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[H. Amekura](https://orcid.org/0000-0003-2148-8431), [A. Chettah](https://orcid.org/0000-0002-9815-0992), [K. Narumi](https://orcid.org/0000-0001-8569-0108), A. Chiba, Y. Hirano, K. Yamada, S. Yamamoto, [A. A. Leino](https://orcid.org/0000-0003-3504-548X), [F. Djurabekova](https://orcid.org/0000-0002-5828-200X), [K. Nordlund](https://orcid.org/0000-0001-6244-1942), N. Ishikawa, N. Okubo, Y. Saitoh

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[Latent ion tracks were finally observed in diamond](https://mdr.nims.go.jp/datasets/09a28200-249c-468d-8f87-624ca2f8d15c)

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Latent ion tracks were finally observed in diamondArticle https://doi.org/10.1038/s41467-024-45934-4Latent ion tracks were finally observed indiamondH.Amekura 1 , A. Chettah 2, K. Narumi 3, A. Chiba3, Y. Hirano3, K. Yamada3,S. Yamamoto3, A. A. Leino 4, F. Djurabekova 4, K. Nordlund 4, N. Ishikawa5,N. Okubo5 & Y. Saitoh3Injecting high-energy heavy ions in the electronic stopping regime into solidscan create cylindrical damage zones called latent ion tracks. Although thesetracks form in many materials, none have ever been observed in diamond,even when irradiated with high-energy GeV uranium ions. Here we report thefirst observation of ion track formation in diamond irradiated with 2–9MeVC60 fullerene ions. Depending on the ion energy, the mean track length (dia-meter) changed from 17 (3.2) nm to 52 (7.1) nm. High resolution scanningtransmission electron microscopy (HR-STEM) indicated the amorphization inthe tracks, in which π-bonding signal from graphite was detected by theelectron energy loss spectroscopy (EELS). Since the melting transition is notinduced in diamond at atmospheric pressure, conventional inelastic thermalspike calculations cannot be applied. Two-temperature molecular dynamicssimulations succeeded in the reproduction of both the track formation underMeV C60 irradiations and the no-track formation under GeV monoatomic ionirradiations.On nuclear fission of a uranium atom, fission fragments—i.e., a pair ofhigh-energy heavy ions, one with a mass number of ~95 and the otherwith a mass number of ~140—are emitted with a total kinetic energy of~170MeV.When suchhigh-energy heavy ions are injected into a solid, ahuge quantity of energy of more than 10 keV nm−1 is deposited alongthe ion trajectory. This high-energy deposition generates cylindricalregions of damage (typically a few nm in radius and around 10μm inlength for each fragment) called “latent ion tracks” (abbreviatedhereafter to “ion tracks”) along the ion trajectories in some materials;however, these ion tracks are not seen in all materials1.It is not only fission fragments that can form ion tracks: tracks canalso be formed by high-energy heavy ions from large- and medium-sized particle accelerators1. High-energy heavy ions of between tens ofMeV and several GeV, which dissipate their energy mostly via theelectronic excitation in solids, are called swift heavy ions (SHIs). Overthe past few decades, the formation of ion tracks by SHIs has been acentral topic of research in ion–solid interactions2–4 in various mate-rials including metals5, metallic compounds6, oxide superconductors7,semiconductors8, inorganic insulators9, and polymers10.The propensity for tracks to form depends strongly on theproperties of the solids. Although there are some exceptions, in gen-eral, the propensity is higher for insulators11 and lower formetals11; thatof semiconductors is in-between8,12,13. Although tracks are formed inmany insulators11, one notable exception has been diamond. It isreported that neither fission tracks14 nor ion tracks1,15 have beenobserved to form in diamonds. The propensity for track formation isgenerally higher in damaged crystals than in corresponding unda-maged crystals (which is known as the pre-damage effect8), becausethe damage reduces thermal conductivity and enhanceselectron–lattice coupling of solids16.However, even in a diamond that had been previously damagedby being irradiated with neutrons to a fluence of 2.5 × 1020Received: 13 November 2022Accepted: 8 February 2024Check for updates1National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0003, Japan. 2Department of Physics, LGMM laboratory, University of 20 Août 1955-Skikda, BP 26, route d’El Hadaiek-Skikda, Skikda 21000, Algeria. 3Takasaki Institute for Advanced Quantum Science, National Institutes for Quantum ScienceandTechnology (QST), Takasaki,Gumma370-1292, Japan. 4Department of Physics andHelsinki Instituteof Physics, University ofHelsinki, POBox43, FI-00014Helsinki, Finland. 5Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan. e-mail: amekura.hiroshi@nims.go.jpNature Communications |         (2024) 15:1786 11234567890():,;1234567890():,;http://orcid.org/0000-0003-2148-8431http://orcid.org/0000-0003-2148-8431http://orcid.org/0000-0003-2148-8431http://orcid.org/0000-0003-2148-8431http://orcid.org/0000-0003-2148-8431http://orcid.org/0000-0002-9815-0992http://orcid.org/0000-0002-9815-0992http://orcid.org/0000-0002-9815-0992http://orcid.org/0000-0002-9815-0992http://orcid.org/0000-0002-9815-0992http://orcid.org/0000-0001-8569-0108http://orcid.org/0000-0001-8569-0108http://orcid.org/0000-0001-8569-0108http://orcid.org/0000-0001-8569-0108http://orcid.org/0000-0001-8569-0108http://orcid.org/0000-0003-3504-548Xhttp://orcid.org/0000-0003-3504-548Xhttp://orcid.org/0000-0003-3504-548Xhttp://orcid.org/0000-0003-3504-548Xhttp://orcid.org/0000-0003-3504-548Xhttp://orcid.org/0000-0002-5828-200Xhttp://orcid.org/0000-0002-5828-200Xhttp://orcid.org/0000-0002-5828-200Xhttp://orcid.org/0000-0002-5828-200Xhttp://orcid.org/0000-0002-5828-200Xhttp://orcid.org/0000-0001-6244-1942http://orcid.org/0000-0001-6244-1942http://orcid.org/0000-0001-6244-1942http://orcid.org/0000-0001-6244-1942http://orcid.org/0000-0001-6244-1942http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-45934-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-45934-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-45934-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-45934-4&domain=pdfmailto:amekura.hiroshi@nims.go.jpneutrons cm−2, additional irradiation with 1.03GeV Bi ions to a fluenceof 2 × 1010 ions cm−2 induced neither track formation norgraphitization17. Zhang et al.-irradiated diamond powder with 1.4GeVU ions to much higher fluences ranging from 5 × 1012 to8 × 1013 ions cm−218. While a higher propensity was expected for dia-mond powder than the bulk crystals, the tracks were not formed in thepowder, but the graphitization was detected.The vanishingly low propensity for track formation in diamond,up to monoatomic GeV heavy ion irradiation, guarantees track-freediamond-anvil cells for applications involving SHI irradiation underhigh pressures15,19. SHI irradiation under high pressures is a powerfultool for studying the properties of minerals deep in the Earth’s crust,and extremely high-energy SHIs are required to pass through a dia-mond cell of 2–3mm in thickness. Although diamonds subjected toextremely high-energyU ion irradiation show ion penetration, no trackformation has been reported. This low propensity for the track for-mation is also applied for the formation of the nitrogen-vacancy (NV)centers in diamond using monoatomic swift heavy ion irradiationintending the quantum applications20.Higher velocity SHIs emit higher energy δ-electrons toward theradial directions, which excite the cylindrical region along the iontrajectories. The radii of the cylindrically excited regions aredetermined by the range of the δ-electrons. Consequently, highervelocity SHIs form the excited regions of larger volumes because oflonger δ-electron ranges, resulting in lower-density excitation.Lower velocity ions result in higher-density excitation, which isadvantageous for track formation. We use the term “velocity effect”in this context21,22.Here, we report the first observation of track formation in dia-monds with C60 fullerene cluster ion irradiation of between 2 and9MeV, corresponding respectively to Se of between 29 and52 keV nm−1. Tracks were not observed under 1MeV C60 irradiation(Se = 21 keV nm−1). High-resolution scanning transmission electronmicroscopy (HR-STEM) observed the amorphization in the tracks andthe partial formation of the crystalline graphite phase. The electronenergy loss spectroscopy (STEM-EELS)mapping detected a π-bondingsignal stronger in the tracks. Since diamonds do not show a meltingtransition at atmospheric pressure23, the application of the conven-tional inelastic thermal spike (i-TS) calculations is not justified. Here,we applied the two-temperature molecular dynamics (TT-MD) simu-lations and succeeded in the reproduction of both the track formationunder 2–9MeV C60 irradiation and the no track formation under GeVmonoatomic ion irradiations. One of the advantages of the TT-MDsimulations is no requirement of the input of the equilibrium meltingtemperature.ResultsThe observation of ion tracks in diamondFigure 1 shows bright field transmission electronmicroscopy (BF-TEM)images of irradiated diamond samples. As described in pastliterature1,15, no one has succeeded in using monoatomic SHIs to formion tracks in diamonds. Figure 1a illustrates this situation: A crystallinediamond was irradiated with monoatomic SHIs of 200MeV Xe14+;however, ion tracks were not observed, whichwas consistent with pastliterature1,15.In contrast, ion tracks were observed in diamond as black dots inFig. 1b under 2MeVC60+ ion irradiation. The areal density of tracks was5.8 × 1010 tracks cm−2, which was comparable to the ion fluence of5 × 1010 C60 cm−2, indicating that one track was generated by one C60ion impact. Irradiation was at an incident angle of 7° from the surfacenormal24. The electronic stopping power Se of 29 keV nm−1 for 2MeVC60 ions in diamond (which was determined as described in the“Methods” section), was identical to that of 200MeV Xe14+ ions(Se = 29 keV nm−1). Despite the identical Se, tracks were observed indiamond irradiatedwith 2MeV C60 ions but not with 200MeV Xe ions.By utilizing 2MeVC60 ions, we have succeeded in forming ion tracks indiamond for the first time.Shapes, dimensions, and the Se threshold of the tracksFigure 2 shows BF-TEM images of diamond samples irradiated with9MeV C602+ ions, with tilting angles of (a) 0° and (b) 30° (see the“Methods” section and Supplementary Methods 1 for the configura-tion). The tilting angle denotes the angle between the TEMobservationdirection and the sample surface normal. The samples were irradiatedwith the C60 ions at an incident angle of 7° from the surface normal24.Figure 2a shows black dots that were later ascribed to ion tracks indiamonds and their overlapping surface craters/hillocks.We evaluatedsome of these dots under over- and under-focus conditions and foundthat the track images (dots) changed fromblack towhite in accordancewith the defocus condition (Supplementary Note 1). The contrastreversal indicates that the dots, i.e., the ion tracks, have a lower densitythan themedium25,26. As shown in Fig. 2a, the tracks observed from thesurface normal direction are not perfectly circles but ellipses. This isprobably due to the ion incident angle being 7° from the surfacenormal since the images of the track sidewalls overlapped with thetrack diameters (see Supplementary Note 2).When the tilting angle is 30°, a long and narrow tail is observed toextend in the same direction from every ellipsoidal track-head(Fig. 2b). These long and narrow tails are ascribed to the track-bodies deeper inside the diamond. The track-bodies are visible withtilting, but not visible without tilting because the track-bodies areoverlapped by the track-heads. The track-bodies are narrower than the(a) 200 MeV Xe14+ => diamond (b) 2 MeV C60+ => diamond Se = 29 keV nm-1Sn = 0.083 keV nm-1Se = 29 keV nm-1Sn = 9.3 keV nm-120 nm20 nmFig. 1 | Bright-field transmission electron microscopy (BF-TEM) images of dia-mond samples irradiated with (a) 200MeV Xe14+ ions and (b) 2MeV C60+ ions.Both images were recorded at the over-focus conditions. Although the electronicstopping power Se is identical with both irradiations, the ion tracks are formedonlyunder C60+ ion irradiation. Sn denotes the nuclear-stopping power.Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 2track-heads, indicating that the tracks consist of a two-step structurewith two different diameters. Possible candidates are surface-craters27or hillocks28 with wider diameters around the surface than the dia-meters of the tracks in depth, as depicted in Fig. 3a. Another possiblecandidate was conical ion tracks, which were observed in Y3Fe5O12irradiatedwith 40.2MeVC60 ions29 and inTiO2with 1390MeVBi ions30,where the track diameters decreased with the depth.Figure 2c–e shows side-views of the tracks in low, medium, andhigh magnifications, respectively. Thick black layers are deposited Ptfilms for surface markers of ~20 nm in thickness, and the tracks areobserved at one side of the Pt markers. To protect the Pt markeragainst the focused ion beam (FIB) milling for sample thinning, a thickcarbon layer was deposited over it.As shown in Fig. 2d, many protrusions were observed at theprotection-layer side of the Pt marker. Judging from the image inten-sity, the protrusions are made of Pt. However, since the Pt layers weredeposited after the irradiations with C60 ions, the protrusions reflectthe shapes of the irradiated surface, probably the shapes of the hillockson the diamond surface. While the Pt thickness was thicker than theheights of the hillocks, the hillocks of quartz crystals have been suc-cessfully detected by this method24. A supporting observation of thismethod is the fact that each Pt protrusion is located on the extensionline of each ion track.It should benoted that a higher density of the tracks is observed inFig. 2c than in Fig. 2d, probably because of the greater thickness of thesample of Fig. 2c. The higher density of the tracks results in higherdensity of the Pt protrusions. Because of the overlap of the protrusionimages due to the higher density, the protrusions are not clearly dis-tinguished from each other in Fig. 2c.Figure 2e exhibits an expanded image of two ion tracks. Since thisfigure is not clear, one cannot judge whether cylindrical or conicaltracks. Therefore, the observed tracks with narrower tails (Fig. 2b)could be ascribed to surface-craters27, hillocks28, or conical tracks29,30.As shown later, a track with three legs was observed by HR-STEM. Toexplain the strange track shapes, we assume the material emissionfrom the track and deposition on the sample surface, which could bemore consistent with the hillocks and craters than the conical tracks.From the indirect observation of the hillocks in Fig. 2d, the hillocks aremost probable.Comparing the mean track diameters determined from the topview with the 0° tilting and those determined from the side view forvarious C60 energies (Fig. 3b) indicates that the mean diametersdetermined from the top views are always wider than the diametersdetermined from the side views. Error bars in Fig. 3b–d represent themean± the standard deviation (SD) of more than fifty tracks for eachcondition. The ion energy dependence of the mean track length isshown in Fig. 3c, indicating that the mean track length increases withthe energy but is quite short, i.e., 52 nm even at the maximum energyof 9MeV or less. The short track lengths are very different from thoseof SHIs.As shown in Fig. 3d, the track formation threshold Se,th of24 keVnm-1 was determined by assuming the relationship8R2track =CðSe�Se,thÞ ð1Þwhere Rtrack and C denote the mean track radius determined from theside views and a constant, respectively. Regarding the determinationof the track diameters from the side-view images, see SupplementaryNote 3. Since tracks were observed with 2MeV C60 ions(e) Side viewsurface marker (Pt)10 nm(d) Side viewprotec�on LayerdiamondhillocksPt(a) Top-view  Tilt = 0��(b) Top-view Tilt = 30�ion incident angle 7�20 nm(c) Side-view 20 nmFig. 2 | BF-TEM images of diamond samples irradiated with 9MeV C602+ ions tofluences of 5 × 1010 or 1 × 1011 C60 cm−2. Top-view images of irradiated diamond areshown with tilting angles of a 0° and b 30° from the surface normal. The C60 ionirradiations were performed with an incident angle of 7° from the surface normal.Side-view images of ion tracks in c low-, d medium-, and e high-magnifications.Thick black layers in c–e are deposited Pt films as surface markers. In d, manyprotrusions are observed at the protection-layer side of the surface maker. Whilethe observed protrusions are made of Pt, the origin of the protrusions can be thehillocks on the diamond surface, made by the ion tracks. e shows an expandedimage of two tracks. All the images a–ewere recorded at the over-focus condition.Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 3(Se = 29 keV nm-1) and higher energies, but not with 1MeV C60 ions(21 keV nm−1), the threshold value of 24 keV nm−1 is justified. However,this threshold of 24 keV nm−1 sounds too lowbecauseKhmelnitski et al.failed in the attempt to form ion tracks with 1.03GeV Bi irradiation(Se = 41.0 keV nm−1)17. As shown in the “Discussion” section, the TT-MSsimulations indicate that this inconsistency can be ascribed to thevelocity effect.High-resolution STEM observationSince ion tracks are formed more efficiently in graphite than indiamond31, it is important to confirm that the tracks are formed indiamondandnot in graphite. Toobtain local information in the vicinityand inside of the tracks, HR-STEM was applied. From lattice fringesobserved by HR-STEM, information on the crystallinity around thetracks is obtained, e.g., whether the tracks are formed in diamond orother phases, and whether the tracks are amorphous or not. For thispurpose, we used a single crystalline diamond samplewith a (100) facefor the HR-STEM observations, because fine alignment among thetrack direction, the zone axis, and the electron beamswasmuch easierusing a single crystal. The sample was irradiated along the [100] zoneaxis with 9MeV C60 ions and observed along the same direction bySTEM. Before the irradiation, the sample was thinned down to 36 nmthick, which is thinner than the mean track length of 52.1 nm with astandard deviation (SD) of 7.3 nm. Since the sample thicknessx = 36 nm is less than themean thicknessminus 2 SD, the probability ofan un-penetrating track P (x < the mean thickness–2 SD) is 2.3%.Therefore, it is almost guaranteed that the deeper ends of all the tracksreach the other side of the sample. This quite thin thickness isimportant to judge whether amorphous regions form in the tracks ornot, while the track formations in such a thin layer could be slightlydifferent from those in bulk.Figures 4a and b indicate STEM-BF images of ion tracks in dia-mond at (a) low and (b) mediummagnification. While many tracks areobserved in Fig. 4a, most of the tracks show white cores and blackshells. Figure 4c is a fast Fourier transform (FFT) pattern of a highmagnification image (not shown), and Fig. 4d was reconstructed fromthe signal inside the red circle in Fig. 4c by filtering the inverse FFT tostress the lattice fringes. While the lattice fringes of diagonal squaresare observed outside the track, which is consistent with the diamondlattice, an amorphous region was observed in the track. Between thetrack core and the diamondmatrix, black regionswere observed. Sinceit is a STEM-BF image, the white core is ascribed to lower density orthinner thickness. Contrary the black track “shells” can be ascribed tohigher-density regions or simply greater thickness. The high-angleannular dark field STEM (HAADF) observationwas also carried out andconfirmed these density/thickness changes as shown in Supplemen-tary Note 4. While this is only speculation, the core became in lowerdensity or lesser thickness due to material emission induced by theFig. 3 | Ion energy dependences of (b) the mean track diameter and of (c) themean track length indiamond. Inb, the trackdiametersdetermined from the top-views (0°) and the side-views are indicated by closed and open circles, respectively.The difference between them indicates the two-step structures of the tracks, whosecandidate structures are schematically shown in (a) as surface craters and hillocks.In d, squared mean radii of the tracks determined from the side views are plottedagainst Se, indicating the track-formation threshold of 24 keVnm−1. In b–d, errorbars represent themean± the standard deviation (SD), of more than fifty tracks foreach condition.Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 4track formation. Parts of the emitted material were deposited at thesurround of the track, and formed thicker regions, which are observedas the black peripheries of the track shown in Fig. 4d. However, furtherstudies are necessary to confirm this speculation.While Fig. 4c shows bright spots of 022- and 004-related diffrac-tions from the diamond lattice, four diffuse spots are observed muchcloser to the center spot than the diamond D022 spots. These spotscannot be ascribed to the diamond but to the graphite G002 andG00-2. Since G002 and G00-2 appear as a pair of spots, the observation ofthe four spots indicates the existence of crystalline graphite grains ofdifferent orientations. HR-TEM observations show both the formationof amorphous regions at the track cores and of the crystalline phase ofgraphite.Chemical bonding inside the ion tracksSince the possible existence of graphite in the track is suggested by thediffuse ring (spots) in the STEM-FFT pattern (Fig. 4c), it is important toknowwhat carbonphase (graphite G or diamondD) is dominant insidethe ion tracks. Since the mean track diameter (from the side view) is7.1 ± 1.3 nm (mean± SD) under 9MeV irradiation, it is possible to useSTEM-EELS tomap the phase inside the tracks because the spot-size ofSTEM-mode of JEM-2100F is 0.5 nm, i.e., much smaller than the meantrack diameter.Figure 5a shows a STEM image of ion tracks in diamonds observedunder conditions optimized for the EELSmeasurements but not for theSTEM observation. The purpose of this low-quality image (Fig. 5a) is toindicate that the line-scanning of STEM-EELS was performed along thegreen line shown. Figure 5b shows the EELS spectra around the C 1sedge. Spectra from literature for graphite and diamond are shown atthe bottom of Fig. 5b by blue and red circles, respectively32. The gra-phite phase shows a characteristic peak at 285 eV, which is ascribed tothe transition from the occupied 1s to an unoccupiedπ* level. Also, thegraphite phase shows a plateau from 295 to 308 eV, while the diamondphase exhibits a valley at 303 eV and an isolated peak at 306 eV.Colored solid curve spectra shown above were detected at variousdistances x from the track center from0 to 30 nmalong the line shownin Fig. 5a. While the intensity depends on the distance, always a faintpeak is observed at 285 eV which is attributed to the π* peak.The experimental EELS spectra I(E) (thin colored curves) in Fig. 5bwere fitted as the sum of the standard data of graphite IG(E) and dia-mond ID(E)32 by adjusting the graphite ratio y, i.e.I Eð Þ= yIGðEÞ+ ð1� yÞIDðEÞ, ð2Þwhere 0 < y < 1. The optimized curves were shown by thin black linesand the optimized ratios y were shown in Fig. 5b. The graphite ratio ywas the highest at the center of the track, which reached y =0.30. Theratio y decreased with the distance from the center of the track.This indicates that non-negligible content of graphite or at leastπ-bondings exist in the track cores. This observation could be consistentwith the observation of broad graphite spots in the FFT pattern shownin Fig. 4c. However, it should be noted that the EELS spectrum(x =0 nm) in Fig. 5b was detected at the center of the track. Further-more, the spot size of our EELS was 0.5 nm, i.e., much smaller than thetrack diameter of 7.1 ± 1.3 nm (the mean± SD), and the tracks areconnected to the other side of the samples. Therefore, the observedEELS spectrum (x =0nm) was detected from the severely irradiatedregion. Even though, the diamond phase of only 30% transforms to thegraphite phase. The 70% are not transformed to graphite after a C60ion impact.Figure 5c indicates the dependences of the π* peak intensity andof the graphite ratio y along the distance from the track center: The π*peak has a maximum at the center of the track and decreases with thedistance from the center up to 7 nm. Beyond the distance of 7 nm, thepeak intensity becomes almost constant even up to 30nm. The ratio yshows almost similar dependence as the π* peak. While the constantintensity of the π* peak outside the track could be ascribed to damageintroduced during the FIB thinning, further increment of the peakinside the track is definitely ascribed to the impact of a C60 ion.Comparing the mean track radius of 3.6 nm for 9MeV C60 irradiationdetected by TEM observations, the EELS line-scanning provided thedamage zone radius of ~7 nm. However, this disagreement can bereasonable because the π* peak represents the distribution of the πbonds, while the tracks represent damage aggregates of nanometricsizes. The spatial distribution of the π bonds may expand wider thanthe radius of the tracks. Different track radii depending on the mea-surement methods, e.g., TEM, XRD, and Raman scattering, werereported by, e.g., Lang et al. 33.Asdescribed, Zhang et al. irradiateddiamondpowderwith 1.4GeVU ions to much higher fluences ranging from 5 × 1012 to8 × 1013 ions cm−2, i.e., 100–1600 times higher than the present study of5 × 1010 ions cm−2. Zhang et al. observed no track formation but thegraphitization18. In this work, the track formation was induced with2–9MeV C60 ion irradiations to the diamond. Partial transitions fromsp3- to sp2-bondings, i.e., graphitization, were observed in the tracks in2 nm(b)(a)(d)d022(c)0 2-20 0-40-2-20 2 20-2 20 0 4[1 0 0]5 nm-1Fig. 4 | Scanning transmission electron microscopy bright-field (STEM-BF)images of ion tracks formed under 9MeV C60 ion irradiation incident to the[100] zone axis of a single crystalline diamond. The ion fluence was 5 × 1010C60 cm−2. a Low and b medium magnification images. c a fast-Fourier transform(FFT) image of a high magnification image (not shown). d was reconstructed fromthe signal inside the red circle in c by filtering the inverse FFT. The sample wasthinned down to ~36 nm thick by FIB milling, which is thinner than the mean tracklength of 52.1 ± 7.3 nm (the mean± SD), excluding the contribution of unirradiatedbottom deeper than the track ends. One of the interplane distances is indicated ind as d022. Since we used a TEM with the spherical aberration correction, theScherzer defocus was not applied.Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 5addition to the amorphization. Furthermore, FFT patterns indicate theformation of crystalline graphite.DiscussionA broadly accepted model for ion track formation is the inelasticthermal spike (i-TS) model22, in which the tracks are considered as aconsequence of the melting/vaporization phase-transition (under theatmospheric pressure) of the target material induced by the high-density energy deposition from a penetrating ion. However, diamondbehaves differently: While the i-TS model presumes the melting tran-sition under atmospheric pressure, diamond melts under extremelyhigh pressure only. When heated at atmospheric pressure, the dia-mond does not melt but transforms to graphite at 2000–2200K23,34and then sublimates itself around 4300K23,35. Therefore, the applica-tion of the i-TS calculations is not justified to diamond. Amore generalapproach is required: Here we have applied the two temperaturemolecular dynamics (TT-MD) simulations: This model describes themotions of C atoms interacting via the interatomic potentials underrapid energy deposition from the electronic system,without assumingany phase transitions such as themelting of diamond or graphitization(see the “Methods” section and Supplementary Note 5). This is incontrast with the i-TS model, where the phase transition temperature,mostly the melting temperature at the equilibrium, should be input.Furthermore, the TT-MD simulations could detect the track formationwithout phase transitions, i.e., without melting and vaporization.Here a C60 ion is modeled as an ion with high Se and quite lowvelocity. To compare the effect of the low velocity of C60 ions and highvelocity of GeVmonoatomic ions, TT-MD simulations were carried outat two different velocities of 4.93MeVu−1 (GeV monoatomic ion) and0.05MeVu-1 (C60 ion) for three different Se (20, 40, and 60 keV nm−1).Figure 6a and b show top- and side-views of simulation cells after thecomputation time of 100 ps from each ion impact. For the high-velocity cases (a), a track was not formed at 20 keV nm-1. In the case of40 keV nm-1, the damage was localized close to the surface only asshown in the side view, indicating that it is no longer a continuoustrack. A continuous track was formed at 60 keV nm−1. Contrary, a trackwas formed even at the lowest Se of 20 keV nm−1 for the low velocitycases (b). With increasing Se, the track diameter increased. The simu-lated tracks look almost spherical from the top, which is nearly con-sistent with low-magnification BF-TEM images (Figs. 1b and 2a) but notwith high-magnification STEM images (Fig. 4).The simulation and experimental results on the track diameterswere plotted in Fig. 6c. Error bars in Fig. 6c represent the mean dia-meter ± SDofmore thanfifty tracks (experimental) andmore than fourregions of one track (simulations) for each condition. Red circlesrepresent simulation results for the low velocity (0.05MeVu−1), whichwell reproduced the experimental track diameters (green circles)under C60 ion irradiations between 2 and 9MeV. An exception was at20 keV nm−1. While the simulated result shows the track formation, ithas not been experimentally confirmed. However, apart from thefidelity of the simulation model, this difference could be ascribed tothe fact that the destruction of C60 molecules by the nuclearcollisions13,29 is not considered in the TT-MD simulations. Due to thenuclear collisions, the mean track length was shortened to 17 nm for2MeV irradiation as shown in Fig. 3c.Khmelnitski et al. reported that tracks were not formed in dia-mondunder 1.03GeVBi irradiation (4.93MeVu−1)17; this observation ofthe null tracks is indicated by a purple triangle in Fig. 6c. Since it wasreported that trackswere not formed indiamondwithU ion irradiationof any energy15, the highestSe attainable byU ions, i.e., themaximum Seat the Bragg peak (Se = 49.3 keV nm-1 at 1.1 GeV U, 4.62MeVu−1), isFig. 5 | Scanning transmission electron microscopy-electron energy loss spec-troscopy (STEM-EELS) of an ion track in diamond. The sample was irradiatedwith 9MeV C602+ ions at a fluence of 5.0 × 1010 C60 cm−2. a A STEM image of iontracks observed under conditions optimized for EELS measurements but not forSTEM. The purpose of this low-quality image a is to indicate that the location of theline-scanning of STEM-EELSwas performed along a green line.b EELS spectra at theC 1s edge. Blue and red spectra at the bottom are literature data of graphite anddiamond, respectively32. Upper spectra were experimentally measured at variousdistances x from the center of the track. Each spectrum was fitted by Eq. (2) as thesum of the standard spectra of graphite and diamond32 with optimizing the gra-phite ratio y. The optimized curves are shownby thin black curves. Theπ* peakwasindicated by a vertical broken line. c The intensity of the π* peak and the optimizedgraphite ratio y are plotted along the distance from the center of the track. Ahorizontal broken line is a guide for the eye.Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 6plotted by a purple square (see Supplementary Note 6). As alreadydescribed, the simulation results indicated almost no track formationat 40 keV nm−1 for the high velocity, which is consistent with theexperiments. While the track formation is predicted at 60 keV nm−1even for the high velocity, it is impossible to confirm, because thehighest Se attainable by a monoatomic ion is 49.3 keV nm−1, whichcorresponds to the Bragg peak of U ion (purple square). Therefore, notrack formation under high-velocity monoatomic ion irradiations isalso reproduced by the TT-MD simulations.Consequently, Fig. 6c has obviously clarified why ion tracks arenot formed with swift monoatomic ions and why tracks are formedwith slow MeV C60 ions at the same Se. The difference is due to thevelocity effect. However, it should be noted that an approximationwasprovided to apply the TT-MD simulations to a C60 ion impact. Whileeach C atom consisting of a C60 molecule is injected to a differentposition within the size of the C60 molecule (the radius of 0.35 nm),sixty C atoms are approximated to be injected to the same position inthe simulations. Since the radius in which 66% of the electronic energyis stored is 0.4 nm for each C ion in the present case, cooperativeenergy deposition is possible between C ions at different sites. How-ever, this effect probably results in the enlargement of the excitationvolumes, i.e., the reduction of the excitation density. The presentsimulations should overestimate the track radii. However, the experi-mental results were well-reproduced by the simulations. We cannotexclude other effects such as the synergy effect between Se and Sn toenhance the track radii.Therefore, the following scheme is proposed for track formationin diamonds. Tracks were formed under 2–9MeV C60 ion irradiation.The track formation thresholdwas estimated tobe24 keV nm-1 for slowMeVC60 ions and ~50 keV nm−1 or higher for fastmonoatomic ions. Thedifferent threshold is primarily ascribed to the velocity effect, which issupported by the TT-MD simulations. However, contributions fromother effects cannot be excluded. Our success in forming ion tracks indiamonds is ascribed to the application of MeV C60 ions, which areslow and have a lower track-formation threshold. HR-STEM observa-tions and EELSmapping indicate that the track regions are amorphousand havemore sp2-bondings than outside the tracks. Broad diffractionof crystalline graphite was also detected by FFT of HR-STEM images.MethodsSample preparationPoly-crystalline and single-crystalline diamond self-standing samples,both of which were grown by the chemical vapor deposition (CVD)technique, were purchased from Element Six Co. At first, the poly-crystalline samples were utilized for all the experiments, then thesingle-crystalline samples of 3mm×3mm×0.25mm in dimensionswere utilized for further HR-STEM and STEM-EELSmeasurements. Thecrystal face of 3mm× 3mm corresponded to the (100) of diamond,while the other faces of 3mm×0.25mm corresponded to the (010)and (001).Optical transmission spectroscopy in the ultra-violet and visibleregions of the poly-crystalline samples was performed and verified theoptical transparency up to the intrinsic bandgap energy of ~5.5 eV36.Also, the CVD growth guaranteed that the samples had little con-tamination from common impurities found in natural diamonds. Evenin polycrystalline, the grain sizes were as large as several micrometersor more. While typical dimensions of the TEM samples were ~5 µm×~10 µm,we seldom recognized the existence of grain boundaries duringthe TEM observations. See Supplementary Note 7 for more details.TEM specimens were prepared in two different configurations(pre-thinned, thinned before ion irradiation; post-thinned, thinnedafter ion irradiation) to observe the top and side views of the iontracks13. See Supplementary Methods 1 for details. The pre-thinnedspecimens were thinned down with 30 keV Ga focused ion beam (FIB)milling to a thickness of ~100nm or thinner and were held on TEMgrids. While the thickness of ~100 nm sounds thick, the low atomicnumber of diamonds assisted the electron transmission. A single-crystalline sample for STEM observations was thinned down to 36 nmin thickness. Then the pre-thinned specimens with the TEM grids wereirradiatedwithC60 ions at an incident angle of 0° or 7° from the surface(c)(a) 4.93 MeV u-120 keV nm-1 40 keV nm-1 60 keV nm-1topside(b) 0.05 MeV u-1topside20 keV nm-1 40 keV nm-1 60 keV nm-16 nmFig. 6 | Two-temperature molecular dynamics simulations of ion track forma-tion in diamond. Top- and side-views of simulation cells are shown for a high(4.93MeV u−1) and b low (0.05MeVu−1) velocity irradiations, at three differentSe = 20, 40, and 60 keVnm−1. The projectiles are injected at the center of the topsurface, and the simulations were performed up to 100ps after the ion impact. Thevisualizations display subsections of the simulation cell at the end of each simu-lation. Atoms are drawn as blue dots using an orthographic projection, and the topview is oriented in the [001] direction while the side view is in [010]. The simulatedand experimental results on the track diameters were plotted in (c). Red circlesrepresent simulation results for low velocity (0.05MeVu−1), which well reproducedthe experimental trackdiameters (green circles) underC60 ion irradiations between2 and 9MeV. The absence of track formation by 1.03GeV Bi ions and by the highestSe of U ions are indicated by a triangle and a square in purple, respectively. Thesimulateddiameters for the high velocity (4.93MeVu−1) are shownby cyan squares.Error bars represent the mean diameter ± SD of more than fifty tracks (experi-mental) and more than four regions of one track (simulations) for each condition.The visualizations were created using the OVITO PRO software49.Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 7normal, to evaluate the top views of the tracks (the track diameterdistributions). The single-crystalline sample for STEM observationswas irradiated along the [001]. In the case of the post-thinned speci-mens, bulk CVD samples were irradiated with C60 ions without thin-ning, and the cross-sectional samples were thinned down by FIBmilling to observe the side views of the tracks (the track length dis-tributions). To identify the surface position of the post-thinned sam-ples, a thin layer of Pt was deposited onto the sample surface beforeFIBmilling. Themethodwasbasically similar towhatwe had applied tocrystalline silicon before13.Because of the much lower sputtering yield of diamond, morethan ten times higher FIB fluence was required for thinning of thesamples compared with Si. Since tracks are embedded in the surfacelayer of the post-thinned samples, the surface layer was protected by athick layer of deposited carbon. Despite this precaution, track layerswere sometimes lost due to the extremely high FIB fluences. Thethinning process was quite time-consuming and required special care.C60 ion irradiationIrradiation of diamond samples with C60 ions was conducted at theTakasaki Institute for Advanced Quantum Science, of the NationalInstitutes for Quantum Science and Technology (QST), using a 3MVtandem accelerator and a newly developed high-flux C60 negative ionsource37. Powder of C60with a purity of 99.5%was used. C60 ions with acharge state of +1 (C60+) were utilized between 1 and 6MeV irradia-tions, while those with a charge state of +2 (C602+) were utilized for9MeV irradiation. Because of the magnetic mass separation, singlycharged ions were free from contamination with fragments. However,doubly charged 9MeV C602+ ions could possibly be contaminated withfragments of singly charged 4.5MeV C30+ ions, because of the samem/q ratio. However, the amount of contaminating 4.5MeV C30+ ionswas negligible compared to the 9MeV C602+ ions. See SupplementaryNote 8 for more details.The samples were irradiatedwith low fluences of 5 × 1010 or 1 × 1011C60 cm−2 to avoid creating overlapping tracks. The ion incident anglewas set to 7° from the surface normal, except for a sample forHR-STEMobservation; an incident angle of 0° was applied. For comparison,some samples were irradiated with 200MeV Xe14+ ions from the tan-dem accelerator at the Japan Atomic Energy Agency (JAEA), TokaiResearch and Development Center.The Se and Sn ofmonoatomic ionswere estimated fromSRIM2013code38. Those of C60 ions were estimated from the following rela-tionship:Si E,C60� �= γiN � SiðE=N,C1Þ ð3Þwhere i = e (electronic)39 or i = n (nuclear)40, andN = 60 is presumed forC60 ions. Although γi ≈ 1 is frequently assumed in Eq. (3), the assump-tion of γe ≈ 1 was recently bolstered by Kaneko’s calculations41. Kanekoconcluded that γe is approximated as a constant of ~0.8 between 2 and10MeV C60 ions41. In this paper, γe = 1 is assumed for Eq. (3). For moredetails, see Supplementary Note 9.TEM observationThreedifferent transmission electronmicroscopes (TEM)were utilizedfor different purposes, while all operated at 200 kV. Bright-field TEMobservation of the two configurations (pre- and post-thinned samples)was conducted using a JEOL JEM-2100 microscope. HR images wereobserved using a JEOL JEM-ARM200F with the spherical aberrationcorrection since thed-valueof diamond [220] is very small as0.126 nm.Scanning TEM (STEM) and electron energy loss spectroscopy (EELS)mapping and the high-angle annular dark field STEM (HAADF) wereconducted using a JEOL JEM-2100F microscope. For the EELS, theenergy loss range between 230.0 and 497.8 eV was detected. To avoidthe sample shift during the EELS measurements, the measurementsoftware compensated the shift with occasionally observing STEMimages. To alternatively carry out both the EELS and STEM, a relativelylong camera length of 20 cm was used for EELS measurements.Two-temperature molecular dynamics simulationsSimulations using the two-temperature molecular dynamics model(TTMD) are performed following the method by Ivanov and Zhigilei42,which is implemented inPARCASMDcode43–45 anddescribed in ref. 46.It incorporates electronic effects into classical molecular dynamicswith a friction termFi =�∇iV ~r� �� �+ ξvi ð4Þwhere Fi is the force acting on the i-th particle, V is the original Tersoffpotential (i.e., without the λ3-term)47, and vi is the velocity. The secondterm provides coupling with the electronic part of the two-temperature model42,Ce Te� �∂Te∂t=∇ Ke Te� � � ∇Te� �+G Te� �Te � T l� �, ð5ÞTe t =0ð Þ=Aðr?Þ ð6Þwhich is solved on a 51 × 51 × 1 finite difference grid over the MDsimulation domain (23 nm× 23 nm× 13 nm) in size. Te is the electronictemperature, C(Te) the electronic heat capacity, and Ke(Te) the elec-tronic heat conductivity, holding the relation Ke(Te) =Ce(Te)De, whereDe is the electronic heat diffusivity. G(Te) is the effective electron-phonon coupling and A r� �describes the electronic temperature afterthe initial electronic collision cascade. The magnitude of the frictionterm ξ is solved by requiring that the total energy of the system (heatequation + kinetic energy in MD simulation) is conserved at eachtimestep. More details are described in Supplementary Note 5.The simulation cells are prepared with a relaxation run using theBerendsen thermo- andbaro-stat48 to 300K,0GPa for 50 ps. The initialenergy deposition is calculated so that the ion passes through the cellin the shortest direction (i.e., 13 nm), and the atoms near the fourremaining outer boundaries are cooled to 300K with a rapidBerendsen thermostat. To simulate the impact, the system is let toevolve for 100ps. After this time, the resulting track radii are deter-mined by measuring the size of the circular, darker regions from thetop views in Fig. 6 by eye. At least fourmarkers around each region areused to determine the radius and the error.Data availabilityThe datasets generated during the current study are available from thecorresponding author on request. Source data are provided withthis paper.Code availabilityThe code and software used in this work are PARCAS, OVITO, QUAN-TUM ESPRESSO, and SRIM which are openly available online from thecorresponding developers and maintainers. OVITO PRO, which is notopen source, was used to create the MD visualizations, but a similaranalysis can be achieved with the open-source version.References1. Lang, M., Djurabekova, F., Medvedev, N., Toulemonde, M. & Traut-mann, C. 1.15— fundamental phenomena and applications of swiftheavy ion irradiations. In Comprehensive Nuclear Materials 2nd edn(eds Konings, R. J. M. & Stoller, R. 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Sci.Eng. 18, 015012 (2010).AcknowledgementsA part of the study was supported by the Inter-organizational AtomicEnergy Research Program through an academic collaborativeagreement among JAEA, QST, and the University of Tokyo. Theauthors are grateful to the crew of the accelerator facilities at QST-Takasaki and at JAEA-Tokai for their help. H.A. was supported byJSPS-KAKENHI Grant number 22K04990. TEM observation was per-formed using the facility of the NIMS TEM station. F.D. acknowledgesResearch Council of Finland SPATEC project #349690. Weacknowledge CSC (Finland) for awarding this project access to theLUMI supercomputer, owned by the EuroHPC Joint Undertaking,hosted by CSC (Finland) and the LUMI consortium through devel-opment access program.Author contributionsK.Na., A.Chi., Y.H., K.Y., and Y.S. have developed the high-flux MeV C60ion beam. H.A. prepared samples. Y.S., A.Chi., Y.H., S.Y., and K.Na.conducted C60 ion irradiation. N.I. and N.O. conducted 200MeV Xeirradiation. H.A. conducted TEM observations. A.Che. carried out i-TScalculations. A.L., F.D., and K.No. carried out TT-MD simulations. All theauthors joined in the discussion of the results and contributed tomanuscript preparation.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-45934-4.Correspondence and requests for materials should be addressed toH. Amekura.Peer review information Nature Communications thanks StephenDonnelly, Weixing Li and the other, anonymous, reviewers for theircontribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-45934-4Nature Communications |         (2024) 15:1786 10https://doi.org/10.1038/s41467-024-45934-4http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Latent ion tracks were finally observed in diamond Results The observation of ion tracks in diamond Shapes, dimensions, and the Se threshold of the�tracks High-resolution STEM observation Chemical bonding inside the ion�tracks Discussion Methods Sample preparation C60 ion irradiation TEM observation Two-temperature molecular dynamics simulations Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information