Graduate Physics Laboratory Handbook: Second Sound in Liquid He
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Scheduling Liquid Helium Delivery

 Liquid Helium is used to provide temperatures at or below 4 K. Transfer of the Helium from the transportation dewar to the experiment dewar will be done only under the supervision of the laboratory coordinator or the TA's. Helium is ordered on Mondays or Wednesdays before 2 PM for delivery on Tuesdays or Thursdays, respectively.

2.2.1 Second Sound In Liquid Helium II

Second sound (heat transmitted in a wave-like manner rather than by diffusion) is observed in liquid Helium II. The velocity is measured by one or more of several techniques (direct, standing wave, etc.) as a function of temperature.

We have devised simple techniques to construct cavity resonators and transducers for this experiment. Please find the description of these techniques in the experiment files.

In order to facilitate the scheduling of liquid helium delivery, please see above.

Second Sound References

1. V. Peshkov, "`Second Sound' in Helium II,"J. Phys. (Moscow) 8, 381 (1944); "Determination of the Velocity of Propagation of the Second Sound in Helium II," J. Phys. (Moscow) 10, 389 (1946). These are the original publications of the observation of second sound.
2. C.T. Lane, H.A. Fairbank, and W.M. Fairbank, "Second Sound in Liquid Helium II," Phys. Rev. 71, 600 (1947). This is the first investigator to publish observations of second sound in the U.S.
3. J. R. Pellam, "Investigations of Pulsed Second Sound in Liquid Helium," Phys. Rev. 75, 1183 (1949). This is the published work using heat pulse transmission in second sound.
4. J. R. Merrill, "Second Sound Experiment for Advanced Laboratories," Am. J. Phys. 36, 137 (1968).
5. P. J. Bendt, "Attenuation of Second Sound in Helium II Between Rotating Cylinders," Phys. Rev. 153, 280 (1967). See Table I. for values of second sound velocity with claimed precision of 1%.
6. Grad. Lab Tech Note, "Second Sound Experiment." Technical details for building a transmitter/receiver pair.
7. A. J. Dessler and W. M. Fairbank, "Amplitude Dependence of the Velocity of Second Sound," Phys. Rev., 104, 6 (1956). One possible extension of the experiment.
8. H.A. Fairbank and C.T. Lane, "A Simple Carbon-Resistance Thermometer for Low Temperatures," Rev. Sci. Instr. 18, 525 (1947).
9. C. T. Lane, "Resource Letter LH-1 on Liquid Helium," Am. J. Phys. 35, 367 (1967). Broad, background bibliography on helium.
10. L.D. Landau and E.M. Lifshitz, Fluid Mechanics, 2nd Ed., (Pergamon Press, New York, 1987), Chapter XVI on Dynamics of Superfluids. See particularly section §141 on the derivation of the "sound" velocities.
11. Helium vapor pressure tables from F.E. Hoare, L.C. Jackson, and N. Kurti, Experimental Cryophysics, (Butterworths, London, 1961).
12. Variatives Specific Heat at low temperatures
13. Saturated Vapour Pressure
14. Thermal Cycle Testing-Carbon Glass Resistor
15. S. Jones,  "Experiment VII: The Final Project"  PHYS 685 12/9/04    Second Sound Transmitter Circuit Project

A liquid helium cryostat and header appropriate for this experiment are available. The general procedure consists of assembling your own sample, checking its condition at various stages of cooling, observing the superconducting transition at zero magnetic fields, and measuring the dependence of the critical field for destruction of superconductivity as a function of temperature. With reasonable care it is possible to take sufficiently precise data to require corrections to the simple quadratic formula for the critical field. Hysteresis in the critical field and a pronounced roundness in the R vs H and R vs T curves are generally observed "non-ideal" effects which challenge students' understanding.

Samples of tin or indium wire are available. A number of more interesting experiments are possible. The experiment could be modified to use lock-in techniques to improve the signal-to-noise ratio.

In order to facilitate the scheduling of liquid helium delivery, please see above.

Superconductivity References

1. H. Kammerlingh-Onnes, Leiden Comm. 120b, 122b, 124c (1911).
2. G. L. Trigg, Landmark Experiments in Twentieth Century Physics, (Dover Publications, Inc., New York, 1975). See Chap. 12 on Superconductivity for a good historical introduction with quotes and figures from the original references. In Grad Lab library.
3. C. Kittel, Introduction to Solid State Physics, 3rd Ed. New York: J. Wiley (1966), Chapter 11 "Superconductivity". QC171.K5.
4. E. Maxwell, "Superconductivity of the Isotopes of Tin", Phys. Rev. 86, 235 (1952).
5. J. D. Livinston and H. W. Schadler, "Effect of Metallurgical Variables on Superconducting Properties", Progress in Materials Science 12, 185 (1965). Pages 185-205 are an excellent introduction to the physical parameters of importance in Type I and II superconductors. A minimum of mathematics is used, but imp ortant results of the BCS and Ginsberg-Landau theories are presented.
6. D. M. Ginsberg, "Resource Letter Scy-1 on Superconductivity," Am. J. Phys. 32, 85 (1964). See especially resources 18, 19, 20.
7. D.M. Ginsberg, "Resource Letter Scy-2 on Superconductivity," Am. J. Phys. 38,  949 (1970).
8. E. A. Lynton, Superconductivity, 3rd Ed., London: Methuen/Barnes and Noble (1969). A relatively painless survey of the theory of superconductivity at an introductory level. Grad Lab copy, #36 is gone. QC612.S8L9.
9. M. Tinkham, Introduction to Superconductivity, New York: McGraw Hill (1996). New edition.
10. D. L. Decker, D. E. Mapother, and R. W. Shaw, "Critical Field Measurements on Superconducting Lead Isotopes," Phys. Rev. 112, 1888, (1958). Shows measured hysteresis effects and mention effect of annealing the sample.
11. D. K. Finnemore, D. E. Mapother, and R. W. Shaw, "Critical Field Curve of Superconducting Mercury," Phys. Rev.118, 127 (1960).
12. L. N. Cooper, "Theory of Superconductivity," Am. J. Phys. 28, 91 (1960). A simple presentation of the ideas in BCS theory.
13. Rev. Mod. Phys. 36 1-328 (1964). Review article. *
14. J. C. Swihart, D. J. Scalapino, and Y. Wada, Phys. Rev. Lett. 14, 106 (1965). Interesting deviations from quadratic fit of critical field with temperature.

Technical and Low-Temperature Technique References

1. L. A. Hall, "Survey of Electrical Resistivity Measurements on 16 Pure Metals in the Temperature Range 0 to 273 K°", National Bureau of Standards Technical Note 365 (1968). Contains NBS Memorandum M-24 on tin and M-26 - M-33 on other metals provid ing data on resistivity as a function of temperature.
2. G. T. Meaden, Electrical Resistance of Metals, New York: Plenum Press (1965). QC611.M5.
3. J. R. Merrill, "An Inexpensive, Easily Wound, Superconducting Magnet for Dip Experiments", Rev. Sci. Instrum. 41, 24 (1970). Q184.R5.
4. G. K. White, Experimental Techniques in Low-Temperature Physics, Oxford: Clarendon (1959). Grad Lab library #76. QC278.W45.
5. A. C. Rose-Innes, Low Temperature Techniques, New York: Van Nostrand (1964). Grad Lab library #134. TP482.R6.
6. C. T. Lane, "Resource Letter LH-1 on Liquid Helium," Am. J. Phys. 35, 367 (1967). Broad, background bibliography on helium.
7. C.T. Lane and H.A. Fairbank, "Pyrex Dewars for Liquid Helium," Rev. Sci Instr. 18, 522 (1947)
8. F. G. Brickwedde, T. R. Roberts, and R. H. Sherman, J. Res. Natl. Bur. Stand. A65, 1 (1960). Gives the "1968 NBS Temperature Scale" including the cryogenic region. Provides tables of vapor pressure of liquid helium versus temperature. These tables are also found in the A.I.P. Handbook, pp. 4-278 to 4-282.
9. T. P. Orlando, et al., Phys. Rev. B 19, 4545 (1979). *
10. B. W. Roberts, J. Chem Phys. Ref. Data 5, 823 (1976). *
11. Hall Generator Installation Instructions
12. Hall Generator Model HGCA-3020 Notes
13. Properties of Helium
14. Data Chart
15. Vapor Pressure of Liquid Helium-4 Graph
16. Low Temperature Techniques

* Missing from archive 6/00

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• Technical Questions contact the Laboratory Coordinator.