J Supercond Nov MagnDOI 10.1007/s10948-013-2305-2

O R I G I NA L PA P E R

X-Ray Diffraction and Cation Distribution Studiesin Zinc-Substituted Nickel Ferrite Nanoparticles

D.V. Kurmude · R.S. Barkule · A.V. Raut ·D.R. Shengule · K.M. Jadhav

Received: 16 April 2013 / Accepted: 28 June 2013© Springer Science+Business Media New York 2013

Abstract Structural and cation distribution studies onNi1−xZnxFe2O4 (with x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0)ferrite nanoparticles by using X-ray diffraction analysis arereported. In this work the Nickel–Zinc ferrites nanoparticlesare synthesized by sol–gel auto combustion using respec-tive metal nitrates and citric acid as fuel for the auto com-bustion reaction. Formation of ferrite nanoparticles havingsingle-phase spinel structure is evident from the obtainedX-ray diffraction patterns. Lattice constant values of theNi1−xZnxFe2O4 ferrite system are found to increase with in-crease of zinc substitution x. Broad and intense XRD peaksin the patterns indicate the nanocrystalline nature of theproduced ferrite samples. Average particle size calculatedfrom most intense Bragg’s reflection (311) using Debye–Scherrer’s formula is found to be 30 nm. The particle sizeis found to decrease with increase in zinc substitution x.Observed X-ray density is found to decrease with increasein zinc substitution x. Bulk density, porosity, and unit cellvolume are also calculated from the XRD data. Distribu-tion of metal cations in the spinel structure estimated fromX-ray diffraction data show that along with Ni2+ ions mostof the Zn2+ ions also occupy the octahedral [B] sites,which are attributed to nanosize dimensions of the ferritesamples.

D.V. KurmudeMilind College of Science, Aurangabad, 431004 M.S., India

R.S. Barkule · A.V. Raut · K.M. Jadhav (B)Department of Physics, Dr. Babasaheb Ambedkar MarathwadaUniversity, Aurangabad, 431004 M.S., Indiae-mail: drjadhavkm@gmail.com

D.R. ShenguleVivekanand Arts, Sardar Dalipsingh Commerce and ScienceCollege, Aurangabad, 431004 M.S., India

Keywords Ni–Zn nanoferrites · Structural and physicalproperties · Cation distribution

1 Introduction

Cubic spinel ferrite is a group of technologically importantmaterials having applications from microwave to radio fre-quencies. The spinel ferrite has general formula of MFe2O4,where M is any divalent ion of metals such as nickel, cad-mium, zinc, magnesium, copper, etc. [1]. Structural, electri-cal, and magnetic properties of these materials effectivelydepend upon their stoichiometry, methods of synthesis, andcationic distributions among the available (A) and [B] sitesof the face-centered cubic (fcc) spinel structure formed byoxygen anions at the corners.

The unit cell of the spinel structure is obtained by dou-bling approximately face-centered cubic oxygen sublatticealong each of the three directions. Of the resulting 64 tetra-hedral (A) sites and 32 octahedral [B] sites, only 8 and 16 areoccupied, respectively, by cations in stoichiometric spinel.The majority of spinel compounds belong to the space groupFd3m (F 4

1/d32/m, No. 227 in the International Tables) [2].Occupation of the tetrahedral site entirely with a divalent

transition metal produces a normal spinel structure, whileoccupation of the octahedral site with the divalent tran-sition metal yields an inverse spinel structure. If divalenttransition-metal ions are present on both (A) and [B] sublat-tices, the structure is of mixed or disordered spinel [3]. Oc-cupation of metal ions at tetrahedral and octahedral sites alsodepends on method of preparation. For example, bulk nickelferrite shows completely inverse spinel structure by occupy-ing octahedral sites with nickel ions, whereas in nanocrys-talline form small fraction of nickel ions is found to exist atavailable tetrahedral sites in a spinel structure.

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Knowledge of cation distribution and spin alignment isessential to understand the magnetic properties of spinel fer-rites. The interesting physical and chemical properties offerrospinels arise from their ability to distribute the cationsamong the available tetrahedral (A) and octahedral [B] sites.Determination of cation distribution at the tetrahedral (A)and octahedral [B] sites has been a subject of many stud-ies. The cation distribution in spinel ferrites can be ob-tained from the analysis of various data obtained from X-ray diffraction [4], Mossbauer spectroscopy [5], Magneti-zation measurements, [6], Electron spin resonance (ESR)[7], Neutron diffraction [8], Thermoelectric [9], and Nu-clear magnetic resonance (NMR) [2]. Quantum mechanicalmethod [10], “Rietveld” refinement [11], and the reflex pro-gram [12] can also be employed to determine the cation dis-tribution in spinels. Methods suggested by Bertaut [13] andFuruhashi [14] are based on a comparison between the X-ray diffraction intensities observed experimentally and thosecalculated for a large number of hypothetical crystal struc-tures. Wet chemically synthesized polycrystalline spinel fer-rites normally consist of fine particles, and they exhibit un-usual physical properties, as compared to their bulk coun-terparts synthesized by conventional ceramic technique [15,16]. Cation distribution is found to vary with method of syn-thesis, valence of cations doped, crystallite size, tempera-ture, etc.

Substituted nickel ferrites have been the subject of exten-sive investigation because of their microwave applications.Many reports are available on pure and substituted nickelferrites synthesized by ceramic technique in bulk form andby wet chemical methods such as coprecipitation, hydrother-mal, citrate precursor method, etc. in nanosize form [17–19].On going through these reports, it is seen that no systematicinvestigation is carried out on the zinc-substituted nickel fer-rite nanoparticles synthesized by sol–gel auto combustionmethod. Effect of zinc and effect of nanosize form on thestructural and physical properties along with cation distribu-tion of nickel ferrite nanoparticles obtained by sol–gel autocombustion technique using citric acid as fuel is rarely stud-ied. In this view, the structural, physical, and cation distri-bution studies of zinc-substituted nickel ferrites synthesizedby sol–gel auto combustion method are undertaken, and theresults obtained are reported in this paper.

2 Experimental

Nickel–zinc ferrite samples with compositional formulaNi1−xZnxFe2O4 (with x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0)were synthesized by sol–gel auto combustion method us-ing AR grade nitrates of nickel, zinc, and ferric [20]. Citricacid is used as fuel. Using citric acid as fuel helps the ho-mogeneous distribution of the metal ions to get segregated

from the solutions [21]. Aqueous solutions of nitrates wereprepared in minimum amount of deionized water. The citricacid solution prepared separately as per the desired stoi-chiometry was then gradually added to the nitrate solutions,and the mixture was stirred continuously for half an hourto have sol. The pH of the sol was adjusted to 7 by drop-wise addition of ammonia to it. In addition to continuousstirring, the sol is heated at 80 ◦C in order to convert it intoviscous brown gel. After the formation of gel the stirringis stopped, and gel is allowed to burn via auto combustionreaction forming the required loose floppy powder of theend product, the ferrite [22]. As prepared ferrite powder wasthen first heated at 150 ◦C for 2 h to remove water contentsin it. After natural cooling, the powder is sintered at 600 ◦Cfor 8 h in order to get the nanocrystalline ferrite powders.Flow chart of the synthesis procedure leading to formationof zinc-doped nickel ferrite is given in Fig 1. A typical chem-ical reaction (with x = 0.2) leading to the final product ofzinc substituted nickel ferrite can be stated as [23]

0.8Ni(NO3)2 +0.2Zn(NO3)2 +2Fe(NO3)3 +(

20

9

)C6H8O7

→ Ni0.8Zn0.2Fe2O4 +(

40

3

)CO2 +

(80

9

)H2O + 4N2

X-ray diffraction study of all Ni–Zn ferrite samples is doneusing PANALYTICAL X-ray Diffractometer (Model: XpertPRO MPD) in 2θ range from 20◦ to 80◦ in step of 0.02◦at room temperature. The cation distribution in the presentferrite system is determined from XRD data using Bertautmethod.

3 Results and Discussion

X-ray diffraction patterns corresponding to Ni1−xZnxFe2O4

ferrite system for x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0, shownin Fig 2, confirm the formation of single-phase cubic spinelstructure for all the samples. All the planes present in XRDpattern were indexed by combining Bragg’s law with planespacing equation for cubic system [24]. Most of the planessuch as (220), (311), (222), (400), (422), (511), and (440)belonging to the cubic spinel structure are found to bepresent in the XRD pattern of the samples under investiga-tion. Moreover, a typical XRD pattern of pure nickel ferriteshows best match with PDF No. 10-325 that of the cubicspinel. The existence of broad peaks in the XRD patterns in-dicates the nanosize dimensions of the prepared ferrite par-ticles [25]. The lattice constant was calculated using the re-lation

a = d

√(h2 + k2 + l2

), (1)

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Fig. 1 Flow chart of the sol–gelauto combustion synthesis ofNi1−xZnxFe2O4 ferritenanoparticles

Fig. 2 X-ray diffraction patterns of ferrite system Ni1−xZnxFe2O4with x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0

where a is the lattice constant, d is the interplanar spacing,and h, k, and l are the Miller indices. The interplanar spacingd is calculated by using the well-known Bragg law of X-raydiffraction, viz.,

nλ = 2d sin θ, (2)

where n is the order of diffraction, λ is the wavelength ofthe X-ray employed, and θ is Bragg’s glancing angle. TheX-ray density dx is calculated using the relation

dx = 8M

NAa3, (3)

where M is the molecular weight of the composition, NA isthe Avogadro number, and a is the lattice constant [26]. Thepercent porosity is determined using the equation

P =(

1 − db

dx

), (4)

where db is the bulk density. The particle size t is calculatedusing the Debye–Scherrer formula

t = 0.9λ

β cos θ, (5)

where β is the full width at half maximum (FWHM) of therecorded XRD pattern, taken in radians. Most intense peak

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(311) is considered for the calculation of particle size as itis the strongest peak appearing at lower diffraction anglesand can be conveniently analyzed by computer fit. Using thevalues of lattice parameter a, the unit cell volume is also de-termined for each sample. The obtained values of the struc-tural parameters are tabulated in Table 1.

3.1 Effect of Zinc Substitution on Structural Parameters

From Table 1 it is clear that the lattice constant a increaseswith zinc substitution as expected. The increasing behaviorof lattice constant with Zn2+ content is because of replace-ment of Ni2+ ions having comparatively smaller ionic radius(0.69 Å) by Zn2+ ions with larger ionic radius (0.74 Å). Thevariation of the lattice parameter a as a function of Zn2+ ionconcentration x in the Ni1−xZnxFe2O4 matrix follows theVegard law [27]. The values of obtained lattice constant arecompared with that generated from the data of the bulk Ni–Zn ferrite samples [28, 29]. These values are also presentedin Table 1. The values are found to be lower than that of bulklattice parameter except for x = 0.8. Variation of lattice con-stant a with Zn content x is shown in Fig 3.

The X-ray density of pure nickel ferrite is found to be5.391 g/cm3, which matches closely with its reported value5.38 g/cm3 [30]. The X-ray density of Ni–Zn ferrites isfound to decrease with zinc substitution from 5.391 g/cm3

to 5.320 g/cm3. The X-ray density depends upon the latticeconstant, which is increased with the increase in Zn con-centration, so the corresponding X-ray density decreasedwith the increase in Zn concentration. A similar trend hasbeen reported in studies of zinc-substituted manganese fer-rite [31]. The values of the bulk density are found to belower than those of the X-ray density values and are at-tributed to the presence of pores formed and developed atthe time of sample preparation and sintering process [32].The change in the density of the prepared ferrite samples isalso attributed to the change in sintering conditions, sinter-ing temperature, particle size, and chemical compositions.The X-ray density, bulk density, porosity, and specific sur-face area values are in agreement with the reported data[33, 34].

Different structural parameters such as hoping lengths(LA and LB), tetrahedral bond length (dAX), octahedralbond length (dBX), tetrahedral edge length (dAXE), sharedoctahedral edge length (dBXE), unshared octahedral edgelength (dBXEU), tetrahedral site radius (rA), and octahedralsite radius (rB) are determined by using the usual relations[35] and summarized in Table 2. The value of oxygen po-sitional parameter is taken as 0.375 Å; ionic radii of Ni2+(0.69 Å), Zn2+ (0.74 Å), Fe3+ (0.645 Å), and O2− (1.32 Å)ions are considered as given by Shannon [36].

3.2 Effect of Zinc Substitution on Particle Size

Particle size of pure nickel ferrite is obtained to be 41 nm.Upon substitution of zinc, it was found to be reduced to aver-age value of 30 nm. The presence of zinc obstructs the crys-tal growth in spinel ferrites. The crystal growth in the solu-tion depends on various parameters, the most important onebeing the molecular concentration of the material approach-ing the surface of the tiny crystal during the growth process.Because of the liberation of latent heat at the surface, thelocal temperature is normally higher than the solution tem-perature. The surface temperature affects the molecular con-centration at the surface of the crystal and, hence, the crys-

Fig. 3 Variation of lattice constant of Ni1−xZnxFe2O4 spinel ferritesystem with zinc content x in bulk and nanoform

Table 1 Lattice constant (a),X-ray density (dx ), bulk density(db), porosity (P ), particle size(t ), and unit cell volumeobtained for theNi1−xZnxFe2O4 spinel ferritesystem

X aexp (Å) dx

(gm/cm3)db

(gm/cm3)P

(%)t

(nm)V

(Å3)Nano Bulk

0.0 8.328 8.340 5.391 2.062 61.75 41 578

0.2 8.356 8.365 5.367 2.233 58.40 32 583

0.4 8.377 8.388 5.357 1.964 63.35 27 588

0.6 8.405 8.408 5.334 1.917 64.07 30 594

0.8 8.428 8.426 5.320 1.761 66.89 30 598

1.0 8.431 8.442 5.344 2.005 62.48 34 599

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Table 2 Hopping lengths (LA and LB), tetrahedral bond length(dAX), octahedral bond length (dBX), tetrahedral edge length (dAXE),shared octahedral edge length (dBXE), unshared octahedral edge length

(dBXEU), tetrahedral site radius (rA), octahedral site radius (rB), andtheoretical lattice constant (ath) for the Ni1−xZnxFe2O4 spinel ferritesystem

X LA LB dAX dBX dAXE dBXE dBXEu rA rB rA(cal.) rB(cal.) ath (Å)

0 2.515 2.436 1.890 2.033 3.086 2.803 2.946 0.570 0.712 0.645 0.668 8.325

0.2 2.522 2.443 1.896 2.040 3.096 2.812 2.956 0.576 0.719 0.655 0.668 8.341

0.4 2.527 2.448 1.901 2.045 3.104 2.820 2.963 0.581 0.724 0.657 0.672 8.354

0.6 2.534 2.455 1.907 2.052 3.114 2.829 2.973 0.587 0.731 0.654 0.678 8.367

0.8 2.540 2.461 1.912 2.058 3.123 2.837 2.981 0.592 0.736 0.649 0.686 8.379

1 2.541 2.461 1.913 2.058 3.124 2.838 2.983 0.593 0.737 0.647 0.692 8.392

tal growth. The formation of zinc ferrite is more exothermicas compared to formation of nickel ferrite. Thus, it is ex-pected that if one introduces zinc in the system, more heatwill be liberated, decreasing the molecular concentration atthe crystal surface and hence obstructing the grain growth[28] and reducing the particle size. Moreover, the reductionin particle size can be related to the electronic configurationof nickel (3d8) and zinc (3d10); obviously, as compared tozinc, nickel, which has incomplete electronic configuration,has more tendencies to interact with legends and O2− an-ions. The lack of d electrons is important because there arevery little covalent interaction and tendency toward exten-sion between Zn2+ and its legends. Thus, introduction ofzinc into nickel obstructs the growth of particle, and hencethe particle size is reduced. Further, the smaller particle sizesof the samples doped with zinc ions are due to lower bondenergy of Zn2+–O2− as compared to that of N2+–O2− [37].The reduction in particle size of a ferrite material producesinteresting changes in ionic distributions of the spinel struc-ture, which in turn can give rise to enhanced magnetic prop-erties.

3.3 Cation Distribution Studies

Distribution of cations among the available tetrahedral (A)and octahedral [B] sites of the synthesized Ni–Zn ferritespinels is estimated by using X-ray diffraction intensity cal-culations as suggested by Buerger [38], and the required for-mulae reproduced here are taken from [39]:

Ihkl = |Fhkl |2 × P × Lp, (6)

where Ihkl is the relative integrated intensity, Fhkl is thestructure factor, P is the multiplicity factor for the plane(hkl), and LP is the Lorentz polarization factor,

Lp = (1 + cos2 θ)

(sin2 θ × cos θ). (7)

To calculate the X-ray diffraction intensities (Ihkl) in-stead of considering all the planes of the spinel, typical

planes, namely (220), (400), (422), and (440), are consid-ered, as these planes are known to be cation-sensitive planes[40]. Instead of arbitrary intensities of individual planes(hkl), the ratios (I440/I422), (I220/I440), (I422/I400), and(I220/I400) are considered to minimize the errors in the re-sults. The intensity ratios (I220/I400 and I422/I400) are foundto be more sensitive to the cation distribution [41]. The ab-sorption and temperature factors are not taken into accountin our calculations because these do not affect the relativeintensity calculations for spinels at room temperature [42].The formulae for the structure factors for the plane (hkl)are taken as reported by Furuhashi et al. [14]. The multi-plicity factors are taken from the literature [24]. The resultsof X-ray intensity calculations for various possible modelsgiving rise to normal to inverse spinels have been tried andwere compared with those observed intensity ratios calcu-lated separately for entire range of zinc substitution from theX-ray diffraction data. The cation distribution for which theobserved ratio agrees well with that of the proposed intensityratios is taken as a correct one. The cation distribution pro-posed for the present nickel–zinc nanoferrites synthesizedby sol–gel auto combustion method is presented in Table 3.

Using the accepted cation distribution, the tetrahedral siteradius (rA(cal)) and octahedral site radius (rB(cal)) are calcu-lated by using the relations

rA(cal) = |CNirNi2+ + CZnrZn2+ + CFerFe3+|, (8)

rB(cal) = 1/2|CNirNi2+ + CZnrZn2+ + CFerFe3+|. (9)

Theoretical lattice constant (ath) is calculated by usingthe formula given by [43]:

ath = 8

3√

3(rA(cal) + r0) + √

3(rB(cal) + r0). (10)

The obtained values of site radii and theoretical latticeconstant ath are presented in Table 2. From Tables 1 and 2it is seen that the values of observed and theoretical latticeconstants are in agreement with each other favoring the es-timated cation distribution [44]. Thus, it confirms that the

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Table 3 Estimated cationdistribution analysis forNi1−xZnxF2O4 spinel ferritesystem

X A-Site B-Site (I422/I400) (I220/I400) Fe[B]Fe(A)

Obs. Cal. Obs. Cal.

0 (1Fe) [1Ni1Fe] 0.42 0.42 0.97 1.20 1.00

0.2 (0.0Ni0.1Zn0.9Fe) [0.8Ni0.1Zn1.16Fe] 0.40 0.45 1.34 1.26 1.22

0.4 (0.26Ni0.0Zn0.74Fe) [0.34Ni0.4Zn1.26Fe] 0.51 0.45 1.85 1.26 1.70

0.6 (0.2Ni0.0Zn0.8Fe) [0.2Ni0.6Zn1.2Fe] 0.59 0.44 2.11 1.21 1.50

0.8 (0.08Ni0.0Zn0.92Fe) [0.12Ni0.8Zn1.08Fe] 0.63 0.41 2.28 1.14 1.17

1 (0.0Ni0.02Zn0.98Fe) [0.0Ni0.98Zn1.02Fe] 0.64 0.40 2.31 1.11 1.04

estimated cation distribution is correct. Figure 2 shows thevariation of theoretical lattice constant ath with the zincsubstitution x. As seen from Fig 2, the experimental lat-tice constant aobs is slightly smaller than that of theoreti-cal lattice constant ath. This is in agreement with the re-ported results [45]. The small deviation between ath andaobs may be due to the presence of some ferrous ions Fe2+(rFe

2+ = 0.078 nm) on octahedral sites with larger radii thanFe3+ (rFe

3+ = 0.0645 nm) [46].Also, from Table 3 it is seen that the pure nickel ferrite

shows the inverse spinel structure as expected with all theNi2+ ions situated at octahedral [B] sites along with half ofthe Fe3+ ions and remaining half of Fe3+ ions at tetrahe-dral (A) sites. Strikingly, it is also seen from Table 3 that al-though Zn2+ ions have strong preference to tetrahedral (A)sites in bulk zinc ferrite, the Zn2+ ions have been found tobe situated at octahedral [B] sites with large degree of inver-sion. This may be attributed to the method of synthesis andnanosize of the prepared ferrite samples.

Hamdeh et al. [47] have reported similar results, wherefine powders of zinc ferrite were produced by the supercrit-ical aerogel method. This process has been shown to pro-duce powders having large structural and chemical disorder.Secondly, portions of the powders were ball milled, causingmuch greater atomic disorder due to mechanical displace-ment of ions under high stress and shear. Battle et al. [48]have studied zinc ferrites prepared by variety of methodsincluding conventional ceramic method and suggested theoccupation of zinc ions at octahedral [B] sites. Further,low-temperature Mossbauer studies indicates a significantamount of deviation of cation distribution from their bulkPreferences. Also, Fe3+ ions have strong preference for thetetrahedral (A) site as compared to octahedral [B] site [49].So formation of pure nickel ferrite is most favorable as bothNi2+ and Fe3+ ions occupy their preferred sites with ease.As zinc is introduced in spite of its preference for (A) site,the Fe3+ ions may be forcing zinc ions to occupy octahe-dral [B] site as is evident from the present cation distributionstudy [28]. It is also reported that large cation redistribu-tions/inversion parameters can be obtained only by placingZnFe2O4 into a nonequilibrium state [50]. It is also reportedfor specific composition of Ni1−xZnxFe2O4 ferrite material

Fig. 4 Variation of zinc occupation level at octahedral [B] site withzinc content x

with x = 0.5 and normal site preferences; its configurationfor bulk form can be written as (Zn0.5Fe0.5) [Ni0.5Fe1.5]O4,which leads to the saturation magnetization value of nearly70 emu/g at room temperature. However, in case of nano-particles of these systems, the cation preferences do nothold good any more. This means that some of the Zn2+will now occupy the octahedral sites and push back Ni2+and Fe3+ to the tetrahedral sites and that the new config-uration can be written as (Zn0.5−xFe0.5−yNiz) [Ni0.5−zZnx

Fe1.5−y ]O4 such that x = y + z. Such a substitution def-initely leads to the lower value of the saturation magneti-zation as 56.01 emu/g. A relatively low value of saturationmagnetization for the sample annealed at 550 ◦C indicatesthat cations are surely deviated from their normal prefer-ences [51]. Figure 4 shows the zinc concentration at octa-hedral [B] site with its substitution level in nickel ferrite.

4 Conclusion

Zinc-substituted nickel ferrite nanoparticlesNi1−xZnxFe2O4

(with x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) were synthesizedsuccessfully by using sol–gel auto combustion technique

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with average particle size of 30 nm. The substitution of Zn2+for Ni2+ ions results in the increasing the lattice constant.The particle size is found to decrease Zn2+ ions. The cationdistribution data suggests the effect of particle size. Nor-mally, Zn2+ ions occupy tetrahedral (A) site, but here it isobserved that Zn2+ ions occupy octahedral [B] site, and itmay be due to the nanosize nature of samples.

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