Elastic Properties of Cr-doped Mn Ferrite

M H Abdellatif,A A Azab

doi:10.1186/s42269-019-0143-5

M H Abdellatif, A A Azab

Open Access

https://doi.org/10.1186/s42269-019-0143-5

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Abstract

BackgroundThe mechanical properties of Mn-Cr ferrite of different compositions are important for industrial applications in everyday life. Ferrites are used in electric choke coils, electric transformers, and many other electronic and optical devices. The elastic properties can be understood by studying the longitudinal sound velocity (Vl) and shear velocity (Vs).ResultsThe longitudinal sound velocity (Vl) and shear velocity (Vs) are measured at room temperature by pulse transmission technique at the frequency of 1659 Hz, which is ideally representing the mechanical properties of the ferrite crystal. The shear sound velocity was found to be around 4 × 103 m∕s while the longitudinal sound velocity was ranging according to the doping concentration from 6 × 103 to 1 × 104 m∕s. The behavior of Young’s modulus (E), rigidity modulus (n), mean sound velocity (Vm), and Debye temperature (θD) is quite similar, where a change in the slope was noticed at Cr concentration higher than 0.7 in the spinel lattice.ConclusionWe have characterized the elastic properties of the spinel structure Mn-Cr ferrite with different Cr ion concentration at a fixed sound frequency using the pulse transmission technique. The longitudinal sound velocity showed an increase with increasing Cr ion concentration, the rigidity constant as well as Debye temperature, Isotropic compressibility, and the acoustic impedance showed behavioral change at Cr ion concentration x = 0.7 which is correlated to the intra-ionic distances change due to the replacement of Fe ions with smaller size Cr ions.

Highlights

IntroductionFerrites have been proven as important compounds that have a wide range of applications in the industry (Abdellatif et al, 2018; Abdellatif et al, 2017), research (Liakos et al, 2016; Abdellatif et al, 2015), physics (Abdellatif et al, 2018; Abdellatif et al, 2015; Abdellatif et al, 2012; Abdellatif et al, 2011), and chemistry of everyday life (Abdellatif et al, 2017; Abdellatif et al, 2016; Abdellatif et al, 2017; Abdellatif et al, 2018; Abdellatif & Azab, 2018)
The Debye temperature θD has been calculated from the Anderson formula
We can fully understand the change of the sound velocity by studying its thermodynamical coordinates, since the response of the solid to the acoustic pulse depends on its interatomic arrangement, in a spinel structure, and there are two main interstitial sites, the octahedral (B) and tetrahedral site (A)

Summary

Introduction

Ferrites have been proven as important compounds that have a wide range of applications in the industry (Abdellatif et al, 2018; Abdellatif et al, 2017), research (Liakos et al, 2016; Abdellatif et al, 2015), physics (Abdellatif et al, 2018; Abdellatif et al, 2015; Abdellatif et al, 2012; Abdellatif et al, 2011), and chemistry of everyday life (Abdellatif et al, 2017; Abdellatif et al, 2016; Abdellatif et al, 2017; Abdellatif et al, 2018; Abdellatif & Azab, 2018). Young’s modulus, the rigidity constant, the mean sound velocity, the transverse sound velocity, and the longitudinal sound velocity are known as the elastic parameters of solid crystals. Those parameters can be used to interpret the behavior of the crystalline solid on the basis of binding energy between atoms. The Debye temperature can be calculated based on the mechanical parameters using the Anderson formula (Lakhani & Modi, 2010). The mechanical properties of Mn-Cr ferrite of different compositions are important for industrial applications in everyday life. The elastic properties can be understood by studying the longitudinal sound velocity (Vl) and shear velocity (Vs)

Results

Discussion

Conclusion