Influence of Ca²⁺ Substitution on Elastic Properties of CaCu₃Ti₄O₁₂ Quadruple Perovskites Determined by Ultrasonic Pulse Echo Selection Technique

The structural, microstructural, optical, and elastic properties of polycrystalline perovskite series, Ca_1+xCu_3–xTi₄O₁₂; x = 0–1.0, have been investigated employing X-ray powder diffractometry, scanning electron microscopy, UV–Vis spectroscopy, and ultrasonic pulse-echo selection technique at 300 K. The primary structural parameter and ultrasonic parameters; longitudinal wave velocity (V₁), the amplitude of transmitted and reflected pulses a_o/a_n were used to calculate porous values of various elastic parameters such as shear wave velocities V_s, mean sound velocity V_m, elastic moduli L, B, G, E, Debye temperature θ, Poisson’s ratio σ, acoustic impedance Z, internal friction Q^–1, absorptivity A, adiabatic compressibility B_a, Lame’s constant λ_L, and Vickers micro-hardness H_v. The elastic constants were emended to a void-free state using eight distinct semi-empirical methods. These models are principally relying on the pore morphology in the material. Depending upon the correction model employed, L_o is found to decrease from ~21.5 to ~39.5%, B_o from ~17.4 to 45.6%, while E_o and G_o are found to decrease from ~22 to 34% on Ca²⁺ substitution (x = 0–0.5) in the system. Besides, the observed increase in different elastic moduli for x = 1.0 composition is found to vary from 0.3 to 7%. The compositional dependency of elastic moduli has been explained in terms of the change in interatomic bonding strength produced by variations in interatomic distances, microstructure, and electronic configuration. The values of Pough’s ratio B_o/G_o, Frantsevich’s ratio G_o/B_o, and Poisson’s ratio σ_o suggest the brittle nature of prepared ceramics.