From Physics 111-Lab Wiki

All pages in this lab. Note To print Full Lab Write-up click on each link below and print separately

I. Nuclear Magnetic Resonance (NMR)

II. Staff Sign-off Sheet (NMR) and Pre-Lab Questions

III. Continuous Wave NMR Equipment

IV. Continuous Wave NMR - The Experiment

V. NMR RF Black Box Circuit Diagram

VI. NMR Frequency Table

VII. NMR Lock In Amplifier

VIII. NMR Scope Program

IX. Pulsed NMR

X. Pulsed NMR Equipment

XI. Pulsed NMR Setup

XII. Pulsed NMR Appendices

Reprints and other information can be found on the Physics 111 Library Site

Before The Lab

View the NMR and Pulsed NMR videos, discuss pre-lab questions with instructor, and get the Staff Sign-off Sheet (NMR) signed.

Discuss the Physics about this experiment with the faculty or the GSI's in the 111-Lab before starting.

You should keep a laboratory notebook. The notebook should contain a detailed record of everything that was done and how/why it was done, as well as all of the data and analysis, also with plenty of how/why entries. This will aid you when you write your report.

Introduction

In 1952 Felix Bloch and Edward Purcell received the Nobel Prize in physics for their discovery in 1945 of nuclear magnetic resonance. Bloch's method of observation is now widely used in many areas of science and technology. NMR is a sensitive probe of the local magnetic field in matter at the location of nuclei, and gives us information about nuclear spins and their surroundings. In the Medical field it is called Magnetic Resonance Imaging to avoid the use of the word "nuclear". This experiment has the following objectives:

1. To observe the phenomena of nuclear magnetic resonance (NMR) of protons in H2O and other liquids
2. To observe the absorption and dispersion line shapes of NMR under slow passage and under non-adiabatic passage conditions, and to study their dependence on concentration of paramagnetic ions added to the liquid
3. To measure the ratio of the magnetic moment of F¹⁹ to that of the proton
4. To use the technique of lock-in detection to get improved signal-to-noise ratios in the NMR detection.

A former student commented, "The best thing that can be said about NMR is that in beginning of the experiment, a student feels overwhelmed by its complexity. As you become more familiar with it, this feeling is replaced by curiosity and eventually understanding." This is to say that while there is a great deal to learn initially about NMR, given time and a lots of effort the pieces do fall into place, and the result is an unusually rewarding laboratory experiment.

To start, you should read Liboff, Bloch's article "Nuclear Magnetism" (Jan. 1955) and Kittel's chapter "Nuclear Magnetism and Masers", pp.499-509, (see Prerequisite Reading Materials), and Reference 4. These are just to get you started; you should look at the other references and articles in the reprints before you write your report. Watch the NMR video before proceeding to the next section.

Prerequisite Reading Materials

Note all reprints are on the Library Site under Physics 111 "Physics 111-Lab Library Site";

1. A. Abragam, Principles of Nuclear Magnetism, Oxford Press, 1961. This is the definitive reference. #QC762.A23
2. F. Bloch, "Nuclear Induction", Physical Review 60, 460, (1946). Bloch's two-coil method is used in this experiment. #QC1. S695 (Pages 460-474;)
3. R. Schumaker and W. A. Benjamin, Introduction to Magnetic Resonance, 1970. Reach Ch. 2 and Ch. 3. #QC762.S34
4. C. Kittel, Introduction to Solid State Physics, John Wiley 5^th Ed. (1976). Read pp. 479-509 for a brief-quantitative expose of the main ideas. #QC176.K51
5. L Yuan and C. S. Wu, Methods of Experimental Physics, Part B, Vol. 5, Academic Press (1963), pp. 104-123 (Section 2.4.1.4). This reference discusses all the ideas necessary to do the experiment, which uses the two-coil Bloch method. #QC33.M48
6. R. Liboff, Introduction Quantum Mechanics, Holden Day, 1980. Sections 11.8 and 11.9 include a simple, direct derivation of NMR, along with a physical interpretation. While Liboff does not use the classical Bloch equations, he does give a good idea of what's going on. #QC174.12.L54
7. S. Walker and H. Straw, Spectroscopy Vol. 1, Macmillian (1962, Ch. 5. (Available in 111 Lab, not to be taken out of the laboratory). #QC451.W2 (Engineering Library)
8. Bloch, Felix "Nuclear Magnetism"; American Scientists: Vol. 43, No. 1, Jan 1955, pp. 48-62.
9. Bloch, F., et al "The Nuclear Induction Experiment"; Physical Review: Vol. 70, Oct 1946, pp. 474-485.(Note: Note check out CRC Table of Physical Constants for valves)
10. Ames, D.P. "Magnetic Resonance": Chapter 9, pp. 8.112-8.127.
11. Hahn, E.L. "Free Nuclear Induction"; Physics Today, Nov. 1953. Pp.4-9.
12. Brewer, Richard G. & Hahn, Erwin L. "Atomic Memory"; Scientific American: Vol. 251, No. 6, Dec. 1984, pp. 50-57.
13. Lowe, I.J., & Whitson, D. "Simple Pulsed Nuclear-Magnetic Resonance Spectrometer"; pp. 335-338.
14. Cohen-Tannoudji, "Quantum Mechanics"; Vol. 1, 1977, Wiley. pp. 443-454.
15. Jacobsohn, Boris A. and Wangsness, Roald "Shapes of Nuclear Induction Signals"; Physical Review: Vol. 73, May, 1948, pp. 942-946
16. Bloembergen, N, Purcell, E. M., Pound, R.V. "Relaxation Effects in Nuclear Magnetic Resonance Absorption"; Physical Review: Vol. 73, Apr, 1948, pp. 679-712
17. NMR Reprints available from the Physics Library or from the 111-Lab share; reserved under 111-LAB
18. Watch the videos on NMR & Pulsed NMR and the video lecture series, called "Transitions" on the 111-Lab Network or from the Physics 111-Lab web site. 111-Lab Videos

Theory

Conceptually this experiment is quite simple, but how the data are recorded is not. It helps to know what we are going to do before we discuss what pieces of equipment we use.

Suppose we place a single nucleus between the south and north poles of the magnet. The magnetic moment of the nucleus forces the nucleus to align in such a way that the north pole of the magnet repels the north pole of the nucleus and the south pole of the magnet repels the south pole of the nucleus. This creates equal and opposite forces that form torque upon the nucleus. The nucleus begins to rotate around the vertical axis. This rotation of the nucleus is called "precession". The frequency of this precession is called the Larmor frequency. In this experiment we will place the sample of protons into the permanent magnet. This will force the protons to precess at the Larmor frequency and induce an electric field in a receiver coil that is wrapped around the sample test tube. At the same time we will apply a radio frequency to the sample. This frequency will be tuned to resonance at the precession frequency. Our goal is to observe the nuclear magnetic resonance of the protons in the sample.

Figure 1:The absorption signal of a magnetic resonant system as a function of magnetic field.

A sample of protons in a magnetic field of strength H₀ has energy levels that are populated according to the Boltzmann distribution. When we send in electromagnetic radiation with photons of energy the system absorbs some of the photons and reduces the total energy in the radiation. is known as the Larmor frequency, the resonance frequency of the system. The gyromagnetic ratio is determined from the ratio at resonance. We are going to measure the frequency, assume the value of , and determine H₀. For a fixed frequency, the resonance curve looks like Figure 1.

How shall we produce this curve so that we can measure H₀ at resonance? We could set to a fixed value and make measurements of (power out)/(power in) for many different values of H, in small enough increments to allow an accurate determination of H₀ from a plot of the data. Of course we could also set H to a fixed value, and make measurements as is varied. We really don't care about the exact values of power - we need only the ratios - but we do need some way of measuring the power, which in our case is at a frequency of about 16 MHz.

However, it is more satisfying and often enlightening to create a plot on an oscilloscope, so we can observe changes immediately as we adjust the equipment parameters. Let's scan H back and forth relatively slowly above and below the resonance value H_o. We will use a scan frequency of 60 Hz. The variation of H in time will look like Figure 2.

Figure 2: Applied Magnetic Field varying at 60 Hz

Let's put this plot together with the first one, to get Figure 3.

Figure 3: Measured signal

Now we will use the concept of "signal" to express the power ratio. We will plot the electric field, rather than the power, of the outgoing radiation at the frequency f_o as a function of time and call it the signal. The amplitude of this signal is a measure of the power absorption in the sample.

Figure 4a: Incident Field

Figure 4b: Resultant Field

The electric field at a frequency of 16 MHz is now modulated in amplitude at a frequency of 60 Hz. The magnitude of the amplitude when plotted in time is a measure of the resonance curve. The function of the detector is to rectify the 16 MHz signal, put it through a low pass filter to remove the 16 MHz component but leave the modulation component at 60 Hz. The signal is sent to an oscilloscope whose sweep frequency is set at 60 Hz. The display shows the amplitude of the modulation as a function of time (really a function of B), and consequently displays the desired resonance curve.

A block diagram with signals at the various stages appears in the next section.

To summarize, we take a liquid sample in a test tube and place it in a magnetic field. We apply a radio frequency magnetic field to the sample by placing it near a transmitter coil, and tune the frequency to resonance at the Larmor frequency, the precession frequency of the protons. As the protons precess, they induce an electric field in a receiver coil wrapped around the sample. The amplitude of the electric field is a maximum when the frequency of the applied RF field exactly matches the Larmor frequency. In a detector circuit we rectify the RF field, filter it to get a DC voltage proportional to the amplitude of the field, and display the voltage on an oscilloscope.

To take data, we set the frequency of the RF to the Larmor frequency for the field produced by the permanent magnet, and then sweep the magnetic field amplitude sinusoidally in time at 60 Hz, above and below the value for resonance (we say that the field is modulated sinusoidally with a frequency of 60 Hz). The detector output is a plot of the resonance curve, the amplitude of the detector signal vs. magnetic field applied to the sample, for a fixed frequency.

Figure 6: Block Diagram.

Figure 7: NMR Head Detail.

Revision 2007.1

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