Room‐Temperature Solid‐State Transformation of Na₄SnS₄ ⋅ 14H₂O into Na₄Sn₂S₆ ⋅ 5H₂O: An Unusual Epitaxial Reaction Including Bond Formation, Mass Transport, and Ionic Conductivity

Abstract

A highly unusual solid‐state epitaxy‐induced phase transformation of Na₄SnS₄ ⋅ 14H₂O (I) into Na₄Sn₂S₆ ⋅ 5H₂O (II) occurs at room temperature. Ab initio molecular dynamics (AIMD) simulations indicate an internal acid‐base reaction to form [SnS₃SH]³⁻ which condensates to [Sn₂S₆]⁴⁻. The reaction involves a complex sequence of O−H bond cleavage, S²⁻ protonation, Sn−S bond formation and diffusion of various species while preserving the crystal morphology. In situ Raman and IR spectroscopy evidence the formation of [Sn₂S₆]⁴⁻. DFT calculations allowed assignment of all bands appearing during the transformation. X‐ray diffraction and in situ ¹H NMR demonstrate a transformation within several days and yield a reaction turnover of ≈0.38 %/h. AIMD and experimental ionic conductivity data closely follow a Vogel‐Fulcher‐Tammann type T dependence with D(Na)=6×10⁻¹⁴ m² s⁻¹ at T=300 K with values increasing by three orders of magnitude from −20 to +25 °C.

The unusual solid‐state transformation of Na₄SnS₄ ⋅ 14H₂O into Na₄Sn₂S₆ ⋅ 5H₂O at ambient conditions is elucidated on the molecular level by combined in situ and ex situ experiments supported by theoretical calculations.

Introduction

Over the last few decades, a large variety of synthetic approaches have been developed for the synthesis of thiostannates or tin sulfides. These include the molten flux approach,[ ¹ , ² ] conventional high temperature reactions,[ ³ , ⁴ , ⁵ ] solvothermal methods,[ ⁶ , ⁷ , ⁸ , ⁹ ] or reactions in liquid media at moderate temperatures.[ ¹⁰ , ¹¹ ] Beside the most common thiostannate anion, [Sn₂S₆]^4‐, which is composed of two edge‐sharing [SnS₄] tetrahedra, a range of further [Sn_nS_2n+x/2]^x− units like [SnS₄]⁴⁻, [Sn₃S₇]²⁻ or [Sn₄S₉]²⁻ are also observed with Sn^IV valence. ^[6] In addition, many examples have been reported for compounds with mixed Sn valence, such as Sn^IV/Sn^II or Sn^IV/Sn^III.[ ¹² , ¹³ , ¹⁴ ] The structural versatility is due to the variable coordination number (CN=4–6) as well as the variable oxidation state of Sn. We recently identified Na₄SnS₄ ⋅ 14H₂O (I) ^[15] as a promising starting material for the preparation of new thiostannates from liquid media.[ ¹⁰ , ¹¹ ] These syntheses yield rather complex anionic species instead of the simple SnS₄ ⁴⁻ anion.[ ¹⁰ , ¹¹ ] We evidenced that I spontaneously undergoes an acid‐base reaction in H₂O and [Sn₂S₆]⁴⁻ is formed under release of H₂S. ^[11] In addition, we successfully used I and mixtures with Na₃SbS₄ ⋅ 9H₂O for the generation of a new Na₄SnS₄ polymorph and Na⁺ superionic conductors Na_4‐xSn_1‐xSb_xS₄ by directed thermal removal of the crystal water molecules at a moderate temperature. ^[16] This powerful and economic synthetic route appears promising for transfer into industrial application provided that certain prerequisites are fulfilled. In particular, the process‐relevant properties of the starting compounds must be known, and suitable candidates should be i) easy to synthesize including scalability, reproducibility and high purity; ii) composed of cheap, earth‐abundant, non‐toxic and sustainable elements; iii) long‐term stable under ambient conditions.

Compound I contains a large amount of crystal water molecules and such compounds tend to decompose slowly. Therefore, we here studied the stability and reactivity of I and surprisingly, we found a slow epitaxial reaction transforming I into Na₄Sn₂S₆ ⋅ 5H₂O (II) at room temperature (RT). In this study, we monitored this unusual structural transformation in the solid state with ex situ X‐ray powder diffraction (XRPD), in situ Raman, in situ IR, and in situ NMR spectroscopy. The multi‐method experimental characterization of this unusual structural transformation is complemented by an investigation of the underlying dynamics with the help of ab initio molecular dynamics (AIMD) simulations and an analysis of the consequences of the transformation on the Na⁺ ion conductivity in both phases.

Results and Discussion

The storage atmosphere plays a crucial role for preserving the integrity of I: at 95 % relative humidity (RH) complete degradation occurs to form a mushy solid within 3 d; at RH=59 % small amounts of Na₄Sn₂S₆ ⋅ 5H₂O (II) were formed after 1 d (Figure S1). Storing the sample in vacuum, Ar or covered by Scotch tape also resulted in a partial transformation (Figure S1). This transformation process was investigated in ambient air (RH: 35‐40 %) collecting XRPD patterns at regular intervals (Figure 1). The initial XRPD pattern demonstrates phase purity of I, reflections of II appeared after 1 d and the amount of II steadily increased but even after 11 d no full transformation was achieved. A two‐phase Rietveld refinement showed that ≈15 wt% of I was transformed into II after 11  d. But one should consider this value with some care because a pronounced preferred orientation in the pattern of I caused by the platelet‐like crystals rather yields an estimate than an exact value.

Figure 1.

XRPD patterns of I recorded at different time intervals in air. Arrows are drawn for highlighting the development of reflections of II.

The full width at half maximum (FWHM) of the reflections does not differ significantly between I and II, most probably pointing at an intra‐crystalline process. Hence, we propose that this structural transformation is thermodynamically driven with I being less stable at RT than II under the storage conditions. This is supported by the observation, that no transformation occurs for months storing I in a freezer (T=−18 °C).

Obviously, a condensation reaction occurs in the solid state involving i) protonation of [SnS₄]⁴⁻ at S²⁻ by proton transfer from H₂O, i. e. an O−H bond breakage occurs, ii) condensation of adjacent [SnS₃SH]³⁻ anions to generate [Sn₂S₆]⁴⁻, and iii) H₂S release as verified using humid Pb acetate paper. These processes are thermally activated including mass transport and diffusion of species in the crystal with a reasonably high ion mobility. For retaining mass balance, amorphous NaOH must be generated according to the chemical Equation 1:

$${\displaystyle 2\mathrm{Na}{}_4\mathrm{SnS}{}_4·14\mathrm{H}{}_2\mathrm{O}\to \mathrm{Na}{}_4\mathrm{Sn}{}_2\mathrm{S}{}_6·5\mathrm{H}{}_2\mathrm{O}+19\mathrm{H}{}_2\mathrm{O}+2\mathrm{H}{}_2\mathrm{S}+4\mathrm{NaOH}}$$ (1)

The structural transformation is accompanied by a significant density increase from 1.856 to 2.445 g/cm³ and is initiated at various nucleation spots in crystals of I as observed by optical microscopy (Figure S2).

Comparing the unit cell parameters of I and II some surprising similarities are identified: the lattice parameters for I are a=8.62311(15), b=23.5067(3), c=11.3086(2) Å and β=110.4827(19)°, while those of II are a=8.45088(3) and c=23.32912(12) Å, i. e. the a‐ and b‐axes of I match well with a‐ and c‐axes of II indicating an epitaxial relation between the structures (Figure 2). The monoclinic space groups (SG) C2/c with disorder of one Na atom and five H atoms ^[15] and Cc ^[17] were reported for I. A redetermination of the structure by single‐crystal X‐ray diffraction (SC‐XRD) shows that SG C2/c is correct (further details in Supporting Information). Structure determination of I at various temperatures (Table S1) reveals a linear unit cell expansion (Figure S4) with increasing temperature and almost isotropic atomic displacement parameters for Na⁺ ions (Figure S5).

Figure 2.

View of the interconnection of different polyhedra in the structures of I (top) and II (bottom). Two‐unit cells along [010] (I) containing the split positions O5, O6 and O7 (left) and O5’, O6’ and O7’ (right) and along [001] (II) are displayed. Only [SnS₄]⁴⁻ and [Sn₂S₆]⁴⁻ units are drawn as polyhedra. Only H atoms involved in special S⋅⋅⋅H−O interactions (dashed lines) are shown (compare text). Purple: Na; gray: Sn; yellow: S; red: O.

In the structure of I, Na1 is octahedrally coordinated by five H₂O molecules and one S²⁻ anion, while Na2/Na3 are in an octahedral environment of six H₂O molecules (Figure 2, top and Figure S6). All bond lengths are in the range of the sum of ionic radii [r _Na (CN=6): 1.02 Å, O²⁻: 1.35 Å, S²⁻: 1.84 Å; Sn⁴⁺: 0.55 Å; Table S2] ^[18] and match literature data.[ ² , ⁵ , ¹⁹ , ²⁰ ] The plausibility of the structure model is also underlined by the global instability index GII, i. e. the root mean squared average bond valence sum mismatch, which is 0.17 and hence in the acceptable range <0.2 both for C2/c as for Cc. The Na⁺ centered polyhedra are connected through common corners and edges to form a 3D structure (Figure 2, top). Only one of the two unique S²⁻ anions of [SnS₄]⁴⁻ has bonds to Na⁺ ions. A special structural feature is the connection of two [SnS₄]⁴⁻ anions by unsymmetrical S⋅⋅⋅H−O bonds with one remarkable short S⋅⋅⋅H bond of 2.36 Å and one longer at 2.57 Å (O−H⋅⋅⋅S angles: 170 and 157°), indicating strong hydrogen bonds (Figure 2, top). This geometric situation may allow protonation of the terminal atoms of the [SnS₄]⁴⁻ anions. Only five H₂O molecules are involved in O−H⋅⋅⋅O bonding, but all in O−H⋅⋅⋅S bonds (Table S3).

Compound II, Na₄Sn₂S₆ ⋅ 5H₂O, (SG: P4₁2₁2) comprises Sn, Na1, Na2, S2, S4, O2 and O3 atoms in general and S1, S3 and O1 in special positions (Figure S7 and Table S4). In the [Sn₂S₆]⁴⁻ anion the Sn‐S_brid bond is longer compared to the Sn‐S_term bonds (Table S5), ^[21] and the angles around Sn indicate a small distortion of the tetrahedra, in agreement with literature.[ ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ ] All S²⁻ anions of [Sn₂S₆]⁴⁻ have bonds to Na⁺: S_brid (S1, S3) have bonds to two Na⁺ and S_term (S2, S4) are involved in one respectively three Na−S bonds (Figure 2, bottom). While the Na−O bonds are similar to those of I, the average Na−S bond is significantly longer but is in agreement with literature data.[ ² , ⁵ , ¹⁵ , ²⁰ ] The Na1O₃S₃ octahedron and the Na2O₂S₃ trigonal bipyramid (Figure 2, bottom and Figure S8) share common edges to form a (Na1Na2)O₃S₆ secondary building unit, which are joined to generate a 3D network structure (Figure 2, bottom). O−H⋅⋅⋅S hydrogen bonding interactions are observed involving only the terminal S atoms of the anion.

The Raman spectra recorded in situ during 26 h show the decrease of intensity of the characteristic band of [SnS₄]⁴⁻ (353 cm⁻¹, band 6 in Figure 3), completely vanishing and the simultaneous appearance of new bands assigned to [Sn₂S₆]⁴⁻ (bands 1‐5 in Figure 3). For a conclusive assignment of the bands DFT calculations were performed and the results are compared to the experimental vibrational frequencies in Table 1. Interestingly, calculation of the free [SnS₄]⁴⁻ anion led to the breathing vibration (A₁) at 267 cm^‐1 at significantly lower frequency than in the experiment (353 cm⁻¹, band 6 in Figure 3). It seems logical that the [SnS₄]⁴⁻ anion should be strongly affected by secondary interactions and therefore in a following calculation two coordinating Na⁺ and the eight most strongly coordinating H₂O molecules were considered. The symmetry reduction led to two different stretching vibrations, one Sn−S stretch with contact to Na⁺ and one without, yielding 338 cm⁻¹ (SnS₂(Na₂)) and 356 cm⁻¹ (SnS₂) fitting well to the experimental values (353 cm⁻¹, FWHM=20 cm⁻¹). Obviously, secondary interactions affect the frequencies of the vibrations.

Figure 3.

Time‐dependent lower frequency Raman spectra of I (2 spectra/h ⋅ 26 h=52 spectra) (top), showing the transformation into II. The strongest six bands are assigned according to results of the calculations (single points and vibrational analysis on SC‐XRD coordinates including coordinating Na⁺ ions and the eight strongest coordinating water molecules for [SnS₄]⁴⁻). The A_g modes for [Sn₂S₆]⁴⁻ with two coordinating Na⁺ ions and the vibrations obtained for [SnS₄]⁴⁻ with next nearest H₂O molecules and Na⁺ ions (bottom).

Table 1.

Experimental vibrational frequencies (cm⁻¹) of [SnS₄]⁴⁻ and [Sn₂S₆]⁴⁻ in I and II and theoretical values for {Na₂[SnS₄](H₂O)₈}²⁻ and {Na₂[Sn₂S₆]}²⁻.

Experiment, Raman (Start)	Experiment, Raman (End)	Simulation[a]	Compound	Mode[b]' (Assignment in Figure 3)
	60/75	68	Na4Sn2S6	Ag
	93	93	Na4Sn2S6 NaOH	Ag Lattice[c]
	104	113/117	Na4Sn2S6	Ag
	123 (m)	149	Na4Sn2S6	Ag(Sn2S2) (5)
	135 (w)		–	–
	214 (w)		NaOH	Lattice[c]
	247 (m)		Na4Sn2S6	Lattice
	289 (m)	282	Na4Sn2S6 NaOH	Ag(Sn2S2) (4) Lattice[c]
	347 (vs)	344	Na4Sn2S6	Ag(Sn2S2) (3)
353 (s)		338/356	Na4SnS4	ν(SnS2)/ν(SnS(Na)2) (6)
	364 (s)	372	Na4Sn2S6	Ag(Sn−S) (2)
	386 (s)	384	Na4Sn2S6	Ag(Sn−S(Na)) (1)

Complete data in Table S6. [a] single points on SC‐XRD coordinates with subsequent vibrational analysis. Only vibrations of the anions listed: [Sn₂S₆]⁴⁻ of a {Na₂[Sn₂S₆]}²⁻ unit for Na₂Sn₂S₆ and the only observable vibration of [SnS₄]⁴⁻ inside {Na₂[SnS₄](H₂O)₈}²⁻ for Na₄SnS₄; [b] 9 A_g (Ra) modes are listed for [Sn₂S₆]⁴⁻ [c] Ref. [29].

For the D _2h symmetric [Sn₂S₆]⁴⁻ anion the vibrational analysis yields Equation 2:

$${\displaystyle \Gamma {}_{\mathrm{vib}}{}^{\mathrm{D}2\mathrm{h}}=4\mathrm{A}{}_{\mathrm{g}}\left(\mathrm{Ra}\right)+2\mathrm{B}{}_{1\mathrm{g}}\left(\mathrm{Ra}\right)+2\mathrm{B}{}_{2\mathrm{g}}\left(\mathrm{Ra}\right)+1\mathrm{B}{}_{3\mathrm{g}}\left(\mathrm{Ra}\right)+1\mathrm{A}{}_{\mathrm{u}}\left(\mathrm{inactive}\right)+3\mathrm{B}{}_{1\mathrm{u}}\left(\mathrm{IR}\right)+2\mathrm{B}{}_{2\mathrm{u}}\left(\mathrm{IR}\right)+3\mathrm{B}{}_{3\mathrm{u}}\left(\mathrm{IR}\right)}$$ (2)

Calculation of vibrations of the free [Sn₂S₆]⁴⁻ anion led to a spectrum with only two vibrations above 300 cm⁻¹ in contrast to the three visible bands between 320 and 400 cm⁻¹ in the experimental spectrum increasing in intensity during the conversion process (bands 1, 2, and 3 in Figure 3). Like for [SnS₄]⁴⁻, to account for the effect of a coordinating environment the two nearest Na⁺ ions were included in the calculations (Figure 3) generating a {Na₂[Sn₂S₆]}²⁻ moiety and the rule of mutual exclusion can be applied for the obtained vibrations (g: Raman active, u: IR active). For the C _i symmetric [Sn₂S₆]⁴⁻ the vibrational analysis results in Equation 3:

$${\displaystyle \Gamma {}_{\mathrm{vib}}{}^{\mathrm{Ci}}=9\mathrm{A}{}_{\mathrm{g}}\left(\mathrm{Ra}\right)+9\mathrm{A}{}_{\mathrm{u}}\left(\mathrm{IR}\right)}$$ (3)

This approach yields a spectrum almost perfectly reproducing the three vibrations above 300 cm⁻¹, including two types of terminal Sn−S stretching modes (bands 1 and 2 in Figure 3) and a ring deformation vibration (band 3 in Figure 3, see also Figure S9). Interestingly, the latter represents the strongest band and was earlier assigned as unspecific Sn−S stretching vibration but no explanation for three bands located above 300 cm⁻¹ was given. The coordination of Na⁺ on the opposite sides leads to decoupled vibrations, both totally symmetric regarding C _i, with different energies. This is in contrast to the A_g vibrations of the free anion, which is also totally symmetric but has the local symmetry D _2h. Accordingly, the lower change of polarizability in case of the A_g (C _i) vibrations then correlates with the lower intensity of the observed Sn−S bands compared to the strong band of the Sn₂S₂ deformation vibration at 347 cm⁻¹. In the higher energy region of the Raman spectra (3500‐500 cm⁻¹) the loss of H₂O during the conversion into II can be seen (Figure S11 and Table S6). Additionally, small amounts of Na₂CO₃, most likely originating from reaction of NaOH (see Equation (1)) and CO₂, was observed.

The H₂O loss during the transformation was monitored by in situ IR spectroscopy. Indeed, during ≈17 h the bands of water (ν(H₂O) at 3600–2900 cm⁻¹ and δ(H₂O) at 1700‐1500 cm⁻¹) vanished (Figure 4, Table S6). Additionally, a progressive absorption at 3520 cm⁻¹ may be explained by NaOH formation during condensation of two [SnS₄]⁴⁻ anions, which is accompanied by evolution of H₂S evidenced by the characteristic smell. The continuous decrease of absorption band intensity for H₂O can be explained by the experimental setup, where the IR chamber is continuously purged with dry N₂, and the reduced H₂O content in II. is done see above

Figure 4.

Time dependent IR spectra of I (6 spectra/h ⋅ 16.7 h=100 spectra), showing the transformation into II, the loss of H₂O and NaOH formation.

Sulfidic compounds such as Na₃PS₄,[ ³⁰ , ³¹ ] Na_3−xPS_4−xCl_x, ^[32] Na₃SbS₄,[ ³³ , ³⁴ ] Na₁₁Sn₂PS₁₂, ^[35] Na_4−xSn_1−xSb_xS₄, ^[36] and Na₃SbS_4‐xSe_x ^[37] were identified as good Na⁺ ion conductors. Therefore, the total ionic conductivities σ _i of I and II were determined from electrochemical impedance spectroscopy (EIS) over the temperature range T=−20 to +25 °C. Even though EIS does not discriminate between H⁺ and Na⁺ ion motion properties, we expect the Na⁺ ions as the dominant charge carriers (compare AIMD simulations). A representative Nyquist plot (T=10 °C) and the equivalent circuit, consisting of one constant phase element (CPE) in parallel with a resistor (R), are shown in Figure 5 (left).[ ³¹ , ³⁸ ] This unit is connected in series to another CPE to contribute for the blocking electrode behavior. σ _i and capacitances C _i obtained at different temperatures (Figure S12 and S13) are shown in Table 2. Both samples exhibit comparable values, for example, σ _i(I)=4.8 μS cm^‐1 and σ _i(II)=3.9 μS cm⁻¹ at T=+10 °C. In the small temperature range, σ _i(I) and σ _i(II) cover several orders of magnitude (Table 2). C _i(I) and C _i(II) are similar between −20 and 25 °C (Table 2) and can be correlated to averaged bulk and grain boundary transport properties (C _bulk≈1×10⁻¹² F and C _{grain boundary}≈4×10⁻⁹ F). ^[39] σ _i(I) and σ _i(II) are lower than values reported for solid‐state Na⁺ ion electrolytes, but reasonably high compared to that of Na₃SbS₄ ⋅ 9H₂O (σ _i=0.5 μS cm−¹ at RT). ^[33] Using the temperature‐dependent data, the activation energies for ionic conduction E _a (Eq. (4)) were calculated using Arrhenius plots (Figure 5, right) according to Equation 4:

$${\displaystyle \sigma {}_{\mathrm{i}}T=A\times \exp (-E{}_{\mathrm{a}}/k{}_{\mathrm{B}}T)}$$ (4)

Figure 5.

Nyquist impedance plots of I and II at +10 °C together with the equivalent circuit for fitting the spectra (left). Arrhenius plots of the ionic conductivity of I and II (right). For the data of I see explanation in the text.

Table 2.

Selected ionic conductivities σ _i and capacitances C _i at various temperatures for I and II.

T [°C]	σ i(I) [S cm−1]	C i(I) [nF]	σ i(II) [S cm−1]	C i(II) [nF]
−20	6.5×10−8	0.08	4.7×10−8	0.06
−10	3.6×10−7	0.08	2.6×10−7	0.06
0	1.5×10−6	0.08	1.1×10−6	0.06
+10	4.8×10−6[a]	0.08	3.9×10−6	0.06
+20	1.0×10−5[a]	0.09	1.1×10−5	0.05
+25	9.9×10−6[a]	0.07	1.7×10−5	0.05

[a] σ _i deviates from linear Arrhenius behaviour, see Figure 5 (right).

A=pre‐exponential factor, σ _i=ionic conductivity, k _B=Boltzmann constant, T=absolute temperature.

An important observation is that σ _i(II) follows the Arrhenius law over the entire temperature range, whereas a deviation from the linear behavior is observed for σ _i(I) at T>10 °C (Figure 5, right). This is caused by transformation of I into II during the measurement, thus a mixture of both compounds was investigated (Figure S14). Therefore, E _a(I) was calculated in the range from −20 to +10 °C, while E _a(II) was obtained for the whole temperature range (Figure S15). Comparable values of E _a(I)=0.91 eV and E _a(II)=0.88 eV are determined, demonstrating similar ionic conduction properties. Like for σ _i, the values for E _a are larger than for, for example, Na₃SbS₄ (0.22‐0.25 eV)[ ³³ , ³⁴ ], Na₁₁Sn₂PS₁₂ (0.39 eV), ^[35] or Na₃SbS_3.75Se_0.25 (0.23 eV). ^[37]

In order to understand the contribution of Na⁺ ion transport properties to the total σ _i, we analyzed the static energy landscape for mobile Na⁺ ions by the bond valence site energy method (BVSE),[ ⁴⁰ , ⁴¹ ] which provides a quick approximate overview on the topology of the migration pathways as well as relevant migration barriers from representative local structure models. The Na⁺ ion transport in both local structure models of I (involving either O5, O6 and O7 or O5’, O6’ and O7’) preferentially follows a robust 2D path perpendicular to [010] (Figure 6) that involves the octahedrally coordinated Na2 and Na3 sites with E _a≈0.82–0.87 eV (depending on the local structure model), while some local structure models suggest an 1D path with a slightly lower migration barrier along [001] for the same Na⁺ ions. With a somewhat higher energy barrier of about 1.1 eV the accessible pathways are expanded to a 3D network. These should be taken rather as upper limits as such static models do not factor in the relaxation of H₂O molecules in response to Na⁺ hops, which depending on temperature may become significant in this compound.

Figure 6.

a) Isosurfaces of constant bond valence site energy for mobile Na⁺ superimposed on a local structure model of I corresponding to Figure 2. Colors as in Figure 2 (Na1: dark violet sphere; Na2: light pink sphere; Na3: magenta sphere. b) Energy landscape for mobile Na⁺ based on the local structure model containing O5’, O6’, O7’. Labels i# refer to interstitial sites ranked by increasing site energy.

DFT relaxations were used to confirm the structure models. When not imposing any symmetry restrictions the relaxation of a local structure model led to a model that was compatible with SG Cc within narrow tolerances. Non‐hydrogen atom positions except the partially occupied Na3 site were also compatible with the finally chosen higher SG C2/c, supporting the plausibility of the observed structure model.

An analogous BVSE landscape for Na⁺ migration in II yields the lowest energy percolating Na⁺ paths as separate 1D paths along the a or b direction with E _a=0.50 eV involving both types of Na⁺ ions that are connected to form a 3D pathway network with E _a=0.72 eV (Figure 7). Compared to the disorder in I, the diffusion in II is hampered by the lack of accessible sites, as all Na sites are fully occupied and the relatively high energy, interstitial sites are too close to be occupied simultaneously.

Figure 7.

a) Isosurfaces of constant bond valence site energy for mobile Na⁺ superimposed on the structure model of II. Colors as in Figure 2 (Na1: light pink sphere; Na2: dark violet sphere), b) Energy landscape for mobile Na⁺ in II. Labels i# refer to interstitial sites ranked by increasing site energy.

AIMD simulations of the relaxed structure model for I have been conducted at T=1200, 800, 600 and 500 K to gain deeper insight into both the initial steps of the reaction mechanism into II and into the Na⁺ conductivity. Due to the high computational effort, the period over which reactions can be monitored in such a 204 atom structure model is limited. Over 30 ps (steps: 1 fs) there was no bond breaking observed. This changed drastically when a water molecule dissociation was manually introduced (by converting two water molecules at a distance of 11.5 Å into OH⁻ and H₃O⁺ groups, followed by a geometry relaxation. Independent of the temperature of the simulation the extra proton was transferred within less than 1 ps to one of the adjacent [SnS₄]⁴⁻ groups creating [SnS₃HS]³⁻ groups, while the proton vacancy at the OH⁻ anion became comparably mobile to the Na⁺ ion through a Grotthuss type mechanism. However, due to the low concentration of dissociated H₂O molecules in I the Na⁺ ions will still remain the dominant charge carriers. For the NVT AIMD simulations at 800 and 1200 K, the lengthening of the Sn−SH bond also led to a temporary breaking of the [SnS₃HS]³⁻ group into [SnS₃]²⁻ and HS⁻ suggesting a likely reaction path for the condensation to [Sn₂S₆]⁴⁻.

Analysis of the mean square displacements of the Na⁺ ions in I demonstrates a somewhat higher local mobility of Na2 and Na3 than of Na1. In line with predictions from the BVSE model (Figure 6), the Na⁺ mobility remains essentially restricted to the x‐z plane and only for T=1200 K a significant contribution from transport along the y direction is noted. In the Arrhenius plot (Figure 8), the mean square Na displacement is converted to a Na⁺ ionic conductivity applying the Nernst‐Einstein equation, i. e. assuming uncorrelated hops. At T=500–1200 K, where a statistically significant ionic motion was observed, E _a for the ion migration appears somewhat smaller and temperature dependent (see curvature of Arrhenius plot). Linear extrapolation of the AIMD results over T=500–1200 K down to 300 K suggest ion diffusion coefficients of D(Na)=7×10⁻¹² m² s⁻¹ and D(H)=6×10⁻¹² m² s⁻¹ at 300 K. At least at elevated temperatures the ionic transport is more accurately described by a Vogel‐Fulcher‐Tammann (VFT) type temperature dependence. AIMD data and σ _i from EIS experiments can effectively be fitted by a common VFT curve (Figure 8), where the temperature dependence of E _a is characterized by a characteristic temperature T ₀ of 145 K. This VFT fit corresponds to a Na⁺ diffusion coefficient of D(Na)=6×10⁻¹⁴ m² s⁻¹ at 300 K. The VFT‐type temperature dependence may be taken as a sign that ionic conductivity may show a temperature dependent transition between a liquid‐like and a solid‐like ion transport.

Figure 8.

Arrhenius plots of experimental and simulation results for the ionic conductivity of I. Low temperature results from EIS (blue diamonds, same data as in Figure 5) and high temperature Na⁺ ionic conductivities from AIMD simulations (red circles) can be interpreted as falling onto a common VFT‐type temperature dependence (dotted line). Solid lines refer to polynomial regressions of the respective data category.

Magic‐angle spinning (MAS) NMR spectroscopy was performed to gain deeper insight into the atomic environments of ¹H, ²³Na, and ¹¹⁹Sn in I and II (Figure 9, full spectra see Figure S16–S18). For I, three signals at δ=61.6 (strong), 68.2 (medium) and 72.8 ppm (weak) are observed for ¹¹⁹Sn. Only one unique Sn is present in this structure and the observation of more than one NMR signal indicates structural disorder, i. e. different atomic arrangements around this unique site. Moreover, the ¹¹⁹Sn MAS NMR experiment lasted ∼17 h and some I is already at the beginning of the phase transformation involving the S²⁻ protonation. This non‐stationary situation leads to different NMR signals resulting from the [SnS₄]⁴⁻ unit in I but also in intermediates with different Sn⋅⋅⋅S⋅⋅⋅H interactions. δ is in the same range as those reported for Na₄SnS₄ and K₄SnS₄ (δ=67.6 and 74 ppm, respectively).[ ¹¹ , ⁴² , ⁴³ ] The ¹H spectrum contains only one narrow intense signal (δ=5.0 ppm), explainable by a high proton mobility. Similarly, in the ²³Na spectrum only one narrow signal (δ=5.0 ppm) occurs indicating fast Na⁺ ion dynamics.

Figure 9.

MAS ¹H, ²³Na, and ¹¹⁹Sn MAS NMR spectra for I (black) and II (red); crosses indicate rotational sidebands.

In the ¹¹⁹Sn MAS NMR spectrum of II (Figure 9, right, bottom) one narrow intense signal of [Sn₂S₆]⁴⁻ is observed at δ=49.8 ppm in agreement with δ=50 ppm of K₄Sn₂S₆. ^[42] A comparable change of the ¹¹⁹Sn NMR shift was reported for [SnS₄]⁴⁻ and [Sn₂S₆]⁴⁻ in solution.[ ¹¹ , ⁴² ] A second weak signal at 76.7 ppm results from minor impurities which were not detected by XRPD. Similarly, the ¹H MAS NMR spectrum of II (Figure 9, left, bottom) contains one strong and one weak signal at δ=3.6 and 4.8 ppm. While in the ²³Na MAS NMR of I only one signal was observed, the spectrum of II (Figure 9, middle, bottom) includes two intensive signals at δ=2.0 (broad) and 7.1 ppm (narrow). Therefore, the temporal averaging of local environments is less effective, i. e. the motion of Na⁺ ions seems to be slower, in agreement with the two different Na⁺ environments (see above).

The phase transformation of I into II was investigated by in situ (static) solid‐state ¹H NMR (Figure 10 and Figure S19). In contrast to the MAS NMR experiments this static measurement was performed in an open tube to prevent the influence of gas pressure due to H₂S and H₂O formation, hence without sample rotation. This yields broader line shapes, making a reliable differentiation of signals from I and II impossible. Therefore, the total integral intensity resulting from superposition of both compounds is plotted in Figure 10. For comparison, solid‐state ¹H NMR was performed for possible other reaction products like NaOH ⋅ xH₂O and NaHCO₃ (Figure S19) with (30 kHz) and without sample rotation. Using sample rotation, one broad signal at about −3.8 ppm could be observed for NaOH ⋅ xH₂O and one broad peak at +13.9 ppm for NaHCO₃. A theoretical intensity loss of ∼82 % is calculated for the complete phase transformation in Equation (1) taking only I and II into account disregarding all other reaction products. Over 100 h of the in situ experiment, a linear loss in integral intensity by ∼31 % is observed (Figure 10, right), suggesting a reaction turnover of ∼38 % over this period (0.38 %/h).

Figure 10.

Time‐dependent in situ solid‐state (static) ¹H NMR experiment of the phase transformation of I (left). Change of the ¹H NMR integral intensity vs. time during the static in situ measurement (right). For further details see the plain text.

Conclusion

We observed an unusual structural transformation of the crystal water‐rich compound Na₄SnS₄ ⋅ 14H₂O into the crystal water deficient sample Na₄Sn₂S₆ ⋅ 5H₂O at RT, which was monitored with time‐resolved XRPD experiments, in situ IR, in situ Raman and in situ ¹H NMR spectroscopy. This transformation is exciting with respect to several aspects: the reaction requires a complex sequence of chemical reactions including O−H bond breakage accompanied by proton transfer to terminal S atoms of [SnS₄]⁴⁻ units, formation of NaOH, movement of adjacent SnS₃SH³⁻ units over several Å, condensation to generate [Sn₂S₆]⁴⁻, release of H₂S, rearrangement of the Na⁺ ions including bond formation. All these processes occur in the solid state without significant changes of the crystal integrity. The reaction is slow and can be suppressed by cooling Na₄SnS₄ ⋅ 14H₂O, indicating that the transformation is a thermally activated process. AIMD calculations support these experimental findings. EIS investigations demonstrate that I and II are moderate ionic conductors, which is underlined by data obtained from BVSE calculations, and the ionic mobility increases by three orders of magnitude between −20 to +25 °C.

Experimental Section

Synthesis of Na₄SnS₄   ⋅ 14H₂O (I): 1.80 g (7.50 mmol) Na₂S ⋅ 9H₂O were dissolved in 5 mL H₂O. 0.655 g (1.87 mmol) SnCl₄ ⋅ 5H₂O also dissolved in H₂O (3 mL) were added dropwise to the Na₂S ⋅ 9H₂O solution. ^[15] The mixture was stirred for 30 min at RT until the generated yellow precipitate was dissolved and a blue‐green solution is formed. To this solution, 4 mL cold (3 °C) pure acetone were added and stored at this temperature for 10 min. The colorless crystals were filtrated with a yield of ≈68 % based on Sn.

Synthesis of Na₄Sn₂S₆   ⋅ 5H₂O (II): 0.750 g (1.27 mmol) Na₄SnS₄ ⋅ 14H₂O was dispersed in 4 mL MeOH and heated for 20 min at 90 °C. The white solid of Na₄Sn₂S₆ ⋅ 5H₂O was filtrated, washed with MeOH and stored in air at room temperature (yield ≈40 % based on Sn). The XRPD pattern shows only reflections of compound II (Figure S7).

Structure Determination: Data for compound I were collected using a XtaLAB Synergy, Dualflex, HyPix diffractometer with Mo‐K _α radiation (λ=0.71073 Å) at 79.9(8) K. Data reduction, scaling and absorption corrections were performed using CrysAlisPro (Rigaku, V1.171.41.93a, 2020). The final completeness is 99.90 % out to 30.078° in θ. A multi‐scan absorption correction was performed using CrysAlisPro 1.171.41.93a (Rigaku Oxford Diffraction, 2020) using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. The structure was solved and the space group C2/c determined by the ShelXT[ ⁴⁴ , ⁴⁵ ] structure solution program using the Intrinsic Phasing solution method and by using Olex2 ^[46] as the graphical interface. The model was refined with version 2016/6 of ShelXL.[ ⁴⁴ , ⁴⁵ ] All non‐hydrogen atoms were refined anisotropically. The O−H H atoms were located in difference maps, their bond lengths were set to ideal values and finally they were refined isotropically with U _iso(H)=1.5 U _eq(O) using the riding model. Selected crystal data and refinement results are summarized in Table S1 and details of the structure determinations are given in the corresponding text in the Supporting Information.

The XRPD pattern of II could be indexed with a tetragonal unit cell with extinction conditions suitable for the space group P4₁2₁2 using TOPAS Academic. ^[47] Using these parameters and an estimated composition based on EDX spectroscopy, the position of the heavy Sn, S and Na atoms could be determined using direct methods as implemented in Expo 2009. ^[48] This initial structure model was subsequently refined by Rietveld methods using a Thompson‐Cox‐Hastings profile function and a 12^th order polynomial background function. Residual electron density was identified by Fourier synthesis and attributed to oxygen atoms representing water molecules coordinated to the sodium atoms. The positions of all atoms were freely refined without any restraints, and the displacement parameters were refined element specifically. The final plot is shown in Figure S7 and some figures of merit are summarized in Table S4. Our structural data derived from the XRPD pattern match very well with those reported in the Supporting Information of Ref. [21].

Deposition Numbers 2142577 (I at 100 K), 2142575 (I at 140 K), 2142574 (I at 180 K), 2142573 (I at 220 K), 2142576 (I at 260 K) and 1984037 (II) contain the supplementary crystallographic data for this paper. These data are provided free of charge by the joint Cambridge Crystallographic Data Centre and Fachinformationszentrum Karlsruhe Access Structures service.

Computational Details: First‐principles DFT calculations for the molecular dynamics simulations were carried out under the generalized gradient approximation ^[49] with the Vienna ab initio Simulation Package[ ⁵⁰ , ⁵¹ ] (for energy minimizations) and with CASTEP ^[52] for the dynamic simulations. Calculations of the vibrational spectra were carried out by using the TURBOMOLE program package. ^[53] Structure optimizations were performed at the PBE05/def2‐TZVPP^[54–56] level of theory and RI approximation[ ⁵⁷ , ⁵⁸ , ⁵⁹ ] to speed up the calculations. To prove that the optimized structure is a minimum on the potential energy surface and for the vibrational frequencies the AOFORCE module was used, ^[60] which is included in the TURBOMOLE program package.

AIMD simulations were conducted for a conventional unit cell Na₁₆Sn₄S₁₆H₁₁₂O₅₆ containing 204 atoms using a 380 eV plane‐wave energy cutoff with time steps of 1 fs in the canonical (NVT) ensemble for four temperatures, 1200 K, 800 K, 600 K and 500 K over 10–30 ps. Additional trials with longer time steps up to 2 fs to facilitate longer simulation periods led to an unphysical behavior of the O−H bonds and thus had to be discarded. For each time step total energy/atom was converged to 2×10⁻⁶ eV and eigen energy was converged to 10⁻⁶ eV. As preliminary simulations of the ordered structure at 800 K did not result in any chemical reaction over the simulation period, AIMD simulations discussed in this work refer to a 204 atoms local structure model comprising a conventional unit cell where the chemical reaction was accelerated by dissociating one water molecule (containing an O(7) atom) into an OH group and a symmetry copy of this water molecule at a distance of 11.5 Å into an H₃O group, followed by a geometry relaxation.

X‐Ray Powder Diffraction: The XRPD patterns were measured with a STOE Stadi‐P diffractometer equipped with a MYTHEN 1 K detector (DECTRIS) in transmission geometry using monochromatized Cu‐K _α1 radiation (λ=1.540598 Å).

Infrared Spectroscopy: IR spectra were recorded at RT on a Bruker Vertex70 FTIR spectrometer using a broadband spectral range extension VERTEX FM for full, mid, and far IR in the range of 6.000‐80 cm⁻¹.

Raman Spectroscopy: Raman spectra were recorded at RT on a Bruker RAM II FT‐Raman spectrometer using a liquid nitrogen cooled, highly sensitive Ge detector, 1064 nm radiation and 4 cm⁻¹ resolution.

Electrochemical Impedance Spectroscopy: EIS was performed using a VSP Essential (BioLogic) and an impedance test cell for solids ASC−A (Sphere™) exhibiting stainless steel pistons as blocking electrodes. The solid compounds were pressed into pellets at RT (p≈120 MPa, diameter d=8.0 mm, thickness h(I)=1.49 mm, h(II)=0.59 mm). The cell was cooled to −20 °C in a climate chamber MK056 (Binder) and three impedance measurements were recorded with an amplitude of 100 mV in a frequency range from 1 MHz to 1 Hz after a resting time of 3.5 h at various temperatures between −20 and +25 °C with T steps of +5 °C. The total ionic conductivity was calculated from the impedance spectra applying fits according to the equivalent circuit shown in Figure 5 (left) using EC‐Lab® V11.33.

Solid‐State MAS NMR Spectroscopy: ¹H, ²³Na, and ¹¹⁹Sn MAS NMR was performed at a magnetic field of 11.7 T, corresponding to resonance frequencies of 500.2 MHz, 132.3 MHz, and 186.5 MHz, respectively. Powder samples were packed into 2.5 mm rotors in argon atmosphere and the spinning speed was 30 kHz. Spectra were acquired with a single‐pulse sequence for ¹H/¹¹⁹Sn and with a Hahn‐echo sequence for ²³Na. The π/2 pulse length was 4.2 μs for ¹H, 2.65 μs for ²³Na, and 1.2 μs for ¹¹⁹Sn. The recycle delay was 15 s for ¹H and 30 s for ²³Na/¹¹⁹Sn. Chemical shifts were referenced to tetramethylsilane for ¹H (0 ppm), an aqueous 1 m NaCl solution for ²³Na (0 ppm), and well crystalline SnO₂ for ¹¹⁹Sn (−604.3 ppm). ^[61]

Conflict of interest

The authors declare no conflict of interest.

Supporting information

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

Supporting Information

Benkada A., Hartmann F., A. Engesser T., Indris S., Zinkevich T., Näther C., Lühmann H., Reinsch H., Adams S., Bensch W., Chem. Eur. J. 2023, 29, e202202318.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.