Whitney, W. M.

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III. LOW TEMPERATURE PHYSICSDr. C. W. GarlandL. J. SlutskyW. M. WhitneyJ. W. WrightA. ATTENUATION OF SOUND IN LIQUID HELIUMIn May 1954, measurements made at the M. I. T. Low Temperature Laboratory byC. E. Chase (1) showed that the attenuation coefficient for sound waves in liquid heliumgoes through a broad maximum in the vicinity of 0.9 0 K before falling to zero at lowertemperatures. At the top of the curve two minor peaks, separated from each otherby a temperature difference of about 0. 1°K, were observed. Earlier work done atCambridge University by Chase (2), which had demonstrated that the anomalous increasein absorption just below 1 °K could be ascribed to a relaxation process, had not revealeda fine structure similar to that found at M. I. T., but the Cambridge measurements hadbeen made at only three temperatures below 1°K, and the additional peak could easilyhave been missed. The peaks on the absorption curve were therefore interpreted asindicating the presence of two separate relaxation mechanisms in the liquid.For his measurements at M. I. T. Chase used a single X-cut quartz crystal, in con-junction with a polished brass reflector, to transmit and receive 20-[sec pulses of soundat a carrier frequency of 12 Mc/sec. All voltages appearing across the crystal,including an additional signal from the output of a pulsed signal generator, wereamplified, detected, and displayed on the sweep of a DuMont 256D A/R oscilloscope.Echo heights were measured by adjusting the calibrated signal generator output untilthe sizes of the comparison pulse and the echo were equal.During the past summer, in the course of an experiment to measure the attenuationas a function of pressure, several attempts were made to reproduce Chase's vapor-pressure data, using the same crystal, crystal holder, and reflector and the sameelectronic measuring techniques. The curves obtained for the attenuation coefficientexhibited minor peaks similar to those reported, but of different magnitudes andseparated by different temperature intervals. Furthermore, the results could not bereproduced from one experimental run to the next.At temperatures for which the attenuation was large, the echo size was correspond-ingly small. The shape of the echo at this low-voltage level was severely distorted bythe presence of considerable amounts of a coherent background clutter (prolonged ringingof the crystal in its fundamental and complex modes after the exciting voltage has dis-appeared), and consequently it was difficult to estimate the pulse height accurately.Moreover it was impossible to tell whether variations in pulse height were to be attrib-uted to changes in attenuation, or to further distortion produced by changes in phasebetween the echo and its background resulting from the slight dependence of the velocityon temperature.(III. LOW TEMPERATURE PHYSICS)The difficulty was resolved by using separate crystals to transmit and receive. Withthe background clutter from the input signal no longer present on the oscilloscope sweep,it was possible to measure the height of the transmitted pulse with much greater preci-sion. There was no noticeable pulse distortion, even for the smallest signals, and theresults obtained could be reproduced. They showed no additional peaks in the attenuationcurve, and within experimental error agreed with Chase's Cambridge values. It nowseems certain, therefore, that the presence of the second peak in the M. I. T. resultswas a spurious effect, and that as the temperature falls below 1 'K, the attenuation coef-ficient rises smoothly to its maximum value.W. M. WhitneyReferences1. C. E. Chase and M. A. Herlin, Phys. Rev. 95, 565L (1954); 97, 1447 (1955).2. C. E. Chase, Proc. Roy. Soc. A220, 116 (1953).

Low Temperature Physics

III. LOW TEMPERATURE PHYSICSDr. C. W. Garland L. J. Slutsky W. M. WhitneyR. Dalven J. W. WrightA. ATTENUATION OF SOUND IN LIQUID HELIUMExploratory measurements were made to determine the attenuation of sound inliquid helium as a function of pressure, in the range of temperature between 0. 20 K and1 K. Short ultrasonic pulses at a carrier frequency of 11. 8 mc were generated in atube containing liquid helium by an X-cut quartz crystal which was operated at resonance.A second crystal, matched with the first, was used as a receiver. Changes in the ampli-tude of the transmitted sound pulses were measured with a comparison pulse, providedby a signal generator with a calibrated, continuously variable output attenuator.Low temperatures were obtained by the adiabatic demagnetization of iron ammoniumalum. In an experiment utilizing magnetic cooling, the demagnetization capsule must bethermally isolated, insofar as it is possible, from the rest of the apparatus. The pathlength over which the sound pulses were transmitted could not be varied conveniently;consequently only changes in the absorption coefficient, as a function of temperature,could be measured directly. Data taken at the vapor pressure could be subsequentlyconverted to absolute values of attenuation by matching them with measurements madeby C. E. Chase (1), above 1oK, at 12. 1 mc, using a variable path length. No informa-tion of this kind was available to aid in adjusting the data at higher pressures, and it wasnecessary to make use of the assumption, valid at vapor pressure, that the absorptionvanishes as the absolute zero of temperature is approached.The results from two successful runs are shown in Fig. III-1. The curve at vaporpressure is in agreement with earlier measurements reported by Chase and Herlin (2),within the experimental error caused by a temperature uncertainty of approximately5 per cent in their experiment, and of about 2. 5 per cent in the present one. Below2.9 2. 80. 8°K the attenuation was found to vary as T , in agreement with the T depend-ence quoted by Chase and Herlin.Measurements were made along the vapor pressure curve at two different signalamplitudes. The branching of the absorption curve at low temperatures provides evid-ence of extra attenuation arising from the nonlinear response of the liquid to signals oflarge amplitude. On the basis of a brief prior investigation of finite-amplitude attenua-tion at 1. 8'K, where the attenuation is low, and from a knowledge of the signal amplitudeused here, it was possible to conclude that, for a given value of the absorption coeffic-ient, nonlinear effects become noticeable for much lower signal intensities at low tem-peratures than at high. This result cannot be explained on the basis of a classicalapproach to the problem of finite-amplitude attenuation, and it may very well have itsorigin in quantum phenomena.(III. LOW TEMPERATURE PHYSICS)VAPOR PRESSURES10-S8.0 ATMOSPHERES05-13 ATMOSPHERES18.3 A0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0TEMPERATURE (*K)Fig. III-1. Attenuation of sound in liquid helium under pressure.An interesting feature of the (low-amplitude) curve taken at vapor pressure is achange in the power law occurring at about 0. 4 0K. Chase and Herlin found a similarchange in the slope of their curve at 0. 30 K. In view of the fact that they used a some-what longer path length, the present results are consistent with their suggestion that theeffect might be connected with the rapid increase of phonon mean-free-paths with decrea-sing temperature. The increase in the power law should occur at a higher temperaturefor a shorter path length, as is observed.A log-log plot of the curve taken at 8. 0 atmospheres shows that the attenuation variesas T A small increase in the power law, not evident in the figure, occurs at 0. 4°K.Since the number of phonons per unit volume decreases rapidly with increasing pressure,with a consequent increase in the mean-free-path, we might have predicted that the in-crease in slope would occur at a higher temperature at this pressure than at vapor pres-sure. Unfortunately, the scatter in the data at low temperatures is a sizeable fractionof the attenuation itself, which is small at this pressure, and it is possible that theapparent change in power law is not significant. Nevertheless, the fact that there isclearly no other knee in the curve at higher temperatures appears to be inconsistent withthe simple phonon mean-free-path interpretation of the effect at vapor pressure. Thewarm-up times for the demagnetizations at 13 and 18.3 atmospheres were, unfortunately,too short to permit the taking of reliable data in the temperature range from approxi-mately 0. 6°K to 0. 8°K; hence the experimental scatter in this region is quite large.These measurements, therefore, throw little light on the problem, although they do indi-cate roughly that the attenuation falls to zero much more rapidly than T3(III. LOW TEMPERATURE PHYSICS)Measurements taken above 0. 80 K are reliable at all four pressures, however, andat these temperatures the attenuation can be discussed as a function of pressure.According to Khalatnikov (3), the absorption coefficient (a) is given for liquid helium,as well as for ordinary liquids, by the expression22pcwhere a is the angular frequency, p the density, c the velocity of sound, Tr the coeffi-cient of ordinary (shear) viscosity, and t the coefficient of second viscosity, containingthe relaxation effects. It is known that, above 1°K, the attenuation calculated fromthe shear viscosity alone is an order of magnitude smaller than the measured value, sothat is the dominant term in the expression in parentheses. The attenuation (a) has acertain substantial pressure dependence arising solely from that of the factor (l/pc3),which is of little interest here. We eliminate it by calculating instead the quantitya' = 2pc3 a/w . Values of a', plotted in Fig. III-2, are seen to decrease approximatelyexponentially with pressure.The only theoretical discussion of the attenuation of sound in liquid helium, based ona definite microscopic picture of the liquid, is that of Khalatnikov (4), who calculatesrelaxation times governing the anomalous attenuation from a consideration of collisionsbetween the elementary excitations of the liquid, phonons and rotons. Unfortunately,he finds it necessary to introduce an adjustable parameter into the theory in order tomake any kind of quantitative approach to the problem; therefore it is not possible tocalculate the pressure dependence of his results. With a suitable choice for the valueof the parameter, Khalatnikov's theory describes the temperature dependence of theattenuation at vapor pressure down to 1°K,but below that temperature it breaks downn 15.0 and predicts an attenuation that falls to zero0 31.20- much more rapidly than T , vanishing\o almost completely (5) at 0. 6 0 K.T 0oo0K In the neighborhood of the relaxation0o peak, the present results can at least be0.80-a \discussed qualitatively from the point of\ view of the specific mechanisms on which0.60 \ Khalatnikov bases his calculations-inelasticphonon-phonon and phonon-roton collisions.0 5 10 5 20 25 A noticeable feature of the data is thePRESSURE (ATMOSPHERES) increase, with increasing pressure, of theFig. 111-2. Pressure variation of temperature at which the maximum attenua-normalized attenuation. tion occurs. One might infer from this(III. LOW TEMPERATURE PHYSICS)result that the relaxation times of the elementary collision processes are increasingwith pressure. This is the behavior to be expected from phonon-phonon interactions.Phonon-roton interactions, however, would produce the opposite effect, since the num-ber of rotons per unit volume increases with pressure, and the phonon-roton mean-free-paths are determined essentially by the roton density. The present results arenot inconsistent with the interpretation that both processes are at work; their net resultis to reduce the strength of the relaxation, with the phonon-phonon interaction havingthe dominant influence in shifting the temperature of the relaxation peak.It is hoped that experiments, now under way, for the purpose of following up someof the problems presented by these preliminary results and extending the measurementsto 2 mc and 6 mc, will help to define more clearly the theoretical problem that wlllhave to be solved if the behavior of the attenuation is to be understood at these tempera-tures.A more detailed account of the experiment described above can be found in refer-ence 6.W. M. WhitneyReferences1. C. E. Chase, Proc. Roy. Soc. (London) A220, 116 (1953).2. C. E. Chase and M. A. Herlin, Phys. Rev. 97, 1447 (1955).3. I. M. Khalatnikov, J. Exp. Theor. Phys. USSR, 23, 21 (1952).4. I. M. Khalatnikov, J. Exp. Theor. Phys. USSR, 20, 243 (1950).5. C. E. Chase (private communication).6. W. M. Whitney, Ph. D. Thesis, Department of Physics, M. I. T., 1956.

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Low Temperature Physics

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