random network amorphous plane together with a crystal axis in\nthe third dimension.\nAs we discussed in Supplementary Note 9, we fully agree with reviewer 2 that\nmedium-range order exists in the amorphous plane of Nb-W-O nanorods. However, it\nis very common for amorphous materials to possess certain medium-range order\n(Nano Letter, 2012, 12, 1081-1086; Nature, 2020, 577, 199–203). This is a hot and\nlong-lasting topic in debating the distinct boundary between amorphous and crystalline\nmaterials. However, we provide new insight to distinguish the boundary between\namorphous and crystalline cases, for which the direction matters.\nmatter is the glass transition. Can the glass transition be observed in this matter by\ndifferential scanning calorimetry? If not, then this matter is paracrystalline rather than\namorphous.\nResponse to Comment 4: We fully agree that differential scanning calorimetry would\nbe interesting to understand the Nb-W-O nanorods. However, Nb-W-O nanorods\n(thickness: 50-200 nm) are grown on SrTiO single crystal substrates (thickness: 0.5\n3\nmm). The amount of Nb-W-O nanorods is negligible compared to the substrate. Thus,\nit is impossible to detect the Nb-W-O signal in differential scanning calorimetry.\nFurthermore, collecting a large enough amount of nanorods from the substrate surface\nto enable differential scanning calorimetry seems extremely challenging.\nComment 5: By the way, some typos can be seen in the manuscript. “F PDF of Nb-W-O nanorods”.\nResponse to comment 5: Thanks for the critical reading. We revised the caption in\nFigure R2 (new Fig. 2).\nComment 6: In summary, the state of matter in this manuscript is still unclear. The\nauthor needs to verify which kind of structure it is, amorphous or paracrystalline?\nResponse to comment 6: As discussed above, we believe that the structure of Nb-W-O nanorods falls under the definition of paracrystal. The state of the Nb-W-O matter\nshows the stacking of the 2D amorphous layer. In the matter along the amorphous\nplane, limited medium-range order is observed with continuous random network, while\nin the vertical direction, the layers are stacked at the specific layer spacing of 3.91 Å.\nWe fully agree that the finding of our structure fits within the paracrystalline definition.\nHowever, we believe that the contribution of our case is to provide new insight to\ndistinguish the boundary between amorphous and crystalline cases, for which the\ndirection matters. This is beyond current understanding in the debate how medium\nrange disorder determines the boundary between amorphous and crystalline materials.\nGeneral Comment: This paper is interesting, though perhaps not as generally\napplicable as the authors imply in their abstract. The manuscript is well-written, and\nthe characterization work seems solid. However, as I describe below, the authors need\nto update their knowledge of oxide structures beyond the year 1932 when Zachariasen\npublished his seminal work on glass structures.\nComment 1:\nMy primary issue with this paper is that it’s not as original as the author’s claims imply.\nWhile the atomic resolution characterization in the current work is excellent, I have\nseen very similar structures (seemingly ordered along one axis) in several previous\nmanuscripts: (none of which are cited by the authors)\n-Miran MozeticÏ, Uros Cvelbar, Mahendra K. Sunkara, and Sreeram Vaddiraju, A\nMethod for the Rapid Synthesis of Large Quantities of Metal Oxide Nanowires at Low\nTemperatures, Adv. Mater. 17, 2138 (2005).\n-Subhra Jana and Robert M. Rioux, Seeded growth induced amorphous to crystalline\ntransformation of niobium oxide nanostructures, Nanoscale, 4, 1782 (2012).\n-Sophia B. Betzler, Ai Leen Koh, Bettina V. Lotsch, Robert Sinclair, Christina Scheu,\nAtomic Resolution Observation of the Oxidation of Niobium Oxide Nanowires:\nImplications for Renewable Energy Applications, ACS Appl. Nano Mater, 3, 9285\n(2020).\nResponse to comment 1: Nb-based oxides and W-based oxide usually form a rod-\nlike structure, as shown in Figure R16 a-b (Nature, 2018, 559, 556-563). In the\nreferences mentioned by reviewer 4 above (Advanced Materials, 2005, 17, 2138;\nNanoscale, 2012, 4, 1782; ACS Applied Nano Materials, 2020, 3, 9285) TEM images\nshow line like structure in all three works and SAED patterns indicate a nanocrystalline\nphase for all of them, as shown in Figure R16 c-e. In fact, the original crystalline\nmaterial Nb W O shows a line like structure in the [010] direction of Nb W O\n18 16 93 18 16 93\ncrystal, as shown in the schematic of atomic ordering of Nb W O crystal (Figure\n18 16 93\nR16 g). Thus, the STEM image of the longitudinal section of the nanorods is only\nevidence for a fixed d-spacing along the longitudinal direction but no proof of the\nstructural similarity. Moreover, the SAED patterns of the references above show a\nnanocrystalline phase for all three nanowire works, which is different from our findings.\n24\n[Figure Redacted]\nFigure R16 a-b SEM image of Nb W O crystal (Nature, 2018, 559, 556-563), c-e\n18 16 93\nTEM and SEAD results from the reference mentioned by reviewer 4 (Advanced\nMaterials, 2005, 17, 2138; Nanoscale, 2012, 4, 1782; ACS Applied Nano Materials,\n2020, 3, 9285), f-g Structural schematic of Nb W O crystal.\n18 16 93\nComment 2:\nGiven that the current paper primarily focuses on structure, I expect to see a much\ndeeper dive into other imaging studies on similar nanowires / materials.\nResponse to comment 2: We added the comparison of the atomic structure of Nb-\nW-O nanorods with traditional Nb-based and W-based nanowire/nanorod structures.\nThe modification of the manuscript related to this part can be seen in line 110 to 112.\nstudy isn’t mentioned by the authors at all: 2D quasicrystals / (semi)rational\napproximates in ternary oxides. Figures 3a, b, and especially Figure 3c look like 2D\ndecagonal quasicrystals to me. I suspect there may be additional disorders introduced\nby substrate and growth effects which may add some randomness to the quasicrystal\nlattice. For example, in Figure 2a, the (pseudo)coherent domain length appears to be\nonly ~4 nm. Either way, the authors certainly need to explain exactly how their\nproposed structural models are similar to and distinct from 2D stacked quasicrystals.\nHere are a few references to get them started (there are many possible references\nhere)\n-https://link.springer.com/content/pdf/10.1007/978-3-642-58434-3_3 (textbook\nchapter)\n-Stefan Förster et al., Quasicrystals and their Approximants in 2D Ternary Oxides,\nphysica status solidi (b) 257, 1900624 (2020).\n-Catalina Ruano-Merchan et al., Stoichiometry-Driven Formation of Two-Dimensional\nTernary Oxides: From Quasicrystal Approximants to Honeycomb Lattice Structures, J.\nPhys. Chem. C 128, 8839 (2024).\nResponse to comment 3: The 5 side rings appear in the transverse section of the\nnanorods which may be considered by reviewer 4 as evidence for quasicrystal.\nHowever, we need to make it clear that Fig.3c in our manuscript is a STEM image of\nNb W O crystalline powder at its [001] projection (the target material for the PLD\n18 16 93\nfabrication). As shown in Figure R17, we found the lower magnification STEM image\n(including Fig.3c in the image) of the Nb W O crystalline at its [001] projection. The\n18 16 93\nSTEM image and its FFT show that the structure is Nb W O crystalline (Schematic\n18 16 93\nof the structure are shown in Figure R16f.) with point and line defects.\nFigure R17 a STEM image of crystal Nb W O (Blue square is Fig.3c), b FFT\n18 16 93\nanalysis of a, c SAED results of crystal Nb W O .\n18 16 93\nby reviewer 4. (Physical Properties of Quasicrystals, 1999, Pages 51-89; Physica\nStatus Solidi (b), 2020, 257, 1900624; Journal Physical Chemistry C, 2024, 128, 8839)\nSame units only point towards the ordered directions. Thus, the order parameter for\nthe quasicrystal units should be 1. We used a reference provided by reviewer 4, to\ncalculate the order parameter of one of the quasicrystals presented in the reference\n(Physica Status Solidi (b), 2020, 257, 1900624). The data collection process is shown\nin Figure R18 and Table 2. The structure has a C12 symmetry. Thus, the angle 𝜃 of\nthe basic units in quasicrystal needs to be processed by the following equation:\n𝑛𝜋 𝜋\n𝜃( = 𝜃 − >𝑛 ∈ ℤ,0 ≤ 𝜃( ≤ A\n9:2;\" 9:2;\" 6 9:2;\" 6\nThe order parameter of the basic units in this quasicrystal can be calculated by the\nfollowing equation:\n∑) 𝑐𝑜𝑠 (12(𝜃( −𝛼) 𝜋\n)*( 9:2;\"\n𝑆 = max>𝑆 (𝛼)A= maxHB BI 𝛼 ∈D0, A\n9:2;\" 9:2;\" 𝑚 6\nUsing the above method, we can obtain the order parameters of different basic units\n(square, rhombus and regular triangle), which is 1. However, we also calculated the\norder parameters of the basic units ((3,0), (4,0), and (5,0/1) rings) of the 2D amorphous\nplane of Nb-W-O nanorods. The results show that the order parameters of all the basic\nunits are quite small, as shown in Table 1. Thus, we can conclude that the structure of\nthe 2D amorphous plane of Nb-W-O nanorods is not a 2D quasicrystal structure but a\n2D amorphous structure with a small proportion of medium-range order in it.\n27\n[Figure Redacted]\nFigure R18 a Quasicrystal schematic (Physica Status Solidi (b), 2020, 257, 1900624),\nb-d Order parameter analysis on the basic units in quasicrystal.\nTable 2 Angle distribution of the basic units in quasicrystal\n0˚ 30˚ 60˚ 90˚ 120˚ 150˚\nSquare 16 0 17 0 19 0\nRhombus 2 4 6 4 2 3\nRegular triangle 39 36 37 35 0 0\nComment 4: Therefore, I cannot accept this manuscript for publication in its current\nform. The authors need to identify precisely how their new observations and models\nextend the existing literature of semi-ordered ternary oxides.\nResponse to comment 4: The semi-ordered ternary oxides in the reference\nmentioned by reviewer 4, either have a crystal structure (same as our Fig.3c, the\ncrystal structure of Nb W O ), or exhibit order (2D quasicrystal structure). 2D\n18 16 93\namorphous plane of Nb-W-O nanorods does not have any of either. It can only be a\n2D continuous random network amorphous plane with a small proportion of medium-\nrange order in it.\nComment 5: “Scanning electron microscopy (SEM) results reveal 2, 1 and 3\norientational growth of Nb-W-O nanorods on Nb-doped SrTiO3 (001), (011) and (111)\nsubstrates, respectively.” This statement is very unclear – what does “2 orientational\ngrowth” etc. mean? While I think I see what the authors are getting at, they should\nclarify that they mean families of nanowire orientation.\nResponse to comment 5: We have revised the sentence into: “Scanning electron\nmicroscopy (SEM) results reveal that Nb-W-O nanorods on Nb-doped SrTiO3 (001),\n(011) and (111) substrates grow in 2, 1, and 3 orientations, respectively.”\nComment 6: Figure 4 caption is way too long. All the captions are too long, but\nespecially this one. Concisely describe your observations and move discussion to the\nmain text.\nResponse to comment 6: We revised the 3D RSM part into 2 Figures, as shown in\nFigure R5 and Figure R6.\nComment 7: \"... defined by the choice of substrate, rather than that it is the result of\nan uncontrolled local phenomenon.\" Could be clarified.\nResponse to comment 7: We deleted this description as we found that the description\nis not relevant.\nGeneral Comment: The authors have fabricated a unique three-dimensional structure\ncomposed of stacked two-dimensional amorphous layers in the Nb-W-O system. By\ntaking advantage of the unidirectional periodicity of this structure, they performed direct\nimaging of the amorphous structure using state-of-the-art STEM techniques. This\napproach, combined with X-ray diffraction, EXAFS, and RSM analyses, enables a\ndetailed structural characterization. A key strength of the study is that the electron\nbeam was aligned parallel to the periodic axis, allowing unambiguous imaging of the\namorphous structures. The experimental work is thorough, and the discovery of a 3D\nstructure possessing 2D amorphous character is noteworthy. However, I have several\nconcerns as listed below:\nResponse to General Comment: We thank Reviewer 5 for the insightful comments.\nWe have revised our manuscript accordingly based on your valuable comments. By\naddressing these issues and incorporating the reviewer’s feedback, we believe that\nour manuscript is now significantly improved.\nComment 1: The authors should address the relationship between their findings and\nprevious work, particularly Ref. 8 (Huang et al., Nano Lett. 12, 1081 (2012)), where a\ntwo-dimensional amorphous SiO film was directly imaged using STEM and shown to\n2\nreproduce the classic Zachariasen model. Although the current study focuses on a\nthree-dimensional structure, the amorphous nature is still essentially two-dimensional.\nThe authors should clearly articulate the scientific advancement beyond previous\nstudies.\nResponse to comment 1: We agree with reviewer 5 that the amorphous nature of\nNb-W-O is 2D amorphous plane and our analysis approach is highly inspired by ref.8\nin the manuscript. The 2D amorphous SiO discovered by Huang et al. is the thinnest\n2\nglass which is included in latest Guinness Book of World Records. However, the\nscientific advancement of our work is the first homogeneous material which shows a\nthree-dimensional structure composed of crystalline stacked two-dimensional\namorphous layers.\nWe revised the introduction as follows: “By taking advantage of the 2-dimensional\nnature of some materials, single-layer amorphous materials, since the first discovery\nby Huang8-9 as the thinnest glass, have expanded greatly including 2D amorphous\ncarbon5,10.”\nwhether three-dimensional amorphous materials exhibit medium-range order (MRO).\nHowever, the present structure is fundamentally a two-dimensional amorphous\nmaterial, and thus may not directly address this question. The authors are encouraged\nto comment on this point and clarify their position.\nResponse to comment 2: We provided a case which combines amorphous\ninformation (2D amorphous plane) and crystal information (crystal third direction) in a\nhomogeneous structure at different directions, which suggests that “degree of order\ndifference at different orientation” can be as important as “degree of order” itself for\ndiscussing a structure between complete amorphous phase to complete crystal phase.\nWe revised the introduction as follows: “The finding of such unique structure proposes\na new insight for the boundary between amorphous and crystalline phases beyond the\ndebate of medium-range order.”\nComment 3:The manuscript claims that the amorphous layers exhibit only short-range\norder (SRO), without MRO. Is this conclusion fully justified? For example, the reduced\npair distribution function G(r) shown in Fig. 2f extends only up to 5 angstrom, making\nit difficult to conclusively determine the absence of MRO. Furthermore, the peak near\n4.8 angstrom might correspond to in-plane amorphous features and could be indicative\nof MRO, especially since it exceeds typical interatomic distances.\nResponse to comment 3: We admit that the unavoidable signal from SrTiO in the\nAfter in depth analysis (inspired by reviewer 2) on the STEM image of the 2D\namorphous plane of Nb-W-O nanorods, we found a small proportion (less than 5%) of\nMRO in it. The determined MRO structure was not originally in the Nb W O lattice,\n18 16 93\nwhich is the reason we didn’t count it as medium-range order in the Nb-W-O system.\nFurthermore, the small proportion of MRO structure (4-side ring clusters) is evidence\nof the ring rearrangement from the original Nb W O crystal.\n18 16 93\nThus, we revised the description as follows:\n“After detailed analysis (Supplementary Note 9, Figs. S42) on the STEM images of 2D\namorphous layers of Nb-W-O nanorods (Fig.3 a-b), we can conclude that MRO exists\nin the 2D amorphous plane of Nb-W-O and the randomness of the 2D amorphous\nplane on SrTiO (011) is less than the one on SrTiO (001). However, both MRO area\n3 3\nproportions are small and considering the small order parameter, we can still conclude\nthat the 2D amorphous plane of Nb-W-O nanorods is a 2D amorphous plane with\n31\ncontinuous random network structure5,8-9 and the randomness of the plane would be\nsimilar when we use the same growth condition even with different oriented SrTiO3\nsubstrate.”.\nHowever, small proportion of MRO can be found in most reported continuous random\nnetwork structures (Nano Letter, 2012, 12, 1081-1086; Nature, 2020, 577, 199–203),\nas shown in Figure R12-14. Thus, we believe we can still define the 2D amorphous\nplane of Nb-W-O nanorods as a continuous random network 2D amorphous layer.\nComment 4: In Figs. 3a and 3b, STEM images of samples grown on SrTiO3 (001) and\n(011) substrates are shown, respectively. Fig. 3b appears more ordered than Fig. 3a.\nCould this reflect a difference in the degree of medium-range order? The authors\nshould address this observation and provide their interpretation.\nResponse to comment 4: Inspired by the comment from reviewer 2, we analyzed the\nMRO area of 2D amorphous planes of Nb-W-O nanorods on SrTiO (001) and (011)\n3\n(Fig.2 a-b), as shown in Supplementary Note 9. The MRO area proportion of 2D\namorphous planes of Nb-W-O nanorods on SrTiO (011) is a bit higher than the one\n3\non SrTiO (001), 3.9% vs. 1.1%.\nthe order parameter of the basic units (different rings) inside the 2D amorphous plane\nof Nb-W-O nanorods, as shown in Supplementary Note 8. The results of the order\nparameter analysis show that the degree of order of basic units in both 2D amorphous\nplanes of Nb-W-O nanorods on SrTiO (001) and (011) is small. And we cannot find a\n3\nhigher degree of order between 2D amorphous plane of Nb-W-O nanorods on SrTiO\n3\n(001) and the one on SrTiO (011) by comparing the order parameter due to the\n3\ninconsistency of the comparison of the order parameters in both cases. Thus,\nadvanced models for analyzing degree of order along different orientations are urgently\nneeded. We plan to analyze this in future studies.\nComment 5: It is possible to extract atomic coordinates from the bright spots in the\nSTEM images and calculate the reduced pair distribution function G(r). I recommend\ncomparing this with the G(r) obtained from XRD measurements. This comparison\nwould help disentangle the contributions from amorphous in-plane structure and\nperiodicity along the stacking direction.\nResponse to comment 5: We have used the model “ePDFpy” (Computer Physics\nCommunications, 2024, 299, 109137) to transfer the SAED results of the amorphous\n32\nmaterials to PDF results. However, the thickness of the Nb-W-O nanorods films is\nsmaller than the electron beam width for SAED analysis. Thus, we could not obtain an\nreliable SEAD result. However, we already listed some areas with MRO in the 2D\namorphous plane and compared them with other reported 2D continuous random\nnetwork amorphous structures. Thus, we believe we can conclude that a low\ncontribution MRO in 2D continuous random network amorphous structure is not\navoidable. We revised the discussion about the existence of “MRO” in our manuscript\nand we focused on the newly identified structure, and its contributions to the existing\nknowledge on the state of solid matter.\nComment 6: It remains unclear what conceptual or structural insights this study offers\nbeyond the compatibility with Zachariasen's model. The authors are encouraged to\nmore clearly state the broader implications of their findings for the structural science of\namorphous materials, particularly in the summary section.\nResponse to comment 6: As discussed above, we present a material that is\namorphous in the plane perpendicular to the nanorod, while being completely ordered,\nand therefore crystalline, along the length of the nanorod (Fig.1 a-c). This periodicity\nalong the third-dimensional axis enabled the direct imaging of the amorphous 2D Nb-\nW-O monolayers, which are found to follow Zachariasen’s model.\nWe believe that the contribution of our case is to provide new insight to distinguish the\nboundary between amorphous and crystalline cases, for which the direction matters.\nThis is beyond current understanding in the debate how medium range disorder\ndetermines the distinct boundary between amorphous and crystalline materials.\nWe revised the summary section as follows: “Our work sheds light on the intricate\ninterplay between order and disorder in solid matter and contributes to the\nunderstanding of the structural properties of amorphous/crystalline systems beyond\nthe debate of medium-range order. As the new material bridges the gap between\namorphous and crystalline matter, its unique properties will open new avenues for\nfuture exploration.”\n33"}, {"round": 2, "reviewer_comments": {"reviewer_1": "This second version of the manuscript greatly improves the understanding of what the authors would demonstrate. After reading the new version, I believe the manuscript can be accepted for publication if the authors address the following two comments.\nComment 1:\nAccording to one of my comment on the previous version, the authors have now defined a clear orientation notation with respect to both the measurement orientation and the crystallographic main directions. Unfortunately, they used the symbol “*” to label the [100], [010] and [001] directions. This is a pity because this symbol is used in crystallography to represent directions in the reciprocal space. Another choice has to be done.\nComment 2:\nOn page 2, the authors wrote that the material under study is amorphous in the x-y plane and this statement refers to the structural model reported Fig. 1 a-c. In fact, not any representation of structure in x-y plane is reported Fig. 1. The authors state that, due to the periodicity in the third direction, such an in plane structure cannot be represented. Nevertheless, in principle, a slice of the structure with a thickness of one atomic plane could evidence this in plane amorphous nature. This must be added.", "reviewer_2": "The reviewer has carefully checked the response to the comments on the manuscript entitled “Crystalline or Amorphous? A Matter of Perspective” by Xia et al.\nAlthough most questions have been properly addressed, the reviewer is unsatisfied with the response to comment 4. In the response to comments 4, the author wrote “The amount of Nb-W-O nanorods is negligible compared to the substrate. Thus, it is impossible to detect the Nb-W-O signal in differential scanning calorimetry. Furthermore, collecting a large enough amount of nanorods from the substrate surface to enable differential scanning calorimetry seems extremely challenging”. In fact, this reply is not true for flash DSC. The desired sample amount for flash DSC is only a few micrograms, and the Nb-W-O signal can be detected by scraping a few pieces of nanorods from the substrate.\nTo determine the nature of this non-crystalline matter, the reviewer still recommends that the authors perform thermal measurements using flash DSC. However, this can be addressed in a future study. The manuscript has been significantly improved and it deserves the publication in Nature Communications.", "reviewer_3": "I am still not entirely convinced about the author's claims of <5% medium range order (MRO) or the novelty of this study. By eye in Figures 1 and 2 I think I see correlations well beyond 5 nm, and I agree with the other referee that the PDF should be extended to longer length scales. By taking these image and looping through all (masked) bright sites, the authors could easily compute an imaging PDF / reduced PDF.\nHowever I feel the authors have done their due diligence to investigate most of questions of myself and the other referees.\nTherefore I am prepared to accept this manuscript for publication, if the authors can fulfill this request:\n-Please upload all of the raw TEM images published in this study to a public repository (such as Zenodo). It's not acceptible to write \"Data Availability - The data that support the findings of this study are available from the corresponding author upon reasonable request.\" anymore and Springer Nature policy requires upload of all data (and analysis codes), here is the policy:\nhttps://www.nature.com/nature-portfolio/editorial-policies/reporting-standards#availability-of-data\nIf the authors won't measure the long range PDF themselves, they must make it possible for the research community to do so (and I will be checking your results after publication!).", "reviewer_4": "I appreciate the authors’ revisions in response to my comments. In particular, the modifications regarding Comments 1, 2, 3, and 4 satisfactorily address my concerns.\nHowever, I still have remaining concerns regarding my previous Comments 5 and 6.\n1. With respect to my previous comment 5, thank you for the clarification regarding the difficulty of obtaining reliable SAED data for PDF analysis. However, I would like to emphasize that the main point of my earlier comment was not about deriving PDF from SAED, but rather about the possibility of extracting atomic coordinates directly from the STEM images and calculating the 2D reduced pair distribution functon(G(r)) from them. This approach does not rely on SAED and would make better use of the STEM data that the authors already possess. By comparing the STEM-derived G(r) with the one obtained from XRD, the authors could provide a more quantitative basis for their discussion of medium-range order (MRO) and disentangle the respective contributions from in-plane amorphous structure and stacking periodicity. Such an analysis would significantly strengthen the manuscript and support the conclusions in a more rigorous way.\n2. With respect to my previous comment 6, I appreciate the authors’ efforts to revise the summary section. However, the response still does not fully address the essence of my concern. The main point was to clarify what conceptual or structural insights this study provides for the field of amorphous materials beyond demonstrating compatibility with Zachariasen’s model. The revision largely restates the anisotropic order–disorder character of the nanorods, but it remains unclear how this observation advances broader understanding. In particular, the authors are encouraged to state more explicitly what the key factor is in distinguishing the boundary between amorphous and crystalline states, and what implications this may have for future studies of amorphous/crystalline systems."}, "author_response": "Response to Reviewer #1\nOverall Comment: This second version of the manuscript greatly improves the understanding\nof what the authors would demonstrate. After reading the new version, I believe the manuscript\ncan be accepted for publication if the authors address the following two comments.\nComment 1: According to one of my comment on the previous version, the authors have now\ndefined a clear orientation notation with respect to both the measurement orientation and the\ncrystallographic main directions. Unfortunately, they used the symbol “*” to label the [100],\n[010] and [001] directions. This is a pity because this symbol is used in crystallography to\nrepresent directions in the reciprocal space. Another choice has to be done。\nResponse to Comment 1: We thank the reviewer for the constructive suggestion. We have\nchanged x*, y*, z* to x’, y’, z’ in the real space to avoid misunderstanding.\nWe have revised the corresponding parts in the revised main text/figures and Supplementary\nNote 1 to clarify those misunderstandings.\nComment 2: On page 2, the authors wrote that the material under study is amorphous in the\nx-y plane and this statement refers to the structural model reported Fig. 1 a-c. In fact, not any\nrepresentation of structure in x-y plane is reported Fig. 1. The authors state that, due to the\nperiodicity in the third direction, such an in plane structure cannot be represented. Nevertheless,\nin principle, a slice of the structure with a thickness of one atomic plane could evidence this in\nplane amorphous nature. This must be added.\nResponse to Comment 2: We thank the reviewer for bringing this to our attention, which has\nbeen modified in the illustration for better understanding. The single layer illustration is shown\nin Figure R1.\nFigure R1 Single layer illustration from the Nb-W-O nanorods. a 2D view, b Transverse section,\nc Longitudinal section.\nWe have replaced Figure 1b with Figure R1b for a better understanding. The new Figure 1 is\nshown below as Figure R2.\nStructure of Nb-W-O nanorods (z axis is the growth direction), b Transverse section (single\natomic layer) of Nb-W-O nanorods, c Longitudinal section of Nb-W-O nanorods, d Schematic\nof the Nb-W-O nanorods on SrTiO (001) substrate, e-f Top and side view SEM images of the\n3 3\n(011) substrate, h-i Top and side view SEM images of the Nb-W-O nanorods on SrTiO (011)\n3\nsubstrate, j Schematic of the Nb-W-O nanorods on SrTiO (111) substrate, k-l Top and side view\ndefined as the [100], [010], [001] directions of SrTiO crystal, details are described in\nOverall Comment: The reviewer has carefully checked the response to the comments on the\nmanuscript entitled “Crystalline or Amorphous? A Matter of Perspective” by Xia et al.\nAlthough most questions have been properly addressed, the reviewer is unsatisfied with the\nresponse to comment 4. In the response to comments 4, the author wrote “The amount of Nb-\nW-O nanorods is negligible compared to the substrate. Thus, it is impossible to detect the Nb-\nW-O signal in differential scanning calorimetry. Furthermore, collecting a large enough amount\nof nanorods from the substrate surface to enable differential scanning calorimetry seems\nextremely challenging”. In fact, this reply is not true for flash DSC. The desired sample amount\nfor flash DSC is only a few micrograms, and the Nb-W-O signal can be detected by scraping a\nfew pieces of nanorods from the substrate. To determine the nature of this non-crystalline\nmatter, the reviewer still recommends that the authors perform thermal measurements using\nflash DSC. However, this can be addressed in a future study. The manuscript has been\nsignificantly improved and it deserves the publication in Nature Communications.\nResponse to general comment: We thank the reviewer for pointing out the capabilities of flash\ndifferential scanning calorimetry, which is unfortunately not available within our institute.\nFurthermore, peeling off the Nb-W-O nanorods from an epitaxial substrate will be challenging\nand future studies can explore the usage of freestanding membranes (Science, 2024, 383, 388-\n394).\nOverall Comment: I am still not entirely convinced about the author's claims of <5% medium\nrange order (MRO) or the novelty of this study. By eye in Figures 1 and 2 I think I see\ncorrelations well beyond 5 nm, and I agree with the other referee that the PDF should be\nextended to longer length scales. By taking these image and looping through all (masked) bright\nsites, the authors could easily compute an imaging PDF / reduced PDF.\nHowever I feel the authors have done their due diligence to investigate most of questions of\nmyself and the other referees.\nTherefore I am prepared to accept this manuscript for publication, if the authors can fulfill this request:\n-Please upload all of the raw TEM images published in this study to a public repository (such\nas Zenodo). It's not acceptible to write \"Data Availability - The data that support the findings\nof this study are available from the corresponding author upon reasonable request.\" anymore\nand Springer Nature policy requires upload of all data (and analysis codes), here is the policy:\nhttps://www.nature.com/nature-portfolio/editorial-policies/reporting-standards#availability-of-data\nIf the authors won't measure the long range PDF themselves, they must make it possible for\nthe research community to do so (and I will be checking your results after publication!).\nResponse to general comment: We thank the reviewer for bringing this issue to our attention.\nWe have uploaded the data and images supporting the findings of this study at Zenodo\nrepository : https://doi.org/10.5281/zenodo.17588010 , which will be made publicly available\nbefore publication of our manuscript.\nWe transferred the STEM images into PDF results, as shown in Figures R3, R4, and R5.\nSupplementary Note 5 and Figures S8-S10 have been added to describe obtained PDF results.\nThe STEM images of the transverse section of the as-grown Nb-W-O nanorods on SrTiO (001)\n3\nand (011) substrates as well as the (001) plane of crystalline Nb W O powder were used to\n18 16 93\nsimulate the PDF results, which are shown in Figures R3 and R4. As shown in Figure R3,\nonly metal ions are clearly displayed in the STEM images. Thus, the PDF results calculated\nfrom STEM images would only reveal the statistics of the metal atom distances. As shown in\nFigure R4, the PDF result of crystalline Nb W O shows a concentrated, periodic\n18 16 93\ndistribution of the metal atom distance. However, the PDF results of the transverse section of\nthe as-grown Nb-W-O nanorods on SrTiO (001) and (011) substrates show a constant G(r) at\n3\n1 after 1 nm atom distance, which provides solid evidence that the transverse section of the as-\ngrown Nb-W-O nanorods on SrTiO (001) and (011) substrates exhibits a 2D amorphous\n3\nstructure.\nThe following sentences have been added to the revised manuscript: “The PDF results\nsimulated from the STEM images are shown in Supplementary Note 5, Fig. S8-10 and only\nreveal the distance distribution between the metal ions. The conventional Nb W O crystal\n18 16 93\nexhibits multiple peaks distributed over distances till 60 Å, while in strong contrast the Nb-W-\nO nanorods on SrTiO (001) and (011) substrates show relatively flat lines after 10 Å. These\n3\nresults confirm the 2D amorphous nature of the transverse section of Nb-W-O nanorods.”\nSrTiO (001) and (011) substrates as well as (c) the (001) plane of crystalline Nb W O\n3 18 16 93\npowder. d-f the atom searching results.\nFigure R4 PDF results of the STEM images in Figure R3 obtained by the atom location data.\nresult from synchrotron XRD of Nb-W-O nanorods on SrTiO (011) substrate.\nNb-W-O nanorods on SrTiO (011) substrate is between 3.5 to 4.1 Å, which spans 2 peaks in\n3\nthe synchrotron XRD result of the same sample. Thus, even the M-O bond and the signal from\nSrTiO appeared in the synchrotron XRD data, next to the M-M bonds from the Nb-W-O\n3\nnanorods.\nOverall Comment: I appreciate the authors’ revisions in response to my comments. In\nparticular, the modifications regarding Comments 1, 2, 3, and 4 satisfactorily address my\nconcerns. However, I still have remaining concerns regarding my previous Comments 5 and 6.\nComment-1. With respect to my previous comment 5, thank you for the clarification regarding\nthe difficulty of obtaining reliable SAED data for PDF analysis. However, I would like to\nemphasize that the main point of my earlier comment was not about deriving PDF from SAED,\nbut rather about the possibility of extracting atomic coordinates directly from the STEM images\nand calculating the 2D reduced pair distribution functon(G(r)) from them. This approach does\nnot rely on SAED and would make better use of the STEM data that the authors already possess.\nBy comparing the STEM-derived G(r) with the one obtained from XRD, the authors could\nprovide a more quantitative basis for their discussion of medium-range order (MRO) and\ndisentangle the respective contributions from in-plane amorphous structure and stacking\nperiodicity. Such an analysis would significantly strengthen the manuscript and support the\nconclusions in a more rigorous way.\nResponse to Comment 1:\nWe transferred the STEM image into PDF results, as shown in Figure R3, R4 and R5.\nSupplementary Note 5 and Figures S8-S10 have been added to describe the obtained PDF\nresults. See the description above answering the same comment by reviewer 3.\nComment-2. With respect to my previous comment 6, I appreciate the authors’ efforts to revise\nthe summary section. However, the response still does not fully address the essence of my\nconcern. The main point was to clarify what conceptual or structural insights this study\nprovides for the field of amorphous materials beyond demonstrating compatibility with\nZachariasen’s model. The revision largely restates the anisotropic order–disorder character of\nthe nanorods, but it remains unclear how this observation advances broader understanding. In\nparticular, the authors are encouraged to state more explicitly what the key factor is in\ndistinguishing the boundary between amorphous and crystalline states, and what implications\nthis may have for future studies of amorphous/crystalline systems.\nResponse to comment 2: Many thanks for raising this point. Distinguishing the boundary\nbetween amorphous and crystalline states is important because it helps us understand how the\natomic structure of a material influences its physical, chemical, and functional properties.\nDetermining this boundary is crucial for interpreting how structure governs behavior in\nmaterials. Understanding where and how this boundary lies enables better control of\ncrystallization and amorphization processes, which are fundamental to materials synthesis,\nthin-film deposition, and annealing. Many emerging materials rely on properties that lie\nbetween amorphous and crystalline regimes. Understanding this boundary helps tune\nperformance for desired applications. Our work opens important new avenues of exploration\nand provides a new platform for computational modeling of the 2D amorphous matter stacking.\nMoreover, accurate determination of amorphous solids in the complete range of disorder is\n7\nimportant to shed new insights in modelling of amorphous/crystalline systems in three-\ndimensional real space.\nWe have added this additional description to the summary section.\n8"}, {"round": 3, "reviewer_comments": {"reviewer_3": "While I still have some reservations, I believe the authors have addressed my comments to a degree satisfactory for publication. I expect this paper will contribute to significant discussion in the disordered materials community. I do understand the PDFs are just from the metal atoms, which is important to point out in the text. I believe these PDFs place the authors' claims on much firmer ground.", "reviewer_4": "The authors have addressed all my comments carefully and satisfactorily. The revised manuscript is significantly improved and is now suitable for publication in Nature communications. I have no further concerns."}, "author_response": ""}]

Decision letter