Synthesis and Growth Mechanism of SiS2 Rods.

The SiS2 rods exhibit a significant anisotropy property applied in a special field such as in the one of all-solid-state lithium-ion batteries and so on. In this work, the orthorhombic SiS2 rods with high chemical/phase purity were prepared by an elemental method, either through a boiling or a steaming process, at 1023-1073 K for 3 h and under the saturated S-vapor pressure (2.57-3.83 MPa) in a closed sealed-tube system. The composition, crystal structure, morphology, and growth mechanism were investigated. Results showed that the growth orientation of SiS2 along the <0 0 1> is intrinsically governed by the crystal structure motif. It could exist in both processes and the latter tends to show in macroscopic morphology. Using the pressure-temperature diagram, structure refinement, pole figures, image analyses, and so forth, factors influencing the purity and growth of SiS2 rods were concluded from the thermodynamics and kinetics viewpoints.

Introduction

Silicon disulfide (SiS2) is an important synthetic compound used in fundamental and applied research. It is one of the important raw materials for sulfide-based solid electrolytes.[1−12] There are five polymorphs of SiS2. One is the ambient-pressure (NP) phase (≤3.83 MPa, 973–1570 K)[10,11,13−18] with an orthorhombic structure (Ibam, Space Group no. 72), which can remain stable up to 6.9 GPa at RT.[10] The other four are high-pressure (HP) phases, while HP1-, HP2-, and HP3-phases are quenchable under ambient conditions. Monoclinic HP1-/HP2-phases (P121/c1, no. 14) form under 2.8/3.5 GPa at 1473 K, respectively. They have different unit-cells (Z = 4 vs Z = 12) and the c value of the former [5.8261(8) Å] is smaller than that of the latter [14.747(2) Å].[11] The tetragonal HP3-phase (I4̅2d, no. 122) forms under 4.0–7.5 GPa at 1373–1703 K.[11,14,15] The trigonal HP4-phase (P3̅m1, no. 164) cannot be obtained by quenching from a high temperature. It can only form through in situ high-pressing (27.5–29.6 GPa) at RT,[10] either from a stable NP-phase or one of the above three metastable HP-phases.

The SiS2 has an extreme-high selling price due to its complex synthesis methods restrained by its sensitivity toward hydrolysis and oxidation to generate the toxic H2S with a penetrating odor.[5,19]

Synthesis methods for NP-SiS2 have been summarized[5] and classified into two groups: compound[3,13,16−20] and elemental[6,10,11,20−22] methods. As for the latter, both silicon (Si) and sulfur (S) sources are elementary substances. It has advantages of easy availability of raw materials, simple process, no environmental pollution, safety, and less corrosion of equipment. At present, the “elemental method” for NP-SiS2 has become the main priority for academic research and scale production. The related reaction takes place at a certain temperature in a sealed quartz or quartz-lined steel container, similarly in a low-/medium-pressure hydrothermal kettle.

There are two routes in the “elemental method”.

The first is with a dual-temperature zone having a temperature gradient between the cold- and hot-ends of the container.[10,11,20,21] The synthesis reaction happens at the hot-end. The S-vapor circulates between the two ends. The ambient reaction pressure (NP) depends on the saturated S-vapor pressure (Psat.@S) at the cold-end rather than the pressure at the hot-end. This route ensures effectively the safe use of quartz tubes. However, it is at the expense of the reaction pressure reduction due to the lower cold-end temperature (vs hot-end temperature). The reaction time has to be extended. The requirement with a longer tube would decrease the effective reaction volume and therefore increase the equipment complexity and difficulty to use.

The second is with a uniform-temperature zone while the NP varies. When NP ≤ Pctrl., the reaction can take place safely (Pctrl.—the control pressure set for safe use of quartz tubes; being equal to 3.83 MPa in this work).where Blocks I–IV correspond to the four P-T relevant quadrants (labeled in Figure , see Section ). The Pi@S is the ideal gas pressure of S calculated by the ideal gas equation (= nSRTVq–1, MPa), where T > Tb.p.@S (717.75 K).[23] The nS is the mole number of S, R is the ideal gas constant (8.3144 J·mol–1·K–1), and Vq is the active volume (dm3). Next, the Pexpl. is the pressure limit of tube explosion. When NP > Pctrl. and meanwhile > Pexpl., quartz tubes would explode (Block IV). In practical application, the Pexpl. value of a commercially available quartz tube is about several megapascals (MPa), far below the tensile strength of a silica rod (∼120 MPa at 923–1073 K).[24,25]

Figure 2

Ambient pressure (NP) via temperature (T) diagram for synthesizing SiS2. Tm.p.@S—melting point of S (388.36 K);[23,32]Tb.p.@S—boiling point of S (717.75 K);[23,32]Te.p.@SiS2—eutectic point of SiS2 (1240 K);[23]Tm.p.@SiS2—melting point of SiS2 (1363 K);[18,19,33]Tb.p.@SiS2—boiling point of SiS2 (1403 K);[19,33]Psat.@S—saturated S-vapor pressure calculated from Rau et al.’s equation,[34] where Tb.p.@S < T ≤ Tb.p.@SiS2; and Psat.@SiS2—saturated SiS2-vapor pressure calculated via HSC software, where T > Tb.p.@SiS2.

By using the uniform-temperature zone, it makes full use of the advantage of pressure increasing (thus enhancing reaction rate) caused by sulfur gasification.[5,6,21,22] Compared to the dual-temperature zone, the reaction temperature here is between that at the hot-end and the cold-end. Therefore, the reaction pressure in the uniform-temperature zone is higher than that in the dual-temperature zone, while the latter depends on the Psat.@S at the cold-end. The route via the uniform-temperature zone can improve the rate constant (k) and conversion rate (η) in an exothermic reaction, which is also applied in this work.

However, there remains still some challenges in the application of the “elemental method”, e.g., low purity of SiS2, set for the safe use of quartz tubes complicated process to eliminate residual S,[6] long production period (soaking for 150 h,[20] 3 d[10,11] or 7 d;[22] calcining for 70–80 h[6] or 12 d[10,11]), too many production procedures,[6] high-temperature/pressure safety problems,[5,6] and detailed growth kinetics of rods (c.f. CdS, ZnO, et al.).[26,27]

We prepared SiS2 2 years before through an “elemental-synthesis gasifying separation” (ESGS) process.[5] This work is to reinvestigate/optimize the control techniques for solid–liquid/solid–gas reactions, chemical/phase-purity and microstructure of SiS2. The chemical (c.f. evaporation) approach using benzene is first used to eliminate residual S to prepare pure SiS2. The growth mechanism of SiS2 rods is proposed.

Materials and Characterization

The preparation flow chart of SiS2 is shown in Figure and the ambient pressure (NP) via temperature (T) diagram for synthesizing SiS2 in Figure .

Figure 1

Preparation of the flow chart of SiS2. (a) Solid–liquid boiling process; (b) solid–gas steaming process.

S Powder

The commercially available S powder (99 wt %, Beijing Xinguang Chem. Reag. Fact., China) was washed first by aqua regia with a HCl/HNO3 ratio of 3:1 (vol %) (36.0–38.0 wt % HCl, Shanghai Chem. Reag. Fact., China; 65.0–68.0 wt % HNO3, Shanghai Chem. Reag. Fact., China). Then, it was washed many times with ultrapure water (>18 MΩ·cm), until no Cl– could be detected in the washing solution and pH = 7. The washed substance was vacuum-dried and sieved through 200 mesh (<74 μm).

Si Powder

A certain number of polysilicon blocks (7N, Xinte Energy Co. Ltd., China) were broken and put into a stainless-steel vessel, together with Fe-balls (ϕ5.9 mm) and ethanol (99.7 wt %, Shanghai Chem. Reag. Fact., China) at the ratio of 1 (Si): 8 (Fe-balls): 1 (ethanol) (wt %). Ball-milling proceeded for 12 h at 150 rpm for revolution and 300 rpm for rotation in a planetary mill (QM-DY9, Nanjing Instr. Fact., China). The Si slurry was washed in sequence by 10 wt % HCl and 6 wt % HF (≥40.0 wt %, Shanghai Chem. Reag. Fact., China). Then, it was washed with ultrapure water and ethanol and vacuum-dried and sieved as the above. The Teflon utensils and containers were used when HF was involved in experiments. As a comparison, some Si powder was prepared by using WC-Co balls (ϕ6.1 mm) for 2 h. Then, the Fe-ball-milled Si powder was denoted as “Si” and the WC-Co-ball-milled Si powder was denoted as “Si#”.

SiS2 Powder

The obtained S and Si powders were mixed at the mole ratio (δ) of 3.3 : 1, that is, δ = 3.3, and then sealed in quartz tubes and vacuumed to 10 Pa with Ar. Each tube (Vq = 0.0121 dm3) contains 2 g of powder, equivalent to that mSi = 34.6 g/dm3. At least three tubes were used for one sample. Quartz tubes were laid diagonally in the furnace at a certain angle of 15°–25°. Half of them contained reactants at a down (D) site (for the solid–liquid boiling process; Figure a) and the other half at an up (U) site (for the solid–gas steaming process; Figure b). Samples were heated at low (L) or high (H) temperature (1023/1073 K) for 3 h then cooled down to RT. Both heating and cooling rates were 5 °C/min. Products were taken out by cutting quartz tubes and then treated (T) with benzene (Sinopharm, China; ≥ 99.5 wt %) in an Ar-filled glovebox (H2O < 0.1 ppm, O2 < 0.1 ppm). Last, they were vacuum-dried and sieved through 200 mesh (<74 μm).[5,28,29] For the following reasons, benzene was used in this work—It is the simplest aromatic hydrocarbon with a stable ring connected by delocalized big π-bonds. The hydrogen atoms on the ring are easy to be replaced but difficult to react with the oxygen in air (at RT). Addition reactions are difficult to proceed while it is used. It does not dissolve or react with the target product SiS2. However, it can dissolve residual S and other impurities.[30]

Samples were labeled hereafter with suffixes such as H, L, U, D, and T to represent those prepared at different conditions, for example, SiS2_HUT refers to the SiS2 prepared at a high (H) temperature of 1073 K, while the quartz tube was at an up (U) site, and treated (T) by benzene.

Chemical compositions were analyzed by an inductively coupled plasma-optical emission spectrometer (ICP Prodigy 7, Leeman Labs Inc., USA). The crystal structure and phase purity were determined by X-ray powder diffraction (XRD) using CuKα radiation (λα1 = 1.54060 Å, 40 kV, 40 mA) in a flat plate θ/2θ geometry with a step size of 0.01313°/step and a time per step of 128.52 s/step (Empyrean, PANalytical B.V., Netherlands). Samples were protected from water and oxygen through a special sample stage (Deen Optics Co., China) with shielding Ar in Kapton tapes.

The structure refinement with spherical harmonics function was performed by the Rietveld method implemented in GSAS/EXIGUI software[31] using the model of Si[S]2 based on an orthorhombic structure (Ibam, ICSD 291210).[11] The preferred orientation of polycrystalline grains was characterized by the texture index (J), texture strength (J1/2), and pole figures.

The microstructure and compositions were tested by a field-emission scanning electron microscope (S-4800, Hitachi Ltd., Japan), and a field-emission scanning/transmission electron microscope equipped with an X-ray spectrometer for energy-dispersive spectroscopy (EDS) (Talos F200S G2, ThermoFisher Sci. Inc., USA).

Results and Discussion

Chemical Purity

31 elements were analyzed by ICP for the acid-pickled raw materials (S and Si) and the synthesized SiS2 powders (Figure ). It showed that the W impurity induced by WC-Co ball-milling was much more difficult to be removed by the acid-pickling process than the Fe induced by Fe ball-milling.[5,28,29] All samples except the Si# (WC-Co-ball-milled Si powder) had a low content of element impurity (<690 ppm; w/o Na) and a low total impurity content (∼99.95 wt % purity; w/o Na). The acid-pickled Si, the synthesized SiS2_LUT, SiS2_HU, and SiS2_HUT had a relatively high content of Na, as a result of a high content of total impurity content. It might come from utensils, containers, or test errors. More studies are underway.

Figure 3

ICP analysis results of the acid-pickled raw materials (S, Si, and Si#) and the synthesized SiS2 powders.

Phase Purity and Crystal Structure

The acid-pickled S was indexed to the orthorhombic α-S8(s) with annular molecules (FdddZ, no. 70; ICSD 63083) (Figure a). At low temperatures (<432 K), the prevailing S-molecular species were those of cycloocta-S, cyclo-S8, and small molecules (from S2 to S8) with minimal and negligible quantities identified in the solid, liquid, and gaseous phases.[34−36] When heated, it will transform to various forms of polymeric S-chains, catena or mixed cyclo-linear, for example, monoclinic β-S8(s) at 369 K, monoclinic λ-S(l) with long-chain molecules near its melting point (Tm.p.@S = 388.36 K), and amorphous μ-S(l) at 432–433 K. Last, it would turn into a gas at its boiling point (Tb.p.@S = 717.75 K).[23,32] The acid-pickled Si was indexed to the cubic phase (Fd3̅mS, no. 227; ICSD 51688). The S and Si started to react below 628–663 K.[22,23,32−37]

Figure 4

(a) XRD patterns of the acid-pickled raw materials (S and Si) and the synthesized SiS2 powders; (b) Final observed, calculated, and difference profiles of the structure for SiS2_HUT via Rietveld refinement. The inset is the crystal-cell view in the direction [0 1 0]; (c) pole figures for the first three allowed reflections in SiS2_HUT, that is, (1 1 0), (2 0 0), and (2 1 1).

Two of the eqs –4 are independent.

XRD patterns of the synthesized SiS2 samples could be indexed to pure (100 wt %) orthorhombic SiS2 phases except for SiS2_HU. The SiS2_HU contained a small amount of residual α-S8, which was easily removed by benzene. All patterns were almost the same, including background, peak positions, shapes, and relative intensities. However, these relative intensities were obviously different with those deduced from the ICSD 291210 (Ibam, no. 72).[11] Thus, the preferred orientation correction[31,38,39] was introduced into the Rietveld refinement of the SiS2_HUT sample (Figure b). The refinement did not show any anomalies. The fit converged with acceptable goodness-of-fit (χ2 = 2.62) and agreement indices (Rp = 5.49%, Rwp = 8.72%, Rexp = 3.34%, and RF2 = 9.14%). The obtained structural and thermal parameters are reasonable (Table ).[11,40]

Table 1

Rietveld Refinement Parameters and Results of the Structure for the SiS2_HUT Sample

ions	type	Wyckoff	x	y	z	Occ.	Uiso (Å2)
Si4+	Si1	4a	0.0000	0.0000	0.2500	1.0	0.029(1)
S2-	S1	8j	0.1178(2)	0.2078(4)	0.0000	1.0	0.035(1)
χ2	Rp	Rwp	Rexp	RF2	Nobs	Nconstr.
2.62	5.49%	8.72%	3.34%	9.14%	5769	0
Space group: Ibam (no. 72); orthorhombic; Z = 4; Mr = 92.2175; ρcal. = 2.0400 g·cm–3. a = 9.6152(6) Å; b = 5.6224(2) Å; c = 5.5543(4) Å; α = β = γ = 90°; V = 300.264(16) Å3.

It showed orthorhombic SiS2 phases could be synthesized through the boiling/steaming process in a uniform-temperature zone (1023–1073 K, 3 h) and under the corresponding saturated S-vapor pressure (Psat.@S = 2.57–3.83 MPa).[34]

The chemical bonds in the orthorhombic SiS2 are anisotropic. Distorted edge-sharing [SiS4] tetrahedra link as chains along the c-axis (the inset of Figure b). There is very rigid covalent bonding between the tetrahedra in the direction [0 0 1], while there is weak ionic and van der Waals bonding with an “open” structure in the other two directions (a and b).[11,40] From the structure refinement with spherical harmonics function, the allowed eighth-order harmonic coefficients (Clmm) were calculated. They are related to the reflection-intensity correction factors that describe the texture effects. Then, the texture index (J) and texture strength (J1/2) which depends on Clmm were concluded, that is, J = 1.6149 (c.f. J = 1 for random, otherwise J > 1; J = ∞ for a single crystal) and J1/2 = 1.2708.

Pole figures present that the statistical orientation distribution of the plane normals from a particular set of planes gives a mapping of the probability of possible grain orientations.[31,38,39]Figure c showed pole figures constructed for the first three allowed reflections in orthorhombic SiS2 with the comparatively low symmetry, that is, (1 1 0), (2 0 0), and (2 1 1), in which the relative populations of planes in various orientations were proportional to the numbers (represent relative intensities of the diffraction signal) against the contour lines.

It confirmed that the synthesized orthorhombic SiS2 powders presented polycrystalline alignment with oriented [0 0 1] texture microstructures.

Microstructure (SEM and TEM/EDS)

Scanning electron microscopy/transmission electron microscopy (SEM/TEM) images and EDS mappings of the acid-pickled Si and the synthesized SiS2 powders are shown in Figure i–viii. The length (L), diameter (D), and length-to-diameter ratio (L/D) of Si and SiS2 rods/particles from SEM image analysis are shown in Figure .

Figure 5

SEM (i–vii), TEM images, and EDS mappings (viii) of Si and the synthesized SiS2 powders. They are as follows: the Fe-ball-milled and acid-pickled Si [i(a) and i(b)]; the SiS2 prepared at a low (L) temperature of 1023 K, while the quartz tube was at a down (D) site [ii(a) and ii(b)], at an up (U) site [iii(a) and iii(b)], or at an up (U) site and then treated (T) by benzene [iv(a) and iv(b)]; the SiS2 prepared at a high (H) temperature of 1073 K, while the quartz tube was at a down (D) site [v(a) and v(b)], at an up (U) site [vi(a) and vi(b)], or at an up (U) site and then treated (T) by benzene [vii(a) and vii(b); viii(a1), viii(b1), and viii(c1)].

Figure 6

Length (L), diameter (D), and length-to-diameter ratio (L/D) of Si and SiS2 rods/particles from SEM image analysis.

The S was kept in the liquid and gaseous states in this work thus the initial size (as opposed to chemical purity) needs not be too concerned.

The acid-pickled Si has a small particle size and a uniform particle size distribution of 3.3 ± 0.9 μm (Figures i and 6). It means that the Fe-based medium for ball-milling Si powder is highly effective for decreasing particle size and maintaining a high chemical purity (by post-acid-pickling).[5,28,29]

SiS2 particles prepared with the quartz tubes at a down (D) site (solid–liquid boiling process, Figure a), whether at low (L) or high (H) temperature (1023/1073 K), have irregular shapes and feature a little rod-like, such as SiS2_LD (Figure ii) and SiS2_HD (Figure v). Their mean particle diameters are 3.8 ± 1.2 μm and 4.9 ± 1.3 μm, respectively (Figure ). The forced-convective S-liquid stirred constantly the solid Si/SiS2 and destroyed the rods (see Section ).

SiS2 particles prepared with the quartz tubes at an up (U) site (solid–gas steaming process, Figure b), whether at low (L) or high (H) temperature (1023/1073 K), have rod-like shapes and feature very little irregular, such as SiS2_LU (Figure iii), SiS2_LUT (Figure iv), SiS2_HU (Figure vi), and SiS2_HUT (Figure vii and viii). The solid–gas steaming process provided a more stable growth environment for the SiS2 rods (see Section ). Their mean particle sizes (length/diameter) are 13.4 ± 4.5/3.8 ± 0.9 μm for SiS2_LU, 12.9 ± 3.0/3.2 ± 0.6 μm for SiS2_LUT, 16.0 ± 5.4/3.9 ± 0.9 μm for SiS2_HU, and 16.8 ± 5.0/4.5 ± 1.3 μm for SiS2_HUT, respectively. The corresponding length-to-diameter (L/D) ratios are 3.5, 4.0, 4.1, and 3.7, respectively. The length increases 19–30% with preparation-temperature increasing, while the diameter increases by varying degrees. Thus, the resulting L/D values change a little (Figure ).

The TEM imagine and EDS mappings of SiS2_HUT (Figure viii) showed a homogeneous elemental distribution of S and Si in SiS2 rods. No impurities were detected.

Comparing the images of SiS2_LU (Figure iii) with SiS2_LUT (Figure iv) and SiS2_HU (Figure vi) with SiS2_HUT (Figure vii), they showed that the residual S could be effectively eliminated through benzene treatment. In addition, the benzene could modify the microstructure and dispersion of SiS2 particles.

Specially, Figure showed that particle diameters of both Si and SiS2 powders were in the same order of magnitude, meaning that the particle diameter of a SiS2 particle depended mainly on that of a Si particle. A single Si-particle (rather than several Si-particles) reacted with liquid/gaseous S and then grew into a rod along a preferred direction.

The preferred orientation of orthorhombic SiS2 has been reported before, such as SiS2 with a fibrous, a needle-shaped, or a pillar-shaped morphology/structure.[3,13,16] However, so far, there is little explanation for the growth mechanism. Some orthorhombic materials with preferred orientation have also been investigated, such as Bi2S3 nanorods[41−43] or nanotubes,[43] Sb2S3 nanorods,[44] BiSCl polygonal tubes, BiSI bundle-rods,[45] and so on. Their growth mechanism was explained to be related to the large surface tension of the solution,[42,43] the large surface energy of products,[41] environment pressure,[44] or the inherent structural characteristics of products.[41,42,44,45]

In this work, the orthorhombic SiS2 powders with an oriented microstructure were prepared through the boiling/steaming process in a uniform-temperature zone (1023–1073 K) and under the saturated S-vapor pressure (Psat.@S = 2.57–3.83 MPa). The relatively high pressure is more favorable for the formation of SiS2-rods in the closed sealed-tube system (which is similar to the hydrothermal one) than that in an open system.[44] The texture had a consequence of the thermal/polycrystalline growth history. The synthesis conditions could affect the macroscopic morphology but could not change the microstructural anisotropy.[45] The intrinsic crystal-structure characteristics, being independent of synthesis conditions, determined the growth orientation of SiS2 rods. The synthesis temperature depended on the particle size of Si, and its dispersing condition in the melted/gasified S.[20] The latter was no doubt excellent in this work.

According to the Bravais’ law, for the orthorhombic SiS2, the observed crystal faces are parallel to the net planes with the highest reticular densities (or smallest mesh areas), that is, (1 0 0); the greater ones are corresponding to the more important forms. During synthesizing, big SiS2 grains preferentially grew into rods on (1 0 0) by consuming small grains on (1 1 0)/(2 1 1), which had low reticular densities (or large mesh areas). Moreover, the ratio of length-to-diameter gradually increased. As stated before, most of the Si–S bonds along the c axis have the shortest bond-length and strongest bond-energy. The SiS2 rods grew along [0 0 1] were rather stable thermodynamically and hard to be cleaved once the Si–S chemical bond was formed. The growth along [0 0 1] was intrinsically governed by the highest surface energy of plane (0 0 1).[41]

Growth Mechanism of SiS2 Rods

According to eq , NP1023 K = Psat., 1023 K@S = 2.57 MPa (

From the thermodynamics viewpoint, there may exist the following reactions to prepare SiS2 by an “elemental method”, for example, at 1023 K (2.57 MPa)–1073 K (3.83 MPa) in this work.

The main reaction to synthesize SiS2(s) (eq ) proceeds below 1993 K and the side reaction to SiS(g) (eq ) starts to proceed when T > 628 K.[33] The former dominates because it has a larger Gibbs free-energy (absolute value) than the latter. Besides, the forward reactions in eqs and 8 would be very difficult to happen below 1993 K (also in this work), while the partial pressures of SiS(g) are 10–3 atm in eq (3,37) and 10–5 atm in eq , respectively.[3,37] This means, if the SiS(g) was generated via eq , it would tend to produce SiS2(s) and Si(s) as in the backward reaction of eq or react with S2(g) to form SiS2(s) as in the backward reaction of eq . Therefore, the contribution of SiS(g) in the “elemental method” (as in this work) to synthesize SiS2(s) can be neglected, which is different from that in a “compound method”.[3,13,16−20]

For the Si–S reactions, there is an interface between reacting phases. In order for the reaction to proceed, three paths take place in series—transport of reactants (Si/S) to the interface, reaction at the phase boundary (PB), and transport of product (SiS2) away from the interface.[46] In addition, the exothermic reactions (eqs and 4) at PB liberate heat (given an adiabatic assumption, e.g., in a uniform-temperature zone in this work), change the boundary temperature and limit the reaction rate (r). Any of these steps may determine the overall reaction rate (r) which depends on the slowest one.

Solid–liquid reaction (boiling process; Figure a): The process was at 1023 K under 2.57 MPa or at 1073 K under 3.83 MPa. Mass-transport rates of reactants (Si and S) and product (SiS2) increased greatly through the forced-convection mass-transport step in the S-liquid. The PB reaction proceeded mainly between the solid Si and S-liquid, while the saturated S-vapor stayed nearby (eq ). Therefore, the dominant factor which determines r was the reaction rate of solid-liquid-PB (rs–l). The PB was fixed by the movement of atoms/molecules across the interface in a way equivalent to the grain growth. In this process, the forced-convective boiling S stirred constantly the solid Si/SiS2 and destroyed the rods, such as SiS2_LD (Figure ii) and SiS2_HD (Figure v).

Solid–gas reaction (steaming process; Figure b): Here, mass-transport rates were governed through the forced-convection mass-transport step in the saturated S-vapor. The PB reaction proceeded mainly between the solid Si and saturated S-vapor, while the S-liquid stayed below (eq ). The dominant factor which determined r was the reaction rate of solid–gas-PB rs–g. When a single Si-particle (surrounded by S-vapor) acted as a heterogeneous reaction surface, the oriented growth of SiS2 occurred, such as SiS2_LU (Figure iii), SiS2_LUT (Figure iv), SiS2_HU (Figure vi), and SiS2_HUT (Figure vii and viii).

Then, consider the reactions from the kinetics viewpoint. The calculations of Rau et al.[34−36] concluded that the mean S-atom number per molecule is 3 in the liquid state [i.e., S3(l)] and 4.7 in the gaseous one [i.e., S4.7(g)] in the range of 1023–1073 K. Referring to eqs and 4, the kinetic equations could be expressed as eq . The relationship among reaction pressure, concentrations of reactant (S)/product (SiS2), and reaction time showed in Table and Figure . Here, the t refers to time. The a, b, and c are initial (t = 0) concentrations of Si(s) (= [Si]0 = 1.23 mol/dm3), S3(l) (= [S3]0), and S4.7(g) (= [S4.7]0), respectively (a ≤ 1.5b + 2.35c). Here, the initial concentration of single S, that is, [S]0 = 4.059 mol/dm3 = 3b + 4.7c, while δ = 3.3. The x, (a – x), (b – ux) and c – ((2–3u)/4.7)x are instantaneous (t = t) concentrations of SiS2(s) (= [SiS2]), Si(s) (= [Si]), S3(l) (= [S3]), and S4.7(g) (= [S4.7]), respectively (0 < x < a). The c values (= [S4.7]0) were calculated by the ideal gas equation under Psat.@S4.7.[34] When the reactions went on at 1023 K, the S-vapor pressure in the tube remained constant (= Psat., 1023 K@S4.7 = 2.57 MPa). However, when the reactions completed 82.9% (= 1.02/1.23 × 100%) at 1073 K, the S-vapor pressure became smaller (between 3.03–3.83 MPa) than Psat., 1073 K@S4.7 (= 3.83 MPa) because all the liquid S had been gasified earlier. The amount of S-liquid was the difference between those of the total S and S-vapor.

Table 2

Kinetic Equations and the Relationship between Initial/Final Concentrations ([C]i/[C]f) of Reactant (S)/Product (SiS2) and Reaction Time (t)

9
t = 0	Conc. (mol/dm3)	a	b	c	0
	[C]i,1023 Ks–l	1.23	0.880	0.302	0
	[C]i,1023 Ks–g	1.23	0.880	0.302	0
	[C]i,1073 Ks–l	1.23	0.680	0.429	0
	[C]i,1073Ks–g	1.23	0.680	0.429	0

Figure 7

Relationship between reaction pressure and concentrations of reactant (S)/product (SiS2).

The bl, ∞ and bg, ∞ correspond to the amount of residual S3(l) and S4.7(g) when the reactions just finished at the synthesis temperature, respectively. The total residual S, that is, Srest = bl, ∞ + bg, ∞ = 3b + 4.7c – a.

The differential-type kinetic equations are as the following:where k refers to the rate constant of reaction.k = kSiS = kSi = (1/u)kS = (4.7/(2 – 3u))kS. The α, β, and γ are the sub-orders of reaction (all > 0). Parallel solid–liquid (eq ) and solid–gas (eq ) reactions proceeded simultaneously as the following:where ks–l and ks–g are the rate constants of the solid–liquid phase-boundary (PB) and solid–gas phase-boundary (PB), respectively. The following superscript symbols have the same meanings. The al and ag correspond to the amount of Si reacted with S3(l) and S4.7(g), respectively.

For the boiling process to synthesize SiS2 at 1023/1073 K and a down (D) site in quartz tubes, eq (same as the following eqs and 15) was the primary reaction.

This was a complete solid–liquid reaction. Where ag → 0, al = a = 1.23 mol/dm3 and u = 2/3. The [S4.7] kept constant (= c = 0.302 mol/dm3) until the end of the reaction. b = (3.3 × 1.23–4.7 × 0.302)/3 = 0.880 mol/dm3.

This was an incomplete solid–liquid reaction. Where ag → 0, al = a = 1.23 mol/dm3 and u = 2/3. The [S4.7] kept constant (= c = 0.429 mol/dm3) until 82.9% (= 1.02/1.23 × 100%) SiS2 was obtained. b = (3.3 × 1.23–4.7 × 0.429)/3 = 0.680 mol/dm3. The S3(l) consumption was 0.680 mol/dm3 and that of S4.7(g) was 0.089 mol/dm3 (= 0.429–0.340 mol/dm3). In other words, the last 17.1% SiS2 was synthesized through a solid–gas reaction.

For the steaming process to synthesize SiS2 at 1023/1073 K and a up (U) site in quartz tubes, eq (same as the following eqs and 17) was the primary reaction.

This was a complete solid–gas reaction. Where al → 0, ag = a = 1.23 mol/dm3 and u = 2/3. The [S4.7] kept constant (= c = 0.302 mol/dm3) until the end of the reaction. The amount of S4.7(g) which reacted with Si(s) equals that of the gasified S3(l), while the latter decreased from 0.880 to 0.060 mol/dm3.

This was a complete solid–gas reaction. Where al → 0, ag = a = 1.23 mol/dm3 and u = 2/3. The [S4.7] kept constant (= c = 0.429 mol/dm3) until 82.9% (= 1.02/1.23 × 100%) SiS2 was obtained. The amount of S4.7(g) which reacted with Si(s) included that of the gasified S3(l) (= 0.680 mol/dm3) and the other S4.7(g) consumption (= 0.429–0.340 = 0.089 mol/dm3). The residual S4.7(g) was 0.340 mol/dm3 and residual S3(l) was zero.

Comparing eq with 15 and eq with 17, the following equations could be obtained (0 < x < 1.23)

Because (0.880–2/3x)/(0.680–2/3x) > 1, β > 0 and the k1023 Ks–l/k1073 Ks–l is slightly less than 1 (according to the Arrhenius rule from the kinetics viewpoint), so r1023 Ks–l/r1073 Ks–l>1. The temperature increasing would result in the decreasing of the solid-liquid-PB reaction rate (rs–l) in the boiling process. In other words, the low temperature is beneficial to the boiling process.

Because the k1023 Ks–g/k1073 Ks–g is slightly less than 1 (same as the above), so r1023 Ks–g/r1073 Ks–g<1. The temperature increasing would result in the increasing of the solid–gas-PB reaction rate (rs–g) in the steaming process. In other words, the high temperature is beneficial to the steaming process.

To sum up, the synthesis method for SiS2 in this work is safe (cf. dangerous H2S and CS2),[3,18,19] economical [cf. expensive Al2S3 and (C2H5S)4Si],[13,18,19] convenient (cf. soaking for 150 h,[20] 3 d[10,11] or 7 d22; calcining for 70–80 h6 or 12 d;[10,11] complicated process[6] to eliminate residual S), and feasible with acceptable requirements for facilities and operations.[5]

Conclusions

In this work, the SiS2 rods were prepared by using the excess sulfur formula either through a solid–liquid boiling process or a solid–gas steaming process.

The relatively high pressure (2.57 MPa@1023 K and 3.83 MPa@1073 K) is more favorable for the formation of SiS2-rods in the closed sealed-tube system (with a uniform-temperature zone) than that in an open system. The chemical (c.f. evaporation) approach using benzene is first used to eliminate residual S to prepare pure SiS2.

The SiS2 rods have controllable microstructure and high chemical/phase purity. The optimized synthesis condition can affect the macroscopic morphology but cannot enough change the microstructural anisotropy.

The gaseous SiS is hardly present in this “elemental method” between 1023 and 1073 K which is different with that in a “compound method”. The SiS2 rods were synthesized through solid–liquid/solid–gas reactions among the Si(s), S3(l), and S4.7(g). The low temperature is beneficial to the solid–liquid reaction and the high temperature to the solid–gas reaction.