Flux Growth of Single-Crystalline Hollandite-Type Potassium Ferrotitanate Microrods From KCl Flux

Hollandite-type crystals have unique and interesting physical and chemical properties. Here, we report the flux growth of hollandite-type single-crystalline potassium ferrotitanate (KFTO) with faceted surface features from a KCl flux. We varied the flux growth conditions, including the kind of flux, holding temperature, and solute concentration for growing faceted crystallites. KCl was found to be the best flux to grow the single-crystalline KFTO particles, while heating at or above 900°C was needed to yield the KFTO single crystals. The crystal growth was only weakly dependent on the solute concentration. Next, we characterized the grown single crystals and discussed the manner of their growth from the KCl flux. TEM images with clear electron diffraction spots indicated that the KFTO crystals grew along the <001> direction to form microrods ~10 μm in size. DFT calculation results indicated that the surface energy of the (100) face is lower than that of the (001) face. Based on these characterization results, we proposed a possible growth mechanism of the KFTO crystals.


INTRODUCTION
Hollandite-type minerals such as silicate exist naturally in the Earth's lower crust and upper mantle and possess significant structural stability (Miura and Iura, 1986). For chemists and physicists, inorganic crystals with hollandite structure are very interesting, because of their unique chemical and physical properties such as fast ion conduction and ion exchange (Michiue and Watanabe, 1999), which allow them to function as solid electrolytes and adsorbents for radioactive elements, respectively (Yoshikado et al., 1995;Aubin-Chevaldonnet et al., 2007;Xu et al., 2016;Tumurugoti et al., 2017;Hassan et al., 2018;Cao et al., 2019). Among these crystals, titanates with hollandite structure possess the stoichiometry of A x (B, Ti) 8 O 16 and tetragonal symmetry, where A is alkali or alkaline-earth cations including K + , Rb + , and Ba 2+ , and B is a trivalent cation in the oxygen octahedron such as Ga 3+ and Al 3+ . Here, we focus on the composition K 1.75 Fe 1.75 Ti 6.25 O 16 (KFTO) from the viewpoints of cost and environmental friendliness. Figure 1 shows its crystal structure. The typical connections of (Fe, Ti)O 6 octahedra form 1-D tunnel sites along the [001] direction, and the K + cations fill in the center of the empty sites and diffuse into the sites. The walls of such tunnels are formed by (2 × 2) octahedra. Generally, hollandite type materials are FIGURE 1 | Crystal structure of hollandite-type K 1.75 Fe 1.75 Ti 6.25 O 16 . K, Fe, Ti, and O atoms are represented by purple, orange, blue, and red spheres, respectively. The crystal structure is visualized using the VESTA program (Momma and Izumi, 2011). synthesized by solid-state reaction (SSR) or hydrothermal reaction (Aubin-Chevaldonnet et al., 2007;Xu et al., 2016;Tumurugoti et al., 2017). However, there are rooms for improvement in crystal quality. Especially, to assess the physical and chemical properties of hollandite type crystals, it is important to prepare KFTO crystals with defined morphology and faceted surface features.
Flux growth is an approach for the nucleation and growth of functional inorganic crystals in molten-salts through the dissolution of ingredients and the precipitation of target crystals. The synthetic flexibility of flux growth conditions can lead to control of size, morphology, and exposed surface features of crystals, and stabilization of intermediate phases (Hayashi et al., 2019). For instance, we have reported the flux growth of platy KTiNbO 5 (Xiao et al., 2016), cuboidal LiMnO 2 , and β-Li 2 TiO 3 (Xiao et al., 2017), which highlights these benefits.
Herein, we comprehensively studied the growth of idiomorphic KFTO crystals from KCl-based fluxes. We explored several flux growth conditions, namely the flux species, holding temperature, and solute concentration in order to yield large KFTO crystals with faceted surface features. The manner of crystal growth in the KCl flux was then studied, and the formation of the single-crystalline KFTO microrods was discussed based on combined experimental and theoretical analysis results.

Growth of KFTO Crystals
All reagents were purchased from Wako Pure Chemical Industries, Ltd., and used without further purification. K 2 CO 3 , Fe 2 O 3 , and TiO 2 (anatase, 98.0%) powders were employed as solutes; while KCl, KOH, and KNO 3 were used as fluxes. In a typical procedure, K 2 CO 3 , Fe 2 O 3 , and TiO 2 were mixed in the molar ratio of 1.00:1.00:7.14 (giving a nominal composition of K 1.75 Fe 1.75 Ti 6.25 O 16 ) and mixed with a flux material at a solute concentration (defined as the molar ratio of KFTO to the flux) between 10 and 80 mol%. The mixture was placed into an alumina crucible with a lid under ambient conditions. Then, the crucible was placed in an electric furnace, heated to a setting temperature of 800-1,000 • C at a heating rate of 300 • C·h −1 , and then maintained for 10 h under air. After the holding, the crucible was cooled to room temperature at an arbitrary setting rate under air. The product was washed with deionized water at room temperature and then dried in air at 100 • C. The resulting KFTO samples are abbreviated as KFTO flux -900, etc. For comparison, KFTO crystals were also prepared via SSR without using the flux according to Equation (1), and the sample is named KFTO SSR . 0.875K 2 CO 3 + 0.875Fe 2 O 3 + 6.25TiO 2 → K 1.75 Fe 1.75 Ti 6.25 O 16 Characterization X-ray diffraction (XRD) patterns were recorded on a Miniflex II or SmartLab powder diffractometer (Rigaku) with monochromated Cu Kα radiation (λ = 0.15418 nm). Field-emission scanning electron microscopy (FE-SEM, JEOL, JSM-7600F) images were collected at an acceleration voltage of 15 kV. Nitrogen adsorption isotherms were obtained at −196 • C using a Belsorp Mini II sorption analyzer (BEL Japan). For TEM observation, a typical single crystal of KFTO was selected and milled to 5 µm × 5 µm × 100 nm using a focused ion beam apparatus (FIB, JIB-4000, JEOL). The TEM images and selected area electron diffraction (SAED) patterns were taken with the incident beam parallel to the exposed dominate facet at an acceleration voltage of 200 kV. To estimate the chemical compositions of the grown KFTO samples, we carried out elemental analysis. In the elemental analyses, 0.010 g of the KFTOs was dissolved in hydrofluoric acid, and the dissolved solution was analyzed using inductively coupled plasma-optical emission spectrometry (ICP-OES, SII, SPS5510). The DFT calculations were performed using the generalized gradient approximation (GGA-PBEsol) + U and projectoraugmented wave methods, as implemented in the Vienna ab initio simulation package (VASP) (Kresse and Furthmuller, 1996a,b;Perdew et al., 2008). The U value for the d-orbitals of Fe was set to 4.0 eV (Jain et al., 2011). An energy cut-off of 500 eV and a 2 × 2 × 8 k-point mesh for the bulk were used for the unit cell of 26 atoms in a tetragonal lattice of K 2 Fe 2 Ti 6 O 16 with I4/m symmetry as the starting structure. Relaxation of the crystal structure was allowed in all calculations, and energies of the final optimized geometries were recalculated to correct for changes of the plane-wave basis during relaxation.
To calculate the surface energy of the bulk and surface models, we considered two low-index surfaces [the (100) and (001) facets] and the stoichiometric composition. In the case of (100) facet with Fe-poor termination, we manually arranged the atoms to maintain the stoichiometric composition. The energy of a slab with a surface facet, E slab , was calculated. The crystallographic symmetry of the top and bottom slab surfaces is essential for achieving a rational computational prediction. The surface energy, γ , is defined as Equation (2).
where A is the surface area of the slab, E bulk is the energy per atom in the bulk model, and N is the number of atoms in the slab model. The slab cells were constructed from the relaxed bulk structure, and their lattice parameters were fixed. To calculate the surface facets, slab thicknesses >20 Å were chosen for all facets with a vacuum thickness of 20 Å.

Crystal Growth
We first examined the effect of different flux species on the growth of KFTO crystals, because the cation and anion in the flux can influence the dissolution of the solutes. Figure 2 shows the XRD patterns of KFTO crystals grown at 900 • C from KCl-KNO 3 , KCl, and KOH fluxes, whose melting temperatures are 580, 771, and 405 • C, respectively. KCl and KNO 3 were mixed in a 1:1 molar ratio. The respective KCl-KNO 3 , KCl, and KOH fluxes might act as K sources, which is known as self-fluxing. The use of KCl-KNO 3 and KOH resulted in the formation of K 2 Ti 6 O 13 as a by-product in addition to KFTO. In contrast, single-phase KFTO crystals were grown from the KCl flux. The difference in product formation could be attributed to the property of the flux, wherein the halide flux would promote the formation of metal complexes in the solution and thereby control the intermediate species. Therefore, from this point on, we only discuss the growth of KFTO crystals from the KCl flux. Next, we examined the growth of KFTO crystals under different holding temperatures. Figure 3 shows the XRD patterns of crystals grown from the KCl flux at 800, 900, and 1,000 • C (solute concentration: 80 mol%), together with those of KFTO SSR synthesized at 900 • C. Heating to 800 • C in the presence of flux resulted in KFTO and an unknown phase. Increasing the holding temperature to 900 and 1,000 • C eliminated this unknown phase, resulting in the single KFTO phase. On the other hand, SSR at 900 • C did not give single-phase KFTO, mainly because the Fe 2 O 3 did not completely react. Figure 4 is the FE-SEM images of KFTO crystals grown at 800, 900, and 1,000 • C and KFTO SSR synthesized at 900 • C. At 800 • C, both anisotropic undefined crystals several µm in size and needle-shaped crystals were observed. In contrast, heating at 900 and 1,000 • C resulted in rectangular crystals with faceted surface features from the KCl  flux, and SSR produced small undefined crystals ∼100 nm in size. The sharp difference in morphology between the KFTO samples shows two important points. The first is that the present optimum temperature for flux growth (900 • C) is ∼300 • C lower than that for the KFTO prepared by SSR (1,200 • C). The second point is that the crystals with well-defined facets were formed possibly due to the formation of intermediate species, as will be discussed later.
The solute concentration dependence of KFTO crystal growth was next studied, while the holding temperature was fixed at 900 • C. Figure 5 shows the XRD patterns of KFTO crystals prepared at 10, 50, and 80 mol% of solute concentrations. At 10 mol%, the diffraction line around 28 • could not be indexed to the KFTO phase, showing the formation of the impurity phase. In contrast, at or above 50 mol%, the singlephase KFTO was observed. According to the FE-SEM images (Supplementary Figure 1), the crystal size and morphology were independent of the solute concentrations, as only singlecrystalline microrods ∼10 µm in size were formed. In summary, we found the best flux growth condition for the KFTO to be: KCl flux, holding temperature of 900 • C, and solute concentration of 50-80 mol%. The KFTO samples were named KFTO-80 and KFTO-50 hereafter.
We estimated the chemical compositions of KFTO-80 and KFTO-50. The weight percentages of K, Fe, and Ti for KFTO-50 were found to be 6.2, 13.7, and 41.5 wt%, respectively, while those of K, Fe, and Ti for the KFTO-80 were 6.4, 13.7, and 42.1 wt%. However, the theoretical contents of K, Fe, and Ti for the nominal composition K 1.75 Fe 1.75 Ti 6.25 O 16 are 9.5, 13.6,

Crystal Growth Process
We carried out TEM observation on the KFTO-50 grown at 50 mol% solute concentration for 10 h at 900 • C, in order to determine the crystal growth direction. A typical single-crystalline microrod was processed as described in the Experimental section. The obtained bright-field TEM image and SAED pattern are shown in Figure 6. The ordered diffraction spots taken along the (100) direction indicate that the crystal was single-crystalline in nature. Observation of the exposed facets suggests that the dominant exposed crystal plane at the bottom side was the (010) plane (left image of Figure 6). As a result, the crystal grew along the <001> direction. A similar result was obtained for KFTO-80, as shown in Supplementary Figure 2. Again, the observed clear diffraction spots indicate its single-crystalline nature. Therefore, growth in the <001> direction was found to be dominant regardless of solute concentration.
To explain this preferred crystal growth direction, we calculated the surface energies for the (100) and (001) planes, and the results are shown in Table 1 while the superstructures of KFTO with (100) and (001) facets are shown in Supplementary Figure 3. We found that the surface energy for (100) plane was 0.8414 J·m −2 , while that for (001) plane was 1.279 J·m −2 . The higher surface energy of the latter means that the <001> growth direction is reasonable. The calculated surface energies were used in Wulff 's constructions to predict the equilibrium morphologies (Wulff, 1901), which are shown in Figure 7. The predicted shape is a rectangular parallelepiped with a longer c-axis. The crystal morphology of the KFTO shown in Figures 4b,c, and Supplementary Figure 1 is a rectangular parallelepiped as well. This similarity in shape indicated that the experimental and theoretical results are highly consistent.
Finally, we briefly propose the possible growth manner of the idiomorphic KFTO microrods. At the initial stage, the KFTO nucleus forms mainly through the solid-state reaction of TiO 2 , Fe 2 O 3 , and K 2 CO 3 . Because Cl − is recognized as a mineralizer in solution-based syntheses through the formation of a metal complex (Bugaris and zur Loye, 2012), the surface of KFTO nucleus undergoes chlorination, followed by the growth of the KFTO crystal along with the <001> direction through the elimination of Cl 2 . The driving force for the flux growth could be the concentration gradient of KFTO resulting from flux evaporation when the mixture was held at 900 • C. The present finding opens the door for the growth of hollandite-type crystals using the chloride-based flux.

CONCLUSION
The flux growth of KFTO crystals from the KCl-based flux was systematically studied. Among the flux examined, pure KCl was found the most suitable for growing single-crystalline KFTO crystals with surface-faceted features. Holding temperature dependence experiments indicated that the heating at or above 900 • C yielded the single-phase KFTO. The crystalline KFTO micro-rods were grown from a KCl, independent of the solute concentration, at 900 • C. The TEM observation results indicated the single crystallinity of KFTO and the crystal growth direction along with the <001> direction. DFT calculation result using the slab model of KFTO showed that the surface energy for the (100) facet was lower than that for the (001) facet. The theoretical equilibrium morphology of KFTO in Wulff 's construction derived from the DFT calculation was in good agreement with the FE-SEM images of KFTO grown from the KCl at 900 • C.

DATA AVAILABILITY STATEMENT
The datasets generated for this study are available on request to the corresponding author.

FUNDING
This work was partially supported by the A Shinshu-Method for Regional Innovation Ecosystem by Industrial Implementation of Innovative Inorganic Crystal Material Technology project of the Program on Regional Innovation and Ecosystem Formation of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan.