Swift heavy ion tracks in alkali tantalate crystals: a combined experimental and computational study

The formation of latent tracks with different damage morphologies in alkali tantalate crystals (KTaO3 and LiTaO3) under the action of the extreme electronic energy loss induced by 358 MeV 58Ni19+ irradiation was studied by experimental characterizations of the lattice damage and numerical calculations using the inelastic thermal spike model. Prism coupling measurements were used to analyze of the refractive index profiles of irradiated regions. This approach is effective and very accurate for determination of the in-depth damage profile and its correlation with the energy loss curves. The calculated spatio-temporal evolution of the energy deposition densities and lattice temperatures theoretically demonstrate the experimentally observed latent tracks in Ni19+-irradiated crystals. Based on the observed damage morphologies of individual and overlapped spherical defects, and discontinuous and continuous tracks, the corresponding threshold values of the electronic energy loss for track damage in alkali tantalate crystals were assessed. For irradiating ions with an energy of 6.17 MeV amu–1, a threshold of ~12.0 keV nm−1 for the production of spherical defects in KTaO3 crystals is indicated, and the threshold for LiTaO3 crystals is less than 12.0 keV nm−1. For irradiating ions with an energy of 2.15 MeV amu–1, owing to the ion-velocity dependence effect, an electronic energy loss of ~13.8 keV nm−1 leads to overlapped spherical defects and discontinuous tracks in KTaO3 and continuous tracks in LiTaO3. Compared with LiTaO3, a relatively higher damage tolerance and critical threshold for track formation in KTaO3 crystals are proven. The determined lattice temperature threshold for continuous track production is 3410 K for KTaO3 and slightly less than 3250 K for LiTaO3, demonstrating that, compared with the melting point, a much higher lattice temperature in the region surrounding the ion path needs to be achieved to produce stable track damage due to the non-negligible effect of melting damage caused by annealing during the cooling process.


Introduction
In the field of radiation research, study of the interactions between energetic ions and solid materials is fundamental to understanding the responses of materials to ion irradiation and the induced effects on microstructure and performance [1][2][3][4]. Irradiating a solid material with swift heavy ions leads to intense electronic excitation and thermal spike responses due to inelastic collisions between moving ions and target electrons [5][6][7]. One of the major consequences of this interaction is the molten phase induced along the path of ion penetration and the subsequent latent track with a width of a few nanometers and length of several tens of micrometers [8][9][10][11].
The properties in such nanoscale regions containing lattice disorder or an amorphous phase are drastically changed and modified compared with the surrounding virgin bulk. Thus, swift heavy ion irradiation is a powerful technique that is utilized to study the undesirable phenomena (creep, swelling, embrittlement, etc) occurring in irradiation environments [12][13][14][15][16] but also has beneficial applications in material modification and device fabrication on the nano-and micrometer scales [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Alkali tantalate crystals (KTaO 3 , LiTaO 3 , etc) with perovskite-like structures exhibit versatile properties that are attractive for numerous applications, such as electro-optic waveguides in microelectronics [32], pyroelectrics in neutron generation [33] and photocatalysts in pollutant degradation [34] and water splitting [35]. According to recent work, the abovementioned properties can be effectively modified by the introduction of ion-irradiation-induced defects and nanostructures [20,36]. Utilizing swift Ni 19+ ion irradiation, the present work focuses on the thermal spike responses and latent track behaviors of alkali tantalate crystals under the action of different ion energies and electronic energy losses. Different damage morphologies, from individual and overlapped spherical defects to discontinuous and continuous tracks, are discussed, and the corresponding threshold values are determined. The temperature threshold is used to define the condition for generation of latent track damage from a thermodynamic perspective, and could be used to discuss the track behaviors corresponding to different electron energy losses and ion velocities under different irradiating ion species and ion energies. In this work, the introduced temperature threshold is demonstrated to be a more fundamental and essential parameter for determining the latent track behaviors; it is broadly applicable and makes the experimental results for different irradiation conditions comparable. Addressing these issues can not only provide a deeper scientific understanding of the puzzling scenario of ion track formation in insulators but also contribute to a foundation and assessment for ion-irradiation applications in the fields of material modification and nanostructure fabrication.

Alkali tantalate crystals and ion irradiation processes
The single-crystal (1 0 0) KTaO 3 (perovskite structure with cubic Pm3m symmetry) and (0 0 6) LiTaO 3 (ilmenite structure with rhombohedral R3c symmetry) samples with dimensions of 10 mm × 10 mm × 0.5 mm were irradiated at 300 K with 358 MeV 58 Ni 19+ at fluences of 1 × 10 12 , 3 × 10 12 and 3 × 10 13 cm −2 , respectively. The swift Ni 19+ ion irradiations were carried out at the Heavy Ion Research Facility in Lanzhou (HIRFL), Institute of Modern Physics, Chinese Academy of Sciences, which has relatively precise energy and fluence calibrations, and could guarantee the repeatability of the irradiation experiment. During the irradiation process, a relatively low Ni 19+ -beam current density and ion flux (8.1 × 10 10 cm −2 s −1 ) were used in order to avoid undesired ion beam annealing and charge accumulation on the samples [37].

Experimental characterizations of latent track damage
The track damage in alkali tantalate crystals induced by swift Ni 19+ irradiation was characterized through prism coupling, Rutherford backscattering spectroscopy in channeling configuration (RBS/channeling), high-resolution x-ray diffraction (HRXRD) and transmission electron microscopy (TEM) techniques. Prism coupling measurements were carried out utilizing a Metricon model 2010 prism coupler in a nearinfrared wavelength band (1539 nm diode laser). In the RBS/ channeling analysis, a 2.0 MeV He + beam with a probe size of 2 mm × 2 mm was extracted from an NEC 2 × 1.7 MV tandem accelerator, and a Si detector located at a scattering angle of 160° relative to the He + beam was used to collect the backscattered He + signal. The HRXRD measurements were performed using a Rigaku Smartlab high-resolution x-ray diffractometer, in which a Cu K α1 anticathode with a Ge monochromator was used to provide a parallel and monochromatic x-ray beam with a wavelength of 1.54 Å. In the measurements, ω-2θ scans were recorded with a step size of 0.0012°. Cross-sectional TEM samples of alkali tantalate crystals were prepared by a standard method including polishing, dimpling and then Ar ion milling with a Gatan 695 precision polishing system, and were observed with an FEI Tecnai G2 F20 transmission electron microscope. The damage characterization experiments were also carried out several times in order to confirm the accuracy and repeatability of the analysis results.

Simulations and analysis of the track damage effect
The electronic energy loss and displacements per atom (dpa) induced by irradiating alkali tantalates with 358 MeV Ni 19+ were determined by using the Stopping and Range of Ions in Matter (SRIM) 2013 full-cascade simulation code [38,39]. In these two crystals, the displacement energies of Li, K, Ta and O atoms were set as default values in the SRIM simulation code (25, 25, 25 and 28 eV, respectively). Based on the results of prism coupling measurements [40], the refractive index profiles in Ni 19+ -irradiated regions were reconstructed by utilizing the inverse Wentzel-Kramers-Brillouin (iWKB) procedure [41,42]. The spatio-temporal evolutions for the energy deposition and lattice temperature induced by electronic energy loss were numerically calculated with the inelastic thermal spike (iTS) model [43,44]. The experimentally observed lattice damage and latent track behavior in alkali tantalate crystals were analyzed based on the iTS calcul ation results.

Experimental characterizations of latent tracks in alkali tantalate crystals
As shown in figure 1(a), the metallographic cross-section images of Ni 19+ -irradiated KTaO 3 and LiTaO 3 samples clearly indicate the regions with irradiation-induced damage. Under 58 Ni 19+ irradiation with a fluence of 3 × 10 12 cm −2 , the LiTaO 3 crystal sample was obviously darker than the KTaO 3 crystal sample at the position of peak electronic energy loss, providing evidence that the transmissivity decreased considerably. Therefore, more severe irradiation damage was observed in the LiTaO 3 crystal than in the KTaO 3 crystal. Electronic energy loss and simulated dpa depth profiles corresponding to 358 MeV 58 Ni 19+ irradiation with a fluence of 3 × 10 13 cm −2 are shown in figure 1(b), as indicated by the black solid curves and red dashed curves, respectively. The peak values of dpa corresponding to 58 Ni 19+ irradiation at a fluence of 3 × 10 13 cm −2 are 0.037 and 0.028 for the KTaO 3 crystal and LiTaO 3 crystal, respectively. Based on the damage accumulation curve [36,45], the disorder levels of the Ta sublattice in KTaO 3 crystal and LiTaO 3 crystal corresponding to the related dpa values are 1.9% and 3.2%, respectively. Owing to the low 58 Ni 19+ fluences (1 × 10 12 , 3 × 10 12 and 3 × 10 13 cm −2 ) and absolute dpa values in the present work, the nuclear energy loss process (S n , elastic collisions between Ni 19+ and target nuclei, dominant at the end of the ion range) would not cause significant lattice damage and could be considered negligible. Thus, the irradiation damage shown in figure 1(a) is ascribed to the intense electronic energy loss process (S e , inelastic collisions between Ni 19+ and target electrons). Under the action of 358 MeV 58 Ni 19+ irradiation, the electronic energy loss in the KTaO 3 and LiTaO 3 surface regions is ~12.0 keV nm −1 , and the maximum electronic energy loss located at the Bragg peak (~18.0 µm depth) is ~13.8 keV nm −1 , as shown in figure 1 In this work, the prism coupling technique was first used to rapidly evaluate the in-depth damage evolution profile in the surface and its correlation with the peak electronic energy loss regions of Ni 19+ -irradiated KTaO 3 and LiTaO 3 samples. Unlike other characterization experiments (RBS/channeling, TEM, etc) limited by large facilities or complex sample preparation processes, prism coupling measurements can be directly carried out on ion-irradiated samples by utilizing a miniature prism coupler. As shown in the schematic diagram in figure 1(c), utilizing the prism coupling technique the light intensity corresponding to TE or TM modes (depending on the axial orientation of the electric field vector) was measured using lasers. When the electronic energy loss located at the Bragg peak produces obvious lattice damage, the refractive index of the buried damaged layer (optical barrier) decreases owing to the damage-induced lattice swelling/disordered ion tracks embedded in the crystalline host matrix; then, the laser beam propagating in the prism can couple into the surface region via an evanescent field effect, leading to a decrease in the output laser power. The presence of sharp drops in the measured light intensity spectrum indicates the production of a buried damaged layer located at the Bragg peak. In addition, the knee point in the light intensity curve corresponds to the refractive index of the region just below the sample surface; thus, a distinguishable change in the surface refractive index measured in the ion-irradiated sample compared with the virgin sample indicates the production of surface damage. The curve shown in the schematic diagram (figure 1(d)) indicates the light intensity obtained by the prism coupling measurement, which is obtained from [46] and used to illustrate the physical mechanism of prism coupling experiments. Therefore, prism coupling measurements can quickly provide basic knowledge about the production of irradiation-induced damage and the evolution of its depth profile in transparent materials.
The prism coupling measurements were carried out utilizing a Metricon model 2010 prism coupler at a visible band (633 nm He-Ne laser) and a near-infrared wavelength band (1539 nm diode laser). The measured light intensity spectra corresponding to 58   , and for the virgin (0 0 6) LiTaO 3 crystal with the rhombohedral ilmenite structure the characteristic peak located at 2θ = 84.33° corresponds to a reflection from the (0 0 1 2) plane (JCPDS card no. 71-0953). Upon increasing the Ni 19+ fluence to 3 × 10 13 cm −2 , the broadening of the main peak in the KTaO 3 sample indicates the production of damage in the buried layer located at the Bragg peak; compared with the HRXRD peak of a virgin sample, the peak obtained from the 58 Ni 19+ -irradiated LiTaO 3 sample exhibited a clear shift to the lower-angle side and broadening behavior. Ion irradiation increased the lattice constant and interplanar spacing, and caused lattice swelling and tensile strain in the track damage region. The HRXRD peak shifted substantially to a lower diffraction angle with an increasing number of connected defects [47]. Thus, with the increase in irradiating 58 Ni 19+ fluence, the irradiation-induced defects and track damage inside the LiTaO 3 crystal increased, and the corresponding peak significantly shifted to a lowerangle side. The structural characterizations obtained from RBS/channeling and HRXRD measurements further confirm the above discussions based on the prism coupling results. In order to describe the accumulation of irradiation-induced damage, one LiTaO 3 sample was also irradiated with 58 Ni 19+ to a fluence of 9 × 10 12 cm −2 . In the initial experiment, based on the RBS/channeling spectra shown in figure 2(b), the Ta sublattice disorder in the surface regions of Ni 19+ -irradiated LiTaO 3 samples was further calculated utilizing a classical approximate expression, where χ i , χ v and χ r are the backscattering yields of the irradiated sample under the channeling condition, and the virgin sample along the channeling direction and with a random orientation, respectively [48]. The Ta sublattice disorders were further calculated utilizing a classical approximate expression. However, the obtained disorder levels of the Ta sublattice are not sufficient to determine the trend between the lattice disorder and irradiating ion fluence. Therefore, one LiTaO 3 sample was further irradiated with 58 Ni 19+ to a fluence of 9 × 10 12 cm −2 . The obtained relative disorder of the Ta sublattice at the LiTaO 3 surface region as a function of the irradiating 58 Ni 19+ fluence (damage accumulation curve) is shown in figure 3(a). In combination with the prism coupling measurements, the relationship between Ta sublattice disorder and refractive index corresponding to different wavelengths is fitted by a polynomial expression, as shown in figure 3(b). Swift heavy ion irradiation can modify the refractive index to facilitate a better understanding of the physical mechanisms of ionmatter interactions, which is essential for designing materials with new functionality for technological applications of novel devices. In this work, the obtained quantitative relationship between the irradiation fluence (lattice disorder) and the refractive index provides the necessary data and evidence for the optical applications of swift heavy ion irradiation.
The damage in KTaO 3 and LiTaO 3 crystals induced by swift Ni 19+ irradiation was directly observed by utilizing the TEM technique. Cross-sectional TEM images taken of the surface and peak electronic energy loss regions in the samples

Numerical calculations of track damage formation with the iTS model
The mechanism of latent track damage in ion-irradiated alkali tantalate crystals is now further discussed using the iTS model [43,44]. Electronic energy deposition from irradiating ions onto target electrons results in an electron cascade via electron-electron interactions. Due to the difference between the electron temperature and lattice temperature, the deposited energy is then transferred from the hot electron subsystem to the cold lattice subsystem through electron-phonon coupling, leading to a local increase in temperature along the ion trajectory. Once the electronic energy loss exceeds a certain threshold, local melting appears, and via a subsequent rapid quenching process a latent track containing a region of lattice damage and an amorphous volume can be formed. The energy and temperature evolutions of the electron and lattice subsystems can be numerically calculated by utilizing the following classical heat diffusion equations: where T e and T a , C e and C a , and K e and K a are the temperatures, specific heat coefficients and thermal conductivities of the electron and lattice subsystems, respectively, g is the electron-phonon coupling parameter and A (r, t) describes the spatio-temporal energy deposition from the irradiating ion onto the electron subsystem. The K a and C a profiles of KTaO 3 and LiTaO 3 crystals as a function of lattice temperature T a used in the calculation process are shown in figures 6(a) and (b) [51][52][53][54][55][56], respectively. For both KTaO 3 and LiTaO 3 , C e was set to 1.0 J cm −3 K −1 and K e was set to 100 W m −1 K −1 , because K e = C e × D e [44], where D e is the electron diffusivity (1.0 cm 2 s −1 ) [57,58]. In [44], based on the experimental results for different materials, the relationship between λ and band gap was fitted. The fitting result indicates that the value of λ appears to be directly related to the inverse of the band gap energy. Based on the band gap energies of KTaO 3 (3.6 eV) and LiTaO 3 (4.7 eV) [35], the values of the electron-phonon mean free path λ could be deduced according to [44]; in this work these were 4.7 nm for KTaO 3 and 4.2 nm for LiTaO 3 . Thus, because λ 2 = C e × D e /g, the g values of the KTaO 3 and LiTaO 3 crystals were set to 4.5 × 10 18 W m −3 K −1 and 5.7 × 10 18 W m −3 K −1 , respectively. The spatio-temporal evolution of the energy deposition densities and lattice temperatures induced by the action of the electronic energy losses were numerically calculated. As shown in figures 6(c)-(f), the lattice temperatures in the surface and peak electronic energy loss regions of the Ni 19+irradiated KTaO 3 and LiTaO 3 crystals increased to 3410 K and 4140 K and 3250 K and 4070 K, respectively, substantially exceeding the melting points (1625 K for KTaO 3 and 1923 K for LiTaO 3 ) and leading to the formation of a molten phase. During the subsequent cooling process, due to recrystallization occurring at the cylindrical crystal-melt interfaces, the radii of the experimentally observed latent tracks (individual spherical defects and discontinuous and continuous cylindrical damage zones shown in figures 4 and 5) are smaller than the radii of the calculated molten regions shown in figures 6(e) and (f). For different penetrating ion energies and electronic energy losses, different energy deposition densities and lattice temperature increments will be achieved, leading to different damage responses and latent track morphologies in KTaO 3 and LiTaO 3 crystals. Unlike the well-understood production of continuous tracks by relatively high electronic energy losses, the formation of individual spherical defects and discontinuous tracks in the irradiated regions is far more complicated. It can be ascribed to statistical fluctuations of the ion charge state owing to electron capture and loss processes along the ion penetration path, and the subsequently induced non-homogeneous energy deposition [59,60]. The statistical fluctuations of the ion charge are immediately followed by corresponding fluctuations of the momentary energy loss (E mom ): if E mom is only slightly higher than the threshold value (E th ) for damage formation, then the capture of electrons by a penetrating ion would reduce E mom to below E th , resulting in an undamaged lattice structure; if E mom is only slightly lower than E th , then the loss of electrons by a penetrating ion would increase E mom to above E th , leading to the production of lattice damage. In this way, when the electronic energy loss is around E th for damage formation, individual spherical defects can be formed; when accompanied by increasing electronic energy loss, discontinuous and continuous latent tracks would be formed. Thus, as shown in figures 4(a) and 5(a), under 58 Ni 19+ irradiation with an energy of 6.17 MeV amu -1 (surface regions), very few individual spherical defects are produced in the surface region of the KTaO 3 crystal, and an E th of ~12.0 keV nm −1 for formation of individual spherical defects in a KTaO 3 crystal is determined in the present work, indicating that the corresponding lattice temperature calculated by the iTS model is the lattice temperature threshold for irradiation damage. Both spherical defects and discontinuous regions of track damage are produced in the surface region of the LiTaO 3 crystal, and the related E th for a LiTaO 3 crystal should be slightly less than 12.0 keV nm −1 , indicating that the corresponding lattice temper ature calculated by the iTS model is slightly higher than the lattice temperature threshold.
Accompanying the reduced ion energy and increased electronic energy loss along the ion penetration path, more significant track damage was produced in the peak electronic energy loss region than in other regions. The E th for track formation is also dependent on ion velocity [49] and decreases upon reducing the ion velocity. Therefore, as shown in figures 4(c) and 5(c), under ion irradiation with an energy of 2.15 MeV amu -1 (peak electronic energy loss regions), the E th for individual spherical defect formation in KTaO 3 and LiTaO 3 crystals should be further reduced and somewhat less than 12.0 keV nm −1 , and the electronic energy loss of ~13.8 keV nm −1 in the present work leads to overlapping spherical defects and the formation of discontinuous tracks in the KTaO 3 crystal and continuous tracks in the LiTaO 3 crystal. In the iTS model, compared with the energies of irradiating ions and electronic energy losses, the induced lattice-temperature evolution is more fundamental and essential to understanding the track damage behavior. As shown in figures 6(e) and (f), the related lattice temperature evolution demonstrates that, compared with the melting points (1625 K for KTaO 3 and 1923 K for LiTaO 3 ), a much higher lattice temperature in the region surrounding the ion path needs to be achieved to produce stable track damage due to the nonnegligible effect of melting damage caused by annealing during the cooling process. Thus, a lattice-temperature threshold for the production of track damage is introduced: 3410 K for the KTaO 3 crystal and slightly less than 3250 K for the LiTaO 3 crystal. The different track behaviors in alkali tantalate crystals under different irradiation conditions (ion energies, velocities and electronic energy losses) could be comparatively studied by calculating and comparing the irradiation-induced spatiotemporal evolution of the lattice temperature with the lattice temperature threshold determined in this work.

Conclusions
In this work, employing 358 MeV 58 Ni 19+ irradiation to produce intense electronic energy loss, the induced damage responses and latent track morphologies in alkali tantalate crystals (KTaO 3 and LiTaO 3 ) were studied. The utilized prism coupling technique has allowed us to obtain a complete refractive index profile, turning this into an effective and accurate method for studying damage behavior. The analysis of the irradiated region is rapidly conducted, providing a basic understanding of irradiation-induced damage behavior in various crystals. According to the iTS model calcul ations, the spatio-temporal evolution of energy deposition densities and lattice temperatures reflects the experimentally observed latent tracks in Ni 19+ -irradiated alkali tantalate crystals. Compared with the melting point, a much higher lattice temper ature in the region surrounding the ion path needs to be achieved to produce stable track damage due to the non-negligible effect of melting damage caused by annealing during the cooling process. More remarkable is the observation of individual and overlapped spherical defects and discontinuous Figure 6. (a), (b) Temperature-dependent thermal conductivities and specific heat coefficients of the KTaO 3 and LiTaO 3 lattice subsystems used for iTS model calculations. Spatiotemporal evolutions of (c), (d) energy deposition densities and (e), (f) lattice temperatures in the surface and peak electronic energy loss regions of Ni 19+ -irradiated KTaO 3 and LiTaO 3 crystals, as numerically calculated using the iTS model. and continuous tracks induced by different electronic energy losses and ion energies; thus the threshold values for the production of track damage with different morphologies were determined. In addition, numerical calculations of the iTS model point out that the lattice temperature along the ion penetration path increases to 3410 K and 3250 K. Therefore, a lattice temperature threshold for track production, which is more fundamental and essential than the energy of irradiating ions and electronic energy loss, is introduced and assessed to be 3410 K for KTaO 3 and slightly less than 3250 K for LiTaO 3 . Compared with the LiTaO 3 crystal, a higher critical threshold value is found for the KTaO 3 crystal, indicating relatively high damage tolerance behavior under the action of extreme electronic energy loss. Our experimental findings and numerical calculations involving the latent tracks not only facilitate a better understanding of ion-solid interactions but also contribute to a foundation for ion-irradiation applications, such as the design and fabrication of nanoscale-to-microscale structures in crystals through swift heavy ion irradiation and subsequent selective chemical etching techniques, tailoring new advantageous features for novel photonic applications.