A study of the EPR spectrum of the Ca(OH)₂:Gd 3+ system as a function of temperature.

University of Windsor University of Windsor

Scholarship at UWindsor

Scholarship at UWindsor

Electronic Theses and Dissertations Theses, Dissertations, and Major Papers

1-1-1973

A study of the EPR spectrum of the Ca(OH)

A study of the EPR spectrum of the Ca(OH)

22

:Gd 3+ system as a

:Gd 3+ system as a

function of temperature.

function of temperature.

Gérald E. Roberge

University of Windsor

Follow this and additional works at: https://scholar.uwindsor.ca/etd

Recommended Citation Recommended Citation

Roberge, Gérald E., "A study of the EPR spectrum of the Ca(OH)2:Gd 3+ system as a function of temperature." (1973). Electronic Theses and Dissertations. 6887.

https://scholar.uwindsor.ca/etd/6887

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N A TIO N A L LIB R A R Y

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BIB U O TH ^C fU E N A TIO N A LE

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NAME OF

TITLE OF THESIS.. .A.

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system. aa^ a fu n c tio n of_ tempejrp tujre._

UNIVERSITY.... Ppiypr??-?Y. pf Windsor.Ifcpdppr,.

OvtZ-tfgJ...

DEGREE FOR WHICH THESIS WAS PRESENTED... ...

L

YEAR THIS DEGREE GRANTED ; ... . 3-973... .*

Permission'is hereby granted to THE NATIONAL LIBRARY

f •

OF CANADA to microfilm this thesis and to lend or sell copies

of the film.

The author reserves other publication Tights, and

neither the thesis nor extensive extracts from it may be

printed or otherwise reproduced without the author's

written permission.

(Signed).

PERMANENT ADDRESS:

f . r . u 7j c - y - , s o % ,

'cn

A STUDY OF THE EPR SPECTRUM OF THE Ca(OH)2 :Gd3+

SYSTEM AS A FUNCTION OF TEMPERATURE

V

by

Gerald E. Roberge

A Thesis

Submitted to the Faculty of Graduate Studies through the Department of Physics in Partial

- Fulfillment of the Requirements for the Degree of Master of Science at

\ the University erf Windsor

Windsor, Ontario

’ 1973

(ey Gerald E* Roberge 1973

447000

f

APPROVED BY:

7 T

T

ABSTRACT

. ■■**. • *

The temperature dependence of the C a ^ H ) ^ G d ^ +

» # ^

system was studied in the 77°K to 375°K range by means of

the electron paramagnetic resonance method at K band ■.

frequency. '

The trigonal-crystal field parameters were fitted

to the \spin-tlairfi'4ta>ni^o

£ B T / '

n 0 . Anm nm • n=0,2,4,6

nr=

0

3

6

(~t |m 1 s n

^ /

using a multi-dimcnsional least squares method. The.

■ ' . ' v

p^araeters which showed temperature dependence were the \ixi 1

parameters 1*20 anc^ ^4 0’ while the b sbowed a very rapid

change at around room Cemperaturc.

£

The values of thectcmporaturc independent

parameters turned out to be:

Rx — Sy — g z = 1.9920 + 0 .0006

. b 6° - (-1.2 + .2) Gauss ^

bfi3 - = (27 + 4) Gauss

b 66 - ( - 1 9 + 2) Gauss

Nq hyperfine stiiicturc was observed,, although the nuclear s

of Gd^~* and G d ^ Y each occurring with — 1 5 abundance, ha

values of ~. Energy level diagrams were drawn, ^showing

perfect linearity for a magnetic field >2 Kgauss and up to

1 5 Kguussr. . ^

iii

\

ACKNOWLEDGEMENTS

.

^ ' 1,

I

The author wishes to thank Dr. F. Holuj for

first proposing this study and for his guidance daring this

work. Thanks are also due to Dr. T. Kwan for his help'

concerning the experimental work' and to my wife, Paulette,

for her assistance in^ recording of ‘data and preparation

p of diagrams. ' * _

IV

TABLE OF CONTENTS

ABSTRACT «

)

ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF TIGURES

CHAPTERS

« •

I.

II.

III.

IV.

V.

INTRODUCTION

CRYSTAL STRUCTURE OF Ca'(OH).

THEORY

A) Electron Paramagnetic Resonance

1. Free Paramagnetic Ion

• 5

-%. Crystal Field

3. Trlvalent Gadolinium Ion

B) Hamiltonian

1. General Form {

^,

2. Spin-Hamiltonian Operator

3- Matrix Elements

INSTRUMENTATION

A) Microwave Circuit

B) Electronic Circuit /

C) Magnetic Field

i

EXPERIMENTAL PROCEDURES AND RESULTS

A) Angular Variation

B) Temperature Variation

C) Results

page

iii

iv

vii-viii

I-2

4

« 4

4

4

4^

5

5

7

8

14

14

16

17

19

19

30

30

page

VI. DISCUSSION AND CONCLUSIONS p 37

A) Crystal Orientation . - : 37

B) Temperature Dependence 37

C) Charge Compensator 40

BIBLIOGRAPHY " ’ 42

APPENDICES ' 42

A. - Magnetic Field Calibration 44

B. Best Fit Data of Spin-Hamiltonian 45 Parameters

VITA AUCTORIS 4 6.

r

\

V

LIST OF TABLES

\

page

II.1 Structural Data for Ca(0H)2 ' . 21

111.1 Table of Tensor Operator Equivalents 11

S' ^ •

111.2 Relationship Between b m and B 11

n nm

111.3 Matrix Elements of Spin-Hamiltonian 12

111.4 Values of Matrix Elements of the t

Tensor Operator Equivalents 13

V.l(a-h) Spectrum Measurements ' ' 22

.. \

-V

.

■

* x

1 '

*

*

vii

Reproduced with permission

7 * *

*

OF FIGURES

page

II.1 C a f O H ^ crystallography 3

IV.1 Block Diagram of Apparatus 15

V.l Angular Variation in XY Plane 20

V. 2 Angular Variation in ZX Plane 21

V. 3 iTypical Spectrum in [1010] Direction

at 60°C - < ₃₁

V,4 Temperature Dependence o f , b^5 Parameter 3.2

V. 5 . Temperature Dependence of Parameter ₃₃

V.6 Temperature Dependence of b Parameter3

4 34

V. 7 Enprgy Levels Diagram Along Y-Axis ₃₅

V. 8 Energy Levels Diagram Along' Z-Axis 36

VI. 1 ModifiefKPlot of Temperature Dependence of b,°/Parameter

Z/ \

38

viii

CHAPTER I

INTRODUCTION

The purpose o f this experiment was to measure the

' *) 3+

temperature dependence of the Ca(0H)2:Gd system from liquid

nitrogen (77°K). to above room temperature (375°K) using the

methods of Electron Paramagnetic Resonance Spectroscopy. The

choice of CatOH)^ was motivated by the fact that it proved to

be a suitable host in which to study temperature effects on

* 1 ?*

the EP& spectra.of (Cu^+ ) and (Mn“'+ ) .

A Jahn-Teller effect having a relatively higl

transition' temperature from the static to the dynamic state

■ 2+

was encountered in the Cu spectrum. Moreover, the dynamic

Jahn-Teller spectruqi turned out to be anisotropic. In the

4

case of the-Mn EPR spedtrum, the spin-Hami 1 tonian

o ^

parameter reversed its sign at 4 5 0-K, while the value of the

ipotropic hyperfine structure tensor component decreased

sizeably with the increase of temfSerature.

* The room temperature investigation of the G d . ' s p e d

had been carried out earlier in this laboratory' . A computer

program, which diagonalizes the Hamiltonian, f?ts the crystal

C'. t

field parameters through a multidimensional Newtoq-Raphson

least square minimization method. The form of live program us

in this investigation is a revised version of that routine.'

- 1

-\

\

s

CHAPTER II

f

-CRYSTAL STRUCTURE OF,Ca(OH>2

' % _

Calcium hydroxide crystal belongs t<? the hexagonal

— 2 1

system (Cdl9 type) with space group P3 — (D,,). There is

■t- m Ja

t

one formula unit per unit cell. The calcium ion occupies

the invariant position (0,0,0) with point symmetry 3m while

the OH complex occupies positions with symmetry 3-rji.

Fig- (II.la) is a projection of the lattice in the

,-.(0001) plane, showing the^ three-fold symmetry axis passing

2+

through the Cn“ sites, while Fig. (II.lb) shows the hexagonal

unit cell. The choice of coordinate system is defined in

Fig. (II.lc). The X, Y and Z axes are parallel to the [ lOlO],

)

[1210] and [0001] di rcctions respectively; the hyuhoxyl ions

thus occupy the two adjacent layers normal to the hexagonal

2+

axis and are sandwiched on either side of the Ca layer.

The folloVing table gives structural data of the

Ca(0il) 9 crystal at 20°C. ^

TAM.E ( IT. 1 ) 4

Unit cell parameter a = 3-591'8 A’

> Unit cell parameter c = 4-9063 A

Structure parameter = 0.2341 A

Structure parameter = O.4248 A

- 2

\

3

-S'

©

B E L O W

ABOVE

'ST

Fig. (II.1)

•'

A '

CHAPTER III

. * THEORY

>

Et^CTRON/PARAMAGNETIC RESONANCE

Free paramagnetic ion

- e. 0

If a free ion-with a resultant electronic angular

momentum J is.placed in a magnetic f i e l d H , the energy levels

. \ ;

of this magnetic dipole are g^ven by

✓ • ,

E .= mjg/^H ' (III.1)

To produce magnetic dipole transitions, such that Anij = + 1»

an alternating R.F. field of frequency v .satisfying the

' • v; , . ‘ " '*

resonance Condition •

hv = g/^H (III. 2)

^ r

is applied at right angles to H. - ,

r * " * *

2 * Crystal Field '

When the paramagnetic ion is placed iri a solid, it

will form bonds with the diamagnetic ligands. These ligands

are charged ions which not only set up internal electric fields,

considered to a good approximation to be static, but also form

chemical bonds. The overall effect on the energy levels is a

splitting of the ground state into a number of components. ‘ As

a result, the orbital and spin degeneracy of the free iori is

partly removed.

3. * Tr^. valent Gadolinium -Ion

1

•

'

7

Gadolinium’ ion has the electronic structure (Xe)4f

so that the ground state o f ^ h e free trivalc^llt iorfvis the

4

-r

-l '

8 7

orbital singlet state ^7 /2 *'*le ^ configuration. When the ion is introduced in C a C O H ^ crystal as an impurity, the

8

ground state becomes since the spin degeneracy is

unaffected by the crystal field.

There is no simple explanation of the

zero-field-splitting, although qualitatively, it is no doubt caused by

high-order processes. Wybourne^ enumerated several, and in

the specific case of ethylsulfate host, two contributed

significantly to the ^ 2 ° P arameber: the fourth-order, involvin

the crystal field linearly, and a second-order, also linear in 7

crystal field but involving the excited 4 f P7/9 state. These,

two mechanisms give" a contribution having an opposite sign to

the experimental b^0 parameter.

B) HAMILTONIAN

1. General form ^

The general form of the Hamiltonian describing the

various interaction^' of each unpaired electron of the free. t

•paramagnetic ion with its surroundings tnay be written

as:-w h e r e :

JC= T + vc + VSL + vss + VN + v2 . . (III.3),

. t»K2 . ■ *' •

• T =/* E -r— is the kinetic energy; sum is over all

7 r f « *

K *

s

K electrons.

^ Z e 2 ' e2

s= - S + --- is the interaction of each C .. r., . s,. v. .

h h xj

i '

electron with the Coulomb field of the-nucleus,

f *

modified _by the repulsive field' of the other

electrons, and summed over all electrons. ^

-VSL = ■ Z \ l . 's^ is the spin orbit coupling which

i •

<• , reduces to X L ' S for Russell-Saunders scheme . V „ _ *=•£ Si ’?.i 3(ri.i‘S i ){ri.i‘SK )

SS ,• — o— ~--- -" c -7— --- : s p m - s p i n

,J -rA r A

ij 13

coupling. , .

Vjj, is the hyperfine term while the electrostatic interaction '

with the quadrupole moment Q of the nucleus is described by

V

follows:

The order of magnitude of these interactions is as

t.

Vr ~ 105 cm 1

c ■ CJ

3 - 1

10 cm for rare earths '

v ss~

1

cm

V.. ~ 10" 1 - 10“ 3 cm" 1 ..

N

V ~ 10"3 cm" 1

Now, when the ion is placed in the crystalline field,

the interaction between the eldctrons of the paramagnetic ion '

and the ligands adds.an -additional term V to the Hamiltonian:

A

V = £ e $(r ) : depends on position of each electron.

X K K •

* — * 1

Finally, if the ion is acted upon by a magnetic field H,

additional interactions arc: *

VH = £ K + electronic interaction

K

Vh = : nUc^ear interaction

7

-2. Spin Hamiltonian Operator

Since the general Hamiltonian is complicated and

avgcward to work, with* it has become general practice to

define a "spin Hamiltonian" in the following way: the EPR

spectrum is looked upon as belonging to a fictitious spin S

and having a degeneracy of 2S + 1. Now, since the crystalline

field is, in general anisotropic, its contributions to the

splitting of the ground state varies with the orientation of

the crystal with respect to the applied external magnetic

field.

'The Hamiltonian may thus *be written:

3C = /ifiS-g-H + £ Bnm Tm + S-3C-I + I* Q-1 - AjgjjI'.H-

(HI. 4)

0 *

where g,; A and Q are second rank tensors

"^nm are *'ensor operator equivalents. They are functions

*

of the effective spin operator S.

Bnm are empi rical parameters. These quantities are fitted

to experimental data.

The first term in Eq. (III.4) is the electronic Zeeman tens,

while the second describes zero-field splitting by the crystal

field. The third term is the hyperfine term, the fourth

being the quadrupole interaction and finally, the last t^rm

describes the nuclear Zeeman splitting.

'' ' ^ f .. * *

" > In the case of C a ^ H ^ t G d , no hyperfine splitting or nuclear Zeeman transitions are observed at the microwave

P-frequency and in the range of magnetic field used.

The electrostatic potential in which the Gd^+ ion

with

finds itself arises from the ligand ions. These are

regarded as point charges such that the potential is a

solution of the Laplace’s equation AV = 0, and is given by

the spherical' harmonics : ».

V = E E E A® r11 = E ; V® (III. 5)

. n ^ n

n X n,m ■

Ct

where: . *

K relates to the electron in the unfilled shell

Y ® (0k„ O is the angular part of the spherical harmonics, n k k

Symmetry considerations define the values that m and n can

t a k e :

— n can only take on values up to 6 since f electrons

(3) """

transform like D of the rotation group and when the

matrix elements V® are computed, the direct product

(3) (3)

D x D involves no representation higher than 6.

- also n can take on even values only since the parity of

,t matrix elements of V m must be even. n

— n = 0 gives \'^ contribution which is an additive constant.that we chose to ignore.

- m can only takb on values m — 0, + 3} + 6 since the

crystal f^ield at the paramagnetic ion possesses axial,

three-fold and six-fold symmetries.

3 - Matrix Elements

We express the crystal field contribution in terms

of angular momentum operator equivalents as follows. In

genera], any tensor may be decomposed into components which

transform independently under rotation of the coordinate

systefti. An*' "irreducible tensor operator" T , with ,nm

components (m = -n, -n + 1, ... , n -- 1, n) additionally

satisfies the commutation relations with the angular

momentum operator J:

[Ji> Tnm] = ia+in 1/2Tnny.1 •> . (III.6)

p > Tnn.J = mTnm '• ’"here J ± r J x ± *■

3y,

Eq. (III.6), in its inverse form, thus generates all of the v

tensor operators. The ones of importance in this case are

listed in Table (III.1). We thus have, substituting in

Eq. (III.4): / ■

" “ % hn ho + V

t

! T1-1 \7J Tn>

Ulhn

m=0, + 3,6

mlfin

/

wh e r e ;

hi - g xHx ± igy 11/

h (| = g Z HZ

The Zeeman term is represented in a frame of reference in

which the g tensor is diagonal; the hyperfine, as well as the

quadrupole and nuclear Zeeman terms have not been included.

The matrix' element's of the crystal field tensor

operators are given by <m,lT |m,»>, where T transform as

J nm J ' nm

the spherical harmonics Y m , h m1 beihg the Z component of

n J

the angular momentum. The non zero terms are the ones for

which**

m = m J - m j.

■ . .. ■ ' ■ . i

- 1 0

-The matrix elements of the spin-Hamiltonian operator are

given in Table (ill.3)* The numerical values of the matrix

elements of the tensor operators are given in Table (XXI.4),

/*

while Table (III.2) gives the relationship between the fitted

parameters B and the more conventional b m parameters.•

nm v n .

"N

11

-•TABLE (III.1)

Table of Tensor Operator Equivalents

T10 - Jz

Tl+1

_J±

T20 = / J ^3JZ2 - J (J + ^

T40 =

J I^b

T4+3 “

^2

II

^60 ~ ~4 / ^3l - 105 C3J( J + 1) - 71Jz^

+ 2l[5J^(J + 1)Z - 25J(J + 1) + 1 4}j z

-5Cj3 (J + l)3 - 8j 2 (j + l)2 + 1 2j (j + 1)}]

t6±3 = ? I / I T tJ+ (llJz2 ' 0 <2 + 1) + 59) Jz 3

~ ■

\

+ {11JZ3 - Q3J(J + 1) +59) J2 )J+]

T = 1 T6

6+6 = S J+

TABLE (III. 2). . .

Relationship Between b m and B

n nm

h °=(l)1/ 2B ■ K h O 315

2 V 20 4.'’ 7 40 6 - ( ~31~ l/ 2 60

\ 3= - F6 0 B43 • b63= -630(|r )1/2B63 b66= 3 1 S 'B66

M a t r i x E l e m e n t s of S p i n -H a m i l t o n i a n

- YZ

-K

t\

m **

4 . -J t*5 $>Q

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

13

-T1 0(7/2)

t40(7/2)

Values

J

‘ 7/2

7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2 7/2

TABLE (III.4)

of Matrix Elements of the Tensor 0perat6r Equivalents

' 7/2

t4 3( 7 / 2 ) .7/2

and 7 /2

(-1) W 7/2) 7/2

7/2 J z -7/2 -5/2 -3/2. -1/2 1/2 3/2 5/2 7/2 -7/2 -5/2 -3/2 -1/2 1/2 3/2 5/2 7/2 r7/2 -5/2 -3/2 -1/2 1/2

7/2 -7/2

7/2 -5/2

and . 7/2- -3 /2 (-l)^_3(7/2) 7/2 -1 /2

7 /2 1 /2

T6 3(7/2)

Matrix Element

-3.500000D 00

-2.500000D 00

-1.500000D 00

-5.OOOOOOD-Ol

5•OOOOOOD-Ol

1. 500000D 00 2.500000D 00.

3.500000D 00

2.5 0 9 9 8 0D 01

-4.661393D 01

-1.075706D 01

3.227118D 01

3 . 7 2 7 H 8 D 01

-1.075706D 01

-4.661393D Q1

2.5 0 9 9 8 0D 01

5.0 1 9 9 6 0D 01

3-»794733D 01 0 . 0

-3-794733D 01^

-5.019960D 01

\

T20(7/2)

60

" 1 1 v and

1.435904D 02

-1.899522D 02

< 0.0

66

and (7/2)

J J

* z Matrix Element

7 /2 -7/2 8.573214D 00

7/2 -5/2 1.224745D 00

7 /2 -3.674235D 00

7/2 -1 /2 -6 .1 2 3 72 4 0 00

7 /2 1 /2 -6.123^24D 00 7 /2 .3 /2 -3.674235D 00

7 /2 5 /2 1.2247450 00

7 /2 7 /2 8.573214D 00

7 /2 -7/2 2.072548D 01

7/2 -5/2 -1.0362740 02

7 /2 -3/2 1.865293D 02 7/2 - 1 / 2 -1.036274D 02 7/2 1 /2 -1.036274D 02

7/2 3/2 1.865293D 02

7/2 5/2 -1.036274D 02

7/2 7/2 2..072548D 01

7/2 -7/2 -1.870829D 00

7/2 -5/2 -2.44^490D 00 7/2 -3/2 -2.7386lpD 00

7/2 -1 /2 - z. 8284270 00

7/2 1 /2 -2.738613D 00

7 /2 3/2 -2.4494900 00

7/2 5/2 -1.870829D 00

7/2 -7/2 2.381176D 02

1.899522D 02 (-1)^(7/2) 7/2 -S/2

-1.435904D 02

2.381176D 02

J represents the initial state of T (7/2) and the final

z .nm ‘ '

state for T m (7/2).

CHAPTER IV

f '

INSTRUMENTATION

The ESR spectrometer used in this experiment was ,

of the balanced bridge .type with the microwave frequency ^

\

stabilized against the sample cavity. A block diagram

describing\the system is shown in Fig. (IV.1). It operated

at a n ominal>frequency of 24GHz. A 1 2 n Varian magnet, o f x

which the field was stabilized against a Hall-effect probe,

provided the magnetic field. The resohant fields were

measured using a proton magnetometer oscillator.

' The following is a brief description of the

principal components of the apparatus used in the experiment.

A) Microwave Circuit:

- Klystron is the microwave source (Varian model VA98M), of

reflex type with a nominal power output of 30mw. The

power supply w a d a Hewlett-Packard (#7l6B). The klystron

was immersed in a) water-cooled oil bath.

1

-Isolator is a microwave ferrite device which makes use of

’ \ ^ ' '

the Faraday effect)to permit transmission of microwaves

in one direction^only.

-Wavemeter cavity is a calibrated, tunable cylindrical' cavity

used as a frequency meter.

- Power attenuator is used to monitor power iricidepb on loaded

cavity in order to avoid saturation.

*

%

r

-Circulator permits transmission of power from one terminal to

the next in sequence. Here, the microwave is transmitted

B

l

o

c

k

D

i

a

g

r

a

m

of

A

p

p

a

r

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O

kH

i

F

i

e

l

d

M

o

d

u

l

a

t

i

o

— 16

-^ . *

to the resonant cavity arm and then to the crystal

detector arm.

-Slide-screw tuner serves to match the impedance of the

klystron arm with the cavity arm. Usually, the cavity ♦

is slightly mismatched in order to bias the detector

crystal.

N

- Resonant cavity was made of a glass tubing whose inner

surface was sputtered with gold. The cavity is coupled

to the microwave arm by a thin copper iris ( ~4mm

diameter)* since the waveguide was' rectangular.

A heater was made of chromel wire and embedded in Sauer

Eisen on the o^ts^de of the bottom plate of the cavity.

The crystal, glued to a hollow quartz pin, could be ^

rotated about an horizontal axis by means of a

gonio-meter. Any orientation of the crystal, relative to

the magnetic field, could thus be attained since the

magnet could be rotated about a vertical axis. Copper­ as

constantan thermocouple wires were inserted in the pin

so that the junction made contact with the crystal. The

cavity operated in the mode.

v.

\ ‘ N

B) Electronic Circuit: ^

-Klystron frequency control is used to stabilize the klystron”^ )

frequency. The principle of operation is the following:

by frequency modulating the reflector, the signal

detected by the. AFC (automatic frequency control) crystal

detector contains a component of the modulating signal;

whose phase and amplitude depends on the difference

between the-klystron and cavity frequencies. This AFC

signal is then fed to a phase sentitive detector (P.S.D.)

The resulting D.C. error voltage is applied to the

reflector of the klystron-.

The klystron stabilizer used was a Teltronic Model KSLP,

the modulating frequency being 70 Khz.

-LQCk-in amplifier compares the phase and frequency of a

\ ■

resonant signal, from the signal crystal detector, with

the original 100 Khz modulation signal. This modulation

signal is generated by an oscillator incorporated in the

lock-in amplifier and used to modulate the magnetic field

by means of two Helmholtz coils placed along side the

cavity, and parallel to the pole faces of the magnet.. The

result is a derivative signal proportional to the

resonant signal, which is displayed on the oscilloscope or

chart recorder as a function of magnetic field. The

Variac is used to regulate 60 Hz’ modulation in oscilloscope

display. The lock-in amplifier used was a Princeton

" * • "

Applied Res^Arch, Model JB-6.

C) Magnetic Field

The magnetic field was produced by a water-cooled

12 inch Yar ian electromagnet with a 3 .5 inch gap and rotating

^ ^ A ,

base. The field was stabilized to 1 part in 10 by'means of

o Fieldial model V-FR2503 (Varian) control unit. The 100 KKf"

signal, originating from the lock-in amplifier, is first

c

power»amplified before being applied to the two Helmholtz

coils-connected in series.

The magnetic field strength was measured by means

of a protdn magnetic resonance the probe of which

consists’ of a marginal oscillator. ' The source of* proton

was a small piece of rubber and the probe was placed at the

center and near the pole-face.

. The correction for difference in field strength

at the polle face and in the center-of the gap, where this

crystal is located, was obtairted by making corresponding 0 field measurements at both positions; these are tabulated

in Appendix•A. Since the differences involved were-less t

than the reproductibility deviations of the E.P.R. lines, the v

J • - $ ‘

average difference was calculated and added as the correction

i - ■ * •

to the measured fields.

CHAPTER V

EXPERIMENTAL PROCEDURE AND RESULTS

A) Angular Variation

The orientation of the crystal was arrived at by

determining the'.Z-axis (C-axis) and the Y-axisj these were

4

-defined by observing the turning point of the J— 5, | > line

in'each case. The coordinates of each axis was plotted on a

Wulff net, thus determining the thre^p'rincipal planes. The

angular variation of the spectrum in the basal (X-Y)

plane-* I .

was accurately measured, using the P.M.R. magnetometer at

intervals of 10 degrees. The results, for the j ~ > — ]-r >

apd | — ] — rg > transitions are given in Fig. (V.l). Next, the angular variation in the X-Z.plane, at

liquid nitrogen temperature, was determined from the spectra

traced-out on a chart ^recorder at intervals of 10 degrees.

This result is given in Fig. (V.2). A comparison with the

room temperature results^ reveals no qualitative difference.

The spectrum was measured accurately at different

orientations and temperatures, always using the same set of

ten orientations at each temperature. These measurements

are given in Tables (V.la) - (V.lh), along with the oricntatio

angles. THETA and PHI, the D.PPH ^standard (free radical a,

a.'-dipheryl (3-picrylhydrazyl) and the temperature (°C). Note

o t '

that the fields are given in Mhz.

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. 24

-C O N V E N T I O N A L P A R A M E T E R S F O K Cil53 + I N C A ( O H ) 2 A T 2 3 G H Z — G E K A L O K 0 B 9 K G E

NUMRRR OF O R I E N T A T I O N S a l O N U M B E R °OF I T E «A7IUNS = 3 T E M P E K A T U K E (C ) =-122.0

SIZE OF M AT R IX = B _ SPIN VALUE* 3.5 NUMBER OF P A K A M E T E K S = 9

DPPH(MMZ)'” 35.6689 3 5 . 5 4 4 7 3 5 . 6 7 8 8 35. 5465 35.5491 35 .5502 35 . 5729 ' 3 5 7 6 7 8 8 -- 3 3 T 6 9 5 8 - ^ 3 7

“6975---THETA 9 0 . 0 ' ^ 9 0 . 0 0.0 90.0 90.0 90 .0 70.0 20.0 20.0 Vu.O

PHI 0.0 90 . 0 90.0 45.0 20.0 70.0 90.0 90.0 0.0 . 0.0

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4 4 . 3 9 9 8 4 4 . 3 B 3 0 17.6352 44.3357 4 4 . 3 7 0 2 4 4 . 3 2 5 8 3 9 . 86bO 1 9 . 2 5 7 9 19.1163 3 9 . 3 5 4 7

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