133
326

 

'THS_

QIIAD:‘<*II FCLE 7£QRAKnE ZIQDIES

“F‘ F‘ A $)\. ,. ‘.-\ I u
dhesfis Yer nae axesmaa 2 .s F”

MICHI IGII‘I STAFE In ”IIIRSITY
Richard Eaiw; I/Zic hel
25353

A

""'"'" .IIIIIlIlIIIIIIIII

THESIS

IIIIII

1293 01743 0319

                    

This is to certify that the

thesis entitled
Quadrupole Resonance Studies
presented by

Richard Edwin Michel

has been accepted towards fulfillment
of the requirements for

Ph. D degree mm.

W“—
Major pro essor

Date October 26, 1956

 

0-169

 

 

._ __..

‘9’"

QUADRUPOLE RESONANCE STUDIES

BY

Richard Edwin Michel

AN ABSTRACT

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of

the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics
1956

 

Approved Wi_%—m

Richard E. Michel

The quadrupole resonance of 0135 has been used to study
certain properties of crystals of p-C5H4612 and 06H501. The
investigations of p-65H4Clg were made at room temperature
while those of 06H5Cl were made at liquid nitrogen tempera-
ture. Both resonances occur in the range of ~34mm The
resonances were detected by means of an internally quenched
superregenerative oscillator.

The Zeeman splitting of the resonance from single cry-
stals of p-06H4612 indicated that there were two directions
of the 6-01 bond.separated by ~.74°, when the crystal was
in the low temperature, orca , phase but that there was only
one direction when the crystal was in the high temperature,
or g , phase. The transition temperature is ~32 'C. The
orientation of the single axis in the II phase with reSpect
to the two in thetx. phase appeared to be either random or
capable of assuming a large number of different values.
Measurements of the line width of the nuclear magnetic re-
sonance of the protons in the same samples indicated that
the reorientation of the C-Cl bond during the phase transi-
tion was accompanied by a similar reorientation of the mole-
cule as a whole.

The samples of 06H5Cl studied contained controlled
amounts of other benzene derivatives. The addition of even
.001 mole fraction of certain impurities reduced the maximum

height of the signal greatly without appreciable broadening

Richard E. Michel

of the line. The effectiveness of the impurity in reducing
the resonmice was measured by the number of molecules which
each impurity molecule would have to make ineffective in
order to bring about the resultant loss in intensity. There
appeared to be a linear relationship between the effective-
ness of the impurities and the difference in volume between
the impurity molecule and the C6H501 molecule. There was
no observable effect due to a difference in the electric

dipole moment of the impurity and resonant molecules.

QUADRUPOLE RESONANCE STUDIES

By

Richard Edwin Michel

A THESIS

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
- Applied Science in partial fulfillment of

the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics
1956

Cepyright by
Richard Edwin Iflchel
1959

ll ; "l lli,

 

ACKNOWLEDGEMENTS

The author wishes to express his

appreciation to Professor R. D. Spence

for his interest and guidance during

the course of this work.

Richard Edwin Michel
candidate for the degree of

Doctor of PhilOSOphy

’

Final examination, October 26, 1950, l p.m., Physics
Conference Room

Dissertation: Quadrupole Resonance Studies

Outline of Studies
Major subject: Physics

Minor subject: Mathematics

Biographical Items
Born, October 31, 1928, Saginaw, Michigan
Undergraduate Studies, Michigan State University, 1946-50

Graduate Studies, Michigan State University, 1950,
cont. 1953-56

Experience: Graduate Assistant, Michigan State University,
1950, 1953, 1954-55. Instructor (temp.).
Michigan State University, 1955-56

Member of Phi Kappa Phi, Sigma Pi Sigma, Society of the
Sigma Xi, The American Physical Society

I.

II.

III.

IV.

TABLE or CONTENTS

THEORY. . . . . .

The Pure Electric Quadrupole Energy States.

The Electric Field Gradient

THE SPECTROMETER.

THE PHASE TRANSITION IN p-C6H4C12 . . . . . .

Zeeman Splitting of the Nuclear Quadrupole

Resonance .

Dipolar Broadening of the Nuclear Magnetic Re-
sonance (NMR) of the Protons in p-C6H4Cl2.

The Experimental Method .

Discussion of the Results

QUADRUPOLE RESONANCE OF IMPURE SAMPLES.

LIST OF REFERENCES

27
29
33

37
4l

52

Tl

I. INTRODUCTION

A nucleus which possesses an electric quadrupole moment

may interact with an electric field if the field is such

 

J
action energy is dependent upon the orientation of the nu-

that not all of its derivatives, jEIi, vanish. The inter-

cleus in the electric field. The presence of such an inter-
action can be observed in optical,1 molecular beam,2 micro-
wave3 and nuclear paramagnetic4 spectroscopy. In all of
these cases, however, the quadrupole energy is small in com-
parison to other energies present in the system and manifests
itself only in fine structure lines and line shapes.

The observation of spectra resulting from nuclear tran-
sitions between energy states whose separation is determined
entirely by the electric quadrupole interaction was first
accomplished by Dehmelt and Kruger.5 The transitions ob-
served were those of the chlorine nuclei in solid trans-
dichloroethylene. In a series of papers6 they have discussed
this experiment along with similar observations of reso-
nances of bromine, iodine and antimony nuclei.

The spectrum which is observed arises from the detec-
tion of a radio-frequency nuclear magnetic resonance absorp-

tion. That is, energy of a radio-frequency field is trans-

ferred to the nuclei by means of an interaction between the

field and the nuclear magnetic moments. The absorption of
energy and the accompanying excitation of the nuclei from

one energy state to another take place when the frequency of
the field satisfies the condition.J=ۤ where AE.is the sepa-
ration of the energy states. In this reapect it is similar
to nuclear paramagnetic resonance, the difference being the
manner in which the energy states are determined. In nuclear
paramagnetic resonance the energy levels are determined by
the orientation of the nuclear magnetic moments in an exter-
nally applied static magnetic field. On the other hand, the
quadrupole states are fixed by the interaction of the nuclear
electric quadrupole moments and an electric field gradient.
Furthermore, the source of the electric field is a charge
distribution within the sample itself. It follows that in
nuclear quadrupole resonance (NQR) the resonant frequency of
a given nucleus varies from com pound to compound.

Much of the work which has been done in NQR has been
concerned with attempts to use these shifts in frequency to
substantiate or extend existing theories of molecular and
crystalline interactions. For instance, Livingston7 has ob-
served that the quadrupole coupling constant, the product of
the nuclear electric quadrupole moment and the maximum field
gradient, increases regularly in the sequence of solid mater-
ials CH2012, CH 013 and C 014. This behavior is in agree-
ment with changes to be expected in the bonds within the

molecule, which will be discussed later, and indicates that

adjacent molecules in the solid have very little effect on
the quadrupole coupling constant in molecular crystals. If
the adjacent molecules did have a large effect, there would
be more random behavior of the coupling constant.

In a somewhat similar vein, investigatorsa'9 have found
that there is a relation between the quadrupole coupling
constant and Hamett's substituent parameter (T’.I The con-
stant is a measure of the electron density in the molecule
and thus should affect the electric field which is seen by
the resonant nucleus.

In contrast to these investigations which are concerned
with changes in the field gradient due to changes in molecu-
lar structure, some workers have observed variations in the
spectrum when the crystal structure has been perturbed.
Duchesne and Monfilslo have observed the NQR of 0135 in
p - 06H4012 when small amounts (10‘3 to 10"2 molar concen-
tration) of p - CgH4Br2 have been added. The two compounds
form a solid solution; however, the difference in size of
the two molecules should produce some strain around the im-
purity molecule. The investigators observed a rapid decrease
of signal intensity and a broadening of the line with in-
creasing concentration of the impurity. They did not ob-
serve a shift in the resonant frequency of the impure samples

with respect to the pure sample. Dean11 has reported that

there is a shift in frequency for molar concentrations of

the order of one-tenth. A shift in the resonant frequency
of 0135 in p - 06H4012 has also been reported by Dautreppe

12 when they subjected the crystal to a pressure

and Dreyfus
of 900 kg/cm2. It would thus appear that even if Livingston's
conclusion, that the surrounding molecules do not play a

large role in determining the resonant frequency, is true,
their fractional importance is large enough to be easily
observed. Their exact role in the production of the field
gradient, however, is still not well understood. The im-
portance of NQR in the investigation of molecular bond
structure would be greatly enhanced if these crystalline
effects were better understood.

It might be mentioned at this point that, although we
have discussed only the case of solid materials, pure quad-
rupole transitions have been observed by Sterzer and Beers13
in vapors of CHBI and CF31. Also Seiden14'has recently pro-
posed that it may be possible to observe such transitions in
liquids which show some anisotropy.

The investigations of this thesis are restricted to
solids and in particular to organic compounds containing one
or more covalently bonded chlorine atoms. The resonances
observed are those of 0135. There are two sections to the
thesis.. In the first part use is made of existing ideas
concerning the electric field gradient at the nucleus to in-

vestigate a phase transition in p - 05H4012 known to exist

at 32°C. In the second part an attempt is made to better
understand the role which the surrounding molecules play in
producing the gradient at the nucleus. A discussion of the
general theory applicable to both parts is given first with
the more specialized discussions given in their respective

sections.

II. THEORY

A. The Pure Electric Quadrupole Energy States

The pure electric quadrupole energy states arise from
an electrostatic interaction between the nuclear charge and
the electric charge surrounding the nucleus. The discussion
given here is merely an outline of the derivation of these
energy states for the particular case of an axially symmetric
electric field. A more complete discussion of the general

case has been given by Pound.15

We begin by considering the total electrostatic inter-
action between two groups of charge, the nucleus and the

surrounding charge.

2 an
(1

 

 

X

fflne subscript “n" refers to the nucleus and the subscript

'NB“ to the charge outside of the nucleus. In terms of the

indicated quantities the electrostatic interaction is given

I QIE‘ACIE'A 87* 9"“ V

: 1

E ST. 1., ILmI.\*(:—I3lt ' 1%}: Wei-“‘1 (1)
Since by definition ”$5 I , the denominator may be expanded

 

in terms of Legandre polynomials.
E = Sm, l4,“ QIr—‘\QIB!\I%,+%Plim°1v~l+%mme>a (2)
,...1 inn,
The first term of the expansion leads to the coulomb energy
which has no orientational dependence and is therefore of no
interest to us. The second term leads to the electric dipole
energy which vanishes for a nucleus which has a symmetrical
distribution of charge. This term has been found to be zero
for all nuclei so far studied. The third term leads to the
quadrupole energy which is the interaction we wish to dis-
cuss. Its value is:
t. -- I. 8.18”as:attainment-Ivan (3)
The angle es“ may be eliminated from the problem by intro-

ducing the Cartesian coordinates through the relation

(4)
EM'R.’ : “ml-\Lme“; : izx‘slxlt:

This gives:

3 ~~X.X.-11U},n (5)
a. ; y, 31‘ij an. I... .. .. a, natjgflibnm
It can be verified that the energy may be expressed in the

following form:

. (6)
Est = ”I; .23 Q“ IVER“.

where,
QLS : ST“QIn:‘V\\K3XML XnS ‘3“ ”'13) 91"“
IVEILS : _ 8’“ Iii—3%) I3xl:xn~,~8;gn1391’,
The advantage of expressing the energy in this manner is
that one can investigate the contribution due to the nucleus
separately from that of the surrounding charge distribution.
Considering (2;; first we see that it is a symmetric
tensor, since the Xaio commute, and that the sum of the
diagonal terms is zero. There is a theorem16 which states
that if two tensors (a) are symmetric, (b) possess a zero
trace and (c) are constructed in the same manner from vec-
tors which satisfy the eame commutation rules with respect
to l: as E and:- , then the matrix elements diagonal in I
of the two tensors will have the same dependence on the mag-
netic quantum number,¥n . That is, if' T33 and 'TE; are

two such tensors then

IIMITMINII = have i <7)

I
Ilw TsIIw‘I = K, S('w.\
where K, and K1 are independent of'm . Since m is a

measure of the orientation of the nucleus, it is §I~€H
which is of interest to us in NQR. We may therefore replace

(Rt; by the following tensor:
Cm = C I. “DATA; ~313IIII] (8)

The constant C.is determined by defining the electric quad-

rupole moment, 1Q , in the following manner

an (II\Q33III\:C[(11-I\I_] (9)

so that

Q-~ - 3.9. I. “II-I. In, ‘Sis III] (10)
”- Inn—u

The second tensor II7§\;3 is also symmetric and real so
that it is possible to find a coordinate system in which it
will be diagonal.17 We shall assume that the coordinate
system chosen originally was the correct choice.

1 1 ll
(VEM = - 573%]:“3Xu-3LLRJ97. ‘ ’
It is easily seen that this tensor is actually the gradient
of an ehectric field as indicated by the symbolism. The
potential arising at a point {5 due to the charge distribu-
tion QKQA is given by:

v .~..I w M

The second derivative of this quantity with respect to KL

J

evaluated at n_:O results in IVE); . We now make the
assumption that IVE); is constant with respect to the nu-
clear orientation. This simplification can not be made in
investigations such as the molecular beam experiments. In
these cases one is concerned with essentially free molecules,
and the orientation of the nucleus certainly may have an
appreciable effect on the remainder of the molecule. In the

case of the NQR, however, the “remainder of the molecule" is

10

the macroscopic crystal and we may conceivably neglect the

effect of the orientation of the nucleus on such a massive

object.
We further restrict the problem to the special case of
E
an axially symmetric field gradient, that is for 3573' : 33%.:

Furthermore, since we are considering the electric field at
the nucleus due to charges outside of the nucleus, the elec-
tric field must satisfy the relation ‘V~§; O . Using these

relations the Hamiltonian of the problem becomes

- LQ“ ‘- 3\¥\1 - I1. (13)
“'4 ‘ unit—h I ' l
where % E ()Ei/Ji.

The Hamiltonian is diagonal in “A and the resulting energy

states which are degenerate in 1v" are

E 3 SIGN, [ 3w‘—t(I-H\1 (14)

h“ “H: Lil-I]

B. The Electric Field Gradient

The spectrum of 0135 resulting from the energy levels
derived in the last section consists of a single line whose
frequency is determined by the relation:

I); : 413352, (15)

 

Thus, if it is assumed that the electric quadrupole moment

ll

of a given nucleus is independent of the nature of the com-
pound of which it is a part, the transition frequency is a
direct measure of the electric field gradient. As is evi-
dent, however, neither the value of the field gradient nor
the quadrupole moment can be determined from a frequency
measurement alone.
Before discussing possible sources of q and their rela-

tive importance, we can consider one aspect of the source
which is entirely general. As has been mentioned before,

the electric field must satisfy Laplace's equation, V. E=O

p.” ‘ .

If the symmetry of the charge distribution is cubic or
spherical, the x, y and 2 directions will be equivalent.

This requires that:

(16)
bx 3t 3?.-
Taken together these two relationships require that:
’ (17)
9‘37 - QEEQ - AEEB :.C>

fi‘bn’B—i
Therefore, for an electric quadrupole interaction to exist,
the charge distribution producing the electric field must
have a symmetry less than cubic.

The charge distribution is normally c0nsidered in two
parts, the valence electrons associated with the nucleus in
question and all other charges surrounding the nucleus. The

division is made in this manner since q is primarily depen-

12

dent upon the valence electrons and the manner in which they
are bonded. The closed shells of electrons surrounding the
nucleus constitute a spherical charge distribution and there-
fore do not contribute to the field gradient.

For the case considered here, covalently bonded 0135,
the field will arise largely from the lack of one 3p elec-
tron in the valence shell. The validity of this division
of the source of q may be inferred from the following com-
parison. The field gradient due to one electronic charge
placed l R0 from the nucleus is iK'Ofr gbg<ka3 assuming
the atom is otherwise undisturbed. It has been shown1
that for the chlorine nucleus the shielding of the surround-
ing electrons should reduce this value to ~"“°‘g.qs9“433
In comparison, the observed field gradient corresponding to
the resonant frequency of 35mc, which is an average value
for the 0-0135 covalent bond, is \lX IO N’- cso/a‘a .

A further illustration of the relative contribution of
the valence electrons and the external charges can be made
by comparing q for the gaseous NaCl and that for a molecule
in which the chlorine is covalently bonded, such as CH301.
In the former case the electron distribution around the
chlorine nucleus is approximately spherical and the electric
field gradient must be attributed to its partner ion, whereas
in the second case there is no distinct charge present and

q must be attributed to the asymmetrical distribution of the

13

chlorine electrons caused by their participation in the co-
valent bond. For Nacl q is known to be less than .I7K10'ri—g
while for gaseous CH301 it is Laxto“7e“%a£.. Thus, for a
covalently bonded chlorine atom, q should be given to a

good approximation by the calculation of only that portion
of q which arises from the participation of the valence
electron in the bond. Even if the approximation is valid,
the calculation has an extremely large uncertainty in itself
since the wave functions of electrons in the molecule are
not known.

18 have considered methods of making

Townes and Bailey
approximate calculations from which one can obtain at least
an idea of the nature of q and in some cases an approximate
value. The nature of the chemical bond between two atoms is
commonly expressed in terms of a set of limiting types which
are more easily visualized. Thus, for example, a bond may
be said to be largely covalent with a certain percentage of
ionic character and a certain percentage of double bonding.
The percentage of the various parts is normally determined
by fitting the available eXperimental evidence into a con-
sistent pattern.

The bond we are concerned with is the 0-61 bond in
chlorine derivatives of benzene, methane and ethane. In
these cases it is largely a single covalent bond. A single

covalent bond is visualized as a shared pair of electrons.

The stabalization of the bond arises from the overlapping

14

of the two electron orbits. In the valence bond method

the wave function for each of the electrons is expressed as
a linear combination of the atomic wave functions of their
respective atoms. The exact combination is chosen so as

to make the bonding as strong as possible. The ground state
of the atom usually makes the most important contribution
with only one or two of the other states contributing to the
bond to any appreciable extent. For the normal single co-
valent chlorine bond there is a mixture of the 33 and 3p
states. Townes and Bailey18 estimate that the character of
this hybrid bond is 20 percent 3s and 80 percent 3pz. The
3P2 orbital has axial symmetry about the z, or bond, direc-
tion and will produce an axially symmetric field gradient at
the chlorine nucleus. The presence of the Es character in
the bond will not affect the symmetry but since the s orbit
has spherical symmetry the field gradient should be reduced.
To see this we can compare q for atomic chlorine where it

should arise from a pure sz orbit to that in CHBGI where it

arises from the s-p hybrid bond.

if
Atomic chlorine (9" 'q no 4...."

04'
CH3Cl I: :3an “Va?

There is also an ionic portion of the bond which can be de-
termined roughly from the difference in the electronegativity
of the two partner atomS. This also will not change the

axial symmetry of the bond but it will reduce the value of

15

the gradient. It is a change in the ionic content which is
assumed to account for Livingston's7 results. As one adds
chlorine atoms in the sequence CH3Cl, CH2012 and CH013 there
is greater competition for the carbon electrons and brings
about a reduction in the ionic character of the bond and an
increase in the value of q and thus the resonant frequency.
In the case of the chloro-benzenes there is a contri-
bution of about 10 percent double bonding. This is reflected
in a more stable compound and in a shortening of the bond
distances. The second bonding orbital is a Px orbital where
the x direction is taken normal to the plane of the benzene
ring. The contribution of this orbital will destroy the

axial symmetry of q. Deanlg has shown that the asymmetry
3i!_ DE;

’7: 3X
.. ._7;E§Ea—

X?
with p-06H4012 the asymmetry will be neglected since the

is “no? , In the work which we do

effects which we are concerned with will not be greatly

changed by the small errors introduced by this assumption.

III. THE SPECTROMETER

One of the fortunate features of NQR is that for many
cases the instrumentation necessary for the observation of
the resonance is relatively simple. The circuit diagram of
the instrument used for the investigations reported on in
this thesis is shown in figure No. 1. It is on internally
quenched superregenerative oscillator., The operation of
this type of oscillator has been discussed in some detail
by Whitehead.20 The basic circuit is that of a pulsed os-
cillator. The oscillations are turned off, or quenched, due
to a build-up of charge on the grid condenser. The time
constant of the RC combination in the grid circuit is too
long to permit the mean grid potential to adjust to the
level of oscillation.

In order that the oscillator will operate effectively
as a receiver the quench frequency should be between 1/100

and l/lOOO of the frequency of oscillation.20

The absorp-
tion frequencies we were interested in were m’35mc which re-
quired a quench frequency between 35 and BSOkc. The quench
frequency is determined to a large degree by the charging
rate of the RC combination on the grid. These componets
were adjusted until the quench frequency was 48kc at which

time the instrument seemed to function properly. The mea-

surement of the quench frequency was made by making use of

.hmpmsoppomam one .H .mam

 

 

 

 

 

 

 

.IAWI
m 11 l_\ .3: .11.."
new .00 _MNMN
O .I—u' Ill, J
.3. one»... 2/
35 lg 26 _ m
i.m .nqddflrllllxanqut 4%

 

usage as

18

the frequency spectrum of the oscillator. The periodic

quenching of the oscillations produces an amplitude modu-
lated signal which contains not only the main oscillation
frequency but also frequencies which differ from it by in-

20 A measurement

tegral multiples of the quench frequency.
of the frequency separation of these so called side band
frequencies thus furnished the value of the quench frequency.
If one starts with the oscillations quenched, the
growth of their peak values up to the point of steady state
oscillation can be expressed by the relation V: V0 fit/b ,
where V5 is the voltage from which the oscillations grow and
b a constant dependent upon the circuit parameters. The re-
sponse of a superregenerative oscillator to a signal from
an external transmitter has been studied in some detail20
and is thought to occur due to the change in V0 caused by
the presence of the external signal. The nature of the rer
sponse depends upon whether the quenching action is interal,
as in our oscillator30r is caused by the application of a
periodic voltage from an external source to some point of
the circuit which causes the oscillations to stop. Further-
more, if the quenching action is external, the form of the
response will be dependent upon the frequency of the quench
voltage. Whatever the form of the response, however, its

source is still thought to be a change in the voltage level

from which the periodic bursts of oscillations grow.

19

The response of the oscillator to the nuclear magnetic
resonance and the nuclear quadrupole resonance of a sample
placed in the tank coil of the oscillator still needs an ex-
planation. It was suggested by Roberts?1 who was the first
to observe that a superregenerative circuit would respond to
nuclear resonance, that one effect of the resonance would
be a change in the value of b in the expression describing
the exponential increase and decay of the oscillation. This
would follow from the lowered Q of the coil due to an ab-
sorption of energy by the sample. Roberts21 also suggested
that in agreement with Block's22 theory there should be a
transient signal induced in the coil by the nuclear magnetic
moments in the sample after it is subjected to the r.f.

pulse of oscillation. The direct measurement of such in-

duced voltages has been made by Hahn23 for the case of nu-

4 for the quad-

clear resonance and by Bloom, Hahn and Herzog2
rupole system. As applied to the superregenerative oscillator,
this effect results in the sample acting as a signal gener-
ator. Thus the detection process should be the same as that

already investigated for the response of the oscillator to

an external signal.

Roberts21 concluded that the latter of the two effects
was the most important in the production of a nuclear re-
sonance signal. Dean19 also assumed that this was the most
important process in the detection of NQR by use of a super-

regenerative oscillator. The argument used by Dean was

20

that, based upon the work of Watkins,25 a pure absorption
could not produce a signal with the strength and signal to
noise ratio actually observed with such an oscillator. His
arguments do not,apparently, apply to the oscillator which
we used for our investigations. This is shown in figure

No. 2 which contains the oscilloscope traces of the output
of the oscillator for two different cases. (The manner in
which the traces are obtained will be explained later). The
first trace resulted from the pure absorption of energy from
the oscillator. This was accomplished by placing a General
Radio wave meter which was adjusted to the oscillation fre-
quency close to the oscillator coil. The resulting signal
certainly indicates that there is a strong response to a
pure absorption by our instrument. Furthermore, the strong
resembhxnce of this signal shape to that of the second trace
which is the 6135 resonance line in p-05H4Clg indicates that
the quadrupole signal may well be determined largely by such
an absorption. The observed signal shape is very similar

to a mixture of the pure absorption and diSpersion curves
which are obtainable by use of an r.f. bridge.

Assuming that the main source of the output signal is
an absorption of energy by the sample, the question still
remains as to just how the output is related to this 1038.
Figure No. 3 shows the variation in the peak values of the
r.f. oscillations and the variation of the mean grid poten-

tial as a function of time. The variation of the mean grid

21

(a)
(b)

Fig. 2. The response of the oscilla-
tor to (a) an absggption meter,
(b) the NQR of Cl in CgHSCl.

 

o I r M_ t->
(a) V5 z//////q\L////////////fi\\v
an,
(b)
\/,> ,_ __,_-_ -._ -7 ,_ ,-___A___ t->

 

Fig. 3. The time variation of (a) the
mean grid voltage, (b) the peak
values of the r.f. oscillations.

22

potential will produce a variation in the plate voltage of
the same frequency and similar shape. The output of the
oscillator can then be taken to be the area of these pulses
multiplied by the frequency at which they occur. There will
be changes in the output correSponding to changes in the
variation of the mean grid voltage.

The mean grid potential is driven negative as the os-
cillations increase due to a collection of electrons on the
grid during the positive sweeps of the oscillations. The
level of oscillations grows until the losses in the circuit
prevent further growth. Meanwhile the grid potential is
still decreasing due to the long time constant of the grid
leak combination and starts a cumulative decrease of the os-
cillations. The growth of the peak values of the oscilla-
tions follows the relation V: v. e”b . Losses in the coil
due to an absorption of energy by the sample would change
the value of b and thus the rate at which the oscillations
build up. This in turn would change the frequency and area
of the mean grid voltage variations and thus the output.

If one assumes that the decay of the oscillations obeys
the same law as the increase, then the period of the quench
frequency is 2t1. The value of t1 is determined by
tfi=b.9n'€? where Vm is the maximum value of the oscillation

and V0 is the voltage level from which the oscillations

grow. To a first approximation the grid voltage rises as

23

a linear function of the time, V : ct. The area of the pul-
ses of grid voltage will be Ag=-%c(2t1)2. The output of the
oscillator, V1, will be proportional to the product of this
area times the frequency of the pulses,l/2t1;

v. = (W) b. a. ‘31-" .

If we assume that any variation in Vols negligible, the ratio
of any two output voltages will be given by v‘/ V). = b‘/b1 .
If none of the circuit parameters have been changed, the
ratio of the b's will be proportional to the ratio of the
losses due to the sample.

As a check on this idea, the maximum height of the out-
put signal was measured for different volumes of 05H501 at
the temperature of liquid nitrogen. Figure 4 shows the rela-
tion between the normalized volume and the normalized signal
height. The relation is linear as is to be expected from the
above discussion when one assumes the losses to be a linear
function of the number of resonant nuclei. It is implicit
in the discussion of some of our results that the maximum
amplitude of the output signal is a linear function of the
number of nuclei contributing to the resonance.

The frequency of the oscillator was varied periodically
so that the condition of resonance was obtained at regular
intervals of time. The resulting periodic change in the plate
current due to the absorption of energy was picked up from the
plate circuit by means of an audio transfacmer and passed through

a detector circuit before being displayed on the oscillo-

 

 

 

Fig. 4. The dependence of the maximum signal height,
S, upon the volume of the sample for CgHSCl.

25

scope. The audio transformer passed the quench frequency
‘without much loss; however, the time constant of the detec-
tor, T~1°0pm, was long enough to rid the signal of the
quench frequency but short enough not to effect the absorp-
tion signal appearing at a low audio frequency.. The peri-
odic appearance of the absorption signal, which allowed it
to be displayed on the oscilloscope, was obtained in the
following manner. The oscillator was adjusted so that its
frequency was equal to the resonant frequency of the nuclei
in the sample being studied. A small condenser whose capa-
citance could be varied periodically by the application of.
a small voltage was placed in parallel with the main tuning
condenser of the oscillator. The small added condenser was
obtained from the Navy altimeter RT-7/APN-l. A 60 cycle
voltage ovaI volt was applied to the condenser causing its
capacitance to vary periodically at this rate. This in turn
varied the frequency of the oscillator at this rate so that
the condition of resonance was swept through periodically
allowing the signal to be displayed on the oscilloscope.

It was found that by operating the heater of the 6H6
in the detector, which had its two sections in parallel,
at ~ 3 volts and also by Operating the heater of the (935'
slightly under 6.3 volts the noise of the instrument could

be reduced considerably without expense to the signal

strength.

26

A measure of the sensitivity of the instrument was ob-
tained from the fact that the smallest size sample of
p-G6H4612 which gave rise to an observable signal was one-

tenth of a cc.

IV. THE PHASE TRANSITION IN p-C6H4012

The observation of a phase transition in p-C6H4612 has
been reported by several authors. Beck and Ebbinghaus26 were
apparently the first to observe it. Their method was to ob-
serve a sample in a test tube as it was gradually cooled
from the melt. They observed that when the sample first
solidified it appeared to have intimate contact with the
glass wall. During subsequent cooling the crystal became
detached from the side of the test tube. The temperature at
which this occurred was quite definite and was assumed to
be the transition temperature of a phase change during which
the sample changed volume. The transition temperature was
found to be 39.500. Several other authors have reported ob-
servable changes in the macroscopic crystal.27'28 The most
recent of which were Danelov and Ovcienk029 who observed the
epeed with which the interface between the two phases moved
through the crystal. They concluded that the transition
temperature was 30.8°C. A different type of evidence of the

30 when he observed

phase transition was given by M. F. Vuks
a change in the Raman spectra at low and high temperatures.
His determination of the transition temperature was 32cb.
If, as it appears, the NQR absorption frequency depends
upon the crystalline arrangement, there also should be a

shift in it as the crystal changes phase. Such a shift has

28

been observed by Dean11

who gives the magnitude of the shift
as 27kc for 0135 at 25°C. Observations have also been made
on the change in orientation of the 0-01 bond during the

31 The determination of the orientation

phase transition.
of the C-01 bond can be made, as will be shown presently,
by observing the NQR of a single crystal in the presence of
a small («230 gauss) magnetic field. The results which
have been obtained have not been entirely conclusive so we
have attempted a further investigation along this line. We
have also followed the orientation of the remainder of the
molecule by means of observations made of the line width of
the nuclear magnetic resonance of the hydrogen atoms situ-
ated on the sides of the benzene ring. Through a comparison
of measurements in the upper phase with those in the lower
phase we have attempted to determine the relation between
the two phases and thus the nature of the transition itself.
Before considering the actual experimental method we
will discuss the basis for the orientational determinations
which have been made. we consider first the Zeeman split-
ting of the NQR of the chlorine nuclei and then the dipolar

broadening of the nuclear magnetic reasonance of the hydro-

gen atoms in p-05H4Clg.

A. Zeeman Splitting of the Nuclear
Quadrupole Resonance
We shall consider the case of an axially symmetric
field gradient and choose as our 2 axis the axis of symmetry.
we may therefore assume that the applied magnetic field lies

in the x, z phase without any loss of generality. The re-

sulting Hamiltonian is:
(18)

H: )60 - LLHL-T-x W9 +Iiu°93
I

where “,0 is the unperturbed Hamiltonian. The matrix of

the perturbation energy is not diagonal in m. The elements

of interest to us are shown below.

(19)
M. 3’; "2: ’é: ‘13:-
ALH B O o
98. -351: (on H
EL U359 -I AAHLI*&ams9 O
V}. -V‘LI i )
ALMIW; '9 kn“ one
"'2’. 0 ”‘4: 3°" 113-:
lflhcm
-3/1 0 O L: 8

According to first order degenerate perturbation theory

the correction to the tB/L levels are given directly by the
corresponding diagonal elements of this matrix. To obtain
the corrections of thei>i levels we must first diagonalize
the sub-matrix involving only these states. This process
results in a mixing of the states ’W\=t)t-._ and the resulting

energy values can no longer be characterized by these states

50

but will be called 31,2. The resulting first order energy

corrections for I=3/2 are thus:
9)

EN/ : inflame (20)
l

h . I
:1 : ifiHLqW19*m\9‘]/t
J

3

Due to the mixing of the energy states MelVl’transitions

are now allowed between \\. l e‘i’ i 34)

 

 

 

 

 

 

 

m-flg / m: ”I.
Mr: {$51, \—I Z: J"-
Mzi’l "'”‘< J ”’1 O
”.2 ”b t. ”V.

The transition frequencies are given by

v (21)
hD’ng :hifgi phone i ng‘iafiear @1961“

|
_ /

)‘ Ugo =“UQ i N H W19 + M.§.[HM«‘0 «“0391 1
Figure No. 5 shows a plot of the shift of the frequency of w
the various Zeeman componets from U22 as a function of the
angle 9 . Now if

‘ (22)

I
NHmez Agitim‘e’rwel "
cxvaB = '/TT
then

y'c- ; VD
The same thing will be true of I}; and VB at cos9: - VJ: .

Thus if the magnetic field lies anywhere on this cone of
directions about the axis of symmetry we should observe a

coalescence of two of the Zeeman lines.

 

eco.

so:

. 0 (Ho soapopsm m mm

63 80.5 mpsmsoasoo swamps one .H0 072% echo

ooo.

 

ace

.3.
a.“ mo wads: SH

om oWHm

 

ooe

 

 

 

Orv l

O.Nl

O.N

 

 

0.?

32

me: with :5150

D

By use of this fact it is possible to determine the

 

z direction in terms of coordinates fixed in the crystal.
In figure No. 6 7, 3:107 are the coordinates fixed in the
crystal and “7' g. and '?| are fixed (in the laboratory.
The axis of the oscillator coil and crystal coincide along
the ‘F ,7. axis. with the magnetic field fixed in the ’7'
direction the crystal is rotated about the ‘fi','?( axis.

If the z direction is such that 6" > 35° then there will
be two Values of 8' (consider only one-half the cone of
directions) for which two of the Zeeman lines will coalesce.
If K' is set halfway between these two values the gradient
should lie in the '7"?J plane. When the magnetic field
is rotated in this plane about the { axis there should
again be two points at which the Zeemal lines coalesce and
they should be mleBO apart. Half-way between these two di-

rections is the axis of the field gradient.

 

 

 

Fig. 6. Coordinate system for the
measurement of the C-Cl di-
rection in p-C6H4012.

b4

\xi

B. Dipolar Broadening of the Nuclear
Magnetic Resonance (NMR) of
the Protons in p-05H4612

It was shown in the previous section how to determine
the 0-01 direction in a single crystal of p-C6H4012. We
will now indicate a method to determine the direction of the
line joining the two protons on the same side of the benzene
ring. If it is found that these two directions change in
the same manner when the crystal undergoes the phase transi-
tion, it will be fairly certain that the molecule as a whole
is undergoing the change and not just the 0-01 bond.

The line width of the protons arises from dipolar
broadening due to surrounding nuclear magnetic moments. The
crystal structure of p-05H4012 in the lower phase has been
determined32 and the environment of the protons based upon
this work is shown in figure No. 7. There is another mole-
cule in the unit cell which has a similar environment but
a different orientation. The analysis given for the mole-
cules shown in figure No. 7 will be equally applicable to
the molecules of the other orientation. From the distances
given in figure No. 7 it was thought that we should include
all four protons in the group of resonant nuclei. The second
moment of the line is used as a measure of the line width

and is obtained from VanVleck'sB} treatment of the problem.

 

 

 

 

Fig. 7.

The environment of the protons

35

36

VanVleck's expression for the second moment due to di-

pole interaction is given below in (gauss)2.

- 1. —L
< (AW: : 3/11\1+‘\t't‘n§ * .ZWM‘OJM') “3h (25)
M3 QHK -(.

+y, "5"»: {- f 16m“) 52(3m‘93w51 "-59
In the above formula g and I are the nuclear g-factor and
spin for the nucleus having resonance, 3.5,]; are the nuclear
g-factors and spins of other nuclear species in the sample,
Pgt is the length of vector connecting nuclei s and t, and

N8 is the total number of nuclei having. resonance in the

sub-group considered. For our case
\ -

I“ /3_ Ia," 3/1

% -‘- 5.58 3‘5: -55

us“:

We shall consider only the interactions of the protons with
the nearest chlorine and the proton-proton interactions:
Hl-Hz, H2-H3 and H3-H4. This gives:
< why)”Q :.: lHS‘ V. Nun‘s, a? 4- ,u (3cmL 9(an

4 .00? I. thy} 93-‘\x+ )3“) affix]

Obviously the second term may be neglected with respect to

(24)

the first. Within a fair degree of approximation the H2-H3
interactions may also be neglected. This results in the line
width being determined by the dipole-dipole interaction of

the two protons on the same side of the benzene ring. The

37

-I.
line width should have a minimum value at €9= U4- 03“ .

Thus, as long as the proton-proton and the C-01 directions
are parallel, the orientation of the magnetic field in the
g ) “7"? coordinates which produce a zero splitting of
Zeeman componets of the NQR of the chlorine nuclei should
‘also produce a minimum line width of the NMR of the protons.
This, of course, is based on the assumption that we can
always attribute the proton line width to the dipole-dipole
interaction of the two protons on the same side of the ben-

zene ring.

C. The Experimental Hethod

Crystal growth. The single crystals investigated were
cylinders ~lO cm long with a diameter of 4/.8cm. There were
no observable crystal faces to indicate crystalline struc-
ture or orientation. The crystals were grown from the melt
in the following manner. A cylindrical form of the desired
size was constructed from aluminum foil and glued to a piece
of glass tubing which ha& been drawn to a very narrow tip
and sealed. The form was filled with molten p-65H4012
(M.P. 55°C) and placed in a vertical furnace kept at approxi-
mately 75 Q}. The furnace was a brass pipe two inches in
diameter and one foot in length wrapped with two feet of
nichrome wire and covered with asbestos insulation. The
form was lowered through the furnace by means of a clock

mechanism at a rate of 0.5cm per hour into a water bath

38

immediately below the furnace. In this method, as the con-
tainer is lowered from the furnace, the tip cools first and
with reasonable luck a single seed crystal is formed in the
very narrow tip. If the container is lowered slowly enough,
all subsequent crystallization takes place on the faces of
this seed and the result is that the entire sample is finally
solidified into a single crystal. The aluminum foil can
easily be removed leaving the crystal free from any con-
straining walls.

The samples were first grown in the same manner but
with the form constructed entirely out of glass tubing.
Since the crystals were quite fragile the glass could not
be removed and the samples had to be investigated while
still enclosed in this form. There was,therefore,a possi-
bility of the rigid walls of the container exerting forces
upon the crystal since there might be a change in volume
during the phase transition. The data presented in this
thesis was obtained from the free samples only.

The phase transition. It was found that most of the
samples grown by the method indicated above were in the low
temperature phase, the at phase. At least they were in the
ex phase after standing at room temperature («v25°c) for a
day. The phase that the crystal was in was determined orig-
inally by a comparison of the transition frequency with
those given by Dean19 for the two phases. Later it was

possible to determine the phase from the nature of the Zeeman

pattern.

39

Consistent results were obtained when the phase transi-
tion @963 was induced by the following method. The crystal
was warmed at v 30°C.for one-half hour in a water bath.

Then the tip of the crystal was placed in water at4~ 45ch
until the Q; phase was observed to begin its growth. This
was noted by‘a somewhat cloudy appearance of the @i phase
and by a sharply defined interface. The crystal was then.
placed in a water bath at ~ 34°C while the (3 phase con-
tinued to grow along the crystal. If the Q> phase was
allowed to grow completely throughout the crystal and if the
crystal was then kept at 35°C for ten to fifteen minutes,
the crystal seemed to be quite stable and would remain in
the Q) phase for a day or two when the crystal was kept at
room temperature. If, on the other hand, the (5 phase was
only allowed to grow along a portion of the crystal, the e(
phase would grow back as soon as the crystal was placed at
room temperature.

Measurements of the molecular orientations before and
after thegphase transitions. In order to make the measure-
ments previously discussed we had to associate a fixed co-
ordinate system with the crystal. The 4? axis was taken to
be the axis of the crystal. The 3 and 47 axes were deter-
mined by clamping the crystal in a brass chuck which was
attached to a disc graduated in degrees, the disc being per-
pendicular to the axis of the crystal. The orientation of

the C-Cl direction with respect to this coordinate system

IE”

4O

varied from crystal to crystal. We were interested, how-
ever, only in the change in orientation of this bond as the
crystal underwent the phase transition. The crystal was
inserted in the tank coil of the oscillator. The axes of
the coil and the crystal, the ft. and ‘? axes, coincided
and lay in the horizontal plane. The source of the magnetic
field was a set of Helmholtz coils designed so that the mag-
netic field could be rotated about in the horizontal plane.
The "f axis was thus taken to lie in the horizontal plane
perpendicular to the '$‘,‘}‘ axes. With the coordinate sys-
tems thus fixed the measurements described previously were
carried out to determine the C-Cl direction. Figure E3.
shows the oscillator with the Helmoltz coils in place.

Once the C-Cl direction was determined it was possible
to transfer the crystal to the nuclear magnetic resonance
appartus with the E, “Z ?' axes still fixed in the crystal.
The apparatus used for this measurement is that described

34 The measurements made did not determine the

by Jain.
proton-proton direction since a rotation of the magnetic
field was not possible. With the magnetic field perpendic-
ular to the axis of the crystal, the crystal was rotated
about its axis and the direction of the magnetic field in
the ‘3 A79 coordinates was recorded for the orientation
which produced minimum line widths. These orientations were
compared with similar measurements for the zero splitting of

the Zeeman componets of the NOE. The phase of the crystal

was changed and the process repeated.

.nodpamoa ma
madoo upaossflmm exp Spa: smmeOApoon one .w .wam

 

 

 

r
-o§'d'-
4.! V

.A.-.-‘

 

 

.0 o
..

-~

~.~..

.

‘ .
' I-
4 x.
‘ '2 U-
2. a

I

 

." »
. ”,1-

0‘

 

 

D. Discussion of the Results
The results of the measurements to determine the C-Cl
direction in both phases of several crystals are given in
Table I. Two directions were found in the e< phase and are
labeled by the subscripts "l" and "2“. Only one direction
was found in the (A phase and is designated by the subscript

. The angle ”If; is the. angle between the L“ and 3‘0“

“-5“
axes. Figure 9 shows typical traces of the Zeeman patterns
of a single crystal of p-06H4Cl2. The top trace is the

pure quadrupole resonance. The middle trace shows two Zeeman
lines from each molecule and the bottom trace shows the two

central lines after they have coalesced. The crystal struc-

ture of p-05H4012 has been determined by Croatto, Bezzi and
32

Bua for the low temperature phase. Their data shows that

there are two molecules to a unit cell and that the 6-01
directions of the two molecules are separated by 74.20. The
average value of "12 for our results is 73.95 WhiCh can be
considered to be in agreement with the x-ray work.- Lutz31
has obtained a value of w12 of 760x2o from the Zeeman
8plitting of the quadrupole resonance signal.

Table II contains the directions of the magnetic field
in the 3'7 plane which resulted in a minimum width of the
proton resonance and also those which resulted in zero
Splitting 0f the Zeeman componets of the chlorine NQR. Data
are Elven for two crystals in both the x and (3 phases.

Althousn there is a very large shift in these directions

g. A. «L
‘

m.mm
m.~nn
a.oa
«.ma
o.~na
m.aa
s.sm
o.mm
o.ae
«.Nm
o.oda
N.HNH

m.os
n43

m.am
n.nm
s.nm
o.~m

«.mna
n.ab

m.sa
so.
o.mm
o.an
n.~m
o.~m
m.ma
m.mw
«,3

o.s~n
o.oon
o.mm~
o.om«

m.an~
o.saa

we.“
m.ssa
m.omn
o.n

o.os~
o.~o~

m.ms~
"yo

o.ms
o.mn
o.naa
o.s~a

as
on...

0.5
has
oswcd
m.wm
use
as
o.wHH
o.mm
no

Nuosmmona so menses a gas Xv
was zH_osom.uuuu use so mmoneomsHo use

n.aa
n.as
m.ss
o.ss
n.ma
a.ss
o.ms
n.na
«.ms
«.ms
o.na

m.sa
.23

o.om
o.on
m.soa
n.3oa

n.nna
n.mn~
o.owH
“.mon
o.~nn
m.ooa
o.nm

H.n~

43

.H mqmga

o.msa
coed
o.ann
o.ana

“.mn
n.am
m.nn
0.3m
m.nnu
0.3m
o.as .
o.nm
in

m.wdn
“.mdn

m.sa
m.sn
o.~n
o.~ma
o.mn~
m.sa
o.am
m.~sn
“.mma
n.mo~

. v0

o.mm
o.mm
m.naa
m.n~a
o.ms
o.mnn
o.o-
m.~aa
o.mna
n.am
n.es
o.em

n
so

Hmpmmno

43

(a) q.....~/\IIIII.
a) w

(c) w

 

Fig. 9. The (a) pure quadrupole signal and (b),
(c) §§pical Zeeman splittings of it for
C1 in a single crystal of p’C6H4012

(a)

(b)

 

Fig. 10. The (a) maximum and (b) minimum line
widths of the proton resonance in a
single crystal of p-C6H4012.

TABLE II

COMPARISON OF POINTS OF ZERO SPLITTING (NQR)
AND POINTS OF MINIMUM LINE WIDTH (NMR)
FOR p-06H4Clz WITH Q»: 90°

 

 

Crystal 01L for Minimum Line Width x for. Zero Splitting

 

l. O O O o O 0
0; phase 164 , 250 , 257 156 , 247 , 268
9 phase 134), 2050 131°, 204°
2. o O O C
as phase 60 , 147 65 , 144

o 0

(aphase 5°, 103° 6 , 106

 

45

during the phase transitions, the proton resonance and the
quadrupole resonance experiments give the same data, for a
given phase, within the accuracy to which the minimum line
width could be determined (0’50). Since it was found that
there are two directions of the CFCl bond in the a: phase,
there should be four points for each experiment (Ooéetkwoo).
A more detailed study of the Zeeman pattern showed that the
fewer points resulted from the accidental superposition Of
two points. The comparison of these results can be inter-
preted to mean that during the phase transition there is a
reorientation of the molecule as a whole and that the proton-
proton and C-Cl directions remain parallel. Figurelo is a
photograph of a typical oscilloscope trace Of the maximum
and minimum line width of the proton resonance. At its
widest point the line is seen to be a badly smeared out
doublet. These conclusions have been substantiated by a re-
cent x-ray analysis of the Q. phase by Houty and Clastre.35
They found that the {3 phase was a triclinic crystal with
one molecule per unit cell and that the structure Of the
molecule was essentially unchanged from that in the'u.phase.
Thus we can say quite definitely that during the phase trans-
sition there is a reorientatiOn Of at least part of the mole-
cules and that their reorientation is not accompanied by a
distortion Of the molecule.

We can increase our knowledge of the nature of the

transition by determining the magnitude of the reorientation.

This should be obtainable from the values of W13 and ”23
for the various crystals investigated. A comparison of
these values, however, fails to show much regularity” The
reorientation in crystal #1 and one part of crystal 6b,
in which the upper phase was allowed to grow from both ends
of the crystal , agree to within 30. This is also true of
crystal #5 and part of crystal #7 although the reorientation
is there crystals differ from that in #1 and #6. The rest
of the fourteen examples show completely different reorien-
tation. This may mean that there arévery many different but
definite ways in which the crystal may change from the M
t'0 the g structure. It may also mean that there is no de-
finite crystallographic relationship between the two phases
and that the two cases mentioned above are mere coincidences.
This lack of a very regular relationship between the
toWO phases is fur ther illustrated by the data obtained for
the last six crystals. The data was taken for the sixth
c>I‘ystal in both phases and listed under 6a, the (5 phase
having grown throughout the crystal. The crystal was re-
turnsd to the a phase where measurements listed under 6b

were made. The orientation of the axes had changed. Per-

haps a more striking result was Obtained when the crystal

was again raised to the «x phase. This was done by starting

the growth of the upper phase from both ends Of the crystal.
The result was that each end of the crystal had a single and
well defined direction of the C-Cl bond but the two directions

Mum‘s.- 31.4

47

were different from one another. This same experiment was
repeated for the seventh crystal with similar results. For
the last two crystals the Q) phase was not allowed to grow
completely through the crystal when measurements were taken
on the Q phase. As the N phase grew back, the C-Cl direc-
tions had their original orientations. However, when the
crystals were again raised to the 9 phase the orientation
Of the single axis was different from the first time. In a
further experiment we submerged crystals in thetx. phase in
a temperature bath of ~ 40°C at which time the Q phase could
be seen to begin its growth at a number of points in the cry-
stals. Once the crystals were entirely in the (3 phase the
Zeeman pattern of their quadrupole absorption signal was Ob-
served. It was found that the magnetic field either elimi-
nated any observable signal or resulted in a Zeeman spectrum
too complicated and weak to be analized in detail but at
least indicative of several different orientations Of the
C-01 direction. This last eXperiment can be explained by
assuming that many of the centers of growth of the Q phase
resulted in little pieces Of crystal with different orienta-
tions. That is, we cal consider this experiment to be merely

an extension of the case in which we allowed the Q phase to
start its growth from the two ends of crystals #6 and #7.
These results seem to substantiate the views obtained from a
comparison of the values Of W13 and W23 that the crystallo-
graphic reorientation during the phase transition may take

place in either a very large or an infinite number of ways.

There was one characteristic of the transition which
appeared to be true from a visual inspection of the crystal
as well as from a check of the resonant frequencies of vari-
ous parts Of the crystals during the time they were changing
phase. The new phase grows from its source in such a manner
that at no time is the entire crystal in a disordered state
halfway between the two phases. Instead, there is one sec-
tion which has not changed its structure at all and another
which has been completely changed. This was certainly sub-
stantiated by the fact that we were able to Obtain normal
signals, as well as Zeeman patterns, from each section Of
the crystal during the time that the interface between the
two phases was moving along the crystal. Even the slightest
irregularities in the crystal structure is sufficient to
effect the signal greatly.

Another characteristic Of the phase transltion which
appears to be definite is that, although there are many
possible orientations for the new phase to take, once a cen-
ter of the new phase has begun its growth all of the Old
phase,which is transformed as a result of the growth of this
center, will undergo the same reorientation. The fact that
the samples were still single crystals after they had under-
gone the transition requires that this be true. The results
0f crystal #6 and #7 further illustrates this view since,
although the two sources Of growth of the(§ produced sec-
tions of the crystal with different orientations, each sec-

tion was a single well ordered crystal.

49

These properties Of the transition suggested a further
experiment to decide if there was any relationship between
the crystal orientations of the two phases. If there is no
relation, then presumably the molecules Of the Old phase can
rotate through any angle to take up the orientation of the
new phase and will do so regardless of their previous orien-
tation. The orientation Of the new phase being determined
by some undesignated parameters.

If the above idea is correct, it should be possible to
start with a polycrystalline sample and produce a single
crystal by merely causing the sample to undergo the phase
transition in such a manner that it starts from only one
source. The term polycrystalline would have to mean a con-
tinuous sample with different sections having various orien-
tations. A sample composed of separate crystals would re-
quire the phase change to start anew in each crystal and
thus would not produce the desired effect. A small (~ 30
gauss) magnetic field was applied to the sample to determine
if it was a single crystal or polycrystalline. A single cry-
stal will give a well defined Zeeman pattern. Each section
Of the polycrystal will also give a Zeeman pattern but since
they have different orientations the separation of the com-
ponets will be different for each section. If the sections

of the crystal with a given orientation are small enough, the

application of the magnetic field ”washes out" the signal.

Typical results are shown in Figures 11 and 12. The pure

50

quadrupole resonances before and after the phase transition
are shown in the first and third traces respectively. The
resonances in the presence of a 30 gauss magnetic field be-
fore and after the phase transition are shown in the second
and fourth traces respectively. The Zeeman lines shown in
the fourth traces are taken to indicate that the sample is
now a single crystal or at least contains a large section
which now has a single orientation. In Figure 11 the sam-
ple was originally in thecx_ phase and in Figure 12 the
sample was originally in the 9 phase. It thus appears that
either the s! '0 (Z or the (IS—e oi transition can produce a
single crystal from a polycrystalline sample. It would thus
appear that there is no fixed relationship between the orien-

tations of the molecules in the two phases.

 

Fig. 11.

 

Fig. 12.

51

Q

V. QUADRUPOLE RESONANCE OF IMPURE SAMPLES

‘

The 0135 resonance was Observed at liquid nitrogen tem-
perature in samples Of C5H501 which contained controlled
amounts of impurities. The maximum height of the resonance
signal was greatly reduced by the addition of even 10"3
molar fraction of certain impurities.

‘ If we assume that the effect on the signal arises from
strains in the crystal due to a difference in size of the
111)purity and resonant molecules, we can make a rough calcu-
lation of the expected change in the signal due to the pre-
sence of the impurity. According to Love36, the strain
around a spherical inclusion in an elastic medium will fall
off as the reciprical of the cube Of the distance from the
inelusion. Although such a model is only a crude approxima-
(tion to our experimental situation it should at least allow
us to determine the nature of the effects.

If the shift in frequency is taken to be proportional
to the strain, then the resonant frequency of a nucleus at
a distance r from the impurity molecule will be J}: V; + '33
We Shall first consider the resulting frequency spectrum

which would be expected in such a .situation from an infi-

nitely sharp line. The number Of molecules lying at a dis-

tance between r and r1- dr is given by:

&N = elm 113-911. (25)

where Q is the density Of molecules. We can express dr in

terms of 93” through the relation for the shift in frequency

due to the strain. This gives‘.

(25)
81.: .. w 1 1
Mir-Va "-
Substitution Of this expression in (25) yields
(27)

N;,‘LE(’\K 9‘ x
g 3 w-m

K Av‘
&N = -—- a

ham
Since for k)o the 9V correSponds to a decrease in frequency
When QN represents an increase in the number of molecules,
the ratio is negative so that v 3%: is positive. This ratio
represents the number of molecules in a given frequency range

Which is merely the frequency distribution which we desire

K
“\V-Vn : (5:53" (28)

This calculation was based upon the assumption that the
eIl‘.".fect of the impurity was strictly radial. We can consider
the case of a simple angular dependence and see if there is

any effect upon the nature Of the results.

The above relation for the dependence of the strain is
bat-8ed upon the fact that the displacement of a molecule at
a distance r from the impurity is proportional to l/r2. If

we now assume that the only strains which will be effective

54

are those which arise from displacements in the Z direction,
the displacements effecting the signal will be given by:

C, i (29)

at: (x1*‘3‘*1;\‘/1v

The corresponding strain in the Z direction will be given by:

 

 

9% - .2... .. Les? - Lu—swg <30)
8?: ‘ n3 rx" ’ ' “3

If now the frequency shift is taken to be proportional to

this strain we have:
- 3m 9 (31)
w- v + h K‘ i

In this case the shift in frequency will not be all in the

Same direction. If we consider R)O then:

(Y-voiko QT" o<9<9°
n-e.< 9 UT
Us“ ‘5‘?
For all other values of 9 K ”=- Vo‘ > 0 ~
For 0( 9 ( -90 the volume included by the surface of con-

Stant frequency V: U”-- C. is given by:
X- -k ‘.-____..M°fl"‘9

‘ “t M9h8u(32)
v. =3°$° SR 9°
_ ‘L‘TE.
"' C.

‘i 3

55

The volume included in the surface of constant frequency

U’z D'b 4 C. for 90 K 9 4 E; is given by:

t
\ m : “tn-mum’s 1'- ‘ (33)
V1 ; 89 S 89" n‘m9999m8m

O O
‘LELE
N5“-

If we take into account the remaining values of 9 , the to-
tal volume inside the surface 1):»; -C. is given by:

3n- n (34)
V. = m E;
With a similar expression for the volume inside the surface
corresponding to the positive shift. The number of mole-
cules between the two surfaces corresponding to VI: Vo’cc

and V1. : Vs -C',_ is given by:

Q R V): m (as)

INK/U}: "JBKVV V0 *’ AV)

QN

I]

AN

Ml ._ <9}!
If we allow LU to become small, the ratio /AU‘ 7 (9T

01" the frequency distribution which we desire:

K (36)
in K v- vb = (a- m"
This is the same form as for the completely radial depen-

dence except that the frequency shift is now allowed in

both directions.

56

The effect of a strictly radial dependence would predict
a shift in the average frequency of the resonance. Dean11
has reported a very slight (613kc) shift in p-O6H4012 when
one-tenth molar fraction of p-C6H4Br2 was added. On the
other hand we found no shift in the resonant frequency for
the impure samples studied. Although the angular dependence
chosen here may not be the correct one, it at least shows
that an unshifted line is possible when some allowance is
made for the anisotropy actually present in the crystal.

The fact that we observe resonances at all in the impure
samples indicates that there is at least a portion of the
crystal in which the frequency is not shifted greatly. For
low concentrations we can surround each impurity by a sphere
01‘ radius R such that 5d? 3 ‘W‘VA =~ °~ 0‘ W , where w
13 the width of the original line. Since the frequency
Shirts in the remaining molecules lie well within the line
Width, we can neglect their actual dependence and assume
that they give rise to an undeviated line. The total volume
of the sample which is contained in the Spheres of radius
(2‘6 about each impurity is:

V“; N; %W_E_ (37)
Where N1 is the number of the impurity molecules. The vol-

ume outside of these regions, v2, will be given by:

57

V1; VO“V\ .2 NO‘U’M' V\

where No is the total number of molecules and 14.. is their

molar volume.. The fractional value of V1 is given by:

8.35 inc. (38)
‘vo‘so‘t'fi‘

where c is the concentration of the impurity. The fraction
lying outside of these volumes is given by 1-9.
If we arbitrarily apply this argument to an infinitely

sharp line of height A it will result in the following shape.

 

 

502RU-9)
{'1‘ 0.39 _ @229
Vo-o‘ V0 Words ”I-

Fig. 13. Broadening of an infinitely sharp line

If we apply such a broadening to a rectangular line of width
2" and height 2A, the function f0 will result in a portion

or the line shape:

(39)
nglFHi—ei worm»
The contribution of fl will result in:
via; I w ' (4O)
8)! . .83;
F\ ; Rem 5w \T.y')‘ , Hell” (y—v')‘

l l .
2 RQQLK‘E‘N 1 ‘39th ”33“,»

The contribution of f2 will result in:

w . ‘0 SV‘
.25. . 99a --—--- (41)
FL 2 Red. 8““ \yuml ) id (ubifl‘
-\.o-o\<v«k)“k VL’N‘K
‘ ‘ 3;..‘2.
: RSWI&* V-vo ’ “SO“LVE-w‘]
Within the range ~ ”*Oxk Jfi {IO-CK the line shape is
given by:
(42)

W

PK”):1H\\-Q\ +IRBK¥C+Ew

For U‘)\u+m or V’x‘w'o‘
—. “1‘0
(3 \U\ - n 90“- v‘m‘ l
Figure 14 shows the approximate line shapes for 9:- 0, V1, \.

8:0 6‘15: 62‘

<——1w—->

 

 

 

 

 

 

Fig. 14. Broadening of a rectangular line

The effect of increasing the concentration of the impurity
is thus to take a certain amount of absorption outside of
the original line width without appreciably broadening the
line as long as the concentration is low since the line
width is determined in this case by the undeviated central
portion.

Our results show very little broadening to the line for
low concentrations although the intensity as measured by the
maximum height of the signal shows a definite decrease. This
can be seen in Figure 15 which shows the signal in 06H501
for increasing concentrations of p-Cthclg. The first trace
is pure C6H501; the second and third are the signals for
. 0017 mole fraction of impurity; the fourth and fifth are
Signals for .0035 mole fraction of impurity.

The fact that the intensity does decrease without great
broadening permits us to apply the following, somewhat crude

IDlienomenological argument which will aid us in discussing
1fohe relative effectiveness of the various impurities. Con-
Sider the impurity molecules to be distributed at random in
the crystal lattice. Also let each impurity molecule so
effect the crystal that it is surrounded by a sphere of ra-
élius R such that molecules of the sample which lie within
this volume do not contribute to the resonance and those
Which lie outside of the volume are unaffected by the im-
purity molecule. The probability that a given lattice posi-

1Lion is occupied by an impurity molecule is c, where c is

 

60

(a)

(b)

(c)

 

Fig. 15. The C135 quadrupole resonance in C6H5Cl
with (a) .0000, (b) .0017 and (c) .0035
mole fraction of p‘06H40120

 

 

 

the molar fraction of the impurity. The probability that a
lattice site is occupied by a resonant type molecule is given
by (l-c)? This molecule will contribute to the resonance only
if every site lying within a sphere of radius R surrounding
it is occupied by a resonant type molecule. If there are

N sites in this volume, the probability that a molecule will

contribute to the resonance is (l - c)N and the signal

Strength, S will be given by:

N 2+
$2. So(\—C\ (3)

Where SO is the signal strength for c: 0. Taking the 108‘

aJr‘ithm of both sides gives:
(44)
«la S/s. z Mum-d

For small 0 the logarithm on the right side may be expanded

in terms of 0 so that:

gyx S/SO Z‘Nc.

Figures 16 and 17 are plots of

(45)

W‘s/5. 9‘ “C- for various

impurities in 05H5Cl. At least until S3: .130 the linear

belation is quite good and the negative slope of the lines
Bhould give the number of molecules made ineffective by the
Dbesence of a given impurity. The deviation from a linear
r‘elation at higher concentrations may arise from the fact

that as more impurity atoms are added their Spheres of in-

tluence may begin to overlap, thus making their overall ef-

fectiveness diminish.

 

 

 

v m-C6H4CIZ as
x C3H5OH '3 5

+ CBH5CH3 zls
’ (tfiHsNH2 ass

 

 

 

-.002 -.004 -.006 - .008 -.OIO
-C
Fig. 16. A logarithmic pl t of the maximum
quadrupole

signal height of the 01

signal in 65H Cl as a function of

the concen ration of various ,
impurities.

 

 

w
0"”

.3

.2

 

N
O CsflsBr 70
X 05H; 208

. p'CGH4C|2 22 o

 

 

-.002 -.004 -.000 -.oos -.010
-c

Fig. 17. A logarithmgg plot of the maximum signal
height of the Cl quadrupole signal in
C6H501 as a function of the concentra-
tion of various impurities.-

63

The signal strength was taken to be the ratio of the
maximum signal height to noise height of the signal trace
appearing on the oscilloscope. In order to obtain a perma-
nent record as well as more accurate measurements, the traces
were photographed with a Land camera and the measurements
made on the photographs. Photographs of the signal from
pure samples were taken regularly in order to take into
account any possible change in the operation of the oscilla-
tor over the period during which data was taken.

The purity of the CgHSCl was Eastman Grade which was
further purified by the method suggested by Vogel.37 The
liquid was washed with concentrated sulfuric acid until the
acid came clear. It was then washed with water, sodium hy-
droxide and water. Finally it was dried over calcium chlo-
ride for twenty-four hours.

The impurities were added to the sample at room temper-
Etture and the sample agitated to insure a good mixture. The
sample holder was a test tube with an index scratch on it
to insure that the same amount of sample was used for each
investigation. About 1 cc of liquid sample was used. The
test tube was held in the vertical tank coil by means of a
<3Orig washer so that the entire volume of the sample was con-
tained within the coil. The sample and coil were immersed
in a bath of liquid nitrogen until the signal stabalized.
It was found that there was no further increase in the sig-

118.1 size or shift in frequency after three minutes. To

64

insure that the temperature of the sample had come to equi-
librium the samples were allowed to cool from four to five
minutes before the signal was recorded. The values given
in Figures 16 and 17 represent the average of three to four
readings at each point.

Work of this same general nature has been reported by
Monfils and Grosjean.38 They observed the effect of impuri-
ties on the 0135 resonance in p-C5H4012. The impurity mole-
cules were of two types; those’which were taken to have the
Same size as p-CgH4012 but a different electric dipole mo-
ment, and those which were taken to have the same electric
dipole moment but differed in size. Their results are shown

in Table III where \er is equivalent to the N of our dis-

TABLE III

RESULTS or MONFILS AND GROSJEAN FOR
VARIOUS IMPURITIES IN p-06H4012

 

h;
k

 

fl

 

 

Impurity Molecule 'U'm (NH; WY (X I03“) (\fx - VQXLX (OH)
13 ~chlorob~romobenzene 87 _ — ~13 ———————————— g:l_—_—
D - dibromobenzene 162 O 4.2
D - bromoiodobenzene 330 O 7.8
D - chlorophenol 135 2.59 O
13 ~ chlorotoluene 204 4.29 O
13 ~ chloroaniline 435 9.04 O

 

\

65

cussion. The volume differences of the first three mole-
cules may be obtained by associating spherical volumes with
each of the Cl, Br and I atoms whose radii are equal to their
respective covalent radii. The difference in volume of the
molecules is then taken to be the difference in the volumes
of the two atoms attached to the benzene ring. The effec-
tiveness of the three impurities, as measured by the value
of UT, , appears to be a linear function of the difference
in volume between the impurity molecule and p-06H4012. This
is shown in Figure 18.

For the last three samples the size of the molecules
were assumed to be equal to that of p-C6H4Cle presumably be-
cause the covalent separation of the atoms in the radicals
substituted for the Cl atom is equal to the covalent radius
of Cl. The value of ‘er for these three compounds shows a
linear dependence upon the square of the dipole moment dif-
ference listed in Table III. It is not too clear, however,
J ust how these values are obtained. For p - chlorotoluene,
the moments of chlorobenzene and toluene were apparentlyd
added. For p-chloroaniline and. p-chlorophenol, however,
it. was not possible to obtain the values given by Monfils and
Grosjean38 by this method. If instead, one considers the to-
tal dipole moment of the molecules, the change should be
eQual to the value of the dipole moments of the impurities

sil'ice the moment of p-05H4012 is zero. For p-chlorotoluene

 

.maodmoolc ear mHSQmHOE meatsmsa esp smmmpmp
mocmsmtae manage mew soc: e> mo mocmesmcme were .wa .wam

oo><

x o
270. on on o. o.

 

zoo. 32;, can =o> ...-. \

:3: 22360 II. x\ x

1:35-: \\
NsGCIOOua o \

.mezcoai. x o \ o

 

00.

com.

00»

00v

and p-chloroaniline the results are £#J= 1.93 X 10"18 and
AA = 2.95 X 10"18 respectively, which are in fair agree-
tnent with those listed by the authors. In the case of
jp-chlorophenol, however, the value of L3}1=2.27,X 10-18 would
certainly destroy any linear dependence on (A POL.

The choice of the covalent radii and separation as a
measure of the size of the radicals attached to the benzene

ring seems strange since we are interested in their effect

 

 

on molecules to which they are connected by weak van der Waals .5
forces. If one treats the first three impurities in the
same manner as before but uses instead the van der Waals
radii, one still obtains a linear relation between change in
volume and effectiveness. Their volumes are plotted in
Figure 18 along with values calculated using the covalent
radii.

When one considers the last three impurity molecules in
the same manner, it becomes doubtful if one can consider
them to be the same size as p-06H4012. The van der Waals
radii of all the radicals is not known, however, for the

CH3 group it is 2.0 A0 as compared to 1.80 A? for the chlo-

 

rine atom. From this point of view it does not seem likely.
that one could obtain much information about the effect of
the electric dipole moment from these impurities since at
least one of them presents a change in volume also.

There are some interesting comparisons which can be

38

made, however, between the results of Monfils and Grosjean

67

and our results. The value of N for p-chlorophenol in
p-C6H4Cle is the same as that for phenol in C5H5CI. There
is similar agreement between the values of N for p-0106H4NH2
and p-CngH4CH3 in p-C5H4012 and the respective values of N
for C5H5NH2 and C5H5CH3 in 05H501. The fact that impurity
Inolecules which differ from the resonant molecule by similar
structural changes have the same effectiveness is an indi-
cation that the impurity molecules in general are distri-

‘buted throughout the crystal as single molecules. It is

 

possible that they could be collected at imperfections or
that groups of them could be merely caught in the crystal
as it solidifies and still be quite effective. However,
that two different binary mixtures would produce the same
grouping or an equivalent one as far as the resonance is
concerned does not seem too likely. It is even more unlikely *
that there should be three examples of this as we have here.
There is further support for the view that the effec-
tive impurities actually form solid solutions with the sam-

 

ples. To be effective in destroying the signal they cer-
tainly must be contained within the crystal. Furthermore
they all possess the characteristic of having a molecular
structure similar to that of the sample. While this is
neither a necessary or sufficient condition for the forma-
tion of a solid solution it is fairly common. Furthermore

it has been found that impurities which differ greatly in
molecular structure are quite ineffective. For instance, J

toluene which has a value of N==200 in C6H5CI had a value of

 

 

68

h1?.§' when used in CHQCIQ. Although many impurities were
zadded to CH2012 none had an N”>40 except CH212 which was

"the only impurity tried with a similar structure and whose
TJ=:220. The relative effects of p, m and o-C6H4012 are also
eaxamples of this. It appears that zm-C5H4012 is more effec-
tsive below .001 mole fraction than for greater concentra-
iLions. This may be explained as being the limit of the solu-
lsility of the impurity in the sample. Such an explanation
lias been given by Monfils and Grosjean38 for similar be-
liavior of p-ClC6H40H and p-CngHhNHe in p—C5H4012.

Figures 16 and 17 Show the plots of In égo versus-c for
“various impurities used in 05H5Cl from which the value of
IN was determined. Figure 19 shows a plot of the values of
N versus the difference in the volume of the impurity and
resonant molecule. The volume difference was calculated in
the same manner as indicated previously by making use of the
van derWaals radii of the substituted group.

One group of molecules, C6H6, p-C5H4Br2, p-06H4012 and
jp-CngHhBr all have the same dipole moment,,.=o , and thus
differ from that of 05H5Cl by the'same amount, Ahamflo“?
IBased upon the conclusion of Monfils and Grosjean38 one would
expect that the plot of N1 versus cur would be a straight
line as it is, but that its intercept at 13""- 0 would be

V 150, whereas it actually appears to be I» o. This would
seem to indicate that the effectiveness of the impurity is

'very low when there is no volume change, regardless of the

 

.Hommmo mam masomaos nuancesa or» semepmp
mosmsmwwap essaoe exp some 2 mo mocmpnmame mSB .ma .wfim

 

00 \(4
3.2.3» on on o. o. n
suemwzsoa o o
.m I Sch 1.
roexooa . 8.
area x .
_szoo >
.mszou o s
com
m 2
Avon
O .uo¢

 

70

difference in dipole moment. This is further substantiated
by the fact that the results for 06H5Br and C5H5I, both of
which possess the same dipole moment as C6H501 ( fx=L7mM§8),
lie on the line defined by the above results.

Our results indicate that in agreement with MOnfils
and Grosjean38 there is a linear dependence between the ef-
fectiveness of the impurity in reducing the signal strength
and the difference in volume of the impurity and resonant
molecules. We find, however, that a difference in the dipole
moment of the two molecules seemsto have little if any

bearing upon the effectiveness of the impurity.

 

Ii

 

 

 

 

7.
8.
9.

10.

11.
12.

l3.
14.
15.
16.

17.

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Goldstein, H. Classical Mechanics. Addison-Wesley
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19. Dean, 0. Thesis. Harvard Univ., 1952.

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21. Roberts, A. Rev. Sci. Instr. 18: 845, 1947.

 

 

22. Bloch, F. Phys. Rev. 70: 460, 1946.

 

23. Hahn, E. L. Phys. Rev. 80: 580, 1950.

24. Bloom, Hahn and HerZOg. Phys. Rev. 97, 1599, 1955.

 

25. Watkins, G. Thesis. Harvard Univ., 1952. f j? ‘

 

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PHYSXCS—MATH LIB!

 

   

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