Ti-Al-Fe
.pdfA.Kostov / JMM 44 B (2008) 49 - 61 |
59 |
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Table 6. Integral Gibbs energy of mixing and excess Gibbs energy for Ti-Al-Fe ternary system at 2000K
xTi |
xAl |
xFe |
ΔGM |
ΔGE |
xAl |
xFe |
ΔGM |
ΔGE |
Cross |
|
|
|
|
Cross |
|
|
|
section A |
|
|
|
|
section B |
|
|
|
|
|
|
|
|
|
|
|
|
0 |
0.9 |
0.1 |
-9400 |
-3994 |
0.7 |
0.3 |
-19831 |
-9674 |
|
|
|
|
|
|
|
|
|
0.1 |
0.81 |
0.09 |
-15759 |
-5488 |
0.63 |
0.27 |
-25446 |
-10899 |
|
|
|
|
|
|
|
|
|
0.2 |
0.72 |
0.08 |
-19806 |
-7161 |
0.56 |
0.24 |
-28374 |
-11927 |
|
|
|
|
|
|
|
|
|
0.3 |
0.63 |
0.07 |
-22525 |
-8583 |
0.49 |
0.21 |
-29790 |
-12523 |
|
|
|
|
|
|
|
|
|
0.4 |
0.54 |
0.06 |
-23877 |
-9442 |
0.42 |
0.18 |
-29807 |
-12521 |
|
|
|
|
|
|
|
|
|
0.5 |
0.45 |
0.05 |
-23771 |
-9543 |
0.35 |
0.15 |
-28437 |
-11833 |
|
|
|
|
|
|
|
|
|
0.6 |
0.36 |
0.04 |
-22159 |
-8806 |
0.28 |
0.12 |
-25693 |
-10440 |
|
|
|
|
|
|
|
|
|
0.7 |
0.27 |
0.03 |
-19048 |
-7269 |
0.21 |
0.09 |
-21600 |
-8395 |
|
|
|
|
|
|
|
|
|
0.8 |
0.18 |
0.02 |
-14490 |
-5088 |
0.14 |
0.06 |
-16180 |
-5828 |
|
|
|
|
|
|
|
|
|
0.9 |
0.09 |
0.01 |
-8482 |
-2536 |
0.07 |
0.03 |
-9360 |
-2939 |
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
|
|
Cross |
|
|
|
|
Cross |
|
|
|
section C |
|
|
|
|
section D |
|
|
|
|
|
|
|
|
|
|
|
|
0 |
0.5 |
0.5 |
-23454 |
-11928 |
0.3 |
0.7 |
-20515 |
-10358 |
|
|
|
|
|
|
|
|
|
0.1 |
0.45 |
0.45 |
-29127 |
-13348 |
0.27 |
0.63 |
-27146 |
-12599 |
|
|
|
|
|
|
|
|
|
0.2 |
0.4 |
0.4 |
-31811 |
-14269 |
0.24 |
0.56 |
-30504 |
-14057 |
|
|
|
|
|
|
|
|
|
0.3 |
0.35 |
0.35 |
-32815 |
-14590 |
0.21 |
0.49 |
-31990 |
-14722 |
|
|
|
|
|
|
|
|
|
0.4 |
0.3 |
0.3 |
-32355 |
-14248 |
0.18 |
0.42 |
-31885 |
-14599 |
|
|
|
|
|
|
|
|
|
0.5 |
0.25 |
0.25 |
-30514 |
-13225 |
0.15 |
0.35 |
-30319 |
-13715 |
|
|
|
|
|
|
|
|
|
0.6 |
0.2 |
0.2 |
-27341 |
-11540 |
0.12 |
0.28 |
-27364 |
-12111 |
|
|
|
|
|
|
|
|
|
0.7 |
0.15 |
0.15 |
-22869 |
-9254 |
0.09 |
0.21 |
-23053 |
-9848 |
|
|
|
|
|
|
|
|
|
0.8 |
0.1 |
0.1 |
-17093 |
-6468 |
0.06 |
0.14 |
-17360 |
-7008 |
|
|
|
|
|
|
|
|
|
0.9 |
0.05 |
0.05 |
-9880 |
-3322 |
0.03 |
0.07 |
-10108 |
-3687 |
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
|
|
Cross |
|
|
|
|
|
|
|
|
section E |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0 |
0.1 |
0.9 |
-9986 |
-4581 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.1 |
0.09 |
0.81 |
-18693 |
-8423 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.2 |
0.08 |
0.72 |
-23814 |
-11168 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.3 |
0.07 |
0.63 |
-26803 |
-12862 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.4 |
0.06 |
0.54 |
-27988 |
-13554 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.5 |
0.05 |
0.45 |
-27527 |
-13298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.6 |
0.04 |
0.36 |
-25506 |
-12153 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.7 |
0.03 |
0.27 |
-21961 |
-10182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.8 |
0.02 |
0.18 |
-16852 |
-7451 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0.9 |
0.01 |
0.09 |
-9978 |
-4032 |
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
|
|
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Table 7. Integral Gibbs energy of mixing and excess Gibbs energy for Ti-Al-Fe ternary system at 2073K
xTi |
xAl |
xFe |
ΔGM |
ΔGE |
xAl |
xFe |
ΔGM |
ΔGE |
Cross |
|
|
|
|
Cross |
|
|
|
section A |
|
|
|
|
section B |
|
|
|
|
|
|
|
|
|
|
|
|
0 |
0,9 |
0,1 |
-9426 |
-3823 |
0,7 |
0,3 |
-19833 |
-9304 |
|
|
|
|
|
|
|
|
|
0,1 |
0,81 |
0,09 |
-15752 |
-5106 |
0,63 |
0,27 |
-25493 |
-10415 |
|
|
|
|
|
|
|
|
|
0,2 |
0,72 |
0,08 |
-19735 |
-6628 |
0,56 |
0,24 |
-28416 |
-11369 |
|
|
|
|
|
|
|
|
|
0,3 |
0,63 |
0,07 |
-22407 |
-7956 |
0,49 |
0,21 |
-29826 |
-11928 |
|
|
|
|
|
|
|
|
|
0,4 |
0,54 |
0,06 |
-23736 |
-8775 |
0,42 |
0,18 |
-29842 |
-11926 |
|
|
|
|
|
|
|
|
|
0,5 |
0,45 |
0,05 |
-23631 |
-8883 |
0,35 |
0,15 |
-28479 |
-11269 |
|
|
|
|
|
|
|
|
|
0,6 |
0,36 |
0,04 |
-22041 |
-8200 |
0,28 |
0,12 |
-25747 |
-9937 |
|
|
|
|
|
|
|
|
|
0,7 |
0,27 |
0,03 |
-18969 |
-6760 |
0,21 |
0,09 |
-21669 |
-7982 |
|
|
|
|
|
|
|
|
|
0,8 |
0,18 |
0,02 |
-14460 |
-4715 |
0,14 |
0,06 |
-16261 |
-5531 |
|
|
|
|
|
|
|
|
|
0,9 |
0,09 |
0,01 |
-8497 |
-2334 |
0,07 |
0,03 |
-9435 |
-2780 |
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
|
|
Cross |
|
|
|
|
Cross |
|
|
|
section C |
|
|
|
|
section D |
|
|
|
|
|
|
|
|
|
|
|
|
0 |
0,5 |
0,5 |
-23471 |
-11525 |
0,3 |
0,7 |
-20577 |
-10048 |
|
|
|
|
|
|
|
|
|
0,1 |
0,45 |
0,45 |
-29245 |
-12890 |
0,27 |
0,63 |
-27347 |
-12269 |
|
|
|
|
|
|
|
|
|
0,2 |
0,4 |
0,4 |
-31964 |
-13783 |
0,24 |
0,56 |
-30769 |
-13722 |
|
|
|
|
|
|
|
|
|
0,3 |
0,35 |
0,35 |
-32989 |
-14099 |
0,21 |
0,49 |
-32291 |
-14393 |
|
|
|
|
|
|
|
|
|
0,4 |
0,3 |
0,3 |
-32542 |
-13775 |
0,18 |
0,42 |
-32206 |
-14290 |
|
|
|
|
|
|
|
|
|
0,5 |
0,25 |
0,25 |
-30708 |
-12789 |
0,15 |
0,35 |
-30646 |
-13435 |
|
|
|
|
|
|
|
|
|
0,6 |
0,2 |
0,2 |
-27538 |
-11160 |
0,12 |
0,28 |
-27682 |
-11871 |
|
|
|
|
|
|
|
|
|
0,7 |
0,15 |
0,15 |
-23060 |
-8948 |
0,09 |
0,21 |
-23345 |
-9658 |
|
|
|
|
|
|
|
|
|
0,8 |
0,1 |
0,1 |
-17263 |
-6250 |
0,06 |
0,14 |
-17604 |
-6874 |
|
|
|
|
|
|
|
|
|
0,9 |
0,05 |
0,05 |
-10005 |
-3207 |
0,03 |
0,07 |
-10272 |
-3617 |
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
|
|
Cross |
|
|
|
|
|
|
|
|
section E |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0 |
0,1 |
0,9 |
-10064 |
-4461 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,1 |
0,09 |
0,81 |
-18944 |
-8299 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,2 |
0,08 |
0,72 |
-24152 |
-11045 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,3 |
0,07 |
0,63 |
-27193 |
-12743 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,4 |
0,06 |
0,54 |
-28405 |
-13444 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5 |
0,05 |
0,45 |
-27948 |
-13200 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,6 |
0,04 |
0,36 |
-25911 |
-12070 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,7 |
0,03 |
0,27 |
-22325 |
-10116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,8 |
0,02 |
0,18 |
-17150 |
-7405 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0,9 |
0,01 |
0,09 |
-10171 |
-4008 |
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
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60 |
A.Kostov / JMM 44 B (2008) 49 - 61 |
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component’s content increasing. Activity of |
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the three components is increasing per |
Acknowledgements |
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sections from A to E and with the |
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temperature increasing, too and according to |
First author would like to thank the |
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the Raoult’s law. |
Alexander von Humboldt Foundation, Bonn, |
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Values for the integral Gibbs energy of |
Germany, for supporting and sponsoring this |
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mixing and integral excess Gibbs energy of |
research work at the IME Institute for |
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Ti-Al-Fe ternary system at 1873K, 2000K |
Process Metallurgy and Metal Recycling, |
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and 2073K are presented in Tables 5, 6 and 7. |
RWTH Aachen, Germany. |
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The enthalpies of mixing values indicate |
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that the strongest chemical interaction |
References: |
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between the components in the investigated |
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Ti-Al-Fe ternary system exists between |
1.Final Conference COST Action 535 |
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aluminium and iron and the weakest between |
Thermodynamics of Alloyed Aluminides |
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titanium and iron. In the case of investigated |
(THALU), 4th Discussion Meeting on the |
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sections from aluminium corner, these values |
Development of Innovative Iron Aluminum |
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are strongly affected by Ti-Fe binary system. |
Alloys, 21 – 24 October 2007, Interlaken, |
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|
Switzerland. |
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3. Conclusions |
2. A.I.Zaitsev, N.E. Zaitseva, N.E. |
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|
Shimko, |
N.A. Artyunyan, S.F. Dunaev, V.S. |
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The thermodynamic calculations in |
Kraposhin, L. Ha Thanh, J. Phys.: Condens. |
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binary alloys Ti-Al, Ti-Fe and Al-Fe, as well |
Matter., 20 (2008) 114-121. |
|
|
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as ternary Ti-Al-Fe at 1873K, 2000K and |
3. M. Seiersten , unpublished work |
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2073K were determined. All three |
(1989), Available in SSOL2 and BIN |
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investigated binary systems have negative |
database. |
|
|
|
|
values for integral Gibbs mixing energy and |
4. U.R. Kattner, B.P. Burton, Phase |
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integral excess Gibbs energy. Activity values |
Diagrams of Binary Iron Alloys, (Ed.) H. |
||||
of the components are less than unity and |
Okamoto, |
ASM International, Materials |
|||
show negative deviation from the Raoult’s |
Park, OH, (1993) pp. 12-28. |
|
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law. Phase diagrams for the investigated |
5. |
M. |
Seiersten, |
COST |
507, |
binary systems are calculated by the use of |
Thermochemical database for light metal |
||||
Fact Sage. |
alloys, Vol.2, (Ed.) I.Ansara, A.T.Dinsdale, |
||||
Providing in mind that no experimental |
M.H.Rand, (1998), Available in COST2 |
||||
data for these systems have been done or |
database. |
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reported, obtained results presented one |
6. B. Predel, Numerical Data and |
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good base for the further thermodynamic |
Functional Relationships in Science and |
||||
analysis and developing in these group of |
Technology, in Landolt-Börnstein - Group |
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innovative iron aluminum alloys. |
IV Physical Chemistry, Volume 5a, (Ed.) |
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The obtained and shown results for the Ti- |
Springer-Verlag, 2006, ISSN 1615-2018. |
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Al-Fe-based system provide complete |
7. Z.-K. Liu, Y.A.Chang, Metall. Mater. |
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thermodynamic determination optimization |
Trans. A, 30A (1999) 1081-1095. |
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of this investigated system. |
8. O. Ikeda, I. Ohnuma, R. Kainuma, K. |
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A.Kostov / JMM 44 B (2008) 49 - 61 |
61 |
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