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FINITE SIZE SCALING OF THE SPECIFIC HEAT
OF 4He IN VYCOR GLASS
R. Joseph, F. Gasparini
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6, supplkment au no 8, Toms 39, aotit 1978, page
C6-310
FINITE SIZE SCALING OF THE SPECIFIC HEAT OF
4HeI N VYCOR GLASSt
R.A.Joseph and F.M. Gasparini
Physics Department, State University o f flew York a t Buffalo, Amherst, New York 14260, USA
R6sumd.- Nous prdsentons des n o u v e l l e s mesures d e l a c h a l e u r s p s c i f i q u e d e l ' h d l i u m c o n f i n d dans du Vycor, e t nous en examinons l e comportement c r i t i q u e . Nous ne trouvons aucune anomalie dans l a r d g i o n oG l ' o n observe que l a d e n s i t d s u p e r f l u i d e d i s p a r a f t avec une l o i en puissance 213. Nous trouvons que l e s r 6 s u l t a t s dans un i n t e r v a l l e d e 0 , 0 2 K a u t o u r de T i s e comportent s u i v a n t l a mhe l o i d ' d c h e l l e que l e s r d s u l t a t s de l ' h l l i u m dans du Nuclepore.
Abstract.- We p r e s e n t new measurements of t h e s p e c i f i c h e a t of helium confined i n Vycor, and examine i t s c r i t i c a l behavior. We f i n d no evidence of anomalies i n t h e r e g i o n where t h e super- f l u i d d e n s i t y has been observed t o v a n i s h w i t h a 213 power law. We f i n d t h a t t h e d a t a w i t h i n 0.02K of T s c a l e i n t h e same way a s t h e d a t a of helium i n Nuclepore.
A
The s p e c i f i c h e a t of helium confined i n Vycor g l a s s was f i r s t measured by Brewer, Champeney and Mendelssohn
111
and subsequently t o a b e t t e r r e s o l u -t i o n by Symonds 121. I n l i g h t of r e c e n t measurements of G1e s u p e r f l u i d d e n s i t y of helium i n Vycor by Kie- w i e t , H a l l and Reppy 131, and t h e d e t e r m i n a t i o n of f i n i t e s i z e s c a l i n g of t h e s p e c i f i c h e a t of helium confined i n Nuclepore f i l t e r s by Chen and Gasparini 141, i t was f e l t t h a t new measurements f o r Vycor were needed t o v e r i f y some new a s p e c t s of t h e behavior of confined helium,
The measurements of t h e s u p e r f l u i d d e n s i t y , ps, show a v e r y s u r p r i s i n g r e s u l t : ps v a n i s h e s a t a temperature of To : 1.955 K w i t h a power law which i s t h e s ~ a s f o r bulk helium, i . e . % (1.955
-
T)'s
with
5
= 0.652
0.03. This b u l k - l i k e behavior l e d t oF u r t h e r t h e d a t a n e a r T should s c a l e a s 141
A
[ ~ ( t , d)
-
C ( t , ta = g ( d o t )-
g(m) ( 1 ) where C i s t h e s p e c i f i c h e a t of c o n f i n e d , C ( t , d ),
o r bulk, C(t,m), helium, t =I
I-
TITXI, and g i s a u n i v e r s a l f u n c t i o n . The confinement s i z e d i s t h e s m a l l e s t dimension i f a l l o t h e r s a r e much l a r g e r t h a n d. The i d e a s of a s h i f t i n t h e temperature of t h e maximum i . e . tmdo = c o n s t a n t , and t h e d e c r e a s e i n magnitude, i . e . Cm= AORnd+
c o n s t a n t,
can be d e r i v e d from e q u a t i o n 1. by s e t t i n g t h e temperature d e r i v a t i v e of C ( t , d) equal t o zero. However, t h e v a l i d i t y of t h e s e r e s u l t s have been observed empiri- c a l l y t o extend t o a much wider range i n t t h a n e q u a t i o n 1.4. Thus t h e y a r e i n a s e n s e independent f e a t u r e s of f i n i t e s i z e s c a l i n g .To. No such anomaly was e v i d e n t i n e x i s t i n g d a t a , but
-
I
t h e s u g g e s t i o n t h a t t h e exponenta
f o r t h e s p e c i f i c20
h e a t might a l s o be b u l k - l i k e , i . e . a = 0 , correspon- d i n g t o a l o g a r i t h m i c anomaly a t t h e same temperature
indeed i t might be argued t h a t i t i s small i n ampli- tude, and only v i s i b l e i n a s m a l l e r temperature range
o o O than had been e x p l o r e d , hence r e q u i r i n g a more careful
measurement.
I f such a n anomaly were found, i t would argue f o r a r a t h e r unique s t a t u s f o r t h e behavior of helium i n Vycor, being q u i t e d i f f e r e n t from t h e behavior ex-
2
0 HELIUM IN VYCOR (THIS WORK1
n p D o ' = o n ~ o
o 3 2 . 8 ~ FILM ON NUCLEPORE
ICHEN, GI\SPARINI)
.do
@b"
%
m
pected.from arguments of f i n i t e s i z e s c a l i n g 151. Ac-
V)
I
c o r d i n g t o t h e s e one would e x p e c t a rounded s p e c i f i c I 1.9 2.0 26
I
h e a t , w i t h a maximum,C,
a t a temperature Tm below TA.TEMPERATURE LK)
t
Mark supported i n p a r t by Research Corporation and NSF through grants f fDMR
7711325 andDMR
7509498A01Fig. 1 : S p e c i f i c h e a t of helium confined i n Vycor g l a s s and s p e c i f i c h e a t of a helium f i l m i n nuclepore f i l t e r s .
Our new d a t a f o r t h e s p e c i f i c h e a t of helium f i l l i n g Vycor g l a s s i s shown i n f i g u r e 1. Here we a l s o show f o r comparison t h e d a t a o f
a
32.8;i
f i l m on Nuclepore f i l t e r s 161. The d a t a i n f i g u r e 1 show no evidence of anomalies. The r e g i o n near 1.955 K where p i s observed t o v a n i s h c a n be expanded and shows no s t r u c t u r e w i t h i n a s c a t t e r of 0.2 %. Simi- l a r l y , t h e r e g i o n n e a r t h e maximum a l s o shows no ano- m a l i e s b u t r a t h e r a rounded maximum. Very n e a r TAt h e d a t a have a s l i g h t shoulder which we b e l i e v e i s due t o a small inhomogeneity i n t h e confinement s i z e . A s i m i l a r behavior was observed i n t h e c a s e of Nucle- p o r e / 7 / . I t t h u s a p p e a r s t h a t t h e s p e c i f i c h e a t does n o t mimic a t a l l t h e behavior of ps, i . e . i t c e r t a i n - l y does n o t behave bulk-like.
To d i s c u s s t h e s c a l i n g a s p e c t s one needs t o determine t h e confinement s i z e . Vycor i s o f t e n charac- t e r i z e d a s a porous m a t e r i a l having a geometry of multiconnected channels of about 60
;i
mean diameter. I f we adopt t h i s model, and n o t e t h a t about 6 of helium n e a r t h e w a l l s does n o t p a r t i c i p a t e i n t h es u p e r f l u i d behavior 181, t h e n t h i s r e s u l t s i n a chan- n e l geometry of 48 diameter. I n t h e work w i t h Nu- c l e p o r e / 4 / it was shown t h a t a s f a r a s s c a l i n g e f f e c t s , c y l i n d r i c a l l y confined helium i s e q u i v a l e n t t o a f i l m of t h i c k n e s s (0.585) x diameter o r 28.1
1
i n t h e p r e s e n t c a s e . T h i s dimension i s c l o s e t o t h a t of t h e f i l m d a t a p l o t t e d i n f i g u r e I . , and i t i s e v i - d e n t t h a t t h e behavior of t h e s e d a t a away from TA i sq u i t e d i f f e r e n t . Indeed on t h e b a s i s of t h e work of r e f e r e n c e 4, we would have expected Tm = 2.00 K and Cm = 18.5 Joule/mole K. The measured v a l u e s of Tm =
2.094
2
0.006 and Cm = 15.72
~ o u l e / m o l e K t h u s do not a g r e e w i t h t h e Nuclepore d a t a . More i m p o r t a n t l y t h e d i s c r e p a n c y i s such t h a t i t cannot be c o r r e c t e d by choosing a d i f f e r e n t c o n f i n i n g s i z e : t h e maximum r e - q u i r e s a s m a l l e r s i z e w h i l e i t s p o s i t i o n r e q u i r e s a l a r g e r one. I n a d d i t i o n t o t h e v a l u e s of C and Tm
m
one o t h e r a s p e c t of f i n i t e s i z e s c a l i n g i s e q u a t i o n1. which was found v a l i d f o r helium i n Nuclepore up t o t 7 0.01, w i t h O = 1.85. The d a t a f o r Vycor both above and below TA, p l o t t e d according t o e q u a t i o n 1 a r e shown i n f i g u r e 2. a l o n g w i t h t h e d a t a f o r Nu- c l e p o r e . It i s c l e a r t h a t t h e d a t a s c a l e v e r y n i c e l y , and hence, a t l e a s t n e a r TA, f i t w i t h i n t h e frameworl of f i n i t e s i z e s c a l i n g .
We a r e g r a t e f u l t o P r o f e s s o r J.Reppy f o r providing u s w i t h t h e sample of t h e Vycor used i n t h i s expe- riment.
Fig. 2 : F i n i t e s i z e s c a l i n g of t h e Vycor d a t a near TA and t h e d a t a f o r helium confined i n Nuclepore f i l t e r s
.
References
/ I / D.F., Brewer, D.C., Champeney, and K. Mendels- sohn; Cryogenics
1,
(1960) 108./ 2 / A . J . , Symonds, unpublished t h e s i s , U n i v e r s i t y of Sussex, 1965.; r e p o r t e d by D.Brewer, Jour- n a l of Low Temp. P h y s i c s
2,
(1970) 205./ 3 / C.W., Kiewiet, H . E . ; H a l l and J . D . ; Reppy Phys. Rev. L e t t .
21,
(1975) 1286./ 4 / T.P., Chen, F.M., Gasparini Phys. Rev. L e t t . % (1978) 331.
151 M.E., F i s h e r , i n C r i t i c a l Phenomena, P r o c e e d i n s of t h e I n t e r n a t i o n a l School of P h y s i c s , "Enrico Fermi" Course 51, e d i t e d by M.S. Green (Academic New York 1971).
/ 6 / T.P.; Chen and F.M., G a s p a r i n i ; Phys.Lett.
62A
(1977) 231./7/ T.P.,Chen; M . J . , D i P i r r o , A.A., Gaeta and F.M., G a s p a r i n i ; J.Low Temp. Phys.
