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## Creator

Nikola Subotić, [Takashi Mochiku](https://orcid.org/0000-0003-2208-4279), [Yoshitaka Matsushita](https://orcid.org/0000-0002-4968-8905), Osamu Takeuchi, Takanari Kashiwagi, Hidemi Shigekawa, Kazuo Kadowaki

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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1557/s43580-022-00292-5[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Crystal growth and characterization of RhPb2 and its related compounds](https://mdr.nims.go.jp/datasets/a61e8d32-8bc2-44f6-b848-ec42c31b2345)

## Fulltext

Crystal growth and characterization of RhPb2 and its related compounds   Nikola Subotić1, Takashi Mochiku2, Yoshitaka Matsushita2, Osamu Takeuchi1, Takanari Kashiwagi1, Hidemi Shigekawa1, Kazuo Kadowaki1   1University of Tsukuba, 1-1-1 Tenoudai, Tsukuba, Ibaraki 305-8573, Japan 2National Institute for Material Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan  Abstract  The physical properties of the intermetallic compound RhPb2 have been unexplored in detail and are controversial so far. Two values of superconducting transition temperatures have been reported experimentally in poly-crystal samples with the I4/mcm structure. Moreover, the recent report of band calculation results showed that RhPb2 with the I4/mmm structure (β-RhPb2) may be a topological superconductor candidate, having a higher Tc ≈ 9.7 K than that of the I4/mcm structure. Therefore, we grew single crystals of RhPb2 and performed X-ray diffraction study and the phase stability by EPMA, and resistivity measurements to clarify this intriguing compound. Surprisingly, the resistivity measurements showed three different values of Tc (1.24 K, 2.32 K, and 6.7 K) despite the same crystal structure (I4/mcm) but different levels of Rh vacancies up to 18%, inspiring that some sort of Rh vacancy ordering may occur.   Introduction  According to the binary phase diagrams [1, 2], the intermetallic compound RhPb2 grows through the peritectic reaction incongruently between 640 and 320°C, and it crystallizes in the I4/mcm structure [CuAl2 (C16) structure]. The same crystal structure was observed [3], where it was shown that RhPb2 becomes superconducting below 2.66 K. On the other hand, according to [4], the Pb-deficient I4/mcm structure becomes superconducting below 1.33 K. Furthermore, Zhang et al. [5] claimed that RhPb2 with the I4/mmm structure (β-Pb2Rh) may be a topological superconductor candidate, with surprisingly high superconductivity transition Tc ≈ 9.7 K. Moreover, a recent single-crystal XRD analysis showed Rh-deficiency rather than Pb-deficiency [6].  Different values of Tc [4‒6] and different space groups [5, 6] indicate that allotropes of RhPb2 might exist, while the phase diagrams [2, 3] show the opposite. According to [2], the two horizontal lines at 320°C and 300°C are doubtful because such phase lines were not observed at least in our present study. Indeed, it is rare to see such two lines so close, and the meaning of 320°C is debatable [2]. The choice to perform band calculation with the I4/mmm structure [5] instead of the I4/mcm structure is unrealistic since the I4/mcm structure of RhPb2 was confirmed experimentally. On the other hand, we would like to note that allotropes of RhSn2 do exist, having the I4/mmm and the I4/mcm crystal structures [2]. Since Sn and Pb are chemically similar elements, RhPb2 with I4/mmm crystal structure symmetry might exist.  The present status of RhPb2 can be summarized in Table 1, emphasizing the topological nature of the materials and their superconducting properties. The preparation of high-quality samples is necessary, which is an arduous task. Poor quality of the samples would make the interpretation of the experimental results difficult or often may lead to erroneous results. Besides the growth of high-quality crystals, a detailed investigation of the phase diagram is required to elucidate the topological nature of RhPb2.   Materials and methods  The single crystals of RhPb2 were grown from the Pb-rich melt (molar ratio Rh:Pb = 1:8) in a steep temperature gradient in the infrared mirror furnace [6, 8]. Before the crystal growth, Rh and Pb were melted in an evacuated quartz tube with a flame torch to homogenize the sample. The sample was put in another quartz tube with coned-shaped bottom to promote uniform crystal growth. The quartz tube was hung in the infrared mirror furnace being attached to the upper shaft which allows rotation and vertical translation of the mounted sample. The focal point of the infrared light was at the upper part of the boule, inducing a steep temperature gradient vertically across the sample. To obtain uniform temperature horizontally, the shaft was rotated slowly (~ 10 r.p.m.). The temperature of the sample was controlled by reducing the intensity of the infrared light, not by the vertical translation of the shaft. The upper part of the boule was heated above 640°C, where the sample become completely liquid. Then, the temperature was slowly reduced with a constant rate of approximately 0.5°C/h to a temperature slightly above 320°C, then it was lowered to room temperature. Due to the steep temperature gradient and the size of the grown boule, crystals have formed both at the lower and upper parts of the grown boule. Those crystals turned out to be RhPb2 by EPMA (see SI). In addition, needle-like crystals have grown in the middle part of the boule. It was evident that the needle-like crystals were not RhPb2 since the crystals were soft, and the color changed due to the exposure in the air (which does not occur for RhPb2), indicating higher concertation of Pb. The preliminary single-crystal XRD analysis showed that needle-like crystals may be RhPb4, which crystallizes in the monoclinic I2/m space group. Detailed results of the XRD analysis can be found in the SI.  This kind of crystal formation was not observed in the previous infrared mirror furnace experiments where the size of the grown boule was smaller (the crystals have formed at the lower part of the boule as it usually does). Initially, the crystals of RhPb2 were tried to be grown with the standard muffle furnace with good temperature control. The initial molar ratio was 1:2 = Rh:Pb with various annealing temperatures. It was shown that even after 2 months of growth, no significant crystal formation was observed. Then, various concertation of Pb was tested and it turned out that a higher concentration of Pb promotes crystal growth. The various temperature gradient methods have been tried such as Bridgman, and Czochalrski, but in the end, the before mentioned method with a high concentration of Pb proved to be successful. It is interesting to note that such a crystal growth method was not reported before, and it turned out to be an ideal way how to grow or induce the formation of various phases of a single compound.  After crushing the grown boule, most of the obtained single crystals of RhPb2 were investigated by EPMA, XRD, and resistivity measurements. The crushed crystals often had irregular shapes, meaning that the cleaving is rather difficult. The standard four-probe method was applied to measure the temperature dependence of resistivity. The silver paste was used to connect the voltage and current terminals. The contact resistivity was typically below 1 Ω. The EPMA measurements were performed with JEOL JXA-8500F. The voltage and probe current were at 15 kV and 5 nA, respectively. For calibration, PbS, Au, and Rh were used. The XRD measurements were conducted with two circle diffractometer Rigaku Xtal Mini II.   Results  The resistivity measurements in most cases showed one superconducting transition around 1.25 K (Fig. 1a). In other cases, the resistivity measurements releveled three superconducting transitions indicating the presence of three different phases (Fig. 1c). The transition widths of 1.25 K are smaller than the other two transitions. The corresponding ΔTc/Tc ratios for the 1.25 K, 2.32 K, and 6.7 K transitions are 0.08, 0.21, and 0.07, respectively. The residual resistance ratio (RRR) in most cases was around 4 while the highest was around 7, which corresponds to the medium quality of the grown crystals. The residual resistance of the measured crystals ranges from 11 to 20 μΩ cm. The linear dependence of the resistivity at higher temperatures was observed.  The crystals, on which the resistivity measurements were performed, were cut and prepared for the EPMA measurements. The 1.25 K transition crystals showed neither Rh nor Pb deficiency within experimental error. Sample C showed its 82.58% occupancy of Rh sites. The results are shown in Table 2. The SEM photographs of crystals on which EPMA measurements were carried out are shown in Fig. 2. The COMPO images and the measurement spots on the surface of the crystals are also shown in SI.  Since sample A contained only one Tc the sample may be homogenous and without vacancies. The other two samples show that the vacancies of Rh may not be distributed homogenously since three different values of Tc were observed. For sample C, if it is assumed that the various values of Tc are due to the variation of Rh vacancies, the 6.61 K transition may be due to the 82.58% occupancy of the Rh sites because the 2.39 K transition is negligible, and the 1.26 K is due to the non-deficient structure. Therefore, the remaining 2.32 K transition is probably due to 96.39% occupancy of the Rh sites.   Discussion and conclusion  The topological superconductor candidate, RhPb2 has been investigated experimentally. The medium-quality crystals were grown by a slow-cooling process in a steep temperature gradient infrared furnace. Besides RhPb2, RhPb4 single crystals were found to exist newly. Its preliminary crystal structure has been determined for the first time to be monoclinic I2/m [a = 6.853(4) Ǻ, b = 5.958(6)Ǻ, c = 13.157(3) Ǻ, β = 98.451(2)°].  The EPMA and XRD measurements indicated that the 1.26 K transition is due to the nondeficient structure, not the Pb-deficient structure reported by [4]. Therefore, the Pb-deficient structure might not occur. The 2.32 K transition may be due to the slight Rh-deficient crystals (around 96%), which may correspond to samples found in Ref. [3]. The situation regarding the 6.7 K transition is more difficult to interpret. It may be due to the even more Rh-deficient crystals (around 18%) according to the EPMA and XRD measurements. If this is true, the question is, under what conditions do such structures form. It would be a unique opportunity to investigate how Tc, lattice constants, topology, and other properties do depend on Rh-deficiency. XRD measurements of 18% and 4% (samples C and B) Rh-deficient crystals will be conducted in the near future to confirm if those crystals belong to the tetragonal I4/mcm space group.  Another possibility is that the 6.7 K transition is due to the presence of Pb or RhPb4. It is unlikely that the 6.7 K is due to the presence of Pb since its Tc is 7.1 K. Grown crystals of RhPb4 could be measured with SQUID or a similar technique to determine the Tc. If the Tc is different from 6.7 K, then it is quite certain that the 6.7 K transition is due to the Rh-deficient structure. To confirm whether RhPb4 belongs to the I2/m space group, analysis of better quality crystals is required. It would be quite interesting to perform the band calculation and inspect the topological properties of RhPb4.  The presence of RhPb2 at both ends of the boule and RhPb4 in the middle of the grown boule indicate that there is a considerable temperature difference across the grown boule due to the steep temperature gradient and the size of the boule. As it turned out, this method is favorable for the formation of various phases since a 6.7 K transition was observed for the first time, besides the 2.3 K and 1.23 K reported in previous studies [3, 4]. The next step is to separate those phases to prove if the Rh-deficiency does influence the superconducting properties of RhPb2. The high concertation of Pb may lead to the Rh-deficiency on the one hand. On the other hand, crystals of Au2Pb and AuPb2 grown under similar conditions do not exhibit deficiency indicating that the deficiency in RhPb2 is due to the nature of the material itself rather than the growth method. To determine if the Pb-rich part of the phase diagram yields Rh-deficiency structures, in the future, ratios near 1:2 will be explored in detail.  XRD measurements did not show that the structure of grown crystals of RhPb2 is a tetragonal I4/mmm. The reason might be that β-Pb2Rh is a metastable state. Even without I4/mmm space group, the known binary phase diagrams Pb-Rh are incomplete. Therefore, a detailed investigation of the phase diagram is required. Annealing of grown crystals at various temperatures could be also quite useful in determining the desired conditions and improving the quality of the grown crystals.  In conclusion, the Pb-rich binary phase diagram of the Pb-Rh system was studied. According to the presently available binary phase diagrams [1, 2], several kinds of single crystals can be grown from the appropriate combi- nation of Pb and Rh. Most of their physical properties turn out to be unexplored, for example, different values of Tc of the intermetallic compound RhPb2. This unexpected result encourages further investigation of RhPb2 as a topological superconductor candidate. It certainly requires better quality of single crystals of RhPb2. In addition, the relation between its corresponding Rh-deficient structures and the physical properties must be understood clearly, elucidating the complex nature of the binary phase diagram Pb-Rh. The results from ARPES and STM measurements should be indispensable for understanding the topological properties of RhPb2 and the related compounds. Furthermore, magnetoresistance measurements could also provide important information about the Fermi surface to reveal the topological nature of RhPb2. Such measurements will be conducted in the near future.   Supplementary Information  The online version contains supplementary material available at https://doi.org/10.1557/s43580-022-00292-5.   Data availability  The data that supports the above-presented results are available from the corresponding author upon reasonable request.   Declarations  Conflict of interest  On behalf of all authors, the corresponding author states that there is no conflict of interest.   References  1. B. Predel, Landolt-Börnstein-Group IV Physical Chemistry 5I (1998)  2. G.R. Watts, Gmelin Handbook of Inorganic and Organic Chem- istry, System Number 64: Rh Rhodium, Supplement Volume A1: Coordination Compounds with O-and N-containing Ligands (Springer-Verlag, Berlin, 1991)  3. M.F. Gendron, R.E. Jones, J. Phys. Chem. Solids 23, 405 (1962)  4. E.E. Havinga, H. Damsma, J. Kanis, J. Less Common Metals 27(3), 281‒291 (1972)  5. J.F. Zhang et al., Phys. Rev. B 99, 045110 (2019)  6. T. Mochiku et al., Acta Crystallogr. E 77, 1327 (2021)  7. W. Quan Sheng et al., TopoMat: a database of high-throughput first-principle calculations of topological materials. Mater. Cloud Arch. (2019). https://doi.org/10.24435/materialscloud:2019.0019/ v2  8. N. Subotić et al., MRS Advances. to be published                      Table 1. Current situation of RhPb2. The I4/mcm structure might have topological properties.     Table 2. The occupancy of the Pb and Rh sites.     The almost non-deficient structure (sample A) showed one transition temperature only, while sample C revealed even more Rh-deficiency compared to [6] with three different Tc. In the table are shown the averaged values assuming that the Pb sites are fully occupied. The atomic percentage of the measured spots along with the COMPO photograph of the samples is shown in the SI     Fig. 1 a. Resistivity plot of Rh0.993Pb2.007 up to 10 K. The residual resistance of ≈ 19 μΩ·cm is not so high while the room temperature resistivity is 142.4 μΩ cm. The transition width is ΔTc=0.1 K. The photograph of the measured crystal is shown in SI. b The resistivity plot of Rh0.993Pb2.007 up to 100 K. Linear dependence is obvious, indicating the metallic behavior of RhPb2. c The resistivity plot of sample Rh0.963Pb2.037 up to 10 K. Three transitions can be observed. The transition width of 1.24 K transition is significantly narrower (0.1 K) compared to the higher temperature transition width (0.5 K). The residual resistance is lower compared to sample Rh0.993Pb2.007. The room temperature resistance is 70.15 μΩ cm which corresponds to the RRR being around 6. The measured single crystal is shown in the SI. d The resistivity plot of sample Rh0.993Pb2.007 up to 150 K. The linear dependence is obvious, same as the previous sample, indicating the metallic behavior of RhPb2.       Fig. 2. SEM photographs of Rh0.993Pb2.007, Rh0.963Pb2.037, and Rh0.825Pb2.125, respectively (from left to right), on which the EPMA measurements were done. The size of Rh0.993Pb2.007 is roughly 600×600 μm2, Rh0.963Pb2.037 around 300×200 μm2, and Rh0.825Pb2.125 approximately 100 × 100 μm2.