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2
Gravity-Sensitive Systems at Equilibrium
CRITICAL PHENOMENA
Near their critical points, ~many-body" systems exhibit long-
range order that greatly exceeds the range of the interparticle
interactions. The characteristic length over which the long-range
order persists is called the correlation length. If all of the thermo-
dynarn~c variables of a many-body system can be held sufficiently
close to those defining the critical point, the correlation length can
approach one millimeter. This long correlation length produces
anomalies in the thermodynamic, transport, and structural prom
erties of the system. These anomalies are remarkably independent
of the choice of system. Exper~rnental and theoretical studies of
these anomalies offer an exciting approach to the general "many-
body problem," which has challenged physics for a very long time.
The same long-range order exhibited in many-body systems
near their critical points also exists in systems that have "second-
order" or cooperative phase transitions. A transition especially
suitable for experimental study is the so-called lambda (~) tran-
sition between normal and superfluid liquid helium, as discussed
later in this section.
Recent interest in critical phenomena has been stimulated by
the new theoretical understanding of these phenomena achieved by
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67
Kenneth Wilson, who applied the Renormalization Group Tech-
nique to the problem. This work led to his being awarded the
Nobel prize. Even though Wilson's work produced specific val-
ues of the coefficients and exponents that characterize the critical
anomalies, the experunents have not yet been able to test the
finer details of the theory. Accurate experimental values of the
predicted quantities require extremely precise measurements un-
der tightly controlled conditions (temperature, pressure, density,
and so on). Otherwise, the experiments are unable to distinguish
between conflicting theories. In some exper~rnents the tempera-
tures of the sample must be uniform, measured, and controlled
to one part in 10~°. On Earth the necessary uniformity cannot
be achieved throughout the sample because of strain produced by
the Earth's gravitational field. Therefore the experiment must be
done in a reduced-gravity environment to permit definitive mea-
surement.
Projects leading to space experiments on matter near critical
points or passing through cooperative phase transitions are now
proceeding in several universities and at the National Bureau of
Standards. Each of these projects involves collaboration with one
of the NASA flight centers. Examples of these experiments follow.
One experiment measures the decay rates of critical fluctu-
ations of a simple fluid (xenon) very near its critical point by
observing the light scattering from thin samples of the fluid. The
experiment cannot be performed on Earth because the very large
compressibility of any simple fluid at its critical point will lead to
a large density gradient in the sample due to the sample's own
weight. In a low-gravity environment the density gradient will be
greatly reduced and it will be possible to keep the entire sample
within one microdegree Kelvin of the critical temperature. Under
these conditions the experiment will provide a definitive test of
the theory of decay rates.
Another experiment measures the viscosity of xenon near its
critical point to develop theoretical models of transport properties
of critical fluids and to provide another test of Renormalization
Group predictions. Still another experiment studies transport
properties, i.e., thermal conductivity and shear viscosity near the
liquid-vapor critical point of 3He arid very near the critical point
of 3He/4He mixtures.
Of all the critical-phenomena experiments now in progress,
the one nearest to flight is the so-called lambda point experiment,
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~8
which measures the heat capacity of liquid helium through its
lambda transition from its superfluid phase into its normal fluid
phase. When conducted in m~crogravity, the experunent has the
potential of measuring and controlling the temperature of the
sample to a few parts in 10~°. It will be possible to take data
points within a few parts in 10~° of the transition temperature,
four orders of magnitude closer than has been achieved on Earth.
This is unport ant because the measurements on Earth do not
approach the transition temperature closely enough to put the
prediction of the Renormalization Group calculation to a stringent
test. By contrast the flight experiment will provide a high-quality
test of the Renormalization Group methodology. This experiment
will be followed by a series of critical point flight experiments,
which are outgrowths of the ground-based projects referred to in
the previous paragraphs.
Since a m~crogravity environment permits an improvement of
four orders of magnitude in precision of measurement on critical
phenomena, it is clear that this new regime must be fully exploited.
Now that the technology for using liquid helium in m~crograv-
ity is being developed to the point where we can operate very
close to the lambda transition, it will be possible to address a host
of other fundamental problems. One such problem is the direct
determination of the correlation length for liquid helium. Another
is the construction of a weak link for superfluid helium that would
allow the study of Josephson effects, which heretofore have been
seen only in superconductivity. A weak link is a connection be-
tween two helium baths that depresses the wave function of the
order parameter but allows the phases on either side to remain
relatecI; such a connection will likely have to be of the order of the
correlation length in size. Attempts have been made to construct
a weak link in ground-based exper~rnents, but without apparent
success perhaps because the correlation length is of the order of
angstroms at temperatures that can be attained on Earth. In a
microgravity environment the correlation length could approach
the size where a weak link could be constructed in a machine shop.
It would be fascinating to see what effect the various forms of
dissipation near the lambda transition would have on the tunnel-
ing rate in such a junction. Indeed, friction could be regulated
by changing pressure or adding 3He. Another situation that will
change with access to microgravity is the structure of the cores
of quantized vortices. The cores will become macroscopic in size
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69
close enough to the lambda transition, profoundly altering their
dynarn~cs. For example, vortex waves, vortex-vortex interactions,
and other phenomena will be altered as the sample reaches the
previously forbidden region close to the lambda point. It is en-
tirely possible that a way may be found to introduce tracers that
will allow the three-d~mensional motions of these vortices to be
visualized. We would then have a direct understanding of the true
nature of quantum turbulence.
Finally, the task group emphasizes the new technology that
will emerge as these critical-phenomena experiments are prepared
for space. In order to take full advantage of reduced gravity,
spacecraft instrumentation is being built that reaches new leveb
of sophistication. For example, the group performing the lambda
point experiment has already invented and built thermometers
that will measure the temperature of the liquid helium sample to
one part in 10~°.
They have also developed the calorimeter and control system
that will maintain the temperature to that precision. This alone ~
a technological feat. Similar innovations will probably attend the
development of other exper~rnents.
MECHANICS OF G1lANU[AR MEDIA
Consider the material behavior of cohesionless granular mate-
riais such as sand, flees, or powders. These materials are very weak
compared to other engineering materials, and therefore have low
failure stresses. Postfailure behavior ~ important in a variety of
scientific and engineering applications, including chemical process
ing of catalytic powders, earthquake engineering, and geophysical
catastrophes such as eruptions and landslides. The presence of
gravity represents a nearly insurmountable obstacle to the meat
surement of failure criteria, failure mode, and microscopic failure
mechanisms on the one hand, and postfailure behavior on the
other. This is so since, in a sample of sufficient size that contin-
uum properties can be measured, the axial stress due to gravity
has caused a stress gradient in the sample. This in turn leads to
an Nonhomogeneous material, since some portions are postfa~lure
and some prefailure. Some Spacelab experiments have already
been proposed to study these materials. The objectives of the
experiment are to make measurements of the stress-deformation
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70
behavior of these material under low confining stresses. Conven-
tional biaxial compression tests with continuous measurement of
load and strain are planned. furthermore, local microscopic pho"
tographic measurements of the motion of individual particles and
grains wail give insight into the grain-level mechanisms of failure.
These results wiB be useful for formulating and testing nonlinear
constitutive equations for such materials.
Representative terms from entire chapter:
liquid helium
