Earth's Field NMR Gradient/Field Coil System by Teachspin: Experiments

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Earth's Field Nuclear Magnetic Resonance (NMR) Gradient/Field Coil System

Newsletter 1 – Transforming Earth's Field NMR
Newsletter 2 – Putting the 'R' Into the Earth's Field NMR
Learn about Earth's Field NMR

Gradient/Field Coil System Brochure
Earth's Field NMR Brochure

Experiments

In addition to making the T₁ measurements done with the original EFNMR1-A more accessible, the Gradient/Field Coil system allows many entirely new types of experiments.

Experiments with the Gradient Coils

Spin-Spin Relaxation Time T₂
With the currents in the gradient coils adjusted to yield decay times on the order of 2 seconds in distilled water, it becomes possible to study the effects on T₂ of doping the water with various impurities. Students may be surprised that NaCl has no effect while CuSO₄, even in very low concentrations, shortens T₂ dramatically. Figure 3 shows our measurements of T₂ as a function of CuSO₄ concentration. These measurements may be compared to measurements of the spin–lattice relaxation time, T₁ at the same concentrations.

NMR Imaging
The gradient coils also allow students to study the basic physics of MRI, magnetic resonance imaging. The one-dimensional image, created with our special seven-section segmented sample is a simple but excellent introduction to the fundamentals of this important medical diagnostic technique.

The basis of all MRI is the use of a deliberate, tailored, magnetic field gradient across the sample. This is accomplished by first creating a "gradient free" environment for the sample and finding the precession frequency. A deliberate gradient is then introduced along the cylindrical axis of the segmented sample. The physical implication of this magnetic configuration is that any proton's x-coordinate in position space has been mapped into the FID signal's frequency-space departure from the originally observed frequency.

The Fourier transform of this signal, shown in Figure 4, makes the various spectral components of the FID signal immediately obvious. This data was taken with only three of the seven sections filled with water. Note the three peaks! Knowing the magnitude and direction of the x-gradient, one can reconstruct the separation of the three water filled cells. Even more information about the sample can be obtained by doping individual sections with different concentrations of CuSO₄ and measuring the signal intensity as a function of polarization time. In MRI lingo, this is known as a T₁ image.

Spin-Echo
The celebrated phenomenon of the spin-echo can be observed using this gradient coil system. Spin-echoes are observed when the sample is in a magnetic field in which field gradients, rather than spin-spin interactions, limit the FID decay time.

To observe a spin-echo using only the gradient coils, the student first optimizes the gradient field for maximum FID decay time. Then, a deliberate x-gradient is applied using the step-change toggle switch. This gradient can be reversed manually, or, by using the step-delay control, after a preset time. Figure 5 shows the result, using a 1 sec step-delay. The FID decay goes to zero in about 200 msec, but, because there is still coherence in the spin system, we can reconstitute the signal as a spin-echo at 2 sec by reversing the gradient. In this TeachSpin apparatus, the term "echo" takes on new meaning since the students can actually hear the echo signal in real time from the speakers in the EFNMR1-A.

Experiments with the Helmholtz Coils

Absolute g-value
The ratio of the magnetic moment to the angular momentum of a nucleus is called the "gyromagnetic ratio" or g-value. It has a unique value for each nuclear species. Simultaneous measurements of the magnetic field and the precession frequency are needed to determine the g-value of any nuclei. Since the Helmholtz coils have a known geometry and number of turns, a calibrated current meter allows an absolute determination of the magnetic field. By measuring the precession frequency of the FID, the absolute g-value can be determined. The gyromagnetic ratio of the proton can be measured to better than 1% precision in absolute units.

"Other" Nuclei
To accommodate the variation in local Earth’s magnetic fields, The EFNMR1-A can be tuned from 1600 to 2600 Hz. However, using the Helmholtz coils and an additional 3 A current regulated power supply, at least four common nuclear moments can be made to precess within this tuning range. Students can experiment with heavy water, phosphoric acid, and other interesting chemicals, some of which have important biological applications. In addition to determining nuclear g-values for ²H, ¹⁹F, and ³¹P, students can study spin-spin as well as spin-lattice relaxation in these materials. Figure 6 shows the FFT signal (on a logarithmic scale) of the ³¹P in phosphoric acid standing over 20 db above the noise.

Vector Addition
A measurement of the precession frequency as a function of Helmholtz-coil current can be fitted to a quadratic model for the vector addition of the Earth's and Helmholtz fields to show quantitatively that magnetic fields are vectors (Figure 7). This analysis also measures any misalignment angle between the Earth's and Helmholtz coil fields.

Learn about Earth's Field NMR.

Earth's Field NMR Gradient/Field Coil System