SOUND-PROPAGATION AND DAMPING IN THE VICINITY OF THE SMECTIC-A-HEXATIC-B PHASE-TRANSITION OF 4-PROPIONYL-4'-N-HEPTANOYLOXYAZOBENZENE

Sound velocity and damping were measured in 4-propinnyl-4'-n-heptanoyl oxyazobenzene above its Sm-A-Hex-B phase transition. The measurements were taken at 1 MHz (velocity) and at 3, 9, 15, and 21 MHz (damping) a s a function of the angle theta between the sound propagation directio n and the normal to the smectic layers. The velocity presents a marked anomaly for theta = 90 degrees, whereas a much smaller anomaly is obs erved for theta = 0 degrees, indicating that the phase transition occu rs essentially within the smectic layers. Analysis of these measuremen ts allows the de Gennes elastic constants A, B, and C to be determined . Like the velocity, the damping presents significant pretransitional effects for theta = 90 degrees, reminiscent of those generally observe d in the vicinity of second-order or weakly first-order phase transiti ons. The damping also increases for theta = 0 degrees when T --> T-A.H ex, but the behavior observed does not resemble the usual critical beh avior. It is shown that this pseudocritical behavior stems essentially from a contribution of the anharmonic effects. The anisotropy of the critical effects on velocity and damping can be explained by the theor y elaborated by Andereck and Swift for the Sm-A-Sm-C transition and tr ansposed to the Sm-A-Hex-B transition. Analysis of the velocity measur ements indicates that the specific-heat exponent is of the order of 0. 6. This value, which is far from that associated with the three-dimens ional XY universality class -0.007 to which this transition should in principle belong, confirms the results obtained by calorimetry. The cr itical relaxation lime is characterized by the dynamic exponent zv sim ilar or equal to 1, which corresponds to conventional critical slowing down.