We decided to try to look for flow through helium by a concptiually different approach [5,6]. Rather than squeezinig the lattice of solid helium directly (if you squeeze a porous rock, no water will come out even though the water may fill all the open and connected pores of the rock), we decided to try to inject atoms from the liquid phase. Typically this is not possible beacuse superfuid heliumin direct contact with the solid would cause a hopelessly large heat flux to the sample cell. We created an enviromnent in which porous glass pennetrated the region of our apparatus that was filled with solid helium. In porous glass the freezing pressure of solid helium is well above the normal 25 bars. Thus, by pressurizing the liquid in the porous glass we could attempt to inject helium atoms into the solid that was in contact with the liquid helium held in the porous glass. Figure 1 is a schematic illustration of the apparatus [5,6].
Figure 1: Cell used to study the growth of solid helium from superfluid helium. Helium is admitted to the solid chamber S through capillaries 1 and 2 (heat-sunk only at 4 K) which first lead to liquid reservoirs atop thin porous glass (Vycor) rods V1 and V2. The reservoirs are heated by heaters H1 and H2. Two capacitance strain gages, one on each side of S measure the pressure of solid, while the temperature is measured by carbon thermometer TC. The pressures of the fill lines are measured by pressure transducers P1 and P2 located outside of the cryostat. A third capillary, 3, was heat sunk in several places including the coldest heat exchanger, bypassing the Vycor and was used to initially fill the cell with liquid helium, which was then frozen.
The principle of operation of the appartus is rather simple. One presurizes one of the fill lines, e.g. #1, and looks for a response on the other fill line, #2. Any change in the pressure observed on the other fill line or the cell implies that atoms had to migrate through the experimental cell, which is filled with solid helium. Thus, any change in the pressure in line #2 indicates that mass moved though the solid helium from line #1 to line #2.
Figure 2: An example of a sample of solid helium (Sample BS; ref 6) showing a flow of mass through solid Helium. The pressure in R1, P1, was increased at t $\approx$ 6 minutes, the regulator feeding helium to line 1 was closed at t $\approx$ 30 minutes, and changes in pressure were observed for about 6 hours. Note that dP2/dT was nearly linear for a substantial duration and independent of P1-P2. A change in the pressure of the solid helium in the cell is also recorded on the in situ pressure gauge C1.
Figure 3: An example of a sample of solid helium that did not show flow. Sample BT was warmed from 400 to 547 mK (from sample BS). The sample at 547 mK did not show flow. In this case the regulator fed atoms into R1 for about 30 minutes, but over 7 hours there was no significant movement of the pressures towards equilibrium. Colder temperatures result in flow; higher temepratueres at nearly the same pressure do not. Samples at temperatures above 600 mK have never shown flow in any of our experiments.