Peter Schmidt-Nielsen
Adam Marblestone
Physics of Information Technology (Spring 2010)

Nuclear quadrupole resonance excitation of p-dichlorobenzene

Introduction: NQR spin resonance phenomena can be conceptualized in much the same way as NMR spin resonances, but they occur with zero external field. This vastly simplifies the experimental constraints on a proof of principle, low-budget experiment. In NMR, an external B field is used to create a net magnitization vector which then rotates as spins are flipped, creating a macroscopically observable signal. In NQR in a solid, the macroscopically visible spin dynamics, in response to rf pulses, comes from the interaction of nuclear spins with electric field gradients in the material, rather than macroscopic polarization by an ambient B field. However, there is a subtlety in that this interaction does not create a net spin polarization in the absence of rf exciation, because the nuclear-spin/electric-field-gradient interaction is insensitive to nuclear spin direction. The result is a set of equations analogous to the Bloch equations for spin dynamics in NMR. This result follows from a full quantum treatment of the interaction of the nuclear quadrupole moment with the electric field gradients in the crystal [1]. Our goal for the project is simply to observe evidence of this effect using a device of our construction.

System Design:

Block Diagram:


Design considerations:

-The sample: p-dichlorobenzene, Cl-35, no need for external B field
-Tuned probe: tunable capacitors, analog and digital, conditions for real and imaginary parts of the impedance
-Isolation for the receiver chain: crossed diodes vs. purely switch based, digital noise, distortion from diodes
-TTL switch control: switching timescales, pulse sequence complexity, insertion loss, isolation
-Pulse sequence: spin echo, FID vs. ringdown
-Signal generation: class E amplifier vs. the power amplifier we are using vs. what we can do with cheap circuit components
-Amplifier noise figures and initial signal detectability: choice of two amplifiers, noise floor of spectrum analyzer, Friis formula for cascaded amplifiers, RF design vs what can be done on a simple PCB, correct "order of operations" when searching for a signal
-Filtering: active vs. passive, amplifier gain bandwidth product, oscillations, impedance matching, microstrip design, small inductors
-Homodyne detection: mixing, nonlinearity in mixer, lowpass and bandpass filtering, spectrum analyzer as homodyne detector
-Electromagnetic shielding: copper boxes, low conductivity of the adhesive, need to solder together joints
-Future versions: Yael's mini-nmr board, fab-able microstrip circuit using fast op-amps, impedance matching "on-chip"

Software:

-screenshot

Estimated System Parameters:

-Relation between applied voltage and field strength, current divider model of probe
-Sample properties
-Relation between field strength and pulse sequence parameters

Materials:

-"Moth Ice" (from any hardware store)
-Sprague Goodman GKG series ceramic trimming capacitors (4.5 - 65 pF) [4X]
-Miniature ceramic flathead screwdriver (for tuning probe without capacitive coupling)
-Copper boxes and vinyl cut copper sheets (for shielding)
-Atmega ATtiny45 microcontroller
-PCB to SMA connectors
-Minicircuits ASW2-50DR SPDT switches [3X]
-Minicircuits ZFL 500LN amplifiers [2X] (can be replaced with high speed op amps, GBP > 500 MHz)

Experimental Progress:

-implemented RF switching from logic board
-implemented matched passive 34 MHz bandpass filter
-implemented matched, tuned coil at 34 MHz, characterized with network analyzer and LCR meter
-constructed full experimental setup
-estimated device parameters (such as probe field strength) in order to estimate initial pulse lengths

-tell the story of our problems and solutions so far...

References:

[1] Bloom, Hahn, Herzog. Free magnetic induction in nuclear quadrupole resonance. Physical Review 97:6 (1955) [the best for basic NQR theory]
[2] Maguire. Towards a Table Top Quantum Computer. MS Thesis, 1999 [RF and NMR wisdom]
[3] Maguire. Microslots: Scalable electromagnetic instrumentation. PhD thesis, 2004 [contains some NQR work]
[4] Robinson. A sensitive nuclear quadrupole resonance spectrometer for 2-60 MHz. 1982 J. Phys. E: Sci. Instrum. 15 814 [good SNR formulas]
[5] Pulsed NMR: Spin Echoes. MIT Junior Lab Manual. http://web.mit.edu/8.13/www/12.shtml; see also related here www.physics.nyu.edu/~physlab/Experimental_Phys/PulsedNMR.pdf [references to the basic designs for observing spin echoes]

Acknowlegements: We would be nowhere on this without huge help from Yael and Rehmi on both design and practical implementation details. Thanks also to Clarissa Zimmerman for walking us through her NMR apparatus in the Bioinstrumentation Lab.

Appendix: raw lab notebook and initial musings

Notebook:

2010-05-16:

-Colors in the pulse programmer: (From left to right on the board, when the SMA connectors are facing toward you.) Pink, Blue, Yellow.

-Can keep blue on (first switch) and modulate yellow (second switch) for nice clean pulses

-Software: http://toothbrush.dyndns.org/transfer/nmr.tar

-Pictures of the setup/components/thoughts as of Sunday:





-power amplifier ups the voltage by a factor of around 20

-passive bandpass, pre-matching:


-measuring inductance of a replica coil using HP 4263A: 0.7 uH
-this makes order of magnitude sense: let's just say between 1 uH and 2 uH including all the wire
-let's say the capacitors are 10 pF (we know they are between 4 and 65 pF):  

((1 / (50 ohm)) * (1 / ((-34 megahertz) * (10 picofarad) * 2 * pi))) / ((1 / (((34) megahertz) * 10 picofarad * 2 * pi)) + ((34 megahertz) * 2 * pi * (1 microhenry))) = 0.0367897627 siemens

-multiply this by the voltage entering the probe circuit to get the current I_inductor through the inductance

-then H = u_0 * 5 turns * I_inductor / 1 cm (approximating crudely as an infinite solenoid)

-so at this point we have all info required to estimate the field in the coil (up to an order of magnitude, say)

2010-05-15:

-The sallen-key filter is going crazy with oscillations (like 90 MHz)... looking at the data sheet, we have only a 35 MHz bandwidth at gain = 2 (140 MHz at gain = 1). I had thought our filter had zero gain, but it turns out it should have 10 dB of gain at the center frequency, as designed.

-Switched to making a passive low pass filter (3rd order butterworth), designed in Qucs

-this was very poorly impedance matched (we have discovered the concept of microstrip lines, but didn't have time to implement that!), but we did a hacked fix on that by adding capacitors out front, and we able to transmit around as much as the filter design software expected

2010-05-14:

-Frequency characteristic of our sallen-key bandpass filter:



-More thoughts on measuring/estimating probe field: we realized there is a current divider inside the probe so it is not quite as simple as current = V/50. Still, knowing coil inductance and the capacitance of our tuning capacitors, we could calculate it from current divider relationship.

-Also, I found Yael's old class E power amplifier optimized for a 34 MHz PQR experiment... this may be way better than the power amplifier we are using, in terms of signal to noise performance...

2010-05-13:

a way to estimate the field strength in the probe, for choosing pulse lengths:




2010-05-11:

Building bandpass filters with AD811 high speed op amp:


Pulsing works; power amp gives us a factor of about 50: 10 mV in to 500 mV peak to peak output
-Observe ringdown after pulse is turned off (see picture):

-Ringdown directly from the probe gets to ~ 1 mV after ~3-5 us, so after ~ 15 us we should be in the clear to see stuff

2010-05-08:

-sample choice: we want to use p-dichlorobenzene, which is a chloro derivative of naphthalene that is less flammable, and is now the primary component of mothballs; it has a resonance at room temperature of 34.27 MHz: [from JAS Smith's paper]

"The material should be carefully
recrystallized, dried, and packed as
densely as possible into a 12 or 14 mm
sample tube with as thin walls as possible
(some manufacturers supply egg-shell glass
which is very suitable for this purpose).
The coil may he made from about 5 turns
18 swg varnished copper wire wound
fairly tightly on the sample tube with a
spacing equal to one wire diameter between
turns; it is advisable to fix the coil
to the tube with an adhesive (of low
dielectric loss) to reduce microphonics (see
Fig. 12 for some commercial rf probes).
The depth of sample in the tube should be
sufficient to overreach the two ends of
the coil by several millimeters. From the
chemist's point of view, nuclear quadrupole
resonance is clearly rather demanding
in the size of sample required. Usually
at least 2-3 g. are required when a search
is being carried out, but there are many
compounds which give strong signal from
as little as 0.1 g."

http://www.sigmaaldrich.com/catalog/ProductDetail.do?lang=en&N4=48524|SUPELCO&N5=SEARCH_CONCAT_PNO|BRAND_KEY&F=SPEC

-we can also get it as: "Excell Para Moth Nuggets (100% 1,4-dichlorobenzene)
were purchased at a local hardware store and used
without further purification"

-for p-dichlorobenzene we have I = 3/2 and we are looking at 35-Cl

-35-cl has g= +0.5479157

-hence gyromagnetic ratio = g * nuclear magneton / hbar = 26 241 971.3 s A / kg

-therefore theta (radians) = sqrt(3) * 26241971 s A / kg * (H1 in tesla) * (pulse length in seconds); this is based on the 1955 paper by Bloom, Hahn and Herzog

-here H1 is defined as follows: H_x = 2*H1*cos(omega*t), so I think we need to watch out for this factor of 2

-the order of magnitude of the applied field from our coil is:

-thus for a pi/2 pulse we have approximate pulse length:

-T1 is around 22 ms in this system (http://prl.aps.org/abstract/PRL/v1/i1/p6_1); I'm not sure what T1 even is in this context, though.

-T2* = 310 us at room temperature ("Measurement of apparent spin-spin relaxation times in nuclear quadrupole resonance using a double pulsed super-regenerative oscillator", Doolan, K. R. & Hacobian, S., Australian Journal of Physics, vol. 28, p.45)

-I think therefore generally we'll be talking tens of microsecond pulses, hundreds of microseconds spacing between pulses: for 0.001 Tesla field we get, in seconds
(pi / 2) / (sqrt(3) * 26 241 971 * 0.0005) = 6.91182596 × 10-5
which is about 70 us

2010-05-07:

-made a 16 turn coil, for which system should have had resonance frequency around 34 MHz, but was in fact around 10 MHz. I am assuming that the problem is stray capacitance--we need to make an elegant board with limited extra capacitance, and strip the coil wire properly so that not so much solder is required! Also, using less turns but thicker gauge wire is a good idea.

-5 turns, length =0.7 cm, width = 1.5 cm should work...

2010-05-04: plan is to make a rough full circuit and see the ringdown (and the noise.....)

2010-05-03:

Tried a no-filtering, no-demodulation receiver stage which was just the two chained pre-amps:
-2.3 uV input through amps gives -53 dBm on spectrum analyzer at 34 MHz
-1 mV input without amps gives -53 dBm on spectrum analyzer at 34 MHZ
-so we're getting ~500 times amplification ~ 26 dB, whereas we should be getting 24*2 = 48 dB

-concluded that we need to chain several and include filtering

Ordering band pass filters:

http://www.minicircuits.com/cgi-bin/modelsearch?model=SIF-30%2B&search_type=model

-also confirmed that naphthalene NQR frequency should be around 34 MHz: Nuclear quadrupole resonance in chloro derivatives of naphthalene

-HOW TO HANDLE NAPHTHALENE: it has a flammable, odorous vapor, and costs $30 per cubic cm solid, approximately from Sigma

-Need to start working on control circuitry, switches, while the filters are on order

2010-05-02:

-For Mothball NQR (a more realistic sample) using (the C1 chlorine 35) the resonance frequency is 34 MHz, so I think we should re-make the probe (the first one having been good for seeing how to construct it).

-r = 6 mm (see 1.1 cm diameter test tube), l = 1 cm, # turns = 16 should give L ~ 2.5 uH and a predicted freq tuning range of 12 - 46 MHz

-Book to get: Nuclear Quadrupole Resonance Spectroscopy by Das and Hahn

2010-05-01:

-Decided to do NQR rather than NMR or ESR

-Made a probe board

-The caps are tunable from 4.5 to 65 pF

-Coil parameters: with vertical flask (1.16 inches  = 30 mm thick ~ 15 ml marking on our flask) we want 105 turns for NQR coil of length = 1 inch gives 717 uH, with freq upper (assuming relative permeability of 1) = 2.8 MHz and freq lower = 740 kHz.

-solenoid calculator: www.mogami.com/e/cad/coil-01.html

-Observed tunable resonance of the probe with the network analyzer:




-Also observed resonance with Smith chart view. Need to learn how to interpret this.

-Resonance does seem tunable: need to tune series cap to get a decent signal size, and both caps affect the resonance frequency

-TNT resonance frequency for NQR is < 1 MHz, hence the parameters we chose

-For future probes, it might be good to order some SMA to PCB mounting connectors

2010-04-16:

-using ZASWA-2-50DR switch, we showed that: a) a single rf input could be switched between two outputs with good isolation, and b) we will need two switches to control the isolation for the probe, and a third for connecting the rf source between the power amp and the mixer, because these switches are not operating in reverse

-Need to use LeCroy as a secret weapon, for time-domain analysis, and still use the rare-Earth magnets

-testing amplifiers on receiver chain (-100 dBm = 0.1 pW ~ 2 uV at 50 Ohms), and amazingly our function generator can output 2 uV so we don't need an attenuator; we didn't manage to see anything on scope with two of them chained together or with one only (ZFL-500ln), each one drew about 56 mA, and the nominal gain of these is 240 dB ~ factor of 250, so we should have been able to see this given that the scope can see mV. probably we're not using it right... even 100 uV didn't give us anything visible on the scope... could it be related to the impedance of the scope? seems doubtful because the scope worked for switching test. OK we might have switched out vs. in...

-actually once we got polarity worked the amplifiers functioned; 80 uV produced 2 mV at 30 MHz; tons of noise though, we are going to need to do spectrum analysis and filtering to make this work

To do: take apart the low pass filter in metal box... I want to see what is inside, and how the impedance matching works, for reference when we may need to make our own filters; debug amplifier signal chain by spectrum analysis and filtering, since it was very sensitive to touching the cables and very noisy; work with Yael on probe design and fabrication advice and other considerations

Initial Musings:

Modeling:
-Qucs program looks like it might be helpful
-Spice has a lot of noise modeling (.noise) that would be helpful

Parts List:

Circuit with switch-based isolation:
-AVR microcontroller (or we may be able to use one of the pulse generators in the lab with a mixer for the modulation, if the pulse generator can program two pulses of unequal length with a given delay, for the spin echo)
-2 RF switches [Mini-Circuits, ASW2-50DR SPDT]
-Power amplifier for transmit chain [we ordered AD811 chips, but probably want something more powerful... 5W is typical, maybe we have a more powerful one like this in the lab?] We're using the ZHL-32A-SMA.
-2 RF amplifiers for receiver [Mini-Circuits ZFL 500LN, we have one already but need to order another]
-several tunable capacitors: Sprague Goodman GKG series ceramic trimming capacitors (Ordered 10 of SG3009-ND)
-cabling
-attenuators?
-metal shielding boxes (also, possibly don't want some components to be in direct contact with the metal box, need internal insulation)
-SMA female-female connector [need a bunch of these quickly!]

Circuit with demodulation:
-splitter [I think we have this]
-mixer [we have this]
-low pass filter [need to order or make this]

Circuit with crossed-diode-based isolation: if we take this approach we can actually use a mixer for the modulation switch, although I am not 100% sure this will work with TTL modulation as opposed to the pulse generator that Sleator was using which relies on a "dc signal"
-lambda/4 length coax!
-crossed diodes in isolation boxes

Also need a circuit for tuning/testing the probe impedance:
-directional coupler with oscilloscope can be used to test if there is any reflection, i.e., if we get matching to 50 ohms
-maybe don't need this: can probably use RF test equipment in the lab to spit out info on the complex impedance of our probe --> can tune to satisfy the conditions on the real and imag parts at resonance as in Yael's thesis

Schematics/Drawings:

One probe option from Yael's thesis:


Switching/isolation method:

Issues/Questions:

-switch-based isolation vs. crossed-diode isolation; can switch-based isolation switch high powers? is there any advantage to the crossed diode approach? it seems more complex at first
-this is from MIT's junior physics lab, note how they use both crossed diodes and switches, and how they use a splitter to simplify their switching protocol:
-for diode based isolation, the lambda/4 cable is critical: it prevents the signal distortion we were worrying about!
-need to think about signal strengths, amplification and attenuation stages
-fabrication of the probe, ground planes; Clarissa clearly did it with just normal capacitors and stuck in a resistor to lower the Q due to ringdown issues after the pulses are turned off

References:

1) www.physics.nyu.edu/~physlab/Experimental_Phys/PulsedNMR.pdf
[absolutely essential reading for understanding our setup; has a good schematics too; by combining this with Yael's simplifications/modifications we should be all set]

2) Get two books:

Electron spin resonance: a comprehensive treatise on experimental techniques By Charles P. Poole

Electron Paramagnetic Resonance: Elementary Theory and Practical Applications by John Weil and James Bolton