Solubility Measurements of NaTaO₃ in Molten Na₂MO₄ (M = Mo, W, and S) and Growth of Milli-Order Crystals at High Frequency

Abstract

Sodium tantalate (NaTaO₃) is an attractive functional material for photocatalysis. To understand its physical properties, significant efforts for milli-sized single-crystal growth of NaTaO₃ have been made. However, the growth was difficult due to the smaller size in solid-state growth or probable decomposition and melting in melt growth. Recently, we grew milli-order NaTaO₃ single crystals in Na₂MoO₄ flux. However, the reproducibility of the growth was not sufficient and hindered the stable supply of the crystal for physicochemical evaluations and further growth. The poor reproducibility was assumed to be due to the inhomogeneous, unstable growth field in response to the external atmosphere provided by nonoptimal experimental conditions. A saturated solution is considered the most suitable crystal growth field because it has the highest solubility and facilitates crystal growth with suppressed nucleation. Since supersaturation is the driving force for crystal growth, we considered that large crystals could be obtained with high frequency if growth could be controlled in the region where solubility changes rapidly. To compile a guideline for crystal growth under the control of supersaturation, the solubility of NaTaO₃ in Na-based fluxes, including Na₂MoO₄, was studied. Using NaTaO₃ molding pellets immersed in molten flux, the solubility curve for NaTaO₃ was successfully measured. Based on the solubility, the optimal experimental conditions, that is, the heating temperature, the slow-cooling section, and the amount of flux as a solvent, were determined. Finally, we demonstrated the growth of NaTaO₃ in Na₂MoO₄ flux and achieved milli-order crystals with high frequency. Our findings regarding the solubility of NaTaO₃ in molten flux may assist in the stable supply of milli-order single crystals for material evaluation and larger crystal growth.

Introduction

Perovskite-type materials formulated as ABO₃ have attracted significant attention as functional materials, for example, for applications in optoelectronics, spintronics, and thermoelectricity.¹⁻⁴ Sodium tantalate (NaTaO₃) is an alkali tantalate compound and belongs to a perovskite-type oxide having an orthorhombic crystal system with lattice constants a = 5.513 Å, b = 7.750 Å, and c = 5.494 Å.^5,6 Considering physicochemical properties, NaTaO₃ has an energy band gap of 4.0 eV^7,8 and exhibits photocatalytic activities such as producing hydrogen from water and decomposing organics under ultraviolet light. In addition, NaTaO₃ can be converted into Ta₃N₅—a visible-light-responsive photocatalyst—by nitriding. It is well-known that the performance of a material depends on its crystallographic characteristics such as crystal size and exposed crystal faces. Thus, understanding the correlation between the functional properties and crystallographic characteristics of NaTaO₃ is important.

The precise functionality of a material can be examined using a single crystal. To date, many growth techniques have been used to grow NaTaO₃ crystals. Hu and Teng grew cubic NaTaO₃ crystals with a nanostep structure on their surfaces using a solid-phase method.⁹⁻¹¹ Lee et al. used hydrothermal synthesis to grow face-developed cubic crystals in the submicrometer order.¹²⁻¹⁴ An et al.¹⁹ demonstrated the flux method, and cubic and cleaved hexahedral crystals were grown when NaCl was used as the flux. These single crystals are significantly small and difficult to measure. The melt method may be another potential method for growing larger crystals; however, the high melting point (1810 °C¹⁵) and probable decomposition melting properties of NaTaO₃ are some limitations of this method. In an alternate method, we addressed the growth of larger NaTaO₃ crystals in molybdate fluxes. The relatively low melting point and high boiling point of molybdate should provide a more active reaction field in liquid than chloride flux, which is easy to volatilize. Thus far, we have succeeded in growing milli-sized plate-like NaTaO₃ crystals using Na₂MoO₄ flux.¹⁶ However, the size reproducibility of crystal growth was low and prevented the stable supply of large single crystals for physicochemical evaluations and seed crystals for further large growth.

These issues were believed to be caused by the sensitivity of the growth field in the flux. Here, we consider sensitivity as a parameter to represent the homogeneity and stability of the growth field in response to an external atmosphere (high sensitivity indicates a fragile reaction field). For example, the heating temperature, oversaturation speed, and flux amount affect convection in the field, homogeneity of crystal growth or nucleation, and the number of nucleation, respectively. These factors should synergistically affect the sensitivity of the growth field. We speculate that the low reproducibility of crystal growth in our previous work was related to the high sensitivity of the growth field because it was far from optimal conditions in flux. The crystal growth process in the flux method consists of multiple steps: dissolution of the flux and the solute, nucleation, and adsorption of the solute. Controlling the supersaturation of the solution is important for the construction of a preferred growth field. If the number of stable nuclei generated through supersaturation increases, then the amount of the solute supplied per crystal decreases and growing crystals becomes difficult. In most cases, a cooling method is used to cause supersaturation. Slow cooling allows more epitaxial growth of crystal nuclei, leading to the growth of large crystals. The solute:solvent ratio is also important for controlling the supersaturation. This is because if the solute:solvent ratio is inappropriate, then stable nuclei cannot be controlled and a sufficient solute amount cannot be supplied to the nuclei. To determine suitable conditions for the slow-cooling region and the solute-to-solvent ratio, solubility must be a key parameter. However, the solubility curve of NaTaO₃ in oxide solvents has not been reported.

The purpose of this study was to understand the solubility of NaTaO₃ in Na-based fluxes. If insights into the solubility of NaTaO₃ in a flux can be provided, then guidelines for effective growth conditions for large NaTaO₃ crystals can be established. In this study, we examined the solubility of NaTaO₃ in oxide fluxes of similar anionic structures, including Na₂MoO₄. Comparing the solubilities in each flux, we discussed the role of anions in solvation. We also demonstrated the crystal growth of NaTaO₃ based on the measured solubility curves.

Experimental Section

Growth of NaTaO₃

NaTaO₃ crystals were grown using Na₂CO₃ (reagent grade, Wako Pure Chemical Industries, Ltd.) and Ta₂O₅ (99.9%, Wako Pure Chemical Industries, Ltd.) as raw materials, and Na₂MoO₄·2H₂O (reagent grade, Wako Pure Chemical Industries, Ltd.) was used as the flux. The experimental conditions are summarized in Table 1, run nos. 1–3 were conducted by the solid-phase method, and run no. 4 was conducted using the flux method. In run no. 4, screening experiments were conducted by varying solute concentrations between 1.7 and 2.7 mol % by 0.1 mol %. The solute concentration is defined as follows:

1

where N₁ and N₂ are the number of moles of the solute (NaTaO₃) and the flux, respectively. The raw materials and flux were weighed at a total preparation weight of 20 g. After dry mixing for 15 min, the materials were placed in a platinum crucible, which was placed in an electric furnace. NaTaO₃ crystals were grown by heating in air with a holding time of 10 h under an arbitrary heating program (heating temperature, heating rate, and cooling rate). If fluxes were used (run no. 4), then the resultant product was washed in hot water to dissolve the flux and isolate the target. The resultant powder was identified using powder X-ray diffraction (XRD; Mini Flex II, Rigaku). The measurement conditions were as follows: 2θ, 10–80°; sampling width, 0.02°; scan speed, 10.0° min^–1; voltage, 30 V; current, 15 mA; X-ray source, Cu Kα line (λ = 1.540562 Å). For the crystal samples grown in run no. 4, the average values of the long and short sides were estimated from their morphologies. It is noteworthy that the crystal shape of the obtained crystals was generally a plate, and the axes of the long and short sides were defined to be parallel to the two-dimensional direction of the plates. Herein, approximately 100–200 crystals were collected, and their optical photographs were taken. The biaxial length of each plate-like crystal was gathered from the optical photographs using the image processing software “MIPAR” (MIPAR Software LLC), and the average length was calculated.

Table 1. Growth Conditions for NaTaO₃ Crystals.

run no.	molar ratio (Na:Ta)	solute concentration (mol %)	heating rate (°C·h–1)	holding temperature (°C)	cooling rate (°C·h–1)
1	1:1	100	200	1000	200
2	1:1.05	100	200	1000	200
3	1:1.1	100	200	1000	200
4	1:1	1.7–2.7	45	1500	5 (>1300 °C)
					150 (<1300 °C)

Preparation of NaTaO₃ Pellets

For the solubility measurements, we prepared powdered samples via compression-molding. Approximately 2.0 g of NaTaO₃ powder prepared in run no. 2 was compacted into a disk shape with an inner diameter of 15 mm using a uniaxial press (100 kN Newton press, NPa System) at 60 kN for 5 min. In addition, the disk-shaped compacts were compressed at 300 kN for 10 min in a cold hydrostatic press (Press-CIP, NPa System Co., Ltd.). The obtained NaTaO₃ pellets were placed on a platinum plate, which was placed in an electric furnace. The pellets were heated to 1000 °C at 200 °C·h^–1 and held for 10 h. The pellets were cooled to 500 °C at 200 °C·h^–1 and then cooled naturally to room temperature in the furnace. The prepared pellets were identified using a fully automated multipurpose horizontal X-ray diffractometer (XRD; SmartLab HTC-R, Rigaku). This instrument was used because the X-ray irradiator and detector move instead of the sample stage, enabling identification of the pellets with few positional errors. The measurement conditions were as follows: 2θ, 10–80°; sampling width, 0.02°; scan speed, 10.0° min^–1; voltage, 40 kV; current, 30 mA. The radiation source was Cu Kα (λ = 1.540562 Å).

Solubility Measurements

The solubility measurements were performed by immersing the prepared NaTaO₃ pellets in the molten flux and recording the dissolution weight. Na₂MoO₄·2H₂O (reagent special grade, Wako Pure Chemical Industries, Ltd.), Na₂WO₄ (reagent special grade, Wako Pure Chemical Industries, Ltd.), and Na₂SO₄ (reagent special grade, Wako Pure Chemical Industries, Ltd.) were used as fluxes based on the flux selection guidelines provided in a previous study.¹⁷ A 30 mL platinum crucible was filled with 25 g of each flux, kept in an electric furnace at 800 °C for 1 h, and then cooled to room temperature. Through this heat treatment, fluxes were melted to solidify at a high bulk density to clarify the liquid-phase interface and accurately determine the pellet immersion position for the solubility measurement by producing a flux solid after melting. The dense flux solid and NaTaO₃ pellets were placed in an electric furnace. A schematic diagram of the experiment is shown in Figure 1. The crucible filled with the dense flux was placed in the center of the pull-up furnace, and the position of the crucible was adjusted such that the pellet was at the center of the crucible (Figure 1A). The crucible was heated to 1100–1500 °C and held at a heating state for 3–10 h. The NaTaO₃ pellet was pulled down by 5–10 cm to the position where the NaTaO₃ pellet could be dipped in the molten flux (Figure 1B). The timing when the NaTaO₃ pellet was dipped was considered as the beginning of temperature holding. NaTaO₃ was pulled up after it was immersed for a certain holding time (Figure 1C). The NaTaO₃ pellet was cooled to 500 °C at a rate of 150 °C h^–1, and then, the pellets were naturally cooled to room temperature in the electric furnace. We found that the NaTaO₃ pellets were scraped but not destroyed after this process. The remaining pellets were weighed, and the solubility was calculated using the following equation:

2

where S is the solubility (mol %), M₁ is the pellet dissolution mole, and M₂ is the flux mole. Moreover, M₁ is equal to the molar change of the NaTaO₃ pellets before and after heat treatment.

Figure 1.

Schematic illustration of the solubility measurement of NaTaO₃ at high temperatures (1100–1500 °C) at procedures (A) before, (B) during, and (C) after immersing the NaTaO₃ pellet in Na₂MoO₄ molten flux.

Results and Discussion

Growth of Single-Phase NaTaO₃ and Fabrication of Its Pellets

Pure NaTaO₃ was required to prepare pure NaTaO₃ pellets; thus, we first examined the synthesis of NaTaO₃ using the solid-phase method, as mentioned in previous studies.^18,19 By changing the mixing ratio of the Na and Ta sources, we synthesized several NaTaO₃ powders at 1000 °C. The XRD patterns of the synthesized NaTaO₃ powders are shown in Figure 2. In the NaTaO₃ powder synthesized with a Na₂CO₃:Ta₂O₅ ratio of 1:1 (run no. 1), the diffraction peaks assigned to NaTaO₃ were observed as the major component. We also observed diffraction peaks attributed to Na₂Ta₄O₁₁ as a Na-poor subphase. By increasing the Na molar ratio such that Na₂CO₃:Ta₂O₅ = 1.05:1 (run no. 2), the XRD peaks attributable to NaTaO₃ were observed as a single phase. A further increase in the Na molar ratio, that is, Na₂CO₃:Ta₂O₅ = 1.1:1 (run no. 3), provided diffraction peaks attributable to Na₃TaO₄ in addition to those of NaTaO₃. We considered that Na atoms were volatilized during heating, leading to a deviation in the ratio of Na and Ta from their initial amounts. As a result, Ta-rich sodium tantalate (Na₂Ta₄O₁₁) was formed under stoichiometric conditions, while pure NaTaO₃ was formed when the Na:Ta ratio was 1.05:1. We also assumed that the Na:Ta molar ratio of 1.1:1 was significantly large as the initial amount, and Na-rich sodium tantalate (Na₃TaO₄) was obtained. This result suggests that the preparation of NaTaO₃ is sensitive to the Na:Ta ratio.

Figure 2.

XRD patterns of the products grown by a solid-state reaction at Na₂CO₃:Ta₂O₅ molar ratios of (a) 1:1 (run no. 1), (b) 1.05:1 (run no. 2), and (c) 1.1:1 (run no. 3). Reference data are shown for comparison: the NaTaO₃ International Centre for Diffraction Data, Powder Diffraction File (ICDD PDF), the Na₂Ta₄O₁₁ ICDD PDF, and the Na₃TaO₄ ICDD PDF.

Next, NaTaO₃ pellets were prepared from the NaTaO₃ powders grown in run nos. 2 and 3 by sintering at 1000 °C. The XRD profiles of these two pellets commonly exhibited only the XRD peaks corresponding to the single phase of NaTaO₃, as shown in Figure S1. Although the NaTaO₃ powder included Na₃TaO₄ when synthesized at a Na₂CO₃:Ta₂O₅ molar ratio of 1.1:1 (run no. 3), the obtained NaTaO₃ pellet was in accordance with pure NaTaO₃ without any impurity phases. This result suggests that Na₃TaO₄ is a less stable phase than NaTaO₃, and Na in Na₃TaO₄ volatilized during sintering to form NaTaO₃.

Solubility Measurements

The solubility of the obtained NaTaO₃ pellets in Na₂MoO₄ flux was measured in the temperature range of 1100–1500 °C, where crystal growth in this flux is expected to be promoted as mentioned in our previous study.¹⁶

Evaporation Amount of Na₂MoO₄ Flux

Na₂MoO₄ evaporation at 1400 and 1500 °C was examined to obtain an accurate flux weight (M₂) in eq 2. After the experiment, the evaporation amounts of 25 g of Na₂MoO₄·2H₂O (according to 21.28 g of Na₂MoO₄) were 0.03 g (0.14 wt %) at 1400 °C and 0.18 g (0.85 wt %) at 1500 °C. Because the evaporation rates at each holding temperature were less than 1 wt %, we ignored the evaporation and considered M₂ as the initial amount of Na₂MoO₄ for the solubility calculations.

Equilibrium Time of the Saturated Solution of NaTaO₃ in Na₂MoO₄

For accurate solubility measurements in fluxes, making a solution to be in equilibrium is necessary, which is in accordance with the saturated solution of NaTaO₃ in the Na₂MoO₄ melt. Thus, we examined the saturation time of NaTaO₃ dissolution in the Na₂MoO₄ flux. Figure S2 shows the immersion time dependence of the solubility of the NaTaO₃ pellet in the Na₂MoO₄ flux at 1400 °C. A NaTaO₃ pellet prepared from NaTaO₃ powder (run no. 2) was used in this experiment. The estimated solubilities at immersion times of 3, 5, and 10 h were 0.75, 0.76, and 0.72 mol %, respectively. Because these values exhibited no drastic change, we concluded that the NaTaO₃ dissolution was already saturated after 3 h. It is known that the time taken to reach soluble equilibrium depends on the diffusion rate of the solute; therefore, longer times are needed at lower temperatures. Considering that 3 h are needed for sufficient immersion at 1400 °C and that the diffusion rate would be lower below this temperature, we thought it reasonable to increase the immersion time to 5 h to ensure saturation at all heating temperatures.

Solubility Curve of NaTaO₃ in Na₂Mo₄ Flux at Each Holding Temperature

The solubility of NaTaO₃ in the Na₂MoO₄ flux was measured at holding temperatures between 1100 and 1500 °C. The immersion time was set at 5 h, which is longer than the saturation time described in the previous section. We used this immersion time because we assumed that it takes longer than 3 h to saturate the solution due to the lower thermal flow of the Na₂MoO₄ melt below 1400 °C. The measured solubility curve of NaTaO₃ is shown in Figure 3. We measured the solubility several times to check the error value and confirmed that the error was less than 5%. Almost no solubility was observed at 1100 °C; however, the solubility of NaTaO₃ gradually increased with increasing holding temperature and finally reached 2.17 mol % at 1500 °C.

Figure 3.

Solubility curve of the NaTaO₃ pellet in the Na₂MoO₄ flux at different holding temperatures between 1100 and 1500 °C. The NaTaO₃ pellet was prepared using the sample from run no. 2.

Solubility Curve of NaTaO₃ in Different Fluxes at Each Holding Temperature

To evaluate the contribution of the fluxes to the solubility, the solubility of NaTaO₃ in other fluxes was also measured. Instead of Na₂MoO₄, Na₂SO₄ and Na₂WO₄ were selected as the fluxes. These compounds are sodium-based oxides with anionic structures similar to those of Na₂MoO₄. From our study,¹⁶ the selected fluxes exhibited lower evaporation amounts than other fluxes, and we considered them suitable to verify the role of flux in this study. Figure 4 shows the solubility curves of NaTaO₃ for each flux after 5 h of immersion. Extrapolation of the solubilities in this temperature region was performed using a polynomial for precise comparison. Here, we used the following function to fit all the solubilities:

3

where S is the solubility of NaTaO₃, T is the heating temperature, and a and b are regression coefficients. The solubility of NaTaO₃ in Na₂WO₄ was 0.76 mol % at 1400 °C, which was similar to that for Na₂MoO₄ (0.77 mol %). However, the solubility at 1500 °C was 1.49 mol %, which was lower than that for Na₂MoO₄ (2.16 mol %). Similarly, the solubility for Na₂SO₄ (0.01 mol %) was the same as that for Na₂MoO₄ (0.04 mol %) at 1100 °C, but it was significantly lower at 1400 °C (0.2 mol %). These results clearly indicate the superior dissolution ability of Na₂MoO₄ as a flux. Generally, the higher the solubility is, the greater the solute availability for crystal growth is. Therefore, a flux with a higher dissolution ability is preferred for the growth of large crystals. Thus, we conclude that Na₂MoO₄ is the most suitable flux for large crystal growth among the three fluxes considered in this study.

Figure 4.

Solubility curves of the NaTaO₃ pellet in Na₂WO₄ and Na₂SO₄ fluxes at holding temperatures between 1100 and 1500 °C. The solubility curve in Na₂MoO₄ flux is also shown for comparison. The NaTaO₃ pellet was prepared from NaTaO₃ powder in run no. 2. The dotted line is an approximation for each flux.

Because the cations of these three fluxes are common, the difference in the anion species (MoO₄, WO₄, and SO₄) contributed to the difference in solubilities of NaTaO₃ in these fluxes. To explain this, we focused on the differences in the ionic character of Ta–O, Mo–O, W–O, and S–O. Equation 4 is used to calculate ionicity (percentage of ionic bonds):

4

where x_A and x_B are the electronegativities of the bimolecular (A–B) bond molecules. By substituting the electronegativity of each element (Ta = 1.50, Mo = 2.16, W = 2.36, S = 2.58, and O = 3.44) into eq 4, we calculated the ionicities of Ta–O, Mo–O, W–O, and S–O, as shown in Table 2. As shown in the table, the ionicity of Mo–O was 33.6%, which is the closest value to that of Ta–O. The similarity in ionicity indicates a similarity in the bonding nature. In other words, similar ionicity should lead to easy dissolution in each other. Therefore, we concluded that one of the factors that determine the difference in the solubility of NaTaO₃ is the similarity of the bonding nature of a bond to that of Ta–O.

Table 2. Calculated Ionicities of the Bonds in the MoO₄, WO₄, and SO₄ Fluxes.

bond	Ta–O	Mo–O	W–O	S–O
ionicity (%)	61.0	33.6	25.3	16.9

Growth of Large NaTaO₃ Crystals Based on Solubility Measurements

Based on solubility measurements, we demonstrated the growth of large NaTaO₃ crystals. The von Weymarn equation for the nucleation rate is shown in eq 5.

5

where V is the nucleation rate, K is a constant, S is the equilibrium solubility of the solute, Q is the solubility of the supersaturated solution, and Q – S is the degree of supersaturation. According to eq 5, the nucleation rate can be reduced by decreasing the degree of supersaturation. In other words, the stable nuclei generated from supersaturation can be suppressed by maintaining the solute concentration near the solubility. Thus, by setting the solute concentration close to the solubility, the reaction field can be optimized to enhance crystal growth rather than nucleation. In the present growth of the NaTaO₃ crystals using the Na₂MoO₄ flux, a solute concentration of approximately 2.17 mol % is suitable for larger crystal growth. In addition, 1300–1500 °C is an important temperature range for effective growth because of the large difference in its solubility in this region. Thus, we expected the following growth conditions to be suitable for growing large NaTaO₃ crystals using the Na₂MoO₄ flux: a holding temperature of 1500 °C, a solute concentration of approximately 2.17 mol %, and a slow-cooling range of 1300–1500 °C. Here, screening experiments were carried out in the range of solute concentration from 1.7 to 2.7 mol % at 1500 °C (run no. 4). As a result, white transparent crystals with well-developed self-shapes were obtained under all experimental conditions. As a representative case, Figure 5a shows an optical photograph of the crystals prepared under the condition where the solute concentration was 2.2 mol %. The crystals exhibited a rectangular plate-like crystal outline. Figure S3 also shows that crystals can be obtained at high frequency with a maximum size of 7.5 × 5.4 mm², which is comparable to that reported in our previous study (8 × 4.7 mm²).¹⁶Figure 5b shows the XRD profiles of the grown NaTaO₃ plate-like crystals. After grinding, the XRD patterns assignable to single-phase NaTaO₃ were confirmed. On the other hand, only the XRD peaks indexed to the (010) and (020) faces were selectively observed for the nonground plate-like crystals. This result indicates the high orientation of the plate face, which corresponds to the b-axis in the single crystal. This crystal morphology has already been reported¹⁶ and is only achieved when the flux method is adopted.

Figure 5.

(a) Optical photograph and (b) XRD patterns of the representative NaTaO₃ crystals grown in the Na₂MoO₄ flux at a solute concentration of 2.2 mol %. The holding temperature and the cooling rate were 1500 °C and 5 °C·h^–1, respectively. Note that this photograph does not display the crystal of maximum size. XRD was measured for the ground sample (powder) and nonground sample (single crystal). A reference XRD profile of NaTaO₃ (ICDD PDF 25-0863) is also shown for comparison. Miller indexes are indicated for the representative peaks.

The mean values of the long and short sides of the 100–200 NaTaO₃ crystals grown at each solute concentration are shown in Figure 6. Through polynomial fitting, we found that both the mean values gradually increased from 1.7 mol % to reach a maximum of approximately 2.2 mol %. At the maximum point, the long- and short-side lengths were 2.44 and 1.25 mm. We also calculated the areas by multiplying these two sides for 100 samples from the maximum value to show the histogram at Figure S4a. D₉₀ was 6.41 mm². In our previous growth study using the Na₂MoO₄ flux, we set the holding temperature and the solute concentration to 1500 °C and 5 mol %,¹⁶ respectively. In this case, the average values were 1.93 and 0.90 mm, respectively. The area distribution is shown in Figure S4b, and D₉₀ was 3.49 mm². These results clearly indicate that the crystal growth guided by the solubility curve achieves large crystals with higher reproducibility. Considering that nucleation can be facilitated by oversaturation, we found that the previous conditions were not suitable for constructing a mild reaction field of dissolution and recrystallization, leading to a less effective growth.

Figure 6.

Solute concentration dependence of averaged long- and short-side lengths of the NaTaO₃ crystals grown in the Na₂MoO₄ flux with a holding temperature of 1500 °C. The dotted lines indicate the fitting curve of each length using polynomial fitting.

The solute concentration at the maximum-size growth was almost identical to the measured solubility at 1500 °C, as shown in Figure 6. The solute concentration dependence of both the sizes can be explained through the relationship between saturation and crystal growth. As mentioned before, it is clear that nucleation generated by supersaturation can be effectively suppressed by growing the solute at a concentration near the solubility. This growth field can lead to an increase in the amount of the solute supplied per crystal nucleus, resulting in the facilitation of the crystal growth. On the other hand, the crystal sizes decreased when the solute concentration differed from 2.2 mol %. At lower solute concentrations, the solute supply from the solution was low. On the higher side, there should be an increase in the undissolved NaTaO₃ particles such that the amount of the solute supplied per crystal decreases. These factors should decrease the growth efficiency.

Finally, we investigated the effect of the cooling rate on the crystal growth in the Na₂MoO₄ flux. We performed the crystal growth of NaTaO₃ in the Na₂MoO₄ flux at a slower cooling rate of 2 °C·h^–1. Here, the growth conditions are as follows: the solute concentrations were 2.2 and 2.3 mol %, which are close to the solubility value (2.17 mol %); the holding temperature was 1500 °C; the temperature region using slow cooling was 1500–1300 °C (see run no. 4 in Table 1). Figure 7 shows the histograms of the mean long-side sizes grown at solute concentrations of 2.2 and 2.3 mol % for the top 100 crystals in each case. For comparison, histograms at a slow-cooling rate of 5 °C·h^–1 are also shown. Statistical information obtained through these histograms is presented in Table 3. At a solute concentration of 2.2 mol %, the crystal sizes were estimated to be 2.31 mm for D₅₀ and 4.23 mm for D₉₀ at a slow-cooling rate of 5 °C·h^–1 (Figure 7a), while they were 2.48 mm for D₅₀ and 4.62 mm for D₉₀ at a slow-cooling rate of 2 °C·h^–1 (Figure 7b). Here, D₅₀ and D₉₀ are the median radius and particle size with a particle ratio of 90% or less, respectively. The average values of the crystal size were also estimated to be 2.61 and 2.98 mm for slow-cooling rates of 5 and 2 °C·h^–1, respectively. A similar tendency was observed when a solute concentration of 2.3 mol % was adopted for the growth (see Figure 7c,d). At a solute concentration and cooling speed of 2.2 mol % and 2 °C·h^–1, respectively, we obtained crystals of over 5 mm diameter more frequently than at other conditions. The increased crystal growth is also confirmed by the statistical values shown in Table 3. We assume that the enhanced size distribution at a slow-cooling rate of 2 °C·h^–1 is due to the uniform supply of the solute in solution to the crystal nucleus. In detail, a decrease in the slow-cooling rate may result in a decrease in the supersaturation rate, which favors the nucleus growth rather than nucleation.

Figure 7.

Histograms of long-side sizes of the NaTaO₃ crystals grown at a solute concentration of 2.2 mol % under slow-cooling rates of (a) 5 and (b) 2 °C·h^–1 and at a solute concentration of 2.3 mol % under slow-cooling rates of (c) 5 and (d) 2 °C·h^–1.

Table 3. Long-Side D₅₀, D₉₀, and the Average Values of the NaTaO₃ Crystals Grown at Solute Concentrations of 2.2 and 2.3 mol % under Cooling Rates of 5 and 2 °C·h^–1a.

indexes in Figure 7	solute concentration (mol %)	cooling speed (°C·h–1)	D50 (mm)	D90 (mm)	average value (mm)
(a)	2.2	5	2.31	4.23	2.61
(b)	2.2	2	2.48	4.62	2.98
(c)	2.3	5	1.93	3.54	2.20
(d)	2.3	2	2.46	4.03	2.79

^aThe indexes are in accordance with those in Figure 7.

Conclusions

In this study, the solubility of NaTaO₃ in the Na₂MO₄ (M = Mo, W, and S) fluxes was measured, and the growth of NaTaO₃ crystals in these fluxes was determined based on the solubility curve. NaTaO₃ pellets were prepared by heat sintering, and the solubility of NaTaO₃ was determined from the change in pellet mass when the pellets were immersed in Na₂MoO₄ flux in the temperature range of 1100–1500 °C. As a result, the solubility of NaTaO₃ in the Na₂MoO₄ flux increased with increasing holding temperature, and it was 2.17 mol % at 1500 °C. Further, the solubilities of NaTaO₃ in fluxes with the same cation were measured to be 1.49 (Na₂WO₄ flux, 1500 °C) and 0.2 mol % (Na₂SO₄ flux, 1400 °C), both lower than that in the Na₂MoO₄ flux. This difference in solubility may be due to the similarity between the ionicities of Ta–O, Mo–O, W–O, and S–O. In our previous study,¹⁶ we discovered an effective flux of Na₂MoO₄ for the growth of milli-order NaTaO₃ crystals. However, there were few guidelines for crystal growth, which limited the yield of milli-order crystals and resulted in reproducibility issues at solute concentrations of 5–10 mol %. In this study, we compiled a crystal growth guideline by recording solubility curves for NaTaO₃ in various molten fluxes, including Na₂MoO₄. This allowed us to find the optimal experimental conditions (a solute concentration of 2.2 mol % and a slow-cooling region at 1300–1500 °C) to construct a saturated reaction field in Na₂MoO₄ flux as a good solvent. As a result, we succeeded in growing milli-order NaTaO₃ crystals with high frequency and good reproducibility.

Knowledge of the solubility obtained through this experiment will be useful for the stable supply of milli-order NaTaO₃ single crystals for physical evaluations and further growth. The difference in the solubility depending on the flux may be an important parameter for clarifying the dissolution mechanism of NaTaO₃ and determining fluxes for the bottom-up enlargement of crystals.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.2c02106.

• XRD patterns of the NaTaO₃ pellets grown by a solid-state reaction at different Na:Ta ratios (Figure S1); immersion time dependence of the solubility of the NaTaO₃ pellet in the Na₂MoO₄ flux at 1400 °C (Figure S2); photograph of NaTaO₃ crystals grown at a solute concentration of 2.2 mol % in Na₂MoO₄ flux with a holding temperature of 1500 °C (Figure S3); histograms of the area of the NaTaO₃ crystals grown at solute concentrations of 2.2 and 5 mol % in the Na₂MoO₄ flux (Figure S4) (PDF)

The authors declare no competing financial interest.