50 MeV Li3+ ion irradiation effect on structural, electrical, and dielectric properties of PVA-based nanocomposite polymer electrolytes

Nanocomposite polymer electrolyte thin films of polyvinyl alcohol (PVA)-orthophosphoric acid (H₃PO₄)-Al₂O₃ have been prepared by solution cast technique. Films are irradiated with 50 MeV Li³⁺ ions having four different fluences viz. 5?×?10¹⁰, 1?×?10¹¹, 5?×?10¹¹, and 1?×?10¹² ions/cm². The effect of irradiation on polymeric samples has been studied and characterized. X-ray diffraction spectra reveal that percent degree of crystallinity of samples decrease with ion fluences. Glass transition and melting temperatures have been also decreased as observed in differential scanning calorimetry. A possible complexation/interaction has been shown by Fourier transform infrared spectroscopy. Temperature-dependent ionic conductivity shows an Arrhenius behavior before and after glass transition temperature. It is observed that ionic conductivity increases with ion fluences and after a critical fluence, it starts to decrease. Maximum ionic conductivity of ～2.3?×?10^?5 S/cm owing to minimum activation energy of ～0.012 eV has been observed for irradiated electrolyte sample at fluence of 5?×?10¹¹ ions/cm². The dielectric constant and dielectric loss also increase with ion fluences while they decrease with frequency. Transference number of ions shows that the samples are of purely ionic in nature before and after ion irradiation.     

Dielectric study on Zn1−x Mg x O ceramic materials prepared by the solid-state route

The present work investigates the structural and dielectric properties of Zn_1?x Mg _x O composites prepared by the standard sintering method at 1200 °C during 24 h and doped with different weight percentages of MgO (x = 0–40 %). For this purpose, the scanning electron microscopy (SEM) was used to study the effect of the magnesium’s proportion on the morphology and crystallinity of the obtained samples. The SEM observations have shown rougher surfaces of the samples covered by grains having prismatic shapes and different sizes. The dielectric properties of the ceramics were investigated by spectroscopic impedance at different temperatures and frequencies, thus showing a frequency-dependent dispersion of the permittivity constants and dielectric losses. From these measurements, the relaxation processes were identified and their activation energies extracted. Dielectric responses were correlated with the microstructure and chemical composition of the ZnMgO composites. The mechanisms of ac conductivity are controlled by the polaron hopping and the electron tunneling models. Concerning the tunneling model, two types corresponding to the overlapping large polaron tunneling model for the composites Zn_0.9Mg_0.1O and Zn_0.8Mg_0.2O and the small polaron tunneling model for the composites Zn_0.64Mg_0.36O (in the frequency range 1.7 × 10⁴ Hz–1 MHz) and Zn_0.6Mg_0.4O were observed. Besides, one type of hopping model corresponding to the correlated barrier hopping for the composites ZnO and Zn_0.64Mg_0.36O (in the frequency range 6 × 10²–1.7 × 10⁴ Hz) was noted.     

DLTS and in situ C–V analysis of trap parameters in swift 50 MeV Li3+ ion-irradiated Ni/SiO2/Si MOS capacitors

Ni/SiO₂/Si MOS structures were fabricated on n-type Si wafers and were irradiated with 50 MeV Li³⁺ ions with fluences ranging from 1×10¹⁰ to 1×10¹² ions/cm². High frequency C–V characteristics are studied in situ to estimate the build-up of fixed and oxide charges. The nature of the charge build-up with ion fluence is analyzed. Defect levels in bulk Si and its properties such as activation energy, capture cross-section, trap concentration and carrier lifetimes are studied using deep-level transient spectroscopy. Electron traps with energies ranging from 0.069 to 0.523 eV are observed in Li ion-irradiated devices. The dependence of series resistance, substrate doping and accumulation capacitance on Li ion fluence are clearly explained. The study of dielectric properties (tan δ and quality factor) confirms the degradation of the oxide layer to a greater extent due to ion irradiation.     

Effects of heavy-ion irradiation on the electrical properties of rf-sputtered HfO2 thin films for advanced CMOS devices

HfO₂-based metal-oxide semiconductor (MOS) capacitors were irradiated with high-energy ion beam to study the irradiation effects in these films. HfO₂ thin films deposited by radio frequency (rf)-sputtering were irradiated with 80 MeV O⁶⁺ ions. The samples were irradiated and characterized at room temperature. Devices were characterized via 1 MHz capacitance–voltage (C?V) measurements using the midgap method. The irradiation induced dispersion in accumulation and depletion regions with increasing fluence is observed. After irradiation, the midgap voltage shift (Δ V _mg) of?0.61 to?1.92 V, flat band voltage shift (Δ V _fb) of?0.48 to?2.88 V and threshold voltage shift (Δ V _th) of?0.966 to?1.96 V were observed. The change in interface trap charge and oxide trap charge densities after 80 MeV O⁶⁺ ions irradiation with fluences were determined from the midgap to flat band stretch out of C?V curves. The results are reported and explained in terms of changes in microstructure and dielectric properties of the HfO₂ thin films after irradiation.     

Effect of 50 MeV Li+3 and 80 MeV C+5 ions’ beam irradiation on the optical,structural, chemical and surface topographic properties of PMMA films*

The self-standing films of polymethyl methacrylate (PMMA) were irradiated under vacuum with 50?MeV lithium (Li³⁺) and 80?MeV carbon (C⁵⁺) ions to the fluences of 3?×?10¹⁴, 1?×?10¹⁵, 1?×?10¹⁶ and 1?×?10¹⁷ ions µm^?2. The pristine and irradiated samples of PMMA films were studied by using ultraviolet–visible (UV–Vis) spectrophotometry, Fourier transform infrared, X-ray diffractrometer and atomic force microscopy. With increasing ion fluence of swift heavy ion (SHI), PMMA suffers degradation, UV–Vis spectra show a shift in the absorption band from the UV towards visible, attributing the formation of the modified system of bonds. E_g and E_a decrease with increasing ion fluence. The size of crystallite and crystallinity percentage decreases with increasing ion fluence. With SHI irradiation, the intensity of IR bands and characteristic bands of different functional groups are found to shift drastically. The change in (E_g) and (N) in carbon cluster is calculated. Shifting of the absorption band from the UV towards visible along with optical activity and as a result of irradiation, some defects are created in the polymer causing the formation of conjugated bonds and carbon clusters in the polymer, which in turn lead to the modification in optical properties that could be useful in the fabrication of optoelectronic devices, gas sensing, electromagnetic shielding and drug delivery.     

Effect of carbon nanotubes implantation on electrical properties of sisal fibre–epoxy composites

In this paper, the effects of carbon nanotubes (CNT) implantation and sisal fibre size on the electrical properties of sisal fibre-reinforced epoxy composites are reported. For this purpose, the epoxy composites reinforced with CNT-implanted sisal fibre of 5 mm and 10 mm lengths were prepared by hand moulding and samples characterized for their electrical properties, such as dielectric constant (ε′), dielectric dissipation factor (tan δ) and AC conductivity (σ_ac) at different temperatures and frequencies. It was observed that the dielectric constant increases with increase in temperature and decreases with increase in frequency from 500 Hz to 5 KHz. Interestingly, the sample having CNT-implanted sisal fibre of 5 mm length exhibited the highest value of dielectric constant than the one with length 10 mm. This is attributed to the increased surface area of sisal fibre and enhancement of the interfacial polarization. At a constant volume and a length of 5 mm of the fibres, the number of interfaces per unit volume element is high and results in a higher interfacial polarization. The interfaces decrease as the fibre length increases, and therefore, the value of ε′ decreases at 10 mm fibre length. The peak value of the dielectric constant decreases with increasing frequency. A continuous decrease in dissipation factor (tan δ) with increasing frequency for all samples was observed, while at lower temperatures, the values of tan δ remains approximately same. The AC conductivity for 5 mm length sisal epoxy composite and 10 mm length sisal fibre–epoxy composites is higher than that of pure epoxy at all the frequencies.     

Synthesis of α-In 2 Te 3 thin films from In/Te bilayer by Si ion irradiation

In this work, In/Te bilayer thin films were prepared using sequential thermal evaporation method and subsequently irradiated using swift heavy ions (SHIs) of 100 MeV silicon (Si) with different fluences (1×10¹³ to 5×10¹³/cm²). The inter-diffusion of In and Te layers was highly controlled by SHI irradiation and the In₂Te₃ formation capability was compared with that of the conventional annealing method. The structural as well as optical properties of a post-sintered SHI-irradiated In/Te bilayer were investigated using X-ray diffraction (XRD) measurements and UV–visible spectroscopy, respectively. We found that irradiated samples showed single-phase In₂Te₃ under post-annealed conditions at 150 °C unlike that prepared using the conventional thermal annealing method, which showed mixed phases under similar conditions. This confirms the effective inter-diffusion in bilayer films by SHI irradiation toward the formation of single-phase In₂Te₃. The estimated optical band gap energy was found to be 1.1±0.5 eV and strongly corroborated the XRD results. In addition, the estimated refractive index (n) value of the SHI-irradiated sample (～3.3) was higher than that of the sample obtained through the conventional annealing method (～2.8). This proves that SHI offers a highly compact nature even at low temperatures. This work has a wide scope for achieving single-phase alloyed films through bilayer mixing by SHI irradiation.     

Influence of Nd:YAG laser irradiation on AC impedance and dielectric properties of lithium ferrite

Polycrystalline samples of Li_0.5Fe_2.5O₄ spinel ferrite have been synthesized by a standard ceramic technique. The samples were irradiated with an Nd:YAG laser to study the effect of laser irradiation on the structural, dielectric and AC impedance properties. The X-ray diffraction results show the formation of a disordered cubic structure after irradiation. The dielectric constant (?′), dielectric loss (?″) and the loss tangent (tan δ ) were measured at room temperature as a function of frequency (f=20 Hz–1 MHz) for the irradiated and unirradiated samples of Li_0.5Fe_2.5O₄ spinel ferrite. The dielectric constant of the irradiated samples is decreased in magnitude compared to the unirradiated samples. It was found that laser irradiation increases the polarization and the resistivity of the samples as a result of electronic rearrangement and lattice defects. The AC conductivity of the samples was derived from the dielectric constant and loss tangent data. The change in AC conductivity is attributed to the creation of lattice vacancies after laser irradiation. The AC impedance analysis was used to separate the grain and grain boundary of the Li_0.5Fe_2.5O₄ spinel ferrite.     

Studies of some physical properties of PrFe0.7Ni0.3O3 thin films after 200 MeV Ag15+ irradiation

PrFe_0.7Ni_0.3O₃ thin films (thickness ~ 200 nm) were prepared by pulsed laser ablation technique on LaAlO₃ substrate. These films were irradiated with 200?MeV Ag¹⁵⁺ ions at various fluencies, ranging from 1 × 10¹¹ to 1 × 10¹² ions/cm². These irradiated thin films were characterized by using X-ray diffraction, dc conductivity, dc magnetization and atomic force microscopy. These films exhibit orthorhombic structure and retain it even after irradiations. The crystallite size (110–137?nm), micro strain (1.48 × 10^?2–1.75 × 10^?2 line^?2?m^?4) and dislocation density (79.7 × 10¹⁴–53.2 × 10¹⁴ line/m²) vary with ion fluencies. An enhancement in resistivity at certain fluence and then a decrease in its value (0.22175–0.21813?Ω?cm) are seen. A drastic change in observed magnetism after ion irradiation is seen. With ion irradiation, an increase in surface roughness, due to the formation of hillocks and other factors, is observed. Destruction of magnetic domains after irradiation can also be visualized with magnetic force microscopy and is in close agreement with magnetization data. The impact on various physical properties in these thin films after irradiation indicates a distortion in the lattice structure and consequently on single-particle band width caused by stress-induced defects.     

Strain modification of AlGaN layers using swift heavy ions

Epitaxial AlGaN/GaN layers grown by molecular beam epitaxy (MBE) on SiC substrates were irradiated with 150 MeV Ag ions at a fluence of 5×10¹² ions/cm². The samples used in this study are 50 nm Al_0.2Ga_0.8N/1 nm AlN/1 μ m GaN/0.1 μ m AlN grown on SI 4H-SiC. Rutherford backscattering spectrometry/channeling strain measurements were carried out on off-normal axis of irradiated and unirradiated samples. In an as-grown sample, AlGaN layer is partially relaxed with a small tensile strain. After irradiation, this strain increases by 0.22% in AlGaN layer. Incident ion energy dependence of dechanneling parameter shows E ^1/2 dependence, which corresponds to the dislocations. Defect densities were calculated from the E ^1/2 graph. As a result of irradiation, the defect density increased on both GaN and AlGaN layers. The effect of irradiation induced-damages are analyzed as a function of material properties. Observed results from different characterization techniques such as RBS/channeling, high-resolution XRD and AFM are compared and complemented with each other to deduce the information. Possible mechanisms responsible for the observations have been discussed in detail.     

On the effect of SHI irradiation on dielectric properties of Y3+xFe5−xO12 (x=0.0–0.6) system

The present work aims to investigate the pre- and post-effect of 50 MeV Li³⁺ ion irradiation at a fluence of 5×10¹³ ions/cm² on the dielectric properties of Y_3+xFe_5?xO₁₂, x=0.0, 0.2, 0.4 and 0.6, garnet system over broad temperature, 300–673 K, and frequency, 100 Hz–13 MHz, ranges. Thermal variation of ac resistivity measurements suggests that the mechanism responsible for conduction in the system is polaron hopping. The observed modifications in dielectric properties after swift heavy ion irradiation are mainly due to the modifications of the metal–insulator contacts due to radiation damage-induced disorder and irradiation-induced point/cluster of defects in the material and also compressive strain generated in the lattice structure. The electric modulus presentation and the complex impedance spectral analysis have been employed to study the relaxation process. The YFeO₃ phase is found to be irradiation hard phase as compared with the garnet phase.     

Effect of MeV electron irradiation on the free volume of polyimide

The free volume of the microvoids in the polyimide samples, irradiated with 6 MeV electrons, was measured by the positron annihilation technique. The free volume initially decreased the virgin value from ～13.70 to ～10.98 Å³ and then increased to ～18.11 Å³ with increasing the electron fluence, over the range of 5?×?10¹⁴ – 5?×?10¹⁵ e/cm². The evolution of gaseous species from the polyimide during electron irradiation was confirmed by the residual gas analysis technique. The polyimide samples irradiated with 6 MeV electrons in AgNO₃ solution were studied with the Rutherford back scattering technique. The diffusion of silver in these polyimide samples was observed for fluences >2?×?10¹⁵ e/cm², at which microvoids of size ≥3 Å are produced. Silver atoms did not diffuse in the polyimide samples, which were first irradiated with electrons and then immersed in AgNO₃ solution. These results indicate that during electron irradiation, the microvoids with size ≥3 Å were retained in the surface region through which silver atoms of size ～2.88 Å could diffuse into the polyimide. The average depth of diffusion of silver atoms in the polyimide was ～2.5 μm.     

Temperature and frequency dependent electrical properties of 50 MeV Li3+ ion irradiated polymeric blends

The polymeric blends of polyvinyl chloride (PVC) and polyethylene terephthalate (PET) with equal composition by weight have been irradiated with 50 MeV Li³⁺ ions at different fluences. The AC electrical properties of polymeric blends were measured in the frequency range 0.05–100 kHz, and at temperature range 40–150 ^°C using LCR meter. There is an exponential increase in conductivity with log of frequency and effect is significant at higher fluences. The value of tan δ and dielectric constant are observed to change appreciably due to irradiation. The loss factor (tan δ) versus frequency plot suggests that the capacitors of polymeric blend of PVC and PET may be useful below 10 kHz. No change in dielectric constant was observed over a wide temperature range up to 150 ^°C. Thermal stability was studied by thermogravimetric analysis. Thermal analysis revealed that chain scission is the dominant phenomena in the polymeric blends resulting in the reduction of its thermal stability. It appears from differential scanning calorimetry studies that the melting temperature decreases as fluence increases. FTIR spectra measurements also revealed that the material suffered severe degradation through bond breaking beyond the fluence of 2.3×10¹³ ions/cm².     

The role of zirconium oxide as nano-filler on the conductivity,morphology, and thermal stability of poly(methyl methacrylate)–poly(styrene-co-acrylonitrile)-based plasticized composite solid polymer electrolytes

The plasticized composite solid polymer electrolytes (CSPE) involving polymer blends poly(methyl methacrylate)-poly(styrene-co-acrylonitrile) (PMMA-SAN), plasticizers ethylene carbonate (EC), and propylene carbonate (PC) with lithium triflate (LiCF₃SO₃) as salt and varying concentration of composite nano-filler zirconium oxide (ZrO₂) is prepared by solution casting technique using THF as solvent. The powder X-ray diffraction (XRD) studies reveal amorphous nature of the CSPE samples. Fourier transform infrared (FT-IR) spectroscopy studies reveal interaction of Li⁺ ion with plasticizers, both C=O and OCH₃ group of the PMMA, while nitrile group of SAN is inert. AC impedance and dielectric studies reveal that the ionic conductivity (σ), dielectric constant (ε’), and dielectric loss (ε”) of the prepared CSPE samples increase with increasing content of ZrO₂ nano-filler up to 6 wt% and decrease with further additions. The temperature dependence of ionic conductivity follows Arrhenius relation and indicates ion-hopping mechanism. The sample Z2 (6 wt% ZrO₂) with relaxation time τ of 8.13?×?10^–7 s possess lowest activation energy (E_a?=?0.23 eV) and highest conductivity (2.32?×?10^–4 S cm^?1) at room temperature. Thermogravimetric analysis (TGA) reveals thermal stability of highest conducting sample Z2 up to 321 °C after complete removal of residual solvent, moisture, and its impurities. Differential scanning calorimetric (DSC) studies reveal absence of glass transition temperature (T_g) corresponding to atactic PMMA for the CSPE Z2, while isotactic PMMA component shows T_g around 70 °C, which is due to increased interaction of filler with PMMA leading to change in its tacticity. Scanning electron microscopy (SEM) analysis reveals blending of PMMA/SAN polymers and lithium triflate salt. The incorporation of nano-filler ZrO₂ leads to change in surface topology of polymer matrix. Rough surface of the CSPE Z2 leads to new pathway for ionic conduction leading to maximum ionic conductivity.     

Mössbauer study of ferromagnetic metallic glasses irradiated by swift heavy ions at temperatures 100 and 300 K

The effect of swift heavy ion irradiation on ferromagnetic metallic glasses Fe₄₀Ni₃₈Mo₄B₁₈ and Fe₇₈Si₉B₁₃ has been studied. The ion beams used are 100 MeV ¹²⁷I and 180 MeV ¹⁹⁷Au. The specimens were irradiated at fluences ranging from 3 × 10¹² to 1.5 × 10¹⁴ ions/cm². The irradiations have been carried out at temperatures 100 and 300 K. The magnetic moments are sensitive towards the irradiation conditions such as irradiation temperature and stopping power of incident ion beam. The irradiation-induced effects have been monitored, by using Mössbauer spectroscopy. The modifications in magnetic anisotropy and hyperfine magnetic field distributions, as an effect of different irradiation temperature as well as different stopping power have been discussed. After irradiation, all the samples remain amorphous and magnetic anisotropy considerably changes from its original in-plane direction. The results show enhancement in magnetic anisotropy in the specimen irradiated at 100 K, as compared to that of irradiated at 300 K. It is expected that at low temperature, the stresses produced in the material would remain un-annealed, compared to the samples irradiated at room temperature and therefore, the modification in magnetic anisotropy would be enhanced. A distribution of hyperfine magnetic field, of the samples irradiated at low temperature, show a small but distinct peak at ～?11 Tesla, indicating Fe-B pairing.     

Effect of proton irradiation on the physical properties of PC/PBT blends

Samples from polycarbonate/poly (butylene terephthalate) (PC/PBT) blends film have been irradiated using different fluences (1?×?10¹⁵– 5?×?10¹⁷ H⁺/cm²) of 1?MeV protons at the University of Surrey Ion Beam Center, UK. The structural modi?cations in the proton irradiated samples have been studied as a function of fluence using different characterization techniques such as X-ray diffraction and UV spectroscopy. The results indicate that the proton irradiation reduces the optical energy gap that could be attributed to the increase in structural disorder of the irradiated samples due to crosslinking. Furthermore, the color intensity ΔE, which is the color difference between the non-irradiated sample and those irradiated with different proton fluences, increased with increasing the proton fluence up to 5?×?10¹⁷ H^+/cm², convoyed by an increase in the red and yellow color components. In addition, the resultant effect of proton irradiation on the thermal properties of the PC/PBT samples has been investigated using thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). It is found that the PC/PBT decomposes in one weight loss stage. Also, the variation of transition temperatures with proton fluence has been determined using DSC. The PC/PBT thermograms were characterized by the appearance of two endothermic peaks due to the glass transition and melting temperatures. The melting temperature of the polymer, T_m, was investigated to probe the crystalline domains of the polymer, since the proton irradiation destroys the crystalline structure so reducing the melting temperature.     

Optical and electrical properties of swift heavy ion beam-irradiated polycarbonate/polystyrene bilayer films

Polycarbonate/polystyrene bilayer films prepared by solvent-casting method were irradiated with 55 MeV carbon ion beam at different fluences ranging from 1×10¹¹ to 1×10¹³ ions cm^?2. The structural, optical, surface morphology and dielectric properties of these films were investigated by X-ray diffraction (XRD), UV–visible spectroscopy, Fourier-transform infrared (FTIR) spectroscopy, optical microscopy and dielectric measurements. The XRD pattern shows that the percentage of crystallinity decreases while inter-chain separations increase with ion fluence. UV–visible spectroscopy shows that the energy band gap decreases and the number of carbon atoms in nanoclusters increase with the increase in ion fluences. The refractive index is also found to decrease with the increase in the ion fluence. Optical microscopy shows that after irradiation polymeric bilayer films color changes with ion fluences. The FTIR spectra evidenced a very small change in cross-linking and chain scissoring at high fluence. Dielectric constant decreases while dielectric loss and AC conductivity increase with ion fluences.     

Effect of 100 MeV O7+ ion beam irradiation on structural,optical and electronic properties of SnO2 thin films

In this paper, we present the impact of swift heavy ion beam irradiation on the structural, optical and electronic properties of SnO₂ thin films. Thin films were deposited using the pulsed laser deposition technique on Al₂O₃ substrates. Atomic force microscopy, X-ray diffraction, UV–visible absorption and temperature-dependent resistivity measurements were performed to explore the morphological, structural, optical and electronic properties of the as-deposited and irradiated samples. The peak intensity of the (200) peak was found to decrease monotonously with increasing irradiation fluence. The band gap energy of the 1×10¹¹ ion/cm² irradiated sample was found to increase. The electrical resistivity of the samples showed a continuous increase with the irradiation fluence.     

Proton-induced changes in Bayfol CR 1-4 nuclear track detector

Samples from the polymeric material Bayfol CR 1-4 have been exposed to 1 MeV protons with fluencies in the range 10¹¹–10¹⁴ ions/cm ². The resultant effect of proton irradiation on the thermal properties of Bayfol CR 1-4 has been investigated using thermo-gravimetric analysis (TGA). The onset temperature of decomposition T ₀ and activation energy of thermal decomposition E _a were calculated, results indicated that the Bayfol detector decomposes in one weight loss stage. In addition, the structural modifications in the proton-irradiated Bayfol samples have been studied as a function of fluence using X-ray diffraction and intrinsic viscosity of the liquid samples. Furthermore, the refractive index was measured for the non-irradiated and irradiated Bayfol samples. The results indicated that the degradation is the dominant mechanism in the fluence range 1×10¹¹–5×10¹⁴ ions/cm ². These results have been compared with those obtained in our previous work for Bayfol CR 6-2.     

Effect of gamma irradiation on the dielectric properties and electrical conductivity of the TlInS<Subscript>2</Subscript> single crystal

The effect of gamma irradiation on the dielectric properties and ac conductivity of a TlInS₂ single crystal with a layered structure has been investigated in the frequency range from 5 × 10⁴ to 3.5 × 10⁷Hz. It has been shown that gamma irradiation of the TlInS₂ single crystal with a dose of 10⁴–2.25 × 10⁶ rad leads to a considerable increase in the dielectric loss tangent tanδ, the real part ɛ′ and imaginary part ɛ″ of the complex permittivity, and the ac conductivity σ _ac across the layers. It has been established that, for all gamma irradiation doses, the TlInS₂ single crystal is characterized by the dielectric loss due to electrical conduction up to a frequency of 10⁷ Hz and by the relaxation loss at a higher frequency. Irradiation of the TlInS₂ single crystal results in an increase in the dispersion of tan δ, ɛ′, and ɛ″. It has been demonstrated that, as the gamma irradiation dose is accumulated in the TlInS₂ single crystal, the density of localized states near the Fermi level N _F increases (from 5.2 × 10¹⁸ to 1.9 × 10¹⁹ eV⁻¹ cm⁻³).