Structural and mechanical properties of AFe2O4 (A = Zn, Cu0.5Zn0.5, Ni0.3Cu0.2Zn0.5) nanoparticles prepared by citrate method at low temperature
Ahmad Gholizadeh
1
(
School of Physics, Damghan University (DU), Damghan, Islamic Republic of Iran
)
الکلمات المفتاحية: Mechanical Properties, Ferrites, Citrate method, X-ray diffraction method, IR spectroscopy,
ملخص المقالة :
In this work, the structural and elastic moduli properties of ZnFe2O4, Zn0.5Cu0.5Fe2O4, and Ni0.3Cu0.2Zn0.5Fe2O4 ferrites prepared by citrate method have been investigated. The structural characterization of the samples is evidence for a cubic structure with Fd-3m space group. The Halder-Wagner analysis was used to study crystallite sizes and lattice strain and also stress and energy density. The cation distribution for each composition has been suggested. The experimental and theoretical lattice constants were found to be in good agreement with each other confirming the agreeability of the suggested cation distribution. The force constants for tetrahedral and octahedral sites have been determined by infrared spectral analysis. The increase in force constants of ZnFe2O4 nanoparticles compared to other samples suggests the elastic properties of this sample is better than the other samples. The values of Young’s modulus, rigidity modulus, bulk modulus, Debye temperature have been determined. In addition, using the values of the compliance sij obtained from elastic stiffness constants, the values of Young’s modulus and Poisson’s ratio along the oriented direction have been calculated for the samples. Consequently, we can conclude the ZnFe2O4 nanoparticles could be more useful in industry applications because of their elastic properties compared to other samples.
Structural and mechanical properties of AFe2O4 (A = Zn, Cu0.5Zn0.5, Ni0.3Cu0.2Zn0.5) nanoparticles prepared by citrate method at low temperature
Abstract
In this work, the structural and elastic moduli properties of ZnFe2O4, Zn0.5Cu0.5Fe2O4, and Ni0.3Cu0.2Zn0.5Fe2O4 ferrites prepared by citrate method have been investigated. The structural characterization of the samples is evidence for a cubic structure with Fd-3m space group. The Halder-Wagner analysis was used to study crystallite sizes and lattice strain and also stress and energy density. The cation distribution for each composition has been suggested. The experimental and theoretical lattice constants were found to be in good agreement with each other confirming the agreeability of the suggested cation distribution. The force constants for tetrahedral and octahedral sites have been determined by infrared spectral analysis. The increase in force constants of ZnFe2O4 nanoparticles compared to other samples suggests the elastic properties of this sample is better than the other samples. The values of Young’s modulus, rigidity modulus, bulk modulus, Debye temperature have been determined. In addition, using the values of the compliance sij obtained from elastic stiffness constants, the values of Young’s modulus and Poisson’s ratio along the oriented direction have been calculated for the samples. Consequently, we can conclude the ZnFe2O4 nanoparticles could be more useful in industry applications because of their elastic properties compared to other samples.
Keywords: Ferrites; Citrate method; X-ray diffraction method; IR spectroscopy; Mechanical properties.
1. Introduction
Soft ferrites have been widely used for different kinds of magnetic devices such as inductors, transformers and magnetic heads for high frequency as their electrical resistivity is higher than those of soft magnetic alloys. Ferrite structure with chemical formula AB2O4 was recognized to be an array of oxide anions with two interstitial cation sites A (tetrahedral) and B (octahedral) sublattices [1]. A and B are divalent and trivalent elements, respectively. The proper elemental selection and occupancy of these sites drastically modify the corresponding physical property. Such modification is attributed to the surroundings generated crystal field. AB2O4 crystallizes at ambient conditions in the cubic spinel structure of space group Fd-3m with 8 f.u. in the conventional unit cell. The cubic unit cell is formed by 56 atoms, 32 oxygen anions distributed in a cubic close-packed structure, and 24 cations occupying 8 of the 64 available tetrahedral sites (A sites) and 16 of the 32 available octahedral sites (B sites) [1].
There are three configurations for the ferrite cation distribution; normal, inverse and mixed spinels. Nickel ferrite (NiFe2O4) and copper ferrite (CuFe2O4) have an inverse spinel structure with Ni2+ and Cu2+ ions at octahedral B sites and Fe3+ ions are equally distributed at tetrahedral A and octahedral B sites. The ferric ions preferentially fill all of the eight A-sites. The remaining eight go on to the B sites, as do the eight Ni2+ ions. The antiferromagnetic interaction orients these eight Fe3+ moments and eight nickel moments antiparallel to the eight Fe3+ moments on the tetrahedral sites. The Fe3+ ion moments will just cancel, but the moments on the nickel ions give rise to an uncompensated moment or magnetization. On the other hand, zinc ferrite (ZnFe2O4) has a normal spinel structure with Zn2+ ions at A sites and Fe3+ ions at B-sites. This is because of the preferences of Zn2+ to occupy the tetrahedral spinel sites forming a normal spinel, while Cu2+ occupies mainly the octahedral [B] sites, and thus, the tetrahedral sites are occupied by half of Fe3+ and CuFe2O4 describes as fully inverse spinel. In the case of Zn1−xCuxFe2O4, where 0 < x < 1, the tetrahedral sites are occupied both by Zn2+ and Fe3+ cations and this spinel structure are denoted as partially inverse [2].
The Zn1−xCuxFe2O4 have been widely studied for their intriguing magnetic and catalytic properties and also for their chemical reactivity. Nowadays, Ni-Cu-Zn ferrites have been the dominant materials for Multi-Layer Chip Capacitors (MLCC) and Multi-Layer Chip Inductor (MLCI) due to its better magnetic properties at high frequency and low sintering temperature [3].
Studies of the elastic constants are important in order to understand the behavior of the engineering materials. Elastic constants related closely to many physical properties of solids, such as acoustic– phonon frequencies, internal stress, Debye temperature, etc. Furthermore, they provide a sensitive probe of phase transitions and an indication of the nature of interatomic and interionic binding forces in the material [4,5]. Further, the elastic properties of Fe3O4 could be important in industrial applications because of their elastic data are very much useful to determine the strength of the materials under various strained conditions. While in basic research, the data are useful obtaining an insight into the structure.
The ultrasonic pulse transmission technique is the most convenient technique for elastic constants and Debye temperature determination [5]. To study the elastic properties of spinel ferrite and garnet systems, a new technique based on the infrared spectroscopy has been developed by Modi et al. [6]. The IR spectra absorption bands mainly appear due to the vibrations of the oxygen ions with the cations producing various frequencies in the unit cell. In certain mixed ferrite materials, as the concentration of the divalent metal ions increases, it gives rise to the structural change or the cations distribution in spinel lattice crystal without affecting the spinel ferrite structure [1]. The structural changes brought by the metal ions that are either lighter or heavier than divalent ions in the ferrites strongly influence the lattice vibration. Also, the vibration frequency depends on the cations’ mass, oxygen distance and the bonding force [5].
There are two ways of expressing the elastic properties of crystals, one in terms of elastic stiffness constants, usually denoted by Cij, where i and j may have the values 1 to 6, and the other in terms of the elastic compliance constants, Sij. In general, there are 36 elastic constants, but in the case of isotropic and homogeneous materials like spinel ferrite and garnet, the elastic stiffness constants can be reduced to three (C11, C12 and C44). The crystal to be compressed or stretched in various directions so that only one component of strain is produced, e.g. a uniform expansion parallel to the x-axis. Usually, to obtain such a change of shape it is necessary to apply simultaneously stretching forces of unequal amount parallel to all three axes. The constant c11, is the ratio under these conditions of the stretching force parallel to the x-axis, to the expansion in that direction. The inverse of the elastic stiffness constants tensor, often called the compliance constants tensor, with components 
can be used to derive the linear compressibilities along the principal axes of the coordinates system.
In this paper, it is tried to explain the structural and elastic properties of AFe2O4 (A = Zn, Zn-Cu, Zn-Cu-Ni) nanoparticles prepared by citrate methods which have been not investigated so far. These compounds have long been the subject of study because of its technological applications as compared to the other ferrites. The strain due to lattice deformation of the samples was estimated by Scherer and Halder-Wagner (H-W) methods. In addition, the elastic moduli properties of the samples have been specified by using a new technique based on the infrared spectroscopy. Finally, the structural and elastic properties of the samples have been compared.
2. Experimental
2.1. Materials and sample preparation
The ZnFe2O4, Zn0.5Cu0.5Fe2O4 and Ni0.3Cu0.2Zn0.5Fe2O4 ferrites were prepared by the citrate precursor method and similar to the recipe reported elsewhere [7-9]. Firstly, a solution containing appropriate concentrations of metal nitrates Fe(NO3)3·9H2O, Zn(NO3)2∙4H2O, Cu(NO3)2∙3H2O, Ni(NO3)2∙6H2O, and citric acid, equal to the total number of moles of nitrate ions and according to Table 1 was evaporated at 50°C, overnight. The homogeneous sol-like substance subsequently was dried at 80°C, overnight. Then, the resulting spongy and friable materials were powdered and subsequently sintered separately under an air-ambient atmosphere at temperature 200°C for 2 h. All the reagents used in this work have been purchased from Merck Inc. For convenience, a list of the abbreviations is given in Table 1. All the chemicals were purchased from Merck and used as received ones without further purification.
Table 1: Moles of the metal nitrates for the preparation of AFe2O4 samplesa.
Sample | Abbreviation | Fe(NO3)3.9H2O | Cu(NO3)2.2H2O | Zn(NO3)2.4H2O | Ni(NO3)2.6H2O |
ZnFe2O4 | ZFO | 0.050 | ------- | 0.0170 | ------- |
Zn0.5Cu0.5Fe2O4 | CZFO | 0.050 | 0.0085 | 0.0085 | ------- |
Ni0.3Cu0.2Zn0.5Fe2O4 | NCZFO | 0.050 | 0.0035 | 0.0085 | 0.0050 |
aMole of the citric acid is considered to be 0.067 in all preparation.
2.2. Physical measurements
The X-ray diffraction (XRD) patterns have been recorded using a Bruker AXS diffractometer D8 ADVANCE with Cu-Kα radiation in the range of 2
= 20-80˚ at room temperature (RT). The XRD data were analyzed using a commercial X’pert package and Fullprof program. XRD profile analysis is a simple and powerful method for evaluating the crystallite size and lattice micro-strain. Two factors determine the breadth of Bragg peak including crystallite size-dependent or strain dependent broadening effects, except instrument-dependent effect. Scherrer’s equation indicates the broadening of the XRD pattern which is attributed to the crystallite size-induced broadening [10].
(1)
Here, βhkl is the full-width at half-maximum of the strongest diffraction peak (311) located at about 35˚. Halder and Wagner have given an approximation to the integral breadth of a Voigt function as [11]:
(2)
Where βL and βG are the Lorentzian and Gaussian components, respectively. In cases of isotropic line broadening, the information on strain (ε) and the crystallite size (D) of the powders have been obtained from βhkl and planar spacing dhkl related to each reflected plane via Halder-Wagner (H-W) method [11]:
(3)
where 
and 
. Finally, the results of Halder-Wagner method are compared with the Scherrer method.
The morphology of the samples was studied by the SEM (Hitachi S4160, Cold Field Emission) analysis. The FT-IR spectra of samples were recorded by using a Perkin-Elmer FT-IR spectrometer in the wave number range from 350 cm-1 to 2000 cm-1.
3. Results and Discussions
3.1 XRD analysis
XRD patterns of the ZnFe2O4, Zn0.5Cu0.5Fe2O4 and Ni0.3Cu0.2Zn0.5Fe2O4 ferrites are shown in Fig. 1. Identification of structure type using X'pert high score package confirms that all the diffraction peaks of the XRD patterns can be quite well indexed to the cubic structure Fe3O4 (JCPDS, 74-2399) with space group Fd-3m. Therefore, all the samples are single-phase. The Miller indices have been added for all peaks in XRD pattern of ZFO.
Fig. 1: X-ray diffraction pattern of ZFO, CZFO and NCZFO nanoparticles.
Accurate estimation of lattice constant has been done using Nelson–Riley (NR) extrapolation method by minimizing both systematic and random error. The values of the lattice parameter obtained from each reflected plane related to the cubic structure were plotted against the NR function [3]:
(4)
The extrapolation of the straight line to F(Ɵ) = 0 or Ɵ = 90° gives an accurate lattice parameter. The results are summarized in Table 2.
The X-ray density (
) of the samples was calculated using formula [12]:
(5)
where M is the molecular weight of sample and N is the Avogadro’s number. The calculated values of are summarized in Table 2.
Table 2: The experimental and theoretical values of lattice parameter, and also ionic radius, and cation distribution of A- and B-sites.
