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First-principles calculations of mechanical properties of TiC and TiN

“…application value. In Table 3, those properties were obtained from the elastic constants of TiC and TiN single crystal, using the VoightReuss-Hill (VRH) averaging scheme [23][24][25][26][27]. The theoretical values for polycrystalline elastic properties in this work agree well with the experimental results.…”

Effect of Ba-site substitution by Sr on ultrasonic velocity and electron–phonon coupling constant of DyBa2−xSrxCu3O7−δ superconductors

“…As the ultrasonic wavelength used in this study was much larger than the average grain size, the polycrystalline ceramic samples can be approximated by an isotropic-elastic medium to calculate the longitudinal and shear elastic moduli [38,40]. In this approximation, the longitudinal and shear moduli are given by C L (= 2 l ) and (= 2 s ), respectively where is the density, l is the longitudinal velocity and s is the shear velocity [40].…”

“…As a comparison to the measured temperature dependent sound velocity curves, one of several anharmonicity models [31,36,37] can be plotted together with the velocity curves to illustrate the extent of deviation of the velocity behavior from the calculated curve at high temperatures [16,38]. The simple model proposed by Lakkad [31] which uses a phenomenological model of anharmonic oscillator together with the Debye lattice vibration spectrum was chosen in this work.…”

Effects of Cd2+ substitution on elastic properties and step-like anomalies in Tl0.9Bi0.1Sr1.8Yb0.2Ca1−Cd Cu1.99Fe0.01o7− superconductors

“…The ultrasonic wavelength of around 200-350 μm used in this study was much larger than the average grain size in all of our sample [32] and the polycrystalline samples were approximated as an isotropic elastic medium to calculate two independent elastic stiffness moduli; the longitudinal, C L (¼ ρv l 2 ) and shear elastic moduli, μ(¼ρv s 2 ), where ρ is the density, v l is the longitudinal velocity and v s is the shear velocity [32,33]. The bulk modulus (B) and Young's modulus (Y) were calculated using the ultrasonic wave velocity values using Eqs.…”