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J O N A S AND

M.J. L U T O N

I N a r e c e n t c o m m u n i c a t i o n , r A r s e n a u l t d i s c u s s e d the p r o b a b l e i m p o r t a n c e of the a c t i v a t i o n e n t r o p y A S in a n a l y s e s of l o w t e m p e r a t u r e d e f o r m a t i o n . H e b a s e d his a r g u m e n t o n a n e v a l u a t i o n of the relation: T

AS(T) : A S o +

f

(OAS/OT)r*dT

[1]

o

t h r o u g h the i d e n t i t y :

( a A s / a r ) r . = ( 1 / T ) ( a A / / / a T)r*

[2]

H e r e ASa, the a c t i v a t i o n e n t r o p y a t a b s o l u t e z e r o , i s z e r o , 2 and AH, the a c t i v a t i o n e n t h a l p y , i s u s u a l l y s t r e s s d e p e n d e n t , a n d m a y also have a M i g h t t e m p e r a ture dependence.a Arsenault concluded that, inasmuch a s (~AH/aT)r, d i d n o t d e p a r t s i g n i f i c a n t l y f r o m z e r o o v e r the e x p e r i m e n t a l r a n g e , the e f f e c t of AS c o u l d f o r all p r a c t i c a l p u r p o s e s b e i g n o r e d . Due t o the lack o f e x p e r i m e n t a l d a t a , A r s e n a u l t d i d n o t i n c l u d e i n h i s i n t e g r a t i o n the r a n g e f r o m 0 ° t o 3 0 ° K , w h i c h is o f c r u c i a l i m p o r t a n c e for s u c h a c a l c u l a t i o n , a s w i l l b e s h o w n b e l o w . He a l s o d i d n o t i n c l u d e i n E q . [1] the i n t e g r a l : T*

f

(aAS/O'r*)Tdl-*

[3]

o

w h i c h can b e e v a l u a t e d t h r o u g h the t e m p e r a t u r e d e p e n d e n c e of the a c t i v a t i o n a r e a A * , a s g i v e n b y : 2

(~AS/a "r*)T = b(OA*/aT)r. T h e a d d i t i o n of t h i s

[4]

t e r m l e a d s t o the e x p r e s s i o n : T

AS(T, "1-*) : A S o + o f (OAS/OT)r*dT T*

+ f (aAS/OT*)Td'r*

[5]

o

J. J. JONAS and M. J. L U T O N are Associate Professor and Research Associate, respectively, Department of Metallurgical Engineering, McGill University, Montreal, Canada. Manuscript submitted June 18, 1971. 3492

VOLUME 2, DECEMBER 1971

o T$

+b

f

[(~A*/or)r*JTdT*

[6]

o

It i s the p u r p o s e of t h i s n o t e t o e v a l u a t e AS m o r e c o m p l e t e l y , t h r o u g h the u s e of r e l a t i o n s 115] a n d [6], a n d t o show that AS i s n o t i n f a c t n e g l i g i b l e a b o v e a b o u t o n e - t e n t h of the D e b y e t e m p e r a t u r e , In a d d i t i o n t o r e l a t i o n s [5] a n d [6] a b o v e , AS c a n b e e v a l u a t e d d i r e c t l y , by m e a n s o f a n a c t i v a t i o n f r e e e n e r g y AG v s T d i a g r a m a n d the e x p r e s s i o n :

AS = - ( a A G / a T ) r , = k(a[T i n (~/~)]/aT)r, [7] H e r e 4, i s the p r e e x p o n e n t t a l i n the r e l e v a n t r a t e e q u a t i o n . In F i g . 1 , a AG-T p l o t i s s h o w n , b a s e d o n s o m e r e c e n t m e a s u r e m e n t s o f the y i e l d s t r e s s o f c~ z i r c o n i u m p e r f o r m e d b y the a u t h o r s . 4 T h e s e m e a s u r e m e n t s w e r e c a r r i e d o u t b e t w e e n 6 2 5 ° a n d 8 2 5 ° C and at h a l f - d e c a d e s t r