10.1007@bf03037871(1)
TRANSCRIPT
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A c t iv itie s in L iq u i d F e A I O a n d F e T i O A ll o y s
R . J . F R U E H A N
T h e s o l u b i l i t y a n d a c t i v i t y o f o x y g e n i n F e - A 1 a n d F e - T i m e l t s a t 16 00 ~ w e r e m e a s u r e d . T h e
a c t i v i t y w a s m e a s u r e d e l e c t r o c h e m i c a l l y u s i ng t h e f ol lo w i n g g a l v a n ic c e i l s :
C r - C r 2 O s ( s ) ] T h O 2( Y 2 O a) i F e - A l - _ O ( l ) , A l 2 O s ( s )
C r - C r z O a s ) l T h O z Y a O s ) ] F e - T i - O _ 1 , s a t u r a t e d w i t h o x i d e )
C r - C r 2 O a ( s ) I Z r O 2 ( C a O ) I F e - T i - _ O ( l , s a t u r a t e d w i t h o x i d e )
A l u m i n u m a n d t i ta n i u m d e c r e a s e t h e s o l u b i l i t y of o x y g e n in l i q u i d i r o n t o a m i n i m u m o f 6 p p m
a t 0 . 0 9 w t o c t A 1 a n d 4 0 p p m a t 0 .9 w t p c t T i , r e s p e c t i v e l y . T h e v a l u e o f t h e i n t e r a c t i o n c o e f f i -
c i e n t s ~ A 1 ) a n d s
T
a r e - 4 3 3 a n d - 2 2 2 , r e s p e c t i v e l y . T h e a c t i v i t y c o e f f i c i e n t o f a l u m i n u m a t
i n f i n i t e d i l u t i o n i n l i q u i d i r o n i s 0 . 0 2 1 , w h i l e t h a t o f t i t a n i u m i s 0 . 0 3 8 . T h e v a l u e o f t h e a l u m i -
n u m e q u i l i b r i u m c o n s t a n t , t h e s o l u b i l i t y p r o d u c t a t i n f i n i t e d i l u t i o n , i s 5 . 6 1 0 -*4 a t 1 60 0 ~ T h e
T hO 2 (Y 2 Oa ) e l e c t r o l y t e e x h i b i t e d i n s i g n i f i c a n t e l e c t r o n i c c o n d u c t i v i t y a t 16 0 0~ d o w n t o o x y g e n
p a r t i a l p r e s s u r e s o f 10 -x6 a t m , w h i c h c o r r e s p o n d s t o a b o ut 0 .3 p p m O i n u n a l l o y e d ir o n .
LUMINUMn d t i ta n i u m a r e t he s t r o n g e s t d e o x i d i z -
e r s c o m m o n l y u s e d in s t e e l m a k i n g . D e s p i t e th e e x t e n -
s i v e w o r k d o n e o n t h e a l u m i n u m a n d t i t a n i u m d e o x i d a -
t i on e q u i l i b r i a i n l i q u i d i r o n , t h e r e s t i l l e x i s t s s o m e
u n c e r t a i n t y o n th e e q u i l i b r i u m d a t a .
T h e e a r l y w o r k o f W e n t r u p a n d H i e b e r* i n d i c a t e d
t h a t t h e o x y g e n c o n t e n t i n F e - T i - O a l l o y s a t 1 6 00 ~ i s
a m i n i m u m o f a b o u t 0 . 00 4 w t p c t a t 0 .2 w t p c t T i .
H a d l e y a n d D e r g e 2 d e t e r m i n e d t h e o x y g e n s o l u b i l i t y
a n d i d e n t i f i e d t h e e q u i l i b r i u m o x i d e p h a s e s . T h e y
c o n c l u d e d t h a t o x i d e p h a s e s w e r e l i q u i d F e O - T i O z u p
t o 0 .0 5 p c t T i , T i O 2 c o n t a i n i n g F e O f r o m 0 . 05 t o 1 p c t
T i , T i 2 O s f r o m 1 t o 5 p c t T i , a n d T i O f o r h i g h e r t i t a n i -
u m c o n t e n t s . T h e y fo u n d t h a t t h e o x y g e n s o l u b i l i t y
r e a c h e d a m i n i m u m o f b e t w e e n 0 .0 0 2 a n d 0 .0 0 4 p c t a t
a b o u t 0 . 5 p c t T i a t 1 6 0 0~ C h i n o e t a l . a c a r r i e d o u t a
s i m i l a r i n v e s t i g a t i o n i n w h ic h t h e y i d e n t i f i e d t h e o x i d e
p h a s e t o b e T i a O s f o r a l l o y s c o n t a i n i n g f r o m 0 .0 0 1 t o
0 .2 p c t T i , T i zO a f r o m 0 .2 t o 2 . 0 p c t , a n d T i O a t h i g h e r
c o n c e n t r a t i o n s . T h e y m a d e a fe w o x y g e n s o l u b i l i t y
m e a s u r e m e n t s w h i c h i n d i c a t e t h a t o x y g e n s o l u b i l i t y
m i n i m u m c o u l d b e a s l o w a s 0 . 0 01 w t p c t . T h e r e h a s
n o t b e e n a d i r e c t d e t e r m i n a t i o n o f th e a c t i v i t y of o x y -
g e n o r t i t a n i u m i n l i q u i d F e - T i - O a l l o y s . U s i n g t h e
r e s u l t s o f H a d l e y a n d D e r g e , C h i p m a n 4 h a s m a d e a
r o u g h e s t i m a t e o f t h e a c t i v i t y c o e f f i c i e n t of t i t a n i u m
a t i n f i n i t e d i l u t i o n (7~ a n d o f t h e i n t e r a c t i o n c o e f f i -
c i e n t e ~T ,
e~T i / d lo g fl~ ~ [ I ]
= \
d ( w t p e t T i ) ] N F e _ ~
w h e r e f o i s a c t i v i t y c o e f f i c i e n t of o x y g e n r e l a t i v e t o
t h a t i n p a r e i r o n . H o w e v e r , h is v a l u e s a r e r o u g h e s t i -
m a t e s s i n c e t h e y r e q u i r e d e x t r a p o l a t i o n o f d a t a w i t h
s i g n i f i c a n t s c a t t e r a n d i t w a s n e c e s s a r y t o a s s u m e a
r e g u l a r s o l u t i o n .
G o k c e n a n d C h i p m a n 5 a n d M c L e a n a n d B e l l 8 m e a -
s u r e d t h e h y d r o g e n - w a t e r v a p o r m i x t u r e s i n e q u i l ib -
r i u m w i th F e - A l - O m e l t s i n a l u m i n a c r u c i b l e s a t r e l -
a t i v e l y h i g h t e m p e r a t u r e s ( 16 9 5 ~ t o 1 8 66 ~ T h e a l u -
m i n u m a n d o x y g e n c o n t e n ts o f l i q u i d i r o n i n e q u i l i b -
r i u m w i t h A 12O a w e r e m e a s u r e d b y d ' E n t r e m o n t e t a l . 7
R. J . FRUEHAN is with the E. C. Bain Laboratory for Funda men tal
Research, U. S. Steel Corp. Research Cente r, Mo nroeville, Pa.
Manuscript s ubm itted April 27, 1970.
a t 1 7 4 0 ~ a n d 1 9 1 0 ~ a n d b y S w i s h e r s a t 1 5 8 0 ~ T h e
u n c e r t a i n ty s t i l l e x i s t i n g fo r t he F e - A l - O e q u i l i b r iu m
i s e x e m p l i f i e d b y t h e w id e r a n g e o f e s t i m a t e s f o r t h e
i n t e r a c t i o n c o e f f i c i e n t e (A 1) a t 1 60 0 ~ G o k c e n a n d
C h i p m a n e s t i m a t e d e~A 1) t o b e - 1 2 c o m p a r e d t o t h e
d ' E n t r e m o n t
e t a l .
e s t i m a t e o f - 1 . 0 .
T h r e e o f t h e m a j o r e x p e r i m e n t a l p r o b l e m s i n h e r en t
i n t h e t e c h n i q u e s u s e d i n p r e v i o u s i n v e s t i g a t i o n s o f t h e
F e - A 1 - O s y s t e m w e r e : i ) a t t a i n m e n t of e q u i l i b r i u m
w i t h t h e g a s p h a s e , i i ) g a s s e p a r a t i o n d u e t o t h e r m a l
d i f f u s io n in t h e r e a c t i o n z o n e , an d i i i) t h e e r r o r s i n -
v o l v e d w it h t h e v a c u u m f u s io n t e c h n iq u e f o r d e t e r m i n -
i n g ox y g e n c o n t e n t s w h e n t h e a l l o y c o n t a i n s s i g n i f i c a n t
a m o u n t s o f a l u m i n u m . A s p o i n te d o u t b y d ' E n t r e m o n t
e t a l . , v t h e
v a c u u m f u s i o n t e c h n i q u e i s n o t s u i t a b l e f o r
o x y g en a n a l y s i s a t h i gh a l u m i n u m c o n c e n t r a t i o n s , b e -
c a u s e o f t h e a b s o r p t i o n o f g a s b y t h e a l u m i n u m d i s -
t i l l e d f r o m t h e s a m p l e a n d t h e v a p o r i z a t i o n o f A1 20
w h i ch c o n d e n s e s a t l o w e r t e m p e r a t u r e s .
T h e s e d i f f i c u l t i e s a r e e l i m i n a t e d b y m e a s u r i n g t h e
a c t i v i t y o f o x y g e n i n t h e m e l t e l e c t r o c h e m i c a l l y b y t h e
u s e o f a g a l v a n i c c e l l e m p l o y i n g a s o l i d o x i d e e l e c t r o -
t y t e a nd a n a l y z i n g f o r o x y g e n b y t he n e u t r o n a c t i v a t i o n
t e c h n i q u e .
T h e g a l v a n i c c e l l s u s e d i n t h e p r e s e n t i n v e s t i g a t i o n
c a n b e r e p r e s e n t e d b y
C r - C r ~ O a ( S ) T h O ~ (Y e O s ) I F e - A 1 - O ( / ) , A 1 2 O a( s) [ I]
C r - C r 2 O s ( S ) T h O e( Y 2O s ) L F e - T i - ~ ( / , s a t u r a t e d
w i t h o x i d e ) [ II ]
C r - C r 2 O s ( S ) Z r O 2 ( C aO ) ] F e - T i - O ( l , s a t u r a t e d
w i t h o x i d e ) [ I II ]
T h e r e l a t i o n s h i p b e t w e e n t h e a c t i v i t y o f ox y g e n ao)
w h i c h i s e q u a l t o w e i g h t p e r c e n t i n p u r e i r o n , a n d t h e
e l e c t r o m o t i v e f o r c e (E in m v ) h a s b e e n d e r i v e d p r e -
v i o u s l y a a n d i s g i v e n b y
l o g a o = 4 . 6 2 - 1 3 , 5 8 0 - 1 0 . 0 3 E [ 2 ]
T
F o r a l l o f t h e F e - A 1 a l l o y s i n v e s t i g a t e d , A 1 20 a w a s
t h e e q u i l i b r i u m o x i d e p h a s e ,
i . e .
a b o v e th e a l u m i n u m
c o n c e n t r a t i o n f o r w h i c h h e r c y n i t e ( F e O . A l t O s) i s th e
s t a b l e o x i d e p h a s e . *~ T h e r e f o r e , t h e o v e r - a l l c e l l r e -
a c t i o n c a n b e r e p r e s e n t e d b y
~Cr2Os s) + A - - Cr s) + ~Alz~:)a s) [3]
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The re lat ion shi p betwe en the acti vity of AI(aA1 ) and E
is given by
nF
log aA1 - 2.3 03R T (Eo - E) [4]
where n (= 3) is the nu mbe r of equival ents per mole, F
is the F ara day constant , and Eo is the elec tromo tive
force a cr os s the elec trolyt e for a pure A1-Ai203 melt .
Since the value of E o could not be det ermi ned ex per i-
ment al ly, b ecause ThO2(YaOa) exh ibi ts s ignificant el ec -
t ron ic conduct iv i ty a t the par t i a l p res sur es o f oxygen
in equi l ibr ium with Al20a and pure alumi num, i t was
calcu la ted f rom the known f ree energ ies o f fo rmat ion
of Cr~Oa an d Al2Oa. 11 The val ue of Eo at 1600~ was
calculated to be - 732 mv.
For Fe-Ti -O (ox ide sa tura ted) a l loys con ta in ing
over 5 wt pct Ti , i t i s genera l ly agreed that 720 is the
equi l ib r ium oxide phase so tha t the over-a l l ce l l re-
ac t ion for these a l loys can be represen ted by
Cr2Oa(s) + 72 ~ ~ Cr + 720 [5]
Ther efor e, for al loys cont aining over 5 wt pct Ti the
act iv i ty o f t i t an ium can be ca lcu la ted f rom the e lec t ro-
mot ive force ,
nF (E ~- E) [6]
log aTi - 2.303RT
where n = 2 and E~ is the calcul ated elec tromot ive
force of the ce l l for the Ti (s ) -TiO(s ) sys tem ( -6 74
my) using the free en ergy values compiled by El l iot t
et a l I t
In ca lcu la t ing the ac t iv i t i es o f a luminum and t i t an i -
um in l iquid i ron, the effect of the third component ,
oxygen , can be neg lec ted s ince i t i s p rese n t in smal l
co n cen t r a t i o n s .
In or de r for Eqs. [2], [4], and [6] to be valid, the
elec t ro ly tes mus t exh ib it ins ign i f i can t e lec t ron ic co n-
duct ivi ty under the condi t ions of their use. ZrO~(CaO)
and ThOa(Y2Oa) have pr ev iou sly been de mon str at ed to
exhibi t insigni ficant ele ctro nic conduct ivi ty at 1600~
at oxygen p re ss ur es as low as 3 10 -~3 atm 9 and at
least 2 10-~6 atm, x2 re spe cti vel y.
EXPERIMENTAL
Three types o f ga lvan ic ce l l cons t ruct ion were used
in inves t iga t ing the Fe-A1-O sys tem. One cons i s ted
of a ThO, (7 wt pct Y2Os) tub e, 2 cm OD by 1 cm ID,
closed at one end. The gen era l const ruct i on of the
o ther two types has been descr ibed in deta i l e l se-
whe re, g Brie fly, a ThOu (7 wt pct Y203) pellet, 4 mm
diam by 4 mm high, was seal ed in one end of a s i l ic a
tube or cement ed in one end of an alum ina tube with
h igh-pur i ty a lumina cement . When a s i l i ca tube was
used, the tube was coated with a thin layer of alumina
in order to protect the s i l ica which would otherwise
be redu ced in the melt . For al l three types of cel ls ,
the tubes were packed with a powder mixture of
Cr-Cr2Os, which acted as the reference electrode.
Contact with the C r-C r20 s elect rode was made with
a p la t inum wi re . As d i scussed prev ious ly , the p la t i -
num wire did not reac t s ignific ant ly with the Cr-C r203
elec trode . Contact with the melt was made with a
co m m erc i a l l y av a il ab le m o l y bd en u m ce rm e t co n t a i n -
ing 80 pct Mo and 20 pct AIaO a. I ts constr uct ion has
been descr ibed prev ious ly f l When using the molybde-
num cermet , as constr ucted, there is no need for a
thermoe lect ro mot ive force corr ec t ion and the cerme t
does not dissolve s ig nifican t ly in the mel t .
The ce l l s used in s tudying the Fe- Ti - O sys tem were
es se nti al ly the sa me in that a ZrO2(CaO) or ThO2(Y2Os)
disk was sealed into a s i l ica tube. The only difference
with the cel ls used was that contact with both the
Cr-Cr~Os electrode and the melt was made with a
molybdenum wi re . As d i scussed prev ious l y , a molyb-
denum contact is sat isfactory in s tudies of this typefl
The in i t i a l i ron used was prepar ed by vacuu m-
carbon deoxid iz ing e lec t ro ly t i c i ron ; the main im pur i -
t i es be ing
Si--0.004 wt pct Mn--0.004 wt pct
Cr--0.005 wt pct 0--0. 004 wt pct
Zr--0 .001 wt pct C--0.002 wt pct
The F e-Al mel t s were con ta ined in h igh-pur i ty re-
crys ta l l i ze d a lumina crucib les whi le the F e-T i mel t s
were conta ined in eith er ThO~ or ZrO2 cr uci ble s. ThO2
and ZrO2 crucib l es are su i t ab le con ta ine rs fo r Fe -Ti -
O (oxide satur ated ) melts s ince both ThO2 and ZrOa are
more s table than the oxides of t i tani um, 11 so that there
i s no s ign i f i can t reduct ion of crucib le ma ter ia l . Also ,
ThOu and ZrO2 do not form a liquid oxide solut ion with
the oxides of tita niu m 13 at 1600~ Hadley and Derge 2
repor ted no not iceab le d i f ference in the concent ra t ion
of oxygen at satu rat ion in Fe -T i al loys when the melts
were held in TiO~ MgO, AlcOa, or ZrO2 cr uc ibl es . The
exper imen ts were car r i ed ou t in a ver t i ca l Mo wi re-
wound res i s t anc e furnace which was cont inuous ly
f lushed wi th pur i f i ed argon . The t emper atur e was
measured wi th a Pt -Pt /10 pct Rh thermocouple .
The exper ime nta l p rocedure was ess en t i a l ly the
same as that desc rib ed previ ously, t4 When the tem-
pera t ure reached 1600~ des i red amount o f a luminum
or t i tanium was added to the melt ; after wai t ing a suf-
f i c ien t t ime to ensu re equ i l ib r ium, about th i r ty min-
utes , a cel l was lowered into the tnel t and an emf
read ing t aken . Stab le rever s ib le rea d ings were ob-
ta ined for as long as th i r ty minutes before removing
the cel ls from the melt . In most case s two cel ls were
used and they agree d within 2 my. Ther e was no s ig-
nificant difference in the s table emf r eadi ng when
differe nt types of cel ls wer e used in the same melt .
In the invest i gat ion of Fe-A1-O, the me lts were in
eq uil ibr ium with the A120 s cru cib le. In the case of
Fe- Ti -O , the equ i l ib r ium oxide phase was formed
by the re act io n of the added t i tanium with the oxygen
in the melt . The pre sen ce of an oxide phase was c on-
f i rmed v i sual ly and when necess ary oxygen was added
in the form of i ron oxide.
Af ter sa t i s fac tory emf read ings were ob ta ined ,
samples of the melt were taken by suct ion into a
si l ica tube, 5 mm ID, and quenched in ice water.
Care was taken in the handl ing and the prep ara t ion
of the sampl es f or an alysi s . Only the middle of the
sample was used for analys i s ; a l l of the sample s
used were sound and upon close e xamin at ion showed
no en t rapped ox ide inc lus ions . The sample s were
cleaned by machin ing off the surface , usual ly reduc-
ing the diame ter to about 4 mm. During machini ng
the surface of the sample was kept cool with acetone
in orde r to avoid surfa ce oxidat ion. The samp les were
analyzed for oxygen by neutron act ivat ion with three
or four de terminat ions made on each sample . The
3404-VOLUME 1,DECEMBER 1970 METALLURGICAL TRANSACTIONS
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sampl es were analyzed for a lum inum or t i t an ium
chemic al ly in the usual mann er .
RESULTS AND DISCUSSION
Fe-A1-O
T h e
so lub i l i ty o f oxygen in Fe-Al mel t s in equ i l ib -
ri um with AlaOs at 1600~ is pre se nt ed in Table I and
plot ted in Fig. 1. The solub i l i ty dec rea ses with in-
cre as in g a luminum conten t to a min im um of about 6
ppm at 0.09 pct Al and then inc re ase s ra pidly. Mini-
mum poi nts in oxide sol ubi l i t ies have been found for
sev era l s imi lar sys tems , Fe- Cr- O !~'~S and Fe- V-O. ~6
This behavior is due to the lowering of oxygen act ivi ty
coeff i c ien t wi th incre as ing a lumi num conten t . These
resu l t s are in reasonable ag ree ment wi th the prev ious
resu l t s a t h igher t emp erat ures o f McLean and Bel l , 6
d ' E n t r e m o n t
e t a l . , 7
and Gok cen and Chipman . 5
T h e
only pre viou s work done nea r 1600~ was that of
Swisher. a The resul t s of Swisher appea r to be inco n-
s i s t en t wi th o ther da ta . At re la t i ve ly high a luminu m
conten t s , h i s measu red oxygen content s are lower than
one would expect for the fol lowing rea sons . For al lo ys
con tai ning up to 10 wt pet A1, he r epo rts les s than 10
ppm of oxygen. Even using a value as s mall as - 0 .7
for e (AI), and the e qui l i briu m consta nt
I f ,
co n cen t r a -
tions of oxygen over 300 ppm w ould be ex pected at 5
wt pct A1. If eo(Al) were mor e nega tive , eve n higher
oxygen concentr at ion s would be expected. Also at
T a b l e I . T h e S o l u b i l i t y a n d A c t i v i t y o f O x y g e n i n F e - A I A l l o y s a t 1 6 0 0 ~
Aluminum, Oxygen
wt pct ppm E, mv -log.f~
0.02 10 -102 0.13
0.06 7 - --
0.07 8 -171 0.44
0.09 5 -187 0.34
0.10 7 - -
0.15 8 -212 0.68
0.35 14 -262 1.22
0.85 31 -310 1.89
1.40 48 -351 2.21
*Relative o unalloyed ronwhere fo = 1.0. Cell I used for all measurements.
A l , w t .
0.01 0.05 0.2 0.5 2.0
1 I I I i I I I
d'ENTREMONT et01 (1910~ - 2 0 0
-2.0 \. ~ 100
_o
" \
50 ~:
-5.0
10 o
SWISHER (1580~
- 2
-4. 0 I J I
-2.0 -I.0 0
10g
( a l
%)
Fig. 1--The solubility of oxygen in Fe-A1 melts in equilibrium
with A1203 at 1600~
Fig. 2--Log f0 vs alu-
minum concentrations
in Fe-A1 melts at
1600~
- 1.0
I I I
)
-2.0 -
] I I
0 0.5 1.0 1.5
A1,
w t .
higher Al concen trat ion the oxygen content would be
g rea t e r .
The er ror in Swisher ' s resu l t s i s be l i eved to ar i se
from his method of oxygen anal ysis . As pointed out
previously, the vacuum fusion technique is subject to
s ign i f i can t er r or a t h igh a luminum conten t s , due to
the absorpt io n of gas by the alumi num dist i l led from
the sample and the vaporizat io n of Al20. This would
account for the low oxygen contents at high alum inum
concent ra t ions 9
The activity coefficient of oxygen (fo) (relative to
unal loyed i ron) is shown as a funct ion of alu minu m
conc entra t ion in Fig. 2. The act ivi ty of oxygen was
d e t e rm i n ed d i r ec t l y f rom t he e l ec t ro m o t i v e m ea s u re -
ment . The value of log fo is approxi mately a l inear
funct ion of compos itio n up to 0.3 wi pct Al. However,
at high alu mi num c onc ent rat ion s log )Co is no lon ger a
l in ear funct ion. This is s imi lar to what was found for
Fe- Cr- O, 14 Fe-V -O, le and Fe- Ti -O to be d i scussed
lat er 9 The sl ope up to 0.3 wi pct Al, e(oAI) , is - 3.90 .
As shown by Lupis and Elliott , 17 the v alu e of e~AI) can
be determined from e(oAI).
: in [71
dN A1 NFe~ 1
M o - - MA I
e~A1) = 230 MA1 e (A1) + [8]
MF e o MF e
where M is the atomi c weight. The value of Eg I) is
4 3 3 .
Simi lar express ions were used for de termin ing
e~l and e~ ). Thes e two quan titie s are - 6.59 and - 433,
respect ive ly .
The inter ac tio n coefficie nt e (A1) at 1600~ de te r-
mined in the pre sen t work ( -3 .9 0) i s to be compared
with the previously determined values of Gokcen and
Chipm an s (- 12), McLe an and Bell e (- 4.6), and
d 'E n t r em o n t
e t a l . ? -
1.0). All the value s, exce pt the
presen t one , were ex t rapola ted f rom h igher t empera-
t u r e s .
The early work of Gokcen and Chipman was l imited
to aluminu m conc entr at ion s less than 0.025 wt pct .
The ir value of e (A1) was b ase d on the depe nden ce of
(H20/Hz)[0% ] on alum inum c oncen trat i on. Their value
i s , therefore , on ly a rough es t imate , co ns ider ing
t h e
smal l a luminum concent ra t ion range and the d i f f i cu l -
t ies in analyzing for such quant i t ies of alumin um.
d 'E n t r em o n t e t a l . bas ed the ir valu es of eo At) on the
dependence of the solu bi l i ty product , K' =( pct Al)~
9 (pct O) s, on alu min um concen trat io n and the avai lable
METALLURGICAL TRANSACTIONS VOLUME 1,DECEMBER 1970-3405
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d a t a o n t h e a c t i v i t y o f a l u m i n u m i n F e - A 1 a l l o y s . Is I n
t h e i r c a l c u l a t i o n s t h e y a s s u m e d l o g f 0 t o be a l i n e a r
f u n c t i o n o f w t p c t A 1 o v e r t h e i r 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 r e f o r e , t h e m a j o r r e a s o n f o r th e d i s c r e p -
a n c y b e t w e e n t h e i r w o r k a n d t h e p r e s e n t w o r k i s t h a t
l o g f o i s n o t a l i n e a r f u n c t i o n o f w t p c t A 1 o v e r 0 . 3 w t
p e t . S i n c e m o r e t h a n h a lf o f t h e d ' E n t r e m o n t
et al.
d a t a w e r e t a k e n a t a l u m i n u m c o n c e n t r a t i o n s a b o v e
0 .5 w t p c t , t h e i r v a l u e w i l l be c o n s i d e r a b l y l o w e r t h a n
t h e i n i t i a l v a l u e w h e r e e(oA1) i s r e l a t i v e l y c o n s t a n t . I t
i s n o t e w o r t h y t h a t t h e v a l u e o f l o g f 0 / p c t A1 d e t e r m i n e r
i n t h e p r e s e n t s t u d y a t t h e h i g h e s t a l u m i n u m c o n c e n -
t r a t i o n i n v e s t i g a t e d ( 1 . 4 p c t ) i s a b o u t - 1 . 5 w h i c h i s i n
f a i r a g r e e m e n t w i th d ' E n t r e m o n t et al. H o w e v e r , i n
t h e c o m p o s i t i o n r a n g e o f m a j o r i n t e r e s t (< 0 .3 p c t A 1)
e~A I) i s c o n s t a n t an d e q u a l t o - 3 . 9 0 . T h i s d i s c r e p a n c y
p o i n t s o u t t h e i m p o r t a n t f a c t t h a t t h e v a lu e o f l o g f i i s
a l i n e a r f u n c t i o n o f j w t p c t o n l y i n t h e l i m i t i n g c a s e ,
a s j w t p c t a p p r o a c h e s z e r o . T h e r e f o r e , a n y c a l c u l a -
t i o n d e t e r m i n i n g e z(J) o r u s i n g e~J m u s t b e d o n e i n t h e
c o m p o s i t i o n r a n g e w h e r e i t s v a lu e i s r e l a t i v e l y c o n -
s t a n t .
T h e r e s u l t s o f M c L e a n a n d B e l l e a r e i n e x c e l l e n t
a g r e e m e n t w i t h t h e p r e s e n t v a l u e c o n s i d e r i n g t he e x -
t r a p o l a t i o n o f M c L e a n a n d B e l l ' s d a t a f r o m 1 72 3~
T h e y u s e d o n l y t w o d a t a p o i n t s , o n e a t 1 8 23 ~ a n d t h e
o t h e r a t 1 72 3~ i n d e t e r m i n i n g t h e t e m p e r a t u r e d e -
p e n d e n c e o f e(0Al ) . I n F ig . 5 , e ~ d ) i s p lo t t e d v s l I T
u s i n g b o th s e t s o f d a t a i n d i c a t i n g t h a t th e r e s u l t s a r e
c o n s i s t e n t w i t h th o s e o f M c L e a n a n d B e l l . T h e t e r n -
Table I . The Activity of Aluminum in Fe-AI Alloys at 1600 ~
Relative to Liquid Aluminum)
Electromotive
NAI Force, mv aAl X 103 -lo g 7A I
0.0004 -10 2 0.083 1.68
0.0015 -171 0.294 1.71
0.0018 -18 7 0.398 1.66
0.0032 -21 2 0.645 1.69
0.0072 -2 62 1.550 1.67
0.0173 -3 10 3.630 1.68
0.0293 -35 1 8.310 1,54
Cell I use d for all measurements.
Table III. Thermodynamic Quantities for Fe-AI-O and Fe-Ti-O Alloys at 1600~
Parame ter Fe-A1-O Fe-Ti-O
e~X) -3 ,90 -1 .12
e(O ) -43 3 -22 2
e(x ) -6. 59 -3.75
e(X ) -43 3 -22 2
gtFe.X --2.21 -0 .6
ax_o -1 9 0 -9 6
e(x ) -0 .091 -0 .014
e(x ) -10 -2 .70
7X 0.021 0.038
h(o ) -9 4 kcal/mole -
h(x - 159 kcal/mo le -
- 1.2 I I . I . - . ~ - - ' l '
- 1.4 WILDER E LL I j O TT I
~ - 1 . 6
- I . 8 b ~ " ~
I I I I I
t 0 0 98 096 0 94 092
N z
Fe
F i g . 3 - - L o g Y AI i n F e - A 1 a l l o y s a t 1 6 0 0 ~
p e r a t u r e d e p e n d e n c e o f e(oA I) f o r th e t e m p e r a t u r e r a n g e
1 6 0 0 ~ to 1 8 2 3 ~ i s g iv e n b y
e~A1 = 20, 60 0
T + 7.15 [9]
T h e h e a t - l i k e t e r m k J ) d e t e r m i n e d f r o m t h e t e m p e r -
a t u r e d e p e n d e n c e o f e j ) h a s b e e n d e f i n e d b y L u p i s a n d
E l l io t t z9 a s
de~ )
j -- 2.3 n d [10]
1 / T
l , 0 )
T h e v a l u e s o f ho AI) d e te r m in e d f r o m E q . [ 9 ] a n d r ~Al
a r e p r e s e n t e d i n T a b l e I II .
T h e a c ti v i t y of a lu m i n u m i n F e- A 1 m e l t s d e t e r m i n e d
f r o m m e a s u r e d e l e c t r o m o t i v e f o r c e s i s p r e s e n t e d i n
T a b l e I I . T h e v a l u e o f Io g 7A 1 i s n o t a l i n e a r f u n c t i o n
o f N AI b ut o f N ~ e a s d e m o n s t r a t e d b y B e l t o n a n d
F r u e h a n f l ~ I n F i g . 3 , l o g TA1 i s p l o t t e d v s N ~ e . T h e
v a lu e o f t~Fe A1 , d e f in e d b y D a r k e n 2 t a s
2
l o g Y A1 = O t F e A 1 N F e + I [11]
c o u ld n ot be d e t e r m i n e d b e c a u s e o f t h e s m a l l c o m p o s i -
t i o n r a n g e i n v e s t i g a t e d . T h e v a l u e o f CrFeA 1 = - - 2 . 2 1
d e t e r m i n e d f r o m t h e w o r k o f B e l t o n a n d F r u e h a n i s
u s e d i n d r a w i n g t h e l i n e in F i g . 3 fo r t h e p r e s e n t w o r k .
T h e v a l u e s e s t i m a t e d b y W i l d e r a n d E l l i o t t za a r e a l s o
g i v e n i n F ig . 3 f o r c o m p a r i s o n .
F o r t h e s m a l l a l u m i n u m c o n c e n t r a t i o n i n v o l v e d i n
a l u m i n u m d e o x i d a t i o n of s t e e l , t h e i n t e r a c t i o n c o e f f i -
c i e n t t e r m i n o l o g y m a y b e u s e d a s a n a p p r o x i m a t i o n
e v e n t h o u g h l o g Y A 1 i s n o t a s t r i c t l y l i n e a r f u n c t i o n o f
NA1 . T h e v a lu e s o f e(A1 ) a n d c ~ ) c a lc u l a t e d f r o m th e
v a l u e o f Cg FeA 1 d e t e r m i n e d b y B e l t o n a n d F r u e h a n a r e
0 .0 91 a n d - 1 0 , r e s p e c t i v e l y . I t s h o u l d b e e m p h a -
s i z e d t h a t t h e s e v a l u e s a r e v a l i d o n l y f o r s m a l l c o n -
c e n t r a t i o n s o f a l u m i n u m s i n c e th e F e - A 1 s y s t e m i s
b e s t r e p r e s e n t e d b y t h e q u a d r a t i c f o r m a l i s m . D a r k e n 22
h a s a l s o d e f in e d q u a d r a t i c f o r m a l i s m c o n s t a n t s f o r
t e r n a r y a l l o y s . T h e c o n s t a n t a A l O d e f i n e d b y Eq . [ 1 2] ,
w h i c h i s v a l i d a t i n f i n i t e d i l u t i o n , i s e q u a l t o - 1 9 0
s (A1) = 2 .30 3 (a A i O -- OtFeO -- aFeA1 ) [12]
T h e v a l u e s o f t h e v a r i o u s p a r a m e t e r s f o r F e - A 1 - O
s y s t e m a t 1 60 0~ a r e s u m m a r i z e d i n T a b l e II I.
T h e a c t i v i t y of a l u m i n u m i n F e -A 1 a l l o y s d e t e r m i n e d
f r o m t h e e l e c t r o m o t i v e f o r c e s i s in g oo d a g r e e m e n t
w i t h t h e p r e v i o u s m a s s s p e c t r o m e t r i c w o r k of B e l t o n
F r u e h a n . T h e s m a l l d i f f e r e n c e i n th e v a l u e s o f l o g yoA1
3 4 0 6 - V O L U M E I , D E C E M B E R 1 9 70 M E T A L L U R G I C A L T R A N S A C T I O N S
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= - 1 . 6 8 in t h e p r e s e n t w o r k c o m p a r e d t o - 1 .6 2 d e t e r -
m i n e d p r e v i o u s l y m a y b e a t t r i b u t e d t o t h e u n c e r t a i n -
t i e s i n t h e f r e e e n e r g i e s o f f o r m a t i o n f o r C r a O 3 a n d
A l a O a . T h e d i f f e r e n c e o f 0 . 0 6 i n l o g ~2A I c o r r e s p o n d s
t o a b o u t 5 0 0 c a l u n c e r t a i n t y f o r t h e o v e r - a l l c e l l R e -
a c t i o n [ 3] . T h i s i s w e l l w i t h i n t h e u n c e r t a i n t i e s i n f r e e
e n e r g i e s o f f o r m a t i o n o f A l a O s a n d C r a O s .
T h e e q u i l i b r i u m c o n s t a n t ,
K ,
a t 1 6 0 0 ~ f o r t h e a l u -
m i n u m d e o x i d a t i o n r e a c t i o n i n l i q u i d i r o n d e t e r m i n e d
f r o m t h e d a t a i n T a b l e I i s 5 . 6 1 0 - t4
2 A 1 ( 1 w t p e t ) + 3 0 ( 1 w t p c t ) = A l a O s ( s ) [ 1 3 ]
3
K = a o a A 1
T h i s v a l u e i s i n r e a s o n a b l e a g r e e m e n t w i t h p r e v i o u s
d e t e r m i n a t i o n s a s d e m o n s t r a t e d i n F i g . 4 . D e s p i t e
s o m e o f t h e i n c o n s i s t e n c i e s i n S w i s h e r ' s a d a t a , a
r e a s o n a b l e e s t i m a t e i s m a d e b y e x t r a p o l a t i n g l o g K '
t o z e r o a l u m i n u m c o n c e n t r a t i o n . T h e l i n e d r a w n i n
F i g . 4 i s c a l c u l a t e d u s i n g t h e f o l l o w i n g t h e r m o d y n a m i c
d a t a :
2 A l ( / )
+ { 02 g)= A h O s
A iF ~ = - - 4 0 1 , 5 0 0 + 7 6 . 9 1 T ( R e f . 1 1 )
O u ( g ) = O ( 1 w t p c t i n F e )
A F ~ = - 2 8 , 0 0 0 - 0 . 6 9 T ( R e f . 1 1 )
A l ( l ) = A 1 (1 w t p c t i n F e )
A F ~ = - 2 7 , 6 0 0 ( a t 1 6 0 0 ~ ( R e f . 2 0 )
5 H ~ = - - 1 5 , 1 0 0 ( a t 1 6 0 0 ~ ( R e f . 2 3 )
A i F ~ = - 1 5 , 1 0 0 - 6 . 6 7 T
T h e f r e e e n e r g y c h a n g e f o r R e a c t i o n [ 13 ] i s , t h e r e f o r e ,
g i v e n b y
A iF ~ = - 2 8 7 , 3 0 0 + 9 2 . 3 2 T [ 1 5 ]
a n d l o g K b y
l o g K = - 6 2 , 7 8 0 / T + 2 0 . 1 7 [ 1 6 ]
A g r e e m e n t o f t h e p r e s e n t w o r k a n d th e p r e v i o u s l y d e -
t e r m i n e d v a l u e s a t t h e l o w e r t e m p e r a t u r e s , l e s s t h a n
1 8 0 0 ~ w i t h t h e c a l c u l a t e d l i n e i s e x c e l l e n t . T h i s
a g r e e m e n t s u p p o r t s b o t h t h e d e t e r m i n a t i o n o f K a n d
t h e v a l u e s u s e d i n c a l c u l a t i n g t h e f r e e e n e r g y o f s o l u -
t i o n o f a l u m i n u m i n F e - A 1 a l l o y s , i . e . t h e f r e e e n e r g y
1900~ 1800"C 170(PC 1600%
-9 I I I I
- I 0 - 9 [ ]
- I I - 9 9
-
13 9 d'ENTREMONTet 01
\
9 McLEAN
BELL
~ ~ ~
I
Cl
GOCKCEN8 CHIPMAN ~ _J
- 14
0 PRESENTSTUDY ~ |
c - ~ 1 7 6 q
44 46 48 50 52 54 56
l i T
x IO
F i g . 4 - - L o g
K
v s 1 / T
K =
a ~ a ~ .
o f s o l u t i o n o f 1 w t p e t A 1 a t 1 6 0 0 ~ 2~ a n d t h e p a r t i a l
m o l a r h e a t o f s o l u t i o n o f a l u m i n u m f l s
A t t e m p t s to m e a s u r e e l e c t r o m o t i v e f o r c e s f o r m e l t s
c o n t a i n i n g m o r e t h a n a b o u t 1 . 4 w t p e t A 1 f a i l e d . T h i s
i s a t t r i b u t e d t o t h e p a r t i a l e l e c t r o n i c c o n d u c t i v i t y i n
t h e T h O a ( Y a O s ) e l e c t r o l y t e a t l o w o x y g e n p r e s s u r e s . I n
m e l t s c o n t a i n i n g m o r e t h a n 1 . 4 w t p c t A 1 , t h e m e a s u r e d
e l e c t r o m o t i v e f o r c e s c o n t i n u o u s l y d e c r e a s e d . T h e d r o p
i n t h e e l e c t r o m o t i v e f o r c e m a y h a v e b e e n d u e to t h e
p o l a r i z a t i o n o f t h e C r - C r a O s e l e c t r o d e c a u s e d b y t h e
o p e n c i r c u i t m a s s t r a n s f e r a c c o m p a n y i n g e l e c t r o n i c
c o n d u c t i v i t y . A t t e m p t s t o d e p o l a r i z e t h e e l e c t r o d e b y
p a s s i n g a r e v e r s e c u r r e n t w e r e u n s u c c e s s f u l . A f t e r
p a s s i n g t h e r e v e r s e c u r r e n t , t h e e l e c t r o m o t i v e f o r c e
- 3 . 0
- 4 . 0
1800"C 1700~ 1600"C
I I I
9 McLEAN 8 BELL
o PRESEN T STUDY
1 I I 1 I J
8 50 52
I / T x I 0 ~
F i g . 5 - - e ~ A I) i n l i q u i d i r o n v s
1 / T .
I
54
T a b l e I V . T h e S o l u b i l i t y a n d A c t i v i t y C o e f f i c ie n t o f O x y g e n i n F e - T i
A l l o y s a t 1 6 0 0 ~
Titanium,
vet pct Oxygen, wt pct E, mv -log fo
(Th02 Crucibles)
0.020 0.0099 108 (111)
0.21 0.0070 78 (III)
0.50 0.0051 -6 0 (II)
0.90 0.0044 -78 (1I)
(ZrO2 Crucibles)
0.010 0.0277 -
0.015 0.0207 -
0.022 0.0106 127 (III)
O. 10 0.0086 74 (III)
0.10 0.0077 72 (Ill ,
0.11 0.0086 50 (IIl,
0.30 0.0046 -25 (I1)
0 .32 0 .0033 -45 ( I | )
0.37 0.0040 -4 3 (II)
0.45 0.0045 -5 8 (11)
0.50 0.0051 -6 0 (11)
0.91 0.0040 -9 7 (11)
1.38 0.0042 -13 0 (II)
1.40 0.0050 -15 7 (11)
1.80 0.0073 -160 (II)
2.50 0.0098 -166 (II)
5.70 0.0150 -21 0 (I1)
7.70 0.0207 -245 (II)
11.0 0.0278 -268 (I1)
12.5 0.0401 -285 (II)
i t )
i i )
0.05
0.07
0.66
0.70
0.03
0.17
0.15
0.30
0.38
0.40
0.45
0.59
0.66
0.78
0.96
1.17
1 . 3 6
1.52
1 . 9 2
2.27
2.47
2.77
( ) indicates cell used.
M E T A L L U R G I C A L T R A N S A C T I O N S V O LU M E I , D E C E M B E R 1 9 7 0 - 3 4 0 7
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- I . 0
T i , w t . %
0 . 01 0 . 1 I I 0
I I I I
I 0 0 0
~. -2.0
-3.0
500
z
I 0 0 ~=
5 0
20
t ] t t 1 0
2 . 0 1 .0 0 1 . 0
10g(wt.% Ti)
Fig. 6--Solubility of oxygen in Fe-Ti alloys at 1600~
T a b l e V . T h e A c t i v i t y o f T i t a n i u m i n L i q u i d F e - T i A l l o y s a t 1 6 0 0 ~
( R e l a t i v e to S o l i d T i t a n i u m )
N, i E, mv aTi X 10~ -log fTi
0.066 -210 3.16 1.33
0.089 -245 4.37 1.30
0.126 -268 6.60 1.28
0.143 -285 8.13 1.25
would dec rea se immed iat ely, a t a ra te of about 0.5
my per sec . The apparent l imi t i ng oxygen press ure
at 1600~ for which ThO2(YzOs) beh ave s as a pr ed om i-
nantly ionic condu ctor is about 1.0 10 ~a atm, cor re-
sponding to about 0.3 ppm oxygen in unalloyed iron.
F e - T i - O
The solubi l i ty of oxygen in Fe-Ti a l loys equi l ibra ted
with a t i tani um oxide phase at 1600~ is pre sen ted in
Table IV and plotted in Fig. 6. The solubili ty is a min -
imum of about 0.004 wt pct a t 0.9 wt pct Ti. These re -
su l t s a re in fa i r agreem ent wi th those of Wentrup and
Hiebe r 1 and Hadley and De rge. z The solu bili t ies re-
po rt ed by Chino e t al. , s < 0.001 wt pct O at 0.1 pct Ti,
a re s igni f icant ly lower than those measu red in the
p r e se n t wor k .
In Fig. 7, log fo is plotted vs wt pct Ti. Log fo is
not a l in ear function of t i tan ium cont ent over the en-
tire compo siti on range studied. The value of e (Ti) a t
inf inite dilution is - 1.12. The corr espo ndin g value of
(Ti) is -- 222.
Eo
For alloys containing over 5 at . pct Ti, the activity
of t i tan ium is calcul ated using Eq. [6], and the resu lts
a re pre sent ed in Table V. In orde r to es t imate the
va lue of ~Ti , the exper imenta l r e sul ts a re p lo t ted in
Fig. 8 in acco rdan ce with Dark en' s ~I quadrati c f orm al -
ism. The composi t ion range of th is inves t iga t ion is too
smal l to te s t the va l id i ty of the quadra t ic fo rmal i sm
for th is sy s tem. However , the resul ts g ive a fa i r l in-
ear re la tio nshi p with C~FeTi equal to approx imat ely
--0.6. Extrap olati ng back to inf inite dilution of t i t ani-
um, the val ue of ~2Ti is 0.038 r el at iv e to solid ti tan ium.
The value of ~TiO calculated, using an equivalent ex-
pre ssi on to Eq. [12] , is - 96. The values of the var i-
ous pa ram ete r s desc r ib ing the the rmody namics of the
Fe-Ti -O sys tem at 1600~ a re summar ized in Table
IH.
The va lue s of the co Ti} (- 222) and ~Ti (0.033) de te r-
mined in the present work a re not in good agreement
I I I I [ I
-I.0
,o
-2.0
O
-3 .0 I I I I I I
0 2 . 0 4 . 0 6 . 0 8 . 0 I 0 . 0 12.0
T i , w t .
Fig. 7--Effect of titanium on the activity coefficient of oxygen
in liquid iron at 1600~
o
P.4
- I . 2
- I . 5
- I . 4
N T i
0 0.1 0.2
I I
J
j
m ~ j s
J
s
J
- I . 5 I I
1 . 0 0 . 8 0 . 6
N 2
F e
Fig. 8--Log TTi (solid referen ce) in Fe- Ti all oys at 1600~
with those estimated by Chipman, s Ti) = - 37 and ~Ti
= 0 .011. However , Chipman 's va lues wer e only es t i -
mated f rom the resul ts of Hadley and Derge s ince the
a c t iv i t i es we r e no t m e a su r e d d i r e c t l y . C ons ide r ing
the assumpt ions which were nece ssa r y for Chipman
(Ti) . this disagreement is under-
o cal cul at e ~2Ti and c o ,
standable .
GENERAL DISCUSSION OF Fe- X-O SYSTEMS
The author has determined the solubili ty of oxygen
and the activ it i es for the Fe- Cr- O, .4 Fe-V- O, 16
Fe-B-O , 18 Fe-AI -O, and Fe-Ti -O sy s tem s. Cer ta in
c ha r a c t e r i s t i c s a nd t r e nds f o r t he se sy s t e m s a r e d i s -
cussed below.
In Fig. 9, log Yo/~ is plotted vs atom fraction of
a l loying e lemen t (Nx) . As N x approach es ze ro , the
f i r s t order in te rac t i on coef f ic ient E~ ) appears to be
a reasonable repres enta t ion of the exper i menta l r e -
su l t s . However , in a l l the sys t ems inves t iga t ed the re
is eventua l ly a marked devia t ion f rom the s imple l in-
ear behavi or . Lupis and Ell iott 24 have i ntroduce d gen -
e r a l i z e d in t e r a c t ion c oe f fi c i e n ts i nc o r po r a t ing h igher
te rms . For the so lu t ions under d iscuss ion , N o ap-
proaching ze r o , the ac t iv i ty coef f ic ient can be repre -
sented by
3408-VOLUME I,DECEMBER 1970 METALLURGICAL TRANSACTIONS
-
7/26/2019 10.1007@BF03037871(1)
7/8
In o : C o < X > + p F > + . . . I t ]
In gener a l the use of a second order in te rac t ion coef f i -
c ient pcX) along with r (X) does not adequa tely r ep re -
sent the exper imenta l cu rves in F ig. 9 . In genera l ,
t h r e e o r e ve n m or e t e r m s a r e ne c e s sa r y t o de sc r ibe
the resul ts . The use of h igher in te rac t i on pa ram ete rs
is not pa r t icu l a r ly use ful s ince the da ta a re bes t de -
sc r ibed by the exper imenta l curves in F ig . 9 and
higher order te rms do not y ie ld any informat ion con-
cerni ng the nature of the solution. The only useful ob-
se rva t i on which can be made f rom the h igher te rms is
tha t for a l l the sys tems inves t iga ted pcX) is positive,
i e
a pos i t i ve c u r va tu r e .
In Table VI the val ues of r (X) are lis ted along with
AFx2os /3 ; the oxi de X2Os was chos en si nce it is the
only oxide phase which exis ts for a l l the a l loying e le -
ments cons ider ed here. As shown in Fig. 10, the mag -
ni tude of c~ ) i nc reas es wi th inc reas ing va lue of
- AFx2 03/3 . However , there does not appear to be any
predic table re la t ionship be tween these quant i t ie s . Sev-
e ra l so lu t ion mode ls have been proposed to predic t the
value of EoX) from the behavior of the binary solutions
or stab il i ty of the oxide phases.ZS'ze None of these mod -
e l s p r e d i c t s c~) with suf f ic ient accuracy for a l l the
sys tems s tudied .
Although there is no dir ect re lat ions hip b etween c o
[
I I I
- 0 . 5
I .0
~ I . 5
2 . 5
oi, o 2 0 3 0 : 4
ATOM FRACTION Cr,V, B, Ti or AI )
Fig. 9--Effect of Cr, V, B, Ti, and AI on the activity coeffi-
cient of oxygen in liqui d Fe-X -O alloys.
T a b l e V I . F e - X - O S o l u t i o n s a t 1 6 0 0 ~
, ~ o
Calculated
Alloying AFX203/3 Quasichemical
Elements kcal/mole O*, ppm N~ Experimental z = 2 z = 8
A1 -85.8 6 0.002 -433 -257 -18
Ti -81.6 40 0.01 -222 -186 -17
B -66.2 80 0.03 to 0.05 -115 -35 -8.6
V -62.0 180 0.03 -29.0 -25 -3.6
Cr -51.9 270 0.07 -8.0 -17 -2.5
O minimum oxygen content.
N - atom fraction of alloyingelement at oxygen solubility minimum.
5 0 0
4 0 0
30O
A
a