1. Introduction

The increasing need to harvest energy from fluctuating energy sources has placed energy storage into a central position for future energy technology scenarios. In the case of large-scale stationary energy storage, sodium batteries seem to have advantages in comparison to lithium batteries in terms of production costs ^[1] due to the abundant availability of sodium and in terms of long-standing experience with large battery systems ^[2,3]. To date, in all sodium battery systems Na⁺-ß''-alumina has been employed for the solid electrolyte membrane. This is insofar surprising, as the processing of ß''-alumina to ceramic tubes is more elaborate, sophisticated and energy-consuming due to the high sintering temperatures ^[4] than for the only existing alternative: ceramics in the Na₂O-P₂O₅-SiO₂-ZrO₂ system. Although these materials have been known since 40 years ^[5,6], to our knowledge there has never been a technological approach to replace ß''-alumina in sodium batteries apart from a very recent comparison of a ZEBRA battery cells ^[7]. Since Na₂O-P₂O₅-SiO₂-ZrO₂ ceramics can be processed at lower temperatures and have higher ionic conductivity ^[8] leading to lower internal cell resistance and the possibility of reducing the operating temperature of ZEBRA batteries ^[7], they are serious candidates for an engineering development integrating them into large batteries. However, reviewing the available literature on these materials in the recent decades reveals that the chemistry of the Na₂O-P₂O₅-SiO₂-ZrO₂ system appears to be rather complex, fragmented and sometimes even contradictory. In the present work, we do not only summarize existing knowledge, but also try to harmonize the individual results.

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2. Ternary and Quaternary Compounds

The Na⁺ super-ionic conductor (NASICON) Na₃Zr₂Si₂PO₁₂ belongs to the solid solution ^[5].

${\rm{N}}{{\rm{a}}_{1 + {\rm{x}}}}{\rm{Z}}{{\rm{r}}_{\rm{2}}}{\rm{S}}{{\rm{i}}_{\rm{x}}}{{\rm{P}}_{3 - {\rm{x}}}}{{\rm{O}}_{12}}\;\;{\rm{with}}\;\;0 < {\rm{x}} < 3$

(1)

Its starting member, NaZr₂P₃O₁₂, also belongs to a series of ternary compositions which can be expressed in a general form as

${\rm{N}}{{\rm{a}}_{1 + 4{\rm{x}}}}{\rm{Z}}{{\rm{r}}_{2 - {\rm{x}}}}{{\rm{P}}_3}{{\rm{O}}_{12}}\;\;{\rm{with}}\;\;0 < {\rm{x}} < 1$

(2)

crystallizing in the rhombohedral NASICON-type structure ^[5,9]. Compositions with distinct numbers of x are listed in Table 1. Since ZrO₂ was frequently observed as a second phase in sintered polycrystalline samples ^[10], Boilot et al. ^[11] reduced the ZrO₂ formation by reducing the zirconium content in the starting composition and found NASICON compositions with zirconium deficiency. Later von Alpen et al. ^[10] and Kohler et al. ^[12] confirmed the zirconium deficiency and proposed the substitution mechanisms

${\rm{N}}{{\rm{a}}_{{\rm{l}} + {\rm{x}}}}{\rm{Z}}{{\rm{r}}_{2 - {\rm{x}}/3}}{\rm{S}}{{\rm{i}}_{\rm{x}}}{{\rm{P}}_{3 - {\rm{x}}}}{{\rm{O}}_{12 - 2{\rm{x}}/3}}\left( {0 < {\rm{x}} < 3} \right)$

(3)

and

${\rm{N}}{{\rm{a}}_{{\rm{l}} + 4{\rm{y}} + {\rm{x}}}}{\rm{Z}}{{\rm{r}}_{2 - {\rm{y}}}}{\rm{S}}{{\rm{i}}_{\rm{x}}}{{\rm{P}}_{3 - {\rm{x}}}}{{\rm{O}}_{12}}\left( {0 < {\rm{x}} < 3\;{\rm{and}}\;0 < {\rm{y}} < 0.75\;{\rm{with}}\;0 < {\rm{x}} + 4{\rm{y}} < 3} \right)$

(4)

respectively, leading to a scientific dispute on the existence of NASICON materials with oxygen and/or zirconium vacancies ^[13,14]. Further crystallographic investigations on single crystals grown from sodium phosphate fluxes revealed a partial replacement of Zr⁴⁺ by four Na⁺ ions up to y = 1 with x = 0 ^[15,16] (see Table 1) and y = 1 with x = 0.5 ^[17]. Therefore Na₅ZrP₃O₁₂ can be regarded as an end member for the pure phosphate, Na₅Zr_1.75Si₃O₁₂ for the pure silicate and Na_5.5ZrSi_0.5P_2.5O₁₂ ^[17], Na₅Zr_1.25SiP₂O₁₂ as well as Na₅Zr_1.5Si₂PO₁₂ for phosphate-silicates. However, crystal growth in the solidus region did not reveal the Zr ↔ Na replacement mechanism ^[18]. Another observed phenomenon in polycrystalline NASICON materials is the occurrence of glassy phases leading to the frequently used term "glass-ceramic" for these materials ^[19]. This phenomenon will be discussed below in more detail.

Besides the solid solution (1), charge compensation of Si ↔ P substitutions can also occur with Zr⁴⁺ vacancies instead of Na⁺ interstitial ions:

${\rm{N}}{{\rm{a}}_3}{\rm{Z}}{{\rm{r}}_{2 - {\rm{x}}/4}}{\rm{S}}{{\rm{i}}_{2 - {\rm{x}}}}{{\rm{P}}_{1 + {\rm{x}}}}{{\rm{O}}_{12}}\left( {0 < {\rm{x}} < 2} \right)$

(5)

This series crystallizes in the monoclinic (x < 0.5) and rhombohedral (x > 0.5) NASICON-type structure ^[20], but also contains glassy amounts ^[21]. In addition, very recently during the synthesis of Na₃Zr₂Si₂PO₁₂ we observed phase stability and high conductivity despite a significant silicon deficiency ^[22]. This leads to a more fundamental consideration as to how substitutions or cation deficiencies in the polyanionic lattice may be compensated. In general, missing positive charges can be compensated by a) oxygen vacancies, b) partial zirconium addition and oxygen vacancies, c) partial sodium addition and oxygen vacancies, d) sodium addition and e) zirconium addition according to the series

${\rm{N}}{{\rm{a}}_3}{\rm{Z}}{{\rm{r}}_2}{\rm{S}}{{\rm{i}}_{2 - {\rm{x}}}}{\rm{P}}{{\rm{O}}_{12 - 2{\rm{x}}}}$

(6)

${\rm{N}}{{\rm{a}}_3}{\rm{Z}}{{\rm{r}}_{2 + {\rm{x}}/2}}{\rm{S}}{{\rm{i}}_{2 - {\rm{x}}}}{\rm{P}}{{\rm{O}}_{12 - {\rm{x}}}}$

(7)

${\rm{N}}{{\rm{a}}_{3 + 2{\rm{x}}}}{\rm{Z}}{{\rm{r}}_2}{\rm{S}}{{\rm{i}}_{2 - {\rm{x}}}}{\rm{P}}{{\rm{O}}_{12 - {\rm{x}}}}$

(8)

${\rm{N}}{{\rm{a}}_{3 + 4{\rm{x}}}}{\rm{Z}}{{\rm{r}}_2}{\rm{S}}{{\rm{i}}_{2 - {\rm{x}}}}{\rm{P}}{{\rm{O}}_{12}}$

(9)

${\rm{N}}{{\rm{a}}_3}{\rm{Z}}{{\rm{r}}_{2 + {\rm{x}}}}{\rm{S}}{{\rm{i}}_{2 - {\rm{x}}}}{\rm{P}}{{\rm{O}}_{12}}$

(10)

respectively. These chemical observations and considerations are worth discussing in a wider frame (see Section 4).

Only very few reports exist on phase relations of series (1) establishing a quasi-ternary system ^[23] and giving relations of the end members in the ternary phase diagrams ^[24,25] which will be summarized in the next subsequent sections. So far, figures of quaternary phase diagrams have only been used to visualize the corresponding system under investigation without considering detailed phase relations ^[10,12,26]. Since the various possibilities of substitutions in NASICON materials, to our knowledge, have never been comprehensively discussed in relation to their neighboring phases, we present a first approach here of a quaternary phase diagram on the basis of existing thermodynamic studies and investigated compositions to date. We are aware that not all available data correspond to each other when they are combined to a unified phase diagram, especially when isothermal phase diagrams were investigated at different temperatures. Nevertheless, focusing on the existing phases appearing in this quaternary system can still provide valuable information for further investigations on this complex family of solid electrolytes known as NASICON.

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3. Ternary Phase Diagrams

In the following, the four ternary phase diagrams will be reviewed. For the sake of briefness, literature on binary systems is not mentioned, because it is cited in the publications of the ternary phase diagrams.

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3.1. The Ternary System SiO₂-ZrO₂-P₂O₅

The detailed investigation of the system SiO₂-ZrO₂-P₂O₅ ^[27] revealed the compositions SiP₂O₇ (in low-and high-temperature form), Si₂P₂O₉, SiO₂ (α-cristobalite), (ZrO)₂P₂O₇ (in metastable and stable form), ZrP₂O₇ (in low-temperature form) and ZrSiO₄. No ternary compounds were found, only an extended phase width for (ZrO)₂P₂O₇ up to (ZrO)₃P₄O₁₃. According to this study, the resulting ternary phase diagram is shown in Figure 1.

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3.2. The Ternary System Na₂O-SiO₂-P₂O₅

A very comprehensive study of the Na₂O-SiO₂-P₂O₅ system was carried out by Turkdogan and Maddocks ^[28]. In total, ten binary sodium-containing oxides and three ternary compounds in the sodium-rich region were found. Among these, the stable composition Na₁₈P₄Si₆O₃₁ is of central importance, because it is linked with the other ternary compositions, a few binary compounds as well as several peritectic and eutectic points. Typically, the peritectics have melting points between 900 and 1000 ℃, whereas the eutectic melting points vary from 1020 ℃ (close to N3S; for abbreviations, see caption of Figure 2) down to 780 ℃ (close to N2S3) on the silicate side. One eutectic on the phosphate side has an even lower melting point (550 ℃ between NP and N5P3).

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3.3. The Ternary System Na₂O-P₂O₅-ZrO₂

After identification of the ternary phosphates in Table 1 ^[5], the first steps towards a ternary Na₂O-P₂O₅-ZrO₂ phase diagram were undertaken by Milne and West ^[29,30]. They also identified N5ZP3 and N2ZP2 (for abbreviations, see caption of Figure 3) as NASICON-type materials as well as a solid solution of Na_5–4xZr_1+xP₃O₁₂ with 0.04 < x < 0.11 at 1000 ℃ and a solubility of Zr⁴⁺ in Na₃PO₄, i.e., Na_3–4xZr_xPO₄, with 0 < x < 0.57 ^[29]. Warhus adopted these results to a ternary phase diagram ^[24] specifying the phase equilibria at 1000 ℃. The main features of the phase diagram were confirmed by Vlna et al. ^[31]. They also found four sodium phosphates, one sodium zirconate and four zirconium phosphates, in contrast to Ref. ^[27] (see Figure 1) but in agreement with Ref. ^[24]. The materials with NASICON-type structure lie on the join N3P-Z3P4 and can be described as Na_9–4yZr_y(PO₄)₃. The end member phases N3P and NZ2P3 then correspond to y = 0 and 2, respectively, while for N5ZP3 and Z3P4 y = 1 and y = 2.25, respectively. The stated compound Na₇Zr_0.5(PO₄)₄ ^[9,30] is part of the solid solution Na_3–4xZr_xPO₄ ^[29] and therefore not explicitly shown in Figure 3.

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3.4. The Ternary System Na₂O-SiO₂-ZrO₂

The first investigation of the system Na₂O-SiO₂-ZrO₂ revealed one sodium zirconate, four sodium silicates, all melting between 800 and 1100 ℃, one zirconium silicate and three ternary compounds (N2ZS, N4Z2S3 and N2ZS2; for abbreviations see caption of Figure 4) ^[32]. In this study, seven eutectic points were also determined varying between 1000 and 1100 ℃. On the basis of these results, the subsolidus relations were determined ^[33,34] including N2S3. Later, Wilson and Glasser identified two more ternary compositions (N7ZS5, N2ZS4) and one additional sodium silicate (N3S4) with a very limited width of thermal stability ^[35]. Therefore, its phase relationships are presented as dash-dotted lines in Figure 4. Considering the phase equilibria at 1000 ℃ ^[24,25], the compounds N7ZS5 and N3S4 are not stable and a narrow region of melt exists (see gray area in Figure 4) indicating that the ternary compounds N2ZS4, N2ZS2 and N4Z2S3 are in equilibrium with the melt, ZS and ZrO₂. Since eutectic points were observed in the sodium-rich region ^[32], the gray area can probably be extended to N4S, also affecting the phase relations of N2ZS.

The frequent observation of glassy phases and ZrO₂ as impurities in NASICON ceramics becomes understandable in Figure 4, because the compound N4Z2S3 is in equilibrium with these observed impurities. However, investigations of NASICON phase formation with different starting materials ^[36] have also shown the appearance of phosphate-rich segregations, predominantly Na₃PO₄, indicating a partial de-mixing of the NASICON material to P-and Si-rich compositions. To avoid these reactions, processing of NASICON should be carried out below 1000 ℃, but higher temperatures are required for obtaining dense ceramics so far.

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4. The Quaternary System Na₂O-SiO₂-P₂O₅-ZrO₂

Using the existing knowledge on the ternary systems as well as the reported stability region of materials crystallizing with NASICON structure, i.e., the solid solutions and individual compositions of single crystals investigated, a tentative three-dimensional phase field of NASICON materials was established in a quaternary phase diagram. It has the shape of a compressed tetrahedron (blue region in Figure 5). Three of the edges of the tetrahedron are defined by the solid solutions (1), (2) and (3), indicated as solid red lines in Figure 5. An additional side of the tetrahedron is defined by the two-dimensional solid solution (4), represented by the mesh of blue lines. In general, the blue tetrahedron displays the chemical formula

${\rm{N}}{{\rm{a}}_{{\rm{l}} + 4{\rm{y}} + {\rm{x}}}}{\rm{Z}}{{\rm{r}}_{2 - {\rm{y}} - {\rm{z}}}}{\rm{S}}{{\rm{i}}_{\rm{x}}}{{\rm{P}}_{3 - {\rm{x}}}}{{\rm{O}}_{l2 - 2{\rm{z}}}}$

(11)

proposed by Rudolf et al. ^[37,38], which contains many possible non-stoichiometric variations (Si/P substitution, Zr/Na substitution, Zr and O deficiency). It should be kept in mind, however, that from the thermodynamic point of view the blue triangle is not strictly a single-phase region. It rather represents a region in which the NASICON phase appears with predominant volume fraction. In most of the compositions, especially those towards high SiO₂ content ^[3], the obtained samples also contain a homogeneous distribution of glassy phase ^[21,39,40]. However, in samples with the NASICON composition Na₃Zr₂Si₂PO_l2 (large black circle in Figures 5 and 6; see arrow in Figure 5) glass formation increases with increasing sintering temperature and dwell time at high temperature ^[26,41], mainly induced by the evaporation of Na₂O from the sample surface leading to ZrO₂ precipitation and partial de-mixing of the NASICON phase ^[42]. Typically, the compositional separation is accompanied by accelerated grain growth due to liquid-phase sintering, which can be used to prepare single crystals with crystal edges of about 50–300 µm ^[12,42,43]. An example of the resulting microstructure revealing the different phenomena in a sintered body is shown in Figure 7.

It is worth noting, however, that the phase formation during sintering in air can lead to different results than during phase diagram studies using closed capsules for annealing samples ^[9,24,41]. The discrepancies mainly result from the different partial pressure of Na₂O to which the samples are exposed. The loss of Na₂O during sintering is frequently compensated by the addition of a sodium source during powder synthesis, but it usually remains unclear as to whether the additional amounts really match the losses during heat treatment. An excess of 10 at.% of sodium can, however, substantially increase the ionic conductivity ^[44] and mainly influences the grain boundary conductivity at ambient temperatures.

Based on the knowledge of appearing additional phases, the green areas in Figure 5 show the regions connecting the edges of the NASICON tetrahedron with binary compounds and single oxides, i.e., ZrO₂ and ZrSiO₄ ^[23], Na₃PO₄ and the sodium silicates ranging from Na₂Si₂O₅ to Na₆Si₂O₇. Depending on the temperature, the phase equilibria may be more extended from SiO₂ to Na₄SiO₄ as indicated by a different transparency of the large triangle in Figure 5. For Zr-deficient and Si-rich NASICON compositions, phase relations were observed towards ternary compounds (N2ZS2 and N2ZS4) ^[23], in analogy to Figure 4 and are shown as yellow areas in Figure 5.

To date, only a few individual compositions, e.g., Na_3.1Zr_l.55Si_2.3P_0.7O₁₁ ^[10,39], Na_5.5ZrSi_0.5P_2.5O₁₂ ^[17], and Na_2.95Zr_l.92Si_1.81PO_11.44 ^[22] have been found outside the blue triangle. Normalizing the latter composition to twelve oxygen ions per formula unit, it can also be written as Na_3.09Zr_2.01Si_1.90P_1.05O₁₂, but the position in the phase diagram remains. Therefore, the stability region of NASICON materials seems to be larger than indicated in Figure 5 and more systematic work is necessary to determine the whole stability region of NASICON materials.

Individual compositions which were refined by single-crystal X-ray or neutron diffraction are shown in Figures 5 and 6 as red squares ^{[12,14,15,16,17,18,19,37,38,42]}. The blue square denotes the unusual composition Na_3.1Zr_l.55Si_2.3P_0.7O₁₁ of von Alpen et al. ^[10] and the light-green squares correspond to the Si-deficient compositions reported by Naqash et al. ^[22]. The dashed red lines starting at the black circle (Na₃Zr₂Si₂PO_l2) indicate the series (6) to (10) as a possible charge compensation mechanism for Si-deficient compositions as mentioned in the introductory part of this paper. The related green squares are located along series (6) (Figure 6). However, a more extended study is necessary to elucidate the phase stabilities and substitution rules in this region of the phase diagram.

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5. Conclusions

With respect to technological application, several conclusions can be drawn from the existing knowledge and Figure 5:

• So far, the highest conductivity of NASICON materials within the discussed quaternary system can be attributed to the region of series (1) with 2 < x < 2.5 ^[5,45], to compositions with similar Si/P ratio but with a Zr deficiency ^[10,39] or Si deficiency ^[22]. In other words, high ionic conductivity is not restricted to series (1) despite the fact that Si-rich compositions and especially those with Zr deficiency show a substantial fraction of glassy phase ^[39]. In turn, this implies that the glass either has a high conductivity or that the glass only exists at high temperatures and crystallizes with a NASICON structure during cooling. Preliminary µ-Raman measurements suggest the latter interpretation (Giarola M and Mariotto G, personal communication, University of Verona). However, since only a few reports are available on "offside" compositions from series (1), more systematic investigations in this region of the phase diagram are necessary to explore the full potential of NASICON materials.

• Taking glass formation as an unavoidable process during component manufacturing, the distribution of the Si-rich glass as an outer shell around the P-rich NASICON crystals (Figure 7) can be used as an intrinsic protection layer against reduction with metallic sodium in battery developments. If a continuous glass film is realized, the higher thermodynamic stability of the silicates can protect the NASICON phase from phosphide formation ^[25,39,46]. Although such glass-rich compositions show very high ionic conductivity ^[10,39], this additional phase contributes to the total resistance like an enlarged grain boundary resistance which should be minimized. In addition, the crystallized glassy phase may have significant influence on the mechanical properties ^[7], which need to be addressed and systematically investigated.

• This thermodynamic benefit of the glass phase also implies a practical drawback: Sintering of ceramics, especially for plates and larger components becomes more difficult. On the one hand, the ceramics tend to stick to the base plate and when thin components are considered, they can easily break during detachment from the base plate. On the other hand, large components like tubes may deform more easily during hanging sintering due to the low mechanical strength of the materials and viscous flow at high temperatures.

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Acknowledgments

The author thanks Prof. Mike A. Scarpulla (University of Utah, Depts. of Electrical & Computer Engineering and Materials Science & Engineering) for helpful initial advice to use the MATLAB software and Dr. Robert Mücke (IEK-1) for important computational support. Sahir Naqash and Dr. Doris Sebold (both IEK-1) are gratefully acknowledged for sample preparations and SEM images, respectively.

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Conflict of Interest

The author declares no conflict of interest related to the content of this publication.

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