Transient Crystal Structure of Oscillating Quartz

Abstract

Piezoelectric quartz oscillators are widely used to provide a stable clock signal for watches and other electric circuits. The electrically induced mechanical vibration of quartz will be caused by ionic displacements of cationic Si and anionic O sublattices against each other. However, the transient and small ionic displacements during the mechanical vibration cannot be observed by usual X-ray structure analysis. The electrically induced mechanical vibration of quartz is resonantly amplified under an alternating electric field with the resonant frequency. We have revealed the amplified lattice strain and ionic displacements in a resonantly vibrating quartz crystal under an alternating electric field by time-resolved X-ray diffraction. The details of the experiment and application of the technique to other piezoelectric oscillators are introduced in this chapter.

1. Introduction

Inorganic crystals that exhibit piezoelectricity are currently used in a wide range of industrial applications, such as oscillators, sensors, transducers, and actuators. Piezoelectricity is the property of crystals that generates an electric polarization P_i = Σ_jd_ijσ_j (i = 1–3) proportional to an applied stress σ_j (j = 1–6). d_ij are the piezoelectric constants that indicate the degree of piezoelectricity. Crystals belonging to 20 of 32 crystal point groups show piezoelectricity. Piezoelectric crystals exhibit also inverse piezoelectricity that generates a strain s_j = Σ_id_ijE_i proportional to an applied electric field E_i.

The most famous and industrially important piezoelectric crystal is quartz (α-SiO₂). Quartz is a naturally abundant mineral and can be synthesized artificially by the hydrothermal method. Quartz oscillates mechanically and electrically at a stable frequency, making it widely used in oscillators to provide reference signals for various devices such as quartz watches. However, quartz has the disadvantage that it cannot be used in high-temperature environments because it undergoes a phase transition from the low-temperature α phase to the high-temperature β phase at 573°C.

The authors have been investigating the mechanism of piezoelectricity of quartz and other piezoelectric crystals and synthesizing new piezoelectric crystals such as langasite-type crystals to develop crystals with high functional piezoelectricity superior to quartz crystals. In this chapter, we introduce transient crystal structures of quartz and langasite-type crystals oscillating under an alternating electric field measured by synchrotron X-ray diffraction [1, 2, 3]. Since inverse piezoelectricity is caused by atomic displacements under electric field, measurement of atomic displacements under an electric field is essential to understand the mechanism of piezoelectricity.

Crystal structure analysis based on X-ray diffraction is a powerful tool to measure atomic displacements in crystals, but highly accurate experiments and analysis are required to measure atomic displacements under electric fields. For example, in the case of a quartz crystal with the thickness of 0.1 mm, when a 1 kV potential difference (10 MV/m in an electric field) is applied between the surfaces, the change in the Si−O bond distance (~0.16 nm = 1.6 Å) is estimated to be only about 10⁻⁶ nm from its piezoelectric constants. This value is two orders of magnitude less than the standard deviations of bond distances (~10⁻⁴ nm) determined by conventional X-ray crystal structure analysis.

2. Time-resolved X-ray diffraction under alternating electric field

In order to measure small atomic displacements in piezoelectric crystals under an electric field, the authors have developed a new method for structure analysis of piezoelectric crystals that utilizes resonance under an alternating electric field [1]. Piezoelectric crystals vibrate mechanically and electrically at a certain natural frequency when an instantaneous stress or electric field is applied. For example, the natural frequency of a common quartz oscillator used in industry is 32,768 (2¹⁵) Hz. When an AC electric field with a frequency equal to this natural frequency is applied, the piezoelectric crystal resonates, producing mechanical and electrical vibrations with a particularly large amplitude. We hypothesized that the resonance under an AC electric field could amplify atomic displacements in piezoelectric crystals to a magnitude that could be measured by X-ray crystal structure analysis. The magnitude of the amplification effect in resonance depends on the quality factor (Q-value) of the crystal defined by 2π[(energy stored in the system)/(energy lost from the system in one period of vibration)]. The larger the Q-value, the smaller the energy dissipation and the greater the amplification effect. The Q-value of piezoelectric crystals used in resonators is particularly high, exceeding 10⁶ for quartz crystals.

Even if the atomic displacements involved in piezoelectricity can be greatly amplified by resonance under an alternating electric field, it is actually impossible to measure them using conventional X-ray diffraction. Conventional X-ray diffraction measures X-ray diffraction images during X-ray irradiation for several seconds to several minutes while the crystal is rotating, so it is impossible to measure instantaneous X-ray diffraction images of piezoelectric crystals vibrating at frequencies from kHz to MHz. Synchrotron radiation (SR) X-rays with high brilliance and short pulse duration are useful for the measurement of instantaneous X-ray diffraction images. SR is an electromagnetic wave emitted tangentially to the trajectory of an electron bunch accelerated to nearly the speed of light when the trajectory is bent by a magnetic field. We have been conducting SR time-resolved X-ray diffraction experiments under an AC electric field at SPring-8, the large SR facility (Hyogo, Japan), to measure transient atomic displacements in piezoelectric crystals resonating under an AC electric field. The shortest pulse duration is about 50 ps. By repeatedly irradiating a piezoelectric crystal resonating under an AC electric field with highly brilliant and short pulse X-rays synchronized with the AC electric field, instantaneous x-ray diffraction images when the atomic displacements reach the maximum can be measured with high accuracy (Figure 1).

Figure 1.

Schematic of time-resolved X-ray diffraction under AC electric field.

3. Transient atomic displacements in quartz oscillator

Transient atomic displacements in a quartz oscillator were successfully measured by the SR time-resolved X-ray diffraction under an AC electric field [1]. Quartz crystal belongs to the trigonal crystal system with the point group 32. There are two types of crystal polymorphs in quartz: right and left quartz, which are enantiomorphs of each other. The industrially used quartz crystal is a right crystal with the space group P3₂21. The crystal structure of the right quartz crystal is shown in Figure 2a. The crystal structure of quartz consists of corner shared SiO₄ tetrahedra with the Si−O bond distance of 1.61 Å, the O−Si−O bond angle of 109 degrees, and the Si−O−Si bond angle of 143 degrees. The direction along the twofold axis is called the X-axis, the direction perpendicular to the twofold and threefold axes is called the Y-axis, and the direction along the threefold axis is called the Z-axis. The X, Y, and Z-axes correspond to the [100], [120], and [001] crystal band axes of the primitive trigonal lattice, respectively. The nonzero piezoelectric constants of the right quartz are d₁₁ = −d₁₂ = −d₂₆/2 = −2.31 pC∙N⁻¹, and d₁₄ = −d₂₅ = −0.727 pC∙N⁻¹ [4]. The right quartz and left are piezoelectrically distorted under the electric field E₁ along the X-axis and E₂ along the Y-axis, but not under the electric field E₃ along the Z-axis.

Figure 2.

(a) Crystal structure of quartz viewed along the twofold axis (square box is the trigonal unit cell), and (b) schematic of AT-cut quartz oscillator.

A commercially available AT-cut quartz oscillator with an oscillation frequency of 30 MHz was used as the sample for the measurement. AT-cut oscillators are plate-shaped crystal (Figure 2b) cut along the plane including the X-axis, which is perpendicular to the direction tilted from the Y-axis to the Z-axis by δ = 35 degrees. It is widely used in industry because of its small temperature variation of oscillation frequency near room temperature. When no electric field is applied, the X, Y, and Z-axes are orthogonal to each other, but when an electric field E is applied along the direction perpendicular to the AT-cut plane, the shear strain given by s₅ = d₂₅E₂ and s₆ = d₂₆E₂ causes a distortion of the angle between the X and Z-axes (β angle) and angle between the X and Y-axes (γ angle) from 90 degrees (Figure 2b). Here, E₂ = Ecosδ. The angle between the Y and Z-axes (α angle) is not distorted under the electric field. The oscillation frequency of an AT-cut oscillator f₀ is given by f₀ = 1664/h (MHz) where h (μm) is the thickness of the crystal. To reduce X-ray absorption and extinction effects, a thin and high frequency AT-cut quartz oscillator with h = 55 μm (f₀ = 30 MHz) was used as a sample.

X-ray diffraction experiments were performed at the SPring-8 beamline BL02B1 [5] using X-rays with a wavelength of 0.4 Å. A large cylindrical curved imaging plate was used as the X-ray detector. First, measurements under a DC electric field were performed. Piezoelectric distortions of β and γ angles from 90 degrees under a DC electric field of E = 36 MV∙m⁻¹ (2.0 kV in potential difference) were −0.002(2) and −0.007(3) degrees, respectively. These values are consistent with the values of −0.001 and −0.008 degrees calculated from the piezoelectric constants. Crystal structures determined from more than 4000 Bragg reflection intensities measured under DC electric fields of E = +36 and −36 MV∙m⁻¹ were compared. However, no differences in the bond distances and angles exceeding their standard deviations were observed.

Time-resolved X-ray diffraction of a resonantly vibrating AT-cut quartz oscillator (Figure 1) was performed by applying a sinusoidal AC electric field with a frequency of 30 MHz and an electric field amplitude of 0.18 MV∙m⁻¹ to the sample. Resonance of the sample was confirmed by detecting the current flowing in the circuit with a current probe and displaying it on an oscilloscope. The resonant sample was irradiated with pulsed X-rays with a pulse duration of ~50 ps at a repetition rate of 26 kHz using an X-ray chopper [6]. In order to synchronize the oscillation of the sample and the pulsed X-rays, the ratio of the resonance frequency of the sample to the repetition frequency of the X-rays must be an exact integer ratio. However, both of the resonance frequency of the sample and the repetition frequency of the X-rays cannot be tuned freely. The authors have synchronized the resonance of the sample with pulsed X-rays by modulating the 30 MHz AC electric field at 26 kHz. This method enables instantaneous measurement of X-ray diffraction images of a resonant sample with a time resolution of less than 1 ns. The period of the resonant sample is 33 ns = 1/30 MHz. By varying the delay time Δt of the alternating electric field to the pulsed X-rays from 0 to 33 ns, the time variation in one period of the X-ray diffraction images of the resonant sample was measured.

Figure 3a shows time dependences of deviations of α, β, and γ lattice angles from 90 degrees (Δα, Δβ, and Δγ) obtained by the least-squares method from the positions of several hundred Bragg reflections measured on the X-ray diffraction images. It can be seen that, during the resonance, α angle remains almost unchanged with time, while β and γ angles oscillate sinusoidally and significantly. The amplitudes of the Δβ and Δγoscillations are 0.10 and 0.15 degrees, respectively. These values are the several tens of times larger than the aforementioned values of −0.002(2) and −0.007(3) degrees under the DC electric field of 36 MV∙m⁻¹. Δβ and Δγ under a DC electric field of 0.18 MV∙m⁻¹ calculated from the piezoelectric constants are −1 × 10⁻⁵ and −4 × 10⁻⁵ degrees, respectively. Thus, the resonance under an AC electric field amplifies Δβ and Δγ by a factor of 1 × 10⁴ and 4 × 10³, respectively.

Figure 3.

(a) Time variation of Δα, Δβ, and Δγ, and (b) Si−O−Si bond angles of AT-cut quartz crystal under AC electric field.

The crystal structures at the delay times Δt = 9 and 25 ns when Δβ and Δγ reach the negative and positive maxima, respectively, were obtained by the least-squares method from more than 3000 Bragg reflection intensities. Comparison of the two crystal structures shows that the Si−O bond distances and O−Si−O bond angles in the SiO₄ tetrahedra do not differ by more than their standard deviations (0.002 Å for the bond distances and 0.1 degrees for the bond angles). However, a clear difference was observed in the Si−O−Si bond angles between the SiO₄ tetrahedra. The triclinic crystal structure of the quartz crystal distorted under an electric field consists of three independent SiO₄ tetrahedra with six independent oxygen atoms (O(1)~O(6)). The six independent Si−O−Si bond angles at Δt = 9 and 25 ns are shown in Figure 3b. The abscissa is the number of independent oxygen atoms 1~6. Among O(1)~O(6), large deformations were observed in the Si−O−Si bond angles, especially around O(2) and O(3).

The large deformation of the Si−O−Si bond angles around O(2) and O(3) can be understood from the displacements of the anionic O atoms under the electric field and the arrangements of the Si−O−Si bonds relative to the electric field. The Si−O bonds have both covalent and ionic characters. The electron density distribution was calculated from the measured X-ray diffraction intensities to estimate the numbers of electrons of each atom. The charge deviations from neutral were +2.8e for Si and −1.4e for O (e is the elementary charge). The Si and O atoms, which are positively and negatively charged, respectively, are expected to be displaced in opposite directions upon application of an electric field. However, each Si atom is covalently bonded to four O atoms in tetrahedral coordination, which makes it extremely difficult to displace the Si atoms by an electric field. O atoms are subject to a large repulsive force due to the Si−O covalent bonds when the displacement direction is parallel to the Si−O−Si plane, but can be displaced relatively easily when the displacement direction is perpendicular to the Si−O−Si plane. Comparing the angles between the electric field and the Si−O−Si planes of O(1)~O(6), O(2), and O(3) with the angles about 66 degrees are the closest to perpendicular. The Si−O−Si bond angles centered on O(2) and O(3) deform with the oxygen displacements in the direction perpendicular to the Si−O−Si planes. The relationship between the crystal structure, electric field, and atomic displacements of O(2) and O(3) is shown in Figure 4.

Figure 4.

Oxygen atomic displacements in AT-cut quartz crystal viewed along the twofold axis under electric field E perpendicular to the crystal plane.

As shown above, the piezoelectric distortion of a quartz crystal under an electric field is caused by the displacement of oxygen ions in the direction perpendicular to the Si−O−Si plane due to the electric field and the accompanying deformation of the Si−O−Si bond angles. Mechanical and electrical vibrations with high Q-values of quartz crystals are caused by the restoring force acting on the Si−O−Si bond angles, which causes a harmonic vibration of the oxygen ions with little damping. The combination of resonant vibration under an alternating electric field and SR time-resolved X-ray diffraction has revealed the transient atomic displacements and mechanism of piezoelectricity in quartz. Using this experimental technique, the authors next performed similar transient atomic displacement measurements under an AC electric field on langasite-type crystals, which are useful as piezoelectric materials for high-temperature applications [2, 3].

4. Applications to langasite-type crystals

Langasite (La₃Ga₅SiO₁₄, LGS) is a piezoelectric crystal belonging to the same crystal point group 32 as quartz and does not show a phase transition until its melting point around 1470°C. Its piezoelectric constants are several times larger than those of quartz, d₁₁ = −5.95, d₁₄ = 5.38 pC∙N⁻¹ [7]. Figure 5a shows the crystal structure of langasite. The space group is P321, and the crystal structure consists of GaO₆ octahedra, GaO₄, and Ga_1/2Si_1/2O₄ tetrahedra, and La atoms coordinated by eight oxygen atoms. La atoms can be substituted with other rare earth (RE) elements such as Pr and Nd, and it is known that the piezoelectric constants decrease as the ionic radius of the RE elements decreases [7, 8, 9, 10]. In Nd₃Ga₅SiO₁₄ (NGS), where La is replaced by Nd, d₁₁ = −4.05, d₁₄ = 2.07 pC∙N⁻¹ [7]. Transient atomic displacement measurements under an AC electric field were performed on LGS and NGS to understand the origin of the change in piezoelectric constants due to RE element substitution, in addition to the mechanism of piezoelectricity in langasite-type crystals. The samples used were a commercially available Y-cut LGS crystal with an oscillation frequency of 28 MHz (thickness: 0.05 mm) and a homemade Y-cut NGS crystal with an oscillation frequency of 13 MHz (thickness: 0.09 mm). X-ray diffraction experiments were performed at SPring-8 BL02B1 using X-rays with a wavelength of 0.3 Å.

Figure 5.

(a) Crystal structure of langasite-type crystal viewed along the twofold axis (square box is the trigonal unit cell), and (b) coordination structure around a RE atom.

The crystal structures of LGS and NGS in the absence of an electric field were analyzed and compared first. There was little difference in the Ga(Si)−O bond distances between them. The RE (La, Nd) atoms are coordinated with eight O atoms, but because the RE atoms are on the twofold X-axis, there are only four independent RE−O bonds (Figure 5b). Among the four types of RE−O bonds, large changes in bond lengths were observed in the two short RE−O bonds due to elemental substitutions. The bond lengths of these two RE−O bonds are 2.355 and 2.508 Å for LGS and 2.301 and 2.431 Å for NGS, respectively, indicating that the substitution of La with Nd shortened the bond distance by more than 0.05 Å. In accordance with the shortening of the bond distances, the Ga−O−Ga bond angles centered on the oxygen atoms of these two types of RE−O bonds were also significantly deformed. The two Ga−O−Ga bonds are the only Ga−O−Ga bonds existing in the crystal structure, which bridging a GaO₆ octahedron and a GaO₄ tetrahedron, and a GaO₄ tetrahedron and a Ga_1/2Si_1/2O₄ tetrahedron, respectively. The bond angles of these two types of Ga−O−Ga(Si) bonds are 114.2 and 122.3 degrees for LGS and 112.6 and 120.3 degrees for NGS, indicating a decrease in the bond angles of about 2 degrees with the substitution of La with Nd. In addition, NGS has a larger deformation of the GaO₆ octahedron from the regular octahedron than LGS. The O−Ga−O bond angles in the GaO₆ octahedron are 90 and 180 degrees when the GaO₆ octahedron is a regular octahedron. The maximum deviations of the O−Ga−O bond angles from 90 and 180 degrees in the GaO₆ octahedron are 12.9 and 13.8 degrees for LGS and 15.2 and 16.2 degrees for NGS.

X-ray diffraction experiments under a DC electric field showed that the lattice deformations of Δβ and Δγ were consistent with the piezoelectric constants, as in the case of quartz. Piezoelectric constants estimated from Δβ and Δγ were d₁₁ = −5.7 and d₁₄ = 5.3 pC∙N⁻¹ for LGS and d₁₁ = −3.8 and d₁₄ = 2.3 pC∙N⁻¹ for NGS. Time-resolved X-ray diffraction experiments under an AC electric field were performed with a sinusoidal AC electric field applied to the sample at the resonant frequency, as in the case of the quartz crystal. The electric field amplitudes were 0.20 MV∙m⁻¹ for LGS and 0.16 MV∙m⁻¹ for NGS. The repetition frequency of the pulsed X-rays was 52 kHz for LGS and 69 kHz for NGS. As in the case of the quartz crystal, the time variation of the X-ray diffraction image of the resonant sample in one period was measured by changing the delay time of the AC electric field to the pulsed X-rays, and the time variation of the lattice constant and crystal structure were investigated from these images.

Figure 6a and b show the time variation of Δβ and Δγ for the LGS and NGS oscillators resonating under an AC electric field. As in the case of the quartz crystal (Figure 3a), a large sinusoidal oscillation was observed in Δγ. The amplitudes of the oscillation in Δγ were 0.10 degrees for the LGS and 0.04 degrees for the NGS, respectively. The difference between the two values can be attributed mainly to the difference in piezoelectric constants as described above. The amplification factor of Δγ under an AC electric field due to resonance is more than 5 × 10² from their piezoelectric constants, but smaller than that of a quartz crystal around 1 × 10⁴. The larger amplification effect in quartz is attributed to its Q-value larger than those of LGS and NGS. The amplification effect of Δβ due to resonance was observed in the AT-cut quartz crystal (Figure 3a), but not in the Y-cut LGS and NGS crystals (Figure 6). An AC electric field was applied along the direction 35 degrees inclined from the Y-axis to the Z-axis in the AT-cut quartz crystal (Figure 2b), while it was applied along the Y-axis in the Y-cut LGS and NGS crystals. Δβ is generated by the atomic displacements perpendicular to the Y-axis, so an electric field component perpendicular to the Y-axis will be necessary to amplify Δβ.

Figure 6.

Time variations of Δβ and Δγ for the (a) LGS and (b) NGS oscillators resonating under AC electric field.

The crystal structures of LGS and NGS resonating under the AC electric field at the delay times when Δγ reached their negative and positive maxima were analyzed and compared. Changes in RE−O bond distances, Ga−O−Ga, and O−Ga−O bond angles from the negative to positive maxima of Δγ are shown in Figures 7 and 8. No changes in the Ga(Si)−O bond distances were observed during resonance for both LGS and NGS. In the triclinic distorted structure with 24 independent RE−O bonds under an electric field, three RE−O bonds in LGS and one RE−O bond in NGS showed a change in their bond distances of more than ±0.01 Å with time (Figure 7a). Among the four types of independent RE−O bonds in the trigonal non-distorted structure, only the longest RE−O bonds with the bond distances longer than 2.85 Å showed a clear time variation in the resonance. The two short RE−O bonds, which vary greatly with RE atomic substitution, show no time variation in the resonance. Focusing on the Ga−O−Ga bond angles, we observed that among the 12 types of Ga−O−Ga(Si) bonds in the distorted state under an electric field, four types of bonds in the LGS and one type of bond in the NGS showed a change in their bond angles of more than ±0.25 degrees with time (Figure 7b). These results indicate that replacing La with Nd significantly reduces the deformation of the RE−O bond distances and the Ga−O−Ga bond angles during resonance as RE−O bond distances are shortened. The decrease in the piezoelectric constants due to the replacement of La with Nd is mainly attributed to the fact that the deformation of the Ga−O−Ga bond angles is prevented due to the shortening of the RE−O bond distances.

Figure 7.

Changes in (a) RE−O lengths and (b) Ga−O−Ga angles under AC electric field for Y-cut LGS and NGS resonators.

Figure 8.

Changes in O−Ga−O angles in (a) GaO₆ octahedra, (b) GaO₄, and (c) Ga_1/2Si_1/2O₄ tetrahedra under AC electric field for Y-cut LGS and NGS resonators.

Next, the deformation of O−Ga−O bond angles in GaO₆ octahedra, GaO₄, and Ga_1/2Si_1/2O₄ tetrahedra in the resonance state was investigated. Of the 15 independent O−Ga−O bonds in the GaO₆ octahedra of the distorted structure under an electric field, no and 5 O−Ga−O bonds showed a time variation of their bond angles greater than ±0.25 degrees in LGS and NGS, respectively (Figure 8a). In the GaO₄ tetrahedra, of the 18 independent O−Ga−O bonds, 5 and 5 O−Ga−O bonds showed a time variation greater than ±0.25 degrees in LGS and NGS, respectively (Figure 8b). In the Ga_1/2Si_1/2O₄ tetrahedra, of the 12 independent O−Ga−O bonds, 2 and 1 O−Ga−O bonds showed a time variation greater than ±0.25 degrees in LGS and NGS, respectively (Figure 8c). The substitution of La with Nd increases the deformation of the GaO₆ octahedra from the regular octahedron and facilitates the deformation of the O−Ga−O bond angles of the GaO₆ octahedra during resonance. The Ga−O−Ga bond angles in NGS are not easily deformed due to the shortening of RE−O bonds, but the GaO₆ octahedra are deformed instead. The deformation of GaO₄ and Ga_1/2Si_1/2O₄ tetrahedra during resonance was observed in both LGS and NGS, but no deformation of SiO₄ tetrahedra during resonance was observed in quartz. Therefore, the O−Ga−O bond is more flexible than the O−Si−O bond, and as a result, the piezoelectric constants of LGS and NGS are larger than those of quartz. However, the piezoelectric deformation of LGS and NGS is caused by the deformation of multiple bonds with different force constants, resulting in greater energy dissipation and lower amplification effect (Q-value) in resonance than those of quartz.

As described above, the mechanism of piezoelectricity and the effect of RE substitution in langasite-type crystals were understood by the combination of resonance phenomena under an AC electric field and SR time-resolved X-ray diffraction. LGS shows larger piezoelectric deformation than quartz due to the deformation of GaO₄ and Ga_1/2Si_1/2O₄ tetrahedra. In NGS, the piezoelectric deformation is smaller because the shortening of the RE−O bond distances prevents the deformation of the Ga−O−Ga bond angles, but instead the GaO₆ octahedral deformation is observed. These findings will be useful for the design and development of piezoelectric crystals with higher functionality than quartz.

5. Summary

In this chapter, we introduce transient crystal structures of quartz and langasite-type crystals resonating under an AC electric field observed by SR time-resolved X-ray diffraction. The method can detect small transient atomic displacements in piezoelectric crystals by resonantly amplifying them under an alternating electric field by a factor of 10³–10⁴. We will use this method for structural analyses of other piezoelectric crystals and expand its range of application.

Acknowledgments

This work was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) (Grants Nos. JP22H02162, JP19H02797, JP16K05017, and JP26870491), Tatematsu Foundation, Toyoaki Scholarship Foundation, Daiko Foundation, and the Research Equipment Sharing Center at the Nagoya City University. The synchrotron radiation experiments were performed at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI).

Conflict of interest

The authors declare no conflict of interest.