J. Phys. Chem. zyxwvu 1984, 88, 5899-5902 5899 Nonllnear Electroacoustic Phenomena: Phonon Echo in &Tartaric Acid and Its Salts Jacek Swiatkiewiczt and Paras N. Prasad* Department of Chemistry, State University of New York at Buffalo, Buffalo, New York zyxw 14214 (Received: June 21, 1984) The phonon echo, also called polarization or electroacoustic echo, is investigated for d-tartaric acid and its diammonium salt as well as for the Rochelle salt by using the two-pulse technique. The dependence of the echo amplitude on the delay time is described by both the anharmonic oscillator model and the model of coupled micromotions of the grains recently proposed by Pouget and Maugin. The echo under the experimental conditions behaves according to the small signal limit. The dependence of the damping factor on the pressure of the surrounding gas and the temperature is used respectively to measure an average speed of sound and to derive the mechanism of damping. Under vacuum, the damping factor is found to depend on the square of the radio frequency (rf) as is expected from an intrinsic loss mechanism. A plot of the temperature dependenceof the damping factor for d-tartaric acid exhibits a maximum. This maximum is explained by a thermally activated acoustic relaxation within the powder particles. The observed deuteration effect both on the shape and the position of the maximum points out the importance of hydrogen motions for the acoustic relaxation in these hydrogen-bonded solids. Introduction The area of nonlinear interaction in organic solids is highly active. The investigation in the past has focused on nonlinear optical effects such as second harmonic generation. The increased interest stems from the recognition that organic solids, rich in zyxwvuts ?r electrons, possess large nonlinear electronic susceptibilities. Although electrostrictive and elasticity tensors are known for many of organic materials, the study of nonlinear interactions in the radio-microwave-frequency range has not been reported so far. Such studies are highly relevant in order to determine any potential application of organic solids as phase shifters or nonlinear mixing devices in the radio-microwave region. One manifestation of the nonlinear electroacoustic interactions in piezoelectric solids is the phonon echo phenomenon. The phonon echo, also called polarization or electroacoustic echo, is a coherent rf pulse emitted at time delay 27, as a response of the system to the pulses of electromagnetic radiation applied at times 0 and zyxwvut T. One or both of the rf pulses applied may be substituted by an acoustic pulse of appropriate frequency. Since the phonon echo cannot be produced by the linear response alone, it is a repre- sentative of nonlinear electroacoustic interactions. The phonon echo can be observed in both single crystals and powdery materials. It has been extensively investigated for in- organic piezoelectric and ferroelectric systems. A comprehensive review of the literature can be found in ref 1 and 2. The investigation of the echo amplitude dependence on the pulse time delay has established separate models for single crystal and powder samples: the parametric field-mode interaction model for the former and the anharmonic oscillator model for the latter kind of sample. These two models have been thoroughly discussed by Fossheim and Holt2 Although the echo phenomenon involves nonlinear effects, any estimation of the respective parameters from the experimental data can be made only after a proper separation of the time-de- pendent relaxation terms. Therefore, a better understanding of the acoustic relaxation process in an organic piezoelectric powder plays a key role in the study of nonlinear electroacoustic effects in organic solids. Recently, we reported the observation of the phonon echo in an organic solid, specifically the d-tartaric acid powdere3 In the present paper, an extensive study of the phonon echo in the powders of d-tartaric acid and its diammonium salt as well as the Rochelle salt is presented. The emphasis of this work is on the interpretation of the echo relaxation time (damping factor). The effect of temperature and pressure of the surrounding gas medium on the time evolution of the echo amplitude is investigated to derive information on the acoustic properties of the material. ‘On leave from the Institute of Organic and Physical Chemistry, Technical University of Wroclaw, Poland. Experimental Section Reagent grade d-tartaric acid and its diammonium salt were crystallized from water and dried. Deuterated d-tartaric acid crystals were prepared by repeated crystallization from D20. The Rochelle salt was made by adding equimolar amounts of KOH and NaOH, in the proper stoichiometric ratio, to a d-tartaric acid solution in water. Dry crystals were ground in a mortar and sieved in order to separate the appropriate size particles (75-150 Mm), The powders underwent an etching procedure which involved a mild sonification of the powder in a solvent. During this treatment, smaller particles which adhere to the major crop of the micro- crystals were separated out. Simultaneous etching and recrys- tallization remove some surface damage induced by grinding the crystals into the powder form. The best results were obtained by using a mixture of methanol and hexane as the solvent for d- tartaric acid. But pure methanol was found to be more effective for the etching of the salt powders. Dried powders were sieved again to thoroughly separate particles smaller than 75 bm. A weighted amount of the powder, which approximately contained 1 zyxw O6 particles, was placed between the disks of the capacitor. The sample cell was evacuated for several hours at room temperature. The measurements were performed under vacuum or in a cell filled with an inert gas. The spectrometer used has been described previ~usly.~ In experiments reported here, we used two rf pulses of equal am- plitude, identical frequency, and constant pulse width (2 11s). Special attention was paid to minimize the signal distortion in the external circuitry. A phase-sensitive detection was used. The preamplifier stage was eliminated for this study. The signal amplitude was kept constant by a scaled attenuator. Therefore, no saturation effect of the receiver was observed. The capacitor containing the sample powder was mounted in a glass container, which allowed us to evacuate the system prior to the measurements. The glass container was immersed in a thermostat bath. The CLTS-2 temperature sensor was located at the opposite side of the grounded electrode of the capacitor. This arrangement minimizes any temperature lag between the powder and the temperature probe during the cooling and heating cycles. Results and Discussion Time Dependence of the Echo Amplitude. The observed de- pendence of the echo amplitude on the variable delay T between the two applied rf pulses is shown in Figure 1 for d-tartaric acid, its diammonium salt, and the Rochelle salt. In each case, a fast ~ ~~~ (1) Pouget, J.; Maugin, G. A. zyxwvu J. Acoust. SOC. Am. 1983, 74, 941. (2) Fossheim, K.; Holt, R. M. ’Physical Acoustics”; Mason, W. P., (3) Swiatkiewicz, J.; Talapatra, G. B.; Kurland, R. J.; Prasad, P. N. J. Thurston, R. N., Eds.; Academic Press: New York, 1982; Vol. 16. Chem. Phys. 1983, 78, 7500. 0022-3654/84/2088-5899$01.50/0 0 1984 American Chemical Society