1. IntroductionThe past few decades have witnessed a tremendous exploration of magnetic materials as a result of their attractive applications in areas such as high frequency technology, absorption of electromagnetic waves, magnetic refrigerator technology, magnetic recording media, and electro–optical devices.[1–6] Hexaferrites are known to be chemically stable, inexpensive and friendly to the environment, which makes them viable candidates for various technological applications.[7–9] The variants of hexaferrites include M-type, Y-type, U-type, W-type, X-type, and Z-type, their corresponding chemical compositions are, respectively, BaFe12O19, Ba2Me2Fe12O22, Ba4Me2Fe36O60, Ba2Me2Fe16O27, Ba2Me2Fe28O46, and Ba3Me2Fe24O41, where Me2 represents a small divalent ion such as cobalt, nickel, zinc or magnesium, strontium or lead may replace the barium.[10] M-type hexaferrites exhibit much better properties and it is easy to synthesize at lower temperatures without the occurrence of secondary phase, such as magnetite (–Fe2O3).[11] M-type hexaferrites possessed magnetoplumbite structure with space group P63/mmc and a unit cell consisting of 2 Ba2+, 24 Fe3+, and 38 O2+ ions. The magnetoplumbite structure consists of a dual layer having RSR*S* stacking sequence. The R and R* stacking sequence consist of hexagonal structure having three distinct layers of oxygen, whereas the S and S* stacking sequence consists of a spinel structure having two different layers of oxygen, the asterisk shows the 180° rotation of that particular stacking sequence.[12]
The properties of hexaferrites depend on factors such as chemical composition, synthesis method, calcination temperature, and duration, nature of substituted ions, impurity and crystallite size.[7,13] Hexaferrites have been synthesized with variety of methods such as micro-emulsion, solid state reaction method, and co-precipitation method. However, the sol–gel method offers several advantages such as compositional homogeneity, low reaction temperature, and time.[14] Usually, the dielectric constant rapidly decreases at low frequency and exhibit frequency independent behavior at intermediate and higher frequencies. El-Sayed et al. synthesized Al-substituted M-type barium hexaferrites using solid state reaction method and observed that the dielectric constant increases with temperature at lower frequencies while temperature independent behavior was observed at higher frequencies.[15] Naeem et al. observed an abrupt decrease of dielectric constant at lower frequencies and frequency independent behavior at higher frequencies in Zr–Cd substituted strontium hexaferrites prepared by the sol–gel method.[16] The optical band-gap may decrease or increase depending on the nature of the substituted ions and characterization method. Kaur et al. studied the magnetic properties and determined the optical band-gap of sol–gel synthesized Gd–Co substituted hexaferrites using UV-vis NIR spectroscopy, the observed optical band-gap ranges from 4.07 eV to 4.28 eV, the optical band-gap initially decreases with substitution and then later increases.[17] Auwal et al. studied the magnetic, hyperfine interactions, and optical properties of La-substituted hexaferrites synthesized by the sol–gel method using diffuse reflectance spectrophotometer (DRS), the calculated band gap falls in the range 1.34 eV to 1.78 eV.[18]
Taking inspiration from the literature review, this work aimed to synthesized Dy3+–Cr3+substituted barium hexaferrites using the sol–gel auto-combustion method and investigates the role of Dy3+ and Cr3+ ions on the dielectric and optical properties. The prepared samples were characterized using x-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), FE-SEM/EDX, and elemental analysis, UV-Vis-NIR spectrophotometer, and impedance analyzer.
4. Results and discussion4.1. X-ray diffraction analysisFigure 1 presents the x-ray diffraction (XRD) spectra of M-type barium hexagonal ferrites with chemical composition Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5). The XRD spectra show well-defined intense and sharp peaks with hkl values (006), (110), (008), (107), (114), (200), (203), (109), (205), (206), (1011), (209), (217), (304), (2011), (2012), (220), (2014), and (317), this indicates the formation of a crystalline hexagonal ferrites phase with no secondary phase such as α-Fe2O3 and the successful substitution of Dy3+ and Cr3+ in the M-type hexagonal structure. The XRD spectra were indexed according to standard JCPDS Card No. 39-1433 and were found to be identical to unsubstituted BaFe12O19 with space group P63/mmc. The values of lattice parameters (a and c), crystallite size (D), volume of unit cell (Vcell), and strain (η) were calculated using Eqs. (1), (2), (3), and (4) respectively, and presented in Table 2.
where
dhkl is the value of
d spacing,
hkl are the miller indices,
β (in radian) is the full width at half maximum,
θ is the Braggs angle,
k is the shape factor which has a value of 1 for hexagonal ferrites, and
λ is the x-ray wavelength having a value of 1.54056 Å. From Table
2, it can be seen that
a,
c, and
Vcell decrease with Dy
3+–Cr
3+ substitution, this could be explained on the basis of the ionic radius of the substituted ions. It has been reported that the values of
a,
c, and
Vcell may decrease if the ionic radii of the substituted ions are smaller than those of the host ions and
vice versa. The ionic radius of Dy
3+ (1.03 Å) is smaller than that of Ba
2+ (1.35 Å); similarly, the ionic radius of Cr
3+ (0.52 Å) is also smaller than that of Fe
3+ (0.64 Å).
[13,14,19–21] This scenario prompts the distortion of the unit cell thereby causing microstructural defects and strain, consequently resulting in the observed decreased
a,
c, and
Vcell values. The
c/
a ratio varies slightly with Dy
3+–Cr
3+ substitution and maintained an approximate value of 3.94 for all samples (Table
2). It has been reported that if the ratio is below 3.98, then the prepared sample can be assumed to exhibit hexagonal structure.
[22,23] Since the
c/
a ratio is less than 3.98 for all synthesized samples, we can assume that the prepared samples exhibit hexagonal structure. The values of crystallite size do not follow a regular pattern with Dy
3+–Cr
3+ substitution (Table
2), and it increases for the sample B2 and decreases for B3. The unsubstituted sample,
i.e. B1 exhibits the lowest crystallite size (22.91 nm). The strain (
η) that is distortion-induced during the synthesis process shows a decreasing behavior with Dy
3+–Cr
3+ substitution, this may be due to enhancement towards pure phase of hexaferrites.
[24]Table 2
Table 2
 Table 2 Values of lattice parameters (a and c), crystallite size (D), volume of unit cell (Vcell), and strain (η) for Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5). .
| x/y |
2θ/(±) |
d/Å |
β/(±) |
a/Å |
c/Å |
c/a |
Vcell/Å3 |
D/nm |
η×10–4 |
| 0.0/0.0 |
30.23 |
2.9541 |
0.399 |
5.90 |
23.27 |
3.9440 |
703.92 |
22.91 |
12.89 |
| 0.1/0.3 |
30.31 |
2.9464 |
0.174 |
5.89 |
23.21 |
3.9405 |
698.51 |
52.54 |
5.60 |
| 0.2/0.5 |
30.39 |
2.9015 |
0.235 |
5.87 |
23.15 |
3.9437 |
693.16 |
38.91 |
7.55 |
| Table 2 Values of lattice parameters (a and c), crystallite size (D), volume of unit cell (Vcell), and strain (η) for Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5). . |
4.2. FTIR analysisFigure 2 shows the room temperature FTIR spectra of Ba1–xDyxFe12–yCryO19 (x = 0.0, 0.1, 0.2, and y = 0.0, 0.4, 0.5) in the range 4000 cm–1 to 400 cm–1. The presence of two absorption bands at 438 cm–1 and 589 cm–1 which are characteristics bands of hexaferrites gives an idea of the formation of the hexaferrite structure.[25] These bands are due to metal–oxygen stretching vibrations (such as Fe–O, Cu–O, Mg–O, and Zr–O) at the octahedral and tetrahedral sites in the hexagonal lattice.[26] The band at 438 cm–1 occurs in the octahedral site whereas the band at 598 cm–1 occurs at the tetrahedral site, the variation in Fe3+–O2+ distances at octahedral and tetrahedral sites cause shifting of the position of the absorption bands towards lower frequency side.[27] The shifts in these absorption bands towards lower frequency occur as a result of the occupation of the substituted cations in the Fe3+ site, the unsubstituted sample (i.e., sample B1) exhibits these bands due to the stretching vibration of Ba–O. The absorption bands in the range 1100 cm–1 to 1500 cm–1 observed in all the samples could be attributed to metal–oxygen–metal (M–O–M) bonds such as Fe–O–Fe bonds; broad absorption band observed at 3459 cm–1 as a result of –OH stretching vibration could be due to the presence of water molecules absorbed by the samples.[28] The observed absorption band at 1649 cm–1 results from H–O–H bending vibration of H2O.[29]
4.3. FESEM, EDX, and elemental mappingThe FESEM micrographs of Ba1–xDyxFe12–yCryO19 (x = 0.0, 0.1, 0.2, and y = 0.0, 0.4, 0.5) are presented in Fig. 3. The average grain sizes for all the samples are around 0.1 m to 0.2 m as estimated from the micrographs. Since the grain sizes obtained from XRD is much smaller than those observed in FESEM, we can assume that the grains agglomerate to form larger ones in all the prepared samples. Clearly, the agglomeration is observed in all the samples which could be attributed to magnetic interaction with other neighboring grains.[30] The micrographs show some crystallites with large shapes close to hexagonal platelet-like and others with rice or rod-like shapes. The shapes of the crystallites are vital for various applications, crystallites with large hexagonal platelet-like shapes are useful as radar absorber materials.[31,32] The crystallites with rice or rod-like shapes may find application in data storage, catalysis, imaging, sensing, and surface enhance Raman scattering.[33] The EDX and elemental analysis for the samples B2 and B3 are shown in Fig. 4. Both the EDX spectra and elemental micrographs confirm the stoichiometry of the prepared samples.
4.4. Optical analysisIn UV-vis NIR spectroscopy, the energy of incident photons is absorbed by electrons in the sample, followed by their excitation from the valence band to the conduction band. The optical properties of Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5) have been investigated using UV-vis spectroscopy in the range 234 nm–766 nm. The spectra of the absorbance as a function of wavelength are presented in Fig. 5. The spectra show absorption peaks at 272, 354, 475, and 726 nm which result from σ–σ*, n–σ*, π–π*, and n–π* transitions. In addition, there were two reflection peaks observed at 418 nm and 690 nm. The reflection peak at 418 nm corresponds to hypochromic shift whereas that at 690 nm corresponds to hyperchromic shift. There is no observation of hypsochromic (blue) shift and bathochromic (red) shift in the spectra. The absorption peak at 726 nm and the reflection peak at 690 nm merge together as Dy3+–Cr3+ is substituted, this shows that the substitution of Dy3+–Cr3+ enhances the absorption by the prepared samples. The optical band gap (Eg) was determined using Tauc relation[34]
 | |
where
α is the absorbance,
h is the Plank constant (6.6260×10
–34 J·s),
ν is the frequency of the incident photon, and
A is a characteristics constant that depends on
n. The values of
n are, respectively, 1/2, 3/2, 2, and 3 for allowed direct, forbidden direct, allowed indirect, and forbidden indirect transitions. Figure
6 shows the plots of
Eg for the synthesized samples. The value of
Eg for all the samples was evaluated by extrapolation of the linear part of the graph of (
αhν)
2 against
Eg. The values of
Eg for samples B1, B2, and B3 were found to be 2.89, 2.71, and 2.39 eV respectively.
From Figs. 6 and 7, we can observe that Eg decreases with increases in Dy3+–Cr3+ substitution. Kaur et al. observed that the variation of Eg relies on factors such as quantum confinement and crystallite size.[12] The Eg observed are higher than those obtained for strontium hexaferrites thin films prepared by laser ablation method.[35]
4.5. Dielectric analysisThe response of nanomaterial to an applied electric field is better understood using impedance spectroscopy. This may present us with vital information regarding conduction mechanism involving ionic, electronic, and interfacial polarization. The parameters calculated from the impedance spectroscopy are complex permittivity (ε*), real part of complex permittivity (ε′), and the imaginary part of complex permittivity (ε″) which are expressed in Eqs. (6), (7), and (8), respectively.[36]
where
is an imaginary number,
Z′ is the real part of complex impedance,
Z″ is the imaginary part of complex impedance,
ω = 2
πf is the frequency, and
C0 is the geometrical capacitance. The complex impedance (
Z*), real part of complex impedance (
Z′), and the imaginary part of complex impedance (
Z″) are, respectively, given in Eqs. (
9), (
10), and (
11)
[37]
where
θ is the phase angle. The ratio of
ε″ and
ε′ represents the dielectric loss tangent (tan
δ) or energy dissipation factor of the nanomaterial.
[10]
The conducting properties of a nanomaterial can be explained on the basis of the following equation
[38]
where
σdc is the frequency-independent part of conductivity,
σac (
σac =
Aωs) is the frequency-dependent part of conductivity,
A is the temperature-dependent constant, and
s is a numerical constant. AC conductivity can be expressed by the following relation
[39]
4.5.1. Dielectric constantThe energy storage ability of hexaferrites is better understood by analyzing ε′. Figure 8 represents the room temperature frequency-dependent ε′ for Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5). The dielectric properties of hexaferrites can be explained on the basis of Maxwell–Wagner model. In accordance with this model, the layers of conducting grains in ferrites is surrounded by layers of poorly conducting grain boundaries.[34] When an electric field is applied at lower frequencies, charge carriers easily migrate through the grains and accumulate at the grain boundaries which result in high interfacial polarization owing to high resistivity and consequently high values of ε′ whereas at higher frequencies, the interfacial polarization drastically decreases to negligible values. At this point, only electronic and dipolar polarization contribute to the values of ε′.[40] All the samples exhibit a high value of ε′ at lower frequencies as compared with intermediate and higher frequencies, space charge polarization, oxygen vacancies, and grain boundary defects are the reason behind the high value of ε′ at lower frequencies.[13] From Fig. 8, it can be observed that ε′ increases with increase in Dy3+–Cr3+ substitution for all the samples, this could be attributed to increased space charge polarization as a result enhancement in electron hopping between Fe3+ and Fe2+ ions.[41] Clearly, ε′ shows a decreasing trend with increase in frequency both at lower and intermediate frequencies for all samples. At higher frequencies, there is an abrupt increase in ε′, this indicates that ε′ is enhanced by Dy3+–Cr3+ substitution at higher frequencies. The increasing behavior of ε′ reduces the penetration depth of EM waves by increasing the skin effect, this means that lower values of ε′ observed in hexagonal ferrites as compared with the ε′ of calcium copper titanate (> 9×103 at 106 Hz) makes them useful for high frequency application.[16,42]
4.5.2. Dielectric loss (tanδ)The dielectric loss (tanδ) shows the nature of energy dissipation of the hexaferrite nanomaterial during the conduction of electrons in the dielectric system. Variation of with frequency at room temperature for Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5) is presented in Fig. 9. Electron hopping produces polarization which varies with the applied electric field; when the polarization lags behind the applied electric field above a certain critical frequency, appears.[43] This is justified by the presence of defects (vacancies and interstitials), impurities, and structural imperfections in the material as a result of substitutions of cation with different valency and ionic radius.[14,15] The prepared samples exhibit high tanδ at lower frequencies; this corresponds to loss of energy. There is high resistivity at lower frequencies as a result of grain boundaries; this scenario prompts the need for more energy in order for electron hopping between Fe3+ and Fe2+ ions to occur. Hence, high δ (or loss of energy) is observed at lower frequencies. Less resistivity is observed at higher frequencies as a result of conducting grains and consequently less energy is required for electron hopping between Fe3+ and Fe2+ ions to occur. Thus, small tanδ (or loss of energy) is observed at higher frequencies.[13, 16] The contribution to tanπ at lower frequencies could be attributed to hopping conduction of electrons whereas the observed tanδ at higher frequencies could be due to the response of defect dipoles to the applied electric field, the defect dipoles arise during the process of calcination as a result of the transition of Fe3+ ions to Fe2+ ions.[44] Resonance or Debye-like relaxation peaks are observed in the samples B2 as well as in B3 at higher frequencies, these peaks occur when the frequency of electron jumping during electron exchange between Fe3+ and Fe2+ ions equals the frequency of the applied electric field.[39] The observed decrease in tanδ after the occurrence of the Debye-like relaxation peaks in the samples B2 as well as B3 at higher frequencies can be explained on the basis of relaxation of the defects dipoles, under the influence of applied electric field the relaxation of these defects dipoles displays a decreasing behavior with increase in frequency and subsequently decreases the tanδ in the higher frequencies side.[45]
4.5.3. Cole–Cole plotThe nature of the grain and grain boundary resistance of the synthesized samples can be observed from the behavior of the curve observed in Cole–Cole plot (also called Nyquist plots), which is a plot of the imaginary part (Z″) versus real part (Z′) of complex impedance (Z*). Figure 10 presents the Cole–Cole plot of Ba1–xDyxFe12–yCryO19 (x = 0.0,0.1,0.2, and y = 0.0,0.4,0.5) at room temperature. The analysis of Cole–Cole plots gives vital parameters which characterized non-Debye-like relaxation behavior.[46] A polycrystalline hexagonal ferrite sample can be thought to consist of grains (or parallel conducting plates) separated by grain boundaries (or resistive plates). A Cole–Cole plot consists of a semi-circle arc starting from the lower frequencies side to the higher frequencies side. The part of the semi-circle at the lower frequency side represents the contribution of the grain boundaries (or grain boundary resistance (Rgb) while the part of the semi-circle at the higher frequency side of the Cole–Cole plot represents the contribution from the grains (or grain resistance (Rg).[47] From Fig. 10, we can observe that there is no higher frequency arc for the samples B1 as well as B2. Hence, we can conclude that there is no or less contribution from Rg towards the dielectric properties for these samples. The arc for the sample B3 extends to the higher frequency side of the plot. This is an indication that there is contribution from Rg towards the dielectric properties for this sample and that the quantity of grains has increased. Consequently, we can expect the sample B3 to be more conducting than the samples B1 as well as B2 since grain boundaries are less conducting than grains. From the forgoing discussion, we can assume that Rgb contributes most to the dielectric properties of the synthesized samples.
4.5.4. AC conductivity (σac)The AC conductivity (σac) of Ba1–xDyxFe12–yCryO19 (x = 0.0, 0.1, 0.2, and y = 0.0, 0.4, 0.5) is presented in Fig. 11. From lower to intermediate frequencies, σac exhibits frequency-independent behavior, this could be attributed to the presence of random distribution of charge carriers through activated electron hopping.[43] At higher frequencies, there is a sudden and abrupt rise in σac of the prepared samples; this behavior correlates with the increase in ε′ at higher frequencies (Fig. 8). Similar to the behavior of ε′, the behavior of σac of hexaferrites depends on electron hopping between Fe3+ and Fe2+ ions at octahedral site. As the frequency of the applied electric field is varied, electron hopping between Fe3+ and Fe2+ ions at octahedral site increases thereby resulting in increased conductivity.[48] The conduction mechanism in hexaferrites has been explained by assuming the process of polarization in hexaferrites to be similar to the process of conduction; in this manner, electron hopping between Fe3+ and Fe2+ ions at octahedral site results in the occurrence of local displacement and the subsequent generation of polarization which is responsible for conduction in hexaferrites.49, 50 Similar to ε′, we can conclude that Dy3+–Cr3+ substitution enhances at higher frequencies.
