MRS Advances
https://doi.org/10.1557/s43580-022-00292-5

ORIGINAL PAPER

Crystal growth and characterization of ­RhPb2 and its related
compounds
Nikola Subotić1 · Takashi Mochiku2 · Yoshitaka Matsushita2 · Osamu Takeuchi1 · Takanari Kashiwagi1 ·Hidemi Shigekawa1 · Kazuo Kadowaki1
Received: 20 April 2022 / Accepted: 19 May 2022
© The Author(s), under exclusive licence to The Materials Research Society 2022

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 theI4/mcm structure. Moreover, the recent report of band calculation results showed that R­ hPb2 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, andresistivity 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 samecrystal structure was observed [3], where it was shown that
­RhPb2 becomes superconducting below 2.66 K. On the otherhand, according to [4], the Pb-deficient I4/mcm structure
becomes superconducting below 1.33 K. Furthermore,
Zhang et al. [5] claimed that R­ hPb2 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 thephase 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* Nikola Subotić
nikolasubotic95@gmail.com
1

University of Tsukuba, 1‑1‑1 Tenoudai, Tsukuba,
Ibaraki 305‑8573, Japan2

National Institute for Material Science, 1‑2‑1 Sengen,Tsukuba, Ibaraki 305‑0047, Japan

present study. Indeed, it is rare to see such two lines so close,
and the meaning of 320 °C is debatable [2]. The choice toperform 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 of­RhSn2 do exist, having the I4/mmm and the I4/mcm crystal structures [2]. Since Sn and Pb are chemically similarelements, ­RhPb2 with I4/mmm crystal structure symmetry
might exist.
The present status of ­R hPb 2 can be summarized inTable 1, emphasizing the topological nature of the materials and their superconducting properties. The preparation ofhigh-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 toelucidate the topological nature of ­RhPb2.

Materials and methods
The single crystals of ­RhPb2 were grown from the Pb-richmelt (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

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N. Subotić et al.
Table 1  Current situation of R
­ hPb2. The I4/mcm structure might have topological properties
References
CompoundSample typeSpace group
Tc
Topology[3]
Rh ­Pb2
Poly-crystal
I4/mcm2.66 KZ2 (1;1,1,1) [7] Dirac, Weyl semimetal,
topological superconductor?

[4]
Rh ­Pb1.9
Poly-crystal
I4/mcm1.33 K–with a flame torch to homogenize the sample. The sample
was put in another quartz tube with coned-shaped bottom topromote uniform crystal growth. The quartz tube was hungin the infrared mirror furnace being attached to the upper
shaft which allows rotation and vertical translation of themounted sample. The focal point of the infrared light wasat 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 (~ 10r.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 washeated above 640 °C, where the sample become completelyliquid. 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. Dueto the steep temperature gradient and the size of the grownboule, crystals have formed both at the lower and upper partsof the grown boule. Those crystals turned out to be R­ hPb2 by
EPMA (see SI). In addition, needle-like crystals have grownin the middle part of the boule. It was evident that the needle-like crystals were not R­ hPb2 since the crystals were soft,and the color changed due to the exposure in the air (whichdoes not occur for ­RhPb2), indicating higher concertationof Pb. The preliminary single-crystal XRD analysis showedthat needle-like crystals may be R
­ hPb4, which crystallizes
in the monoclinic I2/m space group. Detailed results of theXRD analysis can be found in the SI.
This kind of crystal formation was not observed in theprevious infrared mirror furnace experiments where the sizeof the grown boule was smaller (the crystals have formed atthe lower part of the boule as it usually does). Initially, thecrystals of ­RhPb2 were tried to be grown with the standard
muffle furnace with good temperature control. The initialmolar 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

13[5]β-RhPb2
Band calculation
I4/mmm
9.7 K
Topological superconductor[6]
Rh0.95Pb2
Single-crystal
I4/mcm––method was not reported before, and it turned out to be anideal 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 R
­ hPb2 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 othercases, the resistivity measurements releveled three superconducting transitions indicating the presence of three different phases (Fig. 1c). The transition widths of 1.25 K aresmaller than the other two transitions. The correspondingΔTc/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 resistanceratio (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 dependenceof the resistivity at higher temperatures was observed.
The crystals, on which the resistivity measurements wereperformed, 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 inTable 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 surfaceof the crystals are also shown in SI.

Crystal growth and characterization of R­ hPb2 and its related compounds﻿	Fig. 1  a Resistivity plot of R
­ h0.993Pb2.007 up to 10 K. The residualresistance 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 R
­ hPb2. c The resistivity plot ofsample ­Rh0.963Pb2.037 up to 10 K. Three transitions can be observed.
The transition width of 1.24 K transition is significantly narrower

Table 2  The occupancy of the Pb and Rh sites
SampleRh (%)

Pb (%)

Measured Tc (K)A ­Rh0.993Pb2.007
B ­Rh0.963Pb2.037

99.3
96.3

100
100

1.25
1.24
2.32
6.7
1.26
2.39
6.61

C ­Rh0.825Pb2.125

82.5

100

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 theaveraged 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

Since sample A contained only one Tc the sample may
be homogenous and without vacancies. The other twosamples show that the vacancies of Rh may not be distributed homogenously since three different values of Tc wereobserved. For sample C, if it is assumed that the various
values of Tc are due to the variation of Rh vacancies, the6.61 K transition may be due to the 82.58% occupancyof the Rh sites because the 2.39 K transition is negligible, and the 1.26 K is due to the non-deficient structure.

(0.1 K) compared to the higher temperature transition width (0.5 K).
The residual resistance is lower compared to sample R­ h0.993Pb2.007.
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 R
­ hPb2

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, R­ hPb2 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 I 2/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 the1.26 K transition is due to the non-deficient structure, notthe Pb-deficient structure reported by [4]. Therefore, thePb-deficient structure might not occur. The 2.32 K transition may be due to the slight Rh-deficient crystals (around96%), 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

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N. Subotić et al.

Fig. 2  SEM photographs of ­Rh0.993Pb2.007, ­Rh0.963Pb2.037, and­Rh0.825Pb2.125, respectively (from left to right), on which theEPMA measurements were done. The size of R
­h0.993Pb2.007 isroughly 600 × 600 μm2, ­Rh0.963Pb2.037 around 300 × 200 μm2, and­Rh0.825Pb2.125 approximately 100 × 100 μm2

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 spacegroup.
Another possibility is that the 6.7 K transition is due tothe presence of Pb or R­ hPb4. It is unlikely that the 6.7 K isdue to the presence of Pb since its Tc is 7.1 K. Grown crystals of R­ hPb4 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 isdue to the Rh-deficient structure. To confirm whether ­RhPb4belongs to the I2/m space group, analysis of better quality
crystals is required. It would be quite interesting to performthe band calculation and inspect the topological propertiesof ­RhPb4.
The presence of ­RhPb2 at both ends of the boule and­RhPb4 in the middle of the grown boule indicate that there
is a considerable temperature difference across the grownboule due to the steep temperature gradient and the size ofthe boule. As it turned out, this method is favorable for theformation of various phases since a 6.7 K transition wasobserved 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 R­ hPb2. The highconcertation of Pb may lead to the Rh-deficiency on the onehand. On the other hand, crystals of ­Au2Pb and ­AuPb2 grownunder similar conditions do not exhibit deficiency indicating that the deficiency in ­RhPb2 is due to the nature of thematerial 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 indetail.
XRD measurements did not show that the structureof grown crystals of R­ hPb2 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 ofgrown 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 thePb-Rh system was studied. According to the presently
available binary phase diagrams [1, 2], several kinds ofsingle crystals can be grown from the appropriate combination of Pb and Rh. Most of their physical properties turnout to be unexplored, for example, different values of Tc of
the intermetallic compound R­ hPb2. This unexpected result
encourages further investigation of ­RhPb2 as a topological superconductor candidate. It certainly requires better
quality of single crystals of R
­ hPb2. In addition, the relation between its corresponding Rh-deficient structures andthe 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 topologicalproperties of R
­ hPb2 and the related compounds. Furthermore, magnetoresistance measurements could also provide
important information about the Fermi surface to reveal
the topological nature of R
­ hPb2. Such measurements will
be conducted in the near future.

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Supplementary Information The online version contains supplementary material available at https://d​ oi.o​ rg/1​ 0.1​ 557/s​ 43580-0​ 22-0​ 0292-5.
Data availability The data that supports the above-presented results
are available from the corresponding author upon reasonable request.

Crystal growth and characterization of R­ hPb2 and its related compounds﻿	Declarations
Conflict of interest On behalf of all authors, the corresponding author
states that there is no conflict of interest.

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