In situ electron diffraction tomography study of the successive phase transitions in LaTaO_4 nanocrystals

Domain: chemistry
Published: 2026-04-11
Editorial outcome: major_revision

Abstract
The ferroelectric oxide LaTaO4, with a layered perovskite-related structure, exhibits a reversible temperature-dependent phase transition between its low-temperature paraelectric and high-temperature ferroelectric states. Herein, using in situ three-dimensional electron diffraction (3D ED) with atomic-resolution, we resolve the structural evolution of LaTaO4 nanocrystals across four distinct phases during sequential heating treatment (300-500 K). Beyond ab initio structure determination of the known monoclinic (m-LaTaO4) and orthorhombic (o-LaTaO4) phases, we unravel: (i) a, previously undetected, intermediate phase (m'-LaTaO4) with a shorter c-axis transiently stabilized at around 372 K, arising from tilting of TaO6 octahedra; (ii) an incommensurately modulated phase (IC-o-LaTaO4) with a modulation vector q ≈ (0.4669, 0, 0) through a combination of 3D ED and high-resolution electron microscopy imaging. The real-time tracking reveals three first-order phase transitions governed by synergetic Ta-O bond distortion dynamics. These findings establish a hierarchical phase transition model that reconciles previous studies and these single nanocrystal observations.

Introduction
Ferroelectric materials1 exhibit a spontaneous net polarizationP, the direction of which is reversibly switchable under an external applied electric field. Consequently, these material s have garnered substantial interest for capacitor, sensor, actuator, and memory device applications. Ferroelectric materials can be formed via a phase transition from paraelectric phases under specific conditions, which is typically accomplished by symmetry breaking. Although the most widely-used ferroelectric materials adopt the perovskite structure, a wide range of other ferroelectrics exist within layered perovskite-like structures including Ruddlesden-Popper, Dion-Jacobson, Aurivillius and Carpy-Galy families.2,3 The latter can be derived from the perovskite (ABX3) structure by cleaving along the [110] plane and incorporation of additional anions, giving rise to the homologous series with general formula AnBnX3n+2, where n represents the number of perovskite blocks between cleaved planes. Within this Carpy-Galy4 family, the n = 4 materials Sr2Nb2O75 and La2Ti2O76,7 aroused significant attention in ferroelectric and piezoelectric research, due to their very high operating temperatures. Notably however, LaTaO48-12is the sole ferroelectric oxide n = 2 member in this family (although CeTaO4 and PrTaO4 also adopt the Carpy-Galy structure they exclusively form only in the non-polar polymorph); LaNbO4 and all other lanthanide (Ln) tantalates and niobates with ABX4 stoichiometry adopted either the non-perovskite-related fergusonite or scheelite structures.13-15 LaTaO4 is of particular interest as it shares structural similarities with the prototypical ferroelectric fluoride analogue, BaMnF4,16 which exhibits a stable nonpolar monoclinic P21/c phase (m-phase) at room temperature and a stable polar orthorhombic Cmc21 phase at high temperature.17,18 In previous studies of the phase transitions of LaTaO4,17,19 an incommensurately modulated structure was identified between the low temperature m-phase and the high temperature o-phase, accompanied by dielectric anomalies during heating and cooling.

Previous studies on crystal structures and phase transitions of LaTaO4 mainly rely on powder X-ray or neutron diffraction.8,20 However, three-dimensional reciprocal information was projected to one dimension in these techniques, leading to peak overlaps and potential oversight of subtle reflection signals in background noises. These limitations hinder differentiation between similar structures and increase the risk of missing key features. Three-dimensional electron diffraction (3D ED)21,22 is an emerging method developed in the past two decades, which has been applied to structure analysis of various materials including inorganic minerals, proteins, crystalline porous materials, etc.23-26 In particular, in situ 3D ED affords the capability of probing not only crystal structures under various environments, e.g. cryogenic temperatures, electric fields, in situ heating, and in gas and liquid environments, but also the dynamic structure evolution under external stimuli.27-29

Here, we utilised in situ 3D ED to track the successive phase transitions of LaTaO4 nanocrystals during thermal cycling. The temperature-dependent structural evolution was resolved through the analysis of 3D reciprocal lattices. In addition to the three previously reported phases, a previously unreported intermediate monoclinic phase, denoted as m'-LaTaO4 phase, was identified between the monoclinic and incommensurate orthorhombic phases in some nanocrystals. Through ab initio structural solutions, we characterised all crystalline phases and established their relationships. By combining 3D ED data with high-resolution transmission electron microscopy (HRTEM) imaging, we elucidated the incommensurate modulation structure including its modulation vector, thereby providing a comprehensive understanding of various atomic-level structures in LaTaO4.

Results
In situ heating 3D ED of LaTaO4

In previous reports, three phases were identified in LaTaO4 during its sequential phase transitions: a monoclinic phase at room temperature (m-LaTaO4), an orthorhombic phase at high temperature (o-LaTaO4), and an intermediate incommensurately modulated orthorhombic phase (IC-o-LaTaO4). The correlation between the m-LaTaO4 and o-LaTaO4 unit cells can be described by a transformation matrix:

(ao) = (0 2 0) · (am)
(bo) = (0 0 1) · (bm) (1)
(co) = (1 1 0) · (cm)

where ao, bo, co represent the unit cell parameters of o-LaTaO4 and am, bm, cm represent those of m-LaTaO4. The [001] zone axis of o-LaTaO4, denoted as [001]o, is equivalent to the [010] zone axis of m-LaTaO4, denoted as [010]m. For clarification, the subscript of the zone axis indicates the corresponding phase.

In this work, the typical crystal structures of m-LaTaO4 (a = 7.67 Å, b = 5.67 Å, and c = 7.94 Å, β = 101.57°, space group P21/c) and o-LaTaO4 (a = 4.05 Å, b = 15.11 Å, and c = 5.80 Å, space group Cmc21) were successfully determined using 3D ED data (Supplementary Fig. 1 and 2 and Supplementary Table 1). To investigate the phase transition behaviour of LaTaO4 during progressive heating, an in situ heating 3D ED experiment was carefully designed and conducted (Fig. 1), so that 3D ED datasets were collected at preset temperatures with a fixed heating rate of 5 K/min (Fig. 1a) from multiple LaTaO4 nanocrystals (Fig. 1b), followed by an equilibration period of 5 mins at each temperature.

3D ED datasets (Fig. 2a-c) were firstly collected at 300 K, from which a monoclinic unit cell with parameters a = 7.63 Å, b = 5.63 Å, and c = 7.92 Å, β = 101.09° was determined, consistent with previously reported m-LaTaO4. However, analysis of 2D slices from the 3D ED data revealed the presence of numerous diffraction spots with h0l (l = 2n+1), which contradicts the systematic absences expected for the widely reported space group P21/c. Given the composition of heavy atoms (La, Ta) and the high density, this observation is likely attributed to strong dynamical scattering effects. This interpretation is supported by a consistent intensity difference observed between h0l reflections with l = 2n and l = 2n+1 indices. From a property perspective, the assignment of the centrosymmetric P21/c space group remains consistent with the well-documented paraelectric behaviour of m-LaTaO4. The observed reflection conditions were summarised as h0l: l = 2n; 00l: l = 2n; 0k0: k = 2n, shown in Supplementary Fig. 3. During heating, SAED patterns along a fixed orientation of the same crystal were recorded with 0.5 s exposure time. Representative SAED patterns at 360, 380 and 400 K are shown in Fig. 1c-e. At 360 K, SAED patterns displayed sharp diffraction spots from both zero-order Laue zone (ZOLZ) and first-order Laue zone (FOLZ), indexed to the [1̅20] of m-LaTaO4. It is worth noting that some diffraction spots, such as 003 and 003̅, should be systematically absent based on the reported space group P21/c but weak spots are present in the experimental SAED pattern (Fig. 1c, Supplementary Fig. 4). This indicates the existence of strong dynamical scattering, which corroborates with the emergence of h0l (l = 2n+1) reflections in 3D ED datasets.

A line profile was extracted from the diffraction pattern along (001̅) direction (marked by the dotted yellow rectangle in Fig. 1c-e), from 214 to 216̅ reflections (Fig. 1f). By recording SAED patterns along the identical orientation of the same nanocrystal during heating, the evolution of diffraction spots could be tracked (Supplementary Video 1 and 2). Fig. 1g and h show the change in intensity of the reflections shown in Fig. 1f during the heating with an interval of 1 K. No obvious change was observed from 300 to 368 K. In this range of temperature, the unit cells determined from 3D ED datasets remain the same as m-LaTaO4. When temperature was increased to approx. 372 K, the nanocrystal underwent a first change. In the range 368 ~ 380 K, the intensities of strong diffraction spots display a visible fluctuation at around 372 K and gradually stabilize at 380 K. Moreover, the 216̅ reflection (marked with an arrow in Fig. 1g) shows a slight shift. Subsequent 3D ED data analysis at 380 K showed significant intensity reduction in h0l (l ≠ 2n) reflections versus room-temperature data (Supplementary Fig. 5). Since two 3D ED datasets are collected from the same particle, the changes in reflection intensities and positions indicate a potential phase transition.

It is worth noting that the changes in intensity of many other reflections are not so prominent. After careful analysis of the 3D ED dataset at 380 K, a monoclinic phase with parameters a = 7.78 Å, b = 5.65 Å, c = 3.97 Å, and β = 100.94° with a space group of P21 could be determined, denoted as m'-LaTaO4 (Fig. 2d-f). However, this intermediate m'-phase is not very stable and only appears in a narrow temperature range. In many cases, m- and m'-phases might coexist in LaTaO4 nanocrystals. Notably, the m'-phase exhibits such subtle structural differences that it remains undetectable in conventional powder X-ray diffraction (PXRD) and neutron diffraction (PND). This limitation arises from two fundamental factors: Firstly, the pronounced overlap of diffraction peaks between the m- and m'-phases leads to statistical averaging of their respective signals in PXRD/PND patterns, effectively obscuring the weaker m'-phase signatures during analysis. Secondly, the m'-LaTaO4 likely exists only at the nanoscale or within localised structural domains, making it inherently challenging to observe through other characterisation techniques.

As the temperature continues to increase from 380 K, the intensities of diffraction spots remain stable until the second phase transition occurs, from the m'-phase to IC-o phase, at ca. 389 K. In addition to changes in reflection intensities, the positions of 214 and 214̅ reflections also shift (marked with yellow arrows in Fig. 1h). Analysis of in situ 3D ED data at 400 K reveals an orthorhombic unit cell with incommensurate modulation (Fig. 2g-i), where the basic cell parameters (a = 3.95 Å, b = 14.58 Å and c = 5.69 Å) agree well with the reported o-LaTaO4. Distinct ‘zig-zag’ satellite spots appear along the (001) direction with a modulation vector q ≈ (0.4669, 0, 0) in 3D reciprocal space, consistent with the previous study by Howieson et al.17

As the temperature continues to increase to ca. 394 ~ 400 K, the diffraction pattern shows a final change, with variations in reflection intensity only (Fig. 1e). Subsequent 3D ED data (Fig. 2j-l) confirms the formation of the high-temperature orthorhombic phase, o-LaTaO4. The unit cell parameters could be determined as a = 3.92 Å, b = 14.41 Å and c = 5.61 Å (at 500 K), with the space group Cmc21. Notably, these phase transition temperatures (389 or 394 K) are lower than widely-reported ones (~ 440 K8,17). Given the non- negligible volume changes among different phases, from 333.61 Å3 (m-LaTaO4 @300 K), 335.76 Å3 (2×m'-LaTaO4 @380 K), 327.52 Å3 (IC-o-LaTaO4 @400 K) to 316.32 Å3 (o-LaTaO4 @500 K), a possible origin of the change in transition temperatures (Tc) value is strain, that the expansion in unit cell volume during heating may have effect on lattice strains, resulting in a decrease of Tc. The dependence of Tc on unit cell volume have been reported in perovskite such as LaCoO330 And the Tc of ferroelectric (CnH2n+1NH3)2(CH3NH3)n-1PbnBr3n+1 could be decreased by the expansion of unit cells.31 Another possible answer could be the size effect of nanoparticles. Zhong et al.32 hypothesised and validated that Tc would drop as the size of ferroelectric nanoparticles decreases using a Landau phenomenological theory. Lyberatos et al.33 proposed that the Curie temperature of L1o-FePt would decrease as the size decreases based on simulations using a Monte Carlo model.

Structure analysis of LaTaO4 phases

In situ 3D ED datasets of all phases (m-LaTaO4, m'-LaTaO4, IC-o-LaTaO4 (main reflections)and o-LaTaO4) were processed using XDS34 software. Ab initio structure solutions were obtained using direct methods in SIR2019,35 followed by structure refinements using SHELXL36 in OLEX237. Crystallographic details of selected 3D ED datasets at 300, 340, 380, 400, 440, 480 and 500 K are provided in Supplementary Table 2. Structural comparisons of m-LaTaO4, m'-LaTaO4 and IC-o-LaTaO4 (Fig. 3) reveal that, apart from minor La position variations, the main difference of these structures lies in the arrangement of twin TaO6 octahedral blocks (TO). In the m-phase, TaO6 octahedra exhibit an overall out-of-phase tilt around [001]m while in both the m'- and o-phases the octahedral tilting is in-phase along the equivalent axis, [001]m' and [100]o, respectively. As a result, m-LaTaO4 has two types of twin TaO6 octahedra stacked alternately, TOm1 and TOm2 (marked with arrows), along the [001] (or [100]o) direction whilst m'-LaTaO4 and o-LaTaO4 have only one type (TOm' and TOo respectively). The measured angles of Ta–O–Ta (Δθ) in these structures show deviations from 180° (the un-tilted parent Cmcm structure): ΔθTOm1 = 38.462°, ΔθTOm2 = -38.462°, ΔθTOm' = 35.54° and ΔθTOo = 33.34°, respectively (the absolute value of ΔθTOm1 and ΔθTOm2 are equal because of the c-centring symmetry of P21/c). This progressive Δθ change indicates that from m-LaTaO4 to m'-LaTaO4, the TO6 octahedra rotate, with one TaO6 block TOm2 rotating anticlockwise, and the other block TOm1 rotating clockwise, resulting in the alignment of TOm' and TOm' along [001]m. And the overall transition from m-LaTaO4 to o-LaTaO4 has the tendency to a higher degree of octahedral alignment towards an ideal (un-tilted) Cmcm structure. This trend is corroborated by temperature-dependent Δθ analysis (Supplementary Fig. 6 and Supplementary Table 3). Data merging could improve the data completeness but shows little changes on the structure refinement statistics in our cases (Supplementary Table 4).

Regarding the phase transformation from m'-LaTaO4 to IC-o-LaTaO4, a comparison between m'-LaTaO4 and the averaged IC-o-LaTaO4 was conducted, as illustrated in Fig. 3b. Differences could be seen along [010]m', where no obvious rotations of TaO6 octahedra could be identified, but an overall shift of the n = 2 TaO6 layers and La ions along the [001] direction was found. Although the shift is small, ca. 0.36a of the unit cell (~ 1.44 Å), it induces the alignment of La and TaO6 blocks along the [010] direction, resulting in an orthogonal arrangement that drives the structure to a different phase of LaTaO4.

However, mere consideration of only the main reflections does not completely represent the exact structure of IC-o-LaTaO4 as satellite spots were excluded in the structure determination. To further investigate the superstructures, multiple datasets of m'-LaTaO4 and IC-o-LaTaO4 from several repeated experiments were analysed. For IC-o-LaTaO4, accounting for weak diffraction spots revealed an incommensurately modulated supercell along the a-axis. The q vectors from all IC-o-LaTaO4 phases have been determined and summarised (Supplementary Table 5). Furthermore, after introducing a modulation vector in data processing of 3D ED datasets using PETS2 (Fig. 4a and Supplementary Fig. 7a),38 the intensity of satellite spots could be integrated, generating a (3+1)D reflection file rather than a standard hkl file. The 0th slices of IC-o-LaTaO4 in hk0m and h0lm are shown in Supplementary Fig. 8. The first-order satellites could be seen in the IC-o-LaTaO4 dataset, but second-order satellite spots are absent, hence only m = 1 is considered. Similarly, the reflections suffer from strong dynamical scattering, by considering the variation of reflection conditions, the reflection conditions could be summarised as hklm: h+k = 2n, and h0lm: l+m = 2n. The reflection conditions are compatible with superspace group Cmc21(α00)0s0, C2cm(α00)ss0 (Ama2(00g)0ss in the standard setting) and Cmcm(α00)0s0. Cmcm(α00)0s0 was excluded, as its basic space group Cmcm is centrosymmetric, which is incompatible with the widely reported ferroelectricity nature of the high temperature LaTaO4 phase.8,9 For the non-centrosymmetric alternatives, C2cm(α00)ss0 was not selected because its symmetry forbids the modulation of z, which precludes any modulated displacement functions along z in the incommensurately modulated model. Such constraints are incompatible with the tilting-dominated incommensurate modulation. In addition, the C2cm symmetry would impose strict constraints on the local atomic geometry. Therefore, the non-centrosymmetric space group Cmc21(α00)0s0 is selected for the incommensurate modulation. The reflection condition with index could be seen in Supplementary Fig. 9. The structure refinement workflow contains: (1) ab initio solution and refinement using only main reflections; (2) reprocessing reflection data including satellite spots; (3) kinematical structure refinement in JANA202039 by introducing a modulation vector q = (0.4669, 0, 0) and superspace group Cmc21(α00)0s0 (Supplementary Fig. 7b). The refinement statistics are summarised in Supplementary Table 6. The finalised model could be seen in Fig. 4b and c, and the de Wolff sections could be seen in Supplementary Fig. 10.

In the refined incommensurately modulated superstructure model of IC-o-LaTaO4, Ta, O and La atoms exhibit positional variations, resulting in a tilting of TaO6 octahedra and a minor displacement of La (Supplementary Video 3 and 4). The tilting of TaO6 is accompanied by minor deformations, which does not appear to be symmetry-dictated. To give a clear presentation, we built a superstructure model with 22×a (Fig. 4d), in which two types of TaO6 blocks with different orientations were identified. These blocks are alternatively connected and exhibit subtle differences in oxygen displacement magnitude, with variations manifesting a long-range modulation period. To display this structural feature, a colour contrast gradient is introduced in Fig. 4d depending on the extent of oxygen position variation. As the oxygen atoms vary in their positions, there are always regions where unit cells of type A and B show more similar structures. This similarity is followed by a gradual deviation between two types until reaching regions with maximum structural difference. However, if we further extend the scale of the model, one can easily find that the periods are not commensurate. This is where the incommensurate modulation originates. This principle aligns with the formation mechanism of incommensurate structures proposed in our previous study, i.e. that the partial ordering of two or more different blocks is the origin for the formation of the incommensurate structures.17

JANA software has been widely used to determine incommensurately modulated crystal structures, mainly utilizing powder or single-crystal X-ray diffraction and powder neutron diffraction data.40-43 In common cases, electron microscopy primarily provides SAED and HRTEM images from limited orientations. Recently, more exemplar research has been reported on the structure refinement of incommensurately modulated structures using 3D ED, PED, etc.21,44-47 Building upon the ongoing development of 3D ED methodologies, this work presents a further application case, demonstrating its utility for refining an incommensurately modulated structure upon in situ heating scenario. Notably, 3D ED has exhibited a strong capability in identifying modulated structures by offering the advantage of not only free rotation in 3D reciprocal space but also accurate indexing during determining the modulation vectors. Conventionally, determining modulation vectors through either real space or reciprocal space by electron microscopy is usually time-consuming and lacks accuracy. This is because structure modulation determination requires a large number of images taken from different orientations, all of which require accurate indexing prior to satellite spots analysis. Furthermore, SAED patterns represent 2D sections of reciprocal space. The interpretation of satellite spots or weak superlattice reflections could be insufficient due to its limited orientation, making it difficult in correctly determining the incommensurate modulation or other superstructures in these materials. In contrast, 3D ED datasets provide structural information in 3D reciprocal space, enabling unrestricted rotation of reconstructed 3D data and 2D section until the correct modulation vector is identified. In addition, with the exploitation of data processing software, e.g. PETS2,38 the modulation vectors can be reliably determined and refined.

The incommensurate structure was further confirmed through high-resolution TEM (HRTEM) imaging. Fig. 5a-d shows a representative HRTEM image taken along the [001]o direction with its corresponding fast Fourier transform (FFT) pattern and electron diffraction pattern. Analysis of satellite spots observed in the FFT and electron diffraction gives the modulation vector q ≈ (0.4624, 0, 0), which is close to that from 3D ED data (0.4669, 0, 0). A line profile along the [100]o direction (Fig. 5e) reveals prominent intensity variations superimposed on the periodic lattice fringes. Two distinct periods exhibiting wave-like modulations are identified (marked in blue for period 1 and red for period 2 in Fig. 5e). By selecting main Fourier coefficients or satellites in the FFT data and performing inverse Fourier transformation, two different images were obtained (middle and bottom left in Fig. 5e). The corresponding line profile (blue curve in Fig. 5e) of only the main reflections presents an overall even distribution whilst the line profile of the satellite reflections (red curve in Fig. 5e) resembles a harmonic wave, with a ca. 6.5×a period. This abnormal contrast difference originates from atomic-scale structural modulations involving La atomic displacements and cooperative TaO6 octahedra tilting. Moreover, HRTEM observations show good agreement with the proposed structure model (Supplementary Fig. 11), that alternating type A and type B domains exhibit characteristic contrast variations over extended length scales. From the full scale filtered HRTEM images with the FFTs in Supplementary Fig. 12, the wavelike patterns, which indicate the incommensuration in the LaTaO4 structure, are distributed across the whole specimen area.

As a sequential work following the study of IC-o-LaTaO4 carried out by Howieson et al.,17 a comparison with the current work can be made. While no unit cell can be strictly defined for incommensurate structures, an expanded supercell with ordered building blocks (“slabs”) approaching the incommensurate structure serves as a conceptual framework for understanding structure formation.48,49 Unlike the “slab” incommensurate model, which assumes partial ordering of building blocks M (6×a/2) and N (5×a/2) based on SAED and HRTEM observations, this work constructs a single-crystal-level structural description. Specifically, we propose a structure model with quantified atomic position approximation rather than “slab” subunit hypothesis. Meanwhile, differing from conventional refinement of a standard database structure using PND data, this study conducted ab initio structure solution, together with structure refinement using 3D ED data, enabling improved approximation of local structural realism.

Nonetheless, despite the differences, the models in the current work are not at odds with those previously reported, but instead complement the understanding of the incommensurate modulation in LaTaO4. The modulation vector q of IC-o-LaTaO4 is close to the reported vector (0.456, 0, 0), exhibiting consistent SAED patterns along the [001]o direction. HRTEM images reveal two alternating intensity periods with wave-like characteristics (top right in Fig. 5e), suggesting that at least two building blocks contribute to the modulated structure in LaTaO4. It is important to note that both “slab” and our models are approximations of the real structure, as satellite spot intensity arises from atomic displacements across hundreds of unit cells.

Overall, the benefits of in situ heating 3D ED reflect in many extents, that upon progressive heating, it is possible to track the crystal structure evolution and obtain a realistic structure under different environments, effectively capturing phase transition behaviour of LaTaO4 nanocrystals. Moreover, the rapid 3D ED data collection makes it possible to detect subtle changes in structures, enabling discovery of transient phases such as the potential intermediate phase, m'-LaTaO4. In this work, the phase transitions and structural evolution of LaTaO4 were investigated using in situ 3D ED coupled with HRTEM imaging. Upon heating the specimen from 300 K to 500 K, the monoclinic phase (m-LaTaO4) underwent a phase transition to an intermediate phase (m'-LaTaO4) at approximately 372 K. Such a phase transition involves a tilting of TO6 blocks to align with TOm1, generating the intermediate phase structurally analogous to m-LaTaO4 but with a unit cell halved in c. Subsequently, the octahedral layers undergo a shift along the [001]m' direction during the transition to an incommensurately modulated orthorhombic phase (IC-o-LaTaO4) with a modulation along the a-axis and a modulation vector q ≈ (0.4669, 0, 0). A final transition at approximately 394 K yielded the fully ordered orthorhombic phase (o-LaTaO4). The crystal structures of m-LaTaO4, m'-LaTaO4 and the averaged IC-o-LaTaO4 phases were resolved ab initio. Based on 3D ED data and HRTEM image analysis, an incommensurately modulated model of IC-o-LaTaO4 was proposed. The methodology demonstrated in the present work enables investigation of phase transitions with subtle structural changes in many other solid materials.

Methods
Material Synthesis

The m-LaTaO4 specimen was prepared as a polycrystalline powder according to previous literature17 and used as prepared without further purification. A standard synthesis procedure involves: Reagents are dried for 1 hour before use—La2O3 at 1000 °C and Ta2O5 at 600 °C. Stoichiometric quantities of the oxides are mixed via milling at 600 rpm for 1 hour in a planetary ball mill, then pressed into pellets 10 ~ 13 mm in diameter using either 1 tonne uniaxial pressure or 200 MPa isostatic pressure. The pellets are subsequently annealed at 1650 °C for 6 hours.

In situ heating 3D ED experiment

Sample preparation. The original m-LaTaO4 specimen was used in the in situ heating experiment. The sample was crushed and dispersed in anhydrous ethanol. The dispersed sample was dropped onto an in situ chip (Fusion Select by Protochips Co. Ltd.) with a 3×3 mesh and left to allow the complete evaporation of ethanol. It should be noted that the amount of dispersed sample was low to avoid blocking of the mesh apertures.

In situ system setup. The heating procedure was controlled by an in situ heating system, which consists of a heater, an in situ specimen holder (Fusion Select: E-FHDC-VO) and a controlling terminal (controlling software Fusion installed in a PC). The in situ holder was connected to the heater and the controlling terminal. The software checks the connection between in situ chip, heater and the controlling system, and the ‘pass’ feedback indicates the in situ system is ready to perform the experiment. For each in situ chip, a calibration file was provided by the manufacturer in order to calibrate the controller electricity parameters under different temperatures and ramping rates. The calibration file was imported to the controlling software before experiment.

TEM setup. The in situ experiment was performed on JEOL JEM-F200 microscope with an ASI Cheetah 1800 camera and a RIO-16 camera. The microscope, with an acceleration voltage of 200 kV, was aligned before experiment.

In situ heating 3D ED experiment design. The temperature was set to 300 K at the beginning of experiment, then increased with a constant rate of 5 K/min, and paused at 300, 340, 380, 400, 440, 480 and finally 500 K to collect 3D ED data (Figure 1). Temperature stabilization for ca. 5 mins was applied before 3D ED data collection. One single crystal was tracked and its SAED patterns were recorded during the heating procedure.

In situ 3D ED data collection. The in situ 3D ED datasets were collected using the ASI-Cheetah 1800 camera combined with a modified INSTAMATIC data collection software.22,28,50 The continuous rotation electron diffraction (cRED) method was used in data collection and an exposure time of either 0.3 s or 0.5 s was used. Due to the dimension of holder, the collection range was -25 ~ 25°.

HRTEM imaging. HRTEM images were taken with a Gatan RIO-16 detector equipped on a JEOL JEM-F200 transmission electron microscope, operating at 200 kV.

Data processing, structural solution and refinement

3D ED reconstruction. The data processing was performed using PETS238 software, including signal extraction and 3D reconstruction. The reflection diameter for peak search is 10 pixels and I/sigma for 20. The original modulated vector was determined and refined as q = (0.4669, 0.0028, -0.0006). The LaTaO4 phases were recognised, their unit cells and the superspace groups were determined using the reconstructed 3D ED data and reciprocal sections generated by PETS2. The frame geometry and reflection profile were also optimised before integration.

Intensity integration. The intensity integration of diffraction spots was conducted by an XDS software for ab initio structural solution. For the incommensurate phase, the determined unit cell and space group were imported into XDS to extract the diffraction information for structural solution of the basic unit cell and refinement of the periodic crystal structure. Besides, data with the modulation vector with maximum satellite order of 1 were integrated and finalised using an integrate profile for intensity estimation in PETS2 in order to refine the modulated structure.

Structural solution and refinement. The initial structural solutions of m-LaTaO4, m'-LaTaO4 and o-LaTaO4 were obtained using direct methods in SIR201935 and refined using a SHELXL36 program in OLEX237. The averaged structure of IC-o-LaTaO4 was also obtained by this means. To gain an incommensurately modulated structure, a satellite-containing (3+1)D reflection file processed by PETS2 was imported to the refinement of the averaged IC-o-LaTaO4 structure using JANA202039. A least-squares method was used for refinement.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this paper, the authors investigate the structural phase transitions in LaTaO₄ materials using electron diffraction tomography. The study is highly interesting, well-executed, and noteworthy, and I believe it merits prompt publication. I recommend that the Introduction section include more reliable and up-to-date literature to support the classification of LaTaO₄ as a perovskite-type material.\nRegarding the results, I suggest that the phases m-LaTaO₄ and m'-LaTaO₄ be compared with analogous ATaO₄ compounds, such as GdTaO₄, which follows the same phase nomenclature. Are these phases structurally identical to those found in the Gd-based material? Additionally, the authors could discuss the potential implications of conducting similar studies on ceramic powders instead of nanocrystals. What differences might be expected, and what insights could be gained?\nIn summary, I recommend acceptance after minor revisions.", "reviewer_2": "The manuscript describes the analysis of phases and phase transitions arising upon heating of LaTaO4. The information was obtained by in-situ heating of the material and collecting 3D ED data at several temperatures.\nThe basic idea of the manuscript is interesting and worthy of pursuing. It is not new (see e.g. Kamba et al., https://doi.org/10.1103/PhysRevB.95.174103), but, to my knowledge, it has not yet been performed to such an extent in terms of temperature range and number of phases. The experiments also seem to have been performed carefully, and the basic results, in general, appear reliable.\nThe weakest point of the manuscript is the amount of information (or rather the lack of it) on the incommensurate phase. It is claimed to be one of the highlights of the manuscript, but the presentation suffers from a number of flaws.\nFirst, the claim that this is the first case of the incommensurate structure refinement against 3D ED data is almost comically wrong. I know that it is hard to keep track of all the literature, but if the authors want to make such a bold claim, they should do at least a basic literature search to verify the claim is correct. Had they done so, they would have found that refinement of incommensurate structures from 3D ED data is quite common, using both the kinematical approach (which seems to be the approach used in this manuscript) and the more advanced dynamical refinement. Already, the review by Gemmi et al. (2019), cited by the authors, contains a whole section on incommensurate structures with several references to the structure analyses by 3D ED. Since then, the number of results increased, including, e.g. the analysis of vaterite (Steciuk et al., https://www.nature.com/articles/s41598-019-45581-6), or recently belite (Plana-Ruiz et al., https://doi.org/10.1107/S205252062400146X).\nThe second, and more critical, problem is that there is very little to no information provided in the manuscript about the details of the structure determination of the incommensurate structure. While there is an extensive table provided in the SI on the refinement of all non-modulated structures (Table 2 in SI), no such table is available for the incommensurate structure – not even a refinement R-factor is provided. Furthermore, the deposited CIF files correspond only to the periodic structures, and the CIF of the modulated structure is not available. Thus, the only information on the structure is the two videos, which are not sufficient and, upon inspection, they rather raise doubts about the correctness of the structure. The expected main modulation would be the tilting of the octahedra. However, the videos show a rather chaotic variation of the oxygen positions that lead to a strong deformation of the octahedra.\nThird, several points in the manuscript seem to indicate that the authors are not very familiar with the analysis of incommensurately modulated structures. One example for all: The caption to Figure 7 in SI says “Screenshot of JANA2020 in refinement of modulation vectors”. However, this screenshot shows the dialog for modulation functions, not vector.\nIn summary, the manuscript does not contain enough information to make it possible to check if the analysis of the incommensurately modulated phase was performed correctly, and this part needs to be significantly improved before the manuscript can be published. If the authors are not sufficiently familiar with the analysis of the modulated structures, they should seek help of an expert in the field.\nIn the following, I list a few more comments on the manuscript. I use the line numbers as provided in the review document:\nLine 19: “incommensurate modulate phase” is not the correct expression. It should be either “incommensurately modulated phase” or “incommensurate phase”, although the second expression is also not very accurate and somewhat colloquial. The same appears several times throughout the manuscript.\nFig. 1g/h: Why are the two figures shown in different colors? It makes it hard to compare them. In particular, the reflection 21-1 seems to be quite strong at 380 K in Fig. 1g, but it is essentially invisible at the same temperature in Fig. 1h. Where does the discontinuity come from?\nLine 103: directions in reciprocal space should be denoted in round brackets, not square brackets, i.e. “along (00-1)m” direction, not [00-1].\nLine 116: Even after repeated rereading, I do not understand this sentence. Could you please reformulate it to make it clearer?\nLine 129: “…likely exists only at the nanoscale…”: What makes you believe this statement? Why is it “likely”? Is there any evidence?\nLine 198: What do you mean by ex situ heating experiments? These experiments were not mentioned anywhere else in the manuscript.\nLine 205: the reference given for Jana2020 is wrong. Please update the reference to https://doi.org/10.1515/zkri-2023-0005\nLine 206: the wording appears to indicate Supplementary Fig. 7b is related to the modulation vector, but it is not – see my comment on the IC structure analysis above.\nLine 207: “with the the previous” should be “with the previous”\nLine 210: “atoms varies” should be “atoms vary”\nLine 224: “many of which” should be “many of them”\nLine 235: “SAED patterns…represent 2D projections” is not accurate. SAED patterns (just like other diffraction patterns) represent 2D sections of reciprocal space, not projections.\nLine 236: the word “misjudged” does not seem appropriate here. Did the authors mean “missed”?\nLine 254: The expression “Fourier Diffractogram” is not common and not really correct. The (fast) Fourier transform (commonly abbreviated as FFT) of the image is not equivalent to the diffraction pattern (or “diffractogram”). I recommend using the more common and correct “FFT image” or “FFT pattern”\nLine 267: “is” should be “are”\nLine 299: Although I think I understand the meaning of this sentence, it is not grammatically correct. In the way it is written it says “3D ED benefits”, but in fact it is “the benefit of 3D ED”. Please reformulate.\nLine 336: “a calibration file was provided”? What was the calibration file calibrating?", "reviewer_3": "The manuscript “In situ electron diffraction tomography unveils sequential phase transitions in LaTaO₄ nanocrystals” by Wu et al. reports on an electron diffraction-based structural study of intermediate phases emerging during the thermal evolution of LaTaO₄. In principle, the authors could use this data to outline a phase transition path on a PT phase diagram within the low-pressure region. The study is solid, and the main message of the paper is clear. I generally liked the paper and recommend it for publication.\nI have a few minor remarks:\n- I strongly recommend depositing the original data in a public repository (e.g., Zenodo) and including a static link to the data in the manuscript.\n- For such small tilt ranges, was crystal tracking by defocusing the diffraction pattern really necessary?\n- Was any data merging performed to mitigate issues related to poor completeness?"}, "author_response": "Point-by-Point Response to Reviewers’ Comments\nReviewer #1 (Remarks to the Author):\nIn this paper, the authors investigate the structural phase transitions in LaTaO₄ materials using\nelectron diffraction tomography. The study is highly interesting, well-executed, and noteworthy, and\nI believe it merits prompt publication. I recommend that the Introduction section include more\nreliable and up-to-date literature to support the classification of LaTaO₄ as a perovskite-type material.\nRESPONSE: We sincerely thank the reviewer for the positive feedback and constructive suggestion.\nWe have included more explanatory text and up-to-date literatures in the revised manuscript to\nsupport the classification of LaTaO₄ as a perovskite-type material.\nThe following references have been added:\nProperties of Layered Perovskite-Related Titanates, Niobates and Tantalates of the Type A B O\nn n 3n+\n, A′ A B O and A B O . Prog. Solid State Chem. 36, 253-387 (2008).\n2 k−1 k 3k+ 1 m m−1 3m\nModification Strategies towards Better Photocatalytic Performance of Water Splitting. Renew. Sustain.\nEnergy Rev. 119, 109527 (2020).\nEpitaxial LaTaO Films. ACS Applied Materials & Interfaces, 16(47), 65149-65156 (2024).\n4\n12: Howieson, G. W.. Synthesis and characterisation of the geometric ferroelectric LaTaO₄ (Doctoral\ndissertation, The University of St Andrews) (2022).\nLu). Anorg. Allg. Chem, 631, 2377-2382 (2005).\nLaNbO and its Relation to Proton Mobility. J. Solid State Chem. 187, 27-34 (2012).\n4\nRegarding the results, I suggest that the phases m-LaTaO₄ and m'-LaTaO₄ be compared with\nanalogous ATaO₄ compounds, such as GdTaO₄, which follows the same phase nomenclature. Are\nthese phases structurally identical to those found in the Gd-based material? Additionally, the authors\ncould discuss the potential implications of conducting similar studies on ceramic powders instead\nof nanocrystals. What differences might be expected, and what insights could be gained?\nIn summary, I recommend acceptance after minor revisions.\nRESPONSE: We thank the reviewer for the suggestion on taking comparable materials into\nconsideration. We suppose the reviewer refers the M-phase with space group I2/a (standardized\nspace group C2/c, https://materials.springer.com/isp/crystallographic/docs/sd_0305308) and M’\nphase (space group P2/a, ICSD No. 020264, standardized space group P2/c,\nhttps://materials.springer.com/isp/crystallographic/docs/sd_1007447). We have carefully compared\nthe structures of LaTaO with that of GdTaO . However, we found that the connections of TaO\n4 4 6\nblocks in two materials are quite different, corner sharing in LaTaO but edging sharing in GdTaO\n4 4\n(M- and M’-phases), as shown below (Figure R1). Instead, another group of minerals—such as\nBaMnF (J. F. Scott. Rep. Prog. Phys. 1979, 42, 1055; shown in Figure R1d)—exhibits similar\n4\nstructural features as LaTaO , including unit cell parameters, space groups and corner-sharing\n4\noctahedra arrangements (Figure R1). (space group Cmc2 ; a = 4.209, b = 14.708, c = 5.874 Å) but\n1\nalso greater topological similarity to o-LaTaO , particularly in the corner-sharing blocks and the\n4\nalternating alignment of Ba.\nWe agree with the reviewer that similar studies could be conducted on ceramic powders. Some\nceramics undergo phase changes during heating. For example, zirconia changes from a monoclinic\nstructure to a tetragonal structure at around 1170 ℃, and then to a cubic crystal at 2370 ℃. These\nphase changes will affect mechanical properties such as strength and toughness of ceramics. Except\nfor phase transitions, crystallites in ceramic powders might grow larger or recrystallize during the\nheating, which can be traced using TEM imaging. This might bring some new insights to this field.\nFigure R1. Crystal structure models of (a) m-LaTaO ; (b) M-GdTaO ; (c) M’-GdTaO and (d)\n4 4 4\nBaMnF . The connection of [TaO ] octahedra in m-LaTaO and [MnF ] octahedra in BaMnF is\n4 6 4 6 4\nthrough corner-sharing whilst those in GdTaO is through edge-sharing.\nThe manuscript describes the analysis of phases and phase transitions arising upon heating of\nLaTaO4. The information was obtained by in-situ heating of the material and collecting 3D ED data\nat several temperatures.\nThe basic idea of the manuscript is interesting and worthy of pursuing. It is not new (see e.g. Kamba\net al., https://doi.org/10.1103/PhysRevB.95.174103), but, to my knowledge, it has not yet been\nperformed to such an extent in terms of temperature range and number of phases. The experiments\nalso seem to have been performed carefully, and the basic results, in general, appear reliable.\nRESPONSE: We thank the reviewer for the positive and encouraging comments.\n2-1 The weakest point of the manuscript is the amount of information (or rather the lack of it) on\nthe incommensurate phase. It is claimed to be one of the highlights of the manuscript, but the\npresentation suffers from a number of flaws.\nFirst, the claim that this is the first case of the incommensurate structure refinement against 3D ED\ndata is almost comically wrong. I know that it is hard to keep track of all the literature, but if the\nauthors want to make such a bold claim, they should do at least a basic literature search to verify\nthe claim is correct. Had they done so, they would have found that refinement of incommensurate\nstructures from 3D ED data is quite common, using both the kinematical approach (which seems to\nbe the approach used in this manuscript) and the more advanced dynamical refinement. Already, the\nreview by Gemmi et al. (2019), cited by the authors, contains a whole section on incommensurate\nstructures with several references to the structure analyses by 3D ED. Since then, the number of\nresults increased, including, e.g. the analysis of vaterite (Steciuk et al.,\nhttps://www.nature.com/articles/s41598-019-45581-6), or recently belite (Plana-Ruiz et al.,\nhttps://doi.org/10.1107/S205252062400146X).\nRESPONSE: Thank the reviewer for pointing this out. We really apologize for the overstated claim\nand insufficient information provided for the incommensurate phase. The incorrect statement has\nbeen deleted and related references have been added (page 8). and related references (refs 44-47)\nhave been added.\n“JANA software has been widely used to determine incommensurately modulated crystal structures,\nmainly utilizing powder or single-crystal X-ray diffraction and powder neutron diffraction data40-\n43. In common cases, electron microscopy primarily provides SAED and HRTEM images from\nlimited orientations. Recently, more exemplar research has been reported on the structure\nrefinement of incommensurately modulated structures using 3D ED, PED, etc.21,44-47 Building upon\nthe ongoing development of 3D ED methodologies, this work presents a further application case,\ndemonstrating its utility for refining an incommensurately modulated structure upon in situ heating\nscenario.”\n2-2 The second, and more critical, problem is that there is very little to no information provided in\nthe manuscript about the details of the structure determination of the incommensurate structure.\nWhile there is an extensive table provided in the SI on the refinement of all non-modulated structures\n(Table 2 in SI), no such table is available for the incommensurate structure – not even a refinement\nR-factor is provided. Furthermore, the deposited CIF files correspond only to the periodic structures,\nand the CIF of the modulated structure is not available. Thus, the only information on the structure\nis the two videos, which are not sufficient and, upon inspection, they rather raise doubts about the\ncorrectness of the structure. The expected main modulation would be the tilting of the octahedra.\nHowever, the videos show a rather chaotic variation of the oxygen positions that lead to a strong\ndeformation of the octahedra.\nRESPONSE: We thank the reviewer’s comment. We apologize for not providing sufficient\ninformation about the incommensurate structure determination. By referring related reference (Acta\nCryst.. B80,105–116, (2024), ref No. 44) and following the procedures mentioned in the data\nprocessing, structural solution and refinement section, we conducted refinement in our\nincommensurate structure, which gives R values of main reflections 16.18% and first order of\nsatellite spots 31.55%. The refinement results have been summarised in Supplementary Table 5. The\nCIF file was also attached, which could be opened in JANA2020.\nYes, the main modulation comes from the tilting of the octahedra. After conducting the refinement\nagain, a model with clear octahedra tilting could be unravelled, as shown in Figure R2, from the\nrefined incommensurately modulated structure model at t = 0.2 and 0.7 (where t represents the\nposition variable of the modulation wave), a tendency of octahedra tilting could be identified. And\nwe also realise that the “octahedra tilting” is not a tilting of rigid octahedra with a strict restrain of\natoms but a tendency of tilting in octahedra with a certain extent of variation of atomic positions. It\nis also important to mention that the determined incommensurately modulated structure is fully\nconsistent with the previous published neutron diffraction and SAED studies of this material, and\nalso of the related n = 4 compound Sr Nb O (https://doi.org/10.1107/S010876810201741X)\n2 2 7\nFigure R2. A diagram of the refined incommensurately modulated structure of IC-o-LaTaO at t =\n4\n0.2 (yellow) and t = 0.7 (blue) showing the tilting tendency in TaO octahedra.\n6\n2-3 Third, several points in the manuscript seem to indicate that the authors are not very familiar\nwith the analysis of incommensurately modulated structures. One example for all: The caption to\nFigure 7 in SI says “Screenshot of JANA2020 in refinement of modulation vectors”. However, this\nscreenshot shows the dialog for modulation functions, not vector.\nIn summary, the manuscript does not contain enough information to make it possible to check if the\nanalysis of the incommensurately modulated phase was performed correctly, and this part needs to\nbe significantly improved before the manuscript can be published. If the authors are not sufficiently\nfamiliar with the analysis of the modulated structures, they should seek help of an expert in the field.\nRESPONSE: We thank the reviewer for pointing out this. The caption of Supplementary Fig 7b\nshould be “the refinement dialog for modulation functions”. For a better demonstration,\nSupplementary Fig 7b has been replaced by the screenshot of JANA2020, which shows the unit cell\nparameters and superspace group. The caption was also corrected.\nFollowing your suggestions, we also asked for help from an expert in this field (Dr. Zhengyang\nZhou in Shanghai Institute of Ceramics), which helped us to improve this part. We have referred to\nrefinements in incommensurate modulation using JANA from some exemplar papers to ensure a\nmore rigorous description throughout the manuscript to strengthen our presentation regarding the\nincommensurate modulation analysis. Specifically, we made following improvements:\n1. Clarified the description and added more detailed information of the refinement process in\nStructural solution and refinement section (page 12)\n2. Double-checked and corrected the definition and expressions on the refinement of modulation\nvectors in the manuscript (Page 8, 12)\n3. Reproduced the refinement results, and updated the refinement statistics (Page 12,\nSupplementary Table 5, Fig.7-10).\n4. Added some supporting references for this section. (Ref. 44-47)\n2-4 In the following, I list a few more comments on the manuscript. I use the line numbers as\nprovided in the review document:\nLine 19: “incommensurate modulate phase” is not the correct expression. It should be either\n“incommensurately modulated phase” or “incommensurate phase”, although the second expression\nis also not very accurate and somewhat colloquial. The same appears several times throughout the\nmanuscript.\nRESPONSE: We thank the reviewer for pointing this out. All expressions concerning the IC-o-\nLaTaO have been corrected as “incommensurately modulated phase” or “incommensurate\n4\nphase/structure”\n2-5 Fig. 1g/h: Why are the two figures shown in different colors? It makes it hard to compare them.\nIn particular, the reflection 21-1 seems to be quite strong at 380 K in Fig. 1g, but it is essentially\ninvisible at the same temperature in Fig. 1h. Where does the discontinuity come from?\nRESPONSE: The different colour schemes of Figure 1g and h are merely for presenting different\ntemperature ranges. A uniform colour scheme was adopted in the revised version. For the different\nintensities of 21-1 reflection, this is caused by the slight misorientation of the crystal. At 380 K,\napart from the recording of SAED patterns, a 3D ED data collection was conducted, followed by a\nre-alignment of crystal orientation to the original position. A slight misorientation was introduced\nduring the re-alignment of the crystal due to the error of goniometer tilting, which could be\nsupported by the mismatch of 21-3 and 211 reflection intensities. This does not change our\nconclusions as a significant decrease in the intensity of weak diffraction spots was witnessed in 3D\nED dataset at 380 K. Moreover, during the manuscript revision, we found that the data in the contour\nheat map of Figure 1h is shifted by mistake. This has been corrected in the revised manuscript, and\nboth the previous diagram and the corrected diagram are shown in Figure R3, in which the main\ndifference was marked by dashed column. We apologise for this error. Now the correct contour heat\nmaps among 360 ~ 380 K and 380 ~ 400 K were illustrated with a uniform colour configuration in\nthe revised manuscript.\nFigure R3. The wrong contour heat map (left) that was shifted by mistake and the correct (right)\nheat map (See Figure 1 in the main body of the manuscript). The main difference is marked by\ndashed column.\n2-6 Line 103: directions in reciprocal space should be denoted in round brackets, not square brackets,\ni.e. “along (00-1)m” direction, not [00-1].\nRESPONSE: We thank the reviewer's comment. As clarified by the IUCr conventions\n(International Tables for Crystallography, Vol. A & B) and TEM textbooks (e.g., Williams & Carter,\n2009), directions in reciprocal space should indeed be denoted with round brackets (hkl). This has\nbeen corrected in the revised version.\n2-7 Line 116: Even after repeated rereading, I do not understand this sentence. Could you please\nreformulate it to make it clearer?\nRESPONSE: We suppose the reviewer refers the sentence “Of note, such structural changes are\nnot obvious with only reduction of intensity among certain reflections.” We want to claim that the\nintensity change, from relatively strong to weak, is not very prominent to be easily identified as an\nobvious phase transition. To explain this, we propose that there might be another intermediate phase.\nBy taking the corresponding 3D ED pattern at 380 K, we realised that there is an m’-phase. We\nrephrased this sentence to make it clear.\n“It is worth noting that the changes in intensities of many other reflections are not so prominent.\nAfter careful analysis of the 3D ED dataset at 380 K, a monoclinic phase with parameters a = 7.78,\nb = 5.65, c = 3.97 Å, and β = 100.94° with a space group of P2 could be determined, denoted as\n1\nm'-LaTaO (Fig. 2d-f).”\n4\n2-8 Line 129: “…likely exists only at the nanoscale…”: What makes you believe this statement?\nWhy is it “likely”? Is there any evidence?\nRESPONSE: Yes, there is. During analysis of the LaTaO specimen, planar defects, twin defects\n4\nand boundaries could be seen in nanocrystal, see examples of HRTEM images in Figure R4a and b.\nIn another HRTEM image of Figure R4c, apart from a planar defect (marked with yellow arrows)\nthe FFT of area 1 could be assigned to a m’-LaTaO whilst the FFT of area 2 could be assigned to a\n4\nm-LaTaO . However, it is difficult to identify the coexistence of two phases in the SAED pattern,\n4\nas m-LaTaO4 only exist in nanoscale. This indicates that phase transition could exist in nanoscale.\nFigure R4. HRTEM images of LaTaO specimen showing (a) planar defect, (b) a boundary of two\n4\ndomains and (c) planar defect and local structure. The FFT pattern in (d) area 1 and (f) area 2 could\nbe assigned to a (e) m’-LaTaO and a (f) m-LaTaO along 010 zone axis respectively.\n4 4\nFurthermore, in an in situ 3D ED dataset of a single LaTaO nanoparticle specimen (Figure R5a),\n4\nwe found a complex polycrystalline pattern containing an IC phase and a twin m’ phase, as shown\nin Figure R5b. From the 0th slice of h0l of 3D ED pattern (Figure R5c), characteristic satellites could\nbe observed among main reflections, indicating an IC phase. More importantly, a series of additional\ndiffraction spots could be observed. After careful analysis, the additional diffraction spots could be\nassigned to a twining m’ phase. For a better illustration, the main reflections were painted in orange\ncolour, the satellite spots were painted in red and the spots of m’-phase twin were painted with cyan.\nWhite lines indicate the orientation of the twinned phases.\nFigure R5. A LaTaO particle with polycrystalline phases. (a) The morphology of the LaTaO\n4 4\nparticle specimen. (b) The reconstructed 3D ED pattern containing an IC phase and a twinned m’-\nphase in the [001] zone axis. (c) The 0th slice of h0l of 3D ED pattern. (d) The repainted slice\no\nshowing components of main reflection (orange), satellite spots from IC phase (red) and twinned\nm’-phase (cyan). White lines indicate the orientation of the twinned unit cells.\n2-9 Line 198: What do you mean by ex situ heating experiments? These experiments were not\nmentioned anywhere else in the manuscript.\nRESPONSE: Thanks for the comment. We apologize for this misleading sentence. Before we\nconducted in situ experiment, we also carried out an ex situ experiment. The results show a good\nconsistency with our in situ experiments. For brevity, we choose not to mention the ex situ heating\nexperiment. Apologize for the confusion and we have removed the related sentences about ex situ\nin the revised manuscript.\n2-10 Line 205: the reference given for Jana2020 is wrong. Please update the reference to\nhttps://doi.org/10.1515/zkri-2023-0005\nRESPONSE: Thanks for pointing this out. The reference has been updated with the corrected one\nwith ref No. 39.\n2-11 Line 206: the wording appears to indicate Supplementary Fig. 7b is related to the modulation\nvector, but it is not – see my comment on the IC structure analysis above.\nRESPONSE: Thanks for pointing this out. This has been corrected.\n2-12 Line 207: “with the the previous” should be “with the previous”\nLine 210: “atoms varies” should be “atoms vary”\nLine 224: “many of which” should be “many of them”\nRESPONSE: Thanks for pointing out these typos and grammar errors. Correction has been done\naccordingly in the revised manuscript.\n2-13 Line 235: “SAED patterns…represent 2D projections” is not accurate. SAED patterns (just\nlike other diffraction patterns) represent 2D sections of reciprocal space, not projections.\nLine 236: the word “misjudged” does not seem appropriate here. Did the authors mean “missed”?\nRESPONSE: Thanks for pointing this out. Yes, we agree with that SAED patterns represent 2D\nsections of 3D reciprocal space not projections. This has been corrected in the revised manuscript.\nJudging an incommensurate structure by merely taking SAED patterns might be misleading. 3D ED\nprovides a better way to determination of modulation vectors.\nTo avoid confusion, we have changed the sentence to “Furthermore, SAED patterns represent 2D\nsections of reciprocal space. The interpretation of satellite spots or weak superlattice reflections\ncould be insufficient due to its limited orientation, making it difficult in correctly determining the\nincommensurate modulation or other superstructures in these materials.” on page 9.\n2-14 Line 254: The expression “Fourier Diffractogram” is not common and not really correct. The\n(fast) Fourier transform (commonly abbreviated as FFT) of the image is not equivalent to the\ndiffraction pattern (or “diffractogram”). I recommend using the more common and correct “FFT\nimage” or “FFT pattern”\nRESPONSE: Thanks for pointing this out. The term “Fourier Diffractogram” has been changed to\n“FFT pattern” in the revised manuscript.\n2-15 Line 267: “is” should be “are”\nRESPONSE: Thanks for pointing this out. This has been corrected in the revised manuscript.\n2-16 Line 299: Although I think I understand the meaning of this sentence, it is not grammatically\ncorrect. In the way it is written it says “3D ED benefits”, but in fact it is “the benefit of 3D ED”.\nPlease reformulate.\nRESPONSE: Thanks for pointing this out. The sentence has been rephrased as:” Overall, the\nbenefits of in situ heating 3D ED reflect in many extents, ” on page 11.\n2-17 Line 336: “a calibration file was provided”? What was the calibration file calibrating?\nRESPONSE: The calibration file calibrates the actual temperature to the chip, which was provided\nby the manufacturer of in situ chips. To our knowledge, the heating of the in situ chip is achieved\nby applying an electric field to the chip, utilising the thermal effect of the chip's resistance. Therefore,\nthis calibration file is used to calibrate the controller electricity parameters under different\ntemperatures and ramp-up rates. The description of the calibration file has been updated in the “In\nsitu heating 3D ED experiment”, “in situ system” setup section.\nReviewer #3 (Remarks to the Author):\nThe manuscript “In situ electron diffraction tomography unveils sequential phase transitions in\nLaTaO₄ nanocrystals” by Wu et al. reports on an electron diffraction-based structural study of\nintermediate phases emerging during the thermal evolution of LaTaO₄. In principle, the authors\ncould use this data to outline a phase transition path on a PT phase diagram within the low-pressure\nregion. The study is solid, and the main message of the paper is clear. I generally liked the paper\nand recommend it for publication.\nRESPONSE: We thank the reviewer for positive comments.\nI have a few minor remarks:\n3-1 I strongly recommend depositing the original data in a public repository (e.g., Zenodo) and\nincluding a static link to the data in the manuscript.\nRESPONSE: Thanks for the suggestion, and we have deposited our original data in Zenodo\n(https://doi.org/10.5281/zenodo.17154008), including original datasets, crystallographic files such\nas .res, .hkl or .ins files.\n3-2 For such small tilt ranges, was crystal tracking by defocusing the diffraction pattern really\nnecessary?\nRESPONSE: Indeed, in small tilting angles (e.g. ≤ 30°), the specimen drift is not dramatic, and it\nis not necessary for defocusing during data collection if the whole microcrystal is within the\nselected-area aperture. However, tracking specimen through defocusing is still a safer way,\nespecially for 3D ED data collection from local regions (tip of rods, corner of crystals, etc.), or edges\nin relatively large crystals (ED data quality may be bad in central area of large crystals). We might\nnot be able to illuminate the same region without crystal tracking.\n3-3 Was any data merging performed to mitigate issues related to poor completeness?\nRESPONSE: We thank the reviewer for the professional question. All data adopted in the\nmanuscript and Supplementary Information are single datasets without merging. Data merging is a\ngood way to improve the completeness, especially for in situ holders which has only ± 25° tilting\nrange. By accepting the reviewer’s suggestion, we merged data for structure solution of both m- and\no-LaTaO phases. 4 datasets of m-LaTaO under 300 Kand 3 datasets of o-LaTaO under 500 K were\n4 4 4\nmerged to improve data completeness. The resolved structures from the merged data show a great\nimprovement on completeness (from no more than 50 % to 84.7 % for m-LaTaO , and from ~60 %\n4\nto 95.6 % for o-LaTaO ) with relatively low R values. Table 6 in the Supplementary Information\n4\nshows the detailed refinement statistics from the merged data of m-LaTaO and o-LaTaO . The\n4 4\nstructure models from merged data show good consistency with our claimed structure. Comparing\nthe refined structures from merged data with those from single datasets, the R values are similar, e.g.\n18.56% (merged) vs. 19.59 % (single dataset under 300 K) and 20.64 % (merged) vs.17.06 % (single\ndataset under 500 K)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly and satisfactorily addressed all issues raised by the reviewers. I recommend the manuscript for acceptance.", "reviewer_2": "I have reviewed the revised version of the manuscript entitled In situ electron diffraction tomography study of the successive phase transitions in LaTaO4 nanocrystals. I can conclude that the authors put a lot of effort in addressing the my comments and improved the manuscript considerably.\nNevertheless, I have still identified some problems in the analysis of the modulated structure, which require some more attention. I am especially concerned by the determination of symmetry (lines 215+). The manuscript says that the observed systematic absences were of the type hk0m: h+k=2n and h0lm: l+m=2n. Then it is stated that these absences can be attributed to the superspace group Cmc21(a00)000. First of all, the first condition should be written hklm:h+k=2n, because it is induced by the centering and thus applies to all reflections, not only the h0lm subset. Second, these conditions are compatible also with the centrosymmetric space group Cmcm(a00)000. It is not explicitly stated why the non-centrosymmetric space group was selected and the centrosymmetric was not considered. I assume it is because it is known that the high-temperature phase is non-centrosymmetric. It would be good to mention this explicitly in the text. Third and most important: in the supplementary figure 7, an attempt is made to illustrate the systematic absences by circles and crosses in the h0lm section. Unfortunately, the circles and crosses in Fig. s9 are not correct. The condition h0lm: l+m=2n implies that when the main reflection is absent, the associated first-order satellites are present and vice versa. I.e., the circles and crosses form a checkerboard pattern. Please revise the figure.\nLooking at the pattern in Fig. S8b and S9b, I can see a lot of violations of any possible systematic absences. The data obviously exhibit a large amount of multiple scattering - not unusual for such a simple inorganic structure. But it means that the systematic absences must be evaluated with great care. Without having access to the raw data, I cannot make a definitive verdict, but I am convinced the correct systematic absence is h0lm: l+m=2n, and the correct superspace group would then be Cmc21(a00)0s0 (or Cmcm(a00)0s0). I think that this option must be carefully evaluated before it is discarded, ideally by trying to refine a structure model in both space groups, and choosing the better model.\nWhen reviewing the symmetry considerations for the modulated structure, I checked again also the symmetry determination of the non-modulated structures. And I am afraid the same error that might have happened in the assignment of the space group of the incommensurate structure crept in also in the analysis of the m-LaTaO4 phase. The authors argue that additional peaks are visible in the SAED patterns and in the reciprocal-space sections from the 3D ED data, disproving the P21/c space group. However, the SAED pattern shown in Fig. 1c is in an orientation that is very favourable for multiple diffraction into the reflection 00-3, and the reciprocal-space section presented in Fig. S3b shows very clear variation of intensity between the l=2n and l=2n+1 rows. Given the strong dynamical character of the data, these images are, in my opinion, consistent with the space group P21/c, and the only method of distinguising P21 and P21/c is performing the refinement in both and showing that P21 is clearly better than P21/c. But my guess is that P21/c is the better choice.\nMy apologies for not having spotted these problems already in the first round of revisions, but I think the problems are relatively severe and need careful consideration.", "reviewer_3": "All reviewers requests have been addressed, and the manuscript is now ready for publication."}, "author_response": "Point-by-Point Response Letter\nReviewer #1 (Remarks to the Author):\nThe authors have thoroughly and satisfactorily addressed all issues raised by the reviewers. I\nrecommend the manuscript for acceptance.\nResponse: We appreciate the reviewer’s positive comments.\nReviewer #2 (Remarks to the Author):\nI have reviewed the revised version of the manuscript entitled In situ electron diffraction\ntomography study of the successive phase transitions in LaTaO4 nanocrystals. I can conclude that\nthe authors put a lot of effort in addressing the my comments and improved the manuscript\nconsiderably.\nResponse: We appreciate the reviewer’s comments.\n1. Nevertheless, I have still identified some problems in the analysis of the modulated structure,\nwhich require some more attention. I am especially concerned by the determination of symmetry\n(lines 215+). The manuscript says that the observed systematic absences were of the type hk0m:\nh+k=2n and h0lm: l+m=2n. Then it is stated that these absences can be attributed to the\nsuperspace group Cmc21(a00)000. First of all, the first condition should be written hklm:h+k=2n,\nbecause it is induced by the centering and thus applies to all reflections, not only the h0lm subset.\nResponse: We thank the viewer for pointing this out. It has been corrected in the revised\nmanuscript.\n2. Second, these conditions are compatible also with the centrosymmetric space group\nCmcm(a00)000. It is not explicitly stated why the non-centrosymmetric space group was selected\nand the centrosymmetric was not considered. I assume it is because it is known that the\nhigh-temperature phase is non-centrosymmetric. It would be good to mention this explicitly in the\ntext.\nResponse: Thanks for the comment. The centrosymmetric space group Cmcm(a00)000 was\nexcluded because the high-temperature phase is well-established as ferroelectric with a\nnon-centrosymmetric structure, as extensively reported in prior studies (such as Cordrey, K. J. et\nal. Dalton Trans. 44, 10673-10680 (2015) and Cava, R. J. & Roth, R.S. J. Solid State Chem. 36,\n139-147 (1981)). This clarification has been added to the revised manuscript.\n3. Third and most important: in the supplementary figure 7, an attempt is made to illustrate the\nsystematic absences by circles and crosses in the h0lm section. Unfortunately, the circles and\ncrosses in Fig. s9 are not correct. The condition h0lm: l+m=2n implies that when the main\nreflection is absent, the associated first-order satellites are present and vice versa. I.e., the circles\nand crosses form a checkerboard pattern. Please revise the figure.\nResponse: We guess that the reviewer means supplementary Fig. 9 instead of Fig. 7.\nSupplementary Fig 9 have been revised for a better illustration.\nSupplementary Fig. 9 The indexed reflection conditions of h0lm of superspace group\nCmc2 (α00)0s0. The bright red dotted lines indicate the h = 2n indices, the dark red dotted lines\n1\nindicate the h = 2n+1 indices, the bright blue dotted lines indicate the l = 2n indices and the dark\nblue dotted lines indicate the l = 2n+1 indices.\n4. Looking at the pattern in Fig. S8b and S9b, I can see a lot of violations of any possible\nsystematic absences. The data obviously exhibit a large amount of multiple scattering - not\nunusual for such a simple inorganic structure. But it means that the systematic absences must be\nevaluated with great care. Without having access to the raw data, I cannot make a definitive\nverdict, but I am convinced the correct systematic absence is h0lm: l+m=2n, and the correct\nsuperspace group would then be Cmc21(a00)0s0 (or Cmcm(a00)0s0). I think that this option must\nbe carefully evaluated before it is discarded, ideally by trying to refine a structure model in both\nspace groups, and choosing the better model.\nResponse: We thank for the reviewer’s comments. We have discussed about the choice of\nsuperspace group. We are aware that there are a lot of violations of systematic absence because of\nstrong dynamical scattering. For Cmc2 (a00)0s0, the reflection conditions (h0lm: l+m = 2n) are\n1\nstricter than Cmc2 (a00)000 (h0lm: l = 2n). From the h0lm reflection of the IC-o-LaTaO\n1 4\n(Supplementary Fig. 8), assigning the superspace group as Cmc2 (a00)0s0 would exclude more\n1\nreflections than Cmc21(a00)000. Furthermore, the octahedral tilting is extensively believed to be\nthe origin of the phase transition in perovskite-like materials, if Cmc2 (a00)0s0 is selected, the\n1\n“octahedral tilting” incommensurately modulated model would turn out to be a “octahedral\ndeformation”, because the O4 atom would rotate in contradict way because of the symmetry, as\nshown in the Figure below.\nFigure R1. Comparison of incommensurately modulated models using space groups\nCmc2 (a00)0s0 and Cmc2 (a00)000.\n1 1\nBy taking the reviewer’s advice, we tried to perform the refinement using Cmc2 (a00)0s0, and the\n1 1\nreflections are obviously stronger than other reflections. Therefore, we accept the reviewer’s\ncomments. The superspace group and the models have been corrected in the revised manuscripts.\n5. When reviewing the symmetry considerations for the modulated structure, I checked again also\nthe symmetry determination of the non-modulated structures. And I am afraid the same error that\nmight have happened in the assignment of the space group of the incommensurate structure crept\nin also in the analysis of the m-LaTaO4 phase. The authors argue that additional peaks are visible\nin the SAED patterns and in the reciprocal-space sections from the 3D ED data, disproving the\nP21/c space group. However, the SAED pattern shown in Fig. 1c is in an orientation that is very\nfavourable for multiple diffraction into the reflection 00-3, and the reciprocal-space section\npresented in Fig. S3b shows very clear variation of intensity between the l=2n and l=2n+1 rows.\nGiven the strong dynamical character of the data, these images are, in my opinion, consistent with\nthe space group P21/c, and the only method of distinguising P21 and P21/c is performing the\nrefinement in both and showing that P21 is clearly better than P21/c. But my guess is that P21/c is\nthe better choice.\nResponse: We thank the reviewer for the careful examination of our experimental results. As we\nmentioned above, the reflections suffer from strong dynamical scattering, resulting in diffraction\nspots that violate the systematic absence. During structure determination, our initial consideration\nis that the l = 2n +1 reflections are considerably strong (as illustrated in Supplementary Fig. 3), so\na lower symmetry of P2 was selected.\n4\nassigning P2 /c, the R values increase by less than 4 % (19.59 % vs 22.79 %@300 K, and 23.43 %\n1\nvs 25.34 %@340 K). But we are also aware that because of low symmetry of P2 has more atoms\n1\nin asymmetric units and more parameters which may easily lead to lower R values. These\ndifferences in R values are acceptable.\nWe admitted that although l = 2n +1 reflections have intensities, but they are apparently weaker\nthan l = 2n reflections. Therefore, we accept the reviewer’s comment. The space groups of\nm-LaTaO have been changed to P2 /c and the refinement statistics have been corrected in the\n4 1\nrevised manuscript.\nMy apologies for not having spotted these problems already in the first round of revisions, but I\nthink the problems are relatively severe and need careful consideration.\nReviewer #3 (Remarks to the Author):\nAll reviewers requests have been addressed, and the manuscript is now ready for publication.\nResponse: Thanks for the reviewer’s comment."}, {"round": 3, "reviewer_comments": {"reviewer_2": "I have now reviewed the third revision of the manuscript. A lot has improved, and I believe the manuscript is close to its final version.\nI would just appreciate a clearer discussion on the octahedral tilting in the IC phase. In the revised manuscript, it is stated that the octahedra do not tilt, but, instead, deform, as dictated by the new symmetry. However, when seeing the videos of the structure, I do not see deformation, but clear tilting. The tilting is accompanied with some deformation, but the deformation does not seem to be symmetry-dictated, but rather a result of the inaccuracy of the refinement. The discussion about \"deformation, not tilting\", is thus very confusing. Please revise the discussion to make your point clearer.\nFurthermore, I noticed that the the reflection conditions are compatible with yet another space group: C2cm(a00)ss0 (equivalent to Ama2(00g)0ss in the standard setting). I guess this space group can be excluded based on crystallochemistry arguments, but it would be good to mention it clearly in the manuscript. I spent a considerable amount of time trying to figure out if this space group could not be the solution for the \"deformation, not tilting\" problem.\nTo conclude, I think that most flaws of the previous version of the manuscript have been corrected, but please improve the description of the octahedral tilting, to avoid making the impression that the octahedra are not tilted, but deformed."}, "author_response": "Point-by-Point Response Letter\nReviewer #2 (Remarks to the Author):\nI have now reviewed the third revision of the manuscript. A lot has improved, and I believe the\nmanuscript is close to its final version.\nResponse: We sincerely thank the reviewer’s comment.\n1. I would just appreciate a clearer discussion on the octahedral tilting in the IC phase. In the revised\nmanuscript, it is stated that the octahedra do not tilt, but, instead, deform, as dictated by the new\nsymmetry. However, when seeing the videos of the structure, I do not see deformation, but clear\ntilting. The tilting is accompanied with some deformation, but the deformation does not seem to be\nsymmetry-dictated, but rather a result of the inaccuracy of the refinement. The discussion about\n\"deformation, not tilting\", is thus very confusing. Please revise the discussion to make your point\nclearer.\nResponse: We apologize for the confusion caused by our previous wording. In the previous version,\nour description was indeed too arbitrary. In particular, when discussing octahedral tilting, we\nimplicitly referred to completely rigid tilting, which unintentionally overemphasized the presence\nof minor octahedral deformation.\nUpon reconsideration, we agree that the structural modulation in the incommensurate phase is\nprimarily governed by octahedral tilting, while small accompanying deformations are also present.\nThese minor deformations should be regarded as secondary effects rather than symmetry-dictated\nprimary distortion modes.\nWe have therefore revised the discussions in the manuscript (page 8, line 241-243) to clarify that\nthe dominant structural motif is octahedral tilting with minor deformation, and to avoid the\npotentially misleading statement of “deformation, not tilting.” We thank the reviewer for pointing\nthis out.\n2. Furthermore, I noticed that the reflection conditions are compatible with yet another space group:\nC2cm(a00)ss0 (equivalent to Ama2(00g)0ss in the standard setting). I guess this space group can be\nexcluded based on crystallochemistry arguments, but it would be good to mention it clearly in the\nmanuscript. I spent a considerable amount of time trying to figure out if this space group could not\nbe the solution for the \"deformation, not tilting\" problem.\nResponse: We thank the reviewer for this comment. Indeed, the observed reflection conditions are\ncompatible with both Cmc2 and C2cm, which are subgroups of the same space group Cmcm.\nHowever, the refinement did not converge to a physically reasonable model and resulted in strongly\ndistorted TaO octahedra, as shown in Fig. R1a and b. From a crystallography perspective, the C2cm\n6\nsymmetry constrains the bridging oxygen atom at the corner-sharing site of the TaO octahedra,\n6\neffectively forcing it toward a special position. If the oxygen atom deviates from this position, the\nsymmetry operation will generate a symmetry-related equivalent counterpart, giving rise to an\napparent split or duplicated oxygen position under C2cm constraints, as illustrated in Fig. R1c.\nCorrespondingly, structure refinements using C2cm yield unusually large atomic displacement\nparameters (ADPs) for this bridging oxygen site, indicated by arrows in Fig. R1d. This behaviour\nsuggests that the imposed C2cm symmetry does not adequately represent the local geometry, further\nsupporting the exclusion of this space group.\nFig. R1. Structure models of o-LaTaO refined using the C2cm viewed along (a) [100] and (b) [001]\n4\nzone axes. (c) Apparent splitting of the bridging oxygen atom when it deviates from the symmetry-\nimposed special position, with a symmetry-related equivalent position generated under C2cm\nconstraints. (d) A structural model showing large atomic displacement parameters (ADPs) of the\nbridging oxygen atoms after refinement, indicated by arrows.\nIn the superspace description, the current data allow both Cmc2 (α00)0s0 and C2cm(α00)ss0 based\n1\non reflection conditions alone. We understand that C2cm(α00)ss0 may appear particularly relevant\nin the context of the earlier discussion on “deformation, not tilting.” However, inspection of the\nsymmetry restrictions imposed by C2cm(α00)ss0 in JANA shows that both zsin1 and zcos1 are\nsymmetry-forbidden, implying the absence of any first-order modulation along the z direction. This\nis incompatible with the experimentally observed tilting-dominated incommensurate modulation,\nwhich necessarily involves displacements with a z component.\nWe therefore exclude the space group C2cm(α00)ss0. And we have added the corresponding\ndiscussion in the manuscript (page 8, line 225-232)\nTo conclude, I think that most flaws of the previous version of the manuscript have been corrected,\nbut please improve the description of the octahedral tilting, to avoid making the impression that the\noctahedra are not tilted, but deformed."}, {"round": 4, "reviewer_comments": {"reviewer_2": "The authors have properly addressed the remaining problems. From my point of view, the manuscript is now suitable for acceptance."}, "author_response": "Responses: Thanks for your comments. We appreciate your effort to review our manuscript and\ngive us a positive feedback."}]

Decision letter