AC Anderson

B Halpern

BD Josephson

D. S. Betts

DO Edwards

HT Davis

KR Atkins

M. Kuchnir

P Magistris

PVE Mcclintock

R Abe

RC Clark

English

McClintock, Peter V. E.

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LOW TEMPERATURE PHYSICS-LT 13, VOL. 1Edited by K. D. Timmerhaus, W. J. O'Sullivan and E. F. HammelBook available from: Plenum Publishing Corporation227 West 17th Street, New York, New York 10011Measurement of Ionic Mobilities in Liquid3He by a Space Charge Method *Department of Physics, University of LancasterLancaster, EnglandIntroductionThe behavior to be expected of a charged impurity moving in a Fermi fluidwas first discussed in detail by Abe and Aizu 1 and independently by Clark.2 Theyconcluded that, although mobility should be inversely proportional to viscosityat high temperatures (classical limit), a T-2 law should be obeyed in the low-tem-perature (degenerate) limit. Davis and Dagonnier have discussed the situation atintermediate temperatures in terms of quantum mechanical Brownian motion.3These predictions were not borne out by experiment.4,5 In a more recent theoreticalinvestigation Josephson and Lekner6 show that, although the T- 2 law may stillbe expected at sufficiently low temperatures, some form of weaker dependenceshould be observed at higher temperatures. Since there seems to be little consensusas to the form of this weaker dependence or as to the characteristic temperature atwhich one regime might give way to the other, it is important that accurate experi-mental mobility data should be obtained. For negative ions such data are nowavailable down to 17 m°K. 5 However, for positive ions data below I°K,4 measuredby a time-of-flight method, suffer from severe inconsistencies and hysteresis effects,apparently experimentally based. In this paper we describe mobility measurementsdown to O.25°K by a completely different technique: space-charge-limited emissionof ions from a sharp metal point. This method appears to be more accurate thanearlier space charge techniques 7 and avoids the complication of thermal gradientsdue to heating at a radioactive source.Field Emission and Field Ionization in Liquid 3HeThe characteristics of field emission and field ionization in liquid 3He havebeen studied in detai1.8,9 In both cases there is a space-charge-limited regime forwhich the emission is well described byloV = Vo + 98 (R/aKf.l)1/2 i1/2 (1)where Vis the potential in V applied to the tip, Vo is a constant, R is the anode radiusin cm, om is the emission cone angle in steradians, K is the dielectric constant, J,l isthe mobility in cm2 y-1 sec-1, and i is the current in nA. In using Eq. (1)to determinemobilities, the largest uncertainty lies in IX. For emission in vacuum IX :::::: 0.6, but inliquid helium we have found 2.2 < IX < 3.2, the exact value depending on the in-dividual tip. Since mobility changes smaller than 1% can be resolved, it is mostuseful to determine the temperature dependence of the mobility by our space chargemethod and then scale the data to agree with the absolute value of J,l at some particu-lar temperature, obtained by another technique.We have found that emission characteristics can be strongly influenced by thebuild up of thermal gradients in the liquid.9 To avoid this effect, all data reportedhere were taken by applying potential to the tip only just long enough for a chartrecorder to record the current, i.e., about 1.5 sec. A simple calculation shows thatduring this period the average temperature of the liquid rises by typically 30moK.However, the maximum temperature rise probably occurs near the tip where theelectric field is largest, and the change in temperature near the anode in the spacecharge region which controls the emission is presumably much smaller.Details of the apparatus and experimental technique are discussed elsewhere.9The tungsten tips were prepared by electrolytic etching in NaOH solution and weresmoothed in situ by field evaporation. Their radii of curvature were determinedfrom the vacuum field-emission characteristics. Temperature measurement was bya 470-0 Speer carbon resistor immersed in the sample within the anode assembly.It was calibrated against 3He vapor pressure down to 0.45°K and the calibrationwas then extrapolated to 0.25°K. Care was taken to keep the sample pressure constantsince we have found that IX is weakly pressure dependent at low pressures.9Experimental ResultsCurrent-voltage characteristics for both positive and negative emISSIOnarepresented as i1/2_ V plots in Fig. 1 for three different temperatures. Good straightlines are obtained in agreement with Eq. (1), and the intercepts are Vo = 410 ± 20Yand 490 ± 30 Y for negative and positive ions, respectively. Although we can, in1< 1{i 2 (A x 10-8) 25 -o T= 0.985K }" 0.4624 + 0.2811!I 0.985}A 0.4623)( 0.281positiveionsnegativeionsFig. 1. Positive and negative ion emission (currents)1/2as a function of tip potential.principle, determine jJ.(T) by measuring the gradient at a number of different tem-peratures, this is not a convenient method in practice because of the large number ofi(V) readings necessary to determine jJ. at a single temperature.If we rewrite Eq. (1) in the formjJ.(T) = [982R/tXK(V - Va)2] i(T) (2)we see that at constant tip potential, changes in mobility are directly proportionalto changes in emission current. It is convenient to normalize the current by dividingit by (V - Va)2, so that data taken at different tip potentials ought to fall on the sameline. In Figs. 2 and 3 we plot the normalized negative and positive emission currents,respectively, against temperature for three different tip potentials in each case.Almost all the points fall within less than ± 1% of a "best fit" curve drawn throughthe data. Scaling our values of if (v - VO)2 to agree with earlier mobility measure-ments4 at 1.0oK, we obtain the mobilities indicated by the right-hand scales ofFigs. 2 and 3. The error in jJ. relative to its value at 1.0oK is therefore indicated bythe scatter of the data points and the systematic error in its absolute magnitudewill be the ± 10% quoted by Anderson et a/.4DiscussionFrom the linearity of the results shown in Fig. 1we deduce that for both positiveand negative ions the mobility is independent of electric field within our experimentalrange, i.e., up to several kV em -1, which is, as far as we are aware, the highest fieldfor which the ionic mobility in liquid 3He has been measured. Careful scrutiny ofthe data suggests that the change in mobility resulting from a 50% change in averageelectric field is certainly less than 1%. Therefore the fact that the field in which jJ.(T)20+d'..,j_i_ x 1015 (AV-2)A+rJ . 0.028~+(I) .2 +r; 0.02719 (v -Va) .d +~~).L (cm2V·1S·')0.02618.•+P 0.025cI>17..t+0.024d'~+0.023<lI+16 +(JA+ Negative ions0.0220 0 V = 3050 volts15 +A 0.021<lI 2800<lit- + 240014 at-0.020<iFVa = 410 volts 0.019~13 '\ P = 95 torr 0.018,*'i,.12 / 0.0170.016110.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1Fig. 2. Temperature dependence of the (normalized) negativeion emission current.a V = 3100 volts!:> 2900+ 2700Ii-32 ~31L I I I0·2 0·3 0·4 0·5Vo = 490 voltsP = 95 torrFig. 3. Temperature dependence of the (normalized)positive ion emission current.is measured is large and nonuniform has little effect on the reliability of our mea-surements.The variation of /1- with temperature (Fig. 2) agrees well with the earlierresults of Anderson et al.4 in the region of overlap, but the scatter of our data pointsappears to be smaller. The temperature dependence of /1 + (Fig. 3) is certainly notinconsistent with the earlier results,4 but there is such a large scatter in the latter(about ± 10%) that a meaningful comparison is difficult.None of the existing theories predicts correctly the temperature dependence of/1+ or /1- in this temperature range. Only Walden's rule gives the correct sign forthe temperature dependence. Between 1.0 and 2.0oK we find /1- inversely propor-tional to viscosity within experimental error, using the smoothed viscosity dataof Betts et alY Below 1.3°K for /1+ and 1.00K for /1- the observed temperaturedependence is much weaker than that implied by Walden's rule.The minimum in /1+ near O.3°K was unexpected and is very interesting. * Aqualitative explanation can be given in terms of the "helium berg" model of thepositive ion.13 On this model the minimum in the melting curve near 0.3OK 14wouldimply a maximum in the positive ion radius at the same temperature and therefore,neglecting other effects, a minimum in mobility. However, it is hard on this basis tounderstand the shape of the /1+ (T) curve. In particular, the maximum value ofd/1+/ dT occurs near OAoK, at which temperature the melting pressure is only 0.5%above its minimum value and is changing very slowly.Our present mobility-measuring technique avoids complications arising fromthe heat continuously generated by a conventional radioactive source. In contrast,field emission/ionization sources generate no heat whatever except when actuallyemitting current, and they would therefore seem particularly suitable for use infuture experiments at ultralow temperatures. To extend our present investigationto lower temperatures, it is clear that much shorter current pulses will be required.Preliminary experiments in He I are encouraging: we find that pulse durations of 1msec should be quite sufficient to carry out the measurements.ConclusionBetween 0.25 and 2.0oK the mobilities of both positive and negative ions inliquid 3He at low pressure are independent of electric field up to several kV cm - 1.We have measured the temperature dependence of the mobilities with greaterresolution than that of previously published work. For negative ions our resultsare in excellent agreement with the earlier work. For positive ions they are not indisagreement but, with our superior resolution, we have been able to observe adefinite minimum in Jl+ at around 0.3°K. No existing theory gives a satisfactoryaccount of the mobility in this temperature range. In view of the great simplicityand good resolution of our space charge technique it seems highly desirable to extendthe measurements down into the fully degenerate temperature regime, and we proposeto do so at the earliest opportunity.I. R. Abe and K. Aizu, Phys. Rev. 123, 10 (1961).2. R. C. Clark, Proc. Phys. Soc. 82, 785 (1963).3. H. T. Davis and R. Dagonnier, J. Chern. Phys. 44, 4030 (1966).4. A. C. Anderson, M. Kuchnir, and J. C. Wheatley, Phys. Rev. 168,261 (1968).5. M. Kuchnir, P. R. Roach, and J. B. Ketterson, Phys. Rev. A2, 262 (1970).6. B. D. Josephson and J. Lekner, Phys. Rev. Leu. 23,111 (1969).7. P. de Magistris, I. Modena, and F. Scaramuzzi, in Proc. 9th Intern. Can! on Low Temp. Phys. /964.Plenum Press, New York (1965), p. 349.8. P. V. E. McClintock, Phys. Leu. 3SA, 211 (1971).9. P. V. E. McClintock, J. Low Temp. Phys. 11, 15 (1973).10. B. Halpern and R. Gomer, J. Chern. Phys. 51, 1031 (1969).II. D. S. Betts, B. E. Keen, and J. Wilks, Proc. Roy. Soc. A 289, 34 (1966).12. M. Kuchnir, Private communication; M. Kuchnir, J. B. Ketterson, and P. R. Roach, this volume.13. K. R. Atkins, Phys. Rev. 116, 1339 (1959).14. D. O. Edwards, J. L. Baum, D. F. Brewer, J. G. Daunt, and A. S. McWilliams, in Proc. 7th Intern.Can! on Low Temp. Phys. /960. North-Holland, Amsterdam, (1961), p. 610.

Measurement of ionic mobilities in liquid 3He by a space charge method.

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