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.
In this study, we have computed temperature dependent ultrasonic and thermophysical properties of hcp medium entropy alloy Ti-Zr-Hf in temperature range of 0K-900K. Second order and third order elastic constants (SOECs and TOECs) have been calculated using lattice parameters using the Lennard-Jones potential model. With the help of SOECs and TOECs, the elastic parameters such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio have been computed. SOECs were also utilized to determine the ultrasonic velocities at different angle along unique axis. Further, thermophysical properties such as Debye temperature, Debye heat capacity, energy density in temperature range of 0K-900K and thermal conductivity in temperature range of 300K-900K have also been theoretically estimated. Additionally, the ultrasonic attenuation due to phononphonon interaction in both longitudinal and shear mode and thermoelastic mechanism have been computed for chosen alloy in the temperature range 300K-900K and attenuation due to the phonon-phonon interaction was found to be dominating over that due to thermoelastic mechanism
The second and third order elastic constants (SOECs and TOECs) of 4d-transition metal mononitrides XN (X: Zr and Nb) have been computed in the temperature range 0 K–500 K using Coulomb and Born–Mayer potential up to second nearest neighbours. In order to investigate the mechanical stability of XN, the computed values of SOECs have been utilized to find out Young’s modulus, bulk modulus, shear modulus, Zener anisotropy and Poisson’s ratio. Furthermore, the SOECs are applied to compute the wave velocities for shear and longitudinal modes of propagation along ⟨100⟩, ⟨110⟩ and ⟨111⟩ crystallographic orientations in the temperature range 100 K–500 K. Temperature dependent Debye average velocity, ultrasonic Grüneisen parameters (UGPs) and Debye temperature have been evaluated. In present work the thermal conductivity of chosen materials has also been evaluated using Morelli-Slack’s approach. Specific heat and total internal thermal energy have been calculated in the temperature range 100 K–500 K on the basis of Debye theory. Thermal relaxation time, acoustic coupling constants and attenuation of ultrasonic waves due to thermo-elastic relaxation and phonon–phonon interaction mechanisms have been calculated in the temperature range 100 K–500 K. The obtained results of present investigation have been compared with available other similar type of materials.
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