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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 66

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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.