Facet controlled growth mechanism of SnO2 (101) nanosheet assembled film via cold crystallization

Cold crystallization of SnO2 was realized in aqueous solutions, where crystal growth was controlled to form SnO2 (101) nanosheet assembled films for devices such as chemical sensors. The nanosheets grew directly on a fluorine-doped tin oxide substrate without a seed layer or a buffer layer. The nanosheets had a thickness of 5–10 nm and an in-plane size of 100–1600 nm. Moreover, the large flat surface of the (101) facet was metastable. The thickness of the SnO2 (101) nanosheet assembled film was approximately 800 nm, and the film had a gradient structure that contained many connected nanosheets. TEM results revealed that the predominate branch angles between any two connected nanosheets were 90° and 46.48°, corresponding to type I and type II connections, respectively. These connections were consistent with the calculations based on crystallography. Crystallographic analysis clarified the characteristic crystal growth of the SnO2 (101) nanosheet assembled film in the aqueous solution. Furthermore, we demonstrate that the metastable (101) facet can be exploited to control the rate of crystal growth by adjusting the etching condition.

www.nature.com/scientificreports/ facet. In summary, the 3D open nanostructures can promote the penetration and diffusion of water molecules, and the exposed {101} facets can improve the adsorption ability of water molecules. The SnO 2 (101) nanosheet assembled films have been applied to molecular sensors and gas sensors as described above. Their characteristic (101) crystal facets and nanosheet morphology were reported to possess novel functions. However, crystallographic analysis of the SnO 2 (101) nanosheet assembled film has not been reported yet. This article is focused on analyzing the crystal growth and morphology of the SnO 2 (101) nanosheet assembled film. The growth mechanism and crystallographic models of the nanosheet are discussed.

Experimental procedure
Crystallization of the SnO 2 (101) nanosheet assembled film on the FTO substrate. The SnO 2 (101) nanosheet assembled film was formed on the FTO substrate following the conventional method used to make photocurrent conversion type molecular sensors. The FTO substrate (SnO 2 :F, Asahi Glass Co. Ltd., 26 × 50 × 1.1 mm) was blown by air to remove dust and was then exposed to vacuum ultraviolet (VUV) light for 10 min using a low-pressure mercury lamp (PL16-110, SEN Lights Co., air flow, 100 V, 200 W) At a distance of 10 mm from the lamp, the power densities were 14 mW/cm 2 and 18 mW/cm 2 for wavelengths of 184.9 nm and 253.7 nm, respectively. The FTO substrate was covered with paper, stacked, and stored in air at the factory. The FTO surface was hydrophobic with a water contact angle of 96° and was modified with VUV exposure to become a super hydrophilic surface with a contact angle of less than 1°. This was because the VUV exposure decomposed the attached organic molecules that were present in very small amounts on the surface of the FTO substrate. The super hydrophilization effect of VUV exposure has been reported for studies on the modification of a hydrophobic organic monolayers into super hydrophilic hydroxyl groups 16,17 . Hydrophilic surfaces with hydroxyl groups were reported to be very effective at the nucleation and crystal growth of metal oxide in an aqueous solution. Therefore, the FTO substrate was subjected to a treatment that produced super hydrophilic surfaces. SnF 2 (CAS 7783-47-3, FW: 156.71, FUJIFILM Wako Pure Chemical Corporation, No. 202-05485, purity 90.0%) was used as the raw material for the SnO 2 crystals. A total of 200 mL of distilled water was heated to 90 °C in a polypropylene container using a drying furnace (DKN402, Yamato Scientific Co. Ltd.). SnF 2 (870.6 mg) was dissolved in distilled water at 90 °C to a concentration of 25 mM. The FTO substrate was immersed in the middle of the solution with the bottom up, tilted at 15° to the upright. The solution was kept at 90 °C for 24 h. The FTO substrate was taken out of the solution, washed with running distilled water, and subjected to strong air blow. The SnO 2 (101) nanosheet assembled film was crystallized on the FTO surface using this technique.
Characterization of the SnO 2 (101) nanosheet assembled film on the FTO substrate. The surface morphology of the SnO 2 (101) nanosheet assembled film on the FTO substrate was observed with a field emission scanning electron microscope (FE-SEM; JSM-6335FM, JEOL Ltd.) The fractured cross-sectional morphology of the SnO 2 (101) nanosheet assembled film was also observed with the FE-SEM after cutting the substrate. Samples for cross-sectional observation on a transmission electron microscope (TEM; FEI Tecnai Osiris) were prepared by the focused ion beam (FIB) micro sampling method at an accelerating voltage of 10-40 kV. Cross-sectional images of the substrates were obtained with the TEM operating at an accelerating voltage of 200 kV. A sample was prepared to observe the morphology from the direction perpendicular to the substrate. The sample piece was mechanically polished to approximately 20 μm from the glass substrate side. The sample was then thinned by Ar ion milling (liquid nitrogen cooling) at an accelerating voltage of ~ 3 keV. Plane images of the substrate were obtained with the TEM at an accelerating voltage of 200 kV. The crystalline phase was analyzed with an electron diffractometer (ED) installed on the TEM. The lattice spacing, crystal orientation, etc. were analyzed with electron diffraction (ED) and fast Fourier transform (FFT) images. High-angle annular dark field (HAADF) images were also obtained with the scanning TEM (STEM) mode. Elemental mapping images were obtained using an energy dispersive X-ray spectroscopy (EDS) unit integrated in the TEM. The STEM probe size was approximately 1 nm. The dwell time and collection time were 20 μs and 300 s, respectively. Count map images were obtained for tin, oxygen, and aluminum. The samples were fixed using resin containing oxygen, carbon, and aluminum.

Results and discussion
SEM observation of the SnO 2 (101) nanosheet assembled film. The SnO 2 (101) nanosheet assembled film was successfully fabricated on the entire surface of the FTO substrate ( Fig. 1, upper image). The crosssectional image showed that the thickness of the SnO 2 nanosheet assembled film was approximately 800 nm ( Fig. 1, lower image). The FTO layer formed on a glass substrate had a thickness of approximately 1000 nm. The SnO 2 (101) nanosheets uniformly formed on the substrate had a thickness of 5-10 nm and an in-plane size of 100-1600 nm (Fig. 1, upper image). The reaction conditions such as temperature and ion concentration were uniform regardless of the location within the solution. The uniformity of the reaction conditions resulted in uniform nanosheet formation, which is one of the advantages of the solution process. In addition, film formation was realized at room temperature and atmospheric pressure in the aqueous solution with an open-air system. Therefore, the method used in this study can be applied to film formation on the meter size scale or to substrates with complicated shapes, such as uneven substrates, particles, fibers, or meshes. Furthermore, sintering at temperatures of the order of ~ 100 °C, which is usually required in the synthesis of ceramics, was unnecessary. Therefore, this method is applicable to film formation on low heat resistant plastics, carbon materials, metals, glasses, organic materials, biomaterials, etc. because of the room temperature process. www.nature.com/scientificreports/ network of the nanosheets (Fig. 2a). The nanosheets connected with each other to form a porous structure with inner nano/mirco-meter sized spaces; this characteristic nanosheet-assembled structure was produced by the crystal growth of SnO 2 . A large SnO 2 (101) nanosheet with a thickness of 4 nm, an in-plane size of over 300 nm, and an aspect ratio of over 75 was observed at the center of the image (Fig. 2b). Nanosheets with a thickness of 4 nm, an in-plane size of 50 nm, and an aspect ratio of 13 grew from the large nanosheet. A large number of small nanosheets with a thickness of 2 nm, an in-plane size of 10 nm, and an aspect ratio of 5 also grew from the large nanosheet. A SnO 2 (101) nanosheet with a thickness of 3 nm, an in-plane size of over 100 nm, and an aspect ratio of over 33 was observed at the upper area of the image (Fig. 2c). Two dark gray lines were observed in the light gray nanosheet, and these lines were parallel to the in-plane direction. The surface of the nanosheets contained smaller SnO 2 crystals of 1-2 nm in size, which contributed to the characteristic surface of the SnO 2 (101) nanosheet assembled film. The angle between the connected nanosheets was either approximately 90° or 40°-50° (Fig. 2d, HAADF). Tin was detected in the nanosheets (Fig. 2d, Sn), oxygen was observed in the nanosheets and the adhesive glue on the nanosheets (Fig. 2d, O), and aluminum was observed in the adhesive (Fig. 2d, Al). The adhesive was used to fix the sample for the TEM experiments and remained on the nanosheets. The mapping image of tin and aluminum clearly showed their positions in the nanosheets and the adhesive (Fig. 2d, Sn-Al), and the EDS results indicated that the nanosheets contained tin and oxygen.
A network of the SnO 2 (101) nanosheets was also observed in the plane observed TEM images (Fig. 3a), which was formed by the dendritic growth of SnO 2 . The nanosheets connected with various angles. Impurities such as amorphous or spherical particles were not observed (Fig. 3b). However, the adhesive remained on the nanosheets. A high resolution TEM image of the nanosheet showed lattice fringes (Fig. 3c1), while an FFT image contained clear spots, which indicated that the nanosheet was a single crystal of SnO 2 (Fig. 3c2). The lattice spacings were calculated from the spots in the FFT image. The lattice spacing of the plane parallel to the nanosheet was 0.2681 nm, and this plane was assigned to the {101} crystal pane. The FFT image indicated that the nanosheet had a (101) crystal facet, which was consistent with previous studies in which the (101) facet of the SnO 2 nanosheet was observed 10,11,18,19 . The lattice spacing of the crystal plane perpendicular to the nanosheet was 0.2307 nm, and this plane was assigned to the {200} crystal pane of SnO 2 . The stacking direction of the {200} crystal planes was the a-axis of SnO 2 . The lattice spacing of the crystal plane at an angle with the nanosheet was 0.1730 nm, and this plane was assigned to the {211} crystal plane of SnO 2 .
Some SnO 2 nanosheets grew from other SnO 2 nanosheets by dendritic growth and connected with a branch angle of 90° (red circle, type I) (Fig. 4a). The crystal structure and growth direction were affected by the branch angle. Notably, the SnO 2 nanosheets grew directly from other SnO 2 nanosheets without the appearance of an www.nature.com/scientificreports/ amorphous layer, impurity layer, or cracks at the interface. This growth feature contributed to the high mechanical strength, high electrical conductivity, high thermal conductivity, etc. of the film. In addition, some SnO 2 nanosheets grew from other SnO 2 nanosheets with a branch angle of 40°-50° (blue circle, type II) (Fig. 4b,c). The TEM images (Fig. 4) clearly showed the interface structure of the nanosheets. However, the TEM observation direction did not precisely align with the direction of the connected interface line of the nanosheets in these figures. In other words, the observation direction was not parallel to both of the connected nanosheets. The branch angles were evaluated from the TEM image, which was further observed from B = <1 − 1 − 1> of SnO 2 , as shown in Fig. 5. Three large nanosheets were observed in parallel from the upper left to the lower right of Fig. 5a. The FFT images of A, B, C, and D ( Fig. 5b) were calculated from the TEM images in squares A, B, C, and D ( Fig. 5a), respectively. Squares B and C were on one of the three large nanosheets. Square A was on the nanosheet that connected with one of the three large nanosheets containing square B; their branch angle was 90° (Fig. 5a). Square D was on the nanosheet that connected with one of the three large nanosheets containing square C; their branch angle was 40°-50° (Fig. 5a). The FFT images were analyzed to calculate the selected area electron diffraction (SAED) pattern from the direction of B = <1 − 1 − 1> of SnO 2 (Fig. 5c). Thus, the lattice spacings of the nanosheets that were parallel to the large nanosheets in FFT B and C were respectively 0.2762 nm (Fig. 5b, B) and 0.2677 nm (Fig. 5b, C). They were assigned to the {101} crystal plane of SnO 2 to indicate that the nanosheets had a (101) facet. The lattice spacings of 0.2677 nm and 0.3373 nm were assigned respectively to the {101} and {110} crystal plane of SnO 2 (in FFT B). The lattice spacings of 0.2591 nm and 0.3466 nm were assigned respectively to the {101} and {110} crystal plane of SnO 2 (in FFT C). They also provided information on the connections of the nanosheets.
The SnO 2 nanosheet that connected with the large nanosheet with a branch angle of 90° is shown in square A. The lattice spacing of the nanosheet that was parallel to the nanosheets in FFT A was 0.2608 nm (Fig. 5b, A). It was assigned to the {101} crystal plane of SnO 2 to indicate that the nanosheets had a (101) facet. The lattice spacings of 0.2611 nm and 0.3333 nm were assigned respectively to the {101} and {110} crystal plane of SnO 2 (in FFT A). On the other hand, the SnO 2 nanosheet that connected with the large nanosheet with a branch angle of 40°-50° is shown in square D. The lattice spacing of the nanosheet that was parallel to the nanosheets in FFT D was 0.3279 nm (Fig. 5b, D). It was assigned to the {110} crystal plane of SnO 2 .
The crystal planes of the SnO 2 nanosheets that connected with a branch angle of 90° or 40°-50° are shown in the red or blue circle, respectively (Fig. 6a). They were analyzed with the FFT images ( Fig. 5b) and the calculated SAED pattern (Fig. 5c). The crystal growth models of the SnO 2 nanosheets that connected with a branch angle of either 90° (red circle) or 46.48° (blue circle) are shown in Fig. 6b. The two bold lines correspond to the {101} crystal planes from the direction of B = <1 − 1 − 1> of SnO 2 in the red circle (Fig. 6b, right), and their calculated branch angle was 90°. This crystal growth model was based on the branch angle of the type I (90°) connection. Additionally, small nanosheets can grow to connect with the bold lines. A calculated branch angle for that connection was 46.48° (Fig. 6b, right). This crystal growth model was based on the branch angle of the type II (46.48°) connection. The branch angle of 46.48° is clearly shown in the growth model depicted in the blue circle The branch angle of the type II (46.48°) connection was analyzed with a crystal structure analysis program ReciPro (ver. 4.283). The crystal system, laue group, space group, lattice constant of the a-axis, and lattice constant of the c-axis were tetragonal, 4/mmm, P4 2 /mnm, 4.737 Å, and 3.185 Å, respectively. The angle between the (101) and (110) crystal planes was 66.76°. The calculated branch angle of the type II connection was 46.48  The crystal growth model is summarized as follows. The models that were analyzed with FFT images and the calculated SAED pattern indicted that the crystal growth of the SnO 2 nanosheet assembled film was based on dendritic growth. The branch angle of the nanosheets was determined by the crystal structure and growth direction. The nanosheets had two types of connections in which the branch angle was 90° (type I) or 46.48° (type II).
Crystallographic analysis of the SnO 2 (101) nanosheet assembled film with cross-sectional TEM images. The SnO 2 nanosheets were nucleated and grown on the FTO surface to form the SnO 2 (101) nanosheet assembled film (Fig. 7). The glass substrate, at the bottom of the TEM image, had a flat surface. The glass substrate had a dark gray layer of approximately 10 nm and a light gray layer of approximately 20 nm near the interface with the FTO layer. The brightness of the light gray layer was similar to that of the glass substrate. The FTO layer formed on the glass substrate. The thickness of the FTO layer was 500-800 nm, and the thickness of its rough surface was 100-300 nm. The FTO layer had dark gray and light gray regions and was composed of a polycrystal of SnO 2 . The difference in the crystal axis direction of each crystal caused differences in the brightness. The SnO 2 (101) nanosheet assembled film formed on the surface of the FTO layer. The film had a porous structure, its density was lower toward the surface, and its thickness was 500-800 nm.
The nanosheets were small in size and formed a dense structure in the region close to the FTO substrate (Fig. 8a). On the other hand, they were also large in size and formed a porous structure in the region far from the FTO substrate. The film had a gradient structure in the direction perpendicular to the substrate; this gradient structure was one of the characteristics of the film. The nanosheets connected with other nanosheets, i.e., one nanosheet branched and grew from another nanosheet. Many small nanosheets branched and grew from the large nanosheet (red circle, Fig. 8a). Notably, a branch angle of 90° (red circle, Fig. 8a) was observed between the small nanosheet and the large nanosheet. This angle is associated with the type I connection (red circles, Figs. 4a, 6a), and the corresponding model is depicted in the red circle of Fig. 6b. A different branch angle of 46.48° was also observed, as shown in the blue circles of Fig. 8a. This angle is associated with the type II connection (blue circles, Figs. 4b,c, 6a), and the corresponding model is depicted in the blue circle of Fig. 6b.
An SAED pattern was obtained from the interface between the SnO 2 (101) nanosheet assembled film and the FTO layer (Fig. 8b1). Orderly arrays of strong diffraction spots were observed (Fig. 8b2), and they were assigned to the {110}, {100}, or {200} diffraction planes of the SnO 2 crystal from the <− 111> direction. A large SnO 2 crystal of the FTO layer was observed in a TEM image (Fig. 8b1), and it had a flat crystal facet. The large SnO 2 crystals in the FTO layer caused the clear spots. In addition, Debye rings were observed, and they were assigned to the {110}, {100}, or {200} diffraction planes of the SnO 2 crystal. The presence of Debye ring diffraction indicated that the rings originated from the random oriented crystals of the SnO 2 nanosheets.
The branch angle of 90° (type I) was also observed at the interface between the SnO 2 nanosheet and the FTO layer, shown in the red circle (Fig. 8c). Many SnO 2 nanosheets were oriented perpendicular to the surface of the FTO layer. The observed angle between any two SnO 2 nanosheets at the center of the red circle was also 90°. The FTO layer had large surface roughness since the FTO was a SnO 2 polycrystal. Two crystal surfaces in the FTO layer formed an angle of less than 90° (yellow circle, Fig. 8c). In spite of the surface roughness, the SnO 2 nanosheets formed on the surface of the depressed valleys to cover the entire surface of the FTO layer. This is one of the advantages of the solution process.
The SnO 2 nanosheets were also observed from a direction parallel to the plane (Fig. 9a-c), where the crystal lattice fringes were observed. These surfaces contained no cracks or pores and were not covered with amorphous layers or organic layers. The bare SnO 2 crystal was exposed even at the tip of the nanosheet (Fig. 9a). The surface of the nanosheet was exposed to the external atmosphere, which led to the characteristic sensor properties. The thickness evaluated at several points was 4-8 nm (Fig. 9a-c); this thinness provided a high specific surface area 20 www.nature.com/scientificreports/ and also contributed to the weight reduction of the coating film. In addition, this dimension had the effect of increasing the ratio of the nano space to SnO 2 crystal. Furthermore, studies showed that the proportion of the electron depletion layer in the SnO 2 crystal dramatically increased in the semiconductor gas sensor [9][10][11]19 , which resulted in high sensor sensitivity. The interface between the SnO 2 nanosheet and the FTO surface was observed at multiple points. The results indicated that the SnO 2 nanosheets directly formed on the FTO surface without any clearance space (Fig. 10a), and the FTO surface was uniformly covered with the SnO 2 nanosheet assembled film even in the convex area of the FTO surface (Fig. 10a). Therefore, direct nucleation and crystal growth of the SnO 2 nanosheets were realized without a seed layer or a buffer layer, which enables film formation on various substrates [21][22][23] . The magnified areas show the crystal growth of the SnO 2 nanosheets at the initial stage (Fig. 10b,c). The nanosheets were 2-5 nm in thickness and 5-20 nm in length in the region of 50 nm from any point at the interface. These small nanosheets formed a dense structure near the interface, indicating that the nucleation density of the SnO 2 nanosheets was high on the FTO surface. Moreover, the high ion concentration accelerated the nucleation and growth of the SnO 2 nanosheet at the initial stage of the synthesis, causing a high density of the SnO 2 nanosheets on the FTO surface. The magnified images show the crystal lattice fringes of the SnO 2 nanosheets and the FTO layer (Fig. 10d,e). Clearance space, amorphous layers, and cracks were not observed between the SnO 2 nanosheets and the FTO layer even in the high-resolution images.
Many tilted SnO 2 nanosheets were observed near the interface (Fig. 10a-e). However, the number of SnO 2 nanosheets that were tilted to the interface decreased with increasing distance from the interface. The initial nuclei were randomly oriented and thus grew into nanosheets with random orientations. The nanosheets that were tilted to the interface reached another nanosheet. The crystal growth parallel to the interface was suppressed by this attachment to the other nanosheet. On the other hand, the SnO 2 nanosheets that aligned perpendicular to the interface grew to form large nanosheets since they had enough space to grow in the region far from the interface. This is one of the formation mechanisms for the gradient structure of the SnO 2 (101) nanosheet assembled film. The other mechanism is the decreasing ion concentration. Sn ions were used for the nucleation and crystal growth of the SnO 2 nanosheets, and the supersaturation degree gradually decreased as the synthesis progressed. A large number of SnO 2 nanosheets were formed during the initial stage, but the rate of nanosheet formation decreased as the synthesis progressed. Therefore, the depleted ion concentration and reduced supersaturation  24 . In particular, the particles changed their morphology, color, surface area, X-ray diffraction pattern, chemical composition, X-ray photoelectron spectra, etc. with synthesis time, which were caused by the gradual changes in the solution condition. HAADF-STEM images provide contrast information according to factors that affect electron scattering such as sample density, sample thickness, and composition (atomic number) (Fig. 11a). The boundaries of each SnO 2 crystals in the FTO layer were clearly shown. Cracks and impurities near the interface between the FTO layer and the glass substrate were not observed. A black layer of approximately 23 nm in width and a gray layer of 13 nm in width were observed at the interface between the FTO layer and the glass substrate. The glass substrate included light gray spherical areas of 20-200 nm in size, which had a chemical composition and density that was different from the surroundings. The spherical impurity areas were not observed near the interface of approximately 200 nm in width.
The SnO 2 (101) nanosheet assembled film in Fig. 8a was observed with HAADF-STEM (Fig. 11b). The shape of the SnO 2 nanosheets and their connections were clearly observed. The SnO 2 nanosheets and the FTO layer were similar in opacity (white) compared with the glass substrate since they had similar chemical compositions.  www.nature.com/scientificreports/ The nanosized spaces that were surrounded by the nanosheets were also clearly observed in the SnO 2 nanosheet assembled film. Tin was detected in both the SnO 2 (101) nanosheet assembled film and the FTO layer (Fig. 11c, Sn). Oxygen was observed in the SnO 2 (101) nanosheet assembled film, the FTO layer, and the glass substrate, while it was not observed in the gray layer of 13 nm (Fig. 11c, O). A similar signal intensity for fluorine was detected in the SnO 2 (101) nanosheet assembled film and the FTO layer (Fig. 11c, F). The FTO layer was doped with fluorine to obtain high electrical conductivity. Therefore, the SnO 2 (101) nanosheet assembled film contained a fluorine concentration similar to that in the FTO layer. Silicon was observed in the glass substrate and the black layer of approximately 23 nm in width since the glass contained silicon dioxide (Fig. 11c, Si). The gray layer of 13 nm in width contained titanium (Fig. 11c, Ti). Sodium was detected in the glass (Fig. 11c, Na) and was also detected in the FTO layer near the glass. Therefore, sodium was slightly distributed to the FTO layer from the glass. A high concentration of sodium was observed in the glass near the gray layer of 13 nm in width. Spherical areas with a high concentration of sodium were observed in the glass substrate; one such area overlapped with the scale bar and the other area was below the label of sodium (Fig. 11c, Na). Their positions were the same as the light gray spherical areas in the HAADF-STEM image (Fig. 11c, HAADF), indicating that the light gray spherical impurity areas in the HAADF-STEM images corresponded to the glass with a high concentration of sodium. The titanium layer of 13 nm in width suppressed the diffusion of sodium from the glass into the FTO layer, although sodium was slightly detected in the FTO layer.
Discussions on the mechanism of anisotropic crystal growth for the nanosheet. Surface energy calculations for the most stable (110) facet and metastable (101) facet. SnO 2 crystal structures with (110) (Fig. S1, left) or (101) (Fig. S1, right) facet were calculated using the VESTA program 25 with the crystal structure data of SnO 2 (COD ID:1000062, The Crystallography Open Database) 26 . The oxygen ions were bonded to the tin ions to produce a bridge structure in the outermost surface layer of the (101) facet. They can be easily removed 11 . The surface reactivity is strongly associated with surface energy and surface stability, and the metastable surface is unstable and highly reactive.
The morphology and facets of the SnO 2 crystals have been discussed with surface energy calculations. Batzill et al. 27 reported a photograph of a SnO 2 single crystal of approximately 5 mm in size, which was grown by a vapor phase transport reaction 28 1.380, 1.487, 1.554, 1.664, 1.679, 1.758, 1.821, 1.860, 2.217, and 2.366 J m −2 , respectively 31 . The surface energy per crystal face increased in the order (110) < (210) < (101) < (100) < (310) < (321) < (211) < (301 ) < (111) < (001). They also reported that the calculated excess surface energies per unit cell were dominated by the electrostatic contribution and were ordered in the same sequence as the areas of the surface unit cells. In contrast, the thermodynamic quantity of excess energy per unit area was dominated by the relaxation energy of  Precise control of the balance between crystal growth and dissolution can be realized with the proposed facet controlled growth method. Therefore, crystals with metastable crystal facets can be obtained. The anisotropic crystal growth by this method can be applied to various crystal morphology control. An etching agent other than fluorine ions can be also used for etching. In addition, etching can be performed by a change in pH, temperature, raw material, concentration ratio, additives, etc. It can be utilized for anisotropic growth control and morphology control of various crystals including inorganic crystals, organic crystals, biocrystals, metal organic frameworks, etc. to facilitate the development of devices using novel crystal planes and morphologies.
Experimental studies are available to support the mechanism of anisotropic crystal growth for the nanosheet mentioned above. Choi et al. revealed that there were many oxygen vacancies (V o ·· ) and non-stoichiometric Sn 2+ on the (101) facet of the SnO 2 nanosheets compared with the (110) facet of the SnO 2 nanoparticles using X-ray www.nature.com/scientificreports/ photoelectron spectroscopy (XPS) 11 . The oxygen vacancies indicated that the bond strength between oxygen and tin on the (101) facet was low. In addition, it was suggested that oxygen ions on the (101) (101) facet. The (110) facet of the nanoparticles contained 4.1 times more of the stronger oxygen peak component due to chemisorption than the (101) facet of the nanosheet. Therefore, the nanoparticles were covered with an adsorbed oxygen layer, which acted as a barrier to protect the oxygen and tin ions of the (110) facet. This protective effect that suppresses the release of oxygen from the (110) facet contributes to stability. High etching speed of the unstable surface was also observed on TiO 2 , which has the same rutile crystal structure as SnO 2 34 . The converged surface energies were calculated from model systems using GGA and three pseudopotentials 35 (101) and (− 10− 1) facets was modeled with VESTA (Fig. 12a). These two facets were parallel and equivalent and contained surface bridging oxygen ions. The tilted image showed four facets on the sides of the nanosheet (Fig. 12b), which were the equivalent most-stable facets of (110), (− 110), (− 1− 10), and (1− 10). A further tilted image showed the appearance of the nanosheet with two large metastable (101) facets and four narrow and most-stable (110) facets (Fig. 12c).
The fluorine ions in hydrofluoric acid are known to dissolve metal oxides such as SiO 2 or SnO 2 by cleaving the chemical bonds between a metal ion and an oxygen ion. The unstable (101) facets are easily etched with fluorine ions compared with the most-stable (110) facets, and the bridging oxygens are also easily attacked by fluorine ions. Thus, fluorine ions continuously dissolve the (101) facet while the tin ions in the solution stack the (101) atomic layers to promote crystal growth perpendicular to the (101) facet. The crystal growth rate in the direction perpendicular to the (101) facet is determined by the competing dissolution rate determined by the fluorine ions and growth rate determined by the tin ions. The controlled crystal growth rate in the direction perpendicular to the (101) facet was very slow under the conditions in this study. On the other hand, the dissolution rate of the most-stable (110) facet caused by the fluorine ions was low. Therefore, the crystal growth rate in the direction perpendicular to the (110) facet was maintained at a high rate to balance the dissolution rate determined by the fluorine ions and the growth rate determined by the tin ions. The rate of crystal growth perpendicular to the (101) facet was much slower than that perpendicular to the (110) facet due to the difference in stability between the two facets. This difference in growth rate between the (101) facets and (110) facets resulted in the formation of nanosheets with large (101) facets.

Conclusion
The SnO 2 (101) nanosheet assembled film was developed in an aqueous solution. The nanosheets grew directly on the FTO substrate. The thickness of the SnO 2 (101) nanosheet assembled film was approximately 800 nm. The nanosheets had a thickness of 5-10 nm, an in-plane size of 100-1600 nm, and a metastable (101) crystal facet with a large flat surface. The crystal growth model was discussed using TEM images, FFT images, and calculated SAED patterns. Dendritic growth governed the crystal growth of the SnO 2 (101) nanosheet assembled film in which the branch angle of the connected nanosheets was determined by the crystal structure and growth direction, resulting in two types of connections, which were defined by the branch angle of either 90° (type I) or 46.48° (type II). Dendritic growth of the branch structures enabled the formation of the SnO 2 (101) nanosheet assembled film, which possessed a characteristic network of the nanosheets with a high surface area and internal nano spaces.
Furthermore, the mechanism of anisotropic crystal growth of the nanosheet was discussed. The (110) crystal facets were the most stable and possessed high stability toward etching by the fluorine ions in the SnF 2 solution. Therefore, SnO 2 grew along the direction perpendicular to the (110) crystal plane to form stacked (110) crystal planes. On the other hand, (101) crystal facet was metastable, and thus both etching and growth occurred on the (101) crystal facet in the SnF 2 solution, thereby realizing slow crystal growth along the direction perpendicular to the (101) crystal facet. The facet controlled growth method achieved anisotropic crystal growth to produce www.nature.com/scientificreports/ the nanosheet with the large (101) facet. This method can be applied to control the morphology of crystals with metastable facets. In conclusion, the characteristic activity of metastable facets is expected to contribute to the development of various devices.