Synergy of elastic and inelastic energy loss on ion track formation in SrTiO 3

Transcription

1 Synergy of elastic and inelastic energy loss on ion track formation in SrTiO 3 William J. Weber 1,2*, Eva Zarkadoula 2, Olli H. Pakarinen 2, Ritesh Sachan 2, Matthew F. Chisholm 2, Peng Liu 1, Haizhou Xue 1, Ke Jin 1, Yanwen Zhang 2* 1 Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA. 2 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. * wjweber@utk.edu; zhangy1@ornl.gov Irradiation effects in SrTiO 3 At temperatures below ~370 K, irradiation of SrTiO3 with MeV ions leads to a crystalline-to-amorphous transformation due to the production and accumulation of atomic defects created by elastic atomic collision cascades 1-3, and partially disordered states due to ion irradiation exhibit oxygen and cation point defect recovery stages below 350 K 4. Epitaxial recrystallization of irradiation-induced amorphous layers in SrTiO3 is observed for irradiation with 0.2 MeV electrons at 300 to 400 K 3 and with 0.2 to 2.0 MeV ions at 373 to 523 K 1. For swift heavy ions, energy transfer to electrons dominates, and irradiation at 300 K in this energy regime with 92 MeV Xe ions also leads to complete amorphization 5. While individual ion tracks, with diameter of ~5 to 6 nm, have been observed for ions with electronic energy loss values from Present address: School of Physics, State Key Laboratory of Crystal Materials and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Jinan , China 1

2 20 to 50 kev/nm (92 MeV Xe to 2.0 GeV U ions) 5,6, the structure of the tracks remains uncertain, since high-resolution TEM has only revealed a recrystallized structure 5 and smallangle x-ray scattering only indicated a constant track density, different than the matrix, and a sharp boundary between track and matrix 6. Irradiation with swift heavy ions (electronic energy loss values of 19 and 22 kev/nm) at glancing incident leads to the formation of chains of nanosized hillocks 7,8. Sample preparation and ion irradiation details The [100] oriented single crystal SrTiO3 samples (15mm 15 mm 0.5 mm), obtained from MTI Crop. ( were irradiated at 7 off the [100] direction with 900 kev Au ions at 300 K to an ion fluence of 0.13 ions/nm 2, which created a distribution of defects with a damage peak (relative disorder of 0.07) at a depth of ~90-95 nm (Fig. 1a, main text) and an implanted Au profile with a peak concentration (~15 appm) at a depth of ~130 nm. After initial characterization of disorder distribution by RBS/C along the [100] direction, the samples were irradiated with 21 MeV Ni ions at 7 off the [100] direction. The irradiations and RBS/C were conducted at the Ion Beam Materials Laboratory at the University of Tennessee 9. Electronic and nuclear energy loss of the 21 MeV Ni in SrTiO3 were determined as a function of depth using the Stopping and Range of Ions in Matter (SRIM) code 10,11. The average displacement dose in dpa (displacements per atom) for both Ni and Au ions was estimated under full-cascade simulations, assuming a sample density of g/cm 3 with threshold displacement energies of 80 ev for Sr 12, 70 ev for Ti 12, 45 ev for O 13,14 sublattices, respectively. The conversion factor at the damage peak from ion fluence (1 ion/nm 2 ) to dose (dpa) is under the 900 kev Au irradiation at 7 off the surface normal. 2

3 Structural characterization Rutherford backscattering spectrometry in channeling geometry (RBS/C) is sensitive to atomic displacements along major crystallographic channeling directions, where the probing He ions are backscattered from interstitials or disordered atoms, and is used along the crystallographic channels to quantitatively determine irradiation-induced damage in crystalline samples. The virgin sample (as-received, undamaged single crystal wafer), pre-damaged (900 kev Au-irradiated) samples, and Ni-irradiated virgin and pre-damaged samples were characterized by RBS/C along the [100] direction. The measurements were performed using a 3.5 MeV He ion beam with Si detectors located at scattering angles of 155 relative to the incoming beam. The beam energy of 3.5 MeV was chosen due to the lower electronic energy loss in the surface region (0.32 kev/nm as compared with 0.43 kev/nm of a 2.0 MeV He beam), and, therefore, to have less possible influence on the SrTiO3 structure and a wide separation of the damage yield between the Sr and Ti signals for dechanneling analysis 15. HAADF imaging was performed on various samples in a 5th order aberration corrected scanning transmission electron microscope (Nion UltraSTEM200) operating at 200 KV. A detector with an inner angle of 65 mrad was used to collect electrons for HAADF imaging. The electron probe current used in the experiment was 16 pa. As mentioned in the main text, no changes in the track diameter were observed after continuous HAADF imaging. To support this statement, a movie of an ion track exposed for 15 sec under the electron beam is provided as Video S1. The movie was made by stacking sequential HAADF images collected with a 16 pa probe current and exposure time of 5 sec/pixel. The originally collected images were 512 x 512 pixels, and the scanning flyback time was 400 sec between two scanning lines. 3

4 Direct impact model for amorphization from ion tracks If a single ion results in a continuous amorphous track, the increase in the fraction of amorphous phase, fa, with increasing ion fluence,, is given by the direct or single impact model 16,17 : fa = 1 exp(- a ), (1) where a is the amorphous cross section of the track. Because of the pre-existing disorder or damage in the samples prior to irradiation with 21 MeV Ni ions, equation (1) is modified to take into account the local pre-existing disorder, fo, at any given depth. This modified direct impact model is given by: fa = fo + (1 fo) [1 exp(- a )], (2) or more simply: fa = 1 (1 fo) exp(- a ). (3) Equation (3) was used to fit the increase in disorder with ion fluence (Fig. 2a of main text) at different depths to obtain track cross sections, but using only ion fluences up to 0.02 ions/nm 2, as shown in Fig. 1S. The track diameters, dt, shown in Fig. 2b of the main text were readily obtained from the relationship: 4

5 Figure S1. Relative disorder as function of ion fluence at different depths. (Error bars are one standard deviation about the mean measured disorder. Solid lines are fits of Eq. 3 to the data.) a = (dt/2) 2. (4) At ion fluences above 0.02 ions/nm 2, the increase in relative disorder as a function of ion fluence becomes superlinear, exhibiting a more sigmoidal approach to amorphization. This behavior is believed to be due to an increase in track diameter with the accumulation and overlapping of tracks, which is already suggested by the increase in track diameter with initial level of disorder at different depths (Fig. 2b). The accumulation and overlapping of amorphous tracks probably lead to further decreases in the electronic and atomic thermal conductivity, and perhaps an increase in the electron-phonon coupling constant. A model of amorphization that includes this 5

6 change in track diameter with increasing ion fluence will require additional research and simulations. Two-temperature model calculations and molecular dynamics simulations We used an inelastic thermal spike model 18 suitable for insulators to include the electronic energy loss effects in the simulations. In this model, the atomic and the electronic subsystems are coupled and the energy exchange between them is described via a set of heat diffusion equations: one describing the evolution of the electronic temperature, Te, as given by equation (5), and one describing the evolution of the atomic temperature, Ta, as given by equation (6). 1, The hot electrons transfer energy to the lattice via the electron-phonon interactions. The second term on the right side of the equations (5) and (6) represents the energy exchange between the electronic and atomic subsystems due to the difference between Te and Tα. The parameters and are the specific heat coefficients of the electronic and atomic systems, respectively; whereas, and are the thermal conductivities of the electronic and the atomic systems, respectively. The term is the electron-phonon coupling parameter, and, describes the energy deposition from the incident ion to the electrons 19. 6

7 Figure S2. Spatial evolution of temperature with time based on the two-temperature model for 21 MeV Ni ions: (a) defect-free crystalline SrTiO3, and (b) SrTiO3 containing 1.5% defects. For the crystalline configuration, we used 1 J cm -3 K -1 and as previously suggest 18,20, where the electron diffusivity,, of 1 cm 2 s -1 is assumed 18,20. The value of was set equal to 11.2 W m -1 K -1, and a specific heat of J g -1 K -1 is used 21. For the pre-damaged system, irradiation-induced defects are known to scatter phonons and electrons resulting in significant decreases in the thermal conductivity of irradiated ceramics 22,23 ; therefore, we decreased both and by an order of magnitude, which is reasonably consistent with the large changes in thermal conductivity of SrTiO3 due to processing defects 24 or cation nonstoichiometry (a few percent) 25. The value of was calculated, as detailed elsewhere 20, to be W m -3 K -1. We used a value 40% larger, W m -3 K -1, for the pre-damaged sample to account for the decrease in the electron-phonon mean free path due to defects. The time and spatial dependencies of the atomic temperature are shown in Fig. S2a,b for the defect-free system and the system containing 1.5% defects. 7

8 The large scale MD simulations (7 million atoms) were performed using a simulation cell without any defects and a simulation cell containing the equivalent of ~1.5 % Frenkel defects. The Frenkel pairs were introduced randomly in the system, and the system was then relaxed under constant pressure and temperature. We provide two videos of the MD results. In both videos, for clarity, we show only the interstitials in the system, defined using the sphere criterion 26. Strontium atoms are shown in blue, titanium atoms in green, and oxygen atoms in purple. The first video (Video S2) shows the response of the defect-free crystalline SrTiO3 system to the thermal spike from a 21 MeV Ni ion, where only a small number of defects are created and total recombination of the defects occurs after a few ps. The second video (Video S3) shows the evolution of the thermal spike for a 21 MeV Ni ion in the pre-damaged simulation cell, where the conductivities of the atomic and the electronic systems are reduced due to disorder, and where the electron-phonon coupling is stronger. A large number of displaced atoms are produced, most of which return to atomic lattice sites after about 5 ps due to elastic recombination. After a MD simulation time of about 10 ps, the system is relaxed, and a clearly formed ion track is observed along the ion path, i.e., in the z direction. In this video, the reflection of a large amount of energy from the MD boundaries is observed. The MD boundaries cannot absorb the excess energy, and it is reflected back into the system, resulting in the creation of the waves seen in the video. The simulations have been re-run in a larger simulation box (~12 million atoms) to test this effect, and the results of the larger simulation indicate no impact of the waves on the final formation of the amorphous track. Total simulation time was 10 ps for the pristine crystalline system and about 40 ps for the pre-damaged system. For the visualization of the MD results, AtomEye 27 was used. 8

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