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I N V E S T I G A T I O N O F A S U P E R H E A T E D S U P E R C O N D U C T I N G

C O L L O I D

B y

Angela Jane D a Silva

B . A . Sc., University of Br i t i sh Columbia , 1986

A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F

T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F

M A S T E R O F A P P L I E D S C I E N C E

in

T H E F A C U L T Y O F G R A D U A T E S T U D I E S

D E P A R T M E N T O F P H Y S I C S

We accept this thesis as conforming

to the required standard

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A

October 1988

© Angela Jane D a Silva, 1988

In presenting this thesis in partial fulfilment of the requirements for an advanced

degree at the University of British Columbia, I agree that the Library shall make it

freely available for reference and study. I further agree that permission for extensive

copying of this thesis for scholarly purposes may be granted by the head of my

department or by his or her representatives. It is understood that copying or

publication of this thesis for financial gain shall not be allowed without my written

permission.

Department of P«HSK^>

The University of British Columbia Vancouver, Canada

Date OCT- f3> / 88

DE-6 (2/88)

A b s t r a c t

In recent years, there has been increas ing interest in the idea of us ing a superheated

s u p e r c o n d u c t i n g c o l l o i d ( S S C ) as a detector for neut r inos and dark mat te r candidates .

T h e p r i m a r y ob jec t ive of th i s work has been t o invest igate the basic propert ies of an S S C ,

cons i s t ing of 7 um r ad ius t i n grains i m b e d d e d in epoxy, us ing a p u m p e d 4 H e cryostat

w i t h a low v i b r a t i o n a l noise R F - S O U I D readout sys tem. T h e superheat ing-supercool ing

hysteresis curves of the c o l l o i d have been measured in app l ied magnet i c fields ranging

f r o m 3.1 x 1 0 " 4 T to 1.4 x 1 0 ~ 2 T . T h e s u p e r c o n d u c t i n g to n o r m a l phase t r ans i t i on in

i n d i v i d u a l grains ins ide the co l lo id has been observed and the measured s ignal size is

in reasonable agreement w i t h the ca lcu la ted values. F i n a l l y , i t was demons t ra ted that

the c o l l o i d could w i t h s t a n d up to 2 0 M r a d of i - r a d i a t i o n w i t h o u t i n c u r r i n g a significant

change in its supeuondu< t i n g - n o r m a l phase t r a n s i t i o n .

A new type of s ample , cons i s t ing of a p l a n a r a r ray of 1 um th ick meta l squares

depos i ted on a m y l a r substrate , was deve loped . B o t h i n d i u m and t i n were used as a.

f a b r i c a t i o n m a t e r i a l . T h e character i s t ics of such samples were inves t igated , again using

the p u m p e d 4 H e cryos ta t . T h e f u l l Mei s sner effect was o n l y observed for appl ied magnet ic

fields less t h a n 5 > ] 0 " ' T . F o r higher a p p l i e d fields, the samples behaved l ike type-U

superconductor s in the m i x e d state regime, e x h i b i t i n g flux p e n e t r a t i o n and t r a p p i n g .

n

T a b l e of C o n t e n t s

A b s t r a c t i i

L i s t of Tab le s v

L i s t of F i g u r e s v i

A c k n o w l e d g e m e n t v i i i

1 I n t r o d u c t i o n 1

1.1 H i s t o r i c a l P e r s p e c t i v e 1

1.2 Superhea ted S u p e r c o n d u c t i n g C o l l o i d 2

1.3 Present W o r k 4

1.4 Thes i s O u t l i n e 4

2 T h e o r y 6

2.1 E n e r g y D e p o s i t i o n 6

2.2 S i g n a l Size 11

3 A p p a r a t u s

3.1 C r y o s t a t IS

3.2 1 K e l v i n Pot 21

3.3 T h e r m o m e t r y 24

3.4 S u p e r c o n d u c t i n g M a g n e t s 25

3.5 S Q U I D R e a d o u t S y s t e m 26

i i i

3.6 T e m p e r a t u r e C o n t r o l 31

3.7 D a t a A q u i s i t i o n 32

4 E x p e r i m e n t s - C o l l o i d S a m p l e 33

4.1 S a m p l e P r e p a r a t i o n 33

4.2 C o o l - D o w n P r o c e d u r e 37

4.3 E x p e r i m e n t a l Resu l t s 38

4.3.1 Hys teres i s Curves 38

4.3.2 R a d i a t i o n Test 43

4.3.3 R a d i a t i o n Hardness 47

5 E x p e r i m e n t s - P l a n a r A r r a y s 49

5.1 F i l m T h i c k n e s s 49

5.2 S a m p l e P r e p a r a t i o n 51

5.3 I n d i u m A r r a y - E x p e r i m e n t a l Resu l t s 53

5.3.1 Hysteres i s Curves 53

5.3.2 T h e r m a l l y A c t i v a t e d F l u x m o t i o n 55

5.3.3 D i s cus s ion 55

5.4 T i n array - E x p e r i m e n t a l Resu l t s 56

6 C o n c l u s i o n s 59

A F L U X P r o g r a m L i s t i n g 61

B H Y S T E R E S I S P r o g r a m L i s t i n g 64

B i b l i o g r a p h y 67

iv

i

Lis t of Tab les

5.1 T a b l e of some relevant p h y s i c a l propert ies of three m e t a l l i c superconduc

tors 50

v

L i s t o f F i g u r e s

1.1 P h a s e d i a g r a m for a type-1 s u p e r c o n d u c t o r . So l id l ine : superheated t ran

s i t i o n ; dashed l ine : t h e r m o d y n a m i c t r a n s i t i o n ; cha in d o t t e d l ine : super

cooled t r a n s i t i o n

2.2 Difference in the free energy between the n o r m a l and s u p e r c o n d u c t i n g

s tate as a f u n c t i o n of the s u p e r c o n d u c t i n g order parameter i l l u s t r a t i n g

the energy bar r ie r p r o t e c t i n g the superheated s u p e r c o n d u c t i n g state. . . 10

2.3 C o - o r d i n a t e sys tem for s ignal size c a l c u l a t i o n 12

2.4 F l u x t r ans former 15

2.5 E x p e c t e d s ignal size due to a 7 p.m rad ius g r a i n , at a pos i t ion ( R , z ) .

f l i p p i n g in an app l i ed field of 0 .01T . P a r a m e t e r R is the rad ia l p o s i t i o n of

the gra in w i t h respect to the centre of the coi l and z is the ver t i ca l pos i t ion

of the g r a i n w i t h respect to the b o t t o m of the c o i l . So l id l ine : R = 1 .0mm;

c h a i n d a s h e d l ine : R = 1 .2mm; c h a i n d o t t e d l ine : R = 1 .4mm 17

3.6 S c h e m a t i c v iew of the cryosta t 19

3.7 L o w e r c ryos ta t assembly 22

3.8 Set-up for flow i m p e d a n c e tests 23

3.9 S Q U I D m o u n t i n g box . (a) top p la te ( ins ide v iew) and m o u n t i n g bracket ;

(b) S Q U I D c o m p a r t m e n t 27

3.10 P o w e r spec t r a of S Q U I D s ignal for an app l i ed field of 0.03 T . (a) is w i t h o u t

m o u n t i n g box i n s t a l l e d ; (b) is w i t h m o u n t i n g box in s t a l l ed 29

v i

4.11 G r a i n size d i s t r i b u t i o n 34

4.12 Hysteres i s curves for co l lo id sample , (a) is in an app l i ed field of 9.3 x 1 0 - 4 T

a n d (b) is in an a p p l i e d field of 9.3 x 1 C T 3 T 39

4.13 B - T phase d i a g r a m of the co l lo id sample . C i r c l e s : superhea t ing t r a n s i t i o n ;

squares: supercoo l ing t r a n s i t i o n 41

4.14 W i d t h of the superhea t ing phase t r a n s i t i o n of the co l lo id sample as a

f u n c t i o n of app l i ed field 42

4.15 T o t a l s ignal change for the s u p e r c o n d u c t i n g to n o r m a l t r a n s i t i o n in the

c o l l o i d sample as a func t ion of app l ied field 44

4.16 (a) S Q U I D s ignal showing single gra in flips f r o m the superheated co l lo id

under i r r a d i a t i o n of 140keV 7-ra .ys . T h e a p p l i e d field is 0 .014T and the

t e m p e r a t u r e is 3 .09K . (b) P o s i t i o n in the superhea t ing t r a n s i t i o n where

the co l lo id was prepared for measurement shown in (a) 46

4.17 S u p e r h e a t i n g transi t Ion curve for the co l lo id sample in an app l i ed field of

9 . 3 x l ( T 3 T . C i r c l e : before 7 - r a d i a t i o n ; square: after 8.3 M r a d 7 - r a d i a t i o n ;

t r i a n g l e : after 20 M r a d 7 - r a d i a t i o n 48

5.18 Hysteres i s curves for the i n d i u m array, (a) is i n the earth's magnet i c field

a n d (b) is in an a p p l i e d field of 1.6 x 1 0 ~ 3 T . C i rc l e s : t e m p e r a t u r e increas ing

( superhea t ing t r a n s i t i o n ) ; squares: t e m p e r a t u r e decreasing ( supercoo l ing

t r a n s i t i o n ) 54

5.19 Hysteres i s curves for t i n array, (a) is i n the earth 's magnet ic field and

(b) is in an a p p l i e d field of 3.8 x 1 0 _ J T . C i rc l e s : t e m p e r a t u r e increas ing

( superhea t ing t r a n s i t i o n ) ; squares: t e m p e r a t u r e decreas ing ( supercoo l ing

t r a n s i t i o n ) 57

vn

A c k n o w l e d g e m e n t

I w o u l d l ike to t h a n k m y superv i sor . D r . B r i a n T u r r e l l , for his suppor t a n d encouragement

t h r o u g h o u t this w o r k . H e was a lways avai lable to discuss new ideas and results .

A l s o . I w o u l d l ike to express m y apprec i a t ion to M a r k Le G r o s , for his invaluable

ass i s tance w i t h m a n y aspects of the design and c o n s t r u c t i o n of the cryos ta t , as well as

hi s ass istance in p e r f o r m i n g the e x p e r i m e n t a l measurements .

In a d d i t i o n , I w o u l d l ike to take this o p p u r t u n i t y to t h a n k D r . A n d r z e j K o t l i c k i for

t a k i n g the t i m e to read m y thesis and for offering several suggestions to improve i t , the

t e c h n i c a l staff of the depar tment of phys ics who were always w i l l i n g to offer advice and

ass is tance. D r . A n d r z e j D r u k i e r , whose un ique p o i n t of view p r o d u c e d m a n y interest ing

d i scuss ions , and the Science C o u n c i l of B r i t i s h C o l u m b i a , for the i r financial assistance.

F i n a l l y , I w o u l d l ike to t h a n k m y husband for his constant support and wil l ingness to

discuss a l l ideas.

v m

C h a p t e r 1

In t roduct ion

1.1 H i s t o r i c a l Perspec t ive

T w e n t y years ago, the idea of u s ing superheated s u p e r c o n d u c t i n g granules for par t ic le

de tec t ion was put f o r t h by a g roup f rom O r s a y T h e y were the first to report the

o b s e r v a t i o n of a /3-ray s t imula ted t r ans i t ion between the superheated superconduc t ing

state a n d the n o r m a l state. In the i r exper iment , it was demons t ra ted tha t 1 um radius

m e r c u r y gra ins , doped w i t h rad ioac t ive g o l d , were sensi t ive to the / i-rays e m i t t e d f rom

the g o l d . W i t h ev idence for the i rrevers ible s u p e r c o n d u c t i n g to n o r m a l phase t r ans i t i on

u n d e r e l ementary pa r t i c l e interact ions , they suggested that a c o l l o i d of such part ic les

c o u l d po s s ib ly be used as a nuclear par t ic le detector .

S ince that t i m e , m a n y ideas a n d exper iments i n v o l v i n g superheated superconduc t ing

granules have been repor ted . In 1972, D r u k i e r and V a l e t t e '"^ suggested that a co l lo id of

superheated s u p e r c o n d u c t i n g grains (SSC') cou ld be used as a detector for charged par t i

cles. M o t i v a t e d by the poss ible app l i ca t ion to charged par t ic le d e t e c t i o n . B l o t et. a l .

p e r f o r m e d a series of exper iments us ing e lectron beams to induce the superconduct ing

to n o r m a l t r a n s i t i o n in meta l l i c spheres. T h e fo l lowing year , D r u k i e r et. a l . ^ suggested

tha t a SSC' cou ld also be used as a t r ans i t i on r a d i a t i o n detector . In 1978, B e h a r et. a l .

deve loped a " g a m m a c a m e r a " u s ing a co l lec t ion of superheated s u p e r c o n d u c t i n g granules

and a square array of U-shaped p i ck-up coi ls . T h a t same year, the SSC' was proposed as

a poss ib le n e u t r o n detector M o r e recently , the SSC' has been suggested as a neut ra l

1

Chapter 1. Introduction 2

current n e u t r i n o detector a m a g n e t i c m o n o p o l e detector a n d a co ld dark m a t t e r

de tec tor & I 1 0 l .

1.2 S u p e r h e a t e d S u p e r c o n d u c t i n g C o l l o i d

T h e superheated s u p e r c o n d u c t i n g co l lo id ( S S C ) consists of s u p e r c o n d u c t i n g grains , a

few m i c r o n s i n size, i m b e d d e d in a su i tab le d ie lectr ic m a t e r i a l . If the grains are made

of t y p e -1 s u p e r c o n d u c t o r , they can exh ib i t metas tab le states such as superhea t ing a n d

s u p e r c o o l i n g . Such states were observed e x p e r i m e n t a l l y over t h i r t y years ago in t h i n

s u p e r c o n d u c t i n g rods and la ter , in col lect ions of s u p e r c o n d u c t i n g spheres

S u p e r c o o l i n g occurs w h e n a s u p e r c o n d u c t i n g sample remains n o r m a l for a t emp era tu re

be low T,-. the t h e r m o d y n a m i c c r i t i c a l t e m p e r a t u r e , but above T$c. the supercooled t r a n

s i t ion t e m p e r a t u r e . S i m i l a r l y , superheat ing occurs w h e n the s u p e r c o n d u c t i n g state per

sists for a t e m p e r a t u r e above Tr- but be low T$H• the superheated t r a n s i t i o n t empera ture .

T h e phase d i a g r a m is shown in F igure 1.1.

For the SSC' to act as a detector , the co l lo id is p laced in a u n i f o r m magnet ic field

and the grains are m a i n t a i n e d just be low the ir superheated s u p e r c o n d u c t i n g to n o r m a l

t r a n s i t i o n t empera ture ( p o s i t i o n X in the phase d i a g r a m i l lu s t r a ted in F i g u r e 1.1). S ince

the gra ins are s u p e r c o n d u c t i n g , they expel the magnet ic flux v i a the Mei s sner effect.

W h e n an i n c o m i n g pa r t i c l e scatters e la s t i ca l ly off of a nucleus in one of the grains , i t

i m p a r t s a smal l recoi l energy to the nucleus it scatters f r o m . For low enough recoi l

energies 2 0 e V for t i n ) , the nucleus w i l l be b o u n d i n its l a t t i ce site and the energy

w i l l be d i s s ipated as heat . For larger recoi l energies, part of the energy m a y go i n t o

p r o d u c i n g permanent defects i n the l a t t i ce ra ther t h a n p r o d u c i n g heat . T h e majority- of

the energy, however , w i l l cont inue to be d i s s ipated as heat ' '1. If th i s s m a l l a m o u n t of heat

is sufficient, it can break C o o p e r pairs , r e su l t ing i n the de s t ruc t ion of the s u p e r c o n d u c t i n g


F i g u r e 1.1: P h a s e d i a g r a m for a type-1 s u p e r c o n d u c t o r . S o l i d l ine : superheated t rans i t i o n : dashed l ine : t h e r m o d y n a m i c t r a n s i t i o n ; c h a i n d o t t e d l i n e : supercooled t r a n s i t i o n .


state at t h e surface of the g ra in . T h i s leads t o the decay of the screening currents at the

surface a n d the p r o p o g a t i o n of the n o r m a l zone in to the inter ior of the g ra in , a l l owing

the m a g n e t i c flux t o penetra te in to the g r a i n . T h i s change in m a g n e t i c permeab i l i ty

can be measured u s i n g a S Q U I D magnetometer . Since the g r a i n was i n a metastable

superheated state, the change of state is p e r m a n e n t . In this way, a gra in " f l i p " can be

used to detect an event .

1.3 Present Work

T h e p r i m a r y interest of this thesis work has been to s tudy the basic propert ies of a

co l lo id cons i s t ing of t i n grains i m b e d d e d in epoxy. In order to do th i s , it was necessary

to cons t ruct a. p u m p e d 4 H e cryosta t w i t h an R F S Q U I D readout sys tem. In cons t ruc t ing

the c ryos ta t . care was taken in t r y i n g to m i n i m i z e v i b r a t i o n a l noise.

A c o l l o i d sample w7as prepared by m i x i n g 7 /m? radius t in grains i n epoxy. T h e phase

d i a g r a m of the c o l l o i d was then m a p p e d out . T h e sens i t iv i ty of i n d i v i d u a l grams to low

energy -.-rays was d e m o n s t r a t e d . In a d d i t i o n , the r a d i a t i o n hardness of the col lo id has

been d e m o n s t r a t e d .

In an attempt, to improve the character i s t ics achieved w i t h the co l lo id , a new type

of sample was deve loped . A pla.nar array of superconduc t ing squares wa.s produced

using t h i n fi lms of t i n and i n d i u m depos i ted on to m y l a r and s t a n d a r d photo l i thography

technology. T h e character i s t ic s of such samples were then s tud ied .

1.4 Thesis Outline

In chapter 2. two i m p o r t a n t questions i n v o l v i n g the v i a b i l i t y of the co l lo id as a detector

are discussed; how m u c h energy is required to flip a gra in and is a g r a i n flip detectable . In

chapter 3, a de ta i l ed descr ip t ion of the a p p a r a t u s used for the exper iments is presented.


C h a p t e r 4 discusses the p r e p a r t i o n of the co l lo id sample and the subsequent experiments

p e r f o r m e d w i t h i t . C h a p t e r 5 discusses the p repara t ion of the p l a n a r a r ray samples a n d

the subsequent e x p e r i m e n t s per formed w i t h t h e m . C h a p t e r 6 presents a s u m m a r y of

resul t s and conclus ions .

C h a p t e r 2

T h e o r y

In order to d e t e r m i n e whether the co l lo id w o u l d be useful as a detector , two i m p o r t a n t

factors must be cons idered . F i r s t l y , the energy necessary to induce a phase t r a n s i t i o n in

a. g ra in must be c a l c u l a t e d . Secondly , it must be demons t ra ted that a gra in t r a n s i t i o n is.

in fact , detectable . These two factors w i l l be discussed in de ta i l in this chapter .

2.1 E n e r g y D e p o s i t i o n

T o ca l cu la te the energy depos i ted in the detector (g ra in ) , consider an elasitic. co l l i s ion

between the i n c o m i n g par t i c l e and a t i n nucleus . T o e s t imate the recoi l energy depos i ted

in the t in nucleus , a s imp le m o d e l a s suming tha t the nucleus is o r i g i n a l l y at rest is used.

W i t h th i s m o d e l , and conservat ion of energy a n d m o m e n t u m , the recoi l energy is given

where ni and v are the mass and i n i t i a l ve loc i ty ol the i n c o m i n g par t i c l e and M is the

mass of the t i n nucleus .

In order for the gra in to operate as a detector , this recoi l energy must be large enough

to cause the s u p e r c o n d u c t i n g g r a i n to f l ip in to the n o r m a l state. In the " u n i f o r m hea t ing

m o d e l " , th i s means that the energy depos i ted must raise the t e m p e r a t u r e of the gra in

by an a m o u n t A T , where A T is the difference between the gra in t e m p e r a t u r e p r io r to

the co l l i s ion and the t e m p e r a t u r e of the s u p e r c o n d u c t i n g to n o r m a l t r a n s i t i o n as shown

in F i g u r e 1.1.

bv

(2.1)

6

Chapter 2. Theory 7

T o convert the depos i ted energy i n t o a t e m p e r a t u r e change, one must consider the

heat capac i ty of t h e g ra in . N e a r the t r a n s i t i o n t e m p e r a t u r e , the heat capac i ty of the

n o r m a l state is less t h a n that i n the s u p e r c o n d u c t i n g state. T h u s , if the n o r m a l state

heat c a p a c i t y is u sed , the ac tua l t e m p e r a t u r e increase w i l l be overes t imated .

T h e heat c a p a c i t y of a m e t a l is g iven b y

Cv = -yT -r AT 3 (2.2)

where

7 = U-D{iF)k%

D((p) is the dens i ty of states at the F e r m i energy

A 7 is the n u m b e r of a toms

a n d 9 is the D e b y e t e m p e r a t u r e .

T h e first t e r m is the c o n t r i b u t i o n due to the electrons w h i l e the second t e r m is the

c o n t r i b u t i o n due to the phonons . For t i n , 7 - 1.78 x l O ^ J m o ] - 1 K ~ - and A - 2.43 x

1 0 ~ 4 J m o l - 1 K - 4 ' 1 5 J . For temperat ures of the order of 1 K . the first, t e r m dominates so

( C V ) s n - 1-8 x 1 0 - 3 T [ J m o l ^ K - 1 ] (2.3)

F o r a t i n gra in of v o l u m e V" [m 3 ] , the heat capac i ty is then

CSn-9ra,r, ^ 1.8 X l O " 3 ? 1 )

- 1 1 0 T V " [ J K _ 1 ] (2.4)

(2.5)

w h e r e p = 7.28 x 1 0 f a g m - 3 is the dens i ty of t i n and MQ = 118.69 g m o l - 1 is i ts a tomic

w e i g h t . So the t e m p e r a t u r e rise due to the c o l l i s i o n , a s suming a u n i f o r m h e a t i n g mode l ,

Chapter 2. Theory 8

is g iven by

a rr, ETecoll Erecc,H = r ~~" = 11 n r v ( '

C-'Sn — grain 1 lVl \

Since every low tempera ture apparatus has finite t empera ture s t ab i l i ty , AT must be

greater t h a n t h a t t empera tu re s t a b i l i t y in order to insure t h a t any gra in flip is due to

p a r t i c l e in te rac t ions r a ther t h a n t e m p e r a t u r e f luctuat ions . If, for th i s reason, a temper

a ture j u m p of A T > 10 m K is r equ i red , then f r o m E q u a t i o n 2.6 one can see that if the

reco i l energy is of the order of 1.6 x 1 0 _ l b J (1 k e V ) , a t i n g ra in of rad ius 3 pm cou ld be

f l i pped at an o p e r a t i n g t empera ture of 1.5 K (obta inable in a s t andard p u m p e d l i q u i d

4 H e cryos ta t ) . For much lower recoi l energies, e i ther smaller grains a n d / o r lower operat

i n g t empera ture s are necessary in order for the deposited energy to be sufficient to cause

a change of s tate in the g ra in .

It shou ld be noted t h a t the u n i f o r m hea t ing mode l p r o b a b l y gives a conservative

e s t imate of the deposi ted energy requi red since it assumes that the entire grain must be

heated before the t r a n s i t i o n takes place ' ^ v T h a t is. it assumes that the propagat ion of

heat is faster t h a n the propaga t ion of the n o r m a l state and the nue lea t ion of the phase

t r a n s i t i o n a lways starts at the equator , where the magnet ic field is the strongest. It

m a y be, however , that the n o r m a l zone created by the energy deposit m a y be sufficient

to nucleate the t r ans i t i on before the heat spreads through the entire g ra in . T h i s is

charac ter i s t i c of the meta s t ab i l i ty of the superheated state, where an energy barr ier

protect s the s u p e r c o n d u c t i n g state at the surface of the g ra in .

T h e energy barr ier can be seen by cons ider ing F, the difference in the free energy per

u n i t surface between the n o r m a l and s u p e r c o n d u c t i n g states. U s i n g the G m z b u r g - L a n d a . u

equat ions , F for a type-1 superconduc tor can be a p p r o x i m a t e d by

F - = ^ + ^/Mli{2_ _ f{0) + 1 f ( 0 ) 3 } ( 2 7 )

S T T / ( 0 ) 8TT ^ 3 J 3 ' M ; ; '

w here

Chapter 2. Theory 9

H is the app l i ed magnet ic field

HC is the t h e r m o d y n a m i c c r i t i c a l field

A is the L o n d o n pene t ra t ion d e p t h

£ is the coherence length

a,nd / ( 0 ) is the s u p e r c o n d u c t i n g order parameter .

C o n s i d e r i n g F as a funct ion of / ( 0 ) , F has

• an abso lute m i n i m u m at / ( 0 ) = 0, cor re spond ing to the n o r m a l state

• a l o c a l m a x i m u m at f(0) — fmax - y ^ r * where v = , / l — and HSH is the

s u p e r h e a t i n g c r i t i c a l field

• a l o c a l m i n i m u m at / ( 0 ) = / w „ = y^r co r re spond ing to the superheated state.

So the superheated state is protected by an energy barr ier per u n i t surface given by ^

A F = F(fmax)- F ( / „ „ • „ )

4 v ^ / : / / H%H\

- — ( i - v 1 -x 2)(^ + . \ - v 1 ( 2 ' 8 )

and i l l u s t r a t e d in F i g u r e 2.2. T h u s , if the energy deposi t is sufficient to overcome this

bar r i e r , i t can nucleate the s u p e r c o n d u c t i n g to n o r m a l t r a n s i t i o n before the heat spreads

t h r o u g h o u t the ent i re g ra in .

E v i d e n c e of such a loca l h e a t i n g m e c h a n i s m has, in fact , been observed by Gonza lez -

Mes t re s a n d P e r r e t - C a l l i x ' ^ l in the i r exper iment s w i t h re la t ive ly large (4bum < q< <

63/7??!) t in grains i r r a d i a t e d w i t h 5 . 5 M e V o-pa.rtic.les. However , as the par t i c l e size is

r e d u c e d , the size of the n u c l e a t i o n centre approaches the size of the gra in a n d the two

m o d e l s converge.

http://o-pa.rtic.les

F i g u r e 2.2: Dif ference in the free energy between the n o r m a l a n d s u p e r c o n d u c t i n g state as a f u n c t i o n of the s u p e r c o n d u c t i n g order pa rameter i l l u s t r a t i n g the energy barr ier p r o t e c t i n g the superheated s u p e r c o n d u c t i n g state .

.Chapter 2. Theory 11

2 .2 S i g n a l S i z e

It is c e r t a i n l y of interest to ca lcu la te the expected signal size due to a single gra in flip.

It is necessary, in fact , to show tha t the s ignal due to a s ingle g ra in flip can indeed be

detec ted .

It is wel l k n o w n t h a t the d i p o l e field due to a. magnet i c m o m e n t , ??*?., is g iven by

B = — V ( 7 7 l - - ) ( M K S ) (2.9)

For j?? d i rec ted a long the k ax i s , th i s can be r e w r i t t e n in spher ica l co-ordinates as

-< 77? _ COsd £ = — V ( — ) (2.10)

47T ?"-

- 77? B = r ( 2 c o s 0 r + sin0 0) (2.11)

4?T7^

where ??? = |?n|.

For a s u p e r c o n d u c t i n g sphere of rad ius a in an app l i ed m a g n e t i c f ie ld , H,. the mag

netic m o m e n t of the sphere is g iven by

??"? = -2irfj.oHca 3 (2.12)

T h u s , for H, — H,k\ as in F i g u r e 2.3, the d ipo le field due to the s u p e r c o n d u c t i n g sphere

is

B = --n„Ht — ( 2 c o s 0 r + sin9 9) (2.13)

For a loop of rad ius R, centred a b o u t the or ig in in the x y - p l a n e , (ie. ± to He), the

abso lute value of the flux go ing t h r o u g h the loop due to the d ipo le at the or ig in is equal

to the absolute value of the f lux outs ide the loop i n the x y - p l a n e , w h i c h is g iven by

* = / / B(6=-)-da .1^=0 Jr=R 2

= --u0Hea 3 d4> drr U-l(-k)-(k) (2.14) 2 Jo Jn r 6

Chapter 2. Theory 12

F i g u r e 2.3: C o - o r d i n a t e sys tem for s ignal size c a l c u l a t i o n .


s ince, in the x y - p l a n e , 0 = ^ and 0 = — k. E v a l u a t i n g gives

o 3

^ = Ku0He- (2.15)

So the flux t h r o u g h the loop clue to a s u p e r c o n d u c t i n g sphere at the o r i g i n is given by 3

$(o,o) = -nu0He— (2.16)

For a 5 um r ad ius g r a i n , in a 2 .5cm radius loop and an app l i ed field of 0 .01T, flipping

f r o m the s u p e r c o n d u c t i n g state to the norma] state,

A $ ( 0 , o ) = 1-57 x 1 0 " 1 6 W b

= 7.6 x 1 0 _ 2 * 0 (2.17)

where <I>g = 2.07 x 1 0 ~ 1 5 W b is the flux q u a n t a . S ince the re so lut ion of an R F S Q U I D

is < iQ~- J ,ty0, such a flux change cou ld be detected . Hence , the detect ion of single grain

fl ips is. in p r i n c i p l e , poss ible .

T o ca l cu la te the s ignal expected f rom a gra in ins ide the c o l l o i d , one must also consider

gra ins not loca ted at the centre of the p i c k - u p loop . To do t h i s , consider V ( ^ f ^ ) in

car tes ian co-ordinates . M a k i n g thi s change in co-ordinate sy s tem,

V ( - ~ ) = ( x - + y" + z 2)- 5 / 2{-3xzi - Zyzj -f (x 2 + y 2 - 2z 2)k) (2.18) r-

W i t h o u t loss of genera l i ty , one can consider a. g r a i n located at (0, , C] ) . T h e n , reca l l ing

that the a p p l i e d field is in the k d i r e c t i o n and z = 0 i n the x y - p l a n e ,

^(v..--!) = ~7^oHea 3/ d<\> I drr — (2.19) 2 .'o Jo {r- cos- <p + [r s in <p — y i ) - + ) b / -

T h i s in tegra l can eas i ly be eva luated n u m e r i c a l l y .

In order to c a l c u l a t e the ac tua l s ignal size p r o d u c e d by the S Q U I D , the a m o u n t of

flux w h i c h is coup led i n t o the the S Q U I D must be ca l cu la ted . T h e flux coupled to the


S Q U I D , <f>sQ, due to the flux, <f>ext, app l i ed t h r o u g h the t rans former c o i l , or p ick-up loop ,

(see F i g u r e 2.4) is g iven by

M„NtT

<PSQ = -j——f——j—<Pext (2.20) Lir •+ Lsg -f Lid

w here

N{r is the n u m b e r of tu rns i n the t rans former co i l

is the se l f - inductance of the t r ans former coi l

LSjg is the se l f - inductance of the s ignal coi l

Lu is the se l f - inductance of the twi s ted leads

Msa is the m u t u a l i n d u c t a n c e between the signal coi l and the S Q U I D c i rcu i t

and . M ' , " A ' ; V " is ca l led the flux transfer factor .

(See Ref . [33], page 176)

F o r the p i c k - u p coi l used in the g ra in exper iment s (descr ibed i n de ta i l in a later

c h a p t e r ) , = 20 and L1r = 1.84//H. For t i g h t l y twis ted N b w i r e , L ~ 0 .3 / j .H/m, so for

the 2 0 c m leads, Lld 2r 0.06/_/H. For the S H E sys tem 330 R F S Q U I D I 3 1 ' , L$B = 2//.H and

Alss = 2 0 n H . H e n c e , the flux transfer factor , FT'F\ is g iven by

(20 x 1 0 ~ V H ) ( 2 0 ) FTF = — —-—'—=0A (2.21)

(1.84 + 2.0 + 0.06)//H

So 10% of the flux change p r o d u c e d by the change of state of a gra in is a c tua l ly coupled

i n t o the S Q U I D . F o r each $ 0 (2.07 x 1 0 ~ 1 5 W b ) coupled in to the S Q U I D , when o p e r a t i n g

i n the x l O O s e n s i t i v i t y m o d e , an o u t p u t s igna l of 2 volts is p r o d u c e d .

A p r o g r a m , F L U X , was w r i t t e n to ca lcu la te the expected s ignal size due to a gra in

f l ip i n s i d e the c o l l o i d . For a g iven gra in l o c a t i o n ins ide the p i ck-up c o i l , E q u a t i o n 2.19

is c a l c u l a t e d for the g ra in p o s i t i o n w i t h respect to the centre of each loop in the c o i l ;


twisted leads

R F coil signal coil transformer coil (pick-up coil)

F i g i i r e 2.4: F l u x t rans former .


the average of w h i c h is 4>ext. T h i s ex te rna l flux is then m u l t i p l i e d by the flux transfer

f ac tor and conver ted to the voltage s ignal o u t p u t b y the S Q U I D . A plot of the expected

s igna l size as a f u n c t i o n of the gra in p o s i t i o n ins ide the p ick-up co i l is g iven in F igure 2.5.

T h e gra in pos i t ions cons idered have been res tr ic ted to inside the vo lume occup ied by the

c o l l o i d sample . A s can be seen in F i g u r e 2.5, the s ignal size varies by ~ 3 5 % as different

g r a i n pos i t ions t h r o u g h o u t the co l lo id are cons idered . A l i s t i n g of F L U X in provided in

A p p e n d i x A .


F i g u r e 2.5: E x p e c t e d s igna l size due to a 7 um radius g r a i n , at a p o s i t i o n (R , z ) , flipping in an a p p l i e d field of 0.01 T . P a r a m e t e r R is the r ad i a l po s i t i on of the gra in w i t h respect to the centre of the c o i l and z is the ve r t i c a l p o s i t i o n of the gra in w i t h respect to the b o t t o m of the co i l . S o l i d l ine : R - 1 .0mm; cha indashed l ine : R = 1 .2mm; cha indot ted l ine : R = 1 .4mm.

Chapter 3

Apparatus

In this chapter , the cryostat as well as the externa l equ ipment necessary for the exper i

ments w Till be discussed.

A l l of the exper iments were per formed in a. dedica ted p u m p e d 4 H e cryostat . T h e

cryos ta t assembly is first precooled to 77 K w i t h l i q u i d n i t rogen and then to 4.2 K

w i t h l i q u i d h e l i u m . T h e ' ' oven" , a t e m p e r a t u r e regulated copper p la te , is further cooled

t-o a p p r o x i m a t e l y 1 .5 K by t h e r m a l conta.d w i t h a smal l v o l u m e of l i qu id h e l i u m under

reduced piessure (1 K pot ) . T h e t empera t u r e of the oven can be increased and contro l led

by means of a t h e r m a l l y anchored resistive heater contro l led ex te rna l ly . T h e samples were

m o u n t e d on the oven via. a threaded silver co ld finger screwed in to the copper oven plate .

In this m a n n e r , the sample c o u l d be m a i n t a i n e d at any t e m p e r a t u r e in the range 1.5 K

to 4.2 K to w i t h i n -- 2 m K .

3.1 C r y o s l a l

T h e appara tus is shown in F i g u r e .'.>.G. Ii is suspended i r o m the top plate which also forms

the seal for the h e l i u m dewar. T w o p u m p i n g lines pa.ss t h r o u g h the top plate : one for the

> 1 K h e l i u m pot a n d the other for the inner v a c u u m c a n . In a d d i t i o n , there are two other

tubes pass ing t h r o u g h to the v a c u u m c a n : one to fac i l i t a te the cables of a pu l ley assembly

and the other was to be used for m o u n t i n g the S Q U I D . T h e 1 K pot p u m p i n g l ine is

l oca ted centra l ly , whi l e the o t h e r three tubes are arranged a p p r o x i m a t e l y in the corners

of an equ i l a te ra l t r i ang le to prov ide m a x i m u m s t a b i l i t y and r i g id i ty . Since the p u m p i n g

18

Chapter 3. Apparatus 19

vacuum can pump

F i g u r e 3.6: Schemat i c view of the cryostat


speed increases as the t e m p e r a t u r e decreases (see Ref . [20], pg . 315), the d iameter of the

p u m p i n g l ine to the 1 K p o t is reduced as it passes through the top p la te of the v a c u u m

c a n . A l s o , to reduce the r a d i a t i v e heat transfer i n t o the 1 K p o t , a r a d i a t i o n block is

p l a c e d ins ide the p u m p i n g l ine at the top p la te of the v a c u u m can . In a d d i t i o n , t w o

d i sk shaped r a d i a t i o n baffles are soldered to the p u m p i n g lines and access tubes between

the top p la te of the cryostat and the t o p plate of the v a c u u m can. These baffles ensure

that the c o o l i n g power of the evapora t ing h e l i u m is ful ly u t i l i z e d , p a r t i c u l a r l y dur ing the

i n i t i a l transfer of h e l i u m i n t o the cryostat . T h e v a c u u m can , w h i c h encloses the 1 K

p o t , is i m m e r s e d in l i q u i d h e l i u m ins ide the outer h e l i u m dewar . T h e comple te cryostat

assembly, i n c l u d i n g the h e l i u m dewar , is suspended from a w o o d frame w i t h sand-fi l led

s u p p o r l s . A s s e m b l i n g a n d d i sas sembl ing of the apparatus is made poss ib le by the use

of i n d i u m O - r i n g seals for the v a c u u m can (see Ref . [20], pg. 328). T h e copper can has

brass flanges at e i ther end w i t h an inner shoulder to allow precise al ignment, and ease of

i n s t a l l a t i o n of t h e i n d i u m w i r e . Pressure is app l ied by twelve screws evenly spaced a round

the o u l e r edge of each flange. In this m a n n e r , adequate v a c u u m seals were consistently

ach ieved .

It was also desireable to have a demountab le feedthrough for a d d i t i o n a l e lectr ica l

connec t ions i n t o the v a c u u m space. T o this end , a cus tomized ''bolt" 1 w i t h an O - r i n g

groove and a ho le t h r o u g h its centre was m a c h i n e d out of brass . T h e necessary wires

are p laced t h r o u g h the hole and sealed inside w i t h epoxy w h i c h has a. coefficient, of

t h e r m a l e x p a n s i o n m a t c h e d to that of brass. T h e bolt is then f i t ted w i t h an i n d i u m O-

r i n g and inserted in to a ho le on the outs ide of the top plate of the v a c u u m can. Pressure

is a p p l i e d by t h e m a t c h i n g nut on the ins ide of the top plate of the v a c u u m can.

^Chapter 3. Apparatus 21

3.2 1 K e l v i n P o t

For efficient and u n i n t e r r u p t e d opera t ion of the cryos ta t , i t is necessary that the 1 K pot

operate in a cont inuous mode . T o thi s e n d . a cont inuous ly o p e r a t i n g ' 2 2 ' 1 K pot was

des igned ' 2 ' ^ and cons t ruc ted .

T h e 1 K pot was m a c h i n e d out of copper w i t h an in ter ior v o l u m e of 1 5 . 3 c m J (see

F i g u r e 3.7). T h e t e m p e r a t u r e of the pot can be m a i n t a i n e d at a p p r o x i m a t e l y 1.5 K by

p u m p i n g on the l i q u i d h e l i u m w i t h a r o t a r y p u m p . L i q u i d h e l i u m is a d m i t t e d into the

1 K pot t h r o u g h the fill l ine , a 6 1 c m length of 0 .12mm i . d . copper-n icke l t u b i n g w o u n d

in to a. 3 m m diameter co i l c o n n e c t i n g the 1 K pot w i t h the l i q u i d h e l i u m b a t h . T h e 4.2 K

end of the fill l ine is soldered in to a copper tube w i t h a s intered si lver filter to ensure

that, the s m a l l d iameter fill l ine remains unclogged.

F o l l o w i n g the procedure o u t l i n e d in Reference [24], the i m p e d a n c e of the fill l ine

was measured and the coo l ing power of the 1 K pot was ca l cu l a ted . T o test the flow

i m p e d a n c e , the set-up shown in F i g u r e 3.8 was used. A t h i n - w a l l e d , low c o n d u c t i v i t y

stainless steel tube is d y n a m i c a l l y p u m p e d on one end whi l e the other e n d , submerged

in l i q u i d h e l i u m , is c losed, except for the sma l l o p e n i n g in the fill l ine tube be ing tested.

In order to ca lcula te the m o l a r flow rate of the e v a p o r a t i n g ga.s (h4p ). the vo lume flow

rate of the gas at the p u m p outlet (V' a) must be measured . T h e n , since 100 pinoles of

gas (at S T P ) occupies a v o l u m e of 2 . 2 4 c m J ,

T h e c r i t i c a l power per u n i t flow ra te of a cont inuous ly o p e r a t i n g 1 K pot is found to

n4i< = v ; * ( lOOpmoles )

( 2 . 24cm 3 )

be I 2 2- 1 a p p r o x i m a t e l y 4 . 5 m W / ] 0 0 p m o l e s / s e c , thus the coo l ing power can be ca lcu la ted

as ( 4 . 5 m W )

* ( n 4 K ) lOOpmoles / sec


pump outer dewar

germanium resistance thermometer'

calibrated germanium resistance thermometer

pick-up coil

solenoid

vacuum can

SQUID

ead shield

cold finger

resistance thermometer

colloid

7-source

moveable source holder

4 H e bath

SQUID mounting box

F i g u r e 3.7: L o w e r cryostat assembly.


p u m p o u t l e t

p r e s s u r e g a u g e

F i g u r e 3.8: Set-up for flow i m p e d a n c e tests.


P « o K n S [ m W ] = (4.5 * 10 4 ) * 7 i 4 K [ m o l e s e e r 1 ]

For the 0 . 1 2 m m i . d . t u b e used for the f i l l l ine , Vg was f o u n d to be 4 . 2 m L / s w h i c h translates

in to a c o o l i n g power of a p p r o x i m a t e l y 8 . 4 m W . T h i s is m o r e t h a n adequate to compensate

for the expected heat l oad .

3.3 Thermometry

V a r i o u s k i n d s of resistance thermometer s are used to m o n i t o r the t e m p e r a t u r e at several

s trategic po int s in the cryos ta t . These i n c l u d e ca rbon resistors a.s wel l as ca l ibra ted

g e r m a n i u m resistors.

In o rder to make measurements at low tempera ture s , a low power auto resistance

br idge was used. T h e resistance br idge is designed to operate accura te ly at very low sensor

d i s s ipa t ions . T h i s a l lows for accurate t e m p e r a t u r e measurements wi thout excessive heat

loads on the system.

A c a r b o n resistor loca ted near the s u p e r c o n d u c t i n g magnet m o n i t o r s 1 lie t empera ture

of the in ter ior of the v a c u u m can . T h i s provides va luab le i n f o r m a t i o n about the state of

the s y s t e m , p a r t i c u l a r l y d u r i n g the i n i t i a l transfer of l i q u i d h e l i u m as i i indicates when

an e q u i l i b r i u m t e m p e r a t u r e of 4.2 K has been reached. A g e r m a n i u m resistor t h e r m a l l y

anchored to the ] K pot m o n i t o r s the per formance of the pot and can be very helpful in

d i a g n o s i n g certain m a l f u n c t i o n s such as blockage of the fill l ine . If this occurs , he l ium

gas can be condensed i m o the 1 K p o t . a l l o w i n g the exper iment to cont inue .

Severa.1 resistors are m o u n t e d on the oven. A c a l i b r a t e d g e r m a n i u m resistor ' " ^ is

used to m o n i t o r the t e m p e r a t u r e of the oven and to record the t e m p e r a t u r e of the sample.

In a d d i t i o n , two c a r b o n resistors are used in c o n j u n c t i o n w i t h the t e m p e r a t u r e control ler :

one as the sensor a n d the o ther as the heater.


W i t h m e a s u r i n g resistors loca ted in these s trategic pos i t ions , the e x p e r i m e n t a l envi

r o n m e n t can be careful ly m o n i t o r e d . T h i s al lows for quick ident i f i ca t ion of any malfunc

t ions w h i c h m a y o c c u r a n d can assist in the i r d iagnos i s .

3.4 S u p e r c o n d u c t i n g M a g n e t s

T h e m a g n e t i c fields requ i red for the exper iment s are generated by a superconduc t ing

so lenoid loca ted ins ide the v a c u u m can.

F o r the first, set of exper iment s , a f i fty t u r n solenoid was m a d e of N b - T i wire

w o u n d on a c y l i n d r i c a l brass former. A coa t ing of Stycast epoxy was a p p l i e d to the coi l

fo l lowed by several layers of p la s t i c tape . T h e field per uni t current p r o d u c e d by the

so lenoid was measured w i t h a H a l l p robe and was found to be 31gaus s / amp.

Ins ide the v a c u u m c a n , the magnet leads are m a d e of N b - T i wire T h i s mater ia l

was chosen because it w o u l d be s u p e r c o n d u c t i n g d u r i n g magnet opera t ion and hence,

w o u l d not c o n t r i b u t e any Jou le heat ing . T h e magnet leads were soldered to the ends

of the so lenoid w i t h 63 /37 al loy soft solder. In a d d i t i o n , a " s u p e r c o n d u c t i n g short " was

p l aced a.cross the solenoid to a l low the magnet, to operate in a. persistent, current mode .

T h i s s u p e r c o n d u c t i n g shor t , or "pers is tent current s w i t c h " , c o u l d be dr iven norma l (ie.

t u r n e d off) by pas s ing a s m a l l current (~- 3 m A ) t h r o u g h a l k Q resistor in t h e r m a l contact

w i t h t h e N b - T i w i r e . T h e Jou le hea t ing in the resistor w o u l d drive a section of the

s u p e r c o n d u c t i n g w i r e n o r m a l , d i s s ipa t ing the current in the so lenoid . T h i s allows the

m a g n e t to be charged or d i scharged as necessary to produce the required field.

F o r the second set of e x p e r i m e n t s , a m o r e homogeneous field was considered desireable

so a longer so lenoid was c o n s t r u c t e d . T h e new so leno id , m e a s u r i n g 8.4cm i n l ength , was

m a d e of 443 turns of t h i n n e r N b - T i wire ' 2 8 ' w o u n d o n a 2 .5cm d iameter former . In thi s

case, however , the former was not brass b u t ra ther a cy l inder of copper fo i l coated w i t h


S tyca s t epoxy . T h e c o i l i t se l f was also coated w i t h a layer of Stycast e p o x y but no plas t ic

t a p e was used . R a t h e r t h a n so lder ing the magnet leads to the ends of the solenoid, the

c o n n e c t i o n was made v i a a screw j u n c t i o n on a n i o b i u m pla te m o u n t e d at the base of

the magnet . A s before, a I k Q resistor was employed as a persistent, current swi tch . T h e

f ie ld per un i t current p r o d u c e d by the solenoid was measured using an R F S Q U I D and

f o u n d to be 3 8 g a u s s / a m p .

3.5 S Q U I D R e a d o u t Sys tem

T h e change of state of the grains is measured u s i n g a S Q U I D ( S u p e r c o n d u c t i n g Q U a n t u m

Interference D e v i c e ) . A c o m m e r c i a l l y avai lable S H E system 330 R F S Q U I D sys tem

is used. T h i s S Q U I D operates at a f requency of 1 9 M H z and has a m a x i m u m frequency

response of 2 0 k H z .

T h e S Q U I D was o r i g i n a l l y m o u n t e d in the largest stainless steel access tube pass ing

t h r o u g h the t o p p la te of the cryostat into the v a c u u m can. W i t h this arrangement , the

S Q U I D sys tem p e r f o r m e d unsat i s fac tor i ly as adequate heat s i n k i n g for the S Q U I D and

i t s s u r r o u n d i n g sh ie ld ing was di f f icul t to achieve. For this reason, a new S Q U I D m o u n t

wa.s des igned.

S ince the S Q U I D is a. very sensi t ive device, capable of detect ing changes in magnet ic

f ie ld < 1 0 - 1 ° g a u s s (see Ref . [32], pg . 1-1), the S Q U I D mount was m a d e of brass and

t h e n p la ted w i t h a layer of lead a n d Rose's m e t a l to f o r m a superconduc t ing shield

against e x t e r n a l m a g n e t i c fields. A c t u a l l y , the S Q U I D m o u n t consists of two isolated

c o m p a r t m e n t s (see F i g u r e 3.9), w h i c h w o u l d allow 7 for exper iments u t i l i z i n g two S O U I D s .

A s wel l as p r o v i d i n g sh ie ld ing a n d a s table m o u n t i n g p lace for the S Q U I D , the new

m o u n t does, i n fact , p r o v i d e adequate heat s i n k i n g since i t is c l amped against the inner


F i g u r e 3.9: S Q U I D m o u n t i n g box . (a) top p l a te ( ins ide v i e w ) and m o u n t i n g bracket : (b)

S Q U I D c o m p a r t m e n t .


w a l l of the copper v a c u u m can w h i c h is submerged i n the 4.2 K l i q u i d h e l i u m b a t h .

A fur ther advantage of the new m o u n t is the r e d u c t i o n of v i b r a t i o n s of the inner

p o r t i o n s of the c ryos ta t ; since the m o u n t is c l a m p e d to the v a c u u m can , it supresses

free m o t i o n of the in ter ior of the cryos ta t . T o i l lu s t ra te th i s fact , the noise s p e c t r u m

of the a p p a r a t u s was recorded before and after i n s t a l l i n g the new m o u n t i n g box . T h e

S Q U I D s igna l was recorded under steady state condi t ions and then fas t-Fourier trans

f o r m e d . T h e r e s u l t i n g power spec t ra for the two cases in an app l ied field of 0 .03T is

shown in F i g u r e 3.10. T h e d i s sappearance of most of the resonance peaks after i n s t a l l i n g

the m o u n t i n g box c lear ly indicates the r e d u c t i o n of v i b r a t i o n a l noise. T h e r e m a i n i n g

resonance peak at 130Hz is bel ieved to be due to v i b r a t i o n of the entire cryostat insert .

N o i s e spectra were measured in various app l ied fields up to 0 .03T but no dependence on

field was observed .

T h e noise figure is defined here as

where Af is the range in frequency over w h i c h the noise is ca l cu la ted and V ' J ( / ) is the

power s p e c t r u m at. the given frequency. T h e noise figure was ca lcu la ted over the frequency

range 150 H z to 1650 H z and found to be N.• = 6.6 x ] 0 ~ 5 V / \ / H Z . T h i s corresponds to

the noise in the preampl i f i e r of the R F S Q U I D .

A n o t h e r i m p o r t a n t aspect of the S Q U I D sys tem is the design of the p i ck-up loop . In

order to m a x i m i z e the flux transfer to the S Q U I D , the i n d u c t a n c e of the p i ck-up loop

-., shou ld m a t c h the i n d u c t a n c e of the S Q U I D ' s s ignal co i l (see Ref . [33], pg . 176). Page

143 of G r o v e r ' " ^ gives Nagaoka ' s f o r m u l a for c a l c u l a t i n g the i n d u c t a n c e of a single layer

c o i l w o u n d on a c y l i n d r i c a l f o r m :

L\fiB] = 0.004n 2a 2bn 2K

where


f 10.0-1

CM «

rr i -o UJ o. CO UJ to O z

8.0

6.0

4.0

2.0 Hi

0.0

(a)

500 1000 1500 2000 FREQUENCY [Hz]

2500 3000

f 10.0

CM L 8.0 H

2 g 6.0 O UJ a 4.0 H CO UJ

6 2 0

' , 1

(b)

11 ' f l mm m 500 1000 1500 2000 2500 3000

FREQUENCY [Hz]

F i g u r e 3.10: Power s p e c t r a of S Q U I D signal for an app l i ed field of 0.03 T . (a) is w i t h o u t

m o u n t i n g b o x in s t a l l ed ; (b) is w i t h m o u n t i n g b o x in s t a l l ed .

Chapter 3. Apparatus 3 0

a = loop r a d i u s [cm]

b = l ength of co i l [cm]

n = w i n d i n g densi ty [ turns /cm]

K = factor t o account for end effects,

t a b u l a t e d as a f u n c t i o n of ( ^ ) -

F o r the S H E sy s tem 330 used , the induc tance of the signal coi l is 2//.H (see Ref. [32],

pg . 1-1 ). For the o r i g i n a l p i c k - u p loop w o u n d of N b - T i wire

a = 0 .25 c m

b = 0 .3 c m

n = 201 u r n s / 0 . 3 c m — 6 6 t u r n s / c m

B u t b c a n be w r i t t e n as ( n u m b e r of t u r n s ) / ( w i n d i n g dens i ty) so Nagaoka ' s formula be

comes

A* L = 0.004 w 2(0.25):--(66 f K

66

F r o m page 145 of G r o v e r ( 3 4 ' , A ' ( ^ f ) = 0.57. N o w p u t t i n g in the constra int that the

i n d u c t a n c e of the p i ck-up loop should m a t c h the i n d u c t a n c e of the s ignal c o i l , one has

2 = 0 .0047T 2 (0 .25 ) -A ' (66 ) (0 .57 )

w h i c h gives N ^ 20 turns . T h u s a 0 .3cm long , 20 t u r n c y l i n d r i c a l p ick-up loop w i t h a

r a d i u s of 0 . 2 5 c m was c o n s t r u c t e d .

A pers i s tent current swi t ch is also p laced i n the p i c k - u p co i l of the S Q U I D . T h i s is

necessary as w i t h o u t i t , any cur rent i n d u c e d in the p i c k - u p loop wdiile the magnet ic field

is b e i n g changed w i l l not decay, caus ing errat ic b e h a v i o u r in the S Q U I D . T h u s , us ing the


pers is tent current s w i t c h , a p o r t i o n of the p ick-up loop can be d r i v e n n o r m a l whi l e the

magnet i c field is be ing changed. T h i s prevents unwanted currents f r o m be ing induced in

the p i c k - u p loop . O n c e the solenoid has the desired pers i s tent current c i r c u l a t i n g , the

current t h r o u g h the s w i t c h in the S Q U I D loop can be t u r n e d off, a l l o w i n g the loop to

become s u p e r c o n d u c t i n g and sensit ive to any further changes i n magnet i c field due to

g ra in flips.

W h e n the s u p e r c o n d u c t i n g magnet was redesigned, a new p i c k - u p loop was also con

s t ruc ted . R a t h e r t h a n us ing a s ingle coi l l oop , a first order g rad iometer was b u i l t . T h e

g rad iometer a l lows o p e r a t i o n of the S Q U I D even whi l e the magnet i c field is be ing changed

since any current i n d u c e d in the top co i l due to a change in the solenoid field w i l l be

cancel led by the current i n d u c e d in the b o t t o m c o i l . H o w e v e r , as the sample is p laced

ins ide o n l y one of the coils of the grad iometer , a change in the magnet ic field due to a

change of state in the sample induces a net current, in the p i c k - u p loop w h i c h is sensed

by the S Q U I D .

T h e g r a d i o m e t e r consists of two 20 t u r n coils w o u n d in o p p o s i n g d irect ions . E a c h coi l

is 0 .22cm long and has a d i ameter of 0 .5cm. T h e coils are made w i t h t h i n N b - T i wire

and are separated by 0 .9cm. A l t h o u g h a pers istent current swi t ch w o u l d no longer be

necessary d u r i n g field changes, one was nevertheless i n c l u d e d incase flux becomes t r a p p e d

in the coils caus ing erra t ic S Q U I D behav iour .

3.0 T e m p e r a t u r e C o n t r o l

T h e t e m p e r a t u r e of the oven is regula ted w i t h a propor t iona l - in tegra l -d i f f e rent i a l ( P I D )

contro l l e r in c o n j u n c t i o n w i t h a constant current D C res is tance br idge . T h e t empera ture

can be r a m p e d up or d o w n a n y w h e r e between 1.5K and 4 . 2 K by a p p l y i n g a, su i tab le

voltage r a m p to the reference i n p u t of the D C resistance br idge . A p a r t i c u l a r t empera ture


can be m a i n t a i n e d t o w i t h i n 2 m K by s i m p l y a p p l y i n g the necessary constant voltage to

the reference i n p u t . T h e a c t u a l vo l tage requi red depends on the p a r t i c u l a r values of the

sensor a n d reference resistors used.

3.7 Data Aquisition

A n in tegra ted software package, L a b t e c h N o t e b o o k is used i n c o n b i n a t i o n w i t h a

personal c o m p u t e r a n d a 12-bit analogue and d ig i t a l I / O card to record exper imenta l

d a t a .

T h e ou tput vo l tage f rom the S Q U I D is d ig i t i zed a n d stored i n one file as b i n a r y integer

d a t a . T h e value of the ca l ibra ted g e r m a n i u m resistor m o u n t e d on the oven is ou tput by

the res is tance br idge as a vol tage one h u n d r e d t imes smal ler t h a n the resistance value.

T h i s vol tage is also d ig i t i zed and stored i n a second file as b inary integer data .

A f t e r the e x p e r i m e n t , a p r o g r a m is used to convert this b i n a r y da ta into a more

useable f o r m . T h e p r o g r a m . H Y S T E R E S I S , has four m a i n funct ions :

1. convert, b i n a r y S Q U I D data into ac tua l vo l tage values

2. convert, b i n a r y res i s tance d a t a i n t o actual reistance values

3. u s ing res is tor c a l i b r a t i o n f o r m u l a , convert resistance

values i n t o t e m p e r a t u r e data

4. s iore S Q U I D voltage d a t a and t empera ture da ta in a s ingle

hie as real A S C I I values .

O n c e th i s d a t a convers ion has been done, p lo t s of S Q U I D s ignal versus tempera ture can

easi ly be made . A l i s t i n g o f H Y S T E R E S I S can be f o u n d i n A p p e n d i x B .

C h a p t e r 4

E x p e r i m e n t s - C o l l o i d S a m p l e

4.1 S a m p l e P r e p a r a t i o n

T h e gra ins used in the c o l l o i d sample were p r o d u c e d by A . K . D r u k i e r by u l t ra son ic dis

i n t e g r a t i o n of m o l t e n 99.99 % pure t i n . S ize selection was achieved by f i l t e r ing the gra ins ,

suspended i n a l coho l , t h r o u g h a series of progress ively finer wi re meshes. U n f o r t u n a t e l y ,

th i s m e t h o d of sor t ing does not p roduce subsets of grains w i t h a nar row (< 5%) size

d i s t r i b u t i o n . O n c e the gra ins had been sorted, they were stored in an i s o p r o p y l a lcohol

s o l u t i o n .

T h e c o l l o i d was made w i t h grains t h a t were repor ted ly 10 urn to 15 um in d iameter .

A p o r t i o n of the grains were placed on a glass s l ide and examined under an o p t i c a l

m i c r o s c o p e at a magn i f i c a t ion of 2 0 0 x . For the sample e x a m i n e d , the size d i s t r i b u t i o n

was found to be 12 um to 16 um i n d iameter . In a d d i t i o n , a p p r o x i m a t e l y 50% of the

gra ins were not spher ica l , but rather somewhat f lat tened e l l ipsoids . A n o t h e r sample of

these grains was e x a m i n e d w i t h a H O R 1 B A C A P A - 7 0 0 par t ic le size d i s t r i b u t i o n ana lyzer .

T h e H O R 1 B A is an a u t o m a t i c par t ic le size d i s t r i b u t i o n ana lyzer based of the p r i n c i p l e of

l i q u i d phase p h o t o s e d i m e n t a t i o n . T h e resu l t ing size d i s t r i b u t i o n is shown in F i g u r e 4.11.

U n f o r t u n a t e l y , s ince sed imenta t ion rates are dependent on p a r t i c l e shape, and a l l gra ins

are n o t spher i ca l , the H O R I B A results are not 100% re l iab le . Nonetheless , th i s size

d i s t r i b u t i o n agrees reasonably wel l w i t h the o p t i c a l e x a m i n a t i o n .

T o make the co l lo id , t i n grains were m i x e d w i t h Stycast epoxy. T h e first m i x t u r e

33

Chapter 4. Experiments - Colloid Sample 34

30

111 -j CL

< CO

u o

z UJ o cc UJ CL

25

2 0 -

15

10-

5 -

i i i i i i i r 4 7 10 13 16 19 22 25 28 31 34 37 40

GRAIN DIAMETER [microns]

F i g u r e 4 . 1 ] : G r a i n size d i s t r i b u t i o n .


cons i s ted of 0.0735g of gra ins a n d 0.734g of epoxy. A sample of th i s m i x t u r e was smeared

on to a glass s l ide a n d a l lowed to dry. It was t h e n e x a m i n e d under a n o p t i c a l microscope.

T h e t i n gra ins were not we l l separated; c l u m p s of several grains o c c u r r e d frequently. In

an a t t e m p t to reduce the amount of c l u m p i n g , 5 um o p t i c a l a l u m i n a was added to the

g lue m i x t u r e . S ince the a l u m i n a is ne i ther m a g n e t i c n o r s u p e r c o n d u c t i n g , it should not

affect the propert ies of the c o l l o i d .

T h e second m i x t u r e consis ted of 0.082g gra ins , 1.954g epoxy and 0.164g a l u m i n a . A

s a m p l e of th i s m i x t u r e was also smeared on to a glass s l ide and e x a m i n e d . T h e a l u m i n a

a p p e a r e d to help disperse the grains ; fewer c l u m p s were observed, a n d se ldom were more

t h a n t w o grains i n v o l v e d . T h i s m i x t u r e was 3.7% (by weight) t i n gra ins .

A t h i r d , s l i ght ly more d i l u t e m i x t u r e (2 .65%, by weight , t i n gra ins) was then made.

It consis ted of 0.066g gra ins , 2.296g epoxy and 0.127g a l u m i n a . In this sample , the t i n

gra ins were fa i r ly wel l d i spersed . O n l y a few c l u m p s were observed , and aga in , the}7

ra re ly consis ted of m o r e t h a n two grains . T h i s t h i r d epoxy m i x t u r e was used to make

the t o r r o i d a l c o l l o i d used in the exper iments

A copper tube wa.s used to prov ide t h e r m a l contact between the co l lo id and the sliver

co ld f inger. T h e t u b e was fabr ica ted out of a 8 m m x 2 5 m m rectangle of 25 pm th ick

99.99% copper fo i l . T h e copper foil was w r a p p e d a r o u n d the co ld finger and covered

w i t h one layer of p la s t i c t ape f o r m i n g a 2 5 m m l o n g , 2 m m in d i ameter c y l i n d r i c a l tube .

T h e t u b e was then weighed a n d a. r i n g of the t h i r d epoxy-gra in m i x t u r e descr ibed above

was a p p l i e d to the t o p 2 m m of the t u b e . Before i t was app l ied to the copper tube , the

e p o x y m i x t u r e was a l lowed to dry for a p p r o x i m a t e l y two hours a n d then m i x e d w rell.

T h i s was done for t w o reasons; the glue becomes very viscous , w h i c h i n h i b i t s the grains

f r o m se t t l ing in the m i x t u r e and keeps the m i x t u r e f r o m r u n n i n g d o w n the outs ide of the

t u b e . A f t e r b e i n g a p p l i e d to the tube , the glue was a l lowed to d r y overn ight .

W i t h the glue c u r e d , the t u b e was aga in we ighed . S u b t r a c t i n g the weight of the tube


before the glue was a p p l i e d , the mass of the co l lo id was f o u n d to be 0.0025g. S ince the

e p o x y m i x t u r e was 2.7% t i n gra ins , 0.0025g of m i x t u r e conta ins 6.63 x 1 0 ~ 5 g of t i n gra ins .

A s s u m i n g an average gra in radius to be 7 /urn and us ing the densi ty of t i n , 7 . 3 g c . m - 3 , the

mass of an average gra in is 1.05 x 1 0 ~ 8 g . Hence the co l lo id s ample conta ins a p p r o x i m a t e l y

6000 grains.

T h e t o r r o i d a l shaped co l lo id measures ~- 2 m m in l e n g t h , w i t h an inner d iameter of

~ 2 m m and a n outer d i ameter of -~ 2 . 8 m m . Its v o l u m e , t h e n , is

KM™ ^ TT(0.14- - 0.1-)(0.2) [cm 3]

- 6 x 10~ 3 [cm 3] (4.22)

T h e co l lo id conta ins 6.63 x 1 0 ~ 5 g of t i n grains w h i c h corresponds to a v o l u m e of

6.63 x 1 0 " 5 [g] V *• or runs 7.3 [gem 3]

9.1 x H I - 6 [cm 3] (4.23)

T h e v o l u m e f i l l i n g factor . fv, is defined as the v o l u m e of grains per unit v o l u m e of c o l l o i d .

In th i s case. t h e n , fy is g iven by

9.1 x n r 6

fv ^ ~ 0.2% (4.24)

In s u m m a r y , the co l lo id used for the exper iments descr ibed later in th i s chapter has

the fo l lowing character i s t i c s :

1. -~ 6000 t in grains w i t h a m e a n rad ius of ~ 7 fim

2. 2 .65% t i n : 92.26%o stycast : 5.09%. a l u m i n a m i x t u r e (by weight)

3. t o r r o i d a l shape: ~~ 2 m m l o n g , 2 m m inner d i ameter , ~- 2 . 8 m m outer d i amete r

4. v o l u m e f i l l ing factor ~ 0.2%.


4.2 C o o l - D o w n P r o c e d u r e

T h e c o o l i n g of the appara tus is c a r r i ed out in two d i s t i n c t stages:

1. p r e c o o l i n g w i t h l i q u i d n i t rogen

2. f i n a l coo l ing w i t h l i q u i d h e l i u m .

T h e a p p a r a t u s is precooled to 77 K by f i l l i n g the outer h e l i u m dewar w i t h l i q u i d n i t rogen .

T o f ac i l i t a te coo l ing of the inner part s of the cryos ta t . a s m a l l amount of h e l i u m exchange

gas is left in s ide the v a c u u m can . A f t e r a p p r o x i m a t e l y one hour , the n i t rogen is removed

f r o m the dewar by pres sur iz ing w i t h air. T h e dewar is then p u m p e d out and flushed w i t h

h e l i u m ga,s several t imes to ensure that a l l of the n i t rogen has been removed . D u r i n g this

ent ire p rocedure , the 1 K pot is kept s l i ght ly over pressured w i t h h e l i u m gas to prevent

any n i t r o g e n f rom ge t t ing in to the f i l l l ine .

O n c e a l l of the n i t rogen has been removed , the l i q u i d h e l i u m transfer can beg in . A s

the h e l i u m level i n the dewar starts to rise, the exchange gas is p u m p e d out of the v a c u u m

can . O n c e the dewar has been filled, the appara tus cools to 4.2 K in a p p r o x i m a t e l y ten

to twenty m i n u t e s . S ince the h e l i u m exchange gas is difficult, to p u m p out when c o l d , the

v a c u u m can m a y need to be "baked o u t " for five to fifteen minutes . T o do thi s , a 10mA

current is passed t h r o u g h a I k f i heater resistor located ins ide the v a c u u m can. T h i s

heats the exchange gas m a k i n g it easier to p u m p out . O n c e the exchange gas has been

removed , p u m p i n g begins on the 1 K pot . D u e to the pressure g rad ient , l i qu id h e l i u m is

d r a w n i n t o the 1 K pot t h r o u g h the fill l ine a n d the reduced vapour pressure cools the

h e l i u m pot and the oven to a p p r o x i m a t e l y 1.5 K .

T h e ent i re coo l ing p r o c e d u r e as o u t l i n e d above requires between t w o and three hours

to comple te .

Chapter 4. Experiments - Colloid Sample 38 t

4.3 E x p e r i m e n t a l R e s u l t s

4.3.1 Hys te res is C u r v e s

In order to charac ter ize the c o l l o i d sample , its superhea t ing- supercoo l ing hysteresis curve

was measured i n various a p p l i e d fields. Such curves were o b t a i n e d by the fo l lowing

sequence of opera t ions :

1. to ensure t h a t a l l of the grains in the co l lo id were s u p e r c o n d u c t i n g , the col lo id was

cooled to T < 1.5 K i n zero app l ied field (B — 0) ,

2. the desired field was a p p l i e d by se t t ing up the appropr i a t e persistent current in the

so leno id .

3. the t e m p e r a t u r e was s lowly swept u p w a r d by a p p l y i n g a slow pos i t ive voltage r a m p

to the reference input of the t empera ture contro l le r . D u r i n g th i s t empera ture r a m p ,

the S Q U I D s ignal a n d t empera ture were recorded ( superhea t ing t r a n s i t i o n ) ,

4. at the end of the t r a n s i t i o n , the S Q U I D s ignal reaches a constant value i n d i c a t i n g

t h a t a l l of the grains in the sample have flipped (become n o r m a l ) . A t th i s po in t ,

the voltage r a m p was reversed a n d the t empera ture was s lowly swept d o w n w a r d

w h i l e c o n t i n u i n g to record both the S Q U I D s ignal and t e m p e r a t u r e ( supercool ing

transi t i o n ) .

5. at the end of the t r a n s i t i o n , the S Q U I D s ignal returns to its o r i g i n a l constant value,

i n d i c a t i n g t h a t al l of the grains have once aga in become s u p e r c o n d u c t i n g .

T w o such hysteresis curves ' 3 ( ' are shown in F i g u r e 4.12. T h e first curve showrs the

narrow^ hysteresis t y p i c a l of a smal l app l i ed field (B = 9.3 x 1 0 _ 4 T ) . T h e second curve

shows how the hysteresis broadens as the app l ied field is increased (B = 9.3 x 1 0 _ 3 T ) .


0.2 0

> -0.2-_l -0.4-< -0.6-z -0.6-CD -0.8-CO -0.8-Q -1-z> -1.2-o -1.2-CO -1.4-

-1.6--1.8-

1.8

• . . • superheating transit ion*

(a) supercooling transitionj

2.2 2.4 2.6 2.8 3 3.2 TEMPERATURE [K]

3.4 3.6 3.8

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 TEMPERATURE [K]

F i g u r e 4.12: Hysteres i s curves for c o l l o i d sample , (a) is i n an a p p l i e d f ield of 9.3 x 10 4 T

a n d (b) is i n an app l ied field of 9.3 x 10"" J T .


T h e shift i n the superheat ing a n d supercoo l ing t r a n s i t i o n t empera ture as the appl ied

f ie ld is increased is a lso apparent, i n F i g u r e 4.12.

D e s p i t e the differences e x h i b i t e d in the t w o hysteresis curves presented, there are also

s i m i l a r i t i e s w h i c h are c o m m o n to a l l of the hysteresis curves w h i c h were recorded. T h e

basic s t ruc ture of the curves, w h i c h can be best observed in h igher app l ied fields, is i n

fact , independent of appl ied f ie ld . T h e curves were measured i n var ious app l ied fields,

f r o m 3.1 x 1 0 _ 4 T to 1.4 x 1 0 ~ 2 T , a n d , i n each case, the s t ruc ture of the curves was as

fo l lows .

T h e hysteresis is a symmetr i c ; the superhea t ing and supercoo l ing t r a n s i t i o n curves are

different shapes . For a. given a p p l i e d field, the superhea t ing t r a n s i t i o n is much narrower

t h a n the s u p e r c o o l i n g t r ans i t i on . T h e superheat ing t r a n s i t i o n starts w i t h a rounded

shoulder fo l lowed by a very steep region and ends w i t h a re la t ive ly sharp shoulder . O n

the other h a n d , the supercool ing t r a n s i t i o n itself is qu i te s y m m e t r i c . It starts and ends

w i t h a b r o a d shoulder , w i t h a re l a t ive ly s lowly changing region between.

T o charac ter ize the co l lo id , the B - T phase d i agram of the co l lo id can be constructed .

T h a t is . the superheat ing and supercoo l ing t r ans i t i on t empera ture s for each appl ied field

are p l o t t e d . F i g u r e 4.13 shows tha t part of the phase d i a g r a m w h i c h has been m a p p e d out

for the co l lo id sample . Since the t rans i t ions themselves are f a i r ly b road , the t rans i t ion

l e m p e r a l l i r e is taken as the t e m p e r a t u r e hal fway t h r o u g h the t r a n s i t i o n as shown in

F i g u r e 4.12.

A s can be seen in F i g u r e 4.12, the w i d t h of the superhea t ing t r a n s i t i o n increases as

the a p p l i e d field increases. F i g u r e 4.14 i l lus tra tes the l inear dependence of the spread in

the s u p e r h e a t i n g t r a n s i t i o n on the app l ied f ie ld. U s i n g the technique of \ 2 - m i n i m i z a t i o n ,

th i s d a t a was fit to the line

(4.25)


2.5 3 TEMPERATURE [K]

3.5

F i g u r e 4.13: B - T phase d i a g r a m of the c o l l o i d s ample . C i r c l e s : superhea t ing t r a n s i t i o n ;

squares : supercoo l ing t r a n s i t i o n .


APPLIED FIELD [mT]

F i g u r e 4.14: W i d t h of the superhea t ing phase t r a n s i t i o n of the co l lo id s ample as a funct ion

of app l i ed f i e ld .


where AT$H is the fu l l w i d t h of the superheat ing t r a n s i t i o n as shown in F i g u r e 4.12. T h e

fact tha t the w i d t h of the t r a n s i t i o n , AT$H, depends l inear ly on the app l i ed field suggests

t h a t the spread in the t r a n s i t i o n is due to the d i s t r i b u t i o n of l o c a l fields. T h u s , i t may

be poss ib le to reduce the t r a n s i t i o n w i d t h by us ing a u n i f o r m d i s t r i b u t i o n of grains .

T h e change in the S Q U I D signal as the co l lo id goes t h r o u g h the s u p e r c o n d u c t i n g to

n o r m a l phase t r a n s i t i o n also depends l i n e a r l y on the app l ied field. T h i s is expected as

the s ignal due to a g r a i n chang ing state is d i r e c t l y p r o p o r t i o n a l to the app l ied field as

discussed in Sect ion 2.2. F i g u r e 4.15 shows the a m p l i t u d e of the s ignal change, for the

S Q U I D o p e r a t i n g in x l m o d e , a.s a funct ion of the app l ied field for one e x p e r i m e n t a l

r u n . F i t t i n g this da ta to a s tra ight l ine , again us ing the \ " - m i n i m i z a t i o n technique , gives

U s i n g th i s e q u a t i o n , a t o t a l s ignal change of 17 .44V is expected for air app l ied field of

0.01 T . C o n s i d e r i n g the co l lo id to be composed of ~ 6000 gra ins , this corresponds to an

average s igna l size of ~ 0 . 3 V per g ra in for the S Q U I D o p e r a t i n g in the x l O O mode .

T h i s va lue is in reasonable agreement w i t h the expected s ignal size per gra in shown in

F i g u r e 2.5 ( r eca l l ing t h a t the co l lo id covers a length of ~ 2 m m ) .

4 . 3 . 2 R a d i a t i o n T e s t

T h e hysteresis curves descr ibed above examine the bu lk propert ies of the c o l l o i d ; the t r a n

s i t ion of the ent ire sample . It. was also des irable to e x a m i n e the t r a n s i t i o n of i n d i v i d u a l

grains i n d u c e d by 7 - r a d i a t i o n f rom a. r ad ioac t ive source l̂ 'K

T h e r a d i o a c t i v e source used was 9 9 m T c , w h i c h has a ha l f life of 6 hours and decays by

emiss ion of 140 k e V 7 - r a y s . T h e " " ' T c . was supp l i ed ' " ^ i n a 0 .1% sal ine s o l u t i o n , w i t h

0.1 cc. of the so lu t ion h a v i n g an a c t i v i t y of a p p r o x i m a t e l y l O m C i . T h e water was evapo

rated f r o m the so lu t ion and the r e m a i n i n g r ad ioac t ive salts were m i x e d w i t h quick d r y i n g

(4.26)


25-|

APPLIED FIELD [mT]

F i g u r e 4.15: T o t a l s ignal change for the s u p e r c o n d u c t i n g to n o r m a l t r a n s i t i o n in the

c o l l o i d sample as a func t ion of app l i ed f i e ld .


e p o x y a n d p l aced i n the source ho lder . T h e a c t i v i t y of the prepared source was approx

i m a t e l y 5 m C i . T h e p r e p a r e d source was then p laced inside the cryostat , a p p r o x i m a t e l y

2 m m f r o m the co l lo id sample .

In order for the 7 - r a y s to f l ip a g r a i n , the g r a i n must be at a t e m p e r a t u r e just below

its t r a n s i t i o n t e m p e r a t u r e . To achieve thi s , the col lo id was prepared i n the fo l lowing

m a n n e r :

1. to ensure that a l l o f the gra ins were o r i g i n a l l y s u p e r c o n d u c t i n g , the col lo id was

cooled to T < 1 .5K i n zero app l i ed field (B = 0).

2. the des ired field was then a p p l i e d by se t t ing up the necessary persistent current in

the so leno id ,

3. the t e m p e r a t u r e was then increased u n t i l the superheat ing t r a n s i t i o n of the co l lo id

began , and there i t was he ld constant .

At th i s p o i n t , some of the gra ins have a l ready flipped i n t o the n o r m a l state a n d ,

therefore , axe insens i t ive to the r a d i a t i o n . A f r ac t ion of the r e m a i n i n g gra ins , however,

are at a t e m p e r a t u r e ju s t below the i r t r a n s i t i o n tempera ture and s h o u l d , therefore, be

sens i t ive to the r a d i a t i o n .

W i t h the co l lo id p r e p a r e d in such a. m a n n e r , the S Q U I D s ignal was recorded and the

r e s u l t i n g s ignal is shown in F igure 4.16. M o s t of the step sizes are in the range 0.37V

to 0 . 5 3 V . For an a p p l i e d field of 0.01 T ra ther t h a n 0 .014T, this w o u l d correspond to

s igna l sizes in the range 0 . 2 6 V to 0 . 3 8 V . So a.gain, the s ignal size for a single grain f l ip

is consistent w i t h the expec ted value shown in F i g u r e 2.5. T h e anomalous ly large steps

are a t t r i b u t e d to two gra ins f l ipp ing s imul taneous ly .

To c o n f i r m that the observed p h e n o m e n a were indeed gra in flips due to the 7 - r a y s .

t w o tests were p e r f o r m e d . F i r s t l y , the 7 - s o u r c e was moved away f rom the co l lo id sample .


Figure 4.16: (a) SQUID signal showing single grain flips from the superheated colloid under irradiation of HOkeV 7 - rays . The applied field is 0 .014T and the temperature is 3 . 0 9 K . (b) Position in the superheating transition where the colloid was prepared for measurement shown in (a).


A s e x p e c t e d , th i s d ra s t i c a l ly reduced the number of g ra in fl ips observed. Secondly, the

exper iment was repeated the f o l l o w i n g day, after four half-l ives of the 7 - s o u r c e , and again,

the n u m b e r of g r a i n flips was great ly reduced .

It shou ld be n o t e d that a l t h o u g h the energy of the emi t ted 7-rays is 140keV, typ ica l ly ,

o n l y 10-20keV is depos i ted i n a 7 fim r ad ius t i n g ra in ' 3 ^ .

4 .3.3 R a d i a t i o n H a r d n e s s

T o invest igate the r a d i a t i o n hardness of the co l lo id sample, the hysteresis curves were

measured at var ious app l ied fields (us ing the procedure descr ibed in Sect ion 4.3.1) b o t h

before and after i r r a d i a t i n g t h e co l lo id sample w i t h h i g h doses of 7 - r a y s

A f t e r m e a s u r i n g the hysteresis curves of the c o l l o i d for var ious app l ied fields, the

s a m p l e was i r r a d i a t e d w i t h S . 3 M r a d of 7 - r a d i a t i o n by p l a c i n g the sample in a ^ C o

b o m b for 2S0 hours . T h e hysteresis curves were then remeasured and the sample w7as

rep laced in the b U C o b o m b for a further 336 hours , b r i n g i n g the t o t a l r a d i a t i o n dose up

to 2 0 M r a d . T h e hysteresis curves were t h e n , once aga in , remeasured.

T h e i r r a d i a t i o n p r o d u c e d no s ignif icant change in the propert ies of the co l lo id . T h e

s u p e r h e a t i n g t r a n s i t i o n t e m p e r a t u r e rema ined the same a n d , i n fact, the shape of the

ent i re s u p e r h e a t i n g t r a n s i t i o n curve was unchanged . F i g u r e 4.17 shows the superheat ing

t r a n s i t i o n curve for an a p p l i e d field of 9.3 x 1 0 " 3 T before i r r a d i a t i o n , after S . 3 M r a d i r ra

d i a t i o n and after 20 M r ad i r r a d i a t i o n . S i m i l a r curves were measured for var ious appl ied

fields u p to 0.01 4 T , and in a l l cases, the curves measured after the i r r ad ia t ions complete ly

"> over l apped those measured before the i r r a d i a t i o n s . T h u s the co l lo id has been shown to

be r a d i a t i o n h a r d up to 2 0 M r a d .


2-i

F i g u r e 4.17: S u p e r h e a t i n g t r a n s i t i o n curve for the co l lo id sample i n an app l ied field of 9.3 x 10"~ 3 T. C i r c l e : before 7 - r a d i a t i o n ; square: after 8.3 M r a d 7 - r a d i a t i o n ; t r i ang le : after 2 0 M r a d 7 - r a d i a t i o n .

C h a p t e r 5

E x p e r i m e n t s - P l a n a r A r r a y s

In a n a t t e m p t t o reduce the w i d t h of the superheat ing t r a n s i t i o n , a new type of sample

was deve loped . R a t h e r t h a n us ing a co l lo id cons i s t ing of a r a n d o m d i s t r i b u t i o n of v a r y i n g

s ized t in gra ins , i t was decided to invest igate a u n i f o r m , p l anar array of t i n squares. Since

i n d i u m has proper t ie s s i m i l a r to those of t i n (see Tab le 5.1), i t too was considered as a

f a b r i c a t i o n m a t e r i a l . T h e p repara t ion of such samples and the exper iments per formed

w i t h t h e m w i l l be discussed in this chapter .

5.1 F i l m T h i c k n e s s

Before samples could be made , the m i n i m u m thickness of the meta l f i l m had to be

d e t e r m i n e d . In order for the s u p e r c o n d u c t i n g - n o r m a l t r a n s i t i o n to remain first- order ,

the thickness of the f i l m , </, must satisfy ^~ ] >

w h e r e \(T) is the t e m p e r a t u r e dependent penet ra t ion d e p t h . T h e t empera ture depen

dence of the p e n e t r a t i o n depth is g iven by

d > \/5 X(T) (5.27)

MT) = A 0

(5.28) {1 - (T/Tc)4y/-

U s i n g A 0 a n d Tc f rom Tab le 5.1, one can ca lcula te the necessary thickness for a first

order t r a n s i t i o n . For an opera t ing t emp er a t u r e of 3.0 K ,

dt,n > 0.15 um

49

Chapter 5. Experiments - Planar Arrays

i

50

M A T E R I A L

71-

( K ) T-me'.t ( ° C )

P ( g e m - 3 )

Bo ( T )

AL (0 ) (nm)

Ao (nm)

-\ theory

(nm) ( n m )

| t i n 3.72 232 7.28 0.0303 3 4 . 0 ( 2 ) 51.0« b> 54.0 ( c ) 230 { d )

| i n d i u m 3.41 157 7.30 0.0283 15.5 ( f> 64 .0 ' f ) 2 0 0 ( 5 )

a l u m i n u m 1.18 660 2.70 0.0104 1 6 . 0 ( c ' 49.0 i h ) 4 8 . 0 ( c ) 1 6 0 0 ( a )

T a b l e 5.1: T a b l e of some relevant phys i ca l propert ies of three m e t a l l i c superconductors . A^(0 ) is the theore t ica l L o n d o n p e n e t r a t i o n d e p t h w h i l e X Q ^ ' 1 is the e x p e r i m e n t a l l y observed p e n e t r a t i o n d e p t h .

( a ' R . D . P a r k s , E d i t o r , Superconductivity, M a r c e l D e k k e r . Inc. (1969) page 174. ( H T . J . G r e y t a k and J . H . W e r n i c k , J . P h y s . C h e m . Sol ids 25, 535 (1964). ( c ) J . B a r d e e n . P h y s i c a 24, 548 (1958). { i ] J . B u r g e r , G . Deut scher , E . G u y o n and A . M a r t i n e t . P h y s . R e v . A137, 853 (1965). u'< J . Feder and D . S . M c L a c h l a n . P h y s . R e v . 177, 763 (1969). ( / ) J . M . L o c k . P r o c . R o y . Soc. A20S, 391 (1951).

E . G u y o n , F . M e u n i e r and E . S . T h o m p s o n . P h y s . R e v . 156, 452 (1967). i h ) T . F a b e r and A . B . P i p p a r d . P r o c . Roy . Soc. A231, 336 (1955).

Chapter 5. Experiments - Planar Arrays 51

d-indium > 0.23 fim

So to ensure a first order t r a n s i t i o n , the film th ickness should be no less t h a n 0.25 fim .

In a d d i t i o n , for size effects to be u n i m p o r t a n t ^\ d must satisfy

d > 2 . 0 4 £ ( T ) (5.29)

where £(T) is the t e m p e r a t u r e dependent corre la t ion l e n g t h . F r o m Ref. [43]

p r o v i d e d T is close to Tc.

U s i n g £o f r o m Tab le 5.1 a n d an o p e r a t i n g t e m p e r a t u r e of 3.0 K ,

d-iin > 0.62 fim

di«<iivm > 0.74 fim

So a film thickness of 1 fim should m a k e size effects u n i m p o r t a n t , as we l l as ensuring

a first order t r a n s i t i o n .

5 .2 S a m p l e P r e p a r a t i o n

lowever, F o l l o w i n g P e l l a n et. a l . I44', glass was o r i g i n a l l y chosen as a subs tra te m a t e r i a l . He

di f f icul t ies i n c u t t i n g the glass in to pieces smal l enough to fit i n t o the p i c k - u p coi l made

tha t p a r t i c u l a r choice of subs t ra te m a t e r i a l i n a p p r o p r i a t e .

Ins tead , 50 fim. th i ck m y l a r was used as the subs t ra te m a t e r i a l . Since the m y l a r cou ld

be cut w i t h scissors or a r azor b lade , samples cou ld eas i ly be m a d e any size or shape.

O n e piece of m y l a r , — 8 0 c m 2 , was coated w i t h a 1 fim t h i c k layer of 99.999% pure

t i n . A second piece of m y l a r , a p p r o x i m a t e l y the same size, was coated w i t h a 1 fim th ick


layer of 99 .99% pure i n d i u m . B o t h f i lms were v a c u u m depos i ted at r o o m t e m p e r a t u r e at

a pressure of ~ 5 x 1 0 - 6 t o r r .

T h e squares were o b t a i n e d by s t andard photores i s t techniques ; i n s u l a t i o n through a

photores i s t m a s k fol lowed b y chemica l e tching . A negat ive photores i s t , K o d a k T h i n F i l m

Photore s i s t ( K T F R ) , sens i t ive to U V - l i g h t , was used. W i t h a negat ive resist , the exposed

areas r e m a i n after d e v e l o p i n g so a s t a n d a r d mesh cou ld be used as the photomask . A

flat mesh , 3 m m i n d i a m e t e r , measur ing 83 pm between p ixe l centres was used.

T h e K T F R was d i l u t e d w i t h t h i n n e r in the a p p r o x i m a t e p ropor t ions 2 parts K T F R

t o 1 part t h i n n e r . Before a p p l y i n g the resist to a s t r ip of the meta l i zed m y l a r , the meta l

f i l m was d i p p e d in a d i l u t e so lut ion of h y d r o c h l o r i c ac id , r insed in water and al lowed to

d r y : the resist adheres best to a s l ight ly ac idic surface. A few drops of the d i lu ted K T F R

s o l u t i o n was spread on t h e meta l f i l m . T h e film was then suspended ver t i ca l ly and the

resist was a l lowed to dry for ~ 15 minutes . Before expos ing the photores i s t , the film was

b a k e d at 82 ° C to 99 ° C for - 10 minutes .

At th i s p o i n t , the s t r i p of meta l l i zed m y l a r coated w i t h a th in {~~ urns) layer of

photores i s t was cut i n t o s m a l l (--• 3 m m x — 5 m m ) pieces. E a c h piece was then processed

as fo l lows. T h e gr id was p l aced on top of the photores i s t and pressure was appl ied w i t h a.

q u a r t z flat w h i c h al lows the t ransmiss ion of U V - l i g h t . T h e photores is t was then exposed

for 45 seconds w i t h a 4 watt xenon gas U V - l i g h t . F i n a l l y , the resist was developed for

t w o m i n u t e s , r insed in water and a l lowed to dry.

W i t h the array of photores i s t squares p r o t e c t i n g the meta l be low, the undes i red m e t a l

between the squares c o u l d be chemica l ly etched away. T h e etchant used was a m i x t u r e

of 1 part concent ra ted (37%) h y d r o c h l o r i c ac id to 1 part water . T h e t i n samples were

s u b m e r g e d i n t h e etchant for ~ 3 hours w h i l e the i n d i u m samples were etched for ~ 4\

hours . W i t h the e t c h i n g comple te , the photores is t was removed by gent ly r u b b i n g the

s a m p l e w i t h a cot ton swab w r a p p e d w i t h t issue a n d soaked w i t h photores i s t s t r ipper


( d i c h l o r o m e t h a n e ) .

T h e r e s u l t i n g tin sample consis ted of ~ 700 tin squares, 35 ± 2pm x 35 ± 2pm,

separa ted b y 48 ± 2pm. T h e i n d i u m sample also consis ted of ~ 700 squares, but each

square was 56 ± 2pm x 56 ± 2pm separated by 27 ± 2pm.

A s w i t h the c o l l o i d sample , a copper t u b e was used to p rov ide t h e r m a l contact between

the s a m p l e and the s i lver co ld f inger. T h e tube was f abr ica ted f r o m a 8 m m x 4 0 m m

rectangle of 25 pm t h i c k copper f o i l w r a p p e d around the co ld finger and secured w i t h a

r i n g of t a p e f o r m i n g a 4 0 m m l o n g copper t u b e . For added strength a n d r ig id i ty , the tube

j o i n t was coated w i t h a layer of epoxy.

A t one end , a p p r o x i m a t e l y 3 m m of the t u b e was flattened and bent at r ight angles

to the ax i s of the c y l i n d e r . T h i s p r o v i d e d a h o r i z o n t a l p l a t f o r m for m o u n t i n g the planar

samples . S i l i cone grease was used to affix the sample to this p l a t f o r m .

5.3 Indium Array - Experimental Results

5.3.1 Hysteresis Curves

F o l l o w i n g the p rocedure o u t l i n e d in Sect ion 4.3.1, the hysteresis curves of the i n d i u m

array were measured . In zero app l i ed field, w i t h only the earth's magnet ic field present,

the s a m p l e e x h i b i t s comple te M i e s s n e r effect: a l l of the flux is expe l led whi l e the sample is

s u p e r c o n d u c t i n g . T h i s is evident, in the first plot shown i n F igure 5.18 as the t o t a l signal

change for the s u p e r h e a t i n g t r a n s i t i o n is the same size as the to ta l s ignal change for the

s u p e r c o o l i n g t r a n s i t i o n . However , as the a p p l i e d field is increased, on ly par t i a l Meis sner

effect is observed; when the sample re turns to the s u p e r c o n d u c t i n g state, some flux

r e m a i n s t r a p p e d i n the sample . T h e t o t a l s ignal change for the supercool ing t rans i t ion

is m u c h smal ler t h a n the t o t a l s ignal change for the superhea t ing t r a n s i t i o n and the

difference corresponds to the amount of flux w h i c h has been t r a p p e d in the sample . T h i s


CD CO

g ZD o CO

2.5 3 TEMPERATURE [K]

^ 0

< z CD CO

g ZD O CO

-1

•2

3 H

-4 2.6

o o o o o o o o o o o o o n n n n n

'I

OOODOO D D O D D°no D o B

= = •

ii? 8 B B i l i i . o

(b)

O D O D D O O D O C

2.8 3 3.2 TEMPERATURE [K]

3.4 3.6

F i g u r e 5.18: Hys teres i s curves for the i n d i u m array, (a) is in the earth's magnet ic field a n d (b) is in an a p p l i e d field of 1.6x 1 ( T 3 T . C i rc l e s : t empera ture increas ing ( superheat ing t r a n s i t i o n ) ; squares: t e m p e r a t u r e decreas ing ( supercoo l ing t r a n s i t i o n ) .


p h e n o m e n o n is i l l u s t r a t e d in the second plot s h o w n i n F i g u r e 5.18.

5.3.2 T h e r m a l l y A c t i v a t e d F l u x m o t i o n

M o v e m e n t of th i s t r a p p e d f lux can be t h e r m a l l y ac t iva ted . T o demons t ra te this , f lux was

t r a p p e d i n the sample by a p p l y i n g a magnet ic f ie ld whi le the sample was ma in ta ined at a

low t e m p e r a t u r e (T < 1 .5K) . T h e m a g n e t i c f ield was then removed a n d the temperature

was increased . T h e cont inuous change in the S Q U I D s ignal as the tempera ture was

increased was due to the releas ing of the f lux w h i c h had been t r a p p e d i n the sample.

In an a t t empt to induce the s u p e r c o n d u c t i n g to n o r m a l t r a n s i t i o n in i n d i v i d u a l

squares, a r ad ioac t ive ~ 4 1 A m source was p laced inside the cryostat , a few mi l l imetre s

away f r o m the sample . A shut ter , w h i c h cou ld be operated ex terna l ly v i a a pul ley sys

t e m , was used to block the 5 . 5 M e V a-pa.rticles e m i t t e d f r o m the 2 4 1 A m u n t i l the r ad ia t ion

was r e q u i r e d . A field was a p p l i e d w i t h the sample cold (T < 1 .5K) a n d the tempera

ture was t h e n raised u n t i l the phase t r a n s i t i o n s tar ted . T h e t empera ture was then held

cons tant a n d the shutter was opened a l l o w i n g the o-part ic les to hit the sample. T h e

cont inuous change in the S Q U I D o u t p u l s ignal due to the l o c a l heat ing produced by the

o-par t i c le s was i n d i c a t i v e of t h e r m a l l y ac t ivated flux creep rather t h a n discrete transi

t ions in i n d i v i d u a l squares.

5.3.3 D i s c u s s i o n

F o r a l l in tents and purposes , the a r ray of i n d i u m squares behaved l ike a type-II supercon-

' d u c t o r in the m i x e d state regime. T h e r e are several poss ible reasons for such behaviour .

F i r s t l y , the ragged n a t u r e of the edges of the squares, p a r t i c u l a r l y regions w h i c h have

been etched very t h i n , most l i k e l y a l low flux p e n e t r a t i o n and t r a p p i n g . Secondly, the

squares are very close together a n d i n some regions , sma l l amounts of i n d i u m may have

been left between the squares, aga in present ing areas where flux p e n e t r a t i o n may occur .


T h i r d l y , there m a y b e some defects in the evapora ted squares themselves w h i c h act as

f lux p i n n i n g sites.

T o t r y to overcome some of these prob lems , the i n d i u m sample was removed f r o m the

cryos ta t a n d heated ( in an argon a tmosphere to prevent unnecessary o x i d a t i o n ) above the

m e l t i n g t e m p e r a t u r e of i n d i u m . It was h o p e d that by m e l t i n g the i n d i u m , any defects in

the film w o u l d be removed and the edges w o u l d become more r o u n d e d , poss ib ly reduc ing

the flux p e n e t r a t i o n . T h e sample was a l lowed to cool a n d was e x a m i n e d under a n opt ica l

m i c r o s c o p e . N o m a j o r change in s t ruc ture was v i s ib le , a l t h o u g h the surface of each square

d i d a p p e a r to be somewhat m o r e rounded t h a n before i t was m e l t e d .

T h e sample was replaced in the cryostat and the exper iment s were repeated . Unfor

tuna te ly , there were no changes in any of the results .

5.4 T i n a r r a y - E x p e r i m e n t a l R e s u l t s

M e l t i n g the i n d i u m sample had no effect on i ts character i s t ic s . However , m e l t i n g the

sample d i d n o t h i n g to change the spac ing between the squares nor to clean the areas

between the squares. In the t i n sample , the squares where m u c h m o r e separated and the

regions between the squares were very c lean. T h e edges, however, were s t i l l very ragged.

Nevertheles s , the t in sample was m o u n t e d in the c ryos ta t and t r i e d .

T h e hysteresis curves were measured a n d , as w i t h the i n d i u m sample , the fu l l Mei s sner

effect was on ly observed in the earth's magnet ic field. For higher app l ied fields, on ly

p a r t i a l M e i s s n e r effect was seen. F i g u r e 5.19 i l lus tra tes these two cases.

O n c e again the t r a p p e d flux c o u l d be t h e r m a l l y a c t i va ted by b o t h a direct t empera ture

increase of the ent i re sample and t h r o u g h l o c a l h e a t i n g due to in terac t ions w i t h the « -

par t i c l e s . Di scre te steps i n the S Q U I D s igna l due to i n d i v i d u a l t i n squares changing

state were not observed. So , l ike the i n d i u m array, the t i n array behaved l ike a type-II


F i g u r e 5.19: Hysteres i s curves for t i n array, (a) is i n the earth ' s m a g n e t i c field a n d (b) is i n an a p p l i e d field of 3.8 x l ( r 3 T . C i r c l e s : t e m p e r a t u r e increas ing ( superhea t ing t r a n s i t i o n ) ; squares: t e m p e r a t u r e decreas ing ( supercoo l ing t r a n s i t i o n ) .

Chapter 5. Experiments - Planar Arrays

s u p e r c o n d u c t o r i n the m i x e d state regime.

C h a p t e r 6

C o n c l u s i o n s

A p u m p e d 4 H e cryos ta t w i t h an R F - S Q U I D readout sy s tem w i t h low v i b r a t i o n a l noise has

been successful ly cons t ruc ted . T h e cryostat has been designed i n such a way as to a l low

m o d i f i c a t i o n s to the s u p e r c o n d u c t i n g so lenoid , the S Q U I D p i c k - u p c o i l , the rad ioact ive

source ho lder or the sample ho lder to be m a d e w i t h re la t ive ease.

U s i n g this c ryos ta t , a. t o r r o i d a l shaped col lo id cons i s t ing of 7 fim. radius t i n grains

i m b e d d e d in epoxy has been s tud ied . T h e superbea t ing- supercoo l ing hysteresis curves of

the c o l l o i d have been measured and the col lo id ' s B - T phase d i a g r a m has been m a p p e d

out for a p p l i e d fields up to 1.4 x ] 0 ~ 2 T . T h e l inear dependence of b o t h the height and

w i d t h of the superhea t ing t r a n s i t i o n on the appl ied field has been demons t ra ted . T h e

height of the t r a n s i t i o n is expec ted to depend l inear ly on the a p p l i e d field since the signal

f r o m each grain is direct!} ' p r o p o r t i o n a l to the app l ied field as discussed in Section 2.2.

T h e l i n e a r re la t ion between the w i d t h of the superheated t r ans i t i on and the appl ied field

suggests tha t the spread in the t r a n s i t i o n is clue to the d i s t r i b u t i o n of local fields caused

by the d iarnagnet ic interact ions between the superconduc t ing gra ins .

T h e s u p e r c o n d u c t i n g to n o r m a l phase t r ans i t i on in i n d i v i d u a l grains in the co l lo id

was observed exper imenta l ly . B y p repar ing the col lo id in a meta s tab le superheated state.

140keV 7 - r a y s e m i t t e d f rom a 9 S , , ; T c source could be used to induce the phase t r ans i t ion

i n i n d i v i d u a l gra ins . Di scre te steps in the o u t p u t s igna l of the S Q U I D i n d i c a t e d such

t r a n s i t i o n s . T h e observed s ignal size was i n reasonable agreement w i t h the ca lcu la ted

values .

59

Chapter 6. Conclusions 60

F i n a l l y , the r a d i a t i o n hardness of the co l lo id was invest igated . T h e co l lo id was ex

posed to large doses (up t o 2 0 M r a d ) of 7 - r a d i a t i o n and the superhea t ing- supercoo l ing

hysteres is curves were remeasured . These curves comple te ly over l apped the hysteresis

curves measured p r i o r to the i r r a d i a t i o n , thus d e m o n s t r a t i n g the r a d i a t i o n hardness of

the c o l l o i d u p t o 2 0 M r a d .

T o t ry to reduce the w i d t h of the superhea t ing t r a n s i t i o n , a new t y p e of sample was

deve loped and inve s t i ga ted . A p l anar array of 1 pm th i ck i n d i u m squares and a s i m i l a r

a r r a y of 1 pm t h i c k t i n squares were f abr i ca ted . T h e hysteresis curves for both arrays

were measured , b u t i n app l i ed magnet i c fields above 5 x 1 0 ^ 5 T , the samples e x h i b i t e d

f lux p e n e t r a t i o n and t r a p p i n g . O n l y in the earth 's magnet ic f ie ld was ful l Meis sner effect

observed . M o t i o n of the t r a p p e d flux c o u l d be ac t iva ted t h e r m a l l y , e i ther by heat ing the

e n t i r e sample or t h r o u g h loca l hea t ing caused by interac t ions w i t h 5 . 5 M e Y o-part ic les

e m i t t e d f rom a. 2 4 1 A m source. N o discrete t r ans i t ions in i n d i v i d u a l squares were observed

i n e i ther s ample .

A p p e n d i x A

F L U X P r o g r a m L is t ing 1 C FLUX 2 C a program to calculate the average flux through one 3 C loop of a 20 turn, 2.5 mm radius pick-up c o i l starting 4 C at z = 0, due to a superconducting grain located at 5 C (r,z) inside the c o i l and then convert this to the 6 C output signal recorded by the SQUID. 7 C 8 REAL*8 TWOPI, RADIUS, FLUX, SUM, SIGNAL 9 REAL*8 GRSIZE, A, BEXT, FLXFAC, PHIO 10 REAL*8 BLIM, ULIM, GFUN, AUXIN 11 DIMENSION RFLUX(1:10,0:19) 12 REAL*8 RFLUX 13 DIMENSION TEMP(1:10) 14 REAL*8 TEMP 15 REAL RAD, HEIGHT 16 INTEGER R 17 COMMON RADIUS, Rl, Zl 18 C 19 C 20 C VARIABLE DEFINITIONS: 21 C 22 C RADIUS: radius of the pick-up c o i l [mm] 23 C GRSIZE: radius of the grain [m] 24 C PHIO: flux quanta [Wb] 25 C BEXT: applied external f i e l d IT] 26 C A: factor to convert integral to flux in PHIO's 27 C FLXFAC: flux transfer factor of SQUID system 28 C RAD: r a d i a l position of grain in c o i l [mm] 29 C HEIGHT: v e r t i c a l position of grain in c o i l [mm] 30 C 31 C 32 C 33 C i n i t i a l i z e constants - — 34 C 35 RADIUS = 2.5D0 36 TWOPI = 6.283185307 37 GRSIZE = 7.0D-6 38 PHIO = 2.07D-15 39 BEXT = 1.00D-2 40 A = (0.5 * BEXT * (GRSIZE**3) * 1000) / PHIO 41 c (factor of 1000 since loop radius in mm) 42 FLXFAC •= 1.0D-1 43 C 44 C write t i t l e for output 45 C 46 WRITE(6,10) RADIUS, GRSIZE, BEXT 47 10 FORMAT(':'//'SQUID signal due to superconducting grain', 48 + ' at ( r , 2 ) . (SQUID operating in xlOO mode)'/ 49 + 'loop radius = ',1PG8.2,' mm; grain radius = ',1PG8.2, 50 + ' m; f i e l d = MPG8.2," T' // 51 + ' r<mm) z(mm) SQUID signal(V) '/ ) 52 C 53 C calculate flux through loop due to grain at 54 C ( r l , z l ) r e l a t i v e to the centre of the loop 55 C 56 Rl = 1.00 57 DO 100, I « 1,5 58 Z l = 0.00

61

Appendix A. FLUX Program Listing 62

59 DO 200, J = 0,19 60 FLUX = DDBLGS(0.0D0,TWOPI,48,48) 61 C FLUX contains value of double integral (flux through loi 62 RFLUX (I, J) •= FLUX 63 C RFLUX contains value of flux in arbit r a r y units 64 C (multiply by A to get flux in PHIO's) 65 21 = 21 + 0.15789 66 C WRITE(7,20)RFLUX(I,J) 67 C 20 F0RMATUPG16.6) 68 200 CONTINUE 69 Rl = Rl + 0.10 70 100 CONTINUE 71 C 72 C — - calculate SQUID signal for a grain at (RAD,HEIGHT) 73 C — - r e l a t i v e to the bottom centre of the pick-up c o i l 74 C

- r e l a t i v e to the bottom centre of the pick-up c o i l

75 DO 300, R = 1,5 76 RAD = 0.90 + (R * 0.10) 77 WRITE(6,310) RAD 78 310 FORMAT(1F10.3) 79 DO 350, I = 0,9 80 HEIGHT = I * 0.15789 81 K = 19 - I 82 SUM = 0.0D0 83 C sum contributions from each loop in the c o i l due to 84 C grain at (R,J) r e l a t i v e to the centre of each loop 85 DO 400, J = 0,1 86 SUM = SUM + RFLUX(R,J) 87 400 CONTINUE 88 DO 450, J = 1,K 89 SUM = SUM + RFLUX(R,J) 90 450 CONTINUE 91 SUM = SUM / 20.0D0 92 C convert to flux in PHIO's 93 FLUX = A * SUM 94 C take into account flux transfer factor of SQUID system 95 FLUX = FLXFAC * FLUX 96 C 2 vol t s SQUID output per PHI0 input in xlOO mode 97 . SIGNAL = 2.0 * FLUX 98 WRITE(6,351)HEIGHT, SIGNAL 99 351 FORMAT(1 OX, 1F10.3,5X,1PG16.7) 100 C since the c o i l i s symmetric about i t s midpoint, 101 C save values for z > half c o i l length 102 J - 10 - I 103 TEMP(J) = SIGNAL 104 350 CONTINUE 105 C p r i n t out values for z > half c o i l length 106 DO 320, J = 1, 10 107 HEIGHT = 1.42101 + (J * 0.15789) 108 WRITE(6,351) HEIGHT, TEMP(J) 109 320 CONTINUE 110 300 CONTINUE 111 C 112 STOP 113 END 114 C 115 C define a u x i l i a r y functions for caluclating integral 116 C 117 FUNCTION BLIM(Y) 118 COMMON RADIUS, Rl, 21 119 REAL*8 Y, BLIM 120 BLIM ' 0.0D0 121 RETURN 122 END 123 c

Appendix A. FLUX Program Listing 63

124 FUNCTION ULIM(Y) 125 COMMON RADIUS, Rl, Zl 126 REAL*8 Y, ULIM, RADIUS 127 ULIM = 1.0DO 128 RETURN 129 END 130 C 131 FUNCTION GFUN(Y) 132 REAL*8 Y, GFUN 133 GFUN = 1.0D0 134 RETURN 135 END 136 C 137 FUNCTION AUXIN(X,Y) 138 COMMON RADIUS, Rl, Zl 139 REAL*8 X, Y, A, B, C, AUXIN, RADIUS 140 A = ((RADIUS/X)**2)*(DCOS(Y)**2) 141 B = ((RADIUS * DSIN(Y) / X) - Rl)**2 142 C = Zl**2 143 AUXIN = ((A+B-2*C)*(RADIUS**2))/((X**3)*((A+B+C)**2.5)) 144 RETURN 145 END

A p p e n d i x B

H Y S T E R E S I S P r o g r a m L i s t i n g 1 program hysteresis; 2 3 {*** program to prepare plot f i les for the hysteresis ***) 4 {*** curves from data collected during grain experiment ***} 5 6 const 7 MAXLENGTH = 32000; {maximum array size) 8 ZL = 1.37929663984; {constants for temperature conversion) 9 ZU = 2.34213138587;

10 ZUMZL = 0.96283474603; 11 TOVOLTS = 0.004882812; {(20/4096) for voltage conversion) 12 PI = 3.1415926535; 13 14 type 15 arraypointer = 'datatype; 16 datatype = record 17 data : array [1..MAXLENGTH] of integer; 18 end; 19 filetype = f i l e of integer; 20 21 var 22 filename, inlfilename, in2filename, outfilename : string[32]; 23 i n l f i l e , in2file : f i l e of integer; 24 outfile : text; 25 longtemp, temp, longsquid, squid : arraypointer; 26 datalength, numcompress, compindex : integer; 27 j , k : integer; 28 coeff : array [0..7] of real; 29 30 procedure getdata(signal:arraypointer; var inputfile:filetype); 31 { read in data and convert notebook integer to } 32 { pascal integer ) 33 var 34 sig : integer; 35 begin 36 writeln;writeln (1 reading in data '),-37 for j :» 1 to datalength do 38 begin 39 read(inputfile,sig); 40 sig := sig - 2048; (convert integer types) 41 signal'.data[j] := sig; 42 end; 43 writeln; writelnC data input complete ' ) ; 44 end; 45 46 procedure compress(signal, compact:arraypointer); 47 { compress data ) 48 var 49 sig : integer; 50 begin 51 i f numcompress = 1 then 52 begin 53 for j : • 1 to datalength do 54 compact'.data[j] := signal".data[j]; 55 compindex := datalength; 56 exit; 57 end; 58 k :« 0;

6 4

Appendix B. HYSTERESIS Program Listing 65

59 for j := 1 to datalength do 60 i f j mod numcompress = 0 then 61 begin 62 k k + 1; 63 compact^.data[k] := signal".data [j]; 64 end; 65 compindex := k; 66 end; 67 68 function volts(sig:integer):real; 69 { convert integer data to actual voltage value } 70 begin 71 volts := <sig * TOVOLTS); 72 end; 73 74 procedure initialcoeff ; 75 { in i t ia l ize coefficients necessary to convert ) 76 { voltage to temperature ) 77 begin 78 coefftO] := 3.594318; 79 coeff[1] := -2.873505; 80 coeff[2] := 0.632675; 81 coeff[3] := -0.053796; 82 coeff[4] := -0.003860; 83 coeff[5] := -0.003826; 84 coeff[6] := 0.002662; 85 coeff[7] := -0.000467; 86 end; 87 88 function log(x:real):real; 89 { calculate log base 10 of x ) 90 begin 91 i f x <= 0.0 then 92 wr i te ln( ' * * * * * log(x) not defined for x <= 0 * * « * * • ) 93 else 94 log := 0.434294482 * ln(x); Uog(e) * ln(x)} 95 end; 96 97 function arccos (x:real) :real; 98 { calculate arccos(x) ) 99 var

100 arc : real; 101 begin 102 arc := arctan(sqrt((1/sqr(x)) - 1)); 103 i f x < 0 then 104 arc := PI - arc; 105 arccos := arc; 106 end; 107 108 function temperature (volt:real):real; 109 { convert voltage to temperature } 110 var 111 i : integer; 112 t, x, z, arcosx : real; 113 begin 114 z :<= logivolt * 100.0); 115 X := (<z - ZL) - (ZU - z)> / (ZUMZL); 116 arcosx : ° arccos (x); 117 t := coeff [0]; 118 for i := 1 to 7 do 119 t := t + (coeff [i] * cos(i*arcosx)); 120 temperature := t; 121 end; 122

Appendix B. HYSTERESIS Program Listing 66

123 procedure writeout(xint,yint:arraypointer); 124 ( print out signal vs temperature > 125 var 126 v, x, y : real; 127 begin 128 for k := 1 to compindex do 129 begin 130 v := volts(xint~.data[k]); 131 x := temperature(v); 132 y := volts(yint~.data[k]); 133 writeln(outfile,x:12:7,y:12:7); 134 end 135 end; 136 137 begin (hyster) 138 new(longtemp); 139 new(temp); 140 new(longsquid); 141 new(squid); 142 writeCenter run number for f i l e name (\nb\squid#.prn) ') ; 143 read(filename); writeln; 144 inlfilename := '\nb\temp' + filename + ' . p rn ' ; 145 in2filename := '\nb\squid' + filename + ' . p rn ' ; 146 write('enter output filename (default \123\hys#.prn) ') ; 147 read(outfilename); writeln; 148 i f outfilename » ' ' then 149 outfilename := '\123\hys' + filename + ' .prn' ; 150 assign(inlfile,inlfilename); 151 reset( inlf i le) ; 152 assign(in2file,in2filename); 153 reset(in2file); 154 assign(outfile, outfilename); 155 rewrite(outfile); writeln; 156 writeln('temperature f i le is ',inlfilename); writeln; 157 writeln('squid signal f i l e is ',in2filename); writeln; 158 writeln('output f i l e is '.outfilename); writeln; 159 write Center number of data points to read from input f i le ') ; 160 read(datalength); writeln; 161 getdata(longtemp,inlfile); 162 getdata(longsquid,in2file) ; 163 write Center number to compress signal by ' ) ; 164 read(numcompress); writeln; 165 compress(longtemp,temp); 166 compress(longsquid,squid) ; 167 initialcoeff ; 168 writeout(temp,squid); 169 170 close( inlf i le) ; close(in2file); 171 close(outfile); 172 173 end.

B i b l i o g r a p h y

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2 4 A , 721 (1967).

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[3] J . B l o t , Y . P e l l a n , J . C . P i n e a u and J . R o s e n b l a t t , J . A p p l . P h y s . 45, 1429 (1974).

[4] A . K . D r u k i e r , 0 . V a l e t t e , G . W a y s a n d , L . C . L . Y u a n and F . Peter s , L e t t , a l N u o v o

C i m e n t o , 14, 300 (1975).

[5] J . B e h a r , J . M . C a r d i , B . H e r s z b e r g . D . H u e b e r , C . V a l e t t e and G . W a y s a n d ,

J o u r n a l de P h y s i q u e . 39, C6-1201 (1978).

[6! A . K . D r u k i e r , J . Igalson and L . Sniadower , N u c l . I n s t r u m . M e t h o d s , 154, 91

(1978).

[71 A . K . D r u k i e r and L . S todo l sky . P h y s . R e v . D 30, 2295 (1984).

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