|
|
The
Observed Properties of Liquid Helium
at the Saturated Vapor
Pressure
Chapter
5. Third Sound Velocity
The
velocity of third sound in helium II for wavelength long compared to the
thickness of the film, d, is given to good approximation by
where
<ps>/p is the effective superfluid
density in the film, f is the restoring force per unit mass, S is the
entropy, T the thermodynamic temperature and L
the latent heat. The restoring force is
where
is the van der Waals's
attraction between a 4He atom and the substrate and
is a retardation parameter.
The effective superfluid density is less than the bulk density because
of healing effects near the walls, such that
where
is the bulk value and D is a temperature-dependent parameter which has
been determined to have the form
D=a+bTp/ps
with
a = 0.5 layers/K and b=1.13 for glass. Here D and d are in units of atomic
layers. Both constants are determined from experiment. The thickness scale
is determined by the partial pressure P in the sample chamber from the
relationship
d3=[T
ln( P / P0)
where
P0 is the saturated vapor pressure at temperature T.
For very thin films (d < 10 atomic layers, where 1 atomic layer = 3.6
angstroms) retardation effects are negligible and the restoring force
can be approximated by f=3/d4,
so that to first order the velocity becomes
The
parameter D can then be determined by making a plot of
as
a function of d with slope unity and intercept D.
For a substrate which is reasonably smooth on the microscopic scale, the
third sound velocity is relatively independent of the substrate on which
it is measured because
and
d3=[T
ln( P / P0)
so
that the first order
is independent of .
Chronological Bibliography for Third Sound Velocity
1 |
C. W. F. Everitt, K. R. Atkins, and A. Denenstein, "Detection of Third
Sound in Liquid Helium," Phys. Rev. Lett. 8, 161-163 (1962). |
2 |
R.
S. Kagiwada, J. C. Fraser, I. Rudnick, and D. Bergman, “Superflow
in Helium Films: Third Sound Measurements,” Phys. Rev. Lett.
22, 338-342 (1968). |
3 |
I.
Rudnick, R. S. Kagiwada, J. C. Fraser, and E. Guyon, “Third
Sound in Adsorbed Superfluid Films,” Phys. Rev. Lett. 20, 430-434
(1968). |
4 |
D.
Bergman, “Hydrodynamics and Third Sound in Thin He II Films,”
Phys. Rev. 188, 370-384 (1969). |
5 |
K.
A. Pickar and K. R. Atkins, “Critical Velocity of a Superflowing
Liquid-Helium Film Using Third Sound,” Phys. Rev. 178, 389-399
(1969). |
6 |
C.
H. Anderson and E. S. Sabiskey, “Phonon Interference in Thin
Films of Liquid Helium,” Phys. Rev. Lett. 24, 1049-1052 (1970). |
7 |
K.
R. Atkins and I. Rudnick, “Third Sound,” in Progress in
Low Temperature Physics, edited by C. G. Gorter (North Holland Publishing,
1970), Vol. 6, pp. 37-76. |
8 |
D.
Bergman, “Third Sound in Superfluid Helium Films of Arbitrary
Thickness,” Phys. Rev. A 3, 2053-2056 (1971). |
9 |
T.
Wang and I. Rudnick, “Anomalous Attenuation of Third Sound,”
J. Low Temp. Phys. 9, 425-433 (1972). |
10 |
J.
Scholtz, E. MacLean, and I. Rudnick, “Third Sound and the Healing
Length of Helium II Films as Thin as 2.1 Atomic Layers,” Phys.
Rev. Lett. 32, 147-151 (1974). |
11 |
K.
Telschow, T. Wang, and I. Rudnick, “Observation of the Critical
Velocity Peak in Superfluid Films,” Phys. Rev. Lett. 32, 1292-1295
(1974). |
12 |
K.
Telschow, I. Rudnick, and T. Wang, “An Experiment on the Bernoulli
Thinning Effect in Unsaturated Superfluid Films,” J. Low Temp.
Phys. 18, 43-63 (1975). |
13 |
R.
K. Galiewicz, K. L. Telschow, and R. B. Hallock, “Persistent
Currents in Saturated Superfluid 4He Films in the Presence of Third
Sound Resonances,” J. Low Temp. Phys. 26, 147-163 (1977). |
14 |
J.
S. Brooks, F. M. Ellis, and R. B. Hallock, “Direct Observation
of Pulsed Third Sound Mass Displacement Waves in Unsaturated 4He Films,”
Phys. Rev. Lett. 40, 240-243 (1978). |
15 |
D.
T. Ekholm and R. B. Hallock, “Film Thinning in Unstaturated
Superfluid 4He Films During Persistent Flow,” Phys. Rev. B 19,
2485-2487 (1979). |
16 |
P.
H. Roberts, R. N. Hills, and R. J. Donnelly, “Calculation of
the Static Healing Length in Helium II,” Phys. Lett. A 70, 437-440
(1979). |
17 |
D. T. Ekholm and R. B. Hallock, “Thickness Measurements of Unsaturated
Superfluid 4He Films Under Driven and Persistent Flow,” J. Low
Temp. Phys. 42, 339-361 (1981). |
|
|