ON THE POSSIBLE USE OF OPTICAL ROTATION MEASUREMENTS FOR DETECTING WEAKLY IR ACTIVE MODES

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ON THE POSSIBLE USE OF OPTICAL ROTATION

MEASUREMENTS FOR DETECTING WEAKLY IR

ACTIVE MODES

V. Sahni

To cite this version:

JOURNAL DE PHYSIQUE

CoZbque C6, sypplkment au n012, T o m 42, ddcembre 1981 page C6-881

ON THE P O S S I B L E USE OF O P T I C A L ROTATION MEASUREMENTS FOR D E T E C T I N G WEAKLY I R A C T I V E MODES

Nuclear Physics Division, Bhabha Atontic Research Centre, Trombay, Bombay

400 085, India

Abstract.-

IR

a c t i v i t y of normal mode8 of a c r y s t a l is usually m m t e d through r e f l e c t i o n o r tranemiasion meaeuntments. We propose here a n o t h e r way which should be u s e f u l f o r studying modes of weak

IR

a c t i v i t y . The method involves measuring t h e r o t a t i o n angle 8 , of t h e plane o f p o l a r i z a t i o n of a monochro- matic beam of frequency LI)

,

a s t h e beam t r a v e r s e s a c r y s t a l of

t h i c k n e s s d . By etudying 0 a s a function of i n c i d e n t frequency

w one would observe a 'resonance* close t o eaah I R a c t i v e f r e - quency (3 j

.

The method would be f e a s i b l e i f t h e r e i s appre-

c i a b l e transmission o f t h e beam t h a t is t h e o s c i l l a t o r s t r e n g t h of t h e mode i e small. We suggest a system, namely, LiKSOq, where t h i s i d e a could be applied. In p a r t i c u l a r we d i s c u e e how

t h e symmetric s t r e t c h i n g mode of SO which is

IR

i n a c t i v e f o r

a f r e e ion but i e w e a k l y I R a c t i v e i n t h i s c r y s t a l , could be i n v e s t i ~ a t e d using d i f f e r e n t wavelengths of a CO;! l a e e r . P o t e n t i a l i t y of t h e proposed technique f o r i n v e s t i g a t i n g phase t r a n s i t i o n s , wherein c e r t a i n Ramn a c t i v e modee a c q u i r e weak

IR

a c t i v i t y a c m e 8 t h e t r a n s i t i o n a r e mentioned.

1. Introduction.- The infra-red (El) a c t i v i t y of l o n g wave- l e n g t h modes of a a r y s t a l is t r a d i t i o n a l l y i n v e s t i g a t e d v i a t h e f i r a t o r d e r procese involving r e f l e c t ion o r transmiaeion

and a wealth of data h a s been accumulated i n

t h i s way. Here we propose another way of d e t e c t i n g weakly I R a c t i v e modee. The method involve8 monitoring t h e r o t a t i o n 0 of t h e plane of p o l a r i z a t i o n o f a monochromatic beam of frequency

a

(ae it paseea through a c r y s t a l ) as a f i n c t i o n of 0

.

_&om

t h e reeonances which w i l l be e x h i b i t e d by t h i s function it should be p o s s i b l e t o i n f e r t h e IR d i s p e r s i o n frequencies. We w i l l o u t l i n e t h e p h y s i c a l b a s i s of t h e method i n s e c t ion 2 and a l e o p o i n t o u t t h e circumstances when the technique would be feasible. A poeeible t e s t case, where t h e idea8 suggested here could be a p p l i e d , 1e discussed i n s e c t i o n 3 and c e r t a i n remarks a r e made r e g a r d i n g t h e u t i l i t y of t h i s technique i n inoestiga- t i n g c e r t a i n phaee t r a n a i t i o n a .

2. Physical Basis of t h e Method.- It is known t h a t t h e phenomenon of o p t i c a l r o t a t i o n , v i e . r o t a t i o n of plane o f

C6-882 JOURNAL DE PHYSIQUE

p o l a r i e a t i o n of a plane p o l a r i s e d beam i n t r a v e r s i n g a medium, can occur even f o r a medium whoee r e a l d i e l e c t r i c t e n s o r i s i s o t r o p i c ,

3

purely on account of e f f e c t s of s p a t i a l d i e p e r s i o n

.

Born and Huang have shmn t h a t t h i s e f f e c t can cause, i n a c r y s t a l otherwise f r e e from double r e f r a c t i o n , t h e r i g h t and l e f t c i r c u l a r l y p o l a r i z e d b e a m t o t r a v e l w i t h d i f f e r i n g phaee v e l o c i t i e s . Since a plane p o l a r i z e d be= can be expressed a s a s u p e r p o s i t i o n of two such c i r c u l a r l y p o l a r i z e d b e a m , t h e above d i f f e r e n c e i n phase v e l o c i t i e s r e s u l t s i n a r o t a t i o n of t h e plane of p o l a r i z a t i o n a s t h e beam t r a v e r e e s i!he medium. One can show3 t h a t even f o r u n i a x i a l c r y s t a l e when t h e beam

propagate0 along t h e unique axia similar c o n s i d e r a t i o n s hold, and f u r t h e r t h e r o t a t i o n angle 0 i s r e l a t e d t o $ t h r o u g h

e

0 4 .

2)

a

( 1 )

3 t.

where G i e t h e gyration v e c t o r , k a u n i t v e c t o r along t h e beam d i r e c - t i o n and d i s t h e thicknecsa of the c r y s t a l . The c a l c u l a t i o n of t h e

-D

g y r a t i o n v e c t o r G r e q u i r e s one t o c a l c u l a t e t h e wave v e c t o r dependence of d i e l e c t r i c s u s c e p t i b i l i t y Q d P (

3 ,

~ 3 ) ; t h a t i e e f f e c t s of

s p a t i a l d i e p e r s i on have t o be incorporated. E x p l i c i t c a l c u l a t i o n e have been (without i n c l u d i n g t h e damping e f f e c t e ) f o r t h e r i g i d ion model case. It emerges t h a t t h e l e a d i n g ( l i n e a r )

d

dependence o r i g i n a t e s from t h e imaginary p a r t

2

,

(of

a,

(

4,

w

1

), which is 80 antisymmetric t e n s o r , and t h e

-C

components of g y r a t i o n v e c t o r G a r e defined through

( cc

,

4

are c y c l i c o r d e r o f 1,2,3) Within t h e l i m i t of n e g l i g i b l e damping, one can w r i t e a somewhat more g e n e r a l form (than f o r t h e r i g i d ion model) f o r t h e g y r a t i o n v e c t o r

3

and t h i s t u r n s out t o be

-3

(c/f Born and Huangla (44.69)) where

iT

(

i )

i s t h e d i p o l e moment o f t h e j t h mode and w

( 6 )

i t s d i s p e r e ion frequency. (For an

IR

inac-

-?

t ive mode t

( i )

= 0 , hence

8

d e r i v e s c o n t r i b u t i o n only f r o m

IR

a c t i v e modes )

.

3

( ) involves the eigenvectore of t h e die-

Upon using equation (3) i n equation (1) we f i n d t h a t i f we s t u d y t h e

o

dependence of the r o t a t i o n angle 0 , then it would show resonancss cloee t o each diapereion frequency. In t h i s m y , by experimentally measuring t h e r o t a t i o n of plane of p o l a r i z a t i o n of a monochrOmatic beem of frequency t h e d i e p e r e l o n f r e q u e n c i e s of

IR

a c t i v e mode8 can be located. Of couree, it i s obvioue t h a t f o r t h e method t o be prac- t i c a l , the tranemieeion of the beam ehould be appreciable. This means t h a t t h e method would be f e a s i b l e only f o r modes of r a t h e r weak

IR

a c t i v i t y . However, t h e important point t o note is t h a t reeonant charac- t e r of 8 as a function of

o

holds even f o r modes o f weak a c t i v i t y , and hence t h e method could be u s e f u l i n t h e i r study provided t h e attenua-

-1 t i o n c o e f f i c i e n t i s

sw

,C 50 cm

.

3. Test Case and U t i l i t y . - A t e s t i n g ground, where t h e technique suggested i n t h i s paper could be t r i e d , is provided b t h e eystem

f

LiKSOq. T h i s i s a c r y s t a l belonging t o t h e eymmetry C6 a t room tempera- t u r e and t h e r e a r e two molecules p e r u n i t c e l l . In t h e f r e e ion s t a t e we knm t h a t t h e symmetric s t r e t c h i n g mode 3, i s I R i n a c t i v e . In liilG90q,

however, becauee one o f the oxygen atoms is inequivalent compared t o o t h e r t h r e e , t h i s mode t o o a c q u i r e s

IR

a c t i v i t y . Of course, t h e lR

a c t i v i t y is expected t o be extremely weak and so t h e p r e s e n t zm thod could be t r i e d . From Raman measurements it i e known t h a t the frequency of t h i s mode l i e s at 1008 cm-l. A canvenient source of monochromatic r a d i a t i o n w culd t h e n be a

C 4

l a s e r which o f f e r e e e v e r a l wavelengths l y i n g i n the range 960cm-' t o 1060 cm". The beam could be made t o Pam along t h e unique a x i e of t h e c r y s t a l , whose f a c e s a r e c u t s o a e t o be normel t o t h e unique a x i s . By monitoring t h e r o t a t i o n angle 8 a e a f u n c t i o n o f

w

one can see whether

IR

a c t i v i t y of t h e mode can be e e t a b l i e h e d i n t h i e way.

I f t h i s technique proves f e a s i b l e t h e n one could employ it t o etudy phaee t r a n s i t i o n s wherein t h e i n v e r s i o n symmetry is loet/acquired a c r o s s t h e t r a n e i t i o n p o i n t . Often i n such case0 c e r t a i n Raman a c t i v e modes lose/acquire IR a c t i v i t y b u t t h e e f f e c t s a r e r a t h e r weak. In

such s i t u a t i o n s , when t h e v i b r a t i o n a l frequency i s already known from Raman d a t a , t o e s t a b l i s h whether t h e a c q u i s i t i o n of I R a c t i v i t y by t h e mode has occurred o r not could be a s c e r t a i n e d by t h e proposed technique. Referencesi- 1. I. Born and K. Huang, Dynamical Theory of C r y s t a l

t a t t i c e e (Oxford Univ. Preee 1 1954.

2. G. Venkataraman, L.A. Feldkamp and V.C. Sahni, Dynamics of P e r f e c t C r y s t a l s ( M I T P r e s s

,

Cambridge, Mass ) 1975.