Electron Paramagnetic Resonance (EPR)

Associated topics: Microwaves, waveguide, resonant cavity

During this experiment, you will quantitatively observe the phenomenon of magnetic resonance. EPR is a useful tool which allows the observer to deduce many things about a particular sample. EPR reveals the existence of unpaired electrons and (by looking at the hyperfine splitting) one can also determine some characteristics of the orbital of the unpaired electrons.
 

You should read "An Introduction to Electron Paramagnetic Resonance Absorption" by Micro-Now Instrument Co. (there is a copy in the lab).

You should study the appropriate sections of one or more of the reference books (see below), and be familiar with the most basic ideas behind the following:
 

1. The phenomenon of magnetic field (Zeeman) splitting of energy levels.
2. What is the phenomenon of magnetic resonance? What causes it? What happens inside the sample at resonance?
3. What is Paramagnetism? What properties of a sample (atom) are important in paramagnetic resonance?
4. What is a Lande g-factor? What is the spectroscopic-splitting factor or g-value?
5. What is the quantity that is measured experimentally? To which theoretical properties does it relate?
6. What are T₁ and T₂? How are they related to the experimentally measured quantity?
7. What is hyperfine splitting? What causes it?
8. What is crystal field splitting?

You should also become familiar with the basics of microwave technology: Waveguides, attenuators, resonant cavities, circulators, klystron and Gunn diode sources, and diode detectors. See:
 

• D.J.E. Ingram, Spectroscopy at Radio and Microwave Frequencies,

• David J. E.Ingram, Radio and Microwave Spectroscopy,

• Turn on the Lock-in amplifier. Although you can and should change the settings on the lock-in as you do the experiment, the following are suggested as a preliminary setup.  The setup for the SR lock-in is similar.

1. Taking an EPR Spectrum:  You want to plot the output of the lock-in (Y) against magnetic field (X). The X-signal is taken from the VOLTAGE output of the SWEEP CIRCUIT. There are two ranges over which you should take spectra for each sample that you study. First, sweep over a broad range, to determine the general locations of the resonances. Second, for each peak or group of peaks, you should adjust the RANGE setting on SWEEP unit to get an expanded view and, hence, a more accurate value of g for each resonance. RANGE settings versus total magnetic field span is available in the lab.
1. Before recording the broad spectrum, scan through the range 2000-4000 gauss looking for peaks. If none appear, you probably need to increase the sensitivity of the lock-in. If the lock-in saturates while passing through a resonance, decrease the sensitivity.
2. Record the spectrum on the X-Y recorder by sweeping the magnetic field. You must use a sweep rate that does not distort the signal. Remember to note the values of the field (on the gaussmeter scale) at the beginning and end of the trace, so you can calibrate the x- axis. Label each plot with appropriate information (sample, lock-in sensitivity, time constant, etc.).
3. Determine the correct phase setting for the lock-in by sweeping through the resonance in DPPH for various phase settings. What should the phase be set to? Why?
4. After changing samples, you may need to adjust the settings of the following: The sensitivity and time constant of the lock-in, and the tuning of the Gunn diode to the cavity (Appendix 1). If you change the tuning voltage, you should record a new spectrum of DPPH at this setting for calibration.
2. Measurements
1. Record the EPR spectrum of DPPH. Assume that you know that g=2.0035 for DPPH and use this to measure the frequency of the Gunn oscillator. (This frequency is adjustable from 8-10 GHz.)
2. For each of the following samples, record both broad and expanded EPR spectra. Do not change the tuning voltage from the setting used for DPPH. Measure H, the width of the resonance. Calculate the g-factor for each resonance. Compare your results with known values for these quantities. Try to observe hyperfine splitting in at least one sample.
1. charred dextrose
2. CuCl₂ ^. 2 H₂O
3. K₃ [Cr (CN)₅ NO]^.H₂O
4. ruby
3. Study a solution of DPPH in benzene.
4. Record a direct absorption curve (instead of a first derivative) and/or a second derivative for a particular sample, say DPPH.
5. NOTE: Different samples may be available at the time you are doing the experiment.

APPENDIX 1

The Advanced Lab EPR Spectrometer

The resonant frequency of an empty microwave cavity depends only upon its dimensions. (See, for example, D. J. Griffiths, Introduction to Electrodynamics, 2nd Ed., Problem 8.42 on p. 395.) This frequency is altered when material is placed inside the cavity. For this reason, "tuning" the microwave bridge should be carried out with the sample to be studied in place in the cavity. The cavity resonant frequency, about 9 GHz (3 cm wavelength), can be observed to shift by several per cent when the sample is removed. (The frequency range between 8.2 and 12.4 GHz is often referred to as "X-band", originally a radar frequency designation.)
 

With the sample in place, the resonant frequency of the cavity is fixed, and the frequency of the microwave radiation has to be tuned to the cavity frequency. The source of the microwave radiation is a Gunn oscillator (a solid state device), the frequency of which can be changed mechanically (tuning screw) and electrically (voltage on varactor diode). The tuning screw has a major effect; please do not change the setting of this screw. The Tuning Voltage control (top right corner of the Micro-Now 810BR front panel) is used to tune the Gunn oscillator frequency to that of the cavity as follows:

1. On the oscilloscope, push in the X-Y the buttons (Horizantal Mode), making Channel 1 the x-axis and Channel 2, the y-axis (Vertical Mode).
2. Set the function generator (Wavetek 19) for a sine wave of approximately 3 KHz. Connect the output voltage through 50 W load to Channel 1(x-axis) input to the scope, and to J3 (MOD IN - modulation input jack) on the back panel of the Micro-Now 810BR. With the latter connection made, when the CW (continuous wave)/EXT MOD (external modulation) switch on the Micro-Now back panel is put in the EXT MOD position, 3 KHz voltage is added to the Tuning Voltage (on the Gunn varactor); this serves to modulate the Gunn oscillator frequency at 3 KHz and the x-axis of the scope becomes a Gunn oscillator frequency axis.
3. Connect the output of the Micro-Now 810BR preamp (jack on front panel) to scope Channel 1 (y-axis). The detector crystal produces a signal (amplified by the Micro-Now 810BR preamp) which depends upon the microwave power reflected from the cavity. This signal is a minimum when the radiation and cavity frequencies are the same, and one speaks of observing the "cavity dip" on the scope when the cavity resonant frequency falls within the frequency range displayed on the x-axis. (Actually one sees two cavity dips, not quite in phase, corresponding to the right and left sweeps across the scope x-axis.)

The Tuning Voltage control is used to change the central Gunn frequency until the cavity dip appears on the scope. The amplitude of the 3 KHz modulation is then continuously reduced while fine tuning the Tuning Voltage to keep the cavity dip on the scope. The frequency of the Gunn oscillator drifts while the system "warms up"; about an hour is required for the warm-up period.
 

Microwave radiation is brought to, and returned from, the cavity by a section of waveguide. Microwave field excitation impinges upon the cavity at a small hole in that side of the cavity which terminates the waveguide section The size of this hole has been carefully determined to reduce the reflection of microwave energy, but another adjustment is required to minimize the reflected energy - a screw setting which depends upon the "lossiness" of the sample. The screw control serves to match the impedance of the "loaded" cavity to the characteristic impedance of the waveguide. However, the microwave detector requires a minimum current of about 0.3 ma to be flowing through it in order to be sensitive to changes in power, and this is achieved in the Micro-Now System by means of a small amount of microwave power reflected from the cavity; i.e., the screw is set a bit off of the matched impedance point. It is not necessary to change the insertion of the screw from one sample to another unless the samples differ significantly in lossiness.

Water above freezing temperatures is a very strong absorber of microwave energy. Sample cells of special geometry partially overcome the lossiness of aqueous samples, but this delicate glassware will not be employed in the Advanced Lab.
 

In general the signal amplitude increases as the microwave power falling upon the cavity increases. However, when the rate at which the excited state is populated by microwave-induced transitions exceeds the rate of relaxation back to the ground state, the Boltzmann distribution between the two states cannot be maintained, and the signal strength begins to level off. As the power is increased further, the signal is ultimately reduced. This phenomenon is called "saturation" and is often accompanied by a distortion of the resonance. A microwave attenuator enables one to adjust the microwave power traveling down the waveguide. For most samples at room temperature, the relaxation rate is high and saturation is beyond the microwave power available. In this case a different upper limit is placed upon the power; one does not want to "burn out" the detector crystal. A crystal current of 0.1 to 0.2 ma will usually provide a good signal and not harm the detector crystal.