Thursday, May 8, 2014

Lab Book May 8, 2014 Evaporation of Liquid Helium and YBCO Critical Field

Lab Book 2014_05_08 Hamilton Carter

Summary:  A lot of work was done on the YBCO side of the experiment.  YBCO superconducts at 90 degrees Kelvin or so.  If it can be used, then part of the experiment can be done using liquid nitrogen which is much cheaper than liquid hydrogen.  YBCO produces far fewer x-rays than Pb though, and at a far lower energy.  The fiberglass Dewar I hope to use for the pulsed magnetic field experiments was measured and it compares favorably to the originally proposed Pb sample size.  In the event that the pulsed magnetic coil is placed insside the fiberglass Dewar, it's going to evaporate some of the liquid helium.  Calculations were performed to find out how much and what the pressure build up due to this helium would be.  The pressure number seems suspiciously low and needs to be checked.

I’m catching up on some of the to do items from the last two days.
YBCO Experiments
The plan here would be to look for the critical field using the yoke magnet.  If we can find it, then experiments using liquid nitrogen, which is much cheaper than liquid helium, can be performed using both the yoke magnet and the can crusher coil.

Look into the AJP articles about how other people have added contacts.  Re-read the four point contact strategy.
I found a rather skeletal reference that states silver pain can be used to make contacts on YBCO samples.  The do provide contact information for the supplier, however.  They also have a very nice diagram for the four contact resistivity measurement.   The supplier listed is: Silver paint, cat. No. 16031, Ted Pella, Inc., P.O. Box 492477, Redding, CA 96049

The four point measurement works as follows.  A current is sent through the superconductor using the two outer leads.  As long as the superconductor is in its normal state, (resistive to electrical currents), then there will be a measurable voltage created by the current travelling between the two outer leads.  The two inner leads measure that voltage.

The question that still arises is whether or not we can quench the YBCO superconductor using the iron yoke magnet.  Hirsch’s data table indicates we may be able to, but other tables contradict it.  An article written by Tiernan at the University of Massachusetts indicates that granular YBCO has a much lower critical field than single crystal YBCO.  This is a good sign since we have granular samples from CAN superconductor.  There’s another article about measuring the critical current density that may be useful.  It looks like give a granular sample, Hirsch’s number is believable.  The next step is to look at low energy x-ray samples since YBCO gives much smaller energies than Pb.

As far as what energies can be detected using NaI scintillation, the following data is from 1952.

The available YBCO sample is 14 cm in diameter by 6 mm thick.  Assuming a maximal spherical size of a 3 mm radius gives the following maximum energy and flux as predicted by Hirsch’s formulas.
Maximum energy
6339.71 eV
Maximum flux
136.735  events
The maximum energy is in what Wikipedia calls the hard x-ray region.

Pb and Liquid Helium Work
The Pb sample may be placed into the fiberglass Dewar with the pulsing coil mounted either inside or outside the Dewar.  By mounting the coil outside, we can use a larger Pb sample since we don’t have to account for the radius of the pulsing coil.  DeSilva used a gap between the coils and the can to be crushed of minimally 0.5 mm.  The coil was constructed with 3 turns of number 10 copper wire.  The wire has a diameter of 2.588 mm.  The down side of mounting the coil outside is that our maximum magnetic field for a given current though the coil will be reduced.
Aside from the larger possible sample size, and the ease of construction, there’s another advantage to mounting the pulser coil outside the Dewar.  Most of the heat created by the coil pulses won’t wind up being deposited in the liquid helium. 
The proposed Pb sample will fit easily into the fiberglass Dewar.  The neck radius on the Dewar is 4.52 cm and the specified sample radius is 3.8 cm.  These dimensions give almost 7 mm of clearance on either side of the sample, which would seem to be enough room to fit the pulsing coil inside the Dewar.

If the coil does go into the Dewar, then there will be concerns about the amount of liquid helium evaporated per coil pulse and how much pressure will build up.  The following is a diagram of the inside of the fiberglass Dewar used for volume calculations.

Assuming only the tail is filled with liquid helium, that gives us the volume of the large chamber and the neck to fill with evaporate liquid helium.  The volume available is calculated below:

Fiberglass Dewar Dimensions (all in inches) Actual Scaled
Neck Dia 3.5625 0.890625 9.04875 cm
Chamber Dia 8.0625 2.015625 20.47875 cm
Neck Depth 12 3 30.48 cm
Chamber Depth 11 2.75 27.94 cm
Tail Depth 9.75 2.4375 24.765 cm
Neck volume 1960.117
Chamber volume 9202.868
Total volume 11162.98

This volume is to be substituted into the ideal gas state equation,

 where n is the number of moles of helium evaporated per pulse, R is the ideal gas constant, 8.314 cm^3 kPa/K mol, T is the temperature of the gas in degrees Kelvin and V is the volume of the gas in cubic centimeters.  The amount of liquid helium that will be evaporated by each pulse, is

 where m is the mass of helium in grams, E is the energy per pulse in Joules, and Q is the latent heat of liquid helium in J/gram. 

All the parameters used and calculated results are shown in the spreadsheet below.
Avagadros number 6.02E+23 molecues
molar conversion for H 4 g/mole He4
Empty volume above liquid helium 11162.98 cm^3
number of moles 5.952380952 mol
R 8.314 cm^3 kPa/K mole
T in Dewar above Li He 8 K
Specific Heat of Liquid Helium at ~4 K 3 J/gm.K
Latent Heat of Liquid Helium 21 J/gm
Density of liquid helium 125 g/liter
Energy from Pulser 500 J
Evaporation per pulse 23.80952381 gm 0.19048 l
Pressure after pulse 0.035465867 kPa 0.00514 psi

Table 1 Evaporation and pressure buildup
The pressure seems a little low.  I may have underestimated the temperature in the Dewar above the liquid helium.

Experimental Setups
Sample Quench Speed Dewar Sample Size Detector
YBCO Slow Styrofoam LiNi replenished 16mm x 6 mm Film
YBCO Fast Styrofoam LiNi replenished.  Sample holder reinforced for Lorentz forces. 16mm x 6 mm Film
Pb Slow Glass Dewar ~1.74 cm radius NaI
Pb Fast Fiberglass Dewar ~3.81 cm radius NaI

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