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MOTION IN MARTENSITICALLY TRANSFORMED
A15 COMPOUNDS
C. Snead, Jr. Welch, D. Welch
To cite this version:
JOURNAL DE PHYSIQUE
Colloque ClO, suppl&ment au n o
12,T o m e 46, dgcembre 1985
page C10-589
INTERNAL FRICTION DUE T O DOMAIN-WALL MOTION IN MARTENSITICALLY
TRANSFORMED A15 COMPOUNDS
C.L. SNEAD, Jr. AND D.O. WELCH
Brookhaven National Laboratory, Upton, NY 11973, U.S.A.
A b s t r a c t
-
A l a t t i c e i n s t a b i l i t y i n A15 m a t e r i a l s i n some c a s e s Leads t o a c u b i c - t o - t e t r a g o n a l m a r t e n s i t i c t r a n s f o r m a t i o n a t low t e m p e r a t u r e s . The t r a n s - formed m a t e r i a l o r i e n t s i n l a m e l l a e w i t h c a x e s a l t e r n a t e l y a l i g n e d a l o n g t h e<loo>
d i r e c t i o n s p r o d u c i n g domain w a l l s between t h e l a m e l l a e . An i n t e r n a l - f r i c t i o n ( 6 ) f e a t u r e below Tm i s a t t r i b u t e d t o s t r e s s - i n d u c e d domain-wall motion. The magnitude of t h e f r i c t i o n i n c r e a s e s a s t m p e r a t u r e i s lowered below Tm a s ( I - c / a ) i n c r e a s e s , and behaves a s ( 1 - c / a ) ' from Tm down t o t h e s u p e r c o n d u c t i n g c r i t i c a l t e m p e r a t u r e where t h e i n c r e a s i n g t e t r a g o n a l i t y i s i n h i b i t e d . The e f f e c t of s t r a i n i n t h e l a t t i c e i s t o d e c r e a s e t h e domain-wall i n t e r n a l f r i c t i o n , b u t n o t a f f e c t T,. Neutron-induced d i s o r d e r and t h e a d d i - t i o n of some t h i r d - e l e m e n t s i n a l l o y i n g d e c r e a s e b o t h 6 and Tm, w i t h some e l e m e n t s r e d u c i n g o n l y t h e former. L e s s t h a n 1 a t . % H i s s e e n t o c o m p l e t e l y s u p p r e s s b o t h 6 and Tm. M a r t e n s i t i c a l l y t r a n s f o r m e d V pZr d e m o n s t r a t e s low- t e m p e r a t u r e i n t e r n a l - f r i c t i o n and modulus b e h a v i o r c o n s i s t e n t w i t h e a s y B/m w a l l motion r e l a t i v e t o t h e e a s y m l m motion of t h e A15's. For the VpZr, a peak i n 6 i s o b s e r v e d , q u a l i t a t i v e l y i n agreement w i t h e x p e c t e dB l m
w a l l motion. INTRODUCTIONAlthough t h e r e h a s been a v e r y l a r g e amount of work expended on s t u d i e s of m a r t e n s i - t i c t r a n s f o r m a t i o n s , t h e u n d e r s t a n d i n g of t h e m i c r o s c o p i c mechanisms i n v o l v e d s o f a r i s q u i t e poor. To q u o t e P l a n e s e t a l .
111
" I n f a c t , o n l y c e r t a i n t r a n s i t i o n s-
t h o s e found i n t h e A15 compounds-
can be e x p l a i n e d i n terms of m i c r o s c o p i c p r o p e r - t i e s of t h e i r c o n s t i t u e n t s ( i t i s b e l i e v e d t h a t A15 compounds undergo a band Jahn- T e l l e r t r a n s i t i o n /2-41." Even w i t h t h a t , the m i c r o s c o p i c mechanism g i v i n g r i s e t o i n t e r n a l f r i c t i o n a s s o c i a t e d w i t h t h e t r a n s f o r m a t i o n i s n o t known. T h i s p a p e r r e v i e w s some of t h e d a t a on i n t e r n a l f r i c t i o n due t o m a r t e n s i t i c t r a n s f o r m a t i o n s i n A15's, how v a r i o u s m a t e r i a l t r e a t m e n t s a f f e c t t h e f r i c t i o n , a "microscopic" t h e o r yt o e x p l a i n t h e f r i c t i o n , and how t h e d a t a and t h e t h e o r y compare.
Some of t h e A15 compounds undergo a c u b i c - t o - t e t r a g o n a l m a r t e n s i t i c t r a n s f o r m a t i o n . T h i s t r a n s f o r m a t i o n i s a t t e m p e r a t u r e Tm below l i q u i d - n i t r o g e n t e m p e r a t u r e and above t h e s u p e r c o n d u c t i n g c r i t i c a l t e m p e r a t u r e Tc. A s w i t h many m a r t e n s i t i c
t r a n s f o r m a t i o n s , i t i s a s s o c i a t e d w i t h a l a t t i c e i n s t a b i l i t y ( t h e i n s t a b i l i t y of t h e {110} <110> mode w i t h d e c r e a s i n g t e m p e r a t u r e and t h e v a n i s h i n g of t h e s h e a r modulus ( 1 / 2 ) ( C l l - C 1 2 ) a t Tm 15-61. I n Nb3Sn t h e t e t r a g o n a l - p h a s e m a t e r i a l i s composed of twinned domains w i t h c a x e s l y i n g a l o n g
< l o o >
d i r e c t i o n s , and w i t h t h e h a b i t p l a n e o f t h e twin boundary a l o n g (110). A t Tm, t h e c a x i s i s reduced and t h e a and b a x e s e q u a l l y l e n g t h e n e d . The t e t r a g o n a l i t y of t h e m a t e r i a l i n c r e a s e s , however, a st h e t e m p e r a t u r e i s lowered below Tm a s c / a d e c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e down t o Tc where f u r t h e r change i n c / a i s a r r e s t e d 121. For Nb3Sn a t Tc, c / a =
0.9939 w i t h Tm a t 43 K 171. On t h e o t h e r hand, V3Si h a s t h e c a x i s l a r g e r t h a n t h e a and b a x e s and a c / a of 1.0022 w i t h a Tm o f 21 K 171. Note t h a t t h e " t e t r o g a n a l i t y " / ( l - c / a ) l of Nb3Sn i s r o u g h l y 3 times t h a t of VgSi a t t h e i r r e s p e c t i v e Tcl s.
The A15 superconductor NbgSn i s c u r r e n t l y the prime m a t e r i a l f o r the c o n s t r u c t i o n of magnets f o r a p p l i c a t i o n s such a s c o n f i n i n g magnets f o r f u s i o n , and bending magnets f o r t h e Superconducting S u p e r c o l l i d e r . Since these a p p l i c a t i o n s r e q u i r e l a r g e s t r e s s e s on the conductors, knowledge of the low-temperature modulus v a l u e s and mechanical behavior i s needed. The modulus d a t a t h a t a r e taken concomitantly with
the Q - l d a t a a r e , t h e r e f o r e , of s c i e n t i f i c and engineering i n t e r e s t . As the t r a n s f o r m a t i o n t o the t e t r a t r a g o n a l phase i s thought t o be i n t i m a t e l y coupled with both mechanical behavior and t o the superconducting c r i t i c a l p r o p e r t i e s , these s t u d i e s take an added i n t e r e s t .
Figure 1 shows the i n t e r n a l f r i c t i o n of Nb3Sn from 10-400 K. Specimens were p o l y c r y s t a l l i n e 10-pm l a y e r s of Nb3Sn sandwiching a 10-um Nb s u b s t r a t e and c u t i n t o f o i l s . Standard e l e c t r o s t a t i c d r i v e i n f l e x u r e was used a t f r e q u e n c i e s between 100 and 2000 Hz. The high-temperature peaks w i l l be discussed l a t e r . The f e a t u r e of n o t e i s the 2.5 o r d e r of magnitude i n c r e a s e i n 0 - I between T, ( h e r e 49 K) and Tc (18.1 K . (Data were taken f o r temperature ramps i n both d i r e c t i o n and no h y s t e r s i s o r time dependence of Q'l was ever d e t e c t e d . A l l d a t a a r e shown f o r i n c r e a s i n g temperature.) I t i s t h i s f e a t u r e t h a t provides the means of studying v a r i o u s chemi- c a l and mechanical e f f e c t s on the m a r t e n s i t i c transformation.
AIRCO
NbSSn
. .
TEMPERATURE (K1
Fig. 1. Q - l vs. temperature f o r Fig. 2. E f f e c t of i n t e r n a l s t r a i n i n "pure" NbgSn f o i l . NbgSn on the reduced modulus E(T)/E(300 K)
a s a f u n c t i o n of temperature.
One of the f i r s t parameters i n v e s t i g a t e , d was the e f f e c t of s t r a i n on t h e transforma- t i o n . S t r a i n due t o unrelieved deformation i n the s u b s t r a t e was i n v e s t i g a t e d a s shown i n the modulus measurements of Figure 2. Note t h a t t h e modulus s o f t e n s near Tm = 49 K t o a value of "40% of the room-temperature value i n the s t r a i n - f r e e specimen. This modulus s o f t e n i n g r e f l e c t s the i n s t a b i l i t y of the I110 }<110> mode mentioned e a r l i e r . With i n c r e a s i n g i n t e r n a l s t r a i n ( e 0 . 1 and 0.2%) the amount of s o f t e n i n g i s reduced s i g n i f i c a n t l y . Figure 3 shows the e f f e c t s of t h i s s t r a i n on the i n t e r n a l f r i c t i o n . The r e d u c t i o n i n the f r i c t i o n with s t r a i n i s c o n s i d e r a b l e , b u t the main p o i n t to make i s t h a t even though the modulus and the i n t e r n a l f r i c t i o n a r e changed, the transformation temperature Tm i s e s s e n t i a l l y u n a l t e r e d , a s i s expected from a Landau- type theory of the transformation
/a/.
TEMPERATURE ( K ) TEMPERATURE ( K ) F i g . 3. E f f e c t of s t r a i n on Q - ~ a s F i g . 4 . P a r a m e t r i z e d f i t of ~ - ' a ( c / a - 1 ) 2 a f u n c t i o n of t e m p e r a t u r e i n Nb3Sn. f o r t h e low- t e m p e r a t u r e i n t e r n a l f r i c t i o n of two Nb gSn specimens. of "pure" Nb3Sn d a t a a r e f i t w i t h t h i s e x p r e s s i o n w i t h t h e d a t a normalized a t 18 K . T h e r e i s one f r e e p a r a m e t e r , T,. S i n c e c / a d e c r e a s e s w i t h t e m p e r a t u r e , we use p r e v i o u s l y determined v a l u e s
I ? /
i n t h e f i t t i n g . The r e s u l t s a r e shown i n F i g u r e 4. The Tm v a l u e of 49 K , determined from t h e a p p a r e n t h i g h e s t - t e m p e r a t u r e of o n s e t of t h e i n t e r n a l f r i c t i o n does n o t f i t w e l l . The v a l u e Tm = 44.5 K was found t o g i v e t h e b e s t f i t . Note t h a t i s n e a r t h e v a l u e of 43 K u s u a l l y a s s o c i a t e d w i t h t h i s t r a n s f o r m a t i o n from X-ray work / 7 / . The r e g i o n 44-49 K would then seem t o be a t e m p e r a t u r e range d e n o t i n g o n s e t (49 K) and c o m p l e t i o n (44 K) of t h e c u b i c - t o - t e t r a g o n a l t r a n s f o r m a t i o n . Below 44 K , a l l changes i n Q-' a r e a t t r i b u t e d t o changes i n c / a . We w i l l s e e t h a t t h i s t r a n s f o r m a t i o n r e g i o n below Tm can be broadened by d i f f e r e n t t r e a t m e n t s .A15 compounds w i t h maximized c r i t i c a l p r o p e r t i e s a r e c h a r a c t e r i z e d a s h i g h l y o r d e r e d compounds. The q u e s t i o n h a s a r i s e n of what t h e e f f e c t s of d i s o r d e r a r e o,n t h e com- pound's p r o p e r t i e s . S i n c e t h e s e m a t e r i a l s a r e e n v i s i o n e d t o be used i n r a d i a t i o n e n v i r o n m e n t s , f o r i n s t a n c e , t h e radiation-damage-induced d i s o r d e r e f f e c t s become o f paramount importance. F i g u r e s 5 and 6 show t h e e f f e c t s of 400 K r e a c t o r - s p e c t r u m n e u t r o n i r r a d i a t i o n t o Nb3Sn. The p r i m a r y d e f e c t produced a f f e c t i n g d i s o r d e r from
t h i s i r r a d i a t i o n i s t h e a n t i s i t e d e f e c t (A-B i n t e r c h a n g e i n t h e A3B compound) 1 9 1 . '
0 2 0 40 6 0
TEMPERATURE ( K )
I n Figure 5 t h e r e a r e t h r e e main t h i n g s t o n o t e with regard t o the d i s o r d e r e f f e c t s on t h e log decrement 6. The f i r s t i s the decrease i n 6 with fluence. The second i s t h e d e c r e a s e i n Tm with f l u e n c e . R e c a l l t h a t i n t e r n a l s t r a i n reduced 6 b u t did n o t a f f e c t Tm a t a l l . I t i s then c l e a r t h a t d i s o r d e r plays a very d i f f e r e n t r o l e i n changing the c h a r a c t e r i s t i c s of the t r a n s f o r m a t i o n , most probably through the
Neutron Fluence ( 1018n/cm2 ,E> l MeV 1 I 0 5 2.4 0 ~ g ~ ' s ~ o' n 1 J J 1 8 1 5 0 100 3 0 0 8 TEMPERATURE (K)
Fig. 6. Reduced modulus E(T)/E(300 K)
vs. temperature of Nb3Sn f o r s e v e r a l reactor-spectrum f l u e n c e s .
Nb3Sn NEUTRONFLUENCE
( 1 0 ' ~ n / c r n ~ , ~ = 1 4 MeV)
TEMPERATURE (K)
Fig. 7. Log decrement 6 vs. temperature of Nb3Sn f o r s e v e r a l f l u e n c e s of 14-MeV neutrons.
e l e c t r o n i c p r o p e r t i e s of the m a t e r i a l which t o f i r s t approximation a r e n o t a f f e c t e d by s t r e s s . Tm i s seen t o decrease monotonically ( s t i l l p r e s e n t i n t h e curve marked 6 i f the s c a l e i s expanded and l o c a t e d a t "21 K). For f l u e n c e s higher than
3.8 x
lo1*
n/cm2, Tm would, by e x t r a p o l a t i o n , l i e below Tc. Since c / a cannotchange below Tc 121, t h e transformation cannot
,
t h e r e f ore; take place. Thus, d i s o r d e r induced by neutron i r r a d i a t i o n can completely a r r e s t the m a r t e n s i t i c t r a n s f o r m a t i o n .I n a d d i t i o n t o a r e d u c t i o n of 6 and Tm with d i s o r d e r , i t i s a l s o noted from Figure 5 t h a t a s f l u e n c e (and d i s o r d e r ) i n c r e a s e , the shape of the 6 curve 'between o n s e t a t high temperature and Tc changes from convex-right to convex-left: i n o t h e r words,
the ( l - c ~ a ) ~ dependence no longer holds. Indeed, the e n t i r e range f o r the 0.65 x 1818 n/cm2 f l u e p c e t a k e s on the c h a r a c t e r of the 44-49 K region of the u n i r r a d i a t e d case. We think t h i s i s s i g n i f i c a n t and t h a t a f l u c t u a t i o n of d i s o r d e r i n the speci- men c r e a t e s the s i t u a t i o n where a l a r g e r temperature range i s spanned b e f o r e the completion of transformation i s r e a l i z e d . For curves 5 and 6 t h i s temperature span c l e a r l y encompasses Tc.
The e f f e c t of i n c r e a s i n g d i s o r d e r on the mode s o f t e n i n g and t h e r e f o r e the dynamic Young's modulus i s shown i n Figure 6. A l l the moduli a r e normalized t o t h e i r r e s p e c t i v e v a l u e s a t 300 K. S o f t e n g of $O% f o r the "virgin" specimen i s seen t o d e c r e a s e t o only 6% f o r the 13 x 10" n/cm case. For the two h i g h e s t f l u e n c e s shown, t h e r e was no m a r t e n s i t i c transformation. This s i g n i f i c a n t i n c r e a s e i n t h e low-temperature modulus i n r a d i a t i o n environments could have important consequences i n f u s i o n a p p l i c a t i o n s . For the e f f e c t of pure 14-MeV neutrons on the transforma- t i o n , Figure 7 shows t h e i n t e r n a l f r i c t i o n changes with f l u e n c e . S i m i l a r behavior t o reactor-spectrum i r r a d i a t i o n (Figure 5) i s seen, b u t with an i n t e r e s t i n g d i f f e r - ence. The changes of the superconducting Tc s c a l e with damage energy when compar- ing the two types of neutron s p e c t r a (14-MeV neutron "6 times more e f f e c t i v e / l o / ) , whereas the comparison h e r e would g i v e a v a l u e c l o s e r t o 2.
The e f f e c t s of a d d i n g T i t o t h e Nb3Sn compound on t h e low-temperature i n t e r n a l f r i c t i o n a r e s e e n i n F i g u r e 8. Here i t i s noted t h a t 3 a t . % i n t h e m a t r i x com- p l e t e l y s u p p r e s s e s t h e t r a n s f o r m a t i o n by r e d u c i n g Tm below Tc. A s w i t h n e u t r o n i r r a d i a t i o n , T i a l l o y i n g r e d u c e s Tm and t h e magnitude of Q- l . Both Q- and T,
Fig. 8. Low-temperature Q - I v s . t e m p e r a t u r e f o r Nb3Sn
+
xTi f o r s e v e r a l v a l u e s of x.a r e s i m i l a r l y reduced by t h e a l l o y i n g of a few p e r c e n t of Ta b u t w i t h Tm com- p l e t e l y s u p p r e s s e d a t t h e 7 - a t . % l e v e l , i n comparison w i t h 3 a t . % f o r t h e T i . I t i s t o be n o t e d t h a t t h e i n t r o d u c t i o n of T i o r Ta reduce b o t h Tm and Q due t o domain-wall motion. The e f f e c t s of T i a d d i t i o n t o t h e modulus i s seen i n Fig. 9 where t h e r e s u l t s a r e q u i t e s i m i l a r t o t h o s e of t h e n e u t r o n - i r r a d i a t e d specimens.
1.0
Fig. 9. Reduced modulus E(T)/E(300 K)
t i o n was taking place. For the Z r a l l o y , where Tm i s not a f f e c t e d , t h i s broaden- i n g of Tm does not obviously take place. R e s u l t s s i m i l a r t o those of Z r a r e shown i n Fig. 11 f o r Hf a d d i t i o n s . The modulus curves f o r both of these a l l o y s (Zr and Hf) a r e q u i t e s i m i l a r to those of T i i n Fig. 9 , and a r e n o t shown.
L I I I I I I I I
0 10 2 0 30 4 0 50 60 7 0 TEMPERATURE ( K )
Fig. 10. Low- temperature Q" vs. temperature f o r Nb3Sn
+
xZr f o r s e v e r a l v a l u e s of x.t
0 - I I I I I I I 0 10 2 0 30 4 0 50 60 TEMPERATURE (K) Fig. 11. Low-temperature Q- vs. temperature f o r Nb gSn+
xHf f o r s e v e r a l v a l u e s of x.The d i f f e r e n c e i n behavior of Q-I and Tm f o r Ti and Ta a d d i t i o n s on the one hand, and f o r Hf and Z r on the o t h e r a r e q u i t e i n s t r u c t i v e . Where d i s o r d e r i s p r e s e n t i n A15 compounds, whether by a l l o y i n g , r a d i a t i o n damage, o r d e v i a t i o n from stoichiome- t r y , i t i s well known t h a t the e l e c t r i c a l p r o p e r t i e s ( i n c l u d i n g the superconductiv- i t y c r i t i c a l p r o p e r t i e s ) a r e much more s e n s i t i v e to d f s o r d e r on the A s i t e than the B s i t e . / 9 / The connection i s then made t o the a l l o y i n g r e s u l t s here t h a t i t is probable t h a t s i n c e T i and Ta reduce T,, but Hf and Z r do n o t , t h a t Ti and Ta occupy the Nb s i t e s , while Hf and Z r probably occupy the Sn s i t e s s i n c e t h e i r presence does not suppress T,. The EXAFS and TEM evidence f o r s i t e occupation confirms the c o n j e c t u r e f o r the T i and Ta: no d e f i n i t i v e r e s u l t s f o r Hf o r Z r a r e y e t a v a i l a b l e . The major p o i n t regarding t h i s i s t h a t we have here a p o s s i b l e new
t o o l f o r i d e n t i f y i n g the s i t e occupancy of d i l u t e a l l o y i n g a d d i t i o n s , based upon i n t e r n a l - f r i c t i o n measurements.
Since the i n t e r n a l f r i c t i o n from the domain-wall motion i s a c l e a r i n d i c a t o r of t h e presence of transformed m a t e r i a l , we a l s o have a t o o l to t e s t f o r t h e presence of the transformation i n o t h e r A15 m a t e r i a l s . Specimens of VgGa and NbgGe have been t e s t e d . Fig. 12 shows the r e s u l t s f o r VgGa. F i r s t , the degree of modulus ,softening is about h a l f of t h a t of NbgSn. The specimen i s s t r a i n f r e e and i s near stoichiome- t r y and p e r f e c t long-range o r d e r a s a t t e s t e d by i t s value of Tc. Thus, we con- clude from the lack of a low-temperature i n t e r n a l - f r i c t i o n f e a t u r e ( c h a r a c t e r i s t i c of twin-boundary motion) t h a t V3Ga probably does n o t undergo a m a r t e n s i t i c phase transforma t i o n . S i m i l a r lack of i n t e r n a l f r i c t i o n i n NbgGe i s r a t h e r inconclusive due t o the subs t r a te-induced s t r a i n s and d i s o r d e r i n the specimens /11/.
m a r t e n s i t i c t r a n s f o r m a t i o n . The e f f e c t s they found were v e r y s i m i l a r t o t h o s e found by a d d i n g T i o r Ta: i . e . , r e d u c t i o n of i n t e r n a l f r i c t i o n i n t h e t r a n s f o r m e d regime and t h e r e d u c t i o n of T,. The s t r i k i n g f e a t u r e , however, i s t h e c o m p l e t e s u p p r e s -
-
s i o n of T, below Tc f o r hydrogen c o n c e n t r a t i o n s l e s s t h a n 1 a t . % ( s e e F i g . 1 3 ) .
20 30 5 0 100 200 400
TEMPERATURE ( K ) TEMPERATURE (K)
Fig. 12. Log decrement 6 and reduced Fig. 13. Reduced modulus E(T)/E(300 K) modulus E(T)/E(300 k ) f o r V3Ga. v s . t e m p e r a t u r e ( t o p ) and Q-
'
v s . temper-a t u r e ( b o t t o m ) f o r NbgSn w i t h v a r i o u s amounts of hydrogen: ( 1 ) None, ( 2 ) 0.2 a t . % ) , (3) 0.15 a t . % , ( 4 ) 1.8 a t . % , and ( 5 ) 3.0 a t . % (from LeHuy e t a l . 1 1 2 1 ) . A d e p a r t u r e from p r e v i o u s b e h a v i o r i s a l s o n o t e d t h a t t h e r e d u c t i o n of s o f t e n i n g ( F i g . 1 3 , t o p ) does n o t s c a l e w i t h t h e r e d u c t i o n o f T, a s w i t h t h e m e t a l l i c a l l o y s . T h e r e a r e c l e a r l y d i f f e r e n t e f f e c t s b e i n g m a n i f e s t e d by t h e hydrogen i n c l u s i o n s t h a t a r e n o t s e e n i n o t h e r t r e a t m e n t s . T h i s would seem t o be a n i n t e r - e s t i n g and f r u i t f u l a r e a f o r f u r t h e r s t u d y .
F o r t h e A15 m a t e r i a l s , we have o n l y been concerned w i t h i n t e r n a l f r i c t i o n due t o t h e motion of twin b o u n d a r i e s t h a t c o m p r i s e t h e w a l l s between d i f f e r e n t l y o r i e n t e d t e t r a g o n a l domains. The presume t i o n i s t h a t t h e s e b o u n d a r i e s move more e a s i l y under s t r e s s a n d / o r have a much l a r g e r a r e a t h a n do any t e t r a g o n a l / c u b i c (film) domain w a l l s . Dejonghe e t a l . 1141 s u c c i n c t l y o u t l i n e d t h e type of i n t e r n a l - f r i c t i o n r e s p o n s e t o be e x p e c t e d from t h e s e v e r a l p o s s i b l e t y p e s of domain-wall motion i n t h e r m o e l a s t i c a l l y t r a n s f o r m i n g specimens. The A15 r e s u l t s f i t t h e c a s e of e a s y m/m boundary motion, w i t h l i t t l e o r no B/m c o n t r i b u t i o n . The o t h e r major p o s s i b i l i t y f o r f r i c t i o n i n v o l v e s t h e c a s e where B/m motion i s predominant: c a s e s where t h e t h r e s h o l d s t r e s s f o r m/m motion i s h i g h e r t h a n t h a t f o r
B l m ,
o r due t o t h e l a c k o fm/m i n t e r f a c e s .
For t h e c a s e of B / m i n t e r f a c e motion, i n s t e a d of c o n s t a n t ( o r i n c r e a s i n g w i t h c / a ) f r i c t i o n below T,, a ( i l l d e f i n e d ) peak i s e x p e c t e d below Tm. A l s o o t h e r
tion. Also, the modulus begins t o show hardening due t o the transformed m a t e r i a l , which i s f u l l y i n keeping with expected behavior. R e c a l l , t h a t the ~ 1 5 ' s show no such hardening below T,, and t h i s lack of hardening i s a s c r i b e d t o a modulus e f f e c t due t o the easy motion of the m/m domains. The hardening i n t h e
1,
, , , , , , ,
,
,
, , , , , ,
, ,
, ,
, , ,
,107 40 60 80 100 120 140 160 TEMPERATURE (I0 VpZr ---.
480 Hz 2O-x10-~ '\V2Zr, then, i s f u r t h e r evidence of the lack of a m/m l o s s mechanism being p r e s e n t i n t h i s system. This V p Z r system a l s o d i s p l a y s a marked h y s t e r e t i c and h e a t i n g
dependence of the i n t e r n a l f r i c t i o n , t h a t i s c o n s i s t e n t with B/m wall motion ( L .
Snead, to be published).
-10
CONCLUSIONS
-
Y09g
Fig. 14. Log decrement 6 vs. temperature f o r V 2 Z r i n region 2 the m a r t e n s i t i c transformation.08; Reduced modulus E(T)/E(300 K) i s
/ a l s o p l o t t e d .
0 -
The m a r t e n s i t i c phase t r a n s i t i o n Nb3Sn and i t s a l l o y s has been shown t o give r i s e t o a l a r g e i n t e r n a l f r i c t i o n ( Q - ~ ) . Presumably o r h e r A15 compounds, such a s V3Si, which have t h i s type of t r a n s i t i o n w i l l a l s o m a n i f e s t t h i s i n t e r n a l f r i c t i o n . (However, t h e magnitude of
9-l
seems to vary with ( c / a-
I ) ~ ; thus the magnitude f o r V3Si should be a f a c t o r of about 8 s m a l l e r than t h a t f o r Nb3Sn.) The c h a r a c t e r -i s t i c s of t h e i n t e r n a l f r i c t i o n , such a s the dependence on ( c / a
-
a r e c o n s i s - t e n t with i t being caused by the s t r e s s - i n d u c e d motion of the boundaries (domain w a l l s ) between d i f f e r e n t v a r i a n t s of the t e t r a g o n a l phase. Furthermore, these domain w a l l s seem t o be a b l e t o move r e l a t i v e l y f r e e l y under the i n f l u e n c e of t h e s t r e s s , but f u r t h e r understanding of the dynamics of domain-wall motion r e q u i r e a d d i t i o n a l experiments t o c h a r a c t e r i z e the s t r e s s - a m p l i t u d e and frequency dependence of the i n t e r n a l f r i c t i o n . Both the i n t e r n a l f r i c t i o n s t r e n g t h and the s o f t e n i n g of the e l a s t i c modulus a s s o c i a t e d with the m a r t e n s i t i c pliase t r a n s i t i o n were shown to depend s e n s i t i v e l y on the s t a t e of s t r e s s , the degree of d i s o r d e r , the presence of s o l u t e s , and o t h e r f a c t o r s ; thus they w i l l provide u s e f u l t o o l s f o r the f u r t h e r i n v e s t i g a t i o n of t h i s i n t e r e s t i n g phase t r a n s i t i o n i n an important c l a s s of i n t e r m e t a l l i c compounds.ACKNOWLEDGMENTS
This r e s e a r c h was performed under the a u s p i c e s of the U.S. Department of Energy, Division of M a t e r i a l s Sciences, O f f i c e of Basic Energy Sciences under Contract No. DE-AC02-76CH00016.
The experimental work presented h e r e i s l a r g e l y the product of s e v e r a l c o l l a b o r a - t i o n s and independent s t u d i e s . The major people included were J. B u s s i e r e , B.
Berry, B. Faucher, H. Kumakura, and M. Suenaga. The t e c h n i c a l a s s i s t a n c e of B.
Jones and W. Tremel i s g r e a t l y a p p r e c i a t e d .
APPENDIX A. Simple Model f o r the Low-Temperature I n t e r n a l F r i c t i o n and Modulus Defect i n A15 Compounds
e i t h e r the x, y, or z a x e s ) ; the volume f r a c t i o n of each of the d i f f e r e n t types of domain w i l l be denoted by f x , f y , and f,, with f t = f x
+
f y+
f,. Weassume, f o r s i m p l i c i t y , t h a t the applied s t r e s s used i n the measurement of the dynamic modulus does not a l t e r the t o t a l amount o f transformed m a t e r i a l , so t h a t f t is a constant. Furthermore, we assume t h a t the e l a s t i c s t r a i n induced i n an i n d i v i d u a l domain i s much smaller than the t e t r a g o n a l i t y (c/a-1) caused by the martensi t i c transformation.
Again f o r s i m p l i c i t y , consider the e f f e c t of an o s c i l l a t i n g u n i a x i a l t e n s i l e s t r e s s along the z a x i s :
This w i l l induce a component of s t r a i n along the z a x i s , which a l s o o s c i l l a t e s (but not n e c e s s a r i l y i n phase with a,,):
where the f i r s t term r e p r e s e n t s the instantaneous e l a s t i c s t r a i n and the second i s the c o n t r i b u t i o n due t o domain-wall motion. Eo i s the unrelaxed Young's modulus, while the angular brackets r e p r e s e n t a volume average over the various domains as well as the untransformed m a t e r i a l . Af, i s the time-dependent change i n the volume f r a c t i o n of z a x i s domains produced by the consumption or c r e a t i o n of adja- c e n t x- and y-axis domains by domain-wall motion. The i n t e r n a l f r i c t i o n , Q - l , and Young's modulus E , a r e obtained by standard methods /15/ from the in-phase and out-of-phase components of €,,/a,,:
- 2 n
(2
-1) I m (Af,/azz)Q-' = a
,
andE-
The required change i n z-domain volume f r a c t i o n , Af,, i s a complex q u a n t i t y with t h e r e l a t i v e c o n t r i b u t i o n of i t s r e a l and imaginary p a r t s dependent on the d e t a i l s of domain-wall dynamics, about which more l a t e r . I f however, i n general the dynamic response of the domain populations to an applied s t r e s s w i l l be of the form:
Af, a F(a,,) ~ ( w ) A
,
where F(aZ,) i s the (thermodynamic) f o r c e on a domain wall caused by the s t r e s s
u,,,
R(w) i s a frequency-dependent response f u n c t i o n which depends on the mechan-ism of domain-wall motion, and A i s the domain-wall area per u n i t volume. The force
F As found from the change i n the e l a s t i c thermodynamic p o t e n t i a l of the c r y s t a l caused by the displacement of the wall s e p a r a t i n g two types of domain
( w ,
x domain and a z domain); t h i s may be found using the e x p l i c i t expressions f o r t h e e l a s t i c thermodynamic p o t e n t i a l s of the three types of domain given by P i e t r a s s . / l 6 / Thus:and
where a i s a n u m e r i c a l f a c t o r which depends on t h e domain s h a e. I t i s s e e n from Eq. ( 5 ) t h a t t h e i n t e r n a l f r i c t i o n i s p r o p o r t i o n a l t o ( c i a - l ) ' , and t h i s i s observed
2
e x p e r i m e n t a l l y a s shown i n F i g u r e 4. B a s i c a l l y , t h e f a c t o r ( c / a - 1 ) a r i s e s because t h e s t r a i n produced when a domain w a l l move i s p r o p o r t i o n a l t o ( c / a - 1 ) . The p r o d u c t of t h e s e two f a c t o r s e n t e r s i n t o Q-', which i s t h e r e f o r e p r o p o r t i o n a l t o (c/a-1)'. Note t h a t t h e f a c t t h a t t h e t e m p e r a t u r e dependence of Q- i s e s s e n t i a l l y a c c o u n t e d f o r by t h a t of ( c / a - 1 ) ' i m p l i e s t h a t t h e f r e q u e n c y r e s p o n s e f u n c t i o n R(w), and hence t h e domain-wall m o b i l i t y , must depend o n l y weakly on t e m p e r a t u r e .
A s p e c i f i c a t i o n of t h e f r e q u e n c y dependence of t h e i n t e r n a l f r i c t i o n , Q - l , and t h e modulus d e f e c t , < E @ - l ) - l - E , r e q u i r e s a n e x p l i c i t model f o r t h e domain-wall dynamics s o t h a t t h e r e s p o n s e f u n c t i o n R(w) c a n be e v a l u a t e d . For example, i f domain w a l l s a r e r e a s o n a b l y mobile o v e r most of t h e i r e x t e n t , e x c e p t f o r c e r t a i n e d g e s , c o m e r s , e t c . , where they a r e h i g h l y pinned ( b y , f o r example, i n t e r a c t i o n s w i t h g r a i n
b o u n d a r i e s , i n t e r s e c t i n g w i t h o t h e r domain w a l l s , e t c . ) , and i f t h e r e i s no c r i t i c a l s t r e s s which must be overcome p r i o r t o motion, a s d i s c u s s e d by DeJonghe e t a l . / 1 4 / , then a d a m p e d - h a r m o n i c - o s c i l l a t o r model of domain-wall dynamics may be a p p r o p r i a t e . (A r e c e n t t h e o r e t i c a l s t u d y of domain-wall motions i n A15 compounds by Barsch and Krumhansl /17/ s u g g e s t s t h a t t h e s e w a l l s behave a s s o l i t o n s , and t h u s they s h o u l d n o t have s t r o n g " P e i e r l s - N a b a r r o w - t y p e c r i t i c a l s t r e s s e s r e q u i r e d t o s e t them moving.) I n such a harmonic model, domain w a l l s w i l l be c h a r a c t e r i z e d by a n e f f e c t i v e mass m , r e s o n a n c e f r e q u e n c y w g , and viscous-damping c o e f f i c i e n t K ( t o a c c o u n t f o r damping by e l e c t r o n s c a t t e r i n g , phonon e m i s s i o n s , e t c . ) , t h e dynamics w i l l then be c h a r a c t e r i z e d by:
where x i s t h e boundary d i s p l a c e m e n t caused by a f o r c e F. Such dynamics l e a d t o t h e r e s p o n s e f u n c t i o n :
The f r e q u e n c y depedence l e v e l s of t h e i n t e r n a l f r i c t i o n and modulus d e f e c t f o r t h e d a m p e d - h a r m o n i c - o s c i l l a t o r model of domain-wall dynamics a r e then o b t a i n e d by combining Eq. ( 8 ) w i t h Eqs. ( 5 ) and ( 6 ) . F u r t h e r e x p e r i m e n t s a r e r e q u i r e d t o t e s t
t h e p r e d i c t i o n s of t h i s model. REFERENCES
1. A. P l a n e s , J. V i n a l s , and V. T o r r a , P h i l . Mag A.
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501 (1983). 2. R. N B h a t t and W. L. McMillan, Phys. Rev. B14,
1007 (1976). 3. R. N. B h a t t , Phys. Rev. Bg,
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H. Thomas, S p r i n g e r - V e r l a g , 1978, p. 131.
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p. 193; Vol X I I I , p. 29 ( 1 9 7 3 ) .6. M. Weger and I . B . Goldberg, i n S o l i d S t a t e P h y s i c s , ed. by F. S e i t z and D . T u m b u l l ( ~ c a d e m i c P r e s s , NY), Vol. 28, p. 1 (1973).
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M a t e r i a l s , e d . by R.P. Reed and A.F. C l a r k , ( P l e n u m p r e s s , NY), V o l . 28, 1 9 8 2 , p. 655.9 . A. R. S w e e d l e r , C.L. S n e a d , Jr., a n d D. E. Cox, T r e a t i s e o n M a t e r i a l s S c i e n c e a n d T e c h n o l o g y , ed. by T. Luhman a n d D. Dew-Hughes (Academic P r e s s , NY),
5
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