Contains reports on six research projects

Bernstein, B.

Chase, C. E., Jr.

Kolm, H. H.

Mayper, V., Jr.

Sharkoff, E. G.

Wright, J. W.

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IV. LOW-TEMPERATURE PHYSICSProf. M. A. Herlin L. D. Jennings, Jr. D. H. RogersB. Bernstein H. H. Kolm Capt. E. G. SharkoffR. P. Cavileer I. Manning S. WaldronC. E. Chase, Jr. V. Mayper, Jr. W. M. WhitneyE. E. Huber, Jr. J. W. WrightA. DETERMINATION OF THE THERMODYNAMIC TEMPERATURE BY AMAGNETIC METHODThe attempt to use a superconducting solenoid as a field producer was unsuccessfulbecause of the excessive heating of the bath by the current leads. A conventional sole-noid that will be cooled with liquid air has been built instead.J. W. WrightB. THERMAL CONDUCTIVITY OF MAGNESIUMData already taken indicate that the temperature range of interest for thermalconductivity measurements is lower than 1. 5 ° K, and that the points of greatest interestwould lie below 1 *K. In order to make measurements in this region, additional pumpingequipment has been obtained which will permit helium-bath temperatures down toapproximately 0. 9 0 K.The carbon resistor thermometers have been lowered in resistance in order topermit more sensitivity of measurement at the lower temperatures. With the alliedequipment in use at present, the lowered resistance values make the sensitivity slightlylower in the higher temperature range.Professor Morris Cohen of the Metallurgy Department has initiated procurement ofa series of samples containing five different percentages of manganese impurity in puremagnesium. These samples will be reproducible to a high degree so that resultsobtained from them should be significant.It is expected that the measurement of the temperature dependence of the thermalconductivity of these samples, correlated with the electrical resistance data on thesame samples, will give an indication of the nature of the phenomena causing theelectrical resistance minimum.E. G. SharkoffC. PRESSURE DEPENDENCE OF SECOND-SOUND VELOCITY IN THEDEMAGNETIZATION REGIONThe results recently obtained in this experiment have been summarized in a letterto the editor of the Physical Review, and will be published soon. Work is being con-tinued on the problem of the anomalous rise in velocity at very low temperatures as-10-(IV. LOW-TEMPERATURE PHYSICS)reported in the letter and also by De Klerk, Hudson, and Pellam at the Office of NavalResearch-General Electric Cryogenics Conference, Schenectady, New York, October 6and 7, 1952.V. Mayper, Jr.D. MEASUREMENTS OF SECOND-SOUND PULSE AMPLITUDES IN LIQUIDHELIUM IIImproved electronic equipment for observing and measuring second-sound pulseshas been set up, and measurements have been made in liquid helium at 1. 31°K, 1. 33 0 K,and 1.470 K. A scale drawing of the received pulse observed at 1.31°K is shown inFig. IV-1. The time scale is indicated in microseconds. The input to the second-soundtransmitter (carbon film on bakelite backing) was a square voltage pulse of 200-i secduration. The pulse shapes at the other temperatures were similar.i=200 t=400 t=600Fig. IV-1Second-sound pulse at 1. 31 0 K.Measured pulse amplitudes at the peak in the waveform are approximately 1. 5times the theoretically expected amplitude for a nonreflected pulse. This factor shouldbe either 2 in the case of complete reflection or 1 in the case of no reflection. Thisdiscrepancy and the unexpected form of the received pulse are believed to be resultsof the thermal boundary conditions imposed by the type of transmitter and receiverused (the receiver structure is identical with that of the transmitter). To produceboundary conditions more likely to facilitate the making of the desired measurementswithout complications, a different type of receiver has been designed and is beingconstructed.B. Bernstein-11-=(IV. LOW-TEMPERATURE PHYSICS)E. THE VISCOSITY OF LIQUID HELIUMThe Quarterly Progress Report, October 15, 1952, described preliminary experi-ments with an electromagnetically coupled, constant rotation viscosimeter having as itsonly moving part a metallic, cylindrical rotor which is free to rotate about its verticalaxis inside a glass tube in the liquid helium bath. When this rotor is driven by a trans-verse three-phase field, the torque required to maintain constant rotation is proportionalto the slip frequency, which is susceptible to accurate measurement. The major problemencountered in this technique is the construction of bearings which will satisfy tworequirements: They must (a) provide frictional torque which is sufficiently constantcompared to the extremely small viscous torque to be measured, and (b) maintain theposition of the rotor with sufficient accuracy to permit so small a clearance between thecylindrical rotor and the fixed cylindrical boundary as to render the viscous torquemeasurable. The magnetic bearings used in the preliminary experiments described inthe last Quarterly Progress Report satisfied the first but not the second of theserequirements. The best jewel bearings available satisfy the second but not the first.In re-examining the problem of a magnetic bearing, we found that J. W. Beams andothers (1, 2) have developed servomechanically controlled magnetic bearings whichdefinitely satisfy both of our requirements: the bearing torque was not measurable evenat speeds of the order of 50, 000 rps, and the positional stability of the rotors was suchthat no motion was detectable by means of a 50-power microscope. Since a bearing ofthis type is literally frictionless, it may be used to measure the viscosity of liquidhelium by simply recording the deceleration of the rotor when it is coasting freely. Theviscosity can thus be obtained as a function of speed and entirely from measurements ofgeometry and time intervals.We have completed the construction of a magnetic bearing controlled by a first-orderservomechanism similar to that used by Beams which is capable of supporting an ironrotor 0. 5 inch in diameter and 7 inches in length inside a liquid helium Dewar. Theupper extremity of the rotor is positioned by the bearing with complete stability, but itis necessary to provide means for preventing slight pendulation of the lower extremity.Such equipment has been designed and is under construction along with the cryostat andassociated parts and the apparatus for accelerating the rotor.H. H. KolmReferences1. J. W. Beams, J. D. Ross, J. F. Dillon: Rev. Sci. Instr. 22, 77, 19512. J. W. Beams, J. L. Young III, J. W. Moore: J. Appl. Phys. 17, 886, 1946-12-(IV. LOW-TEMPERATURE PHYSICS)F. VELOCITY AND ATTENUATION OF FIRST SOUND IN LIQUID HELIUMBELOW 1 o KApparatus is being constructed for the measurement of the velocity and absorptionof ordinary (first) sound in liquid helium in the temperature range from 0. 1 °K to 1 °K,both under vapor pressure and at higher pressures. The helium is to be cooled by theadiabatic demagnetization of a paramagnetic salt, and the measurements are to be madeby means of an ultrasonic pulse technique at a frequency of 2 Mc/sec. This work is acontinuation of research performed by the author at the Royal Society Mond Laboratory,Cambridge, England (1, 2, 3).C. E. Chase, Jr.References1. K. R. Atkins, C. E. Chase: Proc. Phys. Soc. Sec. A, 64, 826, 19512. K. R. Atkins, C. E. Chase: Report of the International Ultrasonics Conference,Brussels, June 1951, p. 2703. C. E. Chase: Ultrasonic Measurements in Liquid Helium (to be published shortly)-13-

Low-Temperature Physics

Contains reports on five research projects

IV. LOW TEMPERATURE PHYSICSProf. M. A. Herlin E. E. Huber, Jr. J. S. MathisB. Bernstein L. D. Jennings, Jr. Capt. E. G. SharkoffR. P. Cavileer H. H. Kolm W. M. WhitneyC. E. Chase, Jr. J. W. WrightA. DETERMINATION OF THE THERMODYNAMIC TEMPERATURE SCALEBY A MAGNETIC METHODDesign and construction of a liquid-air-cooled solenoid and its associated currentcontrol have been completed. This installation gives continuously variable fields of0 to 2000 gauss over a space approximately 3 inches in diameter and 6 inches long, at2 volts maximum. Boiling of the liquid air is quite moderate at the maximum powerinput of 300 watts.Recently we have been attempting to design a modified helium dewar for use in smallelectromagnet gaps. This dewar (see Fig. IV-1) utilizes a polished copper radiationshield in contact with a liquid air bath at one end to replace the usual outer dewar con-taining liquid air. It is apparent that if the radiation shield can be kept at liquid airtemperatures, it will be at least as effective as the conventional two-dewar system inreducing radiation of heat inward to the helium. For comparable inner dewar size theconventional system would require a magnet gap of approximately 3 inches.J. W. WrightB. ELECTRICAL AND THERMAL CONDUCTIVITY OF MAGNESIUMA series of magnesium samples (extruded rods approximately 0. 5 inch in diameter)was obtained from the Dow Chemical Company. The manganese content of these samplesvaried from 0. 01 percent to 1.1 percent, as shown by spectroscopic analyses furnishedby the Dow Chemical Company. The condition of the manganese impurity in these speci-mens was not accurately known, although this condition did not affect the qualitativeresults obtained.The thermal conductivity of each of the five samples containing manganese impuritywas measured as a function of temperature, and the results are shown in Fig. IV-2.The logarithm of the thermal conductivity of each of the samples at a given temperatureis plotted against the logarithm of the impurity content in Fig. IV-3. For a given tem-perature these points lie on a straight line having a slope of approximately -3/4. Anexception is the sample containing 1. 1 percent manganese, which has a thermal conduc-tivity corresponding to an impurity content of about 0. 5 percent manganese. Thisbehavior can be explained by the fact that a large percentage of the manganese contentin the sample was not in solid solution as a result of the heat treatment in extrusion.The Lorentz number (the product of the thermal conductivity and the electricalresistivity divided by the temperature) is of theoretical interest in relating thermal-18-MATERIAL PYREXSS OTHERWISEDwI-- LLJcrt-o(D0C0wI I-J3.02.52.01.51.01.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0TEMPERATURE (DEGREES K)Fig. IV-1Helium dewar for use insmall magnet gaps.Fig. IV-2Thermal conductivity of magnesium as a function of temperaturewith various amounts of manganese content.KOVAR1/32 INCH TiPOLISHED C(0.01% Mn0.043%Mn0.12% Mn0.29 %Mn1.1 /oMnC1.0w- w(I(flI-0aZcrIrI0.01Thermal conductivity0.1 1.0PERCENT MANGANESE IMPURITYFig. IV-3as a function of manganese content.S--0.29% Mn0.12 % MnE0.043% V01% MnTHEORETICAL VALUEI I  I I I I1.0 1.5 2.0Lorentz number2.5 3.0 3.5TEMPERATURE (DEGREES K)Fig. IV-4as a function of4.0 4.5 5.0temperature.-20-IIA= POINT ON I.1I%Mn CURVEA = POINT ON 0.29%Mn CURVECALCULATED FROM AM.I.1 °/oMn0.29 %/ Mn012%Mn0 N0. 43%Mn0,01% Mn- - 4--I =- % Mnw w .....j. 00 o~0 10 20 30 40TEMPERATURE (DEGREES K)Fig. IV-5Electrical resistivity as a function of temperaturefor various amounts of manganese content.0043% Mn0.01 % Mn0%MnI 1 I Iv0 5 10 15 20TEMPERATURE (DEGREES K)I I I25 30 35Fig. IV-6Resistivity of 0 percent, 0. 01 percent, and 0. 043 percent manganesecontent plotted to a larger scale than in Fig. IV-5.-21-S0800.4rNI2v -(IV. LOW TEMPERATURE PHYSICS)conductivity measurements to electrical resistivity measurements, since this numbershould be a constant in an ideal metal where a mean-free-path can be defined. Curvesof this number as a function of temperature are shown in Fig. IV-4. Electrical resis-tivity data, shown in Figs. IV-5 and IV-6, were taken by J. S. Mathis, who used themethod of H. E. Rorschach, Jr.The plot of the Lorentz number vs temperature shows that the mechanism producingthe electrical resistance minimum effect in magnesium affects the thermal conductivityin the same qualitative way as it affects the electrical resistance, since the values foundare all quite near the value predicted by theory. However, the variation of Lorentznumber with temperature shows a negative second derivative for low impurity content,which increases to a positive value for the highest impurity content examined. Thus,the mechanism does not have the same quantitative effect on the thermal conductivityas it has on the electrical resistivity.E. G. SharkoffC. SECOND-SOUND PULSE AMPLITUDES IN LIQUID HELIUM IIA satisfactory phosphor-bronze, wire-wound receiver for the thermal pulses hasbeen constructed after several trials. The resistance vs temperature curve of thisreceiver has been determined with good reproducibility between 1. 35K and 1. 80 0 K.The amplitudes of second-sound pulses were then measured around 1. 4K as a functionof the power-per-unit-area heat input to the helium. The transmitter used was theoriginal type of graphite coating on Bakelite. The data obtained are given in Table I.The first set of data involved an experimental uncertainty of approximately 10 percentdue in large measure to a low-frequency pickup that made the oscilloscope amplitudecomparisons difficult. The second set was taken after elimination of this pickup, andits experimental uncertainty should be 5 percent or less. The observed pulse ampli-tudes are compared with values to be expected from the formula AT = W/pcc 2 , whereW is the heat input per unit area, p is the density, c is the specific heat, and c2 is thesecond-sound velocity. Actually, the theoretical values listed are calculated as twicethe formula value on the assumption that 100 percent reflection takes place at the Bake-lite receiver backing.A representative second-sound pulse waveform observed at 1. 430K is drawn toscale in Fig. IV-7. A 200-fsec input voltage pulse of the kind used to generate thesecond sound, divided down and put through the receiver amplifying and display system,shows 25 to 30 psec rise and fall times. In Fig. IV-8 the initial received pulse and itsfirst two echoes are roughly drawn. These echoes have undergone one and two reflec-tions from the graphite on the Bakelite transmitter, respectively, in addition to theirreflections from the receiver backing.-22-(IV. LOW TEMPERATURE PHYSICS)Table ITemperature(degrees K)Pulse Amplitudes(degrees)Observed (±10 percent)0.76 x 10-30.76 x 101.40. 730.961.23. 1Theoretical0. 80 X 10-31.340.800.971.212.9Observed (±5 percent)l.26 x 10-31.141.051.231. 14Theoretical1.22 X10-31.201.051.241.14Future plans include lowering the temperature range of these measurements fromabout 1. 2°K down to the lowest degree attainable, using a Distillation Products MB-200oil diffusion pump to achieve greater pumping speeds on the helium.B. BernsteinD. THE VISCOSITY OF LIQUID HELIUMThe frictionless magnetic bearing and its associated equipment have been transferredfrom the temporary bench stand used for preliminary tests to a substantial steel framewhich is to support the cryostat. By weighting the frame and mounting it on absorbentfelt pads, the level of mechanical noise has been reduced to a tolerable level duringnight hours.After some experimentation with a variety of materials, a new design for the rotorwas achieved. It was found that the compressive strength of pyrex is adequate to with-stand the forces arising when iron collars of suitable design shrink onto the taperedextremities of a pyrex centerpiece when the entire assembly is cooled to liquid-airtemperature. A rotor which is concentric to better than 0. 0001 inch has been constructedand has been found to be sufficiently well balanced (dynamically) for use at the speedsin question. Inasmuch as cooling involves a certain hazard of breakage, this rotor willnot be cooled until some measurements have been made at room temperature to verifythe suitability of the present design.H. H. Kolm-23-(IV. LOW TEMPERATURE PHYSICS)t=-O t = 200 /SEC t = 400-SEC t = 600/SECFig. IV-7Second-sound pulse at 1.43 0 K.INITIAL PULSE FIRST ECHO SECOND ECHOFig. IV-8Initial received pulse and echoes.E. VELOCITY AND ATTENUATION OF FIRST SOUND IN LIQUID HELIUMBELOW 10 KThe construction of apparatus for the measurement of the velocity and absorptionof first sound in liquid helium at temperatures below 1°K is being continued.A comparison has been made between experimental results obtained earlier atfrequencies of 2, 6, and 12 Mc/sec and a theory due to Khalatnikov (1,2). This theoryassumes that the anomalously high attenuation of sound in helium II is caused by relaxa-tion processes connected with the establishment of equilibrium in the numbers ofelementary excitations present in the liquid (phonons and rotons). Khalatnikov showsthat two of these processes, phonon-phonon and phonon-roton interactions, are dominant,and that the third possible process, interactions between rotons, is of negligible impor-tance. According to Khalatnikov, the two relaxation times should be of equal order ofmagnitude.Numerical calculations based on the best available values of the many parametersin the theory show that qualitative agreement can be obtained, but that the quantitativeagreement is poor. The best fit to the experimental curves results from the assumptionthat the relaxation time for phonon-phonon interactions is very short compared with that-24-(IV. LOW TEMPERATURE PHYSICS)for phonon-roton interactions. At the frequencies used in the experiments and attemperatures above l°K, this indicates that the attenuation is chiefly due to disturbancesin the equilibrium of the numbers of rotons, and that the phonon gas is in equilibriumat all times. At lower temperatures, however, this picture will be changed. TheKhalatnikov theory shows that both relaxation times are becoming rapidly longer as thetemperature is lowered, and it is probable that the phonon-phonon relaxation time willbecome important at temperatures of the order of 0. 8°K. (The experimental data at0. 85 0 K indicate that even there the frequency dependence of the attenuation is not con-sistent with a single relaxation time.) If this is the case, the curve of attenuation againsttemperature may be expected to exhibit two maxima corresponding to the two relaxationprocesses, one of which has been observed in the neighborhood of 0. 9 0 K and is identifiedwith phonon-roton interactions, and the other, due to phonon-phonon interactions, atsome lower temperature.C. E. Chase, Jr.References1. I. M. Khalatnikov: J. Exptl. Theor. Phys. (U.S.S.R.) 20, 243, 19502. I. M. Khalatnikov: J. Exptl. Theor. Phys. (U.S.S.R.) 23, 8, 1952-25-

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Low-Temperature Physics

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