ti-al-nb system

8/13/2019 Ti-Al-Nb system

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Materials Science and Engineering A 152 ( 1 9 9 2 ) 9 - 1 7 9

Thermodynam ic calculation of the ternary T i A 1 N b system

U . R . K a t t n e r * a n d W . J . B o e t t i n g e r

Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, M D 20899 USA )

Abstract

P h a s e e q u i l i b r i a o f t h e t e r n a r y T i - A I - N b s y s t e m a r e d o m i n a t e d b y t h e l a r g e r a n g e o f h o m o g e n e i t y o f ( f l- T i ,N b ) , t h eb i n a ry i n t er m e t a ll i c c o m p o u n d s o f t h e N b - A I a n d T i - A I s y s t em s a n d t h e f o r m a t io n o f t w o t e r n a r y c o m p o u n d s . T h e

a v a i l a b le t e rn a r y e x p e r i m e n t a l d a t a , t o g e t h e r w i th a t h e r m o d y n a m i c e x t r a p o l a t i o n o f t h e t e r n a r y s y s t e m f r o m t h e b i n a r y

s y s te m s , h a v e b e e n u s e d t o c a l c u l a t e t h e t e r n a r y p h a s e d i a g r a m . T h e m o d e l d e s c r i p t i o n s o f th e G i b b s e n e r g i e s o f m o s t o f

t h e s e c o m p o u n d s a r e g i v e n b y t h e e x i s ti n g c a l c u l a ti o n s o f th e b i n a r y s y s te m s . In o r d e r t o m o d e l a p h a s e w h i c h i s p r e s e n t in

o n l y o n e b i n a r y s y s t e m , b u t h a s a t e r n a r y h o m o g e n e i t y r a n g e , a h y p o t h e t i c a l p h a s e w i t h t h e s a m e s t r u c t u r e w a s a n a l y t i -

c a l ly d e s c r i b e d f o r e a c h b i n a r y s y s t e m . S uc h a p h a s e w o u l d , o f c o u r s e , b e m e t a s t a b l e i n t h e o t h e r b i n a r y s y s t e m s .

C o n s t r a i n t s o n t h e G i b b s e n e r g i e s o f f o r m a t i o n w e r e d e r i v e d f r o m t h e c r y s t a l s t r u c t u r e s o f t h e c o r r e s p o n d i n g o r d e r e d

c o m p o u n d s . T h e s e s a m e c o n s t r a i n t s w e r e e m p l o y e d f o r t h e c o r r e s p o n d i n g p h a s e s i n t h e t e r n a r y s y s t e m . I n a f i n a lo p t i m i z a t i o n s t ep , t e r n a r y p a r a m e t e r s w e r e i n t r o d u c e d a n d a d j u s t e d t o t h e 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 . T h e a s - d e r i v e d

d e s c r i p t i o n o f t h e t e r n a r y T i - A I - N b s y s t e m c a n b e u s e d t o e s t im a t e s i n gl e o r m u l t i p h a s e f i e ld s a n d t h e r m o d y n a m i c

quan t i t i e s w here no expe r im en ta l da t a a r e ye t ava i l ab l e . I t i s a l so use fu l a s an i nd i ca to r o f p rob l em a reas fo r w h icha d d i t i o n a l e x p e r i m e n t a l d a t a a r e r e q u i r e d .

1 . I n t r od u c t i on

T h e T i - A 1 - N b s y s t e m is o f i n t er e s t f o r th e d e v e l o p -

m e n t o f h i g h t e m p e r a t u r e / l o w d e n s i t y i n t e r m e t a l l i c

m a t e r i a l s . K n o w l e d g e o f s t a b l e a n d m e t a s t a b l e p h a s er e l a ti o n s i n m u l t i c o m p o n e n t m a t e ri a l s p r o v i d e s

v a l u ab l e i n f o r m a t i o n f o r t h e d e v e l o p m e n t o f p r o c e s s -

i n g s t r a t e g i e s f o r t h e s e m a t e r i a l s . O n c e d e r i v e d , t h i s

t h e r m o d y n a m i c d e s c r i p t i o n c a n b e u s e d t o p r o v i d e

i n f o r m a t i o n w h i c h i s n o t e a s i l y a c c e s s i b l e t h r o u g h

e x p e r i m e n t a l t e c h n i q u e s , s u c h a s m e t a s t a b l e e x t e n s io n s

o r t h e t e m p e r a t u r e s w h e r e t w o p h a s e s h a v e t h e s a m e

G i b b s e n e r g i e s at a g i v e n c o m p o s i t i o n T , c u r v e s ).

D e s p i t e t h e i r i m p o r t a n c e , t h e p h a s e r e l a ti o n s h ip s o f

t h i s s y s t e m a r e o n l y p a r t i a l l y k n o w n f o r c e r t a i n t e m -

p e r a t u r e r e g i m e s [ 1 - 8 ] . F r o m t h e 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 t h e f o l l o w i n g p o i n t s c a n b e d e t e r m i n e d .

1 ) T h e i n t er m e t a l li c c o m p o u n d s o f th e b i n a r y

N b - A 1 a n d T i - A 1 s y s t em s h a v e r e l a ti v el y w i d e r a n ge s

o f h o m o g e n e i t y i n t h e t e r n a r y s y s t e m .

2 ) T h e c o m p o u n d s N bA 13 a n d T i A I 3 f o r m a c o n -

t i n u o u s D022) o l i d s o l u t i o n .

3 ) A t l e a s t t w o t e r n a r y c o m p o u n d s e x i s t n e a r t h e

c o m p o s i t i o n s T i 2 A 1 N b a n d T i 4A 1 3N b .

4 ) T h e f l- T i, N b ) p h a s e w i t h b. c .c , s t r u c t u r e o r d e r s

t o t h e f l0 -T i , Nb ) w i t h B 2 C s C I ) s t ru c t u re .

* A l s o a t : D e p a r t m e n t o f M a t e r i a l s S c i e n c e a n d E n g i n e e r i n g ,U n i v e r s i t y o f W i s c o n s i n - M a d i s o n , M a d i s o n , W I 5 3 7 0 6 , U S A .

5 ) A m i s c ib i l it y g a p m a y e x i s t i n t h e o r d e r e d f l ,-

T i , N b ) p h a s e .

T h e a v a i l a b l e t e r n a r y e x p e r i m e n t a l d a t a , t o g e t h e r

w i t h a t h e r m o d y n a m i c e x t r a p o l a t i o n o f t h e t e r n a r y

s y s t e m f r o m t h e b i n a r y s y s t e m s , h a v e b e e n u s e d t oc a l c u l a t e t h e t e r n a r y p h a s e d i a g r a m . T h i s a t t e m p t a t

m o d e l i n g t h e T i - A I - N b s y st e m m u s t b e v ie w e d a s

p r e l i m i n a r y . H o w e v e r , i t p r o v i d e s a b a s i s f o r t h e c o m -

b i n a t i o n o f d a t a f r o m s e v e ra l s o u r c e s i n a t h e r m o -

d y n a m i c a l l y c o n s i s t e n t m a n n e r a n d i n d i c a t e s

c o m p o s i t i o n a n d t e m p e r a t u r e r e g i m e s w h e r e f u r th e r

e x p e r i m e n t a t i o n i s e s s e n t i a l . A c o n t i n u e d i n t e r c h a n g e

b e t w e e n c a l c u l a t i o n a n d e x p e r i m e n t a t i o n i s t h e

q u i c k e s t r o u t e t o t h e t r u e d i a g r a m .

2 . H i s t o ry o f c a l c u l a t io n s o f t h e T i A I N b s y s t e m

P r e v i o u s c a lc u l a ti o n s o f t h e T i - A 1 - N b s y s t e m w e r e

b a s e d o n t h e t h e n a c c e p t e d c a l c u l a t i o n s o f t h e b i n a r y

s y s t e m s a n d 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 . I n a f i r s t

c a l c u la t i o n o f t h e T i - A 1 - N b s y s t e m [9 ], th e t h e r m o -

d y n a m i c d e s c r i p t i o n s o f t h e b i n a r y s y s t e m s o f N b - A I

a n d T i - A 1 b y M u r r a y [ 1 0, 1 1] a n d o f T i - N b b y K a u f -

m a n a n d B e r n s t e i n [ 1 2 ] w e r e u s e d . S i n c e t h i s c a l c u l a -

t i o n , t h e e x p e r i m e n t a l d a t a a n d t h e r m o d y n a m i c

d e s c r i p t i o n s o f t h e b i n a ry T i - A 1 a n d N b - A 1 s y s te m s

h a v e b e e n s u b j e c t t o r e v i s io n . F o r t h e c a l c u l a t i o n o f t h e

N b - A I s y s te m , M u r r a y [ 10 ] u s e d p h a s e d i a g r a m a s w e ll

l 0 U . R . K a t t n e r 1 4/. J . B o e t t i n g e r / T e r n a ~ T i - A I - N b s y s t e m

a s t h e r m o d y n a m i c d a t a t o d e r i v e t h e t h e rm o d y n a m i c

de sc r ip t i on f o r t h i s sys t e m . A r e - e va lua t i on o f t he

e xpe r im e nta l da t a f o r t h i s sys t e m sugge s t e d t ha t som e

o f t h e t h e r m o d y n a m i c d a t a a r e i n c o n s i s t e n t w i t h t h e

pha se d i a gr a m da t a . T he c a l c u l a t i on ba se d on t h i s r e -

e v a l u a t i o n y i e l d e d a s i m p l i f i e d t h e r m o d y n a m i c

d e s c r i p t io n a n d a m o r e a c c u r a t e f it b e t w e e n t h e c a l cu -l a t e d a nd e xpe r im e nta l pha se bounda r i e s [ 13] . For t he

T i - A I s y s t e m , n e w e x p e r i m e n t a l r e s u l t s s h o w e d t h a t

( a - T i ) i s i n e qu i l i b r ium wi th t he l i qu id pha se a nd h ighe r

l i q u i d u s t e m p e r a t u r e s w e r e e s t a b l i s h e d f o r t h e c o m -

p o s i t io n r an g e o f 3 5 - 8 0 a t. A l . T h e s e c h a n g e s i n t h e

e xpe r im e nta l pha se d i a gr a m a r e r e f l e c t e d by a se r i es o f

c a l c u l a t ions i n t h e l i t e r a tu r e ( se e Ka t tne r e t a l [14] for a

s u m m a r y ) .

S i n c e t h e a c c u r a c y o f t h e t h e r m o d y n a m i c d e s c r i p -

t i ons o f t he b ina r y sys t e m s is c r uc i a l f o r t he c a l c u l a t i on

o f a t e r n a r y p h a s e d i a g r a m , t h e m o s t r e c e n t c a l c u l a -

t io n s o f t h e b i n a r y N b - A I a n d T i - A 1 s y s t e m s w e r eu s e d f o r a n e w a p p r o x i m a ti o n o f t h e T i - A I - N b s y st em .

T h e se t h r e e c a l c u l a t e d b ina r ie s a r e show n in F ig . 1 .

3 Ava i lab le expe r im enta l da ta

T h e 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 f o r t h e T i - A I - N b

s y s t e m a r e sp a r s e w h e n c o m p a r e d w i th t h e c o m p l e x i t y

of t h is sys t e m . M os t o f t he e xp e r im e n ta l i n f o r m a t ion i s

a va i l a b le f o r t he i so the r m a l se c t i on a t 1200 °C . T h e t i e -

l i ne da t a o f r e fs . 6 a nd 15 a r e i n goo d a gr e e m e nt a nd

e s t a b l ish t he p ha se bou nda r i e s w i th su f f ic i e n t a c c ur a c y .

T h e da t a o f re f . 2 f o r t he (f l- Ti , Nb) - Nb 3A1 - Nb2 AI a nd

Nb 2A I - T iA I - ( T i , Nb)A13 th r e e - ph a se e qu i l ib r i a a r e i n

g e n e r a l a g r e e m e n t w i t h th e p h a s e b o u n d a r i e s i n d i c a t e d

by r e f s. 6 a nd 15 . I t is no t e w or th y t o m e nt ion t ha t t he

t i e -l i ne da t a o f r e f. 6 i nd i c a t e a n i so l a t ed s ing l e - pha se

area n ear th e co mp osi t io n Nb~0A145Ti45. Th is s ing le

pha se i s be l ie ve d t o ha ve t he B 2 ( CsC1) s t r uc tu r e . I t is

a l so kn ow n tha t t he ( fl -T i, Nb) pha se un de r g oe s a n

or de r ing t r a ns i ti on f r om th e d i so r de r e d b .c .c , s t r uc tu r e

to t he o r d e r e d B2 s t r uc tu r e ( f l0 -T i, Nb) i n t he t e r n a r y

sys t e m [ 1, 3 , 6] . T h e oc c ur r e nc e o f two s ing l e - pha se

f i elds w i th t he sa m e c r ys t a l s t r uc tu r e i s sugge s ti ve o f a

misc ibi l i ty gap.

M o s t o f t h e e x p e r i m e n t a l d a t a w h i c h a r e a v a i l a b l e

f o r t he 1100 °C se c t i on de t e r m ine t he ( fl - T i,Nb) - T i3A1

b o u n d a r y . T h e d a t a o f P e r e p e z k o [ 7] s h o w a r e l a ti v e ly

w i d e t w o - p h a s e a r e a , w h i le t h e d a t a o f M u r a l e e d h a r a n

a nd Ba n e r j e e [4 ] show a r e l a t ive ly na r r o w on e . Fur -

the r e xpe r im e nta l da t a r e por t a t i e - l i ne f o r ( / 30-

T i , Nb ) - Nb2A I [ 1 ] , a s w e l l as da t a f o r tw o t i e -t r i ang l e s

( /30- T i ,Nb) - Nb2A1- T iAI [ 16] a nd ( f l 0 - T iNb) - T i3Al -

T iA1 [ 5 ] . T h e c om pos i t i ons o f t he ( f l0 -T i,Nb) pha ser e p o r t e d f o r t h e s e t w o t h r e e - p h a s e e q u i l i b r i a a r e

c o n t r a d i c t o r y t o t h e e x t r a p o l a ti o n o f t h e p h a s e b o u n d -

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F i g . 1 . T h e c a l c u l a te d b i n a r y p h a s e d i a g r a m s . (a ) T i - A I , ( b )N b - A I a n d (c ) T i - N b .

a r y da t a g ive n by P e r e pe z ko [ 7 ] . T h i s c onf l i c t c a n be

r e so lve d i f t he a s su m p t ion i s m a d e t ha t two s ing l e -

ph ase a reas of the ( fl0-Ti , Nb ) p has e a lso exis t a t th ist e m p e r a tu r e . I n t h i s c a se on e ( fl 0- Ti , Nb) wo uld be

U . R . K a t t n e r , W . J . B o e t t i n g e r / T e r n a r y T i - A I - N b s y s t e m 1 1

obse r ve d i n t he t h r e e - p ha se e qu i l ib r i a [ 8 ] , whi l e t he

o th e r ( /30-T i,Nb) wa s o bse r v e d by Pe r e p e z ko [ 7] .

F o r t e m p e r a t u r e s o t h e r t h a n 1 2 0 0 a n d 1 1 0 0 ° C , o n l y

f e w t i e - l i ne da t a a r e a va i l a b l e . For 700 °C , Be nde r sky

e t a l . [8] repor ted t ie - l ine da ta be tween ( /3-Ti , N b ) a n d

T i 2 A I N b , a n d B e n d e r s k y e t a l . [ 5 ] r e por t e d da t a

be tw e e n T ia AI 3Nb a nd T iA1 in e qu i l i b r ium wi th a t r a c eof Ti3AI.

E xpe r im e nta l da t a i nvo lv ing t he l i qu id pha se a r e

a va i la b l e on ly f o r t he T iA l3- r i c h pa r t o f t he qua s ib ina r y

NbA13- T iAi~ se c t i on [ 6 ] . Ba se d on t he o bse r va t i o n o f

pr im a r y f i e lds o f c r ys t a l l iz a t i on a nd p r e l im ina r y d i f f e r-

e n t i a l t he r m a l a na lys i s ( DT A) r e su l t s , Pe r e pe z ko e t a l .

[6 ] p r op ose d a n e s t im a te d l i qu idus p r o j e c t i on .

E xpe r im e nta l r e su l t s ha ve e s t a b l i she d t he e x i s t e nc e

of two t e r na r y c om pou nds : T i2A1Nb [ 17] a nd T i4AI 3Nb

[ 5] . T h e T i~ A 1N b c o m p o u n d h a s a n o r t h o r h o m b i c

o r d e r e d s t ru c t u r e . It is b a s e d o n t e r n a r y o r d e r i n g o f t h e

D0z 9 s t r uc tu r e o f T i3AI whic h is a n o r d e r e d de r iva t i veof h .c .p . The Ti4A13Nb compound has the B82 (Ni2In)

s t r uc tu r e a nd i s be l i e ve d t o ha ve a r e l a t i ve ly sm a l l

r a n g e o f h o m o g e n e i t y . N e i t h e r t e r n a r y c o m p o u n d w a s

obs e r ve d i n a l loys t ha t we r e a n ne a l e d a t 1100 °C [5 , 8]

o r h i g h e r t e m p e r a t u r e s . B e n d e r s k y e t a l . [ 8 ] r e por t e d

t h e o c c u r r e n c e o f t h e T i 2 A I N b c o m p o u n d i n s a m p l e s

t h a t w e r e a n n e a l e d a t a n d b e l o w 9 7 0 ° C , a n d t h e

T i ~ A I ~ N b c o m p o u n d w a s o b s e r v e d i n s a m p l e s t h a t

we r e a n ne a l e d a t 700 °C [5 ].

4 . A n a l y t i c a l d e s c r i p t i o n o f t h e p h a s e s

T h e p h a s e s c o n s i d e r e d i n t h e c a l c u l a t i o n o f t h e

T i - A I - N b s y s te m a r e t h e d i s o r d e re d s o lu t io n p h a s es

( l iquid, ( /3-Ti ,Nb) , ( a -Ti ) and (AI) ) , the ordered inte r -

m e t a l l i c c o m p o u n d s o f t h e N b - A I a n d T i - A 1 b i n a r i e s

(Nb3AI , Nb2A1, (T i , Nb)A I3, T i3A1, T iA1, T iA1 2 and

T i 2A I s) a n d t h e o r d e r e d t e r n a r y c o m p o u n d s (T i2 A 1N b

a nd T i4AI 3Nb) . S inc e t he t r a ns i t i on be twe e n d i s -

o r de r e d ( f l - T i ,Nb) a nd o r de r e d ( f l o - T i ,Nb) i s be l i e ve d

t o b e a s e c o n d - o r d e r t ra n s i ti o n , a n d i n o r d e r t o k e e p

the a na ly t i c a l de sc r ip t i on a s s im ple a s poss ib l e , t he se

two s t r uc tu r e s w i l l no t be d i s t i ngu i she d i n t he p r e se n t

ca lcula t ion; both a re re pres ente d as the ( fl -T i , Nb) p hase .

For t he c a l c u l a t i on o f pha se e qu i l i b r i a , t he G ibbs

e n e r g i e s ( G ) o f t h e p h a s e s p r e s e n t m u s t b e e x p r e s s e d a s

a na ly t i c a l f unc t i ons o f t he va r i a b l e s o f i n t e r e s t , i . e .

c o m p o s i t i o n a n d t e m p e r a t u r e . F o r t h e c a l c u l a t i o n o f

t h e t e r n a r y s y s t e m , t h e t y p e o f e q u a t i o n ( m o d e l ) f o r t h e

p h a s e s e x i s ti n g in t h e b i n a r i es h a s b e e n p r e d e t e r m i n e d

b y t h e t h e r m o d y n a m i c d e s c r i p t i o n u s e d i n t h e c a l c u la -

t i on o f t he b ina r y sys t e m s . I n a l l t h r e e b ina r y sys t e m s

t h e d i s o r d e r e d s o l u t i o n p h a s e s w e r e d e s c r i b e d w i t h

q u a s i - s u b r e g u la r s o l u t i o n m o d e l s . T h e r a n g e s o f h o m o -g e n e i t y o f t h e o r d e r e d i n t e r m e t a l l i c c o m p o u n d s w e r e

de sc r ibe d w i th a sub l a t t ic e m od e l , c ons ide r ing two or

m or e sub l a t t i c e s a nd a l l owing subs t i t u t i on t o oc c ur on

a t l e a s t one o f t he m . Pha se s f o r whic h f e w da t a we r e

a v a il a b le o n t h e i r h o m o g e n e i t y r a n g e s w e r e a s s u m e d t o

be s to i c h iom e t r i c . For t he p r e se n t c a l c u l a t i on , t he

p r o g r a m P M L F K T b y L u k a s e t a l . [18] was us ed. In this

p r o g r a m t h e d i f f e r e n t m o d e l d e s c r i p t i o n s c a n a l l b et r e a t e d w i t h a n e q u a t i o n o f t h e f o r m

G = E a E Yk G k + R T l n y k ) )k

+ ~ A l y p y , l v z , v , i I

Ii l l It

+ Z B o y p Y ,I Y ,jj

v v = yp + ( 1 - yp - yq)

t ,t = Y q + ( 1 - y p - y q )

whe r e i i s t he pha se i nde x ; l i s t he sub l a t t i c e i nde x ;

k, p , q , r a re the spec ies indices ; j i s the polynomia l

i nde x ( b ina r y t e r m s) ; 1 ) i s the po ly nom ia l i nde x ( t e r na r y

t e r m s) ; G i i s t he m o la r G ibbs e ne r g y o f pha se i ; a z s t he

fra ct io n o f su bla ttic e l in ph as e i; Yk, Y~,, Y,~, Yr ar e t he

c o n c e n t r a t i o n o f s p e c i e s , r e f e r r e d t o 1 m o l e o f s u b -

la t t ice s ites ; Gk i s the G ibbs ene rgy of spec ies k; Aj is

t h e G i b b s e n e r g y c o e f f i c i e n t s o f b i n a r y p o l y n o m i a l

t e r m s ; B jj i s t he G ibb s e ne r g y c oe f f i c i e n ts o f t e r na r yp o l y n o m i a l t e r m s ; a n d m , n , o a r e t h e e x p o n e n t s o f

po ly nom ia l t e r m s . T h e Gk , A j a nd Bjj pa r a m e te r s a r e

e i t h e r c o n s t a n t o r l i n e a r f u n c ti o n s o f t h e t e m p e r a t u r e .

T h e e x pon e n t s m , n a nd o a s we l l a s t he i nd i c e s p , q

a nd r a r e g ive n i nd iv idua l ly f o r e a c h j o r j j.

T h e f i rs t t e r m on t he r i gh t - ha nd s ide o f e qn . ( 1 ) r e p -

r e se n t s t he G ibb s e n e r g i e s o f t he spe c i e s a nd t he i r c on-

t r ib u t i o n t o t h e c o n f i g u r a ti o n a l e n tr o p y , t h e s e c o n d a n d

t h i r d t e r m a r e b i n a r y a n d t e r n a r y p o l y n o m i a l i n t e r -

a c t i on e ne r g i e s , r e spe c t i ve ly . T he po lynom ia l i n t e r -

a c t i on t e r m s c ons i s t o f two type s ( as se e n i n T a b le 1 ).

T e r m s i n v o lv i n g p r o d u c t s o f c o n c e n t r a t i o n s o n d i ff e r-e n t s u b l a tt ic e s c o r r e s p o n d t o t h e e n e r g y o f f o r m a t i o n

o f t h e p h a s e w i t h o n l y o n e s p e c i e s p r e s e n t o n e a c h s u b -

l a t t i c e . T e r m s invo lv ing p r oduc t s o f c onc e n t r a t i ons on

t h e s a m e s u b l a tt ic e c o r r e s p o n d t o t h e c h a n g e i n e n e r g y

owing to t h e m ix ing o f t he spe c i e s o n t h i s sub l a t ti c e .

T h e a b o v e e q u a t i o n r e d u c e s t o t h e b i n a r y q u a s i -

subr e gu la r so lu t i on m o de l i f on ly one sub l a t t ic e ( l = 1

a nd a ~= 1 .0 ) is c ons ide r e d . I n t h i s c a se t he spe c i e s c on-

c e n t r a t i on , Yk, i s ide n t i c a l t o t h e e l e m e nta l c on c e n t r a -

t i on , xk , a nd t he r e f o r e , t he va r i a b l e xk i s use d i ns t e a d o f

Yk, an d with

t l = x I + 1 - x , - x 2 ) = x I

1 2 U . R . K a t t n e r , W . J . B o e t t i n g e r / T e r n a r y T i - A I - N b s y s t e m

T A B L E 1 . T h e r m o d y n a m i c d e s c r i p t i o n o f t h e T i - A I - N b s y s t e m (a ll q u a n t i t ie s ar e g i v e n i n J m o l - ~ )

M u l t i p l i e r P a r a m e t e r G ~ , A j o r B H M u l t i p l i e r P a r a m e t e r G k , A / o r B jj

L i q u i d

X N b 0 . 0 0

X A j 0 . 00

Xm i 0 . 0 0

XNt,XAIt NI, - - - 1 0 3 7 3 7 . 1 0 + 2 9 . 4 5 9 0 4 T

XNbXAII~NblIAI 2 8 9 7 1 6 . 2 0 + 8 7 . 9 7 0 0 6 T

X N b X A l l A I 2 1 2 7 7 1 3 . 1 0 + 5 8 . 5 1 1 0 2 T

X-I.iXAIUTi - - 1 2 0 5 2 1 . 0 0 + 4 1 . 1 1 3 7 8 T

XTiXAII AI 1 0 4 6 1 9 . 4 0 + 4 1 . 1 1 3 7 8 T

X T i X N b 1 3 0 5 8 . 2 6

X N b X A I X T i - - 1 0 0 0 0 0 . 0 0

( f l - T i , N b )

XNb - 3 0 0 0 0 . 0 0 + 1 0 . 9 0 9 1 0 T

XAI - - 6 2 8 . 0 0 + 6 . 6 5 9 8 0 T

X fi - 1 4 1 4 6 . 0 0 + 7 . 2 8 8 0 0 T

XNbXAWNI - - 1 3 3 9 8 2 . 5 0 + 4 1 . 6 9 4 2 2 T

X Nb XA ll A I 1 2 5 4 0 1 . 5 0 + 4 1 . 6 9 4 2 2 T

XTiXAI - - 1 2 9 3 9 6 . 7 0 + 4 0 . 0 6 3 1 0 TXTiXNb 1 3 0 7 5 . 0 0

XNb2XA~X.I,i 8 0 0 0 0 . 0 0 + 6 0 . 0 0 0 0 0 T

XNbXAI2XTi - - 1 8 0 0 0 0 . 0 0 + 6 0 . 0 0 0 0 0 T

XNbXAIXTi 2 7 0 0 0 0 . 0 0 + 6 0 . 0 0 0 0 0 T

( a - T i )

XNh - - 1 3 0 0 0 . 0 0 + 9 . 7 0 9 1 0 T

XAj - - 5 1 5 1 . 4 0 + 9 . 6 1 7 8 0 T

x -li - 1 8 3 1 6 . 0 0 + 1 0 . 8 9 8 4 0 T

XNhXAI - - 1 2 0 0 0 0 . 0 0 + 4 0 . 0 0 0 0 0 T

XTiXalt, .ri - - 1 3 9 8 2 3 . 4 0 + 4 5 . 3 9 1 7 4 T

XTiXAIUAI 1 0 7 7 5 3 . 6 0 + 2 1 . 0 2 6 3 0 T

XTiXNI~ 1 3 0 7 5 . 0 0

XNbXAIXTi 1 1 5 0 0 0 . 0 0

( A l )

Xy/~ - 8 0 0 0 . 0 0 + 8 , 7 0 9 1 0 T

xA~ - 1 0 7 1 1 . 0 0 + 1 1 . 4 7 2 8 0 T

XTi 1 2 3 1 6 . 0 0 + 1 0 . 7 9 8 4 0 T

XNbXAI 1 8 5 7 8 3 . 3 0 + 9 2 . 5 7 4 9 0 T

X ,riX Ai - - 1 2 4 2 6 9 . 6 0 + 4 3 . 8 9 6 7 5 T

X T i X N ~ 1 3 0 7 5 . 0 0

N b 3 A I ( t w o s u b l a t t i c e s )

N i o b i u m s u b l at t ic e : a N b = 0 . 7 5

y s b Nb - - 2 4 5 0 0 . 0 0 + 1 0 . 3 5 9 1 0 T

Y A l N b - - 3 1 4 8 . 8 0 + 7 . 8 6 3 0 5 T

y T i N b - - 1 3 6 8 8 . 5 0 + 8 . 1 6 5 6 0 T

y N b Y b Y T iN b 9 8 0 6 . 2 5

A l u m i n u m s u b l a t t i c e : a A~ = 0 . 2 5 T

y y h a~ - 2 4 5 0 0 . 0 0 + 1 0 . 3 5 9 1 0 T

Y A i A I - - 3 1 4 8 . 8 0 + 7 . 8 6 3 0 5 T

Y T i A I 1 3 6 8 8 . 5 0 + 8 . 1 6 5 6 0 T

Y A i g l y N b g l - - 8 6 7 5 . 0 1 + 2 . 4 7 0 1 2 T

y y bA ly T i A r 3 2 6 8 . 7 5

Y Ti AlyA IA I - - 4 0 0 0 . 0 0

P o l y n o m i a l t e r m s b e t w e e n s p e c i e s o n d i f fe r e n t s u b l a tt i c e s

Y N b N b y A i a l 3 5 5 1 8 . 5 0 + 6 . 9 3 6 1 7 T

Y A I N b y N b A I 3 5 5 1 8 . 5 0 - 6 . 9 3 6 1 7 T

yTiYbyAiAI - - 2 6 0 0 0 . 0 0 + 7 . 0 0 0 0 0 T

y A i N b y w iAI 2 6 0 0 0 . 0 0 - 7 . 0 0 0 0 0 T

YNbNbyTiNbyAiAI - - 6 0 0 0 . 0 0

N b 2 A I ( t h re e s u b l a t t i c e s )

N i o b i u m s u b l a tt i ce : a y b = 0 . 5 3 3 3 3 3 4 0

yNbNb - - 2 2 6 6 6 . 7 0 + 1 0 . 1 7 5 6 7 T

y A i N l - - 3 9 8 9 . 0 0 + 8 . 2 6 4 1 3 TYTiNb - - 1 3 5 3 6 . 0 0 + 8 . 4 5 8 1 3 T

Y A i N b y T i N b 8 0 4 6 . 1 5

Y T i N b y A N b - - 1 0 0 0 0 . 0 0

A l u m i n u m s u b l a tt i ce : a a~ = 0 . 3 3 3 3 3 3 3 0

Y N b A I - - 2 2 6 6 6 . 7 0 + 1 0 . 1 7 5 6 7 T

yAiAI - - 3 9 8 9 . 0 0 + 8 . 2 6 4 1 3 T

y Ti AI - 1 3 5 3 6 . 0 0 + 8 . 4 5 8 1 3 T

yAtalyN b AI - - 5 4 9 9 . 8 2 + 1 . 6 6 8 2 5 T

YNbAlyTiAI 5 0 2 8 . 8 5

Y T i A l y a l A I - - 6 0 0 0 . 0 0

N i o b i u m s u b l at t ic e : a Nb = 0 . 1 3 3 3 3 3 3 0

y N b N b 2 2 6 6 6 . 7 0 + 1 0 . 1 7 5 6 7 T

P o l y n o m i a l t e r m s b e t w e e n s p e c i e s o n d i f f e re n t s u b l a t t ic e s

Y N b N b y a l A l y N bN b - - 4 6 8 9 5 . 3 0 + 1 0 . 4 6 5 6 9 T

YAiNbyNbAlyNb N b 1 9 7 4 7 . 4 5

yalYbyalalyNb Nb - - 2 7 1 4 8 . 6 9 + 1 0 . 4 6 5 6 9 T

YTiNbyAiAlYNbNb - - 3 5 2 0 0 . 0 0 + 6 . 2 0 0 0 0 T

YAiNbyyiA lyN b Nb - - 3 5 2 0 0 . 0 0 + 6 . 2 0 0 0 0 T

( T i , N b ) A I ~ ( t w o s u b l a t t i c e s )

( T i , N b ) s u b l a t t i c e : a T M = 0 . 2 5

yNbTM - 8 0 0 0 . 0 0 + 8 . 7 0 9 1 0 T

y a j M - 1 0 7 1 1 . 0 0 + 1 1 . 4 7 2 8 0 T

yl , M - 1 2 3 1 6 . 0 0 + 1 0 . 7 9 8 4 0 T

yNuTNyAI M 1 2 5 0 0 . 0 0

yq-iTNyAiM

1 2 5 0 0 . 0 0yNbfNyTi TM 3 2 6 8 . 7 5

A l u m i n u m s u b l a t t i c e : a AI = 0 . 7 5

Y N b a l - - 8 0 0 0 . 0 0 + 8 . 7 0 9 1 0 T

yAWAI - - 1 0 7 1 1 . 0 0 + 1 1 . 4 7 2 8 0 T

YTiAI - - 1 2 3 1 6 . 0 0 + 1 0 . 7 9 8 4 0 T

Y A i A l Y N b A I - - 5 6 5 9 2 . 5 6 + 3 3 . 8 0 6 5 2 T

yAiAlYTiAI - - 6 1 8 4 9 . 4 6 + 3 6 . 5 3 3 7 0 T

YNbAlyTiA I 9 8 0 6 . 2 5

YNbAlyAiAlYTiAI - - 1 0 0 0 0 0 . 0 0

P o l y n o m i a l t e r m s b e t w e e n s p e c i e s o n d i f f e re n t s u b l a t t ic e s

yNbTNyA~AI - - 5 0 1 3 1 . 9 0 + 1 2 . 1 8 2 8 7 T

YAITNyNbAr 5 0 1 3 1 . 9 0 - - 1 2 . 1 8 2 8 7 T

YTi rNyAiAI - - 4 0 3 4 9 . 6 0 + 1 0 . 3 6 5 2 5 T

y A I T N y T i A I 4 0 3 4 9 . 6 0 - 1 0 . 3 6 5 2 5 T

Y N b T N y T i T N y A IA I - - 1 7 0 0 0 . 0 0 + 6 . 0 0 0 0 0 T

T i z A l 5 ( s t o i c h i o m e t r i c c o m p o u n d )

1 - 3 6 1 6 5 4 . 7 0 + 1 4 5 . 6 6 8 3 0 T

T i A I 2 ( s t o i c h io m e t r i c c o m p o u n d )

1 - 1 6 5 3 1 3 . 2 0 + 6 6 . 8 0 6 3 2 T

T i A I ( t w o s u b l a t t i c e s )

T i t a n i u m s u b l a tt i ce : a v~ = 0 . 5

yNbTi - - 8 0 0 0 . 0 0 + 8 . 7 0 9 1 0 T

yA~T~ - 1 0 7 1 1 . 0 0 + 1 1 . 4 7 2 8 0 T

Y T i T i - - 1 2 3 1 6 . 0 0 + 1 0 . 7 9 8 4 0 T

Y T i T i y A i T i i u T i T i 1 0 2 9 7 8 . 4 0 + 7 .7 9 2 8 2 T

U . R . K a t t n e r , W . J . B o e t t i n g e r / 7 ~ ' rn a o ' T i - A I - N b s y s t e m 1 3

TABLE 1 ( c o n t i n u e d )

Multiplier Paramete r G k, A/ or B i , Multiplier Parameter G k , A j o r Bij

T i t a n i u m s u b l a t ti c e : aTi=0.5 ( c o n t i n u e d )

YTiTiyA iTi l 'A i T i 24001.71 + 7.79282 T

YNbT iyTi AI 6537.50

YNb TiyAiTiyTi I 'i -- 40000.00

Alu min um sublattice: a a~ = 0.5

yNt,al - 8000 .00 + 8.7 0910 T

Y A i A I - - 10711.00+ 11.47280 T

yli al - 123 16. 00+ 10.79840 T

Y N b A l y A i A I 60000.00 + 11.00000 T

Y i l y T i I 28311.63 + 10.85167 T

YNbAlyTiAI 6537.50

Polynomial t e r m s b e t w e e n s p e c i e s o n d i f f e re n t s u b l a t t ic e s

Y N b T i Y i I 42000.00 + 8.00000 T

Y A i T i y N b A I 42000.00 - 8.00000 T

y T i T i y i I 37445.10 + 16.79376 T

yAiTiyTi AA 37445.10-- 16.79376 T

yybTiyTiTiyAIAI -- 20000.00

Ti3AI two sublattices)

Tit aniu m sublattice: a f~ = 0.75

yybTi 13000.00 + 9.70910 T

Y A i l i -5151 .40+9 .61780 T

.YTi ri - 18 31 6. 00 + 10.8 9840 T

y y b T i y A i T i -- 30000.00

y T i f i y A i T i - 71277. 87 + 25.469 98 T

y N b T i y r i r i 9806.25

Alu min um sublattice: a AI = 0.25

Y N b A I 13000.00 + 9.70910 T

Y A i A I 5151.40 + 9.61780 T

Y T i A I - - 18316.00+ 10.89840 T

YNbAlyl iAI 3268.75

Polynomial t e r m s b e t w e e n s p e c i e s o n d i f f er e n t s u b l a t ti c e s

Y N b T i y A i A I - - 38000.00 + 7.00000 T

Y A i T i y N b A I 38000. 00 - 7.00000 T

Y T i T i y A i A I - - 29633. 60 + 6.70801 TyAiriyfi AI 29 63 3. 60 -- 6.7 080 1 T

Y N b T i y . l i l i y A i A I - - 9400.00

T i 2 A I N b t h r e e s u b l a t t ic e s )

Titanium sublattice: a f~ = 0.5

Y N b T i 13000.00 + 9.70910 T

yl] i - 1831 6.00 + 10.89840 T

Y n i T i y I i I i - - 10000.00

N i o b i u m s u b l a t t i c e : a N b = 0 . 2 5

Ynbnh -- 13000 .00 + 9.70 910 T

y-riNB - 183 16. 00 + 10. 898 40 T

Al um in um sublatti ce: a a~ = t.25

ya al -- 5151 .40 + 9.61 780 T

Polynomial t e r m s b e t w e e n s p e c i e s o n d i f f e re n t s u b l a t t ic e s

Y N b T i y N b N b y A i A I - - 38000.00 + 7.00000 T

Y T i T i y T i N b y A i A I - - 29633. 60 + 6.70801 T

y T i T i Y N b N b y A i A I 34000.00 + 7.00000 T

Y N b T i y T i n b y i I 34000.00- 7 .00000 T

Ti4A13Nb stoichiometric c o m p o u n d )

1 - 48000 0.00 + 180.00000 T

v , = x 2 + 1 - x I - x 2 ) = x 2

t h e e q u a t i o n c a n b e r e w r i t t e n a s

G i = x l G 1 + R T l n x I ) ) + x 2 G 2 + R T l n x 2 ) )

n l t l

~ AjXl x,J

I n o r d e r t o p r o v i d e a t h e r m o d y n a m i c d e s c r i p t i o n o f

a b i n a r y p h a s e w h o s e c o m p o s i t i o n a l s t a b i l i t i e s e x t e n d

i n t o t h e te r n a ry r e g i o n t h e G i b b s e n e r g i e s o f t h e

c o u n t e r p h a s e s i n t h e o t h e r b i n a r i e s n e e d t o b e e s t i -

m a t e d . T h e s e c o m p l i m e n t a r y p h a s e s a r e n o t s t a b l e i n t h e

r e s p e c t i v e b i n a r i es u n d e r o r d i n a r y c o n d i t i o n s . F o r t h e

N b - A I a n d T i - A I s y s t em s t h e G i b b s e n er g ie s o f

f o r m a t i o n o f t h e s t a b l e p h a s e s w e r e u s e d t o e s t i m a t e

t h e G i b b s e n e r g y o f f o r m a t i o n o f t h e h y p o t h e t i c a l

m e t a s t ab l e c o m p o u n d s . T h e p h a s e s in t h e T i - N b

s y s t e m e x h i b i t n o o r d e r i n g t e n d e n c y . T h e r e f o r e t h e

G i b b s e n e r g y o f fo r m a t i o n o f th e o r d e re d c o m p o u n d sw a s s e t t o z e r o f o r t h e T i - N b s y s t e m a n d t h e t o t a l

e x c e s s G i b b s e n e r g y w a s s e t e q u a l t o t h a t o f t h e d i s -

o r d e re d c o m p o u n d s .

I n t h e a n a l y t i c a l d e s c r i p t i o n s o f t h e o r d e r e d i n t e r -

m e t a ll ic c o m p o u n d s o f t h e N b - A I a n d T i - A 1 s y s te m s

t h e n u m b e r o f p a r a m e t e r s i n t h e d e s c r i p t i o n w a s m i n i -

m i z e d b y u s i n g c o n s t r a i n t s f o r t h e d i f f e r e n t G i b b s

e n e r g i e s o f f o r m a t i o n . If i n a n o r d e r e d c o m p o u n d a ll

t h e e l e m e n t s a r e a s s u m e d t o o c c u r o n a ll s u b l a t ti c e s o f

t h is c o m p o u n d t h is c o m p o u n d w i ll ex i st o v e r th e

e n t i r e c o m p o s i t i o n r a n g e . T h e s t r u c t u r e s o f m o s t o f

t h e s e c o m p o u n d s a r e o r d e r e d d e r i v a t iv e s o f t h e s tr u c -

t u r e s o f t h e p u r e e l e m e n t s . F o r c o m p l e t e s u b s t i t u ti o n

i e a t t h e c o m p o s i t i o n o f o n e o f th e p u r e el e m e n t s t h e

d e g r e e o f o r d e r i n g i n t h e s e c o m p o u n d s m u s t b e z e r o

a n d t h e G i b b s e n e rg y o f th e s e c o m p o u n d s m u s t t h en

b e e q u a l t o t h e G i b b s e n e r g y o f t h e p u r e e l e m e n t s o f

t h e c o r r e s p o n d i n g c r y s t a l s t r u c t u r e . T h i s i m p l i e s c o n -

s t r a i n t s f o r t h e G i b b s e n e r g y o f f o r m a t i o n o f t h e s u b -

s t it u t io n a l a t o m s . T h e s a m e c o n s t r a i n t s w e r e a p p l i e d t o

t h e t h e r m o d y n a m i c q u a n t i t i e s o f t h e h y p o t h e t i c a l

m e t a s t a b l e c o m p o u n d s i n th e r e s p e c t i v e b i n a r ie s .

14 U . R . K a t t n e r W . J . B o e t t i n g e r / T e r n a r y T i - A I - N b s y s t e m

B e c a u s e t h e h o m o g e n e i t y r a n g e o f th e t e r n a r y

T i4A13Nb c o m p ou nd i s be l i e ve d t o be sm a l l , th i s pha se

i s m o d e l e d a s s t o i c h i o m e t r i c . T h e s t r u c t u r e o f t h e

o r d e r e d T i 2 A I N b p h a s e c a n b e d e r i v e d t h r o u g h

a d d i t i o n a l o r d e r i n g o f t i t a n i u m a n d n i o b i u m o n t h e

t i t a n ium sub l a t t i c e o f Ti3AI . I t wa s t he r e f o r e m ode le d

a s a so lu t i on pha se w i th t h r e e sub l a t ti c e s t he ti t a n ium ,n iob ium a nd a lum inum sub la t t i c e s ) . T h i s pha se r e ve a l s

a s i gn i fi c a n t r a nge o f hom oge ne i ty w i th r e spe c t t o

t it a n i u m a n d n i o b i u m , b u t t h e r a n g e o f h o m o g e n e i t y

Colculo~ed

Liquidus

~ T [ 2 A I 5

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0N b A t . % AI A I

b ° ~E x p e r i m e r ; to l QV T ~ ~ oL i q u i d u s / ~ :

S u r f o c e 7 k v ~

q ,g( # T i , N b

i 2 A I 5

2 , , , / ' ' . °0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

N b A t . % A I A I

F ig . 2 . Th e l i q u i d u s p r o j e c t i o n c i r cl e s , ma x i m u m ; s q u a r e s , m i n i -

m um ) . a ) Ca lcu la ted . b ) In it ia l ly , a f t e r Pe r epe zko et a l . [6],t h e c o m p o s i t i o n o f l i q u id o f t h e b i n a r y t h r e e - p h a s e e q u i l i b ri u mwa s t a k e n f r o m t h e b i n a r y c a l c u l a t io n s .

wi th r e spe c t t o a lum inum i s sm a l l e r . I t wa s , t he r e f o r e ,

a s s u m e d t h a t n i o b i u m a n d t i t a n iu m a t o m s m i x o n l y o n

the t i t a n ium a nd n iob ium sub l a t t i c e s a nd no m ix ing

o c c u r s o n t h e a l u m i n u m s u b l at ti c e. T h u s , t h e T i z A I N b

c om po un d c om pos i t i o n is c ons t r a ine d t o T i , Nb)3AI.

F o r c o m p l e t e s u b s t i t u t i o n o n e i t h e r t h e t i t a n i u m o r

n i o b i u m s u b la t ti c e, t h e d e g r e e o f o r d e r i n g m u s t a g a inb e z e r o a n d t h e G i b b s e n e r g y o f f o r m a t i o n m u s t t h e n

b e i d e n ti c a l to t h e c o r r e s p o n d i n g b i n a r y T i 3 A 1 a n d

Nb3A1 pha se s w i th t he D0j9 s t r uc tu r e .

No a t t e m pt wa s m a de t o d e ve lop a m i sc ib i l it y ga p i n

the f l0-Ti,Nb) ph ase in ord er to f it the da ta of

P e r e p e z k o e t a l . [ 6 ] . For t he p r e se n t c a l c u l a t i on , t he

s impl i f ica t ion o f t r ea t ing the f l-T i, Nb ) and f l0-Ti, Nb )

a s o n e d i s o r d e r e d p h a s e h a s t h e c o n s e q u e n c e th a t t hi s

m i sc ib il i ty ga p w ould ha ve t o oc c u r i n t he f l- Ti , Nb)

pha se . I n t he t h r e e b ina r y sys t e m s , t he f l -T i ,Nb) pha se

on ly f o r m s a m i sc ib i l it y ga p i n t he T i - N b sys t e m a t a

r e la t iv e l y lo w t e m p e r a t u r e . H o w e v e r , t h e e x p e r i m e n t a lda t a sugge s t t ha t t he t e r n a r y m i sc ib il i ty ga p o c c ur s on

the T i ,A l ) - r i c h s ide o f the sys t e m a t r e l a ti ve ly h igh

t e m p e r a t u r e s . I n o r d e r t o o b t a i n t h e s p e ci fi c c u r v a t u r e

o f t h e G i b b s e n e r g y n e e d e d f o r t h e f o r m a t i o n o f a

m i s c i b i l i t y g a p , t h e n u m b e r o f t e r n a r y p o l y n o m i a l

t e r m s w o u l d h a v e t o b e i n c r e a s e d . C o n s i d e r i n g t h e

s im pl i f i c a t i ons a l r e a dy i n t r oduc e d f o r t he a na ly t i c a l

d e s c r i p t i o n o f t h e f l / f l o - T i , N b ) pha se , i nc r e a s ing t he

n u m b e r o f p o l y n o m i a l t e rm s is n o t j u s t if ie d .

A t t he be g inn ing o f t he c a l c u l a t i on , a t t e m pt s we r e

m a d e t o u s e a l e a st s q u a r e s m e t h o d i n o r d e r t o a d j u s t

t h e G i b b s e n e r g y c o e f f ic i e n ts o f t h e p o l y n o m i a l t e rm s .S i n c e th e a m o u n t o f a v a il a b le d a t a w i t h r e s p e c t t o t h e

nu m be r o f a d jus t a b l e t e r m s i s re l a t ive ly sm a l l a nd m o s t

o f t h e s e d a t a c o v e r o n l y t h e t e m p e r a t u r e i n t e r v a l

b e t w e e n 1 1 0 0 a n d 1 2 0 0 ° C , t h e r e s u lt s o f t h e le a s t

squa r e s f i t t i ng c ou ld on ly be use d a s i n i t i a l va lue s f o r

t r i a l a nd e r r o r c a l c u l a t i ons . I n t he t r i a l a nd e r r o r

m e t h o d t h e v a l u e s o f t h e a d j u s t a b l e p a r a m e t e r s a r e

e s t i m a t e d . T h e c h a n g e o f t h e p h a s e b o u n d a r i e s

be tw e e n two s t e ps o f t he c a l c u l a t i on is use d t o e s t im a te

n e w v a l u e s i n o r d e r t o a d j u s t t h e c a l c u l a t e d p h a s e

b o u n d a r i e s t o t h e e x p e r i m e n t a l r e s u l t s . T h e r e p o r t e d

v a l u es o f t h e a d j u s t a b le p a r a m e t e r s w e r e e s t i m a t e d b y

s u c h a t r ia l a n d e r r o r a p p r o a c h .

5 R es u l t s a nd d i s cus s i o n

T h e t h e r m o d y n a m i c d e s c ri p ti o n o f t h e T i - A I - N b

sys t e m i s g ive n i n T a b le 1 . T h i s de sc r ip t i o n wa s use d t o

c a l c u l a t e t he l i qu idus p r o j e c t i on , s e ve r a l i so the r m a l

se c t i ons a nd a n i sop l e th . T he c a l c u l a t e d l i qu idus p r o -

j e c t i o n i s c o m p a r e d w i t h a p r e l i m i n a r y p r o j e c t i o n

e s t i m a t e d b y P e r e p e z k o e t a L [61 in Fig. 2 . The ca lcu-

l a t e d 1400 °C se c t i on is shown in F ig . 3 . T h e c a l c u l a t e d

U. R . Katmer W. J . Boe t t inger / Ternary T i -A I-N b sys tem 15

C a l c u l a t e d ~ ~ / ~ ~o

( ~ T ] , N b ) ° / x

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 I 8 0 9 0 1 0 0

N b A t . % A t ( T [ , N b b A I 3 A I

Fig. 3. Calculated isothermal section at 1400 °C.

i so the r m a l se c t i ons a t 1200 , 1100 a n d 700 °C a r e c om -

p a r e d w i t h t h e e x p e r i m e n t a l t i e - l i n e a n d p h a s e b o u n -

d a r y d a t a a s s h o w n i n F i g s . 4 - 6 . T h e i s o p l e t h a t 2 5

a t .% AI w i th t he e xp e r im e n ta l da t a i s show n in F ig . 7 .

T h e c a l c u l a t e d a n d t h e e s t i m a t e d e x p e r i m e n t a l

l i qu idus p r o j e c t i ons a s g ive n in F igs . 2 ( a ) a nd 2 ( b) a r e

in qua l i t a t i ve a gr e e m e nt . T he c a l c u l a t i on p r e d i c t s

c or r e c t l y t he pha se s oc c u r r ing in t he i nva r i a n t f our -

pha se e qu i l i b r i a . Howe ve r , t he l i qu idus t e m pe r a tu r e s

p r e d i c t e d b y t h e c a l c u l a t i o n f o r t h e p r i m a r y T i A I

r e g i o n a r e l o w e r t h a n t h e t e m p e r a t u r e s f r o m f i r s t

e xpe r im e n ta l re su l t s [ 6 ]. T h i s ha s a s a c ons e qu e nc e t ha t

t h e t e m p e r a t u r e o f t h e c a l c u l a t e d t h r e e - p h a s e e q u i -

l ib r iu m L + ( a - T i ) + T i A d e c r e as e s w i th i n cr ea s in g

n i o b i u m c o n c e n t r a t i o n w h i l e t h e f i r s t e x p e r i m e n t a l

r e su l t s i nd i c a t e t ha t t he t e m pe r a tu r e i nc r e a se s . A

tern ary eutec t ic (L ~ Nb2A I + (Ti , Nb)A13 + TiA I) i s

p r e d i c t e d f o r t he i nva r i a n t e qu i l i b r ium invo lv ing

L + Nb2A1 + ( Ti ,Nb)A13 + T iA l , bu t t he e xpe r im e nta lr e su l t s i nd i c a t e t ha t i t i s a t r a ns i t i on- type r e a c t i on

( L + ( Ti ,Nb)A13 ~ Nb2AI + T iAI ) . T h e c a l c u l a t i on

g i v e s a m a x i m u m f o r t h e t h r e e - p h a s e e q u i l i b r i u m

L + N b 2 A I + T i A 1 c l o se to t h e e u t e ct ic c o m p o s it io n .

S m a ll c h a n g e s o f G i b b s e n e r g i es o f t h e c o m p o u n d s

invo lve d i n t h i s e qu i l i b r ium c ou ld sh i f t t h i s m a xim um

c l o s e r to o r e v e n b e y o n d t h e e u t e c t i c c o m p o s i t io n . I n

the l a t t e r c a se , t he i nva r i a n t e qu i l ib r ium wo uld t he n be

a t ra n s i t io n t y p e a n d t h e m a x i m u m w o u l d o c c u r i n t h e

m e ta s t a b l e t h r e e - pha se e qu i l i b r ium .

T h e c a l c u l a t e d 1400 °C se c t i on r eve a l s a l a r ge r a nge

of hom o ge n e i ty f o r ( # - T i,Nb) . T h i s i s i n a gr e e m e ntwi th e x pe r im e nta l r e su l t s [ 1 ] , wh ic h i nd i c a t e t ha t t h is

G ° ~o

C a l c u l a t e d ~ . ~ o

oooc /

,,o %7 2 0

O 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

N b A t . % A I ( T i ' N b ) A ] 3 A I

E x p e r i m e n t a l ~ ~ ~ R e f . 21 2 0 0 o c o R e f . 6

I s o t h e r m ~ / ~ 0 R e f . 1 5

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

N b A t . % A I A I

F i g . 4 . I s o t h e r m a l s e c t io n a t 1 2 0 0 ° C . ( a ) C a l c u l a t e d . ( b ) E x p e r i -

m e n t a l data and phase boundaries.

r a n g e o f h o m o g e n e i t y i s e v e n l a rg e r. T h e c a l c u la t e d

a nd e xpe r im e nta l pha se b oun da r i e s a gr e e fa i r ly we l l a t

1200 a nd 1100 °C, whi l e t he c a l c u l a t e d t i e -l i ne d i r e c -

t io n s d e v i a t e f r o m t h o s e e x p e r i m e n t a l ly d e t e r m i n e d .

T h e i n c r e a s e d r a n g e o f h o m o g e n e i t y o b s e r v e d f o r t h e

( T i , N b ) A I 3 p h a s e i n t h e t e r n a r y s y s t e m w a s w e l l

m a t c h e d b y t h e c a l c u la t io n a t 1 2 0 0 °C . In t h e p r e s e n t

c a l c u l a t i o n t h e t e m p e r a t u r e o f t h e b i n a r y e u t e c t o i d(a -T i) --*T i3AI + T iA1 de c r e a se s i n it ia l ly w i th i nc r e a s -

ing n iob ium c onc e n t r a t i on . T h i s r e su l t s i n a n i so l a t e d

t e r n a r y ( a - T i) p h a s e f i e l d b e t w e e n T i 3 A I a n d T i A I .

6 U. R . Ka t tner W. J . Boe t t inger I Ternary T i -A I -N b sys tem

C a l c u l a t e d ~

00oc ¢ \I s o t h e r m ~ . / ~ e

/ / ~ / / / / / / S T i A X ~ T i A , 2

0 1 0 2 0 3 0 4 0 5 0 6 0 ' 7 ' 0 I 8 ' 0 ' 9 ' 0 ' 1 ( } 0

N b A t . % A I ( T i , N b )A I ~ A I

E x p e r i m e n t a t ~ / ~

11 o 7 <

I s o t h e r m ~ . / / \/

~ / / / / /~ ) ' / /

~ ' . / / _ -. / - .. / i ~ i _ ~/ ..~x i~~

. ~ . / , i , I , / , / 1 . . . .

• R e f . 1

a R e f . 4t 3 R e f . 5

. , e R e f . 70 ~ / I

' ~u R e f . 1 6

T i ~ , ~ , o/ " . ' ~ . T i A I 2

' K ~ i 2 A I 5

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

A t . % A I A I

Fig. 5 . I sotherm al sec t ion a t 1100 °C. a) Calcula ted . b) Exp er i -m e n t a l da t a a nd pha s e bounda r i e s .

C u l c u l o t e d

7 0 0 ° C

I s o t h e r m

0 1 0 2 0 3 0 '

T ic ) 0

4 0 5 ' 0 6 ' 0

N b2 AI A t . % A I

f i A I 2

o7 0 8 0 9 0 1 0 0

b A~ ~

E x p e r i m e n t a l ~ / \ ~ ~o o R e f . 5

7 0 0 ° 0 ~ / ~ \ \ \' // ~ a T i ) e R e f . 8

I s o t h e r m ~ / / ~ ' - ' i, . ik ~

dko : / , '~ / . . . . . 1~ . , ~. ~

i . . . . , , , o

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

N b A t . % A I A I

Fig. 6 . I sothermal sec t ion a t 700 °C. a ) Calcula ted . b) Expe r i -m e n t a l da t a a nd pha s e b ounda r i e s .

The ag reemen t be tween the ca l cu l a t ed i so the rmalsect ion a t 700 °C and th e experim ental data i s poor.

The s ing l e -phase reg ion o f t he phase deno ted by

Ti2A1Nb exis ts in the p resent calcula t ion a t an ex ces-

s ively h igh n iobium content and, in fact , does notinclude the s to ichiometric composi t ion of Ti~A1Nb.

Thu s the impo rtant (f l-Ti,Nb) + Ti3AI + Ti2AIN bthree-phase equil ibrium also exists at an excessively

h igh n iob ium con ten t . Wi th t he cu r ren t t he rmo-dynam ic descrip t ion of the (f l-Ti,Nb) phase , th e phase

bou nda ries of the (fl-Ti, Nb )-T i3A l, (fl-Ti, Nb)-Ti2A1Nb

and (f l -Ti ,Nb)-NbaAl equ i l i b r i a have ve ry s imi l a r

s lopes and smal l changes in the Gibbs energy of the

Ti2AINb compound wou ld re su l t i n d i f fe ren t t opo lo -

gies for this section. Further experimental effort is

needed to establ i sh the phase boundaries for th is i so-therm al sect ion .

The process of adjust ing the Gibbs energy coeff i -

c i en ts o f t he po lynomia l t e rms showe d tha t t he phaserela t ionships obta ined from the calcula t ion are

ext remely sensi tive to smal l changes in the G ibbs ener-

gies . S imi lar behavior had been previously observeddur ing the ca l cu l a ti on o f t he T i -A I b ina ry sys t em [14,

19]. T he fact that smal l changes in the G ibbs en ergies

U. R. Kattner, 14/.J. Boett inger / Terna O T i-A I-N b system 17

o oo ~

c z o 2

® Re Ti ,n b) AI s

Ca lcu la ted

f . 6 : o L iqu idus

o • o l i d u s

o~ i [ i i i ~ I 1 1 1 1

- 0 ~0 20 50 40 50 60 70

N b A I 3 M o l e T i A I 3

, i i i ,

80 90 1 O0

TiAI 5

Fig. 7. Calculated isopleth at 25 at. AI and experimental data.Note that this section is quasibinary, except on the TiA13-richside.

p o s i t i o n a l a n d t e m p e r a t u r e r e g i o n s i n o r d e r t o e l u c i -

d a t e t h e p h a s e e q u i l i b r i a o f t h i s t e c h n o l o g i c a l l y

i m p o r t a n t s y s te m .

A c k n o w l e d g m e n t s

T h e a u t h o r s w i s h t o t h a n k D r . H . L . L u k a s o f t h e

M a x - P l a n c k - I n s t i t u t f i i r M e t a l l f o r s c h u n g ( S t u t t g a r t ,

F R G ) f o r p r o v i d i n g t h e s o f t w a r e u s e d i n t h e p r e s e n t

a s s e s s m e n t , P r o f e s s o r J . H . P e r e p e z k o o f t h e U n i v e r s i t y

o f W i s c o n s i n - M a d i s o n f o r h e l p f u l d i s c u s s i o n s a n d P r o -

f e s s o r Y . A . C h a n g o f t h e U n i v e r s i t y o f W i s c o n s i n -

M a d i s o n f o r c r i ti c a ll y r e a d i n g t h e m a n u s c r i p t . T h i s

r e s e a r c h w a s p a r t i a l l y s u p p o r t e d ( W . J . B . ) u n d e r

D A R P A O r d e r 7 4 6 9.

r e s u l t i n d i f f e r e n t p h a s e r e l a t i o n s h i p s m a y n o t o n l y

h e lp t o e x p l a in t h e e x p e r im e n ta l d i f f i c u l t ie s i n d e t e r -

m i n i n g t h e a c c u r a te p h a s e d i a g r a m f o r t h e T i - A I - N b

s y s t e m , b u t a l s o e x p l a in t h e d i f f i c u l ti e s o f o b t a in in g a

s a t is f a ct o r y t h e r m o d y n a m i c d e s c r i p to n f o r t h e p h a s e s

i n t h i s s y st e m . A c h a n g e i n t h e t h e r m o d y n a m i c d e s c r ip -

t i o n o f o n e p h a s e a f f e c t s a ll t h e p h a s e e q u i l i b r i a i n v o lv -

in g t h a t p h a s e . I n t h e t r i a l a n d e r r o r c a l c u l a t i o n i t i s

a d v i sa b l e t o m o d i f y o n l y a f e w p a r a m e t e r s b e t w e e n t w o

s t e p s o f t h e c a l c u l a t i o n i n o r d e r t o c l e a r l y r ec o g n i z e t h e

e f f e c t s o f t h e m o d i f i c a t i o n s o n t h e l o c a t i o n s o f t h e

c a l cu l a te d p h a s e b o u n d a r i es . T o m o d e l t h e w i d e h o m o -

g e n e i t y r a n g e s o f t h e o r d e r e d i n t e r m e t a l l ic c o m p o u n d a

l a rg e n u m b e r o f a d j u s t a b l e p a r a m e t e r s h a d t o b e

i n c l u d e d . T h i s l a r g e n u m b e r o f a d j u s t a b l e p a r a m e t e r s

m a k e s t h e t r i a l a n d e r r o r m e t h o d f o r t h e a d j u s t m e n t o f

t h e s e p a r a m e te r s r e l a t i v e ly i n e f f i c ie n t . A s t r a ig h t -

f o r w a r d m e t h o d o f a d j u s t i n g a l l o f t h e p a r a m e t e r s

s i m u l t a n e o u s l y is th e l e a s t s q u a r e s m e t h o d [ 2 0] . H o w -

e v e r, i n o r d e r t o a p p l y t h i s m e t h o d s u c c e ss f u ll y , m o r e

e x p e r im e n t a l d a t a a r e n e e d e d . T h e s e d a t a a r e n o t o n l y

n e e d e d t o c o n s t r a i n t h e p h a s e b o u n d a r i e s a t c e r t a i n

t e m p e r a t u r e s , b u t e v e n m o r e i m p o r t a n t l y , t o e s t a b l i s h

t h e c h a n g e o f t h e p h a s e b o u n d a r i e s o v e r a la r g e r t e m -

p e r a tu r e i n t e r v a l .

6 . C o n c l u s i o n

T h e c a l c u la t e d p h a s e d i ag r a m s o f t h e T i - A 1 - N b

t e r n a r y s y s t e m s a r e u n d o u b t e d l y s u b j e c t e d t o l a r g e

u n c e r t a i n t i e s o w i n g t o t h e l a c k o f s u f f i c i e n t t h e r m o -

d y n a m i c a n d p h a s e e q u i l i b r i a d a t a t o f ix t h e m o d e l

p a r a m e t e r v a l u e s a n d t h e c o m p l i c a t e d p h a s e r e l a -

t i o n s h i p s . H o w e v e r , t h e y d o p r o v i d e v a l u a b l e a n d

u s e f u l i n f o r m a t i o n f o r a l l o y d e v e l o p m e n t a n d i n d e e ds u g g e s t e x p e r i m e n t s t o b e c a r r i e d o u t i n c r i t i c a l corn

R e f e r e n c e s

I L. A . Bendersky and W. J. Boettinger, Mater, Res. Soc. Symp.

Proc., II (1989)45.2 K. Kaltenbach, S. Gam a, D. G. Pinatti, K. Schulze and E .-Th.

Henig, Z. Metallkd., 80(1989) 535.3 H.T . Kester-Weykam p,C. H. W ard, T. F. Broderick and M. J.

Kaufman, Scr. Metall ., 32 (1989) 1697.4 K. Muraleedharan and D. Banerjee, Metall . Trans . A, 20

(1989) 119.5 L. A. Bend ersky, W. J. Boettinger, B: P. Burton, E S. Bian-

caniello and C. B. Shoem aker, Acta Metal l . Mater . , 38(1990)931.

6 J. H. Perepezko, Y. A. Ch ang, L. E. Seitzman , J. C. Lin, N. R.Bond a, T. A. Jewett and J. C. Mishu rda, in Proc. Symp. High

Temperature Aluminides and lntermetall ics, Indianapolis,ASM /TM S-AIM E, M etals Park, OH, 1990, p. 19.

7 J. H. Perepezko, private commu nication, 1990.8 L. A. Bendersky, W. J. Boettinger and A. Roytburd, Ac t a

Metall . Mater. , 39 ( 1991 ) 1959.9 U.R . Kattner, unpub lished results, 1988.

10 J.L . Murray, Alcoa report, 1987.11 J .L. Murray, Metall . Trans . A, 19(1 988 ) 24.12 L. Kaufman and H. Bernstein, Com puter Cah ulation of

Phase Diagrams, Academic Press, New York, 1 970.13 U.R . Kattne r and H. L. Lukas, unpublished results, 1990.14 U. R. Kattner, J.-C . Lin and Y. A. Ch ang, Metall . Trans. A.,

Feb. (1992) accepted fo r publication.

15 D.T. Hoelzer an d F. Ebrahim i, in E. D. Verink Jr., Processingan d Protect ion of High T emp erature Structural Materials,An nua l Re por t, University of Florida, G ainesville, F L 1990,p. 26.

16 L.A . Benderski, private comm unication, 1991.17 D. Banerjee, A. K. Gogia, T. K. Nandi an d V. A. Joshi, Ac t a

Metall., 36 ( 1988 ) 871.B. Mozer, L. A. Bende rsky, W. J. Boettinger and R. G. Row e,Scr . Metal l. M ater ., 24 (19 90 ) 2363.

18 H. L. Lukas, J. W eiss and E.-Th . Henig, C A L P H A D , 6

(1982) 229.19 J. C. Lin, T. Jewett, J. C. Mishurda, Y. A. Chang and J. H.

Perepezko, Second Annual Report, supported by DARPAthrough ONR contract (0014-86-K-075), 1988.

20 H. L. Lukas, E.-Th. Henig and B. Zimm ermann, C A L P H A D ,1 (1977) 225.

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