Introduction

In [1], the concept of structural depolymerization of metal fluoride compounds is formulated, which is the basis for the formation of complex metal fluorides and the formation of their crystal structures. The experimental basis for the concept of structural depolymerization of metal fluoride compounds is the depolymerizing effect of fluoride ions (F−) (provided by fluoride ion donors AF) on metal fluoride compounds (MFn) whose structures contain M − Fb − M bridges.

Transition metal fluorides (MFn) have a polymeric structure with M − Fb − M fluoride bridges in the crystalline state. When a metal fluoride compound MFn containing M − Fb − M bridging bonds is exposed to fluoride ions (F−) that have a greater affinity for the metal (M) than the bridging fluorine atoms (Fb), the M − Fb − M bonds in these compounds are broken, and the originally polymeric structures are sequentially depolymerized. Thus, the formation of complex metal fluorides during the interaction of F− ions with binary (MFn) or more complex fluorides (AxMyFn) can be represented as a process of sequential depolymerization of a metal fluoride compound under the action of fluoride ions. The degree of depolymerization of MFn depends on the molar ratio of the reacting components. The proposed concept of structural depolymerization of metal fluoride compounds is justified on the basis of an analysis of crystal structures of complete series of zirconium and hafnium fluoride complexes [2, 3] with the same cations and on the basis of experimental data of synthesis fluoride complexes of zirconium and hafnium.

To assess the degree of polymerization of the crystal structure of a compound, the ratio between the number of bridging fluorine atoms (Fb) and the number of terminal fluorine (Ft) atoms in the structural fragment of the compound, denoted by the letter ε, is usually used. For example, for the compound TiF4, in which each Ti atom is surrounded by four bridging and two terminal F atoms (structural fragment TiF2/1F4/2), the degree of polymerization of the structure is ε = Fb:Ft = 4:2 = 2. For Cs2[TiF6] with the structural fragment TiF6/1F0/2, in whose structure there are no bridging F atoms, ε = 0.

One of the most important provisions of the concept of structural depolymerization of metal fluoride compounds is the decrease in the degree of polymerization of the crystal structure of the compound with increasing amount of the reacting component providing fluoride ions (F−) in a series of complex fluorides with the same cation. The application of the concept of structural depolymerization [1] of metal fluoride compounds has already been shown in the case of fluoride complexes of zirconium structural depolymerization [4, 5]. Structural depolymerization of uranyl fluoride complexes is discussed in [6].

In 2001, the study was published [7], containing provisions similar to the concept of structural depolymerization of metal fluoride compounds [1]. The authors proposed a practical formalism for the manipulation of solid structures, called “dimensional reduction” [7]. Similar to the concept of structural depolymerization of metal fluoride compounds [1], the proposed dimensional reduction is a general formalism that describes how the framework of a parent compound MXx is degraded upon reaction with an ionic reagent AaX to form a child compound AnaMXx+n [7]. The added X− anions disrupt the M − X − M bridges in an MXx parent compound, resulting in a less tightly bound framework. The possibilities of transforming the crystal structures of different types of compounds are formally considered, but the mechanism causing these transformations is not considered or discussed [4].

Recently, a series of papers have been published dealing with the synthesis and study of the crystal structure of new fluoridotitanates(IV) with alkali metal [8], guanidinium [9], and imidazolium [10] cations.

In [8], a systematic study of the reaction between alkali metal fluorides (AF, A = Li, Na, K, Rb, Cs) and titanium(IV) fluoride (TiF4) in anhydrous hydrogen fluoride (aHF) at ambient temperature and a molar ratio n(AF):n(TiF4) of 3:1 to 1:3 was carried out. The formation of the following types of compounds was observed: A2[TiF6], A2[TiF6]·HF, A[TiF5], A[TiF5]·HF, A3[Ti4F19], A[Ti2F9], A[Ti2F9]·HF, and A3[Ti6F27]. Investigation of their crystal structure showed that they consisted of monomeric [TiF6]2− anions (0-D), polymeric ([TiF5]−)∞ chains (1-D), ([Ti4F19]3−)∞ columns (1-D), ([Ti2F9]−)∞ double chains (1-D), and ([Ti6F27]3−)∞ three-dimensional frameworks (3-D).

In [9], the reaction between guanidinium carbonate (and/or chloride) and TiF4 in aHF was carried out in the molar ratios n([C(NH2)3]+):n(TiF4) from 2:1 to 1:4. Five guanidinium fluoridotitanate(IV) salts were isolated and structurally studied: the already known [C(NH2)3]2[TiF6] and the new complexes [C(NH2)3][Ti2F9], [C(NH2)3]4[Ti4F20], [C(NH2)3]3[Ti6F27]·SO2, and [C(NH2)3]4[H3O]4[Ti4F20][TiF5]4. The crystal structures of the synthesized new guanidinium fluoridotitanates(IV) contain oligomeric [Ti4F20]4− and [Ti6F27]3−, and polymeric ([TiF5]−)∞ and ([Ti2F9]−)∞ anions.

The reactions between imidazole (Im) and TiF4 in aHF in the molar ratios n(Im):n(TiF4) ranging from 2:1 to 1:2 resulted in the formation of five fluoridotitanates(IV): [ImH]2[TiF6]·2HF, [ImH]3[Ti2F11], [ImH]4[Ti4F20], [ImH]3[Ti5F23], and [ImH][Ti2F9] [10]. Their crystal structures were determined by a single-crystal X-ray diffraction method.

In [8], the authors state that, with the exception of compound A2[TiF6], whose structure consists of cations A+ and octahedral monomeric complex anions [TiF6]2−, all other synthesized alkali metal fluoridotitanates(IV) are formed by condensation of TiF6 groups. The same is true for the guanidinium and imidazolium fluoridotitanates(IV) [9, 10].

The study of the initial conditions, the formed fluoridotitanate(IV) salts, and the corresponding crystal structures [8,9,10] allows us to consider the formation of the synthesized fluoride complexes of titanium from the point of view of the concept of structural depolymerization of fluoride metal compounds.

Results and discussion

Structural depolymerization of titanium(IV) fluoride in the system CsF/TiF4/aHF

The structural depolymerization of titanium(IV) fluoride under the action of F− ions of alkali metal fluorides is considered by the example of the study the structural depolymerization of TiF4 in the CsF/TiF4/aHF system. The synthesis of cesium fluoridotitanates(IV) was carried out by the reaction between CsF and TiF4, which has a polymeric crystal structure [11]. When CsF is added to TiF4 in aHF or in another aprotic solvent, structural depolymerization of TiF4 occurs under the action of F− ions, which is illustrated by the breaking of the M − Fb − M bridges in TiF4. The degree of depolymerization of the TiF4 structure depends on the initial n(CsF):n(TiF4) molar ratio of the reacting components.

The crystal structure of TiF4 contains three crystallographically distinct Ti atoms, each of which is octahedrally surrounded by six F atoms [11]. Each TiF6 octahedron in the structure is connected to each of the other two TiF6 octahedra by two cis-located equatorial F atoms to form a [Ti3F15] ring of three vertex-linked octahedra. In addition, each octahedron is connected to two octahedra of the same type by trans-positioned F atoms to form isolated columns. In each TiF6 octahedron of the TiF4 structure, two terminal F atoms occur for four bridging F atoms, and the structural fragment is TiF2/1F4/2. The degree of polymerization of the TiF4 structure is ε = 2 (Table 1).

Table 1 Structural depolymerization of TiF4 in the system CsF/TiF4/aHF
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When CsF is added to TiF4 in aHF at a CsF:TiF4 molar ratio 1:3 or 1:2, titanium fluoride is partially depolymerized, and the CsTi2F9 compound crystallizes from solution (Table 1). The structure of CsTi2F9 consists of Cs+ cations and complex anions ([Ti2F9]−)∞. In the CsTi2F9 structure, the octahedral TiF6 groups connected by cis-vertices form polymeric double chain-like anions ([Ti2F9]−)∞, with each octahedron sharing its three vertices with three other TiF6 octahedra (Fig. 1a). Three bridging F atoms and three terminal fluorine atoms coordinate each Ti atom in the CsTi2F9 structure. The structural fragment of the crystal structure of CsTi2F9 is TiF3/1F3/2, and the degree of polymerization is ε = 1 (Table 1).

Fig. 1
figure 1

Fragments of crystal structures of cesium fluoridotitanates(IV): Cs[Ti2F9] a, Cs3[Ti4F19] b, Cs[TiF5] c, Cs2[TiF6] d

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Changing the CsF:TiF4 ratio in the CsF/TiF4/aHF system to 3:4 is accompanied by an increase in the degree depolymerization of TiF4 and leads to the formation of the compound Cs3[Ti4F19]. The crystal structure of Cs3[Ti4F19] consists of Cs+ cations and polymeric double chain anions ([Ti4F19]3−)∞ (Fig. 1b) [8]. The structure of Cs3[Ti4F19] contains two crystallographically independent Ti atoms [Ti(1) and Ti(2)], each coordinated by six F atoms. In each of the chains, the Ti(1)F6 octahedra are connected by common vertices to two adjacent Ti(2)F6. The Ti(2)F6 octahedra, in turn, are connected via three common vertices to three octahedra — two Ti(1)F6 octahedra in the same chain and one Ti(2)F6 octahedron of the adjacent chain. Thus, in the Ti(1)F6 octahedra, there are two bridging atoms per four terminal F atoms, the structural fragment is TiF4/1F2/2 and ε = 0.5, and in the Ti(2)F6 octahedra, there are three bridging atoms per three terminal F atoms, structural fragment TiF3/1F3/2 (ε = 1). The average degree of polymerization of the Cs3[Ti4F19] structure is 0.75 (Table 1).

CsTiF5, is obtained using an initial molar ratio of CsF:TiF4 = 1:1 (Table 1). The crystal structure of CsTiF5 consists of one-dimensional polymeric zigzag chains ([TiF5]−)∞ (Fig. 1c) formed by vertex-linked TiF6 octahedra and Cs+ cations [8]. Of the six F atoms coordinated to the Ti atom, four are terminal, and two are bridging, and the structural fragment is TiF4/1F2/2. Consequently, the degree of polymerization of the CsTiF5 structure is ε = 0.5 (Table 1).

The final product of structural depolymerization of TiF4 under the action of F− ions in the CsF/TiF4/aHF system is Cs2TiF6, which is formed at a molar ratio of CsF:TiF4 of 2:1 (Table 1). The crystal structure of Cs2TiF6 consists of Cs+ cations and isolated monomeric octahedral [TiF6]2− anions (Fig. 1d) in which all fluorine atoms are terminal [8, 13]. The structural fragment of the Cs2TiF6 crystal structure is TiF6/1F0/2, and the degree of polymerization of the Cs2TiF6 structure is ε = 0 (Table 1).

In the CsF/TiF4/aHF system, structural depolymerization of TiF4 under the action of F− ions converts the TiF4 framework structure with the TiF2/1F4/2 (ε = 2) structural fragment into the CsTi2F9 polymer structure with double chains and the TiF3/1F3/2 (ε = 1) structural fragment and then to the Cs3[Ti4F19] structure with zigzag double chains in which every second bridge bond between the TiF6 groups of one polymer chain and the TiF6 groups of the second chain is missing, with Ti(1)F4/1F2/2 (ε = 0.5) and Ti(2)F3/1F3/2, (ε = 1) (an average degree of polymerization of the Cs3[Ti4F19] structure ε = 0.75). The next product of structural depolymerization of TiF4 is the CsTiF5 compound, the structure of which contains one-dimensional polymeric zigzag ([TiF5]−)∞ chains formed by vertex-linked TiF6 octahedra with the TiF4/1F2/2 structural fragment (ε = 0.5). The final product of the structural depolymerization of TiF4 in the CsF/TiF4/aHF system is the Cs2TiF6 compound with the structural fragment TiF6/1F0/2 and the degree of polymerization ε = 0 (Table 1).

In the series of titanium fluoride compounds TiF4-CsTi2F9-Cs3[Ti4F19]-CsTiF5-Cs2TiF6, the degree of polymerization of the crystal structure of the obtained compounds decreases from ε = 2 (TiF4) to ε = 0 (Cs2TiF6) when the molar ratio of the reacting components in the CsF/TiF4/aHF system changes from 1:3 to 2:1.

Structural depolymerization of titanium(IV) fluoride in the systems [C(NH2)3]2CO3 (and/or [C(NH2)3]Cl)/TiF4/aHF

The reaction between guanidinium carbonate (and/or chloride) with TiF4 in aHF was carried out by two methods [9]. In the first method, aHF was added to a mixture of the guanidinium salt and TiF4 in various molar ratios. In the second method, the required amount of guanidinium salt was preliminarily converted into guanidinium polyhydrogen fluoride [C(NH2)3]F·nHF by interaction with aHF. The latter was then used for the reaction with TiF4 in aHF. [C(NH2)3]F had a depolymerizing effect on TiF4, the degree of depolymerization of TiF4 depending on the initial molar ratio of the reacting components, i.e., n[C(NH2)3]+:n(TiF4).

In the system [C(NH2)3]2CO3/TiF4/aHF at a molar ratio of [C(NH2)3]+:TiF4 1:3 and 1:2, the TiF4 compound undergoes partial depolymerization under the action of F− ions to form [C(NH2)3][Ti2F9]. The crystal structure of [C(NH2)3][Ti2F9] consists of guanidinium cations [C(NH2)3]+ and polymeric anion ([Ti2F9]−)∞ structure similar to polymer chains in the Cs[Ti2F9] structure (Fig. 1a) [8]. Each titanium atom in the ([Ti2F9]−)∞ anion is coordinated by three bridging and three terminal fluorine atoms, forming a TiF3/1F3/2 structural fragment. The degree of polymerization of the [C(NH2)3][Ti2F9] structure is ε = 1 (Table 2).

Table 2 Structural depolymerization of TiF4 in the systems (Gua)2CO3 (and/or (Gua)Cl)/TiF4/aHF
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[C(NH2)3]4[Ti4F20] crystallizes from HF solution when less [C(NH2)3]F was present in the [C(NH2)3]2CO3/TiF4/aHF system. The structure [C(NH2)3]4[Ti4F20] consists of oligomeric tetrameric [Ti4F20]4− anions and guanidinium cations [9]. In the tetrameric anion [Ti4F20]4 (Fig. 2a), two bridging and four terminal F atoms form a structural fragment TiF4/1F2/2. The degree of polymerization of [C(NH2)3]4[Ti4F20] is ε = 0.5.

Fig. 2
figure 2

Fragments of crystal structures of guanidinium fluoridotitanates(IV): [C(NH2)3]4[Ti4F20] a, [C(NH2)3]3[Ti6F27]·SO2 b, [C(NH2)3]4[H3O]4[Ti4F20][TiF5]4 c, 1; c, 2

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As in the CsF/TiF4/aHF system, the final product of TiF4 structural depolymerization in the [C(NH2)3]2CO3/TiF4/aHF system is guanidinium hexafluoridotitanate(IV), [C(NH2)3]2[TiF6] (Table 2). [9, 14]. The Ti atoms in the [TiF6]2− anion are coordinated by six F ligands and form distorted octahedra (structural fragment TiF6/1F0/2). The degree of polymerization of the structure [C(NH2)3]2TiF6 is ε = 0 (Table 2).

In the system [C(NH2)3]2CO3/TiF4/aHF, structural depolymerization of TiF4 under the action of F− ions converts the framework structure of TiF4 with the structural fragment TiF2/1F4/2 (ε = 2) into the [C(NH2)3][Ti2F9] with a polymeric structure of double chains and the structural fragment TiF3/1F3/2 (ε = 1). The next step is the formation of [C(NH2)3]4[Ti4F20], whose crystal structure contains oligomeric tetrameric anions [Ti4F20]4−, with the structural fragment TiF4/1F2/2 and the degree of polymerization ε = 0.5. The final product of structural depolymerization of TiF4 is guanidinium hexafluoridotitanate(IV) [C(NH2)3]2[TiF6] with the structural fragment TiF6/1F0/2 and degree of polymerization ε = 0 (Table 2).

In the system [C(NH2)3]Cl/TiF4/aHF, virtually, the same compounds are formed as in the system [C(NH2)3]2CO3/TiF4/aHF (Table 2) [9]. In the case of large amounts of TiF4 ([C(NH2)3]Cl:TiF4 = is 1:4), the product(s) formed are insoluble in aHF. Crystallization of this insoluble product(s) from SO2 solution led to the formation of the solvated phase [C(NH2)3]3[Ti6F27]·SO2. Its Raman spectrum is very similar to the Raman spectrum of the product insoluble in aHF obtained from a mixture of guanidinium salt and TiF4 at the initial molar ratios of the reagents 1:3 and 1:4. On this basis, the authors of [9] concluded that the insoluble phase in aHF is mainly [C(NH2)3]3[Ti6F27] or its HF-solvate form. The crystal structure of [C(NH2)3]3[Ti6F27]·SO2 contains two crystallographically independent anions [Ti6F27]3−, reminiscent of the column-like structure of TiF4. The oligomeric [Ti6F27]3− anions are formed by six TiF6 octahedra: three TiF6 octahedra, sharing cis-corners form a trimeric ring, and the other three octahedra form the same trimeric ring, connected to the first ring by three bridging fluorine atoms, forming a trigonal prismatic geometry (Fig. 2b) [9]. All Ti atoms in the [Ti6F27]3− anion are bonded to three terminal and three bridging F atoms, and the structural fragment of the [C(NH2)3]3[Ti6F27]·SO2 is TiF3/1F3/2 (ε = 1).

Long-term crystallization from a CH3CN solution of a phase insoluble in aHF, formed in the system [C(NH2)3]Cl/TiF4/aHF at a molar ratio of [C(NH2)3]Cl:TiF4 = 1:4, resulted in few crystals of [C(NH2)3]4[H3O]4[Ti4F20][TiF5]4 [9].The crystal structure of [C(NH2)3]4[H3O]4[Ti4F20][TiF5]4 consists of [C(NH2)3]+ and H3O+ cations as well as tetrameric [Ti4F20]4− and polymeric chain-like ([TiF5]−)∞ anions (Fig. 2, c, 1) [9]. The structure of the tetrameric anion is similar to that in the structure of [C(NH2)3]4[Ti4F20] described above. The second anion in the structure of [C(NH2)3]4[H3O]4[Ti4F20][TiF5]4 is a polymeric chain-like ([TiF5]−)∞, consisting of cis-linked TiF6 octahedra (Fig. 2, c, 2).

Structural depolymerization of titanium(IV) fluoride in the Im/TiF4/aHF system

The reaction between imidazole (Im) and TiF4 in aHF in the molar ratios of 2:1 to 1:2 resulted in the formation of five fluoridotitanates(IV): [ImH]2[TiF6]·2HF, [ImH]3[Ti2F11], [ImH]4[Ti4F20], [ImH]3[Ti5F23], and [ImH [Ti2F9] [10].

In the system Im/TiF4/aHF, in the molar ratios Im:TiF4 1:2 and 2:3, structural depolymerization of TiF4 takes place under the action of F− ions of ImHF, and the [ImH][Ti2F9] salt crystallizes from solution. Its structure consists of ImH+ cations and ([Ti2F9]−)∞ anions with a double-chain geometry structure similar to polymer chains in the Cs[Ti2F9] and C(NH2)3][Ti2F9] structure (Fig. 1a) [8]. The structural fragment is TiF3/1F3/2, and the degree of polymerization is ε = 1 (Table 3).

Table 3 Structural depolymerization of TiF4 in the system Im/TiF4/aHF
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With larger amount of imidazole, the depolymerization of TiF4 increases yielding [ImH]3[Ti5F23], [ImH]4[Ti4F20], (ImH)3[Ti2F11], and (ImH)2[TiF6]·2HF. The former contains pentameric [Ti5F23]3− anion with a unique geometry consisting of five octahedral TiF6 groups (Fig. 3a) [10].

Fig. 3
figure 3

Fragments of crystal structures of imidazolium fluoridotitanates(IV): (ImH)3[Ti5F23] a, (ImH)3[Ti2F11] b

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In [Ti5F23]3−, each of the four octahedra shares two cis-vertices with the neighboring octahedron, forming a tetrameric ring. The fifth octahedron TiF6 shares three vertices with three octahedra of the tetrameric ring, forming the Ti5F23 pentamer (Fig. 3a). The structural fragments of Ti(2)-Ti(5) atoms are TiF3/1F3/2 (ε = 1), and the structural fragment of Ti(1) atom is TiF4/1F2/2, (ε = 0.5) (numbering of Ti atoms according to [10]). The average degree of polymerization of the structure [ImH]3[Ti5F23] is ε = 0.9.

The crystal structures of (ImH)4[Ti4F20] salt (Table 3) consist of [Ti4F20]4− anions (Fig. 2a) and ImH+ cations interacting via hydrogen bonds [10]; the structural fragment is TiF4/1F2/2. The degree of polymerization of the (ImH)4[Ti4F20] structure is ε = 0.5 (Table 3). The (ImH)4[Ti4F20] compound can also be considered as a product of structural depolymerization of [ImH]3[Ti5F23]. Under the action of F− ions, the Ti − Fb − Ti bridges in the pentameric [Ti5F23]3− anion are broken, giving rise to the tetrameric anion [Ti4F20]4−, which forms the basis of the crystal structure (ImH)4[Ti4F20].

Dimeric anions [Ti2F11]3− (Fig. 3b), consisting of two octahedral TiF6 groups sharing a common vertex, are present in the crystal structure of [ImH]3[Ti2F11], which crystallizes in the Im/TiF4/aHF system at a molar ratio Im:TiF4 = 2:1 [10]. In contrast to (C5H5NH)2(H3O)[Ti2F11]⋅H2O [12], whose structure contains only a crystallographically unique [Ti2F11]3− anion, the [ImH]3[Ti2F11] structure contains three crystallographically independent Ti2F11 groups with different conformations and coordination domains. The structural fragment of the [ImH]3[Ti2F11] crystal structure is TiF5/1F1/2, and the degree of polymerization of the structure is ε = 0.2. The [ImH]3[Ti2F11] compound can also be obtained by depolymerization of (ImH)4[Ti4F20] under the action of F− ions, which leads to the rupture of some of the trans-located bridging bonds between TiF6 groups in the Ti4F20 tetramer.

In the Im/TiF4/aHF system with a molar ratio of Im:TiF4 = 2:1, the compound [ImH]2[TiF6]·2HF crystallizes. The structure of [ImH]2[TiF6]·2HF is formed from imidazolium cations [ImH]+, octahedral [TiF6]2− anions, and two HF molecules [10]. The structural fragment of the compound [ImH]2[TiF6]·2HF is TiF6/1F0/2, and the degree of polymerization is ε = 0. The [ImH]2[TiF6] salt can also be obtained as a result of the structural depolymerization of [ImH]3[Ti2F11] in HF solution under the action of F− ions by breaking the Ti–Fb–Ti bridge in the Ti2F11 group.

Conclusions

The structural depolymerization of TiF4, which is the basis for the formation of the crystal structure of fluoride complexes of titanium(IV), was studied in the systems CsF/TiF4/aHF, [C(NH2)3]2CO3 (and/or [C(NH2)3]Cl)/TiF4/aHF, and Im/TiF4/aHF. The compositions of fluoridotitanates(IV) formed in these systems and their crystal structures are considered in terms of the degree of polymerization (ε). With increasing initial amount of fluoride ion donors (AF = CsF or in (Gua)F and ImHF formed in situ) in AF/TiF4 reactions, the degree of polymerization of the crystal structures of the obtained salts decreases. In all systems studied, the final products of TiF4 structural depolymerization are A2[TiF6] salts. The Ti atoms in the [TiF6]2− anion are coordinated by six F ligands and form octahedra. The corresponding structural fragment is TiF6/1F0/2, and the degree of polymerization is ε = 0. The highest degree of polymerization (ε = 2) is present in the crystal structure of TiF4 with structure fragments TiF2/1F4/2.

In conclusion, it should be noted that the proposed concept of structural depolymerization of metal fluoride compounds [1, 4] was considered in [15] as applied to the formation of fluoride glasses. In [16], the structure of fluorindate glasses is discussed on the position of structural depolymerization of “octahedral structures.” In particular, it is indicated that the sequential addition of mono- and divalent metal fluorides to InF3, the structure of which is formed from InF6 octahedral groups linked by vertices, takes place, as in the concept of structural depolymerization of metal fluoride compounds, sequential structural depolymerization: framework (InF3) – layer (InF4−)∞ – (InF52−)∞ chain – isolated [InF6]3− octahedra.