The entropy of thermally activated plastic deformation
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The Entropy of Thermally Activated Plastic Deformation R.J.
p e n d e n c e of t h e f o r c e d i s t a n c e d i a g r a m of t h e s h o r t r a n g e b a r r i e r to d i s l o c a t i o n m o t i o n i s d u e to t h e t e m p e r a t u r e d e p e n d e n c e of t h e s h e a r m o d u l u s . A s a r e s u l t t h e f o l l o w i n g e x p r e s s i o n of e n t r o p y c a n b e o b t a i n e d
AS-
O~ [AC. + raA(r*)bJ, ~1 OT
where 7a
___
A,~I + T - - A ( 7 * ) b
AG=
1
0g
OT
T ~I
.gT"
A(T*) is t h e a c t i v a t i o n a r e a , b is the B u r g e r s v e c t o r , i s the s h e a r m o d u l u s , ra i s t h e a p p l i e d s t r e s s , a n d a H i s the e n t h a l p y . If t h e low t e m p e r a t u r e d e f o r m a t i o n of i r o n a n d neutron-irradiated copper are considered along with E q . [2], t h e n t h e m a g n i t u d e of T A S iS s m a l l . F o r e x a m p l e TAS = 0.037 e v f o r i r o n a t 300~ a n d ~,H0 = 0 . 5 5 e v w h e r e A//~ iS t h e c h a n g e of e n t h a l p y a t r * = 0. In t h e c a s e of n e u t r o n - i r r a d i a t e d copper, T A S = 0.04 e v a t 300~ a n d AHo = 3.0 e v . T h e s e r e suits indicate that for all practical purposes the effect of ,iS c a n b e i g n o r e d , f o r t h e v a l u e o f AS is w i t h i n t h e s c a t t e r of d a t a in t h e d e t e r m i n a t i o n s of a H . H o w e v e r , E q . [2] m a y not c o m p l e t e l y d e f i n e ~ S , f o r t h e r e may be a vibrational entropy component as proposed by G r a n a t o e t a l . '~ T h e r e f o r e , AS m a y n o t b e s m a l l . The entropy can be determined from experimental
ARSENAULT
T H E influence of temperature on the rate of plastic deformation has been studied for many years. Several early investigators have proposed that plastic deformation could be described in terms of an Arrhenius equation, t'2 From these early investigations, a detailed analysis of dislocation motion in terms of the absolute reaction rate theory~ has been performed by a number of investigators.4-~' The main equation in these analyses is as follows; the average dislocation velocity can be deftued as L, = vo exp
k~,a T
['1
Fig. l--The temperature
dependence
of t h e a c t i v a t i o n e n e r g y
of slip at constant effective s t r e s s . (Ref. 12).
where vo is a preexponential factor, and AG is the appropriate Gibbs free energy,s One of the difficulties that a r i s e s when considering the above equation is due to the fact that experimentally it is only possible, in a direct manner, to measure the change in the enthalpy (AH). Therefore, it would be advantageous to rewrite the above equation in terms of AH and the change in entropy (AS). Then it would be possibie to compare the experimentally measured ~XH and the ,x// obtained from a particular model chosen to represent the short range barrier to dislocation motion. Schoeck~ has proposed that AS associated with thermally activated dislocation motion can be determined, for he has assumed that the entire temperature deR. J. AR
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