Structural and magnetic study of Al3+ doped Ni0.75Zn0.25Fe2−xAlxO4 nanoferrites

Materials Research Bulletin 65 (2015) 183–194

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Structural and magnetic study of Al3+ doped Ni0.75Zn0.25Fe2
xAlxO4 nanoferrites L. Wang, B.K. Rai, S.R. Mishra * Department of Physics, The University of Memphis, Memphis, TN 38152,USA

A R T I C L E I N F O

A B S T R A C T

Article history: Received 25 July 2014 Received in revised form 9 January 2015 Accepted 10 January 2015 Available online 14 January 2015

Nanostructured Al3+ doped Ni0.75Zn0.25Fe2
xAlxO4 (x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) ferrites were synthesized via the wet chemical method. X-ray diffraction, transmission electron microscopy, and magnetization measurements have been used to investigate the structural and magnetic properties of spinel ferrites calcined at 950  C. With the doping of Al3+, the particle size of Ni0.75Zn0.25Fe2
xAlxO4 first increased to 47 nm at x = 0.4 and then decreased down to 37 nm at x = 1. The main two absorption bands in IR spectra were observed around 600 cm
1 and 400 cm
1 corresponding to stretching vibration of tetrahedral and octahedral group Fe3+–O2
. Saturation magnetization and hyperfine field values decreased linearly with Al3+ due to magnetic dilution and the relative strengths of Fe–O–Me (Me = Fe, Ni, Zn, and Al) superexchanges. The coercive field showed an inverse dependence on ferrite particle size with minimum value of 82 Oe for x = 0.4. A continuous drop in Curie temperature was observed with the Al3+ substitution. From the Mossbauer spectral analysis and X-ray diffraction analysis, it is deduced that Al3+ for x < 0.4 has no obvious preference for either tetrahedral or octahedral site but has a greater preference for the B site for x > 0.4. In nutshell the study presents detailed structural and magnetic, and Mossbauer analysis of Ni0.75Zn0.25Fe2
xAlxO4 ferrites. ã 2015 Elsevier Ltd. All rights reserved.

Keywords: A. Oxides B. Magnetic properties B. Sol–gel chemistry C. Mossbauer spectroscopy C. X-ray diffraction

1. Introduction Due to their various technological applications, NiZn–ferrites have attracted recently considerable research interest [1]. The performance of these materials in the bulk form with grain dimensions in micrometer scales is limited to a few megahertz frequency due to their higher electrical conductivity and domain wall resonance [2,3]. However, the recent technological advances in the electronics industry demand compact ferrite cores to work at higher frequencies [4]. One way to circumvent this problem is by synthesizing the ferrite particles in nanometric scales before compacting them for sintering. When the size of the magnetic particle is smaller than the critical size for multidomain formation, the particle is in a single domain state. Domain wall resonance is avoided, and the material can work at higher frequencies. In addition, it is known that magnetic properties of ferrites are sensitive to preparation technique and their microstructures [5]. The dielectric and magnetic properties of such ferrites depend strongly on preparation methodology and distribution of cations at the tetrahedral (A) and octahedral (B) sites in the lattice [6–9]. Thus any alteration to the cation distribution in ferrites can alter their electrical and magnetic properties. These atomic level changes in

* Corresponding author. Tel.: +1 901 678 3115; fax: +1 901 678 4733. http://dx.doi.org/10.1016/j.materresbull.2015.01.033 0025-5408/ ã 2015 Elsevier Ltd. All rights reserved.

ferrites can be engineered via doping the desired level of magnetic [10–12] or non-magnetic atoms for cations such as [13–17], which in turn affect the crystal structure, influence Fe(A)–O–Fe(B) interactions, and eventually alter magnetic properties of the compound. Therefore, the selection of appropriate additives is the key to obtaining high performance ferrites. In this work, we present the results of systematic doping of nonmagnetic Al3+ content on the structural and magnetic properties of Ni0.75Zn0.25Fe2
xAlxO4 ferrite synthesized via wet chemical method. AluminumionshavebeenproventohavesubstantialinfluenceonMFerrites (M = Al, Co, Mg, Li, etc.), especially increasing resistivity and reducing eddy current losses [18–20]. In addition, the doping of nonmagnetic Al3+ in NiZn–ferrite not only brings grain refinement but also altersthemagnetic properties toa greatextent[21]. Basedon the earlier studies, Ni:Zn ratio was chosen to be 0.75:0.25 as at this ratio, NiZnFe2O4 ferrite shows high magnetization with a high degree of spin collinearity at A and B sites [22]. The study highlights the site preference of Al3+ in Ni0.75Zn0.25Fe2
xAlxO4 over a wide range of substitution and its influence on the magnetic interaction involved. 2. Experimental One pot method [23] was used to synthesis Ni0.75Zn0.25Fe2
xAlxO4 (x = 0, 0.2, 0.4, 0.6, 0.8, 1). Ni(NO3)2 9H2O, Zn

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Table 1 Stoichiometry of chemicals used in the synthesis of Ni0.75Zn0.25Fe2
xAlxO4. x

0.0 0.2 0.4 0.6 0.8 1.0

Weight in g Ni(NO3)26H2O

Zn(NO3)26H2O

Al(NO3)39H2O

Fe(NO3)39H2O

0.5453 0.5453 0.5453 0.5453 0.5453 0.5453

0.186 0.186 0.186 0.186 0.186 0.186

0 0.188 0.375 0.563 0.750 0.938

2.02 1.818 1.616 1.414 1.212 1.010

(NO3)29H2O, Fe(NO3)39H2O, and Al(NO3)39H2O were mixed in the stoichiometric amount, as listed in Table 1, in 30 ml of distilled water. The solution was ultrasonicated for 30 min. After ultrasonication, the solution was cooled down to the room temperature and then the pH was adjusted around 6.5 using ammonium hydroxide. The solution was then heated at 110  C to get rid of the extra water. The dried solid product was heated at 950  C for 12 h which resulted in a black powder of Ni0.75Zn0.25Fe2
xAlxO4. The X-ray diffraction (XRD) patterns were collected by Bruker D8 Advance X-ray diffractometer using Cu Ka radiation. The particle size and morphology were analyzed using transmission electron microscope at 120 keV. The surface area of the synthesized particles was measured using surface area analyzer (Autosorb-I, Quantachrome). The infrared spectra, FTIR, were collected in transmission mode using Thermo IR100 spectrometer in the wave number range 400–4000 cm
1 on a compacted sample-KBr pellet. The magnetic properties of the samples were investigated at room temperature (RT) using vibrating sample magnetometer (VSM). RT 57Fe Mossbauer spectroscopy was used to derive hyperfine parameters. The Mossbauer spectrometer (SEE Co.) was calibrated against a-Fe foil. The Mossbauer spectra were analyzed using WMoss software from SEE Co.

Fig. 1. The X-ray diffraction patterns of the Ni0.75Zn0.25Fe2
xAlxO4 as function of Al3+ doping. The inset figure shows lattice parameter of Ni0.75Zn0.25Fe2
xAlxO4 as a function of Al3+ doping.

3. Results and discussion 3.1. Structural analysis Fig. 1 shows the XRD pattern of Al3+ doped Ni0.75Zn0.25Fe2
xAlxO4 nanocrystalline ferrites. All the Al3+ substituted nickel ferrites of the various compositions show the desired crystalline cubic spinel phase (ICDD: 01-072-6799) along with minor amount of impurity phase NiO. The inset Fig 1, shows that the peak at 35–37 shifts to a lower angle with increasing Al3+ doping, which indicates lattice contraction with Al3+ substitution. The broader peaks of the spinel phase also suggest the presence of NiZn–ferrite in nanocrystalline form. The lattice parameter and percent composition of ferrite and NiO phase were extracted from the profile fitting of XRD data using TOPAS (Bruker Inc.) and are listed in Table 2. The inset Fig. 1 shows that the lattice parameter “a” linearly decreased at the rate of
0.153 Å per Al3+ ion, thus obeying the Vegard’s law [24]. The decrease in lattice parameter upon Al3+ substitution is due to the smaller ionic radius of Al3+ ion (0.535 Å) with respect to the ionic radius of Fe3+ ion (0.645 Å). From the

line-broadening analysis of (3 11) peak and using Scherrer’s formula [25], the dependence of crystallite size on the Al3+ doping in Ni0.75Zn0.25Fe2
xAlxO4 is plotted in the Fig. 2. The crystallite size increases initially with Al3+ content up to x = 0.4 (47 nm) and then decreases with further addition of Al3+ reaching to a value of 37 nm at x = 1.0. Similar dependence of crystallite size on Al3+ content in ZnFe2O4 has been reported earlier [26]. The inset Fig. 2 shows TEM images of Ni0.75Zn0.25Fe2
xAlxO4 for x = 0.0 and 1.0, cubic shape spinel ferrites. The X-ray density Dx of the samples was determined using the relation [27], Dx = 8M/(NAa3), where M is the molecular weight of the composition, NA is the Avogadro’s number, and “a” is the lattice constant. The multiplication factor 8 was used as there are 8 formula units in a unit cell. The X-ray density decreases with the increasing Al3+ ion content due to rapid decrease in molecular weight of the sample as compared to the lattice shrinkage, Table 2. The surface area measurement performed using nitrogen absorption using BET method show a correspondence with the particle size, having maximum surface area (7.506 m2/gm) for particle with minimum particle size for x = 1.0.

Table 2 Structural parameters derived from X-ray diffraction pattern refinement. x

% Composition NiZnFe2O4

% Composition NiO

“a” (Å)

0.0 0.2 0.4 0.6 0.8 1.0

100 92.93 96.44 95.83 96.30 93.07

0.00 7.07 3.56 4.17 3.70 6.93

8.35361 8.32261 8.29576 8.26582 8.23189 8.20156

(89) (51) (63) (60) (46) (111)

“a-th” (Å)

Dx (g/cm3)

Particle size (nm)

Surface area (m2/gm)

8.3328 8.3038 8.2732 8.2437 8.2177 8.1927

5.382 5.321 5.236 5.157 5.076 4.999

42.97 46.77 46.84 43.57 38.17 37.19

6.467 2.140 1.439 2.358 2.803 7.506

L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

185

octahedral site being connected to the tetrahedral site via oxygen ions shrinks by the same amount as the tetrahedral site expands. This movement of the tetrahedral oxygen is described by the oxygen positional parameter u which is the distance between the oxygen ion and the face of the cube edge along the cube diagonal of the spinel sub-cell. Ferrites, generally have “u” greater than the ideal value of 0.375, assuming center of symmetry at A site at (3/8, 3/8, 3/8) [33]. However, values of u depend on preparation conditions, chemical compositions, and heating procedure [34]. The oxygen positional parameter for each composition were calculated using the following formula and are listed in Table 4 [35]: u3m ¼

1=4R2
2=3 þ ð11=48R2
1=18Þ1=2

u43m ¼ Fig. 2. Particle size as a function of Al3+ content, x, in Ni0.75Zn0.25Fe2
xAlxO4. Inset shows TEM image for sample with (a) x = 0.0 and (b) x = 1.0.

The physical properties of ferrites are sensitive to the cation’s nature, the valance state and their distribution on tetrahedral A and octahedral B sites of the spinel structure. Thus, understanding of the cation distribution is essential in understanding the intricate structural and physical property relationship. In this view, it is important to derive some important structural parameters such as the cation distribution on A and B sites, mean ionic radius per molecules of the A and B sites, oxygen parameter, bond length, and bond angles between cation–oxygen (Me–O) and cation–cation (Me–Me). The amount of Fe3+ ions on the tetrahedral A site and octahedral B site had been estimated via Mossbauer spectral analysis (discussed below) by calculating the integrated area under the Lorentizians corresponding to the A and B sites, which were taken as proportional to the amount of Fe3+ at these sites. Coupled with this information and percent composition determined from XRD analysis, the actual compositions of samples were calculated and listed in Table 3. It is evident from the Table 3 that the actual compositions of the sample are close to the nominal composition of samples assumed during the sample preparation. From Table 3, it is clear that at the low concentration, x  0.6, Al3+ prefers tetrahedral A site and increasingly prefer B site for x > 0.6. Thus, in agreement with other studies, Al3+ ion has tendency to occupy both tetrahedral and octahedral sites, however with greater affinity for the B site [13,15,28] at higher Al3+ content. Furthermore, in confirmation with earlier reports, it was observed that Ni2+ prefers B site [29] whereas Zn2+ prefers A site due to their readiness to form covalent bonds involving sp3 hybrid orbitals [30]. Similar site preferences were observed for Me3+ (Me = Cr3+, Al3+) substitution for Fe3+ in spinel as well [27,31,32]. The perfect spinel lattice has regular arrangement of ions, however, often the structure is distorted due to the imperfections in the lattice. Often the cation is larger than the tetrahedral site which moves oxygen ions slightly to accommodate them. The

2R2
2 ½ra þ rðO
2 Þ 1 pffiffiffi þ 4 3a

where u3m and u43m are the oxygen positional parameter assuming the center of symmetry at A site at (3/8, 3/8, 3/8) and at B site at (1/ 4, 1/4, 1/4). R is the ratio of average bond lengths given as: R¼

B
O < rB þ rðO
2 Þ > ¼ ; A
O < rA þ rðO
2 Þ >

where rA and rB are the mean ionic radius of tetrahedral and octahedral sites per formula molecule given as: rA ¼ ½C Ni RNi þ C Zn RZn þ C Fe RFe þ C Al RAl A

1 rB ¼ ½C Ni RNi þ C Zn RZn þ C Fe RFe þ C Al RAl B 2 where Cx is the fraction of “x” cations. There also exist a relation between ionic radius and lattice constant (ath) which is expressed as: pffiffiffi 8 ath ¼ pffiffiffi½ðrA þ RO Þ þ 3ðrB þ RO Þ 3 3 The theoretical lattice constant, ath, values are listed in Table 2 and are in close agreement with the experimentally derived values from profile fitting of XRD data. Furthermore, site radii RA and RB were obtained from the X-ray diffraction data and above calculated u parameters. The site radii RA and RB were calculated using following relations:   pffiffiffi 1 RA ¼ a 3 d þ 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   1 d 2 RB ¼ a 3d þ
6 2 where d = (u1 + u2/2)
uideal, u1 and u2 are the oxygen parameter of the two ends group members of Ni0.75Zn0.25Fe2
xAlxO4, and uideal = 0.250 Å.

Table 3 The cation distributions obtained for Ni0.75Zn0.25Fe2
xAlxO4 from Mossbauer spectral area analysis and X-ray diffraction pattern analysis. X

A site

B site

Actual composition

0.0 0.2 0.4 0.6 0.8 1.0

[Zn0.25][Fe0.75] [Ni0.09][Zn0.26][Al0.2][Fe0.45] [Ni0.11][Zn0.26][Al0.4][Fe0.23] [Zn0.26][Al0.48][Fe0.26] [Zn0.26][Al0.45][Fe0.29] [Zn0.26][Al0.37][Fe0.37]

[Ni0.75][Fe1.25] [Ni0.65][Fe1.35] [Ni0.63][Fe1.37] [Ni0.74][Al0.12][Fe1.14] [Ni0.74][Al0.35][Fe0.91] [Ni0.74][Al0.63][Fe0.63]

Ni0.75Zn0.25Fe2O4 Ni0.74Zn0.26Fe1.8Al0.2O4 Ni0.74Zn0.26Fe1.6Al0.4O4 Ni0.74Zn0.26Fe1.4Al0.6O4 Ni0.74Zn0.26Fe1.2Al0.8O4 Ni0.74Zn0.26Fe1.0Al1.0O4

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L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

Table 4 Average ionic radii (rA,B), site radii (RA,B), oxygen positional parameter (u), and average bond length of sites (A–O, B–O) for Ni0.75Zn0.25Fe2
xAlxO4 system. x

rA (Å)

rB (Å)

RA (nm)

RB (nm)

u3m (1/4,1/4,1/4)

u43m (3/8,3/8,3/8)

A–O (Å)

B–O (Å)

R

0.0 0.2 0.4 0.6 0.8 1.0

0.665 0.650 0.632 0.618 0.621 0.629

0.659 0.656 0.656 0.652 0.641 0.627

0.1992 0.1983 0.1977 0.1970 0.1963 0.1955

0.1988 0.1979 0.1973 0.1966 0.1959 0.1951

0.2628 0.2622 0.2614 0.2609 0.2616 0.2626

0.3872 0.3868 0.3859 0.3854 0.3862 0.3873

1.985 1.970 1.951 1.938 1.941 1.949

1.979 1.976 1.976 1.972 1.961 1.947

0.996 1.002 1.012 1.017 1.010 0.999

tetrahedrally coordinated A site cations along direction, resulting in an increase in volume of A at the expense of the volume of the B site. For Al3+ doped for Ni0.75Zn0.25Fe2
xAlxO4 samples, the u value decreases with the increase in Al3+ content up to x  0.6. The decrease in u3m value is associated to the replacement of Fe3+ with smaller Al3+ at the A site. However at the higher value of Al3+,

x=0.2

x=0

94

Transmittance (%)

Transmittance (%)

The site radii RA and RB are given in Table 4. It is seen that both RA and RB linearly decrease at the rate of 0.0036 Å per Al3+ atom substitution. The site radii RA is greater than RB. From Table 4, it is evident that the oxygen positional parameter u43m of Ni0.75Zn0.25Fe2O4 is slightly greater than ideal value of 0.375. This indicate that anions have moved away from the

92 90

578.54

88

85 80

416.55

593.97

75

86 400

500

600

700

400

-1

Wavenumber (cm )

99 98 97

416.55

95 94 400

83

424.26

82

601.68

81

500 600 700 -1 Wavenumber (cm )

x=0.8

96 439.69

617.11

92 90 400

84

400

500 600 700 -1 Wavenumber (cm )

98

94

x=0.6

80

100

Transmittance (%)

593.97

96

Transmittance (%)

85

x=0.4

500 600 700 -1 Wavenumber (cm )

Transmittance (%)

Transmittance (%)

100

500 600 700 -1 Wavenumber (cm )

x=1

52 50

624.82

48 478.26 46 400

500 600 700 -1 Wavenumber (cm )

Fig. 3. FTIR spectra of Ni0.75Zn0.25Fe2
xAlxO4.

L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

187

Table 5 Band position and force constant for Ni0.75Zn0.25Fe2
xAlxO4. x

yT (cm
1)

yO (cm
1)

M1 g/mol

M2 g/mol

kT( 102 N/m)

kO( 102 N/m)

0.0 0.2 0.4 0.6 0.8 1.0

578.54 593.97 593.97 601.68 617.11 624.82

– 416.55 416.55 424.26 439.69 478.26

58.22 52.80 47.09 44.46 45.33 47.64

– 113.53 113.47 110.31 103.66 95.55

1.485 1.419 1.265 1.227 1.316 1.417

– 1.046 1.045 1.054 1.064 1.160

kT ¼ 7:62 M1 y2T

determine the saturation magnetization. The strength of this superexchange coupling depends on the bond lengths and bond angles between the cations as listed in Tables 7 and 8. The strength of interactions, exchange interaction, between moments of metal ions on various sites depends on (1) distance between metal ions and oxygen ions linking them and (2) on the angle between these three ions, metal ion–oxygen–metal ion. The greatest interaction is observed for linear arrangement, 180 , of these ions with the shortest interatomic distances. It has been reported earlier that for an undistorted spinel, the A–O–B angles are about 125 and 154 [1]. The B–O–B angles are 90 and 125 but in the latter, one of the B–O distances is large. In the A–O–A case, the angle is about 80 . Therefore, the interaction A–O–B between moments on the A and B sites is strongest. The B–O–B interaction is much weaker and the most unfavorable situation occurs in the A–O–A interaction. In view of this, the bond-distances and bondangle were calculated and are listed in Table 7 and 8, respectively. The inter ionic distances between cation–cation (Me–Me, b, c, d, e and f) and between cation–anion (Me–O, p, q, r, s) were calculated using the experimental value of lattice constant, a, and oxygen

x = 0.0 60

x = 0.2 60 40

10
7 N m

Ms, (emu/g)

x > 0.6, the u value increases due to increasing preferential occupancy of Al3+ at the B site. This trend is also reflected in rA and rB. It is observed from Table 4, that rB is least affected as compared to rA with the substitution of Al3+ up to x 0.6, but rB displays a rapid decrease for x > 0.6, which results from higher substitution rate of Al3+ at the B site. The Fourier transform infrared spectroscopy (FTIR) spectrum was recorded in transmission geometry using (KBr) discs in the range of 400–4000 cm
1. The IR spectra for the samples as a function of Al3+ substitution is shown in Fig. 3. Two major absorption bands are observed between 400–610 cm
1. As per Waldron [36], two bands, yT (590 to 610 cm
1) and yO (400 to 420 cm
1), indicate the stretching of cation–anion bonds in the tetrahedral (A) and octahedral (B) sites, respectively, thus further confirming the formation of the spinel structure. The degree of Fe— O covalent bonding determines the band position for the A and B sites. The Fe—O distance (1.89 Å) at A site is smaller than that of a B site (1.99 Å) [37], thus the covalent bonding Fe—O at A site is more than that at B site which results in vibration stretching at higher wave numbers. Table 5 lists the band position yT and yO as a function of Al3+ substitution. The variation in band position is expected due to altered Fe3+–O2
interaction upon Al3+ substation. The yT and yO bands shift to higher wavenumber value with Al3+ substation. Furthermore band broadening was observed due to statistical distribution of Fe3+, Zn2+, and Ni2+, and Al3+ ions on their respective sites and distribution of vacancies among the octahedral and tetrahedral sites. The force constant kT and kO for the A and B sites, for spinel, is given as [38]:

x = 0.4

40

x = 0.6

20

where, M1 and M2 are the molecular weight of cations on A and B sites, respectively. Table 5 presents the variation of force constant with Al3+ content. The force constant was observed to decrease initially for x up to 0.6 for tetrahedral site while increase for the octahedral site. The observed variation in the force constant values reflect changes in the Fe—O covaleny with lattice contraction upon Al3+ substitution. Fig. 4 shows the room temperature magnetization hysteresis loops for Ni0.75Zn0.25Fe2
xAlxO4 samples. The magnetic parameters saturation magnetization (Ms), remanence (Mr) and coercivity (Hc) extracted from the hysteresis loops are presented in Table 6. It is evident from Table 6 and inset of Fig. 4(a) that the magnetization decreases linearly at the rate of 67 emu/g for x < 0.6 and 39 emu/g for x 0.6 per Al3+ ion. In the mixed NiZn–ferrite, Ni2+ ions occupy B sites [26] whereas Zn2+ ions occupy tetrahedral A sites [39]. Al3+ occupying both the tetrahedral A site and the octahedral B site reduces the magnetic moment of the sublattices. In spinel ferrites, the strong superexchange coupling between A and B sites

x = 0.8 0.0 0.2 0.4 0.6 0.8 1.0 x, (Al content)

x = 1.0

0

110

-20

Hc, (Oe)

10
7 N kO ¼ 10:62 M2 y2O m

M, (emu/g)

20

100 90

-40

80 0.0 0.2 0.4 0.6 0.8 1.0 x, (Al content)

-60 -10x10

3

-5

0 Field (Oe)

5

10

Fig. 4. Room temperature hysteresis loop for Ni0.75Zn0.25Fe2
xAlxO4. The inset figure shows saturation magnetization (a) and coercivity (b) as a function of Al3+ content.

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Table 6 Room temperature magnetic parameters of Ni0.75Zn0.25Fe2
xAlxO4. x

Ms (emu/g)

Mr (emu/g)

Mr/Ms

Hc (Oe)

nB (Bohr magneton)

K1 ( 103)

aY–K (degree)

Tc ( C)

0.0 0.2 0.4 0.6 0.8 1.0

65.40 50.85 38.44 22.48 13.84 6.75

14.49 10.93 7.77 4.89 3.89 1.85

0.22 0.21 0.20 0.21 0.28 0.27

114.3 92.1 82.9 95.7 104.1 109.2

2.76 2.10 1.54 0.88 0.53 0.25


2.66
1.96
1.34
0.78
0.61
0.34

32.80 55.78 68.93 72.32 70.85 63.02

444.8 410.4 372.9 324.7 279.0 175.9

Table 7 Interatomic distance in Ni0.75Zn0.25Fe2
xAlxO4 system. Me–Me

Me–O

x

b (nm)

c (nm)

d (nm)

e (nm)

f (nm)

p (nm)

q (nm)

r (nm)

s (nm)

0.0 0.2 0.4 0.6 0.8 1.0

0.2953 0.2940 0.2931 0.2920 0.2909 0.2897

0.3463 0.3448 0.3437 0.3425 0.3412 0.3398

0.3617 0.3601 0.3590 0.3577 0.3564 0.3549

0.5425 0.5402 0.5385 0.5365 0.5346 0.5324

0.5115 0.5093 0.5077 0.5058 0.5040 0.5019

0.1982 0.1977 0.1978 0.1975 0.1962 0.1946

0.1993 0.1977 0.1958 0.1944 0.1947 0.1953

0.3817 0.3785 0.3750 0.3723 0.3728 0.3740

0.3679 0.3660 0.3644 0.3629 0.3619 0.3609

parameters u3m by the relations listed below. The bond angles were calculated using cosine formula for triangle and is listed in Table 8.

Me-Me Distance

Me-O Distances

a 4

1 p = a( − u ) 2

a 8

1 q = 3a (u − ) 8

d= 3

a 4

1 r = 11a (u − ) 8

e= 3

3a 8

a 1 s = 3 (u + ) 3 2

b= 6

a 4

b= 2

c = 11

The Me–O–Me arrangement is shown schematically in Table 8. In accordance with the decrease in the lattice parameter with Al3+ substitution, it is seen from the Table 7 that the distance between cation–cation and cation–anion decreases in the unit cell. Among the bond angles A–O–B (u1, u2), B–O–B (u3, u4), and A–O–A (u5), it is observed that u1, u2, and u5, first increases up to x = 0.6 and then decreases for higher value of x. An opposite trend was observed for u3 and u4. In view of this, and observation from Table 7 and 8, strengthening of A–O–B and A–O–A and weakening of B–O–B interaction is observed for up to x = 0.6 Al3+ substitution. In the present case, (1) gradual replacement of Fe3+ with non-magnetic Al3+ leads to magnetic dilution, (2) non-equilibrium cation distribution [40,41], and (3) reduced Fe3+(A)–O2
–Fe3+(B) linkages leads to canted spin configuration [42–45]; these combined effects bring reduction in the net saturation magnetization of samples.

The observed change in rate of Ms reduction for x 0.4 with Al3+ content can be explained on the basis of the Yafet–Kittle (Y–K) type magnetic ordering at the B site. According to Y–K model of triangular spin, the B lattice side is divided into two sublattices, B1 and B2, each having equal magnetic moments in magnitude but canted oppositely at the same angle, aY–K, relative to the net magnetization at 0 K. The values of the Y–K angle have been calculated using the formula, nB ¼ MB cosðaY
K Þ
MA

nB ¼

Ms MW 5585

MA ¼ C A;Fe nFe þ C A;Ni nNi MB ¼ C B;Fe nFe þ C B;Ni nNi where nB is the experimental magnetic moment expressed in the unit of Bohr magneton [46]. MA and MB are the Bohr magneton on the A and B sites and CA,Fe and CB,Fe are the concentration of Fe on A and B sites, respectively. The theoretical magnetic moment of Fe (nFe) and Ni (nNi) are 5 and 2 mB. The value of nB and aY–K is listed in Table 6 as a function of Al3+ content. The aY–K angle reaches maximum, 72 at x = 0.6 and then decreases with the further substitution of Al3+. Now the initial rapid decrease in Ms with Al3+ content, x < 0.6, is due to greater Al3+ ions initially occupying the A site. This results in a decrease in the net magnetic moment at A site which increases the canting of the Fe3+ ion moments on B site. The net result is decrease in magnetization. At higher Al3+ content, x 0.6, although Al3+ prefers both A and B site but the rate of increase of Al3+ at B site is higher than that at A site, which leaves the A site with higher moment than the B site. This decreases the canting angle of Fe3+ moments on the B site, thus leading to a slower decrease in magnetization. It is clear that the non-zero aY–K angle suggest that the magnetization behavior for all samples cannot be explained on the basis of Neel two-sublattice model due to non-collinearity of spins on B site. This deviation from Neel type magnetic order leads to reduction in saturation magnetization with Al3+ content as well. The calculated values of Mr/Ms loop squareness ratio are less than 0.50 and is invariant with respect to Al3+ content. These values indicate magnetostatic interactions between particles [47]. This is

L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

189

Table 8 Ideal ion pair configuration in spinel ferrite with optimal distance and angles for effective magnetic interactions [75]. The table also list the calculated bond angles for Ni0.75Zn0.25Fe2
xAlxO4 system.

u1 A–O–B

x

u2 A–O–B

u3 B–O–B

u4 B–O–B

u5 A–O–A

90 79 380 125#11“13#

125#11 13# 154 340 0.0 0.2 0.4 0.6 0.8 1.0

121.20 121.37 121.64 121.79 121.58 121.26

136.30 136.94 137.95 138.52 137.72 136.52

96.34 96.04 95.59 95.34 95.69 96.23

126.68 126.61 126.52 126.47 126.54 126.66

a characteristic of the material having predominantly multidomain grains in them [48]. Thus, it can be concluded that all the compositions investigated contain multidomain grains. The data presented in Table 6 and inset Fig. 4 shows an interesting behavior of Hc with Al3+ content in Ni0.75Zn0.25Fe2
xAlxO4. The coercivity decreases to the lowest value (Hc 80 Oe) at x = 0.4 and then increases with the further increase in Al3+ content reaching a value (Hc 110 Oe) at x = 1.0. It is known that the grain size affect the coercivity of nanoparticles in ferrites [49]. The increase in the grain size up to x = 0.4 (Table 2, Fig. 2) also corresponds to Al3+ content with minimum coercivity. If the grain size is smaller than the domain size, the motion of grain boundary is difficult which is reflected in the increased coercivity of particles for x 0.6. The larger grains tend to consist of a greater number of domain walls. The magnetization/demagnetization caused by domain wall movement requires less energy than that required by domain rotation. As the number of walls increases with grain size, the contribution of wall movement to magnetization or demagnetization is greater than that of domain rotation. Therefore, samples having larger grains are expected to have a low coercivity Hc.

68.96 69.39 70.05 70.42 69.90 69.11

The room temperature anisotropy information of Ni0.75Zn0.25Fe2
xAlxO4 samples were obtained from the “Law of approach” to saturate magnetization. The “Law of approach” describes the relation between magnetization M on the applied magnetic field for H greater than coercive field Hc. The magnetization near the saturation Ms can be written as [50], M = Ms(1
a/H
b/H2) + kH, where M is the magnetization, H is the applied magnetic field, and Ms is the saturation magnetization. The term kH represents the field-induced increase in the spontaneous magnetization of the domains. This term is very small at temperature well below the Curie temperature and may be neglected. The term “a” is generally interpreted as due to microstress and ignored in the high field region, and “b” as due to crystal anisotropy. While K1 is the cubic pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi anisotropy constant and is given as, K1 ¼ mo Ms 105b=8. The numerical coefficient 105/8 applies to cubic anisotropy of random polycrystalline samples. The room temperature experimental data M vs. H is fitted to equation, M = Ms(1
b/H2). An example of a fitting curve for x = 0.6 M vs. H data is shown in Fig. 5. The values of Ms and b were obtained from fitting and were used in calculating K1. Our result for K1 is in agreement with the earlier reports on the

3

x = 0.6

15

Experimental Data Fit to LA

200 3

20

K1 (erg/cm )

M, (emu/g)

250x10

10

150

100

5

50 0.0

0 2

4

6 8 Field (Oe)

10

12x10

3

Fig. 5. “Law of approach” fit to M vs. H data for Ni0.75Zn0.25Fe2
xAlxO4,x = 0.6.

0.2

0.4

0.6

0.8

1.0

x, Ni0.75Zn0.25Fe2-xAlxO4 Fig. 6. Magnetic anisotropy energy as a function of Al3+ content for Ni0.75Zn0.25Fe2
xAlxO4.

190

L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

occupancy on A and B sites, Zn+2 on A site and Ni2+ on B site, the probability distribution were calculated with the distribution of Zn2+–Al3+ on A site and Ni2+–Al3+ on B site as follows

400 PA ðnÞ ¼

1 12! ð2
xÞ12
n xn 4096n!ð12
nÞ!

PB ðnÞ ¼

6! ð1
xÞ6
n xn n!ð6
nÞ!

O

TC, ( C)

350

300

250

200 0.0

0.2

0.4 0.6 x, Ni0.75Zn0.25Fe2-xAlxO4

0.8

1.0

Fig. 7. Curie temperature, TC, as a function of Al3+ content for Ni0.75Zn0.25Fe2
xAlxO4.

nanocrystalline ferrites [51,52]. Fig. 6 shows the variation of K1 as a function of Al3+ content in Ni0.75Zn0.25Fe2
xAlxO4. It is observed that the cubic anisotropy constant decreases in magnitude with the Al3+ content. For thermal analysis, differential scanning calorimetry (DSC) was used to determine the Curie temperature, TC, of samples. It is known from the magnetic theory that when heat is added to the magnetic material, the thermal energy increases phonons and kinetic energy of the valence electrons. Part of thermal energy also disorders spins, which contribute to magnetic specific heat. As temperature increases, a maximum value in the vicinity of the TC may be obtained using DSC analyzer [53,54]. At this temperature magnetization decreases rapidly with increasing randomization of spin alignment. At temperature above TC, ferromagnetic or ferrimagnetic materials becomes paramagnetic. The plot of TC as a function of Al3+ content is shown in Fig. 7 and TC values are listed in Table 6. The TC value of 444  C obtained for Ni0.75Zn0.25Fe2O4 which is in close agreement with the published values [55] however, it is lower than the bulk Tc (490  C). The observed decrease in Tc from the bulk value is due to small particle size effect of the sample resulting from atoms sitting on the surface of nanoparticles lacking he complete coordination. This leads to a reduction in the magnetic ordering, which is manifested in the decreased value of ferrimagnetic ordering temperature (Curie temperature, TC) [56,57]. Marked decrease in TC is observed with the increase in the Al3+ content. The decrease in exchange interaction between iron sublattice with Al3+ replacing Fe3+ ion is the cause for the observed decrease in the TC values. Mossbauer spectroscopy is extremely sensitive to small variations in electron density at the iron nucleus, due to different electronic and structural environments. The 57Fe Mössbauer spectra were recorded at 300 K of Ni0.75Zn0.25Fe2
xAlxO4 nanoparticles. The fitted Mossbauer spectra as a function of Al3+ substitution are shown in the Fig. 8. The hyperfine parameters extracted from the refinement are shown in Table 9. As discussed above, in spinel, the antiferromagnetic A–B coupling is thought to be strongest coupling in the structure. Each A-site Fe is coupled to 12 B-site Fe next-nearest neighbors via superexchange coupling. However, each B-site Fe is coupled to only 6 A-site Fe nearest neighbors. In a spinel, hyperfine magnetic fields at B-site 57Fe nuclei are a function of the occupation of the six nearest tetrahedral A sites. In view of earlier reports of Al3+

where PA(n) is the probability of finding A sites surrounded by twelve octahedral B sites having n cation (Al3+ and Ni2+) distribution with concentration of Al3+, x, in the bulk and PB(n) is the probability of finding B sites surrounded by six tetrahedral A sites having n cation (Al3+ or Zn2+) distribution with concentration x in the bulk [58]. The factor 1/4096 is the normalization factor. The probability distribution PB(n) resulted in four values greater than 5% probability while PA(n) resulted in only one value with 5% probability. The Mossbauer spectrums were fitted with probability values greater than 5% only. All other values were ignored in the fitting process. The Ni0.75Zn0.25Fe2
xAlxO4 Mossbauer spectra were fitted with 5 subspectra, one for A site (A0) and four for B sites (B0–B4). Paramagnetic doublets (C1 and C2) were also added representing some minor impurity in the samples. The fact that superpositions of more than one sextet for the B-sites are required to arrive at an acceptable fit to the data reflects the complex magnetic interactions involved in Ni0.75Zn0.25Fe2
xAlxO4. The area under the Mossbauer subspectrum were used to calculate percent site occupancy of ions and actual chemical composition of Al3+ doped NiZn–ferrite, as discussed below. Table 3, shows the site preference of Fe3+, Ni2+, Zn2+ and Al3+ in Ni0.75Zn0.25Fe2
xAlxO4 derived from area under the Mossbauer sub-spectrum. Considering the fact that in NiZn–ferrites, Zn2+ and Ni2+ has preference for A and B site respectively, the percent site occupancy of Al3+ was calculated using the intensity ratios of the Fe3+ on magnetic A and B sites in Ni0.75Zn0.25Fe2
xAlxO4. The Fe(A)/ Fe(B) intensity ratio is expressed in terms of FWHM and line width as follows [59]: AreaðAÞ GðAÞNðAÞ ¼R AreaðBÞ GðBÞNðBÞ where, Area (A/B) is the total weighted average area of A/B site, R is a scaling factor, G is the line width at full-width-at-half-maximum (FWHM), and N is the number of Fe3+ on a given site. Weighted average area and FWHM were calculated considering the distribution of Fe3+ on each site. For example, weighted area for B site for x = 0.6 samples is calculated by considering, B0–B4 with 4, 4, 3, 5, 2, Fe3+ distribution, respectively as follows. AreaðAB Þ ¼

AB0 4 þ AB1 4 þ AB2 3 þ AB3 5 þ AB4 2 4þ4þ3þ5þ2

FWHM ¼

FWHMB0 4 þ FWHMB1 4 þ FWHMB2 3 þ FWHMB3 5 þ FWHMB4 2 4þ4þ3þ5þ2

ISðdÞ ¼

HF ¼

ISB0 AB0 þ ISB1 AB1 þ ISB2 AB2 þ ISB3 AB3 þ ISB4 AB4 AB0 þ AB1 þ AB2 þ AB3 þ AB4

HFB0 AB0 þ HFB1 AB1 þ HFB2 AB2 þ HFB3 AB3 þ HFB4 AB4 AB0 þ AB1 þ AB2 þ AB3 þ AB4

L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

a.u.

a.u.

191

x = 0.0 -10

-5

0

x = 0.2 5

10

-10

-5

5

10

5

10

5

10

V (mm/s)

a.u.

a.u.

V (mm/s)

0

x = 0.4 -10

-5

0

x = 0.6 5

10

-10

-5

a.u.

V (mm/s)

a.u.

V (mm/s)

0

x = 0.8 -10

-5

0

x = 1.0 5

10

V (mm/s)

-10

-5

0 V (mm/s)

Fig. 8. Room temperature fitted Mossbauer spectra of Ni0.75Zn0.25Fe2
xAlxO4.

First the scaling factor R was obtained using FWHM and linewidths listed from Table 9. Weighted line-widths and area were considered for the B site because of the distribution of sextets on B site. Using values listed in Table 9, for x = 0, the R value obtained was 0.669. Using this R value, number of Fe3+ on A and B sites was calculated. For example, the area ratio of Fe3+(B)/Fe3+(A) for x = 0.6 sample is 2.843 and G (A)/G (B) is 1.0156. Then the number of Fe3+ in A and B sites can be calculated using simple algebra as follows.       NðAÞ AreaðAÞ GðBÞ 1 Constant ¼ ¼ NðBÞ AreaðBÞ R R GðAÞ

therefore,   Constant NðAÞ ¼ NðBÞ R

NðAÞ þ NðBÞ ¼ 2
x where (2
x) iron atoms per unit formula are not occupied by Al3+. Values for N(A) and N(B) were obtained by solving above two simultaneous equations. Thus, for x = 0.6 samples, N(A) and N(B) equals to 0.27 and 1.13 for A and B sites, respectively. Furthermore considering presence of 4.17% NiO secondary phase in x = 0.6 sample, Table 2, it is estimated that the amount of Ni2+ in B site is 0.74 which leaves 0.26 Zn2+ on the A site. The Ni2+ concentration is estimated from the XRD data as follows:

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L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

Table 9 The room temperature Mossbauer parameters of Ni0.75Zn0.25Fe2
xAlxO4. x

Iron site

HF (T)

Wt. avg. HF

IS, d (mm/s)

Wt. avg. IS

DEQ

Line width, G (mm/s), FWHM

Wt. avg. G (mm/s) FWHM

Area

Wt. avg. Area (normalized)

(mm/s) 0.0

A B0 B1 B2 B3 C1 C2

47.6 51.5 49.2 45.0 40.4 00.0 00.0

47.6 45.9

0.27 0.36 0.31 0.35 0.37 -0.33 0.42

0.274 0.361

0.00 -0.03 0.03 -0.01 0.07 1.40 -2.42

0.443 0.351 0.351 0.540 0.668 0.189 0.194

0.443 0.498

0.424 0.131 0.199 0.165 0.075 0.012 0.013

0.416 0.559

0.2

A B0 B1 B2 B3 B4 C1 C2

47.0 50.2 49.9 44.8 41.0 28.1 00.0 00.0

47.0 45.7

0.27 0.31 0.39 0.29 0.34 0.44 0.35 0.32

0.266 0.337

0.03 -0.46 0.22 -0.01 -0.01 -0.49 -2.43 0.0

0.446 0.378 0.365 0.494 0.819 0.233 0.261 0.363

0.446 0.501

0.384 0.121 0.177 0.223 0.129 0.028 0.029 0.011

0.348 0.615

0.4

A B0 B1 B2 B3 B4 C1 C2

46.8 50.3 49.7 44.9 41.8 25.7 00.0 00.0

46.8 44.3

0.28 0.32 0.41 0.27 0.30 0.42 0.31 0.36

0.276 0.307

0.04 -0.33 0.22 0.00 -0.02 -0.46 -2.35 0.00

0.428 0.373 0.308 0.523 0.817 0.595 0.281 0.22

0.428 0.531

0.250 0.097 0.090 0.335 0.249 0.033 0.030 0.006

0.229 0.771

0.6

A B0 B1 B2 B3 B4 C1 C2

45.7 50.2 49.7 43.1 39.2 25.8 00.0 00.0

45.7 42.2

0.29 0.32 0.42 0.27 0.28 0.30 0.26 0.31

0.292 0.292

0.00 -0.34 0.21 -0.03 -0.02 -0.34 -2.19 0.00

0.536 0.424 0.274 0.603 0.861 0.504 0.266 0.267

0.536 0.551

0.282 0.096 0.059 0.348 0.256 0.042 0.033 0.010

0.250 0.711

0.8

A B0 B1 B2 B3 B4 C1 C2

44.0 50.7 49.2 40.7 36.3 25.3 00.0 0

44.0 38.2

0.30 0.32 0.46 0.25 0.26 0.24 0.27 0.36

0.299 0.262

-0.07 -0.29 0.28 -0.01 0.03 -0.20 -2.08 0.00

0.730 0.387 0.179 0.725 0.885 0.895 0.357 0.181

0.730 0.592

0.298 0.065 0.017 0.331 0.241 0.106 0.049 0.006

0.267 0.683

1.0

A B0 B1 B2 B3 B4 C1 C2

40.2 51.0 49.2 35.7 30.8 23.2 00.0 00.0

40.2 31.2

0.32 0.38 0.50 0.25 0.25 0.20 0.25 0.31

0.32 0.241

-0.11 -0.21 0.26 -0.03 -0.05 -0.07 -1.87 0.00

1.000 0.230 0.002 0.844 0.838 1.000 0.433 1.408

1.000 0.536

0.298 0.032 0.001 0.232 0.168 0.197 0.050 0.101

0.276 0.584

In chemical formula of NiZn–ferrite: nðZnÞ þ nðNiÞ ¼ 1 nZn mZn =MZn ¼ nNi mNi =MNi ð1
%NiOÞ where n(Zn) and n(Ni) are the molar number of Zn and Ni per formula unit. MZn and MNi is the molecular weight for corresponding nitrate salts and mZn and mNi is the mass of corresponding nitrate salts used in synthesis, Table 1. For example, for x = 0.6 samples, MZn = 291.45 g/mole, MNi = 290.79 g/mole, mZn = 0.186 g, and mNi = 0.5453 g. This leads to chemical composition for x = 0.6 sample as [Zn0.26][Al0.48][Fe0.26]A[Ni0.74][Al0.12]

[Fe1.14]B. Table 3 presents actual chemical composition for all x values of the samples. In agreement with earlier measurements, Al3+ has preference for both A and B sites over a range of aluminum concentration in support to earlier reports on FeAl2O4 that has been confirmed by Mossbauer and neutron diffraction studies [60,61]. Furthermore it is observed that at low concentration, x  0.4, Al3+ has preference for tetrahedral A site, whereas at higher Al3+ content, Al3+ prefers octahedral B site. The assertion that Al3+ has preferred site occupancy in different substitution range is further confirmed by similar study of non-magnetic Ga3+ substitution in Co–ferrite [62].The behavior of hyperfine magnetic field at A and B sites as a function of Al3+ content is shown in Fig. 9. The hyperfine field values are listed in Table 9. The weighted average hyperfine field were calculated as follows.

L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

193

0.36

480

A site B site

0.34

Isomer shift (δ,mm/s)

440

site-Bo 500

-1

420

HF (x10 T)

-1

Weighted Avg. HF(x10 T)

460

400

450

B1 A

0.32

0.28

B2

400

0.26

B3

350 300

0.0

B4

250 0.2 0.4 0.6 0.8 1.0 x, Ni0.75Zn0.25Fe2-xAlxO4

380 0.2

0.4 0.6 0.8 x, Ni0.75Zn0.25Fe2-xAlxO4

0.2

0.4 0.6 0.8 x, Ni0.75Zn0.25Fe2-xAlxO4

1.0

Fig. 10. Weighted average isomer shift as a function of Al3+ content for Ni0.75Zn0.25Fe2
xAlxO4.

1.0

Fig. 9. Hyperfine field of individual sites (inset) and weighted average hyperfine field as a function of Al3+ content for Ni0.75Zn0.25Fe2
xAlxO4.

HF ¼

A site B site

0.30

HFB0 AB0 þ HFB1 AB1 þ HFB2 AB2 þ HFB3 AB3 þ HFB4 AB4 AB0 þ AB1 þ AB2 þ AB3 þ AB4

The weighted average hyperfine field for both A (HFA) and B (HFB) site as a function of Al3+ content is plotted in Fig. 9. The weighted average values obtained at room temperature, HFA = 480 kOe and HFB = 460 kOe for undoped NiZn–ferrite are in good agreement with those reported by other authors [63,64]. Both A-site and B-site hyperfine fields are observed to decrease with increasing Al3+ content, with B decreasing faster than A. This decrease in hyperfine filed can be understood on the basis of the superexchange interaction and the cations distribution. The magnetic ordering in spinel phases, Neel ordering, is mainly determined by the strong antiferromagnetic A–B interactions while contribution from A–A and B–B interactions is usually weak. In the cation distribution, Zn2+ and Al3+ ions are non-magnetic and do not contribute to the hyperfine field. Also, the Fe3+–O2
–Fe3+ superexchange is stronger than Fe3+–O2
–Ni2+. Thus, HFA and HFB decreases with increasing Al3+ content. However, it is to be noted that HFB decreases faster than HFA for x 0.4. The rapid decrease HFB can be explained on the basis of fraction of cations occupying A or B site. As mentioned above, in spinel, A site is surrounded by 12 B sites and B site is surrounded by 6 A site iron atoms. Initially at low concentration, x  0.4, Al3+ show preference to the A site, but at higher x 0.4, Al3+ show comparatively greater affinity for the B site. This brings fractional changes in number of Fe surrounding either A or B site. For example, for x = 0.6 sample, 19% Fe3+ are at A site and 81% are at B site. This means that A site is surrounded by 9.72 B-site Fe3+ and B-site is surrounded by 1.14 A-site Fe3+. Since the rate of decrease of Fe3+ surrounding B site is significant as compared to that of around A-site, hyperfine field values decrease faster for the B-site than A-site. Such a trend of faster reduction in B site hyperfine field has been reported for ZnxCu1
xFe2O4,

CoGaxFe2
xO4 and other ferrites [65,66]. Furthermore, almost similar decrease in the hyperfine fields of both A and B site with the increase in diamagnetic substitution supports our findings for the preference of Al3+ to both sites.The expected range of isomer shift (IS, d) for Fe3+ with oxygen coordination is given to be between 0.20 and 0.30 mm/s, with an average of about 0.22 mm/s for tetrahedral oxygen coordination and 0.30–0.46 mm/s, with an average of about 0.35 mm/s for the octahedral coordination. The IS values, Table 9, for A and B sites are consistent with the above isomer shift values for spinel ferrites [57,67,68]. The result IS (A) < IS(B) is in agreement with the results of other workers [69,70]. This is interpreted as being due to the large bond separation of Fe3+–O2
for the octahedral ions compared with that for the tetrahedral ions. As the orbitals of the Fe3+ and O2
-ions overlap less, the covalency effect is smaller, and hence the isomer shift is large at the octahedral site. The weighted average IS was calculated as follows and is plotted in Fig. 10. ISðdÞ ¼

ISB0 AB0 þ ISB1 AB1 þ ISB2 AB2 þ ISB3 AB3 þ ISB4 AB4 AB0 þ AB1 þ AB2 þ AB3 þ AB4

A significant change in weighted average isomer shift of Ni0.75Zn0.25Fe2
xAlxO4 is observed with progressive Al3+ doping, which indicate that the s-electron charge distribution of Fe3+ ion is influenced by Al3+ substitution. It is observed that the weighted average isomer shift of B-site decreases linearly at the rate of
0.12 per Al3+ substitution. The A-site IS value increases at the rate of 0.049 per Al3+ substitution. The isomer shift is proportional to the total s-electron charge density at the iron nucleus, which is the sum of the spin-up and spin-down s-electron density; an increasing s-electron density is indicated by a decreasing isomer shift. The observed behavior of IS shift for both sites could be attributed to the competition between lattice site volume and complex nature of bonding [71,72], which all affect the s-electron charge density at the iron nucleus. The decrease in IS for the B site indicate delocalization of the 3d orbitals and consequent decreased shielding of the s-electrons from the nucleus. Upon Al3+ substitution, Fe3+—O2
bond length decreases much rapidly at A-site as compared to B-site. The resulting increased covalency at the A-site decrease the delocalization of 3d electrons and consequent

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L. Wang et al. / Materials Research Bulletin 65 (2015) 183–194

increase shielding of the s-electron from the nucleus, which leads to increase in the IS value.The above structural, magnetic, and Mossbauer results show that Al3+ substitution for Fe3+ leads to grain refinement with affinity of Al3+ for octahedral B site, and reduces saturation magnetization and coercivity thus increasing the magnetic softness of the material. 4. Conclusion The substitution of Al3+ ions in Ni0.75Zn0.25Fe2
xAlxO4 system leads to grain refinement and the formation of nanosized mixed spinel ferrites with particle size in the range of 43–37 nm. The unit cell parameter Ni0.75Zn0.25Fe2
xAlxO4 decreased linearly with the increase in Al3+ concentration due to its small ionic radius. The magnetization value of Ni0.75Zn0.25Fe2
xAlxO4 linearly decreased with the substitution of Al3+ due to magnetic dilution. The coercivity value of Ni0.75Zn0.25Fe2
xAlxO4 was found to have an inverse relationship with the particle size. Mossbauer fits were obtained using the binomial distribution model, suggesting a random substitution of iron ions by Al3+ in tetrahedral and octahedral sites. Results clearly show that grain refinement in ferrites is possible with the doping of non-magnetic ions such as Al3+ [44,73,74]. This study highlighted the structure–property relationships in ferrites. Acknowledgements The work was supported by the funds provided by NSF-CMMI (grant #: 1029780) and NSF-TN-SCORE (grant #: EPS 1004083). References [1] A. Goldman, Modern Ferrite Technology, Van Nostrand Reinhold, New York, 1990, pp. 145. [2] P.I. Slick, in: E.P. Wohlfarth (Ed.), Ferromagnetic Materials, vol. 2, NorthHolland, Amsterdam, 1980, pp. 196. [3] A.S. Albuquerque, J.D. Ardisson, W.A.A. Macedo, M.C.M. Alves, J. Appl. Phys. 87 (2000) 4352. [4] P.S.A. Kumar, J.J. Shrotri, S.D. Kulkarni, C.E. Deshpande, S.K. Date, Mater. Lett. 27 (1996) 293. [5] H. Su, H.W. Zhang, X.L. Tang, Y.L. Jing, Y.L. Liu, J. Magn. Magn. Mater. 310 (2007) 17. [6] K.R. Krishna, D. Ravinder, K.V. Kumar, A. Ch. Lincon, Matter Phys. 2153 (2012) . [7] J.L. Dormann, M. Nogues, J. Phys. Condens. Matter 2 (1990) 1223. [8] N. Rezlescu, E. Rezlescu, C. Pasnicu, M.L. Craus, J. Phys. Condens. Matter 6 (1994) 5707. [9] A.E. Virden, K. O’Grady, J. Magn. Magn. Mater. 290 (2005) 868. [10] K.M. Batoo, Nanoscale Res. Lett. 6 (2011) 499. [11] M.A. Amer, M. El Hiti, J. Magn. Magn. Mater. 234 (2001) 118. [12] R.K. Sharma, O.P. Suwalka, N. Lakshmi, K. Venugopalan, Indian J. Pure Appl. Phys. 45 (2007) 830. [13] A.I. Borhan, A.R. Iordan, M.N. Palamaru, Mater. Res. Bull. 48 (2013) 2549. [14] M. Hashim, S. Kumar, S. Ali, B.H. Kob, H. Chung, R. Kumar, J. Alloys Compd. 51 (2012) 107. [15] V.K. Lakhani, B. Zhao, L. Wang, U.N. Trivedi, H.B. Modi, J. Alloys Compd. 509 (2011) 4861. [16] V.K. Lakhani, T.K. Pathak, N.H. Vasoya, K.B. Modi, Solid State Sci. 1 (2011) 539. [17] I. Sharifi, H. Shokrollahi, J. Magn. Magn. Mater. 334 (2013) 36. [18] A.M. Abo El Ata, S.M. Attia, T.M. Miaz, Solid State Sci. 6 (2004) 61. [19] M. El-Shabasy, J. Magn. Magn. Mater. 172 (1997) 188. [20] P. Raj, S.K. Kulshreshtha, J. Phys. Chem. Solids 31 (1970) 9. [21] T. Raghavender, D. Pajic, K. Zadro, T. Milekovic, P. Venkateshwar Rao, K.M. Jadhav, D. Ravinde, J. Magn. Magn. Mater. 316 (2007) 1. [22] N.S. Satya Murthy, M.G. Natera, S.I. Yousef, R.J. Begum, C.M. Srivastava, Phys. Rev. 181 (1969) 969. [23] F. Li, J. Liu, D.G. Evans, X. Duan, Chem. Mater. 16 (2004) 1597.

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