The crystal-field dependency of sound attenuation in the spin-3/2 ising model

The effects of crystal-field (D) on sound attenuation are considered for the spin-3/2 Ising model by using Onsager theory of irreversible thermodynamics. It is assumed that the sound wave couples to the order-parameter fluctuations, therefore, it decays mainly via order-parameter relaxation process. The order-parameters, magnetization and quadrupole moment, are defined in terms of exact recursion relations (ERR) on Bethe lattice (BL). After our analysis, two relaxation times are obtained and they are used to calculate the sound attenuation coefficient (α). Consequently, the critical behaviors of sound attenuation coefficient are investigated in terms of frequency (w) and Onsager coefficient (γ) for the coordination numbers q=3, 4 ad 6 near the second-order (Tc) and first-order (Tt) phase transition temperatures in the ferromagnetic phase regions for the negative and positive D values and the results are presented on the (kBT/J, α) planes. It is found that the peaks about Tt's are observed at the same temperature, but the peaks about Tc's are observed shifted to lower and higher temperatures in increasing (w)'s and (γ)'s, respectively. In addition, the peaks are also obtained near the tricritical points for all q.