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LOCAL TRICRITICAL BEHAVIOUR IN 3He - 4He
MIXTURES FILMS
J. Laheurte, J. Romagnan, A. Gilabert, J. Noiray
To cite this version:
J. Laheurte, J. Romagnan, A. Gilabert, J. Noiray.
LOCAL TRICRITICAL BEHAVIOUR IN
JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 8, Tome 39, aotit 1978, page C6-349
LOCAL TRICRITICAL BEHAVIOUR IN
3 ~ e-
4 ~ eMIXTURES FILMS
J.P. Laheurte, J.P. Romagnan, A. Gilabert and J.C. Noiray
Laboratoire de Za Matie're Condensde, L.A. 190, Pare VaZrose 06034 Nice Cedex, France.
Resume.- Une etude thdorique dans les films de melange 3 ~ e - 4 ~ e predit un comportement tricritique au voisinage des parois.
Abstract.- Tricritical behaviour in the vicinity of walls is obtained from calculations in 3 ~ e - 'He mixtures films.
In bulk 3 ~ e - 4 ~ e mixture the superfluid tran- sition triggers the instability in the mixturewhich leads to the existence of a tricritical point. The existence of tricritical points in mixtures films remains an open and very interesting question I l l . We present in this work results of numerical calcu- lations which, with reasonable assumption and the help of recent experimental measurements 1 2 1 , give an answer to this question.
In a film of thickness d, the superfluid transition temperature TS is function of pressure P, 3 ~ e concentration X and d :
TS = TS(X, P , d) ( 1 )
In the same way we can write that the criti- cal point of the phase separation curve is defined by :
TC = TC(X, P, d) (2)
In bulk mixtures (d + w) the tricritical temperature Tt defined by TS = T = T fixes the
C t
values Pt et X at the tricritical point. t
It is well known that a reduction of the film thickness d decreases the superfluid tempera- ture transition TS. This effect has been intensive- ly studied in pure 4 ~ e films 131. The influence of the film thickness on phase separation has infortu- nately not been studied. However we do not expect strong effects. Effectively the phase separation curve is a line of first order transitions. The associated nucleation length is small and so we do not expect modification of the phase separation curve as long as d > 1 atomic layer. Even a shape variation of the curve top should not change the critical point location. This assumption is also strongly suggested by recent measurements 121 which indicate that on the scale of a few atomic layers separation occurs like in bulk.
Under such assumption and experimental in-
formation for T (X, P, d) the existence of tri- S
critical behaviour in helium mixtures film can be discussed and even calculated.
First of all, in the case of a thin film with uniform concentration and pressure (a floattingfilm without walls) there is no tricritical point, as TC is not affected by a reduction of d while TS is changed. For such thin films the superfluid criti- cal line ends at a point of the phase separation curve, characteristic of a first order transition.
Fortunately in the laboratory, films are usually adsorbed on walls which play an important role. In the walls vicinity the pressureincreases while 3 ~ e concentration is reduced because of the Van der Waals potential. It is then of crucial im- portance to take into account concentration and pre- ssure inhomogeneities in the film. Recent measure- ments 121 of superfluid transition nucleation in helium mixtures show that equation (1) is also : pS(X(Z), P(Z), TS) dZ = F(TS) ( 3 ) IdS
where pS the superfluid density depends on tempera- ture, local pressure and concentration ; Z is the distance of a He atom to the wall and dS is the so- lid layer thickness. The profiles P(Z) and X(Z) are obtained by calculations 121. The function F(TS) is evaluated from experimental observations of super- fluidity onset in helium mixtures 121.
For a given critical temperature TC, assuming that the values of PC and XC are independant of thickness, we use those measured in bulk mixtures 141.
We find that simultaneously to the formation of a superfluid phase located between dS and we also can get, in some mixtures, a local critical point for phase separation at Z d. The instabili- ty nucleates at the boundary of the superfluidphase
when i t appears. ' h i s phenomenon i s d e f i n e d a s a l o c a l t r i c r i t i c a : behaviour. Such behaviour i s ex- pected when therc i s a s o l u t i o n of equation (3) f o r
T = T and X(d) = XC, P(d) = PC.
S C
F i r s t of a l l looking a t a f i l m i n which t h e su- p e r f l u i d t r a n s i t i o n occurs over t h e a l l t h i c k n e s s we o b t a i n a s o l u t i o n b y numerical i n t e g r a t i o n of (3) The l o c a l t r i c r i t i c a l behaviour e x i s t s i n a f i l m of
t h i c k n e s s 3.6 atomic l a y e r s average 3 ~ e concentra- t i o n <X> = 0.31 a t T = 0.872 K.
t
I t i s a l s o p o s s i b l e , changing t h e average con- c e n t r a t i o n and f i l m t h i c k n e s s , t o g e t a s u p e r f l u i d t r a n s i t i o n only on a t h i c k n e s s d - d which i s a S f r a c t i o n of t h e t o t a l f i l m t h i c k n e s s e - dS. We then a l s o observe t h e t r i c r i t i c a l behaviour a t Z
-
d i n a temperature range .872 (K) ,$ Tt ,$ .83 (K) t h e r e i s no s o l u t i o n f o r a t r i c r i t i c a l behaviour i n m i x t u r e s f i l m s . The temperature Tt depends of c o u r s e on t h e average c o n c e n t r a t i o n i n t h e f i l m and t o t a l t h i c k - n e s s . Our r e s u l t s a r e p r e s e n t e d f i g u r e 1.Fig. 1 : T r i c r i t i c a l temperature Tt v e r s u s f i l m t h i c k n e s s e ( i n atomic l a y e r s ) and average 3 ~ e c o n c e n t r a t i o n <X>.
Our c a l c u l a t i o n s show however c l e a r l y t h a t f o r a l l t h e s e p o i n t s t h e s u p e r f l u i d phase t h i c k n e s s and i t s average c o n c e n t r a t i o n remain unchanged (d
-
d =S 3.6 atomic l a y e r and <X> = 0.31). Our c a l c u l a t i o n s show t h a t l o c a l t r i c r i t i c a l behaviour i s p o s s i b l e i n m i x t u r e s f i l m s . A l i n e of " t r i c r i t i c a l p o i n t s " can even b e o b t a i n e d v a r y i n g c o n c e n t r a t i o n and t h i c k - References / I / Papoular, M., J o u r n a l de Physique
37
(1976) C1- 237./ 2 / Romagnan, J.P., L a h e u r t e , J.P., Noiray, J.C. and S a m , W.F., J o u r n a l of Low Temp.
30
(1978) 425 /3/ S c h o l t z , J.H., Mac Lean, E.D. and Rudnick, I . ,Phys. Rev. L e t t e r s
11
(1974) 147./ 4 / Zinov'eva, K.N., Zh. Eksp. Teor. F i z .
46
(1963)1837, Sov. Phys. JETP
17
(1963) 1235.n e s s
