7.12: NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered inhomogenous by the presence of the sample and the probe, resulting in broadened peaks with extraneous side-bands and poor resolution.

These inhomogeneities are corrected before the spectra are recorded by a process called shimming. A set of shim coils surrounds the probe and generates small magnetic fields depending on the current passed through them. These fields can enhance or oppose B₀ in the vicinity of the sample. Shimming involves manipulating the coil fields to obtain the most uniform magnetic field across the sample, correcting the inhomogeneities. Shimming, optimized pulse sequence parameters, and proper sample preparation ensure good peak shape, low signal-to-noise ratio, and maximum resolution.

The Lorentzian peaks in an NMR spectrum are defined by their position, amplitude, and full width at half maximum.

The peak width of a properly prepared sample in a perfectly homogeneous field is governed by the spin–spin relaxation time alone.

However, the applied magnetic field, B₀, is rendered inhomogenous by the presence of the sample and the probe. This results in broadened peaks with extraneous side-bands and poor resolution.

Magnetic field inhomogeneities are corrected by a process called shimming.

During shimming, current is passed through a set of shim coils surrounding the probe, generating small magnetic fields that enhance or oppose B₀ in the vicinity of the sample.

These shim coil fields are manipulated to obtain the most uniform magnetic field across the sample.

Shimming, along with optimized pulse sequence parameters and proper sample preparation, ensures good peak shape, high signal-to-noise ratio, and maximum resolution.

• NMR (Nuclear Magnetic Resonance) - Technique for resonance and relaxation analysis of magnetic nuclei.
• Free Induction Decay - The exponential decay signal detected in NMR.
• Lorentzian Peak - A spectral peak in the frequency domain via Fourier transform of an exponential decay.
• Shimming - Process of magnetic field correction to enhance NMR resolution by countering field inhomogeneities.
• Fourier Transform of a Lorentzian - The process yielding a spectral frequency peak from the exponential decay in NMR.

• Define NMR - Understanding the techniques involved in NMR (e.g., free induction decay).
• Contrast Free Induction Decay vs Lorentzian Peak - Explain the difference between these two elements of NMR (e.g., relationship of exponential decay to frequency domain peak).
• Explore Examples - Discuss practical examples of shimming in NMR (e.g., correction of inhomogeneities for better resolution).
• Explain Shimming - Explaining how the process of shimming impacts resolution and signal-to-noise ratio.
• Apply Fourier Transform in Context - Understand the use and result of Fourier Transform in a Lorentzian to yield a spectral peak.

• What is NMR and how does free induction decay contribute to it?
• What is a Lorentzian Peak in the context of NMR?
• How does the process of shimming contribute to peak resolution in NMR?

• Students - Deepen your understanding of key NMR concepts and improve your familiarity with scientific terms.
• Educators - Provides a clear framework for teaching complex NMR concepts, including free induction decay, Lorentzian peak, shimming, and Fourier transform.
• Researchers - Relevant in advancing spectral analysis and understanding of magnetic fields.
• Science Enthusiasts - Offers insights into advanced study of magnetic fields and resonance, sparking broader interest and curiosity.