Debye Average Velocity Research Articles

Temperature Dependent Behavior of Elastic and Ultrasonic Proprieties of Transition Metal Carbide Mo2C Superconductor

Abstract: Transition metal carbides exhibit peculiar chemical and physical properties, making them integral to industrial applications that demand performance under high temperatures In the case of the hexagonal transition metal carbide Mo2C superconductor, higher-order elastic constants were calculated to be temperature-dependent using an interactional potential model. Second-order elastic constants are used to determine other allied ultrasonic variables. Second-order coefficients are used to analyze the temperature variation of ultrasonic velocities along the z-direction of the superconductor. Furthermore, the temperature difference of Debye average velocity and thermal relaxation time are considered along the same direction. The temperature dependence of ultrasonic properties is explored in relation to thermal, elastic, and mechanical properties. Ultrasonic attenuation , resulting from phonon–phonon (p–p) interactions, is calculated at different temperatures .The study establishes that thermal conductivity is a core provider of the observed ultrasonic attenuation, particularly at higher temperatures. The mechanical and thermal properties of the Mo2C superconductor are superior at lower temperatures. Keywords:Transition metal carbide superconductor, Thermal conductivity, Ultrasonic properties, Elastic properties, Mechanical properties. PACS numbers: 43. 35. Cg; 62.20.Dc; 63.20.Kr.

Non-Linear Thermophysical Behaviour of Transition Metal Titanium

The propagation of ultrasonic waves in the hexagonal closed packed (hcp) structured lanthanide metal titanium has been investigated in the temperature range 300–1000 K. For this, initially the higher-order elastic constants (second-order elastic constants (SOECs) and third-order elastic constants (TOECs)) were computed using the Lennard-Jones interaction potential model. With the help of SOECs, other elastic moduli such as Young’s modulus (Y), bulk modulus (B), shear modulus (G), Poisson’s ratio (σ) and Pugh’s ratio (B/G) were computed using the Voigt-Reuss-Hill approximation. Three types of orientation-dependent ultrasonic velocities, including Debye average velocities, were evaluated using the calculated SOECs and density of titanium in the same temperature range. Thermophysical properties such as lattice thermal conductivity, thermal relaxation time, thermal energy density, specific heat at constant volume and acoustic coupling constant were evaluated under the same physical conditions. The ultrasonic attenuation due to phonon-phonon interaction is most significant under the chosen physical conditions. The ultrasonic properties of titanium are correlated with thermophysical properties to understand the microstructural features and nature of the material.

Theoretical Investigation on Thermal, Mechanical and Ultrasonic Properties of Zirconium Metal with Pressure

Zirconium (Zr), a metal with an hcp structure, has been investigated for the transmission of acoustic wave in the 0 to 25 GPa operating pressure. For this, the Lennard-Jones interaction potential approach has been used to estimate the higher order elastic coefficients (SOECs and TOECs). This model is used to calculate the 2nd and 3rd order elastic parameters for zirconium metal. With the help of SOECs, other elastic moduli such as bulk modulus (B), Young’s modulus (Y) and shear modulus (G) have been calculated for Zr metal using Voigt-Reuss-Hill (VRH) approximations. Later, applying SOECs as well as zirconium density under the same pressure range, three orientation dependent acoustic velocities, comprising Debye average velocities, have been studied. Basic thermal characteristics such as specific heat at constant volume, thermal conductivity associated with lattice, thermal energy density, thermal relaxation time as well as acoustic coupling coefficients of zirconium metal have been also calculated at same pressure range. The computation is also satisfactory in estimating the ultrasonic attenuation coefficients, arises due to the interaction of phonons, hardness as well as melting temperature under various pressures in this research work.

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

Higher order elastic constants were calculated of the intermetallic GdFeAl ternary compound using Lennard Jones potential approach. With the using of second order elastic constants (SOECs), other elastic moduli; shear modulus, bulk modulus, Young’s modulus, Pugh’s ratio, constants of elastic stiffness and Poisson’s ratio are estimated for mechanical and elastic characterization at room temperature. Born stability and Pugh's criteria are used to examine the nature and strength of the intermetallic ternary compound and found that it is mechanically stable compound. For the investigation of anisotropic behaviour and thermophysical properties, ultrasonic velocities and thermal relaxation time have been also calculated along with different orientations from theunique axis of the crystal. The temperature variation of ultrasonic velocities, Debye average velocity and thermal relaxation time along the z axis is evaluated using SOECs. The ultrasonic properties correlated with elastic, thermal and mechanical properties which is temperature dependent is also discussed. Ultrasonic attenuation was calculated at different temperatures due to phonon –phonon (p –p) interactions. The responsible reason of attenuation is p-p interactions; it was got that the thermal conductivity is a core contributor to the characteristic of ultrasonic attenuation as a role of temperature.GdFeAl ternary compound behave as its purest form at lower temperature and are more ductile demonstrated by the minimum attenuation

Mechanical and thermophysical properties of 4d-transition metal mononitrides

Abstract 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.

Mechanical, Elastic and Thermal Properties of Hexagonal BC<sub>2</sub>N Superhard Material

The ultrasonic properties of the hexagonal BC2N superhard material were studied at temperature-dependent following the interaction potential model. Higher-order elastic constants are used for the determination of other ultrasonic parameters. The temperature variation of the ultrasonic velocities is evaluated along with different angles with z-axis (unique axis) of the crystal using the second-order elastic constants temperature variation of the thermal relaxation time, and Debye average velocities are also calculated along with the same orientation. The temperature dependency of the acoustic properties is discussed in correlation with elastic, thermal, and mechanical properties. It has been found that thermal conductivity and thermal energy density are the main contributors to the behavior of ultrasonic attenuation as a function of temperature. The responsible cause of attenuation is phonon-phonon interaction. Mechanical properties of BC2N superhard material at temperature 400K are better than at other temperatures because, at this temperature, it has low ultrasonic attenuation. Superhard material BC2N has many industrial and engineering applications.

Pressure-Dependent Elastic, Mechanical, and Ultrasonic Analysis of CaAuBi Compound

The Lennard-Jones potential model is used to investigate the effects of pressure on the elastic and ultrasonic properties of CaAuBi half-Heusler compound. Potential model technique approaches is used to evaluate second- and third-order elastic constants of CaAuBi compound at various pressures (0-15 GPa). The pressure dependence of elastic constants is studied and it has been observed that the elastic constants of the half-Heusler CaAuBi compound increase monotonically as pressure is increased. The hexagonal half-Heusler CaAuBi compound is mechanically stable at different pressures according to Born's elastic stability criteria. The Voigt-Reuss-Hill method was used to compute elastic parameters such as Young's modulus Y, shear modulus G, bulk modulus B, and Poisson's ratio ν under various pressures. For the provided pressure range, the second-order elastic constants were also utilized to determine ultrasonic velocities along with z-axis at various angles. The half-Heusler CaAuBi compound's hardness, ultrasonic attenuation, melting temperature, and anisotropy are also determined. The computation have been also satisfactory in estimating the thermal conductivity k(min) and Debye average velocity under varied pressure. Keywords: elastic properties, thermal conductivity, ultrasonic properties, thermo-physical properties.

Pressure and size dependent investigation of ultrasonic and thermal properties of ScRu intermetallic

Abstract The present work is focused on the determination of elastic, mechanical, ultrasonic and thermal properties of ScRu intermetallic under the variation of pressure 0–60 GPa and particle size 5–40 nm. Initially, the second order elastic constants (SOECs) have been computed under a potential model approach, in which interaction potential is defined by Coulomb and Born–Mayer potentials. Later on, the estimation of mechanical, ultrasonic and thermo-physical parameters has been performed using SOECs. The ultrasonic velocities are estimated in the same pressure/particle size range for wave propagation along 〈100〉 crystallographic direction. It is found that elastic constants, ultrasonic velocities, Debye average velocity, specific heat at constant volume, thermal energy density, thermal conductivity and melting point enhance with increase in pressure and decay in particle size in chosen intermetallic. The analysis of the obtained results reveals that the elastic, mechanical and thermal properties of ScRu intermetallic shall enhance effectively under pressure in comparison to decay in particle size.

Mechanical, Thermophysical, and Ultrasonic Properties of Thermoelectric HfX2 (X = S, Se) Compounds

In the present study, ultrasonic and thermophysical behaviour of thermoelectric hexagonal structured HfX2 (X = S, Se) compounds have been analysed by the theoretical evaluation of second and third order elastic constants (SOECs and TOECs) using many body interaction potential model. The computed SOECs have been used to determine the temperature dependent specific heat, thermal energy density, elastic coupling constants, Gruneisen parameters, ultrasonic velocities, Debye average velocity, ultrasonic attenuation, and thermal relaxation time. We have observed that the temperature dependent ultrasonic attenuation and thermal relaxation time for HfX2 are mainly affected by thermal conductivity. The elastic properties of the material are compared with existing data in literature for the validation of the work. The obtained values of elastic stiffness are found very large in comparison to that of other material from transition metal dichalcogenides of group IVB indicating better mechanical properties than the same group materials. Calculated elastic, thermal, and ultrasonic properties are correlated for better characterization of the materials which are useful for thermoelectric and energy transport applications.

Theoretical investigation of the electronic and thermoelectric behavior of CoV2O4 alloy

Density functional theory (DFT) within Wien2k code is utilized to compute the mechanical, thermal, electronic, magnetic and thermoelectric properties of the cubic spinel CoV2O4. The ground state lattice constant of CoV2O4 alloy agrees with previous literature. The calculated elastic constants of CoV2O4 predict that the present alloy is anisotropic, elastically stable and brittle. Beneficial acoustical applications are expected for the present alloy due to its high calculated Debye temperature and average sound velocities values. The longitudinal and transverse sound velocities modes of vibrations are found maximum along [110] directions compared to [100] and [111] directions. The calculated DOS and band structure show that CoV2O4 is electronically stable. The present alloy possesses a total magnetic moment of 12.0 [Formula: see text] and is classified as a half-metallic ferromagnet. CoV2O4 shows [Formula: see text]-type behavior and favors holes as charge carriers. The present alloy owns beneficial thermoelectric properties and can be used in thermoelectric applications.

Elastic and thermal properties of carbides of U, Pu, and Am

In this study, we investigated the behaviors of three representative actinide monocarbides (AnCs, where An = U, Pu, and Am) in terms of their superior mechanical and thermo-elastic properties. Coulomb and Born–Mayer potentials were used to calculate the temperature-dependent second order and third order elastic constants up to the second nearest neighbor. The Voigt–Reuss–Hill approximation was employed to compute the values of Young's modulus (Y), Zener anisotropy ratio (A), shear modulus (G), bulk modulus (B), Poisson's ratio (σ), and Pugh's indicator (B/G) using second order elastic constants. The Born stability criteria and Vicker's hardness parameter (Hν) were analyzed to determine the strength and nature of the materials. The Debye average velocities and Breazeale's nonlinearity parameters were calculated in the temperature range from 100 to 500 K. Thermal properties such as the lattice thermal conductivity, thermal relaxation time, crystal energy density, and acoustic coupling constant were computed at different temperatures and along various directions. The longitudinal and shear components of ultrasonic attenuation were evaluated along the three crystallographic directions comprising <100>, <110>, and <111>. The temperature- and direction-dependent ultrasonic properties were correlated with other thermo-physical properties to extract important information such as the material strength and thermal conductivity in order to assess the microstructural quality and nature of the materials, which are useful for industrial applications.

Ultrasonic study of Laves phase compounds ScOs2 and YOs2

The paper presents computation of second- and third-order elastic constants of Laves phase compounds ScOs2 and YOs2 at room temperature using Lennard-Jones potential model. The thermal relaxation time, ultrasonic velocity, ultrasonic attenuation and other related thermo-physical parameters (Debye average velocity, Debye temperature, thermal conductivity, specific heat and thermal energy density) are also calculated using second- and third-order elastic constants. The obtained elastic and ultrasonic properties of chosen compounds have been likened with the properties of other hexagonal structured materials for complete analysis and characterization.

Pressure- and orientation-dependent elastic and ultrasonic characterisation of wurtzite boron nitride

The present study discloses the evaluation of second-order elastic constants of wurtzite boron nitride (w-BN) at room temperature and at different pressures using the many-body interaction potential model approach. Orientation- and pressure-dependent ultrasonic velocity, thermal relaxation time and other related thermophysical parameters (Debye temperature, Debye average velocity, specific heat and thermal energy density) are also calculated using the evaluated second-order elastic constants. The orientation-dependent thermal relaxation time of w-BN is predominantly affected by the Debye average velocity and is indirectly governed by second-order elastic constants. Thermal relaxation time of w-BN is found to decrease with pressure. Calculated elastic and ultrasonic properties of w-BN are compared with the properties of other wurtzite structured materials for a complete analysis and characterisation of the material.

Elastic and Ultrasonic Properties of Rare-earth Lutetium Monopnictides

We present ultrasonic properties of lutetium monopnictides (LuPn: Pn = As and Sb) with the help of second and third order elastic constants in the temperature range 100–300 K. These elastic constants have been computed using Coulomb and Born–Mayer potential with the help of two basic parameters i.e., nearest neighbor distance and hardness parameter. First these elastic constants are applied to compute some mechanical constants such as bulk moduli (B), shear moduli (G), tetragonal moduli (Cs), Poisson’s ratio (ν) and Zener anisotropy ratio (A). The fracture to toughness ratio i.e., G/B was found greater than 0.57, therefore LuAs and LuSb are brittle in nature. In second part of present investigation we evaluated ultrasonic properties such as wave velocities for longitudinal and shear modes, Debye average velocity, Debye temperature and Gruneisen parameters, thermal relaxation time, thermal conductivity, acoustic coupling constants and ultrasonic attenuation due to phonon–phonon interaction along 〈100〉, 〈110〉 and 〈111〉 orientations. The achieved results of present work are compared and discussed with other rare-earth monopnictides.

Behaviour of elastic and ultrasonic properties of curium monopnictides

The temperature-dependent elastic and ultrasonic properties of curium monopnictides CmPn (Pn = N, P, As, Sb) have been explored in the present investigation. The second- and third-order elastic constants have been calculated using Coulomb and Born–Mayer potentials using lattice and hardness parameters. Mechanical parameters, such as Young’s modulus, bulk modulus, shear modulus, tetragonal modulus, anisotropic factor, and Poisson’s ratio, have been computed with second-order elastic constants. These materials fulfilled the requirement of the Born stability criterion. The toughness or fracture ratio is found to be more than 0.57 in CmPn, which indicates their brittle nature. In addition, the ultrasonic wave velocity, Debye average velocity, Debye temperature, thermal relaxation time, thermal conductivity, acoustic coupling constant, and ultrasonic attenuation have also been computed along ⟨100⟩, ⟨110⟩, ⟨111⟩ directions at room temperature. The results are discussed in correlation with other similar types of the materials.

Ultrasonic wave propagation in ternary intermetallic CeCuGe compound

The elastic and ultrasonic properties of the hexagonal intermetallic CeCuGe ternary compound have been evaluated along unique axis at room temperature. Higher order elastic constants have been calculated for CeCuGe compound using Lennard–Jones interaction potential model. The ultrasonic velocity, Debye average velocity, thermal relaxation time and acoustic coupling constant are evaluated along unique axis of the crystal and the temperature dependent ultrasonic velocities are evaluated along different angles with unique axis of the crystal. Finally temperature dependent ultrasonic attenuation is evaluated to extract important information about the material.

A Density Functional Prediction on Phase Stability, Optical, Elastic and Thermal Properties of Metallic CuZr Intermetallic Compound

An ab-initio investigation on structural, electronic, optical, elastic and thermal properties of CuZr intermetallic compound using full-potential linearized augmented plane wave method in the support of density functional theory at ambient condition have been performed. We have employed the generalized gradient approximation of (PBE) to indulgence the exchange correlation potential by solving Kohn-Sham equations. Total energy of CuZr as a function of the unit cell volume has been calculated using full potential linearized augmented plane wave (FP-LAPW) method in B1, B2 and B3 crystal structure to obtain the ground state properties. The study of different phases regarding their enthalpy vs. pressure variation is also presented. Our calculated structural parameters (a0 = 3.268 Å, B = 119 GPa and B' = 4.95) of CuZr are consistent with both the available experimental (a0 = 3.262 Å) and previously presented theoretical data (a0 = 3.280 Å, B = 121 GPa) for B2-type (CsCl) crystal structure. The results obtained from density of states (DOS) and optical spectra shows that the present compound is metallic. The value of density of states at the Fermi level N (EF) is found to 3.89 states/eV which is determined due to the contribution of ‘d’ like states of Cu and Zr and ‘p’ like states of Zr atom. The second order elastic constants are comparatively studied and an excellent agreement is found with other theoretical data. The trend of calculated elastic constants i.e. C11 - C12 &gt; 0, C11 &gt; 0, C44 &gt; 0, C11 + 2C12 &gt; 0 shows the stability criteria for B2-type (CsCl) crystal structure at ambient pressure. The sound velocities for longitudinal and shear waves, Debye average velocity and Debye temperature have been successfully calculated as a first theoretical prediction.

Effect of temperature dependence ultrasonic velocities and attenuation of GaP nanowires

The higher order elastic constants of the hexagonal wurtzite crystal structure of GaP nanowires have been evaluated using Lennard-Jones potential model at room temperature. The ultrasonic velocity increases with the temperature along particular orientation with the unique axis of crystals. Temperature variation of the thermal relaxation time and Debye average velocities is also calculated along the same orientation. The temperature dependency of the ultrasonic properties is discussed in correlation with elastic, thermal and electrical properties. It has been found that the thermal conductivity is the main contributor to the behaviour of ultrasonic attenuation as a function of temperature and the responsible cause of attenuation is phonon–phonon interaction. The mechanical properties of GaP nanowires at low temperature are better than at room temperature, because at low temperature it has low ultrasonic velocity and ultrasonic attenuation. A particularly interesting case is GaP, which is the only (Ga, In)-V semiconductor with an indirect gap in the bulk phase, and are indispensable in modern microelectronic industries.

Ultrasonic attenuation in rare-earth monoarsenides

The present paper deals with the theoretical calculation of mechanical and thermophysical properties of rare-earth monoarsenides, XAs (X: Np, Pu, Th and U) using elastic constants as the input parameters. These second- and third-order elastic constants (SOECs and TOECs) are determined in the temperature range 100–500 K using Coulomb and Born–Mayer potential upto second nearest neighbours. In order to provide the link between mechanical and dynamical behaviour of crystals, parameters such as Young’s modulus, bulk modulus, Poisson’s ratio etc. are also calculated. In addition, the Cauchy relationship is obeyed by the chosen monoarsenides and are fairly anisotropic, which results in the measurement of longitudinal and shear wave velocities along 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 directions. The toughness/fracture (G/B T) ratio is greater than 0.60, which implies that XAs compounds are brittle at room temperature. Further, the Debye temperature is computed using Debye average velocity as the input parameter. It helps in the characterization of lattice vibrations of a solid. In this work, ultrasonic attenuation due to phonon–phonon interaction (α/f 2)p−p and thermoelastic loss (α/f 2)th are computed for XAs from 100 to 500 K using Mason’s theory. It further helps in evaluating the microstructural properties of the chosen materials. The obtained results indicate that XAs is mechanically stable and are compared with data available in the literature.

Elastic, electronic and optical properties of the cubic fluoro-perovskite KCaF 3 under pressure

The elastic, electronic and optical properties of the cubic fluoro-perovskite KCaF 3 have been calculated using the full potential linearized augmented plane wave based on density functional theory. Exchange and correlation effects are taken into account by a generalized gradient approximation and an orbital independent modified Becke–Johnson potential coupled with generalized gradient approximation. The equilibrium lattice parameter, bulk modulus and its pressure derivative have been obtained using optimization method. The results are in good agreement with the available theoretical and experimental data. The elastic properties such as elastic constants, shear modulus, Young modulus, Poisson’s ratio, $$B/G$$ ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and specific heat have been calculated. The pressure dependence of the elastic moduli has been also evaluated. Furthermore, elastic anisotropic properties for KCaF 3 have been analyzed in the pressure range of 0–40 GPa by calculating directional dependence of the Young’s moduli in the crystal. From calculations of the electronic properties, it is found that the band gap is 10.4 (6.1) eV at the $$R$$ – $$\Gamma $$ direction in the Brillouin zone using modified Becke–Johnson potential coupled with generalized gradient approximation (generalized gradient approximation). The variation of the band gap versus pressure is well fitted to a quadratic function. The calculations show that indirect $$R$$ – $$\Gamma $$ to direct $$\Gamma $$ – $$\Gamma $$ band gap transition occurs at 20 GPa. Moreover, optical properties, such as the dielectric function, refractive index and extinction index, have been calculated for radiation up to 35 eV.