35Cl and 14N Nuclear Quadrupole Resonance in Paradichlorobenzene, Sodium Chlorate, and...

8/10/2019 35Cl and 14N Nuclear Quadrupole Resonance in Paradichlorobenzene, Sodium Chlorate, and Hexamethylenetetra

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Journal of Fedoras, Vol. XXI, No. 1, 1-5, 2015

Additional note

35Cl and 14N Nuclear Quadrupole Resonance in

Paradichlorobenzene, Sodium Chlorate, and

Hexamethylenetetramine

Allen Majewski1*

AbstractPulsed nuclear quadrupole resonance studies were carried out in sodium chlorate, para-dichlorobenzene in35Cl. The 14N nuclear quadrupole resonance (NQR) in hexamethylenetetramine was observed using pulsedtechniques on a home built superheterodyne spectrometer with a hybrid tee bridge configuration. High S/N

was achieved with robust isolation techniques, high quality fast recovery amplifiers, and high Q resonant tank.All studies were conducted using the same apparatus. The superheterodyne was largely unchanged for the

three studies except for the tank section and the pulse protection circuitry between the power amplifier and thereceiver section. An exact calculation of probe parameters was made. Evidence of an non-zero assymetryparameter in HMT was observed, but more research is needed.

1Department of Physics, University of Florida, Gainesville, FL, USA

*Corresponding author: [email protected]

1. The quadrupole coupling constant andNQR transitions

The quadrupole coupling constant Cq of a particular nuclear

site in a solid structure is defined as

Cq=

eQVzz

h =

e2qQ

h (1)

where Vzz =eq is the largest absolute eigenvalue of the diago-nalized electric field gradient tensor for the nucleaus, e is the

electron charge,Qis the quadrupole moment and his plancks

constant.Cqis both site specific (there are often inequivalent

sites of a single atom in a unit cell) and compound specific as

every structure has unique values ofCqfor all its nuclei.We consider a nucleus of spin Sand define

A= e2VzzQ

4S(2S1) (2)

The NQR frequencies can be expressed in terms ofA

q= 3|A|h(2|m|+ 1)

(3)

where m is the lowest of the two levels m and m+1 over which

a transition has occurred. For integral spins there are S unique

transitions. For half integral spins there are I1/2uniquetransitions.

1.1 NQR frequencies for half integral spinsNQR is observed in nuclei withI=3/2,I=5/2and I=7/2.ForI= 1/2, there are no transitions. TheI= 5/2andI= 7/2

are perhaps more complicated, but in the case I= 3/2, there isa degeneracy that causes there to be one frequency of half the

quadrupole coupling constant. For example, 3 5Cl hasI=3/2so there is only 1 transition. Using I=3/2equation 3 above,we obtain

q= 12eVzzQh

=1

2Cq

(4)

for axially symmetric field gradients. For non-axially symme-

tryic gradients, we define the assymetry parameter

=Vxx Vyy

Vzz(5)

The axes are chosen so that |Vzz |> |Vyy |> |Vxx | which ensures0 1. If there is axial symmetry andVyy = Vxx ,Vzz isthe only nonzero component in the diagonalized electric field

gradient tensor, forcing = 0. When is nonzero, the singletransition forI=3/2 is given by

q=1

2

eVzzQ

h(1 +

1

3

2)12 (6)

For = 0 and I= 5/2there are of course two lines for theI1/2 allowed transitions as |m| =1

+q =

3

10

eVzzQ

h(7)


2/8

35Cl and 14N Nuclear Quadrupole Resonance in Paradichlorobenzene, Sodium Chlorate, and

Hexamethylenetetramine 2/8

for 52 3

2and for the 3

2 1

2 case

q =

3

20

eVzzQ

h(8)

1.2 NQR frequencies for integer spinsWe return to equation (2) and begin withI= 1 as is the case for

nitrogen. Axial field gradients with = 0lead to a degeneracyand we find there is a single transition having frequency

q=3

4

eVzzQ

h(9)

For > 0 there are two transitions given by

q =

3

4

eVzzQ

h(1) (10)

2. Experimental

2.1 The superheterodyne NMR spectrometer

Figure 1. Superhet pulse generator section.

The home built superheterodyne spectrometer was used

for all measurements of quadrupole resonance. The pulse

controller runs off a 20 MHz clock controlled by a lawbiew

interface. 20 MHz pulses are mixed down with f+ 20MHzinput and filtered to produce pulses having frequency f. The

pulses are filtered and passed through numerous ad-hoc pro-

cessing elements before being injected into the tank circuit

Figure 2. A typical bridge configuration.

by either the method of a directional coupler or using other

isolation schemes. The receiver section mixes the amplified

NMR signal with f+ 20MHz from the generator4 section,

then mixed the filtered result with the 20 MHz clock signal tofinally resolve f fq where fq is the NQR from the sampletank.

This spectrometer is capable of very high S/N measure-

ments when it is optimized and tweaked for each a particular

purpos. Yet the design of particular bridge circuits and their

corresponding matching networks given a sample, and a target

frequency or search space is a primary challenege in using the

apparatus. It is infeasible to design a very wide-band probe

because a high enough Q is needed to detect the very small

NQR signal. This makes searching for a completely unknown

resonance frequency very difficult - the superhet is simply

not designed for sweeping. For example, a resonant tank

and probe configuration was fashioned for 35Cl resonance in

sodium chlorate at 29.936 MHz. However, the design would

not allow tuning to observe the 37Cl NQR which would be

expected at 23.74 MHz, by taking the ratio of the quadrupole

moments of the nuclei. Another primary difficulty is isolation,

which is achieved in numerous ways, many of which are only

feasible in a narrow bandwidth.Quarter wave transformers

were very effective for the 30 MHz band in sodium chlorate,

but would have bee impossible for implement for the 14N

NQR detection in HMT as the coaxial length needed would


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f + 20 MHz (from NMR generator chain)

I &Q

Demodulator

I

Q

20 MHz reference

Mixer

(-6dB)

Narrow band 20 MHz IF chain

F A

F= narrow band filter

X

Y

NMR Signal Receiver and Detection

A= low noise (20 dB each)

broadband amplifier

From PD of

pulse generator

section

NMR signal

from fast recovery

amplifier (50 dB)

A

OUTPUTS

Filters

Phase shift(contolled by DC

voltage from 10 t

pot on front panel)

20 MHz

ZX05-1+

MIQA-21D+

ZFL-1000LN

SBP-21.4+

JSPHS-26

Figure 3. Superhet receiver section

be far too long. Lumped elements of LC networks that act as

quarter wave transformers were considered, but the hybrid tee

was chosen for HMT measurements.

2.2 NQR measurement in paradichlorobenzene

A number of combinations were used for the bridge and tank

circuit sections for trials with various samples. For the case

of paradichlorobenzene, the bridge circuit includes the use of

a hybrid tee junction (Merrimac HJ-55) as well as matching

network B. These earliest measurements display a lower S/N

than those made in NaClO3despite the NQR amplitude being

larger in para-dichlorobenze because of two disadvantages

of the experimental design used at that time. (1) The hybrid

tee junction for isolation is inferior to a quarter wave section

because the signal power is divided both for the pulse in and

NMR out. (2) A short length of RG-58 coaxial was connected

with BNC from the sample coil to the matching circuit. Thisis inferior to having the sample coil connected directly to

the matching capacitors because of the ambient radiation that

is shielding in the latter case as well as the characteristic

inductance and loss in the cable. Nevertheless NQR was

measured in para-dichlorobenze at 34.2534 MHz. The pulse

width was 20 us and the time between pulses was 7 ms. The

RF amplifier used was Minicircuits ZFL-1000N, and hybrid

tee Marrimac HJ-55.

Figure 4. Response to a transient of paradichlorobenzene.

The pulse width was 20 us, with 2.7 ms between pulses, and

N=100 averages.

2.3 NQR measurement in NaClO3In the summer of 2013 visiting scientist Mikolaw Baranowski

assisted with several improvements to the spectrometer that

produced a high S/N for measurement of NaClO3 35Cl NQR.

Matching network A was chosen instead. Additionally, crosseddiodes were added at the output of the power amp. An audio

frequency amplifier was used after the mixdown, and better

RF amplifiers were used for signal detection. The coil was

placed inside a shielded gunbox along with the matching caps.

Figure 5. Isolation method used for NQR detection inNaClO335Cl NQR. Notice the absence of hybrid tee

junction, which is supplanted by the quarter wave section and

diode switches.

The most important alteration is the use of a quarter wave

transformer for isolation instead of a hybrid tee. Though this is

unfeasible for low frequency NQR in 14N, as the wavelength

is inconveniently long, a quarter wave transformer can be

fashioned quickly with a length of RG-58 coaxial cable. The

length of the cable is just one quarter of the wavelength at

the design frequency times .67, the velocity factor for RG-58.

Crossed diodes D1 and D2 provide optimal power delivery

to the sample with no power allowed to leak back into the

power amp. D3 and D4 short when the pulse is on, ensuring

maximal power transfer to the tank. When the pulse is off,

Dall diodes look like an open circuit, so the NMR signal is

delivered to the fast recovery amplifiers.

The tank circuit used for NaClO3 also differed from that

of dichlorobenzene in the matching circuit configuration. For

the NaClO3test, matching configuration A was used. In this

configuration a series capacitor matches a parallel resonance

with the coil, shown in figure 2. Another contibuting factor


4/8



Figure 6. An audio active filter (left) used in the IF stage is a

JFET preamp cascaded with an LM-386 power amplifier IC.

The audio preamp (right) cosists of 2 MPF-102 JFETs in

common source amplifier followed by a common drain

(source follower).

Figure 7. FID of NaClO3 powder at 29.9260 MHz. The

pulse width was 40 us and time between pulses was 10 ms

with signal averaging N=1000.

to the high S/N of the NQR measurement in NaClO3 as com-

pared with paradichlorobenze is the audio IF amplifier and

active filter used after mixdown. It consist of an LM-386

power amplifier chip (1/4 watt) and a JFET preamplifier stage.

Figure 8. The SNR shown by the power spectrum of the

above FID.

Figure 9. The probe design for the NQR test of NqClO3.

Matching fircuit A was used. S/N was improved by having

the sample connected directly to the matching circuit and

placed in the aluminum enclosure without use of coaxial

connector. The copped loop beside the sample coil is anantenna usefulfor tuning. Together with the normal use of a

directional coupler, the antenna provides amplitude and phase

information useful for finding the correct capacitance values

in a two parameter search space.

3. Calculation of capacitances formatching network A

A precise analysis of the above L-network for impedance

matching is given now. We will examine the impedance of

this reactive L network to characterize the parameter space

of the variables C1, C2, , L, r . The usefulness of such acalculation is to produce a useful set of tables of particular

values ofC1and C2 for which the tank is tunes and matched

given a particular ,L and r. This is necessary because it is

often desirable to test a frequency outside of the bandwidth of

a given tank cconfiguration. A calculation of the capacitances

for achieving a matched condition is essential for the construc-

tion of a proper resonant tank in a given band. Most large

air-variable capacitors have a range up up to 300 pF, making

tuning a difficult or impossible task by briute forcing alone.


5/8



Figure 10. Polycrystalline soldium chlorate sample in a 400

nH coil.

For impedance matching conditions to be satisfied, we

must ensure the imedance looking into the tankZ0=50. Todo so we must enforce the conditions

Re[Z] =50

Im[Z] =0(11)

The total impedance looking into matching network A is

Z= 11

jL+r+ jC2

j

C1(12)

Because the second term in the expression forZhas no realpart

Re[Z] =50

Re[Z] =Re[ 11

jL+r+ jC2]

(13)

So we can treat the first term only to fine Re[Z]

1

jC2+ 1r+jL

= r+jL

1 +jC2(r+jL)

= r+ jL

1C2L2 +jC2r

= (r+jL)

1C2L

2 jC2r

((1C2L2) + jC2r) ((1C2L2) jC2r)

= jC2L

23C2r2+L

+ r

C22L24 +C22r

222C2L2 + 1

(14)

The real part ofZis quadratic inC2and has no dependence

onC1, so we can solve for C2 outright. WithRe[Z] =Z0 wefind

Re[Z] =

r

C22(L24 + r22)2C2L2 + 1 (15)

r

Z0=C22

L24 + r22

2C2L

2 + 1

0=C22L24 + r22

2C2L

2 + 1 r

Z0

(16)

We can now express C2 in terms ofL, , and rand Z0only by solving the quadratic

C2 =L2Z0

L2r4Z0+L24Z20+ r

32Z0

L24Z0+r22Z0

(17)

This suggests that either C+2 or C should be thrown out. Re-

turning to equation (15), we can express Im[Z]by appendingthe term j

C1

Im[Z] = 1

C1+

C2L23C2r2+L

C22L24 +C22r

222C2L2 + 1

(18)

which we set to zero and immediately solve for C1 in terms of

C2

0= 1

C1+

C2L23C2r2+L

C22L24 +C22r

222C2L2 + 1

C1=C22L

24 +C22r222C2L2 + 1

C2L23C2r2+L

C1=

1

2

C22L24 +C22r

222C2L2 + 1

C2r2 +C2L22L

(19)

Inserting each of the two roots of equation (18) into equa-

tion (20) (surprisingly) gives

C1 = r

r2Z0(L22 + r2 rZ0) (20)


6/8



The negative value ofC1is nonsense, confirming thatC2

is the valid solution from the quadratic in C2

C1= r

r2Z0(L22 + r2 rZ0) (21)

C+2 should be thrown out leaving us with

C1= r

r2Z0(L22 + r2 rZ0)

C2=L2Z0

L2r4Z0+L24Z20+ r

32Z0

L24Z0+r22Z0

(22)

The calculation is necessary for the design of probes for vari-

ous frequencies. A very different type of tank circuit would

be needed to locate 14N NQR in HMT which was expected at

3.4 MHz.

1.5 107

2.0 107

2.5 107

3.0 107

5. 1011

1. 1010

1.5 1010

2. 1010

2.5 1010

3. 1010

3.5 1010

C1, C2 15 M Hz ; Z o50; r7; L2610^ 6;

Figure 11.C1(), C2()1-5 MHz;Z0=50;r=7;L=26 106;

4 107

5 107

6 107

7 107

8 107

9 107

1. 1011

2. 1011

3. 1011

4. 1011

C1, C2 51 5 M Hz ; Z o50; r7; L1510^ 6;

Figure 12.C1(), C2()5-15 MHz; Z0=50;r=7;L=15 106;

1.5 108

2.0 108

2.5 108

3.0 108

5. 1011

1. 1010

1.5 1010

C1, C2 51 5 M Hz ; Z o50; r7; L 400 nH;

Figure 13.C1(), C2()15-50 MHz;Z0=50;r=7;L=.4106;

4. 14N NQR measurement inhexamethylenetetramine

4.1 Calculation of circuit parameters for fabricationA test of the 14N NQR resonance in hexamethylenetetramine(HMT) was carried out in order to ensure the superhet was

functional in the50

L>50r

(23)

For f=3.4 MHz withr=7 we find

L>16.7H (24)

For f=2.5MHz,

L>22.2H (25)

As NQR in thiourea is expected for 2 MHz< q< 3 MHz, acoil ofL=26 H was fasioned for the HMT study. The coilwas measured to have a pure reistive r=7 at just 10 KHz.Then the capacitances expected for tuning and matching at

f= 3.4 MHz are given by euqation (21). We have set

r=7;

Z0=50;

L=26 106;

(26)


7/8



We then calculate C1and C2to sanity check the design

C1= r

r2Z0(L22 + r2 rZ0)

= 7

7(2.13e7)250 ((26e6)2(2.13e7)2 + 72 750)

=30.8pF

C2=L2Z0

L2r4Z0+L24Z

20+ r

32Z0

L24Z0+r22Z0

= L2Z0

L24Z0+r22Z0

L2r4Z0+r32Z0 r22Z20

L24Z0+r22Z0

= (26e6)(2e7)250

L2(2e7)450 + 72(2e7)250

(26e6)27(2e7)450 + 73(2e7)25072(2e7)2502

(26e6)2(2e7)450 + 72(2e7)250

=50.5pF

(27)

4.2 Low frequency bridge/tank configuration

First, a coil of inductance grater than 25 H was wound from

40 AWG. With a10 KHz LCRmeter the coil showsL=26 H andr=7 . Following the calcalculation in the previoussection, suitable capacitors were chosen for mounting. The

expected 3.4 MHz signal is too low for the use of quarter wave

isolation. A Merrimac hybrid tee (HJ-17) was used instead.

Care was needed to prevent this high inductance coil from

ringing follopwing the pulse. A 2.7k resistor was placedacross the coil to reduce the Q and prevent spurious ringing.

Additionally, potential mechanical oscillations in the coil were

damped with black putty.

4.3 Construction of resonant tank with variable caps

Variable air gap capacitors with suitable range were mounted

to an aluminum enclosure. The coil was placed on a styrofoam

sheet to elevate it about 2 cm from the ground plane. As

always, the box was clamped tightly to a large metal sheet

under which the master ground lead rests. Ground loops are

detrimental in this bandwidth. All elements need mechanical

stability to maintain consistent tuning.

No IF amplifier was needed. Beats were visible even

without an IF passive filter. Two cascaded AU series Miteq

fast recover amplifiers provided enough gain to easily see the

NQR signal.

Figure 14. HMT coil. 60 turns AWG 40. L =26H

Figure 15. For the HMT study, a hybrid tee was used for

isolation. The aluminum enclosure seen on the near side

contains 10 pairs of crossed diodes in series. The diodes

serve to reject low amplitude noise in the pulses.

4.4 Results

A strong signal was observed at 3305.5 KHz. The signal

seems to have a strong temerpature dependence as would be

expected from NQR. The FID is visible without signal averag-

ing at all, and has a maximum amplitude of nearly 100 mV. In-

terestingly, the presence of beats were observed, which would

indicated a non-zero assymetry factor. Previously, HMT was

known to have = 0. However this determination was doneusing continuous wave methods. It is likely the superhet has

far greater resolution than the instrument used for the his-

torical data. This apparatus could potentially resolve a very

small that others could not. This opens the door for future

research in high resolution NQR of low frequency samples,


8/8



Figure 16. HMT probe circuit. The black putty around the

coil is intended to discourage mechanical oscialltions. The

circuit was fused with paper clips.

even if the sample has already been studied. It remains uncer-

tain why a static magnetic field of 100 gauss does not disruptthe signal entirely as is the case with prior 35Cl measure-

ments. More research is needed to determine whether the

candidate is indeed HMTs 14N NQR line and whether or not

is nonzero.

Figure 17. FID of HMT, taken with no passive filtration in

the IF stage. Pulse width = 40 s, spacing 100 ms, N=500averaging. Evidence of beats indicating a nonzero assymetry

parameter.

Figure 18. FID @ 3.2989 MHz, IF filtered. Beats observed.

Figure 19. 3.3180 MHz



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35Cl and 14N Nuclear Quadrupole Resonance in Paradichlorobenzene, Sodium Chlorate, and...

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