In situ studies of a platform for metastable inorganic crystal growth and materials discovery

Significance

Dense inorganic materials comprise most functional electronic, optical, and magnetic devices. Whereas the discovery of new inorganic materials can increase our technical capabilities and uncover new phenomena, the search is difficult due to their formation at high temperatures where only the most stable (often known) materials can be isolated postreaction. We find a variety of unexpected and unknown materials nucleating at moderate temperatures in molten salts. By probing these processes with in situ diffraction, we are able to identify a large variety of new phases quickly and pave a path to more efficient materials discovery.

Abstract

Rapid shifts in the energy, technological, and environmental demands of materials science call for focused and efficient expansion of the library of functional inorganic compounds. To achieve the requisite efficiency, we need a materials discovery and optimization paradigm that can rapidly reveal all possible compounds for a given reaction and composition space. Here we provide such a paradigm via in situ X-ray diffraction measurements spanning solid, liquid flux, and recrystallization processes. We identify four new ternary sulfides from reactive salt fluxes in a matter of hours, simultaneously revealing routes for ex situ synthesis and crystal growth. Changing the flux chemistry, here accomplished by increasing sulfur content, permits comparison of the allowable crystalline building blocks in each reaction space. The speed and structural information inherent to this method of in situ synthesis provide an experimental complement to computational efforts to predict new compounds and uncover routes to targeted materials by design.

Discovering new materials is a crucial step to address large-scale problems of energy conversion, storage, and transmission and other technological needs whether seeking bulk phases or thin films. Dense inorganic materials are desired for their tunable transport, magnetism, optical absorption, and stability, but their existence in general cannot be predicted with the near certainty of that of metastable organic and organometallic compounds. Whereas the desire to efficiently locate and assemble inorganic materials is great, it is hindered by traditional solid-state synthetic methods—at high temperatures often only the energy-minimum thermodynamic product is obtained. To strive toward an arena where metastable compounds can be discovered rapidly and made systematically, here we conduct reactions within liquid fluxes and use in situ monitoring to capture signatures of new phases, even when they quickly dissolve in the melt.

Convective liquid fluxes (salts, metals, or oxides) can serve as reaction media that aid diffusion and enable rapid formation of compounds at temperatures far below their melting points (1–6). The flux can be nonreactive or reactive; in the latter case the flux itself becomes incorporated into the product (7, 8). This well-established approach has demonstrated the prolific discovery of novel inorganic materials grown out of low-melting fluxes, from oxides and other chalcogenides (9–12), to pnictides (13, 14), to intermetallics (15), many of which cannot be attained by direct combinations of the elements. Despite the variety of metastable phases formed in these reactions, the classical approach is to predetermine a given set of reaction conditions (e.g., time, temperature, and heating and cooling rates) and wait for completion to isolate and identify the formed compounds. It is not possible to observe how the reaction system itself has arrived at the isolated compound, whether the crystalline material formed on heating, on cooling, or on soaking at the given high temperature, nor it is possible to know whether any intermediates were present and, if so, their influence on product formation. This lack of awareness (“blind synthesis”) hinders our ability to identify the new materials or to devise successful synthetic processes for desired and targeted materials. If we are to develop a predictive understanding of synthesis and to more quickly discover new materials, we will greatly benefit from the input of much higher levels of detail in how syntheses proceed.

We show here that in situ synchrotron X-ray diffraction maps of metastable inorganic compound formation in inorganic fluxes reveal complex real-time phase relationships and permit rapid access to new inorganic materials that would be missed using classical approaches. Specifically, we have discovered heretofore unknown phases in systems with simple elemental compositions of Cu and Sn with molten polysulfide salts K₂S₃ and K₂S₅ (melting points 302 °C and 206 °C, respectively) as paradigmatic representatives. Complex copper sulfides have been identified as possible earth-abundant photovoltaics (16) and are a source of exotic charge-density-wave materials, whereas tin chalcogenides form the basis for Cu₂ZnSnS₄ (CZTS) semiconductors (17) and exhibit ion exchange properties useful for heavy metal waste capture (18). We observe a complex phase space: In all but one of our reactions we observe additional crystalline phases in situ that are not present by the end of the reaction (as would be recovered ex situ). Both families of ternary compounds can exhibit a variety of coordinations by sulfur, and the range of properties is accordingly large: In just one of our Cu-containing reactions we found a previously undiscovered 1D metal (K₃Cu₄S₄) similar to heavy-metal capture materials and observed a different 2D metal (K₃Cu₈S₆) and a layered semiconductor (KCu₃S₂).

Our approach can be combined with previous work that probes the formation and stabilization of inorganic materials from liquid media, using structural and spectroscopic data (19, 20). Within a given reaction, we can use temperature as a variable to probe the relationships among phases with the goal of understanding how the structures may be constructed from similar building units. Additionally, in situ studies of crystallization have been shown to be effective at probing the kinetics of oxide and sulfide formation, typically from aqueous solutions (21–23).

The in situ technique we describe here provides rapid diffraction signatures of all crystalline phases formed during processing, including metastable intermediates. Reactions are performed in under 2 h (compared with typical flux reactions on the order of days), but time resolution of the data can be on the order of seconds. This is a route to efficient exploration of composition–temperature spaces that might be predicted to house novel compounds with favorable properties by first-principles (24) or data-mining calculations (25). Because new structure types cannot be easily predicted by computational theory, the approach described here is a necessary experimental tool in now-budding efforts to understand, validate, and expand the materials genome.

A schematic of the in situ capillary furnace used to investigate phase formation during flux reactions is shown in Fig. 1A. The sample tubes, 0.7 mm in diameter, were sealed under vacuum, heated using a resistive coil, and continuously rastered through the synchrotron X-ray beam to maintain uninterrupted X-ray exposure of the sample as it melted and flowed within the tube.

Fig. 1.

Schematic of in situ X-ray diffraction experiment and data analysis. (A) The in situ setup for collecting X-ray diffraction data from melting polysulfide fluxes. The sample tube diameter is 0.7 mm. Two-dimensional patterns are integrated and the 1D data can be fitted using Rietveld refinements to give individual contributions to the diffraction patterns in B. Upon heating, diffraction data are collected continuously, giving the set of patterns in C. These data are divided into regions with distinct phase contributions. A single pattern from each region is shown in D–F, with contributions to each pattern identified.

For each reaction, the accompanying series of raw diffraction patterns provide a real-time monitor of the reaction progress and, to a first approximation, the number of phase formation and dissolution events. The X-ray diffraction pattern from a combination of Cu and K₂S₃ before heating is shown in Fig. 1B and fitted with a Rietveld refinement that confirms the contributions from both reagents. The diffraction patterns collected continuously while heating and cooling this reaction mixture are shown in Fig. 1C. Wholesale changes in the diffraction patterns indicate that the reaction pathway proceeded in a series of steps (color coded in Fig. 1C). First, signatures of the reagent metal and polysulfide appeared (blue region), which all resemble the refined pattern in Fig. 1B. Upon heating, low-Q peaks appeared in the diffraction data (red region). This real-time information (before any analysis) revealed that more complex ternary K–Cu–S phases were forming.

Continued heating led to the disappearance of all Bragg peaks (gray region in Fig. 1C). At this point the ternary sulfides dissolved completely into the molten polysulfide salt flux. After cooling, low-Q peaks again signified the presence of ternary phases (violet region in Fig. 1C). Random variations in peak heights in adjacent patterns provided a morphological clue: The product on cooling formed as large sulfide crystals, leading to sharp diffraction spots rather than powder-averaged rings.

Systematic least-squares refinements account for all crystalline phases present. Phase transformations and amorphous regions (defined by the absence of Bragg peaks) can also be observed in real time by visual inspection. Representative diffraction patterns and their least-squares refinements from each of the four temperature regimes in Fig. 1C are shown in Fig. 1 D–F. Data in Fig. 1D were taken at 320 °C upon heating and the reaction contained two ternary phases: KCu₃S₂ and the previously unknown phase K₃Cu₄S₄.

At the time of the experiment, contributions to the diffraction pattern that do not match known compounds are considered unknown phases to be solved. Three options to identify new phases are as follows:

• i)Deduce structure by chemical analogy to known compounds. This can be accomplished manually or aided by computational tools such as the “Structure Predictor” of the Materials Project (26, 27).
• ii)Grow larger single crystals of compounds that crystallize out of a melt. In the present case, elemental analysis and single-crystal diffraction were used in this study to identify K₄Sn₂S₆ from crystals grown ex situ based on information provided by the in situ experiments.
• iii)Solve structure from powder diffraction, using computational packages such as FOX (28).

In the case of the experiment with data shown in Fig. 1D, the unknown phase K₃Cu₄S₄ was identified by option i: comparison of the isostructural phase Na₃Cu₄S₄.

The diffraction pattern at 600 °C in Fig. 1E, taken from the gray region in Fig. 1B, has no Bragg peaks and represents the amorphous polysulfide melt after dissolution of KCu₃S₂ and K₃Cu₄S₄. A diffraction pattern from cooling at 50 °C is shown in Fig. 1F to contain the 2D metallic compound K₃Cu₈S₆ and the recrystallized flux K₂S₃. Because K₃Cu₈S₆ grew as large crystals, not a powder, Le Bail full-profile fitting (disregarding peak heights but refining peak profiles and peak locations constrained by unit cell symmetry) is shown in Fig. 1F to account for all peak contributions rather than the Rietveld method (29).

The last step in diffraction analysis is to refine every powder pattern sequentially. Using the four diffraction patterns in Fig. 1 D–F and their refined phase contributions as anchors, we performed automated least-squares refinements to the ∼200 diffraction patterns to record the reaction progression as a function of time and temperature and form a “reaction map.” In this manner we identified phase fractions and points of crystallization, melting, and dissolution of all crystalline phases present during in situ reactions of Cu and Sn in fluxes of K₂S₃ and K₂S₅. The resulting panoramic reaction maps are shown in Fig. 2 and discussed subsequently.

Fig. 2.

Reaction maps obtained from sequential refinements to in situ diffraction data. (A) Reactions of Cu + K₂S₃ lead to formation of KCu₃S₂ and the new phase K₃Cu₄S₄ on heating. These dissolve into the melt upon heating, and K₃Cu₈S₆ crystallizes upon cooling. A similar phase progression occurs for Cu + 5K₂S₃ (B), with KCu₃S₂ also forming on cooling. Reactions of Cu + K₂S₅ (C) and Cu + 5K₂S₅ (D) produce the layered phase KCu₄S₃. Reactions of Sn + K₂S₃ (E) produce SnS and the new phase K₆Sn₂S₇ on heating. No ternary phases are observed for Sn + 5K₂S₃ (F). The lowest-melting reaction Sn + K₂S₅ (G) reveals formation of the new phase K₅Sn₂S₈ from a melt upon heating. K₄Sn₂S₆ and K₂Sn₂S₅ crystallize concurrently upon cooling. For Sn + 5K₂S₅ (H), the progression is similar but K₂Sn₂S₅ is absent.

Hidden Compounds upon Heating Cu in K₂S₃

Two in situ reactions of Cu in K₂S₃ (1:1 and 1:5 metal:flux mole ratio) were studied and the time- and temperature-dependent progression of phases is shown in Fig. 2 A and B. The melting of the flux and dissolution of Cu are readily seen in the early minutes of heating. The first formed product was the known phase KCu₃S₂, a valence-precise semiconductor (30), which could be isolated if the reaction were stopped at this point. Soon after, the previously unknown phase K₃Cu₄S₄ appeared. The structures of these phases are closely related and shown in Fig. 3: K₃Cu₄S₄ contains 1D chains of CuS trigonal pyramids. In KCu₃S₂ these chains are linked by tetrahedral CuS₄ units to form a 2D network. The shared structural motifs suggest a common precursor may exist in the melt, and the implication for directing synthesis in regime can be probed by other in situ studies (19, 20). Na₃Cu₄S₄ accommodates extra charge on Cu–S chains but curiously does not exhibit charge-density-wave modulations (31). It is not yet known whether K₃Cu₄S₄ behaves similarly. K₃Cu₄S₄ dissolves into the flux at 410 °C, followed by KCu₃S₂ at 490 °C.

Fig. 3.

Ternary crystal structures observed from in situ synthesis experiments. (Upper) Crystal structures of known phases KCu₃S₂, K₃Cu₈S₆, and KCu₄S₃ are shown, along with the sole previously reported Sn-containing structure K₂Sn₂S₆. (Lower) Structures of four previously unknown phases that were discovered: K₃Cu₄S₄, K₆Sn₂S₇, K₄Sn₂S₆, and K₅Sn₂S₈. (Cu, blue; Sn, gray; S, yellow; K, white).

The power of in situ structural characterization to identify intermediate compounds and events is clear in these systems because both reactions of Cu in K₂S₃ produced different phases on heating vs. cooling, indicating metastable compounds. Cooling from 600 °C led to nucleation of the known 2D metal K₃Cu₈S₆ (32). This phase was accompanied at 426 °C by KCu₃S₂ when additional flux was used (starting composition Cu + 5K₂S₃), Fig. 2B. The two reactions of Cu in K₂S₃ produced one previously unknown ternary phase in less than 4 h of reaction time. If this particular reaction procedure of Cu + K₂S₃ were performed ex situ, no evidence of the formation of KCu₃S₂ and K₃Cu₄S₄ would exist—only K₃Cu₈S₆ would remain. Further control over these reactions requires a grasp of reaction kinetics, either by diffraction or calorimetry, but our approach can provide clues about the (meta)stability of the competing phases. For instance, a separate in situ reaction showed that holding the reaction Cu + K₂S₃ at 320 °C led to disappearance of K₃Cu₄S₄ within minutes whereas KCu₃S₂ persisted unchanged for 10 h until the collection was ended. Increasing the flux ratio to Cu + 5K₂S₃ and holding at 320 °C led to dissolution of KCu₃S₂ back into the melt. Armed with a structural description of these phase transitions, simpler calorimetric techniques (differential thermal analysis) would be a complementary method to probe the energy dependence of these reactions and how they can be tuned via temperature and chemistry.

Distinct Double-Layer Sulfides: Cu in K₂S₅

Quickly establishing phase stability boundaries is a key aspect of effective phase discovery. A change in flux chemistry to K₂S₅ (Fig. 2 C and D) led to the gradual formation of a separate 2D metallic compound KCu₄S₃, even before K₂S₅ had fully melted. The phase KCu₄S₃ bears little structural relationship to KCu₃S₂ and K₃Cu₄S₄ from reactions in K₂S₃. It contains corner-sharing CuS₄ tetrahedra, reminiscent of a double-layer version of the ThCr₂Si₂-type structure that exhibits superconductivity in alkali–iron–pnictide compounds (33). KCu₄S₃ is mixed valence and exhibits holes in the S p-band, but modification/doping reactions to induce a superconducting state have yet to be demonstrated (34). A small amount of digenite Cu_2-δS is formed at higher temperatures. Otherwise the reaction mixture is amorphous after KCu₄S₃ dissolves at 495 °C.

Upon cooling, reactions with metal:flux ratio 1:1 crystallize KCu₄S₃ congruently, indicating that this reaction stoichiometry is a viable medium for growing single crystals of KCu₄S₃. Increasing the flux ratio to 1:5 (Fig. 2D) did not change the phase progression upon heating, but did suppress crystallization of KCu₄S₃ and led to a mixed K–Cu–S glass after cooling at the same rate of 15 °C/min, which is relatively fast for an inorganic synthesis.

Implications for Directed Ternary Copper Sulfide Synthesis

This series of four reactions (∼8 h) produced a total of four ternary phases, one of which is new. We also observed that K₂S₃ and K₂S₅ fluxes produced different sets of phases. In essence, K₂S₅ contains more S–S bonding (average valence only S^0.4−). Note that Cu can be oxidized only to 1+ (35). The only semiconducting phase (KCu₃S₂ with nominal S²⁻ valence) was formed in K₂S₃ fluxes only. Metallic phases K₃Cu₈S₆ and K₃Cu₄S₄ that share the same three-coordinate Cu-S motifs (with subtle modifications) were also observed alongside KCu₃S₂. Using a K₂S₅ flux reduced the oxidizing power of the flux, eliminated three-coordinate Cu⁺, and produced metallic KCu₄S₃, which has a less-negative nominal S valence (S^1.67−) than any other phase seen here. The lack of overlap (no other ternary phases existing alongside KCu₄S₃) implies that there is an intermediate reaction space between K₂S₃ and K₂S₅ that remains ripe for discovery: It may contain coexistence of these ternary phases or entirely new compounds. These maps may also imply that there is a change in character of Cu–S coordination in the melt between K₂S₃ and K₂S₅ that divides reactions forming KCu₄S₃ and those forming three-coordinate ternary copper sulfides.

New Dimer Compounds: Sn in K₂S₃

In situ reactions of Sn in K₂S₃ revealed two new phases in our first 2-h study. These reactions are shown in Fig. 2 E and F and proceeded with the melting of Sn first and then formation of α-SnS before the flux K₂S₃ had finished melting at 302 °C. After melting the flux, α-SnS was converted into the previously unknown phases K₆Sn₂S₇ and K₄Sn₂S₆, which are shown in Fig. 3. The structure of K₆Sn₂S₇ was solved based on chemical analogy to the known valence-precise compound Rb₆Sn₂S₇, which contains corner-sharing dimers of SnS₄ tetrahedra (36).

Isolation and structure solution of K₄Sn₂S₆ was straightforward because rapid in situ reactions of Sn in K₂S₅ revealed that it crystallized congruently from the melt. In this case, the reaction maps provided an immediate “recipe” for growth of clear single crystals. K₄Sn₂S₆ contains SnS₄ tetrahedra that are edge sharing to form [Sn₂S₆]⁴⁻ units. Both structures are shown in Fig. 3. Continued heating led to disappearance of K₆Sn₂S₇ until only K₄Sn₂S₆ remained.

The reaction Sn + K₂S₃ $\to$ 1/2 K₄Sn₂S₆ is stoichiometric, so no liquid flux is necessarily present at 600 °C. However, the chain compound K₂Sn₂S₅ (structure is shown in Fig. 3; it contains a 3D network of corner- and edge-sharing SnS₅ trigonal bipyramids) formed upon cooling without any decline in the amount of K₄Sn₂S₆. The presence of SnS and K₆Sn₂S₇ upon heating suggests that these phases left behind amorphous K-poor or S-rich regions, either of which could lead to formation of K₂Sn₂S₅. Again, kinetic studies may reveal routes to full conversion to K₄Sn₂S₆ in this system.

Increasing the flux ratio to Sn + 5K₂S₃ eliminated the formation of any ternary compounds in these reactions. Only a small amount of α-SnS was formed on heating, which dissolved into the flux, leaving a K–Sn–S glass after cooling at 15 °C/min, analogous to the cooling behavior of the reaction Cu + 5K₂S₅ in Fig. 2D.

New Structure Type from a Melt upon Heating: Sn in K₂S₅

Reactions of Sn in K₂S₅ were the only reactions in this study where there was a small induction time after melting of the flux and Sn (T_m = 232 °C): No crystalline phases were present for a short period upon heating. This “dead time” after 60 min have elapsed is shown in Fig. 2 E and F. This metastable induction region has not been observed before in molten salt synthesis and is surprising given the preference of the Cu-containing reactions to form ternary compounds immediately as the flux melted. Ex situ or calorimetric measurements alone cannot quickly differentiate between melting events that produce new phases vs. amorphous induction periods—they must be informed by structural methods.

The new phase K₅Sn₂S₈ crystallized directly from the amorphous induction region upon heating and its structure was solved from high-resolution powder diffraction. Future studies should probe the generality of this formation mechanism. If such behavior exists in many other chemical syntheses, then it would permit single-crystal growth at very low temperatures and therefore may access a different cache of phases than those formed from cooling at high temperatures.

The 2D compound K₅Sn₂S₈ is shown in Fig. 3 and contains infinite zig-zag chains of corner-sharing SnS₄ tetrahedra, similar to Na₂GeS₃, but with extra space between the chains and accommodating one S₄²⁻ polysulfide chain, effectively creating a phase that is K₄Sn₂S₆ + 1/2K₂S₄ (albeit topologically dissimilar to K₄Sn₂S₆). Continued heating led to formation of K₂Sn₂S₅ and K₄Sn₂S₆. At 430 °C all phases had dissolved, leaving an amorphous melt that persisted until concurrent crystallization of K₄Sn₂S₆ and K₂Sn₂S₅ upon cooling past 460 °C at 15 °C/min. Increasing the flux ratio to Sn + 5K₂S₅ (Fig. 2F) led to a reaction with an induction time before crystallizing K₅Sn₂S₈ and K₄Sn₂S₆. K₂Sn₂S₅ was absent on heating and cooling, so this reaction medium was used in a large ex situ reaction to prepare optically clear single crystals of K₄Sn₂S₆ for structural solution.

Unlike the ternary copper sulfides, the K–Sn–S phases are mostly charge-balanced insulators with nominal S²⁻. The one exception is the new metastable phase K₅Sn₂S₈. This phase has polysulfide units incorporated into the structure alongside the SnS₄ tetrahedra that persist in all other ternary phases we observed. This unique phase forms only after an induction time on heating, so further kinetic and structural studies may reveal novel strategies to prepare tin sulfides with large open channels or a disproportionation of S₅²⁻ chains in the melt that are incorporated into the crystal.

Implications for Materials Synthesis and Discovery

In situ exploratory reactions in inorganic reactive fluxes show that a variety of new phases are waiting to be found even in systems that are well investigated. The method of collecting diffraction data in transmission over the full length of a liquid-filled capillary is a powerful tool for materials discovery in its own right, and these experiments can provide valuable insight whenever inorganic or metastable materials are being synthesized. A single in situ reaction can inform bulk reactions to prepare large crystals, as was done here for K₄Sn₂S₆, especially when the phase is of technical interest or cannot be solved by powder diffraction patterns alone. The eight reaction spaces we show in Fig. 2 represent less than 24 h of diffraction time. Accordingly, we present only a limited composition space, because many other fluxes (K₂S_x) and ratios could be explored. This matrix of reactions is large, but could be performed rapidly using the methods we describe.

Knowledge about the temperatures at which different phases form (or disappear), when combined with the atomic structures of the resulting compounds, provides a unique opportunity to begin to understand the underlying mechanism by which these materials are assembled. For example, the new K₃Cu₄S₄ structure is composed of simple Cu₄S₄ one-dimensional linkages that are joined together to form the more complex 2D Cu–S network seen in KCu₃S₂, raising the possibility that the two phases are closely linked energetically and hence could be tuned to favor one product over another. Increasing the S content leads to formation of KCu₄S₃, using entirely different CuS₄ motifs. Experiments using our in situ technique, when combined with theory, can approach the directed synthesis of targeted materials.

Our observation of ternary phases forming upon heating through an amorphous induction zone in low-melting Sn + K₂S₅ reactions highlights the novel formation mechanisms of metastable phases that remain to be uncovered and understood. Because these phases form from solution, studying the nature of the molecular entities that exist in the melt before crystallization will be a major step toward controlling the formation of inorganic crystals and designing new materials. A full array of local structure techniques will be necessary to probe these processes: In situ Raman and X-ray spectroscopy, real-space high-energy X-ray scattering analyses, NMR, and molecular dynamics simulations can all provide structural and mechanistic guidance, whereas calorimetric studies on the same timescale as our in situ work can inform the kinetics.

The rapid interrogation of temperature–composition space is a natural complement to computational efforts to accelerate materials discovery and design, such as the Materials Genome Initiative. New structure types such as K₅Sn₂S₈ found here cannot be easily predicted by theory and have the potential to greatly expand the library of known materials. Our method allows unfamiliar diffraction patterns to be quickly compared with those of predicted compounds, such as those freely available in the Materials Project (25, 26). This approach should be integrated into arenas where the discovery of complex phases can expand the reservoir of functional materials that dictate the state of the art across energy and other applications spaces.

Methods

Precursor polysulfides K₂S₃ and K₂S₅ were prepared by a tube-in-tube vapor transport technique: Balls of metallic K were loaded into a quartz tube, and an alumina crucible filled with a stoichiometric amount of S was suspended above. This tube was sealed under vacuum with the K-containing end submerged in liquid N₂ to prevent vaporization. Care must be taken to prevent spilling the suspended S onto the K below. The sealed tubes were heated to 300 °C in 12 h, held at that temperature for 4 h, and then air quenched. Ingots of K₂S₃ and K₂S₅ powders were ground and sieved to 150 μm and then ground together with stoichiometric amounts of Cu and Sn inside an N₂ glove box. These mixed powders were loaded into 0.7-mm diameter quartz tubes and sealed under vacuum.

In situ X-ray diffraction was performed at beamline 17-BM of the Advanced Photon Source (APS), using X-rays of wavelength λ = 0.605 Å (20 keV), using a beam size ∼0.3 mm² and a Perkin-Elmer 2D detector and the sample heating environment developed by Chupas et al. (37). The experimental configuration is shown in Fig. 1A. Diffraction data were collected continuously with 30-s collection times, and the sample assembly was continuously horizontally rastered through the beam so that each powder pattern integrates intensity over the powder-filled portion of the capillary. All samples were heated to 600 °C with a slowdown near the melting temperature of the polysulfide salt flux given in SI Text.

High-resolution powder diffraction data were collected on selected products at beamline 11-BM of the APS (λ = 0.414 Å, 40 keV). Rietveld refinements were performed using the EXPGUI front end to GSAS (38), whereas structure solution from powder diffraction data used FOX (28) and TOPAS (Bruker Corporation). Single-crystal X-ray diffraction was performed using a STOE diffractometer, using Mo-Kα radiation. Single crystals of K₄Sn₂S₆ were suspended in Paratone oil and sealed in 0.3-mm diameter glass capillaries to prevent degradation of the samples during data collection. Single-crystal refinements were conducted using SHELX (39). Because the K₄Sn₂S₆ crystals were composites of multiple domains, the space group and approximate atomic positions were extracted using SHELX and then further refined using powder data. In most cases, atomic displacement parameters U_iso given in SI Text are constrained to a single value per atomic species, due to the limited statistics inherent to structure solution by powder diffraction of multiphase samples and moderate-resolution instruments (i.e., 17-BM). Additional structural details and refinement results are included in SI Text.