Computational Study of Ultrasonic Parameters of Hexagonal Close-Packed Transition Metals Fe, Co, and Ni

Abstract

The ultrasonic properties like ultrasonic attenuation, sound velocity in the hexagonal closed packed (hcp) Fe, Co and Ni have been studied along unique axis at room temperature. The second-and third order elastic constants have been calculated for these metals using Lennard-Jones potential. The velocities V L and V S1 have minima and maxima respectively, with 45 • with the unique axis of the crystal, while V S2 increases with the angle from unique axis. The inconsistent behavior of angle dependent velocities is associated to the action of second order elastic constants. Debye average sound velocities of these metals are increasing with the angle and has maximum at 55 • with unique axis at room temperature. Hence when a sound wave travels at 55 • with unique axis of these metals, then the average sound velocity is found to be maximum. The comparison of calculated ultrasonic parameters with available theoretical/experimental physical parameters gives information about classification of these metals.

INVESTIGATION OF INTERMETALLIC GdFeAl TERNARY COMPOUND BY ELASTIC, THERMOPHYSICAL AND ULTRASONIC ANALYSIS

“…The irregular behavior of orientation dependent velocity is due to combined effect of second order elastic constants and density of the material. The nature of the orientation dependent velocity curves in this work is similar to nature of orientation dependent velocity curve found for other hexagonal type's material [25,26]. Thus, the angle dependence of the velocities in intermetallic GdFeAl ternary compound is justified.…”

“…Negative TOECs appear in the previous paper on hexagonal structure ternary compound. Therefore, this applied theory for valuation of higher order elastic constants is justified [25,26]. Also, this theory is applicable for other hexagonally binary and quaternary compounds [27,28].…”

Elastic, Mechanical and Thermophysical properties of Single-Phase Quaternary ScTiZrHf High-Entropy Alloy

“…It is found that the value of Bulk modulus, Young's modulus and Shear modulus of high entropy alloy is smaller than those of other hexagonal alloys [38] (Table 2). Thus, ScTiZrHf high entropy alloy little Stiffness and bonding correspond to other alloys.…”

“…However, third order elastic constants are not compared due to lack of data in the literature but the negative third order elastic constants are found in previous papers for hexagonal structure materials. Therefore, the theory applied for valuation of higher order elastic constants is justified [36][37][38][39]. Hence the applied theory for the valuation of higher order elastic constants is justified.…”

Recovery of Co, Mn, Ni, and Li from spent lithium ion batteries for the preparation of LiNi Co Mn O2 cathode materials

“…The main reason is that the ultrasound reduces the mass transfer resistance for the migration of the cathode materials from PVDF into the liquid, which is known to be controlled by diffusion resistance. [21] In other words, the ultrasonic waves accelerate the convective motion and provide a large amount of energy, which increases the contact area of solid and liquid to speed up the leaching efficiency, facilitating the dissolution of the cathode materials. In addition, the ultrasound promotes the formation of liquid cavitations that blow out the surface of the cathode materials covered by insoluble substances like PVDF, generating a highly reactive surface; the cavitation bubbles are crushed during the adiabatic compression process and release a tremendous amount of energy, helping to improve the leaching efficiency.…”