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He3 cryostat for steady state nuclear magnetic resonance measurements in metals Puls, Manfred Paul 1966

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A Ee CRYOSTAT FOR STEADY STATE NUCLEAR MAGNETIC RESONANCE MEASUREMENTS IN METALS J  by  MANFRED PAUL PULS B.A.Sc., The U n i v e r s i t y of B r i t i s h Columbia, 1964  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA May, 1966  In p r e s e n t i n g t h i s t h e s i s requirements Columbia, for  in p a r t i a l  f u l f i l m e n t o f the  f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h  I agree t h a t  the L i b r a r y s h a l l make i t f r e e l y  r e f e r e n c e and s t u d y .  I f u r t h e r agree  available  that permission f o r  e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s It  i s understood  financial  that copying o r p u b l i c a t i o n of t h i s t h e s i s f o r  g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  Department o f  P-&-ty&c^<3  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada Date  representatives.  Columbia  S^j/^CC  permission  A He  3  ABSTRACT cryostat was designed f o r steady state nuclear  magnetic resonance measurements. The cryostat required 3 3 about one l i t e r of He^ at NTP. This amount of He^ was l i q u i f i e d at 1.2°K, which was the temperature of the surroun 4 ding l i q u i d He  bath, and then pumped on by means of a four-  stage mercury d i f f u s i o n pump. By t h i s procedure, a l i 3 o quid He temperature of 0.35 K was achieved and maintained f o r four hours. The r - f c o i l and sample were i n d i r e c t 3 contact with the l i q u i d He to ensure s u f f i c i e n t heat t r a n s f e r between the two. The temperature of the l i q u i d 3 He was measured by means of vapour pressure measurements 3 of the evaporating He^ and by means of resistance measurements of a carbon resistance i n contact with the l i q u i d 3 He . The system was n o n - r e c i r c u l a t i n g , since a t o t a l , uninterrupted run of four hours was considered long enough 3 f o r most experiments.  The He  could also be r e t r a n s f e r r e d  within 20 minutes a f t e r such a run, and t h i s process could _L  be continued u n t i l i n - s u f f i c i e n t  quantities of l i q u i d He  remained to cool the surroundings.  iii TABLE OF CONTENTS Page i i  ABSTRACT LIST OF ILLUSTRATIONS  iv  ACKNOWLEDGEMENT  v  CHAPTER 1  INTRODUCTION  1  CHAPTER 2  EXPERIMENTAL METHODS AND APPARATUS ...  3  APPENDIX  CRYOSTAT  23  HEAT LEAKS AND PUMPING SPEEDS  28  He?  36  BIBLIOGRAPHY  38  iv. LIST OF ILLUSTRATIONS Figure  Page  1  Resistance measurement by Rubicon potentiometer  10  2  Schematic diagram of steady state meter  16  3  Schematic of He vacuum system  spectro-  cryostat and associated 18  4-  Schematic of pumping l i n e s and cans  24  5  Schematic of r - f c o i l , sample, carbon r e sistance and low temperature seals  26  V  ACKNOWLEDGEMENT  I wish to express my gratitude to Dr. D. LI. Williams f o r the i n i t i a l , h e l p f u l ideas and f o r h i s ready a s s i s tance throughout the course of t h i s work, p a r t i c u l a r l y i n the l a t e r stages when he spent many long hours on helping with the completion of the experiment. I also wish to thank G. A. deWitt f o r the many helpf u l discussions, and J . Lees f o r h i s advice and assistance and the construction of a l l of the glass equipment that went into the b u i l d i n g of the c r y o s t a t .  Further, I would  l i k e to thank a l l those members of the Physics Department, who, through t h e i r advice, helped me i n carrying out t h i s work. This research was _upported f i n a n c i a l l y , i n part, by the National Research Council through grants to Dr. D. L I . Williams and by the Dean's Committee on Research through the award of a s s i s t a n t s h i p s to the w r i t e r .  1. CHAPTER 1L INTRODUCTION _>  Rapid advance [Tints have been made i n recent years i n the  f i e l d of nuclear magnetic resonance ( NMR  ) i n metals'*".  Although much of the e a r l i e r work had been done on powder samples, the size of which was much smaller than the e l e c tromagnetic skin depth, improvements i n the s i g n a l to noise r a t i o of the e l e c t r o n i c equipment made i t possible to investigate NMR the  e f f e c t s on metal single c r y s t a l s .  Some of  early work along t h i s l i n e was pursued by members of  t h i s laboratory on aluminum and t i n at approximately 1.2°K 3 2 y  l i q u i d He  temperature .  I t was f e l t , that a f u r t h e r r e -  duction i n temperature would reveal, p a r t i c u l a r l y i n single c r y s t a l t i n , o s c i l l a t i o n s i n the Knight s h i f t as a function of magnetic f i e l d , much the same sort of o s c i l l a t i o n s , known as de Haas - van Alphen o s c i l l a t i o n s , that are evident 3 i n the e l e c t r o n i c s u s c e p t i b i l i t y . It was with t h i s main a p p l i c a t i o n i n mind, that the 3 He  cryostat to be described i n the subsequent pages was  designed.  However, any other experiment using steady  state methods and r e q u i r i n g low temperatures could eq_ally w e l l be done with i t .  Mostly the same e l e c t r o n i c  equipment,  although somewhat improved, was to be used as i n the e a r l i e r 2 experiments by Jones and Williams , with the notable except i o n of the magnet.  Here, a higher f i e l d magnet was thought  more d e s i r a b l e , since i t would, as well as the lower temperatures, a i d i n i n c r e a s i n g the size of the o s c i l l a t i o n s  2. and f a c i l i t a t e t h e i r detection.  I t would a l s o , of course,  increase the o v e r a l l s i z e of the s i g n a l . an upper l i m i t on the frequency  Unfortunately,  of o s c i l l a t i o n s of the  Pound - Knight - Watkins marginal o s c i l l a t o r to be used was  about 19 Mc./sec. f o r optimum s i g n a l to noise.- opera-  tions.  This frequency corresponds to a magnetic f i e l d  strength f o r t i n of only approximately  12 Kilogauss, which  i s only a small increase i n f i e l d strength over the p r e v i ously used maximum value of 10.1 Kilogauss. The He  cryostat was designed  f o r an uninterrupted run o  of about 3 - 4 hours at approximately  0.4 K.  3 The He  could  also be r e t r a n s f e r r e d a f t e r such a run, and t h i s could be done within a timespan of about 20 minutes.  Two such runs  were then u s u a l l y p o s s i b l e , the l i m i t a t i o n s f o r a t h i r d run being the l i q u i d He  level.  In Chapter 2 the p r i n c i p l e of the cryostat i s explained and i t s features described to give a f a i r l y complete overa l l picture.  Some problems with the magnet and i t s use  are mentioned and a b r i e f d e s c r i p t i o n of the e l e c t r o n i c s i s given.  A t y p i c a l He  run i s described, and an estimate  made of the ultimate temperature obtained with the l i q u i d He  as well as the©length of the run.  The Appendix gives  a more d e t a i l e d d e s c r i p t i o n of the cryostat and f u r t h e r , d e t a i l e d heat leak and pumping speed c a l c u l a t i o n s . The accuracy of these c a l c u l a t i o n s i s also i n v e s t i g a t e d .  3 CHAPTER 2 EXPERIMENTAL METHODS AND APPARATUS  Introduction 3 4 L i q u i d He , an isotope of He , has the advantage of a much higher vapour pressure at low temperatures. For example, at 1.2°K, where the vapour pressure of l i q u i d 4 5 4 He i s 0.63 mm. Hg, that of He i s 19.8 mm. Hg . Hence, LL  while a reasonable  l i m i t to the temperature of l i q u i d He  that can be obtained by pumping on i t s vapour would be about 1.2°K, temperatures of 0.4°K to 0.3°K can u s u a l l y 3 3 be expected when pumping on l i q u i d He . L i q u i d He can thus provide another f a c t o r of four lower temperatures and would be u s e f u l as a coolant i n the range 0.4°K to 0.3°K. 3 3 A d i f f i c u l t y i n using He^ as a coolant i s that He costs about $150 a l i t e r at NTP and hence economy/ demands that only a small amount of the gas be used. Further, care must 3 be taken that the He w i l l c i r c u l a t e i n an i s o l a t e d and 3 l e a k t i g h t part of the system. Since part of the He w i l l v  li.  be immersed i n l i q u i d , sups^rf l u i d He , very stringent conditions are consequently put on the vacuum tightness of t h i s part of the c r y o s t a t . It was thought from the beginning to design as simple a system as possible. Approximately one l i t e r ( NTP ) of 3 He was stored i n cans at low enough pressure that a four-stage mercury d i f f u s i o n pump could a l t e r n a t e l y pump the gas i n t o the condenser pot, or pump on the vapour when 3 the He had condensed. Temperature measurements of the  4 l i q u i d He  were done by vapour pressure thermometry,  using  an o i l manometer f o r the high pressure and a McLeod gauge for  the low pressure measurements.  was used as a check.  A resistance  thermometer  The main part of the apparatus con-  s i s t e d of three storage cans:  two of 5 l i t e r capacity 3 and one of 15 l i t e r capacity i n each of which He was stored at a pressure of 35 mm. Hg. A four-stage mercury d i f f u s i o n pump with a l i q u i d nitrogen trap was used to pump 3 the He from the cans into the condenser pot, and a l t e r 3 nately, to pump on the vapour above the l i q u i d He a f t e r i t had condensed, with the cans used as the backing volume. 3 No r e c i r c u l a t i o n was used as. enough He was a v a i l a b l e to 3 make a reasonably long run.  A f t e r a l l the He  had been  b o i l e d o f f , i t was recondensed and t h i s was continued u n t i l Li.  i n s u f f i c i e n t quantities of l i q u i d He proper c o o l i n g of the. surroundings.  were a v a i l a b l e f o r 1  An o v e r a l l schematic  diagram of the cryostat i s given i n F i g . 3. Cryostat The main features required of the cryostat were 1)  2)  Good thermal i s o l a t i o n of the He^ condenser pot 4 from the l i q u i d He . 3 S u f f i c i e n t l y f a s t pumping speed along the He  3  pumping l i n e to take care of the evaporating He . 3)  Geometry of tubes and cans such that the cryostat would f i t inside a 2.24 i n . magnet pole face gap.  A d e t a i l e d d e s c r i p t i o n of the cryostat i s given i n the  Appendix.  In the following sections only the main  features w i l l be described and. some of the reasons behind  5. .them explained^ The Sample Holder ( Condenser Pot ) As shown i n Fig. the  3, as well as i n Figs. 4- and 5 i n  Appendix, the sample holder was situated at the bottom 3  of  the dewar and provided a place f o r the He  to condense.  It contained the r - f c o i l and sample and a carbon resistance for  temperature measurements.  To ensure that the condensed  3  He to  would flaw around the sample a l u c i t e f i l l e r was used surround and support the sample.  was thermally i s o l a t e d from the He  The sample holder bath by means of a  vacuum jacket. Pumping Lines The sample holder and vacuum jacket were suspended by means of two pumping l i n e s . the  One of them extended through  vacuum jacket into the sample holder, while the other  opened into the vacuum jacket.  To cut down the heat leak  between the top of the vacuum jacket, which was i n contact with the l i q u i d He bath, and the sample holder at 3  l i q u i d He  temperatures, the material used f o r the tubes  was thin-walled s t a i n l e s s s t e e l , which has an extremely low thermal conductivity and good strength.  Room tempera-  ture r a d i a t i o n f u n n e l l i n g into the condenser pot was e l i minated to a degree by placing r a d i a t i o n bends 8 i n . above the  top of the vacuum jacket into each of the pumping l i n e s .  The size of the tubes was chosen as large as possible, the diameter of the tubes increasing towards the high temperature part of the dewar, to ensure s u f f i c i e n t l y f _ s t pumping speeds along the tubes.  Unfortunately, an increase  6 i n the tube diameters increases the heat leak, which i s a l i n e a r function of the c r o s s - s e c t i o n a l area of the tube walls, and a reasonable compromise had to be made.  The  s i z e of the tubes was f u r t h e r l i m i t e d by the size of the l i d s on the vacuum jacket and condenser pot, the l a r g e r ( outer ) l i d being only about one inch i n diameter. Pig. 4- of the Appendix gives a schematic of the above mentioned tubes.  Coaxial Cable A f a i r l y long c o a x i a l cable passed from the dewar cap to the l i d of the vacuum jacket.  The cable was 23 i n .  long and consisted of a }4 i n . OD s t a i n l e s s s t e e l tube which constituted the outer s h i e l d of the cable, and a # 34 copper wire spaced inside the s t a i n l e s s s t e e l tube by means of t e f l o n spacers.  Holes were punched into the tube to  allow the helium to flow into i t .  This was to eliminate  the necessity f o r a s u p e r f l u i d seal and the consequent dangers of a leak, and hence, possible thermal o s c i l l a t i o n s which could have occured otherwise.  The wire was passed  through the two cans by means of platinum to glass seals. No s h i e l d i n g of the wire was considered necessary inside the cans.  At the dewar cap the c o a x i a l cable was passed  through the l i d by means of a Kovar s e a l , the wire terminating i n a housing on top of the cap that contained a BNC connector.  A disadvantage of the coaxial cable was  i t s length, which introduced a d d i t i o n a l and unwanted c a pacitance and inductance into the o s c i l l a t o r c i r c u i t , and  7 consequently resulted i n a loss i n s i g n a l .  However t h i s  was not too serious f o r the material that was  3  studied,  since the szgnal was quite large at l i q u i d He anyway.  temperatures  To reduce the amount of heat leaking into the  sample holder from the l i q u i d He  "bath, the center wire  used here was made of # 34 manganin wire, rather than the copper wire used f o r the rest of the cable.  Manganin has  about the same thermal conductivity as s t a i n l e s s s t e e l at low temperatures, while i t s e l e c t r i c a l conductivity i s good enough to introduce a resistance of l e s s than one ohm f o r a one inch length of wire. The t o t a l amount of heat leaking into the sample holder was c a l c u l a t e d i n the Appendix to be about 110 ergs/sec. In p r a c t i s e , however, i t was found that the true heat leak was c l o s e r to 1500 Temperature  ergs/sec.  Measurement  Since a high degree of accuracy i n measuring the 3 f i n a l temperature of the He  bath, and consequently of the  sample, was not required, the simplest of temperature measurement methods were used. 1)  The methods used were  Vapour pressure measurement of the He^  vapour  above the l i q u i d . 2)  Resistance measurement of a carbon resistance 3 immersed i n the l i q u i d He .  These w i l l now be described. A most r e l i a b l e way of measuring the temperature 3 of the He bath was to measure the vapour pressure above  8  i t . To s i m p l i f y the construction of the apparatus, the tube coming from the manometers, however, was simply 3 joined to the He pumping l i n e at the top, i . e . at the dewqr 3 cap.  Hence the He  vapour pressure that was measured was  that at the top of the pumping l i n e , and allowances had to be made f o r the pressure r i s e down the pumping l i n e due to the pumping action.  Such a c a l c u l a t i o n was made i n  the Appendix. Since the pressure to be measured ranged from about 19 mm. Hg to a few microns of Hg, two gauges had to be used.  One was an o i l manometer used f o r the high pressure  range, and the other a McLeod gauge that had been espec i a l l y designed to measure within the range microns of Hg with reasonable accuracy.  The t o t a l range of t h i s gauge  was from 3.67 mm. Hg to 6.37 X-:10"*^mm. Hg. However, the low pressure reading cannot be taken as too accurate. The 3 vapour pressure values*, of the l i q u i d He bath thus obtained were then used to get the corresponding temperatures by 3  using a vapour pressure - temperature table f o r He that had been experimentally determined by Roberts and Sydo4 r i a k . The pressures given i n t h i s table are the pressures 3 of the He  vapour just above the l i q u i d , while the pres-  sure u s u a l l y read by a manometer are at room temperature. 3 Since the temperature d i f f e r e n c e between the l i q u i d He^ bath and the manometer was considerable, a c o r r e c t i o n would have to be applied, i f the tubing from the manometer reached a l l the way down to the condenser pot, to the a c t u a l 3 manometer pressure above readings, the bath. to obtain This the i s the true thermomolecular equilibrium He vapour v  pressure c o r r e c t i o n , which applies f o r low vapour pressures small connecting tubes, and a large temperature d i f f e r e n c e between the manometer and the bath.  However, since the  manometer tube was a c t u a l l y only attached to the pumping 3 l i n e at the dewar cap where the temperature of the He vapour was close to room temperature,  no thermomolecular  pressure c o r r e c t i o n would be necessary f o r the section of the tube connecting the McLeod gauge to the dewar cap. A c o r r e c t i o n would be needed f o r the tubing inside the dewar reaching down to the condenser pot, but t h i s was a c t u a l l y already included i n the pressure r i s e c a l c u l a t i o n s mentioned previously and given i n the Appendix. The most u s e f u l temperature measuring device was the carbon r e s i s t a n c e , since i t could be used to measure tem3 perature not only at He  temperatures,  but also of the  inside of the dewar while i t was being cooled with l i q u i d nitrogen and l i q u i d He , r e s p e c t i v e l y .  The method con-  s i s t e d simply of measuring the r e s i s t a n c e of a carbon resistance i n s i d e the inner can by means of a Rubicon ' potentiometer, as shown i n F i g . 1.  In order to read the  potentiometer d i r e c t l y i n ohms, the value of the current was set f o r a 100 mv. drop across the standard r e s i s t a n c e . Hence the unknown resistance was obtained by using R. = R u s where R was always picked to be the nearest multiple of s ten above the unknown resistance to be measured and where and E_ were the voltages, r e s p e c t i v e l y , across the unknown ( low temperature ) r e s i s t a n c e and across the standard! resistance.  Hence R. was obtained d i r e c t l y from  10.  &ecac/e. 6 ay  Rt  -WW  fa he  fled  i  i  -  fie  i/£r$infi  JMJ/^C'A  7« Fig. 1  Resistance measurement by Rubicon  potentiometer  pote/rf"i'c*ie^6y  11.  jbhe value of E^..  R^ was obtained at various standard  temperature points such as the l i q u i d nitrogen point, the l i q u i d He^ point at atmospheric pressure ( 4.2°K ) and IL  the  l i q u i d He  3  0  point at 1.2 K.  At l i q u i d He  tempera-  tures, only the lowest value of pressure was c o r r e l a t e d with the resistance measurement.  The resistance used was  a u s e f u l one f o r temperature work below 1°K, since i t had i t s greatest change with respect to temperature i n that range.  Curves of temperature versus resistance of  some Speer carbon resistances were published by Black, Roach, and Wheatley  ( subsequently designated by BRW )  who determined which Speer carbon resistances and grades were most u s e f u l f o r work: below 1°K.  Of those found most  u s e f u l , the 1002 grade, ^ watt, 470 ohms nominal resistance, was used i n t h i s experiment.  Hence i t wasspossible to  check the resistance measurement versus temperature value obtained i n t h i s experiment against the value obtained by BRW.  I t was found that the two agreed within the ob-  tainable accuracy. BRW also published data on the decrease of the r e sistance when the c y l i n d r i c a l axis of the resistance was placed at r i g h t angles to a magnetic f i e l d .  They found  that at 0.3°K and at a f i e l d of 10 Kilogauss the decrease was about 5%»  Since the f i e l d used i n t h i s experiment  was about 12 Kilogauss with a temperature of about 0.35°K the  above c o r r e c t i o n f a c t o r was considered accurate enough  to be u s e f u l i n making the resistance measurement c o r r e c t i o n i n t h i s experiment.  12.  A rough check was also made, to see i f there would be an appreciable Kapitza resistance between the carbon resistance - l i q u i d He  i n t e r f a c e and hence, i f the r e -  sistance readings were, appreciably higher than the actual bath temperature.  Data by Lee and Fairbanks  f o r a Cu-  He^ i n t e r f a c e i n the temperature range 0 . 3 ° K to 2°K were used to make the c a l c u l a t i o n .  I t turned out that f o r the  power input of t h i s experiment the temperature d i f f e r e n c e was completely n e g l i g i b l e .  The r - f C o i l and Sample The sample i n v e s t i g a t e d was a single c r y s t a l of t i n , p  the same that had been studied by Jones and Williams a previous experiment.  in  To s i m p l i f y measurements, i t was  desirable to obtain two signals close together.  This was  done by using two single c r y s t a l s glued together, but whose 0 0 1 axes were oriented at 4 5 ° to each other. c r y s t a l s were of equal s i z e , about  Both  i n . long each.  They  were cut by means of a jeweller saw i n a holder with paraf f i n wax used to support the c r y s t a l .  The wax was used to  eliminate the p o s s i b i l i t y of s t r a i n occuring i n the c r y s t a l while i t was being cut.  A f t e r the two c r y s t a l s were cut  they were etched i n n i t r i c acid and examined f o r s t r a i n boundaries.  About 2 5 turns of # 3 4 copper wire were wrapped  around the sample, making sure that equal numbers of turns were around both c r y s t a l s .  When the sample was attached  to the c o a x i a l cable and the condenser pot l i d , which  13  served as the ground, the approximate p o s i t i o n of the two 001 axes was noted, to allow optimum o r i e n t a t i o n of the magnetic f i e l d with respect to the specimen.  Pump:  3 A mercury d i f f u s i o n pump was used to pump on the He 3  i n the condenser pot and i n the same token to pump the He gas into the condenser pot.  The pump was bought from the  Edwards Company of England ( tradename 2M4 ). The pump consisted :,of four stages and i t s p r i n c i p a l advantage was that i t could pump against a maximum backing pressure of about 35 mm. Hg with l i t t l e reduction i n i t s speed.  Hence  i t was p o s s i b l e to eliminate the use of a mechanical r o tary forepump and the consequent dangers of a leak.  The  speed of the pump was rated at between 30 - 35 l i t e r s / s e c . with a l i q u i d nitrogen trap attached at i t s intake. Magnet The magnet used was purchased from the Magnion company and could be used with either 6>i i n . pole faces and a 1.8 i n . pole face gap up to a f i e l d of about 23 K i l o gauss, or 8YM- i n . pole faces, a 2.24 i n . Pole face gap and a maximum f i e l d of around 18 to 19 Kilogauss.  Since  f i e l d s of around 12 Kilogauss were used i n the experiment, and i t was necessary to have the 2.24 i n . pole face gap, the second: pole faces were used.  Unfortunately, since  the high f i e l d pole faces were on the magnet at the time, these had to be dismounted and the other ones put on.  14.  This .job required three people, p h y s i c a l strength, and a great deal of patience.  A f u r t h e r disadvantage  of having  to change pole faces was that they had to be aligned f o r maximum f i e l d homogeneity.  The adjustment could be made  by means of t i g h t e n i n g the three screws each which held the pole faces, and by adjusting the ^i-shims a f t e r a good homogeneity had been obtained.  The ia-shims were c y l i n d r i -  c a l pieces of metal that could s l i d e i n and out of the center of the magnet pole faces, the adjustment being made by means of a v e r n i e r .  The most s u i t a b l e equipment that  was a v a i l a b l e i n the lab f o r the i n i t i a l alignment, was a 30 Mc/sec. pulse spectrometer designed by W. Hardy''. with a deuterium  Used  sample, the resonance of deuterium was  looked f o r on an o s c i l l o s c o p e .  A pulse apparatus was u s e f u l  f o r t h i s task, since even with very poor homogeneity a s i g n a l can u s u a l l y s t i l l be seen.  A f t e r the s i g n a l was  found the screws were adjusted, with both p-shims f l u s h , u n t i l the s i g n a l indicated maximum f i e l d homogeneity over the 2 cm. long sample. field,  The ju-shims were not changed at t h i s  since the f i e l d at which maximum homogeneity was  desired was around 12 Kilogauss and the ju-shim s e t t i n g would be d i f f e r e n t f o r that f i e l d .  However, the t i g h t -  ness of the screws was not adjusted any f u r t h e r when looking f o r maximum f i e l d homogeneity at other f i e l d s . It was found that i t was u s u a l l y b e t t e r to a l i g n the f i e l d at a higher f i e l d i f no pulse apparatus was a v a i l a b l e do  to t h i s at the f i e l d desired, and then use steady-state equipment f o r the lower f i e l d  alignment.  15.  -For  the 10 to 12 Kilogauss f i e l d alignment a Pound -  Knight - Watkins marginal o s c i l l a t o r steady-state spectrometer designed "by S. Sharma was used, with protons as the sample. l y 7 gauss  A f a i r l y large f i e l d modulation ( approximate) was used i n order to f a c i l i t a t e the seeing of  the s i g n a l , and signal was received by means of an loscope.  Nevertheless, the signal was  oscil-  seen only a f t e r many  laborious and f u t i l e f i e l d sweeps, which were necessary, since no r e l i a b l e current versus f i e l d curves were a v a i lable.  A f t e r seeing the signal ( which was almost  un-  detectably small ) the ja-shims were adjusted u n t i l maximum homogeneity was achieved. 1 part i n 10 .  This homogeneity was close to  It was found that at the lower f i e l d  the ji-shims had to be moved i n towards the center of the magnet to account f o r the decrease i n p u l l i n g force that the magnetic f i e l d exerts on them.  Electronics As shown i n F i g . 2, the e l e c t r o n i c equipment used i n conjunction with the He  cryostat consisted of a stan-  dard Pound - Knight - Watkins marginal o s c i l l a t o r and i t s associated equipment.  The o s c i l l a t o r was i n i t i a l l y b u i l t  by E. P. Jones and subsequently much improved upon by Surrendra Sharma.  The modulation c o i l s , b u i l t by E r i c  Enga, consisted of 100 turns of copper wire each, and when attached i n s e r i e s , could give an undistorted f i e l d of up to 7 gauss.  Pt>Unc{-  Phtte  Defect r Chart tfeccfc&r  Fig.  2 Schematic diagram of steady state spectrometer  17.  Vacuum System As shown i n P i g . 3, the He  3  system was connected to a  vacuum pumping system which was used to evacuate the 3 3 He system before putting He into i t . The pumps used were an o i l d i f f u s i o n pump with a speed of approximately 20 l i t e r / s e c , and a mechanical forepump purchased from the Cenco company ( Hyvac 7 )• The vacuum that was obtained with these pumps on the combined glass and metal system was about 10""^ mm. Hg a f t e r about a day or so of pumping, as measured by a P h i l l i p s gauge that had been c a l i b r a t e d f o r a i r by means of a McLeod gauge up to approximately 6 X 10  mm. H ig.  The e n t i r e system was repeatedly leak  tested, p a r t i c u l a r l y the storage cans and the low temperature tubing inside the dewar, by means of a Veeco He detector.  leak  The low temperature tubing was also leak tested  at l i q u i d nitrogen temperatures. inner l i q u i d He  This was done with the  dewar f i l l e d with He  gas and l i q u i d  nitrogen i n the outer dewar cooling the He  exchange gas.  The leak detector was then attached to pump on the tubes i n s i d e the dewar and the He  count was checked.  A further  test was also made at 1.2°K to check f o r the existence of any s u p e r f l u i d leaks.  The check was made by pumping on  both the vacuum jacket and sample holder and reading the pressure obtained on the P h i l l i p s gauge.  A satisfactory  pressure was considered to be about 10 ^ mm. Hg, a f t e r about h a l f an hour of pumping. Usually, during an actual run, the vacuum pumps were 3 shut o f f form the He system and the pumps were used only  '////// j ///////////////////. ///M* '? e  *i3  ,  '.-  i•  HepompitTf  tint  l/l — , , ^^fgd&ei/>'tfs  rvr  7  va/ve  /y  YL7V /  f/e j**/**j>M£  m ^vacuum  lift  Glass-Metal  C  ..  Jy-rrem  'falfie  eke/- JX 73 ell c/iff. forepump  Qhaf  6IQSS yfy*/e/?t  Jacket i  Hereon defterpot'  00  Pig. 3  Schematic o f He«3 cryostat and associated vacuum system  19 to  pump He  exchange gas out of the vaduum jacket.  I t was  found that i t took almost h a l f an hour to get a pressure reading of 10~^ mm. gauge.  Hg with an a i r c a l i b r a t e d  Phillips  A discussion of the pressure that might a c t u a l l y  be i n the vacuum jacket i s given i n the Appendix under the Heat Leak c a l c u l a t i o n s .  He  3  Run  Before precooling the dewars with l i q u i d nitrogen, the 3 vacuum jacket of the He^ condenser pot was f i l l e d with about IL  2 cm. Hg of He  exchange gas.  I t was found also, that  i t was necessary to have some exchange gas i n s i d e the condenser pot i t s e l f , since l u c i t e i s a poor thermal conductor and hence the cooling of the sample would take a long time. For  a f i r s t run, a f t e r the cans had just been assembled and 4 leak tested, He was used as the exchange gas at about the same room temperature pressure as i n the vacuum jacket. 3  For  any subsequent runs the He  that had remained i n the  tubing was used as the exchange gas. above procedure was two-fold.  The reason f o r the  To check that no s u p e r f l u i d  leaks were present, the pumps were used to pump on the vacuum jacket and sample holder. Consequently, to avoid 3 4 the l o s s of any He exchange gas, He was used instead, and i t was determined whether the pressure i n the sample holder could be pumped low enough i n a reasonable time ( 10""^ mm.  Hg i n/_ an hour ). 1  3 A f t e r each run a l i t t l e He  always remained i n the  condenser pot and tubing above i t .  Since the leak tightness  20.  of the tubing had been determined i n a previous run t h i s , 3  plus some a d d i t i o n a l He , was now used as the exchange gas, and no pumping on the sample holder was attempted. 4 4 A f t e r a l i q u i d He t r a n s f e r , the l i q u i d He was pumped on to a pressure of about 0 . 6 mm. Hg, which corresponds to o 3 T = 1.2 K. The He was then pumped into the condenser 3  pot  by means of the 2M4 and the pressure of the He  checked using the o i l manometer to see i f i t had condensed. This pressure was about 1 9 . 6 mm. Hg.  With the 2M4 s t i l l  pumping into the condenser pot the o i l d i f f u s i o n pump was used to pump out the vacuum jacket. about h a l f an hour.  This usually took  A f t e r a room temperature pressure of  about 1 0 " ^ mm. Hg had ueen reached by the o i l d i f f u s i o n pump on the vacuum jacket, the pumping action of the 2M4 was reversed. To achieve the longest run possible, only one 5 l i t e r can was opened f o r the 2M4 to exhaust the 3  He^ vapour i n t o .  The pumping action was f a i r l y r a p i d and  t h i s can was f i l l e d to about 3 5 mm. Hg i n 5 minutes.-. The can was then closed and the other 5 l i t e r can opened. This one was f i l l e d to about 30 mm. Hg when the pressure build-up became imperceptibly small.  The can was then  closed and the 2M4 was allowed to pump into the 1 5 l i t e r can.  The manometer was shut o f f from the cans and connected  instead to the top of the pumping l i n e .  The McLeod gauge 3  was now used to measure the pressure of the He the  top of the pumping l i n e .  about 6 . 3 7 microns of Hg.  vapour at  The pressure measured was  At t h i s pressure reading the  corrected value of the carbon resistance i n contact with  21.  the He  was measured to be 5.12K.  The He  remained at  t h i s temperature f o r about 4 hours. In the Appendix an estimate i s made of the heat leak into the condenser pot and a value of about 1 1 0 ergs/sec. 3 i s c a l c u l a t e d . This would correspond to a He run of a 3 l i t t l e l e s s than 40 hours, f o r 1 cc. of l i q u i d He . Since the a c t u a l run was only about 4 hours f o r about 1 . 5 cc. of l i q u i d , i t must be assumed that the a c t u a l heat leak was c l o s e r to 1 5 0 0 ergs/sec. 3 the He  The temperature ot  obtained, however, indicated both by the vapour  pressure data and the r e s i s t a n c e measurements, shows that the c a l c u l a t i o n of the pumping speeds was e s s e n t i a l l y correct despite various s i m p l i f y i n g assumptions. the c a l c u l a t i o n s i n v o l v i n g pumping speeds only  Of course apply at  the lowest vapour pressure readings where molecular flow conditions are applicable .  However, pumping speeds c a l -  culated assuming molecular flow conditions are always l e s s than corresponding c a l c u l a t i o n s assuming viscous flow. Hence, the above would correspond to a t h e o r e t i c a l  lower  limit. In the Appendix an estimate was made of the pressure r i s e down the pumping l i n e .  The c o r r e c t i o n obtained was  added onto the vapour pressure reading gotten from the McLeod gauge.  The pressure value thus c a l c u l a t e d gave the 3  corresponding temperature of the l i q u i d He obtained i n t h i s experiment.  that was  I t was f e l t that t h i s correc-  t i o n to the vapdiur pressure data was reasonably r e l i a b l e  22. i n view of the statements made above of the  reliability  of the pumping speed c a l c u l a t i o n s . The value of the temperature  of the l i q u i d He  that  was obtained using the corrected vapour pressure data agrees w e l l within the accuracy of both readings with the resistance measurement data taken from the paper by  BRW.  Prom c a l c u l a t i o n s i n the Appendix t h i s value was approximately 0.35°K, and t h i s temperature f o r about 4- hours.  could be maintained  23  APPENDIX  Cryostat In these sections some of the features of the cryostat which have not been mentioned before or only touched upon w i l l be described i n d e t a i l .  A schematic diagram of  the dewar and i t s associated tubing was i n the previous section.  given i n P i g . 3  Pigs. 4 and 5 i n the following  section each show d e t a i l s of various parts of the jacket. A d e s c r i p t i o n of these parts i s given below except f o r the c o a x i a l cable and sample c o i l , which were described under EXPERIMENTAL METHODS AND  APPARATUS.  Condenser Pot The condenser pot was tube approximately  constructed of a 7/8  i n . copper  2 i n . long, whose walls had been thinned  down to a thickness of about 0.040 i n . i n order to cut down on the amount of metal that had to be cooled.  Copper  was used rather than brass, because the sample holder  was  suspended between the pole faces of an electromagnet, and i t was  e s s e n t i a l that a very non-magnetic material be used,  since a magnetic material would destroy the homogeneity of the magnetic f i e l d .  A f i e l d homogeneity around the sample  of b e t t e r than one part i n 10^ was sary.  considered to be neces-  A copper l i d was hard soldered onto the bottom of  the tube and the sample and carbon resistance were f i t t e d into a l u c i t e c y l i n d e r which sat snugly i n s i d e the copper can.  The purpose of the l u c i t e was mainly to f i l l  out  24  J  //W  bencfs  Solder  Solder  Thin-matted sfa/W/ecr sfeef tubes (type 3 o4 of 3Z8 ) i -Soft folder u  Moo d's Me +al Se /cfer  He ton denser  Ha'J  Fig. 4  So/dtr  Schematic of pumping l i n e s and cans  25  the large a v a i l a b l e space inside the can and to ensure that, even with a small amount of He be around the sample.  l e f t , t h i s would  Hence the hole i n the center of the  l u c i t e was made a b i t l a r g e r than was required f o r the sample, so that part of the l i q u i d He  could run around i t .  The carbon resistance used f o r temperature  measurements  was put d i r e c t l y beside the sample and i n contact with i t . This was to ensure that the temperature  measured by the  resistance was reasonably close to that of the sample. The can was closed o f f at the top by means of a copper l i d which was soldered to the can with Wood's Metal. This was necessary since the can had to be removed from time to time which had to be done without melting the other solder j o i n t s on the l i d .  Four leads coming from the  carbon r e s i s t a n c e were passed through the l i d by means of a f i v e - l e a d platinum to glass s e a l , one lead being extra i n case of one of the others breaking o f f .  Similarly,  the c o a x i a l cable lead was passed through the top using a platinum to glass s e a l . The ground lead from the sample c o i l was soft s o l dered onto the l i d before putting on the can.  Both t h i s  lead and the can i t s e l f were soldered on using a soldering gun, although care had to be taken not to overheat the l i d , as then the soib-solder would melt.  Since Wood's Metal  melts at around 70°C t h i s provided l i t t l e problem; i t was just necessary to stop heating the can and l i d a f t e r the Wood's Metal had started running.  I t was found that the  Wood's Metal solder provided a r e l i a b l e low temperature  26.  #Jf  Cv wire  Seals Condenser  HG?  Carbon teSi's+a ft ce to! + 7 0  JL  ) Lodfc  Fig. 5  //J/er  Schematic of r - f c o i l , sample, carbon r e s i s t a n c e and low temperature" seals ;  I  27 .seal as d i d a l l the other seals mentioned above. Vacuum Jacket Surrounding the sample holder was another copper can, which, when evacuated, thermally i s o l a t e d the sample holder from the l i q u i d He  bath.  Both the can and l i d  were of i d e n t i c a l construction and s i m i l a r l y mounted as the sample holder described above, the only d i f f e r e n c e being an a d d i t i o n a l pumping l i n e s t a r t i n g out of the l i d . of t h i s can, plus the c o a x i a l cable.  The  i n . OD s t a i n -  l e s s s t e e l pumping l i n e was s i l v e r soldered into the l i d . It should be noted that a l l of the s t a i n l e s s s t e e l tubes consisted of type 403 or 328 s t a i n l e s s s t e e l which was picked f o r i t s non-magnetic properties. General Construction of Cryostat 3 A supporting structure had to be b u i l t f o r the. He dewar cap, the various tubing coming out of i t , the valve board, the d i f f u s i o n pumps and the manometers.  The s t r u c -  ture was designed by E. Watchorn and constructed by the Physics Machine Shop.  The structure was b u i l t out of  aluminum angle i r o n and care was taken to make i t as v i b r a t i o n l e s s as p o s s i b l e , since v i b r a t i o n s are a s i g n i f i c a n t source of noise i n the marginal o s c i l l a t o r , and since, a l s o , possibly a s i g n i f i c a n t heat input to the 3 He i s caused by v i b r a t i o n s . The structure was b i g enough so that i t contained two s t a t i o n s , one of which was f o r 3 4 4 He , the other f o r He . The He valve board served both stations.  28. The He  3  system was constructed e n t i r e l y out of metal  while the surrounding l i q u i d He  and l i q u i d nitrogen  dewars were of glass, designed by the Physics Department glass blower, J . Lees.  Heat Leaks and Pumping Speeds-; Introduction To achieve as low a temperature 3  as possible with  the l i q u i d He , i t was necessary to simultaneously optimize the pumping speed of the l i n e above the condenser pot and the heat leak into the condenser pot. 3 The amount of heat leaking into the He condenser pot determines the mass rate of flow ( Q ) of evaporating 3  He .  The temperature  ( pressure ) obtainable by pumping  on the l i q u i d i s r e l a t e d to the mass rate of flow and the combined pumping speed of the pump and tubing between Q  the pump and the condenser pot by Q = S-Pj_« This equation was used to a r r i v e at an estimated value 3 of P-p the vapour pressure of He^ obtainable above the liquid.  Q was calculated from an estimate of the amount  of heat leaking into the sample holder, while S- was calculated from a knowledge of the geometry of the tubes and the temperature  and pressure of the gas being pumped.  Heat Leaks The main sources of heat input from the l i q u i d He bath into the condenser pot were 1) Conduction of heat by helium gas inside the  vacuum jacket. 2)  Heat leak down the s t a i n l e s s s t e e l tube.  3)  Heat leak down the e l e c t r i c a l leads.  4)  Heat leak by r a d i a t i o n .  5)  Heat input from the sample c o i l .  6)  Heat input from the carbon resistance.  Another possible source of heat leak was mechanical 3  v i b r a t i o n s of the l i q u i d He , but since no data could be obtained on this? e f f e c t i t was not estimated.  In the  c a l c u l a t i o n s that follow i t was assumed that the l i q u i d He  5  bath was at 0.3°K and the l i q u i d He  4  bath at 1.2°K.  This was approximately the case i n the actual  experiment.  A large heat input resulted from the conduction of heat by the small amount of helium gas remaining i n the vacuum jacket.  Since the outer mantle of the jacket was  at 1.2°K t h i s was about the only material which had not q yet frozen out.  Using the equation  Q = 0.028 a . o  P m m  (  t h i s heat leak was estimated.  T  - T  2  ) w.cm."  2  ±  The above holds at low  temperatures and pressures f o r approximately p a r a l l e l surfaces ( p__ measured at room temperature  ) f o r helium,  where T-^ = temperature of inside, T = temperature of outside ai = accomodation c o e f f i c i e n t = 2  a  ;  l 2 a  &2 + A /A^( 1 2  )a.  where A , A^ are the areas of the outside and i n s i d e 2  surfaces, r e s p e c t i v e l y , and where the accommodation coeff i c i e n t i n general i s defined by ( T  2  - T  x  ) = a( T  2  -  T-L )  30. where^T-^ i s the temperature  of the gas, T  2  the  temperature  of the surface and T^ an i n t e r mediate temperature  that  the gas molecule has adquired a f t e r bouncing o f f the surface at  T. 2  For our case i t was assumed that 'a' had an upper l i m i t of approximately  and that a-^ = a , since both 2  surfaces were copper of about equal shinyness. p_.__ = 10"^ mm. of Q = 25  Hg, and c a l c u l a t i n g a  ergs/sec. was  Q  Assuming  from above, a value  obtained.  The pressure a c t u a l l y obtained a f t e r % hour of _5 ping was about 10 ' mm.  pum-  Hg, as read by an approximately  a i r c a l i b r a t e d P h i l l i p s gauge.  Garfunkel and W e x l e r ^  estimated that an a i r c a l i b r a t e d P h i l l i p s gauge connected to a jacket containing He  exchange gas at very low pressures  would read a f a c t o r of about 100 higher pressure than  was  a c t u a l l y the case; i . e . f o r a P h i l l i p s gauge reading a pressure a b i t more than 10"  mm.  Hg the pressure of the  -8  4 He Hg.  exchange gas would a c t u a l l y be only about 10  mm.  Hence the heat leak c a l c u l a t e d above may be a b i t too  high by a f a c t o r of 10,  perhaps.  The heat leak down the thin-walled s t a i n l e s s s t e e l 9  pumping tube was c a l c u l a t e d using dQ = A/1 k(T)d_.. This equation can be integrated, assuming knowledge of the f u n c t i o n a l dependence of the thermal c o n d u c t i v i t y of s t e e l with respect to temperature 0.3°K.  i n the range 1.2°K  to  Berman '*' has determined k(T) experimentally i n 1  the range 90°K to 2°K f o r german s i l v e r , constatan, and stainless steel.  Assuming k(T) to vary i n the same manner  31. at the lower temperature as at 2°K and higher, a heat leak i.z  of  Q = A/2 J$  X 10"" T 4  1 , 4 5  d T = 41 ergs/sec.  was c a l c u l a t e d . S i m i l a r calculations as the above were made f o r the e l e c t r i c a l leads going into the condenser pot.  Four  manganin leads of # 40 gauge were used f o r the resistance measurement leads and a lead of # 34 gauge was used f o r the c o a x i a l cable.  Manganin was used, since i t has a  low thermal conductivity, reasonable e l e c t r i c a l conductiv i t y and a small thermoelectric c o e f f i c i e n t .  A l l leads  were connected at top and bottom to platinum i n glass seals.  Since platinum i s as good a thermal conductor at 12  low temperatures as copper  , i t was assumed that the end  points of the manganin wires were at 1.2°K and 0.3°K, r e s p e c t i v e l y , heat leak calculations.were made using t h i s assumption.  Using an average value of k i n the range  1.2°K to 0.3°K of 3 X 10" watts/cm.deg.K f o r manganin , 5  12  a value of 0.1 erg/sec. f o r one # 40 gauge wire was obtained.  To cut down the heat leak, the wires used were  much longer than was necessary.  This was not attempted  with the # 34 wire f o r the coaxial cable although i t could have been done, but with greater d i f f i c u l t y than f o r the above.  The heat leak down t h i s wire was c a l c u l a t e d to be  about 1 e r g / s e c , with the resistance of the wire l e s s than one ohm f o r that length. Heat leaks due to r a d i a t i o n were d i f f i c u l t to e s t i mate.  However, a reasonable upper l i m i t was c a l c u l a t e d  32.  by using the  equation  Q  Q = <rU  - T^  )|  assuming 6 « 1 and making a guess at the actual value of £ . There were two main sources f o r r a d i a t i v e heat leak 1)  Radiation between the walls of the vacuum jacket.  2)  Radiation down the He^  The f i r s t part was the outer wall was  pumping l i n e .  straightforward to c a l c u l a t e , since  always at 1.2°K  0.3°K.  and the inner at  Using the above equation, the heat leak was be about IO" " ergs/sec. f o r an estimated 4  c a l c u l a t e d to  6 = 0 . 0 5 for  shiny copper. To eliminate much of the r a d i a t i o n coming down the pumping l i n e a r a d i a t i o n bend was: put into the tube where i t changed diameter from 3 / 8 i n . OD to 1 i n . OD. was  This bend  about 8 i n . above the l i d f o r the vacuum jacket.  long as the l i q u i d He  l e v e l was  As  above the bend or around  i t , the amount of r a d i a t i o n down the tube was,  at worst,  assuming perfect specular r e f l e c t i o n down the tube, less than the value f o r the vacuum jacket.  has dropped to about 2 cm.  l e v e l of the l i q u i d He r a d i a t i o n bend i t was  However, a f t e r the below the  assumed that the r a d i a t i o n entering  the top of the tube was  at about 30°K.  For t h i s value of  the temperature, the r a d i a t i v e heat leak would be about 3 0 ergs/sec., which i s a considerable increase over the previous value. ly  The above c a l c u l a t i o n s , however, are extreme-  crude and would only give an upper l i m i t to the amount  of r a d i a t i o n readhing the condenser pot. A^ large amount of the heat input to the l i q u i d  He  33. was coming from the power put into the sample c o i l . a high Q c i r c u i t  ( Q ^ 10  For  ) t h i s power input i s given by  the equation  p-f. R where R  1  = 0>L and where L = 3 /ih. , Q = 50,  1  cps., and V = 100 mv. was c a l c u l a t e d .  f = jj- = 19 X  Since the power input v a r i e s as the square  that t h i s l e v e l be kept as low as p o s s i b l e . l e v e l of o s c i l l a t i o n s was  important  Since a low  also most desirable f o r best  signal to noise operations of the marginal  oscillator,  t h i s provided no d i f f i c u l t y . Another source of e l c t r i c a l heat input was the current flowing through the carbon r e s i s t a n c e .  This current  adjusted to be exactly 10 ua. by means of a  was  potentiometer.  Hence t h i s heat input was c a l c u l a t e d to be not more than The heating of the manganin leads can be  considered n e g l i g i b l e , since t h e i r resistance was of  1000  a factor  l e s s than the carbon r e s i s t a n c e .  The t o t a l heat leak, as c a l c u l a t e d above, came to about 130  e r g s / s e c , f o r the case when the r a d i a t i v e heat  leak was at i t s worst.  A value of 110  an acceptable mean value. ter 1500  2,  6  An approximate heat input of 30 ergs/sec.  of the voltage l e v e l across the r - f c o i l , i t was  6 ergs/sec.  10  ergs/sec. would be  However, as mentioned i n Chap-  the experimentally determined heat leak was  about  ergs/sec., which c o n s t i t u t e s a considerable d i s c r e -  pancy between the t h e o r e t i c a l l y c a l c u l a t e d value.  It  i s thought that a possible error i n the t h e o r e t i c a l c a l culations might be the assumed value of the pressure i n  34. the vacuum jacket i n the heat conduction by a gas c a l culations, since the P h i l l i p s gauge reading t h i s pressure was  a c t u a l l y f a r c l o s e r to the pump than to the vacuum  jacket, and part of the tubing between gauge and vacuum jacket consisted of a considerable length of % i n . OD. copper tubing. Pumping Speeds; A general method f o r c a l c u l a t i n g the ultimate pressure obtainable above the l i q u i d He  bath i s to use the equa-  tions® q  and 1/S-  = S-P-L  = 1/S  T  + 1/S_,  where S - = t o t a l pumping speed of the system ( i n 1/sec. ), S^. = room temperature speed of the tubes ( 1/sec. ), S  = e f f e c t i v e room temperature speed of tubes i n s i d e dewar ( 1/sec. ),  and where i t i s assumed that the pressure at the pump mouth i s zero. Garfunkel and W e x l e r ^ have derived the e f f e c t i v e room temperature speed of a s e r i e s of tubes with d i f f e r i n g d i a meters i n a temperature gradient, making the following assumptions 1)  Small P/T gradient.  2)  C y l i n d r i c a l tubes.  3)  Molecular flow conditions apply ( mean f r e e path of molecules » radius of tubes, r ^ ).  4)  End e f f e c t s are n e g l i g i b l e ( length of tube, l » i  r ). ±  They have obtained the equation _ 3ooo  35. and P^ are the temperature and pressure, r e s p e c t i v e l y , at the low temperature end of the tubes.  For the part  of the tubing which was outside the dewar and hence at a Q  reasonably constant temperature the equation S  = 3 0 . 5 r / £ /T/M  1/sec.  3  t  was used, which applies when assumptions 2),3) and 4) are valid.  I t was assumed, when using the above equation, 3  that the He  vapour was cLose to room temperature, i . e .  at a temperature equal to T^.  Hence, knowing S  p  and S^,  and thus S^, and also Q ( i n l i t e r micron / sec. ) i t was possible to c a l c u l a t e a value f o r P^ ( i n microns of Hg ). The values obtained f o r the various pumping speeds were: S  r  = 33.6 l i t e r / s e c ,  = 15.7 l i t e r / s e c .  c a l c u l a t e d to be about 10.1 l i t e r / s e c .  Hence  was  The t o t a l heat  leak c a l c u l a t e d came to about 110 ergs/sec. as c a l c u l a t e d i n the previous section, but as was stated e a r l i e r , the actual heat leak was believed to be c l o s e r to 1500 ergs/sec. Using t h i s value the corresponding evaporation rate of the 3 —5 l i q u i d He was = 4.2 X 10 gm./sec. This value was J  converted to lus^csj. ( l i t e r micron /' sec. ) by using Q = Q  M  X 1/1.5  X 10  5  T/M lusecs.  Hence, Q = 40 lusecs.  was c a l c u l a t e d f o r T = T , which gave P-^ = 3.7 microns p  3  of Hg.  This corresponds to a l i q u i d He  temperature of  about 0.33°K. For the c a l c u l a t i o n of the r i s e i n pressure from the dewar cap to the condenser pot due to the pumping action, the  equation P^ = Q/S  r  was used and i t was assumed, as 3  before, that the temperature of the He  was close to  room temperature once i t had gotten past the dewar cap.  36.  Hence, using the previously c a l c u l a t e d values of Q = 40 lusecs., and S_ = 33.6 l i t e r / s e c , P^, = 1.2 microns of Hg. Hence t h i s pressure r i s e was added to the McLeod gauge reading noted i n Chapter 2. This gave a pressure reading 3 of the He vapour pressure d i r e c t l y above the bath of 7.5 microns of Hg.  It i s believed that the error i n the  pressure drop might be as large as 50%.  Also, the actual  pressure reading i s accurate only to 10%. would give f o r the l i m i t s of the l i q u i d He sure - 1 micron of Hg.  Hence, t h i s 3 vapour pres-  At 0.35°K l i q u i d He^ temperature,  t h i s uncertainty i n the temperature, corresponding to the above uncertainty i n the pressure, i s - 0.005°K.  Hence,  even though the uncertainty i n the vapour pressure deter3 mmation of the He vapour i s rather large, the corresponding 3 uncertainty i n the temperature of the l i q u i d He  i s small  enough to be acceptable. i  _  3 Five l i t e r s of He  were purchased from the Monsanto  company with a quoted t r i t i u m concentration of 8 X 1 0 " . LL  The He  concentration was stated as zero.  Since i t was  f e l t , that t h i s t r i t i u m concentration was too high f o r safe handling of equipment a f t e r i t had come i n contact 3 3 with the He , an attempt was made to p u r i f y the He of the t r i t i u m . This was done by a method devised by Erdman 13  et a l . who used 1% of hydrogen as a c a r r i e r gas and passed 3 4 the He slowly through tubes immersed i n l i q u i d He at 4.2°K. Using t h i s method they achieved a p u r i t y of 6 - 2'  37. parts i n l O ^ from a s t a r t i n g concentration of t r i t i u m of —8 1  1.7  X 10" .  The same equipment as was used by Erdman et  a l . was used i n t h i s experiment with the exception that no attempt was made to measure the concentration of t r i t i u m by means of a Geiger counter. 3 The He  was pumped i n t o a 5 l i t e r can that was con-  structed of a 3 i n . OD brass tube with the ends closed by hard-soldering a brass plate on e i t h e r side. pressure i n the can was approximately  Hence the  one atmosphere.  A  t r i t i u m counter was used to check the concentration of t r i t i u m i n the a i r while dismantling the sample holder to make some changes a f t e r a few runs had been made and no large tjdtium concentration was detected. Hence i t was f e l t that either 3 the He  had been p u r i f i e d or that most of the t r i t i u m had  been pumpeeb back into the cans and what was l e f t was not appreciable enough to r e g i s t e r .  38.  BIBLIOGRAPHY  1.  T.J. Rowland: "Nuclear Magnetic Resonance i n Metals", Pergamon Press ( 1961 ).  2.  E.P. Jones andiD. Llewelyn Williams: 1499 ( 1964 ).  3.  S. Rodriguez:  4.  P.E. Hoare, L.C. Jackson and N. K u r t i , eds.: "Experi-r mental Cryophysics", Butterworths and Co. L t d . , London.  5.  W.C. Black, J r . , W.R. Roach and J.C. Wheatley: S c i . Instr. 35_, 58? ( 1964 ).  6.  D.M.  7.  W.N. Hardy: Phi.D. Thesis, U n i v e r s i t y of B r i t i s h Columb i a ( 1964 ).  8.  S. Dushman: "The S c i e n t i f i c Foundations of Vacuum Technique", J. Wiley, New York ( 1949 ).  9.  G.K. White: "Experimental Techniques i n Low-temperature Physics", Clarendon Press, Oxford ( 1959 ).  Can. J. Phys. 42,  Phys. Letters 4, 306 ( 1963 ).  Lee and H.A.  Fairbank:  Rev. of  Phys. Rev. 116, 1359  ( 1959 ).  10.  M.P. Garfunkel and A. Wexler: 170 ( 1954 ).  Rev. of S c i . I n s t r . 25,  11.  R. Berman:; P h i l . Mag. 42 , 642 ( 1951 ).  12.  R.L. Powell and W.A. Blanpied: "Thermal Conductivity of Metals and A l l o y s at Low Temperature"', National Bureau of Standards, C i r c u l a r 556 ( 1954 ).  13.  K.L. Erdman, L.P. Robertson, D. Axen and J.R. MacDonald: Rev. of S c i . Instr. 34, 1280 ( 1963 ).  

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