Six mineral species are known in the Na2SO4–K2SO4 system: thénardite Na2SO4 (Rasmussen et al. 1996), metathénardite Na2SO4 (Pekov et al. 2019), natroaphthitalite Na3K(SO4)2 (Schipalkina et al. 2020), belomarinaite KNaSO4 (Filatov et al. 2019), aphthitalite K3Na(SO4)2 (Okada and Osaka 1980) and arcanite K2SO4 (McGinnety 1972). Metathénardite is a high-temperature modification of α-Na2SO4 (P63/mmc) stabilized at room temperature by bivalent cations admixture, thénardite transforms in α-Na2SO4 (P63/mmc) at approximately 420°C (Rasmussen et al. 1996). All other minerals of this series undergo a reversible phase transition to high-temperature modifications isotypical with α–K2SO4 and α–Na2SO4 (both – P63/mmc) (Eysel 1973). Crystal structures of α–Na2SO4 and α–K2SO4 were refined using single-crystal X-ray diffraction data collected at 420 and 640°C, respectively (Arnold et al. 1981; Naruse et al. 1987). The geometrical parameters of these minerals are given in Table 1. Both coexistence and coherent conjugation of domains of crystal structures of the compounds of the Na2SO4–K2SO4 series are described in Schipalkina et al. 2021 and references therein.
The crystal structures of Na3K(SO4)2, KNaSO4, K3Na(SO4)2 at ambient conditions have practically the same unit cell parameters as its high-temperature modifications (Table 1). They structures are consisted of complex columns of the KO12, NaO6,MO10 (M = K, Na) and SO4 polyhedra (Moore 1973; 1976; 1981; Hawthorne et al. 2000). Crystal structures of aphthitalite-like minerals can be described as pseudo-close-packed cationic array with hexagonal layers parallel to (001) (O'Keeffe and Hyde 1985; Krivovichev and Filatov 1999; Vegas 2000; Gorelova et al. 2016; Krivovichev 2017; Shablinskii et al. 2021) as well as mixed frameworks consisting of columns formed by octahedral-tetrahedral clusters of the MO6 octahedra that share six vertices with six adjacent SO4 tetrahedra (Shablinskii et al. 2021). These clusters represent the microblocks 1 and 2 derived by Voronkov et al. 1975, which are the “elementary bricks” of the frameworks (Krivovichev 2017). According to the cited paper, these microblocks are modules, or the fundamental building blocks (FBB).
Table 1
Geometrical parameters of aphthitalite-like minerals and
Mineral name
|
Idealized formula
|
Sp. gr.
|
a’, Å
|
a, Å
|
c’, Å
|
c, Å
|
Reference
|
Aphthitalite
|
K3Na(SO4)2
|
P–3m1
|
5.680
|
= a’
|
7.309
|
= c’
|
Okada and Osaka 1980
|
Belomarinaite
|
KNa(SO4)
|
P3m1
|
5.604
|
= a’
|
7.178
|
= c’
|
Filatov et al. 2019
|
Natroaphthitalite
|
KNa3(SO4)2
|
P–3m1
|
5.601
|
= a’
|
7.1507
|
= c’
|
Shchipalkina et al. 2020
|
Möhnite
|
(NH4)K2Na(SO4)2
|
P–3m1
|
5.740
|
= a’
|
7.435
|
= c’
|
Chukanov et al. 2015
|
Metathénardite
|
α–Na2SO4
|
P63/mmc
|
5.347
|
= a’
|
7.0876
|
= c’
|
Pekov et al. 2019
|
α–K2SO4
|
α–K2SO4
(at 640°C)
|
P63/mmc
|
5.917
|
= a’
|
8.182
|
= c’
|
Arnold et al. 1981
|
Bubnovaite
|
K2Na8Ca(SO4)6
|
P31c
|
5.402
|
= 2a’
|
7.337
|
= 3c’
|
Gorelova et al. 2016
|
Hanksite
|
Na22K(SO4)9(CO3)2Cl
|
P63/m
|
5.445
|
= 2a’
|
7.08
|
= 3c’
|
Kato and Saalfield 1972
|
Dobrovolskyite
|
Na4Ca(SO4)3
|
R3
|
5.241
|
= 3a’
|
7.339
|
= 3c’
|
Shablinskii et al. 2021
|
Cuprodobrovolskyite
|
Na4Cu(SO4)3
|
R3
|
5.234
|
= 3a’
|
7.339
|
= 3c’
|
Shipalkina et al. 2023 (accepted)
|
The crystal structures of the α–Na2SO4 and α–K2SO4 high-temperature modifications are consisted of a disordered SO4 tetrahedron and two symmetrically independent sites for alkali cations. It should be noted that a dynamic disorder exists in the structures, which leads to a formation of inherited microblocks. One of the alkali cations occupying the octahedral MO6 (M = Na, K) site is surrounded by six disordered tetrahedra forming the fundamental building block (FBB) (Fig. 1) similar to microblocks found in the mixed (heteropolyhedral) frameworks (Voronkov et al. 1975) (see Fig. 4).
According to (Miyake et al. 1980; Arnold et al. 1981; Eysel et al. 1985; Naruse et al. 1987; Rasmussen et al. 1996; Pekov et al. 2019 and references terrain), the disordered tetrahedron can be represented as the SO4 tetrahedra of different orientations only one of which is possible at a time. Only five orientations of the SO4 tetrahedra were established by an analysis of single-crystal neutron and X-ray diffraction data, which were designated as “up” (apex model) (Fig. 2a), “down” (apex model) (Fig. 2b), “left” (edge model) (Fig. 2c), “tilting” (edge model) (Fig. 2d) and “right” (edge model) (Fig. 2e). In the “apex model”, one of the vertices of the SO4 tetrahedron is oriented up or down randomly in the [001] direction. In the case of the “edge model”, one of the edges of the tetrahedron is parallel to the L3 axis and the remained two vertices lie on the xy¼ mirror plane (Arnold et al. 1981). In the “edge model”, three different orientations can be obtained by a thermally induced rotation of the SO4 tetrahedron around the z-axis by 120°. Thus, in trigonal crystal system it is possible to derive 25 microblocks from the MO6 octahedron (M = Na, K) that shares six corners with six adjacent disordered tetrahedra. This number can be reduced to 15 if one removes the microblocks that can be obtained from others using symmetry operations (see Fig. 3).
After the analysis of the crystal structures of the minerals of the Na2SO4–K2SO4 series similar to high temperature α–Na2SO4 (see Table 1), it becomes clear that all the structures (excluding Na2SO4-Fddd) contain these microblocks with the SO4 tetrahedra in one of the described orientations (see Fig. 5–7), as if the tetrahedron remains in this orientation after a cooling of the high-temperature α–Na2SO4 and K2SO4 modifications. Based on this, one can conclude that the fundamental building block (FBB) of the high-temperature modifications is the “parent” one of the octahedral-tetrahedral microblocks that compose the mixed frameworks of the aphthitalite-like minerals investigated in this work. A transition from the parent block to the inherited one occurs upon cooling of the high-temperature modification that is structurally similar to α–Na2SO4. The parent FBB is consisted of the NaO6 octahedron surrounded by six disordered SO4 tetrahedra (tetrahedron with disordered oxygen atoms) (Fig. 1). Such a disordered tetrahedron has five (“apex model”) or nine (“edge model”) vertices. As it was mentioned above, the disordered tetrahedra can be represented as five different orientations of the ordered SO4 tetrahedra.
Description of the [ M ( T O 4 ) 6 ] microblocks
Let us assign the number 1 to denote the tetrahedron in the “up” orientation (apex model) (Fig. 2a), the number 2 – “down” orientation (apex model) (Fig. 2b), 31, 3 and 32 – “left” (edge model) (Fig. 2c), “tilting” (edge model) (Fig. 2d) and “right” (edge model) (Fig. 2d) orientations respectively due to a reason that they can be obtained from each other by the 120° rotation around the c axis. In these minerals and structurally similar compounds, only the tetrahedron orientations can be used in order to define microblocks since the octahedron maintains the same orientation. Then a microblock of any symmetry can be designated as a set of six digits, where the first three digits correspond to the three upper orientations of the tetrahedra, while the second ones – to the three lower orientations of the tetrahedra, for example, (1)(31)(2)(1)(31)(2). If one combines the microblock designation with its structural formula, there will be (SO4-2)(SO4-2)(SO4-2)Na(SO4-2)(SO4-2)(SO4-2) for aphthitalite and (SO4-31)(SO4-31)(SO4-31)Na(SO4-31)(SO4-31)(SO4-31) for Na2SO4 (Cmcm) if the sodium atom is in the octahedral site. All the microblocks derived by Voronkov et al. 1975 have − 3m or 3m symmetry. As it was mentioned above, if the symmetry of the microblock is 3m, then 25 types of microblocks can be combinatorically derived, which number can be reduced to 15 (Fig. 3).
With a decrease of the symmetry of the microblock, the number of combinatorically derived microblocks increases significantly. If the microblock has trigonal symmetry, then it can be defined by two-digit numbers: the first number corresponds to the upper part of the microblock (one octahedron and three tetrahedra) and the second one corresponds to the lower part of the microblock (one octahedron and three tetrahedra) (Fig. 4).
Indeed, configurations of the tetrahedra in the microblocks could also be of transitional forms. Therefore, the parameters that describe the ideal configurations that can be inherited from the parent (high-temperature) microblock should be pronounced. The M–O–T angles and M–O–T–O torsion angles were chosen as geometric parameters, which were calculated using experimental data for the parent microblock. Ideal parameters for each configuration are given in Table 2.
Table 2
Geometric parameters for different configurations of the SO4 tetrahedra in the microblocks inherited from the parent one.
Configuration
|
M–O–T
|
M–O–T–O
|
1
|
166.8(15)
|
180
|
2
|
166.8(15)
|
90
|
31
|
134.017(3)
|
90
|
3
|
172.38
|
115.94
|
32
|
134.017(3)
|
90
|
It should be noted that these microblocks can be considered as defect closest packings of anions as it was shown by Voronkov et al. 1975.
Temperature-dependent structural transformations in the compounds of the Na 2 SO 4 –K 2 SO 4 system, polymorphic modifications of Ca 2 SiO 4 ( P 6 3 / mmc, Pnma, Pna 2 1 , P21/n), bubnovaite K2Na8Ca(SO4)6and dobrovolskyite Na4Ca(SO4)3consisting of theM(TO4)6microblocks
An internal energy of crystals increases with a temperature growth. As a rule, it is manifested in a decreasing density of a crystal structure: a decrease in coordination number, an increase in bond lengths and size of polyhedra as well as its rearrangement. With a decrease in temperature, a thermal motion of atoms gradually decreases and a degree of their difference increases. Thus, atoms tend to order through different crystallographic sites of a structure.
Many minerals and compounds can be obtained from a melt, and a presence of rigid structural fragments in the melt has been known for a long time. At the same time, these fragments are the modules of which crystal structures can be composed. While crystallizing from a melt and changing configuration upon cooling, the FBBs can construct the related structures that are similar to each other and to their high-temperature “parent” ones.
To show the process of structural transformations from high-temperature modification to a low-temperature one, let us consider a number of examples what happens with microblocks in crystal structures with a decrease in temperature. For such a consideration, it is also convenient to use the compounds of the Na2SO4–K2SO4 system as examples, since all the framework crystal structures are composed of these microblocks.
The transformations of compounds of the Na2SO4–K2SO4 system
According to (Eysel 1973; Belousova et al. 2021), the K3Na(SO4)2 and KNaSO4 compounds upon cooling from the isotypical Na2SO4 (P63/mmc) high-temperature modification transform into the P–3m1 and P3m1 ones at 400 and 480°C, respectively. Probably a similar situation occurs during a cooling of the high-temperature Na3K(SO4)2 phase (P3m1), but this phase exists only as a form of an impurity-stabilized (Cu) modification. The structures of low-temperature modifications consist of the microblocks 11 and 22. As it was mentioned above, these microblocks can be inherited from the parent one upon cooling (Fig. 5). A combination of ionic radii of the [VI]K and [VI]Na atoms is suitable for maintaining the trigonal symmetry of the microblock, which is not the case for the end-members of the Na2SO4–K2SO4 series.
According to high-temperature X-ray diffraction data, the Na2SO4 (P63/mmc) high-temperature modification transforms upon cooling at 240 and 230°C into Pbnm and Cmcm phases, respectively (Rasmussen et al. 1996). At room temperature the Cmcm modification transforms into a modification with the Fddd space group. Structural relation is observed during the cooling. In this case, a microblock is formed that can be inherited from the high temperature modification, but the symmetry of the microblock is lower than trigonal one (Fig. 6). The decrease in the symmetry of the microblock is caused by the fact that the octahedra of the upper and lower microblocks share edges, and not faces or not connected through three SO4 tetrahedra. Such interconnection of the polyhedra is caused by an insufficiently larger ionic radius of the [VI]Na atom to share edges between the octahedra, but at the same time the radius is large enough to prevent a formation of the interconnection with three SO4 tetrahedra. The microblock in the Pbnm polymorphic modification can be denoted as (SO4-32)(SO4-31)(SO4-3)Na(SO4-3)(SO4-31)(SO4-32), and in the Cmcm one as (SO4-31)(SO4-31)(SO4-3)Na(SO4-3)(SO4-31)(SO4-31). The difference between the microblocks is a rotation of one of the tetrahedra by 120°, which is due to a fact that the modification with the Pbnm space group is the intermediate one and exists only in a limited temperature range (230–240 °С).
The high-temperature modification of K2SO4 (P63/mmc) transforms into K2SO4 (Pmcn) upon cooling to 587°C (Arnold et al. 1981). These structures are similar, and a structure of the low-temperature phase consists of microblocks with configurations of the tetrahedrons 1 and 2 as in K3Na(SO4)2 but the symmetry of microblocks is lower than trigonal (Fig. 7). The decrease in symmetry is associated with large ionic radius of the [VI]K atom, which leads to a distortion of the octahedral site and microblock at room temperature. The low-temperature microblock can be denoted as (SO4-1)(SO4-2)(SO4-2)K(SO4-1)(SO4-2)(SO4-2).
The Ca2SiO4 transformations
It is well known that the polymorphic modifications of Ca2SiO4 are structurally similar with the Na2SO4 modifications (Moore 1981), while the high-temperature ones are isotypical (Udagawa et al. 1977; Mumme et al. 1996). Although, sometimes P–3m1 is considered as an alternative space group for the high-temperature phase (Mumme et al. 1996). Upon cooling, the following sequence of polymorphic transformations occurs: P63/mmc (1545–1250°C) → Pnma (1250–1060°C) → Pna21 (1060–680°C) → P21/n (680–630°C) → Pcmn (630°C) (Mumme et al. 1996; Yamnova et al. 2011). In the modification with the Pcmn space group, the microblocks are no longer to exist. All the microblocks in the modifications P63/mmc → Pnma → Pna21 → P21/n contain tetrahedrons in the orientations 1 and 2. The distortion of the microblocks and reduce of its trigonal symmetry are associated with an increase in the coordination number of the Ca atom from 6 to 8 with decreasing temperature, thus it can no longer be in the octahedral site. The microblock in Ca2SiO4 (Pnma) can be denoted as (SiO4-2)(SiO4-1)(SiO4-2)Ca(SiO4-2)(SiO4-1)(SiO4-2), Ca2SiO4 (Pna21) – (SiO4-2)(SiO4-1)(SiO4-2)Ca(SiO4-1)(SiO4-2)(SiO4-1), Ca2SiO4 (P21/n) – (SiO4-1)(SiO4-2)(SiO4-1)Ca(SiO4-2)(SiO4-1)(SiO4-2). Earlier, the modular description of Ca2SiO4 polymorphic transformations was described by Zvyagin and Pushcharovsky (1993).
A description of the microblock in bubnovaite and dobrovolskyite
Mixed frameworks in crystal structures of new minerals discovered by the authors, bubnovaite K2Na8Ca(SO4)6 (Gorelova et al. 2016) and dobrovolskyite Na4Ca(SO4)3 (Shablinskii et al. 2021), are similar with structure of aphtitalite consisted of the microblocks that can be derived from the parent one. In association with dobrovolskite was found petrovite (Filatov et al. 2020). But it should be noted that there are the Ca atoms in the chemical composition of the minerals. Both minerals (bubnovaite and dobrovolskyite) are superstructures related to aphtitalite with a ratio of unit cell parameters of 2×2×3 and 3×3×3.
The [M(SO4)6] microblocks in bubnovaite share corners with the SO4 tetrahedra forming a mixed framework consisted of two symmetrically independent columns elongated through the c axis and located on the L3 axis. The SO4 tetrahedra are presented in the crystal structure in two orientations, 1 “up” and 2 “down”. Therefore, the crystal structure is composed of the microblocks 11 and 22. We will use the designation for a microblock of two digits, since their symmetry is trigonal. The first column of microblocks should be considered as a pseudocolumn, since one of the Na sites has a partial occupation. The sequence of the microblocks in the pseudocolumn is (21)(22)(11)(21)(22)(11), and in a continuous one – (11)(22)(21)(11)(22)(21), which is associated with a disordering of the tetrahedra in the orientation 1 “up” and 2 “down” in one site. The disordering is associated with the partial occupation of the sodium atoms in one of the sites. The microblock 11 is formed when the sodium atoms are in the site. When the site is vacant, the tetrahedron takes the 2 “down” orientation (Fig. 9a).
The second column contains the same disordered SO4 tetrahedron leading to the disordering of the microblocks. The sequence of the microblocks in the column can be denoted as (21)(22)(11)(21)(22)(11) with a high probability or (11)(22)(21)(11)(22)(21) with a low probability (Fig. 9b).
The crystal structure of dobrovolskyite can be described as a three-dimensional framework consisting of the Na–O and Ca–O polyhedra and SO4 tetrahedra. The framework can be described as three symmetrically independent rods elongated through the c axis and composed of the octahedral–tetrahedral clusters formed by one central NaO6 or CaO6 octahedron sharing six corners with six adjacent SO4 tetrahedra (Shablinskii et al. 2021). The first type of rod is located on the L3 axis (x = 0; y = 0), the second (x ≈ 2/3; y ≈ 2/3) and third (x ≈ 2/3; y ≈ 0) type of rods are located on general sites.
In the structure of dobrovolskyite these microblocks sharing corners with the tetrahedra and faces with the octahedra form three symmetrically independent rods elongated through the c axis. These rods are interconnected through the SO4 tetrahedra and form a three-dimensional mixed framework, the Na3O7, Na4O10, Na9O8, Ca1O6 polyhedra are located in the cavities of the framework. Microblocks in all three symmetrically independent rods include the SO4 tetrahedra in all five orientations that can be inherited from the parent block: 1, 2, 3, 31 and 32 (Fig. 2). The first rod is located on the L3 axis, therefore it is convenient to use the designation of two digits for the microblocks with trigonal symmetry. A sequence of the microblocks in the rod from top to bottom is (23)(33)(332)(3231)(3131)(311) (Fig. 10). The microblocks 23 and 33 have formulas (S5O4)3Na12(S6O4)3 and (S1O4)3Na1(S5O4)3, 332 – (S2O4)3Na5(S1O4)3, 3231, 3131, 311 – (S2O4)3Na2(S3O4)3, (S4O4)3Na8(S3O4)3 and (S4O4)3Na10(S6O4)3.
The rods 2 and 3 as well as the microblocks are highly distorted, since they are not located on the L3 axis (Fig. 10).
There are all possible orientations of tetrahedra that can be inherited from the parent microblock of the high-temperature phase in the crystal structure of dobrovolskyite Na4Ca(SO4)3. Almost all the tetrahedra in the crystal structure are disordered. It is supposed that dobrovolskyite is an intermediate quenched high-temperature phase similar with α–Na2SO4 and stabilized by the Cu, Mg and K admixtures.
The different numbers and types of the microblocks in these rods make it possible to explain the formation of the superstructures of dobrovolskyite and bubnovaite in opposite to aphthitalite and α-Na2SO4. The number of such microblocks in one rod in dobrovolskyite and bubnovaite is 6, in aphthitalite − 2, which perfectly correlates with the ratio of the с parameters (3:1) in these minerals. The difference in these microblocks explains the increase in the parameter of the unit cell.
The role of changing of the coordination number of the cation in theM(TO4)6microblock
An increase in the coordination number upon cooling is a well-known mechanism of densification of a crystal structure. Although, some exceptions are known such as several REEBO3 borates (Biryukov et al. 2020). If the coordination number of the cation in the octahedral site in the microblock increases upon cooling, the microblock often reduces its trigonal symmetry. Although, with some distortion of the microblock (11), the coordination number of the cation can be increased to 12 due to the apical vertices of all six SO4 tetrahedra without reducing the symmetry. Such an example is observed in bubnovaite, where the K atom is such a cation (Fig. 11). In the (12) microblock, the coordination number of the cation can be increased to 9 without reducing the symmetry of the microblock due to 3 apical vertices of the SO4 tetrahedra. A similar example can be found in the crystal structure of bubnovaite (Fig. 11). If the coordination number of the cation is not equal to 12 or 9 upon cooling, then the symmetry of the microblock reduces. A good example is the Ca atoms in Ca2SiO4 and the K ones in β-K2SO4, where its coordination number increases to 8, which is accompanied by such an arrangement of tetrahedra where four apical vertices are directed towards the cation and two – away from the cation (Fig. 12). Thus, the inheritance of various microblocks upon cooling is also determined by a type of a cation occupying the octahedral site in the parent block.