Journal of Pure and Applied Ultrasonics

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Temperature Dependent Anharmonic Properties of Calcium Oxide Crystal


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

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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  • Temperature Dependent Anharmonic Properties of Calcium Oxide Crystal

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Authors

Jitendra Kumar
Department of Physics, Govt. Girls P. G. College, Banda-210001, U.P., India
Virendra Kumar
D.A.V. Inter College, Banda-210001, U.P., India
Kailash
Department of Physics, BN PG College, Rath, Hamirpur-210431, U.P., India
S. K. Srivastava
Department of Physics, Bundelkhand University, Jhansi-284128, U.P., India

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.