The depth profile of 150 MeV Ni ⁺¹¹ ions in KBTW crystal was theoretically simulated by SRIM software [41]. Figures 1A, B shows the longitudinal and cross-sectional view respectively post normal irradiation which suggests a nearly homogeneous irradiation effect. The energetic ions while penetrating predominantly loses its energy either via collision with nuclei (Sn) or with the atomic electrons (Se). The energy loss by these two processes in KBTW is summarized in Figure 1C. It is evident that the inelastic interaction with electron (Se) dominates initially upto a depth of 12μ m with a initial maximum value of 1.2 keV/Å. Thereafter, the nuclear interactions start increasing with a maximum at 0.025 keV/Å for penetration depth of 18 μ m. Thus, based on thermal spike model the top layer from surface up to 12μ m can be considered as electron loss layer and from 12μ m to 19μ m as nuclear loss layer. Thus the type of defects and imperfections created by ion track will vary from surface to penetration 17 μm with a straggle of 15 μm.

The Le-Bail analysis of the pristine sample is represented in Figure 2A. As evident from the Le-Bail fitting, all the observed peaks belongs to the orthorhombic B2cb space group-symmetry with a = 5.6085 (12), b = 5.38146), and c = 49.4763) Å, respectively. The structure parameters clearly indicate that crystal structure of KBTW is similar to a typical Aurivillius structures with 5-layered perovskite stacking sandwich between Bi ₂ O ₂ layers. A detailed structural analysis is in communication and hence not discussed in this article. The penetration of ions (20 μm) is much larger than the interaction depth of x-rays in solids and thus explains the observed amorphous nature in irradiated ceramic (Figure 2B, bottom curve). This result is agreement with the SRIM calculations [42, 43].

The tapping mode AFM imaging was carried out to examine the surface effects and is shown in Figures 2C, D for pristine and irradiated sample respectively. The roughness profile for both the samples was measured with the aid of inbuilt processing software. The root mean square roughness of the sample shows nearly 10 times increase post treatment. The sample also shows formation of deep trenches, cracks and grain damage. A visible change is colour towards dark shade can be understood by localized heating caused while loosing of ion energy to the lattice. This result is consistent with other published works in functional ceramics [44-46].

To characterize the microstructural changes, the secondary electron imaging was performed. The unirradiated KBTW ceramic shows a plate like grain morphology, typical of bismuth layered structures Figure 2E. The grain distribution in sintered sample has an average crystallite size of 0.36 μ m. The changes induced by Ni ⁺¹¹ ions in its irradiated counterpart is clearly visible in electron micrograph, Figure 2F. The crystallites are fragmented into smaller grains and the agglomeration to form clusters is also observed. Due to diffused grain boundaries, it is challenging to measure the grain size after irradiation. This irradiation damage can be understood by the distribution of kinetic energy of the ions to the lattice. If the energy imparted is greater than the binding energy, the excessive energy can rise the local temperature resulting in localize melting, resulting in the observed amorphization of the surface [47, 48]. A more information on defect kinetics and grain dynamics during ion-beam exposure, can be gained by in situ measurements [49]. Thus, the combination of XRD, AFM and SEM provides more comprehensive information of surface morphology, and internal damage structure.

The temperature (100K–420 K) and frequency (10 Hz–2 MHz) dependence of the real part of the dielectric constant (ϵ′) for KBTW ceramics before and after irradiation is shown in Figure 3. The ϵ′ was observed to show a low frequency dispersion for KBTW with large values at low frequency (Figure 3B) and decrease monotonically with increase in frequency. The pristine KBTW follows a non-linear modified Debye equation. This equation indicate the presence of multiple relaxation mechanism due to surface boundaries effects, usually dominating at lower frequencies, and also termed Maxwell -Wagner (MW) polarization [5]; [50-52]. The ϵ′ was also observed to show a temperature dependence, and increases with temperature. However, no dielectric phase transition was observed for the pristine KBTW in the performed experimental range of temperature. This frequency and temperature dependence is in agreement with conventional dielectric systems [53-55]. As mentioned in the introduction the dielectric constant is related to the total polarizability by Clausius-Mossotti relation. Different polarization mechanisms such electronic, ionic, orientational, space charge and hopping creates dipoles and add to give total polarizability of the system [5]. The dielectric behavior for irradiated sample can be divided into two parts below and above 350 K. Below the transition temperature, the dielectric constant was observed to show an appreciable decrease in dielectric constant. A comparative change post irradiation at high frequency (2 MHz) is summarized in Table 1. This decrease in dielectric constant is attributed to the introduction of defects by irradiation which provides additional inertia to dipole relaxations.

Notably, the irradiated sample shows an anomalous change with increase in temperature near 350 K indicating a phase transition. This drop in dielectric constant (Irr ϵ′) was observed to show a frequency dependence as well. Interestingly, in irradiated KBTW the dielectric constant further drops to negative value above critical temperature (350 K) at radio frequencies. This anomalous transformation to negative dielectric constant state via SHI irradiation is not reported in literature. In presence of an external electric excitation all the conventional polarization mechanisms (electronic, ionic, orientational, hopping, space charge and spontaneous) aligns in the direction of field. All the induced as well as preexisting dipoles add up to give a positive value of effective dielectric constant. The negative value suggests that the net polarization opposes the external field. In present case the transition was observed above TC, indicating the thermally activated mechanism. This could be understood as either increase in the value of depolarizing.

Field (which opposes the applied field) or creation of new dipolar mechanism induced by SHI plausibly by trapping of charge carriers. A similar response was observed in polycrystalline PrMn O ₃, wherein negative value is explained by modified Drude model which allows the formation of electron-electron pair [56].

Modulus Study: The frequency dependence of imaginary part of the modulus for temperatures above transition temperature shows frequency dependence (Figure 4A). The broad dispersive peak representing a dielectric relaxation is shown by solid symbols for pristine K ₂ Bi ₄ Ti ₄ WO ₁₈. The peak maxima (ω _max) shift towards higher frequency with increase in temperature showing presence of a glassy phase. The irradiated ceramic also exhibit a similar dispersive peak with higher value of M″ and a small change in ω _max. Surprisingly, in addition to a broad dispersive peak several dispersive peaks were observed (Figure 4B). The irradiated ceramic also exhibit a similar dispersive peak with higher value of M″ and a small change inω _max. Surprisingly, in addition to a broad dispersive peak several dispersive peaks were observed. The temperature dependence of frequency maximum (ω _max) follows an Arrhenius relaxation given by ω max = A e ( − E a / K B T ) were E _a is activation energy, K _B is Boltzmann’s constant and T is temperature. A single activation barrier in pristine sample is found at 0.3 eV, while that for irradiated sample is at 0.337 eV. The higher activation energy is in agreement with decrease in value of dielectric constant. Notably, the irradiated sample shows multiple relaxation maxima’s with different barrier height. Thus the potential profile of irradiated samples can be seen as a system with multiple activation energies. As a result different relaxation mechanisms will dominate depending on the signal frequency, and temperature. At high temperature mechanism with high activation energy dominates whereas on decreasing temperature lower barrier hopping will become more probable. These temperature and frequency dependent peak maxima’s shows the presence of multiple dielectric relaxations, which are induced by Ni+11 ion implantation. A similar relaxation is observed in relaxor ferroelectrics, wherein the presence of short range polar nano regions have been known to shows a second order dispersive phase transition to ordered state. It is possible for SHI’s to create defects and local electric order by displacing ions from their equilibrium positions. This isolated short range orders are plausible reason for observed multiple ‘glass-like’ dielectric dispersion [57, 58].

AC Conductivity Study: The frequency dependence of the real part of the ac conductivity, σ′ at different temperatures above transition temperature is shown in Figure 5A. The conductivity was observed to increase with temperature, indicating a thermally activated charge transport in these ceramic. However, a significant enhancement (7 times) in conductivity was also observed post irradiation. This SHI induced enhancement can be understood by introduction of charge carriers by metallic Ni+11 ions. These values are in agreement with the dielectric response. However, no anomalous change in the conductivity (which is related to ϵ ^″) above the transition temperature suggest the dielectric response is intrinsic in nature. The real part of the ac conductivity,σ′ was observed to follow the universal response proposed by Jonscher: σ(ω, T) = σ _dc + Aω ⁿ , where ω is angular frequency, T is temperature, σ _dc is dc conductivity, and A is a constant, and n is a temperature dependent exponent [59]. A deviation from this ‘universal’ response can be seen in the (inset of 5 A)) irradiated samples. The energy imparted by SHIs’ is extremely large and can cause disruption in terms of breaking of bonds, introduction of defects, strain and vacancies. This result in formation of new barrier potentials which when subjected to ac fields display overall increase in macroscopic conductivity and also manifest itself in terms of observed multiple dielectric relaxations in modulus study.

Nyquist Plot analysis: The Nyquist representation in complex impedance plane for pristine and irradiated Aurivillius at 400 K is shown in Figure 5B. The pristine sample shows a portion of semi-circle which can further modeled to calculate the impedance contribution by grain and grain boundaries. In present case this circuit can be seen as combination of one parallel R-C circuit in series with R. This R and R-C represents the grain and grain boundary contributions respectively. However, the electro-chemical impedance for irradiated sample exhibits an unconventional spiral curve. The divergence from true semicircle is reported in many complex systems [60, 61]; but the observation of the helical Nyquist plot is a rare phenomenon. A similar curve is observed in impedance analysis of electrodes in Lithium-ion batteries and is termed as inductive loop [62]. This behavior is usually attributed to the solid - electrolyte interphase and a constant phase element is introduced to understand this behavior [63]. As seen in electron micro-graph, the irradiation has fragmented the grains and distorted the grain boundaries due to high energy transfer. Although not completely understood the combinations of various effects (both surface and bulk) could be responsible for the observed inductive behaviour.

Materials with negative dielectric constant, although allowed by principle of electrodynamics, are not found in nature. Same is true for dia-electric materials, the only counterpart of magnetic phenomena which is missing in the electric order. Nevertheless, these systems have been pursued by the scientific community for long as they exhibit a variety of unusual properties which could revolutionize the existing electronic and photonic technologies. In search of such systems, the first breakthrough was achieved in an artificial structure consisting of a periodic array of copper (non-magnetic) resonators [7]. The interaction of such a composite system with oscillating fields is observed to be analogous to that of neutral plasma. And below the plasma frequency (microwave regime) the system exhibits negative indices. The negative relative permittivity was also observed in Perovskite PrMn O ₃, urea-coated nano-particles, insulating polymers, Modified Rh800 dye, and array of gold nano-rods [56]; [64-66]. In present work the effective dielectric constant was observed to achieve negative values for the irradiated K ₂ Bi ₄ Ti ₄ WO ₁₈ above 350 K. In addition the sample exhibits some unique features such as: the helical Nyquist plot, and multiple dipole relaxations. The seven fold rise in conductivity shows an increase in charge carriers due to impingement of Ni ⁺¹¹ in the insulating matrix of ceramic. This anomalous response observed in bulk properties is clearly due to interplay of many complex dipolar mechanisms. The SHI distorts the homogeneity of the ceramic and is capable of creating defects, charge carriers, dipoles, and shows a plasma like surface effect. As the temperature reaches above a critical value a transition to negative dielectric phase is observed plausibly due to activation of these dipoles.