Coulomb oscillation of a proton in a
Ni-Nb-Zr-H glassy alloy with multiple
junctions
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福原 幹夫
Applied Physics Letters
90
20
203111-1-203111-3
2007
http://hdl.handle.net/10097/47065
doi: 10.1063/1.2739080
APPLIED PHYSICS LETTERS 90, 203111 共2007兲
Coulomb oscillation of a proton in a Ni–Nb–Zr–H glassy alloy
with multiple junctions
Mikio Fukuhara,a兲 Asahi Kawashima, Shinichi Yamaura, and Akihisa Inoue
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
共Received 6 March 2007; accepted 19 April 2007; published online 18 May 2007兲
Electric current-induced voltage oscillation at 500– 560 kHz was observed in the current-voltage
curves of nanoscopic size 共⬃0.9 nm兲 tunnel junctions arranged in a low-capacitance 共⬃1 aF兲,
multiple-junction configuration of 共Ni42Nb28Zr30兲100−xHx 共5.2艋 x 艋 15.2兲 glassy alloys in the
temperature range of 205– 6 K. This behavior appeared to be derived from Coulomb oscillation
resulting from the tunneling of individual protons charging and discharging the vacancy capacitance
of Zr–H-䊐-H–Zr atomic bond arrays among Zr-tetrahedral clusters, where 䊐 is the vacancy barrier,
termed the free volume, in the glassy alloys. © 2007 American Institute of Physics.
关DOI: 10.1063/1.2739080兴
Following the discovery of the single-electron
transistor,1 many research groups have studied the “Coulomb
blockade” effect, in which charge transport through the device occurs in an electron-by-electron manner at low
temperatures.2–4 This means that a single electron on a metallic island can block the flow of another electron if the
charging energy of the island greatly exceeds the thermal
energy kT. Subsequently, the analogous effect of “photon
blockbade” has been proposed for the transport of light
through an optical system, using photon-photon interactions
in a nonlinear optical cavity.5 Observation of strictly quantum effects in optics relies on the existence of strong nonlinear interactions between photons.6 Both Coulomb blockade
effects in mesoscopic systems with nanostructures show nonlinear responses to the externally connected macroscopic
system.
In the present letter, in the light of new developments,
we consider the possibility of a nonlinear proton mode using
a glassy alloy that contains hydrogen. Glassy alloys are
peculiar metallic alloys in that they lack the short-, medium-,
or long-range cyclic order of crystalline alloys on the
nanoscale.7–9 Therefore, the metallic glass is considered to be
a macroscopic material with a mesoscopic system that consists of nanostructures.
For metallic glass that consists of antinomic affinity Zr
and antiaffinity Ni elements for hydrogen,10 a melt-spun
flexible amorphous Ni42Nb28Zr30 membrane with excellent
hydrogen permeability11 was selected. The Ni42Nb28Zr30 material is a typical metal-metal-type alloy that consists of familiar transition elements. Our interest lies in investigating
the temperature-dependent hydrogen effect of electric conduction of the 共Ni42Nb28Zr30兲100−xHx glassy alloys in terms of
Coulomb oscillation. However, there are no previous reports
on this subject for glassy alloys with hydrogen.
The rotating wheel method under an argon atmosphere
was used for the preparation from argon arc-melted ingots of
amorphous Ni42Nb28Zr30 alloy ribbons of about 1 mm width
and 20 ␮m thickness. Hydrogen charging was carried out
electrolytically in 0.5M H2SO4 and 1.4 g / l thiourea
共H2NCSNH2兲 at room temperature and at the current densities of 200 and 500 A / m2.12 The amounts of hydrogen aba兲
Electronic mail: [email protected]
sorbed in the specimens were measured by the inert gas carrier melting-thermal conductivity method.
The structure of the glassy 共Ni42Nb28Zr30兲100−xHx alloy
was identified by x-ray diffraction with Cu K␣ radiation
in the grazing incident mode. The angle of incidence used
was 2°.
The specific electrical resistance of hydrogenated specimens was measured by the four-probe method dc and ac
source 6221, Nano voltmeter 2182A 共Keithley Instruments
Inc.兲 with a dc of ±1 mA at cooling and heating rates of
1 K / min., i.e., 0.017 K/s from 373 to 6 K in He of ambient
pressure 共top loading refrigerated cryostat; JECC Torisha
Co.兲. The distance between the two voltage electrodes was
20 mm. In order to eliminate both the effects of the electromagnetic environment and the quantum fluctuation of electric charge,13 we used a source resistance 共RS兲 of 10 G⍀,
which is much larger than the quantum unit of resistance
RQ = h / e2. Voltage oscillation was measured by an oscilloscope 共pulser/receiver TP-1001; Toshiba Tungaloy兲 and the
power spectrum was analyzed by fast Fourier transform.
Desorpted hydrogen from the specimens was analyzed using
a quadrupole mass spectrometer 共HIRESOM-2SM; Ulvac
Inc.兲.
The electrical resistances of 共Ni42Nb28Zr30兲1−xHx
共x = 0 – 0.22兲 alloys under 1 mA dc with positive sign were
measured during cooling and heating runs. The results are
shown as a function of temperature 共Fig. 1兲. The resistance
of the Ni42Nb28Zr30 alloy without H increased almost linearly
FIG. 1. 共Color兲 Electrical resistivities of the 共Ni42Nb28Zr30兲1−xHx 共x
= 0 – 0.22兲 alloys under 1 mA dc. Insert: Effect of hydrogen on TCR.
0003-6951/2007/90共20兲/203111/3/$23.00
90, 203111-1
© 2007 American Institute of Physics
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203111-2
Fukuhara et al.
FIG. 2. 共Color兲 Abnormal resistivity of the 共Ni42Nb28Zr30兲94.8H5.2 alloy.
with decreasing temperature. The negative temperature coefficient of resistivity 共TCR兲 of −9.86⫻ 10−5 / K indicates a
semiconducting character. The resistivity of the
共Ni42Nb28Zr30兲94.8H5.2 alloy initially showed the similar
negative TCR behavior as the alloy without H, but suddenly
increased to second to third order 共Fig. 2兲 at 170 K, and then
continued with discrete variation down to 115 K. Subsequently, the resistance dropped abruptly on the extended line
of the cooling curve between 373 and 170 K, and then ascended once again as the temperature decreased. In the heating run, the resistivity decreased according to the same curve
as the cooling run, except for an increase between 59 and
170 K 共Fig. 1兲. We observed the similar abnormal resistivity
variations for 共Ni42Nb28Zr30兲92.6H8.4, 共Ni42Nb28Zr30兲90H10,
共Ni42Nb28Zr30兲87.4H12.6, and 共Ni42Nb28Zr30兲84.8H15.2, but not
for 共Ni42Nb28Zr30兲97.8H2.2, 共Ni42Nb28Zr30兲95.5H4.5, and
共Ni42Nb28Zr30兲78.0H22.0 共Fig. 1兲. Consequently, the abnormal
variations in the two runs occurred at restricted hydrogen
concentrations of 5.2– 15.2 at. % H and within the temperature range of 200– 6 K 共insert, Fig. 2兲. The negative TCR
increased linearly as the hydrogen content increased 共insert,
Fig. 1兲.
The abrupt increases noted in the two runs mirror the
metal-to-insulator transitions 共Mott transitions兲 of vanadium
and titanium oxides at the Neél temperature.14 However,
since the voltage showed negative sign and the voltage variation did not follow the Ohmic rule in the restricted temperature range, we observed the variation. The wave pattern and
power spectrum of the representative 共Ni42Nb28Zr30兲94.8H5.2
alloy are shown in Figs. 3共a兲 and 3共b兲, respectively, indicating an ac saw wave with a voltage oscillation of 560 kHz.
The
frequencies
共500– 560 kHz兲
obtained
for
Appl. Phys. Lett. 90, 203111 共2007兲
FIG. 4. 共Color兲 Hydrogen tunneling model 共a兲 for two tetrahedral clusters
and blocking oscillation circuit 共b兲. The solid circles represent Zr atoms
共purple兲, hydrogen atoms 共red兲, and vacancies 共yellow兲.
共Ni42Nb28Zr30兲92.6H8.4,
共Ni42Nb28Zr30兲88.9H11.1,
and
共Ni42Nb28Zr30兲87.4H12.6 are presented in Fig. 3共b兲. The desorbed hydrogen from specimens during dc operation could
not be measured by a quadrupole mass spectrometry. This
result places severe constraints on the possibility of a solid
electrode reaction. Thus it is clear that this abnormal behavior is a dc current-induced ac oscillation, which is associated
with the quantum mechanism of solute hydrogen. This oscillation is suggested to arise from sequential quantized charging of the sample.
Based on the present results, it is possible that the abnormal behavior of interest is a Coulomb oscillation that arises
from the tunneling of an individual proton charging and discharging the capacitance, thereby producing discrete voltage
jumps with second to third order of e / C in Ni–Nb–Zr–H
glassy alloys. In a single-electron tunneling oscillation, the
average frequency of the saw waves is assumed to be
1 GHz,2 provided that the tunneling current is 0.16 nA and
the barrier capacitance is less than 1 fF. If the oscillation is
derived from the tunneling of a proton, it is estimated as
being 543 kHz, taking into consideration the proton mass
共938.256 MeV兲, when the tunneling current is 0.16 nA. This
value is in accordance with the experimental value
共500– 560 kHz兲 关Fig. 3共b兲兴. From the static energy E
= 1836e / C for proton tunneling, we can estimate the capacitance of the vacancy barrier as being ⬃1 aF.
Assuming from the neutron scattering spectra that the
hydrogen atom environment available in hydrated ZrNi glass
is exclusively the four-coordination sites that are surrounded
in a tetrahedral pattern by four Zr atoms,15 we propose a
schematic representation of a microscopic junction between
the Zr-tetrahedral clusters in the Ni–Nb–Zr–H glassy alloy
关Fig. 4共a兲兴. In metallic glasses that consist of antinomic affinity Zr and antiaffinity Ni elements for hydrogen, an atomic
Zr–H-䊐-H–Zr array 关⬃0.9 nm 共Ref. 16兲兴 corresponds to a
single Coulomb blockade tunneling junction, where 䊐 is a
vacancy barrier with electrostatic capacitance C. The glassy
alloy is characterized by an assembly 共free volume兲 of such
vacancies, which are distributed homogeneously among the
clusters. The other constituent element, Ni, is an insulator for
proton conduction, since the Ni–H bonding distance is
longer. The tunneling junction representing a single element
of the array is characterized by a tunneling resistance Rt and
capacitance C in the equipment circuit shown in Fig. 4共b兲.
Thus, the glassy alloy of interest can be considered as an
assembly of low-capacitance, multiple-junction configura-
FIG. 3. 共Color兲 Wave pattern for voltage variation 共a兲 and power spectra 共b兲
for glassy alloys Ni42Nb28Zr30 with 5.2, 8.4, 11.1, and 12.6 at. % H. Insert:
Voltage variation with temperature and hydrogen content.
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203111-3
Appl. Phys. Lett. 90, 203111 共2007兲
Fukuhara et al.
tions. In other words, the cyclic oscillation in Fig. 3 would
be a result of proton resonance among the multiple junctions.
The cyclic oscillation in voltage noted during the cooling
process, which can be interpreted as a Coulomb oscillation,
did not occur until the temperature of the sample was reduced to the critical temperature, at which the electrostatic
charging energy of the vacancy exceeded the thermal energy
kT. The greater the reduction in vacancy size, the more the
electrostatic energy decreased, i.e., the transition shifts to
higher temperature. However, when the glassy alloy absorbed hydrogen under the condition of ⬎7.5 at. %, at which
point hydrogen fully occupied the four-coordination sites
that are surrounded in a tetrahedral arrangement by four Zr
atoms,16 the hydrogen was forced to penetrate into the vacancies and consequently, the tunneling disappeared. Thus,
the Coulomb oscillation of the proton requires an appropriate
ratio of Zr to hydrogen 共Zr:H atomic ratio of 4:1兲.
Cessation of oscillation may be explained by the phase
transition of the electrical circuit. Morimoto17 has reported
that an oscillatory-nonoscillatory transition of discontinuous
waves is induced in a blocking oscillation by connecting a
variable resistor R in parallel to the capacitor that decides the
frequency of the circuit. Therefore, we infer by analogy that
the oscillation ceases when R decreases relative to the circuit
resistance RC due to a decrease in tunneling resistance at low
temperature.
This interesting study provides new insight into the
transport mechanism. Further work is called for.
This work was supported by a Grant-In-Aid for Science
Research in a priority Area “Research and Development
Project on Advanced Metallic Glasses, Inorganic Materials
and Joining Technology” from the Ministry of Education,
Science, Sports and Culture, Japan, and by JSPS Asian
CORE Program.
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