Three-dimensional atomic-scale characterization of titanium oxyhydroxide nanoparticles by data-driven lattice correlation analysis

Kohei Aso; Koichi Higashimine; Masanobu Miyata; Hiroshi Kamio; Yoshifumi Oshima

doi:10.1038/s42004-025-01513-2

. 2025 Apr 28;8:122. doi: 10.1038/s42004-025-01513-2

Three-dimensional atomic-scale characterization of titanium oxyhydroxide nanoparticles by data-driven lattice correlation analysis

Kohei Aso ¹, Koichi Higashimine ², Masanobu Miyata ¹, Hiroshi Kamio ³, Yoshifumi Oshima ^1,^✉

PMCID: PMC12037913 PMID: 40295845

Abstract

Metal oxyhydroxides are essential nanomaterials for recent technologies because of their diverse applications, such as catalysis, adsorbents, and precursors of metal oxides. These applications rely on the controlled crystal structures of metal oxyhydroxides formed via hydrolyzed metal monomers’ condensation. However, characterizing the atomic-scale structures of the metal oxyhydroxides has still been challenging due to their diverse structural types, nanometer-scale sizes, and beam sensitivity. Here, we developed a data-driven analysis approach for atom-resolved transmission electron microscopy images of titanium oxyhydroxide (metatitanic acid) nanoparticles. Lattice spacings and angles were measured for each of the 1300 nanoparticles with random crystal orientations, providing three-dimensional structural information. Our findings reveal their anatase-like structure with alternating layers of titanium dioxide (TiO₂) and titanium hydroxide (Ti(OH)₄) planes. The revealed structure is key to understanding their role as a precursor for metastable anatase TiO₂. Our approach unveils the three-dimensional structure of metal oxyhydroxides with high statistical reliability and low electron dose, paving the way for property understanding and application design.

Subject terms: Synthesis and processing, Structural properties, Imaging studies

Controlling the crystal structures of metal oxyhydroxides is key to their implementation in various technologies, but the required atomic-scale characterization remains challenging. Here, the authors describe a data-driven analysis approach for atom-resolved transmission electron microscopy images that enables the determination of the three-dimensional structure of titanium oxyhydroxide nanoparticles.

Introduction

Metal oxyhydroxides are important nanomaterials for technological and scientific areas due to their diverse properties as adsorbents^1–6, catalysts^7–9, and precursors of metal oxides^10–12. These applications are realized by their various shapes and structures, which are controlled by the condensation reaction process of metal-hydrated monomers. In this process, complex forms by attaching the monomers consisting of a metal cation with coordinated hydroxy (OH) groups and aquo (H₂O) ligands^13–15. When condensation reactions preferentially proceed in a linear direction, the metal oxyhydroxides grow into rod-like structures¹⁶. Similarly, two- and three-dimensional (3D) reactions lead to the sheet and particle-like shape, respectively. Different crystal structures can be formed even for the same chemical compositions, that is, structural polymorphs. The condensation reaction process can be controlled by the type of starting monomers, their concentration, pH, temperature, and so on. Structural analysis is important to understand the growth process and to feed the insight back to the synthesis area, leading to more controllable and new properties of the metal oxyhydroxides. However, certain metal oxyhydroxide structures remain unclear due to their diverse types and nanometer-scale sizes.

Metatitanic acid (MA) is one of such metal oxyhydroxides. MA has structural polymorphs with the chemical composition of H₂TiO₃, including layered and anatase-like structures ^{1–6,10–12}^. The layered MA is considered to be one of the Li-ion sieve adsorbents^1–3. The layered MA is obtained from chemical Li deintercalation and H intercalation of the layered Li₂TiO₃. X-ray diffraction (XRD) analysis revealed that the layered MA consists of alternating layers of H and Ti-O planes, which are sometimes misaligned (stacking faults)¹⁷. In contrast, the anatase-like MA, which is synthesized through hydrolysis and condensation reactions¹², has been used to adsorb U ions^4–6. Such an adsorption is considered to occur at their surface. In addition, the anatase-like MA has been used as an intermediate for syntheses of titanium dioxides (TiO₂) of anatase structure^10–12. The broadened peaks in X-ray diffraction (XRD) profiles suggest the nanoparticle (NP) form with a few nanometers^18,19. Although peak positions correspond to those of the anatase structure, peaks specific to the anatase-like MA were not observed clearly. Infrared spectroscopy results suggest that the MA-NPs contain the OH and H₂O bonds^4,5. However, despite their technological application, existing techniques have not yet provided atomic-scale characterization in understanding the internal structure of the anatase-like MA.

Transmission electron microscopy (TEM) and scanning TEM (STEM) can provide information down to the atomic scale. The improved spatial resolution of (S)TEM and image processing techniques have enabled to obtain 3D structures from the multiple projected (S)TEM images. Single-particle analysis, which classifies and averages more than thousands of TEM images, has successfully revealed the structure of organic molecules three-dimensionally. This technique assumes that the sample has the same structure and shape^20,21. However, it cannot be applied as is to the usual inorganic NPs since they are not all the same in structure and shape. Computed tomography (CT)^22,23 and through-focus methods²⁴ are popular 3D analyses in (S)TEM. These methods reconstruct several dozen images of the same region of interest from different projection directions and at different focus positions, respectively. This multiple acquisition leads to dozens to hundreds of times more electron dose compared to single projection imaging. CT-STEM is used to analyze metal nanoparticles that are durable to electron dose²⁵. However, previous studies reported that aluminum oxyhydroxide (HAlO₂) nanowires suffer from electron beam damage, limiting this approach¹⁶. One of the reasons is that the electron conductance of metal oxyhydroxides is less compared to metal²⁵. The less conductance results in charge accumulation near the illumination area under an electron beam, leading to the breaking of chemical bonds, thermalization, and/or Coulomb explosion.

In this study, we have developed a data-driven lattice correlation analysis for obtaining the structure of MA-NPs from HRTEM images. Since NPs are dispersed with random orientations on a thin film for TEM observation, the lattice patterns can be obtained from different viewing directions. Whereas conventional single-particle analysis classifies the particles in the image into each orientation and accumulates the image patterns, our approach extracts the structural periodicity of each particle. The spacings and angles of two different lattices were measured from a fast Fourier transformation (FFT) pattern of individual single NPs. The procedure is conducted on a thousand NPs. Such lattice correlation dataset provides 3D information on the structure. The structure and shape were further verified by density-functional theory (DFT) calculations. The MA-NPs were found to have an anatase-like structure with alternating stacking of TiO₂ and Ti half-occupied planes along the c-axis. The latter contains H atoms, resulting in the Ti(OH)₄ plane.

Results

Atom-resolved imaging of MA-NPs

We analyzed a commercial powder sample of MA provided by Mitsuwa Chemicals Co., Ltd. The powder XRD pattern is similar to that in the previous reports (Supplementary Note 1 and Fig. S1)^10,26. For (S)TEM observations, the powder sample was dispersed onto a thin carbon support film (see Materials and Methods for details). Preliminary observations suggested that the sample contained primary and secondary NPs (Supplementary Fig. S2). The primary NPs were single-crystalline particles of several nanometers in size. The secondary NPs were aggregates of the primary nanoparticles, and they ranged in size from a few tens of nanometers to several micrometers. In this study, we obtained the STEM images of individual primary MA-NPs. The acquisition conditions are described in detail in Materials and Methods^27,28.

Figure 1a shows an annular dark-field (ADF) STEM image of a primary MA-NP. This MA-NP maintained their structures and shapes (Supplementary Fig. S3). Since the ADF intensity corresponds to the number and mass of atoms aligned in a column along the projection direction^29,30, the brighter peaks correspond to Ti atom columns. The Ti columns form dumbbell-like arrangements. The dumbbells are lined up along their axes and are offset by half a periodicity perpendicular to the stacking direction. This atomic arrangement represents the projected pattern when the anatase structure is viewed from the [010] direction^31–34. Hereafter, the Miller indices of the anatase structure are used to express the lattice planes of the MA-NPs. The intensity gradually decreases from the center toward the edges of the NP. This intensity gradient reflects a 3D shape that thins out from the center. Considering the similarity to the anatase TiO₂ NPs³⁵, the observed MA-NP has four equivalent {101} and {011} facets, as well as {001} facets at the top and bottom. These structural and morphological features were confirmed in several other NPs (Supplementary Fig. S4).

Figure 1b shows an enlarged image of the interior of the NP. The Ti dumbbells exhibit asymmetric intensities, which are not evident in the STEM image simulated for the anatase TiO₂ structure (Supplementary Fig. S4 and Note 2)^34,36,37. Based on the line profile in Fig. 1c, the dumbbells exhibit intensity ratios of ~2:1, compared to the profile of anatase. The asymmetric intensities indicate that one Ti column contains half the atoms of the other. Figure 1d shows the FFT pattern of Fig. 1a. Most spots in the FFT pattern are explained in terms of the periods of the anatase structure. However, the MA-NPs exhibit 002 spots that correspond to ~470 pm, which do not occur in the anatase.

The asymmetric intensity profiles of the Ti dumbbells were reversed or changed to nearly symmetric profiles at several locations (Fig. 1e). In addition, the atomic column intensities were weaker on the inside of the rounded rectangle in Fig. 1a. The weaker intensities seem due to the defects, such as the formation of pores, surface roughness, and/or a half-unit cell shift relative to each other. Such defect structures are observed in most NPs (Supplementary Fig. S5).

Data-driven lattice correlation analysis

The following data-driven lattice correlation analysis was developed to identify the 3D structure of the MA-NPs. HRTEM was utilized here to obtain images in short acquisition times without significant artifactual image distortion. The pixel size of the images was calibrated by using a Si standard thin film sample (see Materials and Methods for details). The MA-NPs maintained their structure and morphology during the observations (Supplementary Fig. S6). The images were obtained from 503 different regions of the sample, including several MA-NPs that are randomly oriented on the supporting film. Further details of the HRTEM imaging are described in Materials and Methods. Individual NPs were identified from each HRTEM image (Fig. 2a)^38–40. In some instances, the detected regions may reflect the shape of the secondary NP. The primary and secondary NPs were distinguished by using the length of the circumference and the smallest polygon that encompasses the detected region (convex hull) (Fig. 2b). The NPs for which the length ratio of the polygon to the circumference is smaller than 1.2 were defined as the primary NPs. The length of the major axis and the aspect ratio were determined for each primary NP by approximating the shape as an ellipse.

Fig. 2 — a Typical HRTEM image of MA-NPs supported on a carbon support film. b NP regions were determined based on the image contrast. The NP regions are separated by different colors. The red line around each region indicates a convex hull. The white cross and white circle correspond to the center position and three times the standard deviation of the Gaussian mask, respectively. c HRTEM image masked for the center NP. d FFT pattern of the masked image.

Structural information of individual NPs—such as the lattice spacings and the angles between two lattices—was obtained from its FFT pattern. The image was masked using a two-dimensional Gaussian distribution function with a standard deviation of 300 pm to include the lattice periodicity of only the target NP (Fig. 2c). The position of each reciprocal-lattice spot was determined in subpixel accuracy by fitting a Gaussian function to the intensity distribution around the spot in the FFT pattern (Fig. 2d). The lattice spacing was calculated by measuring the distance of each corresponding reciprocal lattice spot from the center spot. The relative angle between two lattices was measured to be the angle between the two reciprocal lattice spots. These measurements were performed for 1311 NPs.

The MA-NPs’ morphology is measured from the detected region. The histogram of the major-axis length has a peak at ~5.1 nm (Fig. 3a). The histogram of the aspect ratio, the ratio of the lengths of the major and minor axes, exhibits a peak at ~1.3 (Fig. 3b). The crystallite size was evaluated to be 5.4 and 4.6 nm from full-width half maxima of 004 and 200 peaks in XRD profile, respectively (Supplementary Note 1 and Fig. S1)¹⁹. Our HRTEM analysis is in agreement with the XRD analysis.

Figure 3c shows a histogram of the lattice spacings. The histogram exhibits local maxima at ~190 pm, 240 pm, 350 pm, and 480 pm. The first three correspond to the spacings of the (200), (004), and (101) planes in the anatase structure, respectively. The (002) lattice has a spacing of 480 pm, which can be explained by the asymmetric intensity profiles observed in the STEM image in Fig. 1. The peak at (002) is broadened compared to the other peaks. A possible reason is the contribution of the amorphous carbon of the supporting film. In the FFT pattern, a halo pattern reflecting the short-range order of the amorphous carbon appears around the anatase 002 spots (Supplementary Fig. S7). As a result, the MA-NPs’ (002) peak must be hidden by the tail of the halo pattern.

The correlation was investigated for the several sets of lattice spacings and the angle between two different lattices. The two-dimensional histograms in Fig. 3d–f show the probability of observing two lattices with a certain angular relationship. The atomic model in Fig. 3g shows that the (002) and (004) planes are parallel when viewed from the [010] direction. In Fig. 3d, the histogram with a lattice angle range of 0.0° ± 2.5° (parallel) exhibits two peaks at the intersections of the lattice spacings of 240 pm and 480 pm, which correspond to the (004) and (002) lattice planes of anatase, respectively^37,41. Consequently, the position of the 002 spots is equally divided between 004 spots and the center spot in the FFT patterns (see also Fig. 1d). This combination occurred in 29 NPs (Supplementary Fig. S8). In contrast, the atomic model in Fig. 3g shows that the (101) plane intersects the (002) or (004) plane at an angle of 68.3° when being viewed from the [010] direction. In Fig. 3e, the histogram with a lattice angle range of 68.3° ± 2.5° displays four maxima: at the intersections of 240 pm and 350 pm as well as at 350 pm and 480 pm. Therefore, these maxima in the histogram are explained by a combination of the (004) and (101) lattices with one of the (002) or (101) lattices. This combination was found in 23 NPs (Supplementary Fig. S9). Furthermore, the atomic model in Fig. 3h insists that the (101) plane intersects the (011) plane at an angle of 82.1° when being viewed from [ $\bar{1} \bar{1} 1$ ] direction. In Fig. 3f, the histogram with a lattice angle range of 82.1° ± 2.5° exhibits a peak at the intersection of two identical values of 350 pm, which correspond to the (101) and (011) lattice spacings (Fig. 3f). Such a combination was observed in 30 NPs (Supplementary Fig. S10). The MA-NPs showed sets of (004)−(110) and (110)−(101) similar to those of anatase, respectively. Since these sets of lattice planes are observed from two different orientations, the similarity with the anatase structure can be shown in 3D. On the other hand, the structure of MA-NP is different from anatase in terms of 002 periodicity.

The measurement error is evaluated from the peaks in the histogram, which are distributed along the dimensions of the spacings d₁, d₂, and the angle θ. The standard deviation was evaluated to be less than 12 pm in spacings and 2.5° in angles for the peaks around the intersection of (004), (101), and (011). The detail of the analysis error is described in Supplementary Note 3, Fig. S11, and Table S1.

The lattice combination of (004) and (101) showed minimum deviation in the above combinations. From the peak position in the two-dimensional histogram, lattice spacings of MA-NP were evaluated to be d₀₀₄ = 238 ± 7.7 pm and d₁₀₁ = 350 ± 8.5 pm, where the errors indicate standard deviations. These result in the lattice parameters of c = 952 ± 31 pm and a = b = 376 ± 11 pm. These are consistent with the values of c = 949 pm and a = b = 380 pm evaluated from XRD analysis (Supplementary Note 1 and Fig. S1). In contrast, the lattice parameters of anatase TiO₂ nanoparticles are c = 949 pm and a = b = 379 pm for ~5 nm in size measured by XRD in previous study⁴². The measured lattice parameters of MA-NPs are almost the same as those of anatase TiO₂.

Proposed crystal structure of MA-NP

The experimental results show that MA-NP has an atomic arrangement similar to anatase TiO₂ while Ti-full and Ti-half planes are stacked along [001] direction. A structural model was proposed based on the experimental results. Figures 4a and 4b show a cross-section view of the c-planes. These planes can be explained by octahedrons consisting of center Ti and corner O or OH³³. On the c-plane in Fig. 4a, the octahedrons are arranged in a two-dimensional square lattice. Each octahedron is bonded to its neighboring four octahedrons by sharing O elements at its corners, thereby creating ionic Ti–O bonds. This plane has the same atomic arrangement as the c-plane of anatase TiO₂. In contrast, the number of octahedra is halved in the plane shown in Fig. 4b. These octahedra are not bonded through the O elements but are probably hydrogen-bonded by OH groups. This plane has the composition ratio of Ti(OH)₄. These two kinds of planes are stacked each other along [001] as shown in Fig. 4c. The set of these TiO₂ and Ti(OH)₄ planes is stacked in the c-axis direction with a half period shift in the a-axis and b-axis directions, respectively. The Ti atomic columns at the planes in Fig. 4a and Fig. 4b are aligned at the same position along [001] direction, forming a dumbbell-like shape when viewed along [010] direction (Figs. 1a and 3f). The unit cell of the MA-NP structure is twice as large as the unit cell of anatase TiO₂ along the a, b, and c axes. Note that the lattice parameters of MA-NP are described to be halved in this paper throughout for comparison. The proposed structure can also be explained by a possible growth model through a condensation reaction starting from a monomer (Supplementary Note 4 and Figs. S12−S14).

Theoretical calculations of the proposed structure

The structural model in Fig. 4h was supported by using DFT calculations with generalized gradient approximation^43–47. After evaluating the total electronic energy, the atomic positions and lattice constants were updated to minimize the magnitude of the residual force. It then evaluates the total energy again for the updated structure. These steps were iterated 1000 times. The atomic arrangement as a function of the iteration step is shown in Supplementary Movies S1 and S2⁴⁸. Further details of the DFT calculations are described in the Supporting Text. The calculation converged as the maximum of the residual force per atom is below the threshold of 10⁻⁴ Hartree per Bohr in the last 300 iteration steps (Supplementary Note 5 and Fig. S15). This indicates that the optimized structure is theoretically stable, at least as a local minimum.

Figure 5a shows the optimized structure model viewed along the [100] orientation. The model is visualized using VESTA⁴⁹. The optimized structure belongs to the same tetragonal crystal system as the initial structure. The lattice parameters match with one of the anatase structures calculated using DFT within 2% (Supplementary Table S2). This calculation result agrees with the HRTEM lattice correlation analysis, showing that the lattice parameters of MA-NP match with those of anatase within 1%, except that the unit vectors of the three axes differ by a factor of two. The optimized structure is used for STEM image simulation. Figure 5b shows the simulated image along the [100] orientation. The simulated image reproduces the asymmetric intensities of Ti dumbbells observed in the experimental images (Fig. 1a, Supplementary Fig S16). Furthermore, simulated images along the [111] and [131] orientations also agree with the corresponding experimental images (Figs. S17, and S18).

Fig. 5 — a Atomic model viewed along the [010] direction. Gray, red, and blue spheres represent Ti, O, and H atoms, respectively. b STEM simulation image of the optimized model in (a). Image is viewed along [010] direction. c Cross-sectional view of the Ti(OH)₄ c-plane marked by the green rounded rectangle in (a). Dotted lines indicate hydrogen bonds. The surrounding green rectangle corresponds to that in Fig. 4b. The black solid line outlines the unit cell.

The role of the H elements was discussed from the optimized structure. Figure 5c shows a cross-sectional view of the Ti(OH)₄ plane. The H and O elements that make up each OH group are located on approximately the same c-plane. Each H element is directed toward the O element that belongs to the next OH group, forming a hydrogen bond. Four neighboring OH groups exhibit this arrangement, forming a loop of hydrogen bonds. This loop may stabilize the structure instead of the ionic Ti-O bonding. The hydrogen bonds thus seem to be a key for understanding the structure of the metal oxyhydroxides that are produced through condensation reactions.

Discussions

Electron irradiation effect

In general, the sample sometimes undergoes structural changes during (S)TEM observations due to electron beam irradiation. The causes are mainly divided into knock-on damage and radiolysis²⁵. Although the beam damage of MA-NPs has not been studied in the previous study up to our knowledge, anatase TiO₂ has been actively studied. The structural change from anatase TiO₂ to cubic TiO has been observed under electron irradiation at an acceleration voltage of 300 kV by (S)TEM. The knock-on damage is considered to be the main mechanism^31,50. When the acceleration voltage is 200 kV or less, the radiolysis becomes predominant for metal oxides²⁵. It has been pointed out that evaluating the dose rate is more important than the dose as a condition for sample damage. A lower dose rate leads to avoiding charge accumulation in the sample. The threshold dose rate was estimated to be 1.2 × 10⁹ electrons nm^–2 sec^–1 in STEM observation with an acceleration voltage of 100 kV, where a narrow electron beam is scanned across a sample⁵¹. The structure is changed into cubic TiO beyond the threshold, similar to the case of TEM observation. In contrast, anatase TiO₂ nanoparticles experience structural change under HRTEM observation with a dose rate of 6.2 × 10⁴ electrons nm^–2 sec^–1 and acceleration voltage of 300 kV⁵⁰, where the electron beam is irradiated to the whole field of view. In this study, the dose rate was evaluated to be ~7 × 10⁵ − 2 × 10⁶ electrons nm^–2 sec^–1 for STEM observations and ~3 × 10³ electrons nm^–2 sec^–1 for HRTEM analysis, respectively⁵², at the acceleration voltage of 120 kV. These dose rates are 20 to 500 times lower than those in previous reports. The radiolysis must be suppressed enough. Since no obvious change was observed during (S)TEM observations of the MA-NPs, the irradiation damage can be ignored.

Comparison with other techniques

XRD enables precise determination of lattice spacing within a micrometer to millimeter-scale sample area. However, the diffraction peaks become broadened, and their intensities decrease for nano-sized crystallite¹⁹. The MA-NPs are found to have ~5 nm in size and to include defects, resulting in the broadening of the peak intensity. The (002) peak is a forbidden reflection in anatase and weak intensity in MA, so broadening may have made it less visible as a peak in XRD. Our approach takes advantage of the usage of TEM with high spatial resolution and high interaction of electrons with materials, enabling us to analyze nanometer-scale defective materials.

Among conventional methods, CT-(S)TEM enables the 3D structural analysis of the nanoparticles. The 3D atomic arrangements have been revealed for Au and Pt nanoparticles. Since this approach is performed on individual particles, it leads to a lack of statistical reliability in structural analysis. Furthermore, this method requires multiple images, as described in the introduction part. Au and Pt crystals have benefits in that they are durable to the electron beam due to their electron conductivity and provide high image signals. These benefits are not for transition metal oxyhydroxides with less electron conductivity and light elements. Micro-electron diffraction has been performed to obtain a 3D diffraction pattern by acquiring multiple patterns from various angles and then reconstructing the images. Although this technique allows the structural analysis of proteins with less dose rate of ~1 electron nm^–2 s^–1, the sample is assumed to be a single crystal over the field of view of ~100 nm⁵³. The structural information cannot be analyzed appropriately when the sample has crystallite with a smaller size. 4D-STEM represents another advanced technique, capturing electron diffraction patterns at each scanning point with a single nanometer resolution⁵⁴. This method also takes advantage that the dose rate can be reduced enough to analyze the organic crystals. However, structural information has to be extracted from a huge dataset of diffraction patterns, including the large unwanted areas, such as supporting film and agglomerated nanoparticles. Thus, our approach enables 3D structural determination with statistical reliability and reduced beam damage, which is challenging for conventional methods.

The developed HRTEM lattice correlation analysis allowed us to propose the internal structure of anatase-like MAs in 3D. As mentioned in the introduction part, the anatase TiO₂ NPs can be obtained by the calcination of the MA-NPs as a precursor^10–12. If the four H elements in the Ti(OH)₄ plane of the proposed MA structure are replaced by one Ti atom, the structure is changed to anatase TiO₂. The internal H elements in an MA-NP may be released and replaced by a Ti atom during the calcination. The observed structure of the MA-NP seems important to understanding the role as a precursor of the metastable anatase TiO₂.

Conclusions

A data-driven lattice correlation analysis was developed to reveal the structure of MA-NPs. The structure of MA-NPs is similar to that of anatase TiO₂, but the Ti-filled layers and layers in which only half of Ti occupies are alternatively stacked in the c-axis direction. The structure is proposed to be a stack of TiO₂ and Ti(OH)₄ planes, which was supported by DFT calculation. The structure seems to contribute to understanding of the role as a precursor for metastable anatase titanium dioxide. Our data-driven lattice correlation analysis is a powerful technique for elucidating the complex structure of metal oxyhydroxides with defects. We expect that our technique brings a further structural understanding of metal oxyhydroxides, which will expand their possibilities of diverse applications.

Methods

Sample preparation

The original powder sample exhibits mainly anatase titanium dioxide (TiO₂) reflections as shown in the XRD pattern (Supplementary Note 1 and Fig. S1). We note that although peaks corresponding to brookite TiO₂ are also noticeable ^26,55, the intensities of these peaks are so low that brookite structure was not observed in the (S)TEM observations. The sample for (S)TEM observation was prepared as follows. A powder sample of MA-NPs was dispersed in ethanol using sonication. This solution was dropped onto a grid (STEM Co., Ltd., Japan) for (S)TEM observations. The grid has a ~5 nm thick carbon support film that is thin enough for the observations. After dropping the solution, the grid was dried in a vacuum desiccator (~10³Pa).

STEM observation conditions

STEM observations were carried out using JEM-ARM200F (JEOL, Japan). The accelerating voltage of the electron beam was 120 kV, and the convergence semi-angle of the incident electron probe was 22 mrad. The angular detection range of the annular detector for the forward-scattered electrons was 40–160 mrad. These angles were calibrated by using a silicon (Si) standard sample and the reported lattice constant of Si⁵⁶. To suppress the influence of sample drift during the observations, an image series was acquired with 20 frames at the fast-scanning speed of 3 μsec per pixel. The image size was set to 512 × 512 pixels. The dose rate was evaluated from the current value of the fluorescent screen, scanning speed, and pixel size. The frames were positionally aligned by using the cross-correlation method and were integrated as a single image. The image shift between frames is aligned by rigid registration. It should be noted that the intensity distributions of the atomic columns in Fig. 1a are slightly elongated around the center part or thick part. In contrast, the intensity distributions around the edge part or thinner part are not elongated. The elongation at the thick part is probably because of the slight tilt of the incident electron beam from the crystal zone axis⁵⁷.

HRTEM observation conditions

HRTEM observations were performed using the same machine as employed for the STEM observations. The accelerating voltage of the electron beam was 120 kV. The images were captured using an Orius SC600 (Gatan, US) charge-coupled device camera. The image size was set to be 1336 × 1336 pixels. For the statistical analysis of the HRTEM images, we fixed the image magnification to be ×300,000 to visualize both the overall shapes of multiple NPs with a few nanometers in size and lattice fringes of several hundred picometers. The pixel size was calibrated to be 42.8 pm per pixel at this magnification with the Si standard sample and its reported lattice constant. The dose rate was evaluated from the current value of the fluorescent screen, exposure time of 2 s, and beam size.

Detection of NPs from HRTEM images

The particle shapes were extracted from the HRTEM images with a watershed algorithm that can extract regions with different contrasts from other areas of an image^39,40. The HRTEM images were smoothed with a Gaussian filter with a standard deviation of 0.9 nm to avoid the influence of shot noise and the contrast of the carbon support film. NPs that were partially acquired in the image were excluded because their shapes could not be evaluated accurately. The analysis was carried out by using Python programming language with some libraries (Supplementary Note 6).

Supplementary information

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Description of Additional Supplementary Files

Supplementary Movie 1^{(9.9MB, mp4)}

Supplementary Movie 2^{(8.8MB, mp4)}

Acknowledgements

The authors are grateful to Assoc. Prof. Shun Nishimura of the Japan Advanced Institute of Science and Technology for the discussion on the growth process of NPs. K.A. acknowledges Mr. Yuito Kawamura for his contributions to HRTEM observations.

Author contributions

K.A., H.K., and Y.O. designed this study. K.H. conducted XRD measurements. K.A. and K.H. performed the (S)TEM experiments. K.A. analyzed the (S)TEM data and constructed MA-NP models. M.M. carried out DFT calculations. Y.O. supervised the research. K.A. wrote the first draft. All of the co-authors participated in the discussion for the final manuscript.

Peer review

Peer review information

Communications Chemistry thanks Ahin Roy, Yongsoo Yang, Hyesung Jo, and Nonappa Nonappa for their contribution to the peer review of this work. Peer review reports are available.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The Python codes used in this study are available from the corresponding author upon reasonable request.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

The online version contains supplementary material available at 10.1038/s42004-025-01513-2.

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15.Livage, J., Henry, M. & Sanchez, C. Sol-gel chemistry of transition metal oxides. Prog. Solid State Chem.18, 259–341 (1988). [Google Scholar]
16.Iijima, S., Yumura, T. & Liu, Z. One-dimensional nanowires of pseudoboehmite (aluminum oxyhydroxide γ-AlOOH). Proc. Natl Acad. Sci. Usa.113, 11759–11764 (2016). [DOI] [PMC free article] [PubMed] [Google Scholar]
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36.Barthel, J. Dr. Probe: A software for high-resolution STEM image simulation. Ultramicroscopy193, 1–11 (2018). [DOI] [PubMed] [Google Scholar]
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45.Miyata, M. et al. High-throughput screening of sulfide thermoelectric materials using electron transport calculations with OpenMX and BoltzTraP. J. Electron. Mater.47, 3254–3259 (2018). [Google Scholar]
46.Ozaki, T. Variationally optimized atomic orbitals for large-scale electronic structures. Phys. Rev. B67, 155108 (2003). [Google Scholar]
47.Hamann, D. R., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett.43, 1494–1497 (1979). [Google Scholar]
48.Lee, Y.-T. & Ozaki, T. OpenMX Viewer: A web-based crystalline and molecular graphical user interface program. J. Mol. Graph. Model.89, 192–198 (2019). [DOI] [PubMed] [Google Scholar]
49.Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr.44, 1272–1276 (2011). [Google Scholar]
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52.Egerton, R. F. Dose measurement in the TEM and STEM. Ultramicroscopy229, 113363 (2021). [DOI] [PubMed] [Google Scholar]
53.Nannenga, B. L. & Gonen, T. The cryo-EM method microcrystal electron diffraction (MicroED). Nat. Methods16, 369–379 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]
54.Ophus, C. Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond. Microsc. Microanal.25, 563–582 (2019). [DOI] [PubMed] [Google Scholar]
55.Meagher, E. P. & Lager, G. A. Polyhedral thermal expansion in the TiO₂ polymorphs; refinement of the crystal structures of rutile and brookite at high temperature. Can. Mineral.17, 77–85 (1979). [Google Scholar]
56.Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys.93, 025010 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
57.So, Y.-G. & Kimoto, K. Effect of specimen misalignment on local structure analysis using annular dark-field imaging. J. Electron Microsc.61, 207–215 (2012). [DOI] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Transparent Peer Review file^{(1.8MB, pdf)}

Supplementary Information^{(25.8MB, pdf)}

42004_2025_1513_MOESM3_ESM.pdf^{(117.2KB, pdf)}

Description of Additional Supplementary Files

Supplementary Movie 1^{(9.9MB, mp4)}

Supplementary Movie 2^{(8.8MB, mp4)}

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The Python codes used in this study are available from the corresponding author upon reasonable request.

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[CR15] 15.Livage, J., Henry, M. & Sanchez, C. Sol-gel chemistry of transition metal oxides. Prog. Solid State Chem.18, 259–341 (1988). [Google Scholar]

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[CR18] 18.Vorontsov, A. V. & Tsybulya, S. V. Influence of nanoparticles size on XRD patterns for small monodisperse nanoparticles of Cu⁰ and TiO₂ Anatase. Ind. Eng. Chem. Res.57, 2526–2536 (2018). [Google Scholar]

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[CR21] 21.Kühlbrandt, W. The resolution revolution. Science343, 1443–1444 (2014). [DOI] [PubMed] [Google Scholar]

[CR22] 22.Moniri, S. et al. Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys. Nature624, 564–569 (2023). [DOI] [PubMed] [Google Scholar]

[CR23] 23.Scott, M. C. et al. Electron tomography at 2.4-ångström resolution. Nature483, 444–447 (2012). [DOI] [PubMed] [Google Scholar]

[CR24] 24.Ishikawa, R., Shibata, N., Taniguchi, T. & Ikuhara, Y. Three-dimensional imaging of a single dopant in a crystal. Phys. Rev. Appl.13, 1 (2020). [Google Scholar]

[CR25] 25.Jiang, N. Electron beam damage in oxides: a review. Rep. Prog. Phys.79, 016501 (2016). [DOI] [PubMed] [Google Scholar]

[CR26] 26.Seto, Y. & Ohtsuka, M. ReciPro: free and open-source multipurpose crystallographic software integrating a crystal model database and viewer, diffraction and microscopy simulators, and diffraction data analysis tools. J. Appl. Crystallogr.55, 397–410 (2022). [Google Scholar]

[CR27] 27.Aso, K. et al. Singular behaviour of atomic ordering in Pt–Co nanocubes starting from core–shell configurations. Nanoscale14, 9842–9848 (2022). [DOI] [PubMed] [Google Scholar]

[CR28] 28.Aso, K. et al. Subpercent local strains due to the shapes of gold nanorods revealed by data-driven analysis. ACS Nano15, 12077–12085 (2021). [DOI] [PubMed] [Google Scholar]

[CR29] 29.Williams, D. B. & Carter, C. B. Transmission Electron Microscopy. (Springer US, 2009) 10.1007/978-0-387-76501-3.

[CR30] 30.Crewe, A. V., Wall, J. & Langmore, J. Visibility of single atoms. Science168, 1338–1340 (1970). [DOI] [PubMed] [Google Scholar]

[CR31] 31.Li, Y. et al. Atomic-scale imaging of structural evolution from anatase TiO2 to cubic TiO under electron beam irradiation. Nano Today59, 102532 (2024). [Google Scholar]

[CR32] 32.Han, G., Kim, J. Y., Kim, K. J., Lee, H. & Kim, Y. M. Controlling surface oxygen vacancies in Fe-doped TiO₂ anatase nanoparticles for superior photocatalytic activities. Appl. Surf. Sci.507, 144916 (2020). [Google Scholar]

[CR33] 33.Pauling, L. The principles determining the structure of complex ionic crystals. J. Am. Chem. Soc.51, 1010–1026 (1929). [Google Scholar]

[CR34] 34.Penn, R. L. & Banfield, J. F. Morphology development and crystal growth in nanocrystalline aggregates under hydrothermal conditions: Insights from titania. Geochim. et. Cosmochim. Acta63, 1549–1557 (1999). [Google Scholar]

[CR35] 35.Lazzeri, M., Vittadini, A. & Selloni, A. Structure and energetics of stoichiometric TiO₂ anatase surfaces. Phys. Rev. B63, 155409 (2001). [Google Scholar]

[CR36] 36.Barthel, J. Dr. Probe: A software for high-resolution STEM image simulation. Ultramicroscopy193, 1–11 (2018). [DOI] [PubMed] [Google Scholar]

[CR37] 37.Howard, C. J., Sabine, T. M. & Dickson, F. Structural and thermal parameters for rutile and anatase. Acta Crystallogr. B Struct. Sci.47, 462–468 (1991). [Google Scholar]

[CR38] 38.Vasudevan, R. K., Valleti, S. M., Ziatdinov, M., Duscher, G. & Somnath, S. A processing and analytics system for microscopy data workflows: the pycroscopy ecosystem of packages. Advcd Theory Sims6, 2300247 (2023). [Google Scholar]

[CR39] 39.Van Der Walt, S. et al. Scikit-image: Image processing in python. PeerJ2014, 1–18 (2014). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR40] 40.Neubert, P. & Protzel, P. Compact Watershed and Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation Algorithms. in 2014 22nd International Conference on Pattern Recognition 996–1001 (IEEE, 2014) 10.1109/ICPR.2014.181.

[CR41] 41.Hogan, D. W. & Dyson, D. J. Angles between planes in the hexagonal and tetragonal crystal systems. Micron (1969)2, 59–61 (1970). [Google Scholar]

[CR42] 42.Ahmad, Md. I. & Bhattacharya, S. S. Size effect on the lattice parameters of nanocrystalline anatase. Appl. Phys. Lett.95, 191906 (2009). [Google Scholar]

[CR43] 43.Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. 3865–3868 (1996). [DOI] [PubMed]

[CR44] 44.Miyata, M. & Koyano, M. Transport properties of binary phosphide AgP₂ denoting high Hall mobility and low lattice thermal conductivity. Mater. Res. Express9, 055901 (2022). [Google Scholar]

[CR45] 45.Miyata, M. et al. High-throughput screening of sulfide thermoelectric materials using electron transport calculations with OpenMX and BoltzTraP. J. Electron. Mater.47, 3254–3259 (2018). [Google Scholar]

[CR46] 46.Ozaki, T. Variationally optimized atomic orbitals for large-scale electronic structures. Phys. Rev. B67, 155108 (2003). [Google Scholar]

[CR47] 47.Hamann, D. R., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett.43, 1494–1497 (1979). [Google Scholar]

[CR48] 48.Lee, Y.-T. & Ozaki, T. OpenMX Viewer: A web-based crystalline and molecular graphical user interface program. J. Mol. Graph. Model.89, 192–198 (2019). [DOI] [PubMed] [Google Scholar]

[CR49] 49.Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr.44, 1272–1276 (2011). [Google Scholar]

[CR50] 50.Song, M., Lu, Z. & Li, D. Phase transformations among TiO₂ polymorphs. Nanoscale12, 23183–23190 (2020). [DOI] [PubMed] [Google Scholar]

[CR51] 51.Berger, S. D., Macaulay, J. M. & Brown, L. M. Radiation damage in TiO_x at high current density. Philos. Mag. Lett.56, 179–185 (1987). [Google Scholar]

[CR52] 52.Egerton, R. F. Dose measurement in the TEM and STEM. Ultramicroscopy229, 113363 (2021). [DOI] [PubMed] [Google Scholar]

[CR53] 53.Nannenga, B. L. & Gonen, T. The cryo-EM method microcrystal electron diffraction (MicroED). Nat. Methods16, 369–379 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR54] 54.Ophus, C. Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond. Microsc. Microanal.25, 563–582 (2019). [DOI] [PubMed] [Google Scholar]

[CR55] 55.Meagher, E. P. & Lager, G. A. Polyhedral thermal expansion in the TiO₂ polymorphs; refinement of the crystal structures of rutile and brookite at high temperature. Can. Mineral.17, 77–85 (1979). [Google Scholar]

[CR56] 56.Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys.93, 025010 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR57] 57.So, Y.-G. & Kimoto, K. Effect of specimen misalignment on local structure analysis using annular dark-field imaging. J. Electron Microsc.61, 207–215 (2012). [DOI] [PubMed] [Google Scholar]

PERMALINK

Three-dimensional atomic-scale characterization of titanium oxyhydroxide nanoparticles by data-driven lattice correlation analysis

Kohei Aso

Koichi Higashimine

Masanobu Miyata

Hiroshi Kamio

Yoshifumi Oshima

Abstract

Introduction

Results

Atom-resolved imaging of MA-NPs

Fig. 1. Atomic-resolution STEM ADF image of an MA-NP.

Data-driven lattice correlation analysis

Fig. 2. Analysis flow of lattice correlation analysis.

Fig. 3. Data-driven lattice correlation analysis of the MA-NPs.

Proposed crystal structure of MA-NP

Fig. 4. Proposed crystal structure of an MA-NP.

Theoretical calculations of the proposed structure

Fig. 5. Atomic model of the MA-NP structure after DFT optimization.

Discussions

Electron irradiation effect

Comparison with other techniques

Conclusions

Methods

Sample preparation

STEM observation conditions

HRTEM observation conditions

Detection of NPs from HRTEM images

Supplementary information

Acknowledgements

Author contributions

Peer review

Peer review information

Data availability

Code availability

Competing interests

Footnotes

Supplementary information

References

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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