Sol–gel synthesis of Cr 3+ substituted Li 0.5Fe 2.5O 4: Cation distribution, structural and magnetic properties

Li0.5CrxFe2.5−xO4 powders with fine sized particles were successfully synthesized by sol–gel auto combustion, using lithium nitrate, ferric nitrate, chromium nitrate, and citric acid as the starting materials. The process takes only a few minutes to
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  Materials Chemistry and Physics 126 (2011) 755–760 Contents lists available at ScienceDirect MaterialsChemistryandPhysics  journal homepage: Sol–gel synthesis of Cr 3+ substituted Li 0.5 Fe 2.5 O 4 : Cation distribution, structuraland magnetic properties D.R. Mane a , Swati Patil a , D.D. Birajdar a , A.B. Kadam b , Sagar E. Shirsath c , ∗ , R.H. Kadam d a Department of Physics, Balbhim College, Beed (M.S.), India b Department of Physics, Jawahar Mahavidyalaya, Andoor 413 606 (M.S.), India c Department of Physics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431 004 (M.S.), India d Materials Science Research Lab, Shrikrishna Mahavidyalaya Gunjoti, Osmanabad (M.S.), India a r t i c l e i n f o  Article history: Received 4 July 2010Received in revised form24 November 2010Accepted 13 December 2010 PACS: 75.50.Gg73.63.Bd91.60.Pn Keywords: A. Magnetic materialsB. Chemical synthesisC. TGA–DTAD. Magnetic properties a b s t r a c t Li 0.5 Cr  x Fe 2.5 −  x O 4  powders with fine sized particles were successfully synthesized by sol–gel auto com-bustion, using lithium nitrate, ferric nitrate, chromium nitrate, and citric acid as the starting materials.The process takes only a few minutes to obtain as-prepared Cr-substituted lithium ferrite powders. Theresultant powders were annealed at 600 ◦ C for 4h and investigated by thermogravimeter/differentialthermal analyzer (TG/DTA), X-ray diffractometer (XRD) and vibrating sample magnetometer (VSM). Lat-tice parameter, bulk density and particle size are found to decrease with increasing Cr concentration,whereas X-ray density and porosity showed an increasing trend with the Cr content. Cation distribu-tion indicates that the chromium ion occupy octahedral B-site. The magnetic moments calculated fromNeel’s molecular field model are in agreement in the experiment result, which indicates that the satura-tion magnetization decreases linearly from 37.36 to 4.27emu/g with increasing Cr 3+ content. However,coercivity, it increases with the Cr 3+ substitution. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Theattractivefeaturesoflithiumferrite,suchashighCurietem-perature,highsaturationmagnetizationandsquarehysteresislooppropertiesoffermanyadvantagesoverotherspinelferritesusedinmicrowave and memory core applications [1]. Lithium ferrite is a low-cost substitute to the garnet based materials for microwaveapplications [2,3] and is a promising candidate for cathode mate- rials in rechargeable lithium batteries [4,5]. They are based on the inverse spinel structure with lithium and three-fifths of the totalFe 3+ occupying octahedral sites [6]. Two separate crystallographic forms of Li 0.5 Fe 2.5 O 4  have been isolated; a superstructured formin which the lithium and iron atoms are ordered [7,8] and a dis- ordered form in which lithium and iron have a random statisticaldistribution over all the octahedral positions [9,10].Traditionalsynthesisofferritematerialshasinvolved12ormoresteps, including multiple milling and firing stages [11,12]. Some improvements on the traditional approach has been achieved byprecipitation and hydrothermal synthesis [9,10]. It is well known ∗  Corresponding author. Tel.: +91 2402240950; fax: +91 2402240951. E-mail address: (S.E. Shirsath). thatlow-temperaturesinteringofferritescanbeachievedbyusingactive ultrafine powders synthesized via a wet-chemical method.Amongthewet-chemicaltechniques,sol–gelautocombustionsyn-thesis has proved to be a simple and economic way to preparenanoscale powders [13]. In this technique, a thermally induced anionicredoxreactiontakesplace.Theenergyfromtheexothermicreactionbetweenoxidantandreductantcanbehighenoughtoforma desirable phase within a very short time. In our previous works[14] we have synthesized nanocrystalline CoFe 2 O 4  ferrites usingauto-combustion of nitrate–citrate gel, in which nitrates providedmetal ions and citric acid acted as chelating agent.The effect of replacement of Fe 3+ ions by Cr 3+ ion have beenstudied by various workers [15,16]. Lee et al. studied the magnetic properties and showed magnetic moment and Curie tempera-ture decreases with Cr 3+ substitution [17]. Magnetic properties like remanance and coercivity which are of utmost technologicalimportance could be modified and controlled by Cr 3+ substitution[18].Inaddition,thepropertiesoflithiumferritesarepredominantlygoverned by amounts of substitution and the type and the distri-bution of cations on tetrahedral and octahedral sites. Therefore,appropriate amounts of chromium were added to tailor the prop-erties of lithium ferrites. In the present work, we focus on the 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.12.048  756  D.R. Mane et al. / Materials Chemistry and Physics 126 (2011) 755–760 synthesis of Cr 3+ substituted Li 0.5 Fe 2.5 O 4  (  x =0.0–1.0 in steps of   x =0.2) ferrite powders by the sol–gel auto-combustion technique.In this paper, we report on the synthesis process, characterization,cationdistributionandthemagneticpropertiesofsinteredferritesfrom the nanosized powders. 2. Experimental Nanocrystalline powder of Li 0.5 Cr  x Fe 2 −  x O 4  were prepared by sol–gel auto-combustionmethod.TheA.R.gradecitricacid(C 6 H 8 O 7 · H 2 O),lithiumnitrateLiNO 3 ,chromium nitrate (Cr(NO 3 ) 3 · 9H 2 O) and ferric nitrate Fe(NO 3 ) 3 · 9H 2 O were used asstarting materials. Synthesis was carried out in air atmosphere without protectingby any inert gases. The molar ratio of metal nitrates to citric acid was taken as 1:3.The metal nitrates were dissolved together in a minimum amount of double dis-tilled water to get a clear solution. An aqueous solution of citric acid was mixedwithmetalnitratessolution,thenammoniasolutionwasslowlyaddedtoadjustthepH at 7. The mixed solution was kept on to a hot plate with continuous stirring at90 ◦ C. During evaporation, the solution became viscous and finally formed a veryviscous brown gel. When finally all water molecules were removed from the mix-ture,theviscousgelbeganfrothing.Afterfewminutes,thegelautomaticallyignitedandburntwithglowingflints.Thedecompositionreactionwouldnotstopbeforeallof the citrate complex was consumed. The auto-combustion was completed withinaminute,yieldingthebrown-coloredashestermedasaprecursor.Preparedpowderwas then annealed at 600 ◦ C for 4h.  2.1. Structural and magnetic characterization The dried gels were characterized via thermogravimetric (TGA) and differentialthermalanalysis(DTA)ataheatingrateof10 ◦ C/mininairatmosphere.Thesampleswere powdered for X-ray investigations. Part of the powder was X-ray examinedby Phillips X-ray diffractometer (Model 3710) using Cu-K   radiation (  =1.5405 ˚A).The scanning step was 0.02 ◦  and scanning rate was 2 ◦ /min. 1D detector was usedfor the XRD measurement. The X-ray generator was operated at 40kV and 30mA.A specially processed Si powder sample was used for instrumental standard. The(111) reflection of Si at around 28.5 ◦  indicates that the instrumental broadening isvery small (0.5 ˚A).Magnetic measurements were performed at room temperature using a com-mercialPARCEG&GvibratingsamplemagnetometerVSM4500.Magnetichysteresisloops were measured at room temperature with maximum applied magnetic fieldsup to 0.5T. Magnetic field sweep rate was 5Oe/s for all measurements. Hencemeasurement of hysteresis loops with maximum field of 0.5T took about 2h. Thesamples prepared in powder form were fixed in paraffin in order to exclude themotion of powder in a measuring cap. 3. Results and discussion  3.1. Structural properties In order to determine the possible temperature of decompo-sition, crystallization and phase transformation of as-preparedpowderswasstudiedusingDTA/TGAmeasurementsforthetypicalcomposition Li 0.5 Cr 0.4 Fe 2.1 O 4  in air atmosphere, the temperaturerange was 20–700 ◦ C with a heating rate of 10 ◦ C/min. Fig. 1 shows the DTA/TGA curves for as-prepared Li 0.5 Cr 0.4 Fe 2.1 O 4  powders.The TG data of as-prepared Li 0.5 Cr 0.4 Fe 2.1 O 4  powder prepared bysol–gelcombustionyieldthreestepsfrom25to700 ◦ C.Firststepisfrom room temperature to 380 ◦ C, which is ascribed to the vapor-izationofabsorbedwater.Secondstepisfrom380to600 ◦ C,whichis associated with the residual organic matter including citric acid.The weight loss below 600 ◦ C is due to loss of absorbed waterand the decomposition of organic derivatives. Third step is above600 ◦ C, due to weight loss of as received Li 0.5 Cr 0.4 Fe 2.1 O 4  powder.It indicates that the unreacted metal nitrate is oxidized in thisstep. Moreover, the DTA curve does not show any endothermic orexothermic peaks in the whole temperature range.Fig. 2 represents X-ray powder diffraction patterns of Li 0.5 Cr  x Fe 2.5 −  x O 4  (  x =0.0–1.0 in steps of   x =0.2) for all the samples.It is pertinent to note that superstructure lines were observed inthe XRD pattern (Fig. 2). The superstructures peaks such as (210), (211), (310), (320), (421) are evidence that this sample hasorderedspineltypestructure.Thesesuperstructurelinesarisefromordering of the lithium sublattice and are seen for conventionally 0 100 200 300 400 500 600 700 Temperature (ºC) 1.301.351.401.451.501.551.601.65    D   T   A   (  µ   V   ) T  GA (  m g )   Fig. 1.  TGA/DTA curve of the typical sample (  x =0.4). preparedmaterialsthathavereachedthermodynamicequilibrium[7,8]. Metastable, disordered Li 0.5 Cr  x Fe 2.5 −  x O 4  has been isolatedpreviously by quench techniques [19]. In this material the lithium atomsaredisorderedwithastatisticaldistributionovertheoctahe-dralsitesandsuperstructurelinesarenotobserved.Athigherlevelsof chromium substitution no superstructure lines were observed(Fig.2).Thisindicatesthatthechromiumismostlikelystatistically disordered within the structure and disrupts the ordered lithiumarrangements.Latticeconstant( a )measurement(Fig.3)showsthedecreasein latticeconstantasincreaseinCrcontent  x .Thisunitcellsizevaria-tion could be attributed to the ionic radius of six-fold-coordinatedCr 3+ (0.63 ˚A) being smaller than that of six-fold-coordinated Fe 3+ (0.67 ˚A) [20]. When doped with smaller sized Cr 3+ ions, the spinellithium ferrite will shrink. Doping Cr 3+ ions in a spinel type struc-ture will induce uniform strain in the lattice as the material iselastically deformed. This effect causes the lattice plane spacingto change and the diffraction peaks shift to a higher 2    position.The values of X-ray density ( d x ) have been calculated from themolecular weight and the volume of the unit cell. The variationof X-ray density with Cr content is depicted in Fig. 3. It is evi- dent from Fig. 3 that X-ray density increases with increase in Cr 203040506070 (f)(e)(d)(c)(b)(a)         (        3        1        0        )        (        3        2        0        )        (        2        2        2        )        (        4        2        1        )        (        2        1        1        )        (        2        1        0        )        (        4        4        0        )        (       5        1        1        )        (        4        2        2        )        (        4        0        0        )        (        3        1        1        )        (        2        2        0        )      I  n   t  e  n  s   i   t  y   (  r  a   b .  u  n   i   t   ) 2 θ (degree) Fig.2.  X-raypowderdiffractionforLi 0.5 Cr  x Fe 2.5 −  x O 4 :(a)  x =0.0,(b)  x =0.2,(c)  x =0.4,(d)  i =0.6, (e)  x =0.8 and (f)  x =1.0.  D.R. Mane et al. / Materials Chemistry and Physics 126 (2011) 755–760 757 0.0 0.2 0.4 0.6 0.8 Cr Content x    L  a   t   t   i  c  e  c  o  n  s   t  a  n   t   '  a   '   (   ) 4.764.784.804.82 X-r  a  y d  e n s i   t   y'   d  x '   (   gm /   c m  3   )   Fig. 3.  Variation of lattice constant ‘ a ’ and X-ray density ‘ d x ’ with Cr content  x . content  x , which is related to the decrease in lattice constant withincrease in Cr content  x . The average particle size for each samplewasestimatedusingtheScherrerformula[21]consideringthemost intense peak (311). The particle size is decreases for 35–21nmwith increasing Cr content  x . The increase in broadening of XRDpatterns with increase in Cr substitution confirms the decrease inparticlesize.Thebulkdensity‘ d B ’ofthespecimenshasbeendeter-mined by the Archimedes’s principal [22]. The values of the bulk densityareshowninFig.4.Thebulkdensitywasfoundtodecrease with Cr content  x . In the present series the molecular weight of Li 0.5 Fe 2.5 O 4  spinel ferrite decreases with Cr substitution and vol-ume of the unit cell also decreases, but the rate of decrease of molecular weight is more than that of volume. Therefore, the bulkdensity decreases with Cr substitution in the present case. This ledto increase in porosity. The percentage porosity ‘ P  ’ of the samplewas calculated using the values of X-ray density and bulk density.It is clear from Fig. 4 that density of the samples decreases andthe porosity increases with increase in Cr content  x . The increasein porosity is may also be due the decrease in particle size, whichincreases the grain boundaries of the particle and accordingly theincreaseinporosity.Thehighvaluesofporosityindicatetheporousstructure of the prepared samples of Li–Cr–Fe spinel ferrite.The hopping length for tetrahedral A-site ( L A ) and octahedralB-sites ( L B ) are calculated using the values of lattice constant. Thevariation of hopping lengths with Cr content  x  is shown in Fig. 5. It isobservedfromFig.5thatthedistancebetweenthemagneticions (hoppinglength)decreasesasCrcontent  x increases.Thisbehaviorof hopping length with  x  is analogous with behavior of ‘ a ’ with  x ,and may attributed to the deference in the ionic radii of the con- 0.0 0.2 0.4 0.6 0.8  d B  P Cr content x    B  u   l   k   d  e  n  s   i   t  y   '   d    B    '    (  g  m   /  c  m    3    ) 81012 P  or  o s i   t   y'  P '    (   % )   Fig. 4.  Variation of bulk density ‘ d B ’ and porosity ‘ P  ’ with Cr content  x .  L  A  L B Cr content x    L    A    (    Å   ) 2.9282.9322.9362.9402.944 L  B    (  Å  )   Fig. 5.  Variation of   L A  and  L B  with Cr content  x . stituentions,whichmakesthemagneticionsbecomeclosertoeachother and the hopping length decreases. Using the experimentalvalues of lattice constant ‘ a ’ and oxygen positional parameter ‘ u ’and substituting it into equations discussed elsewhere [23]. Tetra- hedral and octahedral bond length ( d Ax  and  d Bx ), tetrahedral edge,shared and unshared octahedral edge ( d AXE ,  d BXE  and  d BXEU ) werecalculated and the values are given in Table 1. It is observed that thealliedparameterdecreasesasCrcontent  x increases.Thiscouldbe related to the smaller radius of Cr 3+ ions as compared to Fe 3+ ions and the site occupancy of the constituent ions in the presentferrite system.  3.2. Cation distribution The cation distribution in the present system was obtainedfrom the analysis of X-ray diffraction patterns. In this method theobservedintensityratioswerecomparedwiththecalculatedinten-sity ratios. In the present study Bertaut method [24] is used to determine the cation distribution. This method selects a few pairsof reflections according to the expression I  Obs .hkl I  Obs .h ′ k ′ l ′ ∝ I  Calc .hkl I  Calc .h ′ k ′ l ′ (1)where I  Obs .hkl  and I  Calc .hkl  aretheobservedandcalculatedintensitiesforreflection ( hkl ), respectively. In this method the best informationon cation distribution is achieved when comparing experimentaland calculated intensity ratios for reflections whose intensities (i)are nearly independent of the oxygen parameter, (ii) vary with thecation distribution in opposite ways and (iii) do not differ signifi-cantly.In the present work (220), (400), (440) were used to calcu-late intensity ratio. These planes are assumed to be sensitive tothecationdistribution.Thetemperatureandabsorptionfactorsarenot taken into account in our calculations as they do not affectthe intensity calculation. If an agreement factor ( R ) is defined as  Table 1 Tetrahedralbond( d Ax ),octahedralbond( d Bx ),tetraedge( d AXE )andoctaedge(shared d BXE  and unshared  d BXEU ). The error estimate is ( ± 0.002 ˚A).  x d Ax  (Å)  d Bx  (Å) Tetra edge (Å) Octa edge (Å) d AXE  d BXE  d BXEU 0 1.890 2.036 3.086 2.803 2.9520.2 1.888 2.034 3.083 2.801 2.9500.4 1.886 2.031 3.079 2.797 2.9460.6 1.884 2.029 3.076 2.794 2.9430.8 1.881 2.027 3.072 2.791 2.9391 1.879 2.024 3.068 2.787 2.935  758  D.R. Mane et al. / Materials Chemistry and Physics 126 (2011) 755–760  Table 2 Cation distribution and X-ray intensity ratio of Li 0.5 Cr  x Fe 2 − 2  x O 4 .  x  Cation distribution a Intensity ratioA-Site B-Site  I  (220) / I  (400)  I  (400) / I  (440)  I  (220) / I  (440) Obs. Cal Obs. Cal Obs. Cal0.0 (Fe 1.0 ) [Li 0.5 Fe 1.5 ] O 4  1.809 1.721 1.706 1.899 1.797 2.0170.2 (Li 0.01 Fe 0.99 ) [Li 0.49 Cr 0.2 Fe 1.31 ] O 4  2.702 2.541 2.519 2.712 2.656 2.9780.4 (Li 0.02 Fe 0.98 ) [Li 0.48 Cr 0.4 Fe 1.12 ] O 4  1.769 1.632 1.558 1.619 1.657 1.7460.6 (Li 0.03 Fe 0.97 ) [Li 0.47 Cr 0.6 Fe 0.93 ] O 4  2.551 2.803 2.412 2.690 2.539 2.8450.8 (Li 0.04 Fe 0.96 ) [Li 0.46 Cr 0.8 Fe 0.74 ] O 4  2.680 2.425 2.276 2.308 2.298 2.3091.0 (Li 0.05 Fe 0.95 ) [Li 0.45 Cr 1.0 Fe 0.55 ] O 4  2.009 1.701 1.495 1.557 1.493 1.512 a The error estimate is ( ± 0.004). in Eq. (2), the best-simulated structure which matches the actual structure of the sample will lead to a minimum value of   R  and thecorrespondingcationdistributionisobtainedforeach hkl and h ′ k ′ l ′ reflection pair considered. R =   I  Obs .hkl I  Obs .h ′ k ′ l ′  −  I  Calc .hkl I  Calc .h ′ k ′ l ′  (2)The intensities of these are nearly independent of the oxygenparameters. The calculations were made for various combinationsof cations.Todeterminethecationdistributionanditsvariationwithcom-position,itisnecessarytocalculateforeachcompositiontheabovementionedintensityratiosexpectedforgivenarrangementsofthecations and compare them with the experimental values. For thecalculationoftherelativeintegratedintensityofagivendiffractionline from powder specimens as observed in a diffractometer witha flat-plate sample holder, the following formula is valid I  hkl  =  F   2 hkl P  · L P  (3)where  F   is structure factor,  P   is multiplicity factor,  L P  the Lorentzpolarization factor and L P  = 1 + cos 2 2   sin 2 cos 2 2   (4)The atomic scattering factor for various ions was taken from theliterature [25].It should be added that the calculated integrated intensities arevalidat0K.Sincetheobservedvaluesareobtainedatroomtemper-ature, a suitable correction is in principle necessary for the precisecomparison. However, the spinels are high-melting compounds,thethermalvibrationoftheatomsatroomtemperatureshouldnotdiffergreatlyfromthatatabsolutezero.Therefore,inourintensitycalculations no temperature correction was deemed necessary.The cation distribution for each concentration and the sitepreferences of cations distributed among tetrahedral A-site andoctahedral B-site showing the fraction of Li and Fe 3+ ions on eithersites are listed in Table 2. It is known that the Cr 3+ preferentiallyreplacesFe 3+ fromoctahedralsitesbecauseoffavorablecrystalfieldeffects (Cr 3+ 6/5  0 , Cr 3+ 0  0 ) [7]. It can be seen that Cr 3+ ions pre-dominately occupy the octahedral sites, which is consistent withthepreferenceforlargeoctahedralsiteenergy.WithincreasingCr 3+ content, the fraction Cr 3+ ions in octahedral sites increases, whileFe 3+ ions in octahedral sites decreases linearly.The mean ionic radius of the tetrahedral (A) ‘ r  A ’ and octahedral[B] site ‘ r  B ’ can be calculated by modifying the relation discussedelsewhere [1]. Using the values of ‘ a ’, the radius of oxygen ion R 0 =1.32 ˚Aand r  A  inthefollowingexpression,theoxygenpositionalparameter ‘ u ’ can be calculated, r  A  =  u − 14  a √  3 − R 0  (5)The oxygen parameter  u  is a quantitative measure of the dis-placement of an oxygen ion due to substitution of a metal cationinto the tetrahedral (A) site. The relation between oxygen posi-tion parameter ( u ), mean ionic radius of the A-site ( r  A ) and of theB-site ( r  B ) with Cr is shown in Fig. 6. The decrease in ‘ r  B ’ may bedue to the increasingly occupation of the smaller ionic radii of Cr 3+ (0.63 ˚A) ions to the B-sites instead of Fe 3+ (0.67 ˚A) ions. Theslow increase in  r  A  is due the migration of Li (0.78 ˚A) from B-siteto A-site. ‘ u ’ decreases as a function of   x , the decrease of ‘ u ’ is adirect consequence of increasing the trigonal distortion of the B-siteoxygencoordination.IncreasingthemigrationoftheLiionsintothe A-sublattice makes it expand to accommodate these ions. ThisexpansioncreatesoxygenvacanciesintheA-sites,whichincreasesthe trigonal distortion of the B-site oxygen coordination. This isreflected in the obtained high values of ‘ u ’, where the ideal value is0.381 ˚A.  3.3. Magnetic properties Introduction of Cr 3+ ions into lithium ferrite greatly affects themagnetic properties. Fig. 7 shows the plots of hysteresis loops for Li 0.5 Cr  x Fe 2.5 −  x O 4  specimens. This figure indicates that the lithiumferrite is a soft magnetic material, which revealed minimal hys-teresis. The magnetic moment in ferrite is mainly due to theuncompensated electron spin of the individual ion and the spinalignmentsinthetwosublatticeswhicharearrangedantiparallely.In a spinel ferrite, each ion at A site has 12 B-site ions as near-est neighbors. According to Neel’s molecular field model [26], the A–B super exchange interaction predominate the intrasublatticeA–A and B–B interactions. Therefore, the net magnetic momentis given by the sum of the magnetic moments of A and B sublat-tices, i.e.,  M  S = M  B − M  A . For chromium-substituted lithium ferrite,Li + substitutionforFe 3+ ionsatAsite,leadingtoadecreaseintheAsite sublattice magnetization. Moreover, the Fe 3+ ions are replaced 0.0 0.2 0.4 0.6 0.8 1.00.670.680.690.70    r A  r B  u Cr Content x    I  o  n   i  c  r  a   d   i   i   (    Å   ) 0.38650.38700.38750.3880  Ox  y  g en p ar  am e t   er '   u'    (  Å  )   Fig. 6.  Variation of ionic radii of A site ( r  A ), B-site ( r  B ) and oxygen parameter ( u )with Cr content  x .  D.R. Mane et al. / Materials Chemistry and Physics 126 (2011) 755–760 759 -4000-2000020004000-40-30-20-10010203040    M  a  g  n  e   t   i  z  a   t   i  o  n   '   M    S    '    (  e  m  u   /  g   )  Applied field (Oe) (f)(e)(d)(c)(b)   (a) Fig.7.  Variationofmagnetizationwithappliedfield:(a)  x =0.0,(b)  x =0.2,(c)  x =0.4,(d)  x =0.6, (e)  x =0.8 and (f)  x =1.0. by non-magnetic Li + and Cr 3+ ions, leading to a decrease in the Bsitesublatticemagnetization.Therefore,themagnetizationofbothsublattices decreases. The decrease of the B site magnetization isstrongerthanoneofAsite,whichleadstoafallinthenetmagneti-zation. For example, we use the known magnetic moments for Li + (0  B ) and Fe 3+ (5  B ). For Li 0.5 Fe 2.5 O 4 :  M  S   =  M  B  −  M  A  = (0 . 5 × 0 + 1 . 5 × 5)  B − (1 × 5)  B =  2 . 5  B  = 69 . 8Am 2 /kgThis value of magnetization is agrees well with the experi-mentally extrapolated value [27], thus proving the collinear nature of the pure ferrite. Using the cationic distribution of Cr 3+ substituted Li 0.5 Fe 2.5 O 4  (Table 2) and the fact that mag- netic moment of Cr 3+ is 3  B , the Neel’s model leads to a fallin the net magnetization per formula unit. For Li 0.5 Cr 0.4 Fe 2.1 O 4 :  M  S  =  M  B  −  M  A  = (0.48 × 0 + 0.4 × 3 + 1.12 × 5)  B − (0.02 × 0 + 0.98 × 5)  B  = 1.9  B  = 31.27Am 2 /kg.Thisvalueismuchlowerthan that of pure Li 0.5 Fe 2.5 O 4  calculated above. With increasingCr 3+ ions content in chromium-substituted lithium ferrite, thenet magnetization decreased gradually. The magnetic momentscalculated from Neel’s molecular field model are in agreement inthe experiment result, which indicates that the saturation magne-tization decreases monotonically with increasing Cr substitutioncontent. The values of saturation magnetization ( M  S ) decreasefrom 37.36 (Li 0.5 Fe 2.5 O 4 ) to 4.27emu/g (Li 0.5 Cr 1.0 Fe 1.5 O 4 ) (Fig. 8). The observed magnetic moment per formula unit in Bohrmagneton(  B )wascalculatedbyusingtherelationdiscussedelse-where [28]. It is observed from Fig. 9 that, both calculated and observed values of magneton number decreases with increase inCr content  x , suggesting that the structure is collinear [26]. It has been a established fact that the tetrahedral and octahedral sublat-tices of ferrite may be subdivided in such a way that the vectorresultant of the magnetic moments of the sublattices are alignedin such a direction that will influence the effective magnetization.Thus the drastic decrease in magnetization could be explained onthebasisofcollinearspinarrangementaroseduetosubstitutionof Cr ions.The coercive force ( H  C ) is an independent parameter, whichcan be altered by heat treatment or deformation and hence is notdependent on saturation magnetization. In this study, the coerciveforces tend to rise in increasing Cr substitution content, in whichthe values of coercive force varied in the range of 136.9–151.0Oe(Fig. 8). It is clearly observed from Fig. 8 that the coercivity ( H  C )    M  a  g  n  e   t   i  z  a   t   i  o  n   '   M    S    '    (  e  m  u   /  g   ) Cr content x  Ms H C 135138141144147150153  C  o er  c i  v i   t   y '  H  C  '    (   O e )   Fig. 8.  Variation of saturation magnetization and coercivity with Cr content  x . 0.0 0.2 0.4 0.6 0.8 1.00123    M  a  g  n  e   t  o  n  n  u  m   b  e  r   '  n    B    '    (      µ    B    ) Cr content x  Cal. Obs. Fig. 9.  Variation of observed and calculated magnetic moment with Cr content  x . increases as Cr 3+ content  x  increases, this behavior is similar tothat of porosity. Porosity affects magnetization process becausepores work as a generator of demagnetizing field. As the poros-ityincreaseshighfieldisneededtopushthedomainwallandthus H  C  increases.Thesaturationmagnetizationisrelatedto H  C  throughBrown’s relation [29], H  C  = 2 K  1  0 M  S (6)where  K  1  is anisotropy constant,  0  is permeability,  M  S  is magne-tizationand H  C  iscoercivity.Accordingtothisrelation H  C  inverselyproportionalto M  S ,thisisconsistentwithourexperimentalresults.The remanent magnetization ( M  r ) is also an independent param-eter since it is not wholly dependent on saturation magnetization( M  S )andcoerciveforce( H  C ).Thevaluesofremanentmagnetizationvaried in the range of 9.5–1.16emu/g. 4. Conclusions Ultrafine crystals of Cr 3+ substituted Li 0.5 Fe 2.5 O 4  ferrite areprepared at a relatively low temperature (600 ◦ C) via sol–gelauto combustion route. It was found that Cr 3+ ions are easilyincorporated into the lattice of the ferrites and do not inducecrystal-structure changes. Experimental results revealed that thelattice constant and cell volume decrease with the increasing of 
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