Effects of Energetic Carbon-Cluster Ion Irradiation on Lattice Structures of EuBa 2 Cu 3 O 7 − x Oxide Superconductor

: C-axis-oriented EuBa 2 Cu 3 O 7 − x oxide ﬁlms that were 100 nm thick were irradiated with 0.5 MeV C monoatomic ions, 2 MeV C 4 cluster ions and 4 MeV C 8 cluster ions at room temperature. Before and after the irradiation, X-ray diffraction (XRD) measurement was performed using Cu-Ka X-ray. The c-axis lattice constant increased almost linearly as a function of numbers of irradiating carbon ions, but it rarely depended on the cluster size. Cluster size effects were observed in the XRD peak intensity and the XRD peak width. With increasing the cluster size, the decrease in peak intensity becomes more remarkable and the peak width increases. The experimental result implies that the cluster ions with a larger size provide a more localized energy deposition in a sample, and cause larger and more inhomogeneous lattice disordering. As such, local and large lattice disordering acts as a pinning center for quantum vortex; energetic carbon-cluster ion irradiation will be effective for the increment in the critical current of EuBa 2 Cu 3 O 7 − x superconductors.


Experimental Procedure
Thin films of EuBa 2 Cu 3 O 7−x 100 nm thick were produced on MgO substrates by using an RF-magnetron sputtering method [36]. The films were c-axis oriented and the superconducting transition temperature, T c , was around 90 K [36]. The films were irradiated with 0.5 MeV C monoatomic ions, 2 MeV C 4 cluster ions and 4 MeV C 8 cluster ions using a tandem accelerator at Takasaki Advanced Accelerator Research Institute of National Institutes for Quantum Science and Technology (QST-Takasaki) [37]. The ion energy per carbon atom was the same for the monoatomic carbon ion and the two kinds of carboncluster ions (0.5 MeV/carbon atom). The samples were irradiated at room temperature, and along the normal of the film plane.
To observe the irradiation-induced change in lattice structures precisely, the X-ray diffraction (XRD) spectra were measured for each sample before and after the irradiation.
The averaged values of the c-axis lattice constant were estimated by measuring the positions of (001) to (0010) XRD peaks and using the extrapolation function of Nelson and Riley [38].
Thus far, we examined the effect of monoatomic ion irradiation with the energy range of 0.85 MeV-3.8 GeV on the lattice constants of EuBa 2 Cu 3 O 7−x [39][40][41][42]. The thickness of the samples used in our previous study was 300 nm. It is well known that cluster ions fragmentate into mono-atoms during the penetration in targets. To detect more precisely the effect of cluster ion irradiation, the cluster fragmentations have to be reduced as much as possible. Thus, the thickness of EuBa 2 Cu 3 O 7−x samples for the present experiment was 100 nm, which was much smaller than that of our previous samples. Figure 1 shows the wide-scanned XRD spectrum for an unirradiated sample. We can observe several peaks corresponding to the crystal planes perpendicular to the c-axis (parallel to MgO substrate). High peaks around 43 and 95 degrees correspond to the MgO substrate.  Figure 2 shows the effects of C 1 , C 4 and C 8 ion irradiation on (005) XRD peaks. The peaks shift to a lower angle with an increase in ion fluence. Other XRD diffraction peaks also shift to a lower-angle side by the irradiation. The present result indicates that the c-axis lattice constant increases by the irradiation. In Figure 3, the values of ∆c/c 0 are plotted as a function of ion fluence, Φ, where c 0 is the c-axis lattice constant before the irradiation, and ∆c = c(Φ) − c 0 , the irradiation induced change in lattice constant. Here, we especially note the meaning of the ion fluence, Φ. It is the number of carbon atoms per cm 2 , and not the number of cluster ions. To avoid any confusion, we call Φ as "carbon fluence" hereafter.  Although several data in Figure 3 are scattered to some extent, the values of ∆c/c 0 increase almost linearly as a function of carbon fluence, and we do not find any systematic dependence of the c-axis lattice constant change on the cluster size.

Results
In Figure 2, two other effects of the irradiation on the XRD spectra are observed. One is the decrease in peak intensity with increasing the ion fluence, and the other is the broadening of the peaks by the irradiation. Figure 4 indicates the intensity of (005) and (006) peaks, which is normalized by the peak intensity before the irradiation, as a function of carbon fluence. Unlike in the case of averaged c-axis lattice constant, the change in peak intensity by the irradiation shows a strong dependence on cluster size. The peak intensity decreases more rapidly for the irradiation with larger-sized carbon clusters.
The cluster-size dependence can also be found in the irradiation-induced broadening of the diffraction peaks. Figure 5 shows the values of full width at half maximum (FWHM) of (005) and (006) peaks, which are normalized by the value of FWHM before the irradiation, as a function of carbon fluence. As can be observed in the figure, the value of FWHM becomes larger for the irradiation with larger-sized carbon clusters.

Discussion
Thus far, we have reported the irradiation effect of several MeV monoatomic ions (0.85 MeV He, 1.0 MeV C, 0.95 MeV Ne and 2.0 MeV Ar) on the c-axis lattice constant of EuBa 2 Cu 3 O 7−x , and have shown that the increase in lattice constant, ∆c, is proportional to the fluence of monoatomic ions, Φ [40]. In Figure 6, the normalized increments in the lattice constant for unit fluence, (∆c/c 0 )/Φ, are plotted against the nuclear stopping power, S n . The values of S n were obtained by using the SRIM calculation code [43]. In the figure, the present result for 0.5 MeV C 1 ions is also plotted.
where A is a constant. The value of S n corresponds to the energy deposited into the sample by one irradiating ion through elastic collisions. For the irradiation with the fluence of Φ, the total energy deposited through the elastic collisions, E D , is given as: (2) and the change in lattice constant, ∆c/c 0 , is: i.e., the change in lattice constant is proportional to the total energy deposited through the elastic collisions. As Figure 3 shows, the change in lattice constant for C 4 and C 8 cluster ion irradiation shows the same dependence on Φ as for C 1 monoatomic ion irradiation.
Here, we confirm again that the meaning of Φ is the number of carbon atoms/cm 2 (carbon fluence). Therefore, data points for 2 MeV C 4 and 4 MeV C 8 cluster ions in Figure 6 are placed at the data point for 0.5 MeV C 1 ions, and the change in lattice constant, ∆c/c 0 , is determined only by the total energy deposited through the elastic collisions. Although the irradiation-induced change in lattice constant does not show any clustersize dependence, the changes in intensity and FWHM of the XRD peaks clearly depend on the cluster size. As can be observed in Figures 4 and 5, with increasing the cluster size, the peak intensity decreases, and the FWHM of the peaks increases. The C 4 and C 8 cluster ion irradiation results in simultaneous collisions of 4-8 monoatomic carbon ions with target atoms, causing high-density energy deposition in narrow regions near the ion trajectories. With increasing the cluster size, the density of deposited energy becomes more localized and more inhomogeneous in space, although the total energy deposition is the same regardless of cluster size. The present result indicates that localized and inhomogeneous energy deposition by the cluster ions causes local lattice disordering, resulting in the decrease in XRD peak intensity and the peak broadening. On the other hand, the lattice constant decided by the XRD measurement corresponds to the averaged one over a wide area of the sample. Therefore, it is rarely affected by the local/inhomogeneous lattice disordering, but only depends on the total deposited energy by the irradiation. EuBa 2 Cu 3 O 7−x is one of ReBa 2 Cu 3 O 7−x oxides, where Re is a rare-earth element, and a promising superconducting material for industrial applications because of the high superconducting transition temperature, T c . The critical current density, J c , under magnetic field (in-field J c ), which is a maximum current density with zero-resistivity, is the most important parameter for practical applications. It is well known that one-dimensional defective regions (ion-tracks) produced by swift heavy ion irradiation act as intense pinning centers for quantum vortices. A lot of studies for the modification of J c have, therefore, been performed so far by irradiating ReBa 2 Cu 3 O 7−x with GeV heavy ions ( [44] and references therein). Recently, several papers have reported that much lower energy (about 100 keV-MeV) ion irradiation can also be used for the improvement of J c of ReBa 2 Cu 3 O 7−x superconductors [45][46][47][48]. The low-energy ion irradiation introduces point-like defects with a dimension of several nm. The lattice disordering inside and around the point-like defects act as effective pinning sites for quantum vortices. However, the energetic ion irradiation not only improves the critical currents, but also causes the degradation of superconductivity. The increase in the c-axis lattice constant of ReBa 2 Cu 3 O 7−x by energetic ion irradiation is mainly caused by the deficiency of oxygen atoms [48]. The oxygen atom deficiency leads to the decrease in superconducting transition temperature, T c . As the present experiment shows, under the condition of the same increase in c-axis lattice constant (the same oxygen deficiency), larger lattice disordering is locally induced by C-cluster ion irradiation as compared with monoatomic C-ion irradiation. Therefore, the present experimental result suggests that the MeV C-cluster ion irradiation will be useful for the improvement of J c with less degradation of T c .

Summary
EuBa 2 Cu 3 O 7−x oxide films were irradiated with 0.5 MeV/atom C 1 , C 4 and C 8 ions. The XRD spectra were measured before and after the irradiation. The c-axis increases almost proportionally with increasing carbon fluence, or energy deposited through elastic collisions and the cluster-size dependence is rarely observed. The irradiation also induces the decrease in XRD peak intensity and XRD peak broadening, which strongly depend on cluster size. With increasing the cluster size, the peak intensity decreases and the peaks become more broadened. The present experimental result shows that the change in averaged c-axis lattice constant is determined only by the total energy deposited through elastic collisions, but the larger cluster irradiation induces locally larger lattice disordering, which is due to localized and inhomogeneous energy deposition by the cluster ions. Funding: A part of the study was supported by Inter-organizational Atomic Energy Research Program in an academic collaborative agreement among JAEA, QST, and the Univ. of Tokyo.
Data Availability Statement: Datasets acquired during the present research are available from the corresponding author on reasonable request.