HAL Id: jpa-00218031
https://hal.archives-ouvertes.fr/jpa-00218031
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
THE MEASUREMENT OF HEAT CAPACITY BY
THE USE OF A RESISTIVE SQUID
J. Park, A. Vaidya
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplPment au no
8,
Tome
39,
aolit 1978, page
C6-
1228
THE MEASUREMENT
OF
HEAT CAPACITY
BY THE USE
OF
A RESISTIVE SQUIP
J . G . P a r k and A.W. Vaidya
Physics
Department, Imperial CoZZege, London
SW7
2BZ,England
RQsum6.- A f i n d ' u t i l i s e r un SQUID r d s i s t a n t pour mesurer l a c a p a c i t C c a l o r i f i q u e d e d i f f d r e n t s m a t Q r i a u x , nous avons m i s a u p o i n t une mdthode q u i r d d u i t l a c o r r e c t i o n due 1 l a c a p a c i t d c a l o -
r i f i q u e du SQUID l u i - m & e . Nous donnons l e s r s s u l t a t s d e m e s u r e s - t e s t f a i t e s e n t r e 2 e t 6 , 5 K s u r 3 , 8 gm d e c u i v r e p u r .
A b s t r a c t . - I n o r d e r t o t r y o u t a resistive SQUID f o r m e a s u r i n g t h e h e a t c a p a c i t y o f m a t e r i a l s , we have d e v i s e d method i n which t h e c o r r e c t i o n t h a t must b e made f o r t h e h e a t c a p a c i t y of t h e r e s i s t i v e SQUID i t s e l f i s r e d u c e d , We r e p o r t t h e r e s u l t s of a p r e l i m i n a r y t e s t measurement made between 2 and 6.5 K on a 3 . 8 gm specimen o f p u r e c o p p e r .
I n t h e p r e s e n c e o f a n e l e c t r i c c u r r e n t i and I f t h e RSQUID i s s u p p o r t e d i n vacuum i t may be a h e a t c u r r e n t q f l o w i n g t h r o u g h t h e normal m e t a l u s e d t o measure t h e amount o f h e a t f l o w i n g i n t o ( o r r e g i o n N of a r e s i s t i v e SQUID (RSQUID) such a s t h e o u t o f ) a specimen H a t t a c h e d t o i t s u n d e r s i d e . By o n e shown i n f i g u r e 1, t h e d e t e c t o r o u t p u t o s c i l l a - v a r y i n g t h e t e m p e r a t u r e o f H i t s h e a t c a p a c i t y C t e s a t a f r e q u e n c y f g i v e n by t h e J o s e p h s o n r e l a - may be measured / I / . We d e s c r i b e h e r e one method t i o n s h i p f = V / i $ o , where V i s t h e v o l t a g e a c r o s s N. of c a r r y i n g o u t s u c h a measurement i n p r a c t i s e and Thus f = ( i r
+
Kq)/Oo, where r i s t h e e l e c t r i c a l t h e r e s u l t s of a n e x p e r i m e n t t o t e s t i t .r e s i s t a n c e of N and K i s t h e t h e r m a l s e n s i t i v i t y : A t h e r m a l r e s i s t a n c e R1 i s i n s e r t e d between K = Sw, where w i s t h e t h e r m a l r e s i s t a n c e of N and t h e specimen and L , t h e lower p a r t o f t h e RSQUID S i s i t s thermopower. below N. A h e a t e r h l i s a t t a c h e d t o t h e specimen. The t e m p e r a t u r e of measurement i s a d j u s t e d by ano-
t h e r h e a t e r h2 o n U , t h e body of t h e RSQUID above N. The method c a n b e s t b e u n d e r s t o o d by r e f e r e n c e
I t o t h e t h e r m a l " e q u i v a l e n t c i r c u i t " shown i n f i g u - r e l b .
Suppose t h a t t h e specimen h e a t e r i s s u d d e n l y s w i t c h e d on a t a time t = 0 and d e l i v e r s power q l . The f r e q u e n c y f does n o t change immediately t o
F i g . 1 : ( a ) The t o r o i d a l RSQUID used i n o u r e x p e r i - ments. Nb p a r t s a r e shown shaded; s o f t s o l d e r , where i t c o v e r s t h e s u r f a c e s o f t h e c o p p e r p a r t s b and c makes a j o i n t w i t h t h e &Fe r i n g N i s shown by a
t h i c k b l a c k l i n e . The t h i c k n e s s o f N and o f tfie s o l - d e r h a s been exagerated f o r c l a r i t y . T h e upper d i s c a i s p r e s s e d down by 3 s c r e w s , one of which i s shown t h e lower Nb d i s c i s h e l d down by a " D e l r i n l ' p i e c e d . The t h e r m a l r e s i s t a n c e of t h e 3 copper w i r e s by h i c h t h e specimen H i s a t t a c h e d v a r i e s from 3600 KW-'at 2K t o 1000 KW-I a t 6.5 K.
(b) Thermal e q u i v a l e n t c i r c u i t . T h e RSQUID i s t r e a t e d a s though i t c o n s i s t e d o f Q , a n i d e a l de- t e c t o r o f h e a t c u r r e n t whose o u t p u t i s a v o l t a g e o s - c i l l a t i n g a t f r e q u e n c y f , and two o t h e r p a r t s U and L which a r e t h e p a r t s of t h e RSQUID above and below t h e r i n g N r e s p e c t i v e l y . R 2 ( < < R l ) i s t h e t h e r m a l r e - s i s t a n c e between t h e RSQUID and t h e c o n s t a n t tempera- t u r e b a t h To. h l and h z a r e h e a t e r s .
K q ~ / i $ ~ b u t o n l y r e a c h e s t h i s v a l u e a f t e r a s u f f i - c i e n t t i m e T h a s e l a p s e d f o r t h e specimen, and a l l
m
t h e o t h e r p a r t s o f t h e system between i t and t h e b a t h , t o t e a c h e q u i l i b r i u m . The f r e q u e n c y r i s e s from i t s i n i t i a l v a l u e f = f 1 a t t = O ( f l i s s e t t o a c o n v e n i e n t v a l u e of 'L 20 kHz by a d j u s t i n g i) t o f ~ = f l
+
Kq l / $ ~ ~ w h e n t2
T ~ .A c o u n t i n g i n t e r - v a l.r
such t h a t .r > .rm i s chosen and t h e number o f c y c l e s o f o s c i l l a t i o n (n ) t h a t t a k e p l a c e between0
t = 0 and t = ~ c o u n t e d ; t h e n t h e number ( n l ) b e t - ween t = and t = 2T
.
The d i f f e r e n c e n = ( n l - n 0 )i s p r o p o r t i o n a l t o t h e amount o f h e a t r e q u i r e d t o r a i s e H and L t o t h e i r new e q u i l i b r i u m temperatu- r e s , s i n c e t h i s h e a t d o e s n o t p a s s t h r o u g h t h e RSQUID and i s u n d e t e c t e d by i t . Hence n=K(KC+rc)
£land f 2 can be measured i n t h e s t e a d y s t a t e b e f o r e and a f t e r ql has been a p p l i e d . The r e q u i r e d h e a t ca- p a c i t y C may thus be o b t a i n e d once R and c(Rn/R)have been obtained from a s e p a r a t e c a l i b r a t i o n experiment. Here R = R 1
+
R 2 .The s e n s i t i v i t y of our RSQUID, i n which a r i n g 0.07 rmn t h i c k made o f S F e (0.1 a t %) a c t s a s t h e normal r e g i o n N , v a r i e s from 0.8 Hz nW-
'
a t 2 K to 0.45 Hz nw-'at 6 K; i t has a r e s i s t a n c e r of 2 ~ 1 0 - ~ ohms. I n o r d e r t o make counting p r e c i s e t h e d e t e c t o r o u t p u t i s f i r s t f e d t o a phase-locked loop whose output d r i v e s t h e c o u n t e r . Current t o t h e h e a t e r i s a p p l i e d by a l i n e a r g a t e opened a t t = 0 by t h e same t r i g g e r p u l s e t h a t s t a r t s an up-and-down counter. The counter i s r e v e r s e d a t t = T a n d stopped a t t = 2 T S O t h a t i t s r e a d i n g g i v e s n d i r e c t l y . Temperature f l u c t u a t i o n s o f t h e RSQUID, which induce f l u c t u a t i o n s i n f a s h e a t flows t o and f o r through N , a r e a t p r e s e n t made s u f f i c i e n t l y small by pumpingt h e l i q u i d helium b a t h below t h e lambda p o i n t . The background h e a t c u r r e n t g e n e r a l l y corresponds t o a frequency f 2. 100 Hz.
The r e s u l t s o f o u r f i r s t measurements, made on a 3.84 gm specimen of pure copper, a r e shown i n f i g u r e 2, uncorrected f o r t h e h e a t c a p a c i t y of L.
L has a h e a t c a p a c i t y c roughly e q u i v a l e n t t o 4.5gm of copper t h e c o r r e c t i o n f o r i t i s reduced by t h e f a c t o r R 2 / R which i s about 0.05 and i s weakly tem- p e r a t u r e dependant. T h i s small c o r r e c t i o n term ac- counts f o r t h e d i f f e r e n c e between o u r measurements and t h e known h e a t c a p a c i t y of cooper (Holste e t a l . 121. The f i n e n e s s of r e s o l u t i o n we have a c h i e - ved by t h e method even a t t h i s e a r l y s t a g e of de- velopment can be gauged from t h e p o i n t s p l o t t e d on an expanded s c a l e i n f i g u r e 3.
Fig. 3 : The u n c o r r e c t e d h e a t c a p a c i t y a t low tem- p e r a t u r e on an expanded s c a l e .
We s h a l l b e measuring c(R2/R) s h o r t l y i n or- der t o complete t h e measurement of C and p l a n t o reduce t h e c o r r e c t i o n term f u r t h e r by s t a b i l i s i n g t h e temperature of U - which should reduce Rz/R by another o r d e r of magnitude. The method should t h e n be ready f o r a t t a c k i n g i n t e r e s t i n g problems.
References
/
I / Park J . G . , Superconducting r n t e r f erence Devices and t h e i r a p p l i c a t i o n s . (Walter de Gruyter, B e r l i n ; 1 9 7 5 278.Fig. 2 : The r e s u l t s of measurement of t h e t o t a l
h e a t c a p a c i t y , uncorrected f o r addenda, / 2 / H o l s t e J.C., Cetas T.C., and Swenson, C.A., compared with t h e v a l u e of C / T expected Rev. S c i . I n s t .
43
(1972) 670.f o r a 3.8 gm sample of pure Copper ( t h e continuous c u r v e ) .
They c o n s t i t u t e a measurement of t h e q u a n t i t y C +c(R2/R). A t y p i c a l p o i n t i s t h e mean of 10 mea- surements taken w i t h
