Some optical properties of thin films of silver and other metals

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Some optical properties of thin films of silver and other metals

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SOME

OPTICAL

PROPERTIES

SILVER

AND

OP

OTHER

THIN

FILMS

OF

METALS

T h e s is su b m itted to th e U n iv e r s ity o f London f o r th e D egree o f D octor o f P h ilo so p h y hy

D onald Q. Avery A p r il 1950

The ex p erim en ta l work d e sc r ib e d in t h i s t h e s i s was c a r r ie d ou t in th e Departm ent o f P h y s ic s , Royal H olloway C o lle g e , under th e d ir e c t io n o f P r o fe s s o r

S. T o la n sk y , betw een O ctober 1914-7 and January 1950.

ProQuest Number: 10096551

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.

uest. ProQuest 10096551 Published by ProQuest LLC(2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. Microform Edition © ProQuest LLC. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346

Some O p tic a l P r o p e r tie s o f Thin F ilm s o f S ilv e r and o th e r M etals A b s tr a c t In th e l a s t f i f t e e n y ea r s th e re has been a c o n sid e r a b le in c r e a se in th e knowledge o f th e o p t ic a l p r o p e r t ie s o f m etal la y e r s l e s s than 1000 A t h ic k , and the use o f la y e r s produced by ev a p o ra tio n or c a th o d ic s p u t t e r in g has become in c r e a s in g ly common f o r th e d eterm in a tio n o f the o p t ic a l c o n s ta n ts o f m e ta ls. In t h i s work th e in te r fe r o m e tr ic method, o r i g i n a l l y due to T olan sk y, f o r th e d eterm in a tio n o f th e r e l a t i v e phase changes o ccu rrin g on r e f l e x io n a t th e su rfa ce o f a m etal la y e r has been fu r th e r d ev elo p ed , and, cou p led w ith a sim p le photo­ e l e c t r i c d e v ic e f o r th e measurement o f i n t e n s it y changes, has been a p p lie d to the study o f r e f l e x io n a t a number o f s u r fa c e s . The method r e q u ir e s s l i g h t l y tra n sp a r en t la y e r s o f the m etal to form a tr a n s m iss io n in te r fe r o m e te r , and i t i s th e r e fo r e o f p a r t ic u la r im portance to determ ine w ith in what th ic k n e s s l i m i t s the o p t ic a l p r o p e r tie s o f th e s e la y e r s can be taken as c h a r a c t e r is t ic o f th e m etal in b u lk form.

To t h i s

end, a stu d y o f th e v a r ia t io n w ith th ic k n e s s o f th e c h a r a c t e r is t ic s o f non-normal r e f le x io n a t th in s i l v e r la y e r s has been made f o r th ic k n e s s e s betw een 100 and 1000 A. Measurements have a ls o been made u sin g the tech n iq u e o f the o p t ic a l c o n s ta n ts o f copper, t i n , speculum, and a new t i n n ic k e l a llo y .

Some in t e r e s t i n g an om alies in th e o p t ic a l

p r o p e r tie s o f evap orated la y e r s o f t i n have "been ob served . The t h e s i s commences w ith a treatm en t o f th e th eory o f r e f l e x io n a t m etal s u r fa c e s and la y e r s , and th e p r e v io u s work in t h i s f i e l d i s rev iew ed , w ith p a r t ic u la r r e fe r e n c e to measurements on ev a p o ra ted la y e r s , and the v a r ia t io n o f t h e ir p r o p e r tie s w ith t h ic k n e s s .

The ev a p o ra tio n equipm ent and

procedure used are d e s c r ib e d , and the measurement o f la y e r th ic k n e s s e s c r i t i c a l l y d is c u s s e d .

The o p t ic a l tec h n iq u e s are

then d e sc r ib e d , th e in te r fe r o m e tr ic tech n iq u e b ein g a n a ly sed in d e t a i l .

F in a lly the r e s u l t s o f th e exp erim en ts are

m entioned and d is c u s s e d .

C O N T E N T S

PAGE P art I Chap. I Chap. I I C h a p .I ll Chap. IV Chap.V P a rt I I Chap♦I Chap. I I P a rt I I I Chap. I ^ C hap.II C h a p .Ill

P art IV Chap. I Chap.I I C h a p .I ll

THEOPETIGAL AND HISTORICAL REVIEW R e fle x io n a t the su r fa c e o f an A bsorbing Medinm..1 R e fle x io n a t a Thin M e ta llic L ayer................................. 9 The O p tica l C onstants o f M e ta llic S u r fa c e s .............. 16 The O p tica l Behaviour o f M e ta llic L a y e rs...................25 The Experim ents to be d e sc r ib e d in t h i s t h e s i s . . 39 THE PRODUCTION OP THE FILMS AND THE MEASUREMENT OP THEIR'"THICKNESS The E vap oration T ech n iq u e.................................................... Ui The Measurement o f Thin F ilm T h i c k n e s s e s . . .............54 THE OPTICAL TECHNIQUES The Measurement o f I n t e n s it y C o e f f ic ie n t s and E l l i p t i c i t y ....................... 65 The I n te r fe r o m e tr ic Method fo r D eterm in in g R e la tiv e Phase Changes - T h eo r y .. . . 7 4 The In te r fe r o m e tr ic Method f o r D eterm ining R e la t iv e Phase Changes - P r a c t i c e .. 84 THE RESULTS OF .THE EXPERIIVENTS I n tr o d u c tio n ................................................................................. 03 Normal In cid en ce P r o p e r tie s o f F ilm s o f S ilv e r and Aluminium.............................. i0 5 Non-Normal In cid en ce P r o p e r tie s o f Film s o f S i l v e r ....................................................... i i3 The O p tica l P r o p e r tie s o f Copper, T in, Speculum, and a T in -N ic k e l A l l o y . .121

P A R T

I

THIOHSTICAL AND HISTORICAL RB7ISW

REFLEXION AT TEîE SUHFACE 01 M ABSORBING MEDIUM Chapter I .

If p la n e

a beam o f l i g h t , p la n e p o la r is e d a t 45^ t o th e

o f in c id e n c e , i s r e f l e c t e d at th e s u r fa c e o f an absorb­

in g medium, th e r e f l e c t e d l i g h t i s in g e n e r a l e l l i p t i c a l l y p o la r is e d .

Both th e am p litu d es and th e p h a ses o f th e com­

p on en ts o f th e in c id e n t l i g h t p o la r is e d p a r a l l e l and p e r ­ p e n d ic u la r ly t o th e p la n e o f in c id e n c e are changed by r e f l e x io n , th e amount o f th e change in each q u a n tity v a ry ­ in g w ith

th e a n g le o f in c id e n c e . In

order to e x p la in th e se phenomena, th e c l a s s i c a l

e le c tr o m a g n e tic th eo ry must be extended from th e sim p ler ca se o f wave p ro p a g a tio n in is o t r o p ic tr a n sp a r en t m edia, and r e f le x io n at th e boun daries o f such m edia, t o th e more g en er a l case o f p ro p a g a tio n in and r e f le x io n a t th e b oun daries o f is o t r o p ic ab sorbing

m edia.

The change n e c e ssa r y in

M axwell»s eq u a tio n s f o r an e le c tr o m a g n e tic f i e l d i s th a t in a d d itio n to th e ^ displacem ent current" term in th e eq u a tio n s f o r th e e l e c t r i c v e c to r e x i s t i n g in a d i e l e c t r i c , account must a ls o be taken o f a "conduction current" varying w ith th e a p p lie d f i e l d , in th e case o f con d uctin g ( i . e . a b so rb in g) m edia. I t can be shown

(1 , 2, 3)

th a t lAtien th e eq u a tio n s

f o r wave p ro p a g a tio n in an absorbing medium are d evelop ed .

2. r e f l e x io n and r e fr a x io n a t th e boundary betw een an absorbing and a tra n sp a ren t medium can be co m p letely determ ined by th e u su a l eq u a tio n s f o r r e f le x io n and r e fr a x io n between two tra n sp a ren t m edia p ro v id ed th a t a r e f r a c t iv e in d ex having r e a l and im aginary p a r ts i s a ssig n e d to th e ab sorb ­ in g medium. The eq u a tio n fo r th e p ro p a g a tio n o f an e l e c t r o ­ m agnetic wave in th e

d ir e c t io n

in g medium i s of th e

form

where ^ ^ The term p

^2ïïifr. y. ^

o f an a x i s , y , in

an absorb­

i s th e w avelength in vacu o.

r e p r e s e n ts th e am plitude o f th e

v ib r a t io n , v h ic h , a f t e r th e wave h as t r a v e lle d a d is ta n c e ^

in th e medium i s reduced by a f a c t o r

con sta n t k

.

The

i s termed th e A bsorp tion Q o e ff ic ie n t o f th e

medium. I f we c a l l

th e r a t io

o f th e v e l o c i t y o f

propa­

g a tio n in vacuo t o th e v e l o c i t y of p ro p a g a tio n in th e medium, th e R e fr a c tiv e in d ex n , th en th e medium i s com­ p l e t e l y c h a r a c te r is e d by the Complex R e fr a c tiv e in d ex g iv e n by

J \f -

'TX f / -

h fy

The q u a n tity JsT i s r e la t e d , in d is p e r s io n th e o r y , to the d i e l e c t r i c co n sta n t, Z , and th e c o n d u c tiv ity ,

0*80, to

t h e w o r st c a s e .

*002

± .0 0 5 ^ f o r

r e l a t i v e p h a se change i s co rresp o n d s t o

±

X

f o r t h e optimum c a s e 0*30.

I f th e

e x p r e sse d a s an a n g le , t h i s

± 0*7^ fo r th e optimum c a s e , and

±

2

° fo r

T h is coii^ ares u n fa v o u r a b ly w ith t h e e r r o r

in e s t im a t io n o f th e a n g le o f p r in c ip a l in c id e n c e by , O’Bryan of

i

0

*1 ^, and th e e r r o r s in d e te r m in in g th e r e l a t i v e

change o f p h a se b y D rude*s m ethod o f

± .QOl ^

As a m ethod f o r th e d e te r m in a tio n o f r e l a t i v e change o f p h a se th e in t e r f e r o m e t r ic te c h n iq u e h a s one main a d v an ta g e o v er p o la r im e t r ic m ethods in t h a t th e a p p a r a tu s u se d i s sim p le t o c o n s t r u c t , and in e x p e n s iv e .

I t a ls o h a s

t h e a d d it io n a l a d van tage t h a t th e d o u b lin g s can be re co r d e d p h o t o g r ^ h i c a l l y and th e m easurem ents made a t l e i s u r e , a s opposed i o th e la b o r io u s v i s u a l o b s e r v a tio n n e c e s s a r y w ith

9 9. m ost o f th e p o la r im e t r ic m eth o d s.

I h is i s p a r t ic u la r ly

th e c a se vheu th e v a r i a t io n o f

w ith w a v ele n g th i s

r e q u ir e d ,

s in c e th e lAhole v i s i b l e range can be covered

in one p h otograp h o f f r i n g e s o f eq u a l ch rom atic o r d e r , w h i l s t th e p o la r im e t r ic method w ould r e q u ir e a dozen or more s e p a r a te e s t im a t io n s w ith a h a l f shade e y e p ie c e o r s im ila r d e v ic e . A s a g a in s t t h e s e a d v a n ta g e s, th e te c h n iq u e h a s a number o f s e r io u s l i m i t a t i o n s .

The a c c u r a c y o b ta in a b le

d o es n o t approach t h a t o b ta in a b le by Drude ^s m ethod, thou gh from th e p o in t o f v ie w o f th e d e te n u in a tio n o f o p t i c a l c o n s t a n t s t h i s i s n ot q u ite so s e r io u s a drawback a s i t seem s, s in c e we have se en t h a t t h e r e i s l i t t l e n eed f o r v e r y g r e a t a c c u r a c y in t h i s c o n n e c tio n .

P erh a p s t h e m ost

s e v e r e l i m i t a t i o n i s th e f a l l i n g - o f f o f a c c u r a c y w ith d e c r e a s in g r e f l e x i o n c o e f f i c i e n t .

The te c h n iq u e i s l i t t l e

more th a n h a l f a s a c c u r a te f o r d e te im in in g th e r e l a t i v e ch an ges o f p h a se o c c u r r in g on r e f l e x i o n a t m e t a ls such a s Chromium or Copper, a s i t i s f o r m e ta ls l i k e S i l v e r and Alum inium . A noth er d isa d v a n ta g e in c e r t a in c a s e s i s t h a t th e te c h n iq u e r e q u ir e s two l a y e r s , one f o r each s u r fa c e o f th e in t e r f e r o m e t e r .

Now i t i s n o t d i f f i c u l t t o p rod u ce

two la y e r s o f p r a c t i c a l l y i d e n t i c a l o p t i c a l c h a r a c t e r i s t i c s .

loo.

i f t h e y a re so t h ic k a s t o have o n ly a few p e r c e n t t r a n s ­ m is s io n .

The o p t i c a l p r o p e r t ie s o f f i l m s o f t h i s k in d ,

such a s t h o s e u se d f o r g e n e r a l in t e r f e r o m e t r ic work, v a ry b u t s lo w ly w ith t h i c k n e s s .

However i f i t i s d e s ir e d t o

m easure th e v a r i a t io n o f t h e r e l a t i v e change o f p h a se w ith th e t h ic k n e s s , i t i s

found t h a t t h e v a r i a t io n w ith t h ic k n e s s

becom es a p p r e c ia b le a t t h ic k n e s s e s b elo w 3 5 0 and i t i s n ot an e a s y m a tte r t o p ro d u ce two i d e n t i c a l f i l m s .

Even w ith

t h e h o r i z o n t a l e v a p o r a tio n p la n t d e s c r ib e d in P a r t i l . Chap. I , a sm a ll amount o f o x id e or o th e r *scum* on one s id e o f th e f ila m e n t can c a u se a marked d i f f e r e n c e in th e t h ic k n e s s and t h e p r o p e r t ie s o f two v e r y t h in f ilm s produced a t th e same tim e in t h e p l a n t . One m ethod o f overcom ing t h i s d i f f i c u l t y i s t o m atch th e t h in f ilm w ith a f r e s h l y p rep a red t h ic k one whose p r o p e r t i e s , i t w i l l be shown, can be r e l i e d upon t o be t h e same a s o t h e r s m easured o f th e same o rd er o f t h i c k n e s s . The d ou b lin g i s th en d u e, n ot t o t w ic e th e r e l a t i v e p h a se change a t e i t h e r o f two i d e n t i c a l f i l m s , but to t h e sum o f t h e r e l a t i v e p h a se ch an ges due t o th e t h in f ilm and th e t h ic k o n e.

This p r o c e s s m ight a t f i r s t s ig h t appear t o

le a d t o an in c r e a s e d a c c u r a c y , s in c e th e f r i n g e s in th e 'm ixed* in t e r f e r o m e t e r w i l l be s h a ip e r than w ith one composed o f two f i l m s o f low r e f l e c t i o n c o e f f i c i e n t s . d o u b lin g in t h e form er c a s e can be m easured t o

However i f t h e — *004

X ,

lo i.

and t h ic k f ilm s r e l a t i v e p h a se change i s known to

,

th e v a lu e f o r t h e r e l a t i v e p h a se change a t th e t h in f ilm i s o n ly a c c u r a te t o

i* 0 0 6 X .

A f u r t h e r d isa d v a n ta g e o f th e in t e r f e r o m e t r ic m ethod i s th a t i t i s n o t p o s s i b l e t o ca rry o u t th e m easu re­ m en ts w ith o u t rem oving th e f ilm s from th e vacuum in vAiich i t was d e p o s it e d .

T h is means t h a t th e f i l m s may be con­

ta m in a ted d u rin g th e a d ju stm en t o f th e in t e r f e r o m e t e r , e t c . , and f a l s e r e s u l t s e n su e .

I t i s g e n e r a lly p o s s i b l e t o make

t h e com p lete exp erim en t f o r th e m easurem ent o f r e l a t i v e p h a se ch an ge, in c lu d in g m easurem ent o f th e v a r i a t io n w ith w a v e le n g th u s in g f r i n g e s o f eq u a l ch ro m a tic o r d e r , w it h in one h ou r, and so o n ly m e ta ls w hich are r a p id ly co n tam in ated in a i r w i l l u nd ergo any s e r io u s change d u rin g m easurem ent. I t may be p o s s i b l e c o m p le te ly t o overcom e t h i s d i f f i c u l t y by c o v e r in g th e f ilm w ith cedarwood o r o th e r o i l of known r e f r a c t i v e in d e x im m e d ia te ly upon rem oval from th e vacuum chamber, and form in g th e in t e r f e r o m e t e r w ith t h i s o i l b etw een th e p l a t e s .

I t w ould o f co u rse be n e c e s s a r y t o m o d ify th e

in t e r p r e t a t i o n o f any r e s u l t s o b ta in e d t o a cco u n t f o r th e r e f r a c t i v e in d e x o f th e o i l . From th e p o in t o f v ie w o f t h e d e t e im in a tio n o f t h e o p t i c a l c o n s t a n t s o f th e m e t a ls , i t i s

se e n im m e d ia te ly

t h a t t h i s m ethod i s b e s t s u it e d t o t h o s e m e ta ls o f h ig h

102.

r e fle x io n c o e f f ic ie n t ,

,S in c e th e m easurem ents a re m ost

c o n v e n ie n t ly made in t r a n s m is s io n , i t f o llo w s t h a t th e m e ta ls m ust be in th e form o f l a y e r s h a v in g a t l e a s t one or two p e r c e n t . t r a n s m is s io n .

I t m ust be d e c id e d f o r

each m e ta l l a y e r u sed w h eth er or n o t t h e l a y e r s can be c o n s id e r e d c h a r a c t e r i s t i c o f th e m eta l i n b u lk .

The q u e s tio n s

a f f e c t i n g t h i s d e c is io n have been d is c u s s e d in d e t a i l in P art I of th is t h e s is .

PART

IV

THE RESULTS OF TBE EXPERIMENTS

mm

IV I n tr o d u c t io n The ex p er im en ts t h a t have been c a r r ie d ou t u s in g

t h e o p t i c a l te c h n iq u e s d e s c r ib e d , can be grouped under t h r e e h e a d in g s , m easurem ent o f t h e norm al in c id e n c e p r o p e r t ie s o f s i l v e r and alum inium , a stu d y o f th e non-norm al in c id e n c e r e f l e x i o n c h a r a c t e r i s t i c s o f s i l v e r l a y e r e , and th e d e t e r ­ m in a tio n o f th e o p t i c a l c o n s ta n ts o f la y e r s o f co p p er, t i n , speculum and a t i n - n i c k e l a l l o y .

Each o f t h e s e s e c t i o n s

w i l l form th e s u b j e c t o f a s e p a r a te c h a p te r , but s in c e t h e o v e r a ll e x p e r im e n ta l p ro ce d u re was s im ila r in each c a s e , i t can be d e s c r ib e d h e r e . A l l th e l a y e r s u sed were d ^ o s i t e d on t o g l a s s s u b s t r a t e s in e i t h e r o f two e v a p o r a tio n p l a n t s d e s c r ib e d . The p a r t i c u l a r p la n t u se d w i l l be d e s c r ib e d in th e d is c u s s io n o f th e r e s u l t s .

A f t e r d e p o s it io n , th e c o a te d s u b s t r a t e s

were removed from th e vacuum chamber and th e o p t i c a l m easu re­ m ents c a r r ie d o u t im m e d ia te ly .

F i r s t each l a y e r in tu rn

was p la c e d in th e p h o to m eter and th e i n t e n s i t y c o e f f i c i e n t s m easu red, b o th a ta n o im a l in c id e n c e and a t non-norm al in c id e n c e f o r th e d e t e m in a t io n o f t h e e l l i p t i c i t y o f th e l i g h t r e f l e c t e d a t t h e s e a n g le s .

The l a y e r s were th e n combined

w ith each o th e r (o r w ith a f r e s h l y p rep a red t h ic k la y e r o f s i l v e r as d e s c r ib e d in P a r t i l l .

C hapter H I ) t o form an

in t e r f e r o m e t e r f o r th e m easurem ent o f r e l a t i v e p h a se ch an ge.

104. In a l l c a s e s t h e o p t i c a l m easurem ents were co m p leted w it h in two h o u r s o f th e tim e o f d e p o s it io n .

When t h e s e m easu re­

m ents were d on e, in th o s e c a s e s W iere t h e t h ic k n e s s o f th e la y e r was m easu red , a t h in s t r i p

of th e f i l m was removed

and an opaque la y e r d e p o s it e d in th e v e r t i c a l e v a p o r a tio n p la n t in as d io r t a tim e a s p o s s i b l e . S in c e t h e s e m easurem ents w ere made in th e minimum tim e in each c a s e , no s y s t e m a t ic i n v e s t i g a t i o n o f th e v a r i a t io n o f th e o b serv ed q u a n t i t ie s withL tim e h a s been m ade.

The

p o s s i b l e e f f e c t o f any 'a g e in g ' o f th e f ilm d u rin g th e m easurem ents w i l l be d is c u s s e d in each p a r t i c u l a r c a s e . The m easurem ents o f t h e normal in c id e n c e r e f l e x i o n c o e f f i c i e n t s w i l l be d is c u s s e d f i r s t ,

s in c e t h e y a re n o t

c l o s e l y r e la t e d t o th e a p p li c a t io n of t h e te c h n iq u e s d e s c r ib e d to th e m easurem ent o f e l l i p t i c i t y and r e l a t i v e p h a se ch a n g es, v h ic h i s th e main p u rp o se o f th e work.

105. NORMAL. INCIDENCE PROPERTIES OF FILMS OF SILVER M B ALI3MINIIM C hapter I .

The r e f l e x i o n and tr a n s m is s io n c o e f f i c i e n t s a t norm al in c id e n c e o f a number o f f ilm s o f s i l v e r and alum inium have been m easu red .

.S ilv e r f ilm s were p rod uced

in b oth t h e e v a p o r a tio n p l a n t s , alum inium f ilm s in th e v e r t i c a l p la n t o n ly .

The a n g le o f in c id e n c e a t imhioh th e

c o e f f i c i e n t s w ere m easured was in p r a c t i c e 5 ° , but t h e v a r i a t i o n o f th e c o e f f i c i e n t s w ith in c id e n c e f o r u n p o la r is e d lig h t i s

such th a t in a l l c a s e s t h e c o e f f i c i e n t s a t t h i s

a n g le can be ta k en a s th e normal in c id e n c e c o e f f i c i e n t s w it h in th e a cc u r a cy o f t h e s e m easurem ents. The i n t e n s i t y c o e f f i c i e n t s o f th e f ilm s o f s i l v e r f o r in c id e n t l i g h t o f mean w a v elen g th 5400 A a re shown in F ig u r e 3 3 .

The r e f l e x i o n c o e f f i c i e n t s a re p l o t t e d a s

o r d in a t e s , t h e t r a n s m is s io n c o e f f i c i e n t s a s a b s c is s a e . The a d v a n ta g e o f t h i s method o f r e p r e s e n t a t io n o v e r th e more u s u a l p l o t o f th e c o e f f i c i e n t s a g a in s t a t h ic k n e s s a x i s h a s a lr e a d y b een m en tion ed in P a r t I , th is th e s is .

C hapter IV o f

The u n c e r t a i n t i e s in th e t h ic k n e s s m easu re­

m en ts a r e a v o id e d , and th e a b s o r p tio n o f any p a r t i c u l a r la y e r can be q u ic k ly d e t e m in e d from, th e g ra p h , s in c e i t i s r e p r e se n te d f o r any p a r t i c u l a r t r a n s m is s io n c o e f f i c i e n t , by t h e v e r t i c a l d is t a n c e from th e p o in t t o th e l i n e o f s lo p e 45^ w hich r e p r e s e n t s z e r o a b s o r p tio n .

106. In F ig u r e 23, t h e p o i n t s r e p r e s e n t th e f ilm s m easu red, th e t h ic k l i n e i s th e mean o f th e o b s e r v a tio n s o f S tr o n g and D i b b l e , sho^ving t h e v a r i a t io n o f r e f l e x i o n w ith t r a n s m is s io n c o e f f i c i e n t f o r t h e i r film s .

It is

and ^

-ty p e

c le a r a t on ce from F ig u r e 23 t h a t th e f ilm s

m easured h e r e co rresp o n d q u it e c l o s e l y t o th e f ilm s o f S tr o n g and D ib b le . I t i s a l s o o b v io u s from t h i s f i g u r e t h a t th e s c a t t e r o f th e e x p e r im e n ta l p o in t s ab out a mean cu rve i s v e r y much g r e a t e r th an t h e ex p er im en ta l e r r o r a s s o c ia t e d w ith th e m easurem ents f o r each p o i n t , w hich i s n o t g r e a t e r th an

2:

O ' o i . i n th e v a lu e o f e i t h e r c o e f f i c i e n t ,

ih e

c a u se s o f t h e s e d e v ia t io n s were d is c u s s e d vhen th e r e s u l t s o f p r e v io u s w orkers were b e in g compared.

The s c a t t e r o f

th e exp B im ental p o i n t s o f s t r o n g and D ib b le i s shown by t h e v e r t i c a l d o tte d l i n e s in F ig u r e 2 3 , and s in c e th e y m easured a v e r y la r g e number o f f ilm s t h i s o rd er o f d e v ia t io n must be reg a rd ed a s u s u a l when f i l m s a r e produced in t h i s manner.

I t m ust be n o te d , h ow ever, t h a t d e s p it e th e im prove­

ment in t h e p r e s s u r e c h a r a c t e r i s t i c s o f t h e la b o r a to r y e v a p o r a tio n p la n t Yhen t h e c o ld tra p was added ( s e e p a r t I I , C hapter I ) , and th e a b se n c e o f any v i s i b l e c o n ta m in a tio n , th e s c a t t e r o f p o in t s r e p r e s e n t in g f ilm s p rod uced in t h i s p la n t i s no l e s s th a n f o r th o s e prod uced in th e v e r t i c a l p la n t w ith o u t any c o ld t r a p .

oo

SIL V E R CURVES DUE TO STRONG AND DIBBLE

POINTS

80

VERTICAL PLANT LABORATORY

PLANT

=5400A

60

40

20

■20

40

60

80

FIGURE 23.

FIGURE 24 SILVER 0-30

EX PE R IM E N T ST R O N G AND D IB B L E

0-40

RO U A RO THEORY

A = 5400A

2 0 0

t h ic k n e s s

Â

■OO

1 07. ‘H ie f a i r l y good agreem ent shoiwn on t h i s r e p r e s e n ­ t a t i o n b etw een t h e m easured v a lu e s and t h e v a lu e s re co rd ed by S tr o n g , v a n is h e s when t h e r e f l e x i o n c o e f f i c i e n t s m easured a re p l o t t e d a g a in s t a t h ic k n e s s m easurem ent f o r th e f i l m s , o b ta in e d in th e manner d e s c r ib e d .

T h is i s done in F ig u r e

2 4, th e a b s c is s a e b e in g v a lu e s o f th e m ass p e r u n it a rea p r e s e n t i n th e f i l m .

V a lu es o f th e t h ic k n e s s o f th e f i l m ,

d e fin e d in t h e manner d is c u s s e d in P a rt I I , a re a ls o in c lu d e d .

C hapter I I ,

The c o n tin u o u s l i n e r e p r e s e n t s t h e

mean o f th e e x p e r im e n ta l p o i n t s .

The mean o f th e r e s u l t s

o f Rouard ( c^. F ig u r e 4 ) and S tr o n g a r e a ls o shov/n, t o g e t h e r w ith a cu rve c a lc u la t e d from th e v a lu e s o f th e o p t i c a l c o n s t a n t s f o r opaque ev a p o r a te d l a y e r s o f s i l v e r , g iv e n (2 8 ) by Hass . T h is l a t t e r cu rv e was c o n fu te d from t h e fo rm u la e g iv e n in P a rt I , C hapter I I . The agreem ent b etw een th e r e s u l t s o f t h e s e e x p e r im e n ts and th e th e o r y i s p o o r , a s i s a ls o t h e a g r e e ­ ment b etw een S t r o n g 's r e s u l t s and th e t h e o r y .

Here th e

v a lu e s o f th e m ass p e r u n it a r e a o b ta in e d by s t r o n g by w e ig h in g a r e ta k e n a s c o r r e c t

.

No doubt some o f th e

d is c r e p a n c y i s due t o th e d i f f e r i n g m ethods o f t h ic k n e s s m easurem ent em ployed, but a q u e s tio n which rem ains un­ r e s o lv e d i s th e rea so n f o r th e la r g e d i f f e r e n c e s betw een th e work o f s t r o n g and th e w r i t e r , and th e work o f Rouard,

1 08. th e l a t t e r '

8

work a g r e e in g f a i r l y w e ll w ith th e th e o r y

f o r v a lu e s o f t h ic k n e s s g r e a t e r th a n 1 5 0 /7 .

No f u r t h e r

i n v e s t i g a t i o n o f t h i s phenomenon was made, s in c e i t l a y o u t s id e th e sco p e o f t h i s wcrk. The norm al in c id e n c e m easurem ents were p r im a r ily u n d erta k en t o be o f a s s i s t a n c e to w ork ers in t h i s la b o r a t o r y u s in g th e te c h n iq u e s o f m u lt ip le beam in t e r f e r o m e t r y , and in t h i s c o n n e c tio n o n ly v a lu e s o f r e f l e x i o n c o e f f i c i e n t g r e a t e r th a n 0*50 a r e o f i n t e r e s t . th e r e s u l t s by p l o t t i n g

R

The r e p r e s e n t a t io n o f

T

a g a in s t

i s a g a in t h e b e s t

from t h i s p o in t o f v ie w s in c e th e im p o rta n t f a c t o r , t h e a b s o r p tio n f o r a g iv e n t r a n s m is s io n , can be d i r e c t l y o b se r v e d , and no m easurem ents o f t h ic k n e s s a r e r e q u ir e d t o p l o t th e c u r v e . S in c e , i n a l l th e in t e r f e r o m e t r lc done in t h i s la b o r a t o r y , th e l a y e r s a r e d e p o s it e d in th e v e r t i c a l e v a p o r a tio n p l a n t , o n ly f ilm s p rod uced in t h a t p la n t w i l l be d is c u s s e d from t h i s p o in t o f v ie w .

F ig u r e 25 shows t h e

r e s u l t s f o r th e r e f l e x i o n and tr a n s m is s io n c o e f f i c i e n t s f o r a number o f s i l v e r and alum inium f i l m s p roduced in t h e v e r t i c a l p l a n t , f o r th r e e d i f f e r e n t w a v e le n g th s , 4 ,5 0 0 , 5 ,4 0 0 and 6 ,1 0 0 A . Now, t h e maximum i n t e n s i t y o f an in t e r f e r e n c e f r in g e f o m e d in a tr a n s m is s io n in t e r f e r o m e t e r w ith r e f l e c t o r s o f t r a n s m is s io n

T

and a b s o r p tio n

A

is

{ It



FIGURE 25 SILVER AND ALUMINIUM

lO O

4500A

0

0.10

0 2 0

J

0 3 0

0 -9 0

0 8 0

0

C .7 0

0 -7 0

0

O

9 0

6 0

0 6 0

O

0 4 0

G -

8 0

S IL V E R

O lO

0 .2 0

-f 0 3 0

0 4 0



O

-A L U M I N IU M

O lO

02 0

T

0 3 0

0 .4 0

109. In o rd er t o o b ta in t h e maximum i n t e n s i t y , th e r a t io n must be a s sm a ll a s p o s s i b l e . From th e cu rv es o f F ig u r e £5 i t i s seen a t once t h a t s i l v e r f ilm s a r e g r e a t l y s u p e r io r t o alum inium f i l m s a t th e w a v e le n g th s s t u d ie d , th e v a lu e s o f

fo r s ilv e r

f i l m s b e in g r o u g h ly h a l f t h o s e f o r alum inium f i l m s . v a lu e s o f

The

found f o r t h e s e s i l v e r f ilm s a re in v e r y

c l o s e agreem ent w ith some m easurem ents made u s in g d i f f e r e n t o p t i c a l te c h n iq u e s on f i l m s prod uced by e v a p o r a tio n by B r ig h t, J a ck so n , and Kuhn^*^^^. I n s p e c t io n o f F ig u r e 25 r e v e a ls how ever t h a t t h e s e v a lu e s o f th e r a t i o

ta k e n from th e mean cu rv e s

a r e n o t r e p r o d u c ib le t o any g r e a t d e g r e e . t h e e x p e r im e n ta l p o in t s i s

The s c a t t e r o f

such t h a t when s u c c e s s i v e f ilm s

a r e ev a p o ra ted in th e p la n t under a p p a r e n tly i d e n t i c a l c o n d it io n s , v a r i a t i o n s in r a t i o be e x p e c te d f o r s i l v e r f i l m s .

o f up t o 50^ must I t was a t f i r s t th o u g h t

t h a t a la r g e p a r t o f t h i s v a r i a t io n was due t o t h e f a c t t h a t th e a c t u a l p r e s s u r e a t which e v a p o r a tio n ta k e s p la c e i n th e v e r t i c a l p la n t i s n o t known, s in c e th e p r e s s u r e gauge i s i n s e n s i t i v e b elo w

!0

o f E g.

However we

have seen from F ig u r e 25 t h a t f ilm s produced in th e la b o r a t o r y p l a n t , in w hich th e p r e s s u r e s can be m easured c o m p a r a tiv e ly a c c u r a t e ly , show v a r i a t io n s o f th e same o r d e r .

110.

The v a r i a t io n s in th e v a lu e o f

f o r alum inium

f i l m s a re g r e a t e r - o f th e o rd er o f lOO^ in some c a s e s .

A

r e c e n t stu d y o f th e o p t i c a l e f f e c t s o f th e o x id a t io n o f alum inium l a y e r s on ex p o su re to th e atm osp h ere, by ca b re ra and T e r r ie n /^ O ), h a s shown t h a t t h e v a r i a t i o n s a re a lm o st e n t i r e l y due t o t h i s c a u s e .

The o x id a t io n p r o c e s s e s a r e

o n ly com p lete a f t e r s e v e r a l d a y s, and th e ch an ges produced by them in th e f i r s t two h o u rs a f t e r p r o d u c tio n a r e v e r y la r g e . The e x i s t e n c e o f t h e s e v a r i a t i o n s in t h e a b s o r p tio n means t h a t in g e n e r a l u s e , t h i s e v a p o r a tio n p ro ced u re cannot be r e l i e d upon to g iv e s t r i c t l y r e p r o d u c ib le f ilm s f o r in t e r f e r o m e t r ic p u r p o s e s .

In th e g e n e r a l a p p li c a t io n s o f

t h i s te c h n iq u e in t r a n s m is s io n , s o u r c e s o f h ig h i n t e n s i t y a r e u s e d , and an o c c a s io n a l h ig h ly a b so rb in g f i l m i s n o t a s e r io u s h a n d ic a p .

However when an in t e r f e r o m e t e r i s u sed

i n r e f l e x i o n th e v i s i b i l i t y o f th e in t e r f e r e n c e f r i n g e s depends c r i t i c a l l y upon t h e a b so r p tio n o f th e f r o n t s u r f a c e o f th e in t e r f e r o m e t e r ( ) ,

and i t i s o c c a s io n a lly found

t h a t a f ilm i s p rod uced imhioh i s v er y p o o r f o r t h i s p u r p o se . A lso b e c a u se o f t h e s e v a r i a t i o n s , i t seem s o f l i t t l e u s e t o c a l c u l a t e v a lu e s f o r f u n c t io n s r e l a t i n g th e i n t e n s i t y e f f i c i e n c y o f an in t e r f e r o m e t e r t o th e r e f l e x i o n c o e f f i c i e n t of i t s

s u r f a c e s , a s B r ig h t, J a ck so n , and Kuhn have done,

s in c e th e v a lu e s o b ta in e d a r e o n ly r e p r o d u c ib le betw een s u c c e s s i v e e v a p o r a tio n s t o

— 50%.

111.

A noth er p o in t o f i n t e r e s t which a r i s e s from t h e s e r e s u l t s co n cern s th e r a t e o f e v a p o r a tio n ,

s tr o n g

and D ib b le in t h e i r work c a lc u la t e d th e t h ic k n e s s e s o f t h e i r d e p o s it s from m easurem ents on t h e tim e ta k en to d e p o s it th e la y e r and t h e geom etry o f t h e sy ste m ,

"fhey

th e n assumed t h e s e t o be c o r r e c t and 'c o r r e c t e d ' v a lu e s o b ta in e d by w eig h in g t o a g r e e w ith t h e s e v a l u e s ,

in t h e

e x p e r im e n ts d e s c r ib e d h e r e , th e tim e o f d e p o s it io n was m easured in each c a s e .

A t a b l e i s g iv e n b elo w show ing th e

tim e ta k e n to d e p o s it a la y e r and i t s r e f l e x i o n c o e f f i c i e n t . Time ( s e c s ) .

27

20

15

15

12

12

lO

iQ

0*90

0*90

0-86

0 .0 7

0*87

0*77

0*68

Q.62

T h is t a b le ^diows t h a t m easurem ents o f t h e tim e ta k e n t o d e p o s it t h e la y e r a re o n ly a v ery rough g u id e t o th e r e f l e x i o n c o e f f i c i e n t s o b ta in e d .

The r e a so n f o r t h i s ,

in th e com m ercial p la n t , i s t h a t th e s i l v e r w e ts th e molybdenum and sp re a d s o u t t o a d i f f e r e n t a r e a f o r each e v a p o r a tio n , and so t h e a rea o f th e so u rce i s d i f f e r e n t i n each c a s e .

S tr o n g and D ib b le u sed a tu n g s te n s p i r a l

c o a te d w ith s i l v e r , and i t m ight be e x p e c te d t h a t th e so u rc e a r e a in t h i s c a s e i s more c o n s ta n t than w ith a molybdenum b o a t, b u t even so la r g e v a r i a t i o n s in th e r e f l e x i o n c o e f f i c i e n t o f la y e r s # i i c h ta k e t h e same tim e

112.

t o d e p o sit m igh t be e x p e c te d .

I t was f o r t h i s re a so n t h a t

th e v a lu e s g iv e n by S tro n g and D ib b le were changed t o a b a s i s w hich assumed t h e i r w e ig h in g s t o be c o r r e c t .

NQN-NORMAL INGIDENCE PROPERTIES OF PIIMS OF SILYSR C hapter I I .

The e l l i p t i c i t y and r e l a t i v e p h a se change o c c u r r ­ in g on r e f l e x i o n a t la y e r s o f s i l v e r o f v a r io u s t h ic k n e s s e s betw een

100

and 600

in c id e n c e o f up t o 7 0 ° .

h ave b een m easured f o r a n g le s o f T h is stu d y had two main o b j e c t s .

F i r s t , th e v a r i a t io n o f th e q u a n t i t i e s

^

and / Ï

w ith

t h e t h ic k n e s s o f a t h in la y e r h a s n o t been p r e v io u s ly exam ined.

S e c o n d ly , i t was d e s ir e d t o f in d w h eth er th e

p r o p e r t i e s o f l a y e r s o f »in t e r f e r o m e t r ic * t h i c k n e s s e s , th a t i s o n ly s l i g h t l y t r a n s p a r e n t, w ere i d e n t i c a l w ith t h o s e o f t h e s u r fa c e o f a m a t e r ia l in b u lk , and a ls o from th e t h i c k ­ n e s s v a r i a t io n t o d eterm in e th e l i m i t s o f t r a n s m is s io n and t h ic k n e s s , b elo w w hich th e p r o p e r t ie s o f t h e la y e r d iv e r g e d from th o s e o f th e m e ta l in b u lk . In F ig u r e 26 t h e e l l i p t i c i t y o f th e l i g h t r e f l e c t e d from a s i l v e r l a y e r ( 4 5 o t h i c k ,

r e fle x io n c o e f f ic ie n t

0 *90, t r a n s m is s io n 0*04) i s shown f o r v a r io u s a n g le s o f in c id e n c e , th e mean w a v elen g th o f t h e l i g h t b e in g 5400 The e x p e r im e n ta l e r r o r s o f e llip tic ity

^

±

0*01 in any v a lu e o f th e

a r e shown in th e F ig u r e .

The v a lu e s t o be

e x p e c te d f o r r e f l e x i o n a t th e s u r fa c e o f a b u lk m eta l have b een c a lc u la t e d from t h e fo rm u la e o f P a r t i , 1*3

C hapter I ,

, u s in g th e v a lu e s f o r t h e o p t i c a l c o n s t a n t s o f

114. s i l v e r g iv e n by Hass^^^^,

r\ = 0*177,

H « 18*60, (

= 5461A).

These v a lu e s are a ls o p lo t t e d in F igu re 26 and i t i s seen t h a t fo r t h i s f ilm th e v a r ia t io n o f th e measured e l l i p t i c i t y from th e t h e o r e t ic a l v a lu e f o r b u lk s o lv e r o n ly ex c ee d s th e ex p erim en ta l er r o r o f

±

1^

f o r a n g le s o f in c id e n c e above

68°.

The v a r ia tio n o f th e r e l a t i v e p hase r e ta r d a tio n ^

, ex p ressed as a f r a c t io n o f th e in c id e n t w avelen gth

( 5 4 6 1 f t ) , w ith th e a n g le o f in c id e n c e i s shown in F igu re 2 7 . The ex p erim en ta l v a lu e s shown were th o se o b ta in ed u sin g F izean in t e r f e r e n c e f r in g e s in a number o f in te r fe r o m e te r s , th e common c h a r a c t e r is t ic o f -which was th a t th e tr a n s m is s io n c o e f f i c i e n t o f th e la y e r s fo im in g them n ev er exceeded 0*07. No sy s te m a tic v a r ia t io n of th e r e l a t i v e phase r e ta r d a tio n w ith in t h e s e l i m i t s was o b serv ed ,

m F ig u re 27 th e co n tin u ou s

l i n e i s n ot th e mean curve through th e p o in t s , but i s th e th e o r ­ e t i c a l cu rv e, computed f o r th e ca se o f r e f l e x io n a t bulk s i l v e r , u s in g th e v a lu e s o f th e o p t ic a l c o n sta n ts quoted . The v a r ia t io n o f a curve through th e ex p erim en ta l p o in t s from th e t h e o r e t i c a l curve would n o t exceed th e exp erim en tal error o f

±

*002

^

f o r a n g le s of in c id e n c e l e s s than

60°

and o n ly by very l i t t l e more than t h i s f o r th e h ig h e r a n g le s o f in c id e n c e l e s s than

60°

and o n ly by v er y l i t t l e more than

t h i s f o r th e h ig h e r a n g le s o f in c id e n c e . The a n g le o f ( 27 ) p r in c ip a l in c id e n c e found by O’ Bryan' ' i s a ls o p lo t t e d .

FIGURE 26. SILVER OO

.^ T H E O R Y

0 95

= 5400A 090

004

40'

20'

8 0'

60'

J

FIGURE 27 SILVER

o BRYAN,

025 C U R V E -

020 0.15

P O IN T S

-

CALCULATED E X P E R IM E N T A L

A=5 4 0 0 A T< 0 07

C IO G-0 5

20°

40°

60“

80

115. and an e x t r a p o la t io n o f a curve through th e exp erim en tal p o in t s would p a s s v ery n ear to t h i s p o i n t . I t should be n o ted th a t v a lu e s o f ^

shown in

F igu re 27 and in su cceed in g f ig u r e s a re e x p re sse d as a f r a c t io n of th e in c id e n t w a v elen g th , and are d i r e c t l y c a lc u la te d from th e f r a c t io n a l ord er se p a r a tio n of th e doubled in t e r f e r e n c e fr in g e s . ^

These cu rves in d ic a t e a v a lu e o f .

^

= O

, fo r

However, i t can r e a d ily be shown from th e

th e o r y g iv e n in P a rt I ,

Chaps. I and I I

W interbottom^^^^, Born^^^)) th a t f o r and th a t i f th e v a lu e s o f

• Drude^^ ), ft ,

9 = 0 ^ , ^ =

g iv e n h ere are transform ed

in t o a n g u la r m easurement, th en th e a n g le correspon d ing to a g iv e n f r in g e s h i f t i s eq u al t o (

) rad iom s.

T h is

i s o f im portance vhen t h e s e measurements a re u sed to c a l ­ c u la t e v a lu e s fo r th e o p t i c a l c o n s ta n ts , s in c e th e a n gu lar m easure o f

^

i s req u ired f o r s u b s t it u t io n in th e form ulae

o f P a rt I .

In p a s s in g i t may a ls o be m entioned th a t th e

s h i f t o f th e dark bands in a B abinet com pensator, u sed in Drude*s method f o r determ in in g an a n g le i s a ls o equal to ( 9k —

, when tran sform ed in t o ) , th e in te r f e r o m e tr ic

and p o la r im e t r ic methods b ein g a lik e in th a t one cannot d is t in g u is h between a r e l a t i v e p h ase s h i f t o f zero and one

of ^

( V 2).

116. .Also stiown d o tte d in F igu re 27 i s th e curve o b ta in ed by Tolansky in th e o r ig in a l work u sin g th e i n t e r fe r o m e tr io tech n iqu e^ ^ ^ ^ .

T his curve f o llo w s th e p r e s e n t

v a lu e s very c l o s e l y f o r in c id e n c e a n g le s of up t o 60° and th en su dd en ly d iv e r g e s from th e t h e o r e t i c a l cu rv e.

*fhe

r e a l i t y o f t h i s d iv e r g e n c e was c a r e f u lly checked by T olansky, but a th o ro u g h ly s a t i s f a c t o r y e x p la n a tio n f o r i t h as n o t been found.

One p o s s ib le e x p la n a tio n i s th a t i t i s an

fagein g* e f f e c t .

The f ilm s u sed by Tolansky in th e o r ig in a l

experim ent were s e v e r a l months o ld , and i t was su g g ested th a t th e e f f e c t may have been caused by th e p r esen ce o f a f a i r l y t h ic k la y e r of o x id e on th e s u r f a c e .

Some f ilm s

u sed in th e p r e s e n t in v e s t ig a t io n were l e f t in th e open la b o r a to r y f o r p e r io d s o f up to th r e e weeks and re-m easured , but no change was ev er observed o f th e order o f m agnitude of t h is e f f e c t . The v a r ia t io n o f ^

w ith w avelen gth fo r film s

o f t h i s order o f t h ic k n e s s was measured very e a r ly in th e i n v e s t i g a t i o n , u s in g f r in g e s of eq u al chrom atic o rd er. r e s u l t s are shown in F ig u re 28 .

%hen ^

The

i s ex p ressed as

a f r a c t io n of a w a v elen g th , i t d e c r e a se s s t e a d i l y tow ards th e red f o r a l l a n g le s of in c id e n c e , but a s an a n g le , i t rem ains n e a r ly c o n s ta n t. of ^ term ^

i t i s ex p ressed The c a lc u la t io n

from th e m easured w avelength was made assum ing th e in th e eq u a tio n 2 - l 0

o f P a rt i l l to be z e r o , and

F I G U R E 28.

SILVER

025

020

O lO 45

0 05

AA.u. 4500

5000

5500

6000

6500

117. th e f a i r l y c lo s e agreem ent betw een th e v a lu e s taken from t h e f r in g e s o f eg u a l chrom atic order ( F ig . 28) f o r /\ m 5461/? , and th e v a lu e s from th e F izean f r in g e s (F ig , 27) show th a t in f a c t th e term be v e iy sm a ll.

yg f o r s i l v e r must

The exp erim en tal e r r o r s in t h e s e e a r ly

m easurements in F igu re 28 are to o la r g e f o r any fu r th e r c o n c lu s io n s a s t o t h e m agnitude o r sig n o f th e q u a n tity t o be drawn. The v a r ia t io n s o f ^

and

w ith th e th ic k n e s s

o f th e la y e r , a t a f ix e d a n g le o f in c id e n c e f o r a w avelen gth o f 5 4 0 0 /? , are i^own in F ig u r e s 29 and 3 0 . a n g le was 65^.

The in c id e n c e

T his a n g le was chosen a s a compromise

betw een th e d e s ir e f o r a s h ig h an in c id e n c e a n g le a s p o s s ib le t o d ec r e a se th e p e r c e n ta g e e r r o r s in th e measurement o f ^

,

and th e d e c r e a se in e f f e c t i v e s i z e o f th e in te r fe r o m e te r f o r th e measurement o f ^

w ith in c r e a s in g in c id e n c e a n g le .

C onsider f i r s t th e m easurements o f th e e l l i p t i c i t y , ^

, F igu re 29 .

o f th e t h ic k n e s s ,

The e r r o r s cf measurement both o f ^ cL , a re shown in th e f ig u r e , to g e th e r

w ith a t h e o r e t i c a l curve c a lc u la te d u sin g eq u a tio n 2*3 P a rt I . cu rves

and

of

A comparison o f th e t h e o r e t ic a l and ezp erim en ta l ± lo w s

th a t f o r v a lu e s o f

^

between 3oo and 2oO ^ ,

th e exp erim en tal v a lu e s a re h ig h e r than th e t h e o r e t i c a l by a s l i g h t , but s ig n if ic a n t , amount, and f o r v a lu e s of

le s s

than 1 5 0 ^ , th e ex p eriem en ta l v a lu e s a re c o n sid e r a b ly below

lOO _ ^ L K _ M I A L _ C I H _ E O R y J).

•T H E O R Y

E X P E R IM E N T .

080

F I G U R E 29. SILVER

040

020

20 lO O A

30

5 0 300A

200A

F IGURE 3 0

400A

500A

SILVER 5400A

CURVE P O IN T S

CALCULATED E X P E R IM E N T A L

025

020

(TH EO R-C;

BU LK M ETAL»

C IO 0-05 20 lO O A

200A

30

50

4 0 300A

400A

500A

600A

118. th e t h e o r e t i c a l o n e s.

I t appears l i k e l y th a t th e marked

d iv er g en ce o f th e v a lu e s o f p

from th e t h e o r e t ic a l curve

f o r v er y t h in la y e r s i s due to a change in th e o p t ic a l c o n sta n ts o f th e la y e r s im ila r to th a t ob served by Rouard, Krautkramer, e t c . , f o r th e normal in c id e n c e r e f l e x io n c o e ffic ie n ts . •Bie v a r ia t io n o f p

w ith

(i

in F ig u re 29 shows

th a t f o r a la y e r t o g iv e e l l i p t i c i t i e s i d e n t i c a l to w ith in ±

w ith th o s e g iv e n by r e f l e x io n at a b ulk m etal

su r fa c e i t must be a t l e a s t 450/9 t h ic k .

U sing th e data

o f th e p r e v io u s ch a p ter (F ig u r e s 23 and 24) t h i s means th a t th e la y e r must have a r e f le x io n c o e f f i c i e n t g r e a te r th an 0*90 and a tr a n sm is sio n l e s s than 0*04 ( ^ . F ig . 2 6 ). F ig u re 30 shows th e v a r ia tio n of th e r e l a t i v e p h ase ,change, ^

, w ith th e t h ic k n e s s ,

cL .

I t i s seen

th a t w ith in th e l i m i t s o f a ccu racy o f th e experim ent th e r e i s no s ig n i f i c a n t d iff e r e n c e betw een th e ex p erim en ta l p o in t s and th e t h e o r e t ic a l curve down to th e s m a lle s t t h ic k n e s s e s m easured, 125/9 .

I t sh ou ld be n oted t h a t th e exp erim en tal

er r o r in c r e a s e s w ith d e c r e a sin g th ic k n e s s f o r th e rea so n s d is c u s s e d in P a rt I I I ,

Chapter I I I .

Some o f th e s e p o in t s

were o b ta in ed u sin g an in te r fe r o m e te r composed of two la y e r s o f n e a r ly i d e n t i c a l t h ic k n e s s , th e mean th ic k n e s s b ein g

119. g iv e n in th e graph, and o th e r s u sin g one la y e r o f th e t h ic k ­ n e s s shown, and one la y e r g r e a te r than 4 0 0 ^ t h ic k , fo r which a v a lu e o f

tak en from F igu re 27 was u se d ,

be seen from th e graph th a t th e v a lu e o f ^

i t can -

fo r r e f le x io n

a t a la y e r o f th ic k n e s s not l e s s than 3 5 0 A i s th e same as th e v a lu e o f A to w ith in

f o r r e f l e x io n a t th e su r fa c e o f bulk s i l v e r

l€ . In c o n sid e r in g th e u se o f th e te c h n iq u e s d e sc r ib e d

in t h i s work f o r th e d eterm in a tio n o f th e o p t i c a l c o n sta n ts o f bulk m a t e r ia ls , u s in g evap orated la y e r s a s c h a r a c t e r is t ic s u r f a c e s , th e c o n c lu sio n t o be drawn from t h e s e m easure­ m ents i s th a t w h ils t th e la y e r s used in th e in te r fe r o m e te r can have tr a n s m is s io n s o f up t o 0*07 and s t i l l y i e l d v a lu e s of A

eq u al t o th e bulk m eta l v a lu e s , th e v a lu e s o f ^

o b ta in ed d ecr ea se f a i r l y r a p id ly from th e bulk m eta l v a lu e as th e v a lu e o f th e tr a n s m is s io n in c r e a s e s beyond 0*04. When th e tech n iq u e i s u sed w ith m e ta ls , such a s s i l v e r , which shows a c o n ^ a r a tiv e ly low a b so r p tio n in tra n sp a ren t la y e r s , measurements on

yO and

A

can both be made on th e

same la y e r s , o f tr a n s m is s io n say 0 '0 2 .

However, i f h ig h ly

ab sorb in g m e ta ls are to be in v e s t ig a t e d , a tr a n s m is sio n o f o n ly 0*02 y i e l d s a v e r y low v a lu e f o r th e maximum i n t e n s i t y o f th e in t e r f e r e n c e f r in g e s used in th e measurement o f A (dependent upon j / ( / f 4^)^ ) .

For m e ta ls o f t h i s k ind a

more s a t i s f a c t o r y p rocedu re would be t o p rep are a number

120. o f opaque or v ery n e a r ly opaque la y e r s fo r th e measurement of th e e l l i p t i c i t y , and t o p rep are la y e r s o f tr a n sm issio n about 0*05, f o r th e measurement o f th e r e l a t i v e p hase change. F in a lly , i t can be m entioned th a t th e o p t ic a l m easurements g iv e n h e r e , s u g g e s tin g a minimum th ic k n e s s o f 450 A f o r la y e r s o f s i l v e r to be c h a r a c t e r is t ic o f th e bulk m e ta l, i s in agreem ent w ith th e o b s e r v a tio n s o f workers u s in g o th e r te c h n iq u e s , quoted in p a r t I , Chap. TV.

Ck, THE OPTICAL PROPERTIES OF^TIN, SfECUlüM AND A TIN-NICKSL ALLOY

Chapter H I .

The te c h n iq u e s d e sc r ib e d have been u sed to i n v e s t ig a t e th e o p t ic a l p r o p e r t ie s o f copper, t i n , speculum , and a new a l l o y b e lie v e d to be



The m easurem ents

were made on t h ic k ev a p o ra ted la y e r s o f t h e s e m e ta ls and a l l o y s , and th e o p t ic a l c o n s ta n ts c a lc u la te d from th e m easurem ents.

In ord er th a t th e o p t ic a l p r o p e r t ie s observed

cou ld be taken a s th o s e o f th e b u lk m a te r ia l, th e la y e r s were d e p o site d t o th e o rd er s o f t h ic k n e s s (a s in d ic a te d by th e tr a n sm is sio n ) su g g e ste d by th e r e s u l t s d e sc r ib e d in th e p r e v io u s ch ap ter on th e v a r ia t io n of th e p r o p e r t ie s of s i l v e r la y e r s w ith t h e i r t h ic k n e s s e s . The d if f e r e n t m e ta ls and a l l o y s w i l l be d is c u s s e d s e p a r a te ly . Copper. Measurements were made on e ig h t th ic k la y e r s o f copper, produced by ev a p o ra tio n in th e h o r iz o n t a l ev a p o ra tio n p la n t .

Four o f t h e s e la y e r s were opaque, or v er y n e a r ly

so ( T