Third Sound and the Decay of Persistent Currents in Unsaturated 3He-4He Films

Transcription

1 University of Massacusetts Amerst From te SelectedWorks of Robert Hallock May, 198 Tird Sound and te Decay of Persistent Currents in Unsaturated 3He-4He Films Robert Hallock, University of Massacusetts - Amerst Available at: ttps://works.bepress.com/robert_allock/45/

2 PHYSCAL RVW B VLUM 21, NUMBR 9 1 MAY 198 Tird sound and te decay of persistent currents in unsaturated 3He-4He-mixture films D. T. kolm and R. 8. Hallock Laboratory for Low Temperature Pysics, Department of Pysics and Astronomy, University of Massacusetts, Arnerst, Massacusetts 13 (Received 13 August 1979) We report te observation of metastable currents in unsaturated He- He-mixture films. Te decay rate of tese currents is found to be an increasing function of He concentration in te film. A simple model for te role of te He, adequate to explain our observations of te concentration dependence of te tird-sound velocity, does not agree wit te measured decay rates. Te remarkable ability of pure superfluid He to maintain a state of macroscopic metastable flow as been experimentally demonstrated bot in restricted geometries" and in saturated and unsaturated ' films. %e report ere measurements of te velocity of tird sound and of te decay of tese metastable currents for a fixed amount of 4He as a function of He concentration for te case of unsaturated films on a Pyrex substrate. Te results we obtain for te tird-sound velocity disagree wit predictions based on te work of Downs6 but are in reasonable agreement wit a simple model for te role of te 'He. ur results for te metastable flow decay rate as a function of concentration cannot be explained by te simple model and an appeal to previous work ' on pure He. A more detailed teoretical treatment is called for. Te apparatus used for te present work is similar to tat used earlier for work4 5 on pure 4He. A Pyrex ring film flow pat is located in an experimental camber of volume 195 cm3 wic contains.5- and.3-p, m A123 powder of surface area 92 m' to provide a reservoir for te film on te ring. Te effects of capillarity at te powder junctions ave been carefully measured for pure He and become important above a film tickness of approximately four atomic layers in te case of.5-p, m A123. Tese effects depend on te surface tension and must be carefully taken into account in te case of mixtures if te film tickness and 'He concentration in te film are to be known wit confidence. Persistent currents are generated witout rotation and te superfluid flow velocity is measured using te tecniques of Dopplersifted tird sound. n tis tecnique te difference between te upstream and downstream tird-sound velocity, bc, is related to te superfluid velocity v, by C-((p, )/p)v were (p, )/p is te reduced superfluid density' in te film. Te po~er required to generate and detect te tird-sound pulses as no observable effect on te measured rates of decay. A typical measurement begins at a selected temperature T wit a fixed, known amount of 4He in te apparatus. Troug use of a superfluid valve mounted on te experimental camber, a known amount of 'He is added to te pure He film at low temperature. Te valve is sealed, and te apparatus is cycled to 4.2 K to ensure mixing. Subsequent cooling to te temperature T is followed by measurements in te mixture film. Tis process is continued by te addition of furter amounts of 'He. %e report our results below as a function of te average 3He concentration in te film were we ave taken proper account of te concentration gradient induced by te substrate. Te He concentration at te film vapor interface X, as been determined by te dew-point metod of Cester et al. ' Te concentrations X, so determined are in good agreement wit values deduced from sound measurements in te He- He vapor above te film. Te velocity of sound in te vapor as been measured by use of te same source and detectors' used for te measurements of tird sound. Sound pulses of widt &5 p.sec can be readily detected and te observed concentration-dependent time of fligt, v, is related to te vapor concentration Xg by m4 ~X X g = 1 m4 m3 r4 were ~~ is te time of fligt in te case of pure He and m3 and m4 are te masses of atoms of 'He and 4He. Te X~ values so determined are in reasonable agreement wit values generated by te dew-point metod. Te measured Xg values in conjunction wit a conservation of mass argument yield liquid concentration values XL wic are also in agreement wit tose obtained by te dew-point metod. n te case of a static film, measurements of te velocity of tird sound C3 ave been made as a function of added amounts of 'He and ence increasing 'He concentration. Results typical of tose taken at several temperatures are sown in Fig. 1. Te dased line is te result of a calculation of te velocity of tird sound in a mixture film based on te work Te American Pysical Society

3 ' D. T. KHLM AND R. B. HALLCK 21 l5. p 5.5- ~o D suggest tat tis concentration tan predicted. " gradient is smaller Representative results of metastable film current velocity versus time measurements for a number of 'He concentrations are sown in Fig. 2. We ave plotted te relative velocity in eac case to facilitate te comparison. Te decay rate is observed to be an increasing function of 'He concentration. For decays wic are not too strong we find tat an expression of te sort.5 v( r) = v~ [l ( log~ p( r/p) (3) x,.8. 2 FG. 1. Velocity of tird sound as a function of added He. Te pure He film was of tickness d4 =8.1 layers. Te solid curve is based on te simple model described in te text. Te dased curve is obtained from te work of Downs. Te data sown ere are representative of oter data taken at 1.25 and 1.45 K. of Downs. Te solid line is te result of a calculation based on te expression" for pure He were" (P }df l+ TS P fq=qqp(3l3+4d r }/(d +P)td, except tat we ave replaced d4 by d as determined by te metod outlined previously ' and replaced (p, )/p by (p )/p were p as been computed for te mixture film as a function of XL, T, and d based on te measurements of Sobolev and sel'son" for bulk mixtures. Te entropy S in te mixture was calculated from te pure fluid entropies by use of te metod of de Bruyn uboter et al. ' Te latent eat L was obtained from te Clausius-Clapeyron equation and te work of Sydoriak and Roberts. 9 Here + =27 K (layers), ' P-41.7 layers, and d4 is te He film tickness for XL =. Tis simple procedure (wic assumes te sole effect of te added 'He is to modify te value of (p, )lp and cange te film tickness) works surprisingly well. Te Downs calculation seeks to include te effects of 3He troug te inclusion of an additional restoring force wic arises due to a concentration gradient caused by te motion of He in te vicinity of te tird-sound wave. ur results provides an adequate representation of te data. ' We observe g to be a strongly decreasing function of film tickness and a strongly increasing function of te temperature. At large times for strong decays substantial deviations from te beavior of q. (3} are seen. Tese observations are in qualitative agreement ' wit te case of pure He. n particular, g is essentially independent of te starting velocity vt and is a useful quantity to caracterize te data. n Fig. 3 te increase in g wit He concentration is sown for tree temperatures. A simple model to explain tis beavior suggested by our measurements of C3Q is to assume te 'He added simply affects te normal component and film tickness and ence canges te value of (p, )/p at te cosen operating temperature T. f te only effect of te He were te simple modification of (p, }/p and dq we migt ten expect pure qhe results for g at a tickness d and a temperature T' (were T' is te temperature of a pure He film wen (p, )/p= (p )/p ) to be comparable to measurements of g in te mixture film of tickness d and temperature T. Te solid lines in AJ c3 CU C T= 1.35 K x,(x) o. 1.3 v 3. 1 ~ t (sec) o o V v vv v v g ~ V VVV ~ y~ g vv ~ ~ V fl ~ ooo Qggg V VVV ~ ~ ~ J y FG. 2. Decay of metastable film flow as a function of time. n all cases te amount of 4He in te apparatus remained uncanged. XL is te average He concentration in te film were proper account as been taken of te substrate-induced concentration gradient. n all cases studied at tis and oter temperatures te addition of He enanced te decay of te metastable flow.

4 21 THRD SUND AND TH DCAY F PRSSTNT CURRNTS o 56 = 25K 26- oo o' 4 ) CA X CU C l4..4 x, FG. 4. Maximum persistent current velocity attainable in our apparatus as a function of concentration. Te solid line presumes te only role of te He is to modify (p~)/p and cange te film tickness as discussed in te text. l2 oo..4 XL.8. l 2 FG. 3. Te dependence of ( on He concentration for tree temperatures. Te points sown are averages for several measurements at eac concentration value. Te solid curves are expectations based on te simple idea tat te only role of te 3He is to affect (p, )/p and te film tickness. Te dased curves illustrate te cange expected in g if te added 3He beaved instead exactly as additional 4He. also observed tat te maximum attainable persistent current velocity is a strong function of 'He concentration. n te case of pure He te maximum persistent current velocity wic can be generated in our apparatus is a strongly decreasing function of temperature and a weak function of film tickness wic peaks at d4 =1 layers for T =1.45 K. n te case of mixtures te maximum attainable persistent current is sown as a function of concentration in Fig. 4. n tis case te solid line was produced using te effective temperature T' introduced earlier. Here too tere is some discrepancy between our observations and te simple model. n conclusion, we ave presented te first results for te decay of metastable film currents in 'He- He mixtures. n addition we ave reported te systematic measurements of tird-sound velocity as a function of concentration. A simple model explains te tird-sound results wile te results for metastable flow deviate from expectations based on te model and results for He. A detailed teoretical investigation is called for. Fig. 3 are te results of suc an analysis at te tree temperatures and te agreement wit te data is unsatisfactory. t is clear ten tat te presence of te 'He affects te decay of te metastable current in a nontrivial way, and a careful teoretical analysis of te effect of te 'He is required. During te course of tese measurements we ave ACKNWLDGMNTS t is a pleasure to acknowledge te generous assistance provided by J. S. Brooks and F. M. llis during te gourse of tis work. Tis work was supported by te NSF troug Grants No. DMR and No. DM R

5 3916 D. T. KHLM AND R. 8. HALLCK 'J. S. Langer and J. D. Reppy, in Progress in Low Temperature Pysics, edited by C. J. Gorter (Nort-Holland, Amsterdarn, 197), Vol, 6, p. 1. H. Kojima, W. Veit,. Guyon, and. Rudnick, in Low Temperature Pysics-L T13. edited by K. D. Timmeraus, W. J. ' Sullivan,. F. Hammel (Plenum, New York, 1974), Vol. 1, p R. K. Galkiewicz and R. B. Hallock, Pys. Rev. Lett. 33, 173 (1974); H. J. Verbeek,. van Spronsen, H. Mars, H. van Beelan, R. de Bruyn uboter, and K. W. Taconis, Pysica (Utrect) 73, 621 (1974); R. K. Galkiewicz, K. L. Telscow, and R. B. Hallock, J. Low Temp. Pys. 26, 147 (1977); R. K. Galkiewicz and R. B. Hallock, Pys. Rev. B 15, 2671 (1977). 4K. L. Telscow and R. B. Hallock, Pys. Rev. Lett. 37, 1484 (1976). 5D. T. kolm and R. B. Hallock, Pys. Rev. Lett. 42, 449 (1979); Pys. Rev. B 21, 392 (198) {preceding paper). ~J. Downs, P. D. tesis (University of Soutern California, 1974) (unpublised). ~J. H. Scoltz,.. McLean, and. Rudnick, Pys. Rev. Lett. 32, 147 (1974). M. Cester, J. P. Laeurte, and J. P. Romagnan, Pys. Rev. B 14, 2812 (1976). 9n tis metod te relation d +P d = 27(1 Xg/4)/f Tln(P /Pg) l (A1) must be satisfied. Here d is te total film tickness, T is te temperature, P is te total vapor pressure in te apparatus, X~ is te 3He concentration in te vapor, and P~ is te dew point pressure. For eac value of X, at a given temperature tere is a corresponding value for P~ and X~ [see T. R. Roberts and B. K. Swartz, in Helium Tree, edited by J. G. Daunt {io State University, Columbus, 196), p. 158 and S. G. Sydoriak and T. R. Roberts, Pys. Rev. 118, 91 (196)j. Given an initial value for d a calculation determines wat value of X,(Pg, Xg) allows q. (A1) to be satisfied. Tis X, in conjunction wit te properties of te apparatus yields a new value for d. teration is continued until q. (Al) is satisfied by values of d, P~, and Xg wic are eac consistent wit te same value of X,. Te final value of X, is ten used to determined XL taking account of te concentration profile induced by te substrate (Ref. 8). ' Te film tickness in te mixture film d was determined by including te relationsip between capillary condensation in te A123 powder and te film tickness on te Pyrex ring. Since te volume of liquid trapped in te powder is a function of te average concentration X, (troug te effects of surface tension), te film tickness on te Pyrex ring canges wit X,. An increase in X, causes an increase in d. Tis calculation (due to F. M. llis) is insensitive to te specific microscopic geometry. t makes use of te volume of liquid as a function of film tickness wic was empirically determined for pure 4He in te experimental apparatus. ' D. Bergman, Pys. Rev. 188, 37 (1969); Pys. Rev. A 3, 258 (1971). ' See, for example, S. J. Putterman, Superfluid Hydrodvnamics (Nort-Holland, Amsterdam, 1974), Cap. 5. ' V.. Sobolev and B. N. sel'son, JTP Lett. 33, 132 (1971). ' R. de Bruyn uboter, K. W. Taconis, C. Le Pair, and J. J. M. Beenakker, Pysica (Utrect) 26, 853 (196). ' However, simple modification of te Downs teory by te inclusion of te (1+TS/L) term for a mixture furter widens te disparity wit experiment. We select to=6 sec to carry out determinations of ( from q(3) '