Since the discovery of superconducting ternary molybdenum chalcogenides, also known as Chevrel-phase superconductors [1], considerable attention has been devoted to them owing to their high upper critical fields, and low cost of the raw materials in comparision with high temperature superconductors (HTS) [2], [3], [4], [5], [6]. Among the various ternary molybdenum chalcogenides, PbMo₆S₈ (PMS) exhibits the highest critical temperature (T_c ≈ 15 K) and a relatively high upper critical field H_c2 > 50 T [7], [8], [9], [10]. Therefore, PMS is considered as a promising candidate for high-field superconducting magnets in the future.

After decades of investigations on PMS superconducting materials, considerable progress has been achieved for wires, bulks, and films [11], [12], [13], [14], [15], [16], [17], [18]. However, due to the weak intergrain connection [19], [20], the current-carrying performance of PMS has not been effectively improved. Microcracks and the occurrence of second phases at the grain boundaries are the two main factors that have been proposed to affect the intergrain connectivity in the PMS system.

In order to solve this problem, hot isostatic pressing (HIP) has been adopted to reduce the porosity and increase the density of the obtained bulks to improve their intergrain connectivity [21], [22], [23]. However, although PMS bulks with a high denisty have been obtained through the HIP process, the superconducting critical temperature was found to decrease, which was attributed to the shrink in the PMS lattice due to the high pressure or variation in stoichiometry during HIP [21]. In addition, the MoS₂ content was found to increase with increasing pressure [21], which is also the main cause of weak intergrain links. Regarding the problem of the formation of second phases at the grain boundaries, previous studies [20], [24] showed that the grain boundaries of PMS are rich in S and poor in Mo, thus forming a nonsuperconducting MoS₂ or Mo₂S₃ phase, which affects the superconducting properties of the PMS. Therefore, it is difficult to simultaneously improve the intergrain connectivity and increase the PMS superconducting phase content.

In this work, Pb_0.92Mo₆S_7.5 with a high superconducting phase content was chosen as the target material based on previous reports [25]. In order to clarify the formation mechanism of the pores, MoS₂ phase, and other secondary phases in PMS materials, the phase evolution process of PMS was studied in detail. On this basis, a two-step method is proposed to prepare PMS bulks, which can effectively eliminate the pores as well as reduce the content of the MoS₂ phase and other secondary phases. A significant improvement in the intergrain connectivity was achieved.

Pb_0.92Mo₆S_7.5 bulks were prepared via the solid-state sintering method. The starting materials were PbS, Mo, and MoS₂, which were weighed in a glove box filled with argon gas according to the Pb_0.92Mo₆S_7.5 stoichiometric ratio. Then, the powders were poured into a mortar and carefully mixed. Subsequently, the mixed powders were cold pressed into pellets with a diameter of 10 mm and a thickness of 1.5 mm, and they were then sealed into a quartz tube and sintered at different sintering temperatures and different dwell times. For the two-step sintering process, the bulks were firstly sintered at 950 °C for 24 h, then crushed in the glove box, ground into powder, and pressed into pellets again. Subsequently, the pellets were sealed into vacuum quartz tubes, sintered at 950 °C for 48 h, and eventually quenched.

The phase of the sintered bulks was determined via X-ray diffraction (XRD, Bruker D8 Advance) with CuKα (λ = 1.5406 Å) radiation. The lattice parameters and phase composition were analyzed based on the Rietveld refinement performed with the commercial software Fullprof®. The errors of all the refinements were within 7%. The content of each phase F_i was calculated as

where I_i represents the intensity of the diffraction peaks of PMS, MoS₂, Pb, and Mo. ΣI is the total peak intensity of the obtained patterns. The morphology of the sintered bulks was characterized via scanning electron microscopy (SEM, JEOL-6700F). The critical temperature was measured using a superconducting quantum interference device (SQUID, MPMS-XL-7) with a background field of 10 Oe in the temperature range from 4.2 to 20 K on cubic samples with dimension of ∼ 3 × 3 × 3 mm³.

Fig. 1 shows the XRD patterns of the PMS bulks sintered at different temperatures. The diffraction peaks of the starting materials, namely Mo, MoS₂, and PbS, can be observed when they were sintered at 500 °C. Upon increasing the sintering temperature, it can be observed that two main steps are involved in the formation reaction of PMS. In the first step, Mo and PbS react and form MoS₂ and Pb. When the temperature rises to 700 °C, besides the diffraction peaks of the starting materials, namely Mo, MoS₂, and PbS, a low Pb content can be observed at ∼ 31.3°, as shown in Fig. 1 (b). This result implies that PbS can be transformed into elemental Pb below 700 °C. When the sintering temperature exceeds 750 °C, very intense Pb diffraction peaks appear, while the PbS peaks weaken. By prolonging the sintering time to 12 h at 750 °C, the intensity of the Pb diffraction peaks increases, while the PbS diffraction peaks disappear, and the intensity of the Mo diffraction peak decreases accordingly. Since the diffraction patterns shown in Fig. 1 have been normalized with respect to the (002) peak of MoS₂, the change in the peak intensity represents the change in the content of the other phases relative to that of the MoS₂ phase. Therefore, the change in the Pb peak intensity at 750 °C suggests that the Pb content increases because of the chemical reaction between Mo and PbS. When the sample was sintered at 750 °C for 24 h, the peak intensity of the MoS₂ phase increased. By contrast, the Pb content decreased substantially. These results suggest that for the formation of the PMS phase, the kinetic parameters are not the only important factors as dynamic processes, including the elemental diffusion during the reaction and crystallization of new phases, are also key to control the PMS formation.

In the second step, Pb, Mo, and MoS₂ react and are transformed into the PMS phase. A low PMS content can be observed when they were sintered at 750 °C for 24 h, suggesting that the initial formation temperature of PMS is not very high. However, the formation speed is too low at this temperature. The PMS content increases slowly upon further increasing the sintering temperature below 950 °C. When the temperature exceeds 950 °C, PMS is formed rapidly. Therefore, based on the above analysis, for the two steps involved in the sintering process, both the kinetic and dynamic parameters should be considered for the optimization of the sintering process.

Fig. 2 shows the backscatter images of the PMS bulks obtained at different sintering temperatures. The distribution of the starting materials can be observed in the samples sintered at 500 °C and 700 °C. As indicated by the arrows in Fig. 2 (a), the lamellar matrix is MoS₂, the circular spots are Mo particles, and the bright white flakes are PbS. The reaction between the individual components becomes stronger with increasing sintering temperature. After sintering at 750 °C for 24 h, the PMS phase can be observed around the Mo particles, and Pb is distributed in spots, as shown in Fig. 2 (c). Upon further increasing the sintering temperature, the PMS phase content increases, especially when sintering at temperatures above 950 °C, as shown in Fig. 2 (d)-2(f).

The inset in each figure shows the fracture microstructure of each bulk sintered at different temperatures. It can be clearly observed that with increasing sintering temperature, the bulk density decreases due to the formation of many pores. When the temperature rises to 900 °C, the PMS phase can be clearly observed in the form of cubes distributed in the bulk, as shown in the inset of Fig. 2 (e); these results are confirmed by Energy Dispersive Spectrometer (EDS). When the temperature increases to 950 °C, the PMS content increases significantly. At the same time, a large number of pores can be clearly observed in the inset of Fig. 2 (f). The pores are formed due to the disappearance of large quantities of PbS to form Pb, which then reacts with Mo during the heat treatment process. This is also consistent with the abovementioned XRD analysis.

Since a higher sintering temperature is beneficial to the formation of the PMS phase, 950 °C was chosen as the sintering temperature for PMS. Considering that the element diffusion process is also key to control the PMS formation, the influence of the sintering time on the PMS phase formation was systematically studied. The XRD patterns of the PMS bulks sintered for different times are shown in Fig. 3 (a), and the variation in the PMS phase content during the sintering process is shown in Fig. 3 (b). It can be observed that as the temperature reaches 950 °C, the content of the PMS phase is 60%, which is likely to be contributed to by the PMS formation during the heating process. With increasing sintering time, the PMS content increases markedly. No elemental Pb can be observed for a sintering time exceeding 14 h. Additionally, elemental Mo disappears after sintering for 26 h. As shown in Fig. 3 (b), the rate at which the content of the PMS phase increases first rises and then decreases. Therefore, based on the obtained “S-shaped” curve, it can be deduced that the PMS formation process is mainly controlled by the diffusion of elements. In the early heat treatment stage, the bulk has a relatively high density and the diffusion of the element atoms is fast, promoting the formation of the PMS phase; thus, the content of the PMS phase increases rapidly. With the prolongation of the sintering time, the PMS phase grows rapidly in the bulk, resulting in a large number of pores, and the diffusion distance between different elements increases. Therefore, the formation rate of the PMS phase decreases accordingly.

Fig. 4 shows the fracture microstructure of the PMS bulks sintered at 950 °C for different times. At the beginning of the heat preservation stage, large amounts of lamellar MoS₂ phases with dark gray and square PMS phases can be clearly observed in the backscatter image shown in Fig. 4 (a). When the sintering time reaches 40 min, the content of the PMS phase increases significantly, and agglomerated MoS₂ grains are distributed between PMS grain clusters, as shown in Fig. 4 (b). Additionally, numerous pores form in the bulk, and there are also crevices between the PMS grains. As the sintering time continues to increase, both the grain size of the PMS phase and the number of pores gradually increase, while the bulk density decreases significantly. It can be deduced that the agglomerated MoS₂ grains between the PMS grains are continuously reacted with increasing holding time, and the PMS grains are stacked and distributed in the form of clusters. Finally, the MoS₂ phase reacts completely, leaving a large number of pores at the locations where MoS₂ was agglomerated. In addition, there is no external constraint in the formation process of the PMS phase, and the PMS grains grow freely, which results in the formation of crevices among them. When the sintering time reaches 26 h, the grain size of the PMS phase remains basically unchanged, but there are still plenty of pores in the PMS bulks. In general, in the traditional sintering process, massive pores and crevices can easily form during the formation process of the PMS phase. These pores and crevices hinder the diffusion of elements, which leads to a decrease in the PMS formation rate and the presence of raw material residues, such as MoS₂, which acts as a secondary phase. Therefore, the preparation process of PMS bulks needs to be further optimized to obtain PMS bulks with a higher superconducting phase content and a higher density.

Based on the above analysis, it can be inferred that the PMS formation is controlled by both the kinetic and dynamic parameters, and it is difficult to prevent the formation of porous structures during the traditional sintering process. The pores will not only affect the density and mechanical strength of the obtained bulks but also lead to weak intergrain links during the current transport process. Therefore, the preparation process of the PMS bulks needs to be further optimized. In this regard, a two-step sintering method is proposed for preparing PMS bulks with a high density and a high superconducting phase content. Firstly, the PMS embryo was sintered, and then the sintered PMS bulk was ground into powder and pressed again into a pellet for the second sintering process. Fig. 5 shows the XRD patterns of the PMS bulks after the two-step and one-step sintering processes. It can be observed that the main phase in all these bulks can be indexed to the PMS phase. In addition, a low content of the residual MoS₂ phase can be detected, as indicated in the patterns. A decrease in the MoS₂ phase content can be observed after the two-step sintering process compared with the samples that were sintered via the one-step sintering process for 24 and 72 h. The superconducting phase content reaches 99.6%. This confirms that the grinding process involved in the two-step sintering process is beneficial for promoting the reaction. On the other hand, the full width at half maximum (FWHM) of the (122) peak increases significantly after the two-step sintering process, as shown in Table 1, which means that the PMS bulks prepared via the two-step sintering process have a finer grain size than those prepared via the one-step sintering process. As shown in Fig. 5 (c), a shift in the (122) peak toward a higher degree for the sample prepared via the two-step sintering process can be clearly observed compared with the sample prepared via the one-step sintering process, which implies that the lattice parameter of the PMS phase decreases in the former case. After the Rietveld refinement, as shown in Table 1, it can be seen that the lattice parameters a and c of the PMS phase obtained via the two-step sintering process decrease. The decrease in the lattice parameter c from 11.456 Å to 11.444 Å is quite clear.

Fig. 6 shows the fracture morphology of the PMS bulks prepared via the one-step and two-step sintering processes. It can be seen from Fig. 6 (a) that there are numerous lamellar MoS₂ grains in the PMS bulk sintered via the one-step sintering process for 24 h. Additionally, there is a large number of pores also in the bulk. By contrast, the porosity of the PMS bulk is considerably reduced after the second sintering step, and no clear MoS₂ phases can be observed. Furthermore, fine-sized PMS grains were obtained, which may be attributed to the grinding process after the first sintering step. The grain boundary pinning phenomenon of PMS is similar to that of Nb₃Sn [26], [27]; a smaller particle size indicates the presence of more boundaries, which can increase the vortex pinning capacity and increase the current-carrying capacity of PMS at high fields. However, in the S3-72 h sample sintered via the one-step sintering process for the same sintering time (72 h), the agglomerated MoS₂ and pores can still be clearly observed, as shown in Fig. 6 (c). However, it can be seen that the intermediate grinding process promotes the distribution of unreacted MoS₂, which can reduce the porosity and increase the density of the PMS bulks, thereby effectively promoting the formation of the PMS phase.

The temperature dependences of the magnetization (M−T) curves of the PMS bulks obtained via the different sintering processes are illustrated in Fig. 7. The superconducting transition of all the obtained PMS bulks is relatively sharp with a narrow transition width, which suggests the high quality of the obtained PMS bulks. The PMS bulks sintered via the one-step sintering process for 24 and 72 h have the same onset superconducting transition temperature (T_c^onset) of 11.6 K. On the other hand, the bulk prepared via the two-step sintering process exhibits a slightly lower T_c^onset of 11.4 K. Several studies [21], [28] have shown that the T_c of PMS decreases as the lattice constant decreases. Therefore, the decrease in the PMS lattice constant c (see Table 1) results in a decrease in T_c. The change in the lattice parameters should be attributed to the variation in the chemical composition during sintering, which will be systematically studied in our future works.

On the other hand, a pronounced increase in ΔM can be observed. Compared with the ΔM values of 0.6 and 1.09 emu/cm³ measured for the samples sintered via the one-step sintering process for 24 and 72 h, respectively, the ΔM value of bulk prepared via the two-step sintering process, which represents the relative superconducting phase content, has increased to 1.36 emu/cm³. This means that the superconducting phase content of the obtained PMS bulk can be considerably increased when using the two-step sintering process. There are two main reasons for the observed ΔM increase. Firstly, the bulk density increases after the two-step sintering process; therefore, the content of the superconducting phase per unit volume also increases. Secondly, the unreacted elements, such as MoS₂, are redistributed during the intermediate grinding process, which can promote the formation of the PMS phase.

In this work, the formation mechanism of the PMS phase was studied in detail. Two steps were involved, namely the reaction of PbS and Mo to obtain MoS₂ and elemental Pb, and the formation of the PMS phase from Pb, MoS₂, and Mo. It was noticed that both the kinetic and dynamic processes are important for the formation of PMS. Although PMS can form at low temperature, a high-temperature treatment is necessary to promote the diffusion of different elements to increase the rate at which PMS is formed. Additionally, a large number of pores and crevices were formed in the PMS bulks, resulting in porous bulks with a poor intergrain connectivity. The formation of pores and second phases in PMS superconducting materials should be avoided in order to achieve PMS bulks with better properties. Therefore, a two-step sintering process was proposed for preparing PMS bulks with a high density. Using this method, the bulk density and intergrain connectivity of PMS were significantly increased simultaneously. This study provides an effective method for preparing high-quality PMS powders that can be used as precursors, thus establishing a good foundation for fabricating PMS superconducting wires for practical applications in the future.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This research is supported Northwest Institute of Non-ferrous Metal Research Funding (No. YK2117).