Latent ion tracks were finally observed in diamond

Injecting high-energy heavy ions in the electronic stopping regime into solids can create cylindrical damage zones called latent ion tracks. Although these tracks form in many materials, none have ever been observed in diamond, even when irradiated with high-energy GeV uranium ions. Here we report the first observation of ion track formation in diamond irradiated with 2–9 MeV C60 fullerene ions. Depending on the ion energy, the mean track length (diameter) changed from 17 (3.2) nm to 52 (7.1) nm. High resolution scanning transmission electron microscopy (HR-STEM) indicated the amorphization in the tracks, in which π-bonding signal from graphite was detected by the electron energy loss spectroscopy (EELS). Since the melting transition is not induced in diamond at atmospheric pressure, conventional inelastic thermal spike calculations cannot be applied. Two-temperature molecular dynamics simulations succeeded in the reproduction of both the track formation under MeV C60 irradiations and the no-track formation under GeV monoatomic ion irradiations.

Supplementary Figure 4. BF-TEM side-view images of diamond samples irradiated with C60 ions of (a) 2 MeV, (b) 4 MeV, (c) 6 MeV, and (d) 9 MeV.The contrast was modified to clarify the ion track images.model [3], (  ) = ∇(  (  ) ⋅ ∇  ) + (  )(  −   ), ( = 0) = ( ⊥ ) which is solved on a 51  51  1 finite difference grid over the MD simulation domain (23 nm  23 nm  13 nm) in size.  is the electronic temperature, (  ) the electronic heat and   (  ) the electronic heat conductivity, written as   (  ) =   (  )  , where   is the electronic heat diffusivity.(  ) is the effective electron-phonon coupling and ( ⊥ ) describes the electronic temperature after the initial electronic collision cascade.Each grid cell has the same volume   .Within the cell, local lattice temperature   is determined using the kinetic energy.The lattice temperature can be used to resolve the magnitude of the friction term  by requiring that the total energy of the system (heat equation + kinetic energy in MD simulation) is conserved at each timestep [3], The sum goes over all atoms (atomic mass ) in the finite difference cell volume.Each MD timestep contains at least two finite difference timesteps.To stabilize the numerical solver, initially MD timestep of only Δ = 2 × 10 −6 fs is used that gradually grows to Δ = 0.1 fs during the first picosecond.
The parameters of the heat equation are based on an electronic temperature dependent electronic heat capacity that is determined up to 10 5 K using Quantum Espresso [9,10].For these computations, the diamond unit cell is relaxed, and the density of states, () , is The effective electron-phonon coupling can be approximated as (  ) = (  )/, where  is the exponential relaxation rate of the electronic-temperature without spatial gradients.Sadasivam et al. [11] has studied the electron-phonon relaxation based on the semiclassical transport equations using electron-phonon scattering rates as determined by density functional perturbation theory.The relaxation rate is determined by fitting a value of  = 60 fs to the electronic temperature evolution of diamond under uniform excitation (given in the Supplemental Material of Ref. [11], p. 24).The diffusivity value is not well known.We use a value of De =1.3 cm 2 s -1 to be consistent with earlier studies of SHI effects in nitrogen doped diamonds [12].For 1 GeV Au ion (as used in Ref. [12]), continuous tracks appear below De = 1.0 cm 2 s -1 and there is almost no effect above De = 2.0 cm 2 s -1 .We have also tested that value up to De = 1.6 cm 2 s -1 gave similar results to those reported here.
( ⊥ ) is the initial temperature determined by first estimating the initial energy density near the ion trajectory using the delta-ray production formula developed by Chunxiang [13], normalized so that it yields the electronic stopping power as predicted by SRIM 2010 code [14], and translating it to initial temperature by integrating the electronic heat capacity.
The simulation cells are prepared with a relaxation run using the Berendsen thermo-and baro-stat [15] to 300 K, 0 GPa for 50 ps.The initial energy deposition is calculated so that ion passes through the cell in the shortest direction (i.e., 13 nm), and the atoms near the four remaining outer boundaries are cooled to 300 K with a rapid Berendsen thermostat.To simulate the impact, the system is let to evolve for 100 ps.After this time, the resulting track radii are measured visually using at least four different locations at different sides of the track.

determined using a 16 
16  16 Monkhorst-Pack k-point grid with kinetic energy cutoff of 200 Ry and a total of 100 bands.Computations are performed with the Projector-Augmented wave (PAW) technique and the Perdew-Burke-Ernzerhof functional (C.pbe-n-kjpaw_psl.1.0.0.UPF from www.quantum-espresso.org).From () , the chemical potential is solved using the bisection method and conservation of total number of electrons.Once the chemical potential is known, the heat capacity is determined by evaluating   (  ) = ∫ ((  ),  )