富山大学研究推進機構水素同位体科学研究センター研究報告 36：31－38，2016.

論文

Pd–Ag–Rh 三元系合金における磁化率と水素吸収量の相関
赤丸悟士，原正憲

富山大学研究推進機構水素同位体科学研究センター〒930-8555 富山市五福 3190

Relation between the magnetic susceptibility and the amount of absorbedhydrogen for the Pd–Ag–Rh ternary alloy
Satoshi Akamaru, Masanori Hara

Hydrogen Isotope Research Center, Organization for Promotion of Research, University ofToyama
Gofuku 3190, Toyama 930-8555, Japan(Received January 31, 2017; accepted July 14, 2017)
Abstract
The magnetic susceptibility and equilibrium pressure of a Pd–Ag–Rh ternary alloy and hydrogen systemwere simultaneously measured, and the relationship between the magnetic susceptibility and the amount ofabsorbed hydrogen was investigated. The magnetic susceptibility linearly decreased to a value approachingzero with increasing hydrogen content. A high hydrogen content with a magnetic susceptibility close tozero is consistent with a hydride phase. This behavior is similar to that of Pd–Ag or Pd–Rh binary alloys
and hydrogen systems, suggesting that the amount of hydrogen absorbed by the Pd–Ag–Rh ternary alloy
is correlated with its electronic band structure, as in the case of the Pd-binary alloys.

1. Introduction
Palladium metal is well-known as a hydrogen storage material, and various31

赤丸悟士・原正憲

applications related to hydrogen usage have been developed including hydrogen sensing andhydrogen purification systems. Pd-based binary alloys that contain a second transition metal
have been designed to adjust the hydrogen absorption properties, and systematic studies on
Pd-based binary alloys and hydrogen systems have been performed to obtain the relation
between the properties and the alloying elements [1].
The amount of hydrogen absorption in metallic Pd depends on its electronicstructure; the number of unoccupied d-states is correlated with the amount of absorbedhydrogen [2]. Each absorbed hydrogen atom provides an electron to Pd, thereby occupying
the unoccupied d-states of Pd. When the unoccupied d-states of Pd are completely filled withelectrons by the absorption of hydrogen, Pd hydride is formed, which cannot undergo furtherhydrogen absorption.
Alloying Pd with a transition metal is an effective way to control the number ofunoccupied d-states in Pd; the amount of absorbed hydrogen is reduced with the supply ofelectrons from the transition metal to Pd. To determine the relation between the amount ofabsorbed hydrogen and the unoccupied d-states in a Pd alloy, Pd–Ag, and Pd–Rh weresystematically investigated [3]. Because alloying Pd with Ag or Rh corresponds to addition or
removal of electrons from Pd, respectively, the number of unoccupied d-states of Pd can becontrolled without deformation of the electronic band structure of Pd. Magnetic susceptibility
measurements of a Pd alloy with various hydrogen contents can be used to study its
electronic structure. The magnetic susceptibility of a Pauli paramagnet is proportional to thedensity of states at the Fermi level [4]. If the electronic band structure of a Pd alloy isregarded as the same as that of Pd metal, the change in the unoccupied d-states via alloying
and the degree of filling of these d-states by hydrogen absorption can be estimated frommagnetic susceptibility measurements. We previously investigated the magnetic susceptibilityof Pd–Ag and Pd–Rh binary alloys with various hydrogen contents and found that the32

Pd–Ag–Rh 三元系合金における磁化率と水素吸収量の相関

amount of absorbed hydrogen was correlated with the amount of doping electron by alloying,namely the amount of substituting elements [3].
The hydrogen absorption properties of Pd-based ternary alloys have not been
extensively studied; therefore a lack of the information about the effect of a third element on
the hydrogen absorption properties still exists. In the present study, we measured themagnetic susceptibility and the hydrogen absorption isotherm of a Pd–Ag–Rh alloy withvarious hydrogen contents to verify that the model applied to Pd-based binary alloys can beextended to analyze Pd-based ternary alloys.

2. Experimental
The Pd0.92Ag0.06Rh0.02 ternary alloy was used as prepared in previous study [5].
Predetermined amounts of Pd, Ag, and Rh metals were weighed out; then, the mixture wasmelted in an arc melting furnace [5]. The obtained ingot was grounded into powder using afile, and a part of the powder was subjected to X-ray diffraction (XRD) analysis. Then 1 g ofpowder was introduced into a quartz cell connected to the pressure–composition isotherm
measurement system. The quartz cell was evacuated down to 1.0 × 10−4 Pa; future, the311
222

which was described in detail in800

220

measured via the induced method,

Pd0.92Ag0.06Rh0.02

200of the Pd0.92Ag0.06Rh0.02 powder was

1600
Intensity, I / cps

for 2 h. The magnetic susceptibility

111

powder alloy was heated at 523 K

previous papers [3,6].

030
3. Results
Figure 1 shows the XRD

40
50
60
70
80
Diffraction angle, 2 / deg

90

Figure 1 Powder X-ray diffraction patternof Pd0.92Ag0.06Rh0.02 ternary alloy.

33

赤丸悟士・原正憲

pattern of the Pd0.92Ag0.06Rh0.02 alloy.

The XRD data was indexed using a face-centeredcubic structure and no unknown diffraction lines were observed. The lattice constant of thePd0.92Ag0.06Rh0.02 alloy was calculated to be 0.3900 nm. If the Pd0.92Ag0.06Rh0.02 ternary alloy
was regarded as a binary alloy of Pd0.92Ag0.08 and Pd0.92Rh0.08, the lattice constant of
Pd0.92Ag0.06Rh0.02 expected from Vegard’s law would have been 0.3898 nm, which wasconsistent with the measured value. These results indicated that a homogeneous
Pd0.92Ag0.06Rh0.02 ternary alloy with a face-centered cubic structure was obtained.
Figure 2 shows the dependence of both the magnetic susceptibility and equilibriumpressure on the hydrogen content of Pd0.92Ag0.06Rh0.02 (denoted as [H]/[Pd–Ag–Rh]). Theequilibrium pressure sharply increased with increasing [H]/[Pd–Ag–Rh] from zero to 0.04.
This range corresponded to that of the dissolved hydrogen region. The equilibrium pressure3

Pd0.92Ag0.06Rh0.02 powder
T = 302 K

210-96050
40110302010Equilibrium pressure, Pe / kPa

Magnetic susceptibility, ' / 10 m kg-170010000.1 0.2 0.3 0.4 0.5 0.6 0.7
Hydrogen content, [H]/[Pd-Ag-Rh] / -Figure 2 The dependence of both a magnetic susceptibility and an equilibrium pressure
on hydrogen content in the Pd0.92Ag0.06Rh0.02 ternary alloy. The evaluation of the phaseboundary from magnetic susceptibility and equilibrium pressure was performed using thedashed and dotted lines.

34

Pd–Ag–Rh 三元系合金における磁化率と水素吸収量の相関

was maintained between 6 to7 kPa within 0.1 < [H]/[Pd–Ag–Rh] < 0.5, which is generally
called a plateau. Because the equilibrium pressure sharply increased above this value, thehydride phase appeared at [H]/[Pd–Ag–Rh] > 0.6. This behavior was qualitatively the sameas that of Pd-based binary alloys and Pd metal [3,6,7].
The magnetic susceptibility of Pd0.92Ag0.06Rh0.02 was 51 × 10−9 m3/kg. This value isslightly smaller than that of Pd metal. With increasing [H]/[Pd–Ag–Rh], the magnetic
susceptibility linearly decreased to the small positive value of 2 × 10−9 m3/kg at[H]/[Pd–Ag–Rh] > 0.6. The dependence of the magnetic susceptibility on [H]/[Pd–Ag–Rh]
was similar to that found for Pd-based binary alloys and Pd metal [3,6,7].

4. Discussion
Since Pd–Ag and Pd–Rh alloys were found to show paramagnetic behavior [3], andthe magnetic susceptibility of Pd–Ag–Rh was very small in comparison with that of otherPd-based ferromagnetic binary alloys such as Pd–Co and Pd–Ni [8,9], the Pd0.92Ag0.06Rh0.02
alloy is considered to be a paramagnet at room temperature. In addition, we proved in aprevious study [3] that the rigid band model could be applied to Pd–Ag and Pd–Rh systems;
the electronic band structure of Pd metal was not affect by the substituting Ag or Rh, and thedensity of states at the Fermi level for Pd-binary alloys was related only to the change in thenumber of electrons by alloying. Considering that the Ag and Rh content of the Pd ternary
alloy used in this study was low, the rigid band model could be applied to thePd0.92Ag0.06Rh0.02 and hydrogen system. In this section, the magnetic susceptibility of the Pd
ternary alloy will be analyzed based on the rigid band model.
The principal values obtained from Fig.1 and 2 are summarized in Table 1. Thevalues for Pd metal and Pd-binary alloys are also included for comparison. As cn be extracted
from the data, the magnetic susceptibility of Pd0.92Ag0.06Rh0.02 without hydrogen is consistent35

赤丸悟士・原正憲

Table 1. The principal values obtained from Fig.1 and Fig.2. The values for related materials
are also summarized in comparison.
[H]/[Pd–Ag–Rh] at βminfrom χ'χ' withouthydrogenPlateaupressure

Latticeconstant

0.52
0.57
0.62
0.67
0.70

0.49
0.55
0.63
0.65
0.71 1)/10−9m3kg−1
42.2
50.6
64.3
73.9
71.1/kPa
0.639
1.04
2.45
10.3
27.4

/nm
0.39030.3896
0.38900.3886
0.38830.571)

51.3

6.29

0.3900from Pe

Pd0.92Ag0.08
Pd0.96Ag0.04
Pd
Pd0.96Rh0.04
Pd0.92Rh0.08
Pd0.92Ag0.06Rh0.02

0.60

Ref.

[1]
[1]
[1]
[1]
[1]
Thiswork1) the value was obtained by the extrapolation of the magnetic susceptibility at the plateau
region.

with that of the Pd0.96Ag0.04 alloy. Because the magnetic susceptibility of a Pauli paramagnet
is proportional to the density of states at the Fermi level [4], this result suggests that thedensity of states at the Fermi level in Pd0.92Ag0.06Rh0.02 is similar to that in Pd0.96Ag0.04, andthat the number of electrons in both specimens are practically the same.
In the Pd–Ag or Pd–Rh and hydrogen systems, the change in the number ofelectrons induced by Ag or Rh substitution resulted in the change of the terminal of theplateau because the amount of unoccupied d-states in the absence of hydrogen was related tothe minimum hydrogen content at the hydride phase (βmin) [3]. The βmin for Pd0.92Ag0.06Rh0.02
was estimated from the equilibrium pressure; the hydrogen content at the terminal of theplateau was determined at the point where the plateau intersected the extrapolated line of thehydride phase. The obtained value was the same as that for Pd0.96Ag0.04, suggesting that theβmin for the Pd0.92Ag0.06Rh0.02 ternary alloy had the same implications as in the Pd-based
binary alloy.
According to our previous study, the magnetic susceptibility of the Pd alloy reachedzero at βmin, and it kept a small negative value within the hydride phase [3]. Because the36

Pd–Ag–Rh 三元系合金における磁化率と水素吸収量の相関

magnetic susceptibility of Pd0.92Ag0.06Rh0.02 showed a positive value within the measured[H]/[Pd–Ag–Rh] range, the βmin was estimated from the intersection of the extrapolation tozero of the magnetic susceptibility at the plateau region. The estimated value thus obtained
was [H]/[Pd–Ag–Rh] = 0.60, which was consistent with the βmin estimated from the terminalof the plateau. Consequently, the amount of absorbed hydrogen for the Pd ternary alloy wasalso correlated with its electronic band structure. It is worth noting that the magnetic
susceptibility of the Pd0.92Ag0.06Rh0.02 hydride ([H]/[Pd–Ag–Rh] > 0.60) was kept a small
positive value, which was indicative of the existence of a small amount of ferromagnetic
impurities in the Pd ternary alloy. When the magnetic susceptibility data decreased to 2 ×
10−9 m3/kg, the estimated βmin became 0.58, which approached the value obtained from theequilibrium pressure. We tried to estimate the amount of magnetic impurities. As can beextracted from reference [10], the magnetic moments of the constituent atoms in a Pd0.97Fe0.03
alloy were determined to be 3.0μB for Fe and 0.15μB for Pd. The Fe content in the Pd matrix
was estimated to be 0.2at% from the enhancement of the magnetization of Pd by a factor of
1.04 induced by the Fe atoms as magnetic impurities. Accordingly, the amount offerromagnetic impurities could be estimated to be rather small, and the change in theelectronic band structure induced by such impurities can be considered negligible in thisstudy.
In the previous study on Pd–Ag and Pd–Rh alloys, the equilibrium pressure at theplateau systematically changed depending on the number of conduction electrons [3]. In thePd0.92Ag0.06Rh0.02 and hydrogen system, however, the equilibrium pressure at the plateau did
not follow the same trend [3]. Future investigation on the Pd–Ag–Rh alloy with various
element compositions and different hydrogen contents is required to gain a better
understanding on this discrepancy.

37

赤丸悟士・原正憲

5. Conclusions
The magnetic susceptibility of a Pd0.92Ag0.06Rh0.02 ternary alloy and hydrogen systemwith various hydrogen contents was measured. It was found that the magnetic susceptibility
linearly decreased with increasing the hydrogen content and approached zero at the hydride
phase. The hydrogen content at the terminal of the plateau was consistent with that obtainedat the point of zero magnetic susceptibility, suggesting that the βmin of the Pd–Ag–Rh ternary
alloy could be estimated from its magnetic susceptibility measurement, as in the case of thePd–Ag and Pd–Rh binary alloys.

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