Aluminum doped manganese ferrites MnAlxFe2−xO4
with
0.0≤x≤1.0 have been prepared by the double ceramic route. The formation of mixed spinel phase has been confirmed by X-ray diffraction analysis. The unit cell parameter `aO' is found to decrease linearly with aluminum concentration due to smaller ionic radius of aluminum. The cation distributions were estimated from X-ray diffraction intensities of various planes. The theoretical lattice parameter, X-ray density, oxygen positional parameter, ionic radii, jump length, and bonds and edges lengths of the tetrahedral (A) and octahedral (B) sites were determined. 57Fe Mössbauer spectra recorded at room temperature were fitted with two sextets corresponding to Fe3+ ions at A- and B-sites. In the present ferrite system, the area ratio of Fe3+
ions at the A- and B-sites determined from the spectral analysis of Mössbauer spectra gives evidence that Al3+ ions replace iron ions at B-sites.
This change in the site preference reflects an abrupt change in magnetic hyperfine fields at A- and B-sites as aluminum concentration increases, which has been explained on the basis of supertransferred hyperfine field. On the basis of estimated cation distribution, it is concluded that aluminum doped manganese ferrites exhibit a 55% normal spinel structure.
1. Introduction
Spinel
ferrites have been the subject of great interest for the past five decades, because of their wide
range of applications in transformers,
inductors, choke
coils, noise filters magnetic recording heads, and so forth [1]. These ferrites
possessing cubic
close-packed structure of oxygen ions, are described by the formula (A)[B]2O4, where (A) and [B] represent tetrahedral and
octahedral sites, respectively. The site occupancy is often depicted in the
chemical formula as (M1−δFeδ)[Mδ Fe2−δ]O4, where round and square brackets denote the A-
and B-sites, respectively, M represents a metal cation, and ‘δ’
is the inversion parameter. The degree of inversion ‘δ’ for spinel
ferrites is defined as the fraction of tetrahedral (A)-sites occupied by
trivalent cations. Accordingly, for a normal spinel δ=0 and for a
completely inverse spinel, δ=1. The magnetic and the electronic
properties of such a ferrite system depend upon the type of metal cations and their distribution
among the two interstitial sites, that is, A- and B-sites. Therefore, the
knowledge of cation distribution is essential to understand the magnetic
behavior of spinel ferrites. Manganese ferrite is early known to be a mixed
inverse spinel, and the degree of inversion mainly depends upon the method of
preparation. The presence of nonmagnetic ions in these spinel ferrites is found
to alter their magnetic and electronic properties. The addition of metal
cations such as trivalent or tetravalent influences the electronic and magnetic
properties of the ferrite system [2–6]. Various studies
showed that heating might change the distribution of metal cations at the A-
and B-sites of MnFe2O4. It has been reported that by
using neutron diffraction technique, the degree of inversion, that is, the
distribution of the cationic ions between the tetrahedral and octahedral sites
of MnFe2O4 prepared by usual ceramic route was determined
81% normal [7]. However, this value reduced to 33%, when MnFe2O4 was prepared by wet chemical method [8]. Thus, the method of preparation may
play a crucial role in order to obtain the desired electronic and magnetic
properties. Extensive investigations regarding the substitution of metal
cations, for example, Cu2+, Zn2+, Ti2+, Co3+,
and Ni2+ in manganese ferrites
have been reported, giving useful
information about the influence of such metal cations [9–13]. However, no
systematic results regarding the estimation of cation distribution on
substitution of aluminum ion in MnFe2O4 was available. In the present studies, the
cation distribution in tetrahedral and octahedral sites of aluminum substituted
manganese ferrites synthesized via double ceramic route has been determined by X-ray diffraction
and Mössbauer spectroscopic measurements.
2. Experimental
Samples of the mixed spinel ferrites MnAlxFe2.0−xO4 for x=0.0,0.2,0.4,0.6,0.8, and 1.0 were synthesized by usual double ceramic processing technique.
The starting materials were high-purity
analytical reagent grade oxides, Fe2O3, MnO, and Al2O3.
The required compositions were weighed and mixed in a mortar and pestle. The
mixed powders were presintered at 1000°C for 10 hours in the air and allowed to cool to room
temperature at the rate of about 2°C/min. In the final sintering
process, the samples were placed in a furnace at 1300°C for 10 hours
in the air and then
cooled slowly to room temperature at the rate of 2°C/min. The
finally sintered materials were well grounded. To ensure their single-phase
nature, the powder X-ray diffraction studies were made on Regaku X-ray
diffractometer by using Cu-Kα radiation of
wave length 1.54060 Å. Fe57 Mössbauer absorption spectra were
recorded in transmission geometry at room temperature using a multichannel
analyzer with a drive in constant acceleration mode. A Co(Rh)57
source with initial activity of 20 mCi was used. The spectrometer was
periodically calibrated using a natural iron foil as a standard.
3. Results and Discussion3.1. X-Ray Diffraction Analysis
The X-ray diffraction patterns of mixed
spinel ferrites (MnAlxFe2.0−xO4 for x=0.0,0.2,0.4,0.6,0.8, and 1.0) are shown in Figure 1.
X-ray diffraction pattern of MnAlxFe2.0−xO4 system.
The positions of diffraction
peaks from various planes were identified using JCPDS file no. 74-2403. It is
evident from Figure 1 that each ferrite sample exhibits single-phase cubic
spinel structure with Fd-3m (227) space group. The value of the lattice
constant ‘aO’ for all the
samples was determined from the position of principal (311) peak using aO=dhklh2+k2+l2, where h, k, and l are the miller indices.
The observed values of lattice
constant ‘aO’ listed in
Table 1 are slightly smaller than the JCPDS table value of 8.518 Å. The lattice
constant ‘aO’ is found to
decrease linearly with aluminum concentration (x) as shown in Figure 2(a), thereby obeying Vegard’s law [14].
Lattice
constant, density, and volume for MnAlxFe2.0−xO4 system.
Composition (x)
Lattice constant
Volume
X-ray density
(aO ± 0.002) Å
(at ± 0.002) Å
Å3
(dx ± 0.002) gm/cm3
0.0
8.454
8.504
604.23
5.07
0.2
8.417
8.455
596.46
5.01
0.4
8.396
8.407
592.05
4.92
0.6
8.372
8.358
586.84
4.83
0.8
8.348
8.310
581.96
4.74
1.0
8.315
8.261
574.89
4.64
Variation of (a) lattice constant and (b) X-ray density with aluminum ions concentration.
The decrease in lattice constant is
attributed to the fact that the Pauling ionic radius of Al3+ (0.50 Å) is smaller than that of Fe3+ (0.64 Å), which causes the shrinking in the unit cell dimensions. The decrease in ‘aO’ and the shift of reflections toward higher angle
with the increasing aluminum concentration (x)
show that aluminum
atoms have been incorporated into the spinel structure [15].
The X-ray density ‘dx’
was calculated using the formula [16] dx=8MNaO3, where ‘M’ is the molecular weight, ‘N’
is the Avogadro's
number, and ‘aO’ is the lattice constant of the spinel ferrite.
The calculated values of X-ray density are listed in Table 1. The X-ray density
decreases with increasing aluminum concentration (x), as shown in Figure 2(b). The decrease in X-ray density is due
to the decrease in
mass, which overtakes the decrease in volume of the unit cell.
The cation distribution in the
various spinel ferrite systems has been estimated from X-ray diffraction [5, 6], Mössbauer’s
effect [17, 18], and magnetization
measurements [19, 20]. It has been
reported [21, 22] that the best
information in estimation of cation distribution can be achieved by comparing
the experimental and theoretical intensity ratios for reflections (220), (422),
and (400). However, the intensities of (220), (422), and (400) planes are more
sensitive to cations on A- and B-sites [23, 24]. The X-ray
diffraction intensity of the respective planes was calculated using the formula [25] Ihkl=|Fhkl|2⋅P⋅LP, where Ihkl is the relative integral
intensity; Fhkl is the
structure factor; P is the
multiplicity factor; Lp is the Lorentz factor. The structural factors
were calculated by using the equation suggested by Porta and Furuhashi et al.
[26, 27]. The
multiplicity factor and the Lorentz factors were taken from the literature
[16]. The ionic scattering factor reported in the international tables for
X-ray crystallography [28] is used for the calculation of structural factor. It
is well established that the intensity ratios I220/I440 and I400/I440 are considered to be sensitive
to cation distribution [29]. Therefore in the present ferrite system, intensity
ratios of these planes have been used in estimation of cation distribution. The
intensity ratios of these planes were calculated for various cation distributions
using the following expression suggested by Bertaut [21]: (IhklIhIkIlI)obs=(IhklIhIkIlI)cal. For all the samples, the calculated values,
those closest to the experimental observed values, are given in Table 2. The
theoretical lattice constant ‘at’
for all composition was calculated on the basis of estimated cation
distribution by using the relation [30] at=833(rA+rO)+3(rB+rO), where rA and rB are the radii of
the A- and the B-sites, respectively, and rO
is the radius of the oxygen ion O2− (1.48 Å).
The calculated values ‘at’
are nearly equal to the experimental observed value ‘aO’
which confirms the estimated cation distribution (see Table 2). The site radii rA and rB used above were determined using the following: rA=0.446rtetFe3++0.554rtetMn2+,rB=(1.554−x)roctFe3++0.446roctMn2++xroctAl3+. The calculated
values of rA and rB are listed in Table 3. The
value of rA decreases
slowly; however the value of rB decreases noticeably with increasing aluminum concentration. This is due to the
replacement of larger ionic radii (Fe3+) with smaller ionic radii
(Al3+) and their distribution amongst the A- and B-sites. The value
of the oxygen positional parameter ‘u’
was calculated by using the following relation:
rA=aO3(u−0.25)−rO. The determined
values of ‘u’ are listed in Table 3.
The values of the tetrahedral (dAL),
octahedral bond length (dBL),
tetrahedral edge length (dAE), and shared (dBE)
and unshared octahedral edge lengths (dBEU) were calculated by using the experimental values of
lattice constant ‘aO’ and
oxygen positional parameter ‘u’ from
the following [30, 31]: dAL=aO3(u−0.25),dBL=aO(3u2−114u+4364),dAE=aO2(2u−0.5),dBE=aO2(1−2u),dBEU=aO(4u2−3u+1116). Various
calculated X-ray parameters are given in Table 3. It is observed that dAL, dBL, dAE, dBE, and dBEU decrease with increasing
aluminum concentration (x). This is due to the substitution process,
that is, replacement of larger ionic radii (Fe3+) by smaller ionic
radii (Al3+) and their distribution among the A- and B-sites. These
results are in consistent with the reported data [32]. It has been reported
that the jump length ‘L’ (the distance between the magnetic ions) of
electrons influences the physical properties of the ferrite system [33]. Electrons
those are hopping
between B- and A-sites are less probable compared to that between B- and B-sites,
because the distance between the two metal ions placed in B-sites is smaller
than if they were placed one in B-sites and the other in A-sites [34]. ‘L’ of
the A- and B-sites is determined from the following relations [35]: LA=aO34,LB=aO24. It is observed
that ‘L’ of A- and B-sites decreases
with increasing aluminum concentration (x)
as shown in Figure 3.
Cation distribution data calculated from XRD
pattern of the MnAlxFe2.0−xO4 system.
X-ray intensity
I220/I440
I400/I440
Composition
Exp.
Cal.
Exp.
Cal.
Cation distribution
Fe3+(B)/Fe3+(A)
MnFe2.0O4
1.0247
1.1796
0.9622
0.7643
(Fe0.446Mn0.554)A[Fe1.554Mn0446]B
3.48
MnAl0.2Fe1.8O4
1.0348
1.2807
0.9624
0.6902
(Fe0.446Mn0.554)A[Fe1.354Mn0.446AL0.2]B
3.03
MnAl0.4Fe1.6O4
1.0565
1.3772
0.9433
0.6483
(Fe0.446Mn0.554)A[Fe1.254Mn0.446AL0.4]B
2.58
MnAl0.6Fe1.4O4
1.0579
1.4772
0.9257
0.6112
(Fe0.446Mn0.554)A[Fe0.954Mn0.446AL0.6]B
2.13
MnAl0.8Fe1.2O4
1.0780
1.5020
0.8414
0.5711
(Fe0.446Mn0.554)A[Fe0.754Mn0.446AL0.8]B
1.69
MnAl1.0Fe1.0O4
1.0910
1.5700
0.5907
0.5256
(Fe0.446Mn0.554)A[Fe0.554Mn0.446AL1.0]B
1.24
X-ray
parameters (error bar ± 0.002 Å):
tetrahedral and octahedral bond lengths (dAL and dBL) and jump lengths (LA and LB),
tetrahedral edge dAE, and shared and unshared octahedral edges (dBE and dBEU).
Composition (x)
dAL (Å)
dBL (Å)
dAE (Å)
dBE (Å)
dBEU (Å)
LA (Å)
LB (Å)
rA (Å)
rB (Å)
u (Å)
0.0
2.2477
1.9031
3.6704
2.3075
3.0282
3.6607
2.9889
0.7286
1.3514
0.4035
0.2
2.2496
1.8922
3.6737
2.2785
3.0183
3.6436
2.9750
0.7286
1.3253
0.4043
0.4
2.2499
1.8858
3.7453
2.2633
3.0100
3.6359
2.9687
0.7286
1.2993
0.4047
0.6
2.2491
1.8776
3.6727
2.2472
3.0023
3.6252
2.9600
0.7286
1.2732
0.4051
0.8
2.2498
1.8685
3.6739
2.2289
2.9953
3.6147
2.9514
0.7286
1.2473
0.4056
1.0
2.2482
1.8592
3.6712
2.2083
2.9853
3.6005
2.9397
0.7286
1.2213
0.4061
Variation of jump length ‘L’ with aluminum ions concentration.
The decrease in
jump length is due to the decrease in the distance between the magnetic ions by
the substitution of smaller Al3+ ions at the B-sites and is similar
to those reported earlier [4, 32].
3.2. Mössbauer Analysis
57Fe Mössbauer absorption
spectra of mixed spinel ferrite system MnAlxFe2.0−xO4 for x=0.0,0.2,0.4,0.6,0.8, and 1.0 recorded at room temperature
are displayed in Figure 4. The experimental data were fitted using least
square-fitting (NORMOS/SITE) program [36]. Each spectrum exhibits a
superposition of two Zeeman sextets, one sextet corresponding to a higher
magnetic field is attributed to Fe3+ ions on the B-site, and the
other sextet corresponding to lower magnetic field is attributed to Fe3+ ions on the A-site. The refined values of the hyperfine parameters computed
from the Mössbauer spectra are listed in Table 4. In the present ferrite
system, it is observed that on increasing Al3+ ions concentration,
the values of isomer shift (δ) of tetrahedral A-sites
show almost negligible change, indicating that aluminum ions do not enter in
A-sites. The isomer shift of B-sites is greater than A-site and is in agreement
with the reported data [11]. Furthermore, the observed values of isomer shift (δ) are significantly less than the expected
value, 0.5 mm/s for the Fe2+ ions [20]. Hence, the presence of Fe2+ ions in the present ferrite system is ruled out. Thus the electron exchange interaction
(Fe2+↔Fe3++e−) does not occur, and hence
the oxidation state of Fe3+ remains unchanged during synthesis
process. The hyperfine field Hhfs values at B- and A-sites show a gradual decrease with increasing Al3+ concentration (x). This can be explained on the basis of
supertransferred hyperfine field at the central cation that originates from the
magnetic moments of the nearest-neighbor cations, that is, from the intra-sublattice
contributions hAA and hBB and the inter-sublattice contributions hAB and hBA. In the present ferrite
system, the intra-sublattice contributions hAA and hBB are predominant. It has been reported that the intensities corresponding
to (200) and (422) reflections are most sensitive to cations on A-sites
[23, 24]. The X-ray diffraction patterns of the present ferrite system indicate
that the intensity of (220) and (422) reflections remains almost constant as
compared to (311) reflection, suggesting that Al3+ ions do not enter
in the A-sites. The value of isomer shift (δ)
of A-sites remains invariant on substitution of aluminum ions suggesting that Al3+ ions do not replace
Fe3+ ions from A-sites. The introduction of Al3+ ions
that replaces Fe3+ ions from B-sites decreases intra-sublattice
contributions, which in turn decreases the hyperfine field Hhfs values. As nonmagnetic Al3+ ions replace Fe3+ ions, the correct amount of Fe3+ ions occupying A- and B-sites is estimated by determining the area under the Mössbauer absorption spectra through the least square
fitting program. The Fe3+(B)/Fe3+(A) ratio obtained
from the Mössbauer spectra is
in good agreement with those calculated from X-ray intensities. It is observed
that this ratio decreases with increasing aluminum concentration (x) suggesting a decrease in
ferrimagnetic behavior.
Room
temperature Mössbauer’s effect parameters for MnAl x Fe2.0−xO4 system as a function of x.
Composition (x)
site
Isomer shift*
Quadrupole splitting
Hhfs
Area (%)
Fe3+(B)/Fe3+(A)
(δ±0.01) mm/s
(Δ±0.01) mm/s
(±2.0 T)
0.0
B
0.18
0.00
47.71
77.74
3.49
A
0.11
0.00
43.48
22.26
0.2
B
0.17
0.00
47.16
75.15
3.02
A
0.11
0.00
42.71
24.85
0.4
B
0.16
0.00
46.46
72.01
2.57
A
0.10
0.00
42.41
27.99
0.6
B
0.13
0.00
45.34
68.92
2.20
A
0.10
0.00
40.58
31.08
0.8
B
0.12
0.00
42.82
62.88
1.69
A
0.10
0.00
36.94
37.12
1.0
B
0.11
0.00
41.80
55.90
1.26
A
0.10
0.00
36.54
44.10
Isomer*
shift given relative to α-Fe.
Room temperature Mössbauer absorption spectra of MnAlxFe2.0−xO4, for x=0.0,0.2,0.4,0.6,0.8, and 1.0.
4. Conclusion
Aluminum substituted manganese ferrites MnAlxFe2.0−xO4 for x=0.0,0.2,0.4,0.6,0.8, and 1.0 have been prepared by double ceramic processing
technique. The unit cell parameter decreases linearly with the increase of
aluminum concentration (x) due to its
small ionic radius. The cation distribution estimated from X-ray intensity
ratios has been verified by comparing the theoretical and experimental lattice parameters. It is observed that the correct amount of Fe3+ ions occupying B-
and A-sites obtained from Mössbauer spectra is in good agreement with those calculated from
X-ray intensity calculations. The hyperfine magnetic field obtained from the
Mössbauer absorption spectra decreases with increasing aluminum concentration
suggesting the decrease in ferrimagnetic behavior and has been explained on the
basis of supertransferred hyperfine field mechanism. The X-ray determined
parameters, for example, lattice constant, X-ray density, ionic radius, bond
length, jump length of the A- and B-sites, oxygen positional parameter, A-site
edge length, and shared and unshared B-site edge lengths were determined and
found affected by Al3+ ions substitution. On the basis of estimated
cation distribution, it is concluded that the present ferrite system exhibits a
55% normal spinel structure.
Acknowledgments
One of the authors
(R. L. Dhiman) is grateful to Dr.
Alok Banerjee and Dr. R. J. Chaudhary, Scientists, UGC-DAE, Consortium for
Scientific Research, University Campus, Khandwa Road, Indore (MP), India, for
providing experimental facilities.
IgarashiH.OkazakiM.Effects of porosity and grain size on the magnetic properties of NiZn ferrite1977601-2515410.1111/j.1151-2916.1977.tb16092.xLalR.roshandhiman_kuk@yahoo.co.inSumanSharmaN. D.TanejaS. P.ReddyV. R.Structural and magnetic properties of zinc ferrite aluminates2007453231237SinghalS.BarthwalS. K.ChandraK.chandfuc@iitr.ernet.inStructural, magnetic and Mössbauer spectral studies of nanosize aluminum substituted nickel zinc ferrites200629629410310.1016/j.jmmm.2005.01.029PanditA. A.bamuaur@bom4.vsnl.netShitreA. R.bamuaur@bom4.vsnl.netShenguleD. R.bamuaur@bom4.vsnl.netJadhavK. M.bamuaur@bom4.vsnl.netMagnetic and dielectric properties of Mg1+xMnxFe2−2xO4 ferrite system200540242342810.1007/s10853-005-6099-xSinghalS.SinghJ.BarthwalS. K.skbarfph@iitr.ernet.inChandraK.chandfuc@iitr.ernet.inPreparation and characterization of nanosize nickel-substituted cobalt ferrites (Co1−xNixFe2O4)2005178103183318910.1016/j.jssc.2005.07.020Justin JoseyphusR.NarayanasamyA.ansuom@yahoo.co.inShinodaK.JeyadevanB.TohjiK.Synthesis and magnetic properties of the size-controlled Mn-Zn ferrite nanoparticles by oxidation method20066771510151710.1016/j.jpcs.2005.11.015HastingsJ. M.CorlissL. M.Neutron diffraction study of manganese ferrite1956104232833110.1103/PhysRev.104.328SakuraiJ.ShinjoT.Neutron diffraction of manganese ferrite prepared from aqueous solution1967236142610.1143/JPSJ.23.1426RanaM. U.IslamM. U.AbasT.Cation distribution in Cu-substituted manganese ferrites1999412525610.1016/S0167-577X(99)00102-0FengJ.fengjing@hrbeu.edu.cnGuoL.-Q.XuX.QiS.-Y.ZhangM.-L.Hydrothermal synthesis and characterization of Mn1−xZnxFe2O4 nanoparticles2007394110010310.1016/j.physb.2007.02.015MishraS.KunduT. K.tkkundu1968@yahoo.comBarickK. C.BahadurD.ChakravortyD.Preparation of nanocrystalline MnFe2O4 by doping with Ti4+ ions using solid-state reaction route2006307222222610.1016/j.jmmm.2006.04.005FayekM. K.Sayed AhmedF. M.Ata-AllahS. S.ElnimerM. K.MostafaM. F.Crystal, magnetic and electric behaviour of CoMnxFe2−xO4 cubic ferrites199227174813481710.1007/BF01166024WeiQ.-M.wqm99@mails.tsinghua.edu.cnLiJ.-B.ChenY.-J.Cation distribution and infrared properties of NixMn1−xFe2O4 ferrites200136215115511810.1023/A:1012473207424WhinfreyC. G.EckartD. W.TauberA.Preparation and X-ray diffraction data for some rare earth stannates196082112695269710.1021/ja01496a010ToledoJ. A.jtoledo@www.imp.mxValenzuelaM. A.BoschP.Effect of AI3+ introduction into hydrothermally prepared ZnFe2O420001981-223524510.1016/S0926-860X(99)00514-1CullityB. D.1959Reading, Mass, USAAddison-WesleyAta-AllahS. S.ssatallah@hotmail.comKaiserM.Cation distribution, hyperfine parameters and conduction mechanism in the ferrimagnetic system Cu0.5Co0.5GaxFe2−xO4200524261324133510.1002/pssb.200440012RaisA.amr@squ.edu.omGismelseedA. M.Al-OmariI. A.Cation distribution and magnetic properties of nickel-chromium ferrites
NiCrxFe2−xO4(0≤x≤1.4)200524271497150310.1002/pssb.200440022JadhavS. A.Magnetic properties of Zn-substituted Li-Cu ferrites2001224216717210.1016/S0304-8853(00)00580-1ThummerK. P.ChhantbarM. C.ModiK. B.kunalbmodi2003@yahoo.comBaldhaG. J.JoshiH. H.Localized canted spin behaviour in ZnxMg1.5−xMn0.5FeO4 spinel ferrite system20042801233010.1016/j.jmmm.2004.02.017BertautE. F.Etude de la nature des ferrites spinelles1950230213215WeilL.BertautE. F.BochirolL.Propriétés magnétiques et structure de la phase quadratique du ferrite de cuivre195011520821210.1051/jphysrad:01950001105020800EoiskaE.WoiskiW.The evidence of Cdx2+Fe1−x3+[Ni1−x2+Fe1+x3+]O4 cation distribution based on X-ray and Mössbauer data19921321K51K5610.1002/pssa.2211320137LadgaonkarB. P.VaingankarA. S.X-ray diffraction investigation of cation distribution in CdxCu1−xFe2O4 ferrite system199856328028310.1016/S0254-0584(98)00174-6BuergerM. G.1960New York, NY, USAJohn Wiley & SonsPortaP.StoneF. S.TurnerR. G.The distribution of nickel ions among octahedral and tetrahedral sites in NiAl2O4-MgAl2O4 solid solutions197411213514710.1016/0022-4596(74)90108-XFuruhashiH.InagakiM.NakaS.Determination of cation distribution in spinels by X-ray diffraction method19733583009301410.1016/0022-1902(73)80531-7MacGillavryC. H.RieckG. D.LonsdaleK.1968Birmingham, UKKynoch PressInternational Tables for X-Ray Crystallography, Volume IIIOhnishiH.TeranishiT.Crystal distortion in copper ferrite-chromite series1961161354310.1143/JPSJ.16.35YousifA. A.ElzainM. E.MazenS. A.SutherlandH. H.AbdallaM. H.MasourS. F.Mössbauer and X-ray diffraction investigation of Li-Ti ferrites19946295717572410.1088/0953-8984/6/29/014AmerM. A.F57e Mössbauer, infrared and X-ray studies of the system Zn1−xCuxCr0.8Fe1.2O42000181253955010.1002/1521-396X(200010)181:2<539::AID-PSSA539>3.0.CO;2-9AmerM. A.moazamer@yahoo.comMössbauer, infrared, and X-ray studies of Ti-doped CoCr1.2Fe0.8O4 ferrites2003237245947110.1002/pssb.200301652El-SaadawyM.BarakatM. M.Effect of jump length of electrons on the physical properties of Mn-doped Co0.6Zn0.4Fe2O4 ferrite2000213330931110.1016/S0304-8853(99)00806-9RaoK. H.RajuS. B.AggarwalK.MendirattaR. G.Effect of Cr impurity on the dc resistivity of Mn-Zn ferrites19815231376137910.1063/1.329768GlobusA.PascardH.CaganV.Distance between magnetic ions and fundamental properties in ferrites197738C116316810.1051/jphyscol:1977132BrandR. A.Laboratorium für Angewandte Physik, Universität Duisburg, Lotharstr 1, D-4100 Duisburg 1, Germany