Novel High-Temperature Modification of Belomarinaite KNaSO₄: Crystal Structure and Thermal Order–Disorder Phase Transitions

Abstract

Belomarinaite KNaSO₄ (space group P3m1, a = 5.6072(3), c = 7.1781(4) Å and Z = 2) has been studied by high-temperature single crystal X-ray diffraction. The K and Na atoms are disordered, and M1(1c) and M2(1b) sites merge into an M1(2d)(K50%/Na50%) site with increasing temperature, and novel translationsgleiche phase transition of belomarinaite KNaSO₄ (P3m1 → P-3m1) was revealed at 123 °C. Then, the temperature increase leads to phase transition of $P\overline{3}m1$-polymorph of KNaSO₄ to α-KNaSO₄ (P6₃/mmc) at 446 °C, and sodium and potassium atoms in K1(1a) and Na1(1b) sites merged into an M4(2a)(K50%/Na50%) site. Crystal structures of KNaSO₄ were refined at 300, 500 and 750 °C to R₁ = 0.057, 0.056 and 0.048, respectively. The BVS maps and bond-valence energy landscape (BVEL) have been calculated, and the probability of the Na⁺ migration has been predicted using structural data for belomarinaite at 25 °C. The Na⁺ ion migration can occur at 2.14 eV in the ab plane and 2.80 eV along the c axis at 25 °C.

1. Introduction

Belomarinaite, KNaSO₄, is a volcanogenic mineral from the Tolbachic volcano, Kamchatka peninsula, Russia. Belomarinaite crystallizes in a trigonal crystal system (space group P3m1, a = 5.6072(3), c = 7.1781(4) Å and Z = 2). The mineral was reported in [1] as pale-blue to green arborescent aggregates of tabular crystals. It was discovered on the Toludskoe lava field, formed during the Tolbachik Fissure eruption in 2012–2013 (55°45′1.32″ N, 160°19′40.74″ E, altitude 1480 m). The specimen was found in the high part of a lava cave. Data on the Tolbachik Fissure eruption in 2012–2013 are given in [2].

Then, belomarinaite was found in the Arsenatnaya fumarole [3]. These belomarinaite specimens are colorless or white, semitransparent hexagonal tabular or lamellar crystals along with johillerite, nickenichite and calciojohillerite. The most complete list of minerals identified on the Tolbachik volcano is given in the review paper [4].

The thermal behavior of belomarinaite was studied using high temperature X-ray powder diffraction over the temperature range of 30–800 °C and using DSC/TG over the temperature range of 30–1000 °C in [5]. The existence of a high-temperature modification (P6₃/mmc) of this mineral above 446 °C has been demonstrated. It was determined that the volumetric expansion varies for the low-temperature phase within the range of 80−200 × 10^–6 °C⁻¹ and 350–300 × 10⁻⁶ °C⁻¹ for the high-temperature phase.

The crystal structure of the synthetic KNaSO₄ (space group P3m1, a = 5.6066(7), c = 7.177(1) Å, Z = 2 and R₁ = 4.2%) was refined in [6]. The crystal chemistry of related structures has been reviewed in [7,8,9,10,11,12].

The thermal behavior of all compounds of the K₂SO₄–Na₂SO₄ system was studied using thermal analysis and powder high-temperature X-ray diffraction, but only the end-members of the series were studied using single crystal high-temperature X-ray diffraction [13,14,15,16,17,18,19]. In the high-temperature phase (P6₃/mmc), a reorientation of SO₄ tetrahedra (dynamic disorder) is observed, which at different temperatures can be described in the apex and edge models. Thus, it will be interesting to know whether a similar reorientation of SO₄ tetrahedra will be observed for the mineral belomarinaite KNaSO₄, and what model of dynamic disorder will prevail in its crystal structure.

In this study, the thermal behavior of KNaSO₄ was investigated using single crystal high-temperature X-ray diffraction. Crystal structures were refined at 300, 500 and 750 °C. New polymorphic modification of KNaSO₄ ($P\overline{3}m1$) was discovered.

2. Materials and Methods

2.1. Samples

The studied sample is belomarinaite holotype with empirical formula (K_0.95Na_0.92Cu_0.04)Σ_1.91S_1.01O₄ [1]. The suitable crystal of belomarinaite for single crystal X-ray diffraction (0.05 × 0.04 × 0.03 mm) was selected from holotype sample.

2.2. Single Crystal X-ray Diffraction

The thermal behavior of belomarinaite was studied by high-temperature single crystal X-ray diffraction analysis using a Rigaku XtaLAB Synergy-S diffractometer (Rigaku, Tokyo, Japan) (MoKα radiation, 50 kV and 1.0 mA) equipped with high-speed direct-action detector HyPix-6000HE (Rigaku, Tokyo, Japan). The data were collected at 300, 500 and 750 °C. The heating process was controlled by «Hot Air gas blowers» system (Rigaku, Tokyo, Japan). A single crystal of belomarinaite was placed and fixed in quartz capillaries with approximately 10 micron wall thickness. The hemisphere of diffraction data (frame width 0.5°) was collected for each temperature value. The orientation of the crystals was not changed during all temperature measures. The CrysAlisPro software (version 1.171.39.44) was used for the further processing [20]. An absorption correction was introduced by the SCALE3 ABSPACK algorithm [21]. The crystal structures have been solved and refined using Jana 2006 software [22]. The crystal structure of belomarinaite at 300 °C was initially refined in the P3m1 space group. Due to high correlation between coordinates of M1(1c)(Na/K) and M2(1b)(K/Na) sites, the ADDSYM program within the PLATON software package [23] was used for the checking of missing symmetry operations, which led to the crystal structure refinement in the P-3m1 space group. The crystal structure data and refinement parameters for all modifications are shown in

Table 1. Crystallographic data and refinement parameters for belomarinaite at 25, 300, 500 and 750 °C.

Chemical Formula	KNaSO4
Mr	158.1
Crystal system,	Trigonal		Hexagonal
Space group	P3m1	$P\overline{3}m1$	P63/mmc	P63/mmc
Temperature °C	25 [1]	300	500	750
a, c (Å)	5.6072(3), 7.1781(4)	5.6914(6), 7.370(3)	5.669(5), 7.750(3)	5.654(4), 8.353(6)
V (Å3)	195.45(2)	206.73(9)	215.68(8)	231.25(16)
Z	2
Radiation type	Mo Kα
µ (мм−1)	1.87	1.77	1.70	1.58
Diffractometer	Rigaku XtaLAB Synergy-S
No. of measured, independent and observed [I > 3σ(I)] reflections	2069, 713, 664	684, 221, 173	738, 116, 47	1452, 103, 28
Rint	0.012	0.035	0.075	0.082
(sin θ/λ)max (Å−1)	0.851	0.686	0.669	0.682
R(obs), wR(obs), S	0.027, 0.033, 1.95	0.057, 0.088, 3.73	0.056, 0.067, 1.74	0.048, 0.103, 1.16
Parameters	38	21	14	14

. Final atomic positional and displacement parameters (Ų) as well as selected bond lengths are given in

Table 2. Selected bond lengths for belomarinaite at 25, 300, 500 and 750 °C.

25 °C [1]		300 °C		500 °C		750 °C
Bond	Distance, Å	Bond	Distance, Å	Bond	Distance, Å	Bond	Distance, Å
K–O3	2.842(7) × 3	K–O2	2.943(12) × 6	M4–O1	2.724(7) × 6	M4–O1	2.746(12) × 6
K–O4	2.885(7) × 3
K–O1	3.243(2) × 3	K–O1	3.305(2) × 6	M4–O2	2.835(12) × 6	M4–O2	2.66(8) × 12
K–O2	3.254(2) × 3			<M4–O>12	2.78	<M4–O>18	2.69
<K–O>12	3.056	<K–O>12	3.124
Na–O3	2.332(8) × 3	Na–O2	2.405(10) × 6
Na–O4	2.355(8) × 3
<Na–O>6	2.344	<Na–O>6	2.405
M1–O1	2.588(10)	M1–O1	2.59(2)	M3–O2	2.50(3) × 6	M3–O2	2.76(10) × 12
M1–O3	2.816(4) × 6	M1–O2	2.859(3) × 6	M3–O1	2.848(6) × 6	M3–O1	2.83(2) × 6
M1–O4	3.050(8) × 3	M1–O2	3.210(15) × 3	<M3–O>12	2.67	<M3–O>18	2.78
<M1–O>10	2.863	<M1–O>10	2.937
M2–O2	2.388(7)
M2–O2	2.815(2) × 6
M2–O2	3.150(5) × 3
<M2–O>10	2.873
S1–O1	1.378(10)	S1–O1	1.42(2)	S1–O2	1.50(3) × 6	S1–O2	1.37(3) × 12
S1–O4	1.446(4) × 3	S1–O2	1.441(6) × 3	S1–O1	1.358(9) × 3	S1–O1	1.48(2) × 3
<S1–O>4	1.429	<S1–O>4	1.435	<S1–O>9	1.45	<S1–O>15	1.39
S2–O2	1.485(8)
S2–O3	1.458(5) × 3
<S2–O>4	1.465

, Tables S1 and S2, cifs and checkcifs are in supplementary.

2.3. BVS for Na-Ion Transport

BVS maps were calculated for a preliminary assessment of possible Na-ion pathways. The BVS maps at various bond–valence mismatches Z_i − Σ_si (Z_i = 1 for Na⁺, s_i = exp[(R₀− R)/b], where R₀ and b are empirical constants [24], R is the cation–anion distance, and Σs_i is BVS) were calculated using the BondStr program [25] for Na⁺ sites in grids with steps of Δx, Δy and Δz = 0.1 Å in the unit cell with the fixed sites of other atoms. The calculated data were visualized using VESTA software [26].

2.4. Structural Complexity Calculation

The structural complexity measures of different KNaSO₄ modifications were calculated as the amounts of Shannon information per atom (^strI_G) and per unit cell (^strI_G,total) using the methodology discussed in [27,28] and the following equations:

$$I_G={\sum }_{i=1}^K{p}_i{\log }_2{p}_i\left(\frac{bits}{atom}\right)$$

(1)

$$I_{G,total}=-\nu {\sum }_{i=1}^K{p}_i{\log }_2{p}_i(bits/u.c.),$$

(2)

Above, k is the multiplicity of a crystallographic orbit, p_i is the random choice probability for an atom from the ith crystallographic orbit, that is

$$p_i=m_i/\nu ,$$

(3)

where m_i is the multiplicity of a crystallographic orbit relative to the reduced unit cell and ν is the number of atoms in the reduced unit cell. TOPOSPro software was used for the calculations [29].

3. Results and Discussion

3.1. Thermal Order–Disorder Phase Transitions

Belomarinaite KNaSO₄ crystallizes in the P3m1 space group, and in the crystal structure, there are two symmetrically independent ^[4]S (S1 and S2), one ^[6]Na, one ^[12]K, two ^[10]K/Na (M1 and M2) and four O (O1, O2, O3, O4) sites (Figure 1 bottom). Belomarinaite is isotypical with the synthetic compound KNaSO₄ [6]. In the crystal structure of the synthetic compound, the K and Na atoms are ordered at the M2(1b) and M1(1c) sites. In the belomarinaite crystal structure, Na and K are disordered over M1 and M2 sites. Apparently, this is explained by the high-temperature genesis of the mineral. New data on the belomarinaite crystal structure obtained in this work at 300 °C indicate that with increasing temperature, the belomarinaite crystal structure changes slightly and translationsgleiche phase transition occurs. The belomarinaite crystallizes in the $P\overline{3}m1$ space group at 300 °C. The presence of this transition is confirmed by the DSC data of synthetic KNaSO₄, e.g., [10,30,31], and those of belomarinaite [5]; there are three thermal effects at about 123, 446 and 840 °C. It was suggested in [30] for synthetic KNaSO₄ that the first broad endothermic peak corresponds to a second-order phase transition. Thus, according to the high-temperature single crystal X-ray diffraction data, the first peak can be attributed to a P3m1↔ P-3m1 phase transition. Apparently, it is caused by the mobility of Na⁺ and K⁺ cations with increasing temperature. As a result, they are statistically distributed over M1(1c) and M2(1b) sites, which leads to the appearance of an inversion center and the existence of only the M(2d) site (Figure 1 middle). The second and third peaks are attributed to a $P\overline{3}m1$ → P6₃/mmc phase transition and congruent melting of the solid solution, respectively, in accordance with the phase diagram [10].

In contrast to room temperature, in the crystal structure of belomarinaite at 300 °C, due to the presence of an inversion center, the number of symmetrically independent sites decreases: one for ^[4]S, one for ^[6]Na, one ^[10]K/Na (M1) and two for O. The <Na–O> (NaO₆) bond lengths increase from 2.344 Å (25 °C) to 2.405 Å (300 °C), and the <K–O> (KO₁₂) bond lengths increase from 3.056 Å (25 °C) to 3.124 Å (300 °C). The <(Na/K)–O> (M1O₁₀) and <(K/Na)–O> (M2O₁₀) bond lengths are 2.863Å and 2.873Å at 25 °C, respectively (Figure 2). In the $P\overline{3}m1$-polymorph, there is only an M1(2d) site coordinated by ten oxygen atoms with <M1–O> bond lengths equal to 2.937 Å (Figure 2). Na and K atoms are completely disordered in the M1(2d) site—50%/50%, due to its mobility, in contrast to room temperature, where the M1(1c) site is occupied by 78% Na and 22% K, while the M2(1b) site is occupied by 22% Na and 78% K. The <S–O> bonds in the S1O₄ and S2O₄ tetrahedra are in the range of 1.378–1.485 Å at 25 °C and 1.42–1.44 Å at 300 °C (Table 2).

The mineral crystallizes in the hexagonal crystal system, space group P6₃/mmc, Z = 2, at 500 and 750 °C. The process of K and Na disordering occurs in the M3(2d) and M4(2a) sites of the crystal structure without changing the symmetry.

After the $P\overline{3}m1$ → P6₃/mmc phase transition (446 °C) in the crystal structure of the high-temperature polymorph at 500 °C, the number of independent crystallographic sites decreases again. The M1(2d)(Na/K) site is preserved, and it is designated as M3(2d); there is M4(2a)(Na/K) instead of K1 and Na1 sites (Figure 1 top). In both sites, the K and Na atoms are disordered (M3: 50%/50% and M4: 50%/50%). There are S sites and O1 and O2 sites with occupancies of 0.66 and 0.33 (Figure 1). The M4–O bond lengths vary from 2.724 to 2.84 Å (500 °C) to 2.66–2.75 Å (750 °C), and the M3–O bond lengths vary from 2.50 to 2.848 Å (500 °C) to 2.76–2.83 Å (750 °C) (Figure 2). The S–O bonds in the SO₄ tetrahedra are in the range of 1.358–1.50 Å at 500 °C and 1.37–1.48 Å at 750 °C (Table 2). A presence of the short and long S–O bonds can be explained by libration effects, typical for the crystal structures with statistical or dynamical disorder. It is worth noting that the coordinates of oxygen sites differ at temperatures of 500 and 750 °C, which further indicates dynamic disorder.

The temperature dependencies of the unit cell parameters for belomarinaite in the temperature range of 25–800 °C were investigated by our group in [5]. The K and Na atoms are ordered in M1O₁₀ and M2O₁₀ polyhedra in the belomarinaite crystal structure at room temperature. According to [1], the M1O₁₀ and M2O₁₀ polyhedra share faces of 2.4 × 3.4 Ų, and the size of these faces is suitable for Na and K migration at high temperatures. With the temperature increasing, the atoms in the M1O₁₀ and M2O₁₀ polyhedra are disordered, and M1(1c) and M2(1b) sites merge into an M3(2d)(K50%/Na50%) site in the KNaSO₄ ($P\overline{3}m1$) crystal structure (Figure 3). Then, the sodium and potassium atoms in K1 and Na1 sites, which form the rods, merged into an M4(2a)(K50%/Na50%) site at 446 °C. Since the value of the c unit cell parameter is determined mainly by the polyhedra forming the rods (cf. 3.2) along the c axis, the disorder of cations in the M3(2d) site leads to a sharp increase in the a unit cell parameter. Then, the disorder of K1(1a) and Na1(1b) sites leads to a sharp increase in the c unit cell parameter (Figure 3). It should be noted that the migration paths of Na and K ions in the high-temperature phase (P6₃/mmc) pass through both M3(2d) and M4(2a) sites.

3.2. Temperature-Dependent Inheritance of KNaSO₄ Structural Transformations

The crystal structure of KNaSO₄ under ambient conditions consists of complex columns of the KO₁₂, NaO₆, M1O₁₀ and M2O₁₀ (M = K, Na) and SO₄ polyhedra [7,8,9,12]. Crystal structures of belomarinaite and similar (aphthitalite-like) minerals can be described as pseudo-close-packed cationic arrays with hexagonal layers parallel to (001) [32,33,34,35,36,37], as well as mixed frameworks consisting of columns formed by octahedral–tetrahedral clusters of MO₆ octahedra that share six vertices with six adjacent SO₄ tetrahedra [37] (Figure 4).

If the temperature of the crystal increases, the thermal motion of atoms increases, e.g., [38,39], and the areas of solid solutions’ miscibility increases with increasing temperature. The thermal motion of atoms gradually decreases with a decrease in temperature. Therefore, the degree of atom difference increases, and atoms tend to be ordered through different sites in a crystal structure.

The crystal structures of compounds of the Na₂SO₄–K₂SO₄ series were firstly described as consisting of microblocks, including the assumption of the genesis of minerals structurally close to the compounds of this series, as formed from a single type of parent microblock in [40]. The crystal structures of the α-Na₂SO₄ and α-K₂SO₄ sulfates contain disordered SO₄ tetrahedron and two symmetrically independent sites for alkali cations. The parent FBB consists of a NaO₆ or KO₆ octahedron surrounded by six disordered SO₄ tetrahedra (a tetrahedron with disordered oxygen atoms) (Figure 5). The term microblock was proposed in [41]. A microblock [M(TO₄)₆] that consisted of an octahedron interlinked by six vertices with six adjacent tetrahedra was considered a structural unit inherited upon cooling from a high-temperature disordered parent unit [40].

At high temperatures, dynamic disorder exists in the α-Na₂SO₄ and α-K₂SO₄ structures, which leads to the formation of inherited microblocks under cooling. Phase transitions in the Na₂SO₄–K₂SO₄ series are reversible, and therefore, we can describe the subsequences of phase transitions upon cooling, since a high-temperature phase crystallizes from the melt.

The disordered SO₄ tetrahedron can be represented as the five different orientations of SO₄ tetrahedra, and only one is possible at a time [15,16,17,18,19,42] and references terrain (Figure 5). In the trigonal crystal system, 15 types of microblocks were derived that can be obtained by cooling [40] (Figure 5). Some of these microblocks were derived in [41] for heteropolyhedral frameworks, and then, they were described as “elementary bricks” of the mixed octahedral–tetrahedral frameworks [36]. All microblocks derived in 1975 [41] have –3m or 3m symmetry.

All structures in the Na₂SO₄–K₂SO₄ system (excluding Na₂SO₄-Fddd) consist of these microblocks with the SO₄ tetrahedra in one of the described orientations [40]. A transition from the parent block to the inherited block occurs upon cooling of the high-temperature modification that is structurally similar to α-Na₂SO₄. All orientations of the tetrahedra that can be inherited from the parent microblock of the high-temperature phase are in in the crystal structure of dobrovolskyite Na₄Ca(SO₄)₃ [37]. This mineral was found in association with petrovite [43].

The crystal structure of belomarinaite can be described as a three-dimensional framework consisting of K–O, Na–O polyhedra and SO₄ tetrahedra. The framework consists of rods elongated along the c axis which formed by NaO₆ or KO₆ octahedron sharing six corners with six adjacent SO₄ tetrahedra (Figure 1 and Figure 2). These microblocks sharing corners with the tetrahedra and faces with the octahedra form rods along the c axis.

The structures of low-temperature modifications ($P\overline{3}m1$ and P3m1) consist of microblocks 11 and 22, and high-temperature modifications (P6₃/mmc) are formed by parent FBB—the disordered octahedral MO₆ (M = Na, K) site is surrounded by six disordered tetrahedra. Microblock designations are given in accordance with [40].

3.3. Sodium-Ion Migration in KNaSO₄ at Different Temperatures

The BVS maps and bond-valence energy landscape (BVEL) have been calculated, and the probability of the Na⁺ migration has been predicted using structural data for belomarinaite at 25 and 300 °C (Figure 6). The Na⁺ ion migration can occur at 2.14 eV in the ab plane and 2.80 eV along the c axis at 25 °C, and the Na⁺ ion migration can occur at 1.85 eV in the ab plane and 2.21 eV along the c axis at 300 °C. Usually, percolation energy of 1.6 eV for Na⁺ ion migration in compounds is promising for solid-state electrolytes [44]. Previously, experimental studies for this compound showed significant electrical conductivity of the high-temperature phase of KNaSO₄ [30].

Apparently, the fact that all sites for alkali cations in P3m1 and $P\overline{3}m1$ polymorphs are completely occupied makes it difficult for the movement of ions, which leads to high values of activation energy, as well as to small values of conductivity according to the [30] data.

We also calculated possible migration paths of Na ions at 500 °C. Quantitative estimates of migration barriers are not given, since the bond-valence parameters at such a temperature will differ significantly from room-temperature ones. Nevertheless, in our opinion, such a calculation is capable of qualitatively showing the migration paths of Na and K ions at high temperatures. This allows us to conclude that both M3(2d) and M4(2a) cation sites are involved in the migration path of Na and K ions.

3.4. Structural Complexity

The information-based structural complexity parameters [27,45] for different KNaSO₄ modifications are listed in

Table 3. The structural complexity of belomarinaite KNaSO₄ modifications.

Temperature, °C	Space Group	IG (bits/atom)	IG, total (bits/cell)
25	P3m1	3.128	43.793
300	$P\overline{3}m1$	2.271	31.793
500 (edge model) 1	P63/mmc	2.156	34.490
750 (apex model) 1	P63/mmc	2.156	34.490

¹ According to the works [16,18], both models exist simultaneously. But as the temperature increases, the occurrence of the vertex pattern increases.

. Generally, the complexities of the KNaSO₄ polymorphs are consistent with the observations that complexity decreases with increasing temperature [28]. A slight increase in structural complexity in the hexagonal modification can be caused by dynamic disorder in the structure, as a result of which, the oxygen sites are split.

4. Conclusions

The thermal structural evolution of belomarinaite was studied using single-crystal diffraction data. The novel translationsgleiche phase transition of belomarinaite KNaSO₄ (P3m1 → $P\overline{3}m1$) was investigated. The presence of the $P\overline{3}m1$ → P-3m1 phase transition is confirmed by the existence of a broad peak in the DSC curve, first discovered in [31], where the abrupt change in heat capacity was also studied, indicating a second-order transition. The symmetry increases with the increasing temperature in the trigonal–trigonal P3m1→ P-3m1 and trigonal–hexagonal $P\overline{3}m1$ → P6₃/mmc transformations, which is in agreement with the well-known tendency [38,46,47,48]. The K and Na atoms in the M1O₁₀ and M2O₁₀ polyhedra are fully disordered with temperature increasing, and M1(1c) and M2(1b) sites merge into an M1(2d)(K50%/Na50%) site in the P-3m1-polymorph of KNaSO₄ crystal structure. Then, the Na and K atoms in K1(1a) and Na1(1b) sites merged into an M4(2a) (K50%/Na50%) site at 446 °C and disordered phase or solid solution exists above 446 °C. The calculations of the bond-valence energy landscape (BVEL) show the probability of the Na⁺ migration at high activation energy of 2.14 eV in the ab plane and 2.80 eV along the c axis at 25 °C. Therefore, only the high-temperature phase of belomarinaite KNaSO₄ is suitable as a solid-state electrolyte. It has been shown that the crystal structures of KNaSO₄ modifications consist of M(TO₄)₆ microblocks. The inheritance of microblocks from the parent structural unit may help to clarify the genesis of similar minerals.