Tunable Twin Matching Frequency (fm1/fm2) Behavior of Ni1−xZnxFe2O4/NBR Composites over 2–12.4 GHz: A Strategic Material System for Stealth Applications

The gel to carbonate precipitate route has been used for the synthesis of Ni1−xZnxFe2O4 (x = 0, 0.25, 0.5 and 0.75) bulk inverse spinel ferrite powder samples. The optimal zinc (50%) substitution has shown the maximum saturation magnetic moment and resulted into the maximum magnetic loss tangent (tanδm) > −1.2 over the entire 2–10 GHz frequency range with an optimum value ~−1.75 at 6 GHz. Ni0.5Zn0.5Fe2O4- Acrylo-Nitrile Butadiene Rubber (NBR) composite samples are prepared at different weight percentage (wt%) of ferrite loading fractions in rubber for microwave absorption evaluation. The 80 wt% loaded Ni0.5Zn0.5Fe2O4/NBR composite (FMAR80) sample has shown two reflection loss (RL) peaks at 5 and 10 GHz. Interestingly, a single peak at 10 GHz for 3.25 mm thickness, can be scaled down to 5 GHz by increasing the thickness up to 4.6 mm. The onset of such twin matching frequencies in FMAR80 composite sample is attributed to the spin resonance relaxation at ~5 GHz (fm1) and destructive interference at λm/4 matched thickness near ~10 GHz (fm2) in these composite systems. These studies suggest the potential of tuning the twin frequencies in Ni0.5Zn0.5Fe2O4/NBR composite samples for possible microwave absorption applications.

ferrite materials depend on the electron spin arrangement and also on the domain spin orientations. The incident microwave radiation can be absorbed in ferrite materials by exciting spin relaxation process, which may be transferred to host lattice due to spin-lattice coupling. The spin-lattice interaction 25 in spinel ferrites, which strongly affects MW absorption characteristics, depends on the distribution of cations in the crystal structure, which is not only decided by the chemical composition and synthetic route but also by the other parameters including pH of chemical reactions 26 , annealing temperature, the rate of heating/cooling, etc.
The ferrite materials need to be dispersed in suitable binder resin matrix to realize the practical microwave absorbing products. Therefore, studies on MW absorbing composites with dispersed magnetic ferrite materials in polymer/resin matrix has always been a subject of interest 27 . Dispersion of ferrite granules has been attempted in different host matrices viz. epoxy resin 28,29 , polyvinylchloride (PVC) 30 , wax 31,32 etc., wherein the studies have been focused on understanding the variation of electromagnetic characteristics of composites with a loading percentage of filler materials as well as their dispersion behavior. Further, the filler-host matrix interactions facilitate multiple scattering of MW radiation via suspended filler granules which may significantly enhance the MW absorption properties in the composites 33 . Yet, there are numerous challenges in the synthesis of homogeneous composite system e.g. dispersion/suspension of the high-density ferrite powder in liquid resin/wax medium leading to the inhomogeneities in the composites. The elastomeric matrix may provide a relatively better host for uniform dispersion of high-density filler due to the entrapment of heavy ferrite granules in cross-linked rubber structure during mixing and vulcanization process 34 . In spite of these advantages, there are very few studies on ferrite-elastomeric composites, directing to microwave absorption. Considering these advantages, in this report, we have focused our studies on the microwave absorbing properties of Ni 1−x Zn x Fe 2 O 4 ferrite as filler in Acrylo-Nitrile Butadiene Rubber (NBR) elastomeric matrix due to its light weight, flexible nature, high elongation, resistance to the corrosion, good high/low temperature stability (− 20 °C to + 125 °C) and high values of tensile strength. Ni 1−x Zn x Fe 2 O 4 (x = 0, 0.25, 0.50 and 0.75) ferrite powders have been prepared using simple, scalable and energy efficient wet chemical method. As synthesized powders have been annealed at different temperatures to study their size-dependent physical and microwave absorption properties. Flexible sheets were fabricated in NBR host matrix with different loadings fractions in the range of 50-80 weight percent (wt%) of the Ni-Zn ferrite material with optimal Zn concentration showing maximum saturation magnetization and investigated for their reflection loss characteristics in the microwave frequency range of 2-12.4 GHz.

Results and Discussion
The representative XRD spectra are shown in Fig. 1a for Ni 1−x Zn x Fe 2 O 4 (x = 0.50) ferrite powder sample, annealed at 650 °C, 950 °C and 1250 °C temperatures. International Centre for Diffraction Data (ICDD) powder diffraction file (PDF) # 22-106 has been used as a reference for phase identification and all the observed diffraction peaks could be indexed with this reference. The appearance of characteristics spinel phase peaks due to (220), (311), (222), (400), (422), (511) and (440) planes, marked in Fig. 1a, confirm the formation of pure spinel phase of Ni 0.5 Zn 0.5 Fe 2 O 4 annealed at 650 °C. The broadening of XRD peaks for 650 °C annealed powder suggests the formation of ultrafine particles. Further, enhancement of intensities and decrease of respective broadening for these diffraction peaks have been observed with the increase in sequential annealing temperatures at 950 °C and 1250 °C, respectively. The other compositions of Ni 1−x Zn x Fe 2 O 4 (x = 0, 0.25 and 0.75) ferrite powders showed similar XRD spectra (Fig. 1b). However, the diffraction peaks are relatively shifted ~0.26° in 2Ѳ towards lower angle with an increase in Zn 2+ ion concentration from NiFe 2 O 4 to Ni 0.25 Zn 0.75 Fe 2 O 4 as shown in Fig. 1c, attributed to the enlargement of cubic lattice parameter 'a' for these inverse spinel compounds from 8.321A° for pure Ni ferrite (x = 0) to 8.385A° for Ni 0.25 Zn 0.75 Fe 2 O 4 ferrite (x = 0.75) composition, as shown in Fig. 1d. The increased 'a' with Zn 2+ ion concentration is caused by the replacement of Ni 2+ ion (ionic radii ~0.78A°) to the large sized Zn 2+ ion (ionic radii ~0.83A°) in the crystal lattice of cubic NiFe 2 O 4 structure [35][36][37] .
Scanning electron microscope (SEM) micrographs are shown in Fig. 2a,b, for Ni 1−x Zn x Fe 2 O 4 powders (x = 0 and 0.5), annealed at 650 °C, 950 °C and 1250 °C. Ferrite powder samples, annealed at 650 °C, show fine microstructure with spherical particle morphology, Fig. 2a(i). The grain growth has been observed with annealing temperature, resulted into the distorted spherical morphology observed for the powder samples, annealed at 1250 °C, Fig. 2a Fig. 3e and f respectively. The saturation magnetization increases with increasing the annealing temperature for all these compositions except for the Ni 0.25 Zn 0.75 Fe 2 O 4 ferrite powder. The marginal decrease in saturation magnetization has been observed for this composition (x = 0.75) while annealed at 950 °C and then a small increase in value for annealing at a higher temperature ~1250 °C. Similarly, the coercive field values were found to decrease with increase in annealing temperature for all the compositions except for ferrite powder with high Zn content (x = 0.75). The distribution of ions in tetrahedral and octahedral sites takes place during the thermal treatment for the formation of inverse spinel crystallographic phase. The cation ordering increases with increasing the temperature, resulting in the higher saturation magnetization, as observed in samples annealed at 1250 °C 25,39 . Further, saturation magnetization increases initially with an increase in Zn 2+ ion concentration and a significant decrease in value has been observed beyond x = 0.5 for ferrite composition as shown in Fig. 3f. At low concentration of Zn 2+ ions, spin site occupancy reduces at A (tetrahedral) sites due to the presence of non-magnetic Zn 2+ ions, however, net magnetization increases due to the shift of Fe 3+ ions from A site to B (octahedral) sites. The increase in Zn 2+ substitution beyond x = 0.5 resulted in the reduced effective spin A site contributions due to the non-availability of the minimum number of spins sites for the oxygen mediated super-exchange interaction between A and B cation sites, leading to decrease in magnetization value, as observed in the present study 17,37 . Moreover, the annealing temperature has favored grain growth, resulting in the enhanced number of domain walls or even larger domains within the grains. The contribution of a domain wall in magnetization/demagnetization process dominates against domain rotation, as domain wall movement is less energetic than the domain wall rotation 18 . Therefore, such energy competition between domain rotation and domain wall movement in larger grains has led to the lower coercive field values for compositions annealed at high temperature i.e. 1250 °C. The decrease in coercive field values is attributed to the decrease in magneto-crystalline anisotropy with Zn substitution, as substantiated in our experimental observations 40 .
The complex permittivity (ε r * = ε r ′ − jε r ″ ) and permeability (μ r * = μ r ′ − jμ r ″ ) values were computed by Nicolson and Ross algorithm using S-parameters measured through waveguide transmission line technique over MW frequency range (2-12.4 GHz) 41 . The imaginary values of complex EM parameters (ε r ″ , μ r ″ ) represent the MW attenuation/absorption characteristics of material and are depicted on the negative scale, following the standard convention for representing the loss factor. All the Ni 1−   where, λ is the wavelength, μ r * is the complex relative permeability, ε r * is the complex relative permittivity and d is the absorber thickness. Further, the impedance of absorber's top layer should be comparable to the free space impedance Z 0 (377 Ω) to enter the microwaves inside the absorber for its effective attenuation as explained schematically in Fig. 7. Considering the close approximation of matched wave impedance criterion, the reflection loss of absorber should have matched values for absorber thickness (d m ) at λ m /4, to satisfy the destructive interference criterion among surface reflected and metal back-reflected wave with the following dependence, as explained by eqs (3) and (4) (Fig. 7) Fig. 8a-d. FMAR50 sample shows the maximum possible reflection loss value (R.L.) max ~− 4dB at ~8 GHz for 5 mm absorber thickness, which has increased up to ~− 10 dB at ~7 GHz for FMAR60 sample for the same thickness. Similarly, with further increase of ferrite loading (FMAR70), the (R.L.) max value has further increased to ~− 15 dB at 10 GHz, ~20 dB at 8.3 GHz and ~24 dB at 7 GHz for absorber thickness values of ~3.5 mm, 4.0 mm, and 4.6 mm, respectively. It is interesting to note that the absorption peak is shifting towards the lower frequency with increasing the absorber thickness for this composition. The observed shifting in reflection loss, towards lower frequency for FMAR70 composite can be explained using eqs (3 and 4). These relations suggest that absorber thickness will effectively reduce with increasing ε r ′ and tanδ m . The insignificant values of reflection loss observed for FMAR50 and FMAR60 are mainly because of the relatively lower tanδ m , for these composite samples as shown in Fig. 6d. Interestingly, the onset of twin match frequencies (f m1 /f m2 ) has been observed at two different matched thicknesses (t m1 and t m2 ), Fig. 8d, for FMAR80 composite sample. At absorber thickness t m1 = 4.6 mm, the first matched (R.L.) max value is ~− 43 dB at the first matching frequency f m1~5 GHz. With the decrease in absorber thickness, R.L profile has shifted towards higher frequency side with lower (R.L.) max values ~− 22 dB and ~− 26 dB for absorber thicknesses ~4 mm and 3.5 mm, respectively. On further reduction in the absorber thickness at t m2 = 3.25 mm, the second matched (R.L.) max value ~− 43 dB has been observed at the second matching frequency f m2 ~10 GHz.
The existence of such two matching frequencies has been observed earlier in pure ferrite powders, however, in rubber-ferrite composite samples only a single matching frequency has been reported 37,45 . The two possible MW absorption loss mechanism are generally attributed in ferrite materials: (i) relaxation mechanism due to the domain wall motion and (ii) the spin rotational resonance. The domain wall resonance mechanism usually dominates at lower MW frequency range (< 1 GHz), as the relaxation of domain motion does not follow the higher MW frequency beyond 1 GHz, whereas relaxation of spin resonance or ferromagnetic resonance (FMR) dominates at the higher MW frequencies. The maximum loss tangent values observed at ~6 GHz for 1250 °C annealed Ni 0.5 Zn 0.5 Fe 2 O 4 ferrites, is close to the first matching frequency (f m1 ) observed at ~5 GHz for 4.6 mm thick FMAR80 sample as shown in Fig. 8d, and is attributed to the spin resonance relaxation mechanism in these samples 46 . As discussed earlier, the FMR frequencies and thus, MW absorption of Ni-Zn ferrite system depends strongly on chemical composition, synthetic route and post processing conditions. Shi et al. tuned the resonance frequency ~2.54 GHz for Ni spinel ferrite nanoparticles prepared using sol-gel process 47 whereas Zhao et al. adjusted the matching absorption frequencies for Ni-Zn spinel ferrite in the range of ~1-12 GHz by substitution of Cu 2+ /Co 2+ ions 48 . The second matching frequency (f m2 ) has been observed at ~10 GHz for 3.25 mm FMAR80 absorber thickness. The f m2 is independent of resonance frequency and is observed because of matched absorber thickness (λ m /4 ~ 3.25 mm) as given by eq. (4). The R.L. profile associated to f m1 at absorber thickness ~4.6 mm may extend towards the higher frequency side with a decrease in thickness up to 3.5 mm. Whereas, the R.L. profile associated with f m2 may contribute towards lower frequency side with an increase in thickness up to 4 mm. It has been observed that R.L. profiles have both the components of matching frequencies (x.f m1 + y.f m2 ) at these thicknesses, where x and y are the fractional contribution from individual matching frequencies f m1 and f m2 , respectively. At the intermediate absorber thickness of 3.5 mm and 4.0 mm the matching frequency (f M ) behavior follows the trend as given in eqs (5 and 6)  The matching frequencies (f m ) for d = 3.5 mm and 4.0 mm thick FMAR80 samples are 9 and 6 GHz respectively, as shown in Fig. 8d. The fractional contributions (x and y) for d = 3.5 mm thick FMAR80 sample are x = 0.2 and y = 0.8 corresponding to f m1 (5 GHz) and f m2 (10 GHz) respectively. For d = 4.0 mm thick FMAR80 sample, the fractional contributions are x = 0.8 and y = 0.2, corresponding to f m1 (5 GHz) and f m2 (10 GHz) respectively, substantiating the proposed mechanism of twin matching frequencies contribution for microwave absorption in these ferrite-rubber composite samples.

Conclusions
The maximum reflection loss (R.L.) max values increase with loading fraction of Ni 0.5 Zn 0.5 Fe 2 O 4 ferrite powder in these rubber composites, as shown in Fig. 8e. Interestingly, for FMAR80 the desired frequency bandwidth (where R.L. ≥ 10 dB or at least 90% attenuation of MW signal) decreases with absorber thickness as shown in Fig. 8f. The MW absorber at 3.25 mm thickness (corresponding to f m2 ) has the widest bandwidth of ~7 GHz, whereas, at absorber thickness of 4.6 mm, frequency bandwidth window reduced to ~4.2 GHz. In the intermediate thicknesses, the bandwidth lies between this ranges. These studies suggest that the FMAR80 absorber can be used as a tunable MW frequency absorber using the thickness as a controlling parameter for strategic applications such as microwave stealth over the different frequency bands.

Methods
Experimental details. The ferrite powders are prepared using gel to carbonate precipitation method, where the co-precipitations of divalent cations (Ni 2+ , Zn 2+ ) as fine particles of carbonates within hydrated gels of ferric hydroxide has been carried out by adding the alkali solution into the mixed metal salt ions. 1 M solution of FeCl 3 (Merck CAS No. 7705-08-0), NiCl 2 (Merck CAS No. 7718-54-9), ZnCl 2 (Merck CAS No. 7646-85-7) were mixed stoichiometrically, followed by adding dropwise 1 M Na 2 CO 3 solution (Merck CAS No. 497-19-8) while maintaining pH ~9, to realize the co-precipitation. The obtained precipitate was washed and dried in an oven at ~90 °C for 2 hours in the air ambient. The resultant composite powder consists of sub-micron crystalline particles of carbonates, embedded within the amorphous medium of Fe 2 O 3 .xH 2 O (70< x < 110). The composite powder was annealed sequentially at 650 °C, 950 °C and 1250 °C for 3 hours each to obtain final sample, which was used for detailed characterization of the physical and microwave absorption properties. The similar process has been followed to prepare a series of Ni 1−x Zn x Fe 2 O 4 spinel ferrites with x = 0, 0.25, 0.50 and 0.75, to understand the effect of Zn substitution on the physical and microwave absorption properties.
Rubber based microwave absorbing sheets are fabricated using mechanical milling followed by high-temperature compression moulding (HTCM), to get the desired shape and size of composite samples. Initially, 30 g of NBR was thoroughly mixed in two roll mixing mill (TRMM) and Ni 0.5 Zn 0.5 Fe 2 O 4 powder was added in different filler ratio in wt%, as listed in the Table -I  curing of rubber-filler compound, ZnO (05 PHR), Steric Acid (02 PHR) as activator to enhance the effect of accelerator and Trimethyl-Di-Quinoline TDQ (01 PHR) as antioxidant for rubber to prevent it from environmental degradation 29 . After homogeneous mixing, the compounds were transferred into 200 mm × 200 mm × 2 mm (L × B × D) size mould and hydraulically pressed at 150 °C with 30 Ton pressure for 30 minutes. The mould was then allowed to cool down to the ambient temperature and rubber sheet was collected for MW characterization. The loading of ferrite powder (> 80 wt%) in NBR matrix was not possible due to the enhanced brittleness, making difficult to handle the composite materials.
X-ray diffraction measurements (Philips X'Pert Pro) were carried out with CuK α (λ = 1.514 A°) radiation as incident X-ray in 20° to 80° 2θ range, to identify the Ni 1−x Zn x Fe 2 O 4 crystallographic phase. Infrared (IR) spectroscopic studies were carried out using FTIR system (Model: Bruker Vertex 70 V). Shape and morphology of Ni 1−x Zn x Fe 2 O 4 powders were analyzed using Oxford EVO5 Scanning Electron Microscope (SEM) system. The room temperature magnetic hysteresis studies (M-H plots) were carried out using Vibrating Sample Magnetometer (VSM) Model ADE EV-5 for − 2kOe to + 2 kOe magnetic field. Electromagnetic parameters i.e. complex permittivity and permeability values were measured in 2-12.