Abstract
Consequent to the interaction potential model, the high-order elastic constants at high entropy alloys in single-phase quaternary ScTiZrHf have been calculated at different temperatures. Elastic constants of second order (SOECs) helps to determine other ultrasonic parameters. With the help of SOECs other elastic moduli, bulk modulus, shear modulus, Young’s modulus, Pugh’s ratio, elastic stiffness constants and Poisson’s ratio are estimated at room temperature for elastic and mechanical characterization. The other ultrasonic parameters are calculated at room temperature for elastic and mechanical characterization. The temperature variation of ultrasonic velocities along the crystal's z-axis is evaluated using SOECs. The temperature variation of the average debye velocity and the thermal relaxation time (τ) are also estimated along this orientation axis. The ultrasonic properties correlated with elastic, thermal and mechanical properties which is temperature dependent is also discussed. The ultrasonic attenuation due to phonon – phonon (p-p) interactions is also calculated at different temperatures. In the study of ultrasonic attenuation such as a function of temperature, thermal conductivity appears to be main contributor and p- p interactions are the responsible reason of attenuation and found that the mechanical properties of the high entropy alloy ScTiZrHf are superior at room temperature.
Highlights
High-entropy alloys (HEAs) have involved considerable attention as they have first proposed in the physical metallurgy community [1]
ScTiZrHf high entropy alloys had the highest elastic constant values, which are the significant for the material, since they are associated with the hardness parameter
The principle established on simple interaction potential model remains valid for calculating higher-order elastic coefficients for hexagonally structured high entropy alloys
Summary
High-entropy alloys (HEAs) have involved considerable attention as they have first proposed in the physical metallurgy community [1]. Ultrasonic velocities on the basis of angle between direction of propagation and z- axis for hexagonal nanostructured compound are given by subsequent set of equations: VL2 = {C33 cos θ + C11 sin θ + C44 + {[C11 sin θ − C33 cos θ + C44(cos θ − sin θ)]2. The mathematical formulation of ultrasonic attenuation for longitudinal (α)Long and shear waves (α)Shear induced by the energy loss due to electron-phonon interaction is given by: αlong. Where ‘ ’ is the density of nanostructured compound, ‘f’ is the frequency of the ultrasonic wave, ‘ e’ is the electron viscosity and ‘ ’ is the compressional viscosity (which is zero in present case), VL and VS are the acoustic wave velocities for longitudinal and shear waves respectively and are given as: VL = √Cρ33 and VS = √Cρ44. Wherever (α/f2)This the thermoelastic loss, (α/ f2)Land (α/f2)S are the ultrasonic attenuation coefficient for the longitudinal wave and shear wave correspondingly
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