ORIENTATIONAL DYNAMICS OF SULPHATE IONS IN POTASH ALUM

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ORIENTATIONAL DYNAMICS OF SULPHATE IONS IN POTASH ALUM

A. Sood, A. Arora, S. Dattagupta, G. Venkataraman

To cite this version:

A. Sood, A. Arora, S. Dattagupta, G. Venkataraman. ORIENTATIONAL DYNAMICS OF SUL- PHATE IONS IN POTASH ALUM. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-572-C6-574.

�10.1051/jphyscol:19816166�. �jpa-00221244�

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JOURNAL DE PHYSIQUE

ColZoque C6, suppZ6ment au n012, Tome 42, de'cembre 1981 page C6-572

ORIENTATIONAL DYNAMICS OF SULPHATE IONS I N POTASH ALUM

A.K. Sood, A.K. Arora, S. Dattagupta and G. Venkataraman Reactor Research Centre, KaZpakkam 603 102, TamiZ Nadu, I n d i a

P b s t r a c t . - The A i n t e r n a l mode o f s u l p h a t e i o n i n p o t a s h alum i s

'J

s t u d i e d b y Raman s c a t t e r i n g a s a f u n c t i o n o f t e m p e r a t u r e . Cur d a t a s u g g e s t t h a t o v e r a n d a b o v e t h e t h e r m a l l y - a c t i v a t e d r e o r i e n - t a t i o n s o f s u l p h a t e i o n , t h e r e i s a n a d d i t i o n a l o r i e n t a t i o n a l r e l a x a t i o n mechanism w h i c h h a s i t s o r i g i n i n c o o p e r a t i v e i n t e r - a c t i o n b e t w e e n s u l p h a t e i o n s .

1. I n t r o d u c t i o n . - In p o t a s h a l u m (KAl (SO4 )2. 1 2 5 ^{O ) ,} t h e s u l p h a t e i o n h a s two o r i e n t a t i o n s l w i t h t h e S - 0 b o n d s p o i n t i n g t o w a r d s A 1 3 + o r K + w i t h p r o b a b i l i t i e s pl o r p 2 (p1) p 2 ). T h i s c a u s e s a s p l i t t i n g o f t h e A i n t e r n a l mode o f t h e s u l p h a t e i o n i n t o two n e a r 990

In t h i s p a p e r , t h e a r e a r a t i o i.e. t h e r a t i o o f t h e number o f s u l p h a t e i o n s i n t h e two o r i e n t a t i o n s i s s t u d i e d a s a f u n c t i o n o f t e m p e r a t u r e t o u n r a v e l f e a t u r e s related t o r e o r i e n t a t i o n s .

2. Experlmenta1.- S i n g l e c r y s t a l s o f p o t a s h alum w e r e c u t p e r p e n d i - c u l a r t o t h e (100 a x i s i n t o a p a r a l l e l o p i p e d o f a p p r o x i m a t e s i z e 6 X 6 X 5 (mm 3

.

I h e d e t a i l s o f t h e Raman s p e c t r o m e t e r a r e same a s r e p o r t e d e a r l i e r 4

.

The e x p e r i m e n t s w e r e d o n e a t 24 d i f f e r e n t tempe- r a t u r e s b e t w e e n 297 K and 93 K.

3. Fesu1ts.- f i g u r e 1 shows t h e a r e a r a t i o . A t 297 K, we o b t a i n (p1/p2 ⁼2.46 2 0.08, i n a g r e e m e n t w i t h x-ray s t u d i e s 1

.

In o r d e r t o i n t e r p r e t t h e d a t a , weF3ssume f i r s t t h a t i o n s make t h e r m a l l y a c t i v a t e d jumps b e t w e e n t h e two o r i e n t a t i o n s a t r a t e s

p h

y2 ⁼ e x p (-E1/kgT), (1 )

P h

3, ⁼

L6/

^{e x p}^-[ ( E I - E ) / ~ BiJ

7

w h e r e

vo, JJl

a r e t h e a t t e m p t f r e q u e n c i e s . E i s t h e e n e r g y s e p a r a - t i o n b e t w e e n t h e two o r i e n t a t i o n a l p o t e n t i a l minima, and E ' i s t h e b a r r i e r h e i g h t a s s e e n f r o m t h e b o t t o m o f t h e d e e p e r w e l l (see F i g u r e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816166

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Fiq. 1 : A e a r a t i o as a f u n c t i o n o f t e m p e r a t u r e . The d o t s are t h e o b s e r v e d v a l u e s . The d a s h e d l i n e c o r r e s p o n d s t o eq. (3 ) ( d = 0 ) and t h e s o l i d l i n e i s b a s e d o n a model w h i c h < i n c l u d e s a t e m p e r a t u r e -

i n d e p e n d e n t r e l a x a t i o n mechanism (i.e. f#= 0 ).

p h p h

2 ). From d e t a i l e d b a l a n c e , pl = p 2

Y1

, whence

Tne d a s h e d l i n e i n f i g u r e 1 shows t h a t ( 3 ) i s o b e y e d f o r T ,240 K b u t i s i n a d e q u a t e a t l o w e r t e m p e r a t u r e s .

W2 1 C?

-

1 2

0 NI2

ANGLE --+

F5.q. 2 : P h e m a t i c d r a w i n g o f t h e a n g u l a r d e p e n d e n c e o f t h e p o t e n t i a l w e l l i n w h i c h (S04)2- i o n s r e s i d e . 1 a n d 2 r e f e r t o t h e two o r i e n t a t i o n s o f t h e i o n .

m e A r r h e n i u s - t y p e a p p r o a c h b e i n g i n a d e q u a t e , we now p o s t u l a t e t h e e x i s t e n c e o f a n a d d i t i o n a l t e m p e r a t u r e - i n d e p e n d e n t r e o r i e n t a t i o n mechanism, a n d w r i t e t h e r a t e s a s

p h ph

W12 = b$2 + b/ ^{a n d} = %l + j/

A p l a u s i b l e p h y s i c a l o r i g i n o f f i s d i s c u s s e d i n S e c t i o n 5.

4. Raman l i n e shape.- Fbr t h e A i n t e r n a l mode, t h e Gaman l i n e s h a p e 9

i ^Sp r o p o r t i o n a l t o

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JOURNAL DE PHYSIQUE

F ( W 1 . j d t e x p b i w t ) ((((0) it)),

- 0 2

w h e r e Q d e n o t e s t h e v i b r a t i o n a l c o o r d i n a t e . Cwing t o t h e zandom jumps o f t h e two p o s s i b l e o r i e n t a t i o n s , t h e v i b r a t i o n d l f r e q u e n c y o f t h e A mode f l u c t u a t e s b e t w e e n d1 a n d Cd2. Fbr t h i s s i t u a t i o n ,

9

t h e l i n e s h a p e s c a n b e c a l c u l a t e d f r o m 5

A f t e r i n c l u d i n g t h e e f f e c t s o f a n h a r m o n i c i t y a n d i n s t r u m e n t a l r e s o - l u t i o n 4 , eq. (5 ) a l o n g w i t h (1 ), (2 ) a n d (4 1 w e r e u s e d t o c o m p u t e t h e l i n e s h a p e s a n d a l s o t h e a r e a r a t i o s . The p a r a m e t e r s w h i c h r e s u l t e d i n good a g r e e m e n t f o r t h e l i n e s h a p e s a r e : V. ⁼V' =

0

3 X 10" sec-', E = 0.527 KCal/mole, E ' = 1.239 KCalLmole and

6 ⁼1.65 X 10' sec-'. I h e a r e a r a t i o e x t r a c t e d b y s u c h a n a n a l y s i s i s shown w i t h a s o l i d l i n e i n f i g u r e 1. C l e a r l y i t r e p r e s e n t s b e t t e r t h e o b s e r v e d r a t i o s .

5. Q r i q i n o f

.-

^l&now c o n s i d e r t h e o r i g i n o f f

.

^Asd i s c u s s e d i n d e t a i l e l s e w h e r e 6 , c o n c e i v a b l y a r i s e s d u e t c 3 f l i p - f l o p r e l a x a - t i o n , i.e, when i o n i makes t h e o r i e n t a t i o n a l jump 1-2 ( s a y ),

a n o t h e r i o n j s i m u l t a n e o u s l y makes a reverse jump 2-1. C a l c u l a t i o n s 6 show t h a t f l i p - f l o p mechanism d o e s l e a d t o a t e m p e r a t u r e - i n d e p e n - d e n t r a t e

REFERENCES

1. L a r s o n , A.C. a n d Cromer, D.T., P c t a C r y s t . 2 3 793 (1967 1.

2. K r i s h n a n , R S , E r a y a n a n , P. S. and V e n k a t e s h , G,M

,

w o c . F i f t h I n t . Conf. %man a e c . ed. S c h u l z (FRG: W e i b u r g ) .

3. Q s e l , H.H. and Szhumacher, G , ^Chem. ^Fhys. ^Lett. 47, 1'68 (1977 ).

4. S o d , A. K , P r o r a , A.K., Unadevi, V. a n d W n k a t a r a m a n , G , wamana 1 6 , 1 ('1981 1.

5 . Anderson, P. W , ^J. Fhys. %c. J a p a n , 9, 316 (1954 ).

6. % o d , A.K., A r o r a , A-K., I B t t a g u p t a , S. a n d Wnkakaraman, G ,

l b a p p e a r i n J. R y s . C. ( 1 9 8 1 ) .