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3He-induced free vortices in thin superfluid films
Physica B 165&166 (1990) 767-768 North-Holland
3He-INDUCED
FREE VORTICES
IN THIN SUPERFLUID
FILMS
D. Finotellozb, Y. Y. Yub*‘,F. M. Gasparini’ a) Department of Physics, SUNY at Buffalo, Buffalo, NY, U.S.A. b) Department of Physics, Kent State University, Kent, OH, U.S.A. c) Department of Physics, Syracuse University, Syracuse, NY, U.S.A.
We report analysis of measurements of the thermal conductance of 3He-4He mixture fii near the Kosterlitz-Thouless transition. It is found that on the supeffluid side of the transition our data can be understood by the existence of free vortices induced by the addition of 3He to ‘He films.
In 2D helium Bhns near the superfluid transition, heat is transported via a convective mechanism that involves mass transport across the opposite ends of the experimental cell. The superfluid film, driven towards the hot end, evaporates by absorbing latent heat. A pressure gradient drives the gas to the cold end where it recondenses liberating its latent heat. By solving [1,2] the appropriate hydrodynamic equations it has been shown that K, - Mz(~~)(~m)~z(uz~~/~)exp(4xt~‘~/b) and Ks -
JzWO~“,d’l<24~ T)
(5)
(l/Kg+ l/K,)-’
with Kv the largest measurable conductance the experimental cell geometry.
0.351
(2)
(3)
/
I
0.
220
(4)
3( K 3>
FIGURE 1 Full symbols, the highest value of measured conductance, &, for ‘He films of different thickness. Plusses, the temperature dependence of K, for a thick film. The solid line is drawn to guide the eye. The dashed line is a power law fit.
We performed thermal conductance measurements on superfluid helium films whose thickness ranged from 11.7 to 36.5 A. Thicker films up to 156A were studied on a different cell and are discussed elsewhere [4]. Values for the upper conductance, K,,, as function of temperature are shown in Fig. 1. The symbols with the error bars represent K,, for 4He
which for TcT, reduces to * Supported by NSF Grants DMR-8601848 and DMR-8905771 0921-4526/90/803.50
on
0.
T Measurements of the thermal conductance of helium films provide information on the correlation length as well as on the number of free vortices present in the film. Since for T
dependent
(1)
with W/L the perimeter for film flow, I=TS, the latent heat, S, being the entropy, D the vortex diffusion constant, a the vortex core diameter, b a non-universal constant, t=T&-1 the reduced temperature, p s and n the density and viscosity of the gas, d the refluxing channel width, Kr and Ks the superfluid and the gas conductances, and n, the free vortex density. The constant F reflects the proportionality between the vortex density and the correlation length, n, - t-2 - a-2exp(-4xt-W/6)
Km- Ku-
@ 1990 - El sevier Science Publishers B.V. (North-Holland)
D. Finotello, Y.Y. Yu, FM. Gasparini
768
10 A A
n1012 N
A
E
10
A
a
0
_: A A
A
i
??
14.7 A
?? A
AA
T< Tc
A
10-30
’
’
Concen
’
’ ’ ’ ’
1
trat
ion(
2 5%)
FIGURE 2 Deped~~ce of the measured upper conductance on the percent 3He concentration. Dashed line is a calculation for the 14.7 A mixture fihns including the scattering mechanism. gee test. Elms of different thickness. These data seem to be consistent with a ‘IJ dependence suggesting a Kapitza boundary resistance as the mechanism for &. The plusses in Fig. 1 represent data taken at constant thickness but extended over a broad temperature range below T,. The dashed line through these data corresponds to a power-law dependence on T of 235+0.05, again consistent with a boundary resistance rather than a gas flow conductance. Our estimate for this gas flow conductance (Eiq. 2) is Ks=28 W/K or two orders of magnitude higher than measured. We concluded [3] that for pure fihns a Kapitra resistance mechanism is responsible for the upper conductance at T
(6)
through (Y,is concentration dependent. Assuming ee vortices are present for T
IDI
l2 3He
Dens
If2 ‘3 l’t”y ( cmp2)
FIGURE 3 Number of induced free vortices for T
~“W/~“@) - (qqd
+ 1)“
(7)
with K(O)=& the upper conductance in the pure film case. The calculated conductance for the 14.7A mixtures is indicated by the dashed line in Fig. 2. The measured conductance values are clearly lower than what is expected from the scattering mechanism. This ditference is most likely due to the assumption of zero free vortices. We thus suqest that beaides the scattering mechanism, the addition of He induces free vortices on the superfluid side of the transition. From the difference between the calculated and measured data in Fig. 2 we calculate the density of free vortices nr in the film. This is plotted as a function of the number density of ‘He in Fig. 3. Note that for the mixture flhns studied, nr is about one order of magnitude smaller than the 3He number density. We conclude that the decrease in the largest measured conductance is due to the gas scattering mechanism together with the generation of free vortices in the film. REFERENCES (1) V. Ambegaolrar, B. I. Halperin, D. R. Nelson, and E. D. Siggia Phys. Rev. B21,1806 (1980) S. I. Teitel, J. Low Temp. Phys. 46,77 (1982) D. Fiiotello and F. M. Gasparini, Phys. Rev Lett. 55, 2156 (1985) (4) D. Finotello, Y. Y. Yu, and F. M. Gasparini, Phys. Rev. Lett. 57, 843 (1986); to appear in Phys. Rev. B. (5) M. Dingus, F. Zhong, and H. Meyer, J. Low Temp. Phys. 65, 185 (1986).
I:;
3He-INDUCED
FREE VORTICES
IN THIN SUPERFLUID
FILMS
D. Finotellozb, Y. Y. Yub*‘,F. M. Gasparini’ a) Department of Physics, SUNY at Buffalo, Buffalo, NY, U.S.A. b) Department of Physics, Kent State University, Kent, OH, U.S.A. c) Department of Physics, Syracuse University, Syracuse, NY, U.S.A.
We report analysis of measurements of the thermal conductance of 3He-4He mixture fii near the Kosterlitz-Thouless transition. It is found that on the supeffluid side of the transition our data can be understood by the existence of free vortices induced by the addition of 3He to ‘He films.
In 2D helium Bhns near the superfluid transition, heat is transported via a convective mechanism that involves mass transport across the opposite ends of the experimental cell. The superfluid film, driven towards the hot end, evaporates by absorbing latent heat. A pressure gradient drives the gas to the cold end where it recondenses liberating its latent heat. By solving [1,2] the appropriate hydrodynamic equations it has been shown that K, - Mz(~~)(~m)~z(uz~~/~)exp(4xt~‘~/b) and Ks -
JzWO~“,d’l<24~ T)
(5)
(l/Kg+ l/K,)-’
with Kv the largest measurable conductance the experimental cell geometry.
0.351
(2)
(3)
/
I
0.
220
(4)
3( K 3>
FIGURE 1 Full symbols, the highest value of measured conductance, &, for ‘He films of different thickness. Plusses, the temperature dependence of K, for a thick film. The solid line is drawn to guide the eye. The dashed line is a power law fit.
We performed thermal conductance measurements on superfluid helium films whose thickness ranged from 11.7 to 36.5 A. Thicker films up to 156A were studied on a different cell and are discussed elsewhere [4]. Values for the upper conductance, K,,, as function of temperature are shown in Fig. 1. The symbols with the error bars represent K,, for 4He
which for TcT, reduces to * Supported by NSF Grants DMR-8601848 and DMR-8905771 0921-4526/90/803.50
on
0.
T Measurements of the thermal conductance of helium films provide information on the correlation length as well as on the number of free vortices present in the film. Since for T
dependent
(1)
with W/L the perimeter for film flow, I=TS, the latent heat, S, being the entropy, D the vortex diffusion constant, a the vortex core diameter, b a non-universal constant, t=T&-1 the reduced temperature, p s and n the density and viscosity of the gas, d the refluxing channel width, Kr and Ks the superfluid and the gas conductances, and n, the free vortex density. The constant F reflects the proportionality between the vortex density and the correlation length, n, - t-2 - a-2exp(-4xt-W/6)
Km- Ku-
@ 1990 - El sevier Science Publishers B.V. (North-Holland)
D. Finotello, Y.Y. Yu, FM. Gasparini
768
10 A A
n1012 N
A
E
10
A
a
0
_: A A
A
i
??
14.7 A
?? A
AA
T< Tc
A
10-30
’
’
Concen
’
’ ’ ’ ’
1
trat
ion(
2 5%)
FIGURE 2 Deped~~ce of the measured upper conductance on the percent 3He concentration. Dashed line is a calculation for the 14.7 A mixture fihns including the scattering mechanism. gee test. Elms of different thickness. These data seem to be consistent with a ‘IJ dependence suggesting a Kapitza boundary resistance as the mechanism for &. The plusses in Fig. 1 represent data taken at constant thickness but extended over a broad temperature range below T,. The dashed line through these data corresponds to a power-law dependence on T of 235+0.05, again consistent with a boundary resistance rather than a gas flow conductance. Our estimate for this gas flow conductance (Eiq. 2) is Ks=28 W/K or two orders of magnitude higher than measured. We concluded [3] that for pure fihns a Kapitra resistance mechanism is responsible for the upper conductance at T
(6)
through (Y,is concentration dependent. Assuming ee vortices are present for T
IDI
l2 3He
Dens
If2 ‘3 l’t”y ( cmp2)
FIGURE 3 Number of induced free vortices for T
~“W/~“@) - (qqd
+ 1)“
(7)
with K(O)=& the upper conductance in the pure film case. The calculated conductance for the 14.7A mixtures is indicated by the dashed line in Fig. 2. The measured conductance values are clearly lower than what is expected from the scattering mechanism. This ditference is most likely due to the assumption of zero free vortices. We thus suqest that beaides the scattering mechanism, the addition of He induces free vortices on the superfluid side of the transition. From the difference between the calculated and measured data in Fig. 2 we calculate the density of free vortices nr in the film. This is plotted as a function of the number density of ‘He in Fig. 3. Note that for the mixture flhns studied, nr is about one order of magnitude smaller than the 3He number density. We conclude that the decrease in the largest measured conductance is due to the gas scattering mechanism together with the generation of free vortices in the film. REFERENCES (1) V. Ambegaolrar, B. I. Halperin, D. R. Nelson, and E. D. Siggia Phys. Rev. B21,1806 (1980) S. I. Teitel, J. Low Temp. Phys. 46,77 (1982) D. Fiiotello and F. M. Gasparini, Phys. Rev Lett. 55, 2156 (1985) (4) D. Finotello, Y. Y. Yu, and F. M. Gasparini, Phys. Rev. Lett. 57, 843 (1986); to appear in Phys. Rev. B. (5) M. Dingus, F. Zhong, and H. Meyer, J. Low Temp. Phys. 65, 185 (1986).
I:;