Strain susceptibilities and elastic constant anomalies of Tb, Dy, and Ho vanadates

The experimental spectrum and wave functions of the Tb, Dy, and Ho ions in the vanadate crystal field have been used to calculate all strain susceptibilities numerically and to analyze quadrupole vrdering phase transitions. A thorough description of experimental elastic constants $C^{\delta}(T)$ and $C^{\gamma}(T)$ of Tb and Dy vanadates in the tetragonal and rhombic phases, respectively, has been given, and magnetoelastic and pair quadrupole coefficients have been determined. The $B^{\epsilon}$ magnetoelastic coefficient for the zircon structure has been first estimated from acoustic measurement data.