Megacycle Frequency Second Sound Citation Notarys, Harris Anthony (1964) Megacycle Frequency Second Sound. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/560M-XZ14. https://resolver.caltech.edu/CaltechETD:etd-10282008-145450 Abstract Generation and detection of second sound have been extended to 25 Mc/sec using a resonant cavity technique. Investigations show the attenuation coefficient of second sound is proportional to the square of the frequency up to 1.3 Mc/sec at 1.22°K, 4 Mc/sec at 1.47°K, and 10 Mc/sec at 1.9°K - 2.1°K in agreement with Khalatnikov's theoretical predictions and with previous low frequency measurements. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Pellam, John R. Thesis Committee: Unknown, Unknown Defense Date: 24 April 1964 Record Number: CaltechETD:etd-10282008-145450 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-10282008-145450 DOI: 10.7907/560M-XZ14 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4291 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 20 Nov 2008 Last Modified: 19 Jan 2024 23:59 Thesis Files Preview PDF (Notarys_ha_1964.pdf) - Final Version See Usage Policy. 1MB Repository Staff Only: item control page

MEGACYCLE FREQUENCY SECOND SOUND Thesis by Harris A. Notarys In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1964 (Submitted April 24, 196) ii ACKNOWLEDGEMENTS Iam very grateful to Dr. J. R. Pellam for suggesting this problem and providing for me the opportunity to carry out this re- search under his guidance. I should also like to express my appreciation to the National Science Foundation and the Alfred P. Sloan Foundation for assistant- ships and financial support of this research. iii ABSTRACT Generation and detection of second sound have been extended to 25 Mc /sec using a resonant cavity technique. Investigations show the attenuation coefficient of second sound is proportional to the square of the frequency up to 1.3 Me/sec at 1.22%, 4 Me/sec at 1.47°K, and 10 Me/sec at 1.9% - 2.1°%K in agreement with Khalatnikov's theoretical predictions and with previous low frequency measurements. Part iv TABLE OF CONTENTS Acknowledgements Abstract Table of Contents Tntroduction Experimental Apparatus Method of Measurement Results and Discussion Conclusions Appendix A. Megacycle Frequency Second Sound Detectors References 13 at 28 3h CHAPTER I INTRODUCTION In 1940 Tiszat predicted the existence of a new wave motion in a-) Liquid helium IT on the basis of his two fluid model. Independ- ently, in 1941 Landau? also predicted it from his quantum 7 hydrodynamic theory. It was not until Lifshitz’ stressed the thermal wave aspects of this wave motion and showed that the most efficient generation technique for it was a heater, that Peshkov® first observed second sound and measured its velocity. Subsequently, second sound has been investigated in great detail. 9-17 The velocity has been measured by various means and the attenu- ationl?- 2 has been measured by a number of investigators. The theory of second sound attenuation has been derived by Landau and Khalatnikov@' @3 from Landau's theory of liquid helium II and has been found to agree remarkably well with experiment. However, in all the previous experimental investigations of second sound the highest frequencies used were those of Hanson and Pellam’? *% who worked between 100 ke/sec and 280 kc/sec . Hence, the properties of second sound at frequencies above this are open to experimental investigation. Furthermore, the high frequency range of * Frequencies up to 600 ke/sec were reported by Mercereau, Notarys and Pellam!’ using a diffraction technique. However, those fre- quencies were attained in the initial stages of this investigation. second sound could provide a useful tool for the microscopic examination of liquid helium TI (at 25 Me/seec and 1.95%, eg = 7200 8). It was on the basis of these considerations that this investiga- tion was begun. | I CHAPTER II EXPERIMENTAL APPARATUS Because of the high attenuation and short wavelength of second sound at high frequencies, a modified cavity technique was used for this investigation. The cavity consisted of two closely spaced quartz optical flats as the reflecting surfaces, one with a second sound emitter and the other with a second sound detector, and no side walls because of the small angular spreading of the second sound beam. A typical emitter and detector for second sound are shown in Fig. l. The emitter consists of a thin gold film (approximately 100 % thick and 0.32 cm square) evaporated on a rectangular (2.5em x 1.2cm by O.6cm thick) quartz flat (flat to 1/8). ‘The leads to the gold emitting area are 1000 R thick evaporated Sn films which go superconducting and hence, support no voltage drop. ‘The second sound is generated by Joule heat from the gold surface when it is driven with an ac current. The detector” consists of a thin film superconductor less than 800 £ thick and typically 2.5 x 107“cm wide and 0.2hem long evaporated on a quartz flat. The leads are again 1000 R Sn films. With a constant current running through the detector, a temperature fluctuation of the superconductor, while it is in its transition tem- perature region, generates a resistance fluctuation and, hence, a voltage which is amplified and recorded. * See Appendix A. aioe Quartz Flat 100 R Au “™ UU N \\io00 & Sn ASJAAAAYS (EA CZ Baked Au Paint Indium Solder EMITTER Quartz Flat (Puperconductor \n000 & sn WAAAY ANY Baked Au Paint Indium Solder DETECTOR FIGURE 1 Salt strsaud uA & OOL ae & ooor inted vA bows reblf[oe mytbal ASTTIMG tal% stresd totoubnooreque ae & ooor Inted vA boxed tebl[o8 mrthal AOTOSTACT if SAUDIT The quartz flats are spaced by various methods. For spacings greater than 1/2 mn, small quartz spacers are used; between 2.5 x 1073em and 12.5 x 107 3em formvar-coated copper wire is used; and below 2.5 x 107 3om tungsten wire is used. The spaced quartz flats are held in a spring-loaded clamping assembly. Fine coaxial cables from the rest of the electronics are then indium-soldered to baked gold paint films which make electrical contact to the emitter and detector films. A block diagram of the electronic system is shown in Fig. 2. A Signal generator (HP606A, HP20O0CD, or GR1330A) drives a current at rf frequency @/2 through the emitter and a matching resistance, R. A filter is used to suppress any harmonic, w, in the rf current from the signal generator and the frequency is measured by a counter or a meter. Second sound at frequency w is generated by the emitter and causes a resistance fluctuation in the detector at the same frequency. A constant de current and a constant ac current at frequency @, (200 eps - 1 ke/sec from an HP200CD), passed through the detector, change the resistance fluctuation into a modulated rf voltage. (The percent modulation is determined by the ratio of ac current to de current and the resistance properties of the detector.) The voltage from the detector is amplified and demodulated by a radio receiver (National HRO6O). The amplitude of the demodulated signal is then measured on a four cycle wide wave analyzer (GR736A) at Oy or 2059 depending on the percent modulation, and recorded. The temperature is determined by measuring the pressure above the liquid helium bath with an oil manometer (dibutyl phthalate) and LapLloosy SoTUOLPOSTY fo weisepzq yoot” 107.0940 1347 FU] t ("wz <n) (wv) (cn) TazkTBuy TIATZsoay r'0 ~——_—— | aAeM oTpey I (| LC J punog I puoossg 1 boo Ld =A adoosoTTLoso (%o) LOVeLaudy) Teusts J 3 rth T34TTal (2/m) sseg Ioyerauay AOT 14 TeUsTS 4 zequnoy Aouenba ty FIGURE 2 using the "1958 He’ Scale of Temperatures" vapor pressure tables to t re) Sy cc) > S| fo) oO Tang te stotstensD 8 0.f iy”) yousypsr rotay09d eqooaol [road v F & Hnooese Be Bayo8 A vol lente a ° ia Stoson 1-0 eel -roderane0 sresyiend tovisoeh ° a sots19n9 (ges ag”) (MA) (w) tod LET (s\w) totostel tots fed die@ mutloH btyephl t9br029f aolnorsseld to mergstd Aol L al CHAPTER IIT METHOD OF MEASUREMENT The information that can be obtained using the cavity equipment already described will now be considered. As a close approximation to the experimental apparatus an infi- nite plane emitter and an infinite plane perfect reflector, with a small sensing area on it, are assumed. The amplitude of a second sound plane wave traveling the x direction can be expressed in qx Ja(t-x/u,) the form e e » where Q@ is the amplitude attenuation coefficient and Us is the velocity. [Previous measurements of o/w*, which is a function of temperature only, (and not frequency) and Us are given in Fig. 3 for the temperature range to be consid- ered. | For an input power per unit area of (Q/a) cosat at the emitter, the second sound temperature amplitude generated at the detector of the resonant cavity is AT = (2) i 5 1 Sape cos jat~tan’*[eotnen tan 2) a Peta [eosh OD~cos =| 2 2 (1) where (Q/A) power/unit area at the emitter 0 density of liquid helium e specific heat of liquid helium U velocity of second sound aINqeredusy, snsteaA 30/2 pue Cn OOOT (4,) & ood O's Ort OT TT aL T T T T T | ; ie. ( AoypuzeTeuy) n/n | a l et- b ma fe) \ co) \/ Es K aay) : ef IN one | \ — J g | B ae L | _ _ ee — 000¢ (088 /mo) Cn FIGURE 3 LO a amplitude attenuation coefficient of second sound D spacing of cavity plates a) second sound frequency por] O oe (260_\cur) Then, the voltage generated at the detector for a constant ac current, ld e ry cosa, passed through the detector is ' S75 dR av =I, sd AT. cosa, t (2) 3°70 where dR/dT is the slope of the resistance versus temperature curve of the detector and AT, is given by Eq. (1). Hence, the voltage output is proportional to the amplitude of the second sound in the I°g cavity. Notice that the detector is amplitude and phase sensitive and not intensity sensitive! Equation (1), which is a typical equation for a resonant system T*e and approximates the experimental conditions, is now examined. For fixed cavity spacing, D, the resonance condition Pe sug O\4e AGLaNe pembeLecs.e L (xX) O\ i, (Hsueon sug Ley ys) Pia (Wel.ceLesn* worstAg> suq Eey;yew) aDd/2., =nx (where the integer n 21 gives the number of half T‘yst a\4, (KPSTSLUTKOA ) wavelengths in the cavity) can be reached by varying either the fre- quency or the temperature (i.e. velocity). By using the resonance condition for a cavity of known spacing, D, an accurate determina- Ts tion of the velocity and dispersion can be made by 8 ee 9000 1) measuring the fundamental and its harmonics at a fixed Pd (car\26c ) temperature, 2) measuring the resonance temperatures of a fundamental and € GAUDTY ) E P its harmonics. ii On the other hand, the value of the attenuation coefficient ean be determined by measuring the width of the resonance curves ( Aa sath Wi or AD sath) at 1//2 of the peak amplitude and using the relevant expansion of Eq. (1) 1) for the frequency-resonance curve (temperature constant ) AQ. L 2 width ofa? = Seth (3) w@ eu a 2) for the temperature-resonance curve (frequency constant ) AT. du,/at ho od ou" - widt + a (4) a) a a Us where du,/at is the slope of the velocity versus temperature curve of second sound. Hence, for those frequencies that have well-defined resonances, the position of the resonance and its width give accurate measurements of the velocity and attenuation coefficient of second sound. | At higher frequencies, when the resonances are not well-defined, it is necessary to fit the experimental results to Eq. (1) in order to determine the velocity and the attenuation coefficient. For even higher frequencies Eq. (1) loses its resonance features and becomes merely a decaying wave of form 12 It should be noted that in all this, D, the spacing of the cavity, is actually a possible variable, which can be used to vary the limits of the three frequency ranges considered above and, especially, to extend to higher frequencies the well-defined resonance range. Furthermore, use of the variable D (and also w) permits the determination, or at least an estimate of, the reflection coefficient of second sound impinging on a quartz flat [which has been neglected in Eq. (1)]. If two emitters with detectors opposite them are placed in the same cavity, it is possible to determine the misalignment of the cavity by comparing the resonance frequency of the two emitter-detector sets. Also, from the second sound crosstalk between the emitter-detector sets and the variation of D and w, the effect of diffraction and spreading of the second sound beam may be assessed. Consequently, the approximate Eq. (1) permits the determination of the velocity and the amplitude attenuation coefficient of second sound, while the neglected effects of reflection, cavity misalignment, and spreading and diffraction of second sound can be handled experimentally. 13 CHAPTER IV RESULTS AND DISCUSSION A. Second Sound Frequency Range With the described cavity technique, generation and detection of second sound have been extended to the frequencies given below: 7(°K) Second Sound Cavity Spacing, Frequency Observed D (em) (Me/sec) 1.9 - 2. 25 1.62 x 107° 1.76 17 2.93 x 1073 1.47 6.5 2.93 x 107? 1.22 3 2.93 x 1073 Although second sound has now been observed up to these frequen- cies, the actual measurement range is smaller because of two experi- mental difficulties. First, at low frequencies, the frequency and temperature- resonance curves give multiple resonance peaks instead of single resonance peaks. This effect is observed below 1.2 Me/see for D=7.8 x 107 3em at 1.9% - 2.1%, but is not observed down to 160ke/see for D=2.93 x 107%cm below 1.47°K. While this splitting of the peaks is suppressed by increasing the second sound frequency or increasing the cavity spacing, D, emitter-detector geometry changes generally give a variation but little suppression of the splitting. The most significant feature associated with this peak ih splitting is that it gives rise to second sound crosstalk between two emitter-detector sets in the same cavity whereas there is no crosstalk if there is no splitting. The effect appears to be a diffraction effect (possibly similar to laser modes >). Since in Eq. (1), which gives the form of the resonances in the cavity, any diffraction or possible cross modes have been completely ignored, a more careful analysis may show the origin of the difficulty. However, if the measurements are Made with sufficient cavity separation and high enough frequency, the entire problem can be considered an interesting observation to be investigated at some future date. Second, at high frequencies, the electromagnetic fields of the emitter effect the detector either by eddy current heating or magnetic field effects on the superconductor. These effects act on the detector exactly like second sound, and as the frequency increases, become more important, since the second sound signal decreases and the electromagnetic noise increases. Figures 4 and 5 show that at a given frequency, as the temperature in the above 1.9% range is increased, (the attenuation of second sound is increased) the second sound/ electromagnetic noise ratio decreases and the effect becomes more marked. As the temperature is permitted to drift the noise alter- nately adds and subtracts from neighboring resonance peaks, since they are 180° out of phase. Finally, at high enough temperatures for the electromagnetic noise to be larger than the second sound, an oscilia- ting signal results with maxima spaced two second sound resonances apart. Figures 4 and 5 also show the effect as frequency is increased gonAyaWy. aNeos id NODIS | wif tm te web ee aeoc AW for en a ae es i doe if | i | aauvnos i} ~ “ ; | 2 ¢-ofx 62), Supede Ayre mer) r | : ; : : ; : sas/w 9 Asuanbaas punds puoras | ho = _ os - . i i * 4 H N 3 F. y) 24G! ma Lp b3¢1 ba ISVe fd PIG Bh a ! w ' t i Q ain * ih aantine ~ tom eben come Fo nen ae Bete bee a —& ; : j : Zz : | iv] Bae — t a 4 cee Pape ee es Seems _ -.—4 ie oa 3 = agnindwy : i sce fe sie cee eee cermin ete ee elf ene | TZ ase meg A OO} | ayee nm og! = PARE] AM OF alec am rn ern Secon nee wee wow chee dawns 7 ne (w2 ¢.01x% £62 Bupedg Kpaey _ ove Ps doce werner 1 em ! ! i : a 2aSPW € Kovianbaay punos, puoreac VAR ASHOG ATES PALO ALTO CALIE Inte PN ON pore TOSS + osi2 . - Z a 4 4 + ft} /[ a \ ar Oo . ime) iH po ne e—— a - }---—— +e ~ : 2 = fe a a — = 1 7 a4. Oo | és bo ee 7z we H ~ _ { 4 am _ ene = | | 4 aan) ns ane 3 pore ern ens — Toe a es i aeog nw Of | BRIS nua & 3 a) nn —— a a ea Ee | — € on | 2DaSPW BS on _ Rouarbas4 punos puosas | 0 VARIAN ASSOCIATES, PALO ALTO, Cali INSTRUMEN?E DIVISION FIGURE 5 17 and as the cavity spacing is changed. A number of designs of second sound emitters and detectors to minimize inductive and capacitive coupling by geometry were tried, but with no great success. A solu- tion of this problem is to design an emitter which is shielded electromagnetically from the detector. However, for this investiga- tion sufficient information is available without this added subtlety, Since analysis shows that the width of a resonance curve is uneffected (within 1.5%) by pick-up signals less than 60% of the size of the second sound signal. (This analysis consists of determining the ranges of phase and amplitude of a noise signal, added to the second sound signal, which give a resultant with the qualitative features of Fig. 4 and 5.) B. Variation of the Velocity of Second Sound with Frequency The velocity of second sound versus temperature was measured with the cavity system in the frequency range 100 ke/sec to 340 ke/see and the measurements agreed very well (within 1%, which is good agreement for absolute values) with those of Mercereau, Notarys, and Pellam! ; measured by a diffraction technique. The velocity change with frequency was determined by comparing the resonance temperatures of harmonics of the cavity. ‘The results showed: 1.9861°K — |u,/u,|< 0.19 1.87 Me/see - 7.5 Me/see D = 1.6x107dn 2.0385°K |Au,/u,|< 0.15% 300 ke/sec - 7 Me/sec D = 7.83x1072, Hence, up to 7.5 Me /sec the velocity is constant to less than 0.15% at 2°K. 18 C. Variation of ow" with Frequency ow“, which has been found to be independent of frequency up to 100 ke/sec - 280 kc/sec in previous measurements, was measured as a function of frequency at several temperatures. For the determination of ow", the frequency~resonance curves were used below 1.47%, while from 1.9% to 2.1% the temperature-resonance curves were used. In Fig. 6 the measured values of or" from 300 ke/sec to 1.3 Mc/see at 1.22°K are compared to Khalatnikov's“> theoretical 18, 20 values which agree well with experiments up to 20 ke/sec. The values show no change in ow" over the frequency range measured and agree within experimental accuracy with Khalatnikov's theoretical values. It should be noted that the wavelength of second sound, Ags? at 1.22°% and 1.3 Mc/sec is 14.2 x 107 ton while the phonon mean is 1.7 x 107 tem. Hence Btn ~..- By decreasing free path, 2 $s ph? the cavity spacing it may be experimentally possible to examine phonon mean free path effects at 1.22°K. In Fig. 7 the measured values of ofa" from 340 ke/sec to 4 Me/sec at 1.47°K are compared to the values measured by Hanson and Pellam’? from 100 ke/sec to 280 kce/sec. The values show no change in ow" over the frequency range measured and agree within experimental accuracy with the values of Hanson and Pellam. In Fig. 8 the measured values of o/s" from 3 Mc/see to °. 10 Me/sec in the temperature range 1.9°K - 2.1°K are compared to 1 the values measured by Hanson and Pellam 4 from 100 ke/sec to 19 3.0 1 1 | Frequency (kce/sec) O 639 | % V 1277 7“ § 2.0 - N oO i) 1093 ry a Khalatnikov (1952) m Ne 1.5F ~ | ~ 3 | 1.0 | 1.20 1.25 1.30 1.35 t (°K) 2 . ce/oy versus T for Various Frequencies FIGURE 6 eL | 20 | 6 I l O.€ L. { (o9a\o4) yYonsuport Hanson and Pellam (1954) OSE 5k 4 eed Bee .-8 | o.s 8 an S$ & 5 ge Bob 4 es rc ro) (S@e@L) vorxtats Lad - ~~ 3b - aL gv $ = | Frequency (xc/sec) 6 B& 340 + 1704 - 2 681 X 2055 - D 1022 O 3070 Vv 1363 © 4083 5 i 1 | 1.40 L.45 1.50 1.55 O.f fe) @g.1 0€.1 @s.t os. T (*K) (x°) T g o/s versus T for Various Frequencies estoneupesr® ayotisV rot T evarev wo FIGURE 7 Oo SAUDTE (#20L) mallet bas noansH (vea\oL) yoneupert HOF L Ox 2408 180 OYVOE SS0L e804 FFL ee. t 02¢.. eu. f od. (x°) 2 astoneypetd ayobrsV r0t T ayatev Se ks) Y Gauort on, x T0;3 (86¢_\c0) el 3.0 o/ or x 1079 (sec”/em) Frequency (Mce/sec) ©+xQQdbpoo OO ON Aw FW Hanson and Pellam (1954) 1.95 2.00 2.05 2.10 t (°K) or/w versus T for Various Frequencies FIGURE 8 (o92\oM) yoneyport E 4f ¢ ) y 8 Q (#205) mallet fas noaneH Or OL. 20.8 00.8 ee. (a°) & estonsypert avotrsV rot T ayarev TY 8 AAUOTE 0.4 0.8 O.f 8.0 3.0 #.0 £.0 0e.f a\%, x 10,3 (26¢_\cur) a2 280 kc/sec. ‘The values show no change in O/ os" over the frequency range measured and agree with Hanson and Pellam to within experimental accuracy. Hence, the measurements indicate that ow" is independent of frequency up to 1.3 Mc/sec at 1.22%, upto 4 Me/sec at 1.47°K, and up to 10 Me/sec in the temperature range 1.9% - 2.1%. This is in agreement with Khalatnikov's theoretical prediction that above 1.2°K for frequencies below 100 Me/see the attenuation coefficient is proportional to frequency squared. On the basis of Landau's excitation spectrum in liquid helium II, Landau and Khalatnikov found that three terms contributed to the atten- uation of second sound: 1) a first viscosity term which is associated with elastic interactions, 2) a second viscosity term which is associated with the number equilibrium of the excitations through inelastic interactions, 3) an effective heat conductivity term which is as large as the combined first and second viscosity terms. In the analysis it was shown that the longest relaxation times above 1.2°K are < 1078 sec and are associated with the establishment of number equilibrium. Consequently, no dispersion should be observable below 100 Mc/sec. However, this analysis does not take into consid- eration mean free path effects which, Khalatnikov asserts, should oceur at lower frequencies. 23 D. Nonlinear Effects As the amplitude of the temperature oscillations in a cavity increases, the second sound amplitude attenuation coefficient increases. Consequently, in order to obtain the zero power values of aos" (given above), it is necessary to correct for the amplitude of the temperature oscillations. The fractional change of ooo" with input power to the cavity has been found to be linear’? If the amplitude of peu, (AT. .) from Eq. (1) is denoted by AP 55 (amplitude of power /em® necessary to generate the same second sound amplitude in the non-cavity case, i.e., pure traveling wave case), then, the fractional change of a per unit AP os (in watts/em“) for the temperature ranges considered is found experimentally to be a(a/w*)/(a/e0") a(a/a")/ (a/c) No associated change of velocity ( [au,/u,,|<0.002) was observed with Hl fe) fo) a 1.2AP.. 1.33°K - 1.46°K APL, $1.2 watts/cm °. o) 2HAP 1.9K - 2.1°K iH this change of attenuation, e.g., at 1.46°K for AP ,<l-2 watts/em“. Since there is an added attenuation as the second sound amplitude is increased, harmonics of the generated second sound frequency should exist and have been observed. It is possible, with the present technique, to Fourier analyze large amplitude second sound. Conse- quently, by considering the nonlinear terms of the hydrodynamic equations this technique should be a sensitive means of determining their validity. it should be noted that the velocity change due to second sound amplitude effects has been treated theoretically by Khalatnikov@? © and. Temperley”* and has been measured for pulses by Dessler and Fairbank.~° 2h B. Reflection Coefficient In Eq. (1) the effects of the reflection coefficient of second sound impinging -on quartz have been completely neglected. If a reflection coefficient r = eP (r=1, B=0; r=0, B=") is assumed, Eq. (1) takes the form (ay Je) 1 | | wD AT (2 + cos|wt-tan cotn(ab+p) ten) ee ae a [eosh“(ap+8)-cos® vad \ Me é (6) where experimentally r ~ 1, B~ 0. The attenuation coefficient from the resonance curve widths is now given by a 6B AW ath 1 Q a ATyiath 1 %2/AT a rr ete ~ —~3 ray) wD ra) aU, a) oD a ra) Us (7) Hence, aS w or D are increased, the effect of B on ow" is decreased. Within experimental accuracy it was found, by both D and w changes, that below 1.47% there are no measurable losses due to reflection above 160 ke/sec (lower frequencies were not considered). In the 1.9°K-2.1°%K temperature range the same was true above 2 Me/sec. For example, by using Eq. (7) and the scatter of ow" (0.3x 10723) in Fig. 7, ® is found to be less than 5x 107° at 1.47°K. Furthermore, the data for ow" at 1.47°% with a cavity spacing, D, changed to 6.05 x 107 Fom from 2.73 x 107 3om fall within the values given in Fig. 7 giving no observable effect of B 2) With D change. Although the effects of reflection can be ignored under the circumstances of this specific investigation, analysis of reflection in terms of the thermal properties of the materials used and the Kapitza boundary resistance“! permits the determination (or at least an indication of the magnitude) of the thermal properties of quartz and its thermal coupling to liquid helium IT. F. Cavity Alignment Cavity misalignment can be measured by using two emitter-detector sets in the same cavity. Ina typical cavity with separation 6.05 x 107 Fem, using formvar-coated copper wire as spacers, there was a misalignment of 4800 R/em (where 1000 R/em misalignment can be detected). The effect of misalignment should decrease with increasing frequency, i.e., increasing attenuation. For frequencies above 160 ke/sec below 1.47°K and above 2 Mc/seec in the 1.9°%K-2.1°% temperature range, no effect due to misalignment has been observed. G. Critical de Power Effects The second sound generation method used in this investigation has associated with it a steady heat input. Consequently, second sound measurements are valid only when the de power input can flow out of the cavity without affecting it. Measurements of the permissible de power input have been made by examining the temperature in the cavity using the second sound resonance temperatures and also the detector resistance. As an example, the values of these maximum 26 permissible power inputs for a cavity with a spacing of 2.93 xX 107 Fem and an emitter O.32cem square are: 7(°K) Power Input (mw/em”) 1.22 12 1.3 a2 1.4 he 1.9 125 2.0 125 2.1 Sh 2.15 By) 2.1720 0 The powers used during the measurement of u, and ow" of a second sound were well below the values which cause temperature changes in the cavity. However, it should be noted that the ultimate limit of this cavity technique (if not the second sound itself) is the Size to which the spacing can be decreased while still permitting sufficient power to generate measurable second sound. 27 CHAPTER V CONCLUSIONS A beginning has been made in the examination of megacycle fre- quency second sound. Measurements have been made of the attenuation coefficient up to 10 Mc/sec Orn~5 = 18000 at 1.95°K) and the velocity up to 7.5 Me/sec. Although there was too much electro- magnetic noise for measurements to be made, second sound has been generated and detected up to 25 Mce/sec (down to hes = 6000 & at 2.05°K). With a more refined generation technique, higher frequencies appear to be attainable. This presents an excellent opportunity to examine liquid helium II on a microscopic scale with a probe smaller than the wavelength of visible light. 28 APPENDIX A MEGACYCLE FREQUENCY SECOND SOUND DETECTORS Because of the small wavelength, high attenuation, and de heat flow associated with megacycle frequency second sound, most detection schemes used in previous investigations are not applicable. Hence, after careful consideration, a bolometer was chosen to satisfy the stringent requirements of this investigation. Use of a bolometer is a common technique for detecting second sound. In the past the bolometer materials used have fallen into two classes; first, semiconductor materials such as carbon films and germanium, and second, superconductors in the form of phosphor bronze wire °° All the previous investigations have been at low enough frequencies so that there was no problem with thermal response of the materials used. However, approximately 500 ke/sec second sound is the upper frequency limit of these materials without special handling or considerations. Nevertheless, it is possible to extend the use of bolometers as second sound detectors into the megacycle frequency range by using evaporated thin films. The two classes of bolometer materials mentioned above act quite differently at low temperatures. The resistance of a semiconductor rises as the temperature is lowered (approximately as R = red; Cy R, constants) and its high dR/aT is related directly with its high resistance. In fact, for thin films the resistance of pure semiconductors in the liquid helium II temperature range is so high that doping them is necessary to make them usable. On the other hand, 29 the resistance of superconductors, which is generally low, drops to zero within a small temperature range at some transition temperature, To (defined as the temperature at which the resistance is half the normal resistance). Consequently, for impedance matching purposes and in order to minimize electromagnetic coupling between emitter and detector, thin film superconductors were used as the detectors for megacycle frequency second sound in this experiment. A superconductor is useful as a second sound detector only over a small temperature range about its transition temperature, Th where its resistance changes from its normal value, Rw to zero. Consequently, different superconductors with different transition temperatures were used to cover the entire liquid helium II tempera- ture range above 1.2%. In any one experiment second sound was inves- tigated over only a small region of temperature. Although a very large number of superconductors can be used, the ones used for this experiment were films of the compound aupi eH and superimposed 3a films. Au-Sn Thin films of Au,Bi were made by first evaporating approximately 600 of Bi ona 2008 evaporated Au film, .075em wide and O.32em long (both evaporations made at room temperatures). The resultant film was then placed in a pyrex vacuum cell and heated for one hour at about 250°C. This gave a thin film superconductor (Au,Bi) with a normal resistance of 159, a transition temperature of about 1.9}4° » anda dr/at (slope of resistance versus tempera- ture curve) of about 7009/°K with O.1 ma measuring current. (These values are approximate and are given only to indicate the 30 film's properties.) It was found during the investigation that variation of the amounts evaporated and the heating procedures per- mitted production of films which had transition temperatures anywhere from 1.2°K to 2.2°K. The widths of the transitions occurring about 1.9°%K were very narrow, whereas transitions at appreciably lower or higher temperatures were not nearly so narrow. However, the primary value of a compound superconductor is to obtain easily a very high sensitivity near one temperature (in the case of Au,Bi in the temperature range 1.8% - 2.1°K), a function performed very well by Au,Bi. The Au-Sn superimposed films were produced by evaporating (at room temperature) between 300 & and 500 8 of Sn on 100 R au films. The transition temperature was a strong function of the ratio of Sn to Au thickness. For example, a 20 R change in Sn thick- ness ora 10 R change in Au thickness changed the transition tem- perature approximately 0.1%. Furthermore, the length of evaporation and temperature of the boat effected the transition temperature. Consequently, in order to use superimposed films to obtain required transition temperatures reproducibly, it is necessary to be able to repeat, exactly, the evaporation conditions. On the average, it was found that for certain normal resistances it was possible to obtain certain dR/daT values Ry(a) ar/at (9/%K) 2.3 10 a3 120 54 300 - 1200 31 where a measuring current of O.1 ma was used. The normal resist- ances vf the order of 54q were obtained for films 0.32 em long and a length to width ratio of about 15. As seen from the values of dr/dT versus Ry? for very small films very narrow transitions can be obtained, approaching the value for transitions of compounds. However, the primary purpose of using these films is to obtain a good sensitivity over a fairly wide temperature range (approximately 0.2K in this case) and to be able to change the transition tempera- ture easily. Both these functions are performed very well by Au-Sn superimposed films when proper care is taken in their fabrication. The stability of some of the films was noted for approximately two-month periods with repeated cycling to liquid helium temperatures. The results showed that in general: (1) The T, and dr/adT of superimposed Au-Sn films decreased a little but not significantly. (2) For Au,Bi films with 1, inside the 1.8% - 2.0% range there was at most a slight change of TO and dr/dat. However, films with higher To annealed to transition temperatures within the 1.8% - 2.0°K range, while films with lower T, also annealed to still lower transition temperatures till the superconducting proper-~ tiles were gone. Consequently, by using Au-Sn superimposed films it is possible to make stable overlapping second sound detectors to cover the entire temperature range between 1.2°K and 2.2°K with good sensitivity, while for very high sensitivity at particular tempera- 32 tures, compounds (such as Au,Bi at 1.8% to 2.0K) or very small Au-Sn films can be used. Since Eq. (2) shows that the ratio between the voltage, AV, generated at the detector, and the second sound amplitude, ATS 5? is I,dR/dT, this is the value which will be defined as the sensi- tivity of the detector. It is important that it be noted that dR/dT is a function of I (as is tT.) and decreases for very high values of Io: Consequently, when determining TaR/at it is necessary that it be measured directly or that R versus T be measured under the exact conditions of the experiment. Values of the sensitivity are listed for the detectors with typical constant ac currents used in the experiment Detector I ar/ar I (ma) Ry (a) At (°K) (amp o/°K) Au Bi QO. - 0.5 O.1 - 0.5 15 6.5 - 1.3107? Au-Sn 0.01 - 0.05 O.1 - 0.5 23 6.5 - 1.3x107! Au-Sn (small) 0.03 - 0.1 O.1 54 22 - 6.5x10°9 Included with the sensitivity is a measure of the temperature fluctu- ation, ATy? which gives a voltage at the detector equal to the noise of the electronic system at 1.28 Mc/sec which is 6.5 x 1077 volts. 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