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An apparatus for the measurement of the specific heat of cadmium below 1° Kelvin Dunick, John E. 1963

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AN APPARATUS. FOR THE MEASUREMENT- OF THE SPECIFIC KEAX OF CADMIUM BELOW 1° KELVIN  by JOHN: E. DUNICK  A: THESIS' SUBMITTED IN PARTIAL FULFILMENT. OF THE REQUIREfrENTS: EOR THE DEGREE OF. EASTER OF; SCIENCE i n the- Department of Physics:  We accept t h i s , t h e s i s as conforming to the standard required from candidates: for< the degree of MASTER OF SCIENCE.  Members of the Department of Physics THE UNiyERSITYj OF BRITISH COLUMBIA, August;  1963  In presenting the  requirements  British  Columbia,  available mission  for  for  purposes his  for I  agree  reference  extensive  without  this  my w r i t t e n  Department  by the  Library  is  I  this  s h a l l make i t  thesis  agree for  that  that  permission.  of Columbia,.  per-  o r by  copying, or  shall  freely  scholarly  Head o f my Department  understood  of  the U n i v e r s i t y of  further  for f i n a n c i a l gain  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a . Date  in partial fulfilment  and s t u d y .  It  thesis  that.the  copying of  may be g r a n t e d  of  thesis  an advanced d e g r e e a t  representatives..  cation  this  not  be  publiallowed  ABSTRACT;  The e l e c t r o n i c s p e c i f i c heat of Cadmium has been determined by a number of independent workers; using two basic methods; magnetic and c a l o r i m e t r i c .  This thesis.  pursues, the problem by a c a l o r i m e t r i c determination using an aquadag thermometer and a thermal valve.  Production of  low temperatures: i s necessary as the t r a n s i t i o n o f o r t h i s superconductor i s about 0.56  K.  temperature  Hence, the i n t e r e s t  l i e s i n attempting to determine the heat capacity of the metal both i n the normal and superconducting  states.  The experimental method and r e s u l t s f o r s p e c i f i c heat measurements f o r other superconductors, i s ; b r i e f l y  reviewed.  The design of the c r y o s t a t i s discussed i n d e t a i l i n Chapter I I . A. rather unique method of preparing a paramagnetic s a l t p i l l i s also given.  Resistance thermometers, and determination of temp-  erature i s very important and the temperature range i s obtained by a d i a b a t i c demagnetisation. The conclusion and r e s u l t s of t h i s research p r o j e c t i s given i n Chapter I I I .  •vi-  ACKNOWLEDGMENTS  I wish to express my thanks- to Dr.. Volkoff f o r donating the use of the laboratory f a c i l i t i e s f o r the research program. I n d i v i d u a l consideration must be given to Dr.. D..V.. Osborne f o r h e l p f u l advice and to Drs. J..B. Brown and P.W. Matthews, f o r t h e i r encouragement and assistance. S p e c i a l thanks i s given to the laboratory technician, Mr. R. Weissbach, f o r h i s assistance with the t e c h n i c a l d e t a i l s of the experiment.  I also extend, my appreciation to the s t a f f of  the U n i v e r s i t y workshop f o r t h e i r t e c h n i c a l advice.  -ii-  TABLE OF CONTENTS Page ACKNOWLEDGMENTS  i i  LIST. OF TABLES  iv  LIST. OF ILLUSTRATIONS  v  ABSTRACT  vi  INTRODUCTION  1  Chapter I  RESUME OF EXPERI MENTAL. FACTS 1.  S p e c i f i c Heats o f Superconductors  ...  3  2.  Measurements of S p e c i f i c Heat of Superconductors to Determine ....  5  Theory of the L a t t i c e and .Electronic S p e c i f i c Heat at Low Temperatures ....  16  4.. Thermal Valves .............................  24  5.  27  3.  II  3  Cooling by A d i a b a t i c Demagnetisation.  DESIGN OF CRYOSTAT FOR SPECIFIC HEAT WORK.  30  1.  Cryostat and Experimental Space .....  30  2.  Preparation of Cadmium Sample .......  32  3.. Preparation of Paramagnetic S a l t P i l l  33  4.  36  Determination of Temperature:; a. A..C.. Resistance Bridge b. . S u s c e p t i b i l i t y Bridge  I I I SPECIFIC, HEAT OF CADMIUM l ; . Apparatus —Procedures 2.  43 ..............  43  Experimental Results - Conclusions ..  46.  REFERENCES  ...  -ill;-  49  LIST. OF. TABLES Facing Page  Table 1.  Atomic Heat of the Elements at Low; Temperatures.......  -iv-  4  LIST! OF ILLUSTRATIONS Figure  Facing  Page .  1;  Sample Space; and Outer Can  2.  Sample Space, S t a i n l e s s - S t e e l  30 Cage, and  Outer Can  31  3.  Vacuum System  31  4.  Cadmium Sample  32  5..  Magnet  32  6..  S a l t P i l l ivith Lead S t r i p  35  7.  Improved Bridge f o r Low Temperature Measurement.  38  8.  S u s c e p t i b i l i t y Bridge  41  9.  S u s c e p t i b i l i t y Bridge C i r c u i t  42  10.  C a l i b r a t i o n of Aquadag Thermometer ....  11.  Temperature vrs Thermal Conductivity of Lead ...  44i 47  Many research workers have determined the e l e c t r o n i c s p e c i f i c heat of Cadmium.  This i s so as Cadmium was the f i r s t  metal f o r which the t r a n s i t i o n temperature using demagnetisation techniques was discovered. In determining the t r a n s i t i o n ature the e l e c t r o n i c s p e c i f i c heat was found.  temper-  Of more i n t e r e s t ,  the e l e c t r o n i c s p e c i f i c heat can be determined c a l o r i m e t r i c a l l y from the normal s p e c i f i c heat equation i n which the l i n e a r term y i e l d s If.  Samoilov s u c c e s s f u l l y i n v e s t i g a t e d cadmium i n t h i s way.  He used an i n t e r e s t i n g f a c t that a very weak thermal coupling allows one to r a i s e the temperature only of the sample during the short heating period.  A phosphor-bronze thermometer,  calibrated  against the s u s c e p t i b i l i t y of Fe ammonium alum, was also employed. The author wishes to carry out a s i m i l a r experiment using a thermal valve to break thermal contact between the s a l t and sample, and using an aquadag thermometer to determine the temperatures involved. This t h e s i s begins with a b r i e f survey of the work done on s p e c i f i c heats of metals, mostly superconductors, i n the very low temperature region. part.  The developement i s chronological f o r the most  One section deals with the e l e c t r o n i c heat capacity and  t r a n s i t i o n temperatures of superconductors alone.  A b r i e f review  of the p r i n c i p l e s of adiabatic demagnetisation i s also presented concluding Chapter I .  -1-  Chapter I I i s a necessary d i s c u s s i o n of c r y o s t a t design f o r s p e c i f i c heat work. sample and s a l t p i l l .  S p e c i a l a t t e n t i o n i s given to preparing the The a.c. r e s i s t a n c e bridge, monitored by  a recorder, i s discussed along with a s u s c e p t i b i l i t y bridge. The f i n a l c h a p t e r , I I I , deals with the experimental  procedure  f o r determining the s p e c i f i c heat of cadmium both i n the normal and superconducting states.  As the l a r g e s t source of e r r o r i s i n  determining the heat input and the corresponding temperature t h i s subject i s also d e a l t with. the f i n a l chapter.  rise  The r e s u l t s are also found i n  CHARTER I Resume of Experimental Facts Eucken published an a r t i c l e , "Energie and Warmeinhalt", i n 1929 and since t h i s date our knowledge of the s p e c i f i c heat of s o l i d s has s t e a d i l y increased. In 1930 accurate calorimetry i n the l i q u i d helium temperature range began, using thermometric techniques of the vapor pressure of l i q u i d helium and phosphor-bronze thermometers. A c t u a l l y , Kammerlingh Onnes i n 1911 discovered superconductivity i n the metal mercury and he and Hoist attempted to measure the s p e c i f i c heat above and below the t r a n s i t i o n temperature. The s e n s i t i v e phosphor-bronze thermometer, g r e a t l y needed i n t h i s work, entered the scene i n 1931.  Keesom and Van den Ende*  were able to detect a d i s c o n t i n u i t y i n the atomic heat of t i n at the  t r a n s i t i o n temperature. A thermodynamical theory has been put  foreward, connecting l a t e n t heat, changes i n entropy and heat capacity with the magnetic threshold curve. Heat capacity measurements of several elements and a l l o y s have been performed and found to be i n excellent agreement with the threshold curves in many cases. Hence, I f , the e l e c t r o n i c s p e c i f i c heat can-be determined by magnetic or c a l o r i m e t r i c methods.  A detailed  discussion o f the theory i s given i n section 3 o f t h i s chapter. 1.  1.  iLpftalfir. Hftat. ,nf .SupfiTttnnducAnr.s.  Keesom W.H., Van den Ende J.N., Proc. Acad. Sci.. Amst.,35,143,1932  /3/  Table 1. Atomic heat of the elements at low temperatures.  The Atomic Number stands on the left, the Symbol on the right of the tield. Below these are given 0 (° K) and (boldface) y (millijoules/mole deg ). Parenthesis indicates uncertain value. For superconductors, 0 refers to the normal state and y is the best estimate from calorimetric data. 2  O  O  Group Period  1  |  Ha  nib  v„  IVb  i Vllb  VIb  VIII  i  1  1 H  Ilia  lib  B  158  Mg 406  1.8  (1.35)  19 K  20 Ca  11  Na|  4 3/Rb  ;  21  Sc  22  Ti  23 V  27S  273  (0.38)  3.34  8.83  38 Sr 39 Y  40 Zr  24 Cr j 2 5 M n  '402  26  Fe i 27 Co  467  1.54  13.8  i  5.0  1  ]  1  270  252  425  2.95  8.5  2.14 j  55 Cs 56 Ba 57* La 72 Hf 73 Ta 132 231 5.44  87 Fr 88 Ra S9**Ac i  74  j  W  ! 75 Re 76 Os  (379) ! 1.48 i  45 Rh '  i  \  i  i 28  445 5.0  41 Nb 42Mo 1 43 Tc44 Ru  6.7  7  !  77  Ni  Al 418  13  ;  (219)  -  29  Cu  339  30 Zn 308  456  j  \  7.4  ! 0.72  1  8 O 9  14 Si 658  15  P  16 S  17 CI  18 A  46 Pd ! 47 Ag48 Cd  31 Ga  Ge  33  As  34 Se  35 Br  36 Kr  51  Sb  52  53  54 Xe  32  366  0.66  49 In  50 Sn  White Gray  300  109  189  j 10.7  ! 0.66  0.71  1.81  1.82  I  i  Ir | 78 Pt j 79 Au 80 Hg ! 229 6.8  165 | 0.74  * 58—71 Lanthanide Rare Earths ** 90—103 Actinide Rare Earths  F ! 10 Ne  1.46  i i j 275 ! 225  |  He  N  C  (2000)  12  5  6  0  Vila  7  6 Diamond  5  0.226  3  Via  '•  4 Be 1160  2  Va  IVa  2  :  Li  3  lb  I i  Graphite  la  (60-90)  Te  I  212  81 Tl 82 Pb  83 Bi S4 Po  89  94.5  117  3.1  3.0  «0.08)  85 At 86 Rn  -4-  As our primary i n t e r e s t i s i n superconductors a b r i e f account w i l l now be given of a p a r t i c u l a r few.  Those i n d i s c u s s i o n  w i l l be both hard and s o f t superconductors; t i n , , aluminum, lanthanum, t h a l l i u m , vanadium, niobium, and tantalum.  Cadmium,  a s o f t superconductor, i s discussed separately. With reference to Table 1 the s p e c i f i c heats of the above metals are reviewed by Pearlmanf  The choice of Sn, AI, La, T l , V, Nb and Ta f o r  discussion a r i s e s from the f a c t that at the lowest temperatures the e l e c t r o n i c s p e c i f i c heat i n the superconducting s t a t e has: been proven to be exponential i n form rather than cubic.  In  f a c t the emperical r e l a t i o n s h i p i s  and i n addition to being emperically a p p l i c a b l e Cbrak et a l have pointed out that t h i s could be expected to be true f o r a theory i n which the l e v e l s occupied by superconducting electrons are separated by a gap from those occupied by the normal electrons.  The i d e a of an energy gap of the order/\E ~ k T  0  has been discussed f o r many years and recently i n p a r t i c u l a r by F r o h l i c h (1954) and Bardeen (1955) and Biondi, Garfunkel 1  and McCouberg ^ (1956). 5  Further support f o r the energy gap theory was. u t i l i z e d  1. 2.  Keesom P.E., Pearlman N., H. Der Physik, Vol XIV, P. 282 Corak W.S., Goodman B.B., S a t t e r t h w a i t e C.B., Wexler A.. Phy.. Rev. ,96,1442,1954 3.. F r o h l i c h Hi., Phys. Rev., 97,845,1950.. 4. Bardeen J.., Phys. Rev. 97,1724,1955. 5. B i o n d i , M.A.., Garfunkel M.P., McCouberg A.O., Phys. Rev., 101,1427; 1956. t!  -5-  by Tinkham of 3 k T  Q  (1956).  exists.  He concluded f o r lead a gap o f the order  Tinkham measured the r a t i o of power t r a n s -  mitted through t h i n f i l m s i n the normal and superconducting states.. 2.  .Measurements of S p e c i f i c Heat o f SnpercQnduQt,Q£S V> netprrnine  Y  The temperature dependence of the s p e c i f i c heat f o r a normal metal i s of the form (1.1) At low temperatures the l i n e a r , term i s predominant and }f , -4 the  e l e c t r o n i c s p e c i f i c heat term i s of the order of 10  cal/mole  2 deg . I t i s not always possible to separate the e l e c t r o n i c c o n t r i b u t i o n from the t o t a l s p e c i f i c heat with great accuracy. I t i s d e s i r a b l e to have the l a t t i c e s p e c i f i c heat term as small as p o s s i b l e and t h i s occurs, with referenctncto equation (1.1), for metals having large Debye temperatures.  However, most s o f t  superconductors which have e x c e l l e n t superconducting properties have r e l a t i v e l y small 8's. Sh (185) and A l (420) have f a i r l y high 8's and much work has been done on them., The hard superconductors, i n periods IVa and V, have the desired l a r g e r Debye temperatures but are d i f f i c u l t to obtain with i d e a l superconducting p r o p e r t i e s . One very s t r i k i n g f a c t of superconductivity i s that when changing from a normal to a superconducting phase a d i s c o n t i n u t i y 1.  Tinkham -M., Phys. Rev., 104,845,1956.  i n the s p e c i f i c heat appears.  This discontinuous jump occurs  through the t r a n s i t i o n temperature from a value o f jfT to Q  about 3#T . 0  This was f i r s t seen by Keesom and Van den Ende, Z  at Leiden, i n 1932. Shortly a f t e r Keesom and Kok measured the magnitude o f the d i s c o n t i n u i t y i n the s p e c i f i c heat at t r a n s i t i o n to be about 0.0024 cal/mole deg. Also, they noticed that no l a t e n t heat was associated with the t r a n s i t i o n . .  The same jump i n the s p e c i f i c heat was noticed  l a t e r i n t h e i r experiments with t h a l l i u m .  Again, no evidence of  l a t e n t heat during the t r a n s i t i o n was noted. Sn Before World War I I more accurate work was performed by 3 Keesom and Van Laer on t i n .  The t r a n s i t i o n temperature T i s Q  conveniently located i n the He range, T =3.73 K. 0  I f the threshold  magnetic f i e l d i s parabolic i t can be shown that at T ( A O . Xo (1.2) 2T 0  0  corresponding to the jump of the atomic heat.  The value (AC)„ lo i s obtained by extrapolation from atomic heat curves above and below T . ^  from C^C)f by Keesom and Kok i s 10 mj/mole deg^ o and from (1.2) i s 1..4 mj/mole deg . This i s lower than c a l o r i 0  1.  Keesom W.H... Van Den Ende J.N., Proc. Acad. S c i . Amst., 35,143,1932.  2.  Keesom W.B.,  3.. Keesom W.H.,  Kok J.A., Physica, 1,770,1934. Van Laer P.H., Physica, 5,193,1938.  metric value which i s to be expected i n t h i s case. 7  Keesom and Van Laer also i n v e s t i g a t e d t i n . and C /T versus  has been c a l c u l a t e d from t h e i r data where  s  C  n  and C  s  A plot of C n A  are the s p e c i f i c heats o f Sn i n the normal and super-  conducting states.  For the normal metal Keesom expressed C i n n  the usual manner G = A«T -+-yT  (1.3)  3  n  and since the s t r a i g h t l i n e representing G  passes through the  g  3 o r i g i n then C =: AT. . Hence, s  A C - C -C = (A-A')T s  3  n  (1.4)  - Jk?<L-( H dH ) c  c  4TT dT\ dT dT / I n t e g r a t i n g t h i s equation twice leads to a parabolic threshold H ^ H j 1- CTA >  curve  C  Q  2  (1.5)  0  This leads to ^  C  =  S r % J ^ ( 2-2TT DT V  H Cc r  ^ 1 d dT T //  2  ^ 4 T f3(T/T ) - l l 2^T iT r ^ T' 2 L J 2  0  C 2fT [ 3 ( T / T ) ~ l j  (1.6)  2  0  hence, £orT = T  ^ ~  Jm. S 21T T  ( A C ) 0  T  = 0  <1*7>  2  0  2 Y T  o  r  JiS T /dH \ 4ir VdT 0  Cii.8)  2  c  JT  0  From these equations we f i n d that there are several ways i n which Y, the c o e f f i c i e n t o f e l e c t r o n i c atomic heat i n the normal s t a t e can be obtained. H  c  1.  I t i s connected d i r e c t l y with V , T , and m  by (1.8), with the jump i n the atomic heat at the normal  Keesom W.H., Van Laer P.H., Physica, 5,193,1938.  0  -8-  t r a n s i t i o n point, and also with the i n i t i a l slope o f the  1 threshold curve at T  Q  by  (1.8). Daunt and Mendelssohn i n v e s t -  igated Sn as w e l l which showed that the l i n e a r term C -C n  s  is  of the r i g h t order o f magnitude to j u s t i f y i t s i n t e r p r e t a t i o n as the Fermi-Sommerfield  s p e c i f i c heat term. Z  The reader should r e f e r to a review by E i s e n s t e i n f o r a comparison between c a l o r i m e t r i c and magnetic determinations of V. He concludes; that the Y*s obtained from the threshold curve data are frequently i n good agreement with the c a l o r i m e t r i c determinations.  However, i n some cases discrepancies e x i s t with the  magnetic values usually lower than the c a l o r i m e t r i c values. S 3 Kok assumes that f o r C — AT s  t h i s implies a cubic depend-  ence f o r the superconducting e l e c t r o n i c s p e c i f i c heat.  Using  t h i s and (1.7 o r 1.6) one can w r i t e G  s =  3*T  0  (T/T )  3  0  but even i n the case o f t i n , from which data Kok o r i g i n a l l y derived these r e l a t i o n s , a d e v i a t i o n from the s t r a i g h t l i n e on the p l o t o f G /r s  vrs T  2  can be seen around T = 5. 2  The f i t o f Sn data by Keesom and Van Laer to an exponential 1  temperature dependence i s c e r t a i n l y no worse than the f i t to T except i n the immediate neighbourhood of the t r a n s i t i o n point 1. Daunt J.G., Mendelssohn K., Proc. Roy. S o c , A, 160,127,1937. 2.  E i s e n s t e i n J . , Rev. Mod. Phys.,  3.  Kok J.A., Physica,  26,277,1954.  1,1103,1934  4.. Keesom W.H., Van Laer P.H., Physica, 5,193,1938.  -9-  where there are pronounced deviations from the exponential. Corak, Goodman, Satterthwaite, Wexler^have given recent more precise measurements f o r the s p e c i f i c heat of Sn over a more extended range of temperature.  Corak et a l have revealed  that the exponential form i s correct except near T . Q  They have  given the values f o r the constants a and b to be almost the same as f o r vanadium, 9 and 1.5 r e s p e c t i v e l y , f o r the emperical formula f o r the superconducting s p e c i f i c heat as i n equation (1.0). C = s  YT  ae" o b T  0  / T  U. z Keesom and Kok i n v e s t i g a t e d A l i n the temperature range of 1 - 20°K and found Yto  be 1„46 mj/mole deg  2  calorimetrically.  A l data gives a good representation of a sum of a cubic term and a l i n e a r term f o r the s p e c i f i c heat. The value of ( A c ) observed T  r-.O  was 1.9 mj/mole deg" and t h i s corresponds by (1.2) a X o f  0.85.  This i s smaller than e i t h e r the c a l o r i m e t r i c or magnetic determination. 3 Daunt and Heer also made e l e c t r o n i c s p e c i f i c heat measurements and they i n d i c a t e d that i t i s very p l a u s i b l e to a t t r i b u t e the l i n e a r term of C -C n  g  to the Fermi-Sommerfield s p e c i f i c heat Of the  normal s t a t e . 1. 2.  Corak W.S.,  Goodman B.B., Satterthwaite C..B., Wexler A., Phys. Rev., 96,1442,1954. Keesom W.H., Kok J.A., Physica, 1, 770,1934.  3., Daunt J.G., Heer C.V.,  Phys. Rev., 76,715,1949.  -10-  i . 2 Goodman i n h i s p l o t of C /T vrs T shoivs a d i s t i n c t change g  ispresent i n the slope i n d i c a t i n g that again the e l e c t r o n i c s p e c i f i c heat i n the superconducting  s t a t e leads to an exponen-  t i a l equation of the form of (1.0), C = VT S  ae- o b T  0  / T  Goodman i n d i c a t e s , as do others i n t h i s f i e l d , that t h i s form can be expected i f there was a small energy g a p ^ E i n the energy l e v e l spectrum of superconductors atures a term of the form  e~*^^  f o r then at the lowest tempercould be:, expected.  The  constants a and b have been found f o r A l to be 6.9 and 1.28 respectively. La Below 35 K the true T  region extends to about 6 K  z '"' "  "  -  _  according to Parkinson et a l . A c a l o r i m e t r i c determination of 5 gives 6.7 raj/mole deg^ and T  0  4..37 K.  58 mj/mole d e g which corresponds 2  by (1.2).  The value of ( A O  T  is;  to the same value of V given  Lanthanum behaves as do the oabove  superconductors  with respect to the exponential fox*m f o r the superconducting e l e c t r o n i c s p e c i f i c heat, l i Further support f o r the exponential law has been produced by  1.  Goodman B.B.., Conference de Physique des Basses Temperatures,P.506.  2.  Parkinson D.H., Quarrington J.E., Proc. Phys. S o c , A,57,569,1954.  -111 Snider and N i c o l on thallium..Previous i n v e s t i g a t i o n s were made Z  by Keesom and Van den Ende and Keesom and Kok.  Keesom and Kok  were the f i r s t to measure the s i z e of the jump i n the s p e c i f i c heat at T  Q  and detected the absence o f l a t e n t heat during the  transition.  T  Q  1.3 mj/mole deg  was found to be:2.36 K.  By equation (1.2) X -  which agrees e x c e l l e n t l y with the value obtained  by the magnetic threshold f i e l d measurements.  C a l o r i m e t r i c values  which were obtained by a l e a s t squares f i t of Keesom and Kok data above T  0  i s much l a r g e r .  There appears no obvious reason  for t h i s discrepancy. V-Nb-Ta These elements are of i n t e r e s t f o r i n v e s t i g a t i o n of the thermodynamics of the phase t r a n s i t i o n from the normal to the superconducting state.  These hard superconductors have high 9's;  and T 's:which i s an advantage.  A s l i g h t disadvantage i s that T  0  Q  f o r V and Nb f a l l s between 4 - 10 K where no c o o l i n g bath i s a v a i l able.  One d i f f i c u l t y  i s that d i f f e r e n t samples give d i f f e r e n t  r e s u l t s by the same i n v e s t i g a t o r s f o r ao apparent reason.  3 Worley, Zemansky and Boorse i n v e s t i g a t e d V and Ta.  Worley  et a l observed p o s i t i v e deviations i n C/T again i n d i c a t i n g the p o s s i b i l i t y o f the exponential form f o r V.  For Ta, the data of A  Worley et a l agree with those o f Keesom and Desirant i n the normal 66 1.  Snider J.L., N i c o l J . , Phys. Rev. 105, 1242. 1957.  2.  Keesom W.H.,  3.  Worley B., Zemansky M.W.., Boorse T., Phys.. Rev., 91,1567,1953.  4.. Keesom W.H..  Kok J.A., Haag 1, 175,503,595,1934.  Desii-ant B., Physica, Haag 8,273,1941.  -12^  state.  The measurements o f Desirant and Mendelssohn g i v e values  of ( A C )  of 34 and 40 mj/mole deg at T  T o  respectively.. 2  Q  equal to 4.0 and 4.4°K  By (1.2) these correspond to ^ of 4..2 and 4.0  mj/mole deg which are lower than both the c a l o r i m e t r i c and magnetic values. 3 For V Satterthwaite  et a l d i d not report deviations i n C/T  o vrs T . However, the r e s u l t s o f Worley et a l give the emperical exponential equation with constants a and b as 9.17 and 1.5 respectively. Nb was investigated by Brown, Zemansky and Boorse, between 2-20°K. T  i s 8.9°K with # a value o f 8.5 mj/moledeg . 2  0  Although  the data needs r e v i s i o n Nb d i d support the exponential law. E l e c t r o n i c S p e c i f i c Heat - Cadmium The standard method of obtaining heat c a p a c i t i e s i s s i m i l a r to that o f Rayne.*  He used c y l i n d r i c a l samples connected to the  s a l t p i l l by copper wire which i s i n thermal contact by the vane technique.  A: manganin heater was glued to the metal using g l y p t a l .  The magnetic temperature f o r copper s u l f a t e was determined b a l l i s t ically.  The r a t i o o f amounts o f s a l t and metal was chosen i n such  a way that at about 0.5°K they had equal heat c a p a c i t i e s .  The  s p e c i f i c heat o f the s a l t was measured i n a separate experiment. P l o t t i n g C/t vrs T s t r a i g h t lines: were found f o r Cu, Ag, P t , and 1. Rayne J . , Phys. Rev., 95,1428,1954. 2.. Desirant B., Mendelssohn K., Nature, 148.316,1941. 3../Corak W.S.., Satterthwaite C.B., Phys.. Rev., 99,1660,1954. 2  -13-  others. confirming the C = A T V XT. r e l a t i o n s h i p .  From the slopes  of these l i n e s V was found to be i n reasonable agreement. 1 Samoilov determined the s p e c i f i c heat of cadmium i n the following way.. The sample was of c y l i n d r i c a l shape containing a heater, H| , glued i n a h e l i c a l groove on the surface.  The  cadmium was connected to the s a l t p i l l , Fe ammonium alum, by a copper wire, Wj , 0.1 mm d i a . 30 cm long.  The dimensions are  Chosen such that a f t e r demagnetisation i t took about an hour f o r the metal to cool to the temperature of the p i l l .  The advan-  tage i s that f o r a short heating period the heat flow to the s a l t was n e g l i g i b l e  so. that the heat capacity o f the cadmium alone  was measured.  In other words the r e s u l t i n g thermal coupling was  so weak that the heat supplied by the heater during a short period r a i s e d the temperature only of the cadmium.  Hence, i t gives the  heat capacity d i r e c t l y which i s an advantage over Rayne*s method. Some d i f f i c u l t i e s were encountered above 0.5°K since here, the s p e c i f i c heat of the s a l t becomes rather small and helium desorpt i o n from the s a l t begins, so that the temperature r i s e due to heat leak increases appreciably.  One method around t h i s i s tO  connect a second wire W^, s i m i l a r to W^, to a heater 11^. The s a l t was kept at about o.l°K and the temperature of the cadmium was kept at a higher e q u i l i b r i u m temperature by generating a constant 1.  Samoilov B..N.., Doklady Akad. Nauk, 'USSR, 81,791,1951.  -14f-  heat flow through  and V^.  The temperatures involved were measured with a phosphorbronze thermometer which was c a l i b r a t e d against the s u s c e p t i b i l i t y of Fe ammonium alum, the l a t t e r being determined ically.  ballist-  Supply wires to thermometer and heaters were of tinned  constantan.  Copper vanes, i n s e r t e d i n the wires, were embedded  i n the s a l t i n order to decrease the heat leak to the cadmium. The vacuum of the calorimeter was improved with an adsorption pump. The r e s u l t s o f Samoilov's experiments were very good. I t was found that 10 3 C = 1.942 x 10 ( T/300) + n  3 7.11 x 10 T (er<  Accuracy reached i n the superconducting state was small due to the small temperature region i n which measurements could be made, T = 0.56 °K -C  and to the i r r e g u l a r i t i e s i n the phosphor-bronze  thermometer below 0.4°K.  I t also appeared t h a t . C ^ T  but the  p o s s i b i l i t y of a small l i n e a r term was not excluded. The f i r s t metal f o r which T„ ivas discovered with the a i d of 1  demagnetisation technique was Cd. K u r t i and Simon performed the f i r s t experiments using a compressed mixture of a paramagnetic s a l t and cadmium metal.. The t r a n s i t i o n temperature i n zero f i e l d was 0.54°K and the slope of t h i s t r a n s i t i o n curve at T 1.  c  was 100  K u r t i N., Simon F. Nature 133,907,1934. K u r t i N., Simon F., Proc. Roy. Soc. Lond., 151,610,1935 t  -15-  oersted/deg.  The s u s c e p t i b i l i t y of the p i l l consisted of a para-  magnetic term due to the s a l t and a diamagnetic term due to the superconducting cadmium.  The t r a n s i t i o n curve can be derived  from observation of the.heating curves of the p i l L f o r various values of magnetic f i r l d strength.  A second method based on  Mendoza's vane technique has the advantage that a f i e l d can be applied to the metal without i n f l u e n c i n g the temperature of the salt. 1 Smith and Daunt found by the same method a T  c  o equal to 0.602 K.  The t r a n s i t i o n curve could be represented by a parabola H-H  0  [l  - (T/T ) ] 2  c  and H , the c r i t i c a l f i e l d at absolute zero, was c a l c u l a t e d to be Q  33.8 oersted and a slope at T„ of 112 oersted/deg., I f the above equation i s v a l i d then the s p e c i f i c heat of the electrons i n the normal state, assuming a r e v e r s i b l e t r a n s i t i o n , obeys C 3  and0^=6.44 x 10  =^T=  V/dH\ 8ir\dT /T-T  .T c  2  erg/mole deg .  S t e e l e and Hein, applying the same method, i n v e s t i g a t e d small Cd grains of s p h e r i c a l shape.  They found T ~ 0.65°K and c  the slope of the t r a n s i t i o n curve increased as the p a r t i c l e s i z e decreased. T  1. 2. 3.  Using the vane technique Goodman and Mendoza found  to be 0.560°K, H - 28.8 oersted, slope at T_- 103 oersted/deg  Smith T.S., Daunt J.G., Phys. Rev., 88,1172,1952. S t e e l e H..C, Hein R.A., Pys. Rev., 87,708,1952. Goodman B.B., Mendoza E., Phi I.Mag. 42,594,1951.  -16-  and X~  5.35 x 10  erg/mole deg .  Samoxlov also t r i e d the vane technique but found that 2f was 20% lower than h i s previous c a l o r i m e t r i c determinations. He suggested that the d i f f e r e n c e might be due to a small l i n e a r term i n the s p e c i f i c heat i n the superconducting state.  Clement  showed that the discrepancy may also be solved by assuming a small term proportional to T curve. at T = c  3.  i n the magnetic t r a n s i t i o n  Samoilov's r e s u l t s were. T - 0.547°K, H c c  104 oersted/deg and if r 5.56 x 10  0  o  28.4, slope p  erg/mole deg .  Theory of the L a t t i c e and E l e c t r o n i c S p e c i f i c Heat of a formal Metal at Low Temperatures The determination of s p e c i f i c heat and i t s v a r i a t i o n at  low temperatures has been a powerful t o o l i n the study of the s o l i d state.  In the c l a s s i c a l theory, each element of a  l a t t i c e had a thermal energy 6 x J£ kT ( k i n e t i c •+• p o t e n t i a l ) , y i e l d i n g a t o t a l energy per mole E = 3NkT = 3RT  (1.30)  and therefore a constant s p e c i f i c heat C = y  dE/dT ~ 3 R z 6 cal/raole deg  For most elements, reasonable agreement with experiment at room temperature was shown by the emperical law of Dulong and P e t i t , although a notable exception was the case of diamond. 2 Einstein  1. 2.  ftfodel  The recognition by E i n s t e i n  of the relevance of  Samoilov B.N., Doklady Akad. Nauk, USSR, 81,791,1951. E i n s t e i n A., Ann. Phys, Lpz., 22,180,800,1907.  -17-  the quantization of energy levels in a simple (Plandtd oscillator given by, ignoring the zero point energy,e=nhv  showed that  this classical result could only be expected to hold for temperatures not small compared with a characteristic temperature of the lattice, ©p, defined by 9 r £  hv/k where h' and k issthe  Elan&fcand Boltzmann constant respectively..  The lattice was  simulated by an aggregation of N similar, independent, o s c i l l ators of frequency v and Einstein showed:.  C  -  - 1  £  1  2 C - 3R  For T » , ©  E  while i f T  <  9 f e / E  (1.31a)  }  we have E r 3RT, and C ~ 3R in agreement with (1.30), v  then E = 3RT. ( 9 /T. ^ E  E  )  C ^ 3 R ( © /T ) <^'^ 2  v  E  E  (1.52a) (1.32)  thus the specific heat falls rapidly to zero as T diminishes. This rtieroretical deduction added great weight to Nernst's Law, the Third Law of Thermodynamics, from which a basic deduction in its present formulation is the vanishing of the specific heat at absolute zero. It was soon recognized that this Einstein model was too crude an approximation to reproduce the very low temperature specific heat sufficiently accurately.  In particular the very  -18-  rapid decay,  f  f  o  r  x<<: © a r i s e s because a minimum energy, hv,  i s necessary to e x c i t e the lowest mode of the Planck o s c i l l a t o r and the p r o b a b i l i t y diminishes very r a p i d l y as the temperature i s lowered.  Nernst and Lindemann^proposed a g e n e r a l i z a t i o n o f  E i n s t e i n ' s formula (1.33)  with a corresponding expression f o r C . v  This y i e l d e d much  better agreement with experiment down to temperatures o f 20°K. 1 The Nernst-Lindemann formula i s regarded today as a very u s e f u l approximate expression. In h i s o r i g i n a l paper E i n s t e i n i d e n t i f i e d the frequency v with a sharp resonance absorption i n the i n f r a - r e d , but was l a t e r led to consider the general connection with the e l a s t i c v i b r a t i o n s of the c r y s t a l .  Thus, other things being equal a high 0 would  imply strong e l a s t i c binding, that i s a more r i g i d s o l d i . conclusion i s of general v a l i d i t y .  This  E i n s t e i n himself also recog-  nized that the coupling between neighbouring atoms would genera l l y be so strong that the assumption of a monochromatic v i b r a t i o n a l spectrum could only be regarded as a rough approximation.  1.  Nernst W., Lindemann F.A., Phys. Z. 11,609,1910.  1  The Debve Jv|odel Debye's approach was to consider the coupled v i b r a t i o n a l modes of the atomic l a t t i c e , some 3N i n a l l , as forming a continuum of e l a s t i c v i b r a t i o n s running from the longest ivavelengths (v=->0) to a:i short wavelength-limit of the order of the l a t t i c e s t r u c t u r e .  This model leads d i r e c t l y tO  a frequency density d i s t r i b u t i o n dn = 4tt/C v d v Z  2  where C i s the v e l o c i t y of e l a s t i c waves i n the c r y s t a l assumed independent of v and i s o t r o p i c .  Associated with each proper  v i b r a t i o n we have the energy of a Plank o s c i l l a t o r and thus  -V E - 4TTV \  hv°dv  that i s  -  E  3RT.  where a c h a r a c t e r i s t i c Debye temperature, 0 , i s now defined by D  0  D  ~ hv /k. m  At high temperatures ive have E - 3RT again i n agreement with the c l a s s i c a l treatment, but at low temperatures  and the s p e c i f i c heat  1.  3  C ^ 464 (T/© ) y  D  cal/moledeg.  Debye P., Ann. Phys., Lpz. 39,789,1912  -20-  1  Almost simultaneously with Debye's work, Born and v. Karman  discussed the complete dynamical treatment of the proper v i b r a t ions of a l a t t i c e s t a r t i n g from the atomic force constants. B a s i c a l l y , the problem was not new.  Newton f i r s t attacked the  analysis of the v i b r a t i o n of a one-dimensional  l a t t i c e when  considering the v e l o c i t y of sound, and K e l v i n was the f i r s t to consider a d i a t o n i c l a t t i c e of large and small coupled masses. This then y i e l d s two d i s t i n c t v i b r a t i o n a l modes, the acoustic and o p t i c a l  branches.  In t h i s approach the v e l o c i t y of propagation i s no longer constant nor n e c e s s a r i l y i s o t r o p i c and the simple ^ r i f e a t i o n a l frequency density  i s not obtained.  The problem of analysing  the true spectrum f o r a p a r t i c u l a r c r y s t a l i s very complex and d i f f i c u l t to generalize; consequently Debye's much simpler and very elegant approximation has been widely applied to the analys i s and comparison of experimental data. In the Debye theory, ©^ i s of course a constant parameter by d e f i n i t i o n ; however i n presenting experimental data i t has become conventional to d e r i v e values at various  temperatures  for an e f f e c t i v e ©^ necessary to force agreement with the Debye theory and to p l o t thus a curve of ©  D  as a function of  temperature.  I f a substance obeyed the Debye theory p r e c i s e l y then of course ©  D,  1.  would be constant.  Born M.,  v. Karman,  I f t h i s i s not the case w i t h i n e x p e r i -  Phys.. Z. 13,297,1912;: 14,15,1913.  imental error, strictly one may only say that the Debye theory is inapplicable, but in fact this approach is of considerable value when certain types of variation common to a number of substances can be recognized. Electronic Specific Heat  - In the case of the electronic contribution  to the specific heat in metals this term dominates in the temperature range below 1°K. It w i l l be remembered that on the classical theory the thermal status 01 the free or conduction electrons was very unsatisfactory; on the one hand, the concept on an electron gas in the Drude-Lorentz theory of thermal and electrical conductivity seemed very appropriate while, on the other, such a classical gas should have contributed an additional specific heat 3/2 nR cal/gn . atom where n is the number of free electrons per atom. To 1  explain the magnitude of the conductivities a value of  n2rl  was  necessary for simple metals, while no corresponding specific heat was observed. Modern quantum theory, in particular the application of the Pauli exclusion principle in Fermi-Dirac statistics,  showed  however, that except at very high temperatures only a very small fraction of the conduction electrons (those on the surface of the Fermi sphere) can interchange thermal energy with the lattice; consequently at normal temperatures, the electronic specific heat is negligible and the electron gas is said to be degenerate.  f.Iore  -22l generally, however, Sommerfeld has shown that the free electrons should exhibit a specific heat linear in T at low temperatures; this consequently should become significant at sufficiently low temperatures where the lattice contribution is falling roughly 3 as T .  The actual magnitude of the linear term will clearly  depend on the density of electron states near the top of the Fermi distribution and information about the whole energy-band can only be obtained i f measurements can also be make at sufficiently high temperatures and for a l l the electrons to contribute essentially.  This depends of course on the actual degeneracy  temperature and i f this can be approached, so that the electron gas tends to become Maxwellian, then an electronic specific heat of the order of 3/2R should manifest i t s e l f in addition to the classical lattice heat.  This increase is observable in some  metals, particularly the transition elements, but in a simple metal the degeneracy temperature is too high. It is clear that, to separate out the electronic heat at low temperatures, the lattice heat must be known accurately and i t has been customary, for the purpose, to express the specific heat in the form C v  464 (T/9) 4- y'T 3  (1.35)  where the validity of the Debye law for the lattice heat is implicit in the second term. Thus: 1.  Sommerfeld A . , Z.. Phys., 47,1,1923.  -23-  Keesom and Clark found f o r n i c k e l i n the range 1-10°K, C  - 464 (T/413) -*- 1.74xl0" T 3  3  Kok and Keesom f o r platinum and copper between 1.2 and 20 K, C v  464 (T/233) + 1.6xl0* T 3  3  _ 464 (T/335) + 1.78xl0~ T 3  c  4  i  Keesom and van Laer found f o r t i n between 1 and 3 K, C y  464 (T/185) + 4X10" T 3  4  fDuyckaerts f o r cobalt between 2 and 18 K f i n d s , 464 (T/443) + 1.2xl0~ T 8  3  * o Keesom and Kurrelmeyer f o r i r o n between 1.1 and 20.4 K, C - 464 (T/462) + 1.2xl0~ T 3  3  v  ^ o Samoilov f o r cadmium between o.4 and 1.1 K, C  -z 464 (T/300) -V 3  v  7.11xl0" T 4  In most cases, i n f a c t , the experiments have been made at a temperature s u f f i c i e n t l y low to assume reasonably that the Debye continuum has been reached. gas theory predicts Y = 1 0 justifiable,  4  The Sommerfeld f r e e electron  and i t appears therefore quite  to conclude from t h i s data, i n general agreement  with theory, that the density o f states f o r c e r t a i n bands i s much higher i n the t r a n s i t i o n metals than f o r a simple metal l i k e Cu.  1. 2. 3. 4. 5. 6.  Keesom W.U., Clark C.W., Physica, 2,513,1935. Kok J.A., Keesom W.H., Physica, 3,1035,1936. Keesom W.H., van Laer P.H., Physica, 5, 193,1938. Duyckaerts, G., Physica, 6,401,1939. Keesom W.H., Kurrelmeyer 3., Physica, 6,817,1939. Saraoilov 3.N., Doklady Akad. Nauk., USSR, 86,281,1951.  -244. Xhermaj Valve? It is often desirable when cooling by demagnetisation to break the thermal link between salt and sample. suggested by F. Simon.  This was f i r s t  Hence, thermal valves or switches are  very useful for specific heat work as i t allows one to determine the specific heat of the sample directly. 2  Mendoza was the first to construct a practical thermal valve. A very thin copper sheet was actually broken by force to break the heat contact.  Using the fact that the thermal conductivity  of liquid helium becomes poor at lower temperatures, Kurti designed yet another switch.  He connected the salt and sample by a narrow  tube, containing a moveable copper rod, f i l l e d with liquid helium. Hence, heat transfer is good along rod when rod is in proper position.  Otherwise, the heat transfer through the liquid helium  is poor. The fact that the heat conductivity of solid helium is much worse than that of liquid helium can also be employed as a basis J for a thermal valve.  Wilkinson and Wilks increased the pressure in  their cryostat to solidify the helium thereby breaking the heat contact.  Upon melting, the heat contact was restored.  Superconductors by far make the best thermal valves.  The  metal is kept in the normal state by the application of an external 1. 2. 3.  Wilkinson K.R., Wilks J . , Proc. Phys. Soc. Lond., A64,89(1951) Mendoza E . , Ceremonies Langevin-Perrin, P. 67 Paris 1948 Simon F . , Reunion d'etudes sur le magnetisme, Stratsbourg.P. 1(1939)  -25magnetic f i e l d .  Hence, thermal linkage i s very good.  With the  valve below i t s t r a n s i t i o n temperature the external f i e l d i s removed and the valve goes i n t o the superconducting s t a t e p r o v i d i n g a much lower thermal c o n d u c t i v i t y .  The t r a n s i t i o n  temperature  should be w e l l above 1 K and care should be taken that no f l u x i s trapped i n the superconducting state.  A high degree of p u r i t y  i s also e s s e n t i a l . Several independent authors proposed a valve based on the above p r i n c i p l e ; Gorter, Heer and Daunt, and Mendelssohn and Olsen. Heer and Daunt demonstrated  the p r a c t i c a l a p p l i c a t i o n o f the switch  using a tantalum wire (56 cm long, 0*017 era dia.) connecting the s a l t p i l l to the l i q u i d helium bath.  S t e e l e and Hein used a super-  conducting thermal valve, replacing exchange gas, i n t h e i r e x p e r i mentation with superconducting cadmium p a r t i c l e s .  DeVries and  sr  Daunt employed a thermal switch f o r determining the s p e c i f i c heat 3 of He . A f t e r the demagnetisation the heat contact between the s a l t and helium container vras broken allowing the s p e c i f i c heat of the l i q u i d to be measured separately. Cascade demagnetisation i s another a p p l i c a t i o n f o r thermal switches. This has been c a r r i e d out using lead by the following workers; Darby, Hatton, R o l l i n , <<  7  Seymour, S i l s b e e and C r o f t , and Falkner, Hatton and Seymour. 1. Gorter C.J., Ceremonies Langevin-Perrin, P. 76, P a r i s 1948. 2. Heer C.V., Daunt J.G., Phys. Rev.., 76,854,1949. 3. Mendelssohn K„, Olsen J.L., Proc. Roy. Soc. Lond., A63.2.1950. 4. S t e e l e M.C., Hein R.A., Phys. Rev., 87,908,1952. 5. DeVries G... Daunt J.G., Phys. Rev., 93,631,1954. 6. Darby J . , Hatton J . , R o l l i n B„, Seymour E., S i l s b e e H,, Proc. Phys* Soc. Lond*, A64.861,1951. 7. C r o f t A., Faulkner E., Hatton J . , Seymour E., Phil.Mag., 44,289,1953  -26Heer, Barnes, and Daunt give the f o l l o w i n g f i g u r e s f o r pure a  coldworked lead below 1 K, ivhich i s adequate f o r design purposes: K (normal) = 4TW'-cm'deg* K (super) = 0.08 T W: -cm deg 5  The r a t i o of the thermal r e s i s t a n c e of a. wire i n the two states o  a  i s therefore 500:1 at. 0.3 K and 5000:1 at 0.1 K.  To-open and  c l o s e the valve, an external f i e l d of 800-850 gauss i s required. z The f i e l d i s u s u a l l y provided by an external solenoid.  Goodman  used a; superconducting solenoid, niobium, f o r h i s external f i e l d . I t has a c r i t i c a l f i e l d much greater than that.of lead and could produce a f i e l d of 2000 gauss with no power dissipation..  1. Heer C..V.., Barnes T.., Daunt J.G., Rev., s e t . Instrum, 25,1088 2„ Goodman B'.B., Conference de. Physique des Basses Temperatures, P. 506.  -27-  5. Adf.qbi,atic CpQlinq I f U represents the i n t e r n a l energy, T the absolute temperature, S the entropy, H the applied magnetic f i e l d , and E i s the magnetisation of a system then, from the second law of thermodynamics,  For  an isothermal change o f f i e l d TdS = T/^JJ \ U"T / H  For  (reversible) dH  a f i n i t e change o f f i e l d from Hj to Hf, the quantity of heat  Q" may be given by  With 8Lconstant f i e l d , i t i s known that an increase i n temperature of a paramagnetic s o l i d causes a decrease i n magnetisation.. i s negative and heat i s r e j e c t e d when the f i e l d i s increased and i s absorbed when the f i e l d i s decreased isothermally. On the other hand, i f we change: the f i e l d a d i a b a t i c a l l y dH  whence  dH  -28-  Note that i f T and Cg can be assumed to be constant ( i t is almost so at room temperature for most paramagnetic substances)  and so a decrease in temperature w i l l occur i f the field is: decreased adiabatically. The above equations gave rise to the so called magnetocaloric effect and led to the currently used methods of cooling substances to temperatures below, one degree Kelvin.  Debye and Giauque were the  f i r s t to suggest magnetic cooling of paramagnetic salts..  The latter  actually f i r s t performed such cooling experiments in America. The procedure is a fairly simple one in principle.  A para-  magnetic salt, such as Cr K alum, whose magnetic ion&; are sufficiently far apart that Curie's law is valid, is suspended in a vessel containing exchange gas (helium) at the lowest temperature available with a liquid helium bath.  Then a magnetic field is turned on and  after the temperature equilibrium is;; re-established,, the exchange gas:, is pumped out leaving the salt thermally insulated.  Adiabatic  demagnetisation is accomplished either by sivitching off the magnet and rolling i t away from the specimen or the specimen i t s e l f is removed from the poles of the magnet after the current has been cut off.  The next step c o n s i s t s i n a determination of the temperature of the s a l t p i l l .  F o r t h i s purpose, the magnetic s u s c e p t i b i l i t y  i s f i r s t determined f o r f i v e or s i x temperatures i n the known tempei-ature range (as determined by vapour pressure measurements) so that the Curie-Weiss law i s determined accurately.  A p l o t of  the  r e c i p r o c a l of galvanometer d e f l e c t i o n per u n i t of current i n  the  primary of the measuring coiils against (T -&) determines av  s t r a i g h t l i n e whose extrapolation to low temperatures i s boldly c a r r i e d out.  (©is a constant dependent on the c h a r a c t e r i s t i c s  of the substance under c o n s i d e r a t i o n ) .  A' new temperature ( T ) ,  c a l l e d the magnetic temperature i s defined as:. Curie's constant suscepti bi l i ty  ~  In the region where Curie's law holds, T  £2 I.Y i s the r e a l K e l v i n  temperature whereas i n the region around absolute zero, T. i s expected to d i f f e r from T absolute. I n order to determine T from T  , one may use the r e l a t i o n  The p l o t of S vs T can be obtained from the i n i t i a l conditionswhere a known magnetic f i e l d has changed S by a known amount. :  F<*>  S C 0 R A  -  i  Secondary C o i l Cage Outer Can Radiation Trap Aquadag Resistor  SAI.3PLE SPACE ATI) OUTER CAN  CdP Cu— W -  Cadmium Sample Pill Copper B r a i d Wood's Metal J o i n t  CHAPTER I I Design o f Cryostat f o r S p e c i f i c Heat Work 1.  Cryostat and experimental  space.  The c r y o s t a t i s not u n l i k e many that are used f o r demagneti s a t i o n work.. Two glass dewars, an inner and an outer, are e a s i l y assembled c o n c e n t r i c a l l y about the experimental  space.  The dewars are s i l v e r e d except f o r a small s t r i p running the length o f the dewars on both s i d e s . This enables"~one to see the l e v e l of both the l i q u i d nitrogen and l i q u i d helium under experimental conditions. The dewar f l a s k s also have long t a i l s such that a large electromagnet can be r o l l e d i n t o p o s i t i o n . The t a i l s of the dewars, the inner one encumbering the pararmagnetic s a l t p i l l , are e x a c t l y aligned between the poles of the magnet. A s t a t i o n a r y glass vacuum system with o i l and mercury manometers and a P h i l l i p ' s pressure gauge i s an i n t e g r a l part of the c r y o s t a t . The low vacuum s e c t i o n i s obtained by means of a backing pump.  This o f f e r s a pressure of about 0.05 mm.  of Hg to the mercury d i f f u s i o n pump.  A large backing volume,  a; 5 l i t r e r e s e r v o i r , was also i n the backing system so that the rotary pump could be turned o f f when necessary.  The d i f f -  -6 usion purap can produce a pressure of about 10 the experimental space.  mm. of Hg i n  This i s necessary so that the exchange  gas, i n t h i s case helium, can be removed during the demagnetisation process. -30-  SAITLE TUDE  QUIET, CA;:  CAGE a / a - O.D.)  (5/C* German-Silver)  (Crass)  urass  Slits for Support Pins  Frinary Coil  Leads To Sample  Wood's Llctal Joint  Cadniur.1 Sample Space  Secondary Coil  Brass Plug  Copper Draio  Holes f o r Supporting Threads  Primary  Secondary Magnetic Salt P i l l Space  "aciatiou Trap  VJood's iietal ^ Solder Joint for Outer Can Support for Cage  (not drawn to scale)  Screw for Adjusting Tension in Threads  Coil  VACUUM SYSTEM  To Siphon  ^  ^  To Sample Tube  Discharge Tube  Reservoir  Out  <"  Rotary Pump  M : - nanometer  Ha 120"cm  Oil 100 cm  -31  A' mercury and an o i l monoraeter are provided i n order to determine the temperature o f the l i q u i d helium using the vaporpressure technique.  By pumping on the helium one can lower the O  o  temperature from 4.2 K to about 1.3 K. This affords a good i n i t i a l temperature with which to begin an adiabatic demagnetisation.  A. large capacity Kinney mechanical pump i s used to  pump on the helium bath. Also a s u s c e p t i b i l i t y bridge i s a v a i l a b l e to determine the temperature o f the s a l t p i l l b a l l i s t i c a l l y .  Primary and secondary  c o i l s are wound on the can, containing the sample and s a l t . The experimental space i s the region which contains the cadmium sample and the paramagnetic s a l t .  A long German-silver  tube, connecting the high vacuum side o f the mercury  diffusion  pump to the sample space, extends i n t o the bath o f l i q u i d helium. A Wood's metal solder j o i n t vacuum seals a; brass can to the tube. I n s i d e the can i s a s t a i n l e s s cadmium and s a l t .  s t e e l cage which supports the  Also, the leads are taken up the german-silver  tube and out to the r e s i s t a n c e bridge through a wax s e a l .  The  leads, #32 B.fiS.. constantan, are thermally anchored to the cage with  Araldite. The cadmium and s a l t are suspended i n the cage by cotton  fibres. the cage.  Care must be taken that these substances do not touch To insure t h i s the f i b r e s were tightened by turning  a..screw at the base o f the cage.  This tends to keep the suspen-  CADMUf.: SAiiPLE (mass - 55 50G grains) o  Constantan Heater (araldite) Cotton Thread' for Support  3ase for Aquadag Coating (Nail Varnish)  -Insulated Copper Lead for Aquadag Thermometer' (insulation off beneath aquadag)  Aquadag <r Insulated Copper Lead  ( Scale: twice actual size )  MAGNET  sion c e n t r a l l y located. An i r o n core, water-cooled electromagnet with adjustable gap and interchangeable pole pieces was used i n t h i s  experiment.  The magnet was operated at 160 v o l t s and 200 amps, which provided a f i e l d of 21 kilogauss. The 2 ton magnet i s e a s i l y r o l l e d on tracks i n t o p o s i t i o n . 2  >  Preparation of Cadmium Sample The sample of cadmium, f i v e nines pure, was obtained from  COKErCO through our metallurgy department.  I t s masS; i s 55.508  grams.. The mass was determined before and a f t e r adding the heater, aquadag thermometer, and bonding agents so that estimates, of the heat c a p a c i t i e s of these substances could be given.  This  i s important as i t has been shown by Parkinson and Quarrington*" that the heat capacity per gram of A r a l d i t e and Wood's metal o  are both f a r greater than that f o r copper between 2; -20 K.  Thus,  even small amounts of these cements and solders used calorimetry c o n t r i b u t e appreciably to i t s heat capacity and must not be neglected. The heater i s of #32 B.GS.  constantan wire.. Some ten turns  were wound thouroughly about one end of the c y l i n d r i c a l cadmium sample, length 2  d i a . 1/2 , and glued with A r a l d i t e .  Towards  the other end, on the surface, two dabs of n a i l varnish were applied one about a centimeter above the other. 1.  Parkinson, D.H.,  Two  turns of  Quarrington, J.E., Proc. Phys.. Soc,A57,569,1954  -33-  i n s u l a t e d constantan wire were placed p a r a l l e l to each other and running over the n a i l varnish.  Each wire was bared a l i t t l e  over the n a i l varnish so that a t h i n s t r i p of aquadag could be painted between them.  Hence, the two turns of wire acted as  leads with a carbon-suspension r e s i s t o r between them.  Finally  a t h i n coat of varnish was; painted over the aquadag to preserve i t from f l a k i n g o f f . The base of the cadmium was tinned with Wood's metal so that a small lead s t r i p , a superconducting thermal valve, could e a s i l y be attached to the cadmium between i t and the s a l t p i l l . 3.  Preparation pf q P a r ^ g q e t A c S a U  PjU  A very i n t e r e s t i n g and useful method of preparing a s a l t p i l l was suggested to the author by Br. P. Matthews..  The  r e s u l t i n g thermal contact i s nearly 10 times that of a compressed pill. About 65 grams of chromium potassium alum was ground i n t o i/ II  a very f i n e powder.  Two p l a t e glass sections (18 x 6 ) had t h e i r  surfaces roughened with s t e e l wool.. By p l a c i n g small amounts of alum between these plates^ and passing the upper p l a t e over the s t a t i o n a r y lower p l a t e , i n a c i r c u l a r motion, produces, a very f i n e powder indeed.  The g r a i n s i z e very nearly resembles that of f l o u r .  About 80 grams of Apiezon o i l i s added to the powdered s a l t i n a beaker and thouroughly s t i r r e d .  A very f i n e suspension of s a l t  -34-  i n o i l i s desired. A. mixture, a, thick l i q u i d , of 5 grams o f o i l to 4 grams of s a l t i s produced.  This l i q u i d i s a s l u r y .  A s t a i n l e s s s t e e l tube ( 5/8" OD, length 21/2" ) was; chosen to be the p i l l container.  Copper wires embedded i n the  s a l t are necessary f o r thermal contact.  A d e s i r a b l e r a t i o of  the area of copper wire to the area df the tube i s of 5-10%. A r a t i o s o f 7% was achieved by 1250 wires ( *37 B.SS.) . A c t u a l l y 1250 turns of t h i s copper xvire was wound on a c y l i n d r i c a l mandrel ( length 8"'dia. 13/4" ).. The c y l i n d r i c a l solenoid of wire was then cut h o r i z o n t a l l y along the solenoid g i v i n g 1250 wires.  As the ends were taped the wires could be r o l l e d up  t i g h t l y forming a c y l i n d e r of 1250 wires some 6 inches long. The ends were sheared to a convenient length and one end o f the r o l l was put i n t o a s o l i d copper cap, crimped, and soldered i n that p o s i t i o n .  This cap was l a t e r tinned with Woods metal and  was the base f o r thermal contact to the salt.. The bundle ofvstire i s then placed v e r t i c a l l y i n s i d e the s t a i n l e s s - s t e e l tube.. One end of the tube i s f i t t e d with a plug containing a threaded hole and a glass f i l t e r . d i a . and the glass f i l t e r 5/16"' d i a . .  The hole i s 3/32" :  The purpose of the threaded  hole i s to receive the syringe which i s used to f i l l the tube  SALT PILL WITH LEAD STRIl  Lead Strip (tliex-r.ial valve) Wood's Metal Joint  Copper Post H  f%$0Copper wires soldered to Conner Post  5/C Steel Tube (length 3") Cotton Thread for Support  /i8flS>Copper Wires inside Tube Tube Contains 14.2 grans (potassium chrome alum) f i l l i n g 12+5% of available space  Brass Plug (not drawn to scale)  -35-  with the slury.  The glass f i l t e r , a small circular one cut from  a larger one, is designed to pass the o i l from the slury by pumping but to leave the salt particles behind. The tube is now f i l l e d from the bottom up using a syringe. The slury does not tend to flow easily and hence is forced in from the bottom in order to penetrate: the mesh of \»jires. * It also helps to tap the tube while f i l l i n g . .  When f u l l the syringe  is removed and a threaded plug is inserted into the now vacant hole.  Using a rotary pump one pumps on the tube, through the  f i l t e r , and the o i l is extracted and collected in a glass tube.. While pumping the level of the slury drops slightly indicating that as the o i l is extracting and the particles of salt are being compressed onto the copper wires.  A l i t t l e slury is now  added to the open top each time the level drops.  After 21/2  hours the level tends to remain stationary and coagulates. Pumping then ceases and the base plug is removed and is replaced by a similar one in size but i t is a solid one. glued into place with Araldite.  This plug is  When removing the f i r s t plug  one sees that heavy packing has taken place in the salt particles.. This heavy packing about the copper vane of wires is responsible for the good thermal contact. The mass of the extracted o i l a n d unused slury is then determined.  This allows one to determine the mass and volume  -36-  of s a l t used with reference to the volume of free space a v a i l able between the copper wires and s t a i n l e s s - s t e e l tube. t h i s a f i g u r e f o r the packing f r a c t i o n i s found.  From  About 14.2  grams of s a l t f i l l e d 12% of the a v a i l a b l e space and t h i s i s considered to be a good f i g u r e . 4.. Determination, ,qf Teqpeyatur.e- A.C. Resistance Bridge r  A 33 cps r e s i s t a n c e thermometer bridge, s u i t a b l e f o r precise temperature measurements i n the l i q u i d helium range, has been designed as a completely self-contained u n i t .  The  a m p l i f i e r has a gain of 120 db, band width of 0.3 cps, and input impedance of 10k ohms. With a power d i s s i p a t i o n of —8 2xlO~ watts i n the thermometer,  r e s i s t a n c e changes of 0.1  ohm can be detected. For a t y p i c a l r e s i s t a n c e thermometer -6 t h i s corresponds to a temperature change of 4x10  0  K at 2K.  Other features include high r e j e c t i o n of l i n e frequency pickup, short recovery time a f t e r saturation, and a combination gain band-width c o n t r o l which shortens the response time during preliminary operations. This c i r c u i t was: designed by Blake, 1 Chase and Maxwell and the reader i s r e f f e r e d to t h i s paper f o r the c i r c u i t diagram. Carbon r e s i s t a n c e thermometers provide one of the most convenient and accurate methods of measuring small, temperature  %  changes at low temperatures. 1.  Blake C, Chase C.E.,  The authors used a 1/2 watt  Maxwell.!E.., Rev.. S c i . I n s t r . , 29,715(1958)  2.. Clement J.E., Quinnell.E.H., Rev.. S c i . Instr..,, 23, 213(1952)  -37-  carbon r e s i s t o r of room-temperature r e s i s t a n c e of 100 ohms. Near 2K the r e s i s t a n c e i s of the order of 15000 to 20000 ohms. 4 The r e s i s t o r has a temperature c o e f f i c i e n t of about -3x10 ohms/deg. at t h i s temperature.  Such thermometers must be  i n d i v i d u a l l y c a l i b r a t e d , during every run, but t h i s disadvantage i s o f f s e t by t h e i r high r e s o l u t i o n and s i m p l i c i t y of operation.  For greatest p r e c i s i o n these thermometers must be  operated i n a s u i t a b l e bridge c i r c u i t , and the power d i s s i p a t i o n i n them must be kept low. The o s c i l l a t o r i s of conventional design and i t s . o u t p u t i s adjusted to 0.4 v o l t s rms to provide a current of about 1 ua i n the thermometer.  The l i n e a r i t y c o n t r o l adjusts the  amount of feedback to minimize d i s t o r t i o n of the output wave form.  The components of the bridge are shielded from the  o s c i l l a t o r and a m p l i f i e r to minimize pickup and heating e f f e c t s . The f i x e d arras of the bridge are wire-wound r e s i s t o r s of lowtemperature c o e f f i c i e n t . . The decade r e s i s t o r c o n s i s t s of s i x standard decade u n i t s which provides steps of 0.1 to 10k ohms, and i s p a r a l l e l e d by a 250 uuf v a r i a b l e a i r c a p a c i t o r which serves to balance capacity of the thermometer leads.  The  s e t t i n g of t h i s capacitor i s independent of the r e s i s t i v e balance, and need be changed only i f the capacitance i n the  Improved Bridge f o r Low Temperature Measurements W.L. BBISCOE  NOTES: 1 . ALL RESISTORS V, WATT UNLESS OTHERWISE SPECIFIED. 2 . RESISTANCE IN OHMS UNLESS OTHERWISE NOTED. 3 . CAPACITANCE VALUES ONE AND OVER IN MICROMICROFARADS, LESS THAN ONE IN MICROFARADS UNLESS OTHERWISE SPECIFIED. 4 . * INDICATES FULL CLOCKWISE POSITION AS SEEN FROM THE KNOB.  TEST POINT INC.  FIG. 1. Schematic circuit diagram of resistance thermometer.  (extension o f Blake, Chase and Maxwell c i r c u i t to include a means f o r s e l f - i n d i c a t i o n of the bridge n u l l )  -38-  thermometer arm of the bridge changes.  For a schematic diagram  of t h i s r e s i s t a n c e bridge c i r c u i t the reader i s to r e f e r to the literature. A very good m o d i f i c a t i o n of t h i s c i r c u i t has been presented 1 by W. L. B r i s c o e , Improved Bridge f o r Low Temperature Measurements.  Blake, Chase and Maxwell have met the basic requirement  of s e n s i t i v i t y with a very small amount of bridge power; however, i t has been found that i t s usefulness i s l i m i t e d by the need f o r peripheral equipment f o r n u l l i n d i c a t i o n . . Hence, B r i s c o e presents a c i r c u i t as an extension of the Blake, Chase and Maxwell c i r c u i t to i n c l u d e a means f o r s e l f - i n d i c a t i o n of the bridge n u l l . The basic d i f f e r e n c e i s as follows; The output from the o s c i l l a t o r V-6, i n a d d i t i o n to being fed to the bridge, i s also fed to the i n v e r t e r tube V-7A.. The o r i g i n a l p o l a r i t y and the i n v e r t e d p o l a r i t y are placed on the suppressor g r i d s of the phase comparator tubes, V-8 and V-9, r e s p e c t i v e l y .  Type 6AS6 tubes;  are used f o r the phase comparator because of t h e i r r e l a t i v e l y high supressor s e n s i t i v i t y .  A s i n g l e stage of gain, V-4, amp-  l i f i e s the bridge output s u f f i c i e n t l y to operate the c o n t r o l grids of V-8 and V-9 i n p a r a l l e l .  For proper operation the  c i r c u i t i s adjusted so that the a m p l i f i e d bridge s i g n a l i s i n phase with the suppressor s i g n a l on V-9. on one side of the n u l l and i s i n phase with the suppressor s i g n a l on V-8 on the other side of the n u l l . 1.. B r i s c o e W.L.,  With the plates of the comparator h e a v i l y Rev. S c i . I n s t r . , 31,999(1960)  -39-  bypassed, they are e s s e n t i a l l y current sources, and i t i s current d i f f e r e n c e s that are measured by the meter.  The  meter i s also equipped with large e l e c t r o l y t i c capacitors to i n t e g r a t e the noise that comes through the system.  This  i n t e g r a t i o n i s e s s e n t i a l because an impulse at the input causes r i n g i n g or f l u c t u a t i o n s of random phase.. In regard to t h i s noise, a user should not be alarmed i f the noise as seen on a t e s t bench seems excessive, because the noise appears to o r i g i n a t e mostly i n the temperature sampling r e s i s t o r .  When  the temperature of t h i s r e s i s t o r i s reduced to c r y o s t a t i c values, very l i t t l e noise remains. The function of V-7B i s simply to reduce the supply voltage to the proper value f o r the phase comparator.  The  portion of the c i r c u i t leading from the bridge e x c i t a t i o n potentiometer to the bridge proper contains two f i l t e r sections that are used f o r adjusting the phase of the bridge s i g n a l as seen by the comparator. The author of t h i s thesis duplicated the bridge used by B r i s c o e and modified i t s l i g h t l y so that i t t c o u l d be adapted to temperatures below 1 K.  The main modifications were t h r e e -  fold;; an aquadag r e s i s t o r was used as the r e s i s t a n c e  thermometer  i n the bridge, an o s c i l l o s c o p e was always kept i n the c i r c u i t at the point marked t e s t - p o i n t balance, instead of detecting  •40-  the null position vtith a meter a Honeywell recorder was used to monitor the output of the 6AS6*s. The preparation of the aquadag resistor hass already been discussed.  It's room temperature value is about 2500 ohms..  The oscilloscope is very useful in obtaining balance in the bridge before the recorder is switched on., Out of balance signal is very simple to detect at this point.  Also, at a glance,  the scope indicates quickly whether one is cooling or heating. This is very useful in the pre-cooling process and demagnetisation process.as well as the actual heating process in the specific heat measurements.Using a recorder to monitor the phase comparator output is very useful indeed.  Rather than having a sharp null! point  indicating exact balance this section of the circuit was redesigned to give a linear output on each side of balance.  This  was achieved by cutting down the overall gain of the circuit and adjusting the impedance level at this point to match that of the Honeywell recorder. oscilloscope,  After obtaining balance, indication by  the recorder is started and traces any change in  resistance of the thermometer.. The recorder is reliable over the linear portion of the output  of out of balance signal which was  linear up to 500 ohms each side of the null position.. Hence, the  -41-  heating curve i s traced d i r e c t l y but care must be taken i n determining the time lag of the s t y l u s due to the time constant of the. c i r c u i t so that the true heating curve can be a r r i v e d a t . 4.,  Rptisrmi tint i n n  nf  Tpnippraturs-  S u s c e p t i b i l i t y Bridge  Many b a l l i s t i c c i r c u i t s f o r measuring the magnetic temp?-erature and hence the absolute temperature of the chromium potassium alum are r e a d i l y a v a i l a b l e i n the l i t e r a t u r e . . A very s u i t a b l e one i s that given by James Nicol.. This i s a d . c mutual inductance bridge. the  The mutual inductance c o i l ; around  paramagnetic sample i s wound on the brass can i n the e x p e r i -  mental space.  I t consists of a primary and secondary c o i l .  primary i s wound the length of the can.  The  A secondary c o i l i s  u s u a l l y wound over the primary with a l l the compensating inductance at room-temperature.  A common p r a c t i c e i n t h i s laboratory  i s to wind the secondary as two c o i l s of equal turns one i n opposition to the other.  S^ i s wound on the primary, i n the  same d i r e c t i o n , near the bottom o f the can. sample i s placed i n s i d e t h i s c o i l . . about 1/2" above S j .  The paramagnetic  S2 i s wound i n opposition  This i s the compensating inductance network.  Now, only a small amount of compensating inductance need be i n the c i r c u i t at room temperature. The mutual inductor compensating c o i l i s 40 rah i n value..  1.  N i c o l J . , Rev. S c i . I n s t r . , 31, 211(1960)  SUSCEPTIBILITY. BRIDGE  6 ohm 2-24 v o l t  0-  10.A .  °  vV—v^V—  _ 1  200*1. 1000\$  0  Ammeter  Reversing Switch  Ro  1  —sJUJUliLAJULx  •  '  \SJULUJUULSUUUV—  R  p  M  Galvanometer  %  -42-  This i s much l a r g e r than necessary but balance i s e a s i l y obtained. A h e l i - p o t i s used as a shunt i n the primary of t h i s c o i l with the center tap connected to the primary of the s u s c e p t i b i l i t y coil.  The secondary i s i n the galvanometer c i r c u i t and i n s e r i e s  with the s u s c e p t i b i l i t y secondary c o i l s .  The mutual inductance  of the s u s c e p t i b i l i t y c o i l s with respect to the standard o r compensating mutual inductance i s given as Mx =  l . M l B Rp R  R  s  2  This value i s not necessary f o r the operation of the bridge as one need simply balance the c i r c u i t before demagnetisation. The primary was wound with 932 turns o f #37 B.£S; copper wire with p o l y s o l i n s u l a t i o n . was 125 ohms.  Room-temperature dc r e s i s t a n c e  The secondaries were wound with the same wire  separated by a.1/2"'gap.  - had 4500 turns and a dc r e s i s t a n c e  of 600 ohms (room-temperature), w h i l e S2 had the same number o f turns but wound i n opposition.  The brass can was f i r s t sprayed  with a f a s t drying p l a s t i c f i l m to prevent shorting through the t h i n i n s u l a t i o n , which d i d tend to scrape o f f while winding with the lathe.  Each l a y e r o f turns was also p l a s t i c coated.  CHAPTER. I l l S p e c i f i c Heat of Cadmium 1.  Apparatus - Procedures The l a r g e s t source of e r r o r i n s p e c i f i c heat work l i e s i n  determining the heat generated i n the heater c o i l to give the corresponding temperature r i s e .  A known current i i s passed  through a^ constantan heater of 8..4. ohm r e s i s t a n c e .  In the  l i q u i d helium range R v a r i e s by about 0.1% per. degree.  However,  a large r e s i s t o r i n the heating c i r c u i t allows the current be kept constant.  A high p r e c i s i o n voltmeter  to  (Hewlett-Packard)  measures, the voltage drop across the heater c o i l . 2 The heat generated i n the constantan c o i l i s . Q = i R t J where t i s time and J i s the Joule constant.  As R has been  measured with high p r e c i s i o n during the heating i n t e r v a l s and as. i i s . also accurately known the l a r g e s t source of e r r o r i n determining Q l i e s i n the measurement of t.. Hence, the p r e c i s e heating i n t e r v a l must be known.  This i n t e r v a l should not be l e s s than 30  seconds and may be as long as 180 seconds.  P r e c i s i o n switching  and timing was g r e a t l y improved by adapting an e l e c t r i c a l timer (Berkely) accurate to; b e t t e r than 1/10 circuit.  seconds i n t o the heater  Hence, one switch c o n t r o l l e d both heating and timing  so that the timer records the exact time of the heating i n t e r v a l . Currents of O..Jg and 0.15 ma were used over i n t e r v a l s of 30 to 60 seconds and very l i t t l e e r r o r was introduced i n t h i s  way.  Thermometer Bridge - The a.c. r e s i s t a n c e thermometer bridge -43-  -44rperformed well.  During the pre-cooling stage one could readily  detect any temperature change by observing the out of balance signal on the oscilloscope..  The desired effect of adding  exchange gas to the sample space and performing demagnetisations was readily seen in this way. The Honeywell recorder, monitoring the out of balance signal, was only in the circuit when the bridge was very close to balance.  A, Gain control on the bridge allowed full:scale  deflec-  tion of the recorder for a resistance change of 1, 10, or 100 ohm steps on the decade resistance box.. Calibrating the aquadag resistor is a straight-foreward procedure.  Exchange gas was l £ t into the sample space allowing  the cadmium sample to achieve thermal equilibrium with the helium bath at about 4.2°K.  The mercury and o i l manometers were used to  determine the temperature of the helium bath and hence the cadmium by vapour-pressure thermometery.  The mercury or o i l level coiild  be held stationary at various points by adjusting the pumping speed.  At these points with the recorder on a high sensitivity  scale the resistance bridge was accurately balanced and the resistance setting on the decade boxes noted.  In this manner  various temperature and resistance readings were taken between 4.2 and 1..2°K. After a demagnetisation to a lower temperature the bridge  -45was q u i c k l y balanced and the recorder put i n the c i r c u i t . Before any heat was put i n t o the cadmium the recorder was  cali-  brated with the decade r e s i s t a n c e by p u t t i n g the bridge out of balance by 1,2.5, or 10 ohm steps. on the recorder.  This caused a step trace  A f t e r adding a heat pulse at t h i s  temperature  a corresponding temperature r i s e and hence a r e s i s t a n c e change caused a d e f l e c t i o n on the recorder.  This d e f l e c t i o n was  then  easily-evaluated by comparing i t with the known r e s i s t a n c e steps previously recorded.  This c a l i b r a t i o n was repeated often during  each demagnetisation.  The temperature r i s e was of the order of  50 m i l l i d e g r e e s corresponding to a r e s i s t a n c e change of 0.5 ohms i n 20K ohms.. The bridge and recorder u n i t worked very w e l l . S u s c e p t i b i l i t y Bridge - Another method of determining the absolute temperature was attempted by use of a s u s c e p t i b i l i t y bridge. The actual bridge set up was very good.  A l l stray inductance was  completely balanced out at room temperature and at l i q u i d nitrogen temperature which i n d i c a t e d that the bridge would be s u c c e s s f u l l y operable.  With the bridge balanced at about 4.2°K one o  decreases  the temperature through steps to 1.2 K as above using the vapourpressure technique, and records i n c r e a s i n g d e f l e c t i o n s on the galvanometer scale. l i t y curve.  However, t h i s bridgedid not y i e l d a s u s c e p t i b i -  -462.  Experimental Results-Conclusions  S p e c i f i c Heat of Cadmium - The experimental conditions were good and throughout the experiment the apparatus performed w e l l except f o r the recorder trace.  Upon adding heat to the sample  a temperature r i s e was observed on the recorder but when the heat pulse was terminated the recorder returned to i t s : i n i t i a l trace and hence i n d i c a t e d no net temperature change.  Over s i x  demagnetisations t h i s recorder trace p e r s i s t e d f o r some t h i r t y s i x heat pulses. The i n i t i a l d e f l e c t i o n on the recorder c e r t a i n l y i n d i c a t e d a temperature r i s e of the proper magnitude but a f t e r the duration of the heating i n t e r v a l , 30 to 60 seconds, the trace returned to the i n i t i a l  temperature.  Due to the above r e s u l t s the s p e c i f i c heat of cadmium was not able to be found.  Examination of these r e s u l t s i n d i c a t e s that the  thermal contact between the cadmium and the s a l t p i l l via. the lead s t r i p was too good.  The heat pulse d i d not warm up the sample but  leaked away down the thermal valve, even though i n the superconduct i n g state, to the s a l t p i l l . .  The p h y s i c a l dimensions of the lead  s t r i p used (40mm x 5.0mm x 0.27mm) i n conjunction with the equation of the thermal conductivity f o r lead i n the superconducting s t a t e (Chapter I) c l e a r l y i n d i c a t e s that these r e s u l t s were to be expected.  The c r o s s - s e c t i o n a l area of the s t r i p must be decreased some  500 times i n order to achieve proper thermal contact between the  K  0  0  Q  G  CD  . ... {  j  f  i  f  i  0.510  O.fO  O.80  i 1'OQ  Temperature v r s Thermal Conductivity of Lead S t r i p  L>  -47sample and the salt.. This means producing very f i n e lead wire o f the highest p u r i t y .  Unfortunately t h i s lead wire was not immed-  iately available. The data obtained should be a measure of thettermal conducti v i t y of superconducting lead.  Knowing the dimensions o f the lead  and assuming that a l l the heat t r a v e l l e d along i t a f t e r a temperature r i s e was recorded on the recorder a measurement o f the thermal c o n d u c t i v i t y waSiestimated.  From the accompanying graph  a w e l l scattered pattern of points appear. The temperature range o i s from 0.6 to 1.0 K. The cadmium i s i n the normal s t a t e while the lead i s i n the superconducting state.  Unfortunately these -5  points do not f o l l o w a curve and the order of magnitude, 10 watts/cm deg i s not good.  However, the pufcity of the lead and the  heat leaks i n the c r y o s t a t are very important. Thermometer Bridge- The thermometer bridge with the Honeywell recorder was e x c e l l e n t . detected.  Changes of 0.1 ohms i n 20K  were e a s i l y  The aquadag thermometer was very good but had to be  re-coated a f t e r every few runs and c a l i b r a t e d during each run. C a l i b r a t i o n of t h i s thermometer was good but before e x t r a p o l a t i o n below 1.2°K a check of t h i s thermometer v r s a s u s c e p t i b i l i t y thermometer should be performed. S u s c e p t i b i l i t y Bridge- This bridge met with d i f f i c u l t y f o r too reasons: a large pure conductor was i n the compensating c o i l and, the secondary c o i l s repeatedly became open c i r c u i t s upon c o o l i n g to helium  temperatures.  -48Th e bridge could be balanced at room temperature and at l i q u i d nitrogen temperature but a net d e f l e c t i o n of some 4 or 5 o cm p e r s i s t e d at,4..2 K.  This d e f l e c t i o n of a. simple k i c k was i n  e i t h e r d i r e c t i o n depending on the p o s i t i o n of the reversing switch.  However, upon c o o l i n g a double k i c k was observed.. The  f i r s t kick was:;as above and very q u i c k l y reversed i t s e l f and kicked very l a r g e l y i n the opposite d i r e c t i o n .  Upon c o o l i n g the  i n i t i a l throw remained the same but the second one became much larger.. This was obviously the one to measure.. This double kick phenomena i s caused.by the presence of a very pure and large conductor, the cadmium sample, which is,concentriclyy located i n the compensating secondary c o i l .  Upon e x c i t i n g the primary c o i l  eddy currents are set tup and d i e away i n the cadmium which i s detected by the secondary c o i l , As the turns of copper wire were wound on the brass can a p l a s t i c spray was put.on each layer.. I t i s f e l t that a f t e r c o o l ing and,warming the p l a s t i c cracks causing open c i r c u i t s i n the coil.  This p a r t i c u l a r wire i s not good f o r c o i l winding.  The  problem was p a r t i a l l y solved by separating the c o i l s with paper. In f a c t , separating each l a y e r with paper i s b e t t e r s t i l l .  c  -49-  REFERENCES Alekseyevsky N., Migunov L . , J . 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