Structural, magnetic, and dielectric properties of

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CERAMICS INTERNATIONAL

Ceramics International 40 (2014) 6127–6135 www.elsevier.com/locate/ceramint

Structural, magnetic, and dielectric properties of nanocrystalline Cr-substituted Co0.8Ni0.2Fe2O4 ferrite Adel Maher Wahbaa, Mohamed Bakr Mohamedb,n a

Tanta University, Faculty of Engineering, Department of Engineering Physics and Mathematics, Tanta, Egypt b Ain Shams University, Faculty of Science, Physics Department, Cairo, Egypt Received 11 October 2013; received in revised form 3 November 2013; accepted 13 November 2013 Available online 21 November 2013

Abstract The structural, magnetic, and electric properties of Co0.8Ni0.2CryFe2 yO4 (0.00 r y r0.75; step 0.15) prepared via citrate precursor method are investigated. The structural properties of the produced nano-particles were examined through X-ray diffraction (XRD) and infrared spectroscopy (IR). The XRD pattern revealed a single phase cubic spinel structure for all the samples. The crystallite size decreases with increasing Cr content. Magnetic properties were recorded using vibrating sample magnetometer (VSM). The saturation magnetization increased first with y ¼0.15 then decreased continuously with further increase of Cr3 þ content. Quite reasonable cation distribution was proposed for all the samples relying on the experimental results of lattice parameters, magnetization, and IR spectrum. Theoretically estimated lattice parameters and magnetic moments (using Neel's two sub-lattice model) obtained from the proposed cation distribution are in conformity with those experimentally obtained from XRD and VSM results, respectively. Chromium substitution was found to improve ac electric properties, which was revealed by analyzing frequency-dependent ac conductivity and loss factor. & 2013 Elsevier Ltd and Techna Group S.r.l. All rights reserved. Keywords: Cr; Magnetic; Dielectric; Structure

1. Introduction Spinel ferrite nano-particles have been attracting many researchers in the last two decades aiming to investigate the correlations between both magnetic and electric properties with compositional and structural ones. Spinel ferrites are widely used in many applications including information storage systems, magnetic cores, magnetic fluids, electronic devices, microwave absorbers, sensors, magnetic drug delivery, and medical diagnostics. In the nanocrystalline phase, electrical and magnetic properties change drastically compared to the bulk phase produced by the standard ceramic method. Ceramic method has several disadvantages including impurities introduced during the grinding process, poor control of stoichiometric composition, particle-size inhomogeneity, and high sintering temperatures [1]. Nanosized materials have been n

Corresponding author. Tel.: þ20 1014068820; fax: þ 20 226842123. E-mail address: [email protected] (M. Bakr Mohamed).

synthesized using various chemical methods including solgel [2], co-precipitation [3], hydrothermal [4], autocombustion synthesis [5]...etc. Wet chemical methods such as coprecipitation and hydrothermal ones produce high-quality fine powders. However, washing and drying processes with long time of preparation and loss of metal ions reduce their suitability for large-scale production [6]. In the past decade, autocombustion method has extensively been used to synthesize ferrites with several structures via mixing organic compounds with metal nitrates to effectively induce the combustion reaction. Organic compounds include citric acid [7], glycine [8], and urea [9]; all act as the fuel for the autocombustion, while metal nitrates, being cation sources, act as oxidants. Citrate-precursor method produces powders of fine and homogeneous chemical composition, fine size, and high reproducibility at lower ignition temperatures (200–300 1C). Besides acting as a fuel, citric acid is effective in forming complexes with the metal cations [10]. In spinel cubic structures, the unit cell should contain 32 oxygen atoms with 8 tetrahedral (A) and 16 octahedral (B)

0272-8842/$ - see front matter & 2013 Elsevier Ltd and Techna Group S.r.l. All rights reserved. http://dx.doi.org/10.1016/j.ceramint.2013.11.064

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A. Maher Wahba, M. Bakr Mohamed / Ceramics International 40 (2014) 6127–6135

occupied sites [11]. Cobalt and iron ions usually occupy both A and B sites while nickel prefers B sides, a fact that might significantly change with the decrease of the crystallite size. Cobalt ferrite is a hard magnetic material with large coercivity and moderate magnetization and has its own informationstorage applications [12]. Nickel ferrite, on the other hand, is a soft magnetic material, and Ni2 þ has its own effect of decreasing coercivity of Co ferrite due to its lower magnetocrystalline anisotropy and smaller magnetic moment. In addition, partial Co substitution with Ni clearly decreases the ac electric and magnetic losses [13]. The addition of trivalent ions like Al3 þ , Cr3 þ , or both as substituent(s) for Fe3 þ ion to ferrites or other oxides, greatly influences both of their electrical and magnetic properties [14–20]. The main reason for substituting Fe with Cr is to increase the electrical resistivity of the composite, which is an essential demand for reducing electrical or dielectric losses, especially for highfrequency applications. Well known is that the electric and magnetic properties of ferrites are strongly dependent on the crystallite size. The substitution of Fe ions by Cr ones both changes the crystallite size and also the distribution of Fe ions along A and B sites, and thus has its obvious role on controlling and may be tailoring the electric and magnetic properties of ferrites. In this work, nanocrystalline Cr-doped cobalt–nickel ferrite powders have been synthesized by citrate precursor auto-combustion method. The effect of Cr substitution on the structural, magnetic, and ac electric properties has been investigated. 2. Experimental Nanocrystalline ferrites with the general formula Co0.8Ni0.2CryFe2 yO4 (y=0.00, 0.15, 0.30, 0.45, 0.60, 0.75) were prepared by citrate precursor method. Analytical grade metal nitrates Co(NO3)2 6H2O, Ni(NO3)2 6H2O, Cr(NO3)3 9H2O, Fe(NO3)3 9H2O and dehydrated citric acid C6H8O7 were used as starting materials. Stoichiometric amounts of the metal nitrates and citric acid were dissolved in minimum amounts of doubly distilled water. The citric to the whole-metal nitrates molar ratio was chosen to be 1:1 to provide complete combustion with no residues of NO3 ions [21]. Metal nitrates solutions were mixed together and then the citric acid solution was added (to chelate Co2 þ , Ni2 þ , Fe3 þ and Cr3 þ ions) followed by one-hour stirring using a magnetic stirrer. Ammonia solution (NH4OH) was added, at room temperature, to the nitrate–citrate solution drop by drop to adjust the pH value at 6.0 when the solution turned darker and more viscous. This pH value was recorded to provide full combustion, stronger phase formation and absence of any ammonia or nitrates in the final product [22]. Heating was then initialized on a hot plate to evaporate the water till a dry viscous gel was formed. With further heating, self-propagating combustion reaction started within some point in the gel accompanied by a dense evolution of brown gases (mainly nitrogen oxides). The combustion propagated till the whole gel was converted into burnt fluffy ash-like powder. The coarse powder was then collected and slightly ground in an agate mortar to achieve a

fine powder. This fine powder was mixed with a tiny amount of polyvinyl alcohol aqueous solution as a binder and then pressed under a pressure of 285 MPa into pellets of 1 cm diameter and around 2.5 mm thickness. Pellets were sintered at 650 1C with a heating rate of 5 1C/min for 3 h and then furnace-cooled to room temperature. Pellets' surface were polished and coated with silver paste to provide the parallelplate capacitor geometry with the ferrite acting as the dielectric medium. The X-ray powder diffraction patterns of the samples were collected on a Philips diffractometer (X'pert MPD) with a goniometer using Cu-Kα radiation. The diffracted intensities were collected in step-scan mode (step size 2θ ¼ 0.021; counting time 2 s) in the angular range 10–801. The crystal structure and microstructure were refined applying Rietveld profile method, using MAUD program [23]. This program is specially designed to perform a simultaneous refinement of both material structure (lattice parameters, atomic coordinates, occupancy factors, displacement parameters) and microstructure (crystallite sizes (D), and r.m.s. lattice microstrain). The U, V, W parameters of instrumental broadening, instrumental asymmetry and the profile shape of the reflections were estimated for the present setting of the diffractometer using LaB6 standard sample. These instrumental parameters were kept fixed during the subsequent structural and microstructural refinements of the samples. Due to the anisotropy in the crystallite size and microstrain values, profiles with different Miller indices are broadened in different manner and this effect creates problems frequently in Rietveld structure refinements. To consider their influence in the profile shapes, the Popa anisotropic model [24] incorporated in MAUD program has been applied. The process of successive profile refinements modulates the different structural and microstructural parameters of the simulated pattern to fit the experimental diffraction pattern. No absorption correction was taken into consideration and the scattering background was refined with a 5th order polynomial. The bulk density, ρb was measured by the Archimedes method and then compared with that estimated from XRD data, ρXRD. The sample porosity is estimated from the relation P ¼ ð1 ρb =ρXRD Þ 100. The X-ray density is calculated from the formula ρXRD ¼ 8M=N A a3 , where the factor 8 indicates the number of formula units in a unit cell, M is the molar mass, NA is Avogadro's number and a3 is the cell volume. Infrared (IR) spectroscopy (Bruker Tensor 27 FTIR Spectrometer) was used in the range of 200–1000 cm 1 to confirm phase formation, provide a primary assumption of cation distribution, and to check the residual groups of the combustion process, such as NO3 , OH and COOH . The magnetization, remanent field, and the coercive field were measured by tracing M–H hysteresis loops for the powder samples at room temperature using a vibrating scanning magnetometer (VSM) and a magnetic field up to 8 kOe using the LDJ vibrating sample magnetometer model 9600. The ac conductivity and dielectric properties were measured at room temperature using a complex impedance technique using low frequency lock-inamplifier (LIA, SR510) operating in the frequency range


refinement of X-ray data. It can be seen from Table 1 that the oxygen position parameter increases with increasing Cr content. Taking the center of symmetry at ð1=4 1=4 1=4Þ (origin at B-site), the ideal value of parameter u is 0.25, while assuming center of symmetry at ð3=8 3=8 3=8Þ (origin at A-site), uideal is 0.375. For these ideal values the arrangement

0.75

0.60

Intensity (a. u.)

102–105 Hz to measure the voltage drop VR across a standard resistance R and the phase angle ϕ between VR and the current I. The value of R is chosen such that VR do not exceed 1% of the rms value of the applied voltage of the signal provided by the function generator. An evacuated silica tube was used as housing for the pellets to avoid moisture absorption on sample surfaces. Data were collected after stabilizing temperature for at least 10 min. The real part of the dielectric constant was determined from the relation ε′ ¼ V R t s sin f= ðε0 ω RAs Þ, where ts and As are thickness and cross-sectional area of the pellet, respectively, and ε0 is the permittivity of free space. The tangent loss factor was determined from the relation: tan δ ¼ ð1= tan fÞ ¼ ε″=ε′, and the ac conductivity is depicted from the formula: sac ¼ ε0 ε′ ω tan δ.

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3. Results and discussion 3.1. X-ray diffraction analysis

0.45

0.30

10

20

30

40

(440)

(422) (511)

(400)

50

60

(620) (533) (622)

y = 0.00

(222)(311)

(220)

0.15 (111)

XRD patterns of Co0.8Ni0.2CryFe2 yO4 (y ¼ 0.00, 0.15, 0.30, 0.45, 0.60, 0.75) are shown in Fig. 1(a). The peaks can be indexed with space group Fd3m to (111), (220), (311), (222), (400), (422), (511) and (440) planes of a cubic unit cell. All XRD patterns were analyzed by using MAUD program, which is based on Rietveld method [25]. The Rietveld refinement for Co0.8Ni0.2Cr0.6Fe1.4O4 is shown in Fig. 1(b), all the observed peaks in the XRD patterns are allowed Bragg 2θ positions, which confirm that these samples are single phase cubic ferrites. The oxygen positions (x¼ y¼ z ¼ u) were taken as free parameters and all other atomic fractional positions were considered as being fixed. Other parameters such as lattice constants, isothermal parameters, scale factors and shape parameters were considered as free parameters. The site occupancy distribution in spinel ferrite will be obtained from magnetization measurements as we will see later. Table 1 depicts the refinement fitting parameters, lattice parameter a (Å), and oxygen parameter, u, for the studied samples. The lattice parameter, as shown in Fig. 2, first decreases then increases and finally decreases with increasing Cr substitution. This behavior will be explained when considering the proposed cation distribution in magnetic properties section. The oxygen positional parameter or anion parameter (u) depends on the chemical composition, preparation conditions and sintering procedure and can be obtained from Rietveld

70

80

2-theta (degrees)

Fig. 1. (a) X-ray powder diffraction for Co0.8Ni0.2Fe2 yCryO4 (0 ryr 0.75) and (b) Rietveld refinement profile for Co0.8Ni0.2Fe1.4Cr0.6O4 sample performed using MAUD software.

Table 1 Refined values of cell parameters a (Å), ath (Å) (as calculated based on the proposed cation distribution), oxygen positional parameter u, tetrahedral and octahedral bond lengths, tetrahedral, octahedral edge and the hopping lengths at A-and B-sites, LA and LB, respectively of Co0.8Ni0.2CryFe2 yO4 (0.00r yr0.75). y

0.00 0.15 0.30 0.45 0.60 0.75

Lattice parameters aexp (A)

ath (A)

8.3829 8.3745 8.3776 8.3785 8.3788 8.3732

8.3830 8.3745 8.3776 8.3785 8.3788 8.3733

Oxygen position u 0.3779 0.3777 0.3775 0.3786 0.3785 0.3789

Tet. bond dAO 1.8570 1.8522 1.8499 1.8661 1.8655 1.8699

Oct. bond dBO 2.0717 2.0712 2.0737 2.0649 2.0654 2.0608

Tet. edge dAOE 3.0326 3.0246 3.0209 3.0473 3.0464 3.0536

Oct. edge Share dBOE

Unshared dBOEU

2.8950 2.8969 2.9028 2.8771 2.8782 2.8670

2.9642 2.9611 2.9622 2.9628 2.9629 2.9611

LA (A)

LB (A)

3.6299 3.6262 3.6276 3.6280 3.6281 3.6257

2.9638 2.9608 2.9619 2.9622 2.9623 2.9603

6130


of O2 ions corresponds exactly to a cubic closed packing, but in actual spinel lattice, this ideal pattern is slightly deformed. For the present Co0.8Ni0.2CryFe2 yO4 system, u4 0.375 which means that O2 ions move away from the cations in tetrahedral A-site along the 〈111〉 directions due to the expansion of the tetrahedral interstices; correspondingly the octahedral B-sites become smaller. This leads to a decrease in the A–A interaction and an increase in the B–B interaction. From Fig. 2, one can clearly notice that with increasing Cr content, the crystallite size decreases from 77 nm for Co0.8Ni0.2Fe2O4 to 12 nm for Co0.8Ni0.2Cr0.75Fe1.25O4. This decreasing affects the electric properties as will be seen later. The values of the tetrahedral and octahedral bond length (dAX and dBX), tetrahedral edge (dAXE), shared and unshared octahedral edge (dBXE and dBXEU) can be calculated as follows [26,27]: pffiffiffi dAo ¼ a 3ðu 1=4Þ; dBo ¼ a½3u2 ð11=4Þu þ ð43=64Þ1=2 ; pffiffiffi dAoE ¼ a 2ð2u 1=2Þ; pffiffiffi dBoE ¼ a 2ð1 2uÞ; dBoEu ¼ a½4u2 3u þ ð11=16Þ1=2 where a is the lattice parameter and u is the oxygen positional parameter. Inspecting Table 1, one can note that both tetrahedral bond length and tetrahedral edge increase as Cr3 þ increases, while octahedral bond length, shared and unshared octahedral edge decrease. The distance between magnetic ions,

pffiffiffi i.e. hopping length in octahedral site (LA) is LA ¼ a p3ffiffi=4, ffi whereas for the tetrahedral site (LB) it is given by LB ¼ a 2=4 [28]. The variation of hopping lengths with Cr3 þ content is depicted in Table 1. It is evident that hopping length LA and LB both decrease with Cr3 þ content. This is assigned to the substitution process and cation distribution. The values of the bulk density ρb, XRD density ρXRD, and the porosity P for all samples are listed in Table 2. The results show that the porosity increases with decreasing crystallite size. 3.2. FT-IR spectroscopy The FT-IR spectroscopy of the Cr-substituted Co0.8Ni0.2Fe2O4 samples is shown in Fig. 3. Four frequency bands were recorded. The higher frequency band of the range 572– 606 cm 1 corresponds to vibrations of the tetrahedral site and the lower frequency band of the range 381–388 cm 1 corresponds to vibrations of the octahedral site. From Table 2, as Cr content increases, ν1 shifts to higher frequency. The shifting of ν1 to higher wave number is attributed to the stretching of Fe–O bonds. The frequency band, ν4 around 490 cm 1 appears as the amount of Cr3 þ content increases, and it could be attributed to the increasing amount of Cr3 þ O2 complexes due to the decreasing content of

0.75 0.6 0.45

2.4

Lattice parameter, a (A)

60

8.382

50

8.380

40 30

8.378

20

8.376

Crystallite size (nm)

70

8.384

Transmittance (a.u.)

80

8.386

0.3

1.6

0.15 0.0

0.8

10 0.00

0.15

0.30

y

0.45

0.60

0.0 1000

0.75

Fig. 2. Variation of lattice parameter ‘a’ and crystallite size with Cr content y in Co0.8Ni0.2Fe2 yCryO4 system.

800

600 400 Wave number (cm-1)

200

Fig. 3. FT-IR spectra of Co0.8Ni0.2Fe2 yCryO4 nano-ferrite samples.

Table 2 The absorption bands (v1, v2, v3, v4), force constant (kt, ko) and ionic radius of the A- and B-sites (rA, rB), XRD density (ρXRD), bulk density (ρo) and porosity (P) for the Co0.8Ni0.2CryFe2 yO4 (0.00ryr 0.75) samples. y

ν1 (cm 1)

ν2 (cm 1)

ν3 (cm 1)

ν4 (cm 1)

kt 104 (dynes/cm)

k0 104 (dynes/cm)

rA (Å)

rB (Å)

ρXRD (g/cm3)

ρb (g/cm3)

P (%)

0.00 0.15 0.30 0.45 0.60 0.75

572.8 580.6 590.2 597.9 603.7 605.6

381.9 387.7 387.7 385.8 381.9 383.8

235 238 235 238 238 238

– – 489 492 492 492

14.09 14.47 14.94 15.33 15.62 15.70

8.84 9.07 9.03 8.89 8.68 8.29

0.50452 0.50386 0.50284 0.50170 0.50068 0.49945

0.68520 0.68238 0.68415 0.68514 0.68585 0.68447

5.290 5.293 5.274 5.259 5.246 5.243

4.699 4.483 4.363 4.236 4.141 4.048

11.2 15.3 17.3 19.5 21.1 22.8


40

M (emu/g)

Table 3 Magnetic-properties parameters of Co0.8Ni0.2CryFe2 yO4 (0.00r yr0.75) samples

y = 0.00 y = 0.15 y = 0.30 y = 0.45 y = 0.60 y = 0.75

60

20 0 -20 -40 -60 -8

-6

-4

6131

-2

0 2 H (kOe)

4

6

8

Fig. 4. Hysteresis loops illustrating magnetization M as a function of the applied magnetic field H at room temperature for Co0.8Ni0.2Fe2 yCryO4 nanoferrite (0ry r0.75).

Fe3 þ on the B-site. Table 2 shows that, ν3-band is almost constant for all samples; this band is probably the characteristic of the bending vibration involving Fe3 þ and O2 of octahedral complexes [29]. Since the vibration frequency is proportional to the force constant (k); the force constant of tetrahedral site (kt) and octahedral site (ko) were estimated by employing the method suggested by Waldron [30]: k t ¼ 7:62 M 1 ν21 10 2 M2 ν22 10 2 2 where M1 and M2 are the molecular weights of cations in A- and B-sites, respectively. The molecular weights, M1 and M2, have been calculated using the cation distribution data, Table 4. The estimated values of kt and ko are listed in Table 2. As seen from Table 2, the band shift of ν1 to a higher frequency with increasing Cr3 þ content indicates that the force constant increases. ko ¼ 10:62

3.3. Magnetic properties The magnetic hysteresis curves which trace the variation of the magnetization M as a function of the applied magnetic fields H for various Co0.8Ni0.2CryFe2 yO4 samples measured at room temperature, are shown in Fig. 4, in which the applied fields extend to 8 kOe. These curves were used to obtain the saturation magnetization Ms, remanent magnetization Mr, and the coercive field Hc; the whole values are listed in Table 3. Values of the saturation magnetization Ms for the samples were deduced from the extrapolation of the M vs. 1/H curves to 1/H-0. Both magnetization and coercivity showed unexpected increase for the smallest doping with Cr3 þ (y¼ 0.15), and then decreases monotonically with the content of Cr3 þ . This behavior could be explained by a cation distribution proposed on the basis of the experimental data of the magnetization and lattice parameter. The suggested cation distribution is illustrated in Table 4. The values of Ms were used to find out approximate values for the

y

Mr (emu/g)

Ms (emu/g)

Hc (kOe)

nobs B (μB)

K 104 (erg/Oe))

0.00 0.15 0.30 0.45 0.60 0.75

25.0 33.8 25.7 17.4 12.0 8.3

67.2 71.3 61.3 46.7 36.6 27.7

1.100 1.825 1.400 1.160 1.235 1.125

2.823 2.988 2.563 1.946 1.524 1.149

8 13 9 6 5 3

in units of the Bohr magnetic moment per unit formula nObs B magneton, using the formulae [13]: nObs B ¼

MW M s 5585

where MW is the molecular weight for each composition. Those values were to be compared with the theoretical ones nB ¼ MB MA, estimated from the proposed cation distribution, where MA and MB are the A-site and B-site sublattice magnetic moment estimated from the magnetic moment of each element in terms of the Bohr magneton μB (5, 4, 3, 0, 2, 3 and 0 for Fe3 þ , Fe2 þ , Co2 þ , Co3 þ , Ni2 þ , Cr3 þ , and Cr2 þ , respectively). Cations like Co3 þ , Fe2 þ , and Cr2 þ are suggested to be formed upon oxidation and reduction processes during the autocombustion. Quite reasonable matching between the observed magnetic moment and the theoretical one was achieved (Tables 3 and 4). To further confirm the suggested cation distribution, a theoretical estimation of the lattice parameter was operated for each composition and then compared with that obtained by XRD analysis. For each sample the average ionic radii per molecule of the tetrahedral and octahedral sites, rA and rB, were calculated based on the suggested cation distribution of Table 4, using the formulae [31]: r A ¼ ∑ αi r i ; i

rB ¼

1 ∑ αi r i 2 i

where αi is the concentration of the element i of ionic radius ri on the respective side. The ionic radii for Co2 þ (0.58 and 0.745 Å), Ni2 þ (0.55 and 0.69 Å), Fe3 þ (0.49 and 0.645 Å), Fe2 þ (0.63 and 0.78 Å), and O2 (1.361 and 1.381 Å) are taken with reference to both sites [32], with the first value corresponds to that of the A-site. Both Cr3 þ (0.63 Å) and Cr2 þ (0.73 Å) were assumed to occupy only the B-site. Values of rA and rB are listed in Table 2. Theoretical values of the lattice parameter are then calculated from the relation [31] i pffiffiffi 8 h ath ¼ pffiffiffi ðr A þ RO Þþ 3ðr B þ RO Þ 3 3 where RO is the ionic radius of oxygen. For all samples, the values of ath greatly match with those obtained from Rietveld XRD analysis (see Table 1), with a percentage error less than 0.0005%. Fig. 5a, b also shows the variation of the estimated rA and rB with the chromium content and its relation with recorded values of ν1 and ν2 of the IR data. The variation of rB with Cr content is quite similar to the variation of the lattice

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Table 4 Cation distribution of Co0.8Ni0.2CryFe2 yO4 (0.00ryr 0.75) samples. y

Cation distribution

MB

MA

nB

0.00 0.15 0.30 0.45 0.60 0.75

þ þ þ þ þ þ þ þ ðCo20:154 Ni20:011 Fe30:835 Þ½Co20:495 Co30:151 Ni20:189 Fe20:205 Fe30:960 O23:973 2þ 2þ 2þ 3þ 2þ 3þ 2þ 3þ 2þ þ ðCo0:142 Ni0:018 Fe0:840 Þ½Co0:627 Co0:031 Ni0:182 Cr0:018 Cr0:132 Fe0:040 Fe30:970 O23:987 2þ 2þ 2þ 3þ 2þ 3þ 2þ 3þ 2þ 3þ 2 ðCo0:128 Ni0:022 Fe0:850 Þ½Co0:646 Co0:026 Ni0:178 Cr0:053 Cr0:247 Fe0:043 Fe0:807 O3:965 þ þ þ þ þ þ þ þ þ þ ðCo20:114 Ni20:024 Fe30:862 Þ½Co20:626 Co30:060 Ni20:176 Cr20:105 Cr30:345 Fe20:060 Fe30:628 O23:948 þ þ þ þ þ þ þ þ þ þ ðCo20:104 Ni20:022 Fe30:874 Þ½Co20:625 Co30:071 Ni20:178 Cr20:108 Cr30:492 Fe20:088 Fe30:438 O23:938 2þ 2þ 2þ 3þ 2þ 3þ 2þ 3þ 2þ 3þ 2 ðCo0:093 Ni0:018 Fe0:889 Þ½Co0:623 Co0:084 Ni0:182 Cr0:094 Cr0:656 Fe0:098 Fe0:263 O3:946

7.48 7.65 7.24 6.65 6.25 5.91

4.66 4.66 4.68 4.70 4.73 4.76

2.824 2.989 2.564 1.945 1.523 1.148

0.506 610

590

0.502

0.500

0.498

0.00

0.15

0.30

y

rA

580

1

570

0.45

0.60

cm-1

600

1,

rA, A

0.504

0.75

3.4. Dielectric properties

0.688 400

0.684

2,

rB , A

390

cm-1

0.686

380

rB

0.682

2

0.680

increases the anisotropy constant K1 and thus the coercive field Hc shows a sharp rise (Table 3) compared to the non-doped sample, in spite of the small increase of Ms (Hc ¼ 0.98 K1/Ms [36]). Worth to mention is that the sample with y ¼ 0.15 showed maximum values of Mr, Hc, and Ms. With further increase of Cr3 þ (3μB) content, the amount of Fe3 þ (5μB) decreases in the B-site and increases in the A-site, and (MB MA) decreases, due to the reduction of the A–B magnetic interactions. The increase of the coercivity field for the sample with y¼ 0.60 could be explained in terms of the competing effect of the decrease of the crystallite size, with the subsequent increase in porosity, on increasing the anisotropy constant.

0.00

0.15

0.30

y

0.45

370 0.60

0.75

Fig. 5. Variation of (a) tetrahedral and (b) octahedral, v1, v2, rA and rB with Cr content y in Co0.8Ni0.2Fe2 yCryO4 system.

parameter. This confirms the fact that Cr occupies the B-site and it is the deciding factor of the lattice parameter. The Cr-free sample is considered as high cobalt-content ferrite, with the probability of formation of iron cobaltite or different oxidation states of cobalt [33–35], with the subsequent appearance of Co3 þ cation characterized by zero magnetic moment. Furthermore, electron distribution balance tells that Co3 þ cations have to coexist with the Fe2 þ and/or Cr2 þ cations, which has lower magnetic number than Fe þ 3 cation. On the first doping with chromium (y=0.15), a sharp decrease of the Co3 þ and Fe2 þ content is assumed, with a subsequent increase of Co2 þ in B-site. Thus, the magnetic moment of the B-site MB increased and also nB=MB MA did. The increase of Co2 þ in B-site for the sample with (y=0.15)

Fig. 6(a) shows the variation of the dielectric constant (ε′) of our samples as a function of frequency at room temperature. All samples show normal dielectric dispersion behavior, where the dielectric constant decreases with increasing frequency while becomes almost constant at higher frequencies. The decrease of ε′ with frequency can be attributed to the fact that, at low frequencies, ε′ depends on both the deformational and relaxation polarization mechanisms. The deformational polarization depends on the displacement of electrons and ions while the relaxation polarization depends on the orientational or interfacial effects. Fe2 þ ions could be formed by partial reduction of Fe3 þ during the sintering process or with the autocombustion process during sample preparation. The presence of Fe2 þ and Fe3 þ ions at octahedral positions defines ferrites as polar materials. Rotational displacements of the dipoles result in the orientational polarization. The rotation or turning of dipoles can be explained as the interchange of the electrons between the ions, thus the dipoles align themselves with field. The increase in frequency leads to a decrease in orientational polarization, since the molecular dipoles need time to change their orientation in response to the applied field. This decrease tends to reduce the value of ε′ with increasing frequency. Also, the dielectric loss tangent (tan δ) as a function of frequency was studied at room temperature and is depicted in Fig. 6(b). Again the dielectric loss tangent decreases with increasing frequency for each sample. All the samples exhibit dispersion due to the Maxwell–Wagner interfacial type polarization [37–39]. The values of tan δ depend upon a number of factors such as stoichiometry, Fe2 þ content and structural


240

6133

60

0 0.15 0.3 0.45 0.6

160 120

50 ,

200

40

80 30

40 0

0.8

102

103

104

5KHz 10KHz 100KHz

105 0.6

f (Hz) Tan

8

0.4

7 0 0.15 0.3 0.45 0.6

6 5 4

0.2

0.0 4.0x10-5

3 2

3.0x10-5 ac

1

-1

ln

0 102

103

104

105

f (Hz)

2.0x10-5

1.0x10-5

0.0

0 0.15 0.3 0.45 0.6

-8 -10

0.0

-14 -16

6

7

0.2

0.3 0.4 composition (x)

0.5

0.6

Fig. 7. Compositional dependence of (a) real part, (b) loss tangent and (c) ln sac with frequency at room temperature for Co0.8Ni0.2Fe2 yCryO4 (0ry r0.75) nanoferrites.

-12

-18

0.1

8

9

10

11

12

13

Fig. 6. Variation of (a) real part, (b) loss tangent and (c) ln sac with frequency for Co0.8Ni0.2Fe2 yCryO4 (0 ryr 0.75) nano-ferrites.

homogeneity, which in turn depends on the composition and sintering temperature of the samples [40]. Fig. 7(b) indicates that the dielectric loss of the prepared nano particles also

depends upon the composition; it decreases as amount of Cr increases. The conduction mechanism in ferrites is a result of electron and hole hopping between ions of the same element existing in different valence states on octahedral sites [41]. The variation of ac conductivity with applied frequency for all samples is shown in Fig. 6(c). The common feature of semiconductors (and some disordered systems) is that the frequency dependence of conductivity increases approximately linearly [42]. The odd behavior of sac for samples with y¼ 0.45 and y¼ 0.60 at high frequencies is attributed to an experimental error. The angle ϕ for these samples at high frequency is greater than 89.01, revealing highly capacitive nature. Resulting errors in the function cos ϕ, used in determining s, is the source of this odd behavior. Generally, all the samples show an increasing nature in the ac conductivity curve which is consistent with the

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power law: stotal ¼ so ðTÞ þ sðω; TÞ where stotal is total conductivity of the system, s0(T) denotes the dc conductivity which is independent of frequency and s(ω,T) denotes the frequency dependent ac conductivity part. The term s(ω,T) can also be expressed as sAC ¼ Aωs where A is a constant having the units of conductivity, ω is the angular frequency, and s is a temperature dependent constant. Increasing the applied frequency induces an increase in the charge-carrier transfer rate between different localized sites. It also assists the charge carriers to be liberated from different trapping centers. Fig. 7 shows the variation of real and imaginary parts of the dielectric constant, dielectric loss and ac conductivity with Cr composition calculated at selected frequencies at room temperature. It is noticed that dielectric constant and dielectric loss tangent decrease with increasing Cr3 þ substitution. This can be correlated with the fact that the electron hopping between the Fe2 þ and Fe3 þ (n-type) and hole hopping between Co2 þ and Co3 þ (p-type) are responsible for the dielectric polarization and electrical conduction mechanisms. Cr3 þ ions may do not take part in the conduction mechanism but limit the hopping probability by forming stable electrical bonds with Fe2 þ ions, thereby localizing the charge carriers. This localization of Fe2 þ ions hinders the hopping mechanism of electron exchange between Fe2 þ and Fe3 þ ions at B-sites, resulting in a decrease in the dielectric constant and dielectric loss tangent. Similar effect was observed in other ferrites doped with Cr such as Co0.5Mg0.5CrxFe2 xO4 system [43]. At last, it is important to consider the effect of the crystallite size on the conduction mechanism of our system. Decreasing crystallite size with Cr3 þ substitution enhances the effect of the lower conductive grain boundaries compared to the higher conductive grains. This may have the greater contribution to decreasing sac with increasing Cr content. 4. Conclusions The Co0.8Ni0.2CryFe2 yO4 (y¼ 0.00, 0.15, 0.30, 0.45, 0.60, 0.75) samples, with pure single-phase cubic spinel structure, were prepared using citrate precursor method. The variation of the lattice parameter with Cr3 þ content was explained using Rietveld analysis, IR peaks, magnetization, and a proposed cation distribution. Crystallite size was greatly reduced by increasing the Cr content. Except for the sample with y ¼ 0.15, the saturation magnetization decreases with increasing Cr3 þ substitution; an indicative fact that the lesser magnetic Cr3 þ ions substitute Fe3 þ ions in the octahedral sub-lattice of the ferrites. The decrease in the saturation magnetization with Cr3 þ content is attributed to the weakening of the A–B interactions as more iron occupies the A-site. Dielectric properties decreased as the amount of substitution Cr3 þ ions increases due to the reduction in Fe2 þ ions responsible for the conductivity and polarization and due to the reduction of the crystallite size.

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