“…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].…”