3.1. Synthesis and Characterization of Pure and Ba-Substituted Hydrogen Phosphates
As described in
Section 2.1, α-SrHPO
4, and β-SrHPO
4 were prepared at either 50 °C or 5 °C. The substitution of strontium ions with various ratios of barium ions in both the forms of SrHPO
4 was also investigated. The reaction products were analyzed using XRD, and the results are summarized in
Figure 1. With a relatively small molar ratio of barium ions (Ba/Sr = 1/9), the α-form of hydrogen phosphate was obtained at 50 °C. When Ba ions were introduced into SrHPO
4 with molar ratios between 20% and 50% of the total cations, the β-form preferentially precipitated from the reaction mixture regardless of the reaction temperature. On the other hand, at a reaction temperature of 5 °C, the β-form predominately formed regardless of the molar ratio of substitution of barium ions. As shown in
Figure 1, both β-SrHPO
4 and β-SrBa(7/3)HPO
4 were prepared at 5 °C, whereas the others were prepared at 50 °C. As the molar ratio of barium ions increased, the peak position shifted toward the lower angle side, and the peak width tended to broaden. When the ratio of barium ions exceeded 50% of the total cations, barium hydrogen phosphate (BaHPO
4) was separately precipitated from the reaction mixture, and this barium salt was not transformed to the corresponding barium apatite but yielded barium phosphate, Ba
3(PO
4)
2, upon hydrolysis in an alkaline solution.
The products obtained were characterized by powder XRD and analyzed using EXPO2014. Samples of α-SrHPO
4 and α-SrBa(9/1)HPO
4 were characterized by powder XRD, and the diffraction patterns were analyzed by EXPO2014 using the structural parameters of the triclinic system with space group P-1. However, structural refinement using the Rietveld method was intentionally not performed, and all parameters for the EXPO2014 analysis were set at default values. The results of the powder pattern analysis are shown in
Figure 2a,b. Indexing was performed using N-TREOR, and the obtained
hkl data agreed well with the standard data available in the open database [
29]. However, at this point, the lattice parameters did not agree with the published data, as indicated in
Table 1. With these obtained parameter values, the interplanar distance
d(hkl) was calculated according to Equation (4), as shown in
Section 2.5.2. The calculation results are presented in
Table S1a in the Supplementary Materials. The correlations between
d(calc) and
d(obsd) for α-SrHPO
4 and α-SrBa(9/1)HPO
4 are shown in
Figure 2c,d, respectively. Plots of
d(calc) vs.
d(obsd) give the distribution of scattered points along the approximate line and show an identical pattern for both samples.
Because the indexing itself seemed to be correct, the poor correlations between
d(calc) and
d(obsd) were considered to be caused by errors in calculating the lattice parameters. Refinement of the parameters was attempted using the calculation process of the SSISD described in
Section 2.5.2. Each lattice parameter was optimized stepwise to minimize the standard deviation (SD) between the total set of
d(calc) and
d(obsd) values. The results of the optimization are listed in
Table 1, and the details of the calculations are listed in
Table S1b. In
Figure S1a, a decrease in the SD during the calculation process of the SSISD is shown. Through the repetition of seven cycles of optimization, the value of SD decreased by approximately two digits, and the correlation between
d(calc) and
d(obsd) improved dramatically, as shown in
Figure 2e,f.
As shown in
Figure S1b,c, each parameter was optimized to minimize the SD from the initial value obtained by EXPO2014, and each parameter converged gradually as the SD decreased to a reasonable value compared to the standard data. The same process was repeated with the initial parameters set to the default values of (
a,
b,
c,
α,
β,
γ) = (10, 10, 10, 90, 90, 90). As shown in
Figure S1d,e, irrespective of the values of the initial set of parameters, all the parameters converged to virtually the same values as those previously obtained. This example indicates that appropriate values of the lattice parameters can be obtained solely from the information on the crystal system to which the sample belongs and the dataset of accurate peak positions, each of which should be correctly associated with the Miller index. A comparison of the lattice parameters of α-SrHPO
4 and α-SrBa(9/1)HPO
4 is presented in
Table 1. It is evident from the results that the substitution of strontium ions with barium ions resulted in the expansion of the cell volume (Δ
a = +0.058 Å, Δ
b = +0.022 Å, Δ
c = +0.046 Å) while keeping the cell geometry virtually intact (Δα = −0.34°, Δβ = +0.28°, Δγ = −0.04°). This result seems to be reasonable because the size of the barium ion (1.42 Å) is substantially larger than that of the strontium ion (1.26 Å).
When the molar ratio of substituted barium ions exceeded 20% of the total cation, the crystal form changed to the β-form regardless of the reaction temperature, as shown in
Figure 3. Although the observed XRD patterns were rather noisy and might be inappropriate for any precise characterization, they were analyzed using EXPO2014. The results for each sample of β-SrBa(8/2)HPO
4, β-SrBa(5/5)HPO
4 prepared at 50 °C, and β-SrHPO
4 prepared at 5 °C yielded rational values for each lattice parameter, and a fairly good correlation between interplanar distances was observed in each case. In addition, the lattice parameters obtained for β-SrHPO
4 were found to be in fairly good agreement with the published data [
26,
30], as indicated in
Table 2.
Powder XRD analysis of β-SrBa(7/3)HPO
4 at 5 °C revealed relatively broad peak patterns with low resolution and considerably high background contributions. The analysis by EXPO2014 did not provide any reliable results, as shown in
Figure 4a,b. However, in this case, each peak position could be determined with reasonable accuracy, and the same indexing as that in the other homologues was applied for the calculation process of SSISD, with the results reported later in this section.
To demonstrate the usefulness of the SSISD method in the case of the monoclinic system, optimization of each parameter was executed using the initial set of parameters obtained by EXPO2014 analysis for β-SrHPO
4, as shown for the initial set of parameters and the final results in
Table S2a,b. In
Figure S2a, a decrease in the SD during the calculation process of the SSISD is shown. The convergence of each lattice parameter is shown in
Figure S2b,c.
Although the initial set of the lattice parameters obtained by EXPO2014 analysis gave fairly good results (10.24374, 7.99616, 9.31777, 116.803) when compared to the published data (10.239, 7.9992, 9.326, 116.770), SD was further improved. As a result of optimization, the SD improved from 2.28E-3 to 3.65E-5, and the final set of parameters shown in
Table S2b, (10.24014, 8.00096, 9.32837, 116.8184), was found to be in close agreement with that of the published data [
26,
30]. The same calculation process of SSISD was applied to all the remaining β-SrBaHPO
4 samples, and the results are summarized in
Table 2. As indicated in
Table 2, substantial improvements in the SD were obtained in all cases, and even for β−SrBa(7/3)HPO
4, which could not be analyzed using EXPO2014, a reliable set of lattice parameters with an acceptable SD was obtained.
The results shown in
Table 2 are also plotted in
Figure 5, and simultaneous increments of all the lattice parameters with an increase in barium ion content were observed. The slopes of the increments of
a,
b, and
c are identical, implying that the unit cell has isotropic expansion.
3.2. Synthesis and Characterization of Nastrophites
Each SrBaHPO
4 sample obtained using the procedures described above was dispersed in water with equimolar amounts of sodium hydroxide in an ice-cooled bath. The products were observed using FE-SEM, and the results are summarized in
Figure 6. All products consisted of irregularly shaped large granules accompanied by nanosized particles. The average size of the granules appeared to decrease with increasing barium ion content. All the products were identified as nastrophites by elemental analysis and XRD measurements, as discussed later in this section.
The elemental analysis of each product was performed using WDX, and the results are summarized in
Table 3. The observed fluorescence intensities from Na in the nas-trophites were relatively weak, and at low concentrations of Ba ions in the sample, the detection of Ba failed, possibly due to inadequately small amounts of each sample. Nonetheless, the measurements for NaSrPO
4, NaSrBa(7/3)PO
4, and NaSrBa(5/5)PO
4 were consistent with the calculated values for each of the estimated chemical compositions of anhydrous nastrophites. The powder XRD patterns for all the obtained products are summarized in
Figure 7. All XRD patterns agreed well with the standard data for nastrophite [
31]. Although less contamination with the unreacted starting material of the corresponding HPO
4 was observed in some of the samples, the XRD patterns were virtually identical for all samples and were analyzed using EXPO2014. The output charts after the EXPO2014 analysis are summarized in
Figure S3 and the obtained lattice parameters for each sample were summarized in
Table 4.
The lattice parameter
a was also derived using the peak position (2
θ) data with the associated Miller indices acquired by EXPO2014 analysis using the least-squares technique (LSM) mentioned in
Section 2.5.1, and the results are given in
Table 4. An example of the calculation process is presented in
Table S3. The obtained values of the parameters were in good agreement with those obtained by EXPO2014, except in the case of NaSrBs(5/5)PO
4, where the discrepancy between them was not negligible. Because the calculation of lattice parameters by LSM uses only the values of peak positions and once the accurate values are determined, there is no possibility of calculation errors. In this particular sample, the peak separation and baseline settings were both reasonably well processed, and the lattice parameters obtained by LSM should be reliable.
Lattice parameter
a is plotted against the molar ratio of barium ions in the nastrophite crystals in
Figure 8. The LSM calculation revealed a fairly good linear relationship between
a and the molar ratio of Ba except for NaSrBa(8/2)PO
4, which may have originated from the defective crystal structure of this particular sample.
3.3. Synthesis and Characterization of Fibrous Strontium Apatites
The reaction mixture in nastrophite synthesis was left to stand at ambient temperature (22–25 °C)for two weeks, and during this period of reaction time, small quantities of the precipitated product were intermittently collected from each reaction mixture and analyzed by XRD measurement. In the initial stage of the reaction, the precipitated product consisted solely of nastrophite, which was gradually converted to nastrophite. One week after initiation of the reaction, the product was a mixture of equal amounts of nas-trophite and apatite. Two weeks after the start of the reaction, the precipitated product consisted solely of apatite, with no trace of nastrophite.
The morphologies of the reaction products were analyzed using FE-SEM, and the fibrous structures of the products were observed, as shown in
Figure 9. The discovered fibrous architectures were minimally affected by the chemical composition of apatite, and as the molar ratio of barium ions increased, the length of the fibers tended to decrease, while their diameters increased.
Elemental analysis was conducted using both WDX and SEM/EDS, and the results are summarized in
Table 5 and
Figure S4, respectively. The observed chemical compositions for all apatite samples agreed well with the calculated values based on the estimated chemical compositions. Despite the drastic chemical and morphological changes during the course of the reaction, the ratio of the initially introduced barium ions in SrBaHPO
4 synthesis retained its nominal value to the final product of apatite.
The changes in the chemical composition during the transformation from hydrogen phosphates to apatites via nastrophite intermediates were also studied using SEM/EDS measurements, and the results are shown in
Figure 10. The initial molar ratios of Ba/Sr were retained in the final products of the substituted apatites
The powder XRD patterns are shown in
Figure 11. Except for pure SrHAP, all the other samples contained small amounts of β-form of the corresponding SrBaHPO
4, which were derived from the unconverted nastrophite intermediates. These impurities could be removed from the apatites by heating the solution of the reaction mixture at the end of the reaction process before filtration.
The results of the crystallographic analysis for all the apatites prepared in this study are summarized in
Table 6. The powder XRD patterns were analyzed using both EXPO2014 and LSM and the output charts of EXPO2014 analyses and an example showing the calculation process of LSM are shown in
Figure S5 and
Table S4, respectively. The lattice parameters are plotted against the ratio of the substituted barium ions in
Figure 12. A linear relationship was observed between the lattice parameters a, c, and barium ion content. Furthermore, except for SrBa(8/2)HAP, the values of the lattice parameters obtained from both EXPO2014 and LSM agreed well. Although the SD obtained by LSM for SrBa(8/2)HAP improved by one order of magnitude from the value of SD based on the values from EXPO2014, discrepancies in lattice parameters between those obtained by EXPO2014 and those obtained by LSM for this particular sample, SrBa(8/2)HAP, were not negligible, and the deviation from the approximate line for the point given by the LSM results may have originated from the defective crystal structure of this particular sample.
The precise crystalline structure of the fibrous SrHAP sample was further analyzed using TEM-SAED, as shown in
Figure 13. Each of the sharply defined diffraction spots was related to the corresponding
hkl plane, and the line connecting 002 and 00
was found to be parallel to the direction of the extended axis of the fiber. These observations indicate that, the strontium apatite fibers were oriented along the
c-axis direction.