Pressure dependent ultrasonic properties of hcp hafnium metal

Abstract

The elastic and ultrasonic properties have been evaluated at room temperature between the pressure 0.6 and 10.4 GPa for hexagonal closed packed (hcp) hafnium (Hf) metal. The Lennard-Jones potential model has been used to compute the second and third order elastic constants for Hf. The elastic constants have been utilized to calculate the mechanical constants such as Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and Zener anisotropy factor for finding the stability and durability of hcp hafnium metal within the chosen pressure range. The second order elastic constants were also used to compute the ultrasonic velocities along unique axis at different angles for the given pressure range. Further thermophysical properties such as specific heat per unit volume and energy density have been estimated at different pressures. Additionally, ultrasonic Grüneisen parameters and acoustic coupling constants have been found out at room temperature. Finally, the ultrasonic attenuation due to phonon–phonon interaction and thermoelastic mechanisms has been investigated for the chosen hafnium metal. The obtained results have been discussed in correlation with available findings for similar types of hcp metals.

Theoretical Approach to Investigate Temperature Dependent Ultrasonic and Thermophysical Properties of Ti-Zr-Hf Ternary Alloy

“…The temperature dependence of SOECS and TOECs for Ti-Zr-Hf alloy have been evaluated using Lennard-Jones potential method. The formulation for calculation of six independent SOECs and ten independent TOECs is thoroughly discussed in the literature [18]- [21]. The bulk modulus (B), shear modulus (G), Young's modulus (Y) and Poisson's ratio have been computed by Voigt-Reuss-Hill method [22] for hexagonal crystals.…”

“…The bulk modulus (B), shear modulus (G), Young's modulus (Y) and Poisson's ratio have been computed by Voigt-Reuss-Hill method [22] for hexagonal crystals. The ultrasonic velocities in longitudinal (V L ), quasi-shear (V S1 ) and shear (V S2 ) modes along unique axis (c-axis) at different angles of propagation, Debye average velocity (V D ) and Debye temperature (θ D ) can be calculated with the help of higher order elastic constants using the formulation discussed in literature [16], [18], [20], [21]. The RHEAs are used in harsh conditions including high pressure and temperature, so it becomes important to study thermophysical properties such as heat capacity, energy density and thermal conductivity at different temperatures.…”

“…The ultrasonic attenuation in solids and liquids is directly related to the physical properties like elasticity, thermal conductivity, type of bonds and interactions in the material etc. The lead causes for the ultrasonic attenuation in materials at high temperature are phonon-phonon interaction (Akhiezer loss) [21], [26] and loss due to thermo-elastic relaxation mechanism [16], [27]. The formulation for evaluating the ultrasonic absorption coefficient ( ) over frequency ( ) squared due to phonon-phonon interaction for longitudinal and shear modes in terms of the acoustic coupling constant (D) was developed by Mason and Bateman [28] and is given as follows:…”