Elastic moduli of PbZr${\mathrm{O}}_3$ and $\mathrm{Pb}{\mathrm{Mg}}_{\frac{1}{3}}{\mathrm{Nb}}_{\frac{2}{3}}{\mathrm{O}}_3$ between 1.5 and 298 K: Anomalies in $\mathrm{Pb}{\mathrm{Mg}}_{\frac{1}{3}}{\mathrm{Nb}}_{\frac{2}{3}}{\mathrm{O}}_3$; Debye temperatures and heat-capacity interpretation

The transit times of 10-MHz longitudinal and transverse ultrasonic waves have been measured between 1.5 and 298 K for ceramic PbZr${\mathrm{O}}_3$ and $\mathrm{Pb}{\mathrm{Mg}}_{\frac{1}{3}}{\mathrm{Nb}}_{\frac{2}{3}}{\mathrm{O}}_3$. The elastic stiffness moduli deduced therefrom have normal temperature dependences in PbZr${\mathrm{O}}_3$. However, in $\mathrm{Pb}{\mathrm{Mg}}_{\frac{1}{3}}{\mathrm{Nb}}_{\frac{2}{3}}{\mathrm{O}}_3$ the moduli have a broad minimum in the region of the diffuse ferroelectric transition, a very slight dip near 90 K, and an anomalous temperature dependence below 90 K. The latter features may indicate the presence of a phase transition which has not been reported previously. For PbZr${\mathrm{O}}_3$ the elastic Debye temperature ${\Theta }_D^{\mathrm{elast}}$ at 1.5 K is 396±4 K. This value is within experimental error of a recent calorimetric value. For $\mathrm{Pb}{\mathrm{Mg}}_{\frac{1}{3}}{\mathrm{Nb}}_{\frac{2}{3}}{\mathrm{O}}_3$, ${\Theta }_D^{\mathrm{elast}}=382\mathrm{}\pm 8$ K, which is much larger than the calorimetric value, indicating that in $\mathrm{Pb}{\mathrm{Mg}}_{\frac{1}{3}}{\mathrm{Nb}}_{\frac{2}{3}}{\mathrm{O}}_3$ acoustic lattice vibrations cannot account for all of the "Debye" term in the specific heat. It is suggested that anomalies in the specific heat may be due to weak bonding between Pb ions and the Mg${\mathrm{O}}_6$ or Nb${\mathrm{O}}_6$ octahedra and to strains in the samples.