Conversion of Nastrophites to Fibrous Strontium Apatites and Their Crystallographic Characterization

Abstract

Strontium apatite has attracted considerable attention from researchers in various disciplines, including the medical field, owing to its excellent biocompatibility and beneficial effects on enhanced bone regeneration. In addition to their chemical characteristics, morphological aspects of apatite crystals are of great importance because they can exert a significant influence on various biological functions. In this study, a versatile method for the synthesis of fibrous strontium apatite is developed for the first time. Highly crystalline strontium apatite nanofibers were prepared by alkaline hydrolysis of strontium hydrogen phosphate (SrHPO₄) at ambient temperature via nastrophite (NaSrPO₄) intermediates. Some strontium ions in the crystal lattice of strontium hydrogen phosphate were substituted with barium (Ba) ions with various molar ratios up to Ba/Sr = 5/5, and their molar ratios were retained in the final products of the substituted fibrous apatites. The products, including hydrogen phosphates, nastrophites, and apatite nanofibers, were characterized using powder X-ray diffraction (XRD), field emission-scanning electron microscopy (FE-SEM), energy dispersive X-ray spectroscopy (EDS), wavelength dispersive X-ray fluorescence (WDX) analysis, and transmission electron microscopy (TEM) with selected area electron diffraction (SAED). These analyses verified the integrity of the speculated structures of the fibrous apatites. The lattice parameters of apatites and other intermediates were calculated using a newly developed calculation process based on the least-squares method and the results were compared to those of EXPO2014.

1. Introduction

Strontium is one of the trace mineral elements found in our bones that is known to promote bone regeneration. However, its biological role in bone health remains to be determined. On medical fronts, oral administration of strontium ranelate has been effectively prescribed for the treatment of osteoporosis [1,2,3]. The application of strontium ranelate is now expanding to osteoarthritis treatment [4,5,6]. These beneficial effects of strontium ions are based on the mechanism of enhanced bone formation and decreased bone resorption via osteoblast stimulation and osteoclast differentiation inhibition, respectively [7,8,9].

Surface coating of various orthopedic prostheses using strontium apatite is a promising strategy to establish a new generation of artificial implants with therapeutic functions. Recent publications from our laboratory established a novel preparation method for various strontium apatites and their application in surface coatings [10,11,12].

Among the various synthetic routes for the preparation of various types of apatite, conversion of the hydrogen phosphate precursor to the corresponding hydroxyapatite by alkaline hydrolysis has been widely used. For instance, brushite (CaHPO₄·2H₂O)-to-hydroxyapatite conversion [13,14] and monetite (CaHPO₄)-to-hydroxyapatite conversion [15,16,17,18] are among the most frequently utilized wet-chemical syntheses for obtaining hydroxyapatite with excellent purity and controlled morphologies. In our previous study, we treated strontium hydrogen phosphate (SrHPO₄) with alkaline compounds, such as sodium hydroxide, sodium carbonate, and sodium metasilicate, yielding pure strontium apatite, carbonate-substituted strontium apatite, and silicate-substituted strontium apatite, respectively. These methods utilize precursor materials as geometrical templates to design the macroscopic morphology of apatite [15,16,17,18].

The morphological aspects of apatite crystals are also known to play important roles in their physicochemical and biological characteristics, such as protein adsorption [19], cytotoxicity [20], and cellular responses [21,22,23]. Aizawa et al. prepared fiber-shaped hydroxyapatite crystals by heating an octacalcium phosphate precursor at 90 °C for 72 h [22]. This fiber-shaped hydroxyapatite was fabricated as a scaffold for osteoblastic cell culture, and various advantageous effects on cell adhesion, proliferation, and differentiation have been demonstrated [23].

In the present study, fiber-shaped strontium apatite crystals were synthesized, and partial substitution of strontium ions with barium ions was also performed. Since barium is known to act as a muscle stimulant at low concentrations [24] and barium apatite has no cytotoxicity [25], incorporation of barium ions into fibrous strontium apatite might have further beneficial effects on protein adsorption and diagnostic X-ray shielding, among others.

In a recent publication by Boanini et al., various Sr-substituted CaHPO₄ were pre-pared and characterized with superior precision [26]. In their study, strict and accurate crystallographic characterization was performed and highly reliable structural data were reported. However, in various situations encountered daily in the laboratory, the samples to be characterized are frequently of poor quality for analysis and may consist of mixtures of various reaction by-products. This situation makes crystallographic characterization almost impossible to perform. In the context of these circumstances, a convenient method to deduce lattice parameters from a dataset of peak positions associated with proper indexing in a hexagonal system using the least-squares method was recently proposed [10]. In this study, this method was extended to triclinic and monoclinic systems, and its usefulness was examined by applying it to the characterization of some specific reaction products prepared in this study, showing poor resolution and contamination with various impurities, which may usually be unsuitable for conventional XRD analysis.

2. Materials and Methods

All chemicals were purchased from Fujifilm Wako Chemicals (Osaka, Japan).

2.1. Synthesis of SrHPO₄ and Ba-Substituted SrHPO₄

Synthesis of α-SrHPO₄ was carried out by dropwise addition of 250 mL of 1.0 M (NH₄)₂HPO₄ into 500 mL of 0.5 M SrCl₂·6H₂O solution over a period of 1 h at 50 °C under mild stirring at ambient pH conditions. The synthesis of β-SrHPO₄ was carried out in the same manner, except for a reduced reaction temperature of 5 °C. Ba-substituted SrHPO₄ was synthesized using mixed solutions of BaCl₂·2H₂O and SrCl₂·6H₂O with various molar ratios ranging from 1/9 to 5/5 (Ba/Sr ratio). The products were labelled according to the molar ratios of two cations, i.e., SrBa(9/1)HPO₄, SrBa(8/2)HPO₄, SrBa(7/3)HPO₄ and SrBa(5/5)HPO₄, respectively. The reaction was performed at 50 °C, with the exception of SrBa(3/7)HPO₄, which was prepared at 5 °C. The reaction was continued for 2 h after dropwise addition of the (NH₄)₂HPO₄ solution, and the precipitated product was recovered by filtration. The product on the filter was thoroughly washed with distilled water and dried in an oven at 37 °C for seven days.

2.2. Synthesis of Nastrophite Intermediates

At 5 °C under continuous stirring, 0.1 mol of each hydrogen phosphate obtained using the procedure described in Section 2.1 were added to a 200 mL flask and dispersed in 100 mL of distilled water. To this solution, 6 g (0.15 mol) of NaOH dissolved in 30 mL of ice-cooled distilled water was added dropwise over a period of 30 min and kept under mild stirring for an additional 3 h at 5 °C. The product was collected by filtration, washed several times with distilled water, and dried at 37 °C for seven days. All samples were labelled according to the molar ratios of Ba/Sr: NaSrPO₄, NaSrBa(9/1)PO₄, NaSrBa(8/2)PO₄, NaSrBa(7/3)PO₄, and NaSrBa(5/5)PO₄.

2.3. Synthesis of Fibrous Strontium Apatites

Fibrous strontium apatites were prepared directly by the mild alkaline hydrolysis of SrHPO₄ and other Ba-substituted hydrogen phosphates without isolating the corresponding intermediate nastrophites. The procedure is described in Section 2.2. After the addition of NaOH solution at 5 °C, the reaction mixture was left to stand at ambient temperature (22–25 °C) for two weeks. The precipitate was filtered and washed several times with distilled water. The product on the filter was collected, transferred to a flask, washed again with hot water at 75 °C for 30 min, and finally recovered via filtration. The product was dried in an oven at 70 °C for two days. All the samples were labelled according to the molar ratios of Ba/Sr, that is, SrHAP, SrBa(9/1)HAP, SrBa(8/2)HAP, SrBa(7/3)HAP, and SrBa(5/5)HAP, respectively.

2.4. Characterization

Powder X-ray diffraction patterns were collected using a Bruker D8 Discover (Bruker AXS GmbH, Karlsruhe, Germany). Each measurement was performed within a diffraction angle (2θ) range of 10–50°, with a step increase of 0.02° and a scan speed of 2°/min. Cu-Kα radiation with an average wavelength of 0.154184 nm was generated at a tube voltage of 20 kV and tube current of 10 mA.

High-resolution scanning electron microscopy (SEM) images of the Pt-deposited samples were obtained using a field-emission SEM (FE-SEM; JSM-7800F Prime, JEOL, Tokyo, Japan). Transmission electron microscopy (TEM) with selected-area electron diffraction (SAED; JEM-2100F, HRPP, JEOL, Tokyo, Japan) was performed at an acceleration voltage of 200 kV.

Elemental analysis of the products was performed using wavelength dispersive X-ray fluorescence (WDX; ZSX Primus IV, Rigaku, Japan) and energy dispersive X-ray fluorescence (EDS; Octane Plus, Ametek Inc., Berwyn, PA, U.S.A.) attached to a low-vacuum scanning electron microscope (LV-SEM; SU3500; Hitachi High-Tech, Tokyo, Japan).

2.5. Determination of Lattice Parameters

2.5.1. Least-Squares Method (LSM)

Powder XRD patterns were indexed using EXPO2014 [27], and the results were compared with the corresponding standard data supplied either by the Crystallography Open Database (COD) or the Cambridge Crystallographic Data Centre (CCDC). The supplied cif files were visualized using VESTA [28] and the validity of indexing was confirmed by comparing the data obtained by EXPO2014 and VESTA. The validity of the calculated lattice parameters obtained by EXPO2014 was further confirmed by applying them to the well-known equations relating the interplanar distances with the lattice parameters as described later in this section, and the standard deviation (SD) between the observed d(hkl) values and the calculated d(hkl) values was evaluated.

The lattice parameters were also calculated by using the least-squares method described in a previous study [10]. For instance, apatite and nastrophite belong to the hexagonal and cubic systems, respectively. In these cases, the optimized lattice parameters can be obtained directly by optimizing the lattice parameters to minimize the sum of the square of the difference, Q, between $d{\left(hkl\right)}_{obsd}$ and $d{\left(hkl\right)}_{calc}$.

$$Q=\sum {\left(d{\left(hkl\right)}_{obsd}-d{\left(hkl\right)}_{calc}\right)}^2$$

(1)

For the hexagonal (and trigonal) system, the optimized lattice parameters a and c are given by the following equations:

$$a=\sqrt{\frac{a_2^2-a_2{b}_2}{a_2{b}_2-a_3{b}_1}}\hspace{1em}\hspace{1em}c=\sqrt{\frac{a_2}{a_2{b}_2-\frac{a_3}{a^2}}}$$

(2)

where $a_1=\sum x_i^2, a_2=\sum x_i{y}_i, a_3=\sum x_i{z}_i, b_1=\sum y_i^2, b_2=\sum y_i{z}_i$ and $x_i=\frac{4\left(h^2+hk+k^2\right)}{3}, y_i=l^2, z_i=\frac{1}{d_{hkl}^2}$.

Similarly, for a cubic system, the optimized lattice parameter a is given by the following equation:

$$a={\left(\frac{s_1+s_2+s_3}{s_4}\right)}^{0.5}$$

(3)

where

$$x_i=h^2,\hspace{1em}{y}_i=k^2,\hspace{1em}{z}_i=l^2,\hspace{1em}{D}_i=\frac{1}{d_{hkl}^2}$$

$$s_1={\displaystyle \sum }_i{x}_i^2,\hspace{1em}{s}_2={\displaystyle \sum }_i{x}_i{y}_i, s_3={\displaystyle \sum }_i{x}_i{z}_i, s_4={\displaystyle \sum }_i{x}_i{D}_i,$$

The optimized lattice parameters for each hexagonal or cubic system are calculated by Equations (2) and (3), respectively, using the observed values of the d-space and corresponding hkl indices.

2.5.2. Sequential Stepwise Improvement of Standard Deviation (SSISD)

As for α-SrHPO₄, this belongs to the triclinic system, and the application of the least-squares method to obtain all six independent parameters (a, b, c, α, β, γ), whose combination could minimize Q, is virtually impossible. An alternative method to obtain a set of parameters that minimizes Q was developed. In the following explanation, the standard deviation, SD ($=\sqrt{\frac{Q}{N}}$, where N denotes the number of the indexed peaks used for calculation) is chosen instead of Q. Because SD is a function of six parameters, SD (a, b, c, α, β, γ), each of them was sequentially optimized to minimize SD. The initial value of SD₀(a₀, b₀, c₀, α₀, β₀, γ₀) was calculated using the initial set of parameters using the following equation:

$$SD=\frac{\sqrt{\sum {\left(d{\left(hkl\right)}_{obsd}-d{\left(hkl\right)}_{calc}\right)}^2}}{\sqrt{N}}$$

$$\begin{gathered} \frac{1}{d{\left(hkl\right)}_{calc}^2}=\frac{1}{V^2}\{h^2{b}^2{c}^{2}si{n}^2\alpha +k^2{a}^2{c}^{2}si{n}^2\beta +l^2{a}^2{b}^{2}si{n}^2\gamma \\ +2hkab{c}^2\left(\cos \alpha \cos \beta -\cos \gamma \right) \\ +2kl{a}^{2}bc\left(\cos \beta \cos \gamma -\cos \alpha \right) \\ +2hla{b}^{2}c\left(\cos \alpha \cos \gamma -\cos \beta \right)\} \end{gathered}$$

(4)

$$V^2=a^2{b}^2{c}^2\left(1-co{s}^2\alpha -co{s}^2\beta -co{s}^2\gamma +2cos\alpha cos\beta cos\gamma \right)$$

To minimize the value of the SD, the finite difference method was applied. The initial SD₀ can be gradually diminished to a final value of SD_n using the following procedure:

$$\Delta SD\hspace{1em}=\hspace{1em}\Delta S{D}_1\hspace{1em}+\hspace{1em}\Delta S{D}_2\hspace{1em}+\hspace{1em}S{D}_3\hspace{1em}+ \cdots +\hspace{1em}\Delta S{D}_n$$

$$\begin{gathered} S{D}_0-S{D}_n=\left(S{D}_0-S{D}_1\right)+\left(S{D}_1-S{D}_2\right)+\left(S{D}_2-S{D}_3\right) \\ +\dots +\left(S{D}_{n-1}-S{D}_n\right) \end{gathered}$$

Each difference of $\left(S{D}_i-S{D}_{i+1}\right)$ can also be divided into the sum of the differences of the individually (parameter-by-parameter) minimized differences of SD’s.

$$\begin{gathered} \Delta S{D}_{i+1}=S{D}_i\left(a_i,b_i,c_i,{\alpha }_i,{\beta }_i,{\gamma }_i\right)-S{D}_{i+1}\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_{i+1},{\beta }_{i+1},{\gamma }_{i+1}\right) \\ = \left(S{D}_i\left(a_i,b_i,c_i,{\alpha }_i,{\beta }_i,{\gamma }_i\right)-S{D}_i\left(a_{i+1},b_i,c_i,{\alpha }_i,{\beta }_i,{\gamma }_i\right)\right) \\ +\left(S{D}_i\left(a_{i+1},b_i,c_i,{\alpha }_i,{\beta }_i,{\gamma }_i\right)-S{D}_i\left(a_{i+1},b_{i+1},c_i,{\alpha }_i,{\beta }_i,{\gamma }_i\right)\right) \\ +\left(S{D}_i\left(a_{i+1},b_{i+1},c_i,{\alpha }_i,{\beta }_i,{\gamma }_i\right)-S{D}_i\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_i,{\beta }_i,{\gamma }_i\right)\right) \\ +\left(S{D}_i\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_i,{\beta }_i,{\gamma }_i\right)-S{D}_i\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_{i+1},{\beta }_i,{\gamma }_i\right)\right) \\ +\left(S{D}_i\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_{i+1},{\beta }_i,{\gamma }_i\right)-S{D}_i\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_{i+1},{\beta }_{i+1},{\gamma }_i\right)\right) \\ +\left(S{D}_i\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_{i+1},{\beta }_{i+1},{\gamma }_i\right)- \\ S{D}_{i+1}\left(a_{i+1},b_{i+1},c_{i+1},{\alpha }_{i+1},{\beta }_{i+1},{\gamma }_{i+1}\right)\right), \end{gathered}$$

where a_i+1 = a_i ± Δ, a_i ± 2Δ, a_i ± 3Δ, a_i ± 4Δ, ··; b_i+1 = b_i ± Δ, b_i ± 2Δ, b_i ± 3Δ, b_i ± 4Δ, and so on. Because SD is a convex downward function of each parameter, there always exists a numeric optimum for each parameter that minimizes SD, while keeping the other parameters unchanged. The first round of optimization began with the determination of a₁ by observing the variation in the SD caused by a small perturbation of parameter a around the initial value of a₀. This first step was followed by the same processes for the remaining parameters until the final step of determining ${\gamma }_1$ was reached. These six steps in one round were repeated several times until an acceptably small value of SD was obtained.

The overall calculation process is illustrated in Scheme 1.

In the case of β-SrHPO₄, this crystal belongs to the monoclinic system, and the same process was applied using the following equation to calculate the optimum lattice parameters to minimize the value of SD:

$$\frac{1}{d{\left(hkl\right)}_{calc}^2}=\frac{1}{si{n}^2\beta }\left(\frac{h^2}{a^2}+\frac{l^2}{c^2}-\frac{2hlcos\beta }{ac}\right)+\frac{k^2}{b^2}$$

(5)

3. Results

3.1. Synthesis and Characterization of Pure and Ba-Substituted Hydrogen Phosphates

As described in Section 2.1, α-SrHPO₄, and β-SrHPO₄ 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 SrHPO₄ 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 SrHPO₄ 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-SrHPO₄ and β-SrBa(7/3)HPO₄ 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 (BaHPO₄) was separately precipitated from the reaction mixture, and this barium salt was not transformed to the corresponding barium apatite but yielded barium phosphate, Ba₃(PO₄)₂, upon hydrolysis in an alkaline solution.

The products obtained were characterized by powder XRD and analyzed using EXPO2014. Samples of α-SrHPO₄ and α-SrBa(9/1)HPO₄ 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. Summary of crystallographic analyses of α−SrHPO₄ and α−SrBa(9/1)HPO₄.

Lattice	α−SrHPO4			α−SrBa(9/1)HPO4
Parameters	EXPO	SSISD	Lit. [29]	EXPO	SSISD
a (Å)	7.251	7.153	7.184	7.259	7.211
b (Å)	7.188	6.79	6.79	7.228	6.812
c (Å)	6.797	7.222	7.256	6.806	7.268
α (°)	91.27	94.62	94.68	91.11	94.28
β (°)	94.65	104.89	104.97	94.33	105.17
γ (°)	75.01	88.91	88.77	74.86	88.87
V (Å3)	341.1	337.92	340.79	343.73	343.63
Rp’	5.82			7.59
SD	2.71 × 10−1	6.47 × 10−3		2.88 × 10−1	3.21 × 10−3

. 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-SrHPO₄ and α-SrBa(9/1)HPO₄ 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-SrHPO₄ and α-SrBa(9/1)HPO₄ 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 (Δa = +0.058 Å, Δb = +0.022 Å, Δc = +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)HPO₄, β-SrBa(5/5)HPO₄ prepared at 50 °C, and β-SrHPO₄ 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-SrHPO₄ were found to be in fairly good agreement with the published data [26,30], as indicated in

Table 2. Comparison of the results of crystallographic analyses for various β-strontium hydrogen phosphates prepared in this study.

	β−SrHPO4			β−SrBa(8/2)HPO4		β−SrBa(7/3)HPO4		β−SrBa(5/5)HPO4
	EXPO	SSISD	Lit. [30]	EXPO	SSISD	EXPO	SSISD	EXPO	SSISD
a (Å)	10.244	10.240	10.239	10.275	10.297	9.041	10.297	10.37	10.435
b (Å)	7.996	8.001	7.999	8.049	8.075	8.906	8.127	8.145	8.179
c (Å)	9.318	9.328	9.326	9.362	9.369	4.808	9.394	9.494	9.512
α (°)	90	90	90	90	90	90	90	90	90
β (°)	116.8	116.82	116.77	116.93	116.95	102.89	116.66	117.09	116.96
γ (°)	90	90	90	90	90	90	90	90	90
V (Å3)	681.2	682.1	682	690.3	694.4	377.4	702.6	713.9	723.6
Rp’	8.25			9.29		17.77		11.55
SD	2.28 × 10−3	3.65 × 10−5		1.10 × 10−2	8.72 × 10−3	9.95 × 10−1	6.79 × 10−3	1.40 × 10−2	1.30 × 10−3

.

Powder XRD analysis of β-SrBa(7/3)HPO₄ 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-SrHPO₄, 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-SrBaHPO₄ 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)HPO₄, 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 SrBaHPO₄ 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. Summary of elemental analyses of various nastrophites by WDX.

		Na	Ba	Sr	P	O	Ba/(Ba + Sr)	(Ba + Sr)/P
NaSrPO4	calcd	0.140	0.000	0.140	0.140	0.570	0.000	1.000
	obsd	0.060	0.000	0.190	0.140	0.610	0.000	1.357
NaSrBa(9/1)PO4	calcd	0.140	0.010	0.130	0.140	0.570	0.100	1.000
	obsd	0.020	n.d.	0.250	0.130	0.600	n.d.	n.d.
NaSrBa(8/2)PO4	calcd	0.140	0.030	0.110	0.140	0.570	0.200	1.000
	obsd	0.018	n.d.	0.251	0.130	0.601	n.d.	n.d.
NaSrBa(7/3)PO4	calcd	0.140	0.040	0.100	0.140	0.570	0.300	1.000
	obsd	0.102	0.051	0.127	0.131	0.589	0.287	1.359
NaSrBa(5/5)PO4	calcd	0.140	0.070	0.070	0.140	0.570	0.500	1.000
	obsd	0.105	0.078	0.088	0.124	0.605	0.470	1.339

. 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 NaSrPO₄, NaSrBa(7/3)PO₄, and NaSrBa(5/5)PO₄ 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 HPO₄ 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. Comparison of the results of crystallographic analyses for various nastrophites prepared in this study.

	NaSrPO4		NaSrBa(9/1)PO4		NaSrBa(8/2)PO4		NaSrBa(7/3)PO4		NaSrBa(5/5)PO4
	EXPO	LSM	EXPO	LSM	EXPO	LSM	EXPO	LSM	EXPO	LSM
a (Å)	10.54271	10.5478	10.5613	10.5609	10.5618	10.5673	10.6087	10.6087	10.6313	10.6661
V (Å3)	1178.93	1173.51	1178.01	1177.90	1201.61	1180.02	1193.95	1193.95	1201.61	1213.44
SD	5.58 × 10−3	2.70 × 10−3	2.55 × 10−4	2.55 × 10−4	1.29 × 10−2	1.31 × 10−2	2.83 × 10−7	2.83 × 10−7	1.08 × 10−2	1.46 × 10−2
Rp’	8.999		6.840		6.980		8.289		7.901

.

The lattice parameter a was also derived using the peak position (2θ) 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)PO₄, 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)PO₄, 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. Elemental analysis by WDX for various apatite fibers.

Molar Ratio		Ba	Sr	P	O	Ba/(Ba + Sr)	(Ba + Sr)/P
SrHAP	calcd	0.000	0.238	0.143	0.619	0.000	1.667
	WDX	0.000	0.228	0.139	0.633	0.000	1.641
SrBa(9/1)HAP	calcd	0.024	0.214	0.143	0.619	0.100	1.667
	WDX	0.021	0.196	0.132	0.651	0.097	1.647
SrBa(8/2)HAP	calcd	0.048	0.190	0.143	0.619	0.200	1.667
	WDX	0.042	0.174	0.135	0.649	0.194	1.600
SrBa(7/3)HAP	calcd	0.071	0.167	0.143	0.619	0.300	1.667
	WDX	0.068	0.165	0.130	0.638	0.292	1.792
SrBa(5/5)HAP	calcd	0.119	0.119	0.143	0.619	0.500	1.667
	WDX	0.106	0.110	0.129	0.655	0.491	1.674

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 SrBaHPO₄ 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 SrBaHPO₄, 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. Summary and comparison of the lattice parameters for various strontioum apatites prepared in this study.

	SrHAP		SrBa(9/1)HAP		SrBa(2/8)HAP		SrBa(7/3)HAP		SrBa(5/5)HAP
	EXPO	LSM	EXPO	LSM	EXPO	LSM	EXPO	LSM	EXPO	LSM
a (Å)	9.7702	9.7702	9.7971	9.8117	9.8446	9.7883	9.8633	9.8673	9.9200	9.9453
b (Å)	9.7702	9.7702	9.7971	9.8117	9.8446	9.7883	9.8633	9.8673	9.9200	9.9453
c (Å)	7.2816	7.2816	7.2994	7.3462	7.3648	7.3104	7.3812	7.3962	7.4596	7.4560
α (°)	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00
β (°)	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00
γ (°)	120.00	120.00	120.00	120.00	120.00	120.00	120.00	120.00	120.00	120.00
V (Å3)	601.95	601.95	606.76	612.47	618.14	606.58	621.87	623.64	635.72	638.67
Rp’	6.578		9.232		9.223		6.782		8.334
SD	1.31 × 10−6	3.38 × 10−7	8.40 × 10−3	6.08 × 10−3	1.94 × 10−2	4.89 × 10−3	2.79 × 10−3	3.12 × 10−3	4.63 × 10−2	3.30 × 10−3

. 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$\overline{2}$ 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.

4. Discussion

The preparation of strontium hydrogen phosphate in aqueous media is known to produce two different isoforms depending on the reaction temperature [32]. β-SrHPO₄ is thermodynamically more stable than α-SrHPO₄, and upon heating, the α-form transforms into the β-form [33]. Several previous research works described the preparation of β-SrHPO₄ at relatively high temperatures [34,35,36]. However, in a recently published study by Boanini et al., successful preparation of β-SrHPO₄ in an aqueous medium at a low temperature (5 °C) was reported [26]. β-SrHPO₄ selectively precipitates from solution at low temperatures owing to its relatively lower solubility compared to that of α-SrHPO₄ [33]. They studied the effects of the substitution of Sr ions with Ca ions in both α-SrHPO₄ and β-SrHPO₄ structures and found that only 30% of Sr ions were replaced in the β-structure, whereas with the α-structure, complete substitution was possible. In this study, 50% of Sr ions in the β-SrHPO₄ structure were replaced by Ba ions, suggesting that Ba ions might be thermodynamically more stably accommodated in the β-SrHPO₄ crystal lattice than Ca ions.

The formation of fiber-shaped strontium apatite was facilitated by the slow alkaline hydrolysis of nastrophite under mild conditions. The process of fiber formation can be explained by the homogeneous precipitation of apatite crystals from the alkaline solution during the hydrolysis of nastrophite. The lattice parameters of the various strontium apatite fibers prepared in this study were compared with previously published results for various apatites, including hydroxyapatite and barium apatite [10,37,38,39,40,41], and the values of c were plotted against a, as shown in Figure 14. A linear relationship between all apatites was observed, which is consistent with previously published results [10].

The LSM and SSISD calculation methods were developed simply because of their simplicity and ease of use by various researchers who routinely use XRD measurements. The chemical compositions and structures of the materials contained in the samples can be deduced from the information provided by the lattice parameters, and XRD analysis is essential for understanding the various properties of inorganic and organic materials. The simplified calculation methods presented in this paper, such as LSM and SSISD, may aid in resolving various analytical problems associated with the nature of the specific samples to be analyzed.

5. Conclusions

Pure and Ba-substituted fibrous strontium apatites were successfully prepared from hydrogen phosphate precursors via nastrophite intermediates. The process of fiber formation can be explained by the preferential c-axis-oriented crystal growth of apatite during the slow hydrolysis of nastrophite. All the products, including fibrous apatites, their precursors, and intermediates, were characterized by WDX, SEM/EDS, XRD, and TEM-SAED. Their chemical compositions agreed satisfactorily with those calculated composition ratios. The lattice parameters were accurately determined using a newly developed calculation process based on the least-squares method, and the results were compared with those of EXPO2014. Improvements in numeric precision of the lattice parameters were confirmed.