A comparison is made between the predicted and measured magnetic dependence of the specific heat. At ~.4°K the effect in rhenium only becomes visible with the nuclear contribution representing about 25% of the total. It is possible, although the percentage of He3. due to the large difference in the vapor pressure of the two liquids.
Like He3. removed at the still stability of the chemical potential of He4. in .. luid superf requires He 3 to 11 evaporate11 from the condensed region to the .. dilute region across the phase boundary.
Equation (13) is directly related to setting up the osmotic pressure gradient that drives the He3. Because the temperature of the boiler is higher than that of the mixing chamber, the He3. °K and a typical still temperature of 0.75 °K the concentration of He3. in the future it will still be in the order of 1%.
With the material now developed, it is possible to analyze the performance of the dilution cooler.
At any instant, the heat transfer rate between the two sets of phonons is given by With this heat flow, the energy difference between the two baths will stabilize at temperatures T. 33) The quantity U is the internal energy in He4. If the dimensions involved are significantly smaller than the phonon mean free path at low temperatures, there will be little heat exchange between the cold He 3 system and the rest of the material.
However, using the estimate of spheres above as a lower bound and substituting into Equation (30), the boundary resistance R can be expressed in terms of the volume of the copper.
37) Then from Equation (36)
The ratio of specific heats cc/cd is 4.3, so the exchanger on the dilute side will require about four times the volume of copper as on the concentrated side. Note that if the He ratio becomes lower than 70%, the inlet fluid will be superfluid at temperatures corresponding to the main impedance temperature. Using these results and knowing the concentration as a function of temperature (Figure 6), it is possible to infer the vapor pressure of the liquid in the still as a function of still and mixing temperature.
If the still temperature was higher, too much He 4 would be vaporized and if it was lower, the pumping speed would be. reduced due to the reduced vapor pressure.
Instability arises because liquid in the dilute phase becomes heavier as temperature increases. Since for viscous flow the impedance varies as d-4 .. the diameter of the pipe exiting the mixing chamber must be kept small. 0 does not include n 3, so f does not, and the temperature gradient (Equation (50)) is linear in n 3 • The quenched dependence on t from equation (46) is determined by numerical integration.
Note that equation (49) where the conductance term is neglected goes as d -1 • Including the conductance term will.
Chapter III. Details of the Refrigerator Construction
General Characteristics
Then ~ will be independent of T and linearly dependent on d, while K will be linearly dependent on both T and d. The above analysis does not apply in this case. During refilling, the temperature of the pot will rise to 1.7 - 2.0 K. The refilling process takes only two to three 0. minutes and the operation of the dilution cooler is very little disturbed. To calculate this impedance value, the viscosity of He was taken as 3. The molar volume is therefore 37 cc/mol.
As described in the last chapter, the heat exchangers are very crucial for the efficient operation of the dilution refrigerator.
Still Design
The design of the upper part of the still has been the subject of an extensive study by Wheatley et al., (S), the final result of which has been a totally new design concept.C 3 . 0). The nylon provides thermal insulation between the heater and the copper walls of the still. The tunnel diode and tank circuit were located on the bottom of the still as shown in Figure 14.
The resistor is then greased into a hole drilled in the lug at the bottom of the mixing chamber. We also need a joint that will be reliably impermeable to liquid He. • Design 4 of this joint, using a crushed indium gasket as shown in Figure 17b, proved to be very satisfactory. While the refrigerator is maintained at,.., 4°K, the pressure in the insulating vacuum is reduced to,.., 1 X 10 mm Hg over a -5 period of about forty-five minutes.
For the phase boundary to reach the mixing chamber, all He 3 must be pumped from the quiescent side to the inlet side. This results in a shift of the phase boundary towards the still as the condenser cools. This temperature of 78 m°K is only the upper limit of the liquid temperature in the mixing chamber.
At a fixed pumping rate, the result is that the ambient temperature rises as the mixing chamber cools. This line is shown in Figure 8 (line A) and gives a measure of pumping efficiency at the station.
Chapter V. Suggested Improvements
The adjustment would be best when the cooling rate (slope of Figure 18) is large, at temperatures somewhat above the lower limit. This slope and the specific heat of the experimental additions will determine the time constant for the temperature change. There is also an increase in throughput as this occurs so it is possible that the impedance of the line in question is too high.
If the number of heat exchangers is increased, as discussed above, it would probably be worthwhile to build a new mixing chamber. This should be done to ensure the best possible thermal contact between the sample and the mixer at the lowest temperatures. The copper paddles used in the current chamber should be replaced with a copper sponge sintered into the bottom of the new mixing chamber.
The bottom should be made from a single piece of copper with good mechanical connections to which the samples can be attached. A potential problem with this type of stall can be keeping the fluid level from rising. Using a level sensor like ours can be helpful if this problem were to occur.
Chapter VI. Thermometry
Thermometry
- Resistance Thermometers
To establish good thermal contact between the resistor and the part whose temperature is to be measured, the outer insulation layer of the resistor is thinned. If one wants to estimate the temperature difference between the resistor and its surroundings, a measure of the thermal limiting resistance is needed. The output of the bridge was displayed on the y-axis of an oscilloscope with a sensitivity of 20 mvolt/cm.
A signal taken from the primary .. oscillator tap on the rear panel is input into the x-axis input of the. The sensitivity of the coil set is determined by the length and placement of the secondary windings. When winding the first secondary, the number of turns per layer was recorded.
The coils are wound on Bakelite molds with the secondary being a slip fit inside the primary. There is one ground point for the entire system of bridge, oscilloscope and coil sets. 39 Cu wires extending down through the center of the nylon rod and into the CMN chamber.
The resistor to be calibrated is also placed in the middle of this mixture with the axis of the resistor parallel to the axis of. Before calibrating the resistor against the CMN, it was calibrated in the temperature range .41°K - 4.2°K as discussed in Section A-1 of this chapter.
PART II
The Electric Field Gradient
Recall the discussion in Chapter I of this part of the three sources of electric field gradients in metals: (1) the contribution of the crystalline lattice considered as point charges. This will be indicated by qlatt. (2) The contribution of the local conduction electrons contained in a sphere centered at each lattice site. 1 • (3) The shielding or anti-shielding effect of the closed oc. shell core electrons around each lattice point.
From the work of Watson et al. it is predicted that the effect of the conduction electrons will be large. 00 and RQ are the Sterriheimer anti-shielding factors that correct for distortions of the closed-shell core electrons.C55. To consider the value obtained for A in the 12.5 kOe field and further, to predict possible NMR transitions that can be observed, it is necessary to study solutions of the combined Hamiltonian.
Matthias' program was obtained and converted to FORTRAN IVG for use on the IBM 360/75 system here at Caltech.t. From this program the energy levels are obtained as a function of the applied magnetic field and the. A comparison of the results at 12.5 kOe serves as a reasonable check on the self-consistency of our data. The result of this mixing will be that the amplitude of the NMR signal will be reduced from the expected value if, for example, states e and f of Figure 30 are assumed to correspond to pure states of mI = -1/2.
A measurement of the transition between these two levels together with the known level distribution scheme will enable one to extrapolate back to H = 0 and determine the zero field distribution. Finally, regarding metallic rhenium experimental verification and further refinements of the results obtained here.
Kerr, Proceedings of Fifth International Conference on Low Temperature Physics and Chemistry, Madison, Wisconsin, Low Temperature Physics and Chemistry, Madison, Wisconsin, red. Radford, Proceedings of the Seventh International Conference on Low Temperature of the Seventh International Conference on Low Temperature Physics.
Fermi temperature and deviation of the chemical potential from the ideal Fermi-Dirac value as a function of concentration. The center of the magnetic poles is under the bottom of the mixing chamber. The tunnel diode oscillator for the level sensor is mounted on the front of the still bottom as shown.
The heater is mounted on the nylon pedestal which is attached to the stationary bottom with a No. Details of the mixing chamber construction. Power, in microwatts, is applied to the mixing chamber as a function of mixing chamber temperature. The voltage and time scales are shown, as well as the resistance of the thermometer at points a and b.
The heater power is then turned off and the temperature decay of the sample to its original temperature is recorded. The slope of the cooling curve in ohms/sec is shown at each data point. Record of sample Re temperature plot as a function of magnetic field as the field is slowly swept from 0 to 300 Oe.
Plot of the sample temperature Re in the diagram as the field is slowly varied from 300 Oe to O. Energy level for ~ = 90 and 0 angular dependence of the resonant magnetic field for a fixed frequency as a function of the applied field.
FLOW IMPEDANCE
FLOW LIMITING O RI FICE
- CRUSHED INDIUM SEAL
PHASE SHIFTER
MEASURING SET
ADJUST ABLE COMPENSATORS
RHENIUM
