Download Low Field NMR Spectrometer

Low Field NMR Spectrometer
Experimental Lab III
Syed Ali Raza
Roll no: 2012-10-0124
LUMS School of Science and Engineering
Thursday, May, 19, 2011
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Abstract
The ultimate goal of this long project is building an NMR spectrometer with the magnet, electronic detection
circuitry and software. We like to see the FID (fourier induction decay) signal from a test tube containing
water and should be able to measure the relaxation times of the spins.
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Theoretical Background
Nuclear magnetic resonance, or NMR, is a phenomenon which occurs when the nuclei of certain atoms are
immersed in a static magnetic field and exposed to a second oscillating magnetic field. Some nuclei experience this phenomenon, and others do not, dependent upon whether they possess a property called spin.
In NMR, EM radiation is used to ”flip” the alignment of nuclear spins from the low energy spin aligned
state to the higher energy spin opposed state. The energy required for this transition depends on the strength
of the applied magnetic field. With no applied field, there is no energy difference between the spin states, but
as the field increases so does the separation of energies of the spin states and therefore so does the frequency
required to cause the spin-flip, referred to as resonance.
Imagine a nucleus of spin 1/2 in a magnetic field. This nucleus is in the lower energy level (i.e. its
magnetic moment does not oppose the applied field). The nucleus is spinning on its axis. In the presence of
a magnetic field, this axis of rotation will precess around the magnetic field. The frequency of precession is
termed the Larmor frequency, which is identical to the transition frequency.
So a constant field in the xy plane which we would call B0 splits the energy levels, than Our transmitter
oscillator placed perpendicular to B0 generates a pulse of electromagnetic radiation producing a magnetic
field B1 along the x axis.
This is called a 90 degree pulse as the angle is changed from the xy plane to the z-axis, Equilibrium is
re-established via spin-lattice and spin-spin relaxation, a process which takes about 5-6 seconds for protons
and which involves the return of the macroscopic vector M to the z axis, ie the ”flip” angle decays back to
zero (exponentially) in about 5-6 seconds for typical protons. As long as the angle is not 0, the resultant
non-zero vector component of M in the direction of the receiver coil placed on the y axis induces a sinusoidal
current in this receiver. Each set of distinct protons will produce a sine (or cosine) wave whose frequency
matches their precession frequency and the intensity of which is related not only to the phase of the sine
wave but also to the value of q at any instant (ie the magnitude of the y component of M). The signal
detected in the receiver therefore resembles a collection of exponentially decaying sine waves, and is called a
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Free Induction Decay, or FID for short.
An overview of the hardware and the circuitry which is used to transmit and recieve the signal and
analysing it is given in the following diagram.
Figure 1: Spectrometer Overview
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3.1
3.1.1
Experiment
Magnet
Simulating Hallbach Array
A Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side
of the array while cancelling the field to near zero on the other side. For our NMR we arrange our magnets
in a Hallbach Array to get a uniform B-Field in the centre. Our magnets are of 12mm diameter and have
strengths varying from 0.2 Teslas to 0.4 Teslas. We use the software Vizimag to simulate our Hallbach Array.
We arrange 8 of our magnets in a circular array with a 60mm inner diameter. For the purpose of our
simulation I have set the strength of the magnetic field strength of each magnet to be 0.2 Teslas. Below are
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some results.
Figure 2: Hallbach Array
The simulation show that we have a fairly constant field in the centre of the array, the strength of the field
is 0.0233 Teslas. The graphs of the fields in the x axis and y axis directions are shown in figure 5. Figure
5a shows graphs plotted along face to face of the magnet that’s why there is a jump at the boundaries.
However figure 5b has plotted just along the centre of the array. The graphs clearly show a fairly constant
and homogenous field at the centre of the array, in both directions.
This is the best possible 8 magnet arrangement, we tried other arrangements like the one in Figure 6.
The magnets at the diagnols were rotated by an angle of 45 degrees, the field is no longer homogenous and
also the flux density at the centre has been reduced to 0.0186 Teslas instead of the 0.0233 Teslas.
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Figure 3: Hallbach array with field lines simulation
Figure 4: Hallbach array with field strength simulation
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...
(a) Graphs along the boundaries of the Array
(b) Graphs along the centre of the Array
Figure 5: Field Strengths inside the magnets array
Figure 6: Plot with the Diagnol magnets rotated at 45 degrees
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3.1.2
Profiling all magnets
We had a total of 11 magnets which were axially magnetised, we wrapped paper tape and labelled them A,B
.... K. Using a compass, we colour labelled the poles of the magnets, red line represents the north pole and
green line represents the south pole. The field strengths of the magnets were measured using the transverse
probe of a Gauss meter. Figure 7 shows a table of the field strengths of our magnets. According to these
strengths we arranged the magnets to get an optimal field, the arrangement is shown in figure 8 although it
is very difficult to achieve the required homogenous field because each magnet has a different field strength.
Figure 7: Table of field strenghts of magnets
3.1.3
Plotting Field strength of a magnet using PCB machine
We mounted a Gauss meter probe on a PCB machine and then moved it very small distances, using the
computer interface we make the probe traverse both in the horizontal and vertical axis. We took two profiles,
one for each pole and used MATLAB to plot a 3D image and following are the plots obtained. The height is
the strength of the magnetic field and is measured in kilo Gauss, the distances are in the x and y axis and
are measured in milli inches.
3.1.4
Casing of our magnets
We tried to arrange the magnets in a plexi glass casing after drilling holes in a sheet of thick plexi glass. But
the fields at such short distances were very strong, it not only made the handling of the magnets difficult
but it was impossible to prevent them from turning in their positions.
So we machined a Teflon housing with a inner diameter of 60mm, the magnets were arranged in an
Hallbach array and were held tight with the help of aluminium screws, we chose aluminium because it is
non magnetic and easy to machine. The magnets were placed in the casing, the screws enable us to rotate
the magnets on it’s axis and hence we can vary the field flux at the centre of the array to get a sweet spot.
Figure 11 show the photographs of our spectrometers casing. The field was measured using a stand and a
Gauss metre, a field of 0.0662 Teslas was measured at the centre of the Teflon housing.
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Figure 8: Optimal arrangement of magnets
...
(b) Side View
(a) Side View
...
(c) Side View
(d) Top View
Figure 9: South Pole of magnet J
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...
(b) Side View
(a) Side View
...
(c) Side View
(d) Top View
Figure 10: North Pole of magnet J
...
(a) labelled Teflon casing with magnets
(b) eflon casing with magnets
Figure 11: Casing of our magnets
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3.2
3.2.1
Probe Design
Tuner Circuit
The coil acts as an inductor and will provide the B field to the sample that we would place in it, our circuit
should satisfy two conditions. It should be well tuned and well matched, by well tuned we mean that it
resonates at a particular frequency, in our case that frequency is the Larmour frequency. By well matched we
mean impedance matching, the impedance of the antenna tuner should equal the impedance of our source.
By the maximum power transfer theorem if the impedance of the source and antenna is same then maximum
power is transferred in the antenna. We need this because we are using the same coil as the transceiver too,
and we don’t need any power to be reflected from the antenna.
The reactance of a capacitor is given by 1/jwC and that of an inductor is given by jwL. We use elementary circuit analysis and solve the circuit equations to get the following equations, the first equation is for
impedence matching and the second equation is used to find a resonant frequency. We can adjust the values
of the two capaciors for tuning and matching the circuit.
(1 + w2 LC1 )
=R
w(C1 + w2 LC1 C2 )
(1 + w2 LC1 ) = w(C1 + w2 LC1 C2 )R
(1)
(2)
2
w LC1 C2
=1
C1 + C2
(3)
Figure 12: The circuit for the probe
3.2.2
Directional Coupler
This is a very useful device and can be used both for impedance matching and also as a duplexer. A directional coupler or magic tee can be thought of as a four port device, the rf input is at port 1, he LC tank
circuit is at port 2, a dummy load to match the tank circuit impedance of tank circuit (purely resistive) at
port 3 and the output at port 4. The rf input at port 1 splits into port 2 and port 3 and nothing goes to
port 4 if and if only the impedance of port 3 and port port 2 have been matched.
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Figure 13: Directional Coupler
3.2.3
Transmitter
Now We would go over separate parts of the spectrometer overview in figure 1 piece by piece. I would try
to use simple flow charts to explain the working. The first figure shows a very simplistic rough view of
the process, the electronic device must provide a pulse of sufficient power at the proper frequency to do
something to the appropriate nucleii in the sample, a signal would be transmitted to the probe through this
block and then received to be fed into the computer.
Figure 14: Simplistic block diagram
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In the second figure we look at the working of the transmitter, The rf synthesizer is programmed to
generate an rf frequency that is the nmr reference frequency. This signal is routed through the phase shifter
which is controlled by the pulse programmer. The phase shift is to provide pulses along the different axes.
By convention, a phase shift of 0 is an x-phase pulse, a 90 degree phase shift corresponds to a y-phase pulse,
180 degree phase shift is a -x-phase pulse and a 270 degree phase shift is a -y-phase pulse. The pulse programmer’s function is to set the timing of the pulses and delays and to program the phase shifter depending
on the needs of the pulse program that the user has selected. A pulse is issued to the amplifier when the
pulse programmer opens the gate (or closes the switch) and lets the low voltage rf signal proceed to the
amplifier.
Figure 15: Transmitter flow chart
3.2.4
Receiver
After the signal is amplified it goes to the probe. There is a very interesting piece of equipment between the
probe and the power amplifier. This device is called a directional coupler and its function is to route the
signal from the amplifier to the probe When a high power pulse from the amplifier comes into the directional
coupler it is routed to the probe and the coil in order to irradiate the sample. After the pulse is issued
the signal that comes back from the probe goes through the directional coupler but is now routed to the
receiver. Actually, it first goes into a preamplifier, this is to boost the weak nmr signal before it gets lost in
the thermal noise of the cables.
Figure 16: Directional Coupler
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After the signal leaves the directional coupler and preamp, it moves on to the receiver. Via the reference
signal and a 90 degree phase shifter in the receiver, two signals are produced, the real (R) and imaginary (I)
signals. This is known as quadrature detection. The nmr reference signal is used to generate the pulses and
in the receiver to mix the signal down to much lower frequencies. This is also the rotating frame frequency.
This frequency is placed in the middle of the spectrum and signals fall on either side of it. In order to tell
whether or not a signal has a positive or a negative frequency with respect to the reference frequency we
receive two signals that are 90 degrees out of phase. This will allow us to tell what the sign of the frequency
is. Only one signal would not be sufficient.
Figure 17: Flow chart of receiver
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References
Experimental Pulse NMR, Fukushima and Roeder
Electronics and instrumentation for scientists, Malmstadt, Enke, Crouch
Anteena Tuner Calculator
http://www.crystal-radio.eu/entunercalc.htm
http://chem4823.usask.ca/nmr/electronics.html
http://www.cis.rit.edu/htbooks/nmr/bnmr.htm
http://www.chem.ucalgary.ca/courses/351/Carey/Ch13/ch13-nmr-1.html
http://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/nmr1.htm
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