Al and PEG Effect on Structural and Physicochemical Properties of CoFe<sub>2</sub>O<sub>4</sub>

Mostaghni, Fatemeh; Abed, Yasaman

doi:10.1590/1980-5373-MR-2016-0912

Abstract

In this work, pure and Alumina doped cobalt ferrite nanoparticles CoFe_2−xAl_xO₄ (for x = 0.44) have been synthesized by the sol gel method. The influence of alumina doping on the morphological and mechanical properties of CoFe₂O₄ nano-particles were investigated by means of X-ray powder diffraction (XRD) and rietveld analysis. XRD analysis confirmed that the single phase formation of pure nano particles with the expected cubic inverse spinel structure with Fd3m space group and without any impurity phase. Alumina doping were led to a decrease in the crystallite size, lattice parameter, elastic constants and magnitude of moduli. It is explained on the basis of the replacement of Fe ions with half-filled d-shell (3d⁵) and larger radius by Al³⁺ ions with a completely filled shell (2p⁶) and smaller radius.

Keywords:
Spinels; Ferrite; Cobalt ferrite; Rietveld Refinement

1. Introduction

Spinels of the type AB₂X₄ are one of the most interesting and important families of crystalline compounds due to their broad applications in magnetic materials, ceramics, catalysis, etc. Spinels of the type A²⁺B³⁺ ₂O₄ belong to a large group of composite oxides with a cubic symmetry (space group Fd3m), where A and B are cations with variable valence. In natural spinels usually A represents divalent cation, while B represents trivalent cation (A²⁺B³⁺ ₂O₄, so-called 2-3 spinels).¹1 O'Handley RC. Modern Magnetic Materials - Principles and Applications. Hoboken: John Wiley & Sons; 2000.

2 Buschow KHJ, ed. Handbook of Magnetic Materials, Vol. 19. Amsterdam: Elsevier, North Holland; 2011.^-³3 Sun S, Zeng H, Robinson DB, Raoux S, Rice PM, Wang SX, et al. Monodisperse MFe2O4 (M= Fe, Co, Mn) Nanoparticles. Journal of American Chemical Society. 2004;126(1):273-279.

Among spinel composite oxides, spinel ferrite nanoparticles have been studied for many years due to their magnetic and electrical properties. In particular, the CoFe₂O₄ has covered a broad applications including electronic devices, ferrofluids, magnetic drug delivery, microwave devices and high density information storage.⁴4 Amstad E, Textor M, Reimhult E. Stabilization and functionalization of iron oxide nanoparticles for biomedical applications. Nanoscale. 2011;3(7):2819-2843.

5 Desantis C, Siegel R, Bandi P, Jemal A. Breast cancer statistics, 2011. CA: A Cancer Journal for Clinicians. 2011;61(6):409-418.

6 Chen J. High Temperature Polyol Synthesis of Super paramagnetic CoFe2O4 Nanoparticles for Magnetic Resonance imaging Contrast agents. Journal of Inorganic Materials. 2009;24(5):967-972.

7 Bixner O, Lassenberger A, Baurech D, Reimhult E. Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles. Langmuir. 2015;31(33):9198-9204.

8 Grunewald TA, Lassenberger A, van Ostrum PDJ, Rennhofer H, Zirbs R, Capone B, et al. Core-Shell Structure of Monodisperse Poly(ethylene glycol)-Grafted Iron Oxide Nanoparticles Studied by Small-Angle X-ray Scattering. Chemistry of Materials. 2015;27(13):4763-4771.^-⁹9 Kurzhals S, Zirbs R, Reimhult E. Synthesis and Magneto-Thermal Actuation of Iron Oxide Core-PNIPAM Shell Nanoparticles. ACS Applied Materials & Interfaces. 2015;7(34):19342-19352. Cobalt ferrite (CoFe₂O₄) is one of the well known hard magnetic materials which has strong magnetic anisotropy, high magnetostriction, moderate magnetization, high coercivity at room temperature and high chemical stability and good electrical insulation.¹⁰10 El-Shobaky GA, Turky AM, Mostafa NY, Mohamed SK. Effect of preparation conditions on physicochemical, surface and catalytic properties of cobalt ferrite prepared by coprecipitation. Journal of Alloys and Compounds. 2010;493(1-2):415422.

11 Scheffe JR, Allendorf MD, Coker EN, Jacobs BW, McDaniel AH, Weimer AW. Hydrogen Production via Chemical Looping Redox Cycles Using Atomic Layer Deposition-Synthesized Iron Oxide and Cobalt Ferrites. Chemistry of Materials. 2011;23(8):2030-2038.

12 Pervaiz E, Gul IH, Anwar H. Hydrothermal Synthesis and Characterization of CoFe2O4 Nanoparticles and Nanorods. Journal of Superconductivity and Novel Magnetism. 2013;26(2):415-424.^-¹³13 Kurtan U, Topkaya R, Baykal A, Toprak MS. Temperature dependent magnetic properties of CoFe2O4/CTAB nanocomposite synthesized by sol-gel auto-combustion technique. Ceramics International. 2013;39(6):6551-6558. There are different methods which have been reported for the preparation of magnetic nanoparticles of cobalt ferrite.¹⁴14 Sinkó K, Manek E, Meiszterics A, Havancsák K, Vainio U, Peterlik H. Liquid-phase syntheses of cobalt ferrite nanoparticles. Journal of Nanoparticle Research. 2012;14:894-908.

15 Jiang G, Chang Q, Yang F, Hu X, Tang H. Sono-assisted preparation of magnetic ferroferric oxide/graphene oxide nanoparticles and application on dye removal. Chinese Journal of Chemical Engineering. 2015;23(3):510-515.

16 Liu Q, Sun J, Long H, Sun X, Zhong X, Xu Z. Hydrothermal synthesis of CoFe2O4 nanoplates and nanoparticles. Materials Chemistry and Physics. 2008;108(2-3):269-273.^-¹⁷17 Freitas JC, Branco RM, Lisboa IGO, Costa TP, Campos MGN, Jafelicci Júnior M, et al. Magnetic Nanoparticles Obtained by Homogeneous Coprecipitation Sonochemically Assisted. Materials Research. 2015;18(Suppl. 2):220-224.

Cobalt ferrite is a partially inverse spinel with formula (Co_x Fe_1-x)[Co_1-x Fe_1+x]O₄, formed by oxygen atoms in a closed packing structure where, Co²⁺ and Fe³⁺ occupy either tetrahedral or octahedral sites.¹⁸18 Ahmed MA, El-Khawlani AA. Enhancement of the crystal size and magnetic properties of Mg-substituted Co ferrite. Journal of Magnetism and Magnetic Materials. 2009;321(13):1959-1963.

19 Rana S, Philip J, Raj B. Micelle based synthesis of cobalt ferrite nanoparticles and its characterization using Fourier Transform Infrared Transmission Spectrometry and Thermogravimetry. Materials Chemistry and Physics. 2010;124(1):264-269.

20 Ayyappan S, Mahadevan SP, Chandramohan P, Srinivasan MP, Philip J, Raj B. Influence of Co2+ Ion Concentration on the Size, Magnetic Properties, and Purity of CoFe2O4 Spinel Ferrite Nanoparticles. The Journal of Physical Chemistry C. 2010;114(14):6334-6341.

21 Meng YY, Liu ZW, Dai HC, Yu HY, Zeng DC, Shukla S, et al. Structure and magnetic properties of Mn(Zn)Fe2-xRExO4 ferrite nano-powders synthesized by co-precipitation and refluxing method. Journal of Powder Technology. 2012;229:270-275.^-²²22 Deraz NM. Glycine-assisted fabrication of nanocrystalline cobalt ferrite system. Journal of Analytical and Applied Pyrolysis. 2010;88(2):103-109. Several researchers have reported on Ti, Y, Gd, Pr, Zn, Ni and Dy doped cobalt ferrite.²³23 Shobana MK, Nam W, Choe H. Yttrium-doped cobalt nanoferrites prepared by sol-gel combustion method and its characterization. Journal of Nanoscience and Nanotechnology. 2013;13(5):3535-3538.

24 Chae KP, Lee JG, Kweon HS, Lee YB. The crystallographic, magnetic properties of Al, Ti doped CoFe2O4 powders grown by sol-gel method. Journal of Magnetism and Magnetic Materials. 2004;283(1):103-108.

25 Oliveira VD, Rubinger RM, Silva MR, Oliveira AF, Rodrigues G, Ribeiro VAS. Magnetic and Electrical Properties of MnxCu1-xFe2O4 Ferrite. Materials Research. 2016;19(4):786-790.

26 Panda RN, Shih JC, Chin TS. Magnetic properties of nano-crystalline Gd- or Pr-substituted CoFe2O4 synthesized by the citrate precursor technique. Journal of Magnetism and Magnetic Materials. 2003;257(1):79-86.

27 Kambale RC, Song KM, Koo VS, Hur N. Low temperature synthesis of nanocrystalline Dy3+ doped cobalt ferrite: Structural and magnetic properties. Journal of Applied Physics. 2011;110(5):053910.^-²⁸28 Wang L, Li FS. Mössbauer study of nanocrystalline Ni-Zn ferrite. Journal of Magnetism and Magnetic Materials. 2001;223(3):233-237.

The present work is focused on the effects of Al³⁺ doping on the structural, morphological and elastic properties of aluminium ion doped cobalt ferrite obtained via sol-gel method. The X-ray powder diffraction patterns, the microstructure and the elastic properties are discussed as a function of the Al³⁺ doping.

2. Materials and methods

2.1. Material

Iron (III) nitrate nonahydrate Fe(NO₃)₃.9H₂O, cobalt(II) nitrate hexahydrate Co(NO₃)₂.6H₂O and aluminium nitrate nonahydrate-Al(NO₃)₃∙9H₂O as source of metal ions and polyethylene glycol (average molecular weight: 4000, Qualigen) as a surfactant were used. The pH was controlled by amonium hydroxide NH₄OH. All reactants were purchased from Sigma-Aldrich. Deionized water served as reacting medium.

2.2. Synthesis of nanoparticles

Nanocrystalline powders of CoFe_2-xAl_xO₄ (x = 0, 0.4) were prepared by the sol-gel method. In a typical reaction, cobalt nitrate (Co(NO₃)₂.6H₂O), iron nitrate (Fe(NO₃)₃.9H₂O), and aluminum nitrate (Al(NO₃)₃.9H₂O) were individually dissolved in 10 ml of deionized water in their respective stoichiometry. The solutions were then mixed and stirred for 30 minutes at room temperature. In addition, polyethylene glycol (average molecular weight: 4000, Qualigen) served as a surfactant for this reaction and poured into the above mixture. Then, the 25% ammonia solution was added drop by drop and stirred vigorous on a magnetic stirrer. The final pH of the mixture was about 8. The resulting solution was kept under stirring at 60ºC for 1 hour. The obtained gels were dried at 80ºC and calcined at 500ºC for 3 hours.

Crystal structure of nanoparticles was determined by a Bruker make diffractometer, Cu-K_α X-rays of wavelength (λ=1.5406 Å). The XRD patterns were recorded in the 2θ range of 10-90º with a step width of 0.02 s^-1.

2.3. Simulation Analysis

The accelrys materials studio 6.0 visualisation package was used to create the nanoparticles. The X-ray diffraction (XRD) pattern was analysed with the help of reflex module by employing rietveld refinement technique. The XRD pattern of the pure and aluminia doped CoFe₂O₄ was refined using the Fd3m space group. The Castep module was employed to calculate the structural, electronic, and elastic properties of two samples. Generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof was used for all calculations.

3. Results and Discussion

3.1. X-Ray diffraction studies

X-ray diffraction pattern of synthesized aluminia doped and pure CoFe₂O₄ are presented in Figure. 1.

Figure 1
XRD pattern of synthesized CoFe₂O₄ and Al-dopped CoFe₂O₄

Peak details of synthesized nanoparticles sumerised in Table 1 and 2. The sharp and broad peaks in these XRD patterns, confirming the single phase formation of pure nano particles with the expected cubic inverse spinel structure with Fd3m space group and without any impurity phase. It can be observed that the intensities of the 220 planes increase and the intensity of 440 plane decrease with the addition of aluminium indicating the preference of the Co^2+, Fe³⁺ and Al³⁺ ions by the octahedral B and tetrahedral A sites. Indeed, this may be indicated the redistribution of the cations in the nanostructure aluminium cobalt ferrite. From this data it is evident that the ratio of Fe³⁺(oct.)/Fe³⁺ (tet.) changes with addition of Al³⁺ ion. In the present case the cubic phase spinel ferrite structure for two composition is mainly due to deficit of Co²⁺ ions in the octahedral sites(<85%) that leads to the absence of co-operative active Jahn-Teller distortion. The crystallite size of the nano-particles were calculated from the most intense peak (3 1 1) of XRD data using Debye-Scherer equation. The crystallite size of Al³⁺ doped and pure CoFe₂O₄ nano-particles were 18.9 and 24.3 nm respectively. The lattice constants of Al³⁺ doped and pure CoFe₂O₄, calculated from F(θ) were 8.22 and 8.32 repectively.

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Table 1
Peak analysis of XRD pattern of synthesized CoFe₂O₄

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Table 2
Peak analysis of XRD pattern of synthesized Al-dopped CoFe₂O₄

As can be seen, the crystallite size and lattice constant were decreased with alumina doping. Similar results have been reported in the literature.²⁹29 Xu S, Shangguan W, Yuan J, Chen M, Shi J. Preparation and Photocatalytic Properties of Magnetically Separable TiO2 Supported on Nickel Ferrite. Chinese Journal of Chemical Engineering. 2007;15(2):190-195.^,³⁰30 Yousefi MH, Manouchehri S, Arab A, Mozaffari M, Amiri GR, Amighian J. Preparation of cobalt-zinc ferrite (Co0.8Zn0.2Fe2O4) nanopowder via combustion method and investigation of its magnetic properties. Materials Research Bulletin. 2010;45(12):1792-1795. This behavior of the lattice constant with alumina doping is due to the replacement of larger Fe³⁺ ions (0.645 ºA) by smaller Al³⁺ ions (0.535 ºA) in the system.

The x-ray density (ρx) of the samples was determined using relation given by Smith and Wijn: ³¹31 Raghavender AT, Pajic D, Zadro K, Milekovic T, Venkateshwar Rao P, Jadhav KM, et al. Synthesis and magnetic properties of NiFe2-xAlxO4 nanoparticles. Journal of Magnetism and Magnetic Materials.2007;316(1):1-7.^,³²32 Smith J, Wijn HPJ. Ferrites. Eindhoven: Philips Technical Library; 1959.

(1)

ρ_{x} - \frac{8 M}{N_{A} a^{3}}

where, M is the molecular weight of the composition, N_A is the Avogadro's number and 'a' is the lattice constant. As there are 8 formula unit in the unit cell so 8 is included in the formula. The x-ray density (ρx) of alumina doped and pure CoFe₂O₄, were 3.605 and 3.746 g/cm³ repectively.

It can be observed that the x-ray density (ρx) decreased with alumina doping, because the decrease in molecular weight overtakes the decrease in volume of the unit cell.

3.2. Rietveld Analysis

Various structural parameters can be determined from rietveld analysis and are found useful to explain other physical properties.³³33 Louh R, Reynolds TG, Buchanan RC. Ferrite Ceramics. In: Buchanan RC, ed. Ceramic Materials for Electronics. 3rdEd. Boca Raton: CRC Press; 2004. This method is based on a least-squares fit between step-scan data of a measured diffraction pattern and a simulated X-ray-diffraction pattern.

In this study the crystalline structure of the pure and aluminia doped CoFe₂O₄ were analized in detailed by rietveld profile refinement method in reflex module. The XRD patterns for these samples have refined using the Fd3m space group (Figure 2).

Figure 2
Rietveld plot obtained by using the true instrumental function, a: CoFe₂O₄, b: Al_0.44CoFe_1.56O₄.

The fitting quality of the experimental data is assessed by computing the parameters R-pattern factor R_p and the weighted-profile factor R_wp.³⁴34 Young RA. Introduction to the Rietveld Method. In: Young RA, ed. The Rietveld Method. Oxford: Oxford University Press; 1993.

35 Polvakov NE, Leshina TV, Meteleva ES, Dushkin AV, Konovalova TA, Kispert LD. Enhancement of the Photocatalytic Activity of TiO2 Nanoparticles by Water-Soluble Complexes of Carotenoids. The Journal of Physical Chemistry B.2010;114(45):14200-14204.^-³⁶36 Young RA, ed. The Rietveld Method. Oxford: Oxford University Press; 1993. These factors are defined as:

(2)

R_{Wp} - {[\frac{\sum_{i} {(I_{0} - I_{c})}^{2} w_{i}}{\sum_{i} I_{0}^{2} w_{i}}]}^{2} \cdot

(3)

R_{p} - \frac{\sum_{i} |y_{io} - y_{ic}|}{\sum_{i} y_{io}}

Where Io and Ic are respectively observed and calculated integrated Bragg intensities (without background). R_p and R_wp values for pure and aluminia doped CoFe₂O₄ were (6.01, 9.27) and (6.91, 9.30) respectively. The calculated R factors indicated that the models were correct.

Oxygen positional parameter (u) for each composite was calculated using the formulae available in the literature. Where u³3 Sun S, Zeng H, Robinson DB, Raoux S, Rice PM, Wang SX, et al. Monodisperse MFe2O4 (M= Fe, Co, Mn) Nanoparticles. Journal of American Chemical Society. 2004;126(1):273-279.' gives u assuming centre of symmetry at (1/4, 1/4, 1/4) for which u_idea = 0.250 (origin at B-site), while u⁴³43 Sharifi I, Shokrollahi H, Doroodmand MM, Safi R. Magnetic and structural studies on CoFe2O4 nanoparticles synthesized by co-precipitation, normal micelles and reverse micelles methods. Journal of Magnetism and Magnetic Materials. 2012;324(10):1854-1861. give 'u' assuming centre of symmetry at (3/8, 3/8, 3/8) for which u_idea = 0.375 (origin at A-site). These two factors are related by following formula:

(4)

u^{\overset{─}{4} 3 m} - u^{3 m} + \frac{1}{8}

The radius of the tetrahedral and octahedral sites in a spinel ferrite can be calculated using the following formulae: ³⁷37 Toby BH. R factors in Rietveld analysis: How good is good enough? Powder Diffraction. 2006;21(1):67-70.^,³⁸38 Sharma RK, Sebastian V, Lakshmi N, Venugopalan K, Reddy VR, Gupta A. Variation of structural and hyperfine parameters in nanoparticles of Cr-substituted Co-Zn ferrites. Physical Review B. 2007;75(14):144419.

(5)

R_{A} - a \sqrt{3} (u - \frac{1}{4}) - R_{0}

(6)

R_{B} - a {(3 u^{2} - 2.75 u + \frac{43}{64})}^{\frac{1}{2}} - R_{0}

Where R_O is the radius of the oxygen ion (1.32 ºA) and u represents the oxygen positional parameter (table 3).

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Table 3
Edge lengths [Aº], bond lengths[Aº], radius of the tetrahedral and octahedral [Aº], and anion parametes [Aº] of Al-Co-Fe-O system

Using the lattice constant as well as oxygen parameter (u) of each composite, interatomic distances have been calculated from following equations.³⁹39 Goldman A. Modern Ferrite Technology. 2nd Ed. New York: Springer; 2006.^,⁴⁰40 Amer MA, El Hill M. Mössbauer and X-ray studies for Ni0.2ZnxMg0.8-xFe2O4 ferrites. Journal of Magnetism and Magnetic Materials. 2001;234(1):118-125. The calculated values are presented in Table 3.

(7)

\begin{matrix} d_{AE} - a {(2)}^{\frac{1}{2}} (2 u^{\overset{─}{4} 3 m} - \frac{1}{2}) \\ Shared octahedral edge \end{matrix}

(8)

\begin{matrix} d_{BE} - a {(2)}^{\frac{1}{2}} (1 - 2 u^{\overset{─}{4} 3 m}) \\ Shared tetrahedral edge \end{matrix}

(9)

\begin{matrix} d_{BL} - a {[3 {(u^{\overset{─}{4} 3 m})}^{2} - \frac{11}{4} u^{\overset{─}{4} 3 m} + \frac{43}{64}]}^{\frac{1}{2}} \\ Octahedral bond lenght \end{matrix}

(10)

\begin{matrix} d_{AL} - a \sqrt{3} (u^{\overset{─}{4} 3 m} - \frac{1}{4}) \\ Tetrahedral bond lenght \end{matrix}

(11)

\begin{matrix} d_{BEu} - a {[4 {(u^{\overset{─}{4} 3 m})}^{2} - 3 u^{\overset{─}{4} 3 m} + \frac{11}{16}]}^{\frac{1}{2}} \\ Unshared octahedral edge \end{matrix}

It is observed from Table 3 that the doping with alumina brought about a decrease in the values of R_A, R_B, edge lengths and bond lengths. This could be related to the smaller radius of Al³⁺ ion as compared to Fe³⁺ ion. In fact, the ionic radius of the Al³⁺ ion is 0.050 nm, while the ionic radius of the Fe³⁺ ions is 0.064 nm.

The interionic distances between the cations (b, c, d, e, and f) and between the cation and anion (p, q, r and s) were also calculated using the experimental values of lattice constant (a) and oxygen positional parameters (u^3m) (Tables 4 and 5) by the following relations:⁴¹41 Birgani AN, Niyaifar M, Hasanpour A. Study of cation distribution of spinel zinc nano-ferrite by X-ray. Journal of Magnetism and Magnetic Materials. 2015;374:179-181.^,⁴²42 Bhatu SS, Lakhani VK, Tanna AR, Vasoya NH, Buch JU, Sharma PU, et al. Effect of nickel substitution on structural, infrared and elastic properties of lithium ferrite. Indian Journal of Pure and Applied Physics. 2007;45(7):596-608.

(12)

p - a (\frac{5}{8} - u) b - (\frac{a}{4}) 2^{\frac{1}{2}}

(13)

q - a (u - \frac{1}{4}) 3^{\frac{1}{2}} c - (\frac{a}{8}) 11^{\frac{1}{2}}

(14)

r - a (u - \frac{1}{8}) 11^{\frac{1}{2}} d - (\frac{a}{4}) 3^{\frac{1}{2}}

(15)

s - a (\frac{1}{3 u} + \frac{1}{8}) 3^{\frac{1}{2}} e - (\frac{3 a}{8}) 3^{\frac{1}{2}}

(16)

f - (\frac{a}{4}) 6^{\frac{1}{2}}

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Table 4
Inter-ionic distances [Aº], of Al-Co-Fe-O system

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Table 5
Bond angles (degree) of Al-Co-Fe-O system

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Table 6
Elastic constants for Al-Co-Fe-O system

M-O M-M

Table 4 indicates that, both interatomic distances between the cation-anion (p, q, r and s) and between the cations (b, c, d, e and f) decrease with alumina doping. This result is accordance with decrease in unit cell volume.

The bond angles (θ₁, θ₂, θ₃, θ₄ and θ₅) were calculated by simple trigonometric principle using the interionic distances with the help of following formula: ⁴¹41 Birgani AN, Niyaifar M, Hasanpour A. Study of cation distribution of spinel zinc nano-ferrite by X-ray. Journal of Magnetism and Magnetic Materials. 2015;374:179-181.^,⁴²42 Bhatu SS, Lakhani VK, Tanna AR, Vasoya NH, Buch JU, Sharma PU, et al. Effect of nickel substitution on structural, infrared and elastic properties of lithium ferrite. Indian Journal of Pure and Applied Physics. 2007;45(7):596-608.

(17)

θ_{1} - \cos^{- 1} [\frac{p^{2} + q^{2} - c^{2}}{2 pq}]

(18)

θ_{2} - \cos^{- 1} [\frac{p^{2} + r^{2} - e^{2}}{2 pr}]

(19)

θ_{3} - \cos^{- 1} [\frac{2 p^{2} - b^{2}}{2 p^{2}}]

(20)

θ_{4} - \cos^{- 1} [\frac{p^{2} + s^{2} - f^{2}}{2 ps}]

(21)

θ_{5} - \cos^{- 1} [\frac{r^{2} + q^{2} - d^{2}}{2 rq}]

These values are tabulated in Table 5.

It is observed from Table 5 that angles θ₃ and θ₄ decrease while θ₁, θ₂ and θ₅ increase with alumina doping. The observed decrease in θ₃ and θ₄ indicative of weakening of the B-B interaction while increase in θ₁, θ₂ and θ5 suggest strengthening of the A-B and A-A interactions on Al³⁺-substitution in the system.

3.3. Elastic Properties

The elastic constants of solids provide a link between the mechanical and dynamical behaviors of crystals. Cubic crystals have three independent elastic constants: C₁₁, C₁₂, and C₄₄ . In the present work, we studied effect of alumina doping on the elastic constants Cij, bulk moduli B, shear moduli G, Young's moduli Y and the Poisson ratio υ. Values of these factors are computed using the following relationships:⁴³43 Sharifi I, Shokrollahi H, Doroodmand MM, Safi R. Magnetic and structural studies on CoFe2O4 nanoparticles synthesized by co-precipitation, normal micelles and reverse micelles methods. Journal of Magnetism and Magnetic Materials. 2012;324(10):1854-1861.

44 Beer FP, Johnston ER Jr., DeWolf JT. Mechanics of Materials. New York: McGraw-Hill Higher Education; 2006.^-⁴⁵45 Grimvall G. Thermophysical Properties of Materials. 1st Ed. Amsterdam: Elsevier, North Holland; 1999.

(22)

\begin{matrix} B - \frac{B_{v} + B_{R}}{2}, G - \frac{G_{v} + G_{R}}{2}, \\ B_{v} - B_{R} - \frac{C_{11} + 2 C_{12}}{3} \end{matrix}

(23)

\begin{matrix} G_{R} - \frac{5 C_{44} (C_{11} - C_{12})}{4 C_{44} + 3 (C_{11} - C_{12})}, G_{v} - \\ \frac{C_{11} - C_{12} + 3 C_{44}}{5} \end{matrix}

(24)

Y - \frac{9 BG}{3 B + G}, v - \frac{3 B - 2 G}{2 (3 B + G)}

Complate set of the calculated elastic constants for two samples are collected in Table 6.

It can be seen that magnitude of moduli were decreased on Al³⁺ doping. It is explained on the basis of the replacement of Fe³⁺ ions with half-filled d-shell (3d⁵) by Al³⁺ ions with a noble gas outer electron shell (2p⁶) structure which do not contribute to the bond formation.

However it is well known that the cations with a completely filled outer electron shell structure are more stable and less compressible than the cations with a half-filled or a incomplete outer shell. In other word the material is compressed easier when the radius of the ions is longer.Therefore, strength of bonding and magnitude of moduli are expected to decrease.⁴⁶46 Bouhemadou A. Theoretical study of the structural, elastic and electronic properties of the GeX2O4 (X = Mg, Zn, Cd) compounds under pressure. Modelling and Simulation in Materials Science and Engineering. 2008;16(5):055007.^,⁴⁷47 Haines J, Léger JM, Bocquillon G. Synthesis and Design of Superhard Materials. Annual Review of Materials Research. 2011;31:1-23.

4. Conclusions

Pure and Al³⁺ doped cobalt ferrite nanoparticles were successfully synthesized by sol-gel method and thermally treated at 500ºC for 3 hours. XRD and the rietveld analysis showed that two composition were formed into single phase cubic spinel structure. Various structural parameters can be determined from x-ray powder diffraction pattern analysis and are found useful to explain other physical properties. The lattice parameters and the crystallite size were found decreasing with Al³⁺ doping. The strength of the A-B interaction increase while B-B interaction decreases with Al³⁺ substitution for Fe³⁺ in the system. Also magnitude of moduli were decreased on Al³⁺ doping. This is due essentially to the ion size difference among Al³⁺ and Fe³⁺ ions.

5. Acknowledgement

We are thankful to the Payam Noor University for their support and encouragements.

6. References

¹
O'Handley RC. Modern Magnetic Materials - Principles and Applications Hoboken: John Wiley & Sons; 2000.
²
Buschow KHJ, ed. Handbook of Magnetic Materials, Vol. 19 Amsterdam: Elsevier, North Holland; 2011.
³
Sun S, Zeng H, Robinson DB, Raoux S, Rice PM, Wang SX, et al. Monodisperse MFe₂O₄ (M= Fe, Co, Mn) Nanoparticles. Journal of American Chemical Society 2004;126(1):273-279.
⁴
Amstad E, Textor M, Reimhult E. Stabilization and functionalization of iron oxide nanoparticles for biomedical applications. Nanoscale 2011;3(7):2819-2843.
⁵
Desantis C, Siegel R, Bandi P, Jemal A. Breast cancer statistics, 2011. CA: A Cancer Journal for Clinicians 2011;61(6):409-418.
⁶
Chen J. High Temperature Polyol Synthesis of Super paramagnetic CoFe₂O₄ Nanoparticles for Magnetic Resonance imaging Contrast agents. Journal of Inorganic Materials 2009;24(5):967-972.
⁷
Bixner O, Lassenberger A, Baurech D, Reimhult E. Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles. Langmuir 2015;31(33):9198-9204.
⁸
Grunewald TA, Lassenberger A, van Ostrum PDJ, Rennhofer H, Zirbs R, Capone B, et al. Core-Shell Structure of Monodisperse Poly(ethylene glycol)-Grafted Iron Oxide Nanoparticles Studied by Small-Angle X-ray Scattering. Chemistry of Materials 2015;27(13):4763-4771.
⁹
Kurzhals S, Zirbs R, Reimhult E. Synthesis and Magneto-Thermal Actuation of Iron Oxide Core-PNIPAM Shell Nanoparticles. ACS Applied Materials & Interfaces 2015;7(34):19342-19352.
¹⁰
El-Shobaky GA, Turky AM, Mostafa NY, Mohamed SK. Effect of preparation conditions on physicochemical, surface and catalytic properties of cobalt ferrite prepared by coprecipitation. Journal of Alloys and Compounds. 2010;493(1-2):415422.
¹¹
Scheffe JR, Allendorf MD, Coker EN, Jacobs BW, McDaniel AH, Weimer AW. Hydrogen Production via Chemical Looping Redox Cycles Using Atomic Layer Deposition-Synthesized Iron Oxide and Cobalt Ferrites. Chemistry of Materials. 2011;23(8):2030-2038.
¹²
Pervaiz E, Gul IH, Anwar H. Hydrothermal Synthesis and Characterization of CoFe₂O₄ Nanoparticles and Nanorods. Journal of Superconductivity and Novel Magnetism. 2013;26(2):415-424.
¹³
Kurtan U, Topkaya R, Baykal A, Toprak MS. Temperature dependent magnetic properties of CoFe₂O₄/CTAB nanocomposite synthesized by sol-gel auto-combustion technique. Ceramics International 2013;39(6):6551-6558.
¹⁴
Sinkó K, Manek E, Meiszterics A, Havancsák K, Vainio U, Peterlik H. Liquid-phase syntheses of cobalt ferrite nanoparticles. Journal of Nanoparticle Research. 2012;14:894-908.
¹⁵
Jiang G, Chang Q, Yang F, Hu X, Tang H. Sono-assisted preparation of magnetic ferroferric oxide/graphene oxide nanoparticles and application on dye removal. Chinese Journal of Chemical Engineering. 2015;23(3):510-515.
¹⁶
Liu Q, Sun J, Long H, Sun X, Zhong X, Xu Z. Hydrothermal synthesis of CoFe₂O₄ nanoplates and nanoparticles. Materials Chemistry and Physics 2008;108(2-3):269-273.
¹⁷
Freitas JC, Branco RM, Lisboa IGO, Costa TP, Campos MGN, Jafelicci Júnior M, et al. Magnetic Nanoparticles Obtained by Homogeneous Coprecipitation Sonochemically Assisted. Materials Research 2015;18(Suppl. 2):220-224.
¹⁸
Ahmed MA, El-Khawlani AA. Enhancement of the crystal size and magnetic properties of Mg-substituted Co ferrite. Journal of Magnetism and Magnetic Materials 2009;321(13):1959-1963.
¹⁹
Rana S, Philip J, Raj B. Micelle based synthesis of cobalt ferrite nanoparticles and its characterization using Fourier Transform Infrared Transmission Spectrometry and Thermogravimetry. Materials Chemistry and Physics. 2010;124(1):264-269.
²⁰
Ayyappan S, Mahadevan SP, Chandramohan P, Srinivasan MP, Philip J, Raj B. Influence of Co²⁺ Ion Concentration on the Size, Magnetic Properties, and Purity of CoFe₂O₄ Spinel Ferrite Nanoparticles. The Journal of Physical Chemistry C 2010;114(14):6334-6341.
²¹
Meng YY, Liu ZW, Dai HC, Yu HY, Zeng DC, Shukla S, et al. Structure and magnetic properties of Mn(Zn)Fe_2-xRE_xO₄ ferrite nano-powders synthesized by co-precipitation and refluxing method. Journal of Powder Technology 2012;229:270-275.
²²
Deraz NM. Glycine-assisted fabrication of nanocrystalline cobalt ferrite system. Journal of Analytical and Applied Pyrolysis. 2010;88(2):103-109.
²³
Shobana MK, Nam W, Choe H. Yttrium-doped cobalt nanoferrites prepared by sol-gel combustion method and its characterization. Journal of Nanoscience and Nanotechnology. 2013;13(5):3535-3538.
²⁴
Chae KP, Lee JG, Kweon HS, Lee YB. The crystallographic, magnetic properties of Al, Ti doped CoFe₂O₄ powders grown by sol-gel method. Journal of Magnetism and Magnetic Materials. 2004;283(1):103-108.
²⁵
Oliveira VD, Rubinger RM, Silva MR, Oliveira AF, Rodrigues G, Ribeiro VAS. Magnetic and Electrical Properties of Mn_xCu_1-xFe₂O₄ Ferrite. Materials Research 2016;19(4):786-790.
²⁶
Panda RN, Shih JC, Chin TS. Magnetic properties of nano-crystalline Gd- or Pr-substituted CoFe₂O₄ synthesized by the citrate precursor technique. Journal of Magnetism and Magnetic Materials. 2003;257(1):79-86.
²⁷
Kambale RC, Song KM, Koo VS, Hur N. Low temperature synthesis of nanocrystalline Dy³⁺ doped cobalt ferrite: Structural and magnetic properties. Journal of Applied Physics. 2011;110(5):053910.
²⁸
Wang L, Li FS. Mössbauer study of nanocrystalline Ni-Zn ferrite. Journal of Magnetism and Magnetic Materials. 2001;223(3):233-237.
²⁹
Xu S, Shangguan W, Yuan J, Chen M, Shi J. Preparation and Photocatalytic Properties of Magnetically Separable TiO₂ Supported on Nickel Ferrite. Chinese Journal of Chemical Engineering. 2007;15(2):190-195.
³⁰
Yousefi MH, Manouchehri S, Arab A, Mozaffari M, Amiri GR, Amighian J. Preparation of cobalt-zinc ferrite (Co_0.8Zn_0.2Fe₂O₄) nanopowder via combustion method and investigation of its magnetic properties. Materials Research Bulletin 2010;45(12):1792-1795.
³¹
Raghavender AT, Pajic D, Zadro K, Milekovic T, Venkateshwar Rao P, Jadhav KM, et al. Synthesis and magnetic properties of NiFe_2-xAl_xO₄ nanoparticles. Journal of Magnetism and Magnetic Materials2007;316(1):1-7.
³²
Smith J, Wijn HPJ. Ferrites Eindhoven: Philips Technical Library; 1959.
³³
Louh R, Reynolds TG, Buchanan RC. Ferrite Ceramics. In: Buchanan RC, ed. Ceramic Materials for Electronics 3^rdEd. Boca Raton: CRC Press; 2004.
³⁴
Young RA. Introduction to the Rietveld Method. In: Young RA, ed. The Rietveld Method Oxford: Oxford University Press; 1993.
³⁵
Polvakov NE, Leshina TV, Meteleva ES, Dushkin AV, Konovalova TA, Kispert LD. Enhancement of the Photocatalytic Activity of TiO₂ Nanoparticles by Water-Soluble Complexes of Carotenoids. The Journal of Physical Chemistry B2010;114(45):14200-14204.
³⁶
Young RA, ed. The Rietveld Method Oxford: Oxford University Press; 1993.
³⁷
Toby BH. R factors in Rietveld analysis: How good is good enough? Powder Diffraction 2006;21(1):67-70.
³⁸
Sharma RK, Sebastian V, Lakshmi N, Venugopalan K, Reddy VR, Gupta A. Variation of structural and hyperfine parameters in nanoparticles of Cr-substituted Co-Zn ferrites. Physical Review B 2007;75(14):144419.
³⁹
Goldman A. Modern Ferrite Technology 2^nd Ed. New York: Springer; 2006.
⁴⁰
Amer MA, El Hill M. Mössbauer and X-ray studies for Ni_0.2Zn_xMg_0.8-xFe₂O₄ ferrites. Journal of Magnetism and Magnetic Materials. 2001;234(1):118-125.
⁴¹
Birgani AN, Niyaifar M, Hasanpour A. Study of cation distribution of spinel zinc nano-ferrite by X-ray. Journal of Magnetism and Magnetic Materials. 2015;374:179-181.
⁴²
Bhatu SS, Lakhani VK, Tanna AR, Vasoya NH, Buch JU, Sharma PU, et al. Effect of nickel substitution on structural, infrared and elastic properties of lithium ferrite. Indian Journal of Pure and Applied Physics 2007;45(7):596-608.
⁴³
Sharifi I, Shokrollahi H, Doroodmand MM, Safi R. Magnetic and structural studies on CoFe₂O₄ nanoparticles synthesized by co-precipitation, normal micelles and reverse micelles methods. Journal of Magnetism and Magnetic Materials. 2012;324(10):1854-1861.
⁴⁴
Beer FP, Johnston ER Jr., DeWolf JT. Mechanics of Materials New York: McGraw-Hill Higher Education; 2006.
⁴⁵
Grimvall G. Thermophysical Properties of Materials 1^st Ed. Amsterdam: Elsevier, North Holland; 1999.
⁴⁶
Bouhemadou A. Theoretical study of the structural, elastic and electronic properties of the GeX₂O₄ (X = Mg, Zn, Cd) compounds under pressure. Modelling and Simulation in Materials Science and Engineering. 2008;16(5):055007.
⁴⁷
Haines J, Léger JM, Bocquillon G. Synthesis and Design of Superhard Materials. Annual Review of Materials Research 2011;31:1-23.

Publication Dates

Publication in this collection
06 Mar 2017
Date of issue
May-Jun 2017

History

Received
04 Dec 2016
Reviewed
07 Feb 2017
Accepted
18 Feb 2017

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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El-Shobaky GA, Turky AM, Mostafa NY, Mohamed SK. Effect of preparation conditions on physicochemical, surface and catalytic properties of cobalt ferrite prepared by coprecipitation. Journal of Alloys and Compounds. 2010;493(1-2):415422.

[11] ¹¹
Scheffe JR, Allendorf MD, Coker EN, Jacobs BW, McDaniel AH, Weimer AW. Hydrogen Production via Chemical Looping Redox Cycles Using Atomic Layer Deposition-Synthesized Iron Oxide and Cobalt Ferrites. Chemistry of Materials. 2011;23(8):2030-2038.

[12] ¹²
Pervaiz E, Gul IH, Anwar H. Hydrothermal Synthesis and Characterization of CoFe₂O₄ Nanoparticles and Nanorods. Journal of Superconductivity and Novel Magnetism. 2013;26(2):415-424.

[13] ¹³
Kurtan U, Topkaya R, Baykal A, Toprak MS. Temperature dependent magnetic properties of CoFe₂O₄/CTAB nanocomposite synthesized by sol-gel auto-combustion technique. Ceramics International 2013;39(6):6551-6558.

[14] ¹⁴
Sinkó K, Manek E, Meiszterics A, Havancsák K, Vainio U, Peterlik H. Liquid-phase syntheses of cobalt ferrite nanoparticles. Journal of Nanoparticle Research. 2012;14:894-908.

[15] ¹⁵
Jiang G, Chang Q, Yang F, Hu X, Tang H. Sono-assisted preparation of magnetic ferroferric oxide/graphene oxide nanoparticles and application on dye removal. Chinese Journal of Chemical Engineering. 2015;23(3):510-515.

[16] ¹⁶
Liu Q, Sun J, Long H, Sun X, Zhong X, Xu Z. Hydrothermal synthesis of CoFe₂O₄ nanoplates and nanoparticles. Materials Chemistry and Physics 2008;108(2-3):269-273.

[17] ¹⁷
Freitas JC, Branco RM, Lisboa IGO, Costa TP, Campos MGN, Jafelicci Júnior M, et al. Magnetic Nanoparticles Obtained by Homogeneous Coprecipitation Sonochemically Assisted. Materials Research 2015;18(Suppl. 2):220-224.

[18] ¹⁸
Ahmed MA, El-Khawlani AA. Enhancement of the crystal size and magnetic properties of Mg-substituted Co ferrite. Journal of Magnetism and Magnetic Materials 2009;321(13):1959-1963.

[19] ¹⁹
Rana S, Philip J, Raj B. Micelle based synthesis of cobalt ferrite nanoparticles and its characterization using Fourier Transform Infrared Transmission Spectrometry and Thermogravimetry. Materials Chemistry and Physics. 2010;124(1):264-269.

[20] ²⁰
Ayyappan S, Mahadevan SP, Chandramohan P, Srinivasan MP, Philip J, Raj B. Influence of Co²⁺ Ion Concentration on the Size, Magnetic Properties, and Purity of CoFe₂O₄ Spinel Ferrite Nanoparticles. The Journal of Physical Chemistry C 2010;114(14):6334-6341.

[21] ²¹
Meng YY, Liu ZW, Dai HC, Yu HY, Zeng DC, Shukla S, et al. Structure and magnetic properties of Mn(Zn)Fe_2-xRE_xO₄ ferrite nano-powders synthesized by co-precipitation and refluxing method. Journal of Powder Technology 2012;229:270-275.

[22] ²²
Deraz NM. Glycine-assisted fabrication of nanocrystalline cobalt ferrite system. Journal of Analytical and Applied Pyrolysis. 2010;88(2):103-109.

[23] ²³
Shobana MK, Nam W, Choe H. Yttrium-doped cobalt nanoferrites prepared by sol-gel combustion method and its characterization. Journal of Nanoscience and Nanotechnology. 2013;13(5):3535-3538.

[24] ²⁴
Chae KP, Lee JG, Kweon HS, Lee YB. The crystallographic, magnetic properties of Al, Ti doped CoFe₂O₄ powders grown by sol-gel method. Journal of Magnetism and Magnetic Materials. 2004;283(1):103-108.

[25] ²⁵
Oliveira VD, Rubinger RM, Silva MR, Oliveira AF, Rodrigues G, Ribeiro VAS. Magnetic and Electrical Properties of Mn_xCu_1-xFe₂O₄ Ferrite. Materials Research 2016;19(4):786-790.

[26] ²⁶
Panda RN, Shih JC, Chin TS. Magnetic properties of nano-crystalline Gd- or Pr-substituted CoFe₂O₄ synthesized by the citrate precursor technique. Journal of Magnetism and Magnetic Materials. 2003;257(1):79-86.

[27] ²⁷
Kambale RC, Song KM, Koo VS, Hur N. Low temperature synthesis of nanocrystalline Dy³⁺ doped cobalt ferrite: Structural and magnetic properties. Journal of Applied Physics. 2011;110(5):053910.

[28] ²⁸
Wang L, Li FS. Mössbauer study of nanocrystalline Ni-Zn ferrite. Journal of Magnetism and Magnetic Materials. 2001;223(3):233-237.

[29] ²⁹
Xu S, Shangguan W, Yuan J, Chen M, Shi J. Preparation and Photocatalytic Properties of Magnetically Separable TiO₂ Supported on Nickel Ferrite. Chinese Journal of Chemical Engineering. 2007;15(2):190-195.

[30] ³⁰
Yousefi MH, Manouchehri S, Arab A, Mozaffari M, Amiri GR, Amighian J. Preparation of cobalt-zinc ferrite (Co_0.8Zn_0.2Fe₂O₄) nanopowder via combustion method and investigation of its magnetic properties. Materials Research Bulletin 2010;45(12):1792-1795.

[31] ³¹
Raghavender AT, Pajic D, Zadro K, Milekovic T, Venkateshwar Rao P, Jadhav KM, et al. Synthesis and magnetic properties of NiFe_2-xAl_xO₄ nanoparticles. Journal of Magnetism and Magnetic Materials2007;316(1):1-7.

[32] ³²
Smith J, Wijn HPJ. Ferrites Eindhoven: Philips Technical Library; 1959.

[33] ³³
Louh R, Reynolds TG, Buchanan RC. Ferrite Ceramics. In: Buchanan RC, ed. Ceramic Materials for Electronics 3^rdEd. Boca Raton: CRC Press; 2004.

[34] ³⁴
Young RA. Introduction to the Rietveld Method. In: Young RA, ed. The Rietveld Method Oxford: Oxford University Press; 1993.

[35] ³⁵
Polvakov NE, Leshina TV, Meteleva ES, Dushkin AV, Konovalova TA, Kispert LD. Enhancement of the Photocatalytic Activity of TiO₂ Nanoparticles by Water-Soluble Complexes of Carotenoids. The Journal of Physical Chemistry B2010;114(45):14200-14204.

[36] ³⁶
Young RA, ed. The Rietveld Method Oxford: Oxford University Press; 1993.

[37] ³⁷
Toby BH. R factors in Rietveld analysis: How good is good enough? Powder Diffraction 2006;21(1):67-70.

[38] ³⁸
Sharma RK, Sebastian V, Lakshmi N, Venugopalan K, Reddy VR, Gupta A. Variation of structural and hyperfine parameters in nanoparticles of Cr-substituted Co-Zn ferrites. Physical Review B 2007;75(14):144419.

[39] ³⁹
Goldman A. Modern Ferrite Technology 2^nd Ed. New York: Springer; 2006.

[40] ⁴⁰
Amer MA, El Hill M. Mössbauer and X-ray studies for Ni_0.2Zn_xMg_0.8-xFe₂O₄ ferrites. Journal of Magnetism and Magnetic Materials. 2001;234(1):118-125.

[41] ⁴¹
Birgani AN, Niyaifar M, Hasanpour A. Study of cation distribution of spinel zinc nano-ferrite by X-ray. Journal of Magnetism and Magnetic Materials. 2015;374:179-181.

[42] ⁴²
Bhatu SS, Lakhani VK, Tanna AR, Vasoya NH, Buch JU, Sharma PU, et al. Effect of nickel substitution on structural, infrared and elastic properties of lithium ferrite. Indian Journal of Pure and Applied Physics 2007;45(7):596-608.

[43] ⁴³
Sharifi I, Shokrollahi H, Doroodmand MM, Safi R. Magnetic and structural studies on CoFe₂O₄ nanoparticles synthesized by co-precipitation, normal micelles and reverse micelles methods. Journal of Magnetism and Magnetic Materials. 2012;324(10):1854-1861.

[44] ⁴⁴
Beer FP, Johnston ER Jr., DeWolf JT. Mechanics of Materials New York: McGraw-Hill Higher Education; 2006.

[45] ⁴⁵
Grimvall G. Thermophysical Properties of Materials 1^st Ed. Amsterdam: Elsevier, North Holland; 1999.

[46] ⁴⁶
Bouhemadou A. Theoretical study of the structural, elastic and electronic properties of the GeX₂O₄ (X = Mg, Zn, Cd) compounds under pressure. Modelling and Simulation in Materials Science and Engineering. 2008;16(5):055007.

[47] ⁴⁷
Haines J, Léger JM, Bocquillon G. Synthesis and Design of Superhard Materials. Annual Review of Materials Research 2011;31:1-23.

2θ [deg.]	h k l	FwHM [2θ]	d-spacing	a [A]	F(θ)	Cry.size [nm]
30.19	220	0.2460	2.9596	8.37	1.82961	33.4
33.22	310	0.5904	2.6964	8.52	1.62781	14.1
35.56	311	0.3444	2.5245	8.37	1.50955	24.3
43.13	400	0.2952	2.0972	8.36	1.03974	29.0
53.47	422	0.7872	1.7135	8.37	0.90145	11.3
57.08	511	0.3444	1.6133	8.31	0.82074	26.3
62.71	440	0.6000	1.4803	8.37	0.12157	15.5

2θ [deg.]	h k l	FwHM [2θ]	d-spacing	a [A]	F(θ)	Cry.size [nm]
30.75	220	0.1968	2.9068	8.22178	1.77766	41.8
34.36	310	0.2952	2.6099	8.25323	1.56398	28.2
36.20	311	0.4428	2.4811	8.22898	1.47009	18.9
44.04	400	0.7872	2.0559	8.22384	1.16509	10.9
54.47	422	0.7872	1.68453	8.25248	0.87748	11.4
58.23	511	0.3936	1.58429	8.23221	0.79441	23.1
64.11	440	0.7200	1.45126	8.20957	0.68597	13.0

compound	d_Ae	d_BE	d_BEu	d_Al	d_Bl	R_A	R_B	U⁴³	U³
CoFe₂O₄	2.8162	3.0352	2.9140	1.7436	2.0948	0.4236	0.7748	0.371	0.246
CoAl_0.4Fe_1.6O₄	2.7918	3.0196	2.9071	1.7098	2.0924	0.3172	0.7724	0.370	0.245

compound	p	q	r	s	b	c	d	e	f
CoFe₂O₄	2.1132	1.7436	3.3322	3.5833	2.9411	3.4492	3.6025	5.403	5.094
CoAl_0.4Fe_1.6O₄	2.0961	1.7064	3.271	3.5356	2.905	3.407	3.5592	5.338	5.033

compound	θ₁	θ₂	θ₃	θ₄	θ₅
CoFe₂O₄	125.54	165.4	88.24	124.86	84.28
CoAl_0.4Fe_1.6O₄	126.96	167.68	87.72	124.69	85.14

Brasil

Brasil

Al and PEG Effect on Structural and Physicochemical Properties of CoFe₂O₄

Abstract

1. Introduction

2. Materials and methods

2.1. Material

2.2. Synthesis of nanoparticles

2.3. Simulation Analysis

3. Results and Discussion

3.1. X-Ray diffraction studies

3.2. Rietveld Analysis

3.3. Elastic Properties

4. Conclusions

5. Acknowledgement

6. References

Publication Dates

History

compound	C11	C12	C44	B	Y	υ	G
compound	[PA]	[GPA]	[GPA]	[GPA]	[GPA]		[GPA]
CoFe₂O₄	186.08	28.6087	50.2593	81.10	178.4627	0.1333	60.2061
CoAl_0.4Fe_1.6O₄	157.37	12.2987	47.8372	60.65	155.5927	0.0725	56.5492

Brasil

Brasil

Al and PEG Effect on Structural and Physicochemical Properties of CoFe2O4

Abstract

1. Introduction

2. Materials and methods

2.1. Material

2.2. Synthesis of nanoparticles

2.3. Simulation Analysis

3. Results and Discussion

3.1. X-Ray diffraction studies

3.2. Rietveld Analysis

3.3. Elastic Properties

4. Conclusions

5. Acknowledgement

6. References

Publication Dates

History

Al and PEG Effect on Structural and Physicochemical Properties of CoFe₂O₄