Orientation-dependent mutual crystalline and amorphous order in a single phase solid
Rui Xia, Jiantao Li, Yorick A. Birkhölzer, Haoyang Peng, Kangning Zhao, Ruohan Yu, Congli Sun, Lei Zhang, Qi Liu, Sungsik Lee, Tianyi Li, Yang Ren, Jie Zheng, Johan E. ten Elshof, Mark Huijben
TL;DR
Scientists discovered a material that is amorphous in two dimensions but crystalline in the third, showing that order can vary by direction within the same solid.
Contribution
A new material is presented that exhibits coexisting crystalline and amorphous order in different dimensions.
Findings
The material consists of stacked 2D amorphous Nb-W-O monolayers with crystalline stacking in the third dimension.
The amorphous layers follow the Zachariasen model for 2D disorder.
This challenges the traditional distinction between crystalline and amorphous materials.
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…
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Figure 5- —https://doi.org/10.13039/501100003246Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organisation for Scientific Research)
- —https://doi.org/10.13039/501100004543China Scholarship Council (CSC)
- —https://doi.org/10.13039/100006224DOE | LDRD | Argonne National Laboratory (ANL)
- —https://doi.org/10.13039/501100001809National Natural Science Foundation of China (National Science Foundation of China)
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Taxonomy
TopicsTransition Metal Oxide Nanomaterials · Magneto-Optical Properties and Applications · Catalysis and Oxidation Reactions
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 materials lack 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 MO_6_ (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.Fig. 1. Schematics and SEM images of different type Nb-W-O nanorod films.a 3D Schematic of the atomic structure of the Nb-W-O nanorods (Green spheres are niobium ions, orange spheres are tungsten ions and z axis is the growth direction.), b Schematic transverse section (single atomic layer) of Nb-W-O nanorods, c Schematic longitudinal section of Nb-W-O nanorods, d Schematic of the Nb-W-O nanorods on SrTiO_3_ (001) substrate, e–f Top and side view SEM images of the Nb-W-O nanorods on SrTiO_3_ (001) substrate (The blue boxes represents the Nb-W-O nanorods, same as h), g Schematic of the Nb-W-O nanorods on SrTiO_3_ (011) substrate, h–i Top and side view SEM images of the Nb-W-O nanorods on SrTiO_3_ (011) substrate, j Schematic of the Nb-W-O nanorods on SrTiO_3_ (111) substrate, k–l Top and side view SEM images of the Nb-W-O nanorods on SrTiO_3_ (111) substrate. (In this work, x’, y’, z’ are defined as the [100], [010], [001] directions of SrTiO_3_ crystal, details are described in Supplementary Note 1).
Results and discussion
The amorphous-crystalline Nb-W-O phase was prepared by pulsed laser deposition of stoichiometric crystalline Nb_18_W_16_O_93_ (prepared from Nb_2_O_5_ and WO_3_) onto Nb-doped SrTiO_3_ substrates (details in Methods section). SrTiO_3_ 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 SrTiO_3_ (001), (011) and (111) substrates, respectively. Considering the similar lattice constant of the c axis of stoichiometric Nb_18_W_16_O_93_ (3.951 Å) and the lattice constant of Nb-doped SrTiO_3_ (3.905 Å), epitaxial growth of a crystalline phase Nb-W-O was hypothesized. On SrTiO_3_ (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 SrTiO_3_ (011) substrates, nanorod growth occurred in the x’ direction only, leading to a single orientation along the substrate surface. In contrast, for SrTiO_3_ (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 SrTiO_3_ (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 SrTiO_3_ substrates was characterized by Scanning Transmission Electron Microscopy (STEM). For a nanorod on SrTiO_3_ (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 confirms 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 SrTiO_3_ (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 niobium tungsten oxide materials synthesized by traditional calcination (tetragonal tungsten bronze structure with defects)^24–42^.Fig. 2STEM analysis of atomic ordering in Nb-W-O nanorod films.a STEM image of the transverse section of Nb-W-O nanorods on SrTiO_3_ (011) substrate (The red box is the area for Fast Fourier transform (FFT) analysis, same as c.), b FFT image of (a, c) STEM image of the longitudinal section of Nb-W-O nanorods on SrTiO_3_ (011) substrate, d FFT image of (c, e) STEM image of Nb-W-O nanorods on SrTiO_3_ (001) substrate, f Zoomed in STEM image of e at film-substrate interface. (The red line shows the boundary of the two directions in Nb-W-O. The blue box represents the first epitaxial Nb-W-O layer. The yellow circle indicates the step of the substrate.), g PDF of Nb-W-O nanorods on SrTiO_3_ (001), SrTiO_3_ (011), and SrTiO_3_ (111) substrates, h, i EXAFS data of Nb (h) and W (i) of Nb-W-O nanorods on SrTiO_3_ (001) substrate.
The interface (zoomed in from Fig. 2e) between the SrTiO_3_ (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 SrTiO_3_ (001) substrate seems to have grown epitaxially, although the A site cations from the ABO_3_ 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 SrTiO_3_ (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 SrTiO_3_ 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 SrTiO_3_ 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 Nb_18_W_16_O_93_ crystal exhibits multiple peaks distributed over distances till 60 Å, while in strong contrast the Nb-W-O nanorods on SrTiO_3_ (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 NbO_6_^43^ and WO_6_^44^ octahedrons. The intermolecular Nb-O and W-O distances are smaller than values commonly reported in literature^43,44^, which suggests 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 MO_6_ octahedrons.
The medium-range order was compared for as-grown nanorods on SrTiO_3_ (001) (Fig. 3a) and SrTiO_3_ (011) substrates (Fig. 3b), as well as its crystalline counterpart^42^ (Fig. 3c). The cation arrangements in tetragonal tungsten bronze Nb_xW_1-xO_6- 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 NbxW_1-xO_6- ½x, the frequency of occurrence of specific ring-like motifs was quantified, formed by MO_6 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 Nb_18_W_16_O_93_, 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 SrTiO_3_ 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 Nb_18_W_16_O_93_. Moreover, the as-grown Nb-W-O nanorods on SrTiO_3_ (001) and SrTiO_3_ (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 Nb_18_W_16_O_93_ 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 (Nb_18_W_16_O_93_) 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 SrTiO_3_ (001) and (011) substrates are quite small, which indicates high randomness of the amorphous plane of Nb-W-O nanorods on SrTiO_3_ (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 SrTiO_3_ (011) and SrTiO_3_ (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 SrTiO_3_ substrates.Fig. 3. Analysis of elemental ordering in Nb-W-O nanorod films.STEM images of (a, b) the transverse section of the as-grown Nb-W-O nanorods on SrTiO_3_ (001) and (011) substrates as well as (c) the (001) plane of crystalline Nb_18_W_16_O_93_ powder^42^. d Quantified frequency of different ring-like motifs in as-grown Nb-W-O nanorods on SrTiO_3_ (001) and SrTiO_3_ (011) substrates as well as crystalline Nb_18_W_16_O_93_ from (a–c). e–h Rotational distributions of the (3,0), (4,0), (5,0), and (5,1) ring-like motifs in as-grown Nb-W-O nanorods on SrTiO_3_ (001) and SrTiO_3_ (011) substrates as well as crystalline Nb_18_W_16_O_93_, respectively. i High-resolution EDX analysis of the as-grown Nb-W-O nanorods on SrTiO_3_ (011) substrate. Green indicates niobium and orange indicates tungsten. j Magnified region from (i), k the molar Nb fraction at 10 different sites (a–j) in (j).
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 Nb_18_W_16_O_93_ 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 NbO_6_ and WO_6_ 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 SrTiO_3_ 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 SrTiO_3_ (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 Nb^5+^ and tungsten is W^6+^, which suggests MO_6_ 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 (3D RSM) analysis. 3D RSM 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 SrTiO_3_ (011) substrate show a line structure in the qx-qz plane and line structures in different qx-qy slices. Thus, the experimental 3D RSM results match with the simulated 3D RSM results and suggest that the Nb-W-O nanorods on SrTiO_3_ (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 3D RSM simulations of the Nb-W-O nanorods on (011), (001) and (111) substrates were compared in detail with the experimental 3D RSM results.Fig. 43D Reciprocal space mapping (RSM) simulation for Nb-W-O nanorod films.a 3D RSM simulation for the stack of single amorphous layers, b qx-qz projection of (a), c qy-qz projection of (a), d–f Schematic of 3D RSM analysis of Nb-W-O nanorods on SrTiO_3_ (011), (001) and (111) substrates respectively’, g–i 3D RSM simulation for Nb-W-O nanorods on SrTiO_3_ (011), (001) and (111) substrates respectively, j–l Simulation results of (g–i) for limited 3D RSM analysis area respectively. (In this work, x*, y*, z* are defined as the [100], [010], [001] directions of SrTiO_3_ crystal and qx, qy, qz are defined by the calibration peak of SrTiO_3_ which is applied for each 3D RSM analysis^53,54^, as described in Supplementary Note 1).Fig. 53D RSM analysis of structural ordering in Nb-W-O nanorod films.a–c qx-qz projection and qx-qy slice at different qz of the 3D RSM simulation results for Nb-W-O nanorods on SrTiO_3_ (011), (001) and (111) substrates (Fig. 4j–I) respectively, d–f qx-qz projection and qx-qy slice at different qz of the experimental 3D RSM results for Nb-W-O nanorods on SrTiO_3_ (011), (001) and (111) substrates respectively.
SEM analysis of the Nb-W-O nanorods on SrTiO_3_ (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 SrTiO_3_ (011) substrate. Thus, the simulation of the 3D RSM of Nb-W-O nanorods on SrTiO_3_ (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 3D RSM analyses. The 3D RSM’s of Nb-W-O nanorods on SrTiO_3_ (011) substrate are simulated according to the x*-y*-z* coordinate system, as shown in Fig. 4d. Thus, the simulated 3D RSM of Nb-W-O nanorods on SrTiO_3_ (011) substrate results in multiple parallel planes and only one plane was captured in the analysis range, as shown in Fig. 4g, j. For the experimental 3D RSM analysis of Nb-W-O nanorods on SrTiO_3_ (011) substrate, the area around the point of the SrTiO_3_ (011) plane in reciprocal space is measured, as shown in Fig. 5d1. The qx-qz view of the experimental 3D RSM shows a broad intensity distribution over a wide 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 3D RSMs of the Nb-W-O nanorods on SrTiO_3_ (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 wide 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 SrTiO_3_ (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 3D RSM (shown in Fig. 4e). The coordinate system of the 3D RSM analysis for Nb-W-O nanorods on SrTiO_3_ (001) substrate is the same x*-y*-z* coordinate system, as discussed above. Thus, the simulated 3D RSM of Nb-W-O nanorods on SrTiO_3_ (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 3D RSM (shown in Fig. 5e1) with the same intensity range in qz as the previous case including the point of the SrTiO_3_ (001) plane in the reciprocal space, indicating long-range disorder along that axis perpendicular to the substrate surface. In Fig. 5 e2-e5, qx-qy slices of the 3D RSMs of the Nb-W-O nanorods on Nb-doped SrTiO_3_ (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 3D RSM analysis results (Fig. 5e), which further validates directly the plane structure in 3D reciprocal space, which matches the simulated 3D RSM of the crystal stack of the amorphous layers.
Lastly, SEM analysis of the Nb-W-O nanorods on SrTiO_3_ (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 3D RSM of Nb-W-O nanorods on SrTiO_3_ (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 3D RSM results were collected in skew geometry with the scattering vector rotating perpendicular to the (001) plane of the SrTiO_3_ (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 SrTiO_3_ (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 SrTiO_3_ (111) substrate, two extra 3D RSM 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 SrTiO_3_ (111) substrate (Figs. S65–S66). Based on the experimental 3D RSM results on Nb-W-O nanorods on SrTiO_3_ (111) substrate for the three different directions ([001], [110] and [111] directions of SrTiO_3_), 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 SrTiO_3_ (111) substrate. Thus, the parallel planes pattern of the multi-layered 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 SrTiO_3_ (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 3D RSM 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 MO_6_ 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.
Distinguishing the boundary between amorphous and crystalline states is important because it helps us understand how the atomic structure of a material influences its physical, chemical, and functional properties. Determining this boundary is crucial for interpreting how structure governs behavior in materials. Understanding where and how this boundary lies enables better control of crystallization and amorphization processes, which are fundamental to materials synthesis, thin-film deposition, and annealing. Many emerging materials rely on properties that lie between amorphous and crystalline regimes. Understanding this boundary helps tune performance for desired applications. Our work opens important avenues of exploration and provides a unique platform for computational modeling of the 2D amorphous matter stacking. Moreover, accurate determination of amorphous solids in the complete range of disorder is important to shed advanced insights into the modeling of amorphous/crystalline systems in three-dimensional real space.
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, Nb_2_O_5_ (Sigma Aldrich, ~325 mesh, 99.9% trace metals basis) and WO_3_ (Sigma Aldrich, powder, 99.995% trace metals basis) were mixed in a 9:16 molar ratio, which is the stoichiometric ratio of Nb_18_W_16_O_93_ 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 SrTiO_3_ (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 O_2_. 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 SrTiO_3_ (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 Eiger2 R 500 K 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 µm^2^). 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 mm^2^ 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.
Supplementary information
Supplementary Information Description of Additional Supplementary Files Supplementary Video 1 Supplementary Video 2 Supplementary Video 3 Supplementary Video 4 Supplementary Video 5 Supplementary Video 6 Supplementary Video 7 Supplementary Video 8 Supplementary Video 9 Supplementary Video 10 Supplementary Video 11 Transparent Peer Review file