Results and Discussion

Spectrometer calibration:

The unloaded cavity resonance was found to be at a frequency of 9.35 GHz. For reasons yet to be investigated, the cavity resonance frequency did not agree with calculations for the simple cylindrical cavity. The resonance frequency found was nearest to the TE112 mode line. The cavity was not an ideal cavity, so it was expected that the resonance frequency would be lower, but not by the amount measured. It is interesting to note that when the cavity was modeled using concentric cylinders, figure 7, and by using the mode chart in figure 8 to determine the value of the Bessel function, the calculated resonance frequency was 9.36 GHz, which strongly agrees with the measured value. This indicates that the cavity mimics attributes similar to a coaxial cavity.

Figure 7: Geometric Parameter for a concentric cylindrical cavity.

Figure 8: TE – modes in concentric cylindrical cavities

Figure 9: Loaded Cavity Resonance

The spectrometer was tested and calibrated using a sample of 2,2-diphenyl – 1-picrylhydrazyl (DPPH). DPPH was used because of its narrow, but intense resonance line resulting from the free electron associated with one of the nitrogen atoms. The DPPH was placed in the cavity and tuned into resonance. The resonance dip is shown in figure 9, the quality factor (Q) was calculated to be 1870. The absorption resonance due to the unpaired electrons in the DPPH is shown in figure 10. The spectrum was observed at room temperature, 298 K, using X-Band microwaves with a frequency of 9.325 GHz. The magnetic field was swept at a rate of 100 G per minute through a range of 1000 G. The magnetic field was modulated at 20 KHz and the signal was filtered through a phase sensitive lock-in amplifier. The resulting signals observed were the absorption resonance obtained directly through the detector, figure 10(a), and the derivative of the absorption resonance obtained through the lock-in amplifier, figure 10(b). The absorption resonance was observed at a magnetic field strength of 3325 G. Using the fundamental equation of EPR presented in the theoretical section (eq-7), a g-value of 2.0035 is obtained. This agrees with the g-value for DPPH (g = 2.0036 ± 0.0003) to within the experimental error of the accepted value. The g-value measured for DPPH slightly deviates from the g-value of the free electron (g = 2.0023), this indicates that the orbital motion of the nitrogen bound electron is nearly canceled out by the molecular structure of the DPPH. Although the g-value peaks at a field strength of 3325 G, the integrated spectrum reveals that the electrons resonate over a range of magnetic field strengths. This build up and decay of the resonance is due to the magnetic interactions between the electrons and their environment. The number of DPPH molecules in the sample does not allow all of the electrons to transition at one specific energy. Further measurement of the integrated intensity, the area under the signal from the detector, figure 10(a), allows for the calculation of the concentration of EPR active species within the sample. 

Figure 10: Signal observed for DPPH through the detector (bottom) and lock-in amplifier (top)

Synthetic Ruby Experiment:

Our sample was cylindrical in shape with height of 1.3335 cm and a diameter of 0.3193 cm. The color is deep red which suggests impurities of iron as well as chromium. The sample is suspended from a small cut of salt crystal and is adhered with thick grease. It lies inside a glass chamber that protrudes into the cavity. The synthetic ruby sample and the salt crystal are connected to a brass cylinder which is in turn connected to the dewer. The dewer rests on a steel counter and is free to rotate 360 degrees.

We begin testing the ruby by making sure our cavity is resonating as well as possible. This is done by adjusting the waveguide screws and/or the reflector intensity until the absorption dip in out peak displayed on our oscilloscope is as close to the center of the peak, and as close to zero as possible. 

The magnet is then activated and swept for short increments of about 1-2.5 min. We then adjust the sensitivity of the lock-in amplifier until the signal is sufficient. If the ruby derivative peaks are at an appreciable height, approximately 1mV, and the derivative signal looks close to the theoretical derivative signal, then we increase the sweep time to ten minutes with a range on 10000 G. Since we do not know where to define zero, we set the dewer to an arbitrary zero and take data for ten minute sweeps at ten degree increments. 

A Hall probe is attached to the electromagnet and reads off an induced voltage reading in millivolts. A reading of the voltage value from the probe is recorded at each peak. It is crucial to record the position of at least one peak and recommended to record at least two. These will be used later to correlate the peak positions when the time steps are converted to the field strength in Gauss. This recording of the peaks is necessary because the sweep time is never exactly ten minutes.

Figure 11: Lattice Orientation

Our ruby is axially mirrored across a 90 degree range and repetitive across a 180 degree range. This is demonstrated in the isofrequency plot created from laboratory data. Our absorption peaks are believed to be caused by electron spin flips within the Cr+3 because our experiment’s sensitivity level is too low to resolve anything else. We believe that the c-axis of our crystal is likely tilted with respect to the z axis of the dewer that it is hanging from and being rotated with. We conjecture that the only way for the lattice reaction to change, if the lattice is repetitive, is for it to be tilted at different angles to the B field as it is rotated.

Figure 12: detail of Lattice.

As the crystal rotates, different surfaces are “visible” to the magnetic field. In other words, the magnetic flux through the crystalline lattice will be more or less at a glancing angle, depending on the angle of rotation. This causes the peaks to appear at different Gauss readings for different angles within a 90 degree rotation

Figure 13: Isofrequency plot for various orientations of synthetic ruby

Error Analysis:

There were a significant amount of errors involved throughout the duration of this experiment. Beginning with the electromagnet, there were difficulties from the start. When calibrating the magnet, we used a Hall probe was itself calibrated with an uncertain value. The value of the calibration magnet was determined using a current deflection test, which had human error involved. The magnet was then used to calibrate the Hall probe, which was then used to read the strength of the electromagnet to determine the error in the value displayed by the electromagnet.

Error also occurred in the measurement of the klystron frequency because the frequency meter used was switched out midway through the experiment and afterwards the peak value did not match up to the previous one. Currently, we have no explanation for this phenomenon, but obviously, it had an effect on the accuracy of our results.

While recording the data for the peaks in the ruby sample, we took down the voltage values by hand, which created a great source of human error. Some of the peak values were not recorded directly in the middle of the peak and frequently happened slightly after they occurred. This significantly reduced the accuracy of each peak value and since there was not sufficient time to take several sweeps of the same value, no average value could be obtained.