Polarized Target Group
Cathy Wasko
Phys 393 – Independent Study
May 2005
The University of Virginia Polarized Target Group looks to study nuclear spin polarization and the improvement of it in various materials. The group is continuously improving equipment and procedure while exploring different materials and other ways to achieve greater success in experimentation. I specifically learned about the preparation that goes into this experimentation through research, design, and material prep. I also learned about the procedures that take place during the actual experimentation as well as the analysis and recovery that follow the experimentation.
1. Introduction
The main goal of the University of Virginia Polarized Target Group is to provide targets for spin physics particle experiments. The degree of nuclear spin polarization and the time it takes to obtain this value in various materials are of importance. The group aims at improving these characteristics through a variety of methods. One way of increasing these values is through investigating the doping of the target sample. Doping means adding free electrons to the material. This can be done by chemical means or through irradiation. In the past, materials were chemically doped, but doping through irradiation has become more prevalent due its consistency and slower loss of the added electrons. The target group usually dopes by irradiation but will also chemically dope materials as well. This is one of many ways to improve polarization and the time it takes to reach this value.
When looking to improve polarization as well as relaxation times, we concern ourselves with two different types of targets: proton materials and deuteron materials. Some proton targets are polarizable to values of greater than 90% while the best deuteron targets can achieve a maximum polarization of around 40%. We have specific and independent goals for the two different targets.
In proton materials, we look to increase the dilution factor in experimentation. The dilution factor mainly results from unpolarized material such as unpolarized nucleons in the sample. It is calculated by taking the number of polarizable particles over the total number of particles. For example, consider ammonia (14NH3); in this case, three hydrogen and fourteen nitrogen give a factor of 3/17 (=3H/(3H+14N)). Determining the dilution factor and accounting for this in our calculation of the polarization will give us a more accurate value. We also look for improved handling techniques in proton materials. Finally, we experiment with the possibility of polarizing nitrogen in these materials as well as uncovering other polarizable elements in the sample.
With deuteron materials, the main goal is to get polarization up higher. As stated before, the most polarizable of deuteron targets max out around 40%. Our goal is to find ways to improve the polarization in these targets, possibly through changing doping doses or altering experimental values like strength of field or temperature. How these elements effect polarization will be explained later in full detail.
Finding which materials have the best polarization and relaxation times also benefits those not specifically involved with the polarized target group. Once found, these highly polarizable materials are utilized in other physics research like scattering experiments, as well as in other fields, such as in magnetic resonance imaging in the medical setting. As stated before, the group provides materials for spin physics particle experiments. Increased polarization of the targets would lead to an improvement in the quality of their experimentation. Also, improved polarizations of target material can vastly improve the resolution of MRI images. These are just a few benefits of greater polarizations in target material.
2. Theory
Nuclear magnetic resonance is achieved by placing nuclei in a static magnetic field, Bo, thus allowing unpaired spins of the nuclei to align themselves in the direction of the field. How many spins align depends on the strength of the field, the temperature, and the spins themselves. The difference between spins aligned in the direction of the field and spins anti-aligned with the field in the scope of the total number of spins gives rise to the polarization of the material and is represented by the equation
. (1)
N↑ denotes the number of spins aligned with the external magnetic field while N↓ denotes the number of spins not aligned with the field. A positive polarization means that there are more spins aligned with the field, as is obvious from the equation above. The reverse is true for a negative polarization.
Strength of field, the temperature, and the magnetic moment of the spins will all effect the polarization of the material. Intrinsically, a higher magnetic moment leads to a higher natural polarization. Polarization of the target also increases with an increase of the external magnetic field and/or a decrease in temperature. The natural resting polarization of a material when located in a constant magnetic field at a constant temperature is known as thermal equilibrium (TE) polarization. These values can be related with the polarization equation
(2)
for the polarization of spin ½ particles. In this equation, μ is the magnetic moment, Bo is the value of the magnetic field, k is Boltzmann’s constant, and T is the lattice temperature. In our experimentation with the low temperature of ~1.5K and a magnetic field of 5Tesla, the electron polarization is greater than 99% and proton polarization is ~0.5%.
The concept of doping was touched upon but should be explained in further detail. Doping is a method for improving the polarization of the material. One method of polarization involving doping is known as dynamic nuclear polarization (DNP). Through DNP, materials are doped either chemically or through irradiation, and as stated before, the target group has recently been concentrating on materials that have been doped through irradiation. Once doped, there are extra electrons to either align themselves or anti-align themselves with the material’s intrinsic spins. Thus there are four probable states: down-up (↓↑), up-up (↑↑), down-down (↓↓), or up-down (↑↓) (taking the first spin to be the proton and the second to be the electron). The energy of these states denotes the probability of being in each state, with the more probable state being the lower energy state. These states are listed in order of decreasing energy, making the last state the most probable one. Forced transitions between states is the underlying theory of DNP, and if these four were the actual states of the system, there would be forbidden transitions between the states (↑↓) to (↓↑) and (↓↓) to (↑↑). Due to other factors, the actual states of the system are a combination of states, still totaling four states but these forbidden transitions are permitted to occur. Thus there are six transitions: two nuclear spin flip (NMR transitions) where the proton flips, two electron spin flips (EPR transitions) and the two previously forbidden transitions. See Figure 1 below for an illustration of the possible transitions between states.
Once doped and placed in a constant magnetic field and temperature, the material’s spins are in their natural states. The target is then hit with microwaves at a frequency (adding energy to the system) represented by the equation below
(3)
These added frequencies cause the transitions among the states to take place. When this happens, both the spin of the protons and the spin of the electrons are flipped. The relaxation time of the electron spin is much, much less than that of the proton, so the electron transitions back to a state of lower energy in order to be used once again to flip another proton. This act is repeated many times, causing more and more protons to align, thus causing the polarization of
Figure 1 – This shows the possible transitions involved during Dynamic Nuclear Polarization (DNP). This also illustrates the relative energies of each spin orientation as well.
the material to increase. The polarity of the polarization (positive or negative) is the result of the microwave frequency added to the system as shown by equation 3 above.
When it comes to actually measuring this value of polarization, continuous wave nuclear magnetic resonance is utilized. Continuous wave can be employed by either applying a constant frequency while the magnetic field is varied or by keeping the magnetic field constant while the frequency is varied. As explained above, microwaves at a frequency represented by Equation 3 are applied. Thus, the material is situated in a magnetic field of known strength. To measure the polarization of this material, a series resonant LCR circuit is employed, where the inductor (L) is located within or surrounding the target. The circuit is tuned so that it resonates with the same frequency as the resonant or Larmor frequency of the nuclei being. The circuit then spans over a window of frequencies. At resonance, there is a voltage peak which is known as the Q curve. This peak corresponds to the nuclei being polarized, because the peak in power results from certain nuclei either 1) aligning themselves with the field and giving off energy to the system or 2) anti-aligning themselves with the field which requires energy from the system. The Q curve is then subtracted from the overall signal of the material, and resulting curve can be used to determine the polarization of the target. The area under this curve is linearly related to the polarization. Using a calibration constant determined from the earlier temperature equilibrium (TE) polarization, we are able to convert the area under the curve into the polarization value. An example of a proton signal can be seen in Figure 2 below. An example of a deuteron signal can be seen in Figure 3, also below.
Figure 2 – Borane Ammonia Signal – This is a signal of positive proton polarization.
Figure 3 – Deuterated Butanol Signal – This is a signal of positive deuteron polarization.
Finally, a concept mentioned briefly before is that of relaxation. Spin relaxation is the amount of time it takes the nuclear spin to relax back to its natural state relative to the static magnetic field, Bo. As stated before, the material is placed in a static field with an oscillating field pulsed perpendicular to it. The field is continuously oscillating such that the polarization of the material continues to increase to its maximum positive or negative polarization. When the oscillating field is removed, the polarized spins begin to flip back to their natural equilibrated state. This is an exponential decay, as can be seen in Figure 4 below. We are interested in the length of time it takes these spins to return to this state. The longer the length of the relaxation time, the more advantageous the material is to other researchers.
Figure 4 – This is an example of the relaxation of deuterated polyethylene (CD2). This is an exponential decay from the negative and follows the form f(x) = -exp((x-xo)/t)+c. If this were a decay from the positive, it would follow the form f(x) = exp((x-xo)/t)+c. The temperature plotted in this graph ranges from 1.560K to 1.590K, thus fluctuating only 0.03K over nearly 4 hours of relaxation.
With the understanding of what polarization is, how higher polarization is achieved, and how the value of polarization is measured, we move on to the description of the equipment utilized.
3. Equipment
The three components of our experimentation that have been focused on thus far have been the material itself, the applied magnetic fields, and the temperature of the system. We have performed experiments with many different materials which are too extensive to list them all here. The materials that I have been directly involved with through data analysis include deuterated materials: deuterated butanol and deuterated polyethylene (CD2), as well as proton materials: lithium hydride, butanol, polyethylene (CH2), and specifically, borane ammonia (NH3BH3). All of these materials were doped through irradiation.
A magnetic field of 5 Tesla is produced by an Oxford superconducting electromagnet in our cryostat system. Also included in the system is a helium-4 refrigerator. A schematic resembling that of our cryostat system can be seen in Figure 5 below. The colder end of the refrigerator is placed inside the electromagnet. A liquid nitrogen chamber is used to buffer the liquid helium chamber from the outside, in the manner of a heat shield. There also are evacuated areas throughout the system to provide an additional buffer. The helium-4 used in the refrigerator reaches a temperature of 4K in its liquid state at atmospheric pressure. A series of pumps are employed to create a low pressure system in the chamber that houses the liquid helium. This then removes the warm vapor in the chamber and allows the chamber to reach the low temperature of 1K. As explained above, the lower temperature allows for a greater polarization of the materials. Both the liquid nitrogen and liquid helium chambers are manually filled as necessary from outside dewars.
Figure 5 - Schematic of a cryostat system resembling the system used by the polarized target group.
Once cooled down, the system is ready for operation. Target material is placed inside this cryogenic system by way of a target insert. Located along the insert are target cups (in which the material is placed), the NMR coil, and microwave instrumentation. Down the center of the stick are electronics that deliver pulses to the material and carry vital information back to the experimenter. Normally, one or two cups would be loaded with target material, allowing greater experimentation time between times when the stick needs to be pulled for material recovery and reloading.
Finally, the material would be polarized by the method explained above. Most targets are polarized for about two hours to see the maximum polarization achievable in that timeframe. If the material does not respond well, it will not be left in the system that long; however, if the material is responding very well, it may be left in much long.
4. Material Preparation
4.1 Bead Making and Irradiation
Another important task in experimentation is the actual preparation of the material. The material being analyzed begins in a liquid or powder form and is frozen or pressed into a solid state. When beginning in a powdered form, the material can be dissolved in a liquid. A warm bath can be utilized in order to expedite the dissolving process. The liquid material is then dropped by way of a burette or syringe, both tipped with a hypodermic needle, into a bath of liquid nitrogen. The hypodermic needle is employed to insure that the volume of the drop is very small (on the order of mm3), such that many beads will be able to fit into the target cup. When in the nitrogen bath, the beads are kept from attracting to one another and are ushered to the corners of the bath by way of a magnetic spinner. The spinner keeps the liquid moving in a circular fashion, thus causing a current and aiding in the formation of more uniform beads, as well as leading to an easier recovery. Once the beads are made, they are collected into a small bottle and deposited into storage dewars for later use.