School of Physics

Experiment 14. Nuclear MagneticResonance

c©School of Physics, University of Sydney

Updated DJR March 6, 2011

How to do this Experiment: This experiment has been assembled as a double experiment.This experiment counts for double the standard marks and is allotted double the standard time(four weeks). Please review the material linked below before proceeding to the experimentalprocedure.Questions about this experiment can be directed to David Reilly: david.reilly@sydney.edu.au

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1 Objective

This experiment makes use the technique of Pulsed Nuclear Magnetic Resonance (NMR),which is the method used by all modern NMR spectrometers to manipulate and detect nu-clear spins in solids and liquids. You will investigate spin-lattice relaxation (T1) and spin-spindephasing (T2), which are two important mechanisms that characterize the ensemble of spinsin the sample.You will see how these parameters are sensitive to the chemical environment.

2 Pre-work

This is a double experiment and requires substantial prework in order to understand the physicsprior to commencing the experiment. The concepts build on classical mechanics (angular mo-mentum, gyroscopes) as well as electromagnetism and quantum mechanics and condensed mat-ter physics. Depending on your knowledge of these concepts, you may wish to undertake somerevision before tackling the physics of NMR.

A number of resources have been prepared to help you develop in understanding the physics ofNMR. See the documents in the NMR Resource folder:

http://www.physics.usyd.edu.au/ reilly/NMR/NMR.html

It is strongly recommended that you understand the classical mechanics of how a gyroscopeworks.

Intro to Gyroscopes link

An excellent introduction is also provided in the following online resources (available onYoutube).

NMR linkNMR linkNMR linkNMR linkNMR linkNMR linkNMR link

The experiment also makes use of more advanced concepts such as “Spin Echo”, “T1 re-laxation”, “Free induction decay” and “CPMG”. The student should be familiar with theseconcepts prior to commencing experimental work. To assist in developing an understanding ofthese topics, resources have been prepared and are available here:

http://www.physics.usyd.edu.au/ reilly/NMR/NMR.html

The Golden standard textbooks for the field are:

A. Abragam, “Principles of Nuclear Magnetism”, Clarendon, Oxford (1961).C. P. Slichter, “Principles of Magnetic Resonance”

NUCLEAR MAGNETIC RESONANCE 14–3

3 Experimental Setup

3.1 Equipment list

• The Nuclear Magnetic Resonance spectrometer consists of three modules:

– Magnet - in which the sample vial can be inserted.

– Case with power supply - this includes the receiver, pulse programmer, and oscil-lator/amplifier/mixer.

– Oscilloscope to display the nuclear magnetic resonance signal.

• Sample vials containing copper sulphate solution, glycerine, mineral oil, and water.

Figure 14-1 is a simplified schematic diagram of the NMR apparatus that you’ll be using. The

Fig. 14-1 : A schematic diagram of the NMR spectrometer.

diagram doesn’t show all the functions of each module, but it does represent the most importantfunctions of each modular component of the spectrometer.

The pulse programmer creates the pulse that controls the length of the radio-frequency (RF)pulse from the RF Oscillator, as well as triggering the oscilloscope on the appropriate pulse.The RF pulse is amplified and sent to the transmitter coils, which are around the sample. TheRF current in this coil produces a homogeneous 12 Gauss rotating magnetic field at the sample.This is the time-dependent B1 field that produces the 90◦ or 180◦ pulses. Remember that thedirection of the static magnetic field from the permanent magnet is considered to be along thez−axis. Let’s assume that the transmitter coil’s axis is along the y−axis, thus the coil that picksup the NMR signal is along the x−axis. Notice that this pick-up coil is the one tightly woundaround the sample in the diagram.

Any rotating magnetization in the xy−plane induces a voltage in the pick-up coil, which isthen amplified by the receiver circuitry. This amplified radio frequency (15 MHz) signal canbe detected by two separate and different detectors. The box labelled “Detector” in the dia-gram simply outputs the positive amplitude of the RF-signal from the pick-up coil. This is thedetector that you will use to record both the free induction decays and the pulse-echo signals.

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The other detector is a mixer, which multiplies the signal from the pick-up coil with continuousRF-signal from the oscillator. The output frequency is proportional to the difference betweenthe two frequencies. This idea is the same as that of “beats” for sound waves. Two similar (butnot exactly the same) waves will produce a beating sound. In the same way if the signal fromthe pick-up coil and the synthesis are not the same then the output frequency from the mixeris the difference between the two. If the two signals have the same frequency then there willnot be any oscillations from the output of the mixer. The mixture is essential for tuning theapparatus. The dual channel oscilloscope will show both the detector and mixer outputs.

4 Procedure

Note that the bench notes explain the front panel of the spectrometer in more detail.Make sure you refer to them since this will enable you to carry out the experiment withless head-scratching.

4.1 Tuning

The following procedures will enable you to tune the applied frequency so that it equals theresonant frequency of the precessing nuclei.

• Turn on the spectrometer from the spectrometer from the switch at the back. It willdisplay a frequency of 15.40000 MHz.

• Insert the Mineral oil sample in the magnet and set up the following parameters.

– Width of pulse A: 20% of full range .

– Mode: Int

– Repetition time: 100 ms, 100% of full range.

– Number of B Pulses: 0

– Sync A

– A: On, B: Off

– Time constant: 0.01

– Gain: 30%

• We must now tune the spectrometer to the precession frequency of the nuclei. Look atthe trace of the mixer output on the oscilloscope. Adjust the frequency so that there iszero beating (that is, no oscillations) from the mixer output.

• Now tune the receiver input for maximum signal.

• Look at the detected output and adjust the width of pulse A until the Free InductionDecay is a maximum. This is the so called 90◦ pulse. Note that the voltage measured onthe oscilloscope is directly proportional the the magnetization M(t) given in the theorysection of these notes.

• If you double the pulse width the Free Induction Decay should vanish, in which case younow have a 180◦ pulse.

NUCLEAR MAGNETIC RESONANCE 14–5

4.2 Magnetic Field Uniformity

After you have found a free induction decay signal and set the spectrometer for a 90◦ pulse, itis time to find the most uniform part of the magnet. This is the so called “sweet spot”. The twocontrols on the sample carriage allow you to move the sample in the x−y plane. The magneticfield at the sample uniquely determines the frequency of the free-induction decay signal. Themost uniform part produces the longest spin-spin relaxation time, T ∗2 .

• Try different positions by using the the x and y controls on the carriage until you find thepositions where T ∗2 is the longest, i.e. the longest FID. Try to make the detected signalso that it looks like a smooth exponential decay. If there are bumps in the decay, thenit means that you are in a highly non-uniform part of the field. Always check the mixersignal to see that you are on resonance.

• Record this value of T ∗2 , the resonant frequency, and the x and y positions where thesemeasurements were taken. The exponential decay of this FID can be used to determineT ∗2 .

• Note that you will have to change the frequency back to resonance (that is no oscillationson the mixed signal) for each position since the resonant frequency changes with differentmagnetic field strength.

Caution: The magnetic field in the gap changes with the changing room temperature through-out the day. So you must keep an eye on the mixer output in order to ensure that the spectrom-eter is on the resonant frequency.

The field difference (known as field gradient) over the sample can be estimated from T ∗2 as-suming that the field gradient is the major contributor to T ∗2 . For example, for mineral oil thereal T2 is much longer than T ∗2 .

• Determine the change in the magnetic field, ∆B, across your sample by obtaining 1/T ∗2which is equal to change in resonant frequency, ∆f , across the sample.

QUESTION: Explain why the most uniform part will produce the longest T ∗2 .

C 1 .

We will now determine the true spin-spin relation time T2, which is independent of the magneticfield gradient.

4.3 Spin-Spin relaxation time, T2, using only two pulses

• Use a two pulse spin-echo sequence, as outlined in the theory section to measure thespin-spin relaxation time, T2 for the mineral oil. Note that the ORIGIN program caneasily fit exponential decay equations to your data so that you can obtain T2.

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4.4 T2 using CPMG

• Now measure the T2 for mineral oil using the Carr-Purcell-Meiboom-Gill (CPMG) pulsesequence.

• Make sure the M-G switch is on, which is located on the AMP/MIXER module.

• Compare the T2 obtained in this way with the T2 obtained from the previous section.

• Repeat the measurement for glycerine.

C 2 .

QUESTION: Explain the advantage of CPMG over regular Hahn Echo.

C 3 .

There is a relationship between viscosity and T2. There are three oils (thin, medium, and thick)that you can use to qualitatively determine this relationship.

QUESTION: What is the relationship between T2 and viscosity? Explain the physics of thisrelationship, including what you would expect for samples in the solid state.

C 4 .

4.5 Spin-lattice relaxation time, T1

QUESTION: Explain how the “inversion recovery” pulse sequence can be used to measureT1.

C 5 .

Before we make use of the inversion recovery pulse sequence for measuring T1, we will nowexamine a quick method for measuring it. Let’s start with an order of magnitude estimate usingthe mineral oil sample.

• Adjust the spectrometer to resonance for a single pulse free induction decay signal.

• Change the Repetition time, reducing the FID until the maximum amplitude is reducedby about 1/3 of its largest value.

The order of magnitude of T1 is the repetition time that was established in the second stepabove. Setting the repetition time equal to the spin-lattice relaxation time means that the mag-netization does not return to its thermal equilibrium value before the next 90◦ pulse. Thus, themaximum amplitude of the free induction decay is reduced to about 1/e of its largest value.Such a quick measurement is useful since it gives you a good idea of the time constant you aretrying to measure and allows you to set up the experiment correctly the first time.

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4.6 Spin-lattice relaxation time using inversion-recovery

• Using the inversion-recovery two pulse sequence, obtain the spin-lattice relaxation timefor mineral oil and glycerine.

• Note that you will now have to turn on pulse B.

• Also note that the trace of the oscilloscope can be made to start after pulse B by switchingthe “Sync” switch to B on the pulse programmer.

• Compare the results for both the mineral oil and glycerine.

QUESTION: Suggest a reason for why T1 is different for oil and glycerine.

C 6 .