Polymorphism, crystal growth, crystal morphology and

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Crystallography Reviews, 2013 http://dx.doi.org/10.1080/0889311X.2013.838673

Polymorphism, crystal growth, crystal morphology and solid-state miscibility of alkali nitrates R. Benages-Vilau∗ , T. Calvet and M.A. Cuevas-Diarte Departament de Cristallografia, Mineralogia i Dipòsits Minerals, Facultat de Geologia, Universitat de Barcelona, c/Martí i Franquès s/n, Barcelona 08028, Spain (Received 23 July 2013; accepted 22 August 2013) In this review, we recollect and discuss the most relevant advancement in crystallographic aspects of alkali nitrates compounds published since 1975, the year of publication of the last review by Rao et al. about some topics discussed here. This review is focused in five nitrate compounds of the first periodic table column: LiNO3 , NaNO3 , KNO3 , RbNO3 and CsNO3 . For each one, we have compiled the information about crystal structure, polymorphism and phase transition, crystal growth and crystal morphology, and the phase diagram and solid-state miscibility results. Considerable numbers of papers have been published in the last 40 years, in particular in relation to binary phase diagrams and solid-state miscibility of alkali nitrates. A variety of phase diagram descriptions appears in the 10 possible binary combinations for the five compounds. To finish, we discuss and propose a geometric model in order to explain the different binary phase diagrams observed between these compounds. Keywords: polymorphism; crystal growth; morphology; solid-state miscibility; alkali nitrates

Contents

PAGE

1.. Introduction

2

2.. Lithium nitrate 2.1.. Crystal structure, polymorphism and phase transitions 2.2.. Crystal growth 2.3.. Morphology

3 3 3 3

3.. Sodium nitrate 3.1.. Crystal structure, polymorphism and phase transitions 3.2.. Crystal growth 3.3.. Crystal morphology

3 3 7 9

4.. Potassium nitrate 4.1.. Crystal structure, polymorphism and phase transition 4.2.. Crystal growth 4.3.. Crystal morphology

9 9 11 12

5.. Rubidium nitrate 5.1.. Crystal structure, polymorphism and phase transition 5.2.. Crystal growth

13 13 15

∗ Corresponding

author. Email: [email protected]

© 2013 Taylor & Francis

2

R. Benages-Vilau et al. 5.3.. Crystal morphology

15

6.. Caesium nitrate 6.1.. Crystal structure, polymorphism and phase transition 6.2.. Crystal growth 6.3.. Crystal morphology

15 15 17 17

7.. Solid-state miscibility and binary phase diagrams 7.1.. LiNO3 –NaNO3 7.2.. LiNO3 –KNO3 7.3.. NaNO3 –KNO3 7.4.. LiNO3 –RbNO3 7.5.. NaNO3 –RbNO3 7.6.. KNO3 –RbNO3 7.7.. LiNO3 –CsNO3 7.8.. NaNO3 –CsNO3 7.9.. KNO3 –CsNO3 7.10..RbNO3 –CsNO3

18 18 19 19 19 19 19 20 20 20 20

8.. Discussion

21

9.. Conclusions

23

Acknowledgements

23

Notes on contributors

24

References

24

Subject index

30

1. Introduction The general chemical formula for alkali nitrates is XNO3 with X = Li, Na, K, Rb or Cs. Some of them would be interesting from the technological point of view.[1,2] From the chemical point of view, for example, nitrate-based salts were used as heat transfer fluids in concentrated solar power plants. Their basic units are a triangular nitrate group and a spherical alkali atom. These compounds are interesting to study because they have, in principle, a simple structure. Despite this, they can crystallize into a variety of crystalline forms. Some of them would be interesting from the technological point of view. For example, NaNO3 has an extended second-order polymorphic transition,[3] and can be considered a model for the isostructural calcite mineral; γ-KNO3 is a ferroelectric phase;[4] rubidium nitrate has a rich polymorphism with four phases at ambient pressure.[5] On the other hand, LiNO3 and CsNO3 have not been widely studied, but they are important in order to obtain a unified vision of the alkali nitrate family. Polymorphism of alkali nitrates has been extensively reviewed by Rao et al.[6] There, the author recollected all the information available up to 1975 and organized it in tables highlighting the most important conclusions extracted in each technique used to characterize them. Our aim is first to complete Rao et al.’s summary with more recent information about polymorphism and phase transitions. Second, to make a recollection of crystal growth data because we noticed that some interesting work has been published, in fact only NaNO3 and KNO3 are studied because they have several important industrial applications such as fertilizers. Chernov and Sipyagin [7] recorded kinetic parameters of nitrates and sulphates, so that it is our starting point. Third, in this

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review, we have included morphological studies because it is interesting to compare how the final crystal shape varies by only changing the alkali metal. Finally, it is also motivating to include solid solution and phase diagrams in this review, so that we can have a complete vision of structural facts in the alkali nitrates family. Alkali nitrate phase diagrams have been recently calculated by the FACTSalt software developed for over 20 years.[8] In the last 40 years, many papers about crystal structure, polymorphism, phase transition, crystal growth, morphology and solid-state miscibility, including phase diagram determination of the alkali nitrate family, have appeared. Unfortunately, the publications are scattered; therefore, we think that it is essential to have all the information about structural aspects in a single paper. All the crystal structures and morphology of crystals have been depicted by shape software.[9]

2. Lithium nitrate 2.1. Crystal structure, polymorphism and phase transitions ¯ group As Rao et al. [6] have shown, lithium nitrate crystallizes in rhombohedral (calcite type), R3c with Z = 6, a = 4.692 Å and c = 15.22 Å at 298 K. There is no evidence for a phase transition in the thermodynamic properties from 298 K to the melting point.[10] However, discontinuities in the absorption coefficient [11] and changes in electric properties [12] may indicate an orientational disorder transition on nitrate groups just like NaNO3 or NH4 NO3 . After Rao et al., only Wu et al. [13] determined the LiNO3 crystal structure. The authors give a significant variation in the c-parameter as can be seen in Table 1. The unit cell determined by Wu et al. [13] is presented in Figure 1, where blue spheres are lithium ions and red spheres are oxygen atoms. These authors grew the crystal from the melt and despite not having a good single crystal they were able to determine its structure. According to them, LiNO3 is isostructural to both calcite (CaCO3 ) and nitratine (NaNO3 ). No evidence has been found for a high-temperature phase. Moreover, Stromme [33] modelled a positional ordered equilibrium structure of LiNO3 at all temperatures. Accordingly, LiNO3 has only one structure as a function of temperature, as is recollected in Table 1. 2.2. Crystal growth We have not found any paper related to anhydrous lithium nitrate growth because it is deliquescent. Nonetheless, Chernov and Sipyagin [7] gave some kinetic data for LiNO3 · 3H2 O compound, which is not of interest for this review. 2.3. Morphology As far as we know, neither theoretical nor experimental morphology is reported for lithium nitrate crystals. However, we expect that the theoretical growth morphology determined by the Bravais– Friedel–Donnay–Harker (BFDH) method will be equal to that of calcite [34] and nitratine [35] ¯ and {001} forms appear in the because they are isostructural crystals. Therefore, {012}, {012} theoretical growth morphology (Figure 2).

3. Sodium nitrate 3.1. Crystal structure, polymorphism and phase transitions ¯ group with Z = 6; a = 5.0396 Å Sodium nitrate crystallizes in rhombohedral (calcite type), R3c ¯ form and c = 16.829 Å at 298 K.[6] A phase transition from the low temperature II-NaNO3 (R3c)

4 Table 1.

R. Benages-Vilau et al. Crystal data for alkali nitrates polymorphic forms.

Compound LiNO3 LiNO3 NaNO3 NaNO3 NaNO3 NaNO3 NaNO3 NaNO3 KNO3 KNO3 KNO3 KNO3 KNO3 KNO3 KNO3 KNO3 KNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 RbNO3 CsNO3 CsNO3 CsNO3 CsNO3 CsNO3 CsNO3 CsNO3

Form

II II II II II I II α α α α I β III γ IV IV IV IV III III III II II I I II II II II I I I

Space group ¯ R3c ¯ R3c ¯ R3c ¯ R3c ¯ R3c ¯ R3c ¯ R3c ¯ R3m Pmcn Pmcn Pmcn Cmc21 Pnma ¯ R3m ¯ R3m R3m R3m P31 m P31 P31 P31 P31 ¯ Pm3m ¯ Pm3m ¯ Pm3m P31 ¯ R3m ¯ Fm3m ¯ Fm3m P31 m P31 /P32 P31 P31 Pa3¯ Pa3¯

a (Å)

b (Å)

4.692 4.6920 5.0696 5.0655(5) 5.0660(5) 5.070 5.07 5.0889(5) 5.414 9.164 5.4119 9.1567 5.4283 9.1849 10.825 18.351 6.436(1) 5.430(1) 5.43 5.425(1) 5.42 5.487(1) 10.479 10.067 10.474 10.55 10.61 4.39(1) 7.32 4.3718(2) 10.474(1) 10.506(3) 8.84(3) 7.32 7.3150(22) 10.87 10.902(2) 10.931(2) 10.95(2) 4.499 8.98 8.98

c (Å)

Z

12.22 2 15.2149 6 16.829 6 16.577(3) 6 16.593(3) 6 16.82 16.82 8.868(3) 3 6.431 4 6.4213 4 6.5034 4 6.435 16 9.192(2) 4 9.112 9.836(4) 3 19.41 12 9.156(3) 3 7.452 9 7.053 9 7.443 9 7.47 9 7.55 9 1 1 1 7.443(1) 9 7.469(3) 9 9

7.76 7.740(2) 7.763(3) 7.80(2)

1 4 9 9 9 9 1 4 8

T (K)

Year

Reference

298 298 298 100 120 293

1975 1994 1975 2000 2000 1972 1978 2000 1975 1973 1973 2003 1976 1975 1976 1975 1976 1975 2001 1992 1982 1982 1988 1971 1980 1992 1992 1988 1980 1975 1980 1993 1993 1984 1983 1975 1975 1953

[6] [13] [6] [14] [14] [15] [16] [14] [6] [17] [17] [18] [19] [6] [20] [6] [20] [6] [21] [22] [23] [23] [24] [25] [26] [22] [22] [27] [26] [6] [26] [6] [28,29] [30] [31] [6] [6] [32]

563 299 298 373 293 388 424 425 364 298 RT RT 298 403 563 296 372 503 573 568 0.001. Rolf et al. [124] also arrived at the conclusion that KNO3 crystal growth may be described by the random fluctuation model. However, in some experiments, they found that KNO3 follows the constant crystal growth model. This is in accordance with a paper by Wang and Mersmann,[131] who concluded that each crystallite has its own constant crystal growth rate. Similarly, Huang et al. [132] found a linear growth rate model. On the contrary, Graber et al. [66] described a diffusion controlled growth in a perfectly stirred industrial tank. Finally, Zarkadas and Zircar [133] established that the best procedure to have a narrow and reproducible crystal size distribution was by operating schemes that included feed recycling, once through and solid hollow fibre crystallizer in a completely stirred tank with in-series operation mode. With this setup, a mean size between 100 and 150 μm could be achieved, this means 3–4 times lower than those of mixed suspension mixed product removal crystallizers. Soltzberg et al. [134] investigated the formation of dendrites of KNO3 by growing crystals in a thin layer of saturated solution. They found, as expected, that dendrites are formed at high subcooling and that 031, 041 and 051 set of crystallographic directions are preferred for dendritic growth. Fujiwara et al. [135] have grown an oriented crystal (along the a direction of the unit cell) under an a value in the SI unit of Tesla magnetic field with a temperature decrease method. 4.3. Crystal morphology KNO3 crystal morphology has been investigated from both the experimental [136] and theoretical [137] points of view by Van der Voort. Experimentally, the author found that the growth habit changes as the crystallization temperature is increased, maintaining the same subcooling of Tequilibrium – Tgrowth = 0.15 K. The most important forms of KNO3 crystals grown below 305 K are {110}, {111}, {010} and the {021} forms. Conversely, at higher temperatures, van der Voort experimentally found up to six faces. Van der Voort assumed that this difference is due to the water adsorption. Soltzberg et al. [138] calculated the late-growth morphology using only Coulombic interactions. They described good agreement between the calculated and the experimental morphology of KNO3 . Similarly, Rolf et al. [124] calculated the surface tension of up to 10 different forms of KNO3 using only a Coulombic potential and three different negative charges on the oxygen atom. Results are reproduced here in Figure 6. Lovik et al. [139] calculated the surface stability of different KNO3 faces by an ab initio DFT procedure arriving at the result that the {001} form has the lowest surface energy. When drawing the shape, with unrelaxed values of surface energy, a simple parallelepiped {100}, {010} and {001} is obtained. If we use relaxed values, the {110} form also appears as depicted in Figure 6(d). The equilibrium shape is quite different from that proposed by Rolf et al.[124] Conversely, when we simulate the growth shape by the BFDH method, we find a completely different shape where only the {110}, {011} and {010} forms appear (Figure 6(e)). Therefore, deeper calculations may be done and reliable potential functions should be used to establish the equilibrium morphology of KNO3 crystals.

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Figure 6. Upper part: equilibrium morphology of the KNO3 crystal for a different negative charge onto oxygen atoms according to Rolf et al.[124] (a) -1/3; (b) -5/6; (c) -4/3. Lower part: (d) equilibrium form of the KNO3 crystal according to Lovvik [139] and (e) Growth morphology according to the BFDH approach calculated by us.

Figure 7. RbNO3 phases and its transition temperatures according to Rao at al.[6] IV-RbNO3 after Pohl et al. [22] and III-RbNO3 , II-RbNO3 , and I-RbNO3 after Ahtee et al.[26] Unit cells are not at the same scale. All structures are viewed along the 010 direction.

5. Rubidium nitrate 5.1. Crystal structure, polymorphism and phase transition As Rao et al. [6] reviewed, it was established by XRD, DTA, dilatometric, calorimetric, electrical conductivity and optical measurements that RbNO3 undergoes three phase transformations shown in Figure 7. Phase IV, the low-temperature form, is trigonal P31 m, with Z = 9, a = 10.479 Å and c = 7.452 Å, at 298 K.[6] Shamsuzzoha and Lucas [23] pointed out that IV-RbNO3 is isostructural with II-CsNO3 . The authors describe the structure as having nine Rb+ -based pseudo-cubes inside the cell with the NO− 3 groups enclosed. The nitrate groups are closely planar and there is no evidence of rotational disorder. Zhou et al. [28] using magic-angle NMR experiments arrived at

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the conclusion that only one independent nitrate is in the IV-RbNO3 phase unit cell. They obtained and adjusted the unit cell by DFT calculations. It was reported by Rao et al. [6] that III-RbNO3 phase is cubic (CsCl type) with a = 4.36 Å and Z = 1 or with a double cell a = 8.72 Å and Z = 2, furthermore in this phase the NO− 3 ion has a free rotation. On the contrary, Shamsuzzoha and Lucas [24] reviewed that the III-RbNO3 phase is better described by nitrate eight-fold orientational disorder. This means that each cell has a simple nitrate orientation because in this structure, the entropy is not high enough to have a free rotation of the nitrate group. Additionally, Ahtee and Hewat [26] studied phase III-RbNO3 by powder neutron diffraction and concluded that III-RbNO3 phase (from 437 to 492 K) has a cubic CsCl-structure, ¯ with one molecule per unit cell (Z = 1); the authors had a preference for the 12-fold orientaPm3m, tional disorder for the nitrate group (see Figure 9). Thus, three models are proposed for the description of the III-RbNO3 structure. Moreover, the work performed by Shinnaka and Yamamoto [140] suggests that the orientational disorder of the NO− 3 ion did not show an anomaly associated with the dielectric constant in the vicinity of the transition to the higher temperature phase (II-RbNO3 ), but showed a pre-transformation effect towards the lower temperature phase (IV-RbNO3 ). According to Rao et al.,[6] phase II-RbNO3 is rhombohedral with a = 4.8 Å and γ = 70◦ 28 around 520 K, with Z = 1; γ being the angle between aand b can be considered as a deviation factor from a hypothetical cubic unit cell (γ = 90◦ ). However, Ahtee and Hewat [26] and Stromme [141] ¯ Ahtee determined that the II-RbNO3 phase has a rhombohedral unit cell with space group R3m. and Hewat [26] and Yamamoto et al. [142] agreed with this space group choice and proposed an aragonite-type disorder, as is depicted in Figure 9. On the contrary, Shamsuzzoha and Lucas [27] preferred a body-centred cubic structure (a = 8.84 Å, Z = 8 at 517 K). Phase I is cubic (NaCl type) with a = 7.32 Å at ∼573 K with Z = 1 according to Rao et al.[6] Ahtee and Hewat [26] published similar results: I-RbNO3 phase is stable in the region 557–583 K, ¯ with Z = 4. it has a cubic NaCl-type unit cell, Fm3m, Pohl et al. [22] asserted to have found another phase that is stable, at least from 346 K (DTA measurement) to 437 K. Although Fermor and Kjesus [143] report a phase transition at 228 K detected by electric conductivity measurements, Owen and Kenard [144] argued that the anomalous electrical behaviour may be only due to thermal history and that there is not another phase at low temperatures. Finally, Shamsuzzoha and Lucas [24] explain the difficulties of obtaining good single-crystals of phase II and I. Therefore, their structures remain unresolved. Regarding phase transitions, Rao et al. [6] pointed out that observing with light microscopy on heating from phase IV-RbNO3 to III-RbNO3 , the crystals become isotropic, then passing through the III-RbNO3 → II-RbNO3 transition results in cracking of crystals and they become anisotropic again. Around 563 K, crystals become isotropic without further distortion. Using XRD studies, it can be explained that IV-RbNO3 , III-RbNO3 and II-RbNO3 phases are related and the transition between them appears to involve changes in positional randomization of Rb+ . However, Ahtee and Hewat [26] pointed out that these transformations seemed to be associated with the change in orientational disorder of the nitrate group. In contrast, the I-RbNO3 phase is not related to the others, and the transition II-RbNO3 → I-RbNO3 does not imply this randomization. The free rotation disorder had been definitively excluded in all phases. Kawashima and Uchiumi [145] studied the temperature and frequency dependence of the AC conductivity of IV-RbNO3 , III-RbNO3 and II-RbNO3 phases along the b-axis [146] and c-axis,[147] and found anomalies near the transition points for all three transitions. They also studied the optical properties near the transition.[148] Shamsuzzoha and Lucas [24] proposed that IV-RbNO3 → III-RbNO3 and III-RbNO3 → II-RbNO3 phase transitions were accomplished by very small changes of the Rb atom sublattices from pseudo-cubic to cubic. The NO− 3 groups in these structures change from being orientationally ordered to disordered and have a similar eight-fold anion–cation coordination. This was consistent with the molecular dynamics simulation of the IV-RbNO3 → III-RbNO3 phase transition performed by Liu et al.,[21] who found that the transition is initiated by an in-plane

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rotation of NO− 3 ions: nitrate groups remained planar; there is not a free rotation. According to Shamsuzzoha and Lucas [24] the II-RbNO3 → I-RbNO3 phase transition did not have a simple unit cell relationship. However, Yamamoto et al. [142] proposed that the coupling between the orientation of anions and shear strain played an important role in this phase transition, both structures having an eight-fold orientational disorder. Additionally, Chary and Reddy [149] and references therein studied the ionic conductivity versus the temperature. They noticed an increase in conductivity in IV-RbNO3 → III-RbNO3 and II-RbNO3 → I-RbNO3 phase transitions; while for III-RbNO3 → II-RbNO3 phase transitions there was a conductivity decrease. These changes correspond to an increase and decrease in symmetry, correspondingly. Furthermore, Charsley et al. [5] made a careful calorimetric investigation gathering all thermal data about transitions. They also determined the three equilibrium temperatures for the transitions, being 438.0 ± 0.1 K (IV-RbNO3 → III-RbNO3 phase transition), 495.3 ± 0.5 K (III-RbNO3 → II-RbNO3 phase transition) and 557.1 ± 0.1 K (II-RbNO3 → I-RbNO3 phase transition) together with the transition enthalpies. Finally, Dean et al. [30] and references therein, give the high pressure polymorphism of RbNO3 which is not included in this review. 5.2. Crystal growth Chernov and Sipyagin [7] give the kinetic coefficients, exchange fluxes and other parameters for the growth of the (124) and (114) faces of RbNO3 . As far as we know, only Treivus and Franke [150] have studied rubidium nitrate kinetics. They found a linear dependence of the growth rate (V ) versus the excess of mass: V = (8.76 ± 0.75) · 10−7 m in the temperature range of 301.2–297.6 K for the forms {110} and {100}, where m is the excess of mass expressed in mol kg−1 H2 O. We have to highlight here that this method of growth rate measurement is not useful to approach the growth mechanism. 5.3. Crystal morphology As far as we know neither experimental nor theoretical morphological studies have been published over the years: only brief descriptions of experimental habit like that proposed by Franke et al.,[56] where a pseudo-hexagonal habit is described. This habit is in accordance with the BFDH growth morphology calculated by us and shown in Figure 8.

6. Caesium nitrate 6.1. Crystal structure, polymorphism and phase transition As Rao et al. [6] described, caesium nitrate exists in two polymorphic phases. The low-temperature form (phase II, pyroelectric) is trigonal P31 m, with Z = 9, a = 10.87 Å and c = 7.76 Å. The I¯ with a = 4.499 Å with Z = 1 at near 400 K. The I-CsNO3 phase CsNO3 phase is cubic (Pm3m) has also been described with a doubled cell with Z = 8 and a = 8.98 Å belonging to the Pa3¯ space group. We show in Figure 9 the low- and the high-temperature unit cell of CsNO3 . Lucas [31] pointed out that II-CsNO3 is isostructural with IV-RbNO3 . It has a P31 space group with a = 10.95(2) Å and c = 7.80(2) Å, Z = 9. In this sense, the form nine pseudo-cubes within + the unit cell. The NO− 3 groups are closely planar and enclosed by Cs ions pseudo cubes of Cs+ ions. There is no evidence that this phase has rotational disorder. Pohl and Gross [29] redetermined the II-CsNO3 phase at 296 K by single-crystal diffraction. The cell parameters were a little bit different from those reported in the paper by Rao et al. [6] and the space group reported is P31 (or the enantiomorph P32 ). Furthermore, these authors described IV-RbNO3 and II-CsNO3 as isomorphous. As it is described later, a complete solid solution between these two compounds

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Figure 8. The BFDH growth morphology of RbNO3 calculated by us.

Figure 9.

CsNO3 unit cell. Left: phase II.[30] and right phase I.[32] Both viewed along the 100 direction.

is known, thus they are certainly isomorphous.[151] Additionally, Zhou et al.,[28] using magicangle NMR experiments, arrived at the conclusion that only one independent nitrate is in the cell, obtaining an adjusted cell by DFT calculations. Following the review by Rao et al.,[6] phase I is a slightly distorted version of the phase II + structure. The structural difference between them is only due to NO− 3 orientation, Cs ion position being practically the same in both structures. Stromme [141] cited I-CsNO3 as cubic primitive (isostructural with III-RbNO3 ) containing one molecule of metal nitrate per unit cell. The author discusses two possible structures introducing entropic terms in the same manner as he did with all other alkali nitrates.[33,152,153] He concluded that some configurational entropy may exist in this phase. The II-CsNO3 phase undergoes a transition to a I-CsNO3 phase at around 434 K. Charrier et al. [154] made a careful calorimetric gathering of all the thermal data about the transition and also determined the equilibrium temperature for it, being 427 ± 10 K together with the transition enthalpy. These authors [155] found an anomaly in the electric constant near the phase transition. Similarly, Kawashima et al. [156] and Kawashima [157] performed conductivity measurements from room temperature to the melt; they found a discontinuity in the phase transition. Moreover, Tagaki et al. [158] studied the phase transition by Brillouin scattering and concluded that II-CsNO3

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Figure 10. The BFDH growth morphology of CsNO3 calculated by us.

is a real ferroelectric phase. Along these lines, Nautiyal et al. [159] prepared polyvinyl alcohol caesium nitrate composite films in order to study their ferroelectric properties. Liu et al. [21] performed molecular dynamics through the phase transition and found that it is initiated by outof-plane rotation of the nitrate group, thus, the transition mechanism is slightly different from the IV-RbNO3 → III-RbNO3 phase transition even if both the low-temperature (IV-RbNO3 and II-CsNO3 ) and the higher temperature (III-RbNO3 and I-CsNO3 ) forms of these nitrates are isomorphous. Finally, Dean et al. [30] and references therein studied the high pressure polymorphism of CsNO3 . We highlight the three high pressure polymorphs of CsNO3 found by Kalliomäki and Meisalo.[160] These are III, IV and V-CsNO3 phases: all three phases presented the same Pmmn space group but with different axial ratios. 6.2. Crystal growth Chernov and Sipyagin [7] reported the kinetic coefficients, exchange fluxes and other parameters for the growth of the (124) and (114) faces of CsNO3 . Similar to rubidium nitrate, Treivus and Franke [150] have studied caesium nitrate kinetics. They found a linear dependence of the growth rate (V ) as a function of the excess of mass: V = (18 ± 2K) · 10−7 · m in the temperature range of 299.3–297 K for the forms {110} and {100}, where m is the excess of mass expressed in mol kg−1 H2 O. We mention here that this method of growth rate measurement is not useful to approach the growth mechanism. 6.3.

Crystal morphology

As far as we know, neither experimental nor theoretical morphological studies of caesium nitrate crystals have been published over the years. There are only brief descriptions of experimental habit, like that proposed by Pohl [29] that describe the crystal as hexagonal shaped c-axis needles. The BFDH morphology (Figure 10) calculated by us is exactly the same as RbNO3 because they are isostructural materials. From this review we can, thus, construct Table 1 for the alkali nitrates’ polymorphism. We summarize here the more relevant data published after the review by Rao et al.,[4] which is also included.

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Figure 11.

R. Benages-Vilau et al.

Binary phase diagrams of the alkali nitrates taken from the FACTSalt web page.[8]

7. Solid-state miscibility and binary phase diagrams All the phase diagrams between alkali nitrates except NaNO3 –CsNO3 have been compiled by Voskresenkaya in 1970.[161] From this compilation, we can extract that they were determined by a variety of experimental methods, mainly visual and visual-polythermal. Moreover, the NaNO3 – KNO3 phase diagram is by and large the most studied among them, with 20 related publications. After this compilation, it is worth mentioning the work made by Dessureault et al. [162] in 1990 who made a critical evaluation of the thermodynamic data published up to that moment and extracted a new model to simulate inorganic binary systems. In the paper quoted above we could only find LiNO3 –NaNO3 , LiNO3 –KNO3 and NaNO3 –KNO3 ; however, a complete set of the computed phase diagrams can be obtained from the FACTSalt web page.[8] Figure 11 shows a simplified version of all alkali nitrate binary phase diagrams in a systematic way. Here we are only concerned with the general form of the binary systems: i.e. do they present any solid solution region? What is their melting behaviour (solid–liquid equilibrium, eutectic invariant, congruent melting, . . .)? Based on Dessureault’s paper,[162] we first systematically describe the alkali nitrate binary phase diagrams and solid solutions research done after the quoted paper, and subsequently we try to make a classification. 7.1. LiNO3 –NaNO3 Dessurreault et al. [162] proposed that this phase diagram presents a eutectic without a solid solution. Effectively, the research by Bélaïd-Drira et al. [163] agreed very well with these results. However, Maeso and Largo [164] questioned whether a flat solidus measured by thermal analysis necessarily indicates a eutectic behaviour.

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7.2. LiNO3 –KNO3 Dessurreault et al. [162] proposed that this phase diagram presents a eutectic invariant, also without a solid solution. However, Maeso and Largo,[164] as before, highlight the same problem. More recent investigations proposed that an equimolar compound LiK(NO3 )2 exists. In actual fact, Xu et al. [165] and Zhang,[166] working with Raman spectroscopy, confirmed a congruent melting point in this system. Therefore, they proposed two eutectics separated by a congruent melting point. The authors explained that the equimolar composition LiK(NO3 )2 only appears in fast cooling conditions without any disturbance. It is a metastable phase at room temperature and decomposes into the terminal compounds LiNO3 and α-KNO3 . The solid solution was only ¯ and R3c space groups formed by a mixture of LiNO3 and γ-KNO3 . These compounds have R3c respectively; therefore, the solid solution is more plausible than when the α-phase (Pmcn space group) is considered. It appears that this intermediate phase can be stable at high temperature. Unfortunately, we do not have enough information to confirm this hypothesis. 7.3. NaNO3 –KNO3 This is by far the most studied nitrate phase diagram with 150 years of history. Many papers have been published trying to solve a fundamental question: does this phase diagram present a solid–liquid equilibrium or a eutectic behaviour? Research gives evidence to either one or the other melting behaviour. For example, Dessurreault et al. [162] proposed a eutectoid and a minimum of melting point with a complete series of solid solution. Below the eutectoid point, a solid solution is formed only for high concentrations of KNO3 (above 90%). A thorough study of this system can be found in a paper by Benages-Vilau et al.,[102] where the authors demonstrated both experimentally and theoretically a solid–liquid equilibrium with a minimum, immiscibility gap in the solid-state and terminal-solid solutions for both components. 7.4.

LiNO3 –RbNO3

In the FACTSalt web page,[8] it is depicted with an equimolar congruent melting point, two eutectic invariants, and, finally, no miscibility in the solid state. Xu and Chen [167] presented the congruent melting compound LiRb(NO3 )2 . According to these authors, all these three congruently melting compounds in alkali nitrate binary systems (LiK(NO3 )2 , LiRb(NO3 )2 and LiCs(NO3 )2 have the same crystal structure and, consequently, the same coordination and environment of nitrate ions. 7.5. NaNO3 –RbNO3 The FACTSalt web page [8] depicted this phase diagram with one eutectic invariant, one peritectic invariant with an incongruent melting point compound NaRb3 (NO3 )4 and, finally, no miscibility in the solid state. No more data have been found for this system. 7.6. KNO3 –RbNO3 This is the most complex binary phase diagram for this family of compounds. In the FACTSalt web page,[8] it is shown that at low temperature, there is no miscibility in the solid state. Above the first eutectoid, there exists a large solid solution domain with the structure of the potassium nitrate high-temperature polymorph (β-RbNO3 ). For the rubidium rich part there is another eutectoid and another region of solid solution with structure of I-RbNO3 . Xu [168] reported that for compositions above 96% IV-RbNO3 , a solid solution exists at room temperature; the author worked with Raman spectroscopy and assigned the structure of the principal regions of this phase diagram.

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7.7. LiNO3 –CsNO3 In the FACTSalt web page,[8] it is presented by a high-temperature equimolar composition, congruent melting compound and two eutectic invariants. According to this, there is no miscibility in the solid state. Drira et al. [169] studied the system by thermal analysis; they found a similar phase diagram. Xu [167] presented the congruent melting compound LiCs(NO3 )2 detected by Raman spectroscopy. 7.8. NaNO3 –CsNO3 In the FACTSalt web page,[8] a simple eutectic without miscibility in the solid state is reported. This phase diagram presents two regions of solid-state immiscibility due to the CsNO3 phase transition. Jriri et al. [170] reported a similar NaNO3 –CsNO3 phase diagram. Finally, they questioned a fundamental aspect: what is the effect of other nitrates in the second-order transition of NaNO3 ? When we take a look at binary systems containing NaNO3 presented here, we observe that they are described as a eutectic behaviour except for the NaNO3 –KNO3 system. In this last system, the phase transition is KNO3 (β) + NaNO3 (II) → NaNO3 (I). Then a high-temperature solid solution is formed. For the others, the proposed reaction is XNO3(l) + NaNO3 (II) → XNO3(l) + NaNO3 (I), where X = Li, Rb or Cs. 7.9. KNO3 –CsNO3 In the FACTSalt web page,[8] a eutectic invariant with solid-state miscibility in the terminal compositions is stated. Therefore, two eutectoid invariants are also depicted. In contrast, Zamali and Jemal [171] experimentally found a similar phase diagram but only confirmed the eutectoid at high caesium nitrate composition. The other invariant was not detected. 7.10. RbNO3 –CsNO3 In the FACTSalt web page,[8] a eutectoid invariant with a total miscibility at high temperature is shown, and then a minimum of the melting point is proposed. Secco and Secco [172] have demonstrated by XRD that a terminal solid solution exists at least until 10% of the other component at room temperature. Moreover, they proposed a somewhat different phase diagram. Unfortunately, they were not able to completely define all transitions by using thermal analysis. Additionally, Wacharine et al.,[151] also working with thermal analysis, gave a detailed description of this phase diagram which, according to them, is characterized by a eutectic, two eutectoids, and an azeotropic-like invariant, three limited solid solutions, and a continuous solid solution at high temperature. Therefore, their phase diagram proposition is quite different from that proposed in the FACTSalt web page.[8] Nasirov et al. [173] and Asadov and Nasirov [174] determined the equilibrium temperature of the transitions IV–III, III–II and in Rb0.975 Cs0.025 NO3 being 393 ± 0.5 and 421 ± 0.5 K respectively. They also demonstrated that these transitions are not destructive; but only ‘displacive’: in fact, the crystals involved in the transitions maintain their shape. These authors [175] continued their work studying Rb0.9 Cs0.1 NO3 composition. They started with a rhombohedral RbNO3 -based ¯ at 500 K. This, in turn, solid solution (P31 ) which undergoes a transition to a cubic phase (Fm3m) transforms into a new tetragonal phase at 550 K (I4) which has a transition to a cubic phase ¯ at 590 K. Therefore, a new phase domain may be introduced into the system. Nasirov (Fm3m) and Asadov [176] studied the formation rate (solid–solid transformations) of α–β–Rbx K1−x NO3 (with × up to 0.1) with perfect faceted single-crystals as a function of supercooling. They concluded that the growth of transformation is independent from the composition, but obviously depends on the supercooling.

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8. Discussion The polymorphism in alkali nitrates is rich in detail. We find eight different phases at ambient pressure, RbNO3 being the richest with four polymorphs. Evidently, the larger the cation the higher the probability of the nitrate group to be disordered. Notwithstanding, only four out of the 12 phases have been definitively described as being disordered. III-CsNO3 and I-CsNO3 are described as having 12-fold and 8-fold disorder, respectively. Furthermore, many authors have tried to assign either rotational or positional (two-position) disorder to the high-temperature polymorphs of NaNO3 and KNO3 . At high temperature (more entropic energy), the disorder in the ¯ phases of LiNO3 and NaNO3 (the two phases) can have nitrate group is easier. In this sense, R3c some disorder at the highest temperature range of their existence. Additionally, Stromme described all the high-temperature forms as being disordered between the calcite and aragonite structure types.[33,141,152,153] Therefore, it seems probable that all phases present some disorder. The nitrate group is considered planar in all the structures reviewed except for β-KNO3 and II-RbNO3 which are high-temperature phases. It is worth noting how the NO− 3 group local symmetry (D3h ) imposes to the space groups of all phases to have a triad axis, except for α-KNO3 . In this phase, we have two non-equivalent oxygen atoms in the asymmetric unit. For the P31 phases of RbNO3 and CsNO3 at room temperature, there are nine non-equivalent oxygen atoms; in these cases, the triad axes do not pass through any atom, so that equivalent oxygen atoms belong to different nitrate groups (this statement is evident because the nitrate group is planar and the screw axes 31 have a translation of 1/3 c). In the rest of the phases, oxygen atoms within a nitrate group become equivalent. This polymorphic behaviour has repercussions in the phase diagram boundaries. In Figure 11, we notice a high dispersion in the behaviour of binary phase diagrams of alkali nitrates. Therefore, we may ask what the reason is. Can we make a systematic classification to predict the binary behaviour? Oonk [177] made a systematic classification of alkali halide series of the phase diagrams and proposed a rule. He found that the larger the radius difference, the lower is the solubility in the solid state. In this sense, we go from a eutectic invariant with a solid solubility below 1 ppb (at room temperature), through complete miscibility just below the solidus line, to complete solubility at room temperature. In contrast to the alkali halides, where all the compounds analysed crystallize in the cubic system at room temperature, 17 of them have the NaCl struc¯ ture type (Fm3m); we have to manage here with different space groups for the components of the family. Furthermore, here we have the nitrate group complication; it is not a spherical ion. However, we can divide the family of binary phase diagrams into three categories depending on the crystalline system at high temperature: both crystal structures are hexagonal, both are cubic, or one is hexagonal and the other is cubic. We recall m as the mismatch parameter defined by Equation (1): m=

V , Vs

(1)

where V is the absolute difference between the molar volumes of a complete XNO3 formula and Vs is the smaller of the two volumes. In this case, we calculate the molar volume of the high-temperature forms from selected crystallographic data given in Table 1. Then, the misfit parameters for the binary systems (at different temperatures) are given in Table 2. In Table 2, we have separated the alkali series system according to the high-temperature component polymorphs (brown: hexagonal phases; purple: cubic phases; and green: hexagonal-cubic phases). It is worth remembering that in order to have a complete solid solution, components must have the same space group. However, Benages-Vilau et al. [100] have experimentally and theoretically demonstrated that NaNO3 –KNO3 form a continuous solid solution just below the solidus line.[102] This situation is also proposed by FACTSalt [8] and depicted in Figure 11.

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R. Benages-Vilau et al. Table 2.

Misfit values for alkali nitrate systems.

m

Na

K

Rb

Cs

Li Na K Rb

0.37

0.73 0.26

1.02 0.48 0.17

0.87 0.87 0.08 0.08

For the hexagonal system compounds, we can make a cut-off at m = 0.30. For m < 0.30, we have a complete solid solution. On the contrary, with m > 0.30 we obtain eutectic invariants without appreciable terminal solid solution. Finally, for m > 0.40 an intermediate compound is formed. We have to remember here that LiNO3 –KNO3 presents an intermediate compound LiK(NO3 )2 [165–167] that probably has hexagonal symmetry. Therefore, this phase diagram is described by two eutectic invariants. In the cubic phases of the CsNO3 –RbNO3 phase diagram, we observe a complete solid solution even though the components do not have the same space group. For the hexagonal-cubic symmetry phase diagrams, we can also impose the same cut-off m = 0.30. In this case, different crystal systems play an important role; we do not expect total miscibility. However, we propose first, that for m < 0.30 we observe a eutectic with terminal solid solutions. And second, for m > 0.30, we observe a eutectic invariant without a significant solid solution. Furthermore, when m > 0.40, an intermediate compound exists. It is curious that for larger mismatches an intermediate compound forms. But, taking into account different compounds’ symmetry, it is possible that an intermediate compound relaxes the total energy of the system. In FACTSalt web page [8], the CsNO3 –RbNO3 phase diagram is simulated as a minimum of the melting point. However, Wacharine et al. [151] experimentally demonstrated that the CsNO3 – RbNO3 phase diagram has, in reality, a eutectic invariant (among other transitions that we are not interested in). In summary, we can extract the following common conclusions for this whole phase diagram family, taking into account the mismatch parameter m: • m < 0.30: a complete solid solution if the crystal system is the same, or eutectic invariants with terminal solid solutions when the crystal system is different. • m > 0.30: eutectic invariant without solid solution. • m > 0.40: eutectic invariant without solid solution and the intermediate stoichiometric compound. At room temperature, we obtain three kinds of morphologies calculated by the BFDH approach depending on the isostructurality of nitrates. LiNO3 and NaNO3 compounds have the same growth ¯ and morphology as calcite (calculated by the same approach).[34] It consists of the {012}, {0 1 2} {001} forms. Similarly, RbNO3 and CsNO3 also have the same calculated morphology that is built from {100}, {010}, (101} and {011}. KNO3 separates these two morphologies with the {010}, {110} and {011} forms. Only for NaNO3 and KNO3 are there available data for surface energy calculations. The equilibrium morphology derived from these values differs from that (growth morphology) calculated by the BFDH approach. In KNO3 , Lovvik et al. [139] showed that the most important form is {001} and for NaNO3 the equilibrium morphology is composed only by {104} form.[76] Neither of these two forms appeared in the BFDH derivation for their respective compounds.

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Concerning crystal growth measurements, it should be noted that only NaNO3 and KNO3 present some interesting data. Unfortunately, the crystal growth control in these compounds is difficult because their solubility curve slope is very high and, additionally, the supersaturation is difficult to control as Benages-Vilau et al. [59] have demonstrated for NaNO3 . These facts, along with a lack of comparable crystal growth conditions, introduce dispersion in the published results. Further, we have to highlight that much work has to be done in these compounds to have a unified vision of crystal growth data. We need a standard procedure in order to compare the data from all the compounds.

9. Conclusions In this paper, we have reviewed the most important information about crystal structure, polymorphism, phase transitions, crystal growth and morphology, solid-state miscibility and binary phase diagrams among alkali nitrates. Sodium nitrate and potassium nitrate were studied in a deeper way, but more work is needed for a complete and unequivocal description in the fields treated in this review. It is curious that surrounding such simple compounds, there was so much discussion and controversy for the high-temperature polymorph crystal structures. It is clear that some disorder exists there, but the different models proposed from XRD data fit practically with the same confidence for each phase. Consequently, it is not easy to describe the phases properly. Authors have agreed with the diverse phase stability domains; only the γ-KNO3 phase domain is not well described. It is a metastable phase that appears upon cooling the β-KNO3 phase, but its temporal stability depends on many factors as has been reviewed here. Nonetheless, this phase introduces some difficulties in the phase diagram determinations because solid solutions with LiNO3 and II-NaNO3 have been described. Many papers devoted to alkali nitrate phase-diagram determination have been published but a complete experimental determination has not been carried out. Nonetheless, the FACTSalt web page has simulations that seem to be quite correct. From this, and morphological data at high temperature, we propose a general boundary for the mismatch (m) parameter in order to group the different behaviours by taking into account only geometrical data. • m < 0.30: a complete solid solution if the crystal system is the same, or eutectic invariants with terminal solid solutions when the crystal system is different. • m > 0.30: eutectic invariant without solid solution. • m > 0.40: eutectic invariant without solid solution and intermediate stoichiometric compound. Crystal morphology is not extensively studied, but for NaNO3 and KNO3 . For the former, a complete periodic bond chain analysis is made. In contrast, for the latter, some theoretical crystal morphology has been proposed on the ground of the electric charge distribution on different ions. NaNO3 and KNO3 are important in the industrial field, so that industrial crystallization is the most studied part. In contrast, the isothermal growth mechanisms were not studied. Because of this, thermodynamic evaluation was not investigated. Only for NaNO3 has a thermodynamic evaluation of crystal growth been investigated. Furthermore, the intrinsic difficulties found in the control of the experimental parameters may be the reason for the lack of thermodynamic and kinetic data for crystal growth in alkali nitrates.

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Acknowledgements We gratefully thank the Ministerio de Ciencia y Tecnologia for the financial support through the CICYT (MAT2011-27225), the Ministerio de Educación through la Factoria Cristalográfica (Consolider-Ingenio, CSD2006-15), the Generalitat de Catalunya through the Grup Consolidat (2009SGR1307), Xarxa deReferència R + D + I en Material Avançats per l’Energia (XaRMAE), and Abengoa enterprise for the financial support through a CENIT program: Consorcio Solar de I+D ConSOLi+da. The authors also acknowledge the referees and the joint main editor of the journal.

Notes on contributors Dr R. Benages-Vilau was born in 1981 at L’Hospitalet de Llobregat (Barcelona, Spain). He took the Chemistry degree at the University of Barcelona (UB) in 2006, Materials’Engineering at Polytechnique University of Catalonia (UPC). He holds a Master’s degree in Crystallography and Crystallization at International University Menéndez Pelayo and a PhD doctorate in Earth Science. He is the co-author of various papers related to solid-state science. He is interested in crystal growth and crystal morphology of materials as well as phase diagram determination.

Dr Teresa Calvet is associate professor of Barcelona University. She has a degree in Geology and a PhD degree in Science, both from the University of Barcelona. Her basic and applied research activity is mainly focused on the polymorphism and solid-state miscibility of different materials, such as aromatic (benzene derivatives) and long-chain compounds (alkanes, alkanols, fatty acids and other lipid materials) as well as inorganic materials. Thus, her scientific activity is supported by collaborations with internationally recognized research groups from Spain, France, The Netherlands, Italy and Japan, and it appears in many scientific international papers basically belonging to the crystallography, physical chemistry and energy storage fields.

Prof. Miquel Àngel Cuevas-Diarte has a degree in Geology by the Universitat de Barcelona, and a PhD in Science by the University of Barcelona in collaboration with the Université Bordeaux I supported by a grant of the French government. He is working in polymorphism and solid-state miscibility. Fundamental and application works for thermal energy storage and crystallography of food components are complemented. Collaboration with other groups from Spain, France, The Netherlands, Italy and Japan are usual. He was Professor of Crystallography and Mineralogy of the Universitat de Barcelona. He is now Emeritus Professor of the Universitat de Barcelona.

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Crystallography Reviews Subject index Alkali nitrates 1–4, 17, 18, 20, 22, 24 Caesium nitrate 16–18, 21, 31 Crystal growth 1–3, 8, 9, 12, 16, 18, 24–30 Crystal structure 1, 3, 4, 7, 9, 10, 14, 16, 20, 22, 24, 26, 30, 31 Eutectic behaviour 18, 19, 21 Lithium nitrate 3, 26 Lithium-caesium nitrate 16–18, 21, 31 Lithium-potassium nitrate 9, 11, 12, 20, 24, 26, 28, 29–31 Lithium-rubidium nitrate 2, 14, 16, 18, 25, 26, 30 Lithium-sodium nitrate 3, 6–9, 24, 26–29, 31 Miscibility 1, 3, 18, 20–25 Morphology 1, 3, 6, 8, 9, 13, 14, 16, 18, 19, 23–29 Phase diagrams 1, 3, 18, 20, 22–24, 28, 31 Polymorphism 1–3, 9, 14–16, 18, 22, 24, 25, 28, 29 Potassium nitrate 9, 11, 12, 20, 24, 26, 28, 29–31 Potassium-caesium nitrate 16–18, 21, 31 Potassium-rubidium nitrate 2, 14, 16, 18, 25, 26, 30 Rubidium nitrate 2, 14, 16, 18, 25, 26, 30 Rubidium-caesium nitrate 16–18, 21, 31 Sodium nitrate 3, 6–9, 24, 26–29, 31 Sodium-caesium nitrate 16–18, 21, 31 Sodium-potassium nitrate 9, 11, 12, 20, 24, 26, 28, 29–31 Sodium-rubidium nitrate 2, 14, 16, 18, 25, 26, 30

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