UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

³He melting curve thermometer Shinkoda, Ichiro 1983

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A6_7 S55.pdf [ 4.93MB ]
Metadata
JSON: 831-1.0084970.json
JSON-LD: 831-1.0084970-ld.json
RDF/XML (Pretty): 831-1.0084970-rdf.xml
RDF/JSON: 831-1.0084970-rdf.json
Turtle: 831-1.0084970-turtle.txt
N-Triples: 831-1.0084970-rdf-ntriples.txt
Original Record: 831-1.0084970-source.json
Full Text
831-1.0084970-fulltext.txt
Citation
831-1.0084970.ris

Full Text

3  HE MELTING CURVE THERMOMETER by ICHIRO SHINKODA  B.SC,  UNIVERSITY OF BRITISH COLUMBIA,  1981  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in  THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS  We  accept to  this  thesis  the r e q u i r e d  as  conforming  standard  THE UNIVERSITY OF BRITISH COLUMBIA DECEMBER 1983  ©  ICHIRO SHINKODA,  1983  In  presenting  requirements  for  Columbia,  I  available  for  permission  this  in  partial  an a d v a n c e d d e g r e e a t  agree  for  thesis  fulfilment  the U n i v e r s i t y  that  the  Library  shall  reference  and  study.  I  extensive  copying of  this  make  further thesis  her  representatives.  publication  of  allowed without  Department  of  this  thesis  my w r i t t e n  for  is  DECEMBER 3 0 ,  1983  understood  financial  permission.  PHYSICS  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date:  It  Columbia  gain  the  of  British  it  freely  agree for  p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t or  of  that  that  scholarly  or  by  copying  shall  not  his or be  Abstract This  thesis  operation, The  melting  curve  operating  range,  the  melting  He  accuracy  is  for  range the  only  a  choice, 3  6 mK  resolution  curve 0.3%.  satisfies  a convenient of  to  of  the  need  standard 600 mK.  is  of  temperature  strain  gauge i s d e s c r i b e d .  capacitance  b r i d g e w h i c h has a r e s o l u t i o n  of  in  Over most o f  its with  however,  the  a precision  low  Also a r a t i o of  this  thermometer  0.03%,  construction  the  thermometer.  t h e t e m p e r a t u r e measured  thermometer The  the c o n s t r u c t i o n ,  He m e l t i n g c u r v e  thermometer  laboratory  temperature  3  the  and t h e t e s t i n g o f  particular the  decribes  1 ppm i s  transformer described.  i i i  Table of  Contents  Abstract  ..  ii  Table of  Contents  iii  List  of  Tables  v  List  of  Figures  vi  Acknowledgements Chapter  vii  I  T e m p e r a t u r e and T h e r m o m e t r y Below 1.1  1K  1  Introduction  1  1.2 T e m p e r a t u r e 1.3  4  The I n t e r n a t i o n a l  Practical  1.4 T h e r m a l P r o p e r t i e s 1.5  Review o f  Practical  Temperature Scale  a t Low T e m p e r a t u r e T h e r m o m e t e r s Below  8 10  1 K  16  1.5.1  R e s i s t a n c e Thermometry  18  1.5.2  Paramagnetic  21  1.5.3  N u c l e a r Magnetic Thermometry  1.5.4  Vapour P r e s s u r e T h e r m o m e t r y  32  1.5.5  Fixed Point  35  1.5.6  3  He M e l t i n g Curve T h e r m o m e t r y  38  1.5.7  Osmotic P r e s s u r e Thermometry  42  1.5.8  Mossbauer E f f e c t  45  1.5.9  Nuclear O r i e n t a t i o n  Thermometry  Devices  Thermometry Thermometry  1.5.10 Thermal Noise Thermometry  ....25  ...48 54  iv  Chapter 3  II  He M e l t i n g C u r v e 2.1  63  Introduction  63  2 . 2 M a g n e t i c F i e l d Dependence o f 2.3  Impurity  Effects  on t h e M e l t i n g C u r v e  2 . 4 A c c u r a c y and R e s o l u t i o n o f 2.5 S e l f - h e a t i n g  and R . F .  3  75 of  t h e MCT  t h e MCT  82 Cell  84  Sinters  88  3 . 4 P r e s s u r e System  ...91  3.5 Capacitance Bridge 3.6 Choice of Chapter  C o a x i a l Cable f o r  99 Low T e m p e r a t u r e s  111  IV  T h e r m o m e t r y w i t h t h e M e l t i n g C u r v e Thermometer 4.1  79  82  Introduction  3.2 Pressure Transducer 3.3  78  III  He M e l t i n g Curve Thermometer 3.1  70 73  t h e MCT  Sensitivity  2 . 6 T h e r m a l Time Response o f Chapter  t h e M e l t i n g Curve  Introduction  115  4 . 2 O p e r a t i n g t h e MCT 4.3 Comparison of  115  t h e MCT w i t h a Germanium R e s i s t o r  4.4 Conclusion  116 ....122 127  Bibliography  129  A p p e n d i x A - O p e r a t i n g a MCT  133  V  List  I T a b l e of He 3  II III  Melting  of T a b l e s  Curve Parameters  T a b l e of N o i s e C h a r a c t e r i s t i c s Temperatures  of C o a x i a l  T a b l e of Temperatures Thermometers  by  Measured  76 Cable at  Different 113  Different 124  vi  List  1.  of  Figures  A SQUID M a g n e t o m e t e r N o i s e Thermometer  57  2.  3  He M e l t i n g Curve  64  3.  The  85  4.  The P r e s s u r e System f o r  5.  The Flow C r y o s t a t  6.  Circuit  7.  Graph o f  8.  Ratio Transformer  9.  Sensitive  3  He S t r a i n Gauge a MCT  92  Used t o C o o l t h e C h a r c o a l Pump  Diagram of  94  t h e Thermometer P r e s s u r e Gauge  the C a l i b r a t i o n  Curve o f  97  the Thermistor  98  Bridge C i r c u i t  100  Capacitance Bridge  10.  A Three T e r m i n a l C a p a c i t o r  11.  Ground C a p a c i t a n c e s  12.  Equivalent  13.  Schematic of Preamplifier  Circuit  101 ,  in a Ratio Transformer  Bridge  of a R a t i o Tranformer  a High Input  Impedance Low N o i s e  102 104 105 1 08  vi i  ACKNOWLEDGEMENTS  I would in the  l i k e t o acknowledge  the supervision numerous  of t h i s  discussions  project. with  t o thank M.  H u r l i m a n n a n d M.W.  during  running  the  the  National  for  a Postgraduate  the support  B.W.  Statt.  Reynolds  and E n g i n e e r i n g  Scholarship.  W.N.  I have a l s o b e n e f i t e d  of the experiment.  Sciences  of Dr.  Also,  I would  for their Finally  Hardy from like  assistance  I w i s h t o thank  Research Council  o f Canada  1  T e m p e r a t u r e and T h e r m o m e t r y Below 1K  I.  1.1  I n t r o d u c t ion A c c u r a t e measurement  demanding  task;  of  as t h e number o f  low t e m p e r a t u r e s  in d i f f e r e n t  for  methods  standard  experimental the  results  temperature  internationally be  defined  presently  laboratories  accepted p r a c t i c a l the  at  range 3  He  to  1  Scale  .5 K } . low  thesis  the  melting  insensitive 5 kG, i t  essentially  curve  to r f ,  very very  demand of  these  is  to build a  of it  all is  has a f a s t  it  was  has  insensitive thermal  an  s c a l e has y e t  to  mK  to  3  K (the  1979)  the  is  physical  make  accurate  He m e l t i n g  standard  in a  Busch, for  advantage  t o magnetic  response t i m e ,  z e r o p o w e r ( G r e y w a l l and  .5  temperatures.  chosen  the  of  that  temperatures  at  thermometer  fact  In a d d i t i o n ,  s e r v e as a l a b o r a t o r y  First  the  (Metrologia,  f r o m a few mK t o 400 m K ( G r e y w a l l and  reasons.  as  this  by  range  Temperature  thermometry extremely d i f f i c u l t  thermometer  a  intercomparision  temperature  temperature  materials  The p u r p o s e o f  is  increases,  The  complicated  Practical  of  1 K  w h i c h depends on an a c c u r a t e measurement  d e f i n e d o n l y down t o  properties  below  experiments conducted at  grows.  is  for  International  temperatures  Busch,  temperature 1982). a  that  and i t  The  number  fields  1982a).  curve  it as  of is  large  dissipates Secondly,  2  since  the  3  He  thermodynamic minimum curve lab 3  P-T  He  with  melting curve the  2.75  attainable  system.  a  the  immediate p r a c t i c a l The in  the  not by  3  He  same s e n s e  measuring  having  used  present  the  the  dilution  t h e He  the p r e s s u r e ,  temperature  of  of a  difficulties thermometry a t  the  low  has  measure t h e but  and to  one  thermometer  which  given  with  an  e m p h a s i s on  than  the  technical  considers and  the  could  a  occurs  i s of  i s a temperature  no  on  clarifies  be the  aspects  in  the  used  diagram  the  to  review  do of  to  t h e p r e d i c t i o n s and  describe  the  physical meaningful the  other  below  1 K is  characteristics,  of e a c h t h e r m o m e t e r . used  temperature  i s meant by  at temperatures  thermal  is  thermometer.  what  order  It  P-T  briefly  A brief  standard  scales are.  thermodynamic  relies  master  t h e o r i e s which are  summarizes  on  temperature  refrigator,it  describes  temperatures.  thermometers  the  conjunction  lowest  vapour p r e s s u r e  chapter  system  one  in  to t h i s laboratory.  thermometer  to d i r e c t l y  rest  used  in  been p r e v i o u s l y m e a s u r e d u s i n g a p r i m a r y  The  curve,  be  make  below  interest  as  melting  However, s i n c e t h e A - t r a n s i t i o n  m e l t i n g curve  possible  to  standard  the  A l s o , the A - t r a n s i t i o n  in principle  temperature  with  for  3  the p r e s s u r e  point  been c h o s e d  in i t s  l a b o r a t o r y u s i n g a He  corrections.  could  minimum  mK,  a w e l l d e f i n e d minimum  every  compare  necessary  self-calibrating at  point,  t h e r m o m e t e r can apply  has  d i a g r a m , once a v a l u e has  pressure  and  the  melting curve  rather  Chapter the  two  melting  m e a s u r e d p r o p e r t i e s of  3  the m e l t i n g c u r v e . of  The t h i r d  chapter  d e s c r i b e s the c o n s t r u c t i o n  the thermometer, which i s borrowed d i r e c t l y  Busch(1982a). utilize  the  temperatures  The 3  He  final melting  to better  than  chapter curve 0.1  mK  from G r e y w a l l  describes  in detail  thermometer accuracy  a t low  to  how  and to  measure  temperatures.  4  1.2  Temperature There  exists  a  state  of  thermodynamic  w i t h each o t h e r . itself  with  temperature. absolute  the The  second  with a l l  physical  the  system.  of  extrinsic  of  with  heat  temperature  scale  it  (2)  called  defines  the  o f a s y s t e m by  variables  a  the  differentiation of  the  to  a  system  which v a r i e s  temperature.  The  i s an a r b i t r a r y  practical  =  ~  1969)  1  is  internal evaluated  constant.  can be m e a s u r e d by o b s e r v i n g a  that  reproducibly  temperature empirical the  temperature  gas i s u s e d as t h e w o r k i n g s u b s t a n c e  can be shown ( K i t t e l ,  the  system h e l d  e n g i n e can be used t o r e l a t e  —  concerns  quantity,  t h e s y s t e m and E i s  the temperature  reversible  a  the  equilibrium  thermodynamics  thermodynamics  The p a r t i a l  d e f i n e d by s u c h m e a s u r e m e n t s  perfect  of  in thermal  such  (Reif,l965)  entropy  property  monotonically  of  describes  is '  the  Practically,  of  that  3E  is  other  law  scale  T  energy of  postulate  existence  temperature  S  quantity  systems which are  The f i r s t  (D  where  physical  and  scale  scale.  A  thermodymanic scale.  i n a Carnot  If  a  cycle,  5  where T, in  the  and  are  Carnot  temperatures  the  cycle,  thermodynamic and  d e f i n e d by  0  the  and  V  temperatures 0*.  equation  of  are  at  the  s t a t e of  the  points  corresponding the  gas,  (3)  where is  P i s the  the molar  gas.  To  energy  by  pressure, V  gas  constant,  prove  equation  i s the and  n  volume o c c u p i e d  i s the  (2)  number  by  the gas,  of m o l e s  i t i s necessary  of  R  the  to r e s t r i c t  the  (4)  According  to e q u a t i o n ( 2 ) ,  and  the  p e r f e c t gas  the  same v a l u e In  1954,  Measures chose water.  The  arbitrary state  of  ideal  gas,  (5)  at  the  a but  of  10th  of  General  f o r the the  the  non-ideal i t may  s c a l e are  temperature  identical  scale  i f both  have  Weights  and  point.  273.16 K  choice  thermodynamic  temperature  one  value  the  be  gas  Conference  thermodynamic constant,  temperature gas  has  R0  + BP  +  point  of  on  the  equation  of  t e r m s t o t h a t of  the  scale.  i n the  triple  depends d i r e c t l y  correction  written  on  The  form  CP* + ••• >  6  where B, C,...,  are  correction  c a n be c a l c u l a t e d  terms  thermometer,  functions  where  temperature  In  formulation  particle for  systems,  systems  derivation reference that the  in of  to  laws o f  of  equilibrium  thermal  parameter  to sufficient is  the  a c c u r a c y , a gas  used  statistical  to  define  the  of  many  with  physics  thermodynamic  i s postulated  thermodynamics  mechanics  a p p e a r s which each  can  h a s t h e same v a l u e  other.  be  The  entire  accomplished  without  temperature(Kittel,1969).  t o have t h e r o l e can  be  derived  mechanics.  A c o n s t a n t c a n be f o u n d t h a t  mechanical  temperature,  T,  Because  scale.  a parameter  the  temperature.  applicable,  thermodynamic the  of  If  of a temperature, from  relates  statistical  the s t a t i s t i c a l  , w i t h t h e thermodynamic  temperature,  through,  (6)  where  k  is  Boltzmann's  Boltzmann's  Systems used  which  to  definition  Like  c o n s t a n t i s not a fundamental  depends upon t h e c h o i c e  be  constant.  find  of the temperature  c a n be d e s c r i b e d the s t a t i s t i c a l  t h e thermodynamic  which  can  be u s e d  weakly  interacting  gas  constant,  c o n s t a n t , as i t s v a l u e scale.  by s t a t i s t i c a l  mechanics can  mechanical temperature  temperature.  f o r thermometry  the  below  Two  such  and by  systems,  1 K, a r e t h e s y s t e m o f  paramagnetics and the system  of e l e c t r o n s  in  7  a  conductor.  8  1.3  The I n t e r n a t i o n a l A  but  it  gas  Practical  t h e r m o m e t e r measures t h e t h e r m o d y n a m i c  r e q u i r e more c o n v e n i e n t  Bureau I n t e r n a t i o n a l  furnish  a  temperature  as p o s s i b l e  scale  eleven  fixed  the thermodynamic point  gold(1337.58 stardard  thermometer platinum for  K).  with  the region  temperatures  Furthermore,  specified in  C , a  the  in  the  1968,  called  1976).  The s c a l e  is  K)  to  the the  defined  the  range  13.81 K  by  the Planck  temperature  second r a d i a t i o n  places,  and  of  range from  the  freezing point  of  formulae are  The p l a t i n u m  1 0 6 4 . 3 "C,  defined  to  close  and  is  interpolation  the  630.74*C t o  several  IPTS,  and i s as  to  6 3 0 . 7 4 *C,  finally law o f  given  resistance  10% r h o d i u m v e r s u s p l a t i n u m t h e r m o c o u p l e  are  the  t h e IPTS i s  defined  instruments.  The I P T S - 6 8 d e v i a t e s scale  in  The f i x e d p o i n t s  hydrogen(13.81  1 3 3 7 . 5 8 K as t h e r e f e r e n c e for  The a i m o f  end,  w h i c h were a s s i g n e d t h e b e s t v a l u e  temperature.  i s used  created  t h e IPTS o c c u r r e d  Preston,  points,  of  To t h i s  and  scale.  then  IPTS-68(Metrologia,1969,  triple  of  temperature,  technology  scale which i s p r a c t i c a l  revision  temperature  Measures  times.  t o the thermodynamic  The l a t e s t  of  thermometers.  des P o i d s e t  w h i c h has been r e v i s e d s e v e r a l  for  Scale  i s a c o m p l i c a t e d s y s t e m ; t h e demands  science  by  Temperature  the  is  used  higher  radiation  and a v a l u e o f  the  with  0 . 0 1 3 8 8 mK  constant.  from a  the  thermodynamic  summary  of  which  temperature is  given  by  9  Hudson(1980). extend  the  0.5 K t o 1979).  I n an e f f o r t temperature  30. K No  N.B.S. nuclear of  5 7  Co,  Scale  scale  has d e f i n e d a s c a l e  a  Josephson  and M a r s h a k ,  thermometer  1980).  temperatures  Until  below  t h e s c a l e d e f i n e d by  for  of  6 0  Co  to  Provisional  defined(Metrologia,  temperatures 10 mK  to  .5  Bureau  below K  .5  K.  using  a  in a single  thermometer(JNT),  crystal  and  a  CMN  by t h e NO and J N T ( S o u l e n  international  .5 K i s c r e a t e d ,  N.B.S.  "1976  and  been d e f i n e d by t h e  calibrated an  the  was  from  thermometer noise  "  has  des P o i d s e t Measures  susceptibitity  for  Temperature  orientation(NO)  these d e v i a t i o n s  s c a l e b e l o w 30 K,  temperature  International  to correct  this  temperature laboratory  will  scale use  10  1.4 T h e r m a l  Properties  Thermometry well  materials  suffers from  common  At v e r y  n o t o n l y from  technical  to  so t h a t  changes the temperature  t o the K i n e t i c  a  at  of a  due very  to low  the s p e c i f i c  heat  of a l l  very  heat  input  small  of t h e sample.  theory of gases  a lack  problems  a l l materials  low t e m p e r a t u r e s  become v e r y s m a l l ,  drastically identical  .5K  but a l s o  properties  temperatures.  be  below  defined scale,  physical  a t Low T e m p e r a t u r e  By a r g u m e n t s  the conductance,  K, c a n  written as(Kittel,1969)  (7)  where  (C/V)  is  the  average  speed  path.  At  carries  i s determined  sample  the  thermal  temperature. thermal  of the heat  temperatures  The  size.  independent  by  below  speed  second  of  R  6  two b o d i e s  a c c u r a t e and p r e c i s e  temperature  must  the  be c a r e f u l l y  of ,  their  mean  concentration  carriers  is  free of the  or  decreases  thermal often  i n thermal  contact.  measurements on a  Thus,  with  gradients  called  the  essentially  low t e m p e r a t u r e s .  materials  source  volume, v i s t h e  t h e mean f r e e p a t h  a t these  between  thermometer  and 1. i s  impurity  of  resistance,  per u n i t  1 K,  the  conductivity A  heat  carriers,  of the temperature  boundary  resistance,  specific  the  the i s the  Kapitza  To p e r f o r m system,  the  designed with these o b s t a c l e s i n  mind. A firm at  temperatures  install quick to  understanding  a  useful  scan  reduce  thermal  chapter  most  or  more(Kittel).  longer  than  so  3  by  i s equal  no  equation  there  conduction  electrons.  electrons  i s determined  Fermi  by  speed,  v,  is  Here a  and  Ahshcroft  heat  to  is  o f phonons  from is  i s much  heat  the  independent  impurity of  the  not  t h e phonon between  small  there  1976) and  phonon-phonon  proportional  independent  additional  100 K  are  and Mermin,  flow  /T)d,  of  phonons  of phonons  0  The  spacing.  wavelength  the  A t low t e m p e r a t u r e s by  ( 9  t o the s h o r t e s t d i s t a n c e  is relatively  is  used  detailed  i s on t h e o r d e r  o f T,  (7) t h e c o n d u c t i v i t y i s p r o p o r t i o n a l t o  metals,  and  recommended.  In t h e m i l l i k e l v i n s ,  impedance  The s p e c i f i c  is  given  1 K t h e phonon  imperfections  t h e s p e e d of sound  In  temperature  few umklapp c o l l i s i o n s ( is  more  and d i s t h e l a t t i c e  M o r e o v e r , a s t h e number  interactions. T ,  temperature  path,  there  design  system.  for  by Lounasmaa  , i s approximately  Thus below  lattice  boundaries.  to  i s t r a n s p o r t e d by p h o n o n s .  by t h e i m p e r f e c t i o n s .  free  are very  , \  heat  e l e m e n t s t h e Debye  scattered mean  the  i s t h e Debye  For  presented,  9 o f t h e book  insulators,  O  in order  p r o p e r t i e s and some common t e c h n i q u e s  gradients are  dominant wavelength where 0  1 K i s necessary  p r o p e r t i e s of m a t e r i a l s  thermometer i n t o a c r y o g e n i c  of g e n e r a l  information In  below  of the thermal  to  therefore  1,T . 3  transport  by t h e  t h e mean f r e e  p a t h of  concentration.  The  t e m p e r a t u r e and t h e  12  specific  heat  equation  (7)  scattered  by  Fermi  of  electron  gives the  the  The  T,  so  So  f i n a l l y , using  in  a metal  K •  where heat  a  and  number of  o-T  b are  and  (7)  +  b I  <r  is  calculate  constants. electons,  -  2  thermal  annealing process  the  should  is proportional  the  total  heat  to  the to 1/T.  conductance  very  low  t e m p e r a t u r e s a l l the The  Wiedemann-Franz  of  T ,  conductivity,  i s then v a l i d .  Equation  is  (9)  conductivity  highest  is all  sample. be  t  from  the  often  used  more  The to  readily  conductivity.  w i t h the  temperature  conductivity  of  is proportional  t h u s K = aT.  JL = 25nW /K .  the  metal  At  electrical  measured e l e c t r i c a l The  kT  are  Mermin)  the  Lorenz constant  phonons  again  in a metal  l i e within  such e l e c t r o n s  that  j  i £  where  phonons  so  by  (9)  low  whose e n e r g i e s  equation  i s c a r r i e d by  law(Ashcroft  However, t h e  mean f r e e p a t h of  i s given  (8)  «t T.  electrons  surface. that  R  i s p r o p o r t i o n a l ( K i t t e l ) t o T,  the  measured  very  pure  metals To  can  obtain last  the  step  thermal c o n d u c t i v i t y  copper(Lounasmaa). be best  improved  by  r e s u l t s , the  before  mounting  at The  carefully annealing into  the  13  apparatus  because  conductivity apparatus, accurate  copper  not  only  thermal  proportional  the  The  to just  surface  i n thermal  and  separated  between by  the heat  for  dielectrics.  proportional The  thermal  to  the  which  through  between  as p r e d i c t e d ( S u o m i  boundary  a  large  torque.  the  as w o u l d be  been o b s e r v e d  thermal  i n the  if  1/T . 3  to  pressure.  same o r  to  1/T  a  allow  conductance held  resistance  the  to the  applied  The  thermal  similiar materials the  wavelength  f o r metals  and  1/T  which permit  from e q u a t i o n ( 8 ) .  and  temperature  a  to metal  dielectric  be  is have  1968)  i s proportional by  to  dependencies  3  only  expected  bolts  to will  i f the b o l t s are not  I f good m e t a l  the  resistance  et a l ,  together  Thus  as  thermal  metal  A l l these  be  surfaces  surfaces  i s much t h i n n e r t h a n  causes  2  bodies  the  thermal conductance.  to  two  s u r f a c e s i s found  c o n t a c t between m e t a l s  1/T ,  resistance  force,  yield  is proportional  Dirty  the thermal  i n the  i s important  contact i s proportional  proportional  As  also  p o i n t s are deformed u n t i l  s o l i d s made o f t h e  carriers  phonons t o p a s s  these  i s the  a barrier  of.  thermal  i n a s m a l l number o f h i g h s p o t s and  below  t h e r e f o r e so  resistance  Good  but  pressing  irregularities  applied  pressure drops  two  force  s u r f a c e s to touch  area  between  the  is  thermometer  i s b e i n g measured,  conductance to  pressure  force  the  work h a r d e n e d .  is desired.  together(Lounasmaa). t h e two  in  whose t e m p e r a t u r e  thermometry  The  is readily  the  applied  have a  large  tightened  with  c o n t a c t cannot  be made,  14  a large very  t h e r m a l boundary  thin  between  layer the  and E p i b o n d Peterson,  of bonding agent  bodies.  1970).  can be a v o i d e d  resistance  is  nonsuperconductiong  for  this  to solder  solder.  should  be  Furthermore, must  be  taken  the d i f f e r e n t i a l  provide a large  body.  boundary The  has been  resistance  of  well  the  of  the the  account  is  some  metal  can be  not  effort  pieces.  apparatus using  the  together  this  when  resistance  is often  restricted  pieces bolts. used  to  of  t o mean t h e  b e t w e e n l i q u i d h e l i u m and a boundary  resistance  understood(Lounasmaa),  done(Keller,1969).  Kapitza  when  thermal c o n t r a c t i o n  resistance  nature  theoretically  into  minimizing  demountable, all  and  force.  The t e r m K a p i t z a thermal,  plating  the thermal c o n t r a c t i o n  carefully  Sometimes,  gold  varnish,  t h e two p i e c e s  But,  and t h e p i e c e s must be r e a d i l y  7031  a  contact  purpose(Anderson  method f o r  possible  into  using  t o p r o v i d e more t h e r m a l  The most e f f e c t i v e  put  by  A p i e z o n N, G e n e r a l E l e c t r i c  121 have been used  t h e r m a l boundary with a  resistance  A  not  a l t h o u g h much s t u d y  comprehensive  h e l i u m and v a r i o u s  is  solid  review  of  the  s o l i d s was c o m p i l e d by  Harrison(1979). The K a p i t z a condition  of  the  resistance solid.  vacuum  will  greater  than a s i m i l i a r  resistance  of  have  a  is very  A copper Kapitza  sensitive  sample c a r e f u l l y  resistance  untreated piece.  the t r e a t e d  to  an o r d e r Further,  the  surface  annealed of the  in a  magnitude Kapitza  sample can t h e n be d e c r e a s e d by 30% by  15  wiping  the  surface  with  resistivity  , defined  by  resistance  and  approximately 3  He,  or  A  to  K , increases  sinter  of  copper  powder o f 700A d i a m e t e r  about of  per  sinters  the He c e l l 3  surface  area  R T  by an o r d e r  area  Kapitza  between  liquid  i n "He, a n d a m e t a l constant  above 0.7 K.  the Kapitza with  resistance i s  the l i q u i d  Properly  has a s u r f a c e  i n chapter  i s described.  the  approximately  constant  silver.  particles  is  Kapitza  o f m a g n i t u d e between 0.1 and  in contact  or  be g i v e n  of three  is  3  a  6  The  i n thermal contact, i s  3  gram o f s i n t e r . ( H a r r i s o n , will  R  m i x t u r e s of He  method o f d e c r e a s i n g  the surface  made  squared  the  i s approximately  standard  increase  where  ft  The p r o d u c t  0.7 K, and t h e n A  r = R A,  "He, o r d i l u t e  an i n s u l a t o r . 0.1  tissue(Lounasmaa).  t h e same w i t h i n a f a c t o r  liquid  below  is  a  1979).  using  sintered area More  3, when t h e  of a  a  silver meter  information construction  16  1 .5 Review o f P r a c t i c a l  Thermometers  T h e r m o m e t e r s Below j_ K  are  classified  a r e c a p a b l e of measuring primary  thermometers  determine  the  knowledge  of  Secondary against the  the  are  the  a primary  review  standard  temperature.  before  f o r the  particular same  it  may  experiment would be is  that  any  region that  exists  are are  and be  primary  be  interest. calibrated  used  t o measure  third  class  standards,  can  that  the 3  He  tempted  3  He  by  the  i t i s independent  melting curve t o use  they  tedious.  The  only primary  disadvantage  a r e c o m p l i c a t e d and  primary  temperature.  sample,  was once  a l l o t h e r s of of  secondary  superconducting  thermometers. thermometers  t o a c h i e v e a c c u r a t e thermometry, but  very  secondary a  the  Examples  p r e s s u r e , the  under  thermometer  is calibrated,  calibrated. vapour  of  of  although  them  A  measure t h e a b s o l u t e  thermometer  also  the  calibrated  can  be  thermometers.  be  The  previous  of  they  a  secondary  q u a n t i t y m e a s u r e d by  reason  type  point, One  There  called  must  secondary  thermometers fixed  be  of  thermometers  Because the p h y s i c a l  the  the  without  a r t i c l e s ( L o u n a s m a a , Hudson e t a l ) i n c l u d e  thermometer  a  temperature.  t h e r m o m e t e r b e f o r e t h e y can  classification  chosen  in  they  of thermometers which  temperature  temperature  thermometers, which w i l l  the  class  t h e r m o m e t e r s , however, r e q u i r e  thermodynamic  most  thermodynamic  the  thermodynamic  a c c o r d i n g t o the e x t e n t  such  of p r i m a r y  require  in  an  experiments thermometers  substantial  time  per  17  measurement. and  require  major  The  secondary  o n l y a few  disadvantage  possibility  that  seconds with  c o o l e d t o low  have  problem  require  several  convenient The m e r i t s of which and  rest  that  minutes  t o use of  various  per  temperature  secondary  the c a l i b r a t i o n  repeatedly the  thermometers are simple  than  may  per  are  the  chapter  vapour  p r e s s u r e , t h e He  fixed  point  3  Finally,  the  orientation,  are  and  thermometers which  resonance  the  secondary  devoted  they  are  The  to a review  secondary  paramagnetic  thermometers. the  standards covered  pressure, Mossbauer  are d i s c u s s e d .  standards  t o implement  but  m e l t i n g c u r v e , and  secondary  osmotic  The  difficult  is  thermometers.  magnetic  the  and more  thermometers.  are d i s c u s s e d are r e s i s t a n c e , nuclear  is  The  change when t h e d e v i c e i s  measurement,  the p r i m a r y  implement  measurement.  thermometers  temperature. they  to  the  of  the  thermometers  susceptibility, The  3  He  and  "He  superconducting in this  noise,  thermometers  the are  thesis. nuclear primary  18  1.5.1 R e s i s t a n c e Thermometry  The  most common t h e r m o m e t e r s a t c r y o g e n i c t e m p e r a t u r e s  resistance obtain,  thermometers,  and a r e compact  thermometers  because  and e a s y  only a very brief  Phosphorus or a r s e n i c thermometers because over  resistor a  long  i s that  temperature  available The  p e r i o d s of time.  resistors.  expensive  are  insensitive to  than  to  i n c r e a s e s a t lower individual typical  value  radiation  i s 1% c h a n g e  than  o f a germanium as  r e i s i t o r s are  sensors  resistors. or  fields.  is  to better  germanium  thermometer  external  The  are  that  carbon  they  Carbon  much  resistors  p r e s s u r e , but are  magnetoresistance  sensitivity  effect  of the r e s i s t o r ,  so  i s approximately constant or s l i g h t l y  temperatures.  resistor  a r e used as  i t may be u s e d  They have t h e a d v a n t a g e  error  here.  down t o 50 mK.  the temperature  the temperature  The a d v a n t a g e  Commerical  t h e germanium  magnetic  with  i s stable  these  s e n s o r s a t low  i s given  i t has been c a l i b r a t e d ,  easy t o  Although  temperature  calibration  standard.  less  increases  operate.  discussion  most common r e s i s t a n c e  composition  that  their  once  are relatively  doped germanium r e s i s t o r s  w h i c h c a n be u s e d  sensitive  to  a r e t h e most v e r s a t t i l e  temperature,  1 mK  they  are  The  difficult i n the  magnetoresistance  to accurately apparent  predict,  temperature  of  an  but a per  1  T(Lounasmaa). The  r e s i s t o r s most commonly u s e d  f o r t h e r m o m e t r y below  1 K  19  are  Speer(Grade  1001)(Edelstein  Matsushita(ERC-18GJ)(Saito preferred specific The  at  the lower  and S a t o ,  disadvantage  Mess,1965)  1975).  temperatures  h e a t and a r e e a s i e r  one m a j o r  and  The M a t s u s h i t a s  because t h e y have a  to thermally  and  ground  with resistance  than  are  smaller Speers.  thermometers  is  that  they are secondary  t h e r m o m e t e r s and t h u s need t o be  calibrated.  The c a l i b r a t i o n  a typical  few  as  it  is  repeatedly  thermometers thought that  of  hard  and  should  that  In t h i s  calibrated be  can change a  The  task  work.  commerically  trusted  cycled.  is a d i f f i c u l t  and  resistor  accurate requires  checked  calibration a great  laboratory  devices  it  cannot  against  percent  deal  has been  of of  found  be  completely  other  temperature  standards. When m e a s u r i n g t e m p e r a t u r e s taken  to  ensure  that  w i t h the thermal b a t h . thin  waffer  good  thermal  Similiarly, thermally should its  the r e s i s t o r Usually  the  100 mK,  is  care  contact  resistors  the  leads  (Robichaux to  When  remembered t h a t  the  and  resistor  attaching  must  i n good t h e r m a l are  leads  to  Anderson, should to  a  be  to  a  achieve 1969).  carefully  resistor  h e a t i n g a carbon r e s i s t o r  be  contact  ground  and t h e n mounted i n a g o l d p l a t e d h o l d e r  anchored.  be  below  it  can change  calibration. Rf p i c k u p  heating 50 mK.  of If  in the leads  the  resistor;  an e l e c t r i c a l l y  attached this  to  resistors  can be q u i t e  s h i e l d e d room i s n o t  can  substantial available,  cause below low  20  pass into  filters the  ground  cryostat.  excitation by  to  Most  voltages  moving  should  be  resistance  so t h a t t h e r m a l  leads  does  not  resistance.  When s u f f i c i e n t  thermometer  can  be  used  attached  bridges  emf  affect  and  measure  use  spurious  the  precautions to  to a l l leads low emf  measurement  are  taken,  the  temperatures  going a.c.  induced of  the  resistor down  to  power d i s s i p a t e d  in a  3 mK(Lounasmaa) A carbon  useful "rule resistor  Q = T nW/K , 3  is  t o be  3  by  if  of  the the  b e t t e r than  thumb"  i s t h a t the  resistance bridge  should  a c c u r a c y , A T / T , of t h e 10"*(Lounasmaa).  be  less  temperature  than  measured  21  1.5.2  Paramagnetic The  Thermometry  paramagnetic  non-interacting  (10)  *  magnetic  "7"  e  where c i s t h e C u r i e of  a  dilute  thermometry, many the  dipoles  constant.  system  In p r i n c i p l e ,  of paramagnets  into  ( I D  Weiss  *  t-  ©  is  constants,  the  thermometer,  are  used t o determine The  1982)  most  is  a  material  If  but  be  the C u r i e  the  of law  susceptibility  used  for  susceptibility  t h e shape  nearest  absolute  depends  on  o f t h e sample,  and  i t i s instead  u s e d as a  neighbour  good  dipole-dipole is  modified  »  two  constant.  f o r very the  precise  Curie  Weiss  law has  two  are necessary to c a l i b r a t e work s e v e r a l  fixed  points  constants.  single crystal been  The  fixed points  s u i t a b l e paramagnetic  has  by  system  law  Weiss  the  a  i n t o a c c o u n t , e q u a t i o n (10)  fr©  thus only  could  the measured  impurities,  are taken  the C u r i e  where  from  thermometer.  interactions  of  i s described  f a c t o r s such as the m a t e r i a l , contributions  ,  1  but because  secondary  This  susceptibility, %  salt  f o r thermometry(Soulen,  o f c e r i u m magnesium n i t r a t e  extensively  studied(Zimmerman  (CMN). et  al,  22  1980)  and  shown t o obey t h e C u r i e  of  CMN l o s e s t h e r m a l c o n t a c t  crystal 30  mK.  He(Wheatly,  1975,  thermodynamic  powder  of  diameter 3  studies  CMN  The  X  (12)  B  is  in  and a t  J  of  a slurry  8 mK i s  measured s u s c e p t i b i l i t y two  a right  facts  Although done  a  on  single  circular  of  the  in  no  using liquid  careful  powdered crystal  cylinder  have shown a g r e e m e n t  and with  within  powder  CMN, a the  0 . 0 5 mK  is  well  2 mK by  At v e r y  low t e m p e r a t u r e s ,  o f CMN and g r e a s e  40 m i n u t e s ( G r e y w a l l  a few mK t h e d i p o l e - d i p o l e  These  1973) o f  below  -0  a constant.  time constant 3  et a l ,  been  1975) down t o  ~  enviroment  can be r e d u c e d by  1977).  susceptibility  described(Wheatly,  T"  have  fitting  A single  g r e a s e and c o p p e r w i r e s o r  equal to the height  mK.  where  of  Richardson,  comparison(Abesbourne  at  w i t h the  The t h e r m a l b o u n d a r y r e s i s t a n c e  p o w d e r e d CMN i n a s l u r r y 3  law down t o 50 mK.  deviates  limit  the  the  lowest  1982a).  become l a r g e  from  thermal  shows an i n c r e a s e  and B u s c h ,  interactions  the  Curie  temperature  Below  so t h a t Weiss that  as  the  law. can be  measured w i t h a CMN t h e r m o m e t e r . A thermometer smaller  molar  concentration dipole  of  using heat  lanthanum  capacity(Hudson  the paramagnetic  interactions  diluted  ion  is  are less s i g n i f i c a n t ,  et less  CMN(LCMN) al). in the  has  a  Because  the  LCMN,  the  so LCMN can be u s e d  to  23  lower  t e m p e r a t u r e s t h a n CMN.  been  measured(Wheatly,  thermal and  time constant  found  between  The s u s c e p t i b i l i t y  1975)  t o be r o u g h l y c o n s t a n t  by  placing  the  salt  and then measuring  system  a  as  frequency  temperatures ratio  transformer requires  sensitivity  disadvantages small d.c. coils  must In  crystal If  of  field be w e l l  summary, o f CMN  be  mutual  using  system. only  is  3  He  of a s t a t i c a l l y  transformer voltage,  The a d v a n t a g e o f a s q u i d  transformer  i s required shielded  to bias  the s a l t  from ambient magnetic  the s u s c e p t i b i l i t y  the  points  only  thermometer  f o r temperatures  t h e thermometer  is  higher  can e a s i l y  f o r the The  are that a  the  astatic  using  a  single  i n t h e r a n g e 30 mK t o 30 K. 1 K, t h e n  below  1 K.  t h e thermometer A  thermometer  temperatures i s not a  below  that  noise.  thermometer  i s t o be u s e d below  at  replaced  system.  and  a  b u t f o r low  have a l m o s t c o m p l e t e l y  ratio  the  and  1/1000 o f t h e s e n s o r m a t e r i a l  the  at  of  T r a d i t i o n a l l y , the  t h e s q u i d magnetometer thermometer  calibrated  usually  inductance  a ratio  (20-300 Hz) e x c i t a t i o n  as  sensor  of the t e m p e r a t u r e .  calibrated  range,  the  i s a good thermometer  t h e thermometer  must  ( 1 2 ) . The  f o r LCMN i n  i n one o f a p a i r  s q u i d magnetometers  system  same  function  i n d u c t a n c e was m e a s u r e d  audio  the  obey  at 7 minutes f o r temperatures  of the paramagnetic  wound c o i l s  the  to  o f LCMN h a s been m e a s u r e d  susceptibility  measured  low  shown  20 mK a n d 8 mK.  The  mutual  and  o f t h e LCMN h a s  1 K. achieve  In  the  reliable  millikelvin  a resolution  o f a few  24  microkelvin. slurry to  At the very  low mK  range  o f g r e a s e o f H e c a n be u s e d  2 mK.  3  powdered CMN  o r LCMN  t o measure t e m p e r a t u r e s  in a down  25  1.5.3  Nuclear  Magnetic  Nuclear  paramagnetism  temperature  by  paramagnetic magnetic  methods  temperatures order  for  zero  is  similiar The  that  external  they  fields.  B T .  is  less  1%.  than  2  thermometer  situations,thus disadvantage  be  advantage  of  obey  Curie  the  a  finite  the  for electronic using  nuclear  law down t o c a n be  is strictly  external  of the B r i l l o u i n  using  moments  magnetic  of true  f i e l d the  function i s  except  thermometer(NMT) would be  that  the  effective  a c c u r a t e l y c a l c u l a t e d f o r the  the, NMT  of  used  The p r e c e d i n g  In  The n u c l e a r  cannot  that  measure  F o r c o p p e r a t 1 mK and 0.2 T, t h e c o r r e c t i o n  2  a good p r i m a r y  to  The W e i s s c o n s t a n t  to the s e r i e s expansion  the order  used to  i n the m i c r o k e l v i n s .  of  magnetic  be  o f a few m i c r o k e l v i n s .  corrections  constant  can  thermometers.  moments  the  Thermometry  are  is  a  secondary  the nuclear much  magnetic  smaller  Curie  experimental  thermometer.  The  moments i s t h a t t h e  than  the  electronic  p a r a m g n e t i c moments. The  sensor  Weiss c o n s t a n t constraints 1/2,  then  otherwise levels be  as  will  are  the  m a t e r i a l must  there  be o f t h e o r d e r  met.  site  symmetry  will  be  as  0.01  K.  of  several conditions.  of m i c r o K e l v i n  I f the nuclear  due t o t h e e l e c t r i c large  satisfy  the  splitting  only  must  of the n u c l e a r  f i e l d gradients. The s e c o n d  if  spin, I, i s greater nucleus  This  two than  be  cubic  spin  energy  splitting  requirement  The  can  i s that the  26  material  should  magnetic  field  internal  magnetic  the  applied  temperature  The  T,  be  field  which  and  The  by  T  f o r copper good  temperature  not  be  -  same  as  therefore  and  posses and  shorter  temperature  and  i s 1.27  of  are  contact  necessites  have  high  so t h a t  copper  and  an to  spin  lattice a  short  the  lattice.  than  t h e T,  a  <  of  electron  metal,  are  been m e a s u r e d ( H u d s o n e t  Ksec(Anderson  for platinium. between  t h e use  m e t a l must be a v a i l a b l e  ratio  the  the c o n d u c t i o n  c o n s t a n t has  0.0296 Ksec  most common m e t a l s NMT  The  thermal  should  and  would n o t a p p l y  the  natural  of a m e t a l  a r e used  as the  platinium(Richard  and  f o r the  i n very pure  abundance  Redfield,  requirement  sensor  the C u r i e c o n s t a n t w i l l  which  and  The  s u p e r c o n d u c t i n g d u r i n g t h e measurement.  gyromagetic  a  and  lattice  field  local  -^r )  metals  bath  The  interest  two  applied  the  relation  where b i s a c o n s t a n t . several  T,  as  measures the n u c l e a r  the  must  The  i s the  the K o r r i n g a  (13)  element.  A NMT  a r e o r d e r s of m a g n i t u d e  which  t h e r e be  of an  t i m e , T, , between t h e n u c l e a r s p i n  temperature,  1959)  ordered,  t h u s C u r i e ' s law  sensor  insulators.  for  t h e sum  field.  diamagnetic  al)  be  i s not n e c e s s a r i l y  for metals  related  magnetically  would t h e n  magnetic  temperature. relaxation  not  the  sensor  form and  The  nuclei  and be  must  a  large  large.  sensor elements  e t a l , 1973,  of  The of  Dundon e t  27  al,  1973). Although  to  self-calibrate  but  the  al).  The  used  or  t o the  this  impurties  t h a t the  the  nuclear  equilibrium  field  of  145  Until  achievable  of by  be  sensor  material  3%(Hudson  et  measured  by  methods  in  a  small  identical  to  that  t h e r m o m e t e r s and The  i s t h a t the  the  major  difficulty  electronic 1 ppm  can  temperature  field  electronic  or  so t h a t t h e  magnetization be  equal A  to  the  heat  heat  nuclear  capacity,  magetization  time.  capacities  For  state degeneracies  thus  increasing  example, a t  of c o p p e r  by  system at a  A problem with a p p l y i n g a l a r g e magnetic of t h e  are equal  is  field  increases  the  10 mK  the  solution  contribution  to c a l i b r a t e electronic  in  the  thermal nuclear  i n a magnetic  G(Hudson e t a l ) .  the  sensitivity  of  relation,  t o the measured m a g n e t i z a t i o n .  relaxation  electronic  the  in concentrations  lifting spin  the o r d e r can  law.  a l a r g e magnetic  is  and  of  i s to s a t u r a t e the  saturated.  Korringa  sensor  i s m e a s u r e d by  enough t e m p e r a t u r e  fully  i t is possible  techniques.  NMT  contribution  applying  the  Curie's  a static  problem  o n l y of  paramagnetic  using  implementing  low  field  in electronic  nuclear  of  susceptibility  inferred  to  i s usually  resonant  magnetic  thermometer,  thermometer u s i n g the  susceptibility  The applied  i s a secondary  the  accuracy  nonresonant  due  t h e NMT  developement the  static  resonant  of  the  Squid  measurement  methods.  The  was Squid  magnetometer, less  than  magnetometer  the that is  28  usually  used  of  sample  the  resolution  (Bubrman e t a l , 1971) t o measure t h e m a g n e t i z a t i o n in  a  of a t y p i c a l  small  magnetic  system  i s g i v e n by  Sx  AT (14)  At  T  is  of the temperature  usually  static  worse t h a n  method  i s determined  1% (Hudson  over  the  et a l ) .  of the sensor m a t e r i a l  is  by  heating  10"  mm  a magnetic  flux  will  The a d v a n t a g e  during  resonance electronic  very l i t t l e  resonance of  do n o t c o n t r i b u t e  may, however, d i s t o r t  the  energy The  i s due t o n o i s e g e n e r a t e d  eddy  et  a l , 1970)  that  i n copper  w i r e s o f 2.3 x  squid operting  a t 190 MHz and  can  also  The  first  be  measured  method  resonance(NMR) t e c h n i q u e and t h e  impurities,  of  o f one f l u x o n .  methods.  measurement  The  t h e measurement.  a R.F.  fluctuation  wave(CW)  50 uK.  by t h e c a l i b r a t i o n and  i s that  be 1% a t 1 mK  assuming  resonant  magnetic  continuous  larger,  system  nuclear magnetization  different nuclear  rise  diameter  The  to resolve  I t h a s been e s t i m a t e d ( H i r s c h k o f f  temperature 3  thermometer  i n the nonresonant  currents. the  the  The  resonant techniques f o r measuring the  magnetization absorbed  G).  •  =l0mK and B = 10 G, i t i s p o s s i b l e  accuracy  (100  b  =  —  10" *  field  techuique.  the  with  field  is a of a  that  the  frequency a thousand  times  t o t h e measured  the l o c a l  second  is  two  a pulsed  The a d v a n t a g e  magnetization  Lamor  is  by  magnetization.  and b r o a d e n  the l i n e  They width  29  of  the  signal.  The  NMR  technique  by m e a s u r i n g Because  the  standard  magnetization, The  pulse  the nucleus  The  apparatus a  component  at  t h e Lamor  is  is  proportional  perpendicular  j ,  to  i n a time  and  the  induced  are  large,  pulsed the  NMR  tipping  by  the of  tipping  of t h e  because at  small tipping  angles  i n the  steady  0  is  The  the  a  induced  magnetic 1/T  must  adequate.  of  loop  voltage  the  time,  field.  through  be  G). this  relaxation  temperature  temperature  10  A voltage  used  The the  because increases  T h i s reduces t h e FID  nucleus  the  signals  Further,  t e c h n i q u e measures the n u c l e a r m a g n e t i z a t i o n p u l s e , thus  of  nuclear  in  from M t o M c o s ©  are  magnetic  MsinB,  z-axis.  T to T/cos6. low  e  frequency  induced  to  angles  B ,  , i t is desirable  spin-spin  along B  s p i n s from  field,  of t h e o r d e r of a  the  the  here.  et a l )  is  proportional  Small  measure  applying a  x-axis.  the  sample.  c a p a c i t y of t h e  around  the  nuclei  described  x-direction  Msin©  0  is  v o l t a g e , but  to  B and  the m a g n e t i z a t i o n  temperature  induced  both  inhomogeneity  magnetization.  the  2  frequency  determined  voltage  decreasing  thermal  the  the  i s t h e Lamor  B, (Hudson  in  precesses  decays  , where w  Because the  be  by  of t h e  to  a steady  s m a l l as p o s s i b l e ( u s u a l l y  magnetic  which  not  in  of  used  a small angle  i s proportional  as  (FID)  are  will  sample  f o r a time, e  decay  techniques  of  in B .  system  keep B  NMR  i s t i p p e d by  Bcostat)  spin  induction  t h e NMR  magnetizaion  z-direction  to  free  measures the m a g n e t i z a t i o n  the  before before  30  the  temperature  increase  relaxation  time, T  measures  equilibrium  unaffected  by t h e t r a n s i e n t s  temperatures copper  using for  platinium  o f 80  by  The  i s used  eddy c u r r e n t radius  field  B  a  sample,  pulse.  method  which  is  Because  at  shorter Care  T ,  than  the  must be t a k e n when  c a n make C u r i e ' s law  invalid  t h e r m o m e t e r c a n be made s e l f - c a l i b r a t i n g  pulse  return  to find  the  and to  the e l e c t r o n i c  direction  of the f i e l d ,  the  equilibrium.  source of s e l f - h e a t i n g  the  magnetization  observing  heating i n the sensor.  along  NMR  o f 1 msec compared t o  much  impurities  r , volume V, r e s i s t i v i t y  penetration  by t h e  the s p i n - l a t t i c e  pulsed  the  has a  T, by d e s t r o y i n g  to  major  s e c and  the  of  caused  If  specimen.  a "T/2  magnetization  then  i s the best choice.  p u l s e d NMR  direction  short,  temperature  because  measuring  relation  is  measured.  1 K platinium  platinium  The  of  A  a particular  first  v  below  with a T  copper,  ,  is  i n 'the B  time  Then  f o r the Korringa's  temperature. i n t h e thermometer  For a c y l i n d r i c a l  i t s axis  t h e eddy c u r r e n t  i s the  conductor  R, and i n a c h a n g i n g  of  by  magnetic  assuming  full  heating(Lounasmaa)  is  Q  (15)  In  the  temperature  range  of  a  few  mK t o 4 K, t h e p r e c i s i o n  measured w i t h t h e p u l s e d NMR  i s about  0.5%  of the  with  an  31  absolute  accuracy  used(Anufrieu  and  self-calibrated about  2%  depending  Peshor,1972).  using  second  sensor  resonant  sample  is  placed  i n a high,  The  angle  = %  Either  to  B . z  - i% , of t h e sample the r e a l  or imaginary  thermometry. be  field  by  calibration thermometer  h a s an a c c u r a c y  wave  steady  smaller  of  rotating  nuclear  The field  given  B^ = B s i n ^ t  transverse  part  detecting  magnetization  energy  induced  energy  the s p i n system,  into  spins  the  2  Because  CW  absorbed  ~x",  f o r the part  of  the voltage  t h e z and y a x i s by t h e  by B ^ . from  the  radiofrequency  and c a n be m e a s u r e d  method  is  constantly  i f T , i s too long,  t h e s p i n s y s t e m c a n be be h i g h e r  latt ice.  equation.  s y s t e m , and t h e r e a l  t o both  WJ^'B /2  experiment.  at  susceptibility,  of t h e s u s c e p t i b i l i t y ,  the  spin  perpendicular  by Q =  field  p a r t may be m e a s u r e d by CW and used  power a b s o r b e d by t h e  is  (CW).  magnetic  s u s c e p t i b i l i t y , X', c a n be m e a s u r e d by o b s e r v i n g in a coil  NMR  i s d e s c r i b e d by t h e B l o c h  by t h e n u c l e a r  induced  of  much  The i m a g i n a r y  measured  magnetic the  relation  i s continuous  right  can  the NMR  method  a  for  A  the Korringa  B i = Be a n d i s r a d i a t e d w i t h  X  on  3%(Hudson e t a l ) . The  The  of  than  i n an  NMR  injecting  the temperature  the temperature  of  the  32  1.5.3  Vapour P r e s s u r e  The  vapour  thermometer required boiling the  pressure  i n the  to  Thermometry  sense  measure  p o i n t or  that  the  another  latent  Once t h e s e  pressure  can  be  measuring  temperatures  used  versus  values  to f i n d  the  the vapour p r e s s u r e  Durieux,  f o r a monatomic v a p o u r  UU0=  where L  e  constant,  of  the  representing  contain  volume of accuracy the  the of  last  experimental fitting  L=  ln[(2 m)  e  liquid,  v^,  of  data.  are  gas  equation(20)  /h ]  used,  given  p  r  relation  latent  JL  f  R  is  and  ^  s  T  depends on  at T = 0  to the e x p e r i m e n t a l  P-T  the and  f  the  the  molar  constant term  last  and  saturation  can  of  by  entropy,s^,  terms heat  (Dijk  is a correction  vapour  the  When  r a t h e r than  relation  " -y  along  vapour  tabulated values  i s the c h e m i c a l  3  the molar  correction The  5 2  of t h e  thermodynamic  three  K  "  non-ideality integrals  the  the  the  of a s y s t e m .  e  3 2  as a f u n c t i o n of  tabulated  of v a p o r i z a t i o n a t T = 0,  £(T) = InLPVa/R-rJ the  the  pressure-temperature  +  and  gas.  of v a p o u r i z a t i o n and  * f ^T> £ **tT)U^  i s the heat  gas  terms  -  primary is  temperature  to high accuracy  a  thermometer  are  vapour  (20)  not  primary  heat  thermodynamic 1958)  is  t o measure t h e v a p o u r p r e s s u r e  temperature.  temperature  thermometer  two  the  molar  curve.  The  how  accurately  be  obtained  is  determined  data.  Because  from by the  33  magnitude of  the  temperature with to case to  (20) may be u s e d  "He e q u a t i o n 1.5K  with  an  tables  superfluid correction  3  to  He  is  film. for  accuracy  be made.  pressure  size  of  the  sensing  tube  F o r example, of  e t a l , ).  T  up  In t h e  "He for  head  in  as p o s s i b l e . because "He  there  and  the  0.7  is  no  K f o r He 3  sensing  tube  ( G r e y w a l l and B u s c h ,  i s of t h e o r d e r  F o r low  and  1980) must  o f 1 mK  and  can  measured d u r i n g t h e experiment.  The  pressure  the  down i n t o  correction  depends  the c r y o s t a t  a t .5 K f o r a t u b e  on  and c a n be a s  with a diameter  of  and t h e t o p end a t 293 K. The  capacitance pressure  measures t h e vapour p r e s s u r e making  any  correction  thermometer w i t h of  K  correction  h i g h a s a 17 mK c o r r e c t i o n 2mm  to  effect  of the thermomolecular  deceasing  f o r the c a l c u l a t i o n  temperature  1.3  or  with  c o n t r i b u t i o n s makes i t p r e f e r a b l e  preferable  calculated  decrease  o f 0.2 m K ( D u r i e u x  low  pressure  The f i r s t  easily  as  Below  the  thermomolecular  size  (20) may be u s e d  3  temperatures  terms  f o r low t e m p e r t u r e s .  of He, the l a r g e l i q u i d use  be  corrrection  3  to  gauge o f in situ the  H e c a n be u s e d  Gonano  and  and a v o i d s  measured  Adams(l970)  t h e n e c e s s i t y of  pressure.  down t o 0.3 K w i t h  an  Such  a  accuracy  1 %(Lounasmaa). When u s i n g a v a p o u r p r e s s u r e  remember  t h a t t h e vapour  the  system  the  temperature  thermometer  i s in equilibrium  with  i s c o o l e d and t h e v a p o u r p r e s s u r e of  the  liquid.  But,  i t i s important  when  the l i q u i d  c a n be u s e d warming  to  when  to find up,  the  34  temperature  of  the  Furthermore,  liquid.  interface  is  surface.  temperature One been  He  to of  note  found  the the  temperature weight  be  which  below  the  the  of  the temperature the  the  the s u r f a c e  of  vapour-liquid  liquid  below  the  i t ,  the  i s h i g h e r than  the  liquid  "He  vapour  incorrect(Brickledde are everywhere  scale(T62) i s incorrect The  of  of  from  above  surface.  of warning,  to  is different  the temperature  the l i q u i d  at the  temperatures 3  not  Due  temperature  the vapour  the  T58.  corrected  T76  tables(Metrologia,  as  vapour 1979).  t o o low  i t had  p r e s s u r e s c a l e ( T 5 8 ) has et by  been  al, 2%. forced  1960)  giving  Similiarly to agree  p r e s s u r e d v a l u e s a r e g i v e n by  the with the  35  1.5.5  Fixed  Point  A critical device less  once  point  K,  the  a  most  metals  minimun  purposes. device  as  of  An  difficulty  T ,  in  an  1 mK.  The  that  magnetic fixed  as  field.  The  temperatures  field, T ,  H (0), c  in  metals  Not  point  a l l  devices.  hysteresis,  for  and  +0.1  degrades  the  ways.  zero  by  HJJ) « HI*) C l - (.V) ) ' 1  to  calibrate  260-62).  First,  of  temperature  to  magnetic  the  there i s by  the t r a n s i t i o n  is related  can  transition  the performance  a t which  H^fT),  transition  reproducibility  (NBS  transition  point  material  chosen the  mK  d e v i c e i n two the  the  of d i f f e r e n t be  and  thermometry  of t h e same  Furthermore,  field  field  i s that  laboratory  i s only  of  scale  possibility  temperature  magnetic  fixed  very l i t t l e  samples  one  point  depression  c  At  phenomenon.  acceptable  the temperature  requires  ambient  temperature,  temperature  with using superconducting f i x e d  i n a g i v e n sample  ambient  magneic  (21)  are  of d i f f e r e n t  c  superconducting  magnetic  reference  understood.  however, a r e u s e f u l  much as  familiar  a  critical  superconducting device.  the T  the  common  define  temperatures every  as  i s well  supercooling  The  temperature, vary  used  with sharp t r a n s i t i o n s , of  to  be  the s u p e r c o n d u c t i n g phase t r a n s i t i o n  superconductors, Only  can  i t s behaviour  t h a n 0.5  is  Devices  a  occurs  the  critical  field  critical  36  Equation field,  (21) c a n be s o l v e d  using  more e x a c t higher  the f i x e d  relation  precision  The  superconducting.  materials.  be  by s p o t w e l d i n g  maximum  less  than  T  c  fields(  20G)  shield The  due  the  can  c  be  be  gives a used  if  to  through National  not  When  a  i s t o cause  superconductor  i t  with  the  T  is  point  c  due  to  h y s t e r e s i s c a n be T c t o the sensor  a  nucleation  always  greater  magnetic  field.  thermometer magnetic  superconducting to  ensure  field magnetic  that  the t r a n s i t i o n of  than For  to  large  g e n e r a t e d due t o d i f f e r e n t i a l  Bureau  become  Ginzberg-Landau  higher  a c t s as  can of  supercooling  the  When  field  site  transition.  effect  must be t a k e n  are  magnetic  using  t h e maximum a m b i e n t  10 mG(NBS).  employed c a r e  could  depression  materials  fixed  satisfactorily,  and  before  C  The s p o t w e l d e d m a t e r i a l  superconducting  the  T (H)  Practically,  of  T  H, t h e sample must be c o o l e d  calculated  supercooling  depression  is  field,  promotes the s u p e r c o n d u c t i n g The  (21)  than  The BCS t h e o r y  supercool.  the The  can  theory(NBS). diminished  to  below  supercooling  device.  of the ambient  due t o a m a g n e t i c  considerably  lower  a known m a g n e t i c  i s required.  second e f f e c t  supercools  point  than e q u a t i o n  superconductor  and  By a p p l y i n g  t e m p e r a t u r e s w h i c h a r e a few mK  measured  the  f o r T.  the a  perform  should  be  shielding magnetic c o o l i n g of  temperature. Standards  manufactures  a  37  superconducting  fixed  temperatures  below  temperatures  near  respectively,  used  , AuAl,  of c o i l s .  the superconducting  SRM 768's a r e c a l i b r a t e d and  temperature  scale  used  temperature  scale  to within  768 f o r  of  five  have  transiton  a  The m u t u a l  Josephson  secondary  inductance coils  are  transitions. against  junction  a gamma-ray a n i s o t r o p y n o i s e thermometer.  i s claimed to coincide  with the  a few t e n t h s o f a p e r c e n t  The  absolute throughout  range(NBS). The  affected is  SRM  consists  and 5 c o u n t e r w o u n d  thermometer  the  It  the  I n , Be, and W) w h i c h  an a s s e m b l y  the primary c o i l  The  called  0.208 K, 0.161 K, 0.099 K, 0.024 K and 0.015 K  and  to detect  device  0.5 K.  superconductors(Auln  between  point  accuracy  point  by  that  The  a.c.  be  and a m p l i t u d e  used.  the  excitation  imposes  of the e x c i t a t i o n  i s not a s e r i o u s  an e x c i t a t i o n  of  obstacle  current  in  a  It  superconducting voltage  used t o  i n d u c e s eddy  current  and t h e sample h o l d e r s . small  i s seriously  as a l r e a d y d i s c u s s e d .  self-heating  e s t i m a t e d power d i s s i p a t i o n  when  field  measured  inductance of the c o i l s  the s e l f - h e a t i n g  restriction The  the  i n t h e samples  frequency  temperature  magnetic  device.  measure t h e m u t u a l heating  the  by t h e ambient  also affected  fixed  of  The r e q u i r e m e n t  compromise signal the  used,  i n the but t h i s  implementation.  i n t h e SRM 768 i s 8 x 1 0 "  1 1  watts,  o f 29 uA a t a f r e q u e n c y o f 400 Hz i s  38  1.5.6  3  He M e l t i n g C u r v e  The  melting  minimum in  in  curve  Thermometry of  3  the pressure  He  has  mK(Greywall  melting  curve  laboratory  and  the  the melting  individual  could  be  equilibrium melting  scales.  any l i n e a r curve.  slight made.  melting  Once  curve  of  for  comparing o f t h e two  gauge may be c a l i b r a t e d  Even  be i n d e p e n d e n t o f  if  only  c a n be  one  s c a l e of the  equation  applied  point  to  f o r the the  3  He  curve  1  Pm  is  the  melting  ^  ,  pressure,  of the l i q u i d  are  molar volumes of the l i q u i d  the  theoretical  could  one  Clausius-Clapeyron  pressure  change  3  c o r r e c t i o n s t o the pressure The  a  make t h e H e  the pressure  pressure  entropies  If  features  useful  standard.  (23)  where  features:  a t a temperature  The MCT would t h e n  l a b pressure  were t o be u s e d , lab  These  themometer(MCT) a v e r y  points are assigned, against  A transiton  Busch).  temperature  distinct  a t T = .32 K and a d i s c o n t i n o u s  the slope at the s u p e r f l u i l d  2.75  two  be  P (T). m  progress  expressions  derived,  The MCT  and s o l i d ,  then  would  and S  a  s  a r e the molar  and v  and t h e s o l i d  entropies  integration be  4  respectively,  f o r the  then  S  and  h a s been made i n t h e u n d e r s t a n d i n g  and  v  the  volumes  would  themometer.  give Some  of H e ( K e l l e r ) , but 3  s  at melting.  of equation(23) primary  t  39  much s t i l l  remains a mystery.  the  predictions  made  will  be  in chapter  the  presented  Some of  about  the  curve  using another  the m e l t i n g  curve  from m e a s u r e d  equation allows with  (23)(Hudson  t h e MCT  an  The  of  (Greywall  the  To  of  are  date,  i n the  the the  some  melting  thermometer  values  al).  of  alternatives  primary  to give temperature  accuracy  curve  et  t h e o r i e s and  behaviour  2.  melting  the  of  curve  t o measure  or  to d e r i v e  quantities  o n l y method  range  0.3 the  K  i s to d i r e c t l y  calibrate  and  Busch,1982a)  against  other  of a c o n s t a n t  number  3  which  to  1%,  He  in  2  mK  melting primary  thermometers. The atoms  MCT  in  consists  measures the  a  fixed  of  a  volume as  low  volume  standard,  and  required  pressures.  than  the c e l l .  which 3  He  The  be  Because  pressure  of  pressure  must be  prevents capillary.  the  the  temperature pressure  3  He,  The  3  He  cell  the  i s changed.  transducer,  the v e r y  pure  i s c l o s e d by  capillary  at a higher  f u r t h e r in chapter  the  mixture  s y s t e m can measured  pressure  be  curve  as  follows  used t o  in s i t u variation  3  find  because  et  four.  the  the  from b e i n g  A  He  to of  MCT a  the 3  He  temperature al,l952), The  trapped  curve,  temperature. blocked  He  pressure  temperature  the m e l t i n g the  3  with  a plug  b l o c k e d - c a p i l l a r y method(Webb  the m e l t i n g  of  a room t e m p e r a t u r e  f o r compressing  discussed  t r a c e s out  varied.  f o r the  i n a s e c t i o n of  will  then  cell  a system  forms  the  temperature  constant  that  pressure  is the The  capillary  t r a n s m i t t e d up  the  40  Although  some c o m m e r i c a l  the p r e s s u r e ( W e i n s t o c k large  amounts  capacitive and Adam, walls  of  1969).  e t a l , 1962 ) ,  heat.  pressure  The  transducer  capacitor using  1978),  plates.  the  to  of  tend  the lead  vary  i s t o use a  Straty-Adam  type(Straty  the  transducer  ulitilizes  separation the The it the  are  transducer 3  He c e l l  chosen  in  capacitance technique,  The d i a p h r a g m  is  can  be  limited  calibration,  the  choosen  some c a r e .  with  The  pressure  capacitance  General  Radio  corresponding  Co.  with  can Type  pressure  charcoal  3  He  by  be  the  1620-A  pump(Lounasmaa)  by  the  affected capacitor  s e n s i t i v i t y of  a n d Adam,  1969).  standard,  before  absolute  uncertainty f o r the  measured  accuracy in  the  system  must  t o AC/C = 1 0 "  capacitance  resolution  i s compressed  a pressure  As t h e  standard  30 b a r s ( G r e y w a l l a n d B u s c h , The  slightly  w a l l and  i n t h e range of i n t e r e s t ( S t r a t y  must be c a l i b r a t e d  measured  which d e t e c t s o n l y  t o o p i m i t i z e the pressure  c a n be u s e d a s a t h e r m o m e t e r . MCT  a wall or  t h e s e p a r a t i o n o f two w e l l d e f i n e d  guarded ground  capacitance.  dissipate  common method  t h e c a p a c i t a n c e between t h e p l a t e s a n d i s o n l y by  to  made o f B e r y l c o 25 ( C o r r u c c i n i a n d  The change  3-wire  they  most  The c a p a c i t i v e  of a c o n t a i n e r , u s u a l l y  Mountfield,  t r a n s d u c e r s c a n be u s e d t o measure  c a n be a b o u t  of cell be  using a  8  bridge.  The  5 x 10"  bar a t  6  1982a).  to the or  required a  pressures  toepler  using  pump(Johnson  a and  41  Wheatley,1970). kept  below  The i m p u r i t y  600 ppm  ppm(Greywall  level  (Scribner  o f "He i n t h e  He  must  e t a l , 1969) and i s u s u a l l y  be < 20  and B u s c h , 1 9 8 2 a ) .  Many o f t h e a d v a n t a g e s o f t h e MCT have and w i l l  n o t be r e i t e r a t e d , b u t one f u r t h e r  is  that  when b e t t e r  the  t e m p e r a t u r e s measured  t o t h e new  3  been  advantage  measurements o f t h e m e l t i n g  calibration.  using  already  t h e MCT c a n be  listed  o f t h e MCT  c u r v e a r e made, easily  adjusted  42  1.5.7 O s m o t i c The in  P r e s s u r e Thermometry  pressure difference,  "He  and  "He  liquid  P, between a d i l u t e  at  T = 0 connected  mixture  of He 3  by a s u p e r l e a k i s  g i v e n ( L o u n a s m a a ) by  (22)  where  x* i s t h e m o l a r 0  the molar  volume  potential  o f He  liquid. of  3  He  of  c o n c e n t r a t i o n o f He  = n / ( n ^ + n^) , V y ; i s  pure  A^.o i s  3  i n "He and s  3  The f i r s t  term  i n "He, and  the  pressure  of  described  accurately  Fermi  "He.  by t r e a t i n g  once  the  down i n t o  density  of  3  to within  range  in  He  as  a l , 1970)  of pure  the  "He  pressure fountian  i n "He c a n be  Complete  with  analytical  p r e s s u r e o f He  i n "He  3  and c o n c e n t r a t i o n s .  "He  is is  a  primary  known, 3  range.  chemical  quasi-particles  t o e x t r a p o l a t e t h e He  themometer  otherwise  temperature  When t h e t h e r m o m e t e r  is  the scale used  d e v i c e , t h e c o n c e n t r a t i o n , x „ , need o n l y be known  10%(Rosenbaum e t  thermometer  called  3  f o r the osmotic  He  the m i l l i k e l v i n  a transfer  is  p r e s s u r e thermometer  t h e r m o m e t e r c a n be u s e d  as  et  entropy  o f He m o l e c u l e s 3  the  (22) i s t h e o s m o t i c  term  The b e h a v i o u r  t h e whole t e m p e r a t u r e osmotic  i s the molar  second  statistics.(Landau  The  liquid,  of e q u a t i o n  expressions are available over  °He  3  i s useful  a l , 1977).  f o r experiments  The  which  osmotic  study  pressure  the p r o p e r t i e s  43  of  3  He  that  i n "He.  Furthermore,  i t is insensitive T h e r e has  osmotic  been  pressure  been u s e d  mK  mK.  The  mixing  thermometer,  e t a l , 1975)  with a resolution  and  a  away t h e  supplies  temperature  of  3  a  the  He  and  very bulb  tries  to  p u s h He  away,  so  temperature the  attracts  chamber the of  the  so  bulb, the  chamber.  Thus  this  temperature  the  i s equal  to the  pressure balance  infers  between is the  can  an be  order  of  measured  The the  power.  The  pressure  osmotic  the  used  He  pressure bulb  temperature  t o measure  temperature  of  temperature  magnitude  larger.  by  a  using  3  osmotic  between t h e the  the  so t h a t  osmotic  t h e r m o m e t e r m e a s u r e s a low  measuring a temperature higher  power  2  on  "He.  of t h e h e a t e r  thermometer and  of  of  i n the  A heater  until  the  bulb  end  increases  of  the  end.  one  bulb  the chamber d e f i n e s a r e l a t i o n s h i p  of  with  has  range  accuracy  drives  and  A  an  i n the  the h e a t e r  mixing  The  thermometer  but  the  temperature  bulb  chamber.  One  superfuild  that  at  volumes.  have  and  amount  on  two  i n the  thermometers t h a t  other  i s independent  into  the  10 uK  the  small  in  f o r thermometry  pressure  3  He  the  of  advantage  refining  of a c a p i l l a r y  b u l b on  i s above t h e m i x i n g 3  interest  but  the  fields.  characteristics.  thermometer c o n s i s t s  bulb drives  bulb  mK  chamber  heater  intensive  have e n c o u r a g i n g  t o 500  t h e r m o m e t e r has  to l a r g e magnetic no  been d e v e l o p e d ( B l o y e t 50  this  3  He  the the by The  vapour  thermometer. A second  thermometer(Lounasmaa) i n f e r s  the  temperature  by  44  measuring  the  pressure  cylindrical  reservoir  of  given  pure  t h e same t e m p e r a t u r e as t h e  technique cylinder  is and  thus  the  fliud  useful In useful  of  of  levels  in the  the  area  than t h a t  concentration  3  He(x  0  = 0.0004  of  pressure the  the d i l u t e  the  3  of  can  A  thermometer  the osmotic  the  be  to  which  capacitance  "He head i n inferred.  the The  i s made t o be much  He r e s e r v o i r  so t h a t  3  thermometer  pressure  to better with  x  thermometer  i n e x p e r i m e n t s on p r o p e r t i e s  " H e , b u t much more d e v e l o p e m e n t u s e d as a r e l i a b l e  small  0.006)  A  r e g i o n 20 t o 700 mK w i t h an a c c u r a c y  summary  A  "He r e s e r v o i r  He r e m a i n s c o n s t a n t  change.  -  "He c y l i n d e r .  used t o measure t h e h e i g h t  cross-sectional smaller  equation(22).  "He i s c o n n e c t e d by a s u p e r l e a k  a l a r g e chamber c o n t a i n i n g d i l u t e is at  by  of  i s necessary before  g e n e r a l purpose p r i m a r y  the  molar  than  1% as  = 0.0004 of  is  0 . 2 mK.  can be a v e r y dilute it  thermometer.  3  He  can  in be  45  1.5.8  Mossbauer Unlike  Thermometry  the vapour p r e s s r e  thermometer absolute  Effect  does  not  require  temperature scale  The M o s s b a u e r -radiation  effect by  thermometer, any  direct  to i n i t i a l l y  The  emission  lattice  the e f f e c t i v e  themometer  mass i s e s s e n t i a l l y  requires  a  absorb the V - r a d i a t i o n absorber  source  respectively.  the c o l d  absorber  arrangement  is self-calibrating.  thermometer  i s considered.  Mossbauer  al(l969)  system. of  very  little The  Either  energy  Mossbauer  to radiate  the source  and  or  the  i s used because  this  interest.  thermometer Here  only  the  cold-absorber  about source  general  thermometry  t h e p a p e r by K a l i u s e t  i s recommended.  The  cold  Boltzmann measures  absorber  distribution  Mossbauer  absorbing  source  nuclei  I .  sublevels  resonantly  sublevels, m.  hyperfine  system. absorbed  from the ground s t a t e  The h y p e r f i n e  t  hyperfine  is  thermometer  of the n u c l e a r  the temperature of the s p i n  appropriate  state  in  the  or a b s o r p t i o n  infinite.  For d e t a i l s  thermometry  of  the  an a b s o r b e r  c a n be a t t h e t e m p e r a t u r e o f  Usually  and  and  effect  i n which the n u c l e i i s  embedded a b s o r b s t h e momentum, b u t a b s o r b s since  knowledge  calibrate  i s the r e c o i l l e s s  the n u c l e i .  the Mossbauer  and  interaction  so t h a t m  t  in  1^,  and  I  splits  t  the  s t a t e s and  thus  The and  Tf-ray f r o m excites  t o the f i r s t  the t r a n s i t i o n s I-  measures  I  between  respectively.  the  excited  t h e 1^ and occur  an  For  e  into two thin  46  absorbers  the r e l a t i v e  transitions  i n t h e Mossbauer  spectrum  is  g i v e n by  (24)  r \ U j - * ^ -  where  oL i s a c o n s t a n t  square  of  the  coefficient, in  a  sublevel  lattice and  approximation.  C  f o r a given  V " ^ *  U  experiment, C(m^m ) t  normalized  i s the p r o b a b i l i t y  m^  calculated  spin p a r t i c l e s  i s doped w i t h  the d i r e c t  C  appropriately  a n d /^m^)  non-interacting  <V "V  only  assuming  The p r o b a b i l i t y  where u is  n  the t o t a l  the  local  equation sublevels case  magnetic  There  (24), but i fthe nuclear  +  and I  e  have  taking the r a t i o  transitions  one g e t s ,  = 1/2*.  As t h e h o s t  this  nucleus i s a good  n  -7  i s the nuclear  i n t h e sample, a n d B i s in  s t a t e s have a s m a l l number  of  As an example, c o n s i d e r t h e  Then r e c a l l i n g  the property  g-factor, N  i s one unknown c o n s t a n t  t h e n ci need n o t be known.  I,j = 3 / 2  are  . }  magnetron, g  field.  nuclei  effect  - nuclei,  number o f M o s s b a u e r n u c l e i  coeffiecients then  *x  i s the nuclear  field.  existing  i s c a l c u l a t e d a s u s u a l by B/kll  *  the  1% o f t h e M o s s b a u e r  interactions are nuclei  (25)  Clebsch-Gordon  of the system  i n a magnetic  i s the  the Clebsch-Gordan  t h a t C(m^,m ) = C(-m^,-m ) and  of the i n t e n s i t i e s  t  of  fc  the  two  possible  47  (  2  6  )  "  R  where  = -/<,gjiB.  A£ c a n  be  thermometer  /r-%)  R(-V«^-«)  By m e a s u r i n g t h e r e s o n a n c e l i n e  independently  determined.  of  sensory  4 mK a n d 14 mK  and  1 9 7  Au  have  e l e m e n t s made f r o m t h e s e a r e e f f e c t i v e  thermometers  from  Fe  of the  of  disadvantage  events  in  of t h i s  usefulness  of at  implementation  temperature  the  sensor  the  lower  of  is  a  1 9 7  Au(Lounasmaa).  determined  Mossbauer  the absorption  p r o b l e m a n d t h e added limits  the  is  thermometer  requires  self-heating  a n d 7 mK t o 50 mK w i t h  thermometer  f o r accurate  thermometer  severely  Fe  with  5 7  respectively,  5 7  thermometers  The a c c u r a c y  needed  isotropes  so t h a t  2 mK t o 20 mK w i t h  number  4.6- i s m e a s u r e d t h e  Once  i s calibrated.  The most common M o s s b a u e r A£/k  separation,  the  by  spectrum. large  feature  t h e use of t h i s  of  very  factor  The i s a very  long  thermometer.  major time  a n d ,as s u c h ,  temperatures. thermometer  The  The M o s s b a u e r  becomes t h e l i m i t i n g  Mossbauer  total  counting  measurement. of t-rays  the  the  i n the  technical difficult  measuring  times  48  1.5.9  Nuclear Orientation If  the  Thermometry  polarization  of  measured, then the a b s o l u t e Boltzman degree  factor.  of o r d e r i n g  There  a  are several  i n the nuclear  used  temperatures  i s t h e measurement o f  emission  nuclei  for absolute  oriented  of K r a y s _  understood(Krane  from et  spins,  but  the  thermometry(Marshak, the  oriented  Y ray  1973),  can via  field.  thus  the the  method  1982)  at  The  low from  anisotropic  nuclei  the n u c l e a r  primary  be  only  anisotropy  _  radioactive  t h e r m o m e t e r ( N O T ) c a n be u s e d a s a et  system  methods f o r m e a s u r i n g  i n a magnetic  al,  spin  t e m p e r a t u r e c a n be d e d u c e d  extensively  decaying  nuclear  is  well  orientation  thermometer(Berglund  a l , 1972) . Oriented  normalized  nuclear  spin  systems  w i t h a x i a l symmetry have a  s p a t i a l d i s t r i b u t i o n , W(0),  of emi t t e d  "V - r a y s  given  by  (27)  u)tri  where  &  emitted describes the  is and the  coefficients,  *  R  the  angle  the  orientation  initial  temperature  reorientation  -  K  ^ P  between  k  the  the P  the  (cos©) a r e  The  R  The k  the  -rays are  quantities  of the n u c l e i  dependence o f W(0) .  and  d i r e c t i o n the  axis.  orientation  parameters,  t u ^ ) .  B (T) K  and c o n t a i n s a l l  Uk. a r e a n g u l a r momentum  are  angular  Legendre  correlation  polynomials.  49  Only  even  terms  directional the  state  goes  enter  distribution  i n t h e summation of the r a d i a t i o n  of p o l a r i z a t i o n  from  zero  multipolarity oriented  to  the  lesser  of  For  t o know  that  only the  i s of i n t e r e s t  and n o t  The summation  over  2L  of the emitted r e d i a t i o n  nucleus.  sufficient  of the Y-rays.  of k because  o r 21, where L i s t h e  and I i s t h e s p i n  the  purposes  of  this  the  sum  be  calculated  can  k  of the  thesis  i t  is  t o the  necessary accuracy. Consideration variation occurs  of W(T,©)  in radiation  at  &  temperature directions  = and  decay  equation  in  where  unique  P (cos©) nuclei  at  these  i s zero,  k  this  i n NOT a r e C o  (25), i s the only  to  5  from  for Co 6 0  50  Mn,  between  whereas  i s not t r u e .  and  6 0  processes are well  i n d e x m i s summed  temperature  points,  is  at  The two  for  which  u n d e r s t o o d and t h e c o e f f i c i e n t s i n F o r C o , W(T,0) i s g i v e n by 6 0  (oj(j.t^= u'los" + o . o i r f c f . m'ifCm) -  equation  the  W  where ^ ( m ) , t h e p o p u l a t i o n  has  changes  temperature  the r e l a t i o n  (27) c a n be c a l c u l a t e d .  (28)  equal  with  the largest  0" o r 1 8 0 ° . F u r t h e r m o r e ,  most commonly u s e d the  flux  shows t h a t  of the m  th  temperature  I t o - I , where a n d 3 f o r "Mn. 5  0.0  sublevel dependent  I  is  the  Similiarly,  3 H f e i «  as  V  given  /  W  '  by  quantity.  The  nuclear  spin  f o r M n one 5a  50  (29)  The  <uoU,0}=  degree  \  of a l i g n m e n t  = u g*B, the h y p e r f i n e radioactive  a host m a t e r i a l  which  be o f t h e o r d e r o f domains 0.1  The  Some c a r e must  NOT  is  because  be  to a l i g n a  t o the r a t i o  are oriented  i s magnetic.  10 - 30 T  is sufficient  1973),  nuclei  in  internal  iron  group  by a p p l y i n g  a l l the  that  splitting  of  temperature  is  limited  over which because  a p p r o x i m a t e l y AE/k. 55  t h e NOT  it The  is  and  the NMR,  single range  crystal 32 mK  therefore The  of Ho t o 1.2  sensitive  K,  been but AE  t h a t W(T,0) a p p l i e s  used  a t 30 mK.  configurations  Co  E  in iron The  range  a  thermometer  for  temperature 6 0  Recently 1982)  has not y e t been  a c c u r a c y o f t h e NOT  to a point  6 0  nuclei,  a secondary  can  Measured  1967).  only  used(Marshak,  i t must be c o n s i d e r e d  theoretical  experimental  has  for  can be u s e d a s  Mn, are almost completely a l i g n e d  a  and  Shirley,  most commonly  et a l ,  i n the host m a t e r i a l  mK,  i 0.003 mK(Templeton  of  domains.  - 0.01  = 7.945  The  applied  primary thermometer(Krane  = 9.11  can  field  the  for  i s AE/k  into  field  a magnetic  experiments.  AE/k  AE  metals.  by NMR  *Mn i n i r o n  them  local  be m e a s u r e d w i t h h i g h p r e c e s i o n 5  )  M  AE/kT, where  by d i f f u s i n g  taken to ensure  practical  the h y p e r f i n e  The  the  i n the host are a l i g n e d  - 1 T.  field  is related  £ r * + /  splitting.  n  The  - 0.0 0 3 ^  t O-^e&l  Co 1 6 6  and  Ho in  to to cover measured  by  thermometer. the  fact  source, although i n p r a c t i c e  most  approximate  is limited  the  by  condition  quite  51  well.  Also,  detectors are  W(T,0)  have a f i n i t e  cylindrical,  attenuation The  the  when  even  in a thin  foil  in To be  the  high  &n,  avoided the  temperature  the e f f e c t i v e  the  self-heats  at an  absorption  cryostat 1 u C i of  6 0  5ft  with  the  The  field  taken  at a site,  limit  long  this  measured  where n and n  b  implies  times  Mn  e  temperatures order  of  less  i s i g n o r e d ( t h i s i s very  is  not  too  bulky),  Co  i s 630 pW a s o p p o s e d  count. has t o  long  counting  30 m i n u t e s  s h o u l d be  practice(Lounasmaa).  than  magnitude  is  low, t h e f l u x  i s more a c c u r a t e  less  The  count  i s the background  than  in  times  i s t h e number o f p u l s e s  relatively  longer  thermometer  counting  of the temperature.  a  a s i t becomes t o o t e d i o u s  thermometer  Y ray  and  Counting  two,  source  m a t e r i a l must a l s o be  in  e  small,  by an  temperature.  keep t h e s e l f - h e a t i n g o f t h e thermometer kept  only  accurately contributes to  measurements  1  b  detectors  1953).  the  o f NOT i s t h e  = (n + n W(T,0)) ,  2  as the  specimen.  error,  intervals.  -  calculating  whereas a l l  i smodified  measured  of the host  f o r accurate  statistical  angle  the  major d i s a d v a n t a g e  /  W(T,0)  aligning  the s o l i d  effects  account  l  of  in  into  = n  of  As l o n g  K  uncertainty  necessary  area.  detector,  f a c t o r ,Q , i n t h e t h e sum(Rose,  demagnetization  An  form  and measuring  The  to a point  surface  t e c h n i c a l problem  detector the  applies  than  20 mK than small  the  because  the C o . 6 0  as  Of  long  6 0  Co i t  I f the as the  t h e r a d i o a c t i v e s e l f - h e a t i n g of t o 30 pW f o r  1 uCi of  5 a  Mn.  52  The  5fl  Mn  self-heats  electron 110  capture,  than  whereas  6 0  Co  6 0  Co  because  decays  i t decays  through  through  emission  of  Kev e l e c t r o n s . The  most  iron(Sites and  cobalt  have  necessary.  5  "Mn  6 0  Co  hyperfine strongly  is  known  splitting  sensitivity  in  w h i c h have been  ppm  copper(Pratt  sensitive  The to time  a  30  of  a  40  be  Fe  the  single  Kondo  give  field  to less  a l , 1969),  5ft  minutes  per  A a  a t 2 mK,  hyperfine  field,  then t h e  the  maximum  than  Mn doped  the  and a v e r y  the  1  systems ppm  to less  B o t h themometers have been  6 0  is  i t has  Two p o s s i b l e  a r e "Mn doped  range of  Co i s  temperature,  If  to  of i n t e r e s t .  i n t h e range  6 0  crystals.  that  of the applied  and  nickel  a t 2 mK.  field.  5  is  crystal(Thorp  magnetic  is  Mn  If  of the temperature  in  than 1  found  to  1-20 mK. Co  o r *Mn NOTs i s f r o m a few mK s  mK w i t h an a c c u r a c y o f  few  Co  adjusted  region  et  temperature or  in  below  function  i n z i n c ( M a r s h , 1970).  be most  Mn  independent  studied  5 9  5ft  although  e t a l , 1967).  T, o f 7 m i n u t e s  can  the  1972),  and  i n t o hep c o b a l t  upon t h e a p p l i e d as  Co  time of t h e o r d e r of 1 minute  materials, is  5 4  6 0  polarizing  not d i f f u s e  i n Fe h a s a  dependent  hyperfine  pure  will  field  et a l ,  external  relaxation  Kondo  for  used(Cameron  reason f o r p r e f e r r i n g  In  field  material  throughout a hep  t h e n no  spin-lattice whereas  host  been  uniformly  a l , 1970),  further  common  e t a l , 1971, J o h n s o n  distributed et  less  1% when u s i n g  point(Sites  et  a counting  a l ,  1971).  53  Temperatures  below  Kondo m a t e r i a l  as  the  applied  magnetic  alignment  of  several  the  Tesla  1 or  host  be  microKelvin  range(Ono  the  become  nuclei  measured,  it  temperature  need not  et  be  and  measured w i t h a NOT carefully  "brute  to  extend  filds  the  al,l980)°, where When  be  remembered  the  same as  the  NOT  that  of  the down  lattice.  of the  between  temperatures the  of  order to  a the.  technique"  interactions  lower  using  controlling  force  with applied  important.  must  be  The  spin  used  can  film  field.  nuclear  can  2 mK  nuclear  are spin  54  1.5.10  Thermal  Noise  Nyquist(1928) voltage  formulated  generated  conductive  Thermometry a  relation  across a resistor  electrons  i n the r e s i s t o r  between  the  and t h e Brownian using  the  t h e r m o d y n a m i c s a n d t h e law o f e q u i p a r t i t i o n  random  motion of  second  of energy.  law  of  The most  common form o f t h e r e l a t i o n i s  (30)  <V  where  <v (t)>  a n  W>=  is  2  the  fluctucations  squared,  the  i s over  integral  i s measured.  time  mechanical  relation  includes  i  average  of  R i s the r e s i s t a n c e the frequency  Nyquist generalized  quantum  1951)  [ YR^Tdw  effects,  range  the  the  thermal voltage  of the  element,  over which  fluctuations  the voltage to  include  b u t t h e most g e n e r a l t h e r m a l n o i s e  zero-point  fluctuations(Callen  and  Welton,  and i s a s f o l l o w s  (31)  <V,%>=  Furthermore, frequency equation  (%hvR(v)L'/a  the resistance  dependent (31)  to  e  L/ T fc  , ,]  1*  »  R i n (30) h a s been g e n e r a l i z e d  resistance.  reduces  «  In  Nyquist's  the  limit  original  hv/kT equation.  e x p e r i m e n t a l l y measured t h e r m a l n o i s e has a g r e e d v e r y w e l l the  and  theoretical  predictions,  thus  in principle  to a —» 0, The with  thermal noise  55  t h e r m o m t r y c a n be u s e d 1928,  S o u l e n and M a r s h a k , The  of  to define  (31)  difference  the temperature  scale(Johnson,  1980).  i n temperature  f o u n d by  using  (30)  instead  i s g i v e n by  (32)  It  i s calculated  by e x p a n d i n g  powers o f hv/kT, result  using  integrating  a  high  frequency  i s less  measured  is  can  the s e r i e s ,  frequency  then e v a l u a t i n g  the  and  cutoff  a t v- .  then a c c u r a c i e s  be a c h i e v e d by u s i n g  (30)  power  instead  basic  components  a t the temperature  meter.  The  10 - 20 K.  The  of of  a  of  of  is  must  the  temperature  being  of b e t t e r  the  more  at  a of  noise  than  1%  complicated  thermometer(NT) are a an  amplifier,  by  from few the  be w e l l  noise  i s added  so t h a t  the mK.  NT  a  known and  large  correction  Other  difficulties  i f the  in  the frquency response of 1/f  noise  is  t o the n o i s e  of the a m p l i f i e r  the  The  amplifiers  output  i s that  a  signal  temperature.  linearly  a very  and  adds t o a  b e s t room t e m p e r a t u r e  interest,  subtracted  implementation amplifier  of  interest,  noise temperature  from t h e r e s i s t o r  resistor  the  amount o f n o i s e an a m p l i f i e r  temperature  be  cutoff  (31).  be d e s c r i b e d q u a n t i t a t i v e l y  noise  i f the  t  1 mK,  more  and  in  than  resistor  than  i n e q u a t i o n (31)  MHz  The  must  integrand  12.5  relation  can  the  spectrum  the the from  56  thermal  emf's must be  t h e many t e c h i g u e s problems  i s given  At  low  by  ways  to  the  exploit  the  magnetometer t o d i r e c t l y  One  Josephen  j u n c t i o n and  property  of  inferred  f r o m measurements o f  need not  be  The noise( flux  sensing  i s not  null  mK)  measured  (Webb  circuit  i s flux  detector a  maintain  a  active  the  is  noise  voltage  the  so  the  power  without  There are  to  use  to  noise  the  a  squid et  al,  voltage  to a  frequency  frequency:  two  of  voltage(Webb the  and  conversion  The  temperature  is  the  power o u t p u t  of  a m p l i f i e r gain  chacarteristic  known.  The  maintains  these  junctions  signal.  j u n c t i o n ( W e b b e t a l , 1973).  resistor,  which  noise  method  i s to apply  t o use  et  l o c k e d mode t o b a l a n c e  resistor.  L,  method  s q u i d magnetometer NT  0.05  to circumvent  characteristics  measure t h e  The  system  second  to the  various  1973).  the  A d e s c r i p t i o n of  of J o s e p h s o n  t h e measurement o f  device.  the  use  amounts of n o i s e  superconducting  for.  Kamper(1973).  permits  excessive  accounted  w h i c h have been d e v e l o p e d  temperatures,  superconductors adding  carefully  R,  fixed  the  noise  i s connected  is  flux  constant  bandpass  a l , 1973)  c o n s i s t s of  coupled and  achieves  filter  i n the  by  i n the  and  then  using  low the  generated  parts.  The to  a  squid an  squid  The  in  the  temperature inductor,  system,  current  i s processed  integrating  the  in  i s operated  feedback  The  amplifier  squid  to a superconducting  squid.  flux  very  voltage  three  to a Squid. connected  the  as  a  which  needed  to  through  an  mean  square  57  ^  r - > . Vnlll  I (t) ^^^^^ R  L  o  V(0 •R, |  •IVout (0* J ACTIVE FILTER  INTEGRATING MEAN SQUARE VOLTMETER  -L  SQUID  F i g u r e 1. A S q u i d magnetometer n o i s e thermometer c h a r a c t e r i s t i c s a s u s e d by Webb e t a l ( l 9 7 3 ) .  with  low n o i s e  58  voltmeter. v(t),  The  system  o p e r a t e s as f o l l o w ,  induces a c u r r e n t ,  magnetometer  measures a f l u x  t h e n passes a c u r r e n t , in  <Kt),  resistor,  the  in  <^(t)  the  inductor.  = LI(t).  The  current, v'(t)  as  noise temperature  of  the system i s  on t h e w h o l e s y s t e m .  such  a s , R, L , a n d r ,  t h e s y s t e m must be known a c c u r a t e l y absolute  magnetometer  system  flux  equal  to  passes t h r o u g h a processed  by  a  and measured i n a p o w e r m e t e r .  parameters,  an  The f e e d b a c k  then  thermometer.  NT i s  f o u n d by  performing  By s u i t a b l y  adjusting  the noise temperature  t h e s y s t e m can be d e c r e a s e d t o 0 . 0 5 mK. of  squid  I'(t), is  voltage,  The  which generates a  R$, and t h e v o l t a g e  a model c a l c u l a t i o n the  I'(t),  squid.  bandpass f i l t e r The  I(t),  the noise  The  transfer  before  of  function  t h e NT can be used  The a b s o l u t e a c c u r a c y o f  a squid  3%, and i s m a i n l y due t o u n c e r t a i n t i e s  in  L  and R. One a l t e r n a t i v e by  calibrating  be c a r e f u l l y  it  at  i s t o use t h e NT as a s e c o n d a r y a single  fixed point.  The q u a n t i t y since a f i n i t e the  choice  temperature in  a  2000 -  given  The components must  c o m p e n s a t e d o r measured t o a c c o u n t  t h e p a r a m e t e r v a l u e s as t h e t e m p e r a t u r e interest  integration  of of  of  <v  time  parameters.  2  (t)>  2500 sees  and  a  order  There to  of  in  quantity  is a conflict  minimize  the  the s t a t i s t i c a l  a compromise o f precision  changes  is a s t a t i s t i c a l  t h e s y s t e m and t o m i n i m i z e measurement,  for  changes.  i s used. In  thermometer  1%  noise error  an a v e r a g i n g t i m e for  68  %  in  of  of the  59  measurements 20  of  the  t e m p e r a t u r e s between a  few  milliKelvin  and  K have been used(Webb e t a l , l 9 7 3 ) . The  s e c o n d method u l i t i l i z e s  weak l i n k at a  w h i c h has  frequency,  an  the  a p p l i e d d.c.  f, given  fact  that  the  bias voltage,  current V,  in a  oscillates  by  (33)  where e i s t h e biased  with  modulates a voltage. small 10"  1 5  a  The  U,  given  frequency  so  by is  W).  is  a m p l i f i e d by  by The  supplying  power  fluctuations with  Josephson  that  the  usually the  (33) choosen  30  MHz  are  electronics.  spectrum  One  FWHM g i v e n  U  as  the  t o be  5KHz.  The  carrier  way  the  order  then  to  the  into  noise a  of is the  demodulated  interpreting  that  1967)  This  signal  of  is  with  up-conversion.  i s to r e a l i z e  compressed(Burgess,  junction  voltage, v ( t ) ,  j u n c t i o n ( of  parameteric a  noise  s i g n a l i s f u r t h e r a m p l i f i e d and  room t e m p e r a t u r e  resultant  The  equation  amount o f power r a d i a t e d by  junction.  curve  charge.  voltage,  frequency  accomplished  by  electron  the  voltage  Lorentzian  by  (34)  where  <J>  been u s e d  e  i s the to test  quantum of the  noise  flux  equal  t o h/2e.  thermometer t o  10%  The i n the  method range 1  has  60  8 K(Silver The  e t a l , 1967). temperature  measurements  of  measurements  can  the  also  system.  i s calculated  V;  is  and  *?" i s t h e g a t e  to  determined  to  more u s e f u l  than  current the  the  easly  time  the  N  of  the  The  resistor  measureable  the  accuracy, thus In  either  quantities  By t a k i n g  variance  the second case,  can  a be  method i s  the  equations  and c o n s t a n t s ; t h u s t h e  thermometers.  The  i n t h e same e x p e r i m e n t and a v e r a g i n g t h e  resistor  of the  by m e a s u r i n g  frequency  output  the of  t o g e t t h e v o l t a g e by e q u a t i o n ( 3 3 ) . are  thermometer. is  temperature  measurements,  first.  i n the r e s i s t o r  There  made  on t h e i t h t r i a l .  of the frequency c o u n t e r .  desired  c a n be d e t e r m i n e d  system  the  5  the  t h e r m o m e t e r s a r e good p r i m a r y system  ot  ^ R f e T / t f *  number o f f r e q u e n c y  contain  frequency  Zimmerman,1971)  ,  large  v a r i a n c e , o~ >  t h e f r e q u e n c y measurement  (36)  where  from N  3. Is/  v a r i a n c e c a n be r e l a t e d by(Kamper  The  We - O  t-l  where  inferred  as  fj = 1  (35)  be  two  unavoidable  s o u r c e s of u n c e r t a i n l y  The number o f f r e q u e n c y measurements  finite,  therefore,  there  is  a  that  statistical  i n the can  be  error  61  associated show is  w i t h the  that  t h e rms  calculated scatter,  AT  imprecision  of  variance. R m s  ,  Simple  i n the determined  calculation temperature  g i v e n by  (37)  There  i s a count  which  adds  an  extra  contribution  c a n be c o n s i d e r e d t o be calculated(Kamper  and  1 i n the frequency  the  t o the v a r i a n c e .  device  Zimmerman,  noise,  1971)  T ,  measurement The  and  0  effect  has  been  t o be  (38)  When  the  equal  to the u n c e r t a i n t y  of  systematic  correction  resolution  one  finds  that  temperature  i n t h e measurement, t h e n t h e  the measured temperature  the  i n t h e measured  i s not u s e f u l .  T of t h e t h e r m o m e t e r . t h e minimum r e s o l u t i o n  This  o f a NOT  adjustment  sets a limit  Combining  is  (37) and  on  (38),  is  41 T  (39)  To number o f averaging  obtain  a  uncertaintly  f r e q u e n c y measurements time  of  1% i n t h e measured T,  required  i s 1 sec t h e n t h e t o t a l  is  2x10".  If  the the  t i m e n e c s s a r y t o measure  62  the  temperature The  be  a t one  summary,  thermometer  6 hours.  t o 0.5  K with  is  that  it  possibility which  the  noise  troubled  thermometer  requires  nearly  accurately. o f an  undetected  i s undetected.  is  by c o r r e c t i o n s  1% u n c e r t a i n t y .  predicted  to  the  primary  the  temperatures  measured from a  A major d i s a d v a n t a g e of the an  Also,  to  1969).  I t i s c a p a b l e of measuring  mK  temperature  e r r o r s have beeen  range(Stephen,  the l e a s t  temperature.  system  is  unavoidable systematic  i n the m i c r o k e l v i n In  point  hour there  extraneous  to  measure always  noise  a  NT  single  exists  source  few  in  the the  63  II.  2.1  3  He M e l t i n g  Curve  Introduction The  3  He  melting  curve  thermometer(MCT) c h a r a c t e r i s t i c s detail, both  i n order  liquid  and will  the  now  melting  curve  be d i s c u s s e d  in  t o s u b s t a n t i a t e c l a i m s made e a r l i e r .  and s o l i d  Clausius-Clapeyron  < >  3  He  a r e quantum s y s t e m s ,  Although  t h e thermodynamic  equation  1 7 ° - ^  40  some  J  describes  the melting  curve.  I f a l l t h e t e r m s on t h e r i g h t  side  (40)  known,  then  of  constructed  were  by  integrating  procedure(Scribner v^  - v  the  5  curve  and s o l i d  temperatures,  3  is  He.  the  is  At p r e s s u r e s diagram  less of  b u t a t low t e m p e r a t u r e s  transitions  (Halper'in  there  are  A-transition  three in  triple liquid  3  is  there  which  usual  accurately  40  measure shape  entropy bar  not are  Along  c o u l d be  The  Then t h e  than  He  a l , 1978). points  3  to  by t h e m o l a r  interesting,  et  curve  (40).  i n equation (40).  determined  P-T  melting  equation  a l , 1969),  and use t h e v a l u e s  melting  liquid  et  the  hand  of  of the  and  high  particularly several  phase  the melting  curve,  correspond  to  the  H e , t h e B - t r a n s t i o n i n t h e l i q u i d , and  64  Figure 2. G r e y w a l l and  The melting curve of He u s i n g B u s c h (1982a) and G r i l l y ( 1 9 7 1 ) 3  the  results  from  65  the magnetic  transition  and  as  useful  in solid  thermometric  temperatures(Roger  et  the context of t h i s  thesis,  temperature There various  phases  behaves  like  1975),  thus  no  a  e t a l , 1960).  experimentally  semi-classical  The s y s t e m entroy  spin  has a molar  contributions  the  would be e x p e c t e d  a  a  entropy  the entropy The  linear  suggest,  3  He  base  of the liquid  (Legget,  function  of  however, t h a t  the there  of  commences t o s p i n  i t s entropy  Theoretically, magnetic  bcc He  energy  3  He  particles entropy are  the order  i s very small  the entropy  fields  i s that sitting of  very  is  w h i c h c a n be  a  system  at equilibrium  small  as  the  The e n t r o p y  The Debye of  t o d e c r e a s e s as the s p i n s begin t o  of 10"  i s as p r e d i c t e d  of  Rln2(Kittel).  i s 20 K ( H a l p e r i n ) .  3  due t o t h e n u c l e a r d i p o l e - d i p o l e  characteristic  spin  for  so t h a t  by  1/2  of s o l i d  order  be  model o f s o l i d  temperature solid  the  applied(Goldstein).  non-interacting  lattice  below  in this lab.  temperatures. unaffected  low  n o t be c o n s i d e r e d i n  occur  The l i q u i d  the m i l l i k e l v i n be  very  i n the e x p r e s s i o n f o r the entropy  at  sites.  they  Experiments  a b o u t 0.5 K ( S c r i b n e r , 1969),  of  they w i l l  interesting  down t o t h e A - t r a n s i t i o n  should  at  The  at  theories  Fermi-liquid  (Wilks).  to  points  3  (Abel  expected  fixed  of He a l o n g the m e l t i n g c u r v e .  a r e h i g h e r o r d e r terms liquid  very  since  accurate  i t s entropy  temperature  Although  al,l983),  of the r e f r i g e r a t o r s are  He.  3  7  K.  (Halperin  interactions, Above  50 mK,  which  have  t h e measured  e t a l ) , but near  1 mK t h e  66  s u d d e n l y d e c r e a s e s t o 0 . 1 R l n 2 - ( 0 s h e r o f f , 1972).  entropy ordering expected  in  the  because  aproximately large only  solid  the z e r o p o i n t  30%  of  exchange  at  a  motion  of  overlap interactions,  of  the  exchange system  the  3  He,  separation,  into  as t h e  is  results  in  1 mK.  If  account,  t h e same f o r m  than  which  o f t h e o r d e r of  i s taken  has  spin  higher temperature  the n e a r e s t neighbour  nearest neighbour  Hamiltonian  occurs  The  the  spin  Heisenberg  form(Thouless,1965)  (*o  H« -  where J  i s the exchange  atoms i and  j , and  negative.  High  been  described  ^  so  the  J  >  for solid  3  He  transition  first  order t r a n s i t i o n  a t about  1 mk.  the  susceptibility  relative  to  experiments(Bernier  increases.  t h e H e i s e n b e r g model model  and  suggested  Solid  constants  behaviour  2 mk,  neighouring  of  J  but  Delrieu, A complete  of  The  the  the At  the  solid  have  It predicts the  list  the behaviour  shows  low not  second  shown  law, that  a  3  The He  but the  of the d e f f i c i e n c y  of s o l i d  be  a decrease in  Curie-Weiss  1977),  is  is  model p r e d i c t s a  experiments  He  partition  i s g i v e n by Roger e t a l ( 1 9 8 3 ) .  to explain  3  must  by G o l d s t e i n ( 1 9 6 7 ) .  the H e i s e n b e r g model. a t about  two  operator.  expansion  order  susceptibility  between  coupling series  the q u a l i t a t i v e  by  ^  interaction  temperature  found  temperatures  i  I i s the n u c l e a r s p i n  anti-ferromagnetic,  have  -  of  latest  below  30  67  mK  i s that  of a system  o f atoms  i n t e r a c t ions(Roger  et  behaviour  melting  of  the  theoretically, well  al).  Although curve  multiple  the v e r y  is  low  exchange temperature  difficult  the h i g h e r temperature  shape o f He  to  explain  characteristics  solid,  m e l t i n g c u r v e about  3  explained  by  a  i n the  relatively  range  10 mK  particles  are  temperature  independent  gas  the  whose e n t r o p y  solid  between  entropy  the  K where t h e two that  at  solid  constant (Scribner  implies  simple  t o 500  until  are  spin  rapidly.  0.32 and  quite  entropies  The  an  into equation(40)  curve  t o the measured c u r v e .  have t r i e d melting  to predict  the e n t i r e  and  the  the 3  He is  to  ordering  of  is a  degenerate  K and  volume is  i s equal  difference  approximately  K t o z e r o K. the  of  entropy  below 0.3  equal,  t h e m e l t i n g c u r v e has  entropy  be  The  He  molar  from 0.33  are  3  liquid  the q u a n t i t i e s similiar  liquid  can  because  1/2.  rapidly  the  e t a l . , 1969)  The  where due  The  K.  minimum  i s Rln2,  10 mK,  decreses  the  model.  mK,  non-interacting  spins i t decreases  Fermi to  have  understood. The  the  which  At T  =0.32  Clausius-Clapeyron  extrema.  After  integrating  inserting  i t , one  finds  More s o p h i s t i c a t e d  melting curve  but  no  a  models  accurate  c u r v e s have been g e n e r a t e d (Hudson e t a l . ) .  Given  that  i t i s not  certain  accurately  d e s c r i b e the b e h v i o u r  curve,  empricial  an  made a b o u t  the  3  He  approach  even  o f t h e He be  used  t h e newer  along  3  will  melting curve  that  the  to j u s t i f y  thermometer.  theories melting  the c l a i m s  68  Because t h e r e curve,  t h e MCT  i s no c o m p l e t e  i s calibrated  a  primary  thermometer.  of  t h e He m e l t i n g c u r v e the temperature  point  devices.  29.316  0.003 b a r .  r e s u l t s agreed at  the very  t h e minimum function  with  by c o m p a r i n g  i s by G r e y w a l l  scale  They  s e t by NBS  found  curve.  The  with  who  768  pressure  fixed  to  0.001 K.  be  Their  the r e s u l t s and  Busch  of G r i l l y a t fitted  the  and  T  T  =  A  2.752  by H a l p e r i n e t a l .  8  -1  mK,  -1.220 x 10-  a ,  = -44.4713  157.616  a ,  = -365.784  624.330  a „ = -491.348  and B u s c h , and  the A - t r a n s t i o n  The c o e f f i c i e n t s a r e  0.15435  data of G r e y w a l l  melting  data.  8.406 x 1 0 "  a „  t h e SRM  o f 0.318  Greywall  the  32.342 b a r  a  minimum  in  P - P,  a  He  Busch(1982a),  through  and w i t h  found  3  a c c u r a t e m e a s u r e m e n t s made by H a l p e r i n e t a l  5"  coordinates  the  a t a temperature  below t o t h e i r  where  the  the melting cruve  and  low t e m p e r a t u r e s ,  (42)  for  The most r e c e n t and p r e c i s e measurement  3  used  theory  Halperin  ft  .  et  al., deviates  69  from  the  values  mbar, w h i c h temperature thermometer.  given  corresponds to over  most  by  t h e e x p r e s s i o n (42) by 0.5% of  uncertainty the  in  temperature  less  the range  than 2  measured of  the  70  2.2  Magnetic  The  slope  difference  slightly  the  slope  the  3  - s  ,  and  affected the  -  U  1  the  dipole  magnetic  Heisenberg  x <  as  characteristics,  because  mK(Scribner)  and  quantitative be  used  respond  to  predictions  a  of y  -1  3  He  3  He  5t * x  +  The  and J  even  the c o e f f i c i e n t  this applied  the are  at  magnetic  In  3  a l l 1,  mK,  He  as  where  interaction  i n (42)  contains below  40  t h e H e i s e n b e r g model i s  melting  temperature  1  of the 2  i s the  if y  temperatures  fields,  incorrect,  of y  T >  u is  in a  1972).  but  independent  Although  the  solid,  field,  atom.  mK(Trickey,  i s very small,  h i g h magnetic  describing  above  the  is essentially  o r d e r term.  of  \* ox *  i s c o n s i d e r e d i n the region  x as a s e c o n d  incapable  the  c o n s t a n t between n e a r e s t n e i g h b o u r s  conditions  1, t h e e n t r o p y  1968),  t o the e n t r o p y of  i s the magnetic  of  is  1967)  --L<i\  B  moment  i s of the o r d e r  t h e model  +  s  y = Bu/kT.  coupling  experimental  X  the  liquid  field(Goldstein,  is proportional  +  to  the entropy of a Fermi  (Goldstein,  _  and  long  i s proportional  the magnetic  curve  where x = J / k T  and  by  i s g i v e n by  5^  solid  since  Curve  In the H e i s e n b e r g a p p r o x i m a t i o n of  entropy  (42)  melting curve  3  of  He.  Dependence o f t h e M e l t i n g  o f t h e He  s  only  solid  Field  curve,  as  even  t h e H e i s e n b e r g model  to describe field.  At  its can  the m e l t i n g curve the  very  low  71  temperatures, in  the  multi-exchange  t h e model t o g e t s a t i s f a c t o r y  i n t e r a c t i o n s must be agreement  with  the  included observed  behaviour. It for  has  been e x p e r i m e n t a l l y found(Kummer  temperatures  than  4.5  greater  KG  unresolvably  the  small.  as t h e t e m p e r a t u r e be  accurate  1977). as  The  h i g h as  prevented  Gibb's is  easy  kG(Johnson  field  free  can  energy  10 mK,  than  fields  the  pressure  melting  as h i g h as  been m e a s u r e d  e t a l , 1971),  where  and  solid.  M  s  M»- -  will  but  in  magnetic  thermometry  fields problems  i n the presence of a  phases  by c o n s i d e r i n g  in equilibrium.  the It  temperature  ft*  a r e the molar  Neglecting  long  of the d a t a .  magnetized  at a constant  =  as  is  1 % of t h e r e a d i n g (Hummer e t a l . ,  shown t h e r m o d y n a m i c a l l y  of two  12 kG,  less  the measured t e m p e r a t u r e  interpretation  be  t o show t h a t  Ai-r  because  of  that  and m a g n e t i c  the m e l t i n g p r e s s u r e i s depressed  ( 4 3 )  the  i s above better  mK  for fields  m e l t i n g c u r v e has 63  1.35  depression Even  the u s e f u l  That magnetic  to  than  e t al., 1977)  m a g n e t i z a t i o n of the l i q u i d  the m a g n e t i z a t i o n  i t i s small(Goldstein,  1968),  one  of gets  the  Fremi  and  liquid  72  where  v  is  the magnetic the m e l t i n g  approximately field  constant  and  greater  i s i n c r e a s e d , the m a g n e t i z a t i o n  pressure  is  depressed.  than  zero.  As  increases  and  73  2.3  Impurity  The at  a  melting  on t h e M e l t i n q  curve  depressed  increased of  Effects  minimum o c c u r s  pressure  the e f f e c t  of i n c r e a s e d  e t al,(l969) found  melting  curve  temperature  600  ppm  20  ppm t h e n  with of  "He.  that  0.1 K was n o t i c e d  occurs  tend  unresolvably  on t h e s i n t e r  o f t h e amount o f "He w h i c h c a n be  surface  is  the t o t a l  separation The  i n bcc s o l i d  3  He i s t h e c e l l  approximately dimensions, will  still  the area  available.  helium  i s 2.2 A.  of the Greywall  moles, thus,  it  by e s t i m a t i n g  surface area  atom d i a m e t e r  cell of  found  i s smaller  and c a p i l l a r y  assuming t h a t  probably  equal  to  the  i s about  An  onto  a  neighbour  4 A(Keller).  of the s i n t e r  p e r atom  The t o t a l i s about  separation  surface  ina  amount 4x10"*  i n a monlayer i s  c a n be a s h i g h  f r e e z e out onto the s i n t e r  out  nearest  below t h e p l u g  t h e "He c o n c e n t r a t i o n  insures  p e r atom and d i v i d i n g  2  lattice  phase  Furthermore,  frozen  i s 0.5 m .  the spacing  the  than  3  The s u r f a c e a r e a  and Busch type  with  i n t h e He c e l l .  The  a t 29 b a r s  bump a t  curve  small,  3  but  between t h e  melting  i n t h e "He H e m i x t u r e  to solidify  3  on t h e c u r v e ,  t h e "He c o n c e n t r a t i o n be  i n He i s  But a s m a l l  i n the  and  h a s been made  difference  estimate  into  study  p u r e a t t h e low t e m p e r a t u r e s .  3  "He w i l l  No major  no s u b s t a n t i a l  So a s l o n g  temperature  "He c o n c e n t r a t i o n  20 ppm "He a n d 600 ppm.  t h e He i s v e r y  the  the  a t higher  "He c o n c e n t r a t i o n s  t h e bump s h o u l d  separation that  as  ( W e i n s t o c k e t a l . , 1962).  Scribner  a  Curve  in  three  a s 700 ppm a n d i n a monolayer.  74  A m o n o l a y e r o f "He  will  sinter(Harrison).  Most  3  He  with  1 982a).  "He r  impurities  not a f f e c t 3  He  melting  less  than  the K a p i t z a curve 20  resistance  thermometers  ppm(Greywall  of the  have  and  used Busch,  75  2.4  Accuracy  The strain  and  R e s o l u t i o n of the  resolution  gauge u s e d  pressure  o f t h e MCT  t o measure  transducers  1982a, C o r r u c i n i  used  have  curve  i n c r e a s e s as t h e t e m p e r a t u r e  of  v a l u e s of t h e given  beginning to l e v e l  by  ^  This  listed  Greywall  resolution  i n c r e a s e s at the lower i s used  p r e s s u r e m e a s u r e d by the  a c c u r a c y of  (Grilly,1971). at  uncertainty,  and  0.1  mK  accuracy than  the  1 %,  3  =  which  strain  10~ ,  the  0.003 b a r ( G r e y w a l l and  T  =  200  finally  t h e MCT  mK,  3  mK,  at T =  in  the  i n the  mbars this  100  3  mK  accuracy  o f any  He  melting  curve  MCT  i s known t o .  third  seem i n t h e  =  300  mK,  ju.K,  3  the  and  the  I f a good  dead  gauge,  Busch,  then  1982a) o r  corresponds  the  to to  the  better 3  mK  0.3  mK  corresponds  to  temperature. < T < 300  d e p e n d s on  mK  have a u n c e r t a i n t y i n  i f t h e p r e s s u r e i s m e a s u r e d t o an  The  be  the  3  results  3 mbars  measured  range  by  corresponds  mK,  of  the  T  strain  gauge w i l l  Busch,  are  is  7  and  of the m e l t i n g  o f f can  At  Most  down t o a b o u t  temperatures.  to c a l i b r a t e the  uncertainty of  g i v e n Ap/p  A t T = 300  uncertainty,  I,  the  resolution  required  Busch(1982a).  resolution,  tester  o f f as  of  melting.  sensitivitly decreases  in Table  and  at  pressure  leveling  temperature  weight  a  temperature  thermodynamics.  resolution  f o r thermometry(Greywall  than  law  the  pressure  better  where t h e c u r v e  The  d e p e n d s on  the  e t a l , 1978)  .1 ppm.  MCT  mK  Thus is  the  better  a c c u r a c y o f 3 mbar. accuracy  G r e y w a l l and  to  which  Busch(1982a)  76  T A B L E  T, mK 3 4 5 6 7 8 9 10 11 12 14 16 18 20 25 30 35 40 45 50 55 60 65 70 75 80 85  P, bar 34.3330 34.2957 34.2569 34.2171 34.1769 34.1365 34.0961 34.0557 34.0154 33.9752 33.8954 33.8164 33.7383 33.6613 33.4729 33.2907 33.1147 32.9448 32.7808 32.6224 32.4696 32.3222 32.1799 32.0426 31.9102 31.7826 31.6594  I  dP/dTT, bar K mK -36.21 -38.23 -39.39 -40.01 -40.32 -40.44 -40.45 -40.37 -40.25 -40.09 -39.71 -39.26 -38.79 -38.30 -37.05 -35.81 -34.58 -33.39 -32.23 -31.11 -30.02 -28.97 -27.95 -26.96 -26.00 -25.08 -24.18  P, bar  90 95 100 110 120 130 140 150 160 170 180 190  31.5407 31.4262 31.3159 31.1072 30.9136 30.7343 -.30.5685 30.4154 30.2745 30.1452 .30.0268 29.9191  210 220 230 240 250 260 270 280 290 300 310 320 330  29:7336 29.6551 29.5856 29.5248 29.4725 29.4282 29.3918 29.3630 29.3414 29.3267 29.3185 29.3166 29.3204  299  ?9-82,U  dP/dT. bar K -23.32 -22.47 -21.66 -20.10 -18.63 -17.24 -15.93 -14.69 -13.50 -12.37 -11.30 -10.26 -9.27 -8.31 -7.39 -6.51 -5.65 -4.82 -4.03 -3.26 -2.52 -1.81 -1.14 -0.50 0.10 0.66  Table of v a r i o u s p a r a m e t e r s o f t h e m e l t i n g by G r e y w a l l a n d B u s c h ( 1 9 8 2 a ) .  curve  as c a l c u l a t e d  77  measured the m e l t i n g c u r v e pressure  and  a  few  tenths  to  accuracies  of a p e r c e n t  of  i n the  3 mbar  in  temperature.  the  78  2.5  S e l f - h e a t i n g and The  in  self-heating  the  the  coaxial  MCT  heating  used  the  10-  An  nulling  amplitude  of  the  measure noise that on  the  the  i f the  would  RMS,  of  be  joule  RMS the  the  means  order  transducer  signal.  The  1 ppm  I f the  thermal  i n t h e MCT  be  stray  the  voltage.  of  emfs and  r e s o l v a b l e to  with c a r e f u l  power d i s s i p a t i o n  the  d e t e c t i o n s y s t e m must  obscure  excitation  then  v o l t a g e s on  a.c.  resolution  volts  because thermal  otherwise  the c a p a c i t a n c e  2  capacitance  A lock-in  voltages  the u s a b l e  in 2 volts  cables,  1 ppm.  the measurable  v o l t a g e of  operation,  be measured  measured t o  limit  excitation  heating  t o t h e c a p a c i t o r of  limits  requirement  the  The  joule  this  electrical  voltage  connected  the  i n t h e w i r e s , but  to  lower  transducer.  from  t o a minimum t o r e d u c e  during  t o be  originates  MCT  kept  m i c r o v o l t s must is  of a MCT  of t h e  v o l t a g e must be  the c a p a c i t o r .  that  Sensitivity  c a b l e s which are  pressure  excitation  of  R.F.  sets a  excitation  grounding  can  be  less  of than  watts.  1 4  The impedance small little  MCT of  is insensitive  the c a p a c i t o r i n the  c u r r e n t to flow joule  to r . f .  heating.  i n the  lead  noise  because  transducer wires,  allows  thus  the only a  there  is  large very very  79  2.6 T h e r m a l The to  Time R e s p o n s e o f t h e MCT  thermal  a thermal  response  bath  t i m e , t,  i s determined  by  of t h e thermometer a t t a c h e d the  t h e r m o m e t e r , C^, and t h e r e s i s t a n c e ,  heat  capacity  R, t o t h e h e a t  of  the  flow t o bath  by  2r -  (45)  There for  are really  a precise  first heat  two t h e r m a l  consists  o f t h e BeCu of  3  He  the 3  He  The  is  resistance  second  fairly  the  strictly  true at  1972),  but  magnitude  The  3  3  system  large  much s m a l l e r t h a n i n the c e l l  consists  phases  the  very  specific  liquid.  bath,  the  and t h e  of the s o l i d  low  are low  approximation  in  walls and  of  suffice  the  being  liquid  in  T h i s i s not  temperatures(Scribner will  of  liquid  temperatures  equilibrium.  the  the K a p i t z a  The t h e r m a l c o n d u c t i v i t y at  than  o f t h e BeCu  t h e r e f o r e as long as t h e r e i s  He  the  He  The  smaller  c o n t a c t w i t h the heat is  the l i q u i d  considered(Lounasmaa), cell,  gauge.  and t h e c o n d u c t i v i t y  i s in metallic  between  He  of  time.  3  and t h e w a l l s o f t h e c e l l . 3  response  t h e same o r d e r o f m a g n i t u d e a s t h e He  boundary  cell.  liquid  the  an o r d e r  liquid(Lounasmaa)  Because the c e l l  resistance  need t o be c o n s i d e r e d  o f t h e BeCu s t r a i n  i s about  approximately  thermal  systems that  d e t e r m i n a t i o n of the thermal  system  that is  RC^p .  et  for  aL>, these  80  calculations. estimate  of  the  considering 3  He  The  3  He  heat K ),  measured  Kapitza  the  of t h e  thermal  time  constant  of  for T <  1  effective  equation  g i v e s the  2-  =  l  of  the  thermal  U£_P-  100  is  of 3  gets  and  of  time  to  i n square  By  into  the  values  for the  5.6xl0 nT 8  3  silver  10 m K ( G o d f r i n ) , sinter  good  that  i s a t most moles  He  a  thermometer.  temperature  mK,  between  for T >  2  surface area  (45)  (45)  a  the  He  i s introduced  number  resistance  0.24T" A" K m /Watts, 3  3  ( C o r r u c i n n i e t a l , 1978), one  where n i s t h e  2  as h e a t  r e p r e s e n t a t i v e low  capacity,  erg/(mole  R =  constant  using  parameters  effective  time  the m e l t i n g p r o c e s s  s y s t e m , and  the  thermal  He.  The  sinter  where  is  A  is  meters.  Thus  in a melting  curve  be  «**^*s«^ •  AT* The  surface  thermometer The T  of  of  K,  is  i s below  sinter  700  the G r e y w a l l  thermometer c e l l  = 0.05  cell  ares  10 mK,  A and  a t most then  40  R  «  ^=  450  the  thermometer  So is  3  He  at  I f the  34  0.5  bars.  m. 2  Thus f o r  temperature the  of  the  silver  1979)  w  4 K ^  ,  *'J  below at  3  is  t h e K a p i t z a r e s i s t a n c e of  Ulo_x_lo-*  sees.  cm  sees.  AT thus  sinter  Busch(1982a) type  c o n t a i n s 0.09  i s given by(Harrison,  (47)  silver  10 mK,  most  the  thermal  7 minutes.  time  constant  Fortunately, for  of the  operating about  30  conditions sec.  of the c e l l ,  ( G r e y w a l l and  the thermal  Busch,  1982a).  time  constant  82  III.  3.1  He  M e l t i n g Curve  Thermometer  Introduct ion The  3  a pressure bridge  He  melting curve  transducer  circuit  pressure strain  to  thermometer c o n s i s t s with a f i x e d  measure 3  the  He  volume,  transducer  at  35  of  bars  three  a  parts,  capacitance  response,  and  and  pressure several  repeated  transducer  cycling  constant  is  t o low  onto  volume of  the c e l l  pressure  i n the  it  a dilution  cell.  a t low  must  heat  i t must not  must  used  temperature  specific  short;  fitted  cell  requirements;  must have a low  calibrate  the  tempertures  must  be  able  without  so be  remain a  its  too bulky  Because the  strain  furthermore,  regardless  of  capacitance pressure  transducer  required  i n t h e p r e s s u r e measurements  demands  the  1 ppm,  capacitance  drift the  sensitivity  over  a day  transducer  ground  of  the  of of  less  transducer than  1 ppm.  i s approximately coaxial  cables  10 pF is  the and  i t as c h o s e n as  the  i n f o r t h i s MCT.  be m e a s u r e d t o  The that with  Because the c a p a c i t a n c e and 300  the pF,  capacitance  the guarded  be the  gauge of G r e y w a l l  requirements, used  time,  i t can  a l l these  t o be  leak;  thermal  so t h a t  and  constant,  withstand  developing a  that  refrigerator;  to  Busch(1982a) s a t i s f y  the  a  gauge.  satisfy  easily  cell  system to supply  The  it  3  a of to  ground  83  3-wire t e c h n i q u e  must be  not  mask  completely  Fortunately, technique,  the  with mostly The  as  used the  the  of  required resolution  and  readily  pressure  available  tight  over  a p e r i o d of y e a r s  leaks  into  the  purified bars, thin  difficult  3  He  be  i s necessary  necessitates  system  and  Finally,  the  contaminating decisions operate.  so  He  i t .  the  stability  use  be  These  does  transducer.  capacitance  is a  can  refined  be  achieved  instruments.  The  constraints,  s y s t e m must be 3  He  is lost,  requirement  3  and  which  He  leak  no  "He  t h a t t h e volume of  t o p r e s s u r i z e t h e whole  hampers must  capacitance  t h a t o n l y a s m a l l q u a n t i t y of h i g h l y  of v e r y  i n c r e a s e s the  thus 3  the  of  many  so t h a t no  A l s o , the  small  capillaries  has  to c o n s t r u c t .  system.  stray  commerical  s y s t e m of a MCT  it  system  response  measurement  makes  the  so t h a t t h e  time  the  thin  capillary  needed  leak  pressured  to  testing to  requirements  w h i c h makes t h e p r e s s u r e  system  s y s t e m an  35  tubing.  pump of  down  the  bars  forced awkward  to  35 The the  system. without  many  design  system  to  84  3.2 P r e s s u r e The  Transducer  cylindrical  Cell pressure  (1982a) i s shown i n F i g u r e hardened  beryllium  hardened a f t e r atmosphere with strength  3.  copper,  machining  transducer It  type  25.  capacitance  base  was  made  two  OFHC  gauges o f t h e S t r a t y - A d a m s  capacitance  makes t h i s  more  gauge l e s s  designs,  and  but the assembly  first  step  solder  a stainless  0.13  thick  mm  bottom  The  copper.  Unlike  many  type(l969),  this  gauge  the spacing  be a d j u s t e d .  simpler  to  o f t h e gauge  of  silver  the  process  will  0.8 m . 2  cell.  into The  steel  well  sinter  contact  packed  i n the assembly  That  machine  between feature  than  the  i s correspondingly  i n t h e b a s e was t h e n  would a d h e r e  considered  the well; sinter  fill  with  About  corresponds about  N e x t , t h e d i a p h r a g m was e p o x i e d  0.3  The  p l a t e d so t h a t  base  and t h e base.  later.  occupies  silver  capillary  silver  t o the copper  this  line  to  base of t h e thermometer.  between t h e s i n t e r  be  o f t h e gauge was  0.56 mm O.D.  w a l l s t o the copper  metallic  was  bulky  cannot  tensile Pa.  s  He  difficult. The  the  plates  in a  The t r e a t e d BeCu h a s a  of  1/2  The p a r t s were  a t 300 C f o r 2 h o u r s  d o e s n o t have any f l a n g e s , a n d c o n s e q u e n t l y ,  other  from  o f 585 MPa, a n d an Young's modulus o f 1 2 5 x 1 0  thermometer  the  and Busch  constructed  Berylco  by b a k i n g  0.5 % t o 1 % H^.  was  of Greywall  and  form  a  The s i n t e r i n g grams o f s i n t e r  t o a surface area  of  45% o f t h e volume o f t h e t o t h e base u s i n g  Emerson  85  F i g u r e 3. The He S t r a i n Gauge u s e d measure t h e He m e l t i n g c u r v e . 3  3  by  Greywall  and  Busch  to  86  and  Cumming, Type  visocity, to  the  prevent  was  two  the  cured  1266,  epoxy.  p i e c e s were c l a m p e d  epoxy  from  f o r a day  then  a  high  cylinder.  thick.  diaphragm Using  optimum  the  has  sanded w i t h v e r y  10  diamond powder  brass  was  capacitor  plates.  housing  with  placed  on  rested epoxied The  3  He  on  the  i t . The  with  1266  chamber  and  epoxy, and then  test  and  to  that  i s 0.025  maximum  strength  were  finish.  cured  upper  was  cooled  Adams(l969),  for  cm the  pressure  of  machined and  then  Using  onto  the  BeCu  to a  fine  lapped  plate  to cure.  slipped  allowed  solder An  insulating  epoxied  A drop  of  the  onto on  p r e s s u r i z e d t o 34  flux  back s i d e s of  was  to rest  with  inidium solder,  The  the  t h e d i a p h r a g m , and  housing  was  to  from  seal.  to the p l a t e s .  allowed  n i p p l e of  was  was  measured.  flat  epoxy was  and  cell  washing w i t h methanol.  Then t h e  2850 FT  Straty  emery p a p e r ,  for a  epoxy  w i t h He  0.640 cm  tensile  vice  The  bars  tested  epoxy  of  surfaces  fine  the  diaphragm  t o be  removed by  of Type 2850 FT  the  by  the  l e a d s were a t t a c h e d  completely  layer  by  plates  finish,  #32  given  that are  capacitor  crack  the  i s determined  the p r e s s u r e s The  of  sinter.  in a  low  t h e whole a s s e m b l y  pressured  a diameter  formulas  thickness  sensitivity  /cm  and  a very  together  t e s t e d t o 40  Further,  c o n t r a c t i o n s d i d not  The  and  pressure  n i t r o g e n temperature  thermal  the  under a lamp, b e f o r e  l e a k t e s t e d and pressure  tightly  flowing into  He  liquid  B e c a u s e t h e epoxy has  2850 FT  lower the the  bar  to  plate  the the was was  diaphragm, lower  and  the  plate. whole  87  assembly c u r e d days  are  pressure  f o r 2 d a y s under a lamp.  required  for  the  black  and i n a s m a l l c o n f i n e d  epoxy  leads  and  measured. decrease was  pressure  i n the pressure  pressure  in  this  the  3  several t r i a l s  chamber  behaviour  was n o t v e r y  cure  34 b a r s  at  into  i t was  was  of  to LN  a  attached  to  the transducer  was  temperature a  account,  while found  predicable.  pressure  two  s e t , when under  s e n s i t i v i t y was m e a s u r e d .  shift  He  bridge  response  When t h e gauge was c o o l e d  made t o t a k e  after  the  to  that  volume.  A B o o n t o n Type 74C-S8 c a p a c i t a n c e the  I t was f o u n d  which  by  large  Some e f f o r t  decreasing  the  t h e epoxy was c u r i n g , b u t that  the  low  temperature  So, t h e epoxy was a l l o w e d t o  i n s u r e d t h e r e would- be no s h o r t  between t h e p l a t e s w i t h i n t h e w o r k i n g p r e s s u r e  r a n g e o f t h e MCT.  The  room  zero pressure  implies was  capacitance  of  3.15 pF  a p l a t e s e p a r a t i o n of 3.7x10"  gold  thermometer  plated  to  ensure  good  i s mounted on t h e m i x i n g  cm.  3  at  The OFHC c o p p e r  metallic chamber  refrigerator.  (  temperature base  contact  when t h e  of  dilution  the  88  3.3  Sinters S i n t e r s a r e used  the its  Kapitza  smaller  silver  liquid  following  h e l i u m and  Kapitza  of copper  Ag  silver  because  resistances Although  sinter  i t s specific  the w a l l s  for  copper  i s prefered  heat  of  i s two  at  times  a t 0.020 K ( L o u n a s m a a ) .  powder commonly  ultrafine  apparatuses to decrease  i s g i v e n by H a r r i s o n ( 1979).  temperatures  than t h a t  The  the  between  have been u s e d ( L o u n a s m a a ) ,  lower  called  temperature  A summary o f m e a s u r e d  materials  sinters the  resistance  container.  various  i n low  powder 700  used A,  to  form  Type I I and  the was  sinter  is  o b t a i n e d from  company:  Vacuum M e t a l l u r g i c a l Shonan B l d g . n  Comp.  LTD.  14-10  1-Chome, G i n z a , Chuo-ky,  The  virgin  t h e BET a =  .16  Tokyo.  powder has  a s u r f a c e a r e s o f 4.0  method(Allen,1968) nm  2  using  Ar a t L N  as t h e a r e a c o v e r e d by one  a  m /g  as m e a s u r e d  2  temperature  Ar atom.  and  using  A  silver  A 400  powder  is also available  silver  powder t e n d s t o s e l f - s i n t e r ( R o b e r s t o n e t a l . , 1983),  not  clear  that  f r o m t h e same company, but b e c a u s e  a n y t h i n g i s g a i n e d by  u n l e s s v e r y low  temperatures  will  resistance  the  sinter  of  400  A  using  the s m a l l e r  be e n c o u n t e r e d . is  about  one  by  The half  the i t is  powder, Kapitza of  the  89  resistance The the  o f t h e 700 A  silver  powder.  i s prepared The  powder by b a k i n g flushed to  with  cool  silver  silverplate loose  powder  must  sinter, area The  Then  be  with  is  hydrogen  done should  under  pressure  during  sinter.  I f no p r e s s u r e  flakey.  Greywall  will  result The  temperatures times  in a sinter  sintering can  c a n be from  it  is  i tis  allowed  The s u r f a c e t o r e c e i v e t h e layer  of s i l v e r .  diamond d u s t  powder  is  onto  t o be s t r u c t u r a l l y around  not o n l y  results  The  t o remove any  packed  the  s t r o n g , the  4000 p s i . in  a  The  strong  of the s i n t e r per  in  a  be  good avoided  container. heating  vacuum  or  The s i n t e r  because  of  must  sinter to  of 200'C  with a surface area  helium  must  shrinkage  i s a p p l i e d , the r e s u l t i n g  at a temperature  a  as i t e m b r i t t l e s the  c l a i m s t h a t 700 A powder p a c k e d  sintered  while  base.  base of the s i n t e r  and  baking  pressures  pressure  copper  pressure  the s u r f a c e s of the  i n c r e a s e s the surface area  of the s i n t e r sintering  silver  f o r the s i n t e r packed  also  atmosphere;  atmosphere.  the  high packing  but  After  p o l i s h e d with a fine  In o r d e r  moderately  unit  is  presintering  f o r 10 m i n u t e s ,  must be p l a t e d w i t h a t h i c k  flakes.  surface.  of hydrogen.  helium  by f i r s t  a r e removed from  t h e powder a t 380*C  a  sinter  for sintering  oxides  1-2 t o r r  in  sinter(Godfrin).  be  of the will  3600  be  psi  f o r 10 m i n u t e s  o f 2.5  m /g. 2  parameters a r e not very c r i t i c a l .  Sintering  be anywhere from  sintering  100 *C t o 400 "t and  1 m i n u t e t o 15 m i n u t e s .  There  is  a  loss  of  90  surface or  area  longer  stronger.  layers.  sinter  packing.  on  a  choice of well  top  of  it  is b u i l t  one  base.  temperatures  sinter  u n l i k e copper chip  off  in  order  is very  90 "C f o r sinter  along  the  layers even  fragile.  20 m i n u t e s . was  be  sinter,  to obtain  was made by p a c k i n g  the  will  up by p r e s s i n g t h i n  t h e s i n t e r e d powder  parameters  the  to  another,  v i s e and t h e n b a k i n g a t  to the  the higher  sinter, tends  i n t h e MCT c e l l  sintering  if  presumably  Silver  The s i n t e r  Otherwise,  The s i n t e r with  s i n t e r e d powder  be m a c h i n e d because  pressing of  the  times are used, but  mechanically cannot  of  found  the  sinter  With to  this  adhere  91  3.4 P r e s s u r e The the  3  System  pressure  system  f o r a MCT must be a b l e t o p r e s s u r i z e  H e gas up t o 35 b a r s w i t h o u t  able  to  calibrate  minimize  the He s t r a i n 3  the contamination,  stainless  steel  an o i l - l e s s  possibility  o f pump o i l i n  t h e gas  and  gauge w i t h h i g h a c c u r a c y .  a l l p a r t s o f t h e s y s t e m a r e made  and a l l c o n n e c t i o n s  Furthermore,  consists  contaminating  a r e metal  compressor the  to  metal  was d e s i g n e d  system.  The  be To of  seals.  t o p r e v e n t any  pressure  system  o f t h r e e p a r t s , t h e c h a r c o a l pump, t h e v a l v e s a n d c o l d  t r a p network, and t h e c a l i b r a t i o n  gauge.  The  arrangement  is  shown i n F i g u r e 4. The  charcoal  pump  compresses  the  3  He  h e l i u m - 3 when t h e c h a r c o a l i s c o o l e d t o 4 K gas  when  partial  i t  pressure  quantity  of  independent density helium  to  of the helium  helium  gas  3  i s g r e a t e r than charcoal  and i s a b l e  a  t o absorb  t h e end c a p s .  charcoal  dust  from  A small  the  absorb i s  i n t h e pump h a s  stainless  steel  with pyrex  entering the f i l l  torr,  STP  of  F i v e grams o f c h a r c o a l were  wall stainless filter  6  0.43 l i t e r s  w h i c h h a d end c a p s w e l d e d o n .  a n d 0.20 mm  the  As l o n g a s t h e  at 4 K w i l l  17 cm l e n g t h o f 3/8" O.D.  0.020" w a l l ,  desorbing  10"  The c h a r c o a l u s e d  p e r gram when c o o l e d t o 4 K. into  and  warm up t o 30 K.  that  of the p r e s s s u r e .  1.22 mm O.D. of  allowed  of 0.67 g/cm  packed with  is  by a b s o r b i n g t h e  line.  steel  A fill  line  tube of  was w e l d e d t o one  g l a s s wool The o t h e r  prevents  end o f t h e  92  Charcool absorption Q°-2000psl pump  (2)b  Thermistor gauge  Transducer  P  •  Cryogenic Temperature  •  Cell Vacuum  Cold trap  Figure 4. The p r e s s u r e s y s t e m f o r t h e MCT u s e s a c h a r c o a l pump t o c o m p r e s s t h e He t o 35 b a r s . A l l the v a l v e s are bellows valves m a n u f a c t u r e d by Nupro. V a l v e s 1, 2, 3, a n d 4 a r e SS-4BG valves. V a l v e s 5 and 6 a r e SS-4BRG v a l v e s . V a l v e 0 i s a SS-4UG valve. The v a l v e t o t h e vacuum i s a b r a s s b e l l o w s v a l v e . 3  93  fill  line  Nupro will  i s connected  SS-4UG operate  valve. safety  was  room  The after  system  for a  resistor  helium  shown i n  is  designed  has p r e s s u r i z e d i n system  pump  dewar  Fig.  a  5,  since  near the cools  by  The pump t e m p e r a t u r e i s  mounted on t h e pump; i t h a s  of  10  k>* a n d  a  liquid  t o be u s e d  i n the following  a l l the helium  from  the  s l o w l y warmed up w i t h t h e v a l v e V© o p e n .  pressure  and  a  helium  k«v.  t h e pump h a s a b s o r b e d  is  the sorption  t h e pump.  resistance  o f 1140 pump  space  over  with a carbon  resistance  it  helium  temperature  gauge  between t h e v a l v e a n d pump  to cool  The f l o w c r y o s t a t ,  liquid  monitored  assembly  was c h o s e n  insufficient  refrigerator. flowing  The  p s i pressure  w i t h p r e s s u r e s up t o 140 b a r s .  A flow c r y o s t a t there  t o a 0-2000  t o 25 b a r s , t h e  valve  manner:  reservoir,  When t h e whole  is  closed.  The  i s now a d j u s t e d by c r a c k i n g open t h e v a l v e on  t h e pump. The  n e t w o r k o f v a l v e s and c a p i l l a r i e s  t h e h e l i u m c a n be f i l t e r e d flows  into  the small c a p i l l a r y  dilution  refrigerator  set  600  the  at  system  than  tubes.  unexpectedly  The  40 b a r s  steel  network  Also,  (140 b a r s  i n the event  warming up,  a  the  valve  1/4"  swagelok  to operate with pressures  f o r the sorption  When t h e MCT i s n o t i n u s e ,  relief  of the  A l l v a l v e s used i n  bellow valves with  i s designed  so t h a t  nitrogen trap before i t  p s i opens up t o t h e r e s e r v o i r .  are stainless  connectors. less  with a l i q u i d  a r e arranged  helium  pump). is  stored  in  a  94  Bellows Gas return line  3 3He  (il lint  E  Charcoal pump  insu'laWn  .Uquid helium  Copper thermal shield Vacuum line  Super insulation Vacuum can  F i g u r e 5. L i q u i d h e l i u m from a s t o r a g e dewar i s f o r c e d o v e r t h e c h a r c o a l pump and c o o l t h e c o n t e n t s i n i t .  to  flow  95  2570 c c volume a t one b a r p r e s s u r e . The wall  LN  stainless  sieve.  foreign lead  tube  there  i n the He, 3  gases w i l l  filled  with  should  not  the t r a p helps  be formed  into  the r e f r i g e r a t o r .  The  fill  1.22 mm line  O.D.  is  dilution  soldered  to  continues  decrease  constant is  Sensotec with  calibrate  network cell.  mm  to  tube.  3  which  is a capillary  with a  O.D.  a n d 0.15 mm  vacuum  can  capillary  wall  of  becomes a 0.56 mm  thin  the  the O.D.  tube  is  r e q u i r e d t o p r e s s u r i z e the  He  the tube.  plug  i n the tube  Although  to a pressure is  capillaries  the  The  that the s o l i d  system  t h a t no p l u g s o f  small  is  fixed  i t requires several  less  enough  than so  10 mT,  the  t h a t the time  i s of the order  of  10  bars  seconds.  transducer to  a 0.71  3  the  molecular  At the top of the c r y o s t a t  f o r f l o w when t h e p r e s s u r e  a few A  cryostat  down  d a y s t o pump down t h e s y s t e m of  l a r g e amounts o f  narrow  t h e amount o f He  given point along  impedance  be  There the l i n e  wall capillary  s y s t e m , and e n s u r e a  the  14  any  A  0.020"  crushed  t o ensure  the  wall.  refrigerator.  to  in  into  and 0.20 mm  which  0.13 mm  used  line  silver  capillary,  to  t r a p i s an 18 cm l e n g t h o f 1/8" O.D.,  steel  Although  impurities  and  cold  a  Super  0.05% a c c u r a c y ,  t h e He  right  TJE,  3  after  cell.  It  the l a s t  The power s u p p l y  0-600  psi  absolute  repeatibility, is  valve  connected  and d r i f t to  i n the system  f o r the transducer  is  pressure  a  the  i s used pressure  l e a d i n g t o the 10.000  volts  96  supply  with  transducer DVM  with  was  a  i s a 0-30  an i n p u t  calibrated  least  square  (48) millivolts. the to  mV  signal,  gas.  is  When u s i n g must  conductivity  w h i c h must  be  measured 10 V/V.  than  tester  -The o u t p u t with  The  1 o  of a  sensor  by t h e m a n u f a c t u r e .  t o the c a l i b r a t i o n  in  bars  supplied  A by  pressure  a  reading i n reading  of  measurements  output.  the  gas.  diagram  against  a  The c a l i b r a t i o n g r a p h  A  pressure, rather  by  simple  i s shown i n F i g u r e  i s shown  in Figure  6.  gauge c o u l d be  and a l s o w i t h s t a n d  7.  The  to  gauge  a i r as the  The gauge  found  overpressuring  measuring device  t h e r m o c o u p l e gauge u s i n g  b e c a u s e no c o m m e r i c a l  measure m i c r o b a r s  ,  from t h e v o l t a g e  gauge m e a s u r e s t h e of  a.ft-K t«>xu>~% ,  +  and t h e t r a n s d u c e r  t h e gauge, t h e z e r o  be s u b t r a c t e d  i t scircuit  calibrated  designed  ppm.  o.\o7C + \.zcv-fco v  The t h e r m i s t o r  was  10  gives  get the t r u e v o l t a g e  construct,  than  a dead w e i g h t  pressure  transducer  the  less  impedance o f n o t l e s s  with  P-  the  of  f i t of a q u a d r a t i c  the manufacture  where  drift  which t o 35  was can  bars.  97  12 V  12V  F i g u r e 6. One o f t h e t h e r m i s t o r s i s e x p o s e d t o t h e gas whose pressure is t o be m e a s u r e d . The s e c o n d t h e r m i s t o r c o m p e n s a t e s f o r the ambient t e m p e r a t u r e .  98  E  it  0  40  80  120  160  200  220  240  Thermistor Output (mV)  Figure 7. The Thermistor gauge was T h e r m o c o u p l e gauge u s i n g a i r a s t h e g a s .  calibrated  against  a  99  3.5  Capacitance  Bridge  A capacitance  bridge capable  resolution  of  10"  10"  day  is  pF  5  per  coaxial so  cables  that  wire  fairly  insensitive  circuit  the p r a c t i c a l  be  used  The  the  changes the  because  a capacitor enclosed  with  i n a metal  10.  T h e r e a r e many b r i d g e c i r c u i t s  the  direct  the in  capacitance  separate  circuit. Fig.  bridges The  8 i s one  ratio  circuit  of  a  the  300  pf,  Kline  the  (1960) i s  capacitance.  9.  The  i n the  A  circuit  presence  of- t h e  8  can  of  large  properties  of  a  t e r m i n a l r e p r e s e n t a t i o n of shield  i s shown  w h i c h can  3-terminal  to balance  of  i s shown i n F i g u r e  in Figure  three  than  particular,  lead  used  i t makes use The  In  a  less  i s about  H i l l h o u s e and  circuit  of  with  capacitance  used.  t o measure s m a l l c a p a c i t a n c e s  terminal capacitor.  require  lead  i n the  i s shown  10 pF  term d r i f t  system t o g e t h e r  must be  of  layout  capacitances  three  to the  measuring  short  d e s c r i b e d by  schematic  and  a  described.  techniques  three  lead  with  connecting  special  simplified  pF  5  of  the  be  used  figure  t o measure  c a p a c i t o r , but  ground  transformer  capacitance  that  not  does  in  most  capacitance bridge  require  a  in  circuit secondary  bridge. Consider  the  circuit  capacitances  The  output  transformer  and  the  circuit  in  impedance signal  i s 5 *A-+ 5 0 U I . S , where S 2  Figure  11,  are  shown.  generator i s the  where  as  dial  the  of  s e e n by setting  of  ground  the  ratio  the  bridge  the  ratio  100  F i g u r e 8. S c h e m a t i c of t h e ratio transformer circuit. balanced, C = 10SC, where s i s t h e d i a l r e a d i n g of t h e transformer. X  When ratio  Figures* Capacitance bridge for the MCT.  Signal Generator  Isolation Transformer  D  Ratio Transformer  Reference Capacitor  Lock-in Detector  r  *>< DP DT Switch IK  11  Referenc In o.  3  -» Preamp T-  Uxxu)  1:1  ZZ  HeCell  102  B  m on t h e l e f t - h a n d s i d e i s a c a p a c i t o r e n c l o s e d i n a shKlS. On t h e r i g h t ' h a n d s i d e i s i t s s c h e m a t i c representat.cn as a t h r e e t e r m i n a l c a p a c i t o r .  103  transformer. the  order  The of  effectively  The  bridge balance The  circuit C^,  by  the  extent  i s found coupled  in figure  to the  impedance of  1 Megohm, so t h a t t h e  shorted  transformer.  12(a).  output  low  12(b).  ground c a p c a i t a n c e ,  The  v o l t a g e a p p l i e d , E,  the  circuit  ratio  of  t o the  of  C^,  is  ratio  in  to  ,  transformer  the  figure  equivalent  the v o l t a g e , E , ratio  of  , affects  circuit  is  is  the  capacitor,  considering  inductor  bridge c i r c u i t  impedance  t o which the by  the  the  across i s given  by  E  ( 4 9 )  where M  u>=  "  2nf.  aM-a.tU, - u,* U . L * - n * K < - - v *<V>  L , and  L  x  are  related  to the  coupling  inductance  by  H  (50)  where  k  is  •- v J T T L I  a constant  between L , a n d L .  I f the  x  that  there  are  transformer,  k =  capacitances. very  high(Kline  introduced  by  representative  no 1,  depending  inductances  reactance then  the values  t  ratio  Hillhouse). ground f o r the  t h e d e g r e e of  the  are  together  losses,  ratio E /E  In a p r a c t i c a l and  on  as  in  an  i s independent transformer, An  estimate  capacitance ratio  coupled  i s found  transformer  of  the of  coupling  ideal the  so  ratio ground  coupling i s the  error  by s u b s i t u t i n g used  in  the  104  Figure 11. capac i t o r s .  The  ratio  transformer  bridge  with  three  terminal  105  (a)  (b)  F i g u r e 12. S c h e m a t i c s h o w i n g t h e g r o u n d c a p a c i t a n c e ( a ) and equivalent circuit of t h e c o m b i n a t i o n of r a t i o t r a n s f o r m e r the ground c a p a c i t a n c e ( b ) .  the and  106  bridge: pF.  E, /E  effect if  L| = L^=  of  an  500  is the  found  but  be  measurable  In  fact,  simpler  that  capacitance.  them, and It  stray  the  the  that the  are  detector must be  insensitivity  to  sensitive  to  the  w h i c h may  introduce  as  cell  and very  drifts  sudden  1, c o u l d  unknown  that  i s of  design  of  be  and  the  Thus  the  troublesome  the  were  capacitance  no  real  concern.  in  an  arbitrary  the  bridge  i s much  measure  inductances  c o n d i t i o n of value,  100  capacitance  measurement  leads  approximate three  the  He  10 ppm.  is  the  but  in  the  bridge,  this  sensitivity  the  shift  i s not  and i s of  reduced  reproducible.  the 3  by  impedance  what must a c c u r a t e l y  long  capacitors  and  k =  a  balancing  as  shifts  1/2  capacitances  and  up  of  precise  capacitor  to p i c k  and  ground  requires only  of a b r i d g e  t o a MCT,  the  from  measured c a p a c i t a n c e  is vital  between  the  resolution, this  a  shifts  the  by  and  is required,  The  guard c i r c u i t  concern  differ  to a high  unit  no  to  b e c a u s e t h e MCT  capacitance  thus s h i f t s  .999,  measurement  because only  than  k =  ground c a p a c i t a n c e  accurate  desired,  H,  to  be  and  well  terminal  the  the  fluctuations s i g n a l s near  reference  so  that  capacitors. the  shielded.  ground in  the  the  guarded  c a p a c i t o r s are  carefully in  from  the  The  most The  leads  sensitive bridge  capacitance, ground  reference  the  is  but  is  capacitance,  frequency  driving  bridge. The  bridge  Synthesizer,  used  i n the  w h i c h has  an  MCT  circuit  50 oi. o u t p u t  is driven  by  an  HP  impedance, c o n n e c t e d  3330A to a  107  1:1 to  isolation the  that two  transformer  c a s e of there  the  ratio  i s only  one  secondary c o i l s  f r o m one  i s u s e d as  amplifier. t o an  The  the  the  Most of  the  cables.  connecting  However, the  to  the  the  vacuum c a n  3  He  stainless  cell  (i.e.  DT72A of  i n the  from t h e  t o the  tope  coax.  noisy  of It  the has  when c o o l e d  vibrations  induce  to  electrical  i s almost  unaffected  the  is  i t i s poorly  additional The battery the  very  low  voltage. Figure  for balancing  f r o m 60  by  Hz  the  are  magnetic  The 13.  The  low  is  ppm.  can  down  lead  from  semi-rigid  the  semi-rigid temperature  whereas  The  cycle  the  drawback thus  of  requires  pickup.  component  i n an  1  a  nitrogen  60  to  Ratio  iron  box  and to  the shield  noise.  leakage current  schematic  Lock-in  the  that  resistive  p r e a m p l i f i e r uses a S i l i c o n i x gate  PAR  vacuum  cooling.  housed  signal  RG-172U c o a x i a l  signals),  the  are  the  Decade  s h i e l d e d and,  s h i e l d s to reduce  powered p r e a m p l i f e r  system The  that  braided  circuit  the  found  liquid  RG-172U c a b l e RG-172U  are  cryostat  been  ensures There  is linear  circuit of  attached  excitation voltage  seven  1 kHz  top  HR8  i s a Cooner AS636-1SSF c o a x , and  steel  i s very  lead  transformer,  s u p p l i e s the  frequency  is  circuit.  s i g n a l f o r the  Industries  cables  which  transformer  bridge  isolation  second winding  box,  The  i n the  reference  which at a  iron  transformer. ground  Electro Scientific  Transformer,  coax  on  i n a sheet  and  d i a g r a m of leakage  a the  is  U402 J F E T , reasonably  which low  preamplifier required  has  input  noise  i s shown  because  at  a  in low  108  F i g u r e 13. the Johnson  The h i g h i n p u t impedance o f t h e p r e a m p l i f i e r n o i s e c u r r e n t seen by t h e b r i d g e .  reduces  109  frequencies the  gate  the  current.  r e a c t i v e and for  the  its  current  of  order  bias  Johnson  w h i c h has  noise.  decrease An with  The  source  0.5  Meg.  input  the  the  s i g n a l by  number of  1000  * / l 10  either  low  The ground  voltage  so  i f one  of  loops  system.  can the  i s to  avoid  amplifier 1 kHz  s i g n a l i s fed  i s battery  i n the  purely value  l  the  be  is  into  powered  switched  quadrature  of  high  4.5nv/JnT at  preamplifier  that  noise  operational  before  turn potentimeter  capacitor,  shot  is essentially  MjO  800  noise  228,  the  requires a very  t o be  noise  detector.  impedance This  A NE5534  a maximun  lock-in  i s d o m i n a t e d by  resistor(chosen  used to a m p l i f y the  noise  in  to  series  s i g n a l can  be  balanced. The brass wall  reference  vacuum  capacitor  can  which  stainless steel  can  has  attached  and  a  1.5  lb relief  in  the  top  can  at  the  bottom are  evacuated. contact  and  so  with  The  The  the  t u b e s by  the  i t two  hermetically  valve. the  There are leads  found  that  coax  can  three  bottom  cable.  i s c o n n e c t e d by  electrical  the  cables  of  a  three  tubes to a lower b r a s s  that  I t was  microvolts. top  to  consists  s.s.  the  cause  Two  of  are  pressed which  the  O.D.  BNC  of  silver  mounts  capacitor  whole a s s e m b l y liquid  nitrogen  pulses  of  soldered  the  i s wrapped a r o u n d  top  compartments  tubes each c o n t a i n  f i r m l y against  thick The  panel  from t h e  The  voltage  tubes are  cans.  a string  bubbling  3/16"  separate  down t o and  independent.  temperature  vacuum c a n .  sealed two  room  inner the  is in  several to  the  a RG-172U walls  of  cables.  110  The  immoblized  pickup.  cables are  All  clamped  t o the  then  cables  within  body o f  the assembly  prevent  vibrations  causing  inducing  noise.  third  the  bottom The  When  b o t t o m can is  decreases  by  an  a  5 torr  nitrogen  pf.  bath,  microphonic firmly  to s t a n d o f f s i n order in  i s used  due  level  bridge  because  fairly  small  LN  the as  a stability  run.  over  In  cables  and  t h e pumping  to thus  line  to  temperature,  i t s capacitance  reference capacitor i s cooled  fairly  t h a t the  capacitance  change  of  stable  pressure 1 to 2  constant in  i n the bath  falls,  the ground  capacitance  amounts.  mica c a p a c i t o r .  p r e s s u r e must n o t  the course  the  silvered  i n the  i n the d i e l e c t r i c to  pf  a  Because the  probability  change  to  the atmospheric  5 torr  coax,  down  d u r i n g the  reasonable  The the  0.10  that  more t h a n  or  motion  tube  to  r e f e r e n c e assembly are  c o n t a i n s a 31.90  cooled  open LN^  requires than  The  the  insensitive  can.  it  by  fairly  1  ppm,  change by  more  weather,  there  is  will  change  by  not  days. of  the  temperature  i s not  of  seen  by  changes  insulator as the  the  in  liquid  capacitance  slowly  and  by  111  3.6 C h o i c e It  of C o a x i a l  i s a fact,  noise  i s generated  During  the course  it  has  also  Cable  i n a coaxial cable of t e s t i n g  been  cables  nitrogen  Temperature  p e r h a p s n o t g e n e r a l l y known, t h a t  found  amounts o f e l e c t r i c a l liquid  f o r Low  very  they  microphonic.  was c o n d u c t e d .  The s u r p r i s i n g r e s u l t  58,  emit cooled  study  that  inner  of the study  was t h a t  microphonic  were e x a m i n e d a r e t h e RG  tube with tube  tube  of  a shorter  with  four  w h i c h were e p o x i e d had a c o p p e r  soldered  s l i p p e d over  hypodermic  the  of a l l the  172,  RG  needle  the  BNC  coax.  The  3/8"  thick  wall  length  of  1/4"  thin  wall  of the l a r g e r tube.  r i n g s of expended  such  tube. on.  that  tube.  connector  was p i e c e d  RG  of  to the inner  t o the inner  142,  length  end c a p s o l d e r e d  t o i t a BNC c o n n e c t o r  be  a  down t h e c e n t e r  t u b e was c e n t e r e d  attached could  consisted  steel  insulation 3/8"  coax steel  stainless  (to  of the noise  s e m i - r i g i d c o a x , and an "homemade" a i r d i e l e c t r i c  stainless  large  tested.  cables  "homemade"  been  assembly,  were a v a i l a b l e i n t h e l a b  coax was t h e q u i e t e s t a n d l e a s t  t h a t were The  that  being  sharply.  I n some c a s e s , t h e  A brief  of c o a x i a l c a b l e s  coax  are  f o r example).  characteristics  cheapest  capacitor  most c o a x i a l c a b l e s  while  temperature,  a l s o became  i t i s struck  the reference that  noise  when  electrical  ploystyrene  One end o f t h e  The o t h e r  the  center  A f t e r a rubber and  the  through the hose.  The  outer  end had terminal h o s e had tube,  a  The a i r i n s i d e  1 12  the  t u b e was d i s p l a c e d w i t h  the  noise  length of cable capacitance Tektronic  in  bridge  forced  in  through  and  c a b l e s was s t u d i e d by a t t a c h i n g a  of the  then  the  observing  The o p p o s i t e  inner conductor  temperature  are  again  summarized  m e a s u r e d by o b s e r v i n g  i n the on a 5440  only  D.C.  end o f t h e c o a x was s h i e l d e d t o  lightly  with  talked to , while  at l i q u i d in  output  s e t t o permit  c a b l e was i n t u r n t a p p e d  and then  the  used  f r o m p i c k i n g up t h e 60 Hz  w h i s t l e d a t , and f i n a l l y ,  results  preamplifier  scope, which had i t f i l t e r s  Each p a r t i c u l a r pen,  different  t o the input  10 KHz t h r o u g h .  prevent  in  t h a t was  needle. The  to  helium  Table  nitrogen II.  signal.  a  plastic  i t was a t room  temperature.  The i n d u c e d  t h e maximum peak t o peak  The  noise  signal  was  produced  the c a b l e . Our  conclusions  temperature  should  electrical  spikes  as  follows.  n o t be e x p o s e d as  as  pliable  c a b l e s a t low t e m p e r a t u r e s .  therefore cables.  Also,  cable  wrapped  are  low  because i n the  noisier  than  i n t h e t h i c k e r c a b l e and  the wires cables  f o r low n o i s e  r a n g e , one s h o u l d  liquids,  at  T h i s may be due t o t h e f a c t  the better q u a l i t y  a  cable  c a n be i n d u c e d  general  whereas RG 172 h a s a s o f t e r  picking  frequency  a r e more t i g h t l y  in  under more s t r e s s t h a n  dielectric, When  cables  Coax  boiling  100 mV  Thick  the wires  rigid  large  to  cable.  that  or  are  choose  a  i n t h e more have  teflon  ployethylene  flexible as  the  dielectric.  a p p l i c a t i o n s i n the audio flexible  cable  with  a  113  T a b l e II Peak t o peak noise voltage i n coax cables at different temperatures. The a m b i e n t room t e m p e r a t u r e v a l u e s a r e a measure of t h e 60 Hz p i c k up o f t h e c a b l e . The ambient noise at low t e m p e r a t u r e i s a measure of t h e a m b i e n t sound l e v e l i n t h e room.  Coax  Room Temperature Ambient OxV)  "homemade air core RG 142 RG 5 8 Sem- rigid RG 172 RG 172 shielded  18  Tapping (mV) 0.4  Low Temperature ( 7 7 K) Microphonic (MV)  Ambient (<tV)  7  6  0.13  Tapping (mV)  Microphonic UV) 13  nil  9  nil  86  4  44  9  4  nil  87  0.4  nil  nil  0.2  nil  13  13  13  80  0.3  nil  80  0.2  nil  0.9  nil  nil  0.9  nil  nil  11 4  non-teflon to  dielectric;  the poor outer  tube,  f o r example,  braid thin  one by  can  reduce  running  t h e e l e c t r i c p i c k up  the c a b l e  walled ..stainless  inside  steel  tube.  a  due  conducting  11 5  IV.  4.1  Thermometry w i t h  Meltinq  Curve  Thermometer  Introduction This  curve  fixed  chapter  deals  thermometer.  resistor  w h i c h had  point 768,  high  magnetic  because  The  fields  calibration  found  next  appendix  temperature  was  use  of  the  3  He  compared w i t h  768 of  not  directly  same run  also  an  a  40  the  device. the  a  It  discrepancy  The the  section MCT  i n the  and  measured  SRM  768  was  the  involving felt  that  field  might  the  d e s c r i p t i o n can  following the  an  for operation  s e c t i o n , a more c o m p l e t e A.  germanium  compared w i t h  k i l o g a u s s magnetic  procedure  melting  experiment  conducted.  to  as measured by  the  first i t was  the  d e s c r i p t i o n of  the  in  discusses  SRM  MCT  was  alter  given  a test  during  the  A brief  the  p r e v i o u s l y been c a l i b r a t e d a g a i n s t  exposing the  with  As  device.  SRM  is  the  compares  germanium d e v i c e , temperatures.  MCT be the and  1 16  4.2 O p e r a t i n g Before  t h e MCT the  was c i r c u l a t e d the  gas.  was  through  trap  was  was s t i l l then  An  indicated traces  by pumping  argon  because  large  outgassing  3  bridge.  and  3  tranducer  When  cooled  capacitance  decreased  temperature  the  the Sensotec  pressure is  The  the cold  cold  trap  The p r e s e n c e  of  water  was  to  of argon  tested  sieve with  gas was  with i t .  attributed  the capacitance liquid 2.622  transducer  and t h e c o r r e s p o n d i n g zero  of  nitrogen pf,  is  the  w i t h a Boonton  and  c a p a c i t a n c e of the c e l l  therefore the systematic  was  to the  reservoir.  was m o n i t o r e d  to  trap  pump f o r one  was due t o w a t e r ,  down o f t h e r e f r i g e r a t o r ,  A t room t e m p e r a t u r e  3.15 p f .  point  on t h e volume w h i l e  nitrogen.  of t h e l a r g e He  He  cold  3  t h e s y s t e m h a d been p r e s s u r e  the cool  cell  o f t h e g a s r e l e a s e d by t h e m o l e c u l a r  concentration  During  The  The H e i n t h e  n i t r o g e n temperature.  analysis  of  the  i n the c e l l .  t h a t most o f t h e c o n t a m i n a t i o n  expected The  to the r e s e r v o i r .  t o 300 °C a n d pumped on w i t h a d i f f u s i o n  heated  hour.  3  at l i q u i d  3  t h e c h a r c o a l pump s o t h a t t h e r e was o n l y a  of the He l e f t  removed  was c o o l e d down, t h e H e  t r a p t o remove any i m p u r i t i e s i n  returned  3  millitorr  refrigerator  the c o l d  The H e was t h e n  pumped down w i t h  few  of  dilution  capacitance cell  was  temperature,  the  at  the  liquid  was 2.574 p f .  measuring  v o l t a g e output shift,  capacitance  helium At t h i s  essentially  zero  of the transducer  w h i c h must be t a k e n  into  117  account  when  using  the  calibration  table  supplied  by  the  manufacturer. When  the  temperature pump  and  rate  of about slowly  this  cell  transformer meter. About  After  digits  (about  monitored  was u s e d  and c a u s e d  pressure.  was  pressure  from t h e b r i d g e ,  The  was m o n i t o r e d and f i f t h  and t h e n during  fifth  cell  was  decreased  each  cycle  as a f u n c t i o n of the  c y c l e a h y s t e a s i s o f 0.1%  at a given  pressure.  The  time  change t o be t r a n s m i t t e d between t h e  was  Between  so  read  signal.  o f 5 ppm p e r m i n u t e . .  pressure  hysteresis,  15 dBm  fluctuations  s y s t e m a t 30 b a r s the  a  very  short.  However,  2 b a r ) were made, t h e r e l a x a t i o n  (  the  the  pressure  changes  reached,  i n s t e a d o f t h e Boonton  was e x e r c i s e d 5 t i m e s ,  and t h e t r a n s d u c e r  during  affected  of the c e l l  a  the capacitance  temperature  Between t h e t h i r d  for  usefully  To  i n t h e room  was n o t i c e d i n t h e c a p a c i t a n c e required  trap at a  t h e Boonton  28 b a r s  was i n c r e a s e d t o 34 b a r s  The c e l l  capacitance  be  charcoal  0.2 p s i p e r s e c ) .  with  capacitance  the  the c o l d  i n the c a p i l l a r i e s ,  of  could  i n the c e l l  28 b a r s .  cell  by  through  a pressure  the f l u c t u a t i o n s  pressure  the  the c e l l  of plugs  bridge  five  pressure to  compressed  3  The b r i d g e was d r i v e n a t 980 Hz w i t h  because gas  1 K, He was  was c o n t i n u a l l y  process.  f u n c t i o n i n g and m a i n t a i n i n g a  on t h e S e n s o t e c  the presence  the  was  l e t into  o f O.OlmV/sec  detect of  refrigerator  was a b o u t and  sixth  calibrated  if time  large of the  a minute. r u n t h e r e was no m e a s u r a b l e every  0.4 b a r s  between  118  27.5  bars  a n d 34.2 b a r s .  (5!)  Vl.WtfM-  P =  where P i s t h e p r e s s u r e ratio  transformer,  error  less  Because  than  the  temperature, monitored  5-7 6*5-5 -  S *,  and S i s the d i a l  reading  the  p o i n t s w i t h an  calibration the  refrigerator  temperature  ensure  that  the equation  of  Sensotec  calibration.  was r u n n i n g  each  section  the temperature the freezing  of the  at a very was  carefully  a t some p a r t  temperature  high  of the  during the  calibration. 3  He p r e s s u r e  in  pumping  speed  the  refrigerator He  region  the u n c e r t a i n t y i n  the  formed  3  describes  d i d n o t d r o p below  pressure The  i n bars  dilution  to  capillary  In t h a t  was d e c r e a s e d  capillary  near  of the c i r c u l a t i n g a n d so r e d u c i n g  f r e e z e s a t a temperature  pressure pressure  o f 34 b a r s . on  the  growth of t h e s o l i d  t o 33.9 b a r s the  system  of  plug  The  formation  cell  showed no i n c r e a s e  by i n c r e a s i n g t h e 3  0.75 K  (Grilly,  had c o o l e d  of the p l u g  regions  of  1871)  below  The at  a  0.7 K, t h e  t o promote t h e  higher  was v e r i f i e d by t h e f a c t  i n pressure  dilution  a t the s t i l l .  was i n c r e a s e d t o 35 b a r s into  plug  3  o f t h e He-"He  the temperature  When t h e s t i l l  plug  still,  and a He  temperature. t h a t t h e He 3  when t h e e x t r a p r e s s u r e  was  supplied. The 32  best  a n d 34 b a r s .  starting  density corresponds  The p a r t i c u l a r  choice  to pressures  of the s t a r t i n g  between pressure  119  d e p e n d s on t h e t e m p e r a t u r e To  reach  the lower  required(Greywall pressure point for  where  refrigerator  the temperature  and germanium  taken  at  0.5 K.  was t h e n  and  resistors It  the  passage  example,to  null  refrigerator The  was  the  was f r e e l y  There  apparatus  on t h e c o l d  and  thermal  the  resistance  of  A second  was warming  up  regulation  was on t h e c o o l through  the  not c o o l  with the other  appeared finger  shield,  was a b o u t  0.55 K, The  various  point  was  temperature because  i t  at the higher down  cycle.  t h e minumum p o i n t on I t was p o s s i b l e , f o r  6th  digit  while  the  cooling.  compared were a l l s i t u a t e d temperature  the  noticable. to  would  associated  cryostat.  very  bridge  refrigerator  difficulties the  of the temperature  curve  c o o l e d t o about  chamber was r e g u l a t e d .  to maintain  while the r e f r i g e r a t o r  melting  density  30.4 and 38  was t h e n d e c i d e d t o t a k e t h e  t o be v e r y d i f f i c u l t  The  o f t h e minimum  starting  was m e a s u r e d .  measurements w h i l e t h e r e f r i g e r a t o r  temperatures  pressure i s  p r e s s u r e s between  of the mixing  b r i d g e was n u l l e d  carbon  proved  initial  used.  e t a l . , 1978).  dilution  capacitance  The l o c a t i o n  of the to  i s t o be  a higher s t a r t i n g  and B u s c h , 1 9 8 2 a ) .  corresponding  bars(Corrucinni  i n w h i c h t h e MCT  temperatures,  i s independent  densities  The  range  down below experiment  t o be a t h e r m a l  (attached to but  because  on t h e m a s s i v e  100 K, due t o attached  s h o r t between t h e  the  mixing  chamber)  the thermometers mixing  0.100 K, t h e r e s u l t i n g  to  being  chamber and t h e  thermal  gradients  120  are  e s t i m a t e d t o be v e r y From 0.1  taken.  K t o t h e minimum p r e s s u r e p o i n t ,  About  particular  15  minutes  temperature.  temperature  regulator  temperature better  small.  was  than  few  required  Because sensor  regulated  a  was  to  the  s i x r e a d i n g s were  to  regulate  sensitivity  at  of  the  i n c r e a s e s a t low  temperature,  0.05  300  hundredth  mK  of  around  milliKelvin  mK,  at  the  and  the  a  to  lower  temperature. The  thermal  tested  by  measuring  temperature 10  regulation  minutes  better  later.  than  than  a  total  drift  4 ppm,  minute  was  never  very  low  0.03  mbar  measured. 0.05%,  drift  c o o l e d below was  immediately  pressure  due  to  in  the  was  after  the  of  drift  in  capacitance  the  the  regulated  bridge  and  the  Unfortunately  the  100  so t h e t h e r m a l  time c o n s t a n t a t  not  mK,  thermometer  measured.  warmed  i n the s i x t h  the  to  less  i s a measure o f  up.  digit,  i n the p r e c i s i o n  was  The this  two  t a k e n as  corresponds  t o which  absolute  certainty  in  the  measurements to  t h e minimum  a c c u r a c y o f t h i s measurement, however, « was  because  then  gauge.  slowly  uncertainty  was  and  constant  4 ppm  the  mK  measurements a g r e e d  a thermal time The  point,  measurement o f t h e minimum p o i n t  o n l y one  The  two  the system.  of the s t r a i n  chamber by  pressure  achieved at a f i x e d  indicating  temperatures  differed  was The  for  the  A second mixing  the  i n the system  temperature, relaxation  t i m e c o n s t a n t o f t h e thermometer a t 300  the  a was  only  pressure  121  calibration passing  3  through  slipped  because  after  been  the  dewar f e l l , be  increased  minimum was  0.05%.  pressure  filled  with  Immediately  point  i n pressure  p l u g had been o r i g i n a l l y t o 36 b a r s ,  3  further  He  plug  The  plug cell  3  for  the  plug  to  formed, the p r e s s u r e  increased.  the pressure  t h e minimum.  He.  3  after  between t h e He  but as the l i q u i d  by d e c r e a s i n g  t o warm up t h r o u g h  the s o l i d  solid  became t o o g r e a t  the pressure  remedied  attempting  i s only  transducer  the  had  cell  the d i f f e r e n c e  the Sensotec  hold:  can  the  and t h e c e l l  slipped and  o f t h e He  helium The  level in  difficulty  on t h e p l u g  before  122  4.3  Comparison  The ratio  data  equation  the  value  of  1982a). kept  only  probably  good  to  capacity,  the  region.  therefore,  of  the  a  this  A  to  decreases  the  0.05%  zero  over has  uncertainty  Busch,  with  its  response  zero  the  can  with  be  a dead  units  are  diaphragm  full  scale  curve  pressure  associated  the  Sensotec  which  because the of  was  pressure  t h a t the  of p r e s s u r e  the  and  agrees  size  10%  and  shifting  calibrated  a linear  in  by  was  only  MCT  established  the  offset,  by  in  measurements  in  assuming  Furthermore,  shift  The  pressure  Sensotec  probably  of  this  transducer  decreased  t o 0.02%, t h e  slight  Sensotec  i n t h e MCT  be  systematic  is ulitilized gauge  measured by  uncertainty  the  to a pressure  pressure.  figures  amounts  0.02%.  from  0.003 b a r s ( G r e y w a l l  can  the  accurate  gauge  The  MCT  This  Because  transducer  pressure  at  absolute  from  tester  readings  uncertainty  the  i s 29.313  the  value.  corrected. weight  to  s c a l e so t h a t t h e m e a s u r e d  accepted suffers  bar  the of  of d i a l  absolute  due  l a r g e number o f  measurements  series  minumum p r e s s u r e  The  is  t h e minimum  because  pressure  The  0.05%.  t o 0.015  The  a Germanium R e s i s t o r  T h e s e numbers a r e c o n v e r t e d  measurement  corresponds  with  c o n s i s t s of  (50).  29.3067 bar  this  t h e MCT  transformer.  using is  MCT  of  over  point,  with  the  calibration. reproducibility capacitance  of  bridge  the  strain  over  a  gauge and period  of  the a  stability day  may  be  123  questioned.  However, g i v e n  during  cool  the  down  t h a t t h e minumum  cycle  was  pressure  w i t h i n 3 ppm o f t h e minimum  p r e s s u r e m e a s u r e d d u r i n g t h e warming up c y c l e , system  i s probably  Therefore  the  measurement  very  s m a l l ( on t h e o r d e r  drift  may  be  and  to  the  the d r i f t  i n the  o f 1 ppm p e r h o u r ) .  reproducibitiy  ignored  measured  of  the  precision  pressure  of  these  measurements. Two the  thermometers  mixing  germanium carbon  chamber.  resistor  Table  III l i s t s  curve  values  calibration  Scientific  had  germanium r e s i s t o r , susceptibility  run.  II of G r i l l y ( l 9 7 l )  was u s e d  table  f o r t h e MCT a t t e m p e r a t u r e s in  the  the graph  drawn u s i n g t h e v a l u e s g i v e n  for  the  d e v i a t i o n o f t h e T58 s c a l e  scale(see by  using  sec 4.4).  the  below  as  the A  interpolated t o account  t h e thermodynamic  0.318 K  were  found  t h e v a l u e s g i v e n by e q u a t i o n ( 4 2 ) .  Where decoupled  The t e m p e r a t u r e s  which i n  The m e l t i n g  by G r i l l y  from  with the  above 0.318 K.  temperatures  from  been  thermometer.  of the c a l i b r a t i o n  i n Table  2 mK  previously  The SI had been c a l i b r a t e d  given  o f 2 mK was made  Instruments  and a 400 -n. M a t s u s h i t a  resistor  w i t h a CMN  the r e s u l t s  a  5-He3A,  with a Lakeshore  had been c a l i b r a t e d  down s h i f t  Model  against the SI.  t o t h e MCT were a t t a c h e d t o  were  ( C ) . The c a r b o n  768 a n d , a l s o ,  turn  addition  These  resistor(SI),  calibrated SRM  in  the from  temperature  carbon  resistance  thermometer,  t h e s y s t e m , t h e SI and t h e C r e a d i n g , but both  are  C,  i s not  consistent  measure t e m p e r a t u r e s  in  which a r e  Table HI Temperatures measured by different thermometers, s .41538 .434474 .467312 .434474 .441442 .446643 ,455294 .466583  Calculated Pressure (Bars) 31.3947 30.8561 293067 30.6315 30.3518 30.1425 29.4926 29.3363  Corrected Pressure (Bars) 31.4040 30.86 45 29,3165 30.6414 30.3615 30.1523 29.5024 29.3456  MCT Temp. (mK) 589 550. 318 135.5 153.7 169.4 202 288  S1 C Resistance Temp. Resistance Temp. (Kft) (mK) (mK) (XI) 1.845 5 89 2.22.6 589 2 43.7 547 1.948 547 3.177 314 3.965 K 1 36 9.034 128 2.807 K 153 7.485 150 2.1 74 K 170 6.537 165 I.4I7K 200 5.210 199 678.5 283 3.495 289  125  lower  than  located  t h e MCT  measurements.  w i t h a c e n t i m e t e r o f t h e MCT,  gradients  in  the  mixing  r e a d i n g s d e v i a t e s from It  was  the  Because the carbon  noted  that  t h e SI has  can  be  temperatures  shifted  its  higher  end,  calibration  point  show  although previous c a l i b r a t i o n  that,  where  the p o s s i b i l i t y of  chamber  t h e MCT  the  SI  c u r v e has  205.7 mK  point.  w i t h the  fixed  within  a  SRM  768 A  the  768  shifted  and  point  test  K  values d i f f e r d at  calibrated  w i t h t h e MCT,  these  January fact  do  check  was  was  different  the  then  the  1983  c u r v e s o f t h e SI  still  curve  1%,  and  temperature. the  fixed  i s o n l y 0.5  mK  agree agree  needs t o the  it  was  be  MCT.  with  to  the  calibrate  value  the taken  of  the  v a l u e of C  t h e p r e s s u r e minimum.  corresponds  temperature t h e new  not c o n f i r m the v a l i d i t y of  to  the  resistor.  Similiarly,  from  mK,  at  t h e SI  and  interpolated  which  162.6  is shifted  i f t h e SI  germanium  passing through  by  and  temperature  t h e MCT  to  at  January  in  i s t o compare  compared  mK.  fixed  the Lakeshore,  f o r t h e MCT  and  0.318  that  768,  5  SI  The  99.02 mK  as  The  curve  i s the worst.  t o a lower  appears  out.  temperature  is  thermal  by as much as  o f t h e a c c u r a c y of t h e MCT  m e a s u r e d when t h e MCT two  at  then  the Lakeshore  test  C w i t h t h e MCT  It  t h e SRM  possibly  at  2 mK  temperature,  against  small  by  ruled  of t h e SI  I f t h e SI c a l i b r a t i o n  only real  resistance  The  temperature  milliKelvin.  recalibrated The  the agreement  device c a l i b r a t i o n  a g r e e s w i t h t h e SRM  resistor  if  to  a  the  1 SI  a t 205.7 mK curve.  relying  mK is  from  Although  t o t a l l y on  the  126  MCT,  they  do  earlier, to  the  compare  instill  some c o n f i d e n c e  only d e f i n i t i v e  i t s temperature  procedure  scale  with  germanium, and h o p e f u l l y a n u c l e a r the  very  low  temperatures.  in  the  MCT.  As  for checking  t h e SRM  768,  orientation  the  stated  t h e MCT  is  Lakeshore  thermometer  at  127  4.4  Conclusion A  3  He  tested.  m e l t i n g curve thermometer  The p r e s s u r e  0.14 mbars.  At temperatures  t o an u n c e r t a i n t y the  precision  regulators decrease  resolution  is  and the  of  7 yu-K. only  more  measurement.  of  this  less than  the  better  runs,  it  With  measurement, 0,5 mK a t  a  uncertainty  t h e MCT can d e t e r m i n e  50 mK a n d 1 mK a t  pressure  is  somewhat  point,  decreases  where t h e h i g h e s t  accuracy  In fact,  t h a n 0.05%.  pressure  linear  around  decrease the 0.05%.  If  As l o n g as t h e p r e s s u r e 29 b a r s ,  uncertainty  the in  shift the  as  pressure  the  The s h i f t i n g  of  the  value  at  accepted  in the the  most  standard  is  the  validity  of  rescaling  pressure  reasonably scale  measurement  there  might  region  sensitive  t h e r e were a l a r g e d i s c r e p a n c y b e t w e e n t h e  to  to  in  s i n c e near  pressure  is  the accuracy  in the pressure  minimum p r e s s u r e and t h e a c c e p t e d v a l u e , doubt  measurement  the  uncertainty  is necessary,  to  pressure  the temperature accurately  m i n i m u m , t h e t e m p e r a t u r e measured by t h e MCT i s t o the pressure.  300 mK,  standard(which  in  t o agree w i t h the the  of  the  the pressure  0.05%  260 mK.  better  m e a s u r e d minimum p r e s s u r e that  of  is  temperature  in  i s d e t e r m i n e d by t h e room t e m p e r a t u r e p r e s s u r e 0.05%).  MCT  may be p o s s i b l e  uncertainty  The a b s o l u t e a c c a r a c y o f  and  corresponds  temperature  With  calibration of  particular  100 mK, t h i s  At t h e h i g h e r 0 . 1 mK.  estimate  s y s t e m has been b u i l t  will below  measured be  some  the pressure.  But,  128  because of  the determined  the  accepted  rescaling. uncertainty  minimum p r e s s u r e  value,  J u s t how e f f e c t i v e in  the  pressure  a b s o l u t e method o f c h e c k i n g rescaling, standards.  there  is  to  do  a  the is  is  i s with some  shift hard  confidence is  in  of  in  reducing  to determine.  the e f f e c t i v e n e s s calibration  i t s uncertainty  the  The o n l y  the  with primary  the  pressure  temperature  129  BIBLIOGRAPHY 1.  A b e l , W.R.; A n d e r s o n , A.C.; B l o c k , W.C.; J . C , Phys. Rev. J_47, 11 1 ( 1970).  2.  A n d e r s o n , A.C.; P e t e r s o n , R.E. , C r y o g e n i c s 1_0, 430 ( 1970)  3.  A n d e r s o n , A.C.; R e d f i e l d , (1959).  4.  A n u f v i e v , Y.D.; P e s h k o v , V.P., S o v i e t Temp. Phys. 34, 183 ( 1 9 7 2 ) .  5.  B a k e r , G.A.; Phys. Rev.  6.  B a r g e s s , R.E., P r o c . Symposium on t h e P h y s i c s o f S u p e r c o n d u c t i v i t y Reviews, U n i v e r s i t y of V i r g i n i a , C h a r l o t t e s v i l l e , V i r g i n i a (1967).  7.  B e r g l u n d , P.M.; C o l l a n , H.K.; Ehnholm, G . J . ; G y l l i n g , R.G., J . Low Temp. Phys. J5, 357 ( 1 9 7 2 ) .  8.  Berman, R., C r y o g e n i c s 5_, ( 1966).  9.  B l o g e t , P.; G h o z l a n , A.C.; P i e j u c , P.; Sudvuund, M; V a r o q u a n x , E.S.; L e F a r r , D., P r o c . on t h e 1 3 t h I n t . Conf. on Low Temp. P h y s . , Plenum P r e s s , New Y o r k ( 1 9 7 3 ) .  A.G., P h y s .  a n d Wheatby,  Rev.  \±6,  Physics,  583  J.  G i l b e r t , H.E.; E v e r , J . ; R u s h b r o o k e , 164, 800 ( 1 9 6 7 ) .  Low G.S.,  10.  B r i c k l e d d e , F.G.; v a n D i j k , H.; D u x i e u x , M.; C l e m e n t , J.R.; L o g a n , J.K., J . R e s . N.B.S. A 64, 1 ( 1 9 6 0 ) .  11.  Callen,  12.  Cameron, J.A.; C a m p b e l l , J.A.; Compton, J . P . ; G l i n e s , R.A.; W i l s o n , G.V.H., P r o c . Phys. S o c . 90, 1077 ( 1 9 6 7 ) .  13.  C o r r u c c i n i , L.R.; M o u n t f i e l d , K.R.; Sci. Instrum. 49, 314 ( 1 9 7 8 ) .  14.  Dundon, J.M.; S t o l f a , D.L.; G o o d k i n d , J.M., P h y s . Lett. 30, 843 ( 1 9 7 3 ) .  15.  D u r i e u x , M.; van D i j k , J . E . ; t e r H a r m s e l , H.; R e i n , P.C.; Rusby, R.L., Temp. C o n t r o l and Measurement 145, ( l J * 7 l J .  16.  Edertstein,  A.S.; Mess, K.W.,  17.  Ganano, R. (1970).  a n d Adams, E.D. , Rev.  H.B.; W a l t o n , T.A., P h y s .  Rev.  83, 34 ( 1 9 5 1 ) .  S p r e n g e r , W.O.,  Physica  Rev. Rev.  31, 1707 ( 1 9 6 5 ) .  S c i . Instrum.  4J_, 716  130  18.  Goldstein,  L., Phys.  Rev.  1_64,  270  ( 1967).  19.  Goldstein,  L., Phys.  Rev.  1J7j_, 194  (1968).  20.  G r e y w a l l , D.S. 146 ( 1 9 8 2 ) .  and B u s c h , P.A.,  21.  G r e y w a l l , D.S. 509 ( 1 9 8 0 ) .  and B u s c h , P.A.,  22.  Grilly,  23.  Halperin, P.C., J .  W.P.; Rasmussen, F.B.; A r c h i e , C.W.; Low Temp. Phys. 3J_, 617 ( 1 9 7 8 ) .  24.  Harrison,  J.P., J .  25.  H i r s c h k o f f , E.C.; Symko, O.G.; V a n t - H u l l , L . L . ; Wheatby, J . C . , J . Low Temp. Phys. 2, 653 ( 1 9 7 0 ) .  26.  J o h n s o n , R.T.;  27.  J o h n s o n , R.T.; Rapp, R.E.; Phys. 6, 445 ( 1 9 7 2 ) .  28.  K a l u r a s , G.M.; K a t i l a , T.E.; Lounasmaa, O.V., Mossbauer E f f e c t Methodology, I . Gruverman, ed. (Plenum, L o n d o n , 1969), V o l . 5 , p . 2 3 1 .  29.  Kammer, R.B.; M u e l l e r , R.M.; Phys. 27, 319 ( 1 9 7 7 ) .  30.  Kamper, R.A., T e m p e r a t u r e : I t s Measurement and C o n t r o l i n S c i e n c e and I n d u s t r y . 4, 349 ( 1 9 7 3 ) .  31.  Kamper, R.A. 132 ( 1 9 7 1 ) .  32.  K i r k , W.P.' (1971)  33.  K i t t e l , C , Thermal Y o r k , 1969).  34.  K r a n e , K.S.; Murdock, B.T.; Lett. 3_p_, 321 ( 1973).  S t e y e r t , W.A.,  Phys.  Rev.  35.  K r a n e , K.S.; S t e f f e r , R.M.; T a b l e s I I , 351 ( 1 9 7 3 ) .  Wheeler,  Nucl.  Data!  E.R.,  Phys.  Rev.  Lett.  49, —  J.  Low  Temp.  Low  Phys.  Temp.  Sci.  £,  Phys.  Lounasmaa, O.V.;  and  Rev.  615  37,  Instrum.  (1971).  467  Richardson, (1979).  Rosenbaum, R.;Symko,  Wheatby, J . C . , J .  Adams, E.D.,  Zimmerman, J . E . , J .  and Adams, E.D.,  51, ~~  Phys.  J.  Appl.  Rev.  Low  Temp.  Temp.  Phys.  Lett.  Physic^. ( J o h n W i l e y & S o n s ,  R.M.,  Low  O.G.;  43,  27,  392  Inc.,  New  131  36.  L a n d a u , J . ; Tough, J . T . ; B r u b a k e r , N.R.; Phys. Rev. L e t t . 23, 283 ( 1 9 6 9 ) .  Edwards,  D.O.,  37.  L a n d a u , J . ; Tough, J . T . ; B r u b a k e r , N.R.; Phys. Rev. A2, 2472 ( 1 9 7 0 ) .  Edwards,  D.B.,  38.  L e g g e t A . J . , Rev.  39.  Marsh,  40.  Metrologia  5_, 35 ( 1 9 6 9 ) .  41.  Metrologia  1_5, 65 ( 1975).  42.  O s h e r o f f , D.D.; R i c h a r d s o n , R.C.; L e e , D.M., Lett. 28, 885 ( 1 9 7 2 ) .  43.  P r a t l , W.P.; S c h e r m e r , Phys. 1, 469 ( 1 9 6 9 ) .  44.  Preston-Thomas,  H., M e t e r o l o g i a  45.  R i c h a r d s , M.G.; 182 ( 1 9 7 3 ) .  Toffe,  46.  R i c h a r d s o n , R.C., P h y s i c a  47.  R o b e r t s , T.R. (1954).  48.  R o b i c h a u x , J . E . and A n d e r s o n , A.C., Rev. 40, 1512 ( 1 9 6 9 ) .  49.  R o g e r , M.; H e t h e r i n g t o n , Phys. 55, 1 ( 1 9 8 3 ) .  J.H.; P e l r i u m ,  50.  Rose, M.E., P h y s .  £ 1 , 610 ( 1 9 5 3 ) .  51.  Rosenbaum, R.L.; E c k s t e i n , 21 ( 1 9 7 7 ) .  52.  R o s e n b e r g , H.M., J . Low Temp. P h y s . , Low Temp. S t a t e Phys. ( C l a r e n d o n P r e s s , O x f o r d , 1965).  53.  S c r i b n e r , R.A.; P a n c z y k , M.F.; Adams, E.D., J . Phys. 1, 313 ( 1 9 6 9 ) .  54.  S i l v e r , A.H.; Zimmerman, J . E . ; Kamper, R.A., A p p l . Lett, i i , 209 ( 1 9 6 7 ) .  55.  Sites,  J.D., P h y s .  Mod.  Phys.  Rev.  Lett.  47, 331 ( 1 9 7 5 ) . 33A, 207 ( 1 9 7 0 ) .  R.I.; S t e y e r t ,  W.A.,  Low Temp.  C r y o g e n i c s 13,  90B, 47 ( 1 9 7 7 ) .  and S y d o r i a k ,  J.R.; S m i t h , H.A.;  J.  Rev.  1_2, 7 ( 1966).  P.S.; T u r n e r , P.R.,  Rev.  Phys.  S.G., P h y s .  Y.; L a n d a u ,  Rev.  93., 1418  S c i . Instrum.  J.M., Rev.  Mod.  J . , C r y o g e n i c s 1_4_,  S t e y e r t , W.A.,  J.  Solid Low Temp. Phys.  Low Temp.  132  Phys.  4, 605 ( 1 9 7 1 ) .  56.  S o r e l u n , M.I., N o i s e , S.N.O.  57.  Soulen, R.J.  58.  Soulen, R.J., Physica  109-110, 2021 ( 1 9 8 2 ) .  59.  S t e p h e n , M.S., P h y s .  Rev.  60.  Suomi, M.; A n d e r s o n , A.C.; H o l m s t e i n , B., P h y s i c a (1968).  61.  S y d o r i a k , S.G.; R o b e r t s , T.R.; Sherman, R.H., J . R e s . N.B.S., G.B.A., 559 ( 1 9 6 4 ) .  62.  Templeton, J . E . and S h i r l e y , 1_8, 240 ( 1 9 6 7 ) .  D.A., P h y s .  Rev.  63.  Thouless,  Soc.(London)  86,, 893 ( 1 9 6 5 ) .  64.  T r i c k l e y , S.B.; K i r k , 44, 668 ( 1 9 7 2 ) .  65.  van D i j k ,  66.  Webb, F.S.; W i l k i n s o n , K.R.; W i l k s , J . , P r o c . (London) 2J_4, 546 ( 1 9 5 2 ) .  67.  Webb, R.A.; G i f f a r d , R.P.; Wheatby, J . C . , J . Phys. 1_3, 383 ( 1 9 7 3 ) .  68.  W e i n s t o c k , H.; L i p s c h u l t z , F.P.; K e l l e r s , C.F.; Tedrow, P.M.; L e e , D.M. , P h y s . Rev. L e t t . S>, 193 ( 1962).  69.  Wheatby, J . C . , Rev.  70.  Zimmerman, G.O.; A b e s h o u s e , D.R., J . Low Temp. P h y s .  a n d M a r s h a k , H., C r y o g e n i c s 20_, 408 ( 1980).  P.J.,Proc.  H.  1J82, 531 ( 1 9 6 9 ) .  Phys.  W.P.;Adams, E.D., Rev.  a n d D u r i e u x , M. , P h y s i c a  Mod.  Phys.  38, 67  Lett.  Mod.  Phys.  2_4_, ( 1959). Royal Soc. Low Temp.  47, 415 ( 1 9 7 5 ) .  D.J.; Maxwell, E.; K e l l a n d , 41_, 79 ( 1 9 8 0 ) .  133  A p p p e n d i x A 2. O p e r a t i n g  The  a MCT  MCT c o n s i s t s o f t h r e e  pressure  system,  itself.  When  remember  a  few  important  s y s t e m must  not  excede  138 be  the  using  bars(2000 p s i )  epoxy  pressure  should  a l w a y s be l e f t  particular points.  opening  in a sizable  which  sensitive  sensitive the noise  The beat  to  3  and  bridge  noise  sources. is  connections  60 Hz s i g n a l s w i l l lock-in  between  always i n the  pump  where  should  never has  80 C.  reservoir  valve can f u n c t i o n  warming up. vacuum  Finally,  line  could  lost. high  First  resolution, i t  of a l l i t i s very  mainly  associated  with  the c r y o s t a t .  The  supporting  on t h e coax must  by  of  be c o n t i n u o u s  filter the  damping  the  them.  up by t h e i n n e r  multiply  over  3  c a n be r e d u c e d  be p i c k e d  a  the  t o t h e He  the  d e t e c t o r does n o t i m m e d i a t e l y  frquencies  must  n o t be h e a t e d  c a b l e s down i n t o  i n t h e c a b l e s by r i g i d i l y guarding  in  has very  and t h i s  the  and t h e c e l l  the pressure  the r e l i e f  amount o f H e b e i n g  many  one  The c e l l  the valve  of the v a l v e s  i n t r o d u c e d by m i c r o p h o n i c s  The  except  of the r e f r i g e r a t o r  to microphonics,  preamplifier  vibrations  large  to  First,  should  open so t h a t  Because t h e c a p a c i t a n c e is  MCT,  are the  S e c o n d , t h e t h e r m i s t o r gauge  i s operating  i n t h e event  inappropriate  bridge c i r c u i t ,  40 b a r s ,  seal,  when t h e MCT  result  this  35 b a r s .  Third,  properly  capacitance  systems: these  c a n be s t o r e d s a f e l y .  p r e s s u r i z e d above  an  separate  or  conductors. out a l l of the  60 Hz  and  the  134  reference  frequency  bandpass a m p l i f i e r driving  by  of v e r y  the output The  ground  The lock-in  is  low  frequency  the  output  decade  loops  knobs To  can  that  then  the  closer  is  be  beats  bandwidth of  important  chosen  that  be  the the  to minimize  which cannot  through t h a t of is  the the  the  filtered  bridge  least of  is straight  sensitive  to  the  The  decrease  because  ratio  forward.  scale  transformer,  and the  resistor to  setting less  into  give on  signal  of  the  With  the  using  output  the  t o be  setting,  a  zero signal  significant  repeated. t h e g a i n of  is  figures has As  the  of  not  the lock-in  by  branch After  changed,  of t h e  shifted  the zero  nulled  output. has  the  the  the a p p r o r i a t e  I f a d j u s t i n g the q u a d r a t u r e  null  bridge  converge to t h e ' c o r r e c t s e t t i n g ,  zero  has  cryostat.  possible  Then t h e q u a d r a t u r e  onto  procedure  to the  the  preamplifier).  resistance the  continue  transformer.  from  dissipation  a d j u s t i n g the  verifying one  the  is  (This  the  the  always undershot.  and  bridge  of t h e  i s zeroed.  switching  it  bridge  i s separate  d e t e c t o r on  lock-in  Thus  the  o p e r a t i o n of  largest  Hz.  of  number o f g r o u n d  transformer  b r i d g e , because  filters.  g r o u n d of  lock-in the  RC  the  i s 50  frequency  possibility  of  ratio  the  null,  setting  gets  i s increased  appropriately For  the  capacitance, related  MCT,  the d i a l  r e a d i n g need not  r a t h e r , the p r e s s u r e  directly  t o the d i a l  response  setting.  of  be the  converted transducer  to a is  135  Before system  the  i s pumped w i t h  days.  Then  cleaned  the  by  heated  the  while  heater  warm  The  a i r through  solder  joints  elevated  assemblies rest  has  in  the wire  the  system  the  on  heater  flow  that  valves the  sieve are to  The c o l d  trap i s  i s wrapped a r o u n d  the  aboue 45 v o l t s o r flowing  there are soft  the temperature  s h o u l d n o t be  the  to  high  Because  outgassing  sufficiently  the rest  of the  i s pumped down t o l e s s  from  the  low l e v e l , system.  than  two  t h e two  After  the  a few m i l l i t o r r ,  i s shut. trap  at  LN^  temperature,  l e t into  i s monitored  with  3  He  the r e s e r v o i r . the Sensotec  is  passed  The p r e s s u r e  pressure  meter.  o f H e a t STP i s r e q u i r e d t o p r e s s u r i z e t h e MCT.  The  3  main volume o f t h e MCT i s t h e r e s e r v o i r When t h e r e  trap  them.  He, the  for several  molecular  cold  cryostat.  When  decreased  the cold  Two l i t e r s  and  the  3  The c h a r c o a l pump i s warmed up by  t h e t r a p s and then  the  and  pump  s h o u l d n o t be t u r n e d  a r e s e a l e d from  t h e vacuum l i n e  through  pump  the system with  diffusion  pumping  100*C.  of t h e s y s t e m  With  pump  i n the flow c r y o s t a t  above  containers  the  variac  may m e l t .  of  an N ^ t r a p p e d  still  t o 300°C w i t h trap.  filling  charcoal  heating  temperature  cold  initial  i sa sufficient  t o t h e He r e s e r v o i r  pressure  3  i n the tubes  with  q u a n t i t y of He i n 3  and t h e H e s u p p l y 3  i s less  t o t h e c h a r c o a l pump i s c l o s e d .  than  The  a 2.5 l i t e r the  tank  empty  , the  are closed.  10 m i l l i t o r r , cold  trap  volume.  When  the valve is  now  136  heated  t o 300 °C t o d r i v e o f f t h e g a s s e s  pumped w i t h  a diffusion  temperature. The and  the  that  slowly  through  increases  main to  flow  pressure  that  hysteresis pressure four  times.  below  probably gauge  the  the  t r a p and i n t o reading  bridge  require  t o the He  LN  cell  3  as i t c o o l s .  The  cell  shold  be  t o 28 b a r s .  5  be  cycles  rate  A l l the monitored  0.9 K.  The  of  so  that  the  From 34.5 b a r s , t h e  has  the  the  kept  This c y c l e i s repeated  hysteresis  to  a  A record of the capacitance  c a n be o b s e r v e d .  i s connected  3  by 0.01 mV/sec. should  into  The H e  at  d o e s n o t c o o l below  sensitivity  about  loaded  the c e l l  refrigerator  pressure  When t h e  the  to  up t h e a d s o r p t i o n pump.  Sensotec  i s slowly decreased  capacitance  decreased  Boonton  cell.  before  The  to  a  meter,  the  cell  will  the h y s t e r s i s  of the  is insignificant. The  0.3  warming  the r e f r i g e r a t o r  of  in  or f i v e  value  i s monitored  i s i n c r e a s e d t o 34.5 b a r s .  a function  i s attached  3  l o c a t i o n s on t h e d i l u t i o n ensure  returned  a t 1 K, t h e H e i s s l o w l y  the c o l d  the  then  c a n now be c o o l e d down.  the r e f r i g e r a t o r by  is  t o be u s e d .  meter  of the c e l l  refrigerator  cell  should  as  capacitance  the capacitance  With  It  The MCT i s now r e a d y  Boonton  dilution  pump.  on i t s s u r f a c e a n d t h e n  calibration  o r 0.4  run c o n s i s t s of p r e s s u r i z i n g  bar increments The  and measuring  two v a l v e s  the c e l l  leading to the c e l l  the  cell  in  capacitance at  each  point.  form metal t o  metal  s e a l s a t t h e s e a t and t h e r e f o r e , need t o be f i r m l y  closed  137  or  they  34.5  will  leak.  bars.  The  The c e l l formula,  calibration  results.  to  the plug  forming  to  34 b a r on t h i s The  pressure,  liquid.  over  pressure  the  plug  3  increases,  of  and t h i s  the  3  He  the  the plug  refrigerator  is  cooled  When t h e p l u g  is  decreased  c a n be anywhere from 30.5  in  the r e f r i g e r a t o r  below t h e f r e e z i n g  the temperature  o f 0.5 b a r s  pressure  the pressure  tothe  MCT.  When  up  between 28 a n d  + a S + a S , i s fitted  t o c o o l the r e f r i g e r a t o r  the  the  P = a  be c a l i b r a t e d  From 34.5 b a r s ,  circulation  increased  should  i s below  capillary.  If  the  i s not completely relieved  to  i s completely  the  pressure  formed.  of  p o i n t , an growth  in  of  the c e l l  If this  happens,  value  and the  -the o r i g i n a l  further before  point  freezing  i s a p p l i e d t o promote  i s now  the overpressure  f o r m e d , t h e MCT c a n  i s applied.  be  used  as  a  thermometer. The liquid be  helium  allowed  plug  plug  i n t h e dewar d r o p s .  to build This  passing  the  on t h e t o p s i d e o f t h e p l u g  level  to s l i p .  slowly on  pressure  through should  the p r e s s u r e  used  of  checked.  the s t i l l At  should  The p r e s s u r e  up b e c a u s e t h e o v e r  i s especially  be d e c r e a s e d  pressure  important  t h e minimum.  i n c r e a s e s as the  At t h i s  must  not  may c a u s e t h e  when  the  MCT  is  p o i n t , the pressure  t o a few t e n t h s o f a b a r above  t o form t h e o r i g i n a l  t h e end of t h e c a l i b r a t i o n  p l u g and t h e  run, the e n t i r e  be warmed up t o 1 K, s o t h a t t h e p l u g c a n  temperature  refrigerator  melt  and t h e  1 38  He  slowly  And  finally,  3  temperature, the  pressure  bled when  out i n t o the  refrigerator  the r e s e r v o i r i n the c e l l  the r e s e r v o i r  should  through  is  warming  be opened  does not b u i l d  up.  the c o l d up  to the c e l l  trap.  to so  room that  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0084970/manifest

Comment

Related Items