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[Hiroshi Amekura](https://orcid.org/0000-0003-2148-8431), [Norito Ishikawa](https://orcid.org/0000-0002-2217-3645), Nariaki Okubo, Feng Chen, [Kazumasa Narumi](https://orcid.org/0000-0001-8569-0108), Atsuya Chiba, Yoshimi Hirano, Keisuke Yamada, Shunya Yamamoto, Yuichi Saitoh

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[Metallic Ca Aggregates Formed Along Ion Tracks and Optical Anisotropy in CaF2 Crystals Irradiated with Swift Heavy Ions](https://mdr.nims.go.jp/datasets/0561a700-efc3-4177-aeb5-3e54d86652a5)

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Metallic Ca Aggregates Formed Along Ion Tracks and Optical Anisotropy in CaF2 Crystals Irradiated with Swift Heavy IonsCitation: Amekura, H.; Ishikawa, N.;Okubo, N.; Chen, F.; Narumi, K.;Chiba, A.; Hirano, Y.; Yamada, K.;Yamamoto, S.; Saitoh, Y. Metallic CaAggregates Formed Along Ion Tracksand Optical Anisotropy in CaF2Crystals Irradiated with Swift HeavyIons. Quantum Beam Sci. 2024, 8, 29.https://doi.org/10.3390/qubs8040029Academic Editors: Klaus-Dieter Lissand David CohenReceived: 19 August 2024Revised: 20 September 2024Accepted: 31 October 2024Published: 7 November 2024Copyright: © 2024 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).ArticleMetallic Ca Aggregates Formed Along Ion Tracks and OpticalAnisotropy in CaF2 Crystals Irradiated with Swift Heavy IonsHiroshi Amekura 1,* , Norito Ishikawa 2 , Nariaki Okubo 2, Feng Chen 3, Kazumasa Narumi 4 , Atsuya Chiba 4,Yoshimi Hirano 4, Keisuke Yamada 4, Shunya Yamamoto 4 and Yuichi Saitoh 51 National Institute for Materials Science (NIMS), Tsukuba 305-0003, Ibaraki, Japan2 Japan Atomic Energy Agency (JAEA), Tokai 319-1195, Ibaraki, Japan; ishikawa.norito@jaea.go.jp (N.I.);okubo.nariaki@jaea.go.jp (N.O.)3 School of Physics, Shandong University, Jinan 250100, China; drfchen@sdu.edu.cn4 National Institutes for Quantum Science and Technology (QST), Takasaki 370-1292, Gunma, Japan;narumi.kazumasa@qst.go.jp (K.N.); chiba.atsuya@qst.go.jp (A.C.); hirano.yoshimi@qst.go.jp (Y.H.);yamada.keisuke@qst.go.jp (K.Y.); yamamoto.shunya@qst.go.jp (S.Y.)5 National Institutes for Quantum Science and Technology (QST), Inage 263-8555, Chiba, Japan;saito.yuichi@qst.go.jp* Correspondence: amekura.hiroshi@nims.go.jp; Tel.: +81-29-863-5479Abstract: It is known that swift heavy ion (SHI) irradiation induces the shape elongation of metalnanoparticles (NPs) embedded in transparent insulators, which results in anisotropic optical ab-sorption. Here, we report another type of the optical anisotropy induced in CaF2 crystals withoutincluding intentionally embedded metal NPs. The CaF2 samples were irradiated with 200 MeV Xe14+ions with an incident angle of 45◦ from the surface normal. With the increasing fluence, an absorptionband at ~550 nm, which is ascribed to Ca aggregates, increases both the intensity and the anisotropy.XTEM observation clarified the formation of the continuous line structures and the discontinuous NPchains parallel to the SHI beam. Numerical simulations of the optical absorption spectra suggestedthe NP chains but not the continuous line structures as the origin of the anisotropy. The opticalanisotropy in CaF2 irradiated with SHIs is different from the shape elongation of NPs.Keywords: swift heavy ion; CaF2; anisotropic optical absorption; nanoparticles; metal aggregate1. IntroductionA huge number of studies have already been devoted to surface plasmon resonances(SPRs) of metal nanoparticles (NPs) embedded in transparent insulators because thesemetal NPs show much faster optical responses than semiconductors due to the electric fieldenhancement in nanometric regions, etc. [1]. To add further functionality to NPs, it is moreattractive if the SPR can be controlled by the polarization angles of polarized light: e.g.,while the s-polarized light excites the SPR, the p-polarized light of the same frequency doesnot. This can be easily attained if non-spherical nanoparticles (NPs) can be prepared. Forexample, triple-degenerated SPR in a spherical NP is divided into a double-degeneratedtransverse SPR and a single-degenerated longitudinal SPR in a spheroidal NP. However, togain enough signal intensity for certain applications, elongation axes of many spheroidalNPs should be aligned in parallel with each other.In this respect, an attractive phenomenon, called “shape elongation of embeddedNPs”, is known, induced by swift heavy ion (SHI) irradiation [2–4]. SHIs are extremelyhigh-energy ions, e.g., higher than several tens of MeV, where the nuclear energy loss Snis negligible compared to the electronic energy loss Se [5]. Under SHI irradiation, metalNPs embedded in certain matrices, e.g., silica glass (SiO2), show shape elongation alongthe SHI beam direction. Therefore, all the NPs which fulfill the elongation conditions [3,4]show shape elongation toward the same direction. Because of the (quasi)conservationQuantum Beam Sci. 2024, 8, 29. https://doi.org/10.3390/qubs8040029 https://www.mdpi.com/journal/qubshttps://doi.org/10.3390/qubs8040029https://doi.org/10.3390/qubs8040029https://creativecommons.org/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/qubshttps://www.mdpi.comhttps://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0002-2217-3645https://orcid.org/0000-0001-8569-0108https://doi.org/10.3390/qubs8040029https://www.mdpi.com/journal/qubshttps://www.mdpi.com/article/10.3390/qubs8040029?type=check_update&version=2Quantum Beam Sci. 2024, 8, 29 2 of 13of NP volume [3,4], the dimensions of NPs perpendicular to the SHI beam show shapeshrinkage. (Although the mechanism must be different, non-spherical Cu NPs were formedin MgAl2O4 under 60 keV Cu implantation [6].)While the recent major consensus on the elongation mechanism is the movement ofmolten metal through low-density track cores of the matrix [4,7], the ion-hammering (IH)mechanism was believed for long time before then. If IH was involved in the mechanism,the elongation of NPs could be induced in amorphous matrices only, because IH is basicallyinduced in amorphous materials only.While the shape elongation phenomena were confirmed in more than ten metal speciesof NPs [3,4], the species of the matrices are very few and mostly limited to amorphousmaterials such as amorphous SiO2 [2], amorphous Si3N4 [8], amorphous LiNbO3 [9],and amorphous Y3Al5O12 (YAG) [10]. One of the reasons why the amorphous matriceswere used is inevitable: SHI irradiation induces the elongation of NPs, simultaneouslytransforming certain crystalline materials to amorphous ones. Furthermore, NPs are oftenformed in the matrices by ion implantation, which often induces the amorphization of thematrices.In this context, we have prepared Au NPs on the surface of silica glass, which werethen embedded by three different matrices, i.e., In1−xSnxOy (ITO, x ~ 0.1), amorphouscarbon (a-C), and CaF2 [11]. First, Au NPs were prepared on silica substrates by electronbeam deposition of a 3 nm-thick Au film and subsequent rapid thermal annealing. Then,the Au NPs were covered by the three different matrices of approximately 50 nm thickusing magnetron sputtering (ITO and CaF2) and arc deposition (a-C). The Au NPs, halfof which were embedded with three different matrices and the other with SiO2, wereirradiated with SHIs of 200 MeV Xe.ITO half-embedding of Au NPs exhibited an XRD peak of ITO even after the SHIirradiation to a high fluence of 2 × 1014 ions/cm2, indicating that the crystallinity wasmaintained. At the same fluences, the Au NPs half-embedded in ITO exhibit more efficientshape elongation than those fully embedded in silica. Therefore, this observation stronglyconfirmed that the shape elongation of NPs is induced even in a crystalline matrix [11].In contrast, Au NPs half-embedded in a-C showed minimal elongation. While the NPsshowed quite weak elongation on the silica side, they showed almost no elongation on thea-C side. This observation indicated that no elongation was induced even in an amorphousmatrix [11].The results of the NPs half-embedded in CaF2 showed loss of reproducibility. Infact, the CaF2 films showed a very strong purple color due to defects, although theyare relatively thin at around ~50 nm, indicating quite poor crystallinity [11]. In fact,point defects are introduced in CaF2 under various irradiations, including electrons [12],protons [13], SHIs [14–16], and even X-rays [17]. According to Ref. [18], the primary processof the point defect formation in CaF2 is the formation of so-called Frenkel pairs in halides,i.e., F- and H-centers. Particularly, F-centers aggregate with each other and form large Fn-centers, which transform to Ca collides. Concerning the shape elongation phenomenon ofembedded metal NPs, changes in the matrix material induced by SHI irradiation, throughthe point defect formation, have been neglected or at least not considered.In this paper, Ag NPs in CaF2 were prepared using a different method from Ref. [11],i.e., Ag ion implantation on CaF2 single crystals. The formation of Ag NPs in CaF2 wasconfirmed by the observation of SPR of Ag NPs. Furthermore, the shape elongation ofNPs was confirmed as the observation of the anisotropic optical absorption, i.e., the opticalabsorption depending on the polarization angle of the incident light. Since we have alreadysucceeded in forming elongated Ag NPs in YAG crystals by the same procedures, i.e.,200 keV Ag ion implantation and 200 MeV Xe irradiation, the formation of Ag NPs and theelongation in CaF2 have been rigidly confirmed because we have experienced that Ag NPsshowed quite similar spectra, irrespective of the different matrices, i.e., CaF2 and YAG [10].One of the most important observations in Ag NPs in CaF2 is that a new peak around550 nm appeared and the intensity increased under SHI irradiation. The peak was alsoQuantum Beam Sci. 2024, 8, 29 3 of 13observed in CaF2 samples without Ag NPs under SHI irradiation, which exhibited opticalanisotropy. This paper describes the observation of the newly observed peak with theanisotropy, corresponding transmission electron microscopy (TEM) images, and numericalsimulations of the optical spectra.2. Materials and MethodsCalcium fluoride (CaF2) has a crystalline structure of the fluorite type, i.e., in the cubicsymmetry. Single crystals of CaF2 with sizes of 10 × 10 × 1 mm3 were purchased fromATOM Optics Co., Ltd., Shanghai, China. The largest surface of 10 mm × 10 mm corre-sponded to the (001) crystalline plane. Some pieces of the CaF2 crystals were implantedwith 200 keV Ag+ ions from a 400 kV ion implanter in Takasaki Institute for QuantumScience and Technology, QST. An incident angle of 5◦ from the surface normal was appliedto avoid channeling implantation. The ion range and straggling of 200 keV Ag ions inCaF2 in an off-axis implantation were calculated by SRIM 2013 [19] as 75.9 nm and 23.1nm, respectively. Samples were implanted through a 7 mm × 7 mm squared aperture withthe beam scanning frequencies of 89 Hz (horizontal) and 502 Hz (vertical). The implantedAg contents for different samples were evaluated by Rutherford backscattering spectrom-etry (RBS) with 2 MeV He+ ions [20]. The mean value and the standard deviation were(1.02 ± 0.15) × 1017 ions/cm2. While as-implanted samples had already shown an SPR peak,which indicated the formation of Ag NPs, post-implantation annealing was performed in avacuum (~5 × 10−6 Torr) at 800 ◦C for 30 min to minimize the damage.Both the pre-Ag-implanted and virgin CaF2 samples were irradiated with SHIs of200 MeV 136Xe14+ ions from the 20 MV tandem accelerator at the Tokai Research andDevelopment Center, JAEA. The fluence ranged from 1 × 1011 to 2 × 1014 ions/cm2. The(001) face of the CaF2 samples were irradiated with an ion incidence angle of 45◦ fromthe surface normal in order to evaluate the anisotropic optical absorption spectra usinglinearly polarized light [21]. Here, the light polarizations of 0◦ and 90◦ are those parallel andperpendicular to the ion-penetrating plane, respectively, as shown in Figure 1. The stoppingpowers and the projected ranges of the 200 MeV Xe ions in CaF2 were calculated usingSRIM 2013 code [19] and shown in Table 1. The Xe ion provides the electronic stoppingpowers Se of 20.3 keV/nm in CaF2, which was much higher than the track formationthreshold of 5 keV/nm in CaF2 [22], indicating the formation of ion tracks in the presentsamples.Quantum Beam Sci. 2024, 8, x FOR PEER REVIEW 3 of 13   One of the most important observations in Ag NPs in CaF2 is that a new peak around 550 nm appeared and the intensity increased under SHI irradiation. The peak was also observed in CaF2 samples without Ag NPs under SHI irradiation, which exhibited optical anisotropy. This paper describes the observation of the newly observed peak with the an-isotropy, corresponding transmission electron microscopy (TEM) images, and numerical simulations of the optical spectra. 2. Materials and Methods Calcium fluoride (CaF2) has a crystalline structure of the fluorite type, i.e., in the cubic symmetry. Single crystals of CaF2 with sizes of 10 × 10 × 1 mm3 were purchased from ATOM Optics Co., Ltd., Shanghai, China. The largest surface of 10 mm  10 mm corre-sponded to the (001) crystalline plane. Some pieces of the CaF2 crystals were implanted with 200 keV Ag+ ions from a 400 kV ion implanter in Takasaki Institute for Quantum Science and Technology, QST. An incident angle of 5° from the surface normal was ap-plied to avoid channeling implantation. The ion range and straggling of 200 keV Ag ions in CaF2 in an off-axis implantation were calculated by SRIM 2013 [19] as 75.9 nm and 23.1 nm, respectively. Samples were implanted through a 7 mm  7 mm squared aperture with the beam scanning frequencies of 89 Hz (horizontal) and 502 Hz (vertical). The implanted Ag contents for different samples were evaluated by Rutherford backscattering spectrom-etry (RBS) with 2 MeV He+ ions [20]. The mean value and the standard deviation were (1.02 ± 0.15)  1017 ions/cm2. While as-implanted samples had already shown an SPR peak, which indicated the formation of Ag NPs, post-implantation annealing was performed in a vacuum (~5  10−6 Torr) at 800 °C for 30 min to minimize the damage. Both the pre-Ag-implanted and virgin CaF2 samples were irradiated with SHIs of 200 MeV 136Xe14+ ions from the 20 MV tandem accelerator at the Tokai Research and Develop-ment Center, JAEA. The fluence ranged from 1 × 1011 to 2 × 1014 ions/cm2. The (001) face of the CaF2 samples were irradiated with an ion incidence angle of 45° from the surface nor-mal in order to evaluate the anisotropic optical absorption spectra using linearly polarized light [21]. Here, the light polarizations of 0° and 90° are those parallel and perpendicular to the ion-penetrating plane, respectively, as shown in Figure 1. The stopping powers and the projected ranges of the 200 MeV Xe ions in CaF2 were calculated using SRIM 2013 code [19] and shown in Table 1. The Xe ion provides the electronic stopping powers Se of 20.3 keV/nm in CaF2, which was much higher than the track formation threshold of 5 keV/nm in CaF2 [22], indicating the formation of ion tracks in the present samples.   Figure 1. Schematically depicted definitions of the ion-penetrating plane and of the 0° and 90°po-larization of incident lights. (Each pair of triangles indicates the direction of the polarization.) While SHIs are incident to the sample surface with an angle of 45°, light for the absorption measurements is incident normal to the surface. Figure 1. Schematically depicted definitions of the ion-penetrating plane and of the 0◦ and90◦polarization of incident lights. (Each pair of triangles indicates the direction of the polariza-tion.) While SHIs are incident to the sample surface with an angle of 45◦, light for the absorptionmeasurements is incident normal to the surface.Quantum Beam Sci. 2024, 8, 29 4 of 13Table 1. Electronic and nuclear stopping powers at the surface and the projected range of 200 MeV136Xe ions in a CaF2 crystal, calculated by SRIM 2013 [19].200 MeV 136Xe Ions in CaF2 Crystal:Electronic stopping power at the surface Se (keV/nm) 20.3Track formation threshold Se,th (keV/nm) [22] 5Nuclear stopping power at the surface Sn (keV/nm) 0.069Projected range Rp(µm) 16.7Ion velocity E/m (MeV/u) 1.47A dual-beam spectrophotometer was used for the anisotropic absorption measure-ments [21] in the wavelength region of 215–800 nm, with a resolution of 1 nm at roomtemperature. An optical polarizer (extinction ratio < 5 × 10−5 in this wavelength region)was inserted in front of the sample. The results were shown in the form of optical density(−log10 T) without correction for reflection, where T denotes the optical transmittance.Cross-sectional transmission electron microscopy (XTEM) was applied using JEM-2100,JEOL, under an operation voltage of 200 kV. XTEM specimens were thinned down parallelto the ion-penetrating plane using a 30 keV Ga focused ion beam (FIB) after deposition ofprotective carbon layers.3. Results3.1. Anisotropic Optical AbsorptionFigure 2a exhibits the optical density spectra detected by linearly polarized light ofCaF2 crystals including Ag NPs irradiated with 200 MeV Xe14+ ions to a fluence rangingfrom 0 to 2 × 1014 ions/cm2. The optical density is defined as −Log10 T, where T denotesthe optical transmittance. The optical density is a quantity similar to the optical absorptionbut does not include a change in the optical reflectance. Solid and broken curves indicatethe spectra measured with linearly polarized light with the polarizations of 0◦ and 90◦, i.e.,parallel and perpendicular to the ion-penetrating plane, respectively, as shown in Figure 1.The spectra at different fluences are vertically shifted from each other for clarity.In an unirradiated state, a prominent peak was observed at ~420 nm, whose spectralshape did not depend on the polarization angle. Compared with literature data on the SPRpeaks of Ag NPs in silica [23,24] and YAG [10], this peak is ascribed to the SPR of Ag NPs inCaF2. A rise in the optical density below 320 nm is also characteristic of the Ag NPs [23,24].While both the polarization curves at 0◦ and 90◦ fell on the same curve at the fluence of1 × 1011 ions/cm2, a small deviation was observed between them at 1 × 1012 ions/cm2.Increasing the fluence further, the deviation between the curves at the two polarizationsincreased. The SPR peaks at the 0◦ and 90◦ polarizations moved to 430 nm and 400 nm,respectively, at the fluence of 5 × 1013 ions/cm2, while both the peaks were at 420 nm in theunirradiated state. The lower (higher) energy shift of the 0◦ (90◦) peak, i.e., the conservationof the center-of-mass of the spectra, is reasonable, because the Ag NPs elongated in theion-penetrating plane (0◦) and shrank outside of the plane (90◦) [10,23,24].It should be noted again that we, in a previous paper [11], deposited CaF2 films overAu NPs by magnetron sputtering and irradiated them with SHIs. However, probablydue to the considerably low quality of the films, we were not able to judge whether NPswere elongated in CaF2 or not. Here, we report that Ag NPs are elongated in CaF2 by SHIirradiation, although CaF2 could be (partially) amorphized by the 200 keV Ag implantation.Increasing the fluence up to 5 × 1013 ions/cm2, the SPR peaks did not move sig-nificantly and stayed around 420 nm, except for small shifts of less than 20 nm. At2 × 1014 ions/cm2, the peaks largely moved to ~550 nm. However, looking carefully atthe 90◦ curves, small changes had already begun at lower the fluences. A shoulder wasobserved at ~550 nm at the fluences between 1 × 1012 and 5 × 1013 ions/cm2, although noshoulder was observed at 1 × 1011 ions/cm2.Quantum Beam Sci. 2024, 8, 29 5 of 13Quantum Beam Sci. 2024, 8, x FOR PEER REVIEW 5 of 13   Figure 2. Optical density (−Log10 T) spectra of CaF2 crystals (a) with and (b) without embedded Ag nanoparticles, both irradiated with 200 MeV 136Xe14+ ions at an incident angle of 45° from the surface normal, where T denotes the optical transmittance. The fluences ranged from 0 to 2  1014 ions/cm2. Solid and broken curves indicate the spectra measured with linearly polarized light with a polari-zation angle of 0° and 90°, i.e., parallel and perpendicular to the ion-penetrating plane, respectively. The spectra at different fluences are potted in different colors and vertically shifted from each other for clarity. Horizontal lines indicate the offsets of each spectrum. Letters of 2 and 5 in (b) indicate that the spectrum is shown after expansion of two times and five times, respectively. To collect further information, CaF2 crystals not including Ag NPs were irradiated and evaluated in the same manner as the CaF2 crystals including Ag NPs. The spectra are exhibited in Figure 2b. Increasing the fluence, a broad peak with the optical anisotropy appeared and grew at ~550 nm. It is known that irradiated CaF2 crystals show two differ-ent absorption peaks: F-centers at ~380 nm and Ca aggregates at ~550 nm [13,14]. The peak observed at ~550 nm in Figure 2b can be ascribed to Ca aggregates. The F-center peak at ~380 nm is difficult to find in Figure 2b, but a very weak shoulder corresponding to the F-center was observed in our previous report [15]. It is known that Ag NPs in silica show another SPR peak at ~600 nm, when the inter-particle distances are strongly reduced [24,25]. The ~600 nm peak in silica was semi-quan-titatively reproduced by the model developed by Garcia et al. who introduced the effect of the electric fields from adjacent NPs to the Maxwell–Garnett effective medium theory [26]. Therefore, the ~600 nm peak become dominant when the fluence of Ag ion implan-tation increases, i.e., when the inter-particle distances between Ag NPs decrease. How-ever, as shown in Figure 2a, the ~550 nm peak increases when increasing the SHI fluence. We have no idea how to explain the decrease in the inter-particle distances with the in-creasing SHI fluence. In fact, Yamada et al. irradiated high-density Ag NPs, which show a ~600 nm peak, with SHIs. Since the SHI irradiation induced the shape elongation of the NPs, which resulted in an increase in the inter-particle distances, the ~600 nm peak de-creased with the increasing SHI fluence. Furthermore, since the ~550 nm peak is also ob-served in the CaF2 crystals not including Ag NPs, the ~550 nm peak should be ascribed to the Ca aggregates rather than the inter-particle effect of Ag NPs.   Figure 2. Optical density (−Log10 T) spectra of CaF2 crystals (a) with and (b) without embeddedAg nanoparticles, both irradiated with 200 MeV 136Xe14+ ions at an incident angle of 45◦ fromthe surface normal, where T denotes the optical transmittance. The fluences ranged from 0 to2 × 1014 ions/cm2. Solid and broken curves indicate the spectra measured with linearly polarizedlight with a polarization angle of 0◦ and 90◦, i.e., parallel and perpendicular to the ion-penetratingplane, respectively. The spectra at different fluences are potted in different colors and verticallyshifted from each other for clarity. Horizontal lines indicate the offsets of each spectrum. Letters of×2 and ×5 in (b) indicate that the spectrum is shown after expansion of two times and five times,respectively.To collect further information, CaF2 crystals not including Ag NPs were irradiatedand evaluated in the same manner as the CaF2 crystals including Ag NPs. The spectra areexhibited in Figure 2b. Increasing the fluence, a broad peak with the optical anisotropyappeared and grew at ~550 nm. It is known that irradiated CaF2 crystals show two differentabsorption peaks: F-centers at ~380 nm and Ca aggregates at ~550 nm [13,14]. The peakobserved at ~550 nm in Figure 2b can be ascribed to Ca aggregates. The F-center peak at~380 nm is difficult to find in Figure 2b, but a very weak shoulder corresponding to theF-center was observed in our previous report [15].It is known that Ag NPs in silica show another SPR peak at ~600 nm, when theinter-particle distances are strongly reduced [24,25]. The ~600 nm peak in silica was semi-quantitatively reproduced by the model developed by Garcia et al. who introduced theeffect of the electric fields from adjacent NPs to the Maxwell–Garnett effective mediumtheory [26]. Therefore, the ~600 nm peak become dominant when the fluence of Ag ionimplantation increases, i.e., when the inter-particle distances between Ag NPs decrease.However, as shown in Figure 2a, the ~550 nm peak increases when increasing the SHIfluence. We have no idea how to explain the decrease in the inter-particle distances withthe increasing SHI fluence. In fact, Yamada et al. irradiated high-density Ag NPs, whichshow a ~600 nm peak, with SHIs. Since the SHI irradiation induced the shape elongationof the NPs, which resulted in an increase in the inter-particle distances, the ~600 nm peakdecreased with the increasing SHI fluence. Furthermore, since the ~550 nm peak is alsoobserved in the CaF2 crystals not including Ag NPs, the ~550 nm peak should be ascribedto the Ca aggregates rather than the inter-particle effect of Ag NPs.Quantum Beam Sci. 2024, 8, 29 6 of 133.2. Cross-Sectional TEM ObservationWhile Figure 2b shows the optical density spectra of Ca aggregates, Orera and Alcalareproduced the Ca band using Mie theory [27]. While the Ca band shown in Figure 2bshows optical anisotropy, is it explained by the shape elongation of Ca aggregates? Theshape elongation of NPs is efficiently induced when the diameters of the aggregates aremuch larger than the diameters of the ion tracks [28]. In order to judge whether Ca-aggregates are larger than the track diameters or not, and whether the shape elongation isinduced in Ca aggregates or not, TEM observation was conducted.TEM images of CaF2 irradiated with MeV cluster ions [29] and SHIs [30] were previ-ously reported. Figure 3a,b exhibit XTEM images of CaF2 samples which have not beenirradiated with SHIs: (a) and (b) are the images at low and medium magnification, respec-tively. It should be noted that Ag NPs are not included in the samples shown in Figure 3.Regions labelled by “C-layer” are carbon layers deposited on the surface of the CaF2 sam-ples. In the cases of irradiated samples, the “C-layers” were deposited on the irradiatedsurfaces. Therefore, the boundaries between the “C-layers” and the CaF2 samples indicatethe irradiated surfaces. However, this is not the case for Figure 3a,b, since they are notirradiated. The unirradiated samples (Figure 3a,b) exhibited quite rough cross-sections.Line structures were not observed, which are observed in irradiated samples.Figure 3c–e show images of CaF2 samples irradiated with 200 MeV Xe14+ ions to afluence of 1 × 1013 ions/cm2: both (c) and (d) are the images in medium magnificationbut taken at different positions, and (e) is taken with higher magnification. As shown inFigure 3c,d, huge numbers of very thin straight lines parallel to each other were observed,which extended much longer than 500 nm along the depth. The angles of the thin lines tothe irradiated surface were all ~45◦, which is the same as the incident angle of the SHIs.The incident angles of the SHIs are shown by arrows in Figure 3. Note that the incidentangle of FIB thinning was 0◦ from the surface normal, which is 45◦ away from the directionof the thin lines. The observed straight lines are not due to the FIB thinning.Figure 3e exhibits an expanded image of the thin lines: While the lines show con-tinuous cylindrical shapes with a typical width of ~2.9 nm in some parts, they showdiscontinuous chains of NPs with a typical diameter of ~3.6 nm in other parts. At themoment, it is not known which structures, i.e., the continuous lines (shown by brokencircles in Figure 3e) or the discontinuous chains (shown by solid circles), contribute to theanisotropic absorption. The structures responsible for the optical anisotropy must includeCa aggregates.According to previous literature [31], track diameters of CaF2 strongly depend on notonly Se but also the ion velocity. The diameters of 2.5 nm and 6 nm were extrapolated toSe of 20 keV/nm from the data of TEM observations for the velocities of 4 MeV/u and0.1 MeV/u, respectively. Since the 200 MeV Xe ion corresponds to Se = 20.3 keV/nm and1.47 MeV/u, the observed line width of 2.9 nm is comparable to the track diameter.Figure 3f,g exhibit XTEM images at the fluences of 1 × 1012 and 5 × 1013 ions/cm2.The density of the lines looks lower for the lower fluence (Figure 3f) and higher for thehigher fluence (Figure 3g).Quantum Beam Sci. 2024, 8, 29 7 of 13Quantum Beam Sci. 2024, 8, x FOR PEER REVIEW 7 of 13   Figure 3. Cross-sectional transmission electron microscopy (XTEM) images of CaF2 samples without Ag NPs, irradiated with 200 MeV Xe14+ ions to the fluence of (a,b) 0 ions/cm2 (unirradiated), (c–e) 1  1013 ions/cm2, (f) 1  1012 ions/cm2, and (g) 5  1013 ions/cm2. C-layer denotes carbon layers depos-ited on the irradiated surfaces before the FIB thinning. The incident angle of the Xe ions was 45° from the surface normal. Arrows indicate the direction of the penetrating Xe ion beams. In (e), ex-amples of the NP chains and of the line structures are indicated by solid and broken circles. 4. Discussion 4.1. Possible Origins of the Optical Anisotropy It is known that SHI irradiation of CaF2 crystals induces the destruction of CaF2 and the aggregation of Ca atoms as metallic Ca collide [13–15,27]. As exhibited in Figure 3, Figure 3. Cross-sectional transmission electron microscopy (XTEM) images of CaF2 samples withoutAg NPs, irradiated with 200 MeV Xe14+ ions to the fluence of (a,b) 0 ions/cm2 (unirradiated),(c–e) 1 × 1013 ions/cm2, (f) 1 × 1012 ions/cm2, and (g) 5 × 1013 ions/cm2. C-layer denotes carbonlayers deposited on the irradiated surfaces before the FIB thinning. The incident angle of the Xe ionswas 45◦ from the surface normal. Arrows indicate the direction of the penetrating Xe ion beams. In(e), examples of the NP chains and of the line structures are indicated by solid and broken circles.Quantum Beam Sci. 2024, 8, 29 8 of 134. Discussion4.1. Possible Origins of the Optical AnisotropyIt is known that SHI irradiation of CaF2 crystals induces the destruction of CaF2 andthe aggregation of Ca atoms as metallic Ca collide [13–15,27]. As exhibited in Figure 3,SHI irradiation formed two different structures: One was parallel straight lines whichcould be ascribed to the ion tracks but may contain metallic Ca. The widths of the lines areconsistent with those of the ion tracks reported in previous literature [31]. The others arediscontinuous NP chains aligned along the SHI beam direction.First of all, it should be mentioned that the observed optical anisotropy in irradiatedCaF2 crystals is different from that induced by the shape elongation of embedded metallicNPs. It is known that the shape elongation of NPs is efficiently induced when the diametersof NPs are much larger than the widths of the ion tracks [28]. Since the Ca NPs observed inFigure 3e are comparable to the track diameter, large elongation is not expected [28]. Theanisotropic optical absorption of CaF2 induced with SHI irradiation shown in Figure 2b isnot due to the shape elongation of NPs but to another origin. It should be noted that wehave observed shape elongation of reaggregated Zn NPs which were synthesized via thedecomposition of ZnO NPs under SHI irradiation [32]. However, the shape elongation isnot the origin of the optical anisotropy from the CaF2 irradiated with SHIs.Penninkhof et al. [33] observed anisotropic optical absorption induced by SHI irradia-tion but not due to the shape elongation of NPs. They introduced Ag ions to BK7 glass viathe ion exchange of Ag+ ↔ Na+ in a hot salt melt, and they nucleated Ag NPs up to thediameters of 2–15 nm by 1 MeV Xe irradiation. Then the sample was irradiated with 30 MeVSi ions with an incidence of 60◦ off-normal to a fluence of 2 × 1014 ions/cm2. TEM observa-tion indicated that the shape elongation of NPs was not induced but chain-like structuresof NPs, which were less clear compared with those shown in Figure 3, were observed alongthe SHI beam. However, anisotropic absorption was detected. They reproduced the spectrausing FDTD simulations, assuming a linear array of four Ag NPs [33].As already described, the SHI irradiation formed the parallel line structures and theNP chains. An emerging question is which structures contribute the anisotropic absorption.To clarify this, optical absorption spectra of Ca nanorods (prolate spheroids) and Ca NPchains were numerically simulated and compared with the experimental spectra.4.2. Numerical Simulations of Optical Anisotropy SpectraComplex dielectronic functions (CDFs) of bulk Ca and CaF2 were collected fromRef. [34] and [35], respectively. The CDF of NPs is different from that of the bulk counterpartbecause of the size effects. Particularly, the mean-free-path (MFP) confinement of carriersin NPs is one of the most typical size effects in metal NPs embedded in transparentinsulators [1]. While the quantum size effect (QSE) is dominant in semiconductor NPs, it isnegligible in metal NPs, except for very small diameters [1].The CDF of bulk Ca is assumed to be described as a sum of the contribution of the freeelectrons and of the bound electrons, i.e.,εm = ε f + εb, (1)The former is assumed to be described as the Drude type:ε f = 1 −E2pE2 + iEΓ, (2)= 1 −(E2p/E2)− i(E2pΓ/E3)1 +(Γ2/E2) (3)Quantum Beam Sci. 2024, 8, 29 9 of 13where Ep and Γ denote the plasma frequency and the carrier relaxation frequency, respec-tively. When Γ << E, the denominator of Equation (3) is approximated by the unity. Thereal and the imaginary parts of εf are approximated as follows:ε f ,1 = 1 −E2pE2 , (4)ε f ,2 =E2pΓE3 , (5)The real and the imaginary parts of the CDF are plotted in Figure 4a as (1 − ε1) and Eε2versus 1/E2. Well-fitted linearities in both the plots confirm that the CDF of bulk Ca is wellapproximated by the Drude type (Equation (2)). From the slopes of curves, two quantities,Ep and Γ, were determined as 5.82 eV and 0.131 eV, respectively. Orera and Alcala reportedthe values of 5.78 eV and 0.018 eV from different analyses [27]. Since Γ is 0.131 eV inour case, the assumption of Γ << E used in the derivation of Equations (4) and (5) wasvalidated.The carrier relaxation frequency Γ in bulk is the inverse of the carrier relaxation time,i.e., it relates to the MFP of the carriers, which is mostly limited by phonon or defectscattering in the bulk. However, in the case of NPs, the carriers are confined inside of theNPs. Therefore, the MFPs cannot be longer than the diameter of NPs. The carrier relaxationfrequency Γ(d) of NPs depends on the diameter d of NPs, which is described as follows:Γ(d) = Γo +2VFd, (6)where Γo and VF denote the bulk relaxation frequency and the Fermi velocity. A value of1.28 × 108 cm/s [36] was used for VF of Ca.Optical absorption spectra of Ca NPs in CaF2 crystal were calculated by the first-orderMie theory [37] using the CDF of Ca NPs (including the MFP confinement) and the CDFof CaF2 crystal. Calculated spectra for NP diameters of 0.5, 1, 2, 3, and 5 nm are shownin Figure 4b, with comparison to an experimental spectrum. While no peak is recognizedfor the diameter of 0.5 nm, a peak grows when increasing the diameter to 2 nm or larger.While the calculated peak wavelength was 490 nm, the experimental one was 540 nm. Thepeak wavelength does not shift with the increase in diameter, as shown in Figure 4b.The different peak wavelengths between the calculations and the experiments wereexplained by Orera and Alcala assuming a pressure effect on the plasmon frequency, whichwas exerted by the matrix. However, we present another explanation: In the experimentalspectrum, a clear observation of the Ca SPR peak indicates that a high concentration ofCa atoms has aggregated, leaving a strongly damaged CaF2 lattice. While the CDF ofthe perfect CaF2 crystal was used for the calculations, the CDF of the damaged matrixmay strongly change from those of the non-damaged perfect CaF2 crystal. To simulate thechange in the matrix refractive index, the absorption spectra were calculated after changingthe refractive index from ∆n = 0.00 to +0.25 and fixing the NP diameter to 3 nm. As shownin Figure 4c, the peak shift was reproduced around ∆n ~ +0.25. The peak difference betweenthe calculations and the experiments can be ascribed to the damage of the CaF2 lattice.One of the purposes of the numerical simulations of the absorption spectra is to distin-guish which structures contribute to the observed anisotropic spectra, the line structuresor the NP chains. Using the CDF of Ca NPs of 3 nm in diameter, i.e., Equations (2) and(6), and the bound electron contribution εb in Equation (1), anisotropic absorption spectraof both the structures were simulated and shown in Figure 4d. The absorption spectra ofa Ca spheroid and of a pair of Ca spheres were calculated using the Rayleigh theory [38](MQRaylgh-2.0 code [39]) and the generalized Mie theory [40] (MQAggr-1.2 code [41]),respectively. These are because the standard Mie theory is only applicable to a singlespherical NP. Instead, the Rayleigh theory and the generalized Mie theory were applied to asingle spheroidal NP and a pair of spherical NPs, respectively. As mentioned in Figure 4b,c,Quantum Beam Sci. 2024, 8, 29 10 of 13there are discrepancies between the calculated peak wavelengths and the experimentalones. In Figure 4d, calculated spectra were plotted with the wavelength shift of +60 nm foreasy comparisons with the experimental spectra.Quantum Beam Sci. 2024, 8, x FOR PEER REVIEW 10 of 13   experimental ones. In Figure 4d, calculated spectra were plotted with the wavelength shift of +60 nm for easy comparisons with the experimental spectra.     Figure 4. Comparisons of the experimental absorption spectra of an irradiated CaF2 sample with various numerical models. (a) Black dots denote the real and imaginary parts of the CDFs of Ca metal from literature, which were plotted with 1/E2 to determine two important parameters for the Drude model, i.e., the plasma frequency Ep and the relaxation frequency . Red lines show the linear fitting of the dot data by the equations (4) and (5). Using both the parameters and the bound elec-trons’ contribution, the absorption spectra were calculated by the 1st-order Mie theory with the MFP confinement as shown in the upper half of (b). The experimental spectra at 2  1014 ions/cm2 are shown in the lower half. Spectra with different colors correspond to those from NPs with different diameters. In (c), to fit the peak wavelength, the absorption spectra were calculated with modifying the wavelength-dependent refractive index of the damaged CaF2 matrix as n + n. Four spectra with different n between 0 and 0.25 are shown by different colors. (d) The experimental spectra (iii) were compared with two models, i.e., the Ca spheroids (ii) and the closely adjacent Ca NP pair (i). Solid and broken curves denote the spectra at 90° and 0° polarization, respectively. Figure 4. Comparisons of the experimental absorption spectra of an irradiated CaF2 sample withvarious numerical models. (a) Black dots denote the real and imaginary parts of the CDFs of Cametal from literature, which were plotted with 1/E2 to determine two important parameters forthe Drude model, i.e., the plasma frequency Ep and the relaxation frequency Γ. Red lines show thelinear fitting of the dot data by the Equations (4) and (5). Using both the parameters and the boundelectrons’ contribution, the absorption spectra were calculated by the 1st-order Mie theory with theMFP confinement as shown in the upper half of (b). The experimental spectra at 2 × 1014 ions/cm2are shown in the lower half. Spectra with different colors correspond to those from NPs with differentdiameters. In (c), to fit the peak wavelength, the absorption spectra were calculated with modifyingthe wavelength-dependent refractive index of the damaged CaF2 matrix as n + ∆n. Four spectra withdifferent ∆n between 0 and 0.25 are shown by different colors. (d) The experimental spectra (iii) werecompared with two models, i.e., the Ca spheroids (ii) and the closely adjacent Ca NP pair (i). Solidand broken curves denote the spectra at 90◦ and 0◦ polarization, respectively.Quantum Beam Sci. 2024, 8, 29 11 of 13The line structures were approximated by prolate spheroids [38] with a minor axis of3 nm. While the spectra were calculated for various major axes L, only the spectra withL = 10 nm are shown in Figure 4d. While both the 0◦ and the 90◦ spectra show a peakaround 475 nm, the 0◦ spectrum shows another peak around 1000 nm, which correspondsto a mode along the longest axis of the prolate spheroids. Since the experimental spectraare only available up to 800 nm, this is not easily determined. However, it seems thatthe experimental 0◦ spectrum does not show a considerably strong peak around 1000 nm.Hence, the spheroid model does not reproduce the experimental spectra. An analyticalsolution is known for the absorption spectra of an infinitely long cylinder [38,40]. Thespectra were also calculated but qualitatively similar to those of a spheroid: i.e., the infinitelylong cylinder model also does not reproduce the experimental spectra.Another candidate is NP chains, which were simulated by a pair of closely adjacentspherical Ca NPs. As shown in Figure 4d, the pair of NPs reproduced the experimentalspectra well in terms of the spectra’s shapes, peak widths, and the degree of the anisotropyof the absorption. Here, we presumed a quite narrow gap of 0.9 nm between the two NPsin Figure 4d, because only very weak anisotropy was observed with the gap of 3 nm, andalmost no anisotropy with the gap of 6 nm. The spectra of three linearly adjacent NPs werealso evaluated, but the results were qualitatively similar with the pair of NPs.Consequently, the experimental spectra were reproduced by the NP chains but not bythe line structures.5. ConclusionsAg NPs were formed in CaF2 single crystals by implantation of 200 keV Ag+ ions toa fluence of 1 × 1017 ions/cm2, and then irradiated with SHIs of 200 MeV Xe14+ ions toproduce a fluence ranging from 0 to 2 × 1014 ions/cm2. Anisotropic optical absorption wasobserved at the SPR peak of the Ag NPs, which indicated the shape elongation of Ag NPs.In the course of the experiments, we also found that the anisotropic absorption wasdetected from CaF2 crystals not including Ag NPs when irradiated with 200 MeV Xe14+ions. XTEM observation clarified that a huge number of very thin straight lines of ~2.9 nmin width were formed, which can be ascribed to the ion tracks but possibly include theCa aggregates. High-magnification observation indicated that some parts of the lineswere continuous cylinders, and the other parts consisted of arrays of discontinuous CaNPs (typically ~3.6 nm in diameter). No clear elongation of NPs was observed. Theanisotropic optical absorption observed in irradiated CaF2 is not due to the shape elongationof decomposed Ca NPs. From the comparison with the numerical simulations, the opticalanisotropy is due to discontinuous but closely adjacent Ca NPs, but not to continuousCa cylinders.Author Contributions: Conceptualization, H.A.; sample preparation, F.C.; swift heavy ion irradiation,N.I. and N.O.; Ag ion implantation and Rutherford backscattering spectrometry, K.N., A.C., Y.H., K.Y.,S.Y. and Y.S.; optical measurements and TEM observation, H.A.; writing—original draft preparation,H.A.; writing—review and editing, N.I., K.N. and H.A. All authors have read and agreed to thepublished version of the manuscript.Funding: This research was funded by JSPS-KAKENHI, Grant number 22K04990. F.C. thanks supportfrom National Natural Science Foundation of China (NSFC) under Grant No. 12235009.Data Availability Statement: The datasets and materials generated during the current study areavailable from the corresponding author on reasonable request.Acknowledgments: A part of this study was supported by the Inter-organizational Atomic EnergyResearch Program through an academic collaborative agreement among JAEA, QST, and the Uni-versity of Tokyo. The authors are grateful to the crew of the accelerator facilities at QST-Takasakiand at JAEA-Tokai for their help. This work was supported by “Advanced Research Infrastructurefor Materials and Nanotechnology in Japan (ARIM)” of the Ministry of Education, Culture, Sports,Science and Technology (MEXT). Proposal Numbers JPMXP1223NM5040 and JPMXP1224NM5073.Conflicts of Interest: The authors declare no conflicts of interest.Quantum Beam Sci. 2024, 8, 29 12 of 13References1. Kreibig, U.; Vollmer, M. 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MQAggr-1.2; Wissenschaftlich-Technische Software: Aldenhoven, Germany, 2012.Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.https://doi.org/10.1016/S0009-2614(99)01206-3https://doi.org/10.1002/pssa.2210440239https://doi.org/10.1103/PhysRevB.78.125413https://doi.org/10.1016/S0168-583X(98)00515-1https://doi.org/10.1088/1361-6528/aa8778https://doi.org/10.1103/PhysRevB.85.054112https://doi.org/10.1063/1.4829475https://doi.org/10.1063/1.1627936https://doi.org/10.1088/0031-8949/4/6/009https://doi.org/10.1364/AO.41.005275https://doi.org/10.1002/andp.19083300302https://doi.org/10.1002/9783527633135 Introduction  Materials and Methods  Results  Anisotropic Optical Absorption  Cross-Sectional TEM Observation  Discussion  Possible Origins of the Optical Anisotropy  Numerical Simulations of Optical Anisotropy Spectra  Conclusions  References