The solubility of tin in aluminum
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Crystal
S
BF*
BS*
BNi*
BMn*
( U'2)~4/i2
(U'2)~2n
0M(Ni)
0m(Mn)
N6
0.99
0.326 (+-0.020)
0.273 (-+0.015)
0.372 (-+0.020)
0.322 (-+0.015)
0.064A (-+0.002)
0.64A (+-0.001)
434 K (-+14)
452 K (+-12)
M9
0.96
0.328 (-+0.015)
0.216 (+0.020)
0.372 (-+0.015)
0.357 (-+0.020)
0.069A (-+0.002)
0.067 (-+0.002)
407 K (-+10)
429 K (-+14)
*BF is the depressionof peaks obtained from the fundmental peaks, whereasBs is the same factor for superstructure peaks. BMn and BNi are peak depression terms due to displacementsof atoms in a state of partial long range order. The U's are the displacements.For further details see Ref. 11.
peaks are in good agreement except for the longest t i m e s , w h e n t h e c o r r e c t i o n to t h e b r o a d e n i n g of t h e 100 p e a k w a s p r o b a b l y u n r e l i a b l e . No a t t e m p t w a s m a d e to e x a m i n e t h e a n i s o t r o p y of t h e d o m a i n s i z e b y e x a m i n i n g t h e b r o a d e n i n g of o t h e r s u p e r l a t t i c e p e a k s . F o l l o w i n g t h i s s t u d y , t h e d e g r e e of l o n g - r a n g e o r d e r w a s m e a s u r e d v s t i m e a t 400~ a n d 375~ Integrated i n t e n s i t i e s of t h e 100 p e a k w e r e o b t a i n e d w i t h a p l a n i m e t e r . Such m e a s u r e m e n t s w e r e a l s o m a d e d u r i n g t h e d o m a i n g r o w t h a t 452~ There are uncertainties in t h e a n o m a l o u s d i s p e r s i o n c o r r e c t i o n to t h e s c a t t e r ing factors for elements whose absorption edge is c l o s e to t h e w a v e l e n g t h e m p l o y e d . T h e s e , t h e l a c k of a good t e m p e r a t u r e f a c t o r a n d e x t i n c t i o n m a d e it d i f f i c u l t to o b t a i n good v a l u e s of t h e l o n g r a n g e o r d e r p a r a m e t e r " S " f r o m , s a y , t h e r a t i o of 100 to 200 i n t e n sities. Instead the values were normalized at equilibr i u m to t h o s e o b t a i n e d i n R e f . 6 ( r e f e r r e d to h e r e a s S e q ) . T h e r e s u l t s a r e g i v e n in F i g s . 2 a n d 3. H e r e t h e d e f i n i t i o n of " S " i s : 3 (ramA~ 1 ( r fl - m B S=--~, l_rnA /+T\I_mB )
[2]
w h e r e m A i s t h e a t o m i c f r a c t i o n of Ni a n d rc~ i s t h e f r a c t i o n of Ni s i t e s r i g h t l y o c c u p i e d . A l s o s h o w n in F i g s . 2 a n d 3 i s t h e f i t to t h e e q u a t i o n developed by Rothstein: g 1-S 1 - - Seq
- c o t h ( a t + B)
[3]
It i s s e e n t h a t t h i s is a s u i t a b l e f i t to t h e d a t a . N o w i c k a n d W e i s b e r g ~~ h a v e s h o w n t h a t t h e r a t e c o n s t a n t a i s e x p o n e n t i a l l y r e l a t e d to t h e a c t i v a t i o n e n e r g y f o r o r d e r ing. From the data at three temperatures this was det e r m i n e d to b e 65 • 10 k c a l / g - a t o m . Based on these results the heat-treatment for complete order in Table I was developed and tested with two c r y s t a l s of 2 6 . 0 0 at. p e t Mn. At t h e e n d of t h i s heat-treatment the int
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