Synthesis, structural, W-H plot and size-strain analysis of nano cobalt doped MgFe2O4 ferrite

In this study we have investigated structural attribute of Co+2 doped
 MgFe2O4. Synthesis of Mg1-xCoxFe2O4 ferrite was carried out using
 co-precipitation method. The formation of spinal ferrite was confirmed
 through X-ray diffraction. Lattice parameter found to be 8.376748 ? and
 crystallite sizes in the range 180-365 ? are observed. Various parameters
 like dislocation density (?D); mechanical properties (strain), Hopping
 length {tetrahedral site (LA) and octahedral site (LB)}, Bond length (A-O
 and B-O), and Ionic radii (rA and rB) were reported. The W-H plot and
 Size-Strain plots were extensively studied and the results have been
 correlated.


Introduction
Magnetic nano-particles have become subject of intense research because of their applications in high density magnetic recording, in the technological, medical and industrial applications [1]. Spinal ferrite materials attained vast interest because of their unparalleled magnetic, electric and dielectric properties [2][3]. Spinel ferrites with a general chemical formula of MFe 2 O 4 , in which M is one or two of divalent metals, such as Co, Mg, Zn, Ni, etc. [3][4].
Magnesium ferrite has cubic structure and it is a soft magnetic n-type semiconductor material. It finds applications in heterogeneous catalysis, adsorption sensors etc. Magnesium ferrite with a chemical formula of MgFe 2 O 4 has an inverse spinel structure, in which half of the trivalent cations occupy the tetrahedral (A) sites and the other half of the trivalent cations and all of the divalent cations fill the octahedral (B) sites [5]. Because of easy fabrications, high efficiencies, thermal stabilities, and low costs of magnesium-ferrites have the broad in scope of applications from low frequencies to microwave frequencies (devices) [6][7]. The excellent magnetic and electrical properties such as high permeability, high electrical resistivity and low dielectric and magnetic losses these ferrites can be used to fabricate as microwave devices like circulators, insulators and phase shifters [8][9].
To accomplish low dielectric losses, reduce the transmission loss [10] cobalt ferrite is used due to high coercievity, high chemical stability and good electrical insulation. Any change in distribution of cations among tetrahedral site and octahedral site by cations substitution have very dominant effects on the physical properties, the substitutions of magnetic or non-magnetic ions alters the spin order which affects the magnetic and electric properties of ferrite structure and greatly affect the ferrite overall properties [11][12]. The substitution of non-magnetic magnesium ion can modify the properties of cobalt ferrite [12]. The cation distribution according to the earlier reported reveals that magnesium ions exist in both sites (A and B) but have a strong preference for the octahedral (B) site [13].XRD, FTIR and dielectric studies of Mg-Co nano crystalline ferrites (x=0, 0.05, 0.1, 0.15, 0.2, 0.25) were prepared by the sol-gel method [14].
In this work we report the cobalt doped magnesium ferrite (Mg 0.85 Co 0.15 Fe 2 O 4 ) by simple chemical route by co-precipitation method.

Materials and Experimental Procedures
Analytical grade FeCl 3 ·6H 2 O, MgCl 2 ·6H 2 O and CoCl 2 ·H 2 O reagents were weights in molar ratio, in distilled water to produce ionic solution. Ferrite was synthesized from simple low cost co-precipitation method. Ammonia is added drop-wise under constant stirring and a pH of 8 is maintained throughout the reaction. During this method, metal salts converted of into hydroxides and subsequent transformation of metal hydroxide into nano Mg 0.85 Co 0.15 Fe 2 O 4 ferrite. Precipitate is further powdered using mortar and crusher for one hour. Then the sample is heated to 550 o C for 6 hour in muffle furnace to obtain final nano ferrite powder. The structural characterisation of sample was carried by X-ray diffractometer Bruker AXS D8 Advance diffractometer (Cu-Kα radiation). The schematic diagram of the synthesis method with results observed is shown in Fig. 1.

XRD analysis
The XRD pattern of Mg 0.85 Co 0.15 Fe 2 O 4 was shown in Fig. 2 with peaks (220), (311), (222), (400), (422), (511), and (440) respectively. These plains confirm cubic structure of Mg-Co ferrite. The diffraction maximum from Bragg's law is prevailed by: It can be seen that the diffraction peaks are either all even or all odd, which suggests a spinel phase (lattice parameter = 8.376748 Å) for sample and thus validates the cubic structure. The detailed information of sample like lattice parameter (a), and interplanar distances (d) are tabulated in Table I D is size of the particle, λ is the wavelength of x-rays (1.5406 Å), θ is Bragg angle for the peak pure diffraction broadening β. The calculated average crystallite size (D) of samples is 243 Å. The distance between magnetic ions (hopping length) in A site (Tetrahedral) and B site (Octahedral) were calculated by using [15][16]  where a is lattice constant:

Williamson-Hall analysis (W-H plot) and "Size-Strain plot" (SSP) analysis
Assuming the size and strain broadening are additive components of the total integral breadth of a Bragg peak [25]. The distinct angle (θ) dependencies of both effects laid the basis for the separation of size and strain broadening in the analysis of Williamson and Hall [15][16][17]. Fig. 3 shows the variation between the βcos θ vs. sin θ (W-H analysis). The equation (16) represents (linear form) y =mx + c where m = strain and c = 1/D, so that the linear plot of βcos θ vs. sin θ gives the slope as lattice strain (ε) and the intercept as 1/D. The ''size-strain plot" (SSP) is an instrument to interpret the quantity of isotropic nature and micro-strain contribution and the advantage is that less weight is given to data from reflections at high angles, where the precision is usually lower which is shown in Fig. 4. In this approximation, we assume that the ''crystallite size" profile is described by a Lorentzian function and the ''strain profile" by a Gaussian function [15,26]. Accordingly, we have: In Fig. 4 similarly to the W-H methods, the term (d hkl β hkl cosθ) 2 is plotted with respect to (d hkl 2 β hkl cosθ) for the all orientation peaks of Mg 1-x Co x Fe 2 O 4 ferrite (x=0.15) ferrite samples with the cubic spinel structure. Crystallite size and lattice strain were also extracted from the XRD data using Williamson-Hall formula through the following equations. In this case, the equivalence between W-H plot and SSP has been reported in Table III. Results of lattice strain and average crystallite size of samples encountered in good agreement with the value obtained from the equations (Table IV).
Tab. III Micro-strain, Dislocation density, W-H plot and SSP plot calculation.
Tab. IV Calculated values of crystallite size, micro strain and dislocation density using W-H plots, SSP and standard formula.

Texture analysis
The reflection intensities from each XRD pattern contain information related to the preferential or random growth of polycrystalline material, which is studied by calculating texture coefficient TC hkl for all planes using [15][16][17]: Tab. V Texture analysis of Sample.

Sl. No.
Miller where I (hkl) is the measured intensity of X-ray reflection, I 0(hkl) is the corresponding standard intensity and N is the number of reflections observed in the XRD pattern. Texture coefficient is higher than one indicates preferential orientation and also indicates the abundance of grains along the given (hkl) plane. TC (220) has relatively higher value 3.43 than other planes indicating higher orientations of crystallites along these particular planes. TC for different (hkl) planes is demonstrated in Table V. It is observed that, preferential orientation (abundance of grains) in (220) plane direction. The stacking fault probability was calculated by measuring the peak shift and tangent values of diffracting angle: [ ] hkl θ θ π α tan 2 3 45 α-stacking fault coefficient, Δ2θ-difference in standard and observe 2θ values. The detailed analysis of stacking fault probability is shown in Table VI and observed to be for this ferrite as 0.0735.
The growth mechanism of ferrite sample can be estimated by calculating the standard deviation using the equation [17]: (17) where I hkl stands for relative intensity of the (hkl) plane. The estimated standard deviation, σ, in the relative intensity values was calculated and tabulated in Table VII from the values of the five strongest lines, excluding the line with I hkl =100. The calculated value of σ is 45.25, which appears to be relatively depleted showing that heterogeneous nucleation, desorption and adsorption are recessive and the homogeneous nucleation looks predominant [28].

Conclusion
The nano cobalt substituted Mg-ferrite (Mg 0.85 Co 0.15 Fe 2 O 4 ) was successfully synthesized by a coprecipitaion method. Structural properties were investigated by XRD analysis shows cubic single phase spinel with lattice parameter 8.376748 Å and crystallitesize (D) is 243 Å. We have also discussed dislocation density (ρ D ), mechanical properties (strain), hopping length {tetrahedral site (L A ) and octahedral site (L B )}, bond length (A-O and B-O), ionic radii (r A and r B ) and stacking fault probability (α) of Mg 0.85 Co 0.15 Fe 2 O 4 sample. The W-H plot and size strain plots were extensively studied and the results have been correlated. Thus Low-cost chemical method (co-precipitation) technique is a favourable way to obtaining homogeneous nano Mg 1-x Co x Fe 2 O 4 ferrite.