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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)
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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
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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.
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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)
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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)
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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,
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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
Figure 20. 3.3055 MHz
Figure 21. 3.3088 MHz