The determination of the Ti-rich liquidus and solidus of the Ti-Fe system
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the assumpt=on: cbCC_ eliq P - p the SGTE method
"~& ~ _ _ ~ _ ,
1600 1809
- - -
E 1500 a: 1/.00
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~LLIJ1300
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~- 1200
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11oo 1000
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BCC
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0.10
0.15
/0.193 x
MOLE-FRACTION
O. 276,,
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I
0.2
0.25
0.3
OF IRON
Fig. l --The experimental solubihty points and the calculated solidus and liquidus boundaries wtth and without the assumptionof equal heat capacities of the bcc and liquid utanium. phasefl On the other hand, with higher iron contents liquidus temperatures as well as the activities of titanium are significantly lower, and therefore the contamination will have a smaller influence on the DTA results. In order to evaluate the heat of fusion without the van't Hoff equation, which is not useful herein, we need to know the activity of iron in the liquid and bcc phases. After considering the results of various authors on the activity of iron in liquid titanium, we gave greatest emphasis to those of Wagner and St. Pierre,t~ who demonstrated the regular solution behavior of the liquid alloys. Assuming that the bcc solution is also regular, the value of the parameter L~ ibrTIFe can be evaluated at the melting point of pure iron (1809 K) at which the accuracy of the experimental liquidus is already good. Using the distribution coefficient kFc (1809 K) = 0.390 we obtained the value Lb~ TIFe= --21700
(J/tool)
for the interaction parameter in the bcc phase. This value together with the interaction parameter t~ Ll~q,~,~ = - 4 0 6 0 0
(J/tool)
and the Gibbs energy of the liquid iron 3 Ao,~b~--hq L.IFe = 12040 -- 6.558T - 3.675 • 10-:IT 7 make it possible to calculate the heat of fusion at the melting point of titanium. On the other hand, to obtain the best value for the heat of fusion the heat capacities of the bee and liquid titanium must be taken into consideration. The cp of the bcc phase was given by Kohlhaas et al. u and that of liquid phase was evaluated with the SGTE method.J2 The cr of the hep phase, which is also needed by the method, is that of Cash and Brooks,~3 and the Cp of the liquid phase was taken from Yokokawa and Kleppa. ~4 This evaluation gave the result
A~
(1943 K) = 14680
J/mol
VOLUME 18A, SEPTEMBER 1987-- 1679
which is smaller than the estimated value of 16234 J/mol generally used in the calculation of the Ti-based systems, J5 Using the new value for the heat of fusion and the SGTE method, we obtained the following equation for the stability of the liquid titanium: A~
c-'t~q = 2348 + 43.097T + 1.55 • 10-4T 2 - 5.874T In T - 2.396 • 10-2IT 7
[1] This function was employed in the calculation of the Ti-rich liquidus and solidus boundaries from the melting point of titanium down to metastable congruent point (803 ~ 48 at. pct Fe). The calculated phase boundaries, Figure 1, support well the assumption of the regular solution behavior of both the bcc and liquid phases. Instead, if we make the assumption of equal heat capacities, the calculated phase boundaries deviate strongly from the experimental points, a
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