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Japanese Journal of Applied
Physics
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REGULAR PAPERS
Neutron measurement during crushing of LiNbO3
crystals in D2 and H2 atmospheres
To cite this article: Masatoshi Fujii et al 2017 Jpn. J. Appl. Phys. 56 117301
- Neutron Emission from Fracture of
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Atmosphere
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Keisuke Sueki et al.
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Vladimir A Tsarev
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nuclear astrophysics
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View the article online for updates and enhancements.
This content was downloaded from IP address 128.119.168.112 on 24/10/2017 at 14:26
REGULAR PAPER
Japanese Journal of Applied Physics 56, 117301 (2017)
https://doi.org/10.7567/JJAP.56.117301
Neutron measurement during crushing of LiNbO3 crystals in D2 and H2 atmospheres
Masatoshi Fujii1*, Kazumasa Kobayashi2, Yasuyuki Taniuchi3, Kenta Takeuchi4, Michiaki Utsumi4,
Masami Chiba5, Toshiaki Shirakawa6, Tomoko Hashimoto7, and Fumio Shiraishi7
1
Faculty of Medicine, Shimane University, Izumo, Shimane 693-8501, Japan
Graduate School of Engineering, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
3
Graduate School of Science and Technology, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
4
School of Engineering, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
5
Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
6
School of Social Information Processing, Otsuma Women’s University, Tama, Tokyo 206-8540, Japan
7
Institute for Atomic Energy, Rikkyo University, Yokosuka, Kanagawa 240-0101, Japan
2
*E-mail: mstfujii@med.shimane-u.ac.jp
Received April 5, 2017; accepted August 9, 2017; published online October 23, 2017
A study of mechano-nuclear fusion during the crushing of dielectric crystals of LiNbO3 was carried out in three different atmospheres, D2 (101 kPa),
H2 (101 kPa), and vacuum (1 Pa). The number of neutrons emitted during the nuclear fusion reaction was counted in a low background-neutron
environment, 6.49 + 0.02 counts/h, using 16 3He neutron counters with a detection efficiency of 8.6%. The observed neutron counts (+σ) during
crushing in D2, H2, and vacuum were 6.39 + 0.24 counts/h (111 h), 6.87 + 0.20 counts/h (169 h), 5.92 + 0.26 counts/h (89 h), respectively. The
excess counts of neutrons were 0.47 + 0.35 counts/h (significance: 1.3σ) (D2) and 0.96 + 0.33 counts/h (significance: 2.9σ) (H2), assuming that
the count in vacuum was zero. From these results, the upper limits of neutron generation in D2 and H2 were 12.2 and 17.4 neutrons/h with a
confidence level of 95% (1.65σ). © 2017 The Japan Society of Applied Physics
1.
Introduction
It has been reported that a mechanical effect on deuterated
metals1–4) and piezoelectric materials5–9) gives rise to a d–d
nuclear reaction. In this reaction a 2.45 MeV neutron is generated together with a 3He nucleus. For the crushing process
for deuterated metals, e.g., LiD with Zr and deuterated
polypropylene in deuterium gas, neutron emission from the
d–d nuclear reaction has been reported by Lipson and coworkers1,3) Deryagin et al.,2) and Klyuev et al.4) They utilized
materials with high deuterium content to generate the fusion
reaction.
In contrast, we experimentally found a new phenomenon
of neutron emission in a fracturing process for LiNbO3 single
crystals, which are piezoelectric materials, in D2 atmosphere.5) Since then, we have studied the phenomenon under
different experimental conditions and also clarified this
phenomenon in inert gas, H2, atmosphere under the same
experimental conditions as for D2 atmosphere.6) We assumed
that the discharge process was induced by the high voltage in
D2 and H2 gases similarly. We found that neutrons were
generated in D2 but not in H2, where no d–d nuclear reaction
occurred. This means that false signals are not generated from
the discharged D2 or H2 gas caused by a high voltage that
originated from the LiNbO3 crystals in the crushing vessel.
We studied the neutron emission rate at various pressures of
D2 gas.7,8) Neutrons were generated also in D2 gas atmosphere at a pressure of 30 kPa or above at a rate of 108 ±
27 counts=h with a statistical significance of 4σ, but not at
18 kPa or below. This shows that the phenomenon needs D2
gas atmosphere at a certain pressure. We also studied the
dependence of the neutron emission rate on the amount of
LiNbO3 crystals in D2 atmosphere, and excess neutrons were
observed with a 97.1% confidence level.9) In addition we
examined this phenomenon in other piezoelectric materials
but no neutrons were observed.8)
Although we observed neutron generation, the generation
rate was too low to systematically fix the reaction process. To
reduce the background (BG) neutron count, we carried out
fracture experiments in a low-BG facility at The Nokogiriyama Underground Laboratory, The Institute for Cosmic-Ray
Research (ICRR), The University of Tokyo, at Futtsu city,
Chiba Prefecture; the Nokogiri facility was located at a
maximum depth of 100 m water equivalent and 30 m on
average.10) The BG-neutron level at the facility was not low
enough to analyze the fusion phenomenon precisely. In this
paper, we report the neutron emission rate of LiNbO3 crystals
fractured under different atmospheric conditions (D2 and H2
gases, and vacuum as an inert condition) at a facility with a
lower BG-neutron level than that of the Nokogiri facility, to
examine the previous experimental results.
2.
Experimental procedure
LiNbO3 crystals were fractured in a gas-tight vessel (stainless
steel SUS304) using a vibro-mill (ITOH VP-100).5,9) LiNbO3
crystal samples were prepared as 3 in. wafers, cut from a CZ
single-crystal rod having a 〈0114〉 growth direction, which
was manufactured by Sumitomo Metal Mining, Yamaju
Ceramics, and Koto Crystal. The 14-cm-diameter vessel
consisted of three cells (Fig. 1). The centers of the three cells
were positioned 3.25 cm away from the center of the vessel.
The diameter and the depth of each cell were 5 and 8 cm,
respectively. The cells were positioned in such a way that
the central angle among the cells was 120° from the center of
the vessel. The bottom of each cell was hemispheric with a
diameter of 5 cm. The total inner volume of the vessel was
422 cm3.
A steel ball 4 cm in diameter (264 g) was placed together
with 4 g (0.89 cm3; ρ = 4.46 g=cm3 11)) of the crystal into
each cell. The vessel was vibrated vertically at 50 Hz and
an amplitude of 0.8 mm, which was measured using an
LED displacement sensor (Omron Z4W-V25R), such that the
three steel balls jumped up and down in the cells, hitting the
ceiling and the bottom. The crystal was crushed into fine
granules with a diameter of 8 µm on average after 1000 s of
vibration.
117301-1
© 2017 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 56, 117301 (2017)
M. Fujii et al.
15000
CAMAC
16 CHANNEL
ADC
(b) BG
4000
COMPUTER
PREAMPLIFIER 16
PARAFFIN
MODERATOR
10000
Frequency
SHAPER
AMPLIFIER 16
Frequency
(a) source
2000
0
1000
3000
2000
Channel
4000
5000
0
1000
2000
3000
4000
Channel
3 He
COUNTER 16
VIBROMILL
Fig. 2. Pulse height distributions of (a) 252Cf source counts=h accumulated
over 90 min and (b) the BG over 28095 h. The peak position was set at
channel 1500 of the ADC.
LiNbO 3
DRIVER
Fig. 1. Schematic diagram of the experimental apparatus.
We measured the neutron emission rate utilizing LiNbO3
crystals in three different atmospheres, D2 (101 kPa), H2
(101 kPa), and vacuum (1 Pa). The sample wafers were
broken into pieces of about 1 cm2 area before putting them
into each cell. The steel balls were put together with the
crystal pieces into each cell. After the evacuation of the
vessel to less than 1 Pa, the vessel was charged with D2 or H2
gas at a pressure of 101 kPa, or left in vacuum, which is the
control condition. Each fracture experiment, i.e., a fracture
run, continued for 1 h with a fresh sample and fresh gas.
Several fracture runs were carried out in one day. To reduce
the fluctuation of environmental conditions depending on
each data-taking day, we alternately changed the atmospheric
condition within one day of experiments: e.g., D2 → H2 →
vacuum (control) → D2 → H2.
Neutrons were detected using 16 3He proportional counters
(Reuter-Stokes RS-P4-0806-207) with a diameter of 2.54 cm
and an effective length of 15.09 cm at a pressure of 4 atm.
The 16 counters with low noise levels were carefully selected
from 20 counters. They were inserted in a cylindrical paraffin
block with an outer diameter of 46 cm, an inner diameter of
17 cm, and a height of 28 cm (Fig. 1). The paraffin block was
used for thermalizing neutrons to increase detection efficiency. The vessel was set at the center of the paraffin block.
The signals from the 16 3He counters were processed
independently using standard Nim and Camac systems.9,12)
High voltages were supplied to the counters by a 16-channel
high-voltage power supply (HOSHIN HE-1449). Signal
pulses were amplified by 16 charge-sensitive preamprefiers
(Ortec 142PC) and shaped by 4 Nim quad-shaper amplifiers
(HOSHIN N012). The pulse height of each signal was
independently digitized using a Camac analog-to-digital
converter (ADC) in the range between channel 0 and channel
4095 (16 ch, 12 bit ADC for pulse height; HOSHIN C008).
A Nim clock generator (HOSHIN N010) supplied 100 Hz
pulses to a Camac Scalar (KAIZU 3122) for measuring event
intervals. The data of the ADC and scalar was read out by
a personal computer (PC). To generate a trigger signal to
transfer the data into the PC, we utilized a function provided
in the ADC. All the input pulse heights were summed and
the summed pulse height was discriminated at a threshold
voltage. When the summed pulse height exceeded the
threshold, the analogue-to-digital conversion started and the
data of the ADC and the Camac Scalar were transferred to the
PC. The discrimination threshold level was tuned to reject
electrical noises at channel 100 of the digitized value.
The pulse height was calibrated using a 252Cf neutron
source. The full energy deposited to the 3He gas counter by
the thermalized neutrons is 764 keV. Each counter was tuned
to the full energy deposit at channel 1500 of the ADC by the
high-voltage power supply to the counter [Fig. 2(a)]. Since
partial energy of the thermalized neutrons is deposited to the
wall of the counter, signals were distributed in the lower
channels. Zero energy deposit was at about channel 60.
The event data, which included pulse height, scalar count of
each counter set, and event time, were recorded in the PC.
The detection efficiency of neutrons was 8.6%, as measured by the 252Cf source, which was set at the same position
as the vessel, that is, the center of the paraffin block. The
detection efficiency was also verified by a Monte-Carlo
simulation of the neutron transport code of MCNP.8,13)
The mechano-fusion experiment was carried out in a lowBG underground facility of Rikkyo University in Yokosuka
city, Kanagawa Prefecture, to reduce natural BG. The facility
is located at a depth of 80 m water equivalent at least. The
previous experimental location at the Nokogiri facility was
at a depth of 30 m on average.10) Furthermore, to prevent
the mixing of electric noise induced by electric leakage at
the high-voltage connectors of the counters with the signal,
we provided dry air to the counters and kept the condition dry
at less than 50% relative humidity. To check the stability of
environmental conditions, we monitored and automatically
recorded humidity, temperature, and atmospheric pressure at
the counters and electronics every hour.
Figure 2(b) shows the pulse height distribution of a
background measurement accumulated over 28095 h, composed of BG-neutron signals and a base noise independent
117301-2
© 2017 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 56, 117301 (2017)
M. Fujii et al.
5000
15000
Frequency
Poisson
10000
3000
Count
Frequency
4000
2000
5000
1000
0
0
2
4
6
8
0
10 12 14 16 18 20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Counter Number
Counts/h
Frequency
70
D2
35
0
Frequency
of pulse height. The shape and peak position of the distribution coincide with those of the thermalized neutrons from
252
Cf [Fig. 2(a)].
To reduce the base noise level in the BG counts, noise
events were discarded on the basis of software cut criteria.
We selected the events that were generated by the signals
between channel 600 and channel 1599. These signals were
considered as neutron signals. Usually one event is induced
by one signal from a counter. Sometimes, however, (1) all
the counters recorded over channel 100, (2) at least one
counter recorded overflow (>channel 4095) in ADC, (3) two
triggers occurred sequentially within 1 s, or (4) double events
between channel 600 and channel 1599 occurred in one
trigger within 100 ms. We discarded these events. After the
software cut, the base noise in a pulse height spectrum was
diminished in the pulse height distribution.
We also checked the stability of the detection system as
follows. We measured BG-neutrons under the same experimental conditions14) as in the fracture experiment at 1 h
intervals and without vibration at 1 h intervals alternately; this
was called a BG run. Moreover, to check seasonal variation,
we continued the BG run between the one-day experiments.
The vessel contained the fractured sample at the prescribed
pressure of D2 or H2 or in a vacuum. The BG-neutron count
after the software cut was 182208 accumulated over 28095 h.
Thus, the BG-neutron counting rate was 6.49 ± 0.02
counts=h. Compared with the BG-neutron count of 15.69 ±
0.12 counts=h at the Nokogiri facility where we had carried
out our previous studies, the BG-neutron count at the Rikkyo
facility is less than half that at the Nokogiri facility. The
Rikkyo facility is an appropriate place to distinguish the
excess neutron counts from BG-neutron counts.
Figure 3 shows the frequency distribution of the BGneutron counting rate with vibration, accompanied by a
Poisson distribution of a mean value of 6.49. The frequency
distribution is consistent with the Poisson distribution and the
confidence level of the consistency is 75%, as determined by
the chi-squared test. Therefore, statistically, the BG events occurred independently during the fracture experimental period.
Figure 4 shows BG-neutron counts of each of the 16
counters; the total count of all counters is 182208 after the
software cut. The average counting ratio is 0.0625 (= 1=16)
Fig. 4. Total BG count for each counter during 28095 h after the software
cut (BG-neutron). The average counts for one counter is 11388 (dashed line).
H2
45
0
Frequency
Fig. 3. Frequency distribution of the BG counts=h for 28095 h after the
software cut (BG-neutron). The average is 6.49 ± 0.02 counts=h. Bars are the
observed frequency and dots are the Poisson distribution of the mean value at
6.49. From the chi-squared test ( χ 2=ν = 19.9=17), the confidence level of the
consistency is 75%.
Vacuum
25
0
1000
2000
Channel
3000
4000
Fig. 5. Pulse height distribution in D2 (81 h) and H2 (112 h) atmospheres,
and vacuum (65 h) before the software cut.
and the average total count of one counter is 11388. The
deviation of the total count of each counter from the average
count exceeds the standard deviation. Since each counter has
a different efficiency and was placed into a different position
of the paraffin moderator, which resulted in a different ratio
of thermal neutron injection, the average count exceeding
the standard deviation was probably caused by the counting
efficiency for each counter. Each counter worked independently and maintained an almost homogeneous detection
efficiency during the measurement.
3.
Results
We carried out the mechano-nuclear reaction experiment
of the crushed piezoelectric material at the underground
facility with a low BG-neutron. The pulse height distributions
of the fracture runs in D2 (81 h), H2 (112 h), and vacuum (65 h)
are shown in Fig. 5. The neutron count rates (±σ) after
the software cut in D2 (81 h), H2 (112 h), and vacuum (65 h)
were 6.25 ± 0.28, 6.77 ± 0.25, and 5.95 ± 0.30 counts=h,
respectively.
117301-3
© 2017 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 56, 117301 (2017)
M. Fujii et al.
Table I. Excess count rates of neutrons in D2 and H2 were calculated using
the neutron count rates in vacuum, in which no neutron emission was
assumed. The statistical deviation and significance in units of σ are listed.
The number of generated neutrons was calculated from the detection
efficiency of the system, 8.6%. The upper limits for the excess neutrons per
hour at 95% confidence level (1.65σ) are also shown.
Table II. Excess count rates of neutrons in D2 and H2 were calculated
using the neutron count rates subtracted from the count rate in vacuum, in
which no neutron emission was assumed. The statistical deviation and significance in units of σ are listed. The number of generated neutrons was calculated from the detection efficiency of the system, 8.6%. The upper limits for
the excess neutrons per hour at 95% confidence level (1.65σ) are also shown.
Atmosphere (duration)
D2 (81 h)
Excess counts=h
Significance=σ
Generated neutrons=h
Upper limit (95% CL) of generated neutrons=h
Atmosphere (duration)
D2 (111 h)
H2 (112 h)
0.30 ± 0.41 0.83 ± 0.39
0.7
2.1
3.5 ± 4.8
11.3
9.6 ± 4.5
17.1
Excess counts=h
Significance=σ
The count rates of excess neutrons in D2 and H2 are
calculated as follows: the neutron count rate in gas atmosphere is subtracted from that in vacuum, which is assumed
to be the BG-neutron rate for the following reasons.14,15)
For low count rate measurement, extreme care is taken not
to change the conditions of the detection system and its
environment. Thus, we use the same chamber that contains
new crystals but in vacuum, i.e., no gases (D2 or H2), as a
control experiment. The atmosphere change from D2 or H2
to vacuum is the smallest change between the neutron
generation condition and the control condition; there is no
neutron generation in vacuum. Moreover, we carried out
measurements in D2, H2, and vacuum within the same day to
eliminate fluctuations of environmental conditions, temperature, humidity, and atmospheric pressure, which cause the
variations of detector efficiency and electric noise rate of
electronics. Thus, we adopt the neutron rate in vacuum as
the BG-neutron rate. The excess rates are 0.30 ± 0.41 (D2)
and 0.83 ± 0.39 counts=h (H2), as listed in Table I with other
calculated results. The significance levels of the excess in
D2 and H2 are 0.7σ and 2.1σ, respectively. The number
of generated neutrons is calculated from the detection
efficiency of the system, 8.6%. The numbers of generated
neutrons are 3.5 ± 4.8 (D2) and 9.6 ± 4.5 neutrons=h (H2).
Therefore, the upper limits of the number of generated
neutrons at the 95% (1.65σ) confidence level for D2 and H2
became 11.3 (= 3.5 + 7.8) and 17.1 (= 9.6 + 7.5) neutrons=h,
respectively.
To increase the statistical significance of the events, we
added some vibration runs of the BG run, which continued
for approximately 1 month, to the fracture runs. We used
the first three runs since the crystal was still fresh and the
atmosphere maintained. As a result, the counting duration
of the fracture process increased to 30, 57, and 24 h in D2,
H2, and vacuum, respectively. The total neutron counts in
D2 (111 h), H2 (169 h), and vacuum (89 h) were 6.39 ± 0.24,
6.87 ± 0.20, and 5.92 ± 0.26 counts=h, respectively. The
standard deviation decreased by 0.04 for D2, 0.05 for H2,
and 0.04 for vacuum. Adding the neutron counts of the first
three vibration runs of the BG run to those of the fracture
runs improved the statistical significance of the excess
counts.
As listed in Table II, the counts of excess generated
neutrons were 0.47 ± 0.35 (D2) and 0.96 ± 0.33 counts=h
(H2), assuming that the count in vacuum was zero. The
significance levels of the excess neutrons in D2 and H2
H2 (169 h)
0.47 ± 0.35 0.96 ± 0.33
Generated neutrons=h
Upper limit (95% CL) of generated neutrons=h
1.3
2.9
5.4 ± 4.1
12.2
11.1 ± 3.8
17.4
were 1.3 and 2.9σ, respectively. The numbers of generated
neutrons were 5.4 ± 4.1 (D2) and 11.1 ± 3.8 neutrons=h (H2)
calculated from the detection efficiency of 8.6%. Finally,
from these values, the upper limit of the number of generated
neutrons at the 95% (1.65σ) confidence level became 12.2
(= 5.4 + 6.8) (D2) and 17.4 (= 11.1 + 6.3) neutrons=h (H2).
4.
Discussion
Neutron generation in D2 atmosphere
The hypothetical process of this phenomenon has been conjectured to be as follows. The high voltage generated across
the LiNbO3 crystal by the crushing force accelerates ions that
induce the d–d nuclear reaction. Deuterium atoms are ionized
by a mechanochemical process owing to the high electric
field at the surface,16) and the deuterons are accelerated by the
field through a vacuum channel, which is created by the
fracture of the crystal. A similar acceleration phenomenon
was observed by Dickinson et al.,17) wherein charged
particles were emitted from the deformation and fracture of
a polycrystalline Ti metal and deuterated Ti. Collision occurs
between an accelerated deuteron and a deuterium atom,
which leads to a nuclear reaction. We postulate this model of
the generation of a neutron as
4.1
d þ d ! 3 He ð0:82 MeVÞ þ n ð2:45 MeVÞ:
ð1Þ
Aside from the mechano-nuclear reaction, Taniuchi et al.18)
and Taira19) carried out an experiment on inertial electrostatic
confinement fusion.20,21) They observed neutron emission
rates of 102–105 s−1 at low accelerating voltages of 10–30 kV
applied by a DC-power supply between a spherical electrode
of 2 cm diameter and a cylindrical chamber of 20 cm diameter
under D2 atmosphere at 0.1–1 Pa.
4.1.1 Estimation of generated voltage. We calculate
the reaction rate using the mechanochemical process.9) First,
we estimate the voltage generated across a LiNbO3 crystal by
the pressure generated upon hitting the crystal with a steel
ball. The crystal has a high piezoelectric strain constant,
d15 = 6.92 × 10−11 C=N, and a relatively low dielectric
constant, κ(T11) = 85.2 × εo C=(V·m). These result in a high
generated voltage. When a pressure X is exerted on an area of
the crystal,22) an electric field, E = (Xd15)=κ(T11), is generated
between the two ends of the crystal. If the pressure is
X = 0.02 N=µm2 on a crystal of 5 µm thickness, the generated
voltage is V = 10 kV. Eventually, the gravitational force of
the 264 g steel ball on a 5 × 5 µm2 area generates pressure
X = 0.1 N=µm2, yielding 50 kV.
117301-4
© 2017 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 56, 117301 (2017)
M. Fujii et al.
10-2
R ¼ Nc f Nt d­d ¼ 6:3 neutrons=h:
ð2Þ
This rate may be detectable in a lower BG-neutron
environment.
4.2 Neutron generation in H2 atmosphere
Although a similar acceleration process in D2 atmosphere
probably occurs in H2, it is difficult for the p–p nuclear reaction to proceed under normal conditions. Thus, we searched
for other hypothetical reaction pathways involving the proton
under moderate conditions.
4.2.1 Consideration of one-step reaction. We use the
LiNbO3 crystal as a minute acceleration apparatus, which
includes a large number of atoms, Li, Nb, and O, compared
with the atmospheric atom, H, in the vessel. We considered
the possibility of a reaction including the participation of the
7
Li atom, and examined a nuclear reaction that generates a
neutron;
7
7
p þ Li ! Be þ n:
ð3Þ
This reaction has a large σp-Li value, 0.3 b (∼ 2 MeV),24)
but has a relatively high threshold energy of 1.64 MeV.25)
In our crushing system using the piezoelectric acceleration
mechanism, the incident protons do not have enough energy
to overcome the threshold energy. Thus, this reaction
pathway does not contribute to neutron generation in the
crushing process in H2 atmosphere.
4.2.2 Hypothesis of two-step reaction. There are no
direct nuclear reaction pathways leasing to the generation
of neutrons between p and other atoms. Thus, we considered
a successive two-step reaction. In the first step, α particles,
which have enough energy to induce the second step,
are emitted, and the particles collide with the second
target atom. The second step occurs and neutrons are
generated.
We present the following as the first step:26,27)
p þ 7 Li ! 2 ð8:62 MeVÞ;
Q ¼ 17:25 MeV;
p-Li ¼ 4:3 108 1:4 104 b ð25 keV­106 MeVÞ: ð4Þ
The second step is
þ 7 Li ! 10 B þ n
ðEth ¼ 4:38 MeVÞ:
ð5Þ
4He
scenario. Deuterons ionized by charged particles emitted
from the fractured piezoelectric material were accelerated
inside a crack before vacuum degradation. Then, during the
passing of accelerated deuterons through a 101 kPa deuterium
atmosphere of a target region, the d–d nuclear reaction
occurs.9) The crushing force turns the crystal of 2.67 cm3
(= 0.89 cm3 × 3) into powder. If each grain volume is set at
5 × 5 × 5 µm3, then the number of grains is Nc = 2.1 × 1010.
The cross section of the d–d nuclear reaction is σd–d = 20 µb
at an average collision energy of 10 keV.23) The thickness
of the target region is assumed to be 5 µm; thus, the number
of included deuterons Nt is 2.7 × 1016 deuterons=cm2 at
101 kPa. The accelerated deuterons pass through the target
region without substantial energy loss during the ionization process. If a deuteron is accelerated at f = 0.15 Hz
by each grain of the crystal, the reaction rate is calculated
to be
Production Rate /s-1
4.1.2 Estimation of neutron generation rate for D2
system. We postulate the following d–d nuclear reaction
10-3
10-4
10-5
10-6
20
25
30
35
40
45
50
Proton energy /keV
Fig. 6. α Particle production rate from 7Li (p,α) α reaction.
The second step has a large σα-Li value (0.1 b at 6 MeV), but
has a large threshold energy of 4.38 MeV.24,28,29) The first
step generates α particles, each with an energy of 8.62 MeV.
The particles have enough energy to overcome the threshold
of the second step (5). It is possible for the α particles emitted
in the first step (4) to generate neutrons that collide with 7Li
atoms.
Next, we estimate the generation rate of neutrons by the
two-step reaction. The emission rate of α particles from the
first step (4) can be calculated using
Z E0
R ¼ 2Nc f Nt p-Li ðEÞðdE=dxÞ1 dE;
ð6Þ
0
where 2Nc × f is the number of incident protons per unit time,
Nt is the number density of the target, and dE=dx is the
stopping power of incident particles. A lower energy region
of the reaction cross section in Eq. (4), σp-Li(E ), is calculated
using an S-factor
SðEcm Þ ¼ 65ð1 þ 1:82 103 Ecm
þ 2:51 106 E2cm Þ ðkeVbÞ;
ð7Þ
p-Li ðEcm Þ ¼ SðEcm Þ=Ecm expð2Þ;
ð8Þ
where Ecm is the center of mass energy and 2 ¼ 88:12=
26)
E1=2
The fitted dE=dx of the proton in the LiNbO3 crystal
cm .
with the SRIM code30) is
dE=dx ð7:531 104 E 0:4114 Þ ðkeV=cmÞ:
ð9Þ
We calculate the emission rate of α particles using the
same parameters as those in D2: the rate of incident proton
particles, Nc × f = 2.1 × 1010 × 0.15 s−1, and the number
density of the target 7Li atom, Nt = 1.684 × 1022 cm−3, which
was calculated from the density of LiNbO3, ρ = 4.46 g cm−3,
and the isotope ratio of 7Li, (92.5%). By substituting the
values of Nc × f and Nt, and the results of Eqs. (8) and (9)
into Eq. (6), we obtain the emission rate of α particles
(Fig. 6).
The emission rate of neutrons from the second step (5) can
be calculated using
Z E0 ¼8:625MeV
Rn ¼ N Nt -Li ðEÞðdE=dxÞ1 dE; ð10Þ
Eth ¼4:38MeV
where Nα is the number of incident α particles per unit
time and Nt is the number density of the target 7Li atom.
The reaction cross section at a lower energy region for
Eq. (5), σα-Li(E ), is calculated using the following S-factor:
117301-5
© 2017 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 56, 117301 (2017)
M. Fujii et al.
n Production rate /s-1
10-7
for Scientific Research from the Ministry of Education,
Culture, Sports, Science and Technology Japan, and
Funds of Tokutei Kenkyuhi at Tokyo Metropolitan
University.
10-8
10-9
10-10
10-11
20
25
30
35
40
45
50
Proton energy /keV
Fig. 7. Neutron generation rate from the 7Li (p,α) α reaction succeeding
the 7Li (α,n)10B reaction.
SðEcm Þ ¼ 5:15 10ðEcm Þ5 1:0 103 ðEcm Þ4
þ 8:39 103 ðEcm Þ3 3:31 104 ðEcm Þ2
þ 6:42 104 ðEcm Þ 4:92 104 ðMeVbÞ
ð2:89 Ecm 5:22 MeVÞ; ð11Þ
which was obtained by fitting to the data.29) The fitted dE=dx
of α in the LiNbO3 crystal with the SRIM code30) is
dE=dx ð1:493 103 E 0:662 Þ ðMeV=cmÞ
ð4:00 E 8:625 MeVÞ:
ð12Þ
We calculate the emission rate of neutrons using the same
parameters as those in D2. The rate Nα of incident α particles,
which are isotropically emitted from the LiNbO3 grains with an
energy of 8.625 MeV (Fig. 6). By substituting Nt (= 1.684 ×
1022 cm−3), σα-Li(E) of Eqs. (8) and (11), and dE=dx of
Eq. (12) into Eq. (10), we obtain the dependence of the production rate of neutrons on incident proton energy (Fig. 7).
Finally, we obtain the neutron generation rate for the twostep reaction as 1.71 × 10−2=h. Although the second step has
a large σα-Li(E), the total emission rate of neutrons is small,
similar to σp-Li(E) of the first step.
5.
Conclusions
We examined the neutron emission from LiNbO3 single
crystals crushed in different atmospheres (D2 and H2
gases, and vacuum) at the lower BG-neutron facility of
Rikkyo University. The numbers of generated neutrons were
5.4 ± 4.1 (significance: 1.3σ) (D2) and 11.1 ± 3.8 neutrons=h
(significance: 2.9σ) (H2). We observed no statistically significant neutron generation in either D2 or H2 atmosphere. The
upper limits of the neutron generation rate in D2 and H2
atmospheres with a 95% (1.65σ) confidence level were 12.2
and 17.4 neutrons=h, respectively.
Acknowledgments
This work was partially supported by a Grant-in-Aid
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