LT 21 Proceedings of the 21st International Conference on Low Temperature Physics Prague, August 8-14, 1996

Part S1 - Quantum Fluids and Solids: Liquid Helium

T h e o s m o t i c p r e s s u r e o f s a t u r a t e d 3 H e - 4 H e m i x t u r e s , p o l a r i z e d by d i l u t i o n

Alexandre Rodrigues b and Gerard Vermeulen a

Centre de Recherches sur les tr~s Basses Tempdratures, BP 166, 38042 Grenoble-C6dex 9, France

b l)epartamento de Fisica, Universidade Federal de Pernambuco, Cidade Univcrsitaria, 50.671.901 Recife, PE, Brasil

Liquid 3He has been cooled (T = 10-15 mK) and polarized by means of a 4He circulating dilution refrigerator. The polarization becomes stationary at 0.15, 7 times the equilibrium polarization in our external field of 7 T. Based on the behavior of the refrigerator as a polarizer, we claim that the molar susceptibilities of coexisting concentrated and dilute 3He are equal at a pressure of 2.6 =1= 0.04 bar. We have measured the osmotic pressure in the dilute phase as a function of the polarization of the concentrated phase up to 0.15. Applying the Clausius-Clapeyron equation for the field dependence of the osmotic pressure gives the susceptibility of the saturated dilute phase. Our results agree with NMR experiments on the dilute phase by Ahonen et al. after multiplying their results by 0.9.

1. I N T R O D U C T I O N Tile experimental study of highly polarized liquid

3He and liquid 3He-4He mixtures with a concentra- tion larger than 0.01 is only possible if the polar- ization, P, is out of equilibrium. In this case, the molar chemical potentialsz Pt and #$ of .3He-r and 3Iiej. (up and down) are different. It is convenient to define an effective field, B = Bc + (#.f - tq.) ~2NAT, where Be is the external field, NA Avogadro's num- ber and ")' the nuclear magnetic moment of 3He. P can be measured but the only way to have access to B is through other thermodynamic quantities. We report measurements of the osmotic pressure, H, in the dilute phase (3Hed) of a phase separated 3He-nile mixture as a function of the polarization, P3r of the concentrated phase (3Hee). In such a polarized mix- ture with equilibrium between the two phases, we have/Lact : ~34t, p3c$ : /~3d$ and B : B3c = B3d. II(B) is given by

( O i l ) = xs(m3d--rn3c) (1) b-B p,r (1 - =,) v40 '

where p is the preasure, T the temperature, mZd = NaTPzd and m3c = NATP3c, x, the 3He concentra- tion in the saturated dilute phase and v40 the molar volume of pure 4lie.

Fig. 1 shows the mixing chamber of the 4Iie cir- culating dilution refrigerator and the osmotic pres-

Figure 1: Experimental set-up

sure gauge. 4He is injected into the mixing chamber (nearly completely filled with 3Hec) to form droplets of ZHea, which fall into the heat/polarization ex- changer. Ideally, the 3Hec entering the mixing cham- ber is in equilibrium with the 3Hen droplets by ex- change of polarization and heat. Thus, the liquid polarizes if P3c(B) > P3a(B) [1] and it cools because tile enthalpy of 3Hed is bigger than of 3Hec. P3c

- the liquid is 3Hec for more than 99 % - is mea- sured by a NMR coil outside the mixing chamber and T by a vibrating wire viscometer. The osmotic pressure gauge [2] is connected to the injection capil- lary. There may be temperature, concentration and

Czechoslovak Journal of Physics, Vol. 46 (1996), Suppl. $1 2,4]

41

" 40.9"

S" 40.8 II

40.7

40.6

40.5 0 50 100 150 200

p32 (%2)

0.35

0.3

0.25

0.2

~ T ~ * , Ramm et al.

. . . . . -T~*u, Ahonen et al.

x - - - T ~ d , Ahonen scaled *

@ * �9 Tjd, H(P3~) 1 I 1

0 5 10 15 p (bar)

Figure 2: II(Pae, T = 0) versus P~c for different 3He circulation rates, ha, at p = 10 bar.

Figure 3: T~*, T~*d, T~* d rescaled (T~* c = T~d at p = 2.6 bar) and T~* d at 10 and 16 bar obtained from II.

polarization gradients between the phase separation interface and the liquid in the gauge, but the liquid adapts itself to keep P4 and hence H constant : II measured by the gauge equals II at the interface.

2. R E S U L T S

X3~ = X3d at p = 2.6 4- 0.04 bar, since circulation of 4He decreases P in the mixing chamber at p < 2.6 bar and increases P at p > 2.6 bar with respect to equilibrium.

Fig. 2 shows II(P3c, T = 0) versus P ~ for differ- ent 3He circulation rates, ha, at p = 10 bar. T in- creases with increasing P3r due to irreversible heating by magnetic relaxation and spin diffusion. Therefore, we have subtracted H(T) [2] from the experimental data. We draw attention to : (1) H decreases faster than quadratic in P3e and (2) II decreases and T increases with increasing n3. Effect (2) is due to mutual friction between 3He present in the injection capillary and the superfluid 4He flow. Both, the de- crease of H and the increase in T can be explained consistently by mutual friction and we are able to take this into account. Effect (1) could indicate a po- larization dependence of the susceptibility. We have analyzed our data at p = 10 and p = 16 bar in tile quadratic region (P < 0.07) to obtain X3d- Fig. 3 shows T*, defined by P = 7 B / k B T * , versus p for :~H% [3] and 3l'Ied [4]. Also shown is the data of ref. [4] multiplied by a factor 0.9 (tile absolute value of the data may be oil by 7 % [4]), so that X3~ = X3d at p = 2.6 bar. Our valucs of T,~ at p = I0 and

p = 16 bar agree with the scaled data. Analysis of the experimental data for II(T) on the phase separa- tion line of ref. [2] by means of a Clausius-Clapeyron equation similar to Eq. 1 leads to the effective mass, rn~d : 2.56, 2.96 and 3.28 at 0.26, 10 and 20 bar. Finally, we obtain 1 + F~' for 3Hed : 0.89 =1= 0.01 independent of p.

3. C O N C L U S I O N

If we assume that X3d is constant and X3r = X0 (1 + tiP'c) - fl > 0 for metamagnet ic and fl < 0 for paramagnetic behavior - we calculate never a de- crease of II that faster than quadratic in P3r as in Fig. 2. We find that II decreases always slower than quadratic in Pz~, if [fl[ is sufficiently large. Presently, we cannot exclude experimental errors due to either a non-linear NMR-spectrometer or thermal gradients between the 3Hea-ZHer interface and the viscometer. If II really behaves as in Fig. 2, it can only be ex- plained by a paramagnetic behavior of 3Hed.

R E F E R E N C E S [1] A. Rodrigues and G. Vermeulen, J. Low Temp.

Phys. 101 (1995) 151. [2] J. Landau, J .T. Tough, N.R. Brubaker and D.O.

Edwards, Phys. Rev A 2 (1970) 2472. [3] H. Ramm, P. Pedroni, J.R. Thompson and H.

Meyer, J. Low Temp. Phys. 2 (1970) 539. [4] A.I. Ahonen, M.A. Paalanen, R.C. Richardson

and Y. Takano, J. Low Temp. Phys. 25 (1976) 733.

242 Czech. J. Phys. 46 (1996), Suppl. $1