Journal of Pure and Applied Ultrasonics

Jitendra Kumar ¹, S. K. Shrivastava ², Kailash ³

Affiliations
1 Department of Physics, Rajkiya Mahila Snatakottar Mahavidhyalaya, Banda-210001, IN
2 Department of Physics, Bundelkhand University, Jhansi-284001, IN
3 Department of Physics, B.N. P.G. College, Rath, Hamirpur-210431, IN

Abstract

The calcium oxide crystal possesses well developed fcc structure and is divalent in nature. Oxides and silicates make up the bulk of the Earth's mantle and crust, and thus it is important to predict their behavior for the study of seismic and volcanic activities. The second order elastic constants (SOECs) were computed using Coulomb and Born-Mayer potential in the temperature range 100-1000 K. The ultrasonic velocities were calculated using these values of second order elastic constants and density ρ. In this study temperature dependent velocities in calcium oxide have been calculated along <100>, <110> and <111> crystallographic directions and the results are presented graphically and discussed in depth.

Keywords

Micro Structural Properties, Seismic and Volcanic Activities, Acoustic Wave Velocities, Second Order Elastic Constants.

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Jitendra Kumar ¹

Affiliations
1 Department of Physics, Rajkiya Mahila Snatkottar Mahavidyalaya, Banda-210 001, IN

Abstract

The acoustic wave velocities have been calculated using the values of second order elastic constants (SOECs) and density ρ. In this study first the second order elastic constants for some oxides CdO, CoO and FeO which possess face centered cubic crystal structure are computed and then acoustic wave velocities has been obtained along different crystallographic directions starting from 100K to an elevated temperature 1000K. The results thus obtained are presented graphically, compared and discussed. The relations presented can be applied to all materials likely to exist in the earth's mantle and crust with rock-salt structure and therefore provide a useful means of considering the properties of rock-forming compounds.

Keywords

Elastic Constants, Ultrasonic Velocity, Face Centered Cubic.

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Jitendra Kumar ¹

Affiliations
1 Department of Physics, Govt. Girls P.G. College, Banda-210001, U.P., IN

Abstract

Ultrasonic applications cover a number of fields of human importance like medical, research, industry, defence and many more. Although ultrasound competes with other forms of medical imaging, such as X-ray techniques and magnetic resonance imaging, it has certain desirable features. Ultrasonic methods offer the possibility to identify and characterize microstructure properties, as well as defects in the materials, controlling material behavior on the basis of physical mechanisms that forecast the properties of the materials, structural inhomogeneities, elastic constants, precipitates, dislocations, grain phase transformation, porosity, cracks, electrical resistivity, thermal conductivity, specific heat, and many other physical properties are well connected with temperature-dependent ultrasonic parameters.

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Jitendra Kumar ¹, Virendra Kumar ², Kailash ³, S. K. Srivastava ⁴

Affiliations
1 Department of Physics, Govt. Girls P. G. College, Banda-210001, U.P., IN
2 D.A.V. Inter College, Banda-210001, U.P., IN
3 Department of Physics, BN PG College, Rath, Hamirpur-210431, U.P., IN
4 Department of Physics, Bundelkhand University, Jhansi-284128, U.P., IN

Abstract

The Calcium oxide crystal possesses well developed structure of the NaCl-type and is divalent in nature. Oxides and silicates make up the bulk of the Earth's mantle and crust, and thus it is important to predict their behaviour. The elastic energy density for a deformed crystal can be expanded as a power series of strains using Taylor's series expansion. One can get this expansion starting from nearest neighbour distance and hardness parameter utilizing Coulomb and Born-Mayer potentials for face centred cubic crystal symmetry. The coefficients of the quadratic, cubic and quartic terms are known as the second, third and fourth order elastic constants (SOECs, TOECs and FOECs) respectively. When the values of second and third order elastic constants and density for any material at a particular temperature are known; one may get ultrasonic velocities for longitudinal and shear waves in different crystallographic directions which give important information about its anharmonic properties.
The theory obtained is applied to get the higher order elastic constants for Calcium oxide crystal at different higher temperatures and the results obtained are presented graphically and discussed widely.

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