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AgZn system β - β' order-disorder phase transition
Scripta METALLURGICA
Vol. 12, pp. 1115-1120, 1978 Printed in the United States
AgZn SYSTEM
--
Pergamon Press,
Inc.
ORDER-DISORDERPHASE TRANSITION
D e l i a A r i a s and Jorge E, K i t t l ComisiSn Nacional de Energ[a AtSmica Av. del L i b e r t a d o r 8250 1429 Buenos A i r e s , A r g e n t i n a (Received September 28, 1978)
I.
Introduction
In t h e r e g i o n of e q u i a t o m i c c o m p o s i t i o n t h e AgZn system has a b o d y - c e n t e r e d c u b i c d i s o r d e r e d ~ phase above 274°C, On quenching from above 274°C o r d e r s t o t h e CsCI ~ structure, Slow c o o l i n g from above 274°C or upquenching and isothermal a n n e a l i n g in t h e range I00-274°C produces a t r i g o n a l ~o s t r u c t u r e ( I ) , The r e p l a c e m e n t of Ag by Au or Cu in amounts h i g h e r than J at~ i n c r e a s e s t h e s t a b i l i t y of t h e o r d e r e d c u b i c / 3 ' phase and d e c r e a s e s t h e s t a b i l i t y of t h e ~ o
phase u n t i l
complete d i s a p p e a r a n c e of t h i s
phase.
The o r d e r - d i s o r d e r t r a n s f o r m a t i o n t e m p e r a t u r e TO, has been s t u d i e d s e v e r a l times. Muldawer (3) d e t e r m i n e d p - - j C ~ ' o r d e r i n g t e m p e r a t u r e f o r the t e r n a r y a l l o y s AgSo_xZnsoAux (x=2,4-3.5-5.0 a t ~ ) by i n v e s t i g a t i n g s u p e r l a t t i c e line intensities. An e x t r a p o l a t i o n of t h e s e v a l u e s t o x=O g i v e s a v a l u e of TO=S45°K f o r AgZn. R e s i s t i v i t y measurements at high temperature have been used by Brookes and Smith (4) to detect the order-disorder t r a n s i t i o n in AuSO_xZn5oAux (x=3-4.5-I015 a t ~ ) and p r e d i c t To=S23°K from t h e t e r n a r y a l l o y s , Kachi et el (5) determined t h e order-disorder t r a n s i t i o n temperature in alloys, usin 9 a modified Sykes-type adiabatic calorimeter. E x t r a p o l a t i n 9 , t h e y o b t a i n e d TO=496°K.
Ag53-xZn47Cux (x=3-4-13 a t % . . . )
Measurements of e l e c t r i c a l resistivity changes d u r i n g quenching have been used by Mc I . C l a r k - M e r r i m a n and Wayman (6) t o d e t e r m i n e TO in AgsoZnso , t h e average v a l u e f o r t e n d e t e r m i n a t i o n s b e i n 9 518°K. A b r i a t a (7) has p r e d i c t e d To=SO3°K~7°K in AgsoZn50 based on t h e v a l u e of the e l e c t r i c a l resistivity diff e r e n c e between ~ a n d # ' D i f f e r e n t a u t h o r s have d i s c u s s e d t h e j~ ' and 5 o phase s t a b i l i t y at d i f f e r ent t e m p e r a t u r e s . For Orr and Rovel (8) t h e -~o phase is s t a b l e at room tempera t u r e in t h e 50 at~Zn a l l o y ; so are t h e 4 6 . 3 - 4 8 . 6 - 5 0 . 7 at~Zn f o r Noguchi ( 9 ) . K i n g - M a s s a l s k i (10) and B r o w n - S t e w a r t ( 1 1 ) , s t u d y i n g t h e 50 a t ~ and 48-50 at~Zn r e s p e c t i v e l y , h a v e suggested t h a t the p t phase remains s t a b l e at room temperature. Measurements of e l e c t r i c a l resistivity and s p e c i f i c heat in AgsoZn~o have been used by A b r i a t a (7) and he e s t i m a t e d from t h e s e data t h a t t h e # ~ phase is s t a b l e between O°K and 270°K,
0036-97~S/78/121115-05502.0O/O C o p y r i g h t (e) 1978 Pergamon P r e s s
1116
ORDER-DISORDER
TRANSITION
Vol.
12, No.
12
T O was o b t a i n e d a v e r a g i n g more t h a n 20 r e s u l t s in each c o m p o s i t i o n ~. D e t e r m i n a t i o n s o f TO f o r ~ - ~ t o r d e r i n g a r e shown in F i g . 2 and T a b l e I , R e s u l t s o f T O a r e r e p r e s e n t e d in F i g . 3 and f o r p u r p o s e s o f c o m p a r i s o n , t h e r e s u l t s o b t a i n e d in CuZn (13) have a l s o been r e p r e s e n t e d . T O r e p o r t e d by A b r i a t a ( 7 ) and by Kachi e t al ( 5 ) c o i n c i d e with our r e s u l t s , within the experimental error, 4~ We c o n s i d e r e d T O t o be t h e v a l u e where d f / d T o b t a i n s a maximum c o n s i d e r i n g t h a t near t h e t r a n s i t i o n point TO, the derivative of the electrical resistivity w i t h r e s p e c t t o t h e t e m p e r a t u r e i s r e l a t e d (14): a) t o t h e d e r i v a t i v e o£ t h e Ion9 r a n g e o r d e r p a r a m e t e r w i t h r e s p e c t t o t e m p e r a t u r e , w h i c h i s monot~ n o u s l y i n c r e a s i n g f u n c t i o n and has a maximum v a l u e as we a p p r o a c h T O From t h e low t e m p e r a t u r e s ; and b) t h e d e r i v a t i v e of t h e s h o r t rang e o r d e r p a r a m e t e r w i t h r e s p e c t t o t e m p e r a t u r e , w h i c h i s a maximum a t t h e second o r d e r t r a n s i t i o n point in bcc o r d e r e d a l l o y s ( 1 5 ) . 400
TEMPERATURE °K /,00 500 '
i
~
I
'
TEMPERATURE °K 500 600
I
600
I
i
I
L
I
4&5 at % Zn
51 at % Z. m
.=;
/~,
i-
© v=s0~C/~g
..j
~c _ _ L
~ 100
I , 200 TEMPERATURE °C
100
[
200
300
TEMPERATURE °C
300
Fig, 2, R e s i s t i v i t y vs temperature curves For quenching £ r o m ~ t o ~ ' ,
Fig, I. Resistivity vs t e m p e r a t u r e curves. Different h e a t i n g and c o o l i n g F r o m ~ , ~ ' and ~ o c o r r e s p o n d i n g t e 5l a t ~ Z n .
Cu-Zn
73o~ D
F i g . 3. O r d e r - d i s o r d e r critical t e m p e r a t u r e dependence on composition
510
--
calculated -.-.calculated (Bragg-Williams) (Quasichemical) - - ca I cu I ated (Kirkwood) eCuZn (13)
s00 uJ
~- 4 g o
• AgZn ( 6 ) IIA9 5__xZnA5oAu x ( 4 ) AAgZn ( 7 )
&BO I
45
Zn
5O ATOMIC %
x t h i s work
55
Vol.
12,
No.
12
ORDER-DISORDER TRANSITION
1117
By u s i n g t h e f o u r t h c o o r d i n a t i o n s p h e r e a p p r o x i m a t i o n , Geychenco and Kanyuka ( 1 2 ) have s t a t e d t h a t in t h e AgZn system t h e ~ t phase is t h e most s t a b l e phase a t low t e m p e r a t u r e s , The p u r p o s e o f o u r work was t o measure t h e o r d e r - d i s o r d e r t e m p e r a t u r e in bcc AgZn a l l o y s w i t h d i f f e r e n t c o m p o s i t i o n and t o e s t i m a t e t h e range o f composition where e was s t a b l e w i t h r e s p e c t t o ~ o at O°K. 2.
Experimental
procedure
A l l o y s were p r e p a r e d u s i n g 9 9 , 9 9 9 + p c t A9 and Zn. The a l l o y i n g e l e m e n t s were w e i g h e d c a r e f u l l y and t h e n m e l t e d i n q u a r t z t u b e s u n d e r p a r t i a l pressure of argon. The a l l o y s were mixed by s h a k i n g t h e t u b e s w h i l e t h e metal was molten. The assumed c o m p o s i t i o n of t h e a l l o y s was used whenever w e i g h t l o s s e s were l e s s t h a n 0 . 1 ~ , In some cases M i c r o p r o b e and wet a n a l y s i s were employed to further ensure the alloy composition. The i n g o t s were s e a l e d in q u a r t z t u b e s c o n t a i n i n g argon and homogeneized f o r 1200 hs a t 600°C, After cooling t h e y were c o l d r o l l e d w i t h i n t e r m e d i a t e 350°C a n n e a l i n g , Sheet samples 0.1 mm t h i c k were p r e p a r e d . S t r i p s m e a s u r i n g IxO. Ix50 mm were used f o r t h e e l e c t r i c a l resistivity measurements. C u r r e n t and v o l t a g e l e a d s were made o f t h e same a l l o y s and 0 . 2 mm c a l i b r a t e d C u - C o n s t a n t a n t h e r m o c o u p l e w i r e s were w e l d e d t o t h e samples. To r e t a i n t h e ~ t phase t h e a l l o y s were h e a t t r e a t e d f o r 20 m i n u t r e s a t 350-400°C in a s i l i c o n e o i l b a t h and quenched t o room t e m p e r a t u r e . The h e a t i n g and c o o l i n g from ~o, ~ ' and ~ were made in t h e same s i l i c o n e oil bath. The changes in t e m p e r a t u r e and r e s i s t i v i t y were r e c o r d e d c o n t i n u o u ~ l y u s i n g a X-Y r e c o r d e r . To measure t h e o r d e r - d i s o r d e r t e m p e r a t u r e t h e samples were quenched a t 3 0 ° C / s e c in a i r s t r e a m , Samples f o r m e t a l l o g r a p h i c e x a m i n a t i o n were m e c h a n i c a l l y p o l i s h e d w i t h d i ~ mond (O.25/Z~J~), or in some cases w i t h a l o g KCN s o l u t i o n u s i n g a v o l t a g e o f 1525V ( a . c . ) . 3,
The o r d e r - d i s o r d e r
temperature
We r e c o r d e d r e s i s t i v i t y - t e m p e r a t u r e c u r v e s in 9 a l l o y ~ over t h e c o m p o s i t i o n r a n g e 45-51 at%Zn. E x p e r i m e n t s were made c o o l i n g from 400-450°C at 3 0 ° C / sec. This cooling velocity was enough t o s u p p r e s s ~ - ~ and / 3 ' - 0 reactions. Metallographies were made on e v e r y sample t o v e r i f y t h e ~ Samples had in a l l c a s e s t h e c l a s s i c a l p ~ phase p i n k c o l o r .
~w
reaction.
To u n d e r s t a n d t h e r e s i s t i v i t y b e h e v i o u r of t h e changes on c o o l i n g is n e c essary to take into account the following points: a) For T < T 0, neap t h e critical t e m p e r a t u r e , a , r a p i d d e c r e a s e o f 2 P i s o b s e r v e d as T d e c r e a s e s . This is a s s o c i a t e d t o i n c r e a s i n g t h e l o n g - r a n g e o r d e r ~ b) For T ~ T 0, where ~ =0, ( T ) i s a l i n e a r f u n c t i o n of T ( a l m o s t a s t r a i g h t line), c) In t h e r e a c t i o n ~-~o the difference in t h e e l e c t r i c a l resistivity is much s m a l l e r t h a n in #-#~ (ordering) and # ' - 50 ( c r ~ s t a l l c ~ 3 r a p h i c changes and some o r d e r i n g ) transitions, In F i g , I are shown h e a t i n g and c o o l i n g c u r v e s oF ~ z , ~ a n d ~ o p h a s e s . Cooling curves with different c o o l i n g r a t e s have been s u p e r i m p o s e d t o show these differences.
1118
ORDER-DISORDER
TRANSITION
TABLE
I t was v e r y d i f f i c u l t to suppress the #--~o r e a c t i o n in a l l o y s w i t h c < 45 at%Zn w h i l e f o r c above 51 at%Zn t h e s a m p l e s were
~ ' phase s t a b i l i t y
In t h e e q u i a t o m i c AgZn a l l o y s A b r i a t a (7) has measured t h e s p e c i f i c h e a t b e tw e e n 80°K and 543°K f o r t h e 3 0 p h a s e , and b e t w e e n 270°K and 380°K in t h e ~o p h a s e . As t h e s p e c i f i c h e a t of t h e )r3t phase between 880-540°K c a n n o t be m e a s u r e d , A b r i a t a e s t i m a t e d t h e c o n f i g u r a tional entropy (Sc) for the ~ ' phase from CuZn specific
h e a t c u r v e s assuming t h a t
the
12, No. 12
I
Compos i t i on c (at%Zn)
very brittle.
4.
Vol.
TO ( ° K )
45 46.5 47 48 48.5 49,5 5O 50,5
493 494 496 498 501 5O4 5O6 5O4
+ ~ + + + + + +
5 4 4 4 4 4 4 4
51
503 + 4
l o n g and
short range order parameters ( ~Zand ~l)represent identical configurational s t a t e s in b o t h a l l o y s and t h a t Sc is common t o AgZn and CuZn, F i g . 4a. He estimated the vibrational component o f t h e e n t r o p y (Sv) f o r t h e # " phase u s i n g Kopp-Newman ( 1 6 ) r u l e s f o r T > Troom and a D e b y e t s f u n c t i o n f o r T < Troom. From t h e c a l c u l a t e d v a l u e s of the e n t r o p y at d i f f e r e n t t e m p e r a t u r e s , F i g . 5a, t a k i n g TO=545°K as t h e t e m p e r a t u r e where ~G ~ - ~ G # = A G ~ 5 ° = O , and i n t e g r a t i n g
¢# ~T
~,.)
---O.6
300°K _,~
TEMPERATURE(°K) /*00 /*50 500 s ~,-- --5d%
350 ,.
. . . : 506 . . °K. ca) TcCSO'/,)
-(15
/T 545°K
=
(c) Tc(42'/,):4as °K T~(/*ov,) :/*?s OK
.
~ ~ _h
~
I , : 1 /
0.6
0.7
550 -'
II
I I
.
////$:
////
/
U~'):s0'/, ;.0 ~(~.): 4S_v,
I
I
0.9
; ; I
~.z R
(11"
t
I
1.0
1.1
ture at d i f f e r e n t sition.
0.4 0.2
compo-
Fig. 5 . A S ~ t
S~°. S ~ '
vs t e m p e r a t u r e
at differe n t t e m p e r a t u r e s , a) 50
0
A~J+)-
~-0.2 -0~
F i g , 4. C o n f i g u r a t i o n a l entropy ~#t) vs t e m p e r ~
-%- #~(s°°/')
0,6
omr
(14
C(d'i:~'].J0.2
REDUCED TEMPERATURE(~¢)
mr
.
Tc "" ~(c') :/.2'1. -'~0.3
d' c' b' a' 08
(I)
"1~6 O.S
,"
//// _.,
dT
-I
s~. . . fFT~i . /*O' ~ / . f
(b) Tc(/*5%)=/*g/* °K
-0.3 (d) -0.2 -0.1
"~5° AS (T)
~
100
I
t_
0 _ _ ~ _
200 300 400 TEMPERATURE ( ° K )
~(\\ I
500
~, ,
II
at%Zn; b) 45 at%Zn; c) 42 at%Zn; d) 40 at%Zn.
Vol.
12, No.
12
ORDER-DISORDER
TRANSITION
he c o n c l u d e d t h a t t h e p " phase i s s t a b l e between 0 - 2 7 0 ° K , 544°K and t h e ~ p h a s e above 544°K, Fig. 6a.
1119
phase between 270-
To e x t e n d t h e s e r e s u l t s f o r n o n - e q u i a t o m i c 45-42-40 at%Zn a l l o y s , we have calculated ~S P~5° at different t e m p e r a t u r e s assuming t h a t t h e change w i t h c o m p o s i t i o n in t h e v i b r a t i o n a l component o f e n t r o p y i s much s m e l l e r t h a n t h e c o r r e s p o n d i n g change in t h e c o n f i g u r a t i o n a l component. The c o n f i g u r a t i o n a l entropy SC vs T was determined using Kirkwood's approximation up to (w/kT) 2. For the order-disorder tempereture T O we used the values in Table I and the long range order parameter was calculated from the Cowley's approximation (17). In Figs. 4 b,c,d and 5 b,c,d are plotted Sc vs T and S vs T for different compositions. From ec. (1) and Fig. 5 we derived the free energy change vs temperature between 42 and 50 at~Zn. The conclusion is that the ~ t phase is stable at O°K in this range of composition and, for symetric consideration, up t o 52 at%Zn. Fig. 6.
I
120 80
I
I
I
I
~.~%
30:~_ 50 %
u
~sY,1 l
t
LD
0
r ""'-.42'/, -40 "
"
VS t e m p e r a t u r e a t d i f f e r e n t compos i t i o n s .
°/0 ...................... -.-2-;-2..-:;..-~.-..•
100
200
300
40O 5O0 TEMPERATURE °K Conclusions
I . The d e t e r m i n a t i o n o f T O f o r d i f f e r e n t c o m p o s i t i o n s in b i n a r y a l l o y s , t h u s avoiding extrapolation from t e r n a r y a l l o y s , has become p o s s i b l e by t h e elimination of the ~ (~')~ 3 o reaction. Within experimental errors,measured r e s u l t s agree t o a g r e a t e x t e n t w i t h t h e t h e o r e t i c a l expected values. 2. From t h e e s t i m a t i o n s made in s a c . 4, we c o n c l u d e t h a t t h e ~3 e phase is s t a b l e a t O°K between 42 and 52 at%Zn. Acknowledgements The a u t h o r s a r e i n d e b t e d t o Dr. J. A b r i a t a f o r a l l o w i n g us t o use some of his results prior to publication and v e r y u s e f u l d i s c u s s i o n s and comments. F i n a n c i a l s u p p o r t by t h e Programa M u l t i n a c i o n a l de M e t a l u r g l a sponsored by t h e O r g a n i z a t i o n of American S t a t e s i s g r a t e f u l l y acknowledged. References I.
I.G.
Edmunds and M.M. Q u r a s h i , A c t a
Crystal loft.
41 417 ( 1 9 5 1 ) .
1120
ORDER-DISORDER
TRANSITION
2. M. Hansen and K. Anderko, C o n s t i t u t i o n
of Binary A l l o y s ,
Vol.
12, No. 12
McGraw-Hill,
New
York (1968).
3. L. Muldawer, J. Appl. Phys, 22, 663 (1951). 4. M.E. Brookes and R.W. Smith, S c r i p t a Met. 3, 667 (1969). 5. M. Yono, H. Asano, N. Nakanishi and S. Kachi, Trans. Japan I n s t . Metals 8, 277 (1967). 6. H. Mc l . C l a r k , E.A. Merriman and C.M. Wayman, Acre Met. 17, 719, 1969. 7. J. A b r i a t a , PhD T h e s i s , Cuyo U n i v e r s i t y (1970). 8. R.L. Opt and J. Rovel, Acta Met. I0, 1935 (1962). 9. S. Noguchi, Journ. of the Phys. Soc. of Japan I I , 1844 (1962). IO. H.W. King and T.B. Massalskl, Trans. AIME 242, 1353 (1968). I I . L.C. Brown and M.J. Stewart, Trans. AIME 242, 1353 (1968). 12. V.V. Geychenko and A.K. Kanyuka, Fiz. Metal. M e t a l l o v e d . 38,5, 918 - 38,6, 1146 (1974). 13. Sykes and W i l l k i n s o n , J. I n s t . Metals 61, 223 (1937). 14. M.A. K r i v o g l a z and Z.A. Matysina, S o v i e t Phys. Jetps, l, IO3 (1955). 15. R. Kikuchi and H. Sato, Acta Met. 22, IO99 (1974). 16. J.M. Ziman, E l e c t r o n s and Phonons, Oxford U n i v e r s i t y Press (1962). 17. J.M. Cowley, Phys. Rev. 77, 669 (1950); 120, 1648 (1960); 138A, 1384 (1965).
Vol. 12, pp. 1115-1120, 1978 Printed in the United States
AgZn SYSTEM
--
Pergamon Press,
Inc.
ORDER-DISORDERPHASE TRANSITION
D e l i a A r i a s and Jorge E, K i t t l ComisiSn Nacional de Energ[a AtSmica Av. del L i b e r t a d o r 8250 1429 Buenos A i r e s , A r g e n t i n a (Received September 28, 1978)
I.
Introduction
In t h e r e g i o n of e q u i a t o m i c c o m p o s i t i o n t h e AgZn system has a b o d y - c e n t e r e d c u b i c d i s o r d e r e d ~ phase above 274°C, On quenching from above 274°C o r d e r s t o t h e CsCI ~ structure, Slow c o o l i n g from above 274°C or upquenching and isothermal a n n e a l i n g in t h e range I00-274°C produces a t r i g o n a l ~o s t r u c t u r e ( I ) , The r e p l a c e m e n t of Ag by Au or Cu in amounts h i g h e r than J at~ i n c r e a s e s t h e s t a b i l i t y of t h e o r d e r e d c u b i c / 3 ' phase and d e c r e a s e s t h e s t a b i l i t y of t h e ~ o
phase u n t i l
complete d i s a p p e a r a n c e of t h i s
phase.
The o r d e r - d i s o r d e r t r a n s f o r m a t i o n t e m p e r a t u r e TO, has been s t u d i e d s e v e r a l times. Muldawer (3) d e t e r m i n e d p - - j C ~ ' o r d e r i n g t e m p e r a t u r e f o r the t e r n a r y a l l o y s AgSo_xZnsoAux (x=2,4-3.5-5.0 a t ~ ) by i n v e s t i g a t i n g s u p e r l a t t i c e line intensities. An e x t r a p o l a t i o n of t h e s e v a l u e s t o x=O g i v e s a v a l u e of TO=S45°K f o r AgZn. R e s i s t i v i t y measurements at high temperature have been used by Brookes and Smith (4) to detect the order-disorder t r a n s i t i o n in AuSO_xZn5oAux (x=3-4.5-I015 a t ~ ) and p r e d i c t To=S23°K from t h e t e r n a r y a l l o y s , Kachi et el (5) determined t h e order-disorder t r a n s i t i o n temperature in alloys, usin 9 a modified Sykes-type adiabatic calorimeter. E x t r a p o l a t i n 9 , t h e y o b t a i n e d TO=496°K.
Ag53-xZn47Cux (x=3-4-13 a t % . . . )
Measurements of e l e c t r i c a l resistivity changes d u r i n g quenching have been used by Mc I . C l a r k - M e r r i m a n and Wayman (6) t o d e t e r m i n e TO in AgsoZnso , t h e average v a l u e f o r t e n d e t e r m i n a t i o n s b e i n 9 518°K. A b r i a t a (7) has p r e d i c t e d To=SO3°K~7°K in AgsoZn50 based on t h e v a l u e of the e l e c t r i c a l resistivity diff e r e n c e between ~ a n d # ' D i f f e r e n t a u t h o r s have d i s c u s s e d t h e j~ ' and 5 o phase s t a b i l i t y at d i f f e r ent t e m p e r a t u r e s . For Orr and Rovel (8) t h e -~o phase is s t a b l e at room tempera t u r e in t h e 50 at~Zn a l l o y ; so are t h e 4 6 . 3 - 4 8 . 6 - 5 0 . 7 at~Zn f o r Noguchi ( 9 ) . K i n g - M a s s a l s k i (10) and B r o w n - S t e w a r t ( 1 1 ) , s t u d y i n g t h e 50 a t ~ and 48-50 at~Zn r e s p e c t i v e l y , h a v e suggested t h a t the p t phase remains s t a b l e at room temperature. Measurements of e l e c t r i c a l resistivity and s p e c i f i c heat in AgsoZn~o have been used by A b r i a t a (7) and he e s t i m a t e d from t h e s e data t h a t t h e # ~ phase is s t a b l e between O°K and 270°K,
0036-97~S/78/121115-05502.0O/O C o p y r i g h t (e) 1978 Pergamon P r e s s
1116
ORDER-DISORDER
TRANSITION
Vol.
12, No.
12
T O was o b t a i n e d a v e r a g i n g more t h a n 20 r e s u l t s in each c o m p o s i t i o n ~. D e t e r m i n a t i o n s o f TO f o r ~ - ~ t o r d e r i n g a r e shown in F i g . 2 and T a b l e I , R e s u l t s o f T O a r e r e p r e s e n t e d in F i g . 3 and f o r p u r p o s e s o f c o m p a r i s o n , t h e r e s u l t s o b t a i n e d in CuZn (13) have a l s o been r e p r e s e n t e d . T O r e p o r t e d by A b r i a t a ( 7 ) and by Kachi e t al ( 5 ) c o i n c i d e with our r e s u l t s , within the experimental error, 4~ We c o n s i d e r e d T O t o be t h e v a l u e where d f / d T o b t a i n s a maximum c o n s i d e r i n g t h a t near t h e t r a n s i t i o n point TO, the derivative of the electrical resistivity w i t h r e s p e c t t o t h e t e m p e r a t u r e i s r e l a t e d (14): a) t o t h e d e r i v a t i v e o£ t h e Ion9 r a n g e o r d e r p a r a m e t e r w i t h r e s p e c t t o t e m p e r a t u r e , w h i c h i s monot~ n o u s l y i n c r e a s i n g f u n c t i o n and has a maximum v a l u e as we a p p r o a c h T O From t h e low t e m p e r a t u r e s ; and b) t h e d e r i v a t i v e of t h e s h o r t rang e o r d e r p a r a m e t e r w i t h r e s p e c t t o t e m p e r a t u r e , w h i c h i s a maximum a t t h e second o r d e r t r a n s i t i o n point in bcc o r d e r e d a l l o y s ( 1 5 ) . 400
TEMPERATURE °K /,00 500 '
i
~
I
'
TEMPERATURE °K 500 600
I
600
I
i
I
L
I
4&5 at % Zn
51 at % Z. m
.=;
/~,
i-
© v=s0~C/~g
..j
~c _ _ L
~ 100
I , 200 TEMPERATURE °C
100
[
200
300
TEMPERATURE °C
300
Fig, 2, R e s i s t i v i t y vs temperature curves For quenching £ r o m ~ t o ~ ' ,
Fig, I. Resistivity vs t e m p e r a t u r e curves. Different h e a t i n g and c o o l i n g F r o m ~ , ~ ' and ~ o c o r r e s p o n d i n g t e 5l a t ~ Z n .
Cu-Zn
73o~ D
F i g . 3. O r d e r - d i s o r d e r critical t e m p e r a t u r e dependence on composition
510
--
calculated -.-.calculated (Bragg-Williams) (Quasichemical) - - ca I cu I ated (Kirkwood) eCuZn (13)
s00 uJ
~- 4 g o
• AgZn ( 6 ) IIA9 5__xZnA5oAu x ( 4 ) AAgZn ( 7 )
&BO I
45
Zn
5O ATOMIC %
x t h i s work
55
Vol.
12,
No.
12
ORDER-DISORDER TRANSITION
1117
By u s i n g t h e f o u r t h c o o r d i n a t i o n s p h e r e a p p r o x i m a t i o n , Geychenco and Kanyuka ( 1 2 ) have s t a t e d t h a t in t h e AgZn system t h e ~ t phase is t h e most s t a b l e phase a t low t e m p e r a t u r e s , The p u r p o s e o f o u r work was t o measure t h e o r d e r - d i s o r d e r t e m p e r a t u r e in bcc AgZn a l l o y s w i t h d i f f e r e n t c o m p o s i t i o n and t o e s t i m a t e t h e range o f composition where e was s t a b l e w i t h r e s p e c t t o ~ o at O°K. 2.
Experimental
procedure
A l l o y s were p r e p a r e d u s i n g 9 9 , 9 9 9 + p c t A9 and Zn. The a l l o y i n g e l e m e n t s were w e i g h e d c a r e f u l l y and t h e n m e l t e d i n q u a r t z t u b e s u n d e r p a r t i a l pressure of argon. The a l l o y s were mixed by s h a k i n g t h e t u b e s w h i l e t h e metal was molten. The assumed c o m p o s i t i o n of t h e a l l o y s was used whenever w e i g h t l o s s e s were l e s s t h a n 0 . 1 ~ , In some cases M i c r o p r o b e and wet a n a l y s i s were employed to further ensure the alloy composition. The i n g o t s were s e a l e d in q u a r t z t u b e s c o n t a i n i n g argon and homogeneized f o r 1200 hs a t 600°C, After cooling t h e y were c o l d r o l l e d w i t h i n t e r m e d i a t e 350°C a n n e a l i n g , Sheet samples 0.1 mm t h i c k were p r e p a r e d . S t r i p s m e a s u r i n g IxO. Ix50 mm were used f o r t h e e l e c t r i c a l resistivity measurements. C u r r e n t and v o l t a g e l e a d s were made o f t h e same a l l o y s and 0 . 2 mm c a l i b r a t e d C u - C o n s t a n t a n t h e r m o c o u p l e w i r e s were w e l d e d t o t h e samples. To r e t a i n t h e ~ t phase t h e a l l o y s were h e a t t r e a t e d f o r 20 m i n u t r e s a t 350-400°C in a s i l i c o n e o i l b a t h and quenched t o room t e m p e r a t u r e . The h e a t i n g and c o o l i n g from ~o, ~ ' and ~ were made in t h e same s i l i c o n e oil bath. The changes in t e m p e r a t u r e and r e s i s t i v i t y were r e c o r d e d c o n t i n u o u ~ l y u s i n g a X-Y r e c o r d e r . To measure t h e o r d e r - d i s o r d e r t e m p e r a t u r e t h e samples were quenched a t 3 0 ° C / s e c in a i r s t r e a m , Samples f o r m e t a l l o g r a p h i c e x a m i n a t i o n were m e c h a n i c a l l y p o l i s h e d w i t h d i ~ mond (O.25/Z~J~), or in some cases w i t h a l o g KCN s o l u t i o n u s i n g a v o l t a g e o f 1525V ( a . c . ) . 3,
The o r d e r - d i s o r d e r
temperature
We r e c o r d e d r e s i s t i v i t y - t e m p e r a t u r e c u r v e s in 9 a l l o y ~ over t h e c o m p o s i t i o n r a n g e 45-51 at%Zn. E x p e r i m e n t s were made c o o l i n g from 400-450°C at 3 0 ° C / sec. This cooling velocity was enough t o s u p p r e s s ~ - ~ and / 3 ' - 0 reactions. Metallographies were made on e v e r y sample t o v e r i f y t h e ~ Samples had in a l l c a s e s t h e c l a s s i c a l p ~ phase p i n k c o l o r .
~w
reaction.
To u n d e r s t a n d t h e r e s i s t i v i t y b e h e v i o u r of t h e changes on c o o l i n g is n e c essary to take into account the following points: a) For T < T 0, neap t h e critical t e m p e r a t u r e , a , r a p i d d e c r e a s e o f 2 P i s o b s e r v e d as T d e c r e a s e s . This is a s s o c i a t e d t o i n c r e a s i n g t h e l o n g - r a n g e o r d e r ~ b) For T ~ T 0, where ~ =0, ( T ) i s a l i n e a r f u n c t i o n of T ( a l m o s t a s t r a i g h t line), c) In t h e r e a c t i o n ~-~o the difference in t h e e l e c t r i c a l resistivity is much s m a l l e r t h a n in #-#~ (ordering) and # ' - 50 ( c r ~ s t a l l c ~ 3 r a p h i c changes and some o r d e r i n g ) transitions, In F i g , I are shown h e a t i n g and c o o l i n g c u r v e s oF ~ z , ~ a n d ~ o p h a s e s . Cooling curves with different c o o l i n g r a t e s have been s u p e r i m p o s e d t o show these differences.
1118
ORDER-DISORDER
TRANSITION
TABLE
I t was v e r y d i f f i c u l t to suppress the #--~o r e a c t i o n in a l l o y s w i t h c < 45 at%Zn w h i l e f o r c above 51 at%Zn t h e s a m p l e s were
~ ' phase s t a b i l i t y
In t h e e q u i a t o m i c AgZn a l l o y s A b r i a t a (7) has measured t h e s p e c i f i c h e a t b e tw e e n 80°K and 543°K f o r t h e 3 0 p h a s e , and b e t w e e n 270°K and 380°K in t h e ~o p h a s e . As t h e s p e c i f i c h e a t of t h e )r3t phase between 880-540°K c a n n o t be m e a s u r e d , A b r i a t a e s t i m a t e d t h e c o n f i g u r a tional entropy (Sc) for the ~ ' phase from CuZn specific
h e a t c u r v e s assuming t h a t
the
12, No. 12
I
Compos i t i on c (at%Zn)
very brittle.
4.
Vol.
TO ( ° K )
45 46.5 47 48 48.5 49,5 5O 50,5
493 494 496 498 501 5O4 5O6 5O4
+ ~ + + + + + +
5 4 4 4 4 4 4 4
51
503 + 4
l o n g and
short range order parameters ( ~Zand ~l)represent identical configurational s t a t e s in b o t h a l l o y s and t h a t Sc is common t o AgZn and CuZn, F i g . 4a. He estimated the vibrational component o f t h e e n t r o p y (Sv) f o r t h e # " phase u s i n g Kopp-Newman ( 1 6 ) r u l e s f o r T > Troom and a D e b y e t s f u n c t i o n f o r T < Troom. From t h e c a l c u l a t e d v a l u e s of the e n t r o p y at d i f f e r e n t t e m p e r a t u r e s , F i g . 5a, t a k i n g TO=545°K as t h e t e m p e r a t u r e where ~G ~ - ~ G # = A G ~ 5 ° = O , and i n t e g r a t i n g
¢# ~T
~,.)
---O.6
300°K _,~
TEMPERATURE(°K) /*00 /*50 500 s ~,-- --5d%
350 ,.
. . . : 506 . . °K. ca) TcCSO'/,)
-(15
/T 545°K
=
(c) Tc(42'/,):4as °K T~(/*ov,) :/*?s OK
.
~ ~ _h
~
I , : 1 /
0.6
0.7
550 -'
II
I I
.
////$:
////
/
U~'):s0'/, ;.0 ~(~.): 4S_v,
I
I
0.9
; ; I
~.z R
(11"
t
I
1.0
1.1
ture at d i f f e r e n t sition.
0.4 0.2
compo-
Fig. 5 . A S ~ t
S~°. S ~ '
vs t e m p e r a t u r e
at differe n t t e m p e r a t u r e s , a) 50
0
A~J+)-
~-0.2 -0~
F i g , 4. C o n f i g u r a t i o n a l entropy ~#t) vs t e m p e r ~
-%- #~(s°°/')
0,6
omr
(14
C(d'i:~'].J0.2
REDUCED TEMPERATURE(~¢)
mr
.
Tc "" ~(c') :/.2'1. -'~0.3
d' c' b' a' 08
(I)
"1~6 O.S
,"
//// _.,
dT
-I
s~. . . fFT~i . /*O' ~ / . f
(b) Tc(/*5%)=/*g/* °K
-0.3 (d) -0.2 -0.1
"~5° AS (T)
~
100
I
t_
0 _ _ ~ _
200 300 400 TEMPERATURE ( ° K )
~(\\ I
500
~, ,
II
at%Zn; b) 45 at%Zn; c) 42 at%Zn; d) 40 at%Zn.
Vol.
12, No.
12
ORDER-DISORDER
TRANSITION
he c o n c l u d e d t h a t t h e p " phase i s s t a b l e between 0 - 2 7 0 ° K , 544°K and t h e ~ p h a s e above 544°K, Fig. 6a.
1119
phase between 270-
To e x t e n d t h e s e r e s u l t s f o r n o n - e q u i a t o m i c 45-42-40 at%Zn a l l o y s , we have calculated ~S P~5° at different t e m p e r a t u r e s assuming t h a t t h e change w i t h c o m p o s i t i o n in t h e v i b r a t i o n a l component o f e n t r o p y i s much s m e l l e r t h a n t h e c o r r e s p o n d i n g change in t h e c o n f i g u r a t i o n a l component. The c o n f i g u r a t i o n a l entropy SC vs T was determined using Kirkwood's approximation up to (w/kT) 2. For the order-disorder tempereture T O we used the values in Table I and the long range order parameter was calculated from the Cowley's approximation (17). In Figs. 4 b,c,d and 5 b,c,d are plotted Sc vs T and S vs T for different compositions. From ec. (1) and Fig. 5 we derived the free energy change vs temperature between 42 and 50 at~Zn. The conclusion is that the ~ t phase is stable at O°K in this range of composition and, for symetric consideration, up t o 52 at%Zn. Fig. 6.
I
120 80
I
I
I
I
~.~%
30:~_ 50 %
u
~sY,1 l
t
LD
0
r ""'-.42'/, -40 "
"
VS t e m p e r a t u r e a t d i f f e r e n t compos i t i o n s .
°/0 ...................... -.-2-;-2..-:;..-~.-..•
100
200
300
40O 5O0 TEMPERATURE °K Conclusions
I . The d e t e r m i n a t i o n o f T O f o r d i f f e r e n t c o m p o s i t i o n s in b i n a r y a l l o y s , t h u s avoiding extrapolation from t e r n a r y a l l o y s , has become p o s s i b l e by t h e elimination of the ~ (~')~ 3 o reaction. Within experimental errors,measured r e s u l t s agree t o a g r e a t e x t e n t w i t h t h e t h e o r e t i c a l expected values. 2. From t h e e s t i m a t i o n s made in s a c . 4, we c o n c l u d e t h a t t h e ~3 e phase is s t a b l e a t O°K between 42 and 52 at%Zn. Acknowledgements The a u t h o r s a r e i n d e b t e d t o Dr. J. A b r i a t a f o r a l l o w i n g us t o use some of his results prior to publication and v e r y u s e f u l d i s c u s s i o n s and comments. F i n a n c i a l s u p p o r t by t h e Programa M u l t i n a c i o n a l de M e t a l u r g l a sponsored by t h e O r g a n i z a t i o n of American S t a t e s i s g r a t e f u l l y acknowledged. References I.
I.G.
Edmunds and M.M. Q u r a s h i , A c t a
Crystal loft.
41 417 ( 1 9 5 1 ) .
1120
ORDER-DISORDER
TRANSITION
2. M. Hansen and K. Anderko, C o n s t i t u t i o n
of Binary A l l o y s ,
Vol.
12, No. 12
McGraw-Hill,
New
York (1968).
3. L. Muldawer, J. Appl. Phys, 22, 663 (1951). 4. M.E. Brookes and R.W. Smith, S c r i p t a Met. 3, 667 (1969). 5. M. Yono, H. Asano, N. Nakanishi and S. Kachi, Trans. Japan I n s t . Metals 8, 277 (1967). 6. H. Mc l . C l a r k , E.A. Merriman and C.M. Wayman, Acre Met. 17, 719, 1969. 7. J. A b r i a t a , PhD T h e s i s , Cuyo U n i v e r s i t y (1970). 8. R.L. Opt and J. Rovel, Acta Met. I0, 1935 (1962). 9. S. Noguchi, Journ. of the Phys. Soc. of Japan I I , 1844 (1962). IO. H.W. King and T.B. Massalskl, Trans. AIME 242, 1353 (1968). I I . L.C. Brown and M.J. Stewart, Trans. AIME 242, 1353 (1968). 12. V.V. Geychenko and A.K. Kanyuka, Fiz. Metal. M e t a l l o v e d . 38,5, 918 - 38,6, 1146 (1974). 13. Sykes and W i l l k i n s o n , J. I n s t . Metals 61, 223 (1937). 14. M.A. K r i v o g l a z and Z.A. Matysina, S o v i e t Phys. Jetps, l, IO3 (1955). 15. R. Kikuchi and H. Sato, Acta Met. 22, IO99 (1974). 16. J.M. Ziman, E l e c t r o n s and Phonons, Oxford U n i v e r s i t y Press (1962). 17. J.M. Cowley, Phys. Rev. 77, 669 (1950); 120, 1648 (1960); 138A, 1384 (1965).