Table of Contents
{ ${/download/attachments/201098661/Magnet.png?version=1&modificationDate=1546979577000&api=v2}$ | In 1946 nuclear magnetic resonance (NMR) in condensed matter was discovered simultaneously by Edward Purcell at Harvard and Felix Block at Stanford using different techniques. Both groups observed the response of magnetic nuclei, placed in a uniform magnetic field, to a continuous wave radio frequency (RF) magnetic field as the field was tuned through resonance. In 1950 Ervin Hahn, a young postdoctoral fellow at the University of Illinois, explored the response of magnetic nuclei in condensed matter to pulse bursts of these same RF magnetic fields. Hahn was interested in observing transient effects on the magnetic nuclei after the RF bursts. During these experiments, he observed a spin echo signal after a two-pulse sequence. This discovery, and his brilliant analysis of the experiments, gave birth to a new technique for studying magnetic resonance. These discoveries and advances have opened up a new form of spectroscopy which has become one of the most important tools in physics, chemistry, geology, biology, and medicine. Magnetic resonance imaging scans (abbreviated MRI – the word “nuclear” was removed to relieve the fears of the scientifically uninformed public) have revolutionized radiology. This imaging technique is completely noninvasive, produces remarkable three-dimensional images, and gives physicians detailed information about the inner working of living systems. |
References
[2] C. P. Slichter, Principles of Magnetic Resonance, Springer, New York, 1996.
1 Goals
Pulsed nuclear magnetic resonance (PNMR) is an experimental technique used to study the response of magnetic nuclei to an applied magnetic field. In this experiment you will learn the physics of how PNMR works and will make measurements of two characteristic relaxation time constants for protons in a mineral oil sample. These two time constants – and the techniques used to measure them – form the basis of medical MRI imaging.
Specifically, your goals for this experiment include the following:
- to learn to use the Pulse Programmer apparatus and the large, water-cooled electromagnet;
- to establish a resonance in samples of mineral oil and teflon, and to use these measure the gyromagnetic ratio of the proton and of fluorine nuclei, respectively;
- to measure the _T_2 relaxation time in mineral oil using the Hahn spin-echo method; and
- to measure the _T_1 relaxation time in mineral oil using the inversion-recovery method.
2 Theory
| Here we wish to examine the effect of magnetic fields on protons and other particles having magnetic moment and angular momentum. It is noteworthy that the underlying physics of nuclear magnetic resonance is very similar to that of electron spin resonance and optical pumping. |
We will first look at the behavior of a spinning magnetic dipole moment in an external magnetic field, then we will extrapolate that behavior to a large ensemble of protons.
2.1 Behavior of a single particle in an external magnetic field
It is useful to model nuclei as spinning bar magnets with an intrinsic magnetic dipole moment, μ, and an angular momentum, L.
In free space, a magnetic moment, μ, is free to point in any direction. However, if an external magnetic field B is present, μ will try to align itself with the external field. When we consider the effect of conservation of angular momentum, we find that μ will not fully align with B, but will instead precess about the axis defined by B. This behavior is analogous to a spinning top precessing in a gravitational field.
In a material containing large numbers of such nuclei, the sum of all the aligned nuclear dipole moments results in a net (bulk) magnetization in the sample. It is the magnitude of these bulk magnetizations, and their behavior over time which is measured in PNMR. Of particular interest are the characteristic times associated with the following:
- How long does it take a randomly oriented ensemble of magnetic nuclei to become aligned? This time scale is _T_1, known as the spin-lattice relaxation time. - How long does it take for nuclei precessing in phase to get completely out of phase due to nearest neighbor interactions? This is _T_2, known as the spin-spin relaxation time.
The rest of the theory section will focus specifically on protons (hydrogen nuclei), though it is generally applicable to any magnetic nuclei.
2.1.1 A spinning magnetic dipole in an external magnetic field
Consider the behavior of a bar magnet with dipole moment μ in a magnetic field B as shown in Fig. 1. When placed in an external magnetic field B, the dipole will feel a torque given by