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This is to certifg that the

thesis entitled

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PURE EEC'I‘RIC QUADRUPOLE SPECTRA

IN CHLORINE COMPOUNDS

By

RICHARD E. MICHEL

A THESIS
Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requiremente
for the degree of.

MASTER OF SCIENCE

Department of Physics

1953

 

.f , (.- f‘ I
/,/ 5/; 9"

Acknowledgement

I wish to thank Professor Robert D.
Spence for the suggestion of this
problem and for hie helpful direction

toward its completion.

P
\ A v (\ \f‘r
term) C W

I.

II.

III.

Table of Contente

Intoduction l

The Theory of Pure Electric Quadrupole Spectre.
A. The Quadrupole Interaction Energy

3. The Surrounding Electric Field

0. The Principle of Quadrupole Reeonance

JOIN

The Detection of Pure Electric Quadrupole Spectre.
A. The Super-Regenerative Oecilletor 8
B. Preformance of the Spectrometer lO

I . IN TRODUC TION

The coulomb interaction and the quadrupole interaction are the
two predominate means by which a nucleus may be coupled with a
surrounding electric field. The latter type of coupling trill be
present. for a nucleus possessing an electric quadrupole moment.
if the surrounding field has symmetry lower than cubic. The presence
of such an interaction has been observed as fine structure in
microwave spectroscopyl a nd nuclear magnetic resonance?“ investigations.

Transitions which occur directly between energy levels of the
nucleus arising solely from the quadrupole interaction give rise to
shat is known as pure electric quadrupole spectra. The first
successful observation of such transitions was made by Dehnelt and
Kruger:5 in solid trans-diochlorethylene by use of an externally
quenched regenerative oscillator. Soon afterwards investigations

’4 using a very single self quenched super-

were made by Livingston
regenerative circuit. The use of the latter circuit for the detection
of pure electric quadrupole spectre forms the subject matter of this
thesis. A brief review of the theory of quadrupole spectra will

be presented first.

II. THE THEORY OF PURE ELECTRIC QUADRUPOLE SPECTRA.

A. The Quadrupole Interaction Energy

The electric quadrupole moment of the nucleus is a measure of
the non-spherical charge distribution in the nucleus. The physical
picture which is commonly given to represent the quadrupole moment
is a nucleus which has uniform charge density and the shape of
either a prolate or an oblate spheriod. The former has a positive
quadrupole moment and the latter a negative one. In either case
the charge distribution is symmetric about the spin axis. From a
classical electrostatic viewpoint the conception of the quadrupole
interaction energy is quite straightforward. The total interaction
energy of the nucleus with the surrounding charge distribution is
given by:

E a S vmu St-
‘Where\MMbis the potential of the surrounding charge distribution
at the element of volume 87“ of the nucleus and 9m is the charge
density of the nucleus. The expression for the potential may be
expanded by'a Taylor's expansion thus giving the total energy as
the sum of the energy terms:
E :. E.+E1+E3+~-~— -

E3 is then considered to be the electric quadrupole energy. The
first two terms are taken as the coulomb and electric dipole
interactions respectively.

While the above argument gives a fairly clear physical

conception of the interaction energy. the value of E0 used is
based on quantum-mechanical considerations. This value for a field

axially symmetric in the 2: direction is:
EQC‘W = y‘t :Kiift? L 5"”‘1- I (ll‘g
Where IL is the nuclear spin,~xv is the projection of I: on the
E axis and may take on the values - 3: to‘ I , a is the electronic
chargefi‘z} is the field gradient evaluated at the nucleus “@5229 is
the quadrupole coupling constant. (Q is the nuclear electric
quadrupole moment defined by:

hi} ‘7'. 3 a}. (“Sudan-”QM 327“
Where 5%.is the angle between “stand the 2 axis.

There are some features of this expression which may be
interpreted physically. Notice that the projection of I in the 2
direction appears to the second power, thus the energy expressions
forirwtare the same. This should be expected since this is really
a Stark splitting and is dependent only on the angle which the spin
vector makes with.the I} axis, not its direction. .Also it is seen
that if 2;; thenF—Q: o . Since for spherical and cubic symetry of
the fi.1d1:i°’ no quadrupole spectra would be expected for such
cases. Also forI=fi the value of EQ‘ 0 thus eliminating from

consideration all nuclei with spin of one-half.

B. The Surrounding Electric Field

In the above expression for the quadrupole interaction energy
the field considered is that arising from all surrounding charge
distribution. There are two sources of the field, the valence

electrons associated with the nucleus and the charges of neighboring

-3-

atoms and ions. The valence electron.may not be a g_electron

since this leads to a spherical charge distribution. Townes and
DaileyR have calculated the relative effects of a valence p

electron and an electronic charge placed lFiofrom a chlorine nucleus.
The effect of the electronic charge being one-half percent of the
valence electron. One of the principle causes of the small effect
is the shielding of external charges by the closed shells of
electrons. The valence electron which approaches the nucleus more
closely is not so affected. Thus the interaction energy for a
given.nucleus should remain fairly constant as the nucleus is placed

in different compounds. That this is so is indicated by the values

of the electric quadrupole coupling constant given below":6
Compound Nucleus qu no
50012 013‘ 6h.18
3. 63.78
P0013 Cl . 87.96
3% 57.88
032012 018% 71.98
03013 01 . 76.62
3; 76.:0
cgsqc1 Cl 69.2u

Although indicating a relative stability of the interaction energy
this data also shows that the effect of the surrounding field is
large enough for investigations to be made of these fields by use

of this type of data. It is also evident that if the surrounding
field were time dependent that the width of the resonance line would
be too large to be observable. Thus pure electric quadrupole spectra

are observed only in solids.

-h—

C . The Principle of Quadrupole Resonance

From quantum-mechanical considerations. M , the projection
of the nuclear spin in the 2: direction, may take on only the
values ~I/‘I4‘, ' ~ - - T4, *I . For a given nuclear spin there will
be several values offéu which are referred to as the energy levels
of the nucleus. .A nucleus which possesses£%§*4 energy is said to
be in the Mg‘ energy state. mu- 1: physically pictured as a
definite orientation of the nucleus in the electric field.

If energy is added to the nucleus it is possible to raise it
from a lower state to a higher one. Not many nuclei will change
their state, however. unless the energy added is exactly equal to
the energy separation of the two states. This is the resonance
phenomena which allows us to measure exactly the energy separation
of the quadrupole splitting. In order to add energy to the nucleus
use is made of the magnetic properties of the nucleus. Each nucleus

has associated with it a magnetic moment, A , which is given by:

“Al : ng—figfie

M is the proton mass and ‘3 is a constant called the gyromagnetic
ratio which is characteristic of the nucleus. An externally applied
ngnetic field will interact with M thus presenting a means of
supplying energy to the nucleus.

From the Bohr relation. asaky . a nucleus may be raised from
a lower to a higher energy state when a quantum of electromagnetic
radiation is absorbed. When the frequency of the radiation. v- . is

such that:

EquA ‘ Equ‘) 1 LG).

n“.—

there will be a large amount of energy absorbed from the external

field since many of the nuclei will undergo a transition. The

detection of this loss of energy from the external field gives rise

to the resonance absorption line. A given resonance line is

identified by the frequency. V0 , at which the absorption takes place.
As an example consider a nucleus for which 'I ‘ 57L . The

associated quadrupole energies are:

qua) : sebum
e. mm .5 {431$ is. Q]

Sq {if l/ij‘ 11 "’ H/lni‘a‘ {2162A

The energy diagram appears as:

'/
Msig).

E0 ‘ ‘ ,
_ Y M: i 3/7-
.- t M : ‘L 1/1.

E0 represents the energy of the nucleus in the absence of the

 

 

 

surrounding electric field.

we have spoken of adding electromgnetic energy to the
system; however. as will be pointed out later, the energy is
absorbed from the coil of an oscillating tank circuit. Since
the magnetic properties of the circuit are usually associated

with the coil it would seem logical to consider the transitions

--6--

magnetic in nature and caused. as has been indicated. by an
interaction between the oscillation external field and the
magnetic moment of the nucleus. The selection rule for a
magnetic dipole transition is Aer—l I so the expected spectrum

would consist of two lines:

a}:
\

93/ ‘ (7:0 3; & (tie. Q]
3

V34.“ 2 3&0:- JL {2% 91
This is the spectrum observed by Dehmelt8 for several iodine compounds.
It is well to emphasize that the nature of this transition
is magnetic and is the same type of transition as is found in
nuclear magnetic resonance experiments. The electric quadrupole
causes the formation of the energy levels but is not concerned

with the transitions between levels.

III. THE DETECTION OF PURE ELECTRIC QUADRUPOLE SPECTRA

A. The Super-Regenerative Oscillator

The circuit shown in Figure l is the spectrometer used in our
investigations. .A qualitative description of its operation will
be given here; amore comprehensive discussion of the super-regenerative
oscillator in resonance investigations has been given by 8.1. Tahsin.9

A.superbregenerative oscillator is a radio frequency oscillator to
which an audio frequency quenching voltage is applied which causes
the circuit to go into and out of oscillation. The quenching voltage
may be applied externally. usually to the plate of the tube: or. as
in this circuit. the components may be chosen so that intern a1 voltages
are produced which result in a quenching action. The result of the
quenching voltage is to produce a very sensitive detector since
during the time when the oscillations are decaying and building up
the plate current is very sensitive to any changes of energy in the
tank circuit. The coil of the tank circuit furnishes an oscillating
magnetic field whose frequency may be readily changed by merely
tuning the tank circuit.

In order to view a resonance absorption line on an oscilloscope
one further component has been added to the circuit. If the sample
were placed in the tank circuit coil and the condenser tuned through
the resonant frequency,1h,, there would appear a signal on the oscilloscope
as the resonance was passed; however, if the circuit was left tuned
at 1%) there would be no signal as there would be no change in

the plate current. In order to observe the signal visually a

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vibrating condenser has been placed in parallel with the tuning
condenser. The capacitance of this condenser may be changed
periodically at any low audio frequency. Thus if we tune the
tank circuit to resonance and then add the periodic change of
the vibrating condenser the resonance condition will be swept
through periodically which will allow the absorption line to

be observed visually.

The block diagram of Figure 2 shows the entire spectometer
circuit. The Select-O—Ject is a commercial filter; it is used to
reject the unwanted amplitude modulation.which is produced as
a result of the frequency modulation of the vibrating condenser.
The Hewlett—Packard audio oscillator furnishes the power to
drive the vibrating condenser. .Ls the lower limit of the
Select-O-Ject is 80 cps the modulating frequency has to be kept
higher. The modulating frequency was normally around 120 cps.

The super-regenerative oscillator was constructed in the
case which contained the vibrating condenser: the latter was
taken from a Navy altimeter. BT-7/APNBI. The sample coil was
made from 6-7 turns of number 58 copper wire wound on a
one-half inch diameter. The coil was shielded by'a one inch
brass cup and was connected to the oscillator by means of a
rigid coaxial line consisting of one—half inch brass pipe and
numbermSO brass wire approximately seven.inches long. Three
teflon washers were used to hold the inner conductor in place.

Later the length of the connecting line was reduced to

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two and one-half inches so that the inductance of the tank circuit
would be concentrated in the coil where the losses take place

and not distributed along the coaxial line. The small vernier
condenser was added to give a smoother sweep through the resonance

condition.

3. Performance of the Spectrometer
To test the instrument the resonance lines associated with

013‘ and 6137 in GHCl3 were first sought as they were known to

exist at:
0135' 0137
88.8081 mc 80.1921 mc
38.2536 mc 80.1800 me

Only one line would be expected from each nuclei since
they'both have a nuclear spin of three-halves. The presence
of two lines has been explained6 by considering that there are
two non-equivalent positions for the Cl nucleus to take in the
molecule.

The tank coil of the spectometer was immersed in.a beaker
of GHClz which was then frozen by placing it in a mixture of
acetone and dry ice. No results were observed. A.possible
reason for the negative results is that the sample was not
frozen solid enough. The temperature of the freezing mixture
was -77’°O and the freezing point of CH013 is ~63.8 .0. The
surrounding electric field may still have had a time dependency.”

which broadened the line width beyond the point where it could

-10-

be observed. The resonance lines had been originally observed at
-l96 0C so liquid nitrogen was next used to freeze the sample.
One of the resonance lines was observed but the tuning condenser
proved too coarse to adjust carefully at resonance. Once the
vernier capacitance was added both lines were observed.

In sweeping the field searching for the resonance line other
signals were detected from other radio frequency oscillators in
the building and even from what is thought to be a local radio
station. To discriminate between the "false” signals and the
quadrupole resonance the following trick was used.

Pound2 has discussed the result of introducing a small external
magnetic field to a single crystal in which a quadrupole resonance
line is being observed. The result is to shift the frequency. The
magnitude of the effect, however. is dependent on the angle between
the magnetic and electric fields. .As our sample was polycrystalline
the effect of introducing a small magnetic field was to widen the line
until it disappeared. Thus the quadrupole line was distinguishable
from the other signals picked up by the oscillator.

The form of the observed signal as the tank circuit was tuned
through resonance was unusual enough that its description is shown
in Figure 3. As shown, a single line appears and splits into two
lines. Whenb.r . the frequency of the tank circuit without the
vibrating condenser. equals Pb , each of the original lines is now
two equally spaced lines. The signal when set at this condition

proved to be smaller and less stable than when the one line was observed.

-11-

 

 

 

 

 

 

 

 

 

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FIGURE 3

To measure the frequency of the resonance line the tank circuit
was first tuned so that‘ur coincided with Y; . The signal of a
Gertsch FM-l frequency meter was mixed.with the resonance signal.
There appeared successively on the oscilloscope as the meter was
tuned through the resonant frequency a series of signals which
were symmetric in amplitude about a central signal. Frequency
measurements were made with this central signal superimposed on
the resonant line.

It was at this point that the main.weakness of this type of
detector came to light. The resonant frequency readings were not
consistent. The reason for this lies in the very nature of the
instrument. The quenching of the oscillations produces side bands
which may also detect the signal. With an internally quenched
oscillator the only way it might b e possible to determine the
frequency at which the detection is taking place is by comparing
the amplitudes of the signals. In our case we were not able to
do so.

Several additional compounds were checked at dry ice and
acetone temperatures; the frequency being swept from 20-50 me.

No results were found in C6H50001 or.Lneline. CHCl C3012 would

2
not freeze with our freezing mixture although its freezing point
is ~M3.8”’C. The metal probe perhaps conducted too much heat into
the sample. CHCIZCOOH conducted to such an extent that it stopped
the oscillations. Finally a line was observed in solid bensyl
chloride (063603201) at liquid nitrogen temperatures. The

approximate position of the line being 33.6 mo.

In an.sttempt to repeat the experiment using benzyl chloride
of only technical purity the line could not be found. Once a
0.P.8. sample was used again.the line was easily obtained. Although
the reason why the impure sample failed to give resonance is not
known it is possible that para-magnetic ions were present which
had the same effect as our externally'applied field.

In an attempt to measure the resonant frequency with certainty
peredichlerbenzene, a solid at room temperature, was used as our
sample. The vernier capacitance of the tank circuit was connected
to a 1 rpm motor which was geared down 1 to 10. The main tuning
condenser was set close to the resonant line and the vernier was
then.drivsn.threugh resonance with the signal being recorded on
s.Hillivsc recorder» Preliminary work with this method indicates
that the side bands of the oscillator can be detected. If so the
uncertainty of the frequency measurements can be removed.

If this is done the circuit presents a very simple means by which

the quadrupole spectre may be observed.

-13-

Bibliography

Gordy, Simone and Smith. EL- 33;. 71+. 2M3 (1911\8)

Pound. 11. v.. m. 513;. 79. 685 (1950)

Dehmelt and Kruger, Naturwise. 37. ill (19%)

Livingston. 3.. £21.33 _IfT_. 1. £333. §£_i_. RR, 5-100 (1992)

Townes and Bailey, £313. 923;. 131112. 20. 3‘? (1%.?)

Livingston. 3.. 131. 3g. 82. 2249 (19:1)

Xichuchi and Wanda, 11?; m 3915 (1952)

Dennelt, H. 0.. g. m. 130, 356 (1951)

Tahein. S. 1.. "The Theory of the Use of the Super-Regenerative

Receiver for the Detection of Nuclear Magnetic Resonance” 15,
22 Masters Thesis. M. S. C. (19‘71)

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