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On the interaction of foreign interstitial atoms with vacancies in α-Fe and group-V transition metals
Scripta
METALLURGICA
ON THE
Vol. ii, pp. 817-823, 1977 P r i n t e d in the U n i t e d States
INTERACTION
OF F O R E I G N
IN e-FE
AND
INTERSTITIAL
GROUP-V
ATOMS
TRANSITION
METALS
Pergamon
WITH
(Received
June
24,
Inc.
VACANCIES
*
M . M o n d i n o and A . S e e g e r ** de F i s l c a Dr. Jos@ B a l s e i r o , C e n t r o A t 6 m i c o , B a r i l o c h e , Rio Negro, The A r g e n t i n e
Instituto
Press,
S.C.
de
1977)
I. I n t r o d u c t i o n R e c e n t work on q u e n c h i n g of i r o n - m o l y b d e n u m alloys (I), on the r e c o v e r y of positron annihilation, i n t e r n a l f r i c t i o n , and r e s i s t i v i t y of n e u ~ g n - i r r a d i a t e d iron (2-4), on the M S B b a u e r effect of iron foils i m p l a n t e d with " ~ X e (5), as w e l l as on h i g h - v o l t a g e e l e c t r o n m i c r o s c o p y (6), h i g h - t e m p e r a t u r e p o s i t r o n annihil a t i o n (7), and s e l f - d i f f u s i o n of pure iron (8) has shown, with i n c r e a s i n g certainty and p r e c i s i o n , that in e - i r o n the m o n o v a c a n c y m i g r a t i o n enthalpy, Hyv , is not very d i f f e r e n t from the m o n o v a c a n c y f o r m a t i o n enthalpy H~V. The best p r e s e n t v a l u e for the d i f f u s i o n c o e f f i c i e n t of m o n o v a c a n c i e s in iron b e t w e e n 400K and 550K is given by (7) -I = a2ViV = 0.5 exp(- 1.28 eV/kT) cm2s (I) DIVIo (a = 2 , 8 6 " 1 0 m = l a t t i c e p a r a m e t e r , VIV = m o n o v a c a n c y jump f r e q u e n c y ) **~. Comp a r i s o n of Eq.(1)with the l o w - t e m p e r a t u r e d i f f u s i o n c o e f f i c i e n t s of i n t e r s t i t i a l l y d i s s o l v e d c a r b o n atoms (9) DC =
exp(-0.81
e V / k T ) c m 2 s -I
,
(2)
D N = 1.26"10 -3 e x p ( - 0 . 7 6
e V / k T ) c m 2 s -I
,
(3)
or n i t r o g e n
1.67-10 -3
atoms
(9)
shows that at t e m p e r a t u r e s b e t w e e n 300K and 40OK, at w h i c h c a r b o n and n i t r o g e n atoms in e - i r o n are q u i t e m o b i l e , m o n o v a c a n c i e s are v i r t u a l l y i m m o b i l e . This means that in this t e m p e r a t u r e range a s u p e r s a t u r a t i o n of m o n o v a c a n c i e s may act as traps for m i g r a t i n g carbon or n i t r o g e n atoms *z** The h y p o t h e s i s that v a c a n c i e s in i r r a d i a t e d iron may form traps for c a r b o n was first made and s u p p o r t e d by e x p e r i m e n t a l e v i d e n c e in a series of papers by D a m a s k and c o l l a b o r a t o r s (12-15). The recent d e v e l o p m e n t s m e n t i o n e d above s u p p o r t s t r o n g l y the c o r r e c t n e s s of this h y p o t h e s i s . A n a l o g o u s e v i d e n c e for the t r a p p i n g
Dedicated
to W . K 6 s t e r
**
Permanent
address:
on the
occasion
of his
80th
birthday
(22.11.1976).
*~*
At 473K Eq.(I) p r e d i c t s of-magnitude estimate
*~**
The same is p r e s u m a b l y also true for o x y g e n ( m i g r a t i o n e n e r g y ( 0 . 9 8 ± 0 . I 0 ) e V (9,10)), but o w i n g to the e x t r e m e l y low s o l u b i l i t y of o x y g e n in e-Fe o b s e r v a t i o n s a n a l o g o u s to those on C and N p r o v i d i n g u n e q u i v o c a l e v i d e n c e for t r a p p i n g by v a c a n c i e s are a p p a r e n t l y not a v a i l a b l e .
Max-Planck-lnstitut fur M e t a l l f o r s c h u n g , I n s t i t u t fur P h y s i k , P o s t f a c h 80 06 65, D - 7 0 0 0 S t u t t g a r t 80, G e r m a n y . ~ i V = 1 4 s -I in s a t i s f a c t o r y a g r e e m e n t ~iv~Is -I from M 6 B b a u e r m e a s u r e m e n t s
817
with (5).
the
order-
818
VACANCIES
of n i t r o g e n
by
vacancies
IN T R A N S I T I O N
METALS
in n e u t r o n - i r r a d i a t e d
a-Fe
Vol.
was
found
II, No.
somewhat
later
9
(161
The p r e s e n t note d e a l s m a i n l y w i t h the c o n s e q u e n c e s of the t r a p p i n g of carb o n or n i t r o g e n by m o n o v a c a n c i e s for the p h y s i c a l m e t a l l u r g y of a - i r o n , in part i c u l a r for the d e t a i l e d u n d e r s t a n d i n g of the s o - c a l l e d c o l d - w o r k r e l a x a t i o n p e a k a s s o c i a t e d w i t h c a r b o n and n i t r o g e n ( S e c t . 2 ) . R e l a t e d p h e n o m e n a w i l l be t r e a t e d briefly (Sect.3). R e c e n t p o s i t r o n a n n i h i l a t i o n w o r k on Ta (17) i n d i c a t e s that in the G r o u p - V t r a n s i t i o n m e t a l s v a c a n c i e s are less m o b i l e than i n t e r s t i t i a l f o r e i g n a t o m s , too. S i m i l a r p h e n o m e n a as in ~ - F e are e x p e c t e d . We s h a l l d i s c u s s the a v a i l a b l e e x p e r i m e n t a l e v i d e n c e in S e c t . 4 . 2.
The
Cold-Work
Relaxation
in ~ - I r o n
(Snoek--KSster
Relaxation)
This r e l a x a t i o n p r o c e s s was f i r s t o b s e r v e d in c o l d - w o r k e d iron at a b o u t 450K by S n o e k (18) ( w o r k i n g at 0.2 Hz) and l a t e r by W e s t (19) (mechanical after-effect m e a s u r e m e n t s ) and by K~ (20), w h o u s e d (as S n o e k ) i n t e r n a l - f r i c t i o n measurements. It was s t u d i e d in c o n s i d e r a b l e d e t a i l by K S s t e r , B a n g e r t , and H a h n (21) by m e a n s of i n t e r n a l f r i c t i o n . T h e s e a u t h o r s (21) o b t a i n e d s t r o n g e x p e r i m e n t a l e v i d e n c e that the p r o c e s s is c a u s e d by an i n t e r a c t i o n of i n t e r s t i t i a l l y d i s s o l v e d n i t r o g e n (or c a r b o n ) a t o m s w i t h d i s l o c a t i o n s g e n e r a t e d d u r i n g the p l a s t i c d e f o r m a t i o n . In o r d e r to a v o i d p o s s i b l e c o n f u s i o n w i t h o t h e r r e l a x a t i o n p r o c e s s e s i n t r o d u c e d by c o l d - w o r k i n g , we f o l l o w the n o m e n c l a t u r e of N o w i c k and B e r r y (22) and r e f e r to the r e l a x a t i o n p h e n o m e n o n in q u e s t i o n as the Snoek-- K S s t e r r e l a x a t i o n . The o r i g i n of the Snoek-- K S s t e r r e l a x a t i o n was c l a r i f i e d f u r t h e r by S c h o e c k (23), who s h o w e d that it r e s u l t s f r o m the m o t i o n of d i s l o c a t i o n s c o n t r o l l e d by the d i f f u s i o n of s u r r o u n d i n g i n t e r s t i t i a l f o r e i g n atoms. A l t h o u g h S c h o e c k ' s t h e o r y a c c o u n t s w e l l for the m a i n f e a t u r e s of the Snoek-- K 6 s t e r r e l a x a t i o n , o t h e r m e c h a n i s m s h a v e s u b s e q u e n t l y b e e n p r o p o s e d in the l i t e r a t u r e (for b r i e f s u r v e y s and c r i t i c i s m s of such a t t e m p t s see N o w i c k and B e r r y (22) and D e B a t i s t (24)). F u r t h e r m o r e , it has b e e n c l a i m e d (25) that i n t e r s t i t i a l l y d i s s o l v e d c a r b o n atoms do not c o n t r i b u t e to the Snoek-- K S s t e r r e l a x a t i o n and t h a t the p r e s e n c e of c a r b o n even r e t a r d s the d e v e l o p m e n t of the r e l a x a t i o n p r o c e s s a s s o c i a t e d w i t h n i t r o g e n . T h i s w o u l d be d i f f i c u l t to u n d e r s t a n d on the b a s i s of S c h o e e k ' s t h e o r y s i n c e the t h e o r y s h o u l d be equally a p p l i c a b l e to c a r b o n and n i t r o g e n i n t e r s t i t i a l s . On the o t h e r h a n d , K a m b e r , K e e f e r and W e r t (26) h a v e d e m o n s t r a t e d that c a r b o n does give rise to the Snoek-- K 6 s t e r r e l a x a t i o n in c o l d - w o r k e d iron. C l o s e r i n s p e c t i o n of the e x p e r i m e n t a l d a t a shows that t h e r e are i n d e e d c h a r a c t e r i s t i c d i f f e r e n c e s in the p r o p e r t i e s of the Snoek-- K S s t e r r e l a x a t i o n a s s o c i a t e d w i t h n i t r o g e n or c a r b o n . W h e n s t u d y i n g the r e l a x a t i o n p r o c e s s by int e r n a l - f r i c t i o n m e a s u r e m e n t s in a t o r s i o n p e n d u l u m , in n i t r o g e n - l o a d e d samples one finds the i n t e r n a l - f r i c t i o n m a x i m u m a l r e a d y f u l l y d e v e l o p e d w h e n the t e m p e r a t u r e of the m a x i m u m is r e a c h e d (26). By c o n t r a s t , in the case of c a r b o n the h e i g h t of the i n t e r n a l - f r i c t i o n p e a k i n c r e a s e s f u r t h e r d u r i n g a n n e a l s at t e m p e r a t u r e s a b o v e the m a x i m u m even u n d e r c o n d i t i o n s w h e r e , as a r e s u l t of a n n e a l i n g at, say, 3 7 0 K the c a r b o n S n o e k p e a k has d i s a p p e a r e d , i n d i c a t i n g that t h e r e w e r e no i s o l a t e d i n t e r s t i t i a l c a r b o n atoms left in s o l i d s o l u t i o n (26). In the r e m a i n d e r of this s e c t i o n we s h a l l s h o w that the d i f f e r e n c e s just described correlate well with internal-friction and p o s i t r o n ~ a n n i h i l a t i o n obs e r v a t i o n s on n e u t r o n - i r r a d i a t e d s p e c i m e n s (2-4) and that they m u s t be a t t r i b u ted to d i f f e r e n c e s in the i n t e r a c t i o n s of m o n o v a c a n c i e s w i t h c a r b o n or n i t r o g e n atoms. This m e a n s that t h e y are not due to d i f f e r e n t m e c h a n i s m s of t h e Snoek-K S s t e r r e l a x a t i o n a s s o c i a t e d w i t h t h e s e f o r e i g n i n t e r s t i t i a l atoms. The key to the q u a n t i t a t i v e s t u d y of the i n t e r a c t i o n of f o r e i g n i n t e r s t i t i a l a t o m s w i t h v a c a n c i e s in s - i r o n a p p e a r s to be the i n t e r n a l - f r i c t i o n peak detected in 1965 by W a g e n b l a s t and S c h w a r t z (27) in n e u t r o n - i r r a d i a t e d iron c o n t a i n i n g 0 . 0 1 1 5 wt% C ( t h e i r peak V, p e a k t e m p e r a t u r e 400K at 30 Hz) on the h i g h - t e m p e r a ture side of the c a r b o n S n o e k peak. T h e y a s c r i b e d this r e l a x a t i o n p r o c e s s to the r e o r i e n t a t i o n of a carbon-- m o n o v a c a n c y c o m p l e x w i t h the c a r b o n l o c a t e d off the c e n t r e of the v a c a n c y . This i n t e r p r e t a t i o n has r e c e n t l y r e c e i v e d s t r o n g s u p p o r t f r o m p o s i t r o n a n n i h i l a t i o n s t u d i e s and i n t e r n a l f r i c t i o n m e a s u r e m e n t s (2,3). W e l l e r et al. (2) s h o w e d that the c o m p l e x g i v i n g rise to W a g e n b l a s t and S c h w a r t z N
Vol.
Ii,
No.
9
VACANCIES
IN T R A N S I T I O N
METALS
819
p e a k V ( n a m e d C-X by W e l l e r et al. (2)) is c a p a b l e of t r a p p i n g p o s i t r o n s , though less s t r o n g l y t h a n i s o l a t e d m o n o v a c a n c i e s . This constitutes direct evidence, which Wagenblast a n d S c h w a r t z c o u l d not p r o v i d e , that the i n t r i n s i c d e f e c t s in the r e l a x i n g c o m p l e x are i n d e e d v a c a n c i e s r a t h e r t h a n s e l f - i n t e r s t i t i a l s ~. In n e u t r o n - i r r a d i a t e d i r o n d o p e d w i t h n i t r o g e n an i n t e r n a l - f r i c t i o n relaxat i o n p e a k ( n a m e d N-X) is o b s e r v e d at a b o u t the same t e m p e r a t u r e as the C-X p e a k ( 3 6 3 K at I Hz) a n d a t t r i b u t e d to the r e o r i e n t a t i o n of a n i t r o g e n - m o n o v a c a n c y c o m p l e x (3). The a n n e a l i n g c h a r a c t e r i s t i c s of the two p e a k s d i f f e r m a r k e d l y ; the annealing temperature of the N - X p e a k is a b o u t 80K l o w e r t h a n that of the C-X peak. W e l l e r a n d D i e h l (3) g i v e e x p e r i m e n t a l e v i d e n c e that the a n n e a l i n g o c c u r s by.dissociation of the c o m p l e x e s w i t h a c t i v a t i o n e n t h a l p i e s H ~ S ~ _ = 1.4 eV and ~V IsC s = 1.6 eV. HI In the p r e s e n t c o n t e x t it is i m p o r t a n t to note that at u s u a l h e a t i n g r a t e s IV-C c o m p l e x e s do p r a c t i c a l l y not d i s s o c i a t e at the t e m p e r a t u r e of the Snoek-K 6 s t e r p e a k , w h e r e a s the IV-N c o m p l e x e s do. S i n c e at t h e s e t e m p e r a t u r e s the N interstitials are v e r y m o b i l e (comp. E q . ( 3 ) ) t h e y m a y m i g r a t e v i r t u a l l y instan ~ t a n e o u s l y to d i s l o c a t i o n s and c o n t r i b u t e to the Snoek-- K 6 s t e r r e l a x a t i o n . A f u r t h e r i n c r e a s e of the t e m p e r a t u r e does not i n c r e a s e the c o n c e n t r a t i o n of n i t r o gen a t o m s s u r r o u n d i n g the d i s l o c a t i o n s . The s i t u a t i o n is q u i t e d i f f e r e n t , h o w e v e r , in the case of c a r b o n - d o p e d iron. Cold-working generates both dislocations and v a c a n c i e s . The c a r b o n a t o m s that d u r i n g the w a r m - u p m i g r a t e d to v a c a n c i e s r a t h e r t h a n to d i s l o c a t i o n s do not cont r i b u t e to the h e i g h t of the Snoek-- K 6 s t e r p e a k in the f i r s t w a r m - u p . In o r d e r to d e v e l o p the c a r b o n Snoek-- K 6 s t e r p e a k f u l l y the s p e c i m e n s h a v e to be a n n e a l e d at t e m p e r a t u r e s w e l l in e x c e s s of t h o s e at w h i c h the Snoek-- K 6 s t e r r e l a x a t i o n is u s u a l l y m e a s u r e d . We thus see that the a b o v e - m e n t i o n e d differences in the an~ nealing behaviour of the Snoek-- K 6 s t e r r e l a x a t i o n s c a u s e d by n i t r o g e n or c a r b o n find a v e r y s i m p l e and n a t u r a l e x p l a n a t i o n . If the v a c a n c y c o n c e n t r a t i o n is v e r y
After suitable corrections for the n e i g h b o u r i n g S n o e k p e a k s and for b a c k g r o u n d e f f e c t s the s h i f t of the p e a k t e m p e r a t u r e b e t w e e n the i n t e r n a l - f r i c t i o n measurem e n t s of W a g e n b l a s t and S c h w a r t z (27) and of W e l l e r and D i e h l (3) (at I Hz) g i v e s us the r e l a x a t i o n t i m e of the r e o r i e n t a t i o n of the c a r b o n - - m o n o v a c a n c y complex TIV_C = T exp(1.03 eV/kT) (4) with T ~ 10-15s. The a c t i v a t i o n enthalpy(presumably u n c e r t a i n by a b o u t ± 0 . 1 5 eV) a g r e e s w e l l w i t h the v a l u e s d e r i v e d by W e l l e r and D i e h l (3) by o t h e r a r g u ments. Eq.(4) predicts a relaxation time of a b o u t 5 m i n ( w h i c h can be i n v e s t i g a t e d by m a g n e t i c or m e c h a n i c a l after-effect measurements) at 297K. This is distinctly l o w e r t h a n the t e m p e r a t u r e r a n g e of the a f t e r - e f f e c t in n e u t r o n irradiated samples attributed to the IV-C r e l a x a t i o n by B l y t h e (28), w i t h whose assignment we,hence, c a n n o t a g r e e . The m a g n e t i c a f t e r - e f f e c t expected f r o m the r e o r i e n t a t i o n of the IV-C a p p e a r s to h a v e b e e n i d e n t i f i e d r e c e n t l y in neutron-irradiated s - i r o n in the t e m p e r a t u r e r a n g e p r e d i c t e d by Eq.(4)(W.Mensch and J . D i e h l , p e r s o n a l c o m m u n i c a t i o n ) . A mechanical a f t e r - e f f e c t in the t i m e and t e m p e r a t u r e r a n g e p r e d i c t e d by Eq.~) a p p e a r i n g a f t e r s t r a i n i n g i r o n w i r e s at a b o u t 350K to 37OK was i n v e s t i g a t e d by W e s t (19). By a time-- t e m p e r a t u r e transformation he f o u n d the a c t i v a t i o n enthalpy of this p r o c e s s to be 0.91 eV, in r e a s o n a b l e a g r e e m e n t w i t h the a b o v e v a l u e . Thus W e s t (19) m a y h a v e b e e n the f i r s t to o b s e r v e the IV-C or IV-N r e l a x a t i o n . It s h o u l d thus be p o s s i b l e to m o n i t o r the IV-C r e l a x a t i o n (and t h e ]V-N relaxation) by m a g n e t i c or m e c h a n i c a l after-effect measurements at t e m p e r a t u r e s at w h i c h the f o r e i g n i n t e r s t i t i a l atoms still move relatively s l o w l y . This m a y p e r m i t a m o r e d e t a i l e d s t u d y of the f o r m a t i o n of t h e i n t e r s t i t i a l - - v a c a n c y c o m p l e x e s t h a n has b e e n p o s s i b l e so far (comp. (3)).
820
VACANCIES IN TRANSITION METALS
Vol.
! 1, No. 9
high c o m p a r e d with the d i s l o c a t i o n d e n s i t y , it may even h a p p e n that the c a r b o n Snoek-- K S s t e r peak is u n d e t e c t a b l y small d u r i n g the first w a r m - u p . I n d e e d , already Snoek (18) has n o t e d that c a r b u r i z e d iron gives rise to a v e r y m u c h w e a k e r c o l d - w o r k r e l a x a t i o n than n i t r o g e n l o a d e d samples. 3. R e l a t e d ture
In this s e c t i o n we that are n a t u r a l l y
Experiments
d i s c u s s some e x p l a i n e d by
on ~-Fe
further observations reported the ideas o u t l i n e d in Sect.2.
in the
litera-
a) ~ £ £ £ X ~ Z _ e £ _ £ ~ e ~ : _ 9 ~ _ ~ ! ~ E £ ~ z ~ £ ~ _ ~ z i ~ e ~ _ ~ _ ~ e ~ _ i ~ i ~ i 2 ~ . After f a s t - n e u t r o n i r r a d i a t i o n at about 170K, the e l e c t r i c a l r e s i s t i v i t y of c a r b u r i z e d iron shows r e c o v e r y stages at about 240K, 320K, 425K, 535K and 575K (13). Of these, the first one (being the s m a l l e s t of the five) may w e l l be i n t r i n s i c in nature, as d i s c u s s e d in one of the p r e c e d i n g papers (7). The 320K stage was a t t r i b u t e d to t r a p p i n g of c a r b o n i n t e r s t i t i a l s by v a c a n c i e s and the 425K stage to the " n o r m a l " p r e c i p i t a t i o n of the excess c a r b o n into a m e t a s t a b l e c a r b i d e (12). The l a t t e r stage is i n d e e d m u c h more p r o n o u n c e d "in w e a k l y i r r a d i a t e d or u n i r r a d i ated q u e n c h e d s a m p l e s than in s t r o n g l y i r r a d i a t e d s p e c i m e n s (13). atoms
The 535K stage finds its n a t u r a l e x p l a n a t i o n in the from v a c a n c i e s . A s s u m i n g that the d e t r a p p i n g rate ~o exp( =
d e t r a p p i n g of is given by
diSS/kT) -
MIV_C
carbon (5)
,
w h e r e ~o= I013s -I, we e s t i m a t e from the 5 min a n n e a l i n g i s o t h e r m s ((13), Fig.5) a d i s s o c i a t i o n enthalpy H ~ S 8 of 1.6 eV - 1.7 eV, in quite good a g r e e m e n t w i t h W e l l e r and D i e h l ' s (3) e s t i m a t e of 1.6 eV, b a s e d on the a n n e a l i n g of the IV-C c o m p l e x as s t u d i e d by i n t e r n a l f r i c t i o n , and also with r e c e n t M S B b a u e r e x p e r i ments (5) *. As one e x p e c t s from this i n % e r p r e t a t i o n , the c o r r e s p o n d i n g stage in nitrogen-doped neutron-irradiated iron is s h i f t e d to lower t e m p e r a t u r e by about l O O K (16). The final (575K) r e c o v e r y stage gives about the right n u m b e r of jumps for the free m i g r a t i o n of m o n o v a c a n c i e s . F u j i t a and D a m a s k (13), who did not have q u a n t i t a t i v e i n f o r m a t i o n on the v a c a n c y d i f f u s i o n c o e f f i c i e n t , a d d u c e d indeed a d d i t i o n a l a r g u m e n t s in favour of this i n t e r p r e t a t i o n but r e j e c t e d it f i n a l l y b e c a u s e the r e c o v e r y stage appears only in c a r b u r i z e d s p e c i m e n s and not in dec a r b u r i z e d ones (13). In the o p i n i o n of the p r e s e n t authors this o b s e r v a t i o n is an a r g u m e n t s u p p o r t i n g r a t h e r than r e f u t i n g the m e c h a n i s m of m o n o v a c a n c y m i g r a tion for the final r e c o v e r y stage. Since c a r b o n i n t e r s t i t i a l s are v i r t u a l l y imm o b i l e at the t e m p e r a t u r e of s e l f - i n t e r s t i t i a l m i g r a t i o n , they may p r o v i d e w i d e ly d i s p e r s e d t r a p s for s e l f - i n t e r s t i t i a l s . This means that in c a r b u r i z e d s a m p l e s v a c a n c i e s have a h i g h e r chance to escape r e c o m b i n a t i o n w i t h s e l f - i n t e r s t i t i a l s than in d e c a r b u r i z e d s p e c i m e n s . Hence the r e c o v e r y stage a s s o c i a t e d w i t h free m i g r a t i o n of v a c a n c i e s s h o u l d i n d e e d be more p r o n o u n c e d in c a r b u r i z e d iron than in d e c a r b u r i z e d iron, in a g r e e m e n t with the o b s e r v a t i o n s (13). b) Preci . . . . . . . . Takeyama
i t a t i o n of c a r b i d e s and n i t r i d e s ( h i g h - v o l t a g e e l e c t r o n m i c r o s c o p y ) " and T a k a h a s h i s t u d i e d p r e c i p i t a t i o n in s o l u t i o n - q u e n c h e d F e - O . O 2 5 wt%C
~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* The s i m p l e s t m o d e l for the d i s s o c i a t i o n of the ( i n t e r s t i t i a l m i g r a t i o n enthalpy H~ < HIV) gives HdiSs
iv-i
= My + H~v_ i
interstitial-- vacancy the r e l a t i o n s h i p
complex
(6)
The b i n d i n g enthalpyH~ v i may be d e t e r m i n e d by c a l o r i m e t r i c m e a s u r e m e n t s . Arndt and D a m a s k (14) foun~ - H~V_ C = 0.41 eV. The a g r e e m e n t w i t h the v a l u e H~V_C = 0.8 eV f o l l o w i n g from Eq.(6) i s p o o r . This may have two reasons: (i) The c a l o r i m e t r i c m e a s u r e m e n t s gave too low a v a l u e for the b i n d i n g enthalpy. (ii) T h e r e is an a d d i t i o n a l energy b a r r i e r for the e s c a p e of the i n t e r s t i t i a l s from the v a c a n c y traps that is not t a k e n into a c c o u n t in Eq.(6).If the b i n d i n g enthalpy m e a s u r e d by A r n d t and D a m a s k (14) is c o n s i d e r e d as c o r r e c t , this a d d i t i o n a l e n e r g y b a r r i e r amounts to about 0.4 eV.
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( 2 9 , 3 0 ) and F e - O . 0 3 w t % N a l l o y s ( 3 0 , 3 1 ) t h a t w e r e i r r a d i a t e d at r o o m t e m p e r a t u r e w i t h 6 5 0 k e V e l e c t r o n s in a h i g h - v o l t a g e electron microscope and subsequently a n n e a l e d at h i g h e r t e m p e r a t u r e s . T h e f o r m a t i o n of c a r b i d e s and n i t r i d e s w a s v e r y m u c h r e t a r d e d in the i r r a d i a t e d p a r t s of the s p e c i m e n s . T h i s is a t t r i b u t e d to the t r a p p i n g of C and N by r a d i a t i o n - i n d u c e d d e f e c t s , in p a r t i c u l a r vacancies. The a u t h o r s c o n c l u d e t h a t IV-N p a i r s b e g i n to d i s s o c i a t e at a b o u t 470K (31), w h e r e a s the d i s s o c i a t i o n of the IV-C p a i r s t a k e s p l a c e d u r i n g 10 m i n a n n e a l s b e t w e e n 510K and 6 2 0 K (29). T h e s e o b s e r v a t i o n s are in g o o d a g r e e m e n t w i t h t h e d i s s o c i a t i o n enthalpie~ o b t a i n e d by W e l l e r and D i e h l (3). L. G r o u p - V
Transition
Metals
It has r e c e n t l y b e e n s h o w n (17) that in Ta, as in ~ - F e , t h e m i g r a t i o n enthalpy of m o n o v a c a n c i e s e x c e e d s that of c a r b o n , n i t r o g e n , or o x y g e n i n t e r s t i t i a l atoms. The same m a y be e x p e c t e d for the o t h e r G r o u p - V B m e t a l s , Nb and V. In the p r e s e n t s u b s e c t i o n we d i s c u s s e x p e r i m e n t s on t h e s e m e t a l s in the l i g h t of the r e s u l t s obt a i n e d on ~-Fe. B o o n e and W e f t (32) as w e l l as v a n O o i j e n and v a n d e r Goot (33) h a v e i d e n t i f i e d t h e n i t r o g e n Snoek--K6ster p e a k in Nb (at a b o u t 80OK, w o r k i n g at f z I Hz). The o b s e r v a t i o n (32) t h a t this p e a k d e v e l o p s f u l l y o n l y w h e n the p e a k t e m p e r a ture has b e e n c o n s i d e r a b l y exceeded,indicates t h a t n i t r o g e n in Nb b e h a v e s s i m i l a r l y to c a r b o n in ~ - F e , e . g . , that it is r a t h e r f i r m l y t r a p p e d by v a c a n c i e s . By c o n t r a s t , o x y g e n in Ta and Nb a p p e a r to b e h a v e like n i t r o g e n in ~-Fe. S c h o e c k and M o n d i n o (34) i d e n t i f i e d a p e a k in Ta at a b o u t 570K w i t h the o x y g e n Snoek-- K 6 s t e r r e l a x a t i o n . This p e a k as w e l l as an a n a l o g o u s one in Nb w a s a l s o o b s e r v e d by d e L a m o t t e and W e r t (35). The p e a k is f u l l y d e v e l o p e d d u r i n g t h e f i r s t w a r m - u p a n d b e g i n s in fact to a n n e a l out as s o o n as the p e a k t e m p e r a t u r e has b e e n e x c e e d e d . This s u g g e s t s that 0 is not v e r y f i r m l y b o u n d to m o n o v a c a n cies in Nb. This c o n c l u s i o n is s u p p o r t e d by the f o l l o w i n g o b s e r v a t i o n (36): O x y g e n a t o m s that h a d p r e s u m a b l y b e e n t r a p p e d by m o n o v a c a n c i e s during quenching of Nb f r o m n e a r the m e l t i n g p o i n t r e t u r n into s o l i d s o l u t i o n (contributing to the 0 S n o e k p e a k ) d u r i n g 5 m i n a n n e a l s at 570K. Quenching experiments s i m i l a r to t h o s e just m e n t i o n e d (36) h a v e r e c e n t l y b e e n p e r f o r m e d on v a n a d i u m (37). In this case it has b e e n s h o w n that lh a n n e a l ing b e t w e e n 6 5 0 K a n d 8 0 0 K is r e q u i r e d for the o x y g e n to r e t u r n into s o l i d solution. T h i s r e t u r n of 0 into s o l i d s o l u t i o n is a c c o m p a n i e d by a d e c r e a s e of the e l e c t r i c a l resistivity, indicating that intrinsic defects (presumably the monovacancies) a n n e a l out s i m u l t a n e o u s l y . The a v a i l a b l e e v i d e n c e s u p p o r t s the v i e w t h a t this d e c r e a s e is due to the a n n e a l i n g out of t h e v a c a n c i e s i m m e d i a t e l y f o l l o w i n g the b r e a k - u p of t h e IV-O c o m p l e x e s (37). H e r e t h e s i t u a t i o n a p p e a r s to be s i m i l a r to the b r e a k - u p of the C-X and N - X c o m p l e x e s in ~ - F e (3). A r e l a x a t i o n p r o c e s s w i t h an a c t i v a t i o n enthalpy of a b o u t 1.5 eV that m i g h t w e l l be a s s o c i a t e d with the reorientation of the IV-0 c o m p l e x was f o u n d in n e u t r o n - i r r a d i a t e d vanadium (38). T h i s r e l a x a t i o n p r o c e s s lies c l o s e to the n i t r o g e n S n o e k p e a k , a n d it may h a v e b e e n h i d d e n by it in o t h e r e x p e r i m e n t s . By a r g u m e n t s a n a l o g o u s to t h o s e u s e d for ~ - F e (4) we may c o n c l u d e that t h e m i g r a t i o n enthalpy of m o n o vacancies in v a n a d i u m lies b e t w e e n that of o x y g e n (1.25 eV (39)) and an u p p e r l i m i t of 2.3 eV d e d u c i b l e f r o m the a n n e a l i n g out of the IV-0 c o m p l e x e s . The p r e c e d i n g considerations s u p p o r t s t r o n g l y the v i e w that the G r o u p - V transition m e t a l s are i n d e e d v e r y s i m i l a r to ~ - F e , b o t h w i t h r e s p e c t to the magnitude of the m o n o v a c a n c y migration e n e r g y and the b i n d i n g of f o r e i g n i n t e r s t i t i a l a t o m s to v a c a n c i e s . Nevertheless, q u i t e a few q u e s t i o n s r e m a i n open, p a r t l y o w i n g to the fact that the a v a i l a b l e e x p e r i m e n t a l d a t a are far less comp l e t e t h a n in the case of ~-Fe. E . g . , v a n O o i j e n and v a n der Goot (33) r e j e c t Schoeck and Mondino's (34) a s s i g n m e n t of the o x y g e n Snoek-- K 6 s t e r r e l a x a t i o n in Ta (and also the a n a l o g o u s one in Nb) and a t t r i b u t e i n s t e a d an i n t e r n a l f r i c t i o n p e a k at h i g h e r t e m p e r a t u r e s to this p r o c e s s . L i k e w i s e , t h e i r r e s u l t s on the n i t r o g e n Snoek-- K 6 s t e r r e l a x a t i o n are o n l y p a r t i a l l y in a g r e e m e n t w i t h the f i n d i n g s of B o o n e and W e r t (32). In o r d e r to c l a r i f y t h e s e as w e l l as s o m e r e l a t e d questions, ultra-high-vacuum measurements on c a r e f u l l y c h a r a c t e r i z e d specimens are r e q u i r e d .
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5. Conclusions Previous work has e s t a b l i s h e d that in ~-Fe a) m o n o v a c a n c i e s are less mobile than carbon, nitrogen, or oxygen i n t e r s t i t i a l atoms , b) diffusing carbon and nitrogen interstitials may be trapped by m o n o v a c a n c i e s , c) nitrogen-- vacancy pairs dissociate more easily than carbon-- vacancy pairs. In the present
paper
it is shown
that
these
results
account
for
(i) the o b s e r v a t i o n that in a-Fe the nitrogen Snoek-- K S s t e r r e l a x a t i o n (alias nitrogen cold-work peak) is always fully developed during the first w a r m - u p , whereas in l o w - f r e q u e n c y i n t e r n a l - f r i c t i o n m e a s u r e m e n t s full d e v e l o p m e n t of the carbon Snoek-- KSster r e l a x a t i o n requires annealing above the peak t e m p e r a t u r e ; (ii) the differences in carbide or nitride f o r m a t i o n of carbon- or nitrogendoped a-Fe as observed in h i g h - v o l t a g e electron m i c r o s c o p y f o l l o w i n g r o o m - t e m perature electron irradiation; (iii) the annealing b e h a v i o u r perature neutron irradiation.
of carbon-
or n i t r o g e n - d o p e d
a-Fe
after
low-tem-
The good agreement b e t w e e n the o b s e r v a t i o n s on the Snoek-- KSster r e l a x a t i o n and the results a)-c) used in c o n j u n c t i o n with Schoeck's theory gives a d d i t i o n a l support to Schoeck's i n t e r p r e t a t i o n of the Snoek-- KSster relaxation. In particular, it is c o n c l u d e d that the theory holds both for n i t r o g e n and carbon ~ n t e ~ acting with d i s l o c a t i o n s in ~-Fe. In a-Fe the energy b a r r i e r for the d i s s o c i a t i o n of carbon-- m o n o v a c a n c y is distinctly larger than the carbon-- vacancy b i n d i n g energy obtained from calorimetric m e a s u r e m e n t s on neutron-irradiated samples.
pairs
There are strong reasons to believe that results a) and b) apply to the Group-V t r a n s i t i o n metals (vanadium, niobium, tantalum), too. A perusal of the available literature indicates that in these metals the oxygen-- vacancy pairs dissociate more easily than the nitrogen-- vacancy pairs. D i f f e r e n c e s in the Snoek-- KSster r e l a x a t i o n may be u n d e r s t o o d in an analogous fashion as i n d i c a t e d above for G-Fe, but further work is clearly necessary. References I. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12 13 14 15 16. 17. 18. 19. 20. 21.
Y.Ikeda, T.Gotoh, K.Abiko, and H.Kimura, Crystal Lattice Defects 5, 163 (1974% M.Weller, J.Diehl, and W . T r i f t s h £ u s e r , Solid State C o m m u n i c a t i o n s 17, 1223 (1975). M . W e l l e r and J.Diehl, Scripta Met. I0, I01 (1976). J.Diehl, M.Weller, and U.Merbold, S c r i p t a Met.~ 811~ this issuel S . R . R e i n t s e m a , M S , b a u e r Studies of I m p l a n t a t i o n Damage in Iron and Nickel, P r o e f s c h r i f t , R i j k s u n i v e r s i t e i t te G r o n i n g e n 1976. M.Yoshida, M.Kiritani, and F.E.Fujit~ J . P h y s . S o c . J a p a n 39, 170 (1975). D.Herlaeh, K.Maier, H . - E . S c h a e f e r , M.Weller, A.Seeger, and J.Diehl, S c r i p t a Met., 803, this issue. G.Hettich, M.Mehrer, and K.Maier, Scripta M e t . , 795~ this issue, J.R.G. da Silva and R . B . M c L e l l a n , Mater. Science E n g i n e e r i n g 26, 83 (1976). W.Frank, H . - J . E n g e l l , and A.Seeger, Z . M e t a l l k d e 58, 452 (1967). W.Frank, H . - J . E n g e l l , and A.Seeger, T r a n s . M e t . S o c . AIME 242, 749 (1968). H . W a g e n b l a s t and A . C . D a m a s k , J.Phys.Chem. Solids 23, 221 (1962). F . E . F u j i t a and A.C.Damask, Aeta Met. 12, 331 (1964). R.A.Arndt and A . C . D a m a s k , Acta Met. 12, 341 (1964). H . W a g e n b l a s t , F.E.Fujita, and A . C . D a m a s k , Acta Met. 12, 347 (1964). M.Wuttig, J . T . S t a n l e y , and H . K . B i r n b a u m , p h y s . s t a t . s o l . 27, 701 (1968). K.Maier, H.Metz, D.Herlach, H . - E . S c h a e f e r , and A.Seeger, submitted to Phys.Rev. Letters. D.L.Snoek, Physica 8, 711 (1941). W.A.West, T r a n s . A m e r i c . l n s t . M i n . M e t a l l . E n g r s 167, 192 (1946). T.S.K~, A m e r i c . l n s t . M i n . M e t a l l . E n g r s . T e c h n - P u b l . N o . 2370 (1948). W.KSster, L.Bangert, and R.Hahn, E i s e n h ~ t t e n w . 25, 569 (1955).
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Ii, No.
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IN T R A N S I T I O N METALS
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22. A . S . N o w i c k and B.S.Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York and London, 1972. 23. G.Schoeck, Acta Met. 11, 6]7 (1963). 24. R.DeBatist, Internal Friction of Structural Defects in Crystalline Solids, N o r t h - H o l l a n d , A m s t e r d a m and London, 1972. 25. D . T . P e t a r r a and D.N.Beshers, Acta Met. 15, 791 (1967). 26. K.Kamber, D.Keefer, and C.Wert, Acta Met. 9, 403 (1961). 27. H.Wagenblast and J.C.Schwartz, Acta Met. 13, 42 (1965). 28. H,J.Blythe, p h y s . s t a t . s o l . ( a ) 20, 619 (1973). 29. T . T a k e y a m a and H.Takahashi, J . P h y s . S o c . J a p a n 35, 939 (1973). 30. T . T a k e y a m a and H.Takahashi, Fundamental Aspects of R a d i a t i o n Damage in Metals, edited by M . T . R o b i n s o n and F.W.Young, Jr., ERDA report CONF-751006, Oak Ridge (Tenn.), Vol. 2, p. 1100. 31. T . T a k e y a m a and H.Takahashi, J . P h y s . S o c . J a p a n 38, 1783 (1975). 32. D.H.Boone and C.A.Wert, J . P h y s . S o c . J a p a n 18, Suppl.l, 141 (1963). 33. D.J.van Ooijen and A.S.van der Goot, Philips Res.Repts. 22, 150 (1967). 34. G.Sehoeck and M.Mondino, J . P h y s . S o c . J a p a n 18, Suppl.l, 149 (1963). 35. E.de Lamotte and C.Wert, J . P h y s . S o c . J a p a n 19, 1560 (1964). 36. A . G . A r a k e l o v , M.S.Blanter, A.Ye.Kissil' , L.A.Kovaleva, and l.T.Stekachev, F i z . m e t a l . m e t a l l o v e d . 35, 826 (1973). 37. A . G . A r a k e l o v , M.S.Blanter, A . Y e . K i s s e l ' , L.A.Kovaleva, and P.A.Khandarov, F i z . m e t a l . m e t a l l o v e d . 40, 71 (1975). 38. M.Eto, Y.Matsuo, S.Ishino, and Y.Mishima, J . N u c l . M a t e r i a l s 52, 309 (1974). 39. G.H6rz, Z.Metallkde. 59, 712 (1968).
METALLURGICA
ON THE
Vol. ii, pp. 817-823, 1977 P r i n t e d in the U n i t e d States
INTERACTION
OF F O R E I G N
IN e-FE
AND
INTERSTITIAL
GROUP-V
ATOMS
TRANSITION
METALS
Pergamon
WITH
(Received
June
24,
Inc.
VACANCIES
*
M . M o n d i n o and A . S e e g e r ** de F i s l c a Dr. Jos@ B a l s e i r o , C e n t r o A t 6 m i c o , B a r i l o c h e , Rio Negro, The A r g e n t i n e
Instituto
Press,
S.C.
de
1977)
I. I n t r o d u c t i o n R e c e n t work on q u e n c h i n g of i r o n - m o l y b d e n u m alloys (I), on the r e c o v e r y of positron annihilation, i n t e r n a l f r i c t i o n , and r e s i s t i v i t y of n e u ~ g n - i r r a d i a t e d iron (2-4), on the M S B b a u e r effect of iron foils i m p l a n t e d with " ~ X e (5), as w e l l as on h i g h - v o l t a g e e l e c t r o n m i c r o s c o p y (6), h i g h - t e m p e r a t u r e p o s i t r o n annihil a t i o n (7), and s e l f - d i f f u s i o n of pure iron (8) has shown, with i n c r e a s i n g certainty and p r e c i s i o n , that in e - i r o n the m o n o v a c a n c y m i g r a t i o n enthalpy, Hyv , is not very d i f f e r e n t from the m o n o v a c a n c y f o r m a t i o n enthalpy H~V. The best p r e s e n t v a l u e for the d i f f u s i o n c o e f f i c i e n t of m o n o v a c a n c i e s in iron b e t w e e n 400K and 550K is given by (7) -I = a2ViV = 0.5 exp(- 1.28 eV/kT) cm2s (I) DIVIo (a = 2 , 8 6 " 1 0 m = l a t t i c e p a r a m e t e r , VIV = m o n o v a c a n c y jump f r e q u e n c y ) **~. Comp a r i s o n of Eq.(1)with the l o w - t e m p e r a t u r e d i f f u s i o n c o e f f i c i e n t s of i n t e r s t i t i a l l y d i s s o l v e d c a r b o n atoms (9) DC =
exp(-0.81
e V / k T ) c m 2 s -I
,
(2)
D N = 1.26"10 -3 e x p ( - 0 . 7 6
e V / k T ) c m 2 s -I
,
(3)
or n i t r o g e n
1.67-10 -3
atoms
(9)
shows that at t e m p e r a t u r e s b e t w e e n 300K and 40OK, at w h i c h c a r b o n and n i t r o g e n atoms in e - i r o n are q u i t e m o b i l e , m o n o v a c a n c i e s are v i r t u a l l y i m m o b i l e . This means that in this t e m p e r a t u r e range a s u p e r s a t u r a t i o n of m o n o v a c a n c i e s may act as traps for m i g r a t i n g carbon or n i t r o g e n atoms *z** The h y p o t h e s i s that v a c a n c i e s in i r r a d i a t e d iron may form traps for c a r b o n was first made and s u p p o r t e d by e x p e r i m e n t a l e v i d e n c e in a series of papers by D a m a s k and c o l l a b o r a t o r s (12-15). The recent d e v e l o p m e n t s m e n t i o n e d above s u p p o r t s t r o n g l y the c o r r e c t n e s s of this h y p o t h e s i s . A n a l o g o u s e v i d e n c e for the t r a p p i n g
Dedicated
to W . K 6 s t e r
**
Permanent
address:
on the
occasion
of his
80th
birthday
(22.11.1976).
*~*
At 473K Eq.(I) p r e d i c t s of-magnitude estimate
*~**
The same is p r e s u m a b l y also true for o x y g e n ( m i g r a t i o n e n e r g y ( 0 . 9 8 ± 0 . I 0 ) e V (9,10)), but o w i n g to the e x t r e m e l y low s o l u b i l i t y of o x y g e n in e-Fe o b s e r v a t i o n s a n a l o g o u s to those on C and N p r o v i d i n g u n e q u i v o c a l e v i d e n c e for t r a p p i n g by v a c a n c i e s are a p p a r e n t l y not a v a i l a b l e .
Max-Planck-lnstitut fur M e t a l l f o r s c h u n g , I n s t i t u t fur P h y s i k , P o s t f a c h 80 06 65, D - 7 0 0 0 S t u t t g a r t 80, G e r m a n y . ~ i V = 1 4 s -I in s a t i s f a c t o r y a g r e e m e n t ~iv~Is -I from M 6 B b a u e r m e a s u r e m e n t s
817
with (5).
the
order-
818
VACANCIES
of n i t r o g e n
by
vacancies
IN T R A N S I T I O N
METALS
in n e u t r o n - i r r a d i a t e d
a-Fe
Vol.
was
found
II, No.
somewhat
later
9
(161
The p r e s e n t note d e a l s m a i n l y w i t h the c o n s e q u e n c e s of the t r a p p i n g of carb o n or n i t r o g e n by m o n o v a c a n c i e s for the p h y s i c a l m e t a l l u r g y of a - i r o n , in part i c u l a r for the d e t a i l e d u n d e r s t a n d i n g of the s o - c a l l e d c o l d - w o r k r e l a x a t i o n p e a k a s s o c i a t e d w i t h c a r b o n and n i t r o g e n ( S e c t . 2 ) . R e l a t e d p h e n o m e n a w i l l be t r e a t e d briefly (Sect.3). R e c e n t p o s i t r o n a n n i h i l a t i o n w o r k on Ta (17) i n d i c a t e s that in the G r o u p - V t r a n s i t i o n m e t a l s v a c a n c i e s are less m o b i l e than i n t e r s t i t i a l f o r e i g n a t o m s , too. S i m i l a r p h e n o m e n a as in ~ - F e are e x p e c t e d . We s h a l l d i s c u s s the a v a i l a b l e e x p e r i m e n t a l e v i d e n c e in S e c t . 4 . 2.
The
Cold-Work
Relaxation
in ~ - I r o n
(Snoek--KSster
Relaxation)
This r e l a x a t i o n p r o c e s s was f i r s t o b s e r v e d in c o l d - w o r k e d iron at a b o u t 450K by S n o e k (18) ( w o r k i n g at 0.2 Hz) and l a t e r by W e s t (19) (mechanical after-effect m e a s u r e m e n t s ) and by K~ (20), w h o u s e d (as S n o e k ) i n t e r n a l - f r i c t i o n measurements. It was s t u d i e d in c o n s i d e r a b l e d e t a i l by K S s t e r , B a n g e r t , and H a h n (21) by m e a n s of i n t e r n a l f r i c t i o n . T h e s e a u t h o r s (21) o b t a i n e d s t r o n g e x p e r i m e n t a l e v i d e n c e that the p r o c e s s is c a u s e d by an i n t e r a c t i o n of i n t e r s t i t i a l l y d i s s o l v e d n i t r o g e n (or c a r b o n ) a t o m s w i t h d i s l o c a t i o n s g e n e r a t e d d u r i n g the p l a s t i c d e f o r m a t i o n . In o r d e r to a v o i d p o s s i b l e c o n f u s i o n w i t h o t h e r r e l a x a t i o n p r o c e s s e s i n t r o d u c e d by c o l d - w o r k i n g , we f o l l o w the n o m e n c l a t u r e of N o w i c k and B e r r y (22) and r e f e r to the r e l a x a t i o n p h e n o m e n o n in q u e s t i o n as the Snoek-- K S s t e r r e l a x a t i o n . The o r i g i n of the Snoek-- K S s t e r r e l a x a t i o n was c l a r i f i e d f u r t h e r by S c h o e c k (23), who s h o w e d that it r e s u l t s f r o m the m o t i o n of d i s l o c a t i o n s c o n t r o l l e d by the d i f f u s i o n of s u r r o u n d i n g i n t e r s t i t i a l f o r e i g n atoms. A l t h o u g h S c h o e c k ' s t h e o r y a c c o u n t s w e l l for the m a i n f e a t u r e s of the Snoek-- K 6 s t e r r e l a x a t i o n , o t h e r m e c h a n i s m s h a v e s u b s e q u e n t l y b e e n p r o p o s e d in the l i t e r a t u r e (for b r i e f s u r v e y s and c r i t i c i s m s of such a t t e m p t s see N o w i c k and B e r r y (22) and D e B a t i s t (24)). F u r t h e r m o r e , it has b e e n c l a i m e d (25) that i n t e r s t i t i a l l y d i s s o l v e d c a r b o n atoms do not c o n t r i b u t e to the Snoek-- K S s t e r r e l a x a t i o n and t h a t the p r e s e n c e of c a r b o n even r e t a r d s the d e v e l o p m e n t of the r e l a x a t i o n p r o c e s s a s s o c i a t e d w i t h n i t r o g e n . T h i s w o u l d be d i f f i c u l t to u n d e r s t a n d on the b a s i s of S c h o e e k ' s t h e o r y s i n c e the t h e o r y s h o u l d be equally a p p l i c a b l e to c a r b o n and n i t r o g e n i n t e r s t i t i a l s . On the o t h e r h a n d , K a m b e r , K e e f e r and W e r t (26) h a v e d e m o n s t r a t e d that c a r b o n does give rise to the Snoek-- K 6 s t e r r e l a x a t i o n in c o l d - w o r k e d iron. C l o s e r i n s p e c t i o n of the e x p e r i m e n t a l d a t a shows that t h e r e are i n d e e d c h a r a c t e r i s t i c d i f f e r e n c e s in the p r o p e r t i e s of the Snoek-- K S s t e r r e l a x a t i o n a s s o c i a t e d w i t h n i t r o g e n or c a r b o n . W h e n s t u d y i n g the r e l a x a t i o n p r o c e s s by int e r n a l - f r i c t i o n m e a s u r e m e n t s in a t o r s i o n p e n d u l u m , in n i t r o g e n - l o a d e d samples one finds the i n t e r n a l - f r i c t i o n m a x i m u m a l r e a d y f u l l y d e v e l o p e d w h e n the t e m p e r a t u r e of the m a x i m u m is r e a c h e d (26). By c o n t r a s t , in the case of c a r b o n the h e i g h t of the i n t e r n a l - f r i c t i o n p e a k i n c r e a s e s f u r t h e r d u r i n g a n n e a l s at t e m p e r a t u r e s a b o v e the m a x i m u m even u n d e r c o n d i t i o n s w h e r e , as a r e s u l t of a n n e a l i n g at, say, 3 7 0 K the c a r b o n S n o e k p e a k has d i s a p p e a r e d , i n d i c a t i n g that t h e r e w e r e no i s o l a t e d i n t e r s t i t i a l c a r b o n atoms left in s o l i d s o l u t i o n (26). In the r e m a i n d e r of this s e c t i o n we s h a l l s h o w that the d i f f e r e n c e s just described correlate well with internal-friction and p o s i t r o n ~ a n n i h i l a t i o n obs e r v a t i o n s on n e u t r o n - i r r a d i a t e d s p e c i m e n s (2-4) and that they m u s t be a t t r i b u ted to d i f f e r e n c e s in the i n t e r a c t i o n s of m o n o v a c a n c i e s w i t h c a r b o n or n i t r o g e n atoms. This m e a n s that t h e y are not due to d i f f e r e n t m e c h a n i s m s of t h e Snoek-K S s t e r r e l a x a t i o n a s s o c i a t e d w i t h t h e s e f o r e i g n i n t e r s t i t i a l atoms. The key to the q u a n t i t a t i v e s t u d y of the i n t e r a c t i o n of f o r e i g n i n t e r s t i t i a l a t o m s w i t h v a c a n c i e s in s - i r o n a p p e a r s to be the i n t e r n a l - f r i c t i o n peak detected in 1965 by W a g e n b l a s t and S c h w a r t z (27) in n e u t r o n - i r r a d i a t e d iron c o n t a i n i n g 0 . 0 1 1 5 wt% C ( t h e i r peak V, p e a k t e m p e r a t u r e 400K at 30 Hz) on the h i g h - t e m p e r a ture side of the c a r b o n S n o e k peak. T h e y a s c r i b e d this r e l a x a t i o n p r o c e s s to the r e o r i e n t a t i o n of a carbon-- m o n o v a c a n c y c o m p l e x w i t h the c a r b o n l o c a t e d off the c e n t r e of the v a c a n c y . This i n t e r p r e t a t i o n has r e c e n t l y r e c e i v e d s t r o n g s u p p o r t f r o m p o s i t r o n a n n i h i l a t i o n s t u d i e s and i n t e r n a l f r i c t i o n m e a s u r e m e n t s (2,3). W e l l e r et al. (2) s h o w e d that the c o m p l e x g i v i n g rise to W a g e n b l a s t and S c h w a r t z N
Vol.
Ii,
No.
9
VACANCIES
IN T R A N S I T I O N
METALS
819
p e a k V ( n a m e d C-X by W e l l e r et al. (2)) is c a p a b l e of t r a p p i n g p o s i t r o n s , though less s t r o n g l y t h a n i s o l a t e d m o n o v a c a n c i e s . This constitutes direct evidence, which Wagenblast a n d S c h w a r t z c o u l d not p r o v i d e , that the i n t r i n s i c d e f e c t s in the r e l a x i n g c o m p l e x are i n d e e d v a c a n c i e s r a t h e r t h a n s e l f - i n t e r s t i t i a l s ~. In n e u t r o n - i r r a d i a t e d i r o n d o p e d w i t h n i t r o g e n an i n t e r n a l - f r i c t i o n relaxat i o n p e a k ( n a m e d N-X) is o b s e r v e d at a b o u t the same t e m p e r a t u r e as the C-X p e a k ( 3 6 3 K at I Hz) a n d a t t r i b u t e d to the r e o r i e n t a t i o n of a n i t r o g e n - m o n o v a c a n c y c o m p l e x (3). The a n n e a l i n g c h a r a c t e r i s t i c s of the two p e a k s d i f f e r m a r k e d l y ; the annealing temperature of the N - X p e a k is a b o u t 80K l o w e r t h a n that of the C-X peak. W e l l e r a n d D i e h l (3) g i v e e x p e r i m e n t a l e v i d e n c e that the a n n e a l i n g o c c u r s by.dissociation of the c o m p l e x e s w i t h a c t i v a t i o n e n t h a l p i e s H ~ S ~ _ = 1.4 eV and ~V IsC s = 1.6 eV. HI In the p r e s e n t c o n t e x t it is i m p o r t a n t to note that at u s u a l h e a t i n g r a t e s IV-C c o m p l e x e s do p r a c t i c a l l y not d i s s o c i a t e at the t e m p e r a t u r e of the Snoek-K 6 s t e r p e a k , w h e r e a s the IV-N c o m p l e x e s do. S i n c e at t h e s e t e m p e r a t u r e s the N interstitials are v e r y m o b i l e (comp. E q . ( 3 ) ) t h e y m a y m i g r a t e v i r t u a l l y instan ~ t a n e o u s l y to d i s l o c a t i o n s and c o n t r i b u t e to the Snoek-- K 6 s t e r r e l a x a t i o n . A f u r t h e r i n c r e a s e of the t e m p e r a t u r e does not i n c r e a s e the c o n c e n t r a t i o n of n i t r o gen a t o m s s u r r o u n d i n g the d i s l o c a t i o n s . The s i t u a t i o n is q u i t e d i f f e r e n t , h o w e v e r , in the case of c a r b o n - d o p e d iron. Cold-working generates both dislocations and v a c a n c i e s . The c a r b o n a t o m s that d u r i n g the w a r m - u p m i g r a t e d to v a c a n c i e s r a t h e r t h a n to d i s l o c a t i o n s do not cont r i b u t e to the h e i g h t of the Snoek-- K 6 s t e r p e a k in the f i r s t w a r m - u p . In o r d e r to d e v e l o p the c a r b o n Snoek-- K 6 s t e r p e a k f u l l y the s p e c i m e n s h a v e to be a n n e a l e d at t e m p e r a t u r e s w e l l in e x c e s s of t h o s e at w h i c h the Snoek-- K 6 s t e r r e l a x a t i o n is u s u a l l y m e a s u r e d . We thus see that the a b o v e - m e n t i o n e d differences in the an~ nealing behaviour of the Snoek-- K 6 s t e r r e l a x a t i o n s c a u s e d by n i t r o g e n or c a r b o n find a v e r y s i m p l e and n a t u r a l e x p l a n a t i o n . If the v a c a n c y c o n c e n t r a t i o n is v e r y
After suitable corrections for the n e i g h b o u r i n g S n o e k p e a k s and for b a c k g r o u n d e f f e c t s the s h i f t of the p e a k t e m p e r a t u r e b e t w e e n the i n t e r n a l - f r i c t i o n measurem e n t s of W a g e n b l a s t and S c h w a r t z (27) and of W e l l e r and D i e h l (3) (at I Hz) g i v e s us the r e l a x a t i o n t i m e of the r e o r i e n t a t i o n of the c a r b o n - - m o n o v a c a n c y complex TIV_C = T exp(1.03 eV/kT) (4) with T ~ 10-15s. The a c t i v a t i o n enthalpy(presumably u n c e r t a i n by a b o u t ± 0 . 1 5 eV) a g r e e s w e l l w i t h the v a l u e s d e r i v e d by W e l l e r and D i e h l (3) by o t h e r a r g u ments. Eq.(4) predicts a relaxation time of a b o u t 5 m i n ( w h i c h can be i n v e s t i g a t e d by m a g n e t i c or m e c h a n i c a l after-effect measurements) at 297K. This is distinctly l o w e r t h a n the t e m p e r a t u r e r a n g e of the a f t e r - e f f e c t in n e u t r o n irradiated samples attributed to the IV-C r e l a x a t i o n by B l y t h e (28), w i t h whose assignment we,hence, c a n n o t a g r e e . The m a g n e t i c a f t e r - e f f e c t expected f r o m the r e o r i e n t a t i o n of the IV-C a p p e a r s to h a v e b e e n i d e n t i f i e d r e c e n t l y in neutron-irradiated s - i r o n in the t e m p e r a t u r e r a n g e p r e d i c t e d by Eq.(4)(W.Mensch and J . D i e h l , p e r s o n a l c o m m u n i c a t i o n ) . A mechanical a f t e r - e f f e c t in the t i m e and t e m p e r a t u r e r a n g e p r e d i c t e d by Eq.~) a p p e a r i n g a f t e r s t r a i n i n g i r o n w i r e s at a b o u t 350K to 37OK was i n v e s t i g a t e d by W e s t (19). By a time-- t e m p e r a t u r e transformation he f o u n d the a c t i v a t i o n enthalpy of this p r o c e s s to be 0.91 eV, in r e a s o n a b l e a g r e e m e n t w i t h the a b o v e v a l u e . Thus W e s t (19) m a y h a v e b e e n the f i r s t to o b s e r v e the IV-C or IV-N r e l a x a t i o n . It s h o u l d thus be p o s s i b l e to m o n i t o r the IV-C r e l a x a t i o n (and t h e ]V-N relaxation) by m a g n e t i c or m e c h a n i c a l after-effect measurements at t e m p e r a t u r e s at w h i c h the f o r e i g n i n t e r s t i t i a l atoms still move relatively s l o w l y . This m a y p e r m i t a m o r e d e t a i l e d s t u d y of the f o r m a t i o n of t h e i n t e r s t i t i a l - - v a c a n c y c o m p l e x e s t h a n has b e e n p o s s i b l e so far (comp. (3)).
820
VACANCIES IN TRANSITION METALS
Vol.
! 1, No. 9
high c o m p a r e d with the d i s l o c a t i o n d e n s i t y , it may even h a p p e n that the c a r b o n Snoek-- K S s t e r peak is u n d e t e c t a b l y small d u r i n g the first w a r m - u p . I n d e e d , already Snoek (18) has n o t e d that c a r b u r i z e d iron gives rise to a v e r y m u c h w e a k e r c o l d - w o r k r e l a x a t i o n than n i t r o g e n l o a d e d samples. 3. R e l a t e d ture
In this s e c t i o n we that are n a t u r a l l y
Experiments
d i s c u s s some e x p l a i n e d by
on ~-Fe
further observations reported the ideas o u t l i n e d in Sect.2.
in the
litera-
a) ~ £ £ £ X ~ Z _ e £ _ £ ~ e ~ : _ 9 ~ _ ~ ! ~ E £ ~ z ~ £ ~ _ ~ z i ~ e ~ _ ~ _ ~ e ~ _ i ~ i ~ i 2 ~ . After f a s t - n e u t r o n i r r a d i a t i o n at about 170K, the e l e c t r i c a l r e s i s t i v i t y of c a r b u r i z e d iron shows r e c o v e r y stages at about 240K, 320K, 425K, 535K and 575K (13). Of these, the first one (being the s m a l l e s t of the five) may w e l l be i n t r i n s i c in nature, as d i s c u s s e d in one of the p r e c e d i n g papers (7). The 320K stage was a t t r i b u t e d to t r a p p i n g of c a r b o n i n t e r s t i t i a l s by v a c a n c i e s and the 425K stage to the " n o r m a l " p r e c i p i t a t i o n of the excess c a r b o n into a m e t a s t a b l e c a r b i d e (12). The l a t t e r stage is i n d e e d m u c h more p r o n o u n c e d "in w e a k l y i r r a d i a t e d or u n i r r a d i ated q u e n c h e d s a m p l e s than in s t r o n g l y i r r a d i a t e d s p e c i m e n s (13). atoms
The 535K stage finds its n a t u r a l e x p l a n a t i o n in the from v a c a n c i e s . A s s u m i n g that the d e t r a p p i n g rate ~o exp( =
d e t r a p p i n g of is given by
diSS/kT) -
MIV_C
carbon (5)
,
w h e r e ~o= I013s -I, we e s t i m a t e from the 5 min a n n e a l i n g i s o t h e r m s ((13), Fig.5) a d i s s o c i a t i o n enthalpy H ~ S 8 of 1.6 eV - 1.7 eV, in quite good a g r e e m e n t w i t h W e l l e r and D i e h l ' s (3) e s t i m a t e of 1.6 eV, b a s e d on the a n n e a l i n g of the IV-C c o m p l e x as s t u d i e d by i n t e r n a l f r i c t i o n , and also with r e c e n t M S B b a u e r e x p e r i ments (5) *. As one e x p e c t s from this i n % e r p r e t a t i o n , the c o r r e s p o n d i n g stage in nitrogen-doped neutron-irradiated iron is s h i f t e d to lower t e m p e r a t u r e by about l O O K (16). The final (575K) r e c o v e r y stage gives about the right n u m b e r of jumps for the free m i g r a t i o n of m o n o v a c a n c i e s . F u j i t a and D a m a s k (13), who did not have q u a n t i t a t i v e i n f o r m a t i o n on the v a c a n c y d i f f u s i o n c o e f f i c i e n t , a d d u c e d indeed a d d i t i o n a l a r g u m e n t s in favour of this i n t e r p r e t a t i o n but r e j e c t e d it f i n a l l y b e c a u s e the r e c o v e r y stage appears only in c a r b u r i z e d s p e c i m e n s and not in dec a r b u r i z e d ones (13). In the o p i n i o n of the p r e s e n t authors this o b s e r v a t i o n is an a r g u m e n t s u p p o r t i n g r a t h e r than r e f u t i n g the m e c h a n i s m of m o n o v a c a n c y m i g r a tion for the final r e c o v e r y stage. Since c a r b o n i n t e r s t i t i a l s are v i r t u a l l y imm o b i l e at the t e m p e r a t u r e of s e l f - i n t e r s t i t i a l m i g r a t i o n , they may p r o v i d e w i d e ly d i s p e r s e d t r a p s for s e l f - i n t e r s t i t i a l s . This means that in c a r b u r i z e d s a m p l e s v a c a n c i e s have a h i g h e r chance to escape r e c o m b i n a t i o n w i t h s e l f - i n t e r s t i t i a l s than in d e c a r b u r i z e d s p e c i m e n s . Hence the r e c o v e r y stage a s s o c i a t e d w i t h free m i g r a t i o n of v a c a n c i e s s h o u l d i n d e e d be more p r o n o u n c e d in c a r b u r i z e d iron than in d e c a r b u r i z e d iron, in a g r e e m e n t with the o b s e r v a t i o n s (13). b) Preci . . . . . . . . Takeyama
i t a t i o n of c a r b i d e s and n i t r i d e s ( h i g h - v o l t a g e e l e c t r o n m i c r o s c o p y ) " and T a k a h a s h i s t u d i e d p r e c i p i t a t i o n in s o l u t i o n - q u e n c h e d F e - O . O 2 5 wt%C
~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* The s i m p l e s t m o d e l for the d i s s o c i a t i o n of the ( i n t e r s t i t i a l m i g r a t i o n enthalpy H~ < HIV) gives HdiSs
iv-i
= My + H~v_ i
interstitial-- vacancy the r e l a t i o n s h i p
complex
(6)
The b i n d i n g enthalpyH~ v i may be d e t e r m i n e d by c a l o r i m e t r i c m e a s u r e m e n t s . Arndt and D a m a s k (14) foun~ - H~V_ C = 0.41 eV. The a g r e e m e n t w i t h the v a l u e H~V_C = 0.8 eV f o l l o w i n g from Eq.(6) i s p o o r . This may have two reasons: (i) The c a l o r i m e t r i c m e a s u r e m e n t s gave too low a v a l u e for the b i n d i n g enthalpy. (ii) T h e r e is an a d d i t i o n a l energy b a r r i e r for the e s c a p e of the i n t e r s t i t i a l s from the v a c a n c y traps that is not t a k e n into a c c o u n t in Eq.(6).If the b i n d i n g enthalpy m e a s u r e d by A r n d t and D a m a s k (14) is c o n s i d e r e d as c o r r e c t , this a d d i t i o n a l e n e r g y b a r r i e r amounts to about 0.4 eV.
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( 2 9 , 3 0 ) and F e - O . 0 3 w t % N a l l o y s ( 3 0 , 3 1 ) t h a t w e r e i r r a d i a t e d at r o o m t e m p e r a t u r e w i t h 6 5 0 k e V e l e c t r o n s in a h i g h - v o l t a g e electron microscope and subsequently a n n e a l e d at h i g h e r t e m p e r a t u r e s . T h e f o r m a t i o n of c a r b i d e s and n i t r i d e s w a s v e r y m u c h r e t a r d e d in the i r r a d i a t e d p a r t s of the s p e c i m e n s . T h i s is a t t r i b u t e d to the t r a p p i n g of C and N by r a d i a t i o n - i n d u c e d d e f e c t s , in p a r t i c u l a r vacancies. The a u t h o r s c o n c l u d e t h a t IV-N p a i r s b e g i n to d i s s o c i a t e at a b o u t 470K (31), w h e r e a s the d i s s o c i a t i o n of the IV-C p a i r s t a k e s p l a c e d u r i n g 10 m i n a n n e a l s b e t w e e n 510K and 6 2 0 K (29). T h e s e o b s e r v a t i o n s are in g o o d a g r e e m e n t w i t h t h e d i s s o c i a t i o n enthalpie~ o b t a i n e d by W e l l e r and D i e h l (3). L. G r o u p - V
Transition
Metals
It has r e c e n t l y b e e n s h o w n (17) that in Ta, as in ~ - F e , t h e m i g r a t i o n enthalpy of m o n o v a c a n c i e s e x c e e d s that of c a r b o n , n i t r o g e n , or o x y g e n i n t e r s t i t i a l atoms. The same m a y be e x p e c t e d for the o t h e r G r o u p - V B m e t a l s , Nb and V. In the p r e s e n t s u b s e c t i o n we d i s c u s s e x p e r i m e n t s on t h e s e m e t a l s in the l i g h t of the r e s u l t s obt a i n e d on ~-Fe. B o o n e and W e f t (32) as w e l l as v a n O o i j e n and v a n d e r Goot (33) h a v e i d e n t i f i e d t h e n i t r o g e n Snoek--K6ster p e a k in Nb (at a b o u t 80OK, w o r k i n g at f z I Hz). The o b s e r v a t i o n (32) t h a t this p e a k d e v e l o p s f u l l y o n l y w h e n the p e a k t e m p e r a ture has b e e n c o n s i d e r a b l y exceeded,indicates t h a t n i t r o g e n in Nb b e h a v e s s i m i l a r l y to c a r b o n in ~ - F e , e . g . , that it is r a t h e r f i r m l y t r a p p e d by v a c a n c i e s . By c o n t r a s t , o x y g e n in Ta and Nb a p p e a r to b e h a v e like n i t r o g e n in ~-Fe. S c h o e c k and M o n d i n o (34) i d e n t i f i e d a p e a k in Ta at a b o u t 570K w i t h the o x y g e n Snoek-- K 6 s t e r r e l a x a t i o n . This p e a k as w e l l as an a n a l o g o u s one in Nb w a s a l s o o b s e r v e d by d e L a m o t t e and W e r t (35). The p e a k is f u l l y d e v e l o p e d d u r i n g t h e f i r s t w a r m - u p a n d b e g i n s in fact to a n n e a l out as s o o n as the p e a k t e m p e r a t u r e has b e e n e x c e e d e d . This s u g g e s t s that 0 is not v e r y f i r m l y b o u n d to m o n o v a c a n cies in Nb. This c o n c l u s i o n is s u p p o r t e d by the f o l l o w i n g o b s e r v a t i o n (36): O x y g e n a t o m s that h a d p r e s u m a b l y b e e n t r a p p e d by m o n o v a c a n c i e s during quenching of Nb f r o m n e a r the m e l t i n g p o i n t r e t u r n into s o l i d s o l u t i o n (contributing to the 0 S n o e k p e a k ) d u r i n g 5 m i n a n n e a l s at 570K. Quenching experiments s i m i l a r to t h o s e just m e n t i o n e d (36) h a v e r e c e n t l y b e e n p e r f o r m e d on v a n a d i u m (37). In this case it has b e e n s h o w n that lh a n n e a l ing b e t w e e n 6 5 0 K a n d 8 0 0 K is r e q u i r e d for the o x y g e n to r e t u r n into s o l i d solution. T h i s r e t u r n of 0 into s o l i d s o l u t i o n is a c c o m p a n i e d by a d e c r e a s e of the e l e c t r i c a l resistivity, indicating that intrinsic defects (presumably the monovacancies) a n n e a l out s i m u l t a n e o u s l y . The a v a i l a b l e e v i d e n c e s u p p o r t s the v i e w t h a t this d e c r e a s e is due to the a n n e a l i n g out of t h e v a c a n c i e s i m m e d i a t e l y f o l l o w i n g the b r e a k - u p of t h e IV-O c o m p l e x e s (37). H e r e t h e s i t u a t i o n a p p e a r s to be s i m i l a r to the b r e a k - u p of the C-X and N - X c o m p l e x e s in ~ - F e (3). A r e l a x a t i o n p r o c e s s w i t h an a c t i v a t i o n enthalpy of a b o u t 1.5 eV that m i g h t w e l l be a s s o c i a t e d with the reorientation of the IV-0 c o m p l e x was f o u n d in n e u t r o n - i r r a d i a t e d vanadium (38). T h i s r e l a x a t i o n p r o c e s s lies c l o s e to the n i t r o g e n S n o e k p e a k , a n d it may h a v e b e e n h i d d e n by it in o t h e r e x p e r i m e n t s . By a r g u m e n t s a n a l o g o u s to t h o s e u s e d for ~ - F e (4) we may c o n c l u d e that t h e m i g r a t i o n enthalpy of m o n o vacancies in v a n a d i u m lies b e t w e e n that of o x y g e n (1.25 eV (39)) and an u p p e r l i m i t of 2.3 eV d e d u c i b l e f r o m the a n n e a l i n g out of the IV-0 c o m p l e x e s . The p r e c e d i n g considerations s u p p o r t s t r o n g l y the v i e w that the G r o u p - V transition m e t a l s are i n d e e d v e r y s i m i l a r to ~ - F e , b o t h w i t h r e s p e c t to the magnitude of the m o n o v a c a n c y migration e n e r g y and the b i n d i n g of f o r e i g n i n t e r s t i t i a l a t o m s to v a c a n c i e s . Nevertheless, q u i t e a few q u e s t i o n s r e m a i n open, p a r t l y o w i n g to the fact that the a v a i l a b l e e x p e r i m e n t a l d a t a are far less comp l e t e t h a n in the case of ~-Fe. E . g . , v a n O o i j e n and v a n der Goot (33) r e j e c t Schoeck and Mondino's (34) a s s i g n m e n t of the o x y g e n Snoek-- K 6 s t e r r e l a x a t i o n in Ta (and also the a n a l o g o u s one in Nb) and a t t r i b u t e i n s t e a d an i n t e r n a l f r i c t i o n p e a k at h i g h e r t e m p e r a t u r e s to this p r o c e s s . L i k e w i s e , t h e i r r e s u l t s on the n i t r o g e n Snoek-- K 6 s t e r r e l a x a t i o n are o n l y p a r t i a l l y in a g r e e m e n t w i t h the f i n d i n g s of B o o n e and W e r t (32). In o r d e r to c l a r i f y t h e s e as w e l l as s o m e r e l a t e d questions, ultra-high-vacuum measurements on c a r e f u l l y c h a r a c t e r i z e d specimens are r e q u i r e d .
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5. Conclusions Previous work has e s t a b l i s h e d that in ~-Fe a) m o n o v a c a n c i e s are less mobile than carbon, nitrogen, or oxygen i n t e r s t i t i a l atoms , b) diffusing carbon and nitrogen interstitials may be trapped by m o n o v a c a n c i e s , c) nitrogen-- vacancy pairs dissociate more easily than carbon-- vacancy pairs. In the present
paper
it is shown
that
these
results
account
for
(i) the o b s e r v a t i o n that in a-Fe the nitrogen Snoek-- K S s t e r r e l a x a t i o n (alias nitrogen cold-work peak) is always fully developed during the first w a r m - u p , whereas in l o w - f r e q u e n c y i n t e r n a l - f r i c t i o n m e a s u r e m e n t s full d e v e l o p m e n t of the carbon Snoek-- KSster r e l a x a t i o n requires annealing above the peak t e m p e r a t u r e ; (ii) the differences in carbide or nitride f o r m a t i o n of carbon- or nitrogendoped a-Fe as observed in h i g h - v o l t a g e electron m i c r o s c o p y f o l l o w i n g r o o m - t e m perature electron irradiation; (iii) the annealing b e h a v i o u r perature neutron irradiation.
of carbon-
or n i t r o g e n - d o p e d
a-Fe
after
low-tem-
The good agreement b e t w e e n the o b s e r v a t i o n s on the Snoek-- KSster r e l a x a t i o n and the results a)-c) used in c o n j u n c t i o n with Schoeck's theory gives a d d i t i o n a l support to Schoeck's i n t e r p r e t a t i o n of the Snoek-- KSster relaxation. In particular, it is c o n c l u d e d that the theory holds both for n i t r o g e n and carbon ~ n t e ~ acting with d i s l o c a t i o n s in ~-Fe. In a-Fe the energy b a r r i e r for the d i s s o c i a t i o n of carbon-- m o n o v a c a n c y is distinctly larger than the carbon-- vacancy b i n d i n g energy obtained from calorimetric m e a s u r e m e n t s on neutron-irradiated samples.
pairs
There are strong reasons to believe that results a) and b) apply to the Group-V t r a n s i t i o n metals (vanadium, niobium, tantalum), too. A perusal of the available literature indicates that in these metals the oxygen-- vacancy pairs dissociate more easily than the nitrogen-- vacancy pairs. D i f f e r e n c e s in the Snoek-- KSster r e l a x a t i o n may be u n d e r s t o o d in an analogous fashion as i n d i c a t e d above for G-Fe, but further work is clearly necessary. References I. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12 13 14 15 16. 17. 18. 19. 20. 21.
Y.Ikeda, T.Gotoh, K.Abiko, and H.Kimura, Crystal Lattice Defects 5, 163 (1974% M.Weller, J.Diehl, and W . T r i f t s h £ u s e r , Solid State C o m m u n i c a t i o n s 17, 1223 (1975). M . W e l l e r and J.Diehl, Scripta Met. I0, I01 (1976). J.Diehl, M.Weller, and U.Merbold, S c r i p t a Met.~ 811~ this issuel S . R . R e i n t s e m a , M S , b a u e r Studies of I m p l a n t a t i o n Damage in Iron and Nickel, P r o e f s c h r i f t , R i j k s u n i v e r s i t e i t te G r o n i n g e n 1976. M.Yoshida, M.Kiritani, and F.E.Fujit~ J . P h y s . S o c . J a p a n 39, 170 (1975). D.Herlaeh, K.Maier, H . - E . S c h a e f e r , M.Weller, A.Seeger, and J.Diehl, S c r i p t a Met., 803, this issue. G.Hettich, M.Mehrer, and K.Maier, Scripta M e t . , 795~ this issue, J.R.G. da Silva and R . B . M c L e l l a n , Mater. Science E n g i n e e r i n g 26, 83 (1976). W.Frank, H . - J . E n g e l l , and A.Seeger, Z . M e t a l l k d e 58, 452 (1967). W.Frank, H . - J . E n g e l l , and A.Seeger, T r a n s . M e t . S o c . AIME 242, 749 (1968). H . W a g e n b l a s t and A . C . D a m a s k , J.Phys.Chem. Solids 23, 221 (1962). F . E . F u j i t a and A.C.Damask, Aeta Met. 12, 331 (1964). R.A.Arndt and A . C . D a m a s k , Acta Met. 12, 341 (1964). H . W a g e n b l a s t , F.E.Fujita, and A . C . D a m a s k , Acta Met. 12, 347 (1964). M.Wuttig, J . T . S t a n l e y , and H . K . B i r n b a u m , p h y s . s t a t . s o l . 27, 701 (1968). K.Maier, H.Metz, D.Herlach, H . - E . S c h a e f e r , and A.Seeger, submitted to Phys.Rev. Letters. D.L.Snoek, Physica 8, 711 (1941). W.A.West, T r a n s . A m e r i c . l n s t . M i n . M e t a l l . E n g r s 167, 192 (1946). T.S.K~, A m e r i c . l n s t . M i n . M e t a l l . E n g r s . T e c h n - P u b l . N o . 2370 (1948). W.KSster, L.Bangert, and R.Hahn, E i s e n h ~ t t e n w . 25, 569 (1955).
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22. A . S . N o w i c k and B.S.Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York and London, 1972. 23. G.Schoeck, Acta Met. 11, 6]7 (1963). 24. R.DeBatist, Internal Friction of Structural Defects in Crystalline Solids, N o r t h - H o l l a n d , A m s t e r d a m and London, 1972. 25. D . T . P e t a r r a and D.N.Beshers, Acta Met. 15, 791 (1967). 26. K.Kamber, D.Keefer, and C.Wert, Acta Met. 9, 403 (1961). 27. H.Wagenblast and J.C.Schwartz, Acta Met. 13, 42 (1965). 28. H,J.Blythe, p h y s . s t a t . s o l . ( a ) 20, 619 (1973). 29. T . T a k e y a m a and H.Takahashi, J . P h y s . S o c . J a p a n 35, 939 (1973). 30. T . T a k e y a m a and H.Takahashi, Fundamental Aspects of R a d i a t i o n Damage in Metals, edited by M . T . R o b i n s o n and F.W.Young, Jr., ERDA report CONF-751006, Oak Ridge (Tenn.), Vol. 2, p. 1100. 31. T . T a k e y a m a and H.Takahashi, J . P h y s . S o c . J a p a n 38, 1783 (1975). 32. D.H.Boone and C.A.Wert, J . P h y s . S o c . J a p a n 18, Suppl.l, 141 (1963). 33. D.J.van Ooijen and A.S.van der Goot, Philips Res.Repts. 22, 150 (1967). 34. G.Sehoeck and M.Mondino, J . P h y s . S o c . J a p a n 18, Suppl.l, 149 (1963). 35. E.de Lamotte and C.Wert, J . P h y s . S o c . J a p a n 19, 1560 (1964). 36. A . G . A r a k e l o v , M.S.Blanter, A.Ye.Kissil' , L.A.Kovaleva, and l.T.Stekachev, F i z . m e t a l . m e t a l l o v e d . 35, 826 (1973). 37. A . G . A r a k e l o v , M.S.Blanter, A . Y e . K i s s e l ' , L.A.Kovaleva, and P.A.Khandarov, F i z . m e t a l . m e t a l l o v e d . 40, 71 (1975). 38. M.Eto, Y.Matsuo, S.Ishino, and Y.Mishima, J . N u c l . M a t e r i a l s 52, 309 (1974). 39. G.H6rz, Z.Metallkde. 59, 712 (1968).