Hydrothermal topotactic epitaxy of SrTiO3 on Bi4Ti3O12 nanoplatelets: understanding the interplay of lattice mismatch and supersaturation

The engineering of epitaxial, two-dimensional (2D) nano-heterostructures has stimulated great interest owing to an expectation of better functional properties (e.g., photocatalytic, piezoelectric). Hydrothermal topotactic epitaxy is one of the promising synthetic approaches for their preparation, particularly the formation of a highly ordered, epitaxial interface and possibilities for the preparation of anisotropic nanostructures of symmetrical materials. The present study highlights the key parameters when steering the alkaline, hydrothermal, topochemical conversion process from Bi4Ti3O12 nanoplatelets to the intermediate, epitaxial, SrTiO3/Bi4Ti3O12 nano-heterostructures and the final SrTiO3 nanoplatelets by balancing the lattice mismatch and the supersaturation. An atomic-scale examination revealed the formation of an ordered epitaxial SrTiO3/Bi4Ti3O12 interface with the presence of dislocations. The SrTiO3 grows in islands for a stoichiometric amount of Sr (Sr/Ti = 1) and the growth resembles a layer-by-layer mode for surplus Sr content (Sr/Ti ≥ 12). The latter enables SrTiO3 overgrowth of the Bi4Ti3O12 basal surface planes, protecting them against dissolution from the top and consequently ensuring the preservation of the platelet morphology during the entire transformation process, the kinetics of which is controlled by the base concentration. A developed understanding of this particular transformation provides the guiding principles and ideas for designing other defined or complex epitaxial heterostructures and structures under low-temperature hydrothermal conditions.


Introduction
Understanding the reaction mechanisms and nucleation-crystallization phenomena remains one of the most reliable fundamentals for the engineering of nanostructures with enhanced functional characteristics. Thanks to improvements in the resolution of the scanning-transmission electron microscope (STEM), which enables the examination of nanostructures at the atomic level, it is now possible to elucidate the formation mechanisms of even very complex particle architectures. The purpose of the established knowledge is to combine the crystallization principles and exploit them in the design of new, tailored structures or heterostructures. Recently, various heterostructural particles with complex or dened 1-dimensional (1D) or 2-dimensional (2D) morphologies and a tailored spatial composition are attracting increased attention because of their potentially unique or enhanced functional characteristics, which can be implemented in many elds, including photocatalysis and ferroelectric/piezoelectric applications. [1][2][3][4][5][6] For example, the construction of effective direct Z-scheme heterostructural photocatalysts by combining two compounds with proper relative band alignments and connected by an epitaxial interface is expected to result in improved photocatalytic performance due to the formation of the interfacial electric eld that contributes to the better separation of e − -h + pairs and the preservation of a high redox ability. 4 2D structures are of particular interest in photocatalysis since their low thickness enables rapid charge transport to the surface and a large 2D area possesses many active sites or provides the maximum face contact when coupling with other photocatalysts in the formation of 2D/2D heterostructures. 1,2 Considering the enhanced charge mobility at a highly ordered, atomically sharp interface, photocatalysts based on chemically bonded heterostructures with epitaxial contact are expected to show better performance and higher stability compared to physically mixed composite materials. 2,5,6 These facts were illustrated by the construction of 2D/2D Bi 2 WO 6 /BiOI epitaxial heterostructures by Wang et al.,2 who demonstrated that this material exhibits improved visiblelight photocatalytic activity for the oxidation of NO, compared to that of the individual counterparts. The importance of heterojunction systems is not limited to the application of particulate heterostructures in photocatalysis. Heterostructural lms are important constituents of optical devices such as photodetectors and photodiodes. [7][8][9] For example, self-powered photodetectors with enhanced performance can be constructed from p-n heterojunctions (p-CuS-ZnS/n-SrTiO 3 ), in which photogenerated electron-hole pairs are effectively separated due to a built-in electric eld, which results in a stable photocurrent without the need for external power. 7 Apart from a p-n junction, the built-in ferroelectric eld for the improved separation of photo-induced carriers could also be achieved by means of the intrinsic, self-polarization of a ferroelectric lm. This was realized in a high-performance UV photodetector based on a mesoporous TiO 2 layer on ferroelectric BaTiO 3. 8 A transparent Schottky photodiode constructed from AgNi nanowires (highwork-function electrode), spin-coated on a SrTiO 3 single crystalline wafer is another example of the advanced architecture of a perovskite-based, multifunctional optical device that enables simultaneous, bias-free, short-wavelength blue-light detection and transparent ultraviolet-light shielding. 9 When designing heterostructured particles, we must consider that two compounds can form a heteroepitaxial interface under the condition that there is a crystallographic orientation relationship with a sufficiently small lattice mismatch between them. 2 This natural restriction limits the number of possible material combinations, which are further reduced in the case of the necessary, well-dened 2D or 1D morphologies. Namely, several materials, especially those with a high crystallographic symmetry, do not show a spontaneous tendency for growth in anisotropic 1D or 2D morphologies because these are far from their equilibrium form. [10][11][12] One of the strategies to overcome these limitations is offered by the topochemical conversion reactions of 1D or 2D template precursor particles, which in the transformation process convert to new materials with inherited template morphologies. The prerequisite condition for a successful topochemical conversion is that the precursor and objective material are in an orientational relationship or possess similar structural units. 11,12 Several such kinds of topochemical conversion reactions have been explored in molten-salt media at temperatures between 660°C and 1100°C. 11,13-17 A typical example is the formation of MTiO 3 (M = Ba, Sr, Pb) perovskite platelets from MBi 4 Ti 4 O 15 or Bi 4 Ti 3 O 12 platelets in molten NaCl/KCl in the temperature range 660-1100°C. 10,13,15,17 From the energy-consumption standpoint, it would be much more convenient if this type of transformation would be possible in aqueous media at a much lower temperature of hydrothermal synthesis. Different solubilities/stabilities of the precursor/template structure and objective phase in aqueous media, different lattice mismatches with respect to that at high temperature do not guarantee that every conrmed topochemical conversion performed in molten salt could be simply transferred to aqueous media. In the case of good crystallographic matching between the template and the target phase, and their appropriately low solubility in the media, the transformation under hydrothermal conditions is expected to proceed through the epitaxial growth of a new phase on the template. This results in the formation of a clear heteroepitaxial interface between the phases at an intermediate stage of the transformation and the pseudo-morphic replacement of the template by the product aer complete conversion. [18][19][20] The main advantage of such a hydrothermal topochemical reaction compared to that in molten salt is that negligible diffusion in the solid-state lattice at typical hydrothermal temperatures enables the formation of heterostructures with a well-dened interface. Therefore, by selecting a proper combination of template, its morphology and the target material, we can design versatile, well-dened heterostructures (e.g., 2D/2D) or structures (e.g., 1D, 2D) through a partial or complete hydrothermal topochemical transformation, respectively.
Compared to epitaxial thin-lm heterostructures grown by physical vapor deposition, the formation of particulate epitaxial heterostructures from solutions has never been studied in such detail, although the latter requires similar considerations of epitaxy, lattice mist, defect formation, etc. The particle transformation under hydrothermal conditions can be even more complex and sensitive to changes in the conditions, since the template is usually dissolving, while also serving as a substrate for epitaxial growth. 18 Furthermore, the role and importance of supersaturation is something that must be considered and understood to guide this kind of transformation process. 21 The current understanding of such a transformation process is limited, and this investigation aims to bridge this knowledge gap through a detailed study of the hydrothermal topochemical transformation of Bi 4 Ti 3 O 12 platelets to SrTiO 3 with the shape maintained. Bi 4 Ti 3 O 12 belongs to the Aurivillius phases, which exhibit a layered structure and are key materials in many elds (piezoelectric, ferroelectric, photocatalysis). 22-25 SrTiO 3 with a highly symmetrical crystal structure is an important, multifunctional perovskite material, which depending on doping, oxygen stoichiometry and strain state, can possess versatile characteristics, like microwave dielectric tunability, ferroelectricity, high electronic conductivity, photocatalytic behavior, oxygen conductivity and others. 10 Recently, SrTiO 3 -based composites have become more signicant in photocatalysis, following their use in large-scale hydrogen generation based on solar energy, as demonstrated by the Domen group. 26,27 Thermodynamically, SrTiO 3 adopts a cubic perovskite structure and their synthesis with 2D structures is limited. Syntheses of anisometric, 2D SrTiO 3 crystallites were mainly initiated by the use of SrTiO 3 platelets for the fabrication of preferentially oriented, textured ceramics. In addition to 2D structures of Sr 3 Ti 2 O 7 and SrBi 4 Ti 4 O 15 , Bi 4 Ti 3 O 12 platelets were also shown to be an appropriate template precursor for the preparation of SrTiO 3 platelets through a topochemical conversion reaction, which until recently was solely studied in molten-salt (NaCl/KCl) media at 1050-1200°C. 10,16 In analogy with the alreadyreported topochemical conversion of Bi 4 Ti 3 O 12 platelets into SrTiO 3 platelets in molten salt at 1100°C, 16 our group was the rst to design the hydrothermal conditions for the Bi 4 Ti 3 O 12 nanoplatelets to transfer to SrTiO 3 nanostructures with a preserved 2D-platelet morphology at a much lower temperature of 200°C. 28 We also showed that the SrTiO 3 /Bi 4 Ti 3 O 12 heterostructural platelets that formed at an intermediate stage of transformation have a promising photocatalytic H 2 evolution, 15-times more than commercial SrTiO 3 nanopowders. 29 We disclosed that the transformation from Bi 4 Ti 3 O 12 to SrTiO 3 platelets proceeds through the dissolution of Bi 4 Ti 3 O 12 and the epitaxial growth of SrTiO 3 over the basal surface planes of the template with the formation of the epitaxial SrTiO 3 /Bi 4 Ti 3 O 12 heterostructures and SrTiO 3 platelets at the intermediate and completed transformation stages, respectively. In the present study we gain further unprecedented insights into this transformation process through an atomic-scale examination of the SrTiO 3 /Bi 4 Ti 3 O 12 interface, an assessment of the relevant lattice mists and an evaluation of the role and importance of supersaturation in controlling the nucleation and crystallization processes and consequently the transformation pathway. This investigation is one of the few fundamental studies on understanding the formation mechanism of epitaxial, heterostructural SrTiO 3 /Bi 4 Ti 3 O 12 and SrTiO 3 platelets that will pave the way for the design of other epitaxial nano-heterostructures and anisotropic nanostructures under hydrothermal conditions.

Synthesis of Bi 4 Ti 3 O 12 template platelets
Bi 4 Ti 3 O 12 template nanoplates were synthesized by a moltensalt method from KCl/NaCl salt, Bi 2 O 3 nanopowder, and TiO 2 nanopowder (0.500 g), so that the molar ratio of NaCl : KCl : Bi 2 O 3 : TiO 2 was 50 : 50 : 2 : 3. 25,28,29 Heating and cooling rates were 10°C min −1 and the reaction temperature was 800°C with a holding time of 2 h. Aerwards, Bi 4 Ti 3 O 12 particles were washed with deionized water to remove the salt, 2 mol L −1 HNO 3 to remove the secondary phases, and nally, once again with deionized water to ensure a neutral pH. 13 The product particles were freeze-dried under vacuum conditions.

Transformation of Bi 4 Ti 3 O 12 into SrTiO 3 /Bi 4 Ti 3 O 12 and SrTiO 3
The transformation reactions were performed under stirring hydrothermal conditions in a Berghof high-pressure reactor with a Teon (PTFE) insert. In a typical procedure, Bi 4 Ti 3 O 12 platelets were admixed (0.057 mol L −1 ) into a water solution containing dissolved SrCl 2 $6H 2 O. The suspension was sonicated for 10 minutes. Aerwards, the suspension was quantitatively transferred to a PTFE-lined insert and subsequently a concentrated NaOH solution was added. Both the NaOH solution and the dispersion of Bi 4 Ti 3 O 12 platelets were cooled down to room temperature (25°C) before mixing. Finally, deionized water was added to the line mark in the PTFE insert to achieve a 70% lling. The concentrations of the reagents in the precursor suspension before the hydrothermal reactions are presented in Table S1. † The concentration of Bi 4 Ti 3 O 12 was the same (c Bi 4 Ti 3 O 12 = 0.00102 mol L −1 ) in all experiments, while the concentration of the NaOH (c NaOH ) solution was 2 mol L −1 or 6 mol L −1 and the concentration of SrCl 2 $6H 2 O varied from 0.00306 mol L −1 to 0.07344 mol L −1 , corresponding to a variation of the initial Sr/Ti molar ratios from 1 : 1 to 24 : 1. The initial Sr/Ti ratio refers to the molar ratio of the added strontium precursor to the overall Ti in Bi 4 Ti 3 O 12 . No other titanium compound was added. The reactions were performed under stirring conditions at 200°C with a duration from 1 hour to 12 hours. Aer the reaction, the system was cooled naturally. The product was washed with water by centrifugation (until pH = 7), soaked in 30 mL of 1 mol L −1 HNO 3 for 5 min, and washed again with water (again until pH = 7). In the end, the washed product was freeze-dried to obtain a ne powder product.

Characterization
X-ray powder diffraction and X-ray diffraction (XRD) for the platelets cast on a single-crystalline silicon substrate were collected with an X-ray diffractometer (Empyrean, Malvern PANalytical) with CuKa 1 radiation (l = 1.5406 Å). The percentages of SrTiO 3 in the SrTiO 3 /Bi 4 Ti 3 O 12 heterostructures were estimated based on the intensity ratios of the (200) diffraction of SrTiO 3 to (008) and (0014) diffractions of Bi 4 Ti 3 O 12 to evaluate the progress of the transformation. These calculations were performed from the XRD patterns of the platelets cast on singlecrystalline silicon substrates. The average weight percentages of SrTiO 3 in the synthesized samples were inferred from the calibration curve, which was made based on XRD patterns of the mixtures of SrTiO 3 and Bi 4 Ti 3 O 12 platelets with known weight ratios of both components. The XRD measurements for the calibration curve were also performed for the platelets cast on the single-crystalline silicon substrate. Using this method, the majority of the platelets were preferentially oriented parallel to the sample holder (single-crystalline silicon), thus giving reproducible intensities of the (008) and (0014) diffractions of Bi 4 Ti 3 O 12 and (200) diffractions of SrTiO 3 , that are parallel to the substrate in this platelet orientation.
The morphologies of the platelets were examined with a scanning electron microscope (SEM) (Schottky FEG, Verios HP 4G, Termo Fischer, USA) operated at 2 kV and 13 pA with a beam deceleration (2 kV) as well as a probe Cs-corrected scanningtransmission electron microscope (STEM Jeol ARM 200 CF, JEOL, Japan) operated at 200 kV.
STEM investigations were performed on the platelets from the top-down and the cross-sectional (edge on) views. For the top-down examinations, powder samples were dispersed in absolute ethanol, sonicated for 15 minutes and a droplet of dispersion was applied to the lacey carbon-coated copper grid. As-prepared platelets spontaneously align with their largest surface parallel to the carbon grid. Any further thinning was not necessary in this case. For edge-on observations of the platelets in cross-section, a small amount of sample powder was mixed together with epoxy resin for the preparation of lamellae. The electron transparency of the lamellae was achieved by mechanical polishing and ion milling in an automatic tripod polisher (Gatan PIPS Model 691, USA). The samples were coated with 2 nm of carbon before STEM observation (PECS, Model 682, USA).

Theoretical and experimental background for controlling Bi 4 Ti 3 O 12 -to-SrTiO 3 transformation under hydrothermal conditions
The prerequisite condition for hydrothermal topochemical conversion is good crystallographic matching between the template and the precipitating new phase, which enables a high nucleation rate and epitaxial growth of the latter on the template, which dissolves through the advancement of the process and as a result, the precursor phase is progressively replaced by the new phase. 18,19 Therefore, to control the coupling of template dissolution and epitaxial growth, it is important to know the characteristics of the template and its dissolution in the media, as well as to understand all the solution and interfacial processes. In the presented Bi 4 Ti 3 O 12to-SrTiO 3 transformation, detailed considerations of these parameters are given below.
The Bi 4 Ti 3 O 12 template platelets that were subject to the Bi 4 Ti 3 O 12 -to-SrTiO 3 transformation studies exhibited an average side length of 1-2 mm and thickness of 50-100 nm. These were typical dimensions of the platelets grown in molten NaCl/KCl salt at 800°C for 2 hours (Fig. 1). 28,29 The STEM examination of the Bi 4 Ti 3 O 12 platelets conrmed their layered structure, with alternation of the pseudo-perovskite ([Bi 2 Ti 3 O 10 ] 2− ) blocks and the bismuth oxide ([Bi 2 O 2 ] 2+ ) layers, whereby the latter exclusively terminated the basal surface planes of the as-prepared platelets, while both types of structural units were exposed at the lateral surface (Fig. 1c). According to the STEM analysis, typical platelets contain few or no planar defects and have atomically at, basal surface planes. Steps are more frequently present close to the platelet's edge and at the lateral surfaces ( Fig. 1b and c). Such a morphological development stems from the anisotropic layer-by-layer growth of the Bi 4 Ti 3 O 12 platelets during their synthesis in molten salt.
The mechanism of the hydrothermal conversion from Bi 4 Ti 3 O 12 platelets to SrTiO 3 platelets in alkaline media under high supersaturation conditions is described in detail in our previous study 29 and briey summarized below. The transformation process proceeded through two main chemical reactions: the dissolution of Bi 4 Ti 3 O 12 according to eqn (1) and the crystallization of SrTiO 3 , expressed by eqn (2). 18,29 Dissolution of Bi 4 Ti 3 O 12 : Crystallization of SrTiO 3 :  BIT orientational relationships dictates the (100) SrTiO 3 growth on the basal surface planes of (001)-oriented Bi 4 Ti 3 O 12 platelets. Control over the process can be exerted based on a consideration of classical nucleation theory and eqn (3), which denes that the nucleation barrier (Dg n ) is proportional to the third power of the interfacial free energy (a) and inversely proportional to the square of the natural logarithm of supersaturation (S) ((ln S) 2 ). 21,30,31 In the case of highly crystalline Bi 4 Ti 3 O 12 platelets, the major contribution to the interfacial free energy comes from the lattice mists of the Bi 4 Ti 3 O 12 and SrTiO 3 pairs of lattice planes from above-mentioned orientational relationships. In the studied system, supersaturation (eqn (4) is dened as the ratio between the product of activities of the dissolved species ([Ti(OH) 6 )] 2− (aq) and Sr 2+ (aq)) immediately before the SrTiO 3 formation and the thermodynamic solubility product (K s ) of SrTiO 3 . 18,29 Dg n f a 3 In accordance with eqn (3) and (4), higher concentrations of [Ti(OH) 6 ] 2− (aq) and Sr 2+ (aq) (i.e. higher supersaturation) promote the nucleation of SrTiO 3 on Bi 4 Ti 3 O 12 . In our previous study, a high supersaturation condition was achieved by using 12-times more Sr than needed for the stoichiometric transformation and a high concentration of NaOH (6 mol L −1 ), which provides a sufficiently high concentration of [Ti(OH) 6 ] 2− (aq) (eqn (1)) through the dissolution of pseudo-perovskite layers of the Bi 4 Ti 3 O 12 platelet (Fig. S1, ESI †). These empirically determined, high supersaturation conditions, enable a low nucleation-energy barrier (eqn (3)), resulting in a high nucleation rate of SrTiO 3 on the basal surface planes of the Bi 4 Ti 3 O 12 platelets, with the formation of the SrTiO 3 protective layer, which restricts Bi 4 Ti 3 O 12 dissolution mainly from the lateral sides. This results in the formation of a groove, which deepens with the progress of the reaction, while the epitaxial SrTiO 3 layers on both basal surfaces thicken (Fig. S1, ESI †). 29 When the Bi 4 Ti 3 O 12 inside the groove dissolves to the last perovskite layer, SrTiO 3 also starts to grow epitaxially from the inner side. This is inferred based on the captured monoatomic bismuth layer that extends along the completely converted platelet part. 29 So, the reaction proceeds from Bi 4 Ti 3 O 12 via the SrTiO 3 /Bi 4 Ti 3 O 12 epitaxial heterostructure until a complete pseudo-morphic transformation to (100)-oriented SrTiO 3 with the preservation of the overall platelet morphology through the entire conversion process. The nal SrTiO 3 platelets, which consist of two parallel, partially intergrown platelets, reect the transformation process (dissolution of Bi 4 Ti 3 O 12 from the lateral side and epitaxial growth of SrTiO 3 on both basal surface planes (Fig. S1, ESI †)). With these initial ideas, we gain new mechanistic insights into the transformation process, by empirically probing the role of different factors in eqn (3), such as the interfacial free energy (a) and supersaturation (S).

Role of the interfacial free energy
The interfacial free energy (a) in the numerator of eqn (3), is a combination of the energy due to the difference in chemical bonding at the interface and the strain energy due to incoherent ordering at the interface. These characteristics comprise lattice mismatch. In general, interfacial energy (a) is lower when the two phases (i.e., epitaxial layer and substrate) are crystallographically well aligned and coherent. 21,32 The mists in our system were evaluated for the [ Table 2, represent unavoidable contributions to the interfacial free energy (eqn (3)) for the growth of the SrTiO 3 on the basal surface plane of the Bi 4 Ti 3 O 12 platelet. In general, in the process of epitaxial growth, the mist can be eliminated/reduced by elastic strain or accommodated by mist dislocations. The latter are formed when the mist is too large to be completely eliminated by elastic strain. 35 To evaluate how the calculated mists (Table 2) are manifested across the SrTiO 3 /Bi 4 Ti 3 O 12 interface, we performed a high-angle annular darkeld (HAADF) STEM analysis of the interface in partially transformed platelets (aer 2.5 h at 200°C in 6 mol L −1 NaOH with Sr/Ti = 12). The results are shown in Fig. 2. The images reveal that SrTiO 3 grows epitaxially on the pseudo-perovskite layer of the Bi 4 Ti 3 O 12 substrate and not on the [Bi 2 O 2 ] 2− layer, which is the termination layer of the asprepared Bi 4 Ti 3 O 12 platelets. 29 We analyzed the Bi 4 Ti 3 O 12 platelets before and aer exposure to NaOH at 200°C for 1 hour and conrmed that the latter treatment removes the surface [Bi 2 O 2 ] 2− layer (Fig. S2, ESI †). We believe that the removal of the     Magnied images of the areas around the mist dislocations ( Fig. 2b and d) show a locally, slightly fuzzy contrast, which indicates that the crystal structure of the last pseudo-perovskite layer of the Bi 4 Ti 3 O 12 is slightly disturbed around the dislocation cores due to the strain imposed on the substrate by the SrTiO 3 layer with the larger unit cell. On the other hand, the SrTiO 3 layer seems to be relaxed aer a few atomic layers.
Based on the HAADF HR STEM micrographs ( Fig. 2b and d) we believe that the SrTiO 3 growth starts with the deposition of Sr 2+ ions, followed by the deposition of the perovskite TiO 6 2− octahedra. The growth continues with the next layer of Sr 2+ and so on. This atomic-scale insight at the SrTiO 3 /Bi 4 Ti 3 O 12 interface could also be one of the reasons why higher Sr/Ti ratios also play such a benecial role in the preservation of the platelet morphology during the transformation process. Due to the competition between the template dissolution and the epitaxial growth process, the rapid deposition of the rst layer of Sr 2+ ions over the naked pseudo-perovskite-terminated basal surface plane is important for the protection of the platelet against dissolution from the top and also for the continuation of the epitaxial growth. Higher Sr 2+ (aq) concentrations (c Sr 2+ ) accelerate the diffusion of the Sr 2+ ions to the surface, facilitating the formation of the rst and subsequent Sr 2+ layers.
Additional information about the growth mechanism was obtained from the top-down STEM examination of the SrTiO 3 / Bi 4 Ti 3 O 12 platelets aer a short conversion time (200°C/1 hour, Sr/Ti = 12, 6 mol L −1 NaOH) (Fig. 3). It can be seen from Fig. 3b that in the rst layers (thickness of 1-2 structural units) SrTiO 3 epitaxial growth occurs with the formation of crystallite islands.  (Fig. 3). Aer 1-2 unit cells the  Nanoscale Advances crystallites appear to be larger (Fig. 3b). This is in accordance with the cross-sectional STEM observation ( Fig. 2b and d), which reveals that the inuence of dislocations vanishes aer two structural units.

Role of supersaturation
In general, the degree of supersaturation determines the nucleation-and-growth mechanism, and therefore its control is extremely important in the tailoring of the crystallization particle morphologies 31 and thin-lm growth of functional materials from solutions. 38 , while for the concentration of Sr 2+ , we speculate that larger amounts of strontium render more dissolved Sr 2+ , which can participate in the formation of SrTiO 3 . Theoretically, it is possible to predict the equilibrium concentrations of aqueous species (supersaturation) with thermodynamic modelling. In the literature, this was already performed for the formation of SrTiO 3 from simple TiO 2 -based precursors (anatase, rutile, hydrous TiO 2 $xH 2 O gel) and strontium precursors (Sr(NO 3 ) 2 , Sr(OH) 2 $8H 2 O). 18,40,41 However, for the present system, dealing with the transformation from Bi 4 Ti 3 O 12 to SrTiO 3, any accurate thermodynamic modelling is hampered by the complexity of the system arising from several possible side reactions (formation of other bismuth titanium compounds (e.g. Bi 12 TiO 20 )), the illunderstood chemistry of Bi(OH) 3 and accordingly the lack of  reliable thermodynamic data. For this reason, the supersaturation in this study was considered at the empirical level. Based on the observed morphological development and our understanding of the general effects of supersaturation on nucleation and growth, it is possible to make a rough comparison of the supersaturations under different conditions. The smallest selected Sr/Ti ratio was 1, because at least a stoichiometric Sr/Ti ratio is needed for a complete transformation from Bi 4 Ti 3 O 12 to SrTiO 3 . Systematic studies were also performed for Sr 2+ (aq) concentrations that signicantly exceed the stoichiometric ratio (i.e., Sr/Ti = 3, 12, 24), while NaOH concentrations were varied from 2 mol L −1 to 6 mol L −1 . The growth and phase compositions were examined aer 2.5 and 12 h.
3.3.1. Transformation control at a lower base concentration (2 mol L −1 NaOH). Fig. 4a and S3, ESI, † show the typical growth mode of SrTiO 3 on Bi 4 Ti 3 O 12 aer 2.5 h of hydrothermal reaction at Sr/Ti = 1 and in 2 mol L −1 NaOH. Based on this lower NaOH concentration, compared to the 6 mol L −1 NaOH in our previous study, 29 a slower dissolution rate of Bi 4 Ti 3 O 12 and consequently a lower concentration of Ti(OH) 6 2− are anticipated. This, together with Sr/Ti = 1, is expected to provide lower supersaturation conditions compared to that formerly reported, where Sr/Ti was 12. 29,42 Considering that the major Bi 4 Ti 3 O 12 platelets remained undissolved, the ratio of Sr 2+ (aq) to [Ti(OH) 6 ] 2− (aq) at the beginning of the process is much higher than stoichiometric. The growth of square-like SrTiO 3 islands on the Bi 4 Ti 3 O 12 template platelets is evident in Fig. 4a. Compared to conditions with higher Sr/Ti ratios (Fig. 4), at Sr/Ti = 1 the SrTiO 3 islands are larger, thicker, isolated and appear more frequently close to the edge of the basal surface plane of the Bi 4 Ti 3 O 12 platelet ( Fig. 4a and S3, ESI †). In many cases the edges of the platelets are partially or even completely rimmed by  SrTiO 3 (Fig. S3c, ESI †). The corresponding morphological development is in accordance with the atomistic observation of the Bi 4 Ti 3 O 12 platelet's morphology, as well as with the theory of nucleation and crystal growth. As observed by STEM and SEM (Fig. 1), several steps are present at the lateral surfaces of the Bi 4 Ti 3 O 12 platelet, while at the basal surface planes, the steps are rarely in the middle but more frequently close to the edge ( Fig. 1b and c). According to classical nucleation-crystallization theory, the kink sites at the steps are the most favorable location for the incorporation and dis-incorporation of structural units. 30,43 As a consequence the dissolution of the pseudoperovskite [Bi 2 Ti 3 O 10 ] 2− blocks and bismuth oxide ([Bi 2 O 2 ] 2+ ) layers of the Bi 4 Ti 3 O 12 platelets proceeds faster from the lateral side and the higher population of steps with kink sites close to the edge of basal surface planes are also the most favorable sites for the beginning of SrTiO 3 growth. Additionally, the solubility product for the SrTiO 3 formation at these places is expected to be exceeded earlier than in the middle of the basal surface plane because the dissolution of the pseudo-perovskite [Bi 2 Ti 3 O 10 ] 2− blocks started from the lateral side and, consequently, the areas close to the edge are at least at the beginning of the process subjected to higher [Ti(OH) 6 ] 2− (aq) concentrations. Therefore, the preferential growth of SrTiO 3 close to the edge is also a consequence of a higher initial local supersaturation that triggers the on-set of SrTiO 3 nucleation preferentially there. But, the SrTiO 3 islands that are grown in lines imply the start of SrTiO 3 growth at the kink sites in the steps, which were initially present on the basal surface plane of the Bi 4 Ti 3 O 12 platelets (Fig. 4a). Fig. 4 clearly shows that the SrTiO 3 coverage of the basal surface plane of Bi 4 Ti 3 O 12 platelets increases with increments of the Sr/Ti ratio. The appearance of the SrTiO 3 growths become more layer-by-layer-like and the individual islands are becoming less discernible at Sr/Ti = 24 ( Fig. 4d and S4, ESI †). Actually, the morphological development evident from Fig. 4ad indicates polynuclear 2D growth, which is a consequence of the high nucleation rates at sufficiently high supersaturation. 31 Even more, the distinct increase in the number of islands with the increase of strontium (Sr/Ti ratio) is assumed to reect the same trend in supersaturation (Fig. 4a-c). In other words, this also implies that at a dened NaOH concentration, higher initial Sr/Ti ratios could be correlated with a higher concentration of Sr 2+ in the solution and with a higher supersaturation. The SrTiO 3 islands are the largest and the thickest in the case of the lowest Sr/Ti = 1, which provides the worst protection of the Bi 4 Ti 3 O 12 basal surface plane. In addition, the system with Sr/Ti = 1 presumably in the series of Sr/Ti ratios ensures the lowest supersaturation, which is also expected to show the steepest decrease in the progress of SrTiO 3 growth, which preferentially continues in areas already covered with SrTiO 3 . Namely, the nucleation-energy barrier (eqn (3)) is lower for the growth of SrTiO 3 on SrTiO 3 (no mist, in eqn (3): a 3 ∼ negligible) than for the growth of SrTiO 3 on Bi 4 Ti 3 O 12 ( Table 2). The explanation why higher c Sr 2+ enables better SrTiO 3 overgrowth over the basal surface planes of the Bi 4 Ti 3 O 12 platelet is not solely established based on the formation of the rst Sr 2+ protective layer, but a clear elucidation is also evident from eqn (3). Since it is expected that higher c Sr 2+ ensures higher supersaturation (S), providing larger term (ln S) 2 in the denominator of eqn (3) and consequently a lower nucleation energy barrier. As a result, an increase of the 2D nucleation rate with an increase of the Sr/Ti ratios and continued 2D polynuclear growth of SrTiO 3 on Bi 4 Ti 3 O 12 is evident from Fig. 4.
In the XRD patterns of the SrTiO 3 /Bi 4 Ti 3 O 12 heterostructures obtained aer 2.5 hours of reaction ( Fig. 5a and S5a, ESI †), regardless of the initial Sr/Ti ratios, the Bi 4 Ti 3 O 12 diffractions dominate over those of SrTiO 3 . This is according to expectations because the SrTiO 3 layers on the Bi 4 Ti 3 O 12 are still thin and a major part of Bi 4 Ti 3 O 12 remained unreacted aer this short time at 200°C in 2 mol L −1 NaOH. A signicant advance of the transformation to SrTiO 3 was observed aer a 12 hour-reaction ( Fig. 5b and S5b, ESI †). Almost pure SrTiO 3 was obtained at Sr/ Ti = 1 (∼98% SrTiO 3 and 2% Bi 4 Ti 3 O 12 remains), whereas the amount of unreacted Bi 4 Ti 3 O 12 increased with Sr excess (Fig. 5b). For example, the remains of Bi 4 Ti 3 O 12 are 27% at Sr/Ti = 3 and further increases to 42% and 58% for Sr/Ti = 12 and 24, respectively. The unreacted Bi 4 Ti 3 O 12 is clearly visible as the lighter core phase in the backscattered electron (BSE) images in Fig. 6 and S6, ESI. † These results indicate that higher Sr concentrations impede the conversion from Bi 4 Ti 3 O 12 to SrTiO 3 . The transformation is the fastest for Sr/Ti = 1, that among the studied Sr/Ti ratios yield the lowest supersaturation, which limits the SrTiO 3 growth predominantly in regions close to the edge (for nucleation the most favorable places), while the middle parts of the Bi 4 Ti 3 O 12 basal surface planes remained unprotected against dissolution. Hence, the supply of [Ti(OH) 6 ] 2− (aq) is not restricted to a long diffusion path from the groove (as in the case of higher supersaturation (Fig. S1, ESI †) 29 and the SrTiO 3 growth continues, predominantly on the initially formed SrTiO 3 layer around the platelet edges. The described transformation process is also supported by the formation of SrTiO 3 frame-like platelets ( Fig. 6a and S6a, ESI †). The integrity of the SrTiO 3 /Bi 4 Ti 3 O 12 platelets aer a 12-hour reaction in 2 mol L −1 NaOH is still impaired for Sr/Ti = 3, but much better preserved for Sr/Ti = 12 and 24 ( Fig. 6 and S6, ESI †). The latter conditions enable the best preservation of morphology, but the sluggishness of the reaction signicantly extends the time needed for complete conversion to SrTiO 3 (Fig. 5b). All these observations emphasize that higher Sr concentrations (Sr/Ti = 12, 24) are needed to direct the nucleation and growth of SrTiO 3 over the whole basal surface planes of the Bi 4 Ti 3 O 12 platelets. When these are entirely protected by SrTiO 3 , the supply of [Ti(OH) 6 )] 2− (aq) for further SrTiO 3 growth is limited by the dissolution of pseudo-perovskite blocks from the groove, which deepens with the progress of the reaction and consequently the reaction is slowed down.
The above-described growths of (100) SrTiO 3 on the (001) Bi 4 Ti 3 O 12 platelets in some respects resemble the epitaxial growth of thin lms on chemically different, dissimilar crystalline substrates, where the structural matching and supersaturation play a key role and determine the type of growth mode. The latter, depending on the lattice mismatch, varies from layer-by-layer growth for a negligible mist (Frank-van der Merwe) to layer-plus-island growth (Stranski-Krastanov) or island growth (Volmer-Weber) for a perceptible mist. 30 Our results clearly demonstrate that conditions with Sr/Ti $ 12 are capable of balancing the 1.4% -2.1% mist ( Table 2) and direct the SrTiO 3 growth over the whole basal surface planes of Bi 4 Ti 3 O 12 and consequently ensure the preservation of the platelet morphology through the process.
3.3.2. Transformation control at a higher base concentration (6 mol L −1 NaOH). To achieve a complete transformation in a reasonable time, the dissolution of pseudo-perovskite blocks has to be accelerated. In view of reaction 1, this can be realized by a higher concentration of base (NaOH). Bi 4 Ti 3 O 12 is therefore expected to dissolve more and faster in 6 mol L −1 NaOH, providing higher concentrations of [Ti(OH) 6 ] 2− (aq) compared to that in 2 mol L −1 NaOH. Nevertheless, the Bi 4 Ti 3 O 12 dissolution should still be slow enough that the platelets can still serve as the substrate for the epitaxial growth of SrTiO 3 . A qualitative evaluation of the stability of the Bi 4 Ti 3 O 12 platelets in 6 mol L −1 NaOH at 200°C revealed no drastic change in the general dimensions of the platelets, even aer a 15 hour treatment under such conditions. 29 Nevertheless, according to the STEM observation hot NaOH causes a relatively rapid removal of the [Bi 2 O 2 ] 2+ termination layer (Fig. S2, ESI †). Similar to 2 mol L −1 NaOH, the transformation rate from Bi 4 Ti 3 O 12 to SrTiO 3 and the accompanying morphological development were also systematically examined in 6 mol L −1 NaOH and at various initial Sr/Ti ratios (i.e., Sr/Ti = 1, 3,12,24). A comparison of the XRD patterns, shown in Fig. 5 and 7 (Fig. S5 and S7, ESI †), revealed that for a particular Sr/Ti ratio the transformation to SrTiO 3 is much faster for reactions performed in more concentrated NaOH solutions. For example, in 6 mol L −1 NaOH (200°C) for the system with initial Sr/Ti = 1, the complete transformation to SrTiO 3 occurs in less than 2.5 hours (Fig. 7a and S7a, ESI †), while approximately 12 hours is needed for the initial Sr/Ti = 12 ( Fig. 7b and S7b, ESI †). However, for initial Sr/Ti = 24, a considerable amount (20%) of Bi 4 Ti 3 O 12 remained untransformed (SrTiO 3 /Bi 4 Ti 3 O 12 ) aer a 12-hour reaction under the same conditions (6 mol L −1 NaOH, 200°C) (Fig. 7b, S7b and S8, ESI †).
In the series of Sr/Ti ratios, the experimental conditions with Sr/Ti = 1 also presumably provide in 6 mol L −1 NaOH the lowest supersaturation, a decrease of which with the progress of SrTiO 3 formation is more notable than for those with higher Sr/Ti ratios. This reects in the morphology of the formed SrTiO 3 particles (nanostructures), which at Sr/Ti = 1 in some cases considerably deviate from the initial template (Fig. 8a). Nanocubes, nanoblocks and various plate-like irregular morphologies were observed. It must be mentioned that in none of these SrTiO 3 nanostructures was the characteristic groove observed, indicating that the growth of SrTiO 3 does not occur simultaneously on both basal surface planes of the Bi 4 Ti 3 O 12 , and the dissolution is also not restricted exclusively from the lateral side. This means that SrTiO 3 continues to grow on initially nucleated SrTiO 3 regions on the Bi 4 Ti 3 O 12 platelet, while unprotected areas of the template dissolve. Similar to the 2 mol L −1 -NaOH-experiments, also under higher base concentrations, better SrTiO 3 coverage and protection of the basal surface planes ( Fig. 8 and 9) were observed at conditions with higher Sr/ Ti ratios.

Formulation of the growth mechanism
The above results, presented in Fig. 4, 6, 8 and 9, demonstrate that when the transformation from Bi 4 Ti 3 O 12 to SrTiO 3 is performed in alkaline (2 mol L −1 or 6 mol L −1 NaOH) aqueous solutions at 200°C with Sr/Ti $ 12, the intermediate SrTiO 3 / Bi 4 Ti 3 O 12 and nal SrTiO 3 structures could well maintain the platelet morphology of the initial Bi 4 Ti 3 O 12 template. The conditions with higher Sr/Ti ratios enable better protection of the basal surface planes against degradation from the top and the SrTiO 3 nucleation and growth occur over the entire basal surface planes, while the Bi 4 Ti 3 O 12 dissolution proceeds from