INTRODUCTION:
Nano ferro spinels are a group of commercially important materials due to their excellent electrical and magnetic properties. The pure and doped NiCuZn ferrites have been the issue of extensive research because of their applications in electronic devices.1,2The ferrites with low loss at higher frequencies are used in pulse transformers, inductances, reflection coils, antennas and modulators, etc. Therefore efforts are being made to develop a low-power loss material operating in the MHz region in accordance with the miniaturization of electronic devices. NiCuZn ferrites with their ease of preparation and versatility for use in wide variety applications are commercially very attractive.
These ferrites are used in the surface mount devices (SMD) and multilayer chip inductors (MLCI) due to their high electrical resistivity and excellent soft magnetic properties at high frequencies.3,4Ferrites are also used in field of heterogeneous catalysts because of their significant electrical and magnetic catalytic properties.5-7The elastic moduli represent the mechanical strength and thermal shock resistance of sample.8 Ultrasonic pulse transmission method is used to determine the elastic constant.9 Recently a new approach to study the elastic properties through the IR spectroscopy was reported.10-13 In the present work we presented the elastic properties of NiCuZn spinel ferrites doped with chromium.
EXPERIMENTAL:
NiCuZnspinel ferrites doped with chromium, with composition of Ni0.2Cu0.2Zn0.6Fe2-xCrxO4(x=0.0 to 1.0 in steps of 0.2) were prepared by the sol-gel auto-combustion method.14 Prepared powders of all the precursor samples were sintered at 500 °C for 4 h to obtain the final product. The elemental stoichiometry determined by energy dispersive analysis of X-ray (EDAX). The crystallographic structures were identified by Phillips X-ray diffractometer (Model 3710). The IR spectra of all samples were recorded in the range 200 to 800 cm-1 using Perkin Elmer infrared spectrophotometer. Morphology and structure of the powder samples were studied on JEOL-JSM-5600 N Scanning Electron Microscope (SEM) and on Philips (model CM 200) Transmission Electron Microscope (TEM). The elastic properties of the samples were determined using infrared spectroscopy data and structural data.
RESULTS AND DISCUSSION:
Elemental Analysis:
The elemental stoichiometry determined by energy dispersive analysis of X-ray (EDAX).Figure 1 shows the EADX pattern of the typical sample x = 0.6.
Fig. 1. Typical EDAX pattern for sample x = 0.6
It is observed that the theoretical and observed atomic percentage of Ni2+, Cu2+, Zn2+, Cr3+, Fe3+ and O2- are in good agreement with each other which indicates that the prepared samples are in good stoichiometry proportion.14
X-ray diffraction:
Figure 2 represents typical XRD pattern for sample x = 0.4 confirmed the formation of cubic spinel structure of single phase without additional peaks corresponding to any other phases.
Fig. 2. Typical XRD patterns for sample x = 0.4
Infrared spectroscopy:
Typical IRspectrum of sample x=0.6 shown in Figure 3. The higher frequency bands (ν1) observed in the range of 610-568 cm-1 while lower frequency bands (ν2) observed in the range of 491-388 cm-1. High frequency bands (610-560 cm-1) assigned to the tetrahedral and low frequency bands (491-388 cm-1) assigned to the octahedral complex.15
Fig. 3: Typical IRspectrum of sample x=0.6
The force constants corresponding to the tetrahedral and octahedral complexes are calculated by using the standard formulae given below: 16
(i)
(ii)
Where, KO is the force constant on octahedral site, Kt is the force constant on tetrahedral site, M1molecular weight of tetrahedral site, M2molecular weight of octahedral site, n1 the corresponding center frequency on tetrahedral site, and n2 the corresponding center frequency on octahedral site. The force constants corresponding to the tetrahedral and octahedral complexes increases with chromium content x.
Fig. 4: Variation in values of RA and RB with chromium substitution
The average force constant K (K=Kt+Ko/2) is tabulated in Table 1. The bond lengths RA and RB have been calculated using the formula given by Gorter.17 The variation in values of RA, and RB are illustrated in Fig. 4 indicates decreases in RA, and RB with chromium content x.
SEM and TEM:
Fig. 5: SEM and TEM image of sample (x=0.8)
Typical Scanning electron micrograph (SEM) and Transmission electron micrograph (TEM) of the sample x=0.8 are shown in Fig. 5. It is observed from the SEM and TEM images that the prepared samples are amorphous and porous in nature with slightly agglomeration.
Elastic properties:
The elastic properties of the series Ni0.2Cu0.2Zn0.6Fe2-xCrxO4(x=0.0 to 1.0 in steps of 0.2) were determined using infrared spectroscopy data. Elastic moduli and Debye temperature were determined through IR data and structural data of spinel ferrite samples.10-13 The stiffness constant C11 was calculated using relation.16
(iii)
Where K is average force constant and a is lattice constant.
(iv)
Where, where r is Poisson ratio and ‘a’ is the lattice constant. The Poisson ratio is function of pore fraction. Using equation iii and iv the stiffness constant is calculated and the values are tabulated in Table 1. The variation in stiffness constant is illustrated in Fig. 6.
Fig. 6: Variation in stiffness constants with chromium content x
It is observed from Table 1 and Fig. 6 that both the stiffness constant increases with increase in chromium substitution. The values of Poisson’s ratio are decreased with the increasing chromium substitution. These two stiffness constants are further used to calculate the various elastic constants such as; Young’s modulus (E), bulk modulus (K) and modulus of rigidity (G).7,11 The variation in Young’s modulus (E), bulk modulus (K) and modulus of rigidity (G) are presented in Table 1 and Fig. 7. It can be observed from Fig. 7 that the values of Young’s modulus (E), bulk modulus (K) and modulus of rigidity (G) increased with chromium substitution. This increase in elastic moduli correlated to the strengthening in the interatomic bonding between Fe and chromium ions with increase in chromium composition x.
Fig. 7: Variation in elastic modulus with chromium content x
The longitudinal wave velocity (VL) and Shearing wave velocity (VS) calculated using following equations,
(v)
(vi)
where G is rigidity modulus with correct zero pore fraction. The values of Vland Vs used to calculate mean wave velocity (Vm),18 which used to calculate Debye temperature (θE) using formula: 19
(vii)
where h is Plank’s constant, k is Boltzmann’s constant, M is molecular weight, q is number of atom in the unit formula and Vm mean wave velocity.