Controlled Growth of SrxBa1−xNb2O6 Hopper‐ and Cube‐Shaped Nanostructures by Hydrothermal Synthesis

Abstract Controlling the shape and size of nanostructured materials has been a topic of interest in the field of material science for decades. In this work, the ferroelectric material SrxBa1−xNb2O6 (x=0.32–0.82, SBN) was prepared by hydrothermal synthesis, and the morphology is controllably changed from cube‐shaped to hollow‐ended structures based on a fundamental understanding of the precursor chemistry. Synchrotron X‐ray total scattering and PDF analysis was used to reveal the structure of the Nb‐acid precursor, showing Lindqvist‐like motifs. The changing growth mechanism, from layer‐by‐layer growth forming cubes to hopper‐growth giving hollow‐ended structures, is attributed to differences in supersaturation. Transmission electron microscopy revealed an inhomogeneous composition along the length of the hollow‐ended particles, which is explained by preferential formation of the high entropy composition, SBN33, at the initial stages of particle nucleation and growth.


Introduction
Controlling the size and morphologyi sa ni mportant aspect of materials ynthesis of functional materials, especially at the micro-to nanometer scale, as this is directly linked to material properties. [1] Thus, understanding and furthermore controlling the underlying mechanismsg overning the size and shape of crystalline materials is imperative. [2] Among av ariety of methods for synthesizing crystalline materials, wet chemicals ynthesis routes, especially hydrothermal, are low-cost,l ow-temperature and scalable methods to prepare functional materials, and have been widely studied to understand crystal growth. [3] This work focuseso nf undamental understanding of crystal growth under hydrothermal conditions. Intricate structures and morphologies from hydrothermal/ solvothermals ynthesish ave been reported without the use of templates and/or templating agents. This shows the spontaneous formation of complex structures under specific conditions. Some examples are;c ubic hopper crystalso fC u 2 O [4] and PbTe, [5] hexagonal tubes of NaYbF 4 [6] and ZnO, [7] dendrite-like BaTiO 3 , [8] tower-like KNbO 3 , [9] and morphology-tuningb y doping of a-Fe 2 O 3 with various cations. [10] Almost as many explanations of possible growth and formation schemese xist as there are reportedw orks, even though many of them could possibly be explained by classical growth theory.
From classical growth theory,c rystalsg row by the addition of monomers (atoms, molecules, or small clusters)f rom the surrounding solution or vapor phase. [11] Based on the Bergeffect, [12] we know that there is ah igher supersaturation at crystal edges and corners, thus the growth is faster at the edges and corners comparedt ot he crystal facets. Still, at low supersaturation, there is an equilibrium between the growth rate of the edges and corners and at the facets, giving crystal shape symmetry reflecting the unit cell of the material with macroscopically flat facets (polyhedral). On the other hand, when the supersaturation is high, this equilibrium can be perturbated, so that the edges and corners are growing at a higherr ate than the crystal facets. This is ak inetic effect to reduce the high supersaturationb yt he formation of al arger surfacearea and is referredt oa san interfacial instability.
The view of crystal growth based on classical growth theory and changes in supersaturation as af unction of temperature and pressure can account for the formation of many crystals shapes:t he kinetic effect can lead to intricately shaped crystals, sometimes referred to as skeletal crystals, due to an inter-facial instability. [13] Some examples are dendritic crystals observed for ice [14] and metals, [15] and hopper crystals observed for some naturally occurring minerals, [13a] synthetic bismuth, [16] and NaCl. [17] Furthermore, for ice crystals, am yriado fn aturally occurring morphologies are observed, includingh ollow structures. [14] In general, with increasing interfacial instability,t he degree of complexity of the final morphology increases (polyhedral!hoppers!dendrites). However, classical growth theory is derived for one-component or simple binary systems, and the complexity must necessarily increasef or wet chemical synthesis with the addition of solvent-crystal interactions, surfactants and mineralizers. Thisa dditional complexity gives an extra dimension for crystal engineering. [18] As an example for such growth of shaped crystals under complicated hydrothermal conditions, we selected aS r x Ba 1Àx Nb 2 O 6 (SBN100x)s ystem, af erroelectric tungsten bronze( TTB) with as econd-order Jahn-Te ller polarization mechanism. [19] This system has received considerable attention due to electro-optical properties [20] and cation disorder. [21] We have previously reported a template-free hydrothermal synthesis of SBN (x = 0.2-0.6). [22] With ap recursor slurry corresponding to SBN40 we observed formationo fc ube-shaped particles (ca. 500 500 nm) for reactions at 300 8C, whereas for SBN20w eo bserved the formation of elongatedh ollow particles (apparently hollow by scanning electron microscopy,S EM) for the same reaction conditions. Similar hollow structures were also observed for higher Sr fractions when the reaction temperature was decreased. Ah igher specific surfacea rea (m 2 g À1 )i se xpectedf or the hollow particles compared to the cubes, whichi si nteresting with respect to the photocatalytic activity of SBN, [23] meriting further investigation into the formation andg rowth of these structures.
In this work we complement our previous in situ study [22] with new experiments and characterization, in addition to discussing some of the previousf indings in an ew setting( explaining the formation of hopper-crystals). The hollow structures were characterized by transmission electronm icroscopy (TEM) with ac ombination of high-angle annular dark-field scanning TEM (HAADF-STEM) and energy-dispersive X-ray spectroscopy( EDS). The amorphous structure of the Nb-acid used as precursor was investigated by synchrotron X-ray total scattering andp air distribution function (PDF) analysis,w hich gives valuable insight into the early formation stages of SBN. We show,t hat based on af undamental understanding of the precursor chemistry, we can control the growth mechanism and thus the particlem orphologyo fS BN, by tuning the Nb-supersaturation of the system, both with chemical (Sr:Ba ratio) and kinetical means(reactiont emperature).

Experimental Section
Synthesis:N ominal composition Sr x Ba 1Àx Nb 2 O 6 (x = 0.2 and 0.4) was prepared following ap reviously described route. [22] Strontium nitrate (Sigma-Aldrich, Oslo, Norway, 9 9.995 %) and barium nitrate (Sigma-Aldrich, Oslo, Norway, 9 9.999 %) were mixed with an iobic acid (Nb-acid) aqueous dispersion and pH was adjusted to 12.4 with aqueous ammonia solution (Sigma-Aldrich, Oslo, Norway, 25 wt %s olution). The Nb-acid was prepared by precipitation from an ammonium niobate (V) oxalate hydrate (Sigma-Aldrich, Oslo, Norway, 9 9.99 %) aqueous solution with addition of ammonia solution to pH ca. 11.T he precursor slurries were prepared for each experiment by first weighing out Nb-acid, then adjusting the pH to 12.4 by adding ammonia solution, before adding the stoichiometric amounts of nitrates and diluting with water to at otal volume of 5mL. This gave afinal Nb-concentration of about 0.25m. The reactions in this work were performed in at ube coil synthesis setup, as described by Skjaervø et al. [24] The setup consists of a 316 Ls teel tube coil that is filled with the precursor slurry and connected to ah igh-pressure liquid chromatography (HPLC) pump (Shimadzu LC-10ADVP,S himadzu Corporation, Kyoto, Japan) with Swagelok tubes and fittings, using distilled water as pressure media. The coil was heated in af luidized sand bath (Omega FSB-3, Omega Engineering, Norwalk, USA) and the temperature was controlled using aPID controller.Anoverview of the synthesis parameters for the experiments conducted are presented in Ta ble 1. The nomenclature is SBNXX TYYY Z, where XX refers to the Sr mole fraction in the precursor slurry times 100, YYY the reaction temper- ature and Zt he reaction time for the coil experiments and "in" for the in situ experiments (described in the next paragraph). After the reaction, the samples were collected, washed with distilled water by centrifugation and decanting, before drying at 105 8Cf or about 12 h.
The samples referred to as in situ experiments in this work were performed in our previous work, [22] and are included here for completeness (samples in Table 1e nding with "i n"). In short, the reaction vessel for these experiments was as apphire capillary heated with ah ot air stream instead of the steel coil and fluidized sand bath used for the ex situ experiments. The same HPLC pump as described above was used for pressurization. The experiments were conducted at the Swiss-Norwegian Beamlines (BM01), European Synchrotron and Radiation Facility (ESRF), Grenoble, France, and reaction time was optimized for each experiment for best utilization of the allocated beam time. The key differences between the coil setup used in this work and the in situ setup used previously is the reaction vessel (steel tube coil vs. single-crystal sapphire capillary) and heating rate (ca. 20 sv s. ca. 1min to reach set point temperature). Further experimental details for the in situ experiments and the in situ setup are reported in previous papers. [22,25] The coil, and the in situ setups show comparable results with similar reaction conditions as presented in Figures S1 and S2 in Supporting information.
Characterization:P hase purity was investigated by X-ray powder diffraction (XRD) using aB ruker D8 Advance Da-Vinci equipped with aL ynxEye detector working in Bragg-Brentano geometry.D iffraction patterns were recorded with Cu Ka radiation (l = 1.5406 ), astep size of 0.0138 and an integration time of 0.75 susing avariable divergent slit.
Scanning electron microscopy (SEM) was performed on af ield emission FEI APREO SEM. An in lens secondary electron detector with an acceleration voltage of 5keV and ac urrent of 25 pA was used. TEM was performed on ad ouble-corrected JEOL JEM ARM200F with ac old field emission gun. The acceleration voltage was set to 200 kV.T he beam convergence angle was 27 mrad and the HAADF-STEM images were acquired using ac ollection angle of 51-203 mrad. EDX spectra were acquired using aJ EOL Centurio SDD detector (solid angle 0.98 sr), using an energy-dispersion of 10 eV per channel. The EDS data were analyzed using HyperSpy (version 1.4.1). [26] Samples for both SEM and TEM were prepared by making ad ispersion of the dried particles in distilled water using ultrasound bath. The dispersions were then dropped onto the sample holder and let dry for 12-24 h. The sample holders were a FIB stub and ah oley carbon copper grid for SEM and TEM, respectively.
Specific surface area (m 2 g À1 ), was measured by nitrogen adsorption and calculated using the BET method for SBN20 T300 1hand SBN40 T300 1husing aT ristar 3000 (Micrometrics Instrument Corporation, Norcross, USA). The samples were degassed at 200 8Cf or 17 htor emove adsorbed water prior to measurements.
X-ray total scattering data for pair distribution function (PDF) analysis was collected on BL08W at SPring-8, Japan using a16inch Per-kinElmer XRD 1621 CN3 ES series flat panel detector and l = 0.10765 (115 keV) with as ample to detector distance of % 53 cm. [27] Sample to detector distance, and geometry of the setup were calibrated using aN IST CeO 2 standard. X-ray total scattering was collected for the as-prepared Nb-acid dispersion, the same Nb-acid dispersion vacuum-dried at room temperature (this was done for improving the scattering signal) and the fully crystalline samples from the coil experiments (see Ta ble 2). The vacuum dried powder sample and SBN samples were packed in Kapton tubes (OD 1.05 mm, ID 1.00 mm, Goodfellow,E ngland) for the X-ray measurements. Am easurement was done with an empty Kapton tube with same dimensions for background subtraction. Wider tubes (OD 1.90 mm, ID 1.80 mm) were used for the Nb-acid dispersion experiments, and aK apton tube with the same dimensions filled with a1%a queous ammonia solution (the dispersions consisted of Nb-acid in a1%a queous ammonia solution having a Nb-concentration of ca. 0.9 m)w as used for background subtraction. Data treatment (masking parasitic regions like beam stopper, and integration from 2D-to 1D-data) was done using pyFAI (version 0.17.0) [28] and Jupyter Notebook (version 5.7.8). [29] xPDFsuite [30] was used for background subtractions and corrections, before Fourier transformation into PDF using aQrange up to 15 and 29.5 À1 for the Nb-acid samples and SBN, respectively (note that Qi st he moment transfer of scattering particle). TOPAS (Bruker AXS version 6) in launch mode was used to fit models to the resulting PDFs, using jEdit (version 4.3.1) as the text editor for writing macros for TOPAS. [31] The structural model used for SBN, is described in Supporting Information.

Results
All the experiments yielded phase pure SBN, as represented by the X-ray diffractogram of SBN40 T300 1h shown in Figure 1a). All materials show high crystallinity,e xcept SBN40 T200 1h where two broad features showing the presence of amorphous phase as seen in Figure 1b). This is in good agreement with our in situ findings, where this reaction took over 2h to complete, whereas for the other experiments conducted in this work the reactions was completed well within 1h. [22] The X-ray diffraction patterns for the coil synthesis experiments and the PDFs are presented in Figure S3 and Figure S4, respectively,i nt he Supporting Information. The Srfractions (referring to x in the chemical formula Sr x Ba 1Àx Nb 2 O 6 )o btained from the PDF analysis are presented in Ta ble 2, while the remaining results are presented in Ta ble S1.

Structure of the Nb-acid precursor
PDFs of both the as-prepared Nb-acid used as precursor and the vacuum-dried Nb-acid are presented in Figure 2a and b. Except for some intensity differences, and as mall shift of the 3.7 peak (towards higher r-values for the as-prepared Nb-acid), the two PDFs look similar.T hat is, the vacuum drying did not change the amorphous structure of the Nb-acid. Four main features can be observed in both PDFs, ab road peak at 1.9 ,t wo close peaks at 3.3 and 3.7 ,a nd ap eak at 4.7 .T he 1.9 peak is assigned to NbÀO atomic pairs in an octahedral configuration, the 3.3 and 3.7 peaks are assigned to NbÀNb pairs of edge-sharing octahedra, and the 4.7 is assigned to the second coordination sphere of NbÀNb pairs of edge-sharing octahedra. In addition to these apparent peaks, some weaker correlations are observed between 5a nd 8 . The Lindqvist-ion can be described as as uperoctahedron, consisting of 6e dge-sharing NbO 6 octahedra, see Figure 2c,w ith reported characteristic features at about 2.0 (NbÀOd istance in octahedra), 3.4 (NbÀNb distance between edge-sharing octahedra) and 4.7 (NbÀNb distance diagonal), [34] and is thus ac andidate for the structure. Af it of ac luster model of the Lindqvist-ion to our PDF data is presented in Figure 2a and b.
To fit the peaks at 3.3 and 3.7 ,the Lindqvist-ion has been stretched slightly along one of its three equivalent axes in our model. It is known that alkali metal-ions coordinate around the Lindqvist-ion, [33a] and it is not unlikely that the NH 4 + -ion can do the same. If the NH 4 + -ion only coordinates on some of the Lindqvist-ion faces (as is the case for Li/Na/K), this could explain the perturbation, or stretching of the Lindqvist-ion. It can be seen that the four main features (1.9, 3.3, 3.7, and 4.7 )a re present, and that the intensities are fitted fairly well with the Lindqvist-ion model. It therefore seems clear that aL indqvist-like ion is the main motif or building block in the Nb-acid used. The weaker correlations between 5a nd 8 could be as ignature of coordinated NH 4 + -ions (which are not included in our model). Another explanation could be ap artly condensation of Lindqvist-ions, which could then also contribute the peak at 3.7 ,ifthe Lindqvist-ions were linked through corner-sharing NbO 6 octahedra with an Nb-O-Nb angle of 1548 (calculated from the observed distances). For example, the decaniobate is a well-known (two edge-sharing Lindqvist-ions, [Nb 10 O 28 ] 6À )p olyoxometalate, although normally stable only at lower pH values than used in this work. [33c] Characterization of size and morphology SEM images of the materials prepared by the coil synthesis are presented in Figure 3. For SBN40 with ar eaction temperature of 300 8Cc ube-shaped particles with as ize of about 500 nm are observed for both reaction times. By decreasing the reaction temperature from 300 to 200 8Cw ith ar eaction time of 6h the particles become more elongated, with ac ross section with similar dimensions as the cubes formed at 300 8C. In the case of SBN40 T200 1h,l arge amorphous agglomerates are observed, which is in good agreement with the XRD pattern. In addition, elongated, apparent non-amorphous features like rod-shaped SBN could be observed in the amorphous agglomerates. Decreasing the Sr fraction in the precursor slurry yields elongated particles with ah ollow or hollow-ended structure. Even though some small dimples can be observed on the facets of the SBN40 materials, it is clear that the hollow structures appear upon lowering the Sr content in the precursor slurry.T he hollow features for SBN20 at 300 8Cb ecome less pronounced with increasing reaction time, making the particles more cube-like. The surface areas measured for SBN20 T300 1h and SBN40 T300 1h were 14.5 AE 0.1 and 15.4 AE 0.1 m 2 g À1 ,r espectively. SEM images of the materials prepared by the in situ setup are presented in Figure 4. Cube-shaped particles with as ize of about 500 nm are observed for SBN40 at 300 8C, and with decreasing temperature to 225 8Cw eo bserve as light elongation of the particles. At 200 8C, am orphology similar to the hollow structure of SBN20 is observed. For SBN30 as imilar trend is observed as for SBN40, with cube-shaped particles at high temperature, and more hollow-like structures with decreasing temperature. In case of SBN30, the transition from the cube-shaped particles to the hollow structures occurs at ah igher temperature than for SBN40, with the formation of hollow structures even at 225 8C. Hollow structures are clearly present at all temperatures for SBN20 from the in situ setup. In addition to the pronounced effect of composition, the in situ experiments also demonstrate ac lear temperature effect, where al ower reaction temperature promotes the formation of the hollow structures. These findings are summarized in the phase diagram in Figure 5, illustrating the formation of hollow structures as af unction of Sr-fraction in the precursor slurry and the reaction temperature.

Characterization of hollow structures with TEM
High-angle annular dark-field (HAADF) scanning TEM of two representative particles from SBN20 T300 1h are presented in Figure 6   (the corresponding bright field images are presented in Figure S5 in Supporting Information). Contrast in HAADF-STEM is directly linked with the thickness of the particles assuming constant average Zn umber.F rom these images it is clear that the particles are not hollow all the way through, but consists of as olid center with hollow ends (intensity profiles across the images are presented in Figure S5).  EDS scans for Ba L a ,N bL a and Sr L a along four different lines on the particles, with as chematically representation of the compositional variation, are presented in Figure 6k.A long the horizontal direction no compositional differences are observed, neither when scanning across the middle of the particle, (Figure 6d and j) nor towards the ends with the hollow structure (Figure 6e and i).I nt he vertical direction, little to no compositional difference is observed in the center of the particles (Figure 6b,c ,gand h), but as ignificant decrease in Sr content is observed towards the hollow ends, while the Nb content stays constant throughout. Am inor increase in the Ba content is evident with the decrease in the Sr content. In the regions where the Sr and Ba counts are close to constant (center of particles), the Sr:Ba ratio is approximately 0.3:0.7.
From electron diffraction ( Figure S6 in Supporting Information) it is shown that the length of the hollow structures is along the crystallographic [001]-direction, and that the [1 00]-and [0 10]-directions (these are equivalent in the tetragonal unit cell) are pointing towards the edges. Hence the facets are normal to the [110]-direction (full description in Figure S6).

Discussion
Single phase SBN, possessing ah ollow microstructure was successfully synthesized using ah ydrothermal route. It was shown that the structures were not hollow throughout, but consisted of a solid core with hollow ends. Furthermore, the morphology is highly tunable with the synthesis parameters (reaction temperature and Sr fraction in the precursor slurry) from the hollow-ended structures to cubes and rod-like structures. The hollow-ended structures are observed only for low Sr-fractions (SBN20) at 300 8C, but for aw ider range of Sr-fractions (SBN20 to SBN40) at 200 8C. It is clear that both alow Sr fraction in the precursor slurry and alow reaction temperature promotes the formation of the hollow-ended structures. The hollow-ended structures possess ahigh specific surface area (SBN20 T300 1h), but not higher than cubes (SBN40 T300 1h). This is in good agreement with the macroporous nature of the hollow-ended structures, and the limitations of nitrogen adsorption and the BET method to measure the effect of macropores. [36] Growth mechanism of hollow-endedSBN The hollow-ended structures presented here are similar to snow crystals [14a] and olivine in the SiO 2 -Al 2 O 3 -CaO-MgO system from glass cooling experiments, [37] and can be referred to as af orm of hopper crystal. This crystal shape indicates formation under high supersaturation and rapid growth relative to the conditions giving cube-or rod-shaped crystals. As Nb-species have the lowest solubility of the three cations (Nb 5 + ,S r 2 + and Ba 2 + ), we propose that the concentration of Nb will be the determining factor for the supersaturation in our system, and the discussion will be focused around this. If we first consider the reactions at 300 8Cw ith varying Sr-fraction in the precursor slurry,o nly SBN20 is forming hollow-ended structures. Hence the supersaturation increases with decreasing Sr-fraction, since the hopper-growth mechanism is promoted only at higher supersaturations. Knowing that our Nb-acid precursor consists of motifs of the Lindqvist-ion, [33a,d] we infer from the observations that the solubility of this ion increases with decreasing Sr fraction, giving the higher supersaturation. Normally,t he solubility of salts increases with increasing size difference between the ions (Lindqvist-ion is large, and therefore closer in size to Ba 2 + than  . High-angle annular dark field (HAADF-STEM) images of two hollow ended rods from SBN20 T300 1hin a) and f). Grey dashed linesinaand f shows where the EDS line scanswere performed, with the corresponding EDS data in panels b), c), d), e), g), h) i) and j). Black dotted lines in panels b), c), d), e), g), h) i) and j) are guides for the eyes,p lotted at 0.3, 0.7, and 0.85, respectively.F or Nb L a the data have been normalizedt othe maximum value, while Ba L a and Sr L a havebeen normalized to the sum of Ba and Sr countswith the assumption that Nb L a is constant where there are no thickness gradients. In k) as chematicrepresentation of the intensity distributions, Nb L a ,SrL a and Ba L a are shown. Indicatedi st he area in the center of the particles with ah omogenouscomposition.
Chem. Eur.J.2020, 26,9 348 -9355 www.chemeurj.org 2020 The Authors. Published by Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Sr 2 + ), so one would expect the Lindqvist-ion to be more soluble with higher Sr fractions from this simple consideration. However, for the Lindqvist-ion the opposite trend is observed for salt-complexes formed with alkali metal ions. The solubility of these saltcomplexes increases going down in the periodic table, for example, solubility increases with decreasing size difference (solubility increases Li < Na < K < Rb < Cs), [33a, 38] just as indicated for the alkaline earth cations in this work. The Sr:Ba fraction is thus observed to give chemical control over the growth mechanism of SBN, where the system can be pushed into the hopper-growth regime with decreasing Sr-fraction. Similar effects have been observed for NaCl crystals growing from an aqueous solution, where an abrupt change from layer-by-layer growth forming cubes to ah oppergrowth mechanism was observed as af unction of increasing supersaturation estimated at the time of nucleation, [17] and crystallization of struvite (NH 4 MgPO 4 ·6H 2 O) where morphology control was obtained by controlling the supersaturation of the system. [39] If we now look at the reactions at 200 8C, the hollow-ended structures were observed also for SBN40 and SBN30 in addition to SBN20. Using the same argument as above, SBN20 has ar elatively higher supersaturation than SBN30 and SBN40 also at 200 8Cb ecause of the lower Sr-fraction. We propose that with the lower reaction temperature and thus slower kinetics, al arger supersaturation is needed to overcome the nucleation barrier.T his shifts the nucleation to occur at ar elatively higher supersaturation for all compositions, making SBN20, SBN30 and SBN40 all nucleate in the hopper-growth region. In addition to the chemical control, the growth mechanism can therefore be controlled also by the kinetics via the reaction temperature.
Some additional general comments to the mechanism of hopper growth are worth including. Hopper growth occurs under high supersaturation, and the initial rapid growth is limited by the surface area of the growing particles. The hopper growth mechanism is a way for the system to quickly increase the surface area of the growing particles, making the growth diffusion-limited. [17] Ar apid initial growth of SBN was observed for the in situ experiments, [22] in good agreement with the proposed hopper growth mechanism. Ag rowth rate order of 3i sr eported for the hopper growth of the NaCl crystals which is comparable to the values around 2.5 that we reported for SBN, [22] further supporting the proposed hoppergrowth mechanism in this work. Ag eneral scheme for the growth mechanism is presented in Figure 7.
For the growth of the cube-and rod-shaped particles observed at high temperatures and/or high Sr-fractions in the precursor slurry we propose ac lassical layer-by-layer growth mechanism. The change from cube-to more rod-shaped particles observed for SBN40 with decreasing reaction temperature is rationalized with slower kinetics at lower temperatures, promoting the formation of the most stable shape (Wulffconstruction). [22] Composition of hollow-ended rod-shaped SBN It is clear from the EDS line scans that there is ac hange in composition (Sr:Ba ratio) along the vertical direction of the rods, where the Sr-fraction is decreasing towards the edges. It is interesting to notice that this is not ag radual decrease from the middle of the rods, but it has as harp onset in the region close to where the hollow structures start. In the horizontal direction, little to no change in composition is observed. The non-hollow center of the particles has ac lose to homogenous composition, with aS rf raction of % 0.3 (based on the relative intensities of Sr and Ba). In our previous work, the average composition of the SBN formed had Srfractions of 0.35 AE 0.1 for precursor slurry compositions ranging from 0.2 to 0.5. [22] In this work we report average Sr-fractions of % 0.25 and % 0.34 for precursor solution of 0.2 and 0.4, respectively.SBN33 is the composition with potentially the highest configurational entropy, [21,40] making it the energetically favored composition from an entropy point of view.N onetheless, from our data (EDS and PDF analysis in this work and Rietveld refinement in our previous work [22] ), it seems clear that SBN33 is nucleating and growing at the initial stages of the reaction, irrespective of the composition in the precursor slurry,f or the syntheses described here. In case of SBN20, there is al imit on how much SBN33 can form, before Sr becomes significantly depleted, and SBN with ah igher Ba fraction is formed, explaining the decrease in Sr-fraction towards the edges of the hollow-ended structures.

Conclusions
We have investigated the growth mechanisms for cube-and hollow-ended shaped particles of SBN made by hydrothermal synthesis. We show that the morphology can be tuned with the Sr:Ba ratio in the precursor slurry and the reaction temperature. As tructure strongly related to the Lindqvist-ion for the Nb-acid precursor was demonstrated by X-ray total scattering. Based on this knowledge, we could rationalize both the composition and temperature dependence on the formation of the hollow-ended structures based on relative changes in supersaturation, and ac hange from layer-by-layer to ah opper growth mechanism at high supersaturations. The hollow-ended SBN structures are more Sr deficient towards the edges in the long direction, explained by ap referential formation of SBN33 at the initial stages of the reaction. . Schematic illustration of the effect of supersaturationont he growth mechanism of SBN. Blue arrows indicate the nucleation rate of new layers, and black arrows the completion of these layers. At high supersaturation the nucleation rate is much higher than the rate of completion, leading to higher growth rates at the edges andcorners.