Crystal structures, phase transitions and thermal expansion properties of NaZr2(PO4)3–SrZr4(PO4)6 solid solutions

Ying Liua, Maxim S. Molokeevbcd, Quanlin Liua and Zhiguo Xia*a
aThe Beijing Municipal Key Laboratory of New Energy Materials and Technologies, School of Materials Sciences and Engineering, University of Science and Technology Beijing, Beijing 100083, China. E-mail: xiazg@ustb.edu.cn; Fax: +86-10-82377955; Tel: +86-10-82377955
bLaboratory of Crystal Physics, Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk 660036, Russia
cSiberian Federal University, Krasnoyarsk, 660041, Russia
dDepartment of Physics, Far Eastern State Transport University, Khabarovsk, 680021, Russia

Received 10th December 2017 , Accepted 10th January 2018

First published on 15th January 2018


Crystal structure evolution and temperature-dependent phase transition of solid solutions are much desired for the understanding of the optimization of functional properties. Herein, the NASICON-type NaZr2(PO4)3–SrZr4(PO4)6 solid solutions with the formula Na(2−2x)Srx[ ]xZr4(PO4)6 (0 ≤ x ≤ 1), where [ ] represents the vacancy, were prepared by the sol–gel method, and their crystal structures, phase transitions and thermal expansion properties were investigated in detail. In the range of x = 0.3–0.35, there is a reversible structural phase transition R[3 with combining macron]cR[3 with combining macron] and the different structural models of the R[3 with combining macron] phase and R[3 with combining macron]c phase were built to better understand the phase transition mechanism. We determined the phase transition boundary between the R[3 with combining macron]c and R[3 with combining macron] structures and predicted the phase transition temperature of Na(2−2x)Srx[ ]xZr4(PO4)6 with any x for further investigation of controlled physical properties. The results indicated that Na0.5Sr0.75[ ]0.75Zr4(PO4)6 showed a near zero thermal expansion in the temperature range of 450–600 K, which can find potential applications.


1 Introduction

Remarkable progress in different fields of science and technology is boosting the discovery of new solid state materials with optimized functional properties.1–3 And investigations based on the crystal structure and temperature-dependent phase transition of new solid solutions are very important for the studies of physical properties, such as photoluminescence properties,4–8 electrical properties9–13 and thermal expansion,14–19 especially for inorganic solid state compounds with an open-framework structure. The NASICON structure is among those and consists of a rigid three-dimensional framework of (PO4)/(SiO4) tetrahedra sharing common corners with MO6 octahedra and containing interstitial ions, including alkali and alkaline earth metal ions, located in a three-dimensionally linked interstitial space.20 As for the NASICON structures, the fast Li-ion conductor lithium zirconium phosphate LiZr2(PO4)3 has been studied for fast-ionic conductivity. For example, Al doped LiZr2(PO4)3 has been reported for the stability of the highly conducting rhombohedral phase, a decrease in the intensity of impurity phase and an increase in the Li-ion concentration with Al doping, which finally results in a high total Li-ion conductivity;21 sodium scandium phosphate Na3Sc2(PO4)3 has been reported for the pronounced luminescence property. For example, Im's group reported an Na3–2xSc2(PO4)3:xEu2+ phosphor that showed blue emission and did not exhibit thermal quenching even up to 200 °C.22 NaZr2(PO4)3 family compounds have been studied to evaluate the thermal expansion and, for example, it has been reported that Pb2/3FeZr(PO4)7/3(SO4)2/3 possessed a low thermal expansion with the average linear coefficient of thermal expansion αav = 1.7 × 10−6 °C−1 in the temperature range from −120 to 200 °C.23

Among the NASICON-type solid state compounds, NaZr2(PO4)3 and SrZr4(PO4)6, both of which belong to the NaZr2(PO4)3 (NZP) family, crystallize in rhombohedral structures but with space groups R[3 with combining macron]c and R[3 with combining macron], respectively. The NZP family ceramics have drawn considerable attention due to their interesting properties, including anisotropic thermal expansion,24–26 high ionic conductivity,27,28 and being hosts for the immobilization of nuclear waste.29,30 From a previous report, the interstitial ions in the structure play an important role in the thermal expansion of the NZP family ceramics: larger ionic radii or fewer interstitial ions result in lower thermal expansion and some solid solutions in the NZP family are expected to be candidates for structural materials.31 Although several groups have investigated the thermal properties and crystallographic structures of a wide variety of the NZP family ceramics from room temperature (RT) to 1000 °C,32–35 studies have seldom been focused on structural phase transformations of the NZP family of solid solutions which is closely related to negative thermal expansion.36

In this investigation, we designed and synthesized the nominal Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0, 0.25, 0.3, 0.35, 0.5, 0.75, and 1) solid solutions, where [ ] represents the vacancy, by the sol–gel method and the samples were mainly characterized by in situ variable temperature powder X-ray diffraction (VT-XRD). The structures, phase transitions and thermal expansion were explored in detail. In the present work, the phase transition boundary between the R[3 with combining macron]c and R[3 with combining macron] structures in the NaZr2(PO4)3–SrZr4(PO4)6 solid solutions has been identified for intermediate x, which can help one to further explore controlled physical properties in the NASICON-type compound family.

2 Experimental section

2.1 Materials and synthesis

A series of Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0, 0.25, 0.3, 0.35, 0.5, 0.75, and 1) compounds were prepared by the sol–gel method37–39 from NaNO3 (A. R., Aladdin), ZrOCl2·8H2O (A. R., Aladdin), NH4H2PO4 (A. R., Aladdin), and Sr(NO3)2 (A.R., Aladdin). Briefly, NaNO3, Sr(NO3)2, and ZrOCl2·8H2O were dissolved in distilled water, and, then, the NH4H2PO4 aqueous solution was slowly added to the first solution with continuous stirring. At room temperature, the resulting mixture was in the viscous slurry form which was heated at 80 °C for 1 h for gelation. The resulting gel was dried at 150 °C for 4 h, ground, calcined at 700 °C for 6 h, and then finally sintered at 1100 °C for 5 h in a tube furnace. After cooling the furnace to room temperature, the samples were ground into fine powders for subsequent characterization.

2.2 Characterization

The samples of Na(2−2x)Srx[ ]xZr4(PO4)6 with different compositions were characterized using a D8 Advance X-ray diffractometer (XRD, Bruker Corporation, Germany) operating at 40 kV and 40 mA with monochromatized CuKα radiation (λ = 1.5406 Å). The scanning rate (2θ range of 10° to 60°) for phase identification was fixed at 8° min−1 and the step size of 2θ was 0.013° and the counting time was 5 s per step for Rietveld analysis. Crystal structure solving and Rietveld refinements were performed using TOPAS 4.2 software.40 The energy-dispersive X-ray spectroscopy (EDS) and mapping measurements of the selected sample NaSr0.5[ ]0.5Zr4(PO4)6 were performed at room temperature using a scanning electron microscope (SEM, JEOL JSM-6510). Additional X-ray diffraction (XRD) patterns were recorded for Na0.5Sr0.75[ ]0.75Zr4(PO4)6 and NaSr0.5[ ]0.5Zr4(PO4)6 powder samples under heating in the range of 298–1073 K in order to obtain cell parameters dependent on temperature and find the phase transition temperature and thermal expansion properties. The in situ variable temperature powder X-ray diffraction (VT-XRD) data were collected on an X′Pert MRD diffractometer with a high-temperature reactor chamber (AntonPaar XRK 900) attached.

3 Results and discussion

3.1 Composition dependent phase transition analysis

Fig. 1a presents the XRD patterns of Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0, 0.25, 0.3, 0.35, 0.5, 0.75, and 1) solid solutions. Furthermore, the XRD patterns were analyzed by Rietveld refinement with difference Rietveld plots (ESI Fig. S1), and the refined crystallographic information files are provided in the ESI. All refinements are stable and give low R-factors (Table 1 and Fig. S2). The coordinates of atoms and main bond lengths are given in Tables 1S and 2S, respectively. The main parameters of processing and refinement results are presented in Table 1, and the crystallographic information files (CIF) of these samples are given in the ESI. The results indicate that compounds with x = 0 and x = 1 are well indexed by rhombohedral unit cells with parameters close to those of NaZr2(PO4)3 (R[3 with combining macron]c)41 and SrZr4(PO4)6 (R[3 with combining macron]),42 respectively. Therefore, there should be a phase transition boundary R[3 with combining macron]cR[3 with combining macron] anywhere in the range of x = 0–1. In the pattern of the sample with x = 1 (R[3 with combining macron]), two strong peaks (0 0 3) and (1 0 1) are found (the marked region in Fig. 1a and b), which should be absent in the phase x = 0 (R[3 with combining macron]c) due to the extinction rule: (h 0 l), l = 2n + 1. By careful checking of the appearance of these peaks, we can suggest the existence of the phase transition R[3 with combining macron]cR[3 with combining macron] in the narrow range of x = 0.3–0.35 (Fig. 1b). Therefore, the crystal structure of NaZr2(PO4)3 (R[3 with combining macron]c) was taken as the starting model for the Rietveld refinement of the patterns recorded for x = 0, 0.25 and 0.3, while the crystal structure of SrZr4(PO4)6 (R[3 with combining macron]) was taken for the Rietveld refinement of the patterns obtained for x = 0.35, 0.5, 0.75 and 1. However, some difficulties arose with the structural models of x = 0.35, 0.5, and 0.75. In the SrZr4(PO4)6 structure, there is only one Sr site which can be occupied by Sr/Na, but, in this case, the chemical formula can be written as Na(1−x)SrxZr4(PO4)6 which does not satisfy the charge balancing and is inconsistent with the composition Na(2−2x)Srx[ ]xZr4(PO4)6 due to a lack of Na ions. Hence, the crystal structure of the R[3 with combining macron] phase should have an additional site occupied by (1 − x) Na ions. The morphology of the selected sample NaSr0.5[ ]0.5Zr4(PO4)6 was studied by SEM analysis (Fig. 2a); relatively uniform crystalline particles were found. Also, the EDS elemental mapping technique was used to test the composition uniformity in Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0.5), as shown in Fig. 2b–f. It is evident that Na, O, P, Sr and Zr are homogeneously distributed over the as-obtained particles.
image file: c7qi00782e-f1.tif
Fig. 1 (a) Powder XRD patterns of various members of the solid solution Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0, 0.25, 0.3, 0.35, 0.5, 0.75, and 1). With an increase in x, the R[3 with combining macron] phase appears gradually which is marked by the blue dashed arrows. (b) The selected diffraction peaks from 10° to 22° of powder patterns of Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0, 0.25, 0.3, 0.35, 0.5, 0.75, and 1) which are marked by a black oval in (a). The appearance of structural peaks (0 0 3) and (1 0 1) at x = 0.35 reveals the phase transition boundary R[3 with combining macron]cR[3 with combining macron] (also written as R[3 with combining macron]cR[3 with combining macron] hereafter and in the figure) between x = 0.3 and x = 0.35.

image file: c7qi00782e-f2.tif
Fig. 2 SEM image (a) of Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0.5) along with EDS elemental mapping for different elements, Na (b), O (c), P (d), Sr (e) and Zr (f).
Table 1 Main parameters of processing and refinement of the Na(2−2x)Srx[ ]xZr4(PO4)6 sample
x xrefined Chemical formula Sp. gr. Cell parameters Z Rwp, Rp (%), χ2 RB, %
0 0 NaZr2(PO4)3 R[3 with combining macron]c a = 8.80898 (7) Å 2 9.17 1.96
c = 22.7706 (2) Å 6.73
V = 1530.23 (3) Å3 1.55
0.25 0.13(2) Na1.5Sr0.25[ ]0.25Zr4(PO4)6 R[3 with combining macron]c a = 8.8035 (1) Å 2 9.87 2.11
c = 22.8502 (3) Å 7.11
V = 1533.66 (5) Å3 1.67
0.3 0.15(2) Na1.4Sr0.3[ ]0.3Zr4(PO4)6 R[3 with combining macron]c a = 8.7949 (2) Å 2 11.12 2.37
c = 22.9068 (6) Å 8.11
V = 1534.47 (8) Å3 1.88
0.35 0.14(1) Na1.3Sr0.35[ ]0.35Zr4(PO4)6 R[3 with combining macron] a = 8.7926 (2) Å 2 10.52 2.67
c = 22.9186 (5) Å 7.85
V = 1534.47 (7) Å3 1.78
0.5 0.30(1) NaSr0.5[ ]0.5Zr4(PO4)6 R[3 with combining macron] a = 8.7714 (3) Å 2 12.84 3.88
c = 23.058 (1) Å 9.77
V = 1536.3 (1) Å3 2.18
0.75 0.645(8) Na0.5Sr0.75[ ]0.75Zr4(PO4)6 R[3 with combining macron] a = 8.7417 (2) Å 2 9.83 2.49
c = 23.2083 (5) Å 7.51
V = 1535.91 (6) Å3 1.60
1 1 SrZr4(PO4)6 R[3 with combining macron] a = 8.70925 (5) Å 2 7.94 2.18
c = 23.3371 (2) Å 5.89
V = 1532.99 (2) Å3 1.35


To further elucidate the crystal structure and composition dependent phase transition, the Fourier difference map FobsFcalc which represents a difference electron density for the Rietveld refinement of structure with x = 0.75 (Fig. 3) was depicted. The map indicates a noticeable maximum at (0 0 1/2) and other symmetry-related sites. It should be noted that namely this site is also occupied by Na+ ions in NaZr2(PO4)3 (R[3 with combining macron]c); however, the SrZr4(PO4)6 (R[3 with combining macron]) compound has no Sr2+ ions in this site. Therefore, to provide linear evolution from Na(1−x)SrxZr4(PO4)6 (x = 0.35) to SrZr4(PO4)6 (x = 1), it was decided to refine only (1 − x) Na in this site for all compounds with x = 0.35, 0.5, and 0.75. Moreover, the (0 0 0) and (1/2 0 0) sites should differ in the R[3 with combining macron] phase and, as it seems, they should not be occupied by Sr/Na simultaneously. So, finally, the structure of the R[3 with combining macron] phase has two sites: (1) (0 0 0) occupied by (1 − x) Na and (x) Sr and (2) (0 0 1/2) occupied by (1 − x) Na and (x) vacancy. The structural model of the R[3 with combining macron]c phase has only one site Sr/Na which was occupied by (1 − x) Na, (x/2) Sr and (x/2) vacancy.


image file: c7qi00782e-f3.tif
Fig. 3 Fourier difference map of Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0.35) with a maximum at (0 0 1/2) and some other symmetry related points which are marked by blue arrows. All these sites in the R[3 with combining macron] phase should be occupied by (1 − x) Na+ ions and (x) vacancy.

Based on the refinement results, the dependences of cell parameters of Na(2−2x)Srx[ ]xZr4(PO4)6 on x (Sr2+ concentration) are shown in Fig. 4, which reveals two interesting features. Firstly, the cell parameter a (Fig. 4a) and c (Fig. 4b) have a fracture at x ∼ 0.33, which is in good agreement with the phase transition R[3 with combining macron]cR[3 with combining macron] previously found in the narrow range of x = 0.3–0.35 using the analysis of (0 0 3) and (1 0 1) reflection intensities. Secondly, with an increase in the Sr2+ concentration (x), the cell parameter a decreases (Fig. 4a), while c increases (Fig. 4b). Such a behavior leads to the nonlinear cell volume (V) dependence on the Sr2+ concentration (x) (Fig. 4c) and, even in the range of x = 0.7–1, V decreases with an increase in x despite the fact that the ion radius of Sr2+ (CN = 6, 1.18 Å) is larger than that of Na+ (CN = 6, 1.02 Å). Therefore, we can speculate the existence of a negative thermal expansion (NTE) effect in the compounds Na(2−2x)Srx[ ]xZr4(PO4)6 at x = 0.7–1. It should be noted that the refined values of x are slightly smaller than the expected ones (Table 1 and Fig. 4d); so the real concentration interval of such NTE compounds can be 0.5–1 instead of 0.7–1. Anyway, the expected and refined values of Sr concentrations are comparable and the overall increase trend in the Sr2+ concentration is consistent (Fig. 4d).


image file: c7qi00782e-f4.tif
Fig. 4 Dependences of cell parameters (a) a, (b) c and (c) cell volume V per x. (d) Dependence of the refined value xrefined of the Sr concentration in the compounds Na(2−2x)Srx[ ]xZr4(PO4)6 per suggested concentration x. Ideally, all points should lie in the straight line which is depicted by the dashed line in Fig. 4(d). In our case, there is some deviation from the suggested chemical formula, but the overall trend of the Sr concentration increase is the same.

Theory group investigation of the phase transition R[3 with combining macron]cR[3 with combining macron] using the ISODISTORT program43 revealed that the transformation can be described by the emergence of instability at the (0 0 0) k7-point (Γ) of the Brillouin zone of the high-symmetry R[3 with combining macron]c unit cell (hereinafter the designation of irreducible representations (irrep) and points of the Brillouin zone are given in accordance with reference books).44,45 The Γ2+ irrep drives this phase transition, and the transformation can be written as image file: c7qi00782e-t1.tif, where η is the critical order parameter. The analysis presents that this irrep allows a continuous phase transition and, indeed, there is no jump of cell volume or cell parameters when the phase transition occurs (Fig. 4a–c). It should be noted that the phase transition leads to charge ordering and splitting of positions. For example, the Na site in the R[3 with combining macron]c structure splits into two sites for the R[3 with combining macron] phase: Na1 at the (0 0 0) site and Na2 at the (0 0 1/2) site. Namely, these two sites were suggested during building the structural model of Na(2−2x)Srx[ ]xZr4(PO4)6 in the R[3 with combining macron] phase though the pure SrZr4(PO4)6 (R[3 with combining macron]) has only one filled site (0 0 0) and one vacancy site (0 0 1/2).

Taking into account all obtained information, we can build a model of structural transformation for NaZr2(PO4)3 doped with Sr2+ ions (Fig. 5). The compound NaZr2(PO4)3 crystallizes in the R[3 with combining macron]c group with only one Na site in the asymmetric part of the unit cell. Low Sr2+ concentration in the range of x = 0–0.3 doesn't lead to space group changing and only the ionic replacement (2Na+ ↔ Sr2+ + vacancy) happens. The higher Sr2+ concentration level leads to the phase transition and the Na site splits into two cation sites. The Na1 site is occupied by (1 − x) Na and (x) Sr ions, while the Na2 site is occupied by (1 − x) Na and, so, again the replacement scheme (2Na+ ↔ Sr2+ + vacancy) is valid. The vacancy part in the Na2 site increases with an increase in x up to total disappearance of any ion in this site at x = 1 (Fig. 5).


image file: c7qi00782e-f5.tif
Fig. 5 Crystal structure modification from Na2Zr4(PO4)6 to SrZr4(PO4)6 through Na(2−x)Srx[ ]x(PO4)6. Phase transition R[3 with combining macron]cR[3 with combining macron] with charge ordering and splitting of positions happens in the range of x = 0.3–0.35.

3.2 Temperature dependent phase transition and thermal expansion property

In order to prove the existence of NTE in these compounds, the temperature dependent XRD patterns of two representative powder samples, NaSr0.5[ ]0.5Zr4(PO4)6 (Fig. S1) and Na0.5Sr0.75[ ]0.75Zr4(PO4)6 (Fig. S2), were measured and they are given in the ESI. Some interesting facts were revealed in this investigation. First of all, the measurements made for the sample x = 0.5 clearly show that the cell parameter a decreases under heating (Fig. 6a), with the coefficients of thermal expansion (CTE) −3.0 × 10−5 K−1 (R[3 with combining macron]) and −2.1 × 10−5 K−1 (R[3 with combining macron]c) (298–1073 K), which proves the linear negative thermal expansion in this crystallographic direction. Comparatively, the sample x = 0.75 shows the cell parameter a decreasing in (NTE) the range of 300–450 K, near zero thermal expansion (ZTE) in the range of 450–600 K and, at higher temperatures, the cell parameter a increasing with the coefficient of thermal expansion varied from −6.4 × 10−6 to 3.1 × 10−6 K−1 (298–1073 K) (Fig. 7a). Such behavior is extremely unusual and near zero thermal expansion is a very useful property because ceramics of this composition will be less strained under heating/cooling which leads to a good mechanical feature. It should be noted that the point x = 0.75 is in close vicinity to the point corresponding to the maximum of the V(x) curve (Fig. 4c). Thus, one can suppose that the Sr2+ concentration (x) at which the compounds have such an unusual property can be located near this maximum, i.e. x = 0.6–0.8.
image file: c7qi00782e-f6.tif
Fig. 6 Temperature dependences of (a) cell parameter a; (b) cell parameter c; (c) cell volume V and (d) net area of the superstructure peak (101) of Na(2−2x)Srx[ ]xZr4(PO4)6, x = 0.5.

image file: c7qi00782e-f7.tif
Fig. 7 Temperature dependences of (a) cell parameter a; (b) cell parameter c; (c) cell volume V and (d) net area of the superstructure peak (101) of Na(2−2x)Srx[ ]xZr4(PO4)6, x = 0.75.

Secondly, it can be seen that NaSr0.5[ ]0.5Zr4(PO4)6 has a phase transition R[3 with combining macron]cR[3 with combining macron] upon heating at T ∼ 700 K, because the intensity of the superstructure peak (101) becomes zero (Fig. 6d) and all cell parameters and the cell volume possess jumps at this temperature (Fig. 6a–c). Thus this transition cannot be of the second order type. The Na0.5Sr0.75[ ]0.75Zr4(PO4)6 sample has no phase transition in the temperature region of 25–800 °C (Fig. 7a–d), but the extrapolation presents that the intensity of the superstructure peak (101) should become zero at ∼1100 K (Fig. 7d). It should be noted that the sample Na(2−2x)Srx[ ]xZr4(PO4)6 (x ∼ 0.32) should have such a phase transition at room temperature T ∼ 300 K (Table 1 and Fig. 4a–c), and all the three points (x = 0.32, T = 300 K), (x = 0.5, T = 700 K), and (x = 0.75, T = 1100 K) lie on one straight line (Fig. 8). This line is the phase transition boundary between R[3 with combining macron]c and R[3 with combining macron] and it can provide us the means for prediction of the phase transition temperature in Na(2−2x)Srx[ ]xZr4(PO4)6 with other x.


image file: c7qi00782e-f8.tif
Fig. 8 Linear increase of the phase transition temperature with an increase in Sr concentration x.

4 Conclusion

In summary, we have designed and synthesized the NASICON-type Na(2−2x)Srx[ ]xZr4(PO4)6 (0 ≤ x ≤ 1) solid solutions by the sol–gel method and studied the crystal structures, thermal expansion properties and phase transitions of samples using XRD techniques. Notably, the ZTE property is achieved in Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0.75) in the temperature range of 450–600 K. In the range of x = 0.3–0.35, there is a structural phase transition R[3 with combining macron]cR[3 with combining macron]. The structure of the R[3 with combining macron] phase has two sites: (0 0 0) occupied by (1 − x) Na and (x) Sr and (0 0 1/2) occupied by (1 − x) Na and (x) vacancy, while the structural model of the R[3 with combining macron]c phase has only one site Sr/Na which was occupied by (1 − x) Na, (x/2) Sr and (x/2) vacancy. In the temperature range of 298–1073 K, the CTE of NaSr0.5[ ]0.5Zr4(PO4)6 was −3.0 × 10−5 K−1 (R[3 with combining macron]) and −2.1 × 10−5 K−1 (R[3 with combining macron]c), while Na0.5Sr0.75[ ]0.75Zr4(PO4)6 exhibited a near zero thermal expansion in the range of 450–600 K and the CTE ranges from −6.4 × 10−6 to 3.1 × 10−6 K−1 (298–1073 K) which suggests their potential application as specific structural materials. Finally, we determined the phase transition between the R[3 with combining macron]c and R[3 with combining macron] structures and predicted the phase transition temperature of Na(2−2x)Srx[ ]xZr4(PO4)6 at arbitrary x.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The present work was supported by the National Natural Science Foundation of China (Grants 91622125, 51722202 and 51572023) and the Natural Science Foundations of Beijing (2172036), and M. Molokeev acknowledges support of the Russian Foundation for Basic Research (17-52-53031).

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Footnote

Electronic supplementary information (ESI) available: The crystallographic information files (CIF) of Na(2−2x)Srx[ ]xZr4(PO4)6 (x = 0, 0.25, 0.3, 0.35, 0.5, 0.75, and 1), and the high temperature (50–800 °C) dependent XRD patterns and the composition dependent Rietveld refinements of some mentioned samples, coordinates of atoms and main bond lengths of some mentioned compounds. See DOI: 10.1039/c7qi00782e

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