Temperature dependent ultrasonic properties of aluminium nitride

Hexagonal wurtzite structured aluminium nitride has been characterized by the theoretical calculation of ultrasonic attenuation, ultrasonic velocity, higher order elastic constants, thermal relaxation time, acoustic coupling constants and other related parameters in temperature range 200-800 K for wave propagation along the unique axis of the crystal. Higher order elastic constants of AlN at different temperatures are calculated using Lennard-Jones potential for the determination of ultrasonic attenuation. A decrease in ultrasonic velocity with temperature has been predicted, which is caused by reduction in higher order elastic constants with temperature. The temperature dependent ultrasonic properties have been discussed in correlation with higher order elastic constants, thermal relaxation time, thermal conductivity, acoustic coupling constants and thermal energy density. Anomalous behaviour of the attenuation is found at 400 K. On the basis of attenuation, the ductility and performance of AlN have been studied.     

Size dependent ultrasonic properties of InN nanowires

The ultrasonic properties of single crystalline indium nitride nanowires (InN NWs) are studied for wire size (diameter) 6–100 nm at 300 K following the interaction potential model. Ultrasonic attenuation, ultrasonic velocity, acoustic coupling constant and thermal relaxation time are calculated using higher order elastic constants and thermal conductivity of the nanowires. The analysis of size dependent thermal relaxation time and ultrasonic properties shows that above the 20 nm diameter, InN nanowire tends towards its bulk material property. The third order polynomial is found to be best fit for size variation of thermal relaxation time. The ultrasonic attenuation as a function of size of the nanowires is found to be mainly affected by the thermal conductivity of the nanowires of different sizes.     

Ultrasonic wave propagation in rare-earth monochalcogenides

The ultrasonic attenuation in thulium monochalcogenides TmX (X=S, Se and Te) has been studied theoretically with a modified Mason’s approach in the temperature and range 100 K to 300 K along 〈100〉, 〈110〉 〈111〉 crystallographic directions. The thulium monochalcogenides have attracted a lot of interest due to their complex physical and chemical characteristics. TmS, TmSe and TmTe are trivalent metal, mixed valence state, and divalent semiconductor, respectively. Coulomb and Born-Mayer potential is applied to evaluate the second- and third-order elastic constants. These elastic constants are used to compute ultrasonic parameters such as ultrasonic velocities, thermal relaxation time, and acoustic coupling constants that, in turn, are used to evaluate ultrasonic attenuation. A comparison of calculated ultrasonic parameters with available theoretical/experimental physical parameters gives information about classification of these materials.      

Propagation of ultrasonic waves in neptunium monochalcogenides

The ultrasonic attenuation and acoustic coupling constants due to phonon–phonon interaction and thermoelastic relaxation mechanisms have been studied for longitudinal and shear waves in B₁ structured neptunium monochalcogenides NpX (X: S, Se, Te) along 〈1 0 0〉 direction in the temperature range 100–300 K. The second and third order elastic constants (SOEC and TOEC) of the chosen monochalcogenides are also computed for the evaluation of ultrasonic parameters. The ultrasonic attenuation due to phonon–phonon interaction process is predominant over thermoelastic relaxation process in these materials. The ultrasonic attenuation in NpTe has been found lesser than other materials NpS, NpSe and GdY (Y: P, As, Sb and Bi). The semiconducting or semimetallic nature of neptunium monochalcogenides can be well understood with the study of thermal relaxation time. Total ultrasonic attenuation in these materials is found to be quadratic function of temperature. The nature of NpTe is very similar to semimetallic GdP. The mechanical and ultrasonic study indicates that NpTe is more reliable, perfect, flawless material.     

Elastic and ultrasonic properties of single crystalline nickel nanowires

In the present paper, we have theoretically calculated the non linear elastic constants of single crystalline Ni NWs at very broad temperature range 20–300 K validating simple interaction potential model. The temperature dependent ultrasonic attenuation and other related properties are determined using their second and third order elastic constants (SOECs/TOECs). Where possible, the results are compared with experiments from literature. There is a correlation between the thermal conductivity and ultrasonic attenuation in the temperature range 100–300 K. Also, a correlation between the resistivity and ultrasonic attenuation in the temperature range 40–100 K has been established validating the theoretical approach.     

Elastic waves at the (0 0 1) and (1 1 0) surfaces of AlN, GaN and InN

We have studied the acoustic waves in the (0 0 1) and (1 1 0) surfaces of AlN, GaN and InN. We have employed the surface Green function matching method and different sets of calculated elastic constants available in the literature for these materials, because no experimental values are available. Important differences are found for the velocities of the bulk and surface acoustic waves coming from these sets of elastic constants, in such a way that they could be easily measured by ultrasonic and Brillouin techniques. These results together with the expressions obtained here for the velocities of the acoustic waves in high symmetry directions could be used to determine the elastic coefficients of these materials.     

Temperature dependent physical effects of ultrasonic wave in beryllium chalcogenides

Temperature dependent physical effects of ultrasonic wave viz. ultrasonic attenuation due to interaction of sound wave and thermal phonons, thermoelastic loss and dislocation damping have been studied in beryllium chalcogenides (BeX, X = S, Se and Te) in the temperature range 50-500 K, along three crystallographic directions of propagation viz. [1 0 0], [1 1 0] and [1 1 1] for longitudinal and shear modes of propagation. Second and third order elastic moduli have been obtained using electrostatic and Born repulsive potentials and taking hardness parameter and nearest neighbour distance as input data. Gruneisen numbers, acoustic coupling constants and drag coefficients have been evaluated for longitudinal and shear waves along different directions of propagation and polarization. The results have been discussed and compared with the available data. It has been found that the temperature dependence of ultrasonic attenuation follows the temperature variation of diffusion coefficient and is mainly dominated by phonon-phonon interaction.     

Macroscopic polarization and thermal conductivity of GaN

We theoretically investigated the effect of macroscopic polarization (sum of spontaneous and piezoelectric polarization) on the thermal conductivity of wurtzite GaN. Macroscopic polarization contributes to the effective elastic constant of the GaN and thus modifies the phonon group velocity. We used the revised phonon velocity to estimate the Debye frequency and temperature. Different phonon scattering rates were calculated as functions of the phonon frequency. The thermal conductivity of GaN was estimated using revised parameters such as the phonon velocity and phonon relaxation rate. The revised thermal conductivity at room temperature increased from 250 to 279 W m⁻¹ K⁻¹ due to macroscopic polarization. The method we developed can be used for thermal budget calculations for GaN optoelectronic devices.     

The structural, elastic and thermodynamical properties of zinc-blend structure InN from first principles

A theoretical study of the structural, elastic and thermodynamic properties of the cubic zinc-blende (ZB) structure InN are presented in this paper by performing first principles calculations within local density approximation. The values of lattice constant, bulk modulus and its pressure derivatives and elastic constants are in excellent agreement with the available experimental data and other theoretical results. It is found that the ZB structure InN should be unstable above 20 GPa mechanically. The pressure and temperature dependencies of the bulk modulus, the heat capacity and the thermal expansion coefficient and the entropy S, as well as the Grüneisen parameter are obtained by the quasi-harmonic Debye model in the ranges of 0-1500 K and 0-25 GPa.     

Theoretical study of temperature dependent lattice anharmonicity in TlCl and TlBr

Effect of temperature on ultrasonic attenuation in BCC structured (CsCl-type) thallium halides (TlCl and TlBr) have been investigated in a wide temperature range 50–500 K for longitudinal and shear modes along [1 0 0], [1 1 0] and [1 1 1] directions of propagation. Starting with nearest neighbour distance and repulsive parameter and taking interactions up to next nearest neighbours, second and third order elastic moduli have been evaluated, which in turn have been used for evaluating thermal relaxation time, Gruneisen numbers, acoustic coupling constants, ultrasonic velocity and ultrasonic attenuation. Ultrasonic attenuation in these bcc structured crystalline materials has been found less than the fcc crystalline materials. The results have been discussed and compared with available data.     

Acoustic waves in (0 0 1) anisotropic polytype heterostructures

We have studied the acoustic waves of (0 0 1) polytype heterostructures formed by slabs of cubic crystals. We have considered symmetric and asymmetric heterostructures formed by AlN, GaN and InN in the zinc-blende structure due to the potential applications of these materials. The anisotropy of the materials has been taken into account and the different propagation directions ranging from the [1 0 0] to the [1 1 0] have been considered. We obtain the dispersion relations for different propagation directions. The coupling between the spatial components of the elastic displacements is different for symmetry and general propagation directions. The spatial localization of the modes in the heterostructures has also been obtained.     

Effect of temperature on non-destructive wave propagation in potassium halides

Temperature dependence of ultrasonic attenuation is investigated for potassium halides in the temperature range 100–400 K. These calculations are done for KCl, KBr and KI for longitudinal and shear waves along the 〈1 1 1〉 direction. The non-linearity coupling parameters and thermal relaxation time have also been obtained for these crystals. In the present investigation, it has been found that phonon–phonon interaction is the dominant cause for ultrasonic attenuation.     

Low temperature elastic constants and Debye temperature of NbO2

The transit times of ultrasonic waves have been measured in single crystal NbO₂ from 295 K down to 1.5 K for quasilongitudinal and shear waves propagating in the [100] direction and down to 160 K for eight other waves. Values are obtained for the C₄₄ elastic constant and for an elastic constant combination which is approximately equal to C₁₁ for temperatures down to 1.5 K and for C₁₁, C₁₂, C₁₃, C₁₆, C₃₃, and C₆₆ down to 160 K. These results are used to deduce 0 K values for the elastic constants and an elastic Debye temperature of 596 ± 7 K at 1.5 K. The acoustic mode heat capacity calculated from the latter is significantly smaller than the heat capacity measured by Wenger and Keesom at low temperatures. Following Wenger and Keesom, the difference is attributed to phasons (excitations involving the phase modulation of charge density waves). An average velocity is deduced for the phasons.     

Vibrational properties of (0 0 1) III-V nitride superlattices

We study the acoustic waves of superlattices grown along the [0 0 1] direction and formed by slabs of cubic III-V nitride. We consider structures formed by combining AlN, GaN and InN in the zinc-blende structure because of the possible applications of these materials. The anisotropy of the materials has been taken into account and the different propagation directions including symmetry directions and general directions have been considered. The dispersion relations for these propagation directions have been obtained. The evolution of gaps along the propagation directions is studied. Total gaps for some propagation directions and frequency ranges are found in GaN-InN superlattices.     

Acoustic waves in (001) InN–AlN and InN–GaN superlattices

We study the acoustic waves of (001) InN–AlN and InN–GaN superlattices. We obtain the dispersion curves for various symmetric and general orientations of the wavevector parallel to the interfaces. The results reveal the impact of the elastic anisotropy due to the zinc-blende structure of the constituent materials. It is found that for certain material parameters and orientations, the dispersion curves exhibit wide gaps with potential for the existence of surface localized waves.     

Temperature dependence of elastic moduli for solid C60

The attenuation and velocity of ultrasonic waves (at a frequency of ～4 MHz) along the 〈111〉 and 〈100〉 directions in solid C₆₀ single-crystal samples are measured in the temperature range 100–300 K. The temperature dependences of the complete set of elastic constants for C₆₀ fullerite are determined from the experimental data. It is shown that the specific features in the behavior of the elastic moduli near the orientational phase transition temperature are associated with different contributions of the relaxation processes to the effective elastic moduli. The activation volume and deformation potentials for the ground and excited states of the C₆₀ low-temperature phase are evaluated from the results obtained in this work and the data available in the literature.     

Green's function approach to paraelastic relaxation

The dynamical behavior of the elastic constants of a crystal containing paraelastic defects is investigated theoretically. A two-level model for the paraelastic defect is adopted, and the coupling between the defect and the lattice vibrations is considered to be strong. The imaginary part of the elastic compliance tensor is calculated by the Green's function method using the Feynman graph technique. It is shown that the change of the elastic compliance due to the defects is in general a superposition of the Debye-type relaxation and of resonant absorption of the acoustic waves. Expressions for the linewidth of the resonance and the Debye relaxation time are derived.     

Acoustic properties of multiferroic BiFeO<Subscript>3</Subscript> over the temperature range 4.2–830 K

The longitudinal acoustic wave velocity and attenuation in BiFeO₃ ceramics have been measured by ultrasonic pulse-echo technique at a frequency of 10 MHz in the temperature range from 4.2 K to 830 K. The anomalies observed in the sound velocity and attenuation behavior versus temperature are attributed to the assumed relaxation in the temperature range 200–500 K and antiferromagnetic phase transition at higher temperatures. Order parameter fluctuations along with magnetostriction are discussed as the factors determining the acoustic wave velocity anomaly in the vicinity of the antiferromagnetic phase transition point.     

Surface acoustic waves and elastic constants of InN epilayers determined by Brillouin scattering

The surface acoustic wave velocity in InN has been experimentally determined by means of Brillouin scattering experiments on c ‐ and m ‐face epilayers. From simulations based on the Green's function formalism we determine the shear elastic constants c₆₆ and c₄₄ and propose a complete set of elastic constants for wurtzite InN. The analysis of the sagittal and azimuthal dependence of the surface acoustic wave velocity indicates a slightly different elastic behavior of the m ‐face sample that basically affects the c₄₄ elastic constant. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

First-principles study of elastic and thermo-physical properties of kesterite-type Cu2ZnSnS4

The lattice constants and elastic constants of the kesterite-type Cu₂ZnSnS₄ have been calculated using density-functional theory (DFT). The calculated lattice constants are in good agreement with the experimental data. The calculated elastic constants indicate that the bonding strength along the [1 0 0] and [0 1 0] directions is as strong as the one along the [0 0 1] direction. The high B/G ratio shows that the kesterite-type Cu₂ZnSnS₄ compound has ductile behavior. Finally, using the Debye model, the volume, bulk modulus and heat capacity as a function of temperature for the kesterite-type CZTS have been estimated at different pressures. The Debye temperature and Gruneisen parameter are 157 K and 2.28 at 300 K temperature, respectively. The present results can give some information for the design of the kesterite-type CZTS compounds, and these can also be used to stimulate future experimental and theoretical work.