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NMR Spectroscopy: Bulk Magnetization

Nuclei possessing a non-zero spin and thus a magnetic moment display Larmor precession when placed in a static magnetic field (B). Real samples are composed of a very large number of nuclei. The magnetic moment of the entire sample, called the bulk magnetization (M), is the vector sum of the individual nuclear magnetic moments.

Just as an individual nuclear magnetic moment, μ, precesses about B, similarly the bulk magnetization precesses about B.

Unlike μ, which can never be perfectly aligned along B, the bulk magnetization can become perfectly aligned along B. This situation occurs when the μx and μy components of all the various nuclei become randomly distributed and perfectly offset each other.

The following comparison might be helpful:

Nuclear Magnetic MomentBulk Magnetization
μx and μy oscillate as a consequence of precession
μz = ℏ γ mI
|μ| never equals μz
μ is not aligned along B
μ is constantly changing
Mx = My = 0
Mz = |M| = Meq
M is perfectly aligned along B and is static

μx and μy oscillate as a consequence of precession
μz = ℏ γ mI
|μ| never equals μz
μ is not aligned along B
μ is constantly changing
Mx and My oscillate as a consequence of precession

Mz does not equal |M|
M is not perfectly aligned along B
M is constantly changing

Larmor Frequency

The rate of precession is related to the intrinsic properties of the nuclei (γ) and the strength of the static magnetic field (B):

ν = γ B / 2π

The frequency of precession (ν) has units of Hz (that is, cycles per sec),

It is possible to detect the precession of the bulk magnetization by placing a detector in the xy plane. A detector, represented by the red or blue disk in the animation below, is simply a coil of wire. If one passes a current through a coiled wire, a magnetic field is induced. Conversely, if a coil is placed in a changing magnetic field, a current (and consequently a voltage) is induced in the coil. This is the mode of detection in NMR spectroscopy. Note that the detector signal is proportional to the rate of change of the bulk magnetization (dM/dt) and not the bulk magnetization itself.


Enable one of the detectors and observe how the detector's signal varies with the position of the bulk magnetization.

If both detectors are enabled, observe how the signals are 90o out of phase with each other, which allows on to identify the direction of precession.

Allow the animation to run for awhile and then measure the Larmor frequency from the graph. Pressing the left mouse button will display the cursor position. Measure the period for the signal; the frequency (in Hz) is the reciprocal of the period.

The time scale for the animation is much smaller than the real time scale. The graph display time in nanoseconds (1 nsec = 10-9 sec). The simulation has been slowed drastically to facilitate visualization.

The simulation is for 1H, for which γ = 2.675222 x 108 sec-1 T-1. Use your measured frequency to calculated the magnitude of B.



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© Copyright 2013-2014, David N. Blauch