Mechanical and Thermal Properties of Praseodymium Monopnictides: An Ultrasonic Study

Abstract

We have computed ultrasonic attenuation, acoustic coupling constants and ultrasonic velocities of praseodymium monopnictides PrX ( X : N , P , As , Sb and Bi ) along the 〈100〉, 〈110〉, 〈111〉 in the temperature range 100–500 K using higher order elastic constants. The higher order elastic constants are evaluated using Coulomb and Born–Mayer potential with two basic parameters viz. nearest-neighbor distance and hardness parameter in the temperature range of 0–500 K. Several other mechanical and thermal parameters like bulk modulus, shear modulus, Young's modulus, Poisson ratio, anisotropic ratio, tetragonal moduli, Breazeale's nonlinearity parameter and Debye temperature are also calculated. In the present study, the fracture/toughness (B/G) ratio is less than 1.75 which implies that PrX compounds are brittle in nature at room temperature. The chosen material fulfilled Born criterion of mechanical stability. We also found the deviation of Cauchy's relation at higher temperatures. PrN is most stable material as it has highest valued higher order elastic constants as well as the ultrasonic velocity. Further, the lattice thermal conductivity using modified approach of Slack and Berman is determined at room temperature. The ultrasonic attenuation due to phonon–phonon interaction and thermoelastic relaxation mechanisms have been computed using modified Mason's approach. The results with other well-known physical properties are useful for industrial applications.

Temperature Dependence of Elastic and Ultrasonic Properties of Sodium Borohydride

“…The achieved results of elastic constants have been applied to compute the mechanical constants [20] like bulk modulus (B), shear modulus (G), tetragonal modulus (C S ), Poisson's ratio (σ ) and Zener anisotropic ratio (A) using following formulae:…”

Origin of sawtooth domain walls in ferroelectrics

“…As a matter of fact, in order to understand the sawtooth domain walls, we propose a minimal model with just short-range interaction between opposite dipoles and long-range Coulomb interaction due to bound charges arising from the head-tohead dipoles, and following a similar approach as the effective Hamiltonian [39][40][41][42][43][44] to simulate 2D and 3D ferroelectric materials. We assume that (i) electric dipoles of opposite directions already exist in the system, and (ii) a boundary exists between the two groups of opposite dipoles (see the Coulomb energy and the short-range interaction as Fig.…”