Dynamic critical phenomena in ammonium halide crystals

Abstract

All available ultrasonic and hypersonic data on N${\mathrm{H}}_{4}$Br, N${\mathrm{H}}_{4}$Cl, and N${\mathrm{D}}_{4}$Cl have been analyzed over a wide range of temperature, pressure, and frequency in the disordered cubic phase $D$, the "ferro-ordered" cubic phase ${O}_{c}$, and the "antiferro-ordered" tetragonal phase ${O}_{T}$. The acoustical absorption and dispersion in the disordered phase can be interpreted in terms of a single relaxation time $\ensuremath{\tau}$ that exhibits critical behavior $\ensuremath{\tau}\ensuremath{\sim}\ensuremath{\Delta}{T}^{\ensuremath{-}\ensuremath{\theta}}$ near the order-disorder transition. The resulting values of the critical exponents $\ensuremath{\theta}$ confirm the existence of a master phase diagram for these systems. In the tetragonal regime (N${\mathrm{H}}_{4}$Br at 1 atm) the experimental value $\ensuremath{\theta}=1.38$ for $T>{T}_{c}$ corresponds quite well with the critical exponent $z\ensuremath{\nu}$, describing order-parameter relaxation for $n=3$ fixed points in Hohenberg and Halperin's model $A$. In the $D\ensuremath{-}{O}_{c}\ensuremath{-}{O}_{T}$ triple-point regime (N${\mathrm{H}}_{4}$Cl at 1 atm, N${\mathrm{H}}_{4}$Br at 1.88 kbar) the experimental value $\ensuremath{\theta}=1.0$ corresponds to $z\ensuremath{\nu}$ given by conventional theory, which is appropriate for model $A$ near higher-order critical points. In the multicritical regime (N${\mathrm{D}}_{4}$Cl at 1 atm, N${\mathrm{H}}_{4}$Cl at 1.5 kbar, N${\mathrm{H}}_{4}$Br at 3.25 kbar) the experimental values of $\ensuremath{\theta}(1.1 \mathrm{to} 1.2)$ associated with this $D\ensuremath{-}{O}_{c}$ multicritical point cannot be easily interpreted in terms of currently available theory. The critical relaxation times were obtained using acoustical relaxation strengths that are independent of temperature, and several pieces of experimental evidence are presented in support of this method of analysis.