3D dynamic structure of a Pt nanoparticle on SrTiO₃ (001) during in-situ heating atomic-resolution ADF STEM imaging

Abstract

Noble metal nanoparticles supported on semiconducting substrates have long been used in heterogeneous catalysis. A central objective in this field is to identify the active sites for catalysis, which requires precise determination of the 3D atomic structure of nanoparticles on substrates. Furthermore, it has widely accepted that catalytic active sites undergo dynamic structural changes under reaction conditions. However, direct observation of such 3D dynamic structures at the atomic scale, particularly under elevated temperatures and reducing environments, remains a challenge. Here, we present the 3D atomic structure of an epitaxially grown platinum nanoparticle, consisting of 263 Pt atomic sites, supported on an atomically flat SrTiO₃ (001) surface, using single-projection atomic-resolution scanning transmission electron microscopy (STEM) combined with quantitative statistical analysis. In-situ heating experiments under reduced atmosphere reveal that the Pt atoms with lower coordination numbers are mobile within the second-nearest-neighbor atomic sites, and we describe the 3D dynamic atomic structure of the Pt nanoparticle by the distribution of partial occupation of Pt atoms. Furthermore, we perform density functional theory calculations based on the experimentally reconstructed 3D atomic structure and find that excess negative charges accumulate at the lower CN atomic sites, which likely serve as catalytically active sites.

Active sites in nanocatalysts undergo dynamic structural changes under reaction conditions. Here, the authors use quantitative scanning TEM to reconstruct the 3D dynamic structure of a Pt nanoparticle, identifying excess negative charges accumulated at lower-coordination Pt atomic sites.

Introduction

The catalytic activity of noble metal nanoparticles (NPs) supported on semiconducting substrates is primarily influenced by the electronic structure of the NPs¹. Consequently, the size and geometric structure of the NPs strongly affect their catalytic activity². As the size of the metal NPs is reduced to below a few nanometers, charge transfer between the NPs and the substrate increases, significantly enhancing their catalytic activity³. Therefore, downsizing NPs is crucial for enhancing catalytic activity, and the effects of size on their performance have been extensively studied⁴. Beyond size, the active site is the most fundamental concept in heterogeneous catalysis to understand catalytic mechanisms, and the geometric structures of NPs, such as heterointerface atomic configurations, facet planes, and coordination number (CN), play a role in determining catalytic activity. To elucidate active sites in NPs, it is essential to determine the three-dimensional (3D) atomic structure of NPs. Electron tomography has been widely used to determine the 3D atomic structures of NPs, including monatomic and high-entropy alloys^5,6. These NPs are typically pseudo-free-standing, supported by a thin carbon film, allowing us to reconstruct their 3D atomic structures with minimal interference from the substrate. However, in a heterogeneous catalytic system, it is essential not only to determine the 3D atomic structures of NPs but also to understand the atomic structure at the heterointerface between the NPs and substrate. This necessitates an alternative approach for reconstructing 3D atomic structures of NPs supported on a semiconducting substrate.

In the last decade, it has been widely accepted that the active sites in NPs undergo dynamic structural changes during catalytic reactions owing to temperature or atmosphere, and therefore, it is important to investigate the 3D atomic structural dynamics in NPs. Atomic-resolution annular dark-field scanning transmission electron microscopy (ADF STEM) has been employed to investigate the atomic structures of NPs⁷. Owing to the Z-contrast nature (Z is the atomic number)⁸, the number of atoms in a projection is countable by quantitatively analyzing the Z-contrast intensity^9,10. However, determining the 3D atomic structure of NPs supported on substrates remains a significant challenge, as it requires separately quantifying the Z-contrast intensities of both the NPs and the substrate. Here, we show the 3D atomic structure of a Pt NP supported on an atomically flat SrTiO₃ (001) surface, using in-situ heating atomic-resolution ADF STEM imaging from a single projection combined with the quantitative statistical analysis within the framework of the Markov chain Monte Carlo (MCMC) method. On the basis of our statistical analysis, we reconstruct the 3D atomic structure of the Pt NP and determine the atomic structure of the heterointerface between the Pt NP and SrTiO₃ (001) surface. The experimentally reconstructed 3D atomic structure is then evaluated by density functional theory (DFT) calculations, and we investigate the interfacial atomic structure, their charge density distribution and catalytic activity (d-band model) for each atomic site in the Pt NP. In the time-resolved ADF STEM imaging at high temperatures, we frequently observed Pt atom jumps in the Pt NP, suggesting that Pt atoms are actively moving under the reduced atmosphere (high vacuum). Since multiple Pt atom exchange processes cannot be distinguished, it is difficult to accurately track all the movements of individual Pt atoms. Although the temporal resolution in STEM can be improved using the recent fast-scanning electron probe system^11,12, the signal-to-noise ratio (SNR) in each frame becomes significantly reduced, which makes quantitative analysis challenging. Therefore, we quantitatively analyze the Z-contrast intensity in the time-averaged ADF STEM image to elucidate the dynamics of the 3D atomic structure of the Pt NP using a statistical approach. We also investigate the interfacial atomic structure between the Pt NP and the SrTiO₃ (001) substrate. Furthermore, we perform DFT calculations based on the experimentally reconstructed 3D atomic structure of the Pt NP and elucidate the relationships between the CN, charge transfer, and catalytic activity at each atomic site using d-band model analysis.

Results and discussion

Atomic-resolution ADF STEM imaging of Pt NPs on SrTiO₃ (001)

Figure 1a shows a plan-view ADF STEM image of Pt NPs dispersed on the atomically flat SrTiO₃ (001) surface¹³. To avoid charging the TEM sample, specimen damage, and hydrocarbon contamination due to electron beam irradiation, we performed in-situ heating of the sample at 483 K in a high vacuum (8 × 10^–7 Pa)¹⁴. In addition to the periodic lattice contrasts of the Sr and Ti-O atomic columns, the brighter objects covering the SrTiO₃ (001) surface correspond to the Pt NPs. As indicated by the white arrows in Fig. 1a, the contrast of the SrTiO₃ (001) substrate changes abruptly in the [010] direction, corresponding to the bunching step on the SrTiO₃ (001) surface. The red ellipses in Fig. 1a indicate that the shape of Pt NPs is not perfectly circular, and we approximated the projected NP geometries as ellipses and calculated average diameters along the major and minor axes. Figure 1b shows the histogram of the average diameters of Pt NPs (total number: 159), and the average diameter of Pt NPs is 1.76 ± 0.4 nm, corresponding to 4 ± 1 unit cells of SrTiO₃ (d₁₀₀ = 0.39 nm). As can be seen in the ADF STEM image, most of the Pt NPs are slightly elongated along the <100> and <110> directions of SrTiO₃, and we measured the long-to-short side ratio (LS ratio) of the Pt NPs. Figure 1c shows the LS ratio distribution of the Pt NPs. The circularly symmetric Pt NPs have the highest frequency (≈28%, LS ratio <1.1), and the frequency of the larger LS ratio gradually decreases. These Pt NPs on SrTiO₃ (001) have high crystallinity. As shown in Fig. 1d, f, we found two types of representative orientation relationships between Pt NPs and the SrTiO₃ (001) substrate: (001)[100]_Pt || (001)[100]_SrTiO3 and (110)[001]_Pt || (001)[1-10]_SrTiO3. The Pt atom locations in Fig. 1d exactly match the atomic columns of SrTiO₃, including Sr, Ti-O, and O atomic columns. Therefore, the orientation relationship in Fig. 1d is determined to be (001)[100]_Pt || (001)[100]_SrTiO3. The lattice mismatch is considerably as small as [d_100,Pt, d_100,SrTiO3] = 0.46%, and therefore, the (001) stacking Pt NPs can be grown epitaxially on the SrTiO₃ (001) substrate. The atomic configuration of Fig. 1f is complex, making it difficult to identify the crystal orientation of the Pt NP. However, when the intensity of the SrTiO₃ substrate is subtracted from Fig. 1f, the (110) stacking of the Pt NP becomes visible, as shown in Fig. 1g. We note that image subtraction is possible because the atomically flat SrTiO₃ provides uniform Z-contrast intensity in large area¹². The orientation relationship in Fig. 1f is determined to be (110)[001]_Pt || (001)[1-10]_SrTiO3. Although the Pt NPs were annealed at a low temperature (483 K), the crystallinity of the Pt NPs is considerably higher than those on the TiO₂ (110) substrate¹⁴. This is because the lattice mismatches between Pt NPs and SrTiO₃ (001) are less than 0.5%, which is 10 times lower than the case in TiO₂ (110) substrate (minimum lattice mismatch: –6.4%)¹⁴.

Fig. 1. The size and shape distribution of Pt NPs on SrTiO₃ (001).

a Atomic-resolution ADF STEM image obtained from Pt NPs supported on SrTiO₃ (001) surface, viewed along the [001] direction. b The histogram of the average diameters of Pt NPs (total number: 159), and the average diameter of Pt NPs is 1.76 ± 0.4 nm. c The histogram of the LS ratio of the Pt NPs. d, e Atomic-resolution ADF STEM image of (001) stacking Pt NP and the subtracted SrTiO₃ periodic lattice contrast. f, g Atomic-resolution ADF STEM image of (110) stacking Pt NP and the subtracted SrTiO₃ periodic lattice contrast. The scale bars in (a) and (d–g) are 5 nm and 1 nm, respectively. Source data are provided as a Source Data file.

3D reconstruction of the Pt NP on SrTiO₃ (001)

To reconstruct the 3D atomic structure of a Pt NP, we first count the number of projected Pt atoms on the SrTiO₃ (001) substrate using a single ADF STEM image. Owing to the incoherent nature of Z-contrast imaging, the Z-contrast intensity is described by a 3D convolution of the point spread function and an object function. According to previous reports, the Z-contrast intensity increases monotonically with the number of atoms along the atomic column^9,15,16. In the present case, the number of Pt atoms per column is limited (less than 5 atoms)^9,15. Therefore, the Z-contrast intensity should increase almost linearly with the number of Pt atoms, indicating that the number of Pt atoms can be counted and the 3D atomic structure of the Pt NP on the SrTiO₃ (001) substrate can be reconstructed. Figure 2a shows an atomic-resolution ADF STEM image containing a single (001) stacking Pt NP, and the Pt atoms are well located on the Ti-O, Sr, and O atomic columns, respectively. To accurately evaluate the Z-contrast intensity, we choose the (001)-stacking Pt NPs because it is epitaxially grown on the SrTiO₃ (001) substrate and has a dominant orientation relationship in this system. To quantify the Z-contrast intensity, we perform 2D Gaussian fitting for the respective atomic columns and use the integral of the fitted 2D Gaussian function as the atomic column Z-contrast intensity (see Methods). In a standard gradient descent fitting algorithm for 2D Gaussian fitting, there are two critical issues: (i) the fitted parameters may be trapped at the local minima because the algorithm strongly depends on the initial value, and (ii) it is difficult to estimate the fitting error. To overcome these issues, we perform a 2D Gaussian fitting for the Z-contrast intensity using a random walk Metropolis-Hastings (RWMH) algorithm as a framework of the Markov chain Monte Carlo (MCMC) method^13,17. In the RWMH algorithm, more than 10⁶ Metropolis sweeps (fitting trials) are used for each atomic column, allowing thorough exploration of possible solutions in a large parameter space. Furthermore, the accepted Metropolis sweeps are stored and used to estimate the fitting errors, and the solution (integral of 2D Gaussian profile) is then given as a probability density function (PDF) rather than a single value in the gradient descent algorithm. Note that the sampling number is quite high, and the PDF will have a Gaussian distribution. As shown in Fig. 2a, Pt atoms are located at three distinct atomic sites: (i) Ti-O (blue), (ii) Sr (green), and (iii) O (red). The numbers of fitted atomic columns are 144 for Ti-O, 144 for Sr, and 44 for O atomic columns, respectively. To accurately count the number of Pt atoms, it is necessary to calibrate the scale of quantified Z-contrast intensity. Several methods have been reported for this purpose, including absolute intensity scaling¹⁸ and intensity histogram classification^13,16, and we adopt the latter approach. Here, we construct the histograms by summing all the PDFs (total PDF) for the Ti-O, Sr, and O atomic columns, respectively. It is important to note that a histogram is highly dependent on the choice of bin size, therefore we optimize the bin size by minimizing the L² cost function¹⁹.

Fig. 2. Counting the number of Pt atoms by statistical approach on Z-contrast intensity.

a Atomic-resolution ADF STEM image containing a (001) stacking Pt NP. The atomic structure model of SrTiO₃ is overlaid: Sr (green), Ti (blue), and O (red). b–d The bin-optimized total PDF (blue dots) for Ti-O, Sr, and O atomic columns, respectively. The colored solid lines (light blue to pink) in each panel are the deconvolved Gaussian profiles, and the red line is the summation of the deconvolved Gaussian profiles (see Supplementary Note 4). The Gaussian profiles as marked by black arrows correspond to irregular peaks (non-integer). e The number of Pt atoms at each atomic column, and Ti-O, Sr, and O atomic columns are labeled with diamonds, squares and circles, respectively. The scale bars in (a) and (e) are 1 nm and 5 Å, respectively. Source data are provided as a Source Data file.

Figure 2b–d shows the bin-size-optimized total PDF (blue dots) for the Ti-O, Sr, and O atomic columns, respectively. Owing to the extensive Metropolis sweeps, we have more than 10⁷ sampling points, which is sufficient for statistical analysis. To classify the number of Pt atoms from the total PDFs, it is necessary to deconvolve the total PDFs into multiple Gaussian profiles. However, the distribution of the total PDFs is exceptionally complicated, containing many peaks that partially overlap. Therefore, we again implemented the RWMH algorithm to uniquely deconvolve them into multiple Gaussian profiles¹³. The best-fit deconvolved Gaussian profiles and their summation are shown as solid-colored lines (light blue to pink) and red lines, and the summation of the multiple Gaussian profiles reproduces the total PDFs very well. To count the number of Pt atoms, we first checked the linearity of the integrated intensity intervals between Gaussian profiles (peak-to-peak distances). The integrated intensity intervals (arb. units) between the neighboring Gaussian profiles are estimated to be 147.2 ± 18.9, 150.5 ± 10.8, and 143.4 ± 18.8 (standard error of the mean) for Ti-O, Sr, and O atomic columns, respectively, suggesting that the integrated intensity intervals maintain good linearity and we can count the number of Pt atoms from the integrated intensity. With this classification, we found that the projected number of Pt atoms per atomic column is less than 5, and the numbers are given in the bottom of Fig. 2b–d, respectively. However, we also found several irregular peaks (black arrows in Fig. 2b–d) located between regular intervals. These peaks may indicate the non-integer numbers of Pt atoms (partial occupation), which will be discussed in the next section. For the Ti-O atomic columns, we found 6 regular peaks, corresponding to the number of Pt atoms from #0 to #5, as indicated by the numbers at the bottom of Fig. 2b. Most of the Ti-O atomic columns have no Pt atoms, and therefore the frequency at the Gaussian profile #0 is the highest. For the Sr atomic column, there are clear tail broadening on both sides at the peak #0 (red arrows), which is not observed at the peak #0 in the Ti-O atomic columns. We therefore added two Gaussian profiles, which significantly improved the goodness of fit (χ-squared test). The classified Sr atomic columns for these two subside peaks are in the bulk region and not related to Pt atoms, and moreover, the integrated intensity intervals are smaller than that of a single Pt atom, suggesting that these atomic columns contain Sr atomistic defects. According to a previous report, Sr mono-vacancies (V_Sr) and adatoms (A_Sr) can form on the surface, and therefore we conclude these subside peaks correspond to V_Sr and A_Sr, respectively¹³. The other peaks are assigned to Pt atoms of #2 to #5, except for three peaks marked with black arrows. Interestingly, there is no Gaussian profile #1, and hence, the Pt NP on Sr atomic columns should have more than two Pt atoms. Compared with the Ti-O and Sr atomic columns, the total PDF of O atomic columns have much more complex profiles. The best-fitted total PDF contains 10 Gaussian profiles, and 5 Gaussian profiles (black arrows) are irregular profiles. The maximum number of Pt atoms is #5, which is consistent with those of the Sr and Ti-O atomic columns.

Here, we discuss the Gaussian profiles corresponding to the non-integer numbers, as indicated by the black arrows in Fig. 2b–d. In our experiments, we sequentially acquired 30 frames with a fast scan, and, for the statistical analysis, these frames were averaged to enhance the SNR²⁰. In these frames, we frequently observed Z-contrast intensity variation at Pt atomic columns, suggesting that individual Pt atoms moved due to the thermal annealing or electron probe scanning. The frequency of Pt atomic jumps is relatively high, and hence Pt atoms should move on the surface rather than in the NP. By tracking Pt atom jumps, the lower limit of the Pt atom jump frequency is estimated to be ≈3 frames (see Supplementary Fig. 1). Although we cannot completely ignore the effects of electron-beam irradiation, the observed dynamic structural changes of the Pt NP are primarily governed by sample heating (see Supplementary Note 1). Therefore, the observed non-integer Gaussian profiles (black arrows) can be interpreted as the partial occupation of Pt atoms in the total observation time. Since the SNR for each frame is considerably low, it is difficult to reconstruct the 3D structure as a function of time. However, in the time-averaged frame, we can statistically analyze the spatial distribution of dynamic Pt atoms in the NP, and we describe the 3D dynamic structure of the Pt NP in terms of the partial occupation of Pt atoms (non-integer numbers). Hereafter, we use the terms full and partial occupation (non-integer) of atomic sites to describe the dynamic behavior of Pt atoms. Figure 2e shows the projected number of Pt atoms in each atomic column, where Ti-O, Sr, and O atomic columns are labeled with diamonds, squares and circles, respectively, and the color of these labels corresponds to the number of projected Pt atoms. The Pt NP consists of 263 Pt atomic sites, including 42 are partially occupied. The diameter of the Pt NP is 1.96 nm, and the projected shape along the [001]_Pt is nearly octagonal. At the perimeter of the Pt NP, we found two types of the termination planes (colored rectangles in Fig. 2e): TiO₂ {100} plane (blue rectangles) and O₂ {110} plane (red rectangles). We note that, as an exception, Sr-Ti-O (1-10) plane terminates at the top-left of the Pt NP (green rectangle). The perimeter of the Pt NP is dominantly terminated by the Ti or O atomic columns, and the termination of the Sr atomic column could be unstable. This could be the reason why the number of Pt atoms on the Sr atomic column starts with #2 rather than #1. It is noteworthy that the structure of the SrTiO₃ can be described as the alternative stacking of SrO and TiO₂ layers along the [001] direction, and the surface termination of SrTiO₃ (001) should be TiO₂ layer under the present annealing condition^21,22. Since we know the number of Pt atoms in each atomic column, we can reconstruct the 3D atomic structure of the Pt NP on SrTiO₃ (001) surface from a single projected image. The Pt NP has AB stacking along the [001]_Pt direction, and there are two locations of the first layer of Pt atoms on the TiO₂ surface termination: O or mixture of Sr/Ti atomic columns. However, the minimum number of the Pt atom at Sr atomic column is #2, and hence the first layer of Pt atom should be on O atomic column, which agrees well with recent X-ray standing-wave analysis²³. Therefore, we reconstruct the 3D atomic structure of Pt NP on the O atomic columns of SrTiO₃ (001) substrate, and the reconstructed structural model is shown in Fig. 3a, where silver and gold spheres correspond to the full and partially occupied Pt atoms. The Pt NP has a dome shape, with a diameter and height of 1.96 nm and 1.76 nm, respectively, where the height is determined by reasonably assuming the Pt NP has an fcc atomic structure. The reconstructed dome shape is also confirmed from similar Pt NPs by the cross-sectional ADF STEM imaging in the same sample. Figure 3b–d shows the reconstructed 3D structural model of the Pt NP, viewed along [100]_Pt, [110]_Pt, and [130]_Pt, respectively, and the atomic bonds are drawn between the nearest-neighbor atomic sites that are partially occupied. The partially occupied atomic sites are mostly adjacent to each other and form a local network, suggesting that the Pt atoms move within the second nearest neighbors at 483 K. With the aid of electron beam irradiation, the Pt NP is virtually exposed to the reduced atmosphere, and the locally connected partial occupation site could be considered as active sites for chemical reaction. In Fig. 3b, c, we find two distinct facet planes: {001}_Pt and {110}_Pt. The (010)_Pt plane corresponds to the triple-phase boundary, which differs from the case of Pt/TiO₂ (110) heterointerface. The measured contact angles in Pt/TiO₂ (110) and Pt/SrTiO₃ (001) are 120° and 90°, respectively, and the wettability of the Pt NP on the SrTiO₃ (001) surface is much higher than that on the TiO₂ (110) surface¹⁴.

Fig. 3. Reconstructed 3D atomic structure of a Pt NP on SrTiO₃ (001) surface.

a 3D reconstructed atomic structure model of the Pt NP and the surface defects on SrTiO₃ (001), where silver and gold spheres correspond to full and partial occupation of Pt atoms. b–d 3D reconstructed atomic structure model of the Pt NP, viewed along the [100]_Pt, [110]_Pt, and [130]_Pt, respectively. e The coordination number distribution of the Pt NP for full (blue) and partial (red) occupation, respectively. f, g The CN number maps of the Pt NP in top and side view, respectively. h–k The CN map of the Pt NP in each range: 10 ≤ CN ≤ 12, 7 ≤ CN ≤ 9, 4 ≤ CN ≤ 6, 2 ≤ CN ≤ 3, respectively. l Bonds with under-coordinated CN (≤6) Pt atoms. Source data are provided as a Source Data file.

Figure 3e shows the coordination number (CN) distribution of the Pt NP for full (blue) and partial (red) occupation. Since Pt NPs have an fcc atomic structure, the CN in the core region should be 12. However, the fraction of the CN between 10 and 12 is only 55.1%, and the fraction of the under-coordinated Pt atoms is 25.1% (7 ≤ CN ≤ 9), 16.0% (4 ≤ CN ≤ 6), and 3.8% (2 ≤ CN ≤ 3), respectively. Therefore, 45% of the Pt atoms are located at the surface or sub-surface of the Pt NP. According to the Wulff construction structural model of the semi-spherical Pt NP (see Supplementary Fig. 4), 39.8% of Pt atoms are located at the surface (CN < 10), and the experimentally determined value (45%) is close to the Wulff construction model. However, 20% of Pt atoms in our reconstructed model contain much lower CN (2 ≤ CN ≤ 6) compared with those in the Wulff model (6 ≤ CN ≤ 8), which is attributed to the surface roughness of the observed Pt NP. This surface roughness may be reduced by annealing the sample at higher temperatures. It is noteworthy that the partially occupied Pt atomic sites have much lower CN than those in full occupation, which could accelerate dynamic structural transformation of the Pt NP. Figure 3f, g shows the CN maps of the Pt NP in top and side views, respectively. From the top view, the surface is not fully covered by the under-coordinated atomic sites but has several atomic sites with the CN larger than 10. This is because the Pt NP has several deep atomic holes, and the surface is rough at the atomic level. Figure 3h–k shows the spatial distribution of Pt atoms as a function of CN ranges: (h) 10 ≤ CN ≤ 12, (i) 7 ≤ CN ≤ 9, (j) 4 ≤ CN ≤ 6, (k) 2 ≤ CN ≤ 3, respectively. The CN distribution of the Pt NP has a core-shell structure, and the diameter and height of the core region (CN ≥ 10) are 1.54 nm and 1.38 nm, respectively. The surface of the Pt NP is mostly covered by the Pt atoms with the lower CN (≤6), and the Pt atoms located on the top surface (away from the heterointerface) have the lowest CN. As shown in Fig. 3l, the partially occupied and lower CN (≤6) atomic sites have connected to each other as a network, and these atomic sites are locally configured on {111}_Pt planes and {001}_Pt planes. It is noteworthy that the local networks between the lower CN (≤6) atomic sites are strongly related to the partial occupation sites, and these atomic sites have high mobility and could be active sites for catalytic properties.

Here, we discuss the size-dependent atomic dynamics of Pt NPs on oxide substrates. Single Pt atoms exhibit high mobility and diffuse two-dimensionally on the oxide surface. However, small Pt clusters such as Pt trimers cannot freely diffuse on the oxide surface for the following reasons: (i) Pt atoms prefer to bond with oxygen atoms and avoid bonding with cations (e.g., Sr, Ti), and (ii) the Pt trimer maintains an equilateral triangular shape due to metallic bonding¹². In addition to these constraints, the effective mass increases with the size of the Pt cluster, reducing the mobility of larger clusters. For example, the diffusion coefficient of a Pt trimer is three orders of magnitude smaller than that of a single Pt atom on the TiO₂ surface. The present Pt NP contains more than 200 atoms and is located on the oxygen atomic columns at the heterointerface, suggesting that the Pt NP cannot move on the SrTiO₃ (001) surface (requires higher temperatures for their movements). However, compared with the Wulff construction model, the surface of the Pt NP is defective and its CNs are considerably lower.

Evaluation of catalytic activity by DFT calculations

To investigate the catalytic activity of these defective atomic sites, we performed DFT calculations using the experimentally reconstructed 3D atomic structure, in which all partially occupied sites were filled by Pt atoms. As discussed above, there are two possible configurations for the first layer of Pt atoms either on O atomic columns or on a mixture of Sr/Ti atomic columns. Our DFT calculations reveal that the Pt NP on O atomic columns is energetically more stable than that on mixed Sr/Ti atomic columns (total energy difference: 16.64 eV), and hence, the surface of the SrTiO₃ is terminated to be TiO₂ layer. This result indicates that the observed Pt NP represents the typical structural characteristics of (001)-stacking Pt NPs on the SrTiO₃ (001) substrates. Figure 4a, b shows the Bader charge distribution for the relaxed atomic structure of the Pt NP on the SrTiO₃ (001) surface, with colors corresponding to the Bader charge at each atomic site. Although slight structural relaxation is observed, the height of the Pt NP is estimated to be 1.72 nm (1.76 nm in the experimental estimation), and the theoretical structure agrees well with the experimental results. As shown in Fig. 3, the low-CN atomic sites are located at the top surface region, and these sites tend to accumulate excess negative charge. To clarify the relationship between atomic CN and charge deviation, we show the Bader charge as a function of CN for each atomic site in Fig. 4c. Although the magnitude of the Bader charge strongly depends on the local atomic configuration, the excess negative charge generally increases with decreasing CN and reaches a maximum at CN = 3. The Bader charge is close to zero at atomic sites with CN = 10–12, but the negative charge increases markedly at undercoordinated sites. Previous theoretical studies have examined charge transfer from oxide substrates to Pt NPs, however, these were typically based on idealized Wulff construction models that differ significantly from realistic atomic configurations. In contrast, our DFT calculations, based on the experimentally reconstructed 3D atomic structure, estimate the total excess charge of the Pt NP to be –0.58 q_e (q_e: elementary charge). It is noteworthy that the direction and magnitude of charge transfer between oxides and Pt NPs can depend strongly on the crystallographic orientation of the heterointerface²⁴. We further performed DFT calculations using the d-band model (see Methods), which is a fundamental model for predicting the catalytic activity of metals^25,26. In the d-band model, metal atoms with a higher d-band center (average d-band energy) form stronger bonds with reactant molecules, which is indicative of higher catalytic activity. Figure 4d shows the d-band centers of Pt atoms as a function of the CN, and Fig. 4e, f shows the corresponding partial density of states (PDOS) of Pt atoms that have minimum and maximum d-band centers, respectively. Pt atoms with lower CNs exhibit higher d-band centers, promoting stronger bonding with reactant molecules. Since Pt atoms with lower CNs have smaller overlap integrals with the surrounding atoms²⁶, these atoms exhibit higher d-band center and potentially greater catalytic activity.

Fig. 4. Charge density distribution by DFT calculations.

a, b Top and side views of the relaxed 3D atomic structure of the experimentally reconstructed Pt NP, and colors correspond to the Bader charge at each atomic site. c Bader charge at each atomic sites as a function of the CN. d The positions of the d-band center for each Pt atom as a function of the CN, where the blue line represents the linear fit. e, f The respective PDOS (s-, p-, d-orbitals) of the Pt atoms with the highest and lowest d-band centers, as indicated in (d). The solid vertical lines indicate the position of the d-band center. The Fermi level is set to 0 eV. Source data are provided as a Source Data file.

In summary, we have demonstrated the reconstruction of the 3D atomic structure of the Pt NP on the SrTiO₃ (001) substrate using single-projection ADF STEM imaging in combination with quantitative statistical analysis of Z-contrast intensity. By identifying partially occupied Pt atomic sites, we revealed that the Pt NP exhibits dynamic structural behavior at high temperatures. Using the experimentally reconstructed 3D atomic structure of the Pt NP, we performed DFT calculations and found that the Pt NP is negatively charged, and the excess negative charge is localized at low-CN atomic sites (partially occupied atomic sites). These undercoordinated atomic sites are likely to serve as active sites for molecular adsorption and catalytic reactions. In this study, we applied these analyses to a single Pt NP, and further analyses of various Pt NPs are required to understand the general behavior of Pt NPs. The present dynamic 3D structural analysis combined with DFT calculations for supported NPs can provide a framework for understanding the distribution of active sites and their catalytic activity.

Methods

Electron microscopy experiments

A commercially available single crystal of SrTiO₃ (001) (Shinkosha Co. Ltd.) was cut into a disk with a diameter of 3 mm using an ultrasonic cutter. The disk was mechanically polished and dimpled at the center of the disk. In the final step, the disk was thinned by low-voltage Ar ion beam milling at 500 V. The electron-transparent thin TEM sample was annealed at 573 K for 3 h to remove hydrocarbon contamination on the surface. Subsequently, the sample was annealed in air at 1373 K for 1 h to form an atomically flat step-terrace surface on the SrTiO₃ (001) surface. We note that the present annealing condition (annealing temperature and time) was investigated using topographic imaging by atomic force microscopy and reflection high-energy electron diffraction analysis. The annealed TEM sample was transferred to an ultrahigh vacuum chamber (7 × 10^–7 Pa, Pascal Co. Ltd.), and Pt NPs were deposited on the SrTiO₃ (001) surface by vacuum evaporation at room temperature. Before mounting the sample, the double-tilt heating TEM holder (JEOL Ltd.) was annealed in a high vacuum at 1073 K for 2 h to remove hydrocarbon and metal oxide contamination. We performed in-situ sample heating at 483 K in a high vacuum (8 × 10^–7 Pa) to avoid hydrocarbon contamination and sample charging. After loading the TEM sample into the microscope, we began annealing the sample at 483 K. To suppress specimen drift (thermal instability) induced by the temperature increase, we waited for 1 h before acquiring atomic-resolution STEM images. The sample temperature was maintained at 483 K during STEM observations. Atomic-resolution ADF STEM images were acquired with an ARM300CF installed at the University of Tokyo, equipped with a cold-field emission gun and a JEOL Delta-type corrector operated at 300 kV. To enhance surface sensitivity (higher depth resolution), the illumination half-angle was set to 40 mrad, and the collection angle for the ADF detector was 77–200 mrad. The beam current and exposure time were 11.9 pA and 2 µs per pixel, respectively. To improve the signal-to-noise ratio, images were acquired sequentially over the same area (30 frames). Sample drift between frames was compensated by non-rigid registration, and the image intensity was averaged over the frames.

Quantitative statistical analysis¹³

The Z-contrast intensity was evaluated by fitting with a 2D Gaussian function at each atomic column. The 2D Gaussian function has six parameters of w_i:= {a_i, b_i, x_i, y_i, σ_ix, σ_iy}

$$G_i\left(w_i;x,y\right)=a_i\cdot \exp \left(-\frac{{\left(x-x_i\right)}^2}{{2\sigma }_{ix}^2}-\frac{{\left(x-y_i\right)}^2}{{2\sigma }_{iy}^2}\right)+b_i$$ 1

where i is the index for the atomic column, and the parameters of a_i, b_i, x_i, y_i, σ_ix, σ_iy for each i are amplitude, background, peak position, and standard deviations for x- and y-directions, respectively. The integrated intensity for an atomic column can be evaluated by the following 2D integral using the optimum parameter set:

$$\widehat{I_i}={\iint }_{-\infty }^{\infty }{G}_i\left(x,y\right)\mathrm{d}x\mathrm{d}y=2\mathrm{\pi }\widehat{a_i}\widehat{{\sigma }_{ix}}\widehat{{\sigma }_{iy}}$$ 2

To find the optimal parameter set of $\widehat{w_i}$, we used the RWMH algorithm for 2D Gaussian fitting. In this algorithm, we can simultaneously estimate the global minimum parameter set and the fitting error. We performed 1,100,000 profile fitting by the RWMH algorithm, including 100,000 burn-in sweeps for each atomic column. Since there are a large number of sampling points in the parameter space, the optimal parameters can be expressed as a PDF. To evaluate the 2D Gaussian integrated intensity, we added all the PDFs obtained from each atomic column (total PDF). As shown in Fig. 2b–d, the total PDF contains multiple peaks, and the integrated intensity can be classified by peak deconvolution. We performed peak deconvolution of the total PDF with mixed Gaussian profiles:

$$g\left(x;q_m\right)={\mathrm{\Sigma }}_{m=1}^M{a}_m\cdot \exp \left(-\frac{{\left(x-p_m\right)}^2}{2{\sigma }_m^2}\right)$$ 3

where m is the index for Gaussian profiles (m = 1, 2, …, M), a_m, p_m, σ_m² (q_m = {a_m, p_m, σ_m}) for each m are the amplitude, peak position, and variance, respectively. To determine the number of Gaussian profiles (M), we examined several cases, e.g., M = 8–11 for the total PDF of Ti-O atomic column (Fig. 2b). The fitting degree is evaluated by the sum of squares of residual:

$${\chi }^2\left(M\right)={\mathrm{\Sigma }}_p\left({\mathrm{\Sigma }}_i\mathrm{PD}{\mathrm{F}}_i\left(x\right)-g\left(x;q_m\right)\right)$$ 4

As can be seen in Fig. 2b–d, the total PDFs have considerably complicated profiles. Therefore, we performed peak deconvolution with the RWMH algorithm, using 1.1 × 10⁷ including 10⁶ burn-in sweeps, which is 10 times more sampling than the 2D Gaussian fit. We then determined the number of peaks with the minimum χ²(M), and the best fits are shown in Fig. 2b–d. After classification, we checked the linearity between the integrated intensity intervals, and the number of Pt atoms is counted. Although the deconvolved Gaussian profiles are not completely separated, there are small overlaps between neighboring Gaussian profiles (see Supplementary Fig. 8). The probability-equal-integrated-intensity I^eq(m, m + 1) with the neighboring two Gaussian profiles {σ_m, p_m}, {σ_m + 1, p_m + 1} can be determined by the weighted internal division:

$$I^{\mathrm{eq}}\left(m,m+1\right)=\frac{{\sigma }_{m+1}{p}_m+{\sigma }_m{p}_{m+1}}{{\sigma }_m+{\sigma }_{m+1}}$$ 5

These I^eq(m, m + 1) values are given at the bottom of Fig. 2. Except for a few non-integer numbers of Pt atoms, the atom counting precisions are better than 68% confidential interval.

Density functional theoretical calculation

DFT calculations were performed using the projector-augmented-wave (PAW) method implemented in the Vienna Ab-Initio Simulation Package (VASP 6.5.1)^27–29. The generalized gradient approximation functional parameterized by Perdew, Burke, Ernzerhof (GGA-PBE) was used³⁰. An energy cutoff of 420 eV was used for the plane-wave basis set. The initial structural model was based on the experimentally reconstructed Pt NP model. The structural model of Pt NP on SrTiO₃ (001) substrates consists of 263 Pt atoms and SrTiO₃ (001) slab containing two layers, including 72 Sr atoms, 72 Ti atoms, and 216 O atoms. The vacuum layer is 15 Å to remove the interaction between periodic images. The structural relaxation was performed until the residual forces were below 0.001 eV Å⁻¹. Bader charges were evaluated using the Bader code^31,32. Excess Bader charges were calculated by subtracting the original valence charge from the computed Bader charge. The average d-band energy (d-band center) ε_d of each Pt atom was evaluated using DFT calculations. The d-band center is defined as

$${ϵ}_d=\frac{{\int }_{-\infty }^{\infty }{g}_d\left(ϵ\right)\cdot \left(ϵ-{ϵ}_{\mathrm{f}}\right)\mathrm{d}ϵ}{{\int }_{-\infty }^{\infty }{g}_d\left(ϵ\right)\mathrm{d}ϵ}$$ 6

where ε is one electron energy, g_d(ε) is the partial density of states of the d-orbitals of a specific Pt atom, and ε_f is the Fermi level. We checked the energy convergence of DFT calculations for a Pt NP on a SrTiO₃ substrate with respect to the different number of SrTiO₃ layers and the different vacuum widths. Supplementary Fig. 6a shows the energy difference between the Pt NP with its first layer on oxygen atomic columns (E_O/O) and on Sr and Ti atomic columns (E_Sr/Ti). Our result shows that the energy difference (E_O/O - E_Sr/Ti) converges to within 0.5 eV for more than two layers of SrTiO₃ substrate. Supplementary Fig. 6b shows the relative energy of the Pt NP with different vacuum widths. The energy converges to within 0.2 eV for vacuum widths exceeding 15 Å.

Statistics and reproducibility

As shown in Fig. 1a, there are numerous Pt NPs on the SrTiO₃ (001) substrate. We observed more than one hundred NP with (001) and (011) stacking, as shown in Figs. 1d–g and 2a, e. Although we analyzed one specific Pt NP of Fig. 2a, e, the present result should be reproducible because we implemented RWMH algorithm, where we performed 2D Gaussian fitting more than 10⁶ sweeps for each atomic column. For the analysis of CN in Fig. 3e, the lattice constant of bulk Pt is used as the threshold distance to calculate CN at each atomic site. Although the CN values at surface atomic sites may be slightly affected by the choice of threshold distance, the most trend is independent from the selection of the threshold distance.

Author contributions

R.I. designed and directed the study, performed electron microscope experiments, and wrote the paper. R.I., R.K., and K.K. analyzed the data. T.F. performed first principles calculations and data analysis. Y.I. and N.S. contributed to the discussion and suggestions.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data that support the findings of this study are available from the corresponding author upon request. Unprocessed raw data are provided as Supplementary Data 1. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-69767-5.