Tasks for Allen Majewski to complete by December 31, 2014
DRAFT
A.
14N NQR
(1) Make a receiving coil suitable for NQR detection of 14 N nuclei. Goal L in range 10-20
H. Coil diameter of the order of 0.75-1.0 in, using AWG 38-40 enameled copper
wire.
(2) Make a resonant circuit using this coil to provide a high Q and use a capacitive
transformer to match to 50 Ohms
(3) Integrate the above into a hybrid tee bridge operating at about 4 MHz and
demonstrate the matching.
(4) Look for 14N NQR in hexamethyl-tetramine (HTM) which is the simplest standard
example for a rom temperature signal.
Write up all steps at every stage with dates and simple descriptive notes in laboratory log
book.
B. Write a short 4-6 page description of your successful test of 35Cl and Cl37 NQR from
samples of NaClO3 and para-dichlorobenzene. Include spectra of the signals from
signal averaging.
Pulsed nuclear quadrupole resonance studies were carried out in sodium chlorate, paradichlorobenzene (35Cl), and hexamethylene-tetramine (14N). All studies were conducted using
the home-made superheterodyne spectrometer. The apparatus was largely unchanged for the
three studies except for the tank section and the pulse protection circuitry between the power
amplifier and the receiver section.
The bridge circuit configuration used for measurement of NQR in para-dichlorobenzene.
However a number of combinations were used for the bridge and tank circuit sections in the
various measurements. Above you see the bridge circuit used in the case of paradichlorobenzene. These earliest measurements display a lower S/N than NaClO3 despite the
NQR amplitude being larger in para-dichlorobenze because of two disadvantages. (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. This is 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.
In 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.
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=100.
The SNR shown by the power spectrum of the above FID.
The bridge circuit configuration used in measurements of sodium chlorate 35Cl NQR. Notice
the absence of hybrid tee junction, which is supplanted by the quarter wave section and
diode switches.
The NaClO3 tank. S/N was improved by having the sample connected directly to the matching
circuit and placed in the aluminum enclosure without use of coaxial connectors.
The tank circuit used for NaClO3 also differed from that of NaClO3 in the matching circuit
configuration. In this circuit, a series capacitor matches a parallel resonance with the coil, as
shown below.
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 Cm, Ct, ω, L, r and produce some useful set of tables for lab, in which the relationship
between Cm and Ct is known for a given ω L and r, where r is a pure resistive parameter in
series with the coil inducatance.
For impedance matching conditions to be satisfied, which for us means 50 ohms real we must
enforce
Im_Z = 0
Re_Z = R := 50 ohms
with
Z_coil = j ω L + r
So the total impedance is
Z_tot = -j / (Cm ω) + Z_coil || Z_Ct = Re_Z + j Im_Z = R + j 0 = 50
Note:
* Z_m is the impedance of the matching cap only
* Z_t is the impedance of the tuning cap only
* the notation A || B means “A parallel B” and A || B = ( 1/A + 1/B)^(-1)
Since Z_coil has a real and an imaginary part, the expression for total impedance is .
Z_tot = -j / (Cm ω) + Z_coil || Z_Ct = Re_Z + j Im_Z = R + j 0 = 50
So I did it by hand, and with mathematica, and iteratively found what I consider decently short
code with reasonably concise expressions. I prefer using mathematica because it allows the
dynamic adjustment of the parameters L, and r to instantly output the capacitances as a
function of frequency. Calculation is on the internet here and printed below.
(*You may copy and paste all of this text including the comments.Just \
run this entire block in mathematica in a single input.It should \
output the capacitances and sliders for you to adjust the other \
parameters.##### 2014 www.altoidnerd.com #####*)Clear[w, L, r, f, Z, \
Zform, ImZ, ReZ, T, M, Tminus, Tplus, Mminus, Mplus, Ma, ALL, tunem, \
tunep, matchm, matchp]
(*To avoid subscripts,we denote the tuning capacitance as T and the \
matching capacitance as M.The coil inductance is L.For the NMR probe \
topology shown in the image \
http://altoidnerd.files.wordpress.com/2014/04/img42.gif the general \
form for the impedance looking into the tank while r is in series \
with L is*)
(* The type
Z = 1/(I*w*M) + 1/(1/(I*w*L + r) + I*w*T);
(*Looking at the output of*)
Zform = ComplexExpand[Z];
(*Will yield the real and imaginary parts.The rest comes from \
enforcing Re{Z}=Z0 and Im{Z}=0*)
ReZ = r/((r^2 +
L^2 w^2) (r^2/(r^2 +
L^2 w^2)^2 + (T w - (L w)/(r^2 + L^2 w^2))^2));
ImZ = (-(1/(M w)) - (T w)/(r^2/(r^2 +
L^2 w^2)^2 + (T w - (L w)/(r^2 +
L^2 w^2))^2) + (L w)/((r^2 +
L^2 w^2) (r^2/(r^2 +
L^2 w^2)^2 + (T w - (L w)/(r^2 + L^2 w^2))^2)));
Solve[ReZ == Z0, T];
Solve[ImZ == 0, M];
(*The resulting quadratic for the capacitance T requires us to \
discard the value with a plus sign before the square root.These \
solutions lead to negative values of capacitance for M (the matching \
cap).I have kept the variables defined,but excluded them in the \
output.*)
Tminus = Dynamic[(L w^2 Z0 Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2])*1.00/(r^2 w^2 Z0 + L^2 w^4 Z0)];
Tplus = Dynamic[(L w^2 Z0 +
Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 - r^2 w^2 Z0^2])/(r^2 w^2 Z0 +
L^2 w^4 Z0)];
Ma[T_] := (-1 + 2 L T w^2 - r^2 T^2 w^2 L^2 T^2 w^4)/(w^2 (-L + r^2 T + L^2 T w^2));
Mminus = Dynamic[(
(-1 + (2 L w^2 (L w^2 Z0 Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2]))/(r^2 w^2 Z0 +
L^2 w^4 Z0) - (r^2 w^2 (L w^2 Z0 Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2])^2)/(r^2 w^2 Z0 +
L^2 w^4 Z0)^2 - (L^2 w^4 (L w^2 Z0 Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2])^2)/(r^2 w^2 Z0 +
L^2 w^4 Z0)^2)/(w^2 (-L + (r^2 (L w^2 Z0 Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2]))/(r^2 w^2 Z0 +
L^2 w^4 Z0) + (L^2 w^2 (L w^2 Z0 Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2]))/(r^2 w^2 Z0 + L^2 w^4 Z0)))
)*1.00];
Mplus = Dynamic[(-1 + (2 L w^2 (L w^2 Z0 +
Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2]))/(r^2 w^2 Z0 +
L^2 w^4 Z0) - (r^2 w^2 (L w^2 Z0 +
Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2])^2)/(r^2 w^2 Z0 +
L^2 w^4 Z0)^2 - (L^2 w^4 (L w^2 Z0 +
Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2])^2)/(r^2 w^2 Z0 +
L^2 w^4 Z0)^2)/(w^2 (-L + (r^2 (L w^2 Z0 +
Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2]))/(r^2 w^2 Z0 +
L^2 w^4 Z0) + (L^2 w^2 (L w^2 Z0 +
Sqrt[r^3 w^2 Z0 + L^2 r w^4 Z0 r^2 w^2 Z0^2]))/(r^2 w^2 Z0 + L^2 w^4 Z0)))];
f = Dynamic[w/(6.28319)];
{"f = " Dynamic[f] }
{Slider[Dynamic[w], {10^6, .2001*10^9, .001*10^6}, ImageSize -> 800],
"w = " Dynamic[w],
Slider[Dynamic[L], {.2*10^-6, 50*10^-6, 1.0*1.0010*10^-7},
ImageSize -> 800], "L =
" Dynamic[L],
Slider[Dynamic[r], {.001, 300, .001}, ImageSize -> 800],
"r =
" Dynamic[r],
Slider[Dynamic[Z0], {1, 300, 1}, ImageSize -> 800],
"Z0 =
" Dynamic[Z0]}
r = 7.000;
Z0 = 50;
L = 26.000*10^-6;
w = 2.00*10^7;
Q = Dynamic[(L*1.00)*w/r];
{"tunecap=", Tminus, "matchcap=", Mminus, "Q=", Q}
C. Write a short summary of your correspondence with the theorists at Oxford on the
predictions for the 35 Cl NQR signal in DTN and suggest reasons why it should be so
much lower than the standard signals normally seen in the range of 27-31 MHz for
organic crystals.
As the NQR frequency at a given nuclear site is directly proportional to Vzz (the electric field
gradient, or stretching), crystals with a high degree of symmetry will have low NQR frequencies.
Tim Green of oxford calculated the EFG tensor for nuclear in DTN as well as in NaClO3 using the
GIPAW method with CASTEP software. Inspection of the crystal structure superficicially
indicates a widely symmetric nuclear distribution about the chlorine sites. Evidence for the
validity of his calculations is that the prediction for NaClO3 35Cl NQR matches observation
remarkably well. Furthermore, the NQR frequencies calculated for 14N in DTN match those
observerved in crystalline thiourea from literature (david h. smith and r. m. cotts) which puts
NQR in 14N in pure thiourea at 2.6 MHz and 2.0 MHz for inequivalent sites.
For NaClO3, CASTEP arrived at an average NQR frequency (over 4 sites) of 28.9 MHz. For
chlorine in DTN, CASTEP calculated NQR at 8.5 MHz (unrelaxed) and 4.5 MHz (relaxed). For 14N
in DTN, the calculation yields 2.9 MHz and 1.6 MHz for inequivalent sites in the relaxed EFG
calculation. The difference between the relaxed and unrelaxed calculation lies in the structural
data preparation. In the unrelaxed case, structure data from direct measurements in literature
is fed directly into CASTEP and used. In the relaxed case, the structure parameters itself are
adjusted using GIPAW, and then the EFG is calculated.
Correcting the data from cotts for 0K using a linear approximation, I find the NQR frequency
lines up with 2.55 MHz.