MRS Advances
https://doi.org/10.1557/s43580-022-00440-x

ORIGINAL PAPER

Investigation of the ternary phase diagram of Au–Pb–Rh compounds
Nikola Subotić1 · Takashi Mochiku2 · Yoshitaka Matsushita2 · Mitsuaki Nishio2 · Osamu Takeuchi1 ·Hidemi Shigekawa1 · Kazuo Kadowaki1
Received: 20 October 2022 / Accepted: 27 November 2022
© The Author(s), under exclusive licence to The Materials Research Society 2022

Abstract
The ternary phase diagram of the Pb-rich Au–Pb–Rh system has been studied from a viewpoint of the formation of intermetallic compounds. We indeed discovered two new compounds with the nominal chemical formula of ­AuPb2Rh2 and­AuPb4Rh5. They are revealed by XRD study to possess a similar crystal structure with each other having an orthorhombic
crystal structure with Pmma symmetry. The resistivity measurements of ­AuPb2Rh2 show double superconducting transitions
at 2.8 K and 1.7 K, while A­ uPb4Rh5 did not above 1.1 K. The significant shift of stoichiometric ratio of Au and Rh observedin both compounds suggests strongly that vacancy structures and site exchange, in particular, the ­AuPb4Rh5 compound, may
play an important role in the physical properties of these compounds.

Introduction
Recently, the topological nature of the electronic state ofmatter has attracted much theoretical as well as experimental attention, because it has emerged newly as a quantum
state of matter in solid-state physics [1–4]. Materials thatpossess such behavior, for example, resistanceless surface
current, may be expected as the most valuable for practical application. According to the band calculations, so far,many materials have been listed and nominated as candidate materials [5–7]. For this purpose of the study, we havechosen the ternary intermetallic compounds including Pb
and 4d or 5d transition metal elements as the main work
field because Pb is the heaviest stable element, nonradioactive, easy to handle, forming stable compounds with 4d and5d elements, with large spin-orbital interaction, a common
cheap metal, etc.
The binary phase diagram Pb-Rh has been investigated[8, 9]. According to [8] the stable intermediate compounds
are ­RhPb4, ­RhPb2, ­Rh4Pb5, RhPb, and ­Rh3Pb2. Besides thebefore-mentioned compounds, according to [9], ­Rh5Pb7 and­Rh3Pb are stable. The superconducting properties of R
­ hPb2* Nikola Subotić
nikolasubotic95@gmail.com
1

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

2

National Institute for Material Science, 1‑2‑1 Sengen,Tsukuba, Ibaraki 305‑0047, Japanmight be influenced by Rh deficiency [10, 11]. RhPb belongs
to the CoSn-type structure, exhibiting a flat electronic bandthat could induce unconventional superconductivity, magnetism, and topological behaviors [12]. ­Rh4Pb5 might also
exhibit topological properties since its topological Z­ 2 index
is (0;1,0,1) [13], while, according to [14], ­Rh4Pb5 is a topological crystalline insulator.
Compared to the binary phase diagram Pb–Rh, the binary
phase diagram Au–Pb is simpler. According to [15], the following intermediate states are stable: A­ uPb2, ­Au2Pb, and­AuPb3 while one metastable state A­ u2Pb3 has been reported.
Among them, A­ u2Pb is a topological superconductor candidate [16] having three different phases at a lower temperature, while the ­Z2 index related to the ­AuPb3 compound is(1;1,1,1) [13]. It is interesting to note that similar controversy exists regarding the superconducting transition temperatures of ­AuPb2 and ­AuPb3 as in the ­RhPb2 case. The
binary phase diagram Au-Rh has no stable intermediate
compounds.
Considering the above-mentioned binary systems for
Pb–Rh and Au–Pb, we started to look for compounds fromhigher concentrations of Pb in the ternary system, because
Pb is expected to promote intermediate compounds to forma flux, which may also interact as a component of the intermetallic compounds.

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N. Subotić et al.

Materials and methods

Table 1  EPMA results for the crystals extracted from the grownboule with corresponding ratios of starting materials

The examined molar ratios were as follows:
1:4:1 = Au:Pb:Rh, 3:5:1 = Au:Pb:Rh, 2:8:1 = Au:Pb:Rh,
2:2:1 = Au:Pb:Rh. The raw materials of Au and Pb were
99.9% purity in shots while Rh was 99.9% purity in powder form (300 mesh), purchased from Furuuchi Chemical
Co, Japan. Before the crystal growth, the corresponding
amount of the material was heated gently and melted in an
evacuated quartz tube by the flame torch. The melted ingot
was put in another evacuated quartz tube and heat-treatedwith the following temperature profile in a standard muffle
furnace; 900 ºC for one day, decreasing to 800 ºC with aconstant rate of 5 ºC/h and then decreasing to 650 ºC witha constant rate of 1 ºC/h.
After opening all the quartz tubes, the grown boules were
spalled for further investigation. It was interesting to see
many shiny crystals on the surface of the broken boules inall cases we studied. These crystals were extracted fromthe piece of the fragment and used for EPMA, XRD, andresistivity measurements. The standard four-point contact
method was applied to measure the temperature dependenceof resistivity. The silver paste was used to connect the voltage and current leads. The contact resistance was typicallybelow 1 Ω. The EPMA measurements were performed withJEOL JXA-8500F. The voltage and probe current were at
15 kV and 5 nA, respectively. For calibration, PbS, Au, andRh were used. The XRD measurements were conducted withtwo circle diffractometer Rigaku Xtal Mini II.

Initial molar ratio

Au (%)Pb (%)

Rh (%)

1:4:1 = Au:Pb:Rh
1:4:1 = Au:Pb:Rh
3:5:1 = Au:Pb:Rh
3:5:1 = Au:Pb:Rh
2:2:1 = Au:Pb:Rh
2:8:1 = Au:Pb:Rh

11.7
0.5
15
18.1
10.1
4.6

42.6
60.6
42.5
43.5
41.4
71.4

45.7
38.9
42.5
38.4
48.5
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Results
The many pieces of crystals were separated mostly bymechanical force, but in some cases, crystals can be foundin the derbies of the sample. Although they are small (≤ 1­mm3), they can be used for the EPMA, XRD, and resistivity measurements.
The EPMA results are shown in Table 1. It is interesting
to see that almost all crystals showed a high concentrationof Rh even though the initial amount was the smallest. The
COMPO images of the samples can also be found in the
SI. For the 281 sample, only one measurement spot waschosen (results will be confirmed in near future). Crystals
from the 141 sample might be assigned to ­AuPb4Rh5 whilethe 351 sample to ­AuPb2Rh2.
The single crystal XRD analysis has been performed
for the two crystals as mentioned in Table 1. They werethe crystals grown from 141 and 351 compositions (sameas shown in Fig. 1a) and b)). The results were presented
in Fig. 2. It is interesting to note that both crystals belong
to the orthorhombic system with the same Pmma space

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In the table, the averaged values are shown. The more detailed data
are shown in SI

Fig. 1  a An optical photograph of the grown crystal from the starting composition of 1:4:1 = Au:Pb:Rh. The crystal grows at the surface of the boule, whereas no crystal is found inside the boule. The
size of the crystal is approximately as large as 12 × 4 × 2 ­mm3. b An
optical photograph of the spalled boule with the initial compositionof 3:5:1 = Au:Pb:Rh. Large triangular plate-like crystals of more thana few millimeters in size were found inside the boule. The crystals
seem to be cleavable because the same-sized crystal appears on both
surfaces of the crushed boule almost every time. c An optical photograph of the spalled boule grown from the starting compositionof 2:2:1 = Au:Pb:Rh. Many needle-like crystals can be seen inside
the boule. The length of the needle can be as large as ~ 5 mm with awidth of ~ 1 mm in diameter. d A COMPO image of the needle-likecrystal extracted from the separated crystal grown from the starting
composition of 2:8:1 = Au:Pb:Rh

group and the chemical formula can be identified to be­AuPb2Rh2 and ­AuPb4Rh5. As seen from the crystal structures, the b lattice parameter of ­AuPb4Rh5 is almost double
compared with that of ­AuPb2Rh2, indicating the formation of ordered vacancies structure and exchange of atomic
positions along the b-axis by forming twinning pair of thebasic unit cell of ­AuPb2Rh2. As a result, it seems that thestructure of ­AuPb4Rh5 can adopt more site exchange of Au
and Rh atoms in the middle of the unit cell in ­AuPb4Rh5.

Investigation of the ternary phase diagram of Au–Pb–Rh compounds﻿	Fig. 2  The results of XRD analysis of crystals 141 and 351. After
careful refinement, the chemical compositions ­AuPb4Rh5 (141) and­AuPb2Rh2 (351) were determined. The schematic atomic arrangements of the unit cell are shown. The Pb atoms are marked in blue,
Rh in green, and Au in pink color. Crystal structures are quite similar(same space group) with different b lattice constants (about 2 times
larger) and the total occupancy of the Au site for the A­ uPb4Rh5 is 1.
Rh deficiency can be also observed in both cases which are not substituted by Au atoms, similar to ­RhPb2 [10, 11]This may also be supported by the evidence that thechemical stoichiometry of A
­ uPb2Rh2 is naturally shiftedfrom 1:4:5. Furthermore, it is found that the Rh atoms areslightly deficient as pointed out in previous work on ­RhPb2[10, 11]. A more detailed crystal structure analysis will befound elsewhere [17].
In Fig. 3 the temperature dependence of resistivity on
samples 351 and 141 is shown. The resistivity at room temperature of the 141 sample is 640 μΩ cm while for the 351

sample is 81.6 μΩ cm. The residual resistance for both samples is high (around 480 μΩ cm for 141 sample and around
65 μΩ cm for 351). The corresponding RRR for 141 and351 samples is 1.33 and 1.25, respectively. The 141 sample
did not exhibit superconductivity down to 1.1 K while 351
had two transitions (2.8 K and 1.73 K). The ΔTc for the
1.73 K transition is 0.17 K while for the 2.8 K transition is
1.2 K. The corresponding ΔTc/Tc ratios are 0.098 and 0.42,
respectively. The resistivity dependence on the temperature

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N. Subotić et al.

Fig. 3  a The low-temperature part of the resistivity plot of sample
351. The residual resistance is around 65 μΩ cm while the room temperature resistivity is 81.6 μΩ cm. The photograph of the measured
crystal is shown in the inset. The resistivity plot up to 100 K is shownin the SI. The transition width of the 2.8 K transition (1.2 K) is wider
than the 1.73 K transition (0.12 K). b Resistivity plot of 141 sample up to 100 K. The sample did not exhibit superconductivity above
1.1 K. The linear dependence indicates the metallic behavior of 141
sample. The photograph of the measured crystal is shown in the inset

at higher temperatures is nearly linear. For 351 sample, thehigher temperature part of the resistance is shown in SI
where around 42 K, a slight kink can be observed.

Discussion and conclusion
The Pb-rich part of the Au-Pb-Rh ternary phase diagram has
been investigated for the first time. Evidently, it becomesmuch more complicated; however, we have much morechances to find new compounds as expected. Indeed, we
have so far discovered that two new compounds ­AuPb2Rh2
and ­AuPb4Rh5 can form in the Pb-rich ternary Au–Pb–Rh
system.
In most cases, the grown crystals were rich in Rh eventhough the initial composition did not have such an amountof Rh. The highest concentration of Au in the measured
crystals was not higher than 20% even though there weresome cases where the initial concentration of Au was higher.
This suggests that during the crystal growth phase separation might occur. In future, the phase diagram near thenominal concentration and narrower temperature range will
be explored. In such conditions, the crystal quality shouldbe improved by reducing the observed deficiency. Also,

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annealing the grown crystals at various temperatures willprobably yield interesting results as well.
According to EPMA results, the crystals that weregrown from the initial molar ratio of. 2:1:2 = Au:Rh:Pb and1:1:4 = Au:Rh:Pb had similar compositions indicating thatthe ­AuPb4Rh5 forms at higher temperatures (around 850ºC). At lower temperatures, the current situation is not clear,but the resistivity measurements indicate that other compounds are forming. Therefore, it is possible that at lower
temperatures, other compounds form for the molar ratio of
2:2:1 = Au:Pb:Rh since those crystals are forming differently
compared to the 1:4:1 = Au:Pb:Rh case (the crystals haveformed on the surface opposite to the needle-like crystals
forming inside the bulk). Moreover, the crystals that weregrown from the 2:8:1 = Au:Pb:Rh ratio are interesting since
the small concentration of Au suggests that doping of ­RhPb3
occurred but according to [8, 9], ­RhPb3 does not exist or
doping of Rh-deficient R­ hPb2 occurred. The Au-Rh-rich partof the phase diagram was not investigated, but it is expectedthat other compounds may form.
As for the superconductivity, uncertainty on the Tc still
remains. This tendency is also similar in the binary systems of Au–Pb and Rh–Pb. R­ hPb2 and related Rh-deficient
structures have Tc = 1.26 K and 2.3 K, respectively [10],while ­Au2Pb 1.18 K [16]. The situation regarding A­ uPb3and ­AuPb2 is similar to R
­ hPb2 since the reported Tc valuesof those compounds do not agree with each other [18–20].
According to [19], the Tc of A
­ uPb2 is 4.42 K. On the other
hand, [18] indicates that the 4.42 K transition is due to­AuPb3 while ­AuPb2 becomes superconducting below 3.15 K.
Surprisingly, ­AuPb4Rh5 is not superconducting above 1.1 K.
For the ­AuPb2Rh2, its superconducting transition might be
1.7 K or 2.8 K. Although the main frame of the unit cellstructure of ­AuPb2Rh2 and A­ uPb4Rh5 is very similar as
seen in Fig. 2, the superconductivity transition behavior isvery different. Therefore, one may ask how the Tc of thesecompounds is influenced by the Rh and Au deficiency andoccupancy. Similar behavior was observed for ­RhPb2 [10].
One may think a possibility that A­ uPb4Rh5 and A­ uPb2Rh2
can be derived from R­ h3Pb2 doped with Au. However, thisis unlikely since the crystal structure of ­Rh3Pb2 is hexagonal[8, 9]. Furthermore, there is a possibility that the binary
phase diagram Rh–Pb may lack some crucial information
because of its incompleteness [8, 9]. Certainly, we needmore careful study in the ternary Au–Pb–Rh system.
As mentioned in the introduction, some compounds fromthe binary phase diagrams Au–Pb and Rh–Pb are supposed
to have nontrivial topological properties. For the ternaryAu–Pb–Rh system, this situation may be similar. Two newcompounds found in this study can also be such candidates
for nontrivial topological materials. For example, the binary­Au2Pb system has intensively been studied as a possible nontrivial topological surface state [16, 21–24]. It is suggested

Investigation of the ternary phase diagram of Au–Pb–Rh compounds﻿	to investigate theoretically and experimentally these newcompounds. This was another motivation to discover newcompounds.
In conclusion, the preliminary investigation of the ternary phase diagram Au–Pb–Rh has been performed andsucceeded in discovering two new compounds ­AuPb4Rh5
and ­AuPb2Rh2. According to the XRD results, they belong
to the orthorhombic crystal system (space group Pmma).
­AuPb4Rh5 is not superconducting above 1.1 K. The observed
transition at 1.7 K and 2.8 K might be due to the different Rh
deficiency and Au occupancy of A
­ uPb2Rh2. In this sense, it
is so curious to ask how nonstoichiometry, caused mainly
by vacancies, affects the occurrence of superconductivity.
To reveal such an interesting issue, the annealing study ofthe crystals under various conditions might be crucially
important.
Supplementary Information The online version contains supplementary material available at https://d​ oi.o​ rg/1​ 0.1​ 557/s​ 43580-0​ 22-0​ 0440-x.
Acknowledgments The author would like to thank Takanari Kashiwagi
for the valuable discussion and support.
Data availability The data that support the above-presented results areavailable 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.

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