Scripta METALLURGICA et MATERIALIA
24, pp. 2019-2022, 1990 Printed in the U.S.A.
Pergamon Press plc All rights reserved
BEHAVIOUR OF TiAI INTERMETALLIC
T.K.Nandy, D.BanerJee and A.K.Gogia Defence Metallurgical Research Laboratory Hyderabad - 500 258, India. (Received June (Revised August
I, 1990) 14, 1990)
Introduction The deformation of ordered alloys may be strongly influenced by alloying additions through their effect on both the anisotropy of electron charge density (1-3) as well as antiphase boundary energy (4). In order to assess alloying effects, it is therefore important to know the specific site occupancy of the additive. Ochiai et al (5) have developed a simple Bragg-Williams model to theoretically evaluate site preferences in Ni~AI and we have subsequently adopted this model to examine site occupance in b~th the ~ ( T i ~ A I ) and ~(B2) phases of TidAl - X alloys where X is a ~ stabillsing add~tio~ (6). This ~aper deals with t~e application of the thermodynamic model to the TiAI (~) phase. Substantial work has recently been published on the effect of ternary additions on the ductility of this phase(7). Thermodynamic The structure follows:
for assessing site occupancy in TiAI which has is derived on the basis of the work by Ochiai et al
an L1 (5) a~
An LI^ crystal with N atoms contain N/2 atoms of each A and B. Consider NXc atoms of Va ternary element C substituting for A atoms. The n u m b e r of nearest neighbour bonds of each kind (NAA , NBB etc.) are NAA
NCC = 4NX C
NAB = 4N(I-2Xc) NAC = 4NXc(I-2Xc) NBC = 8NX C Thus ~otal bond energy when C replaces A atoms is H_ ~. = N(I-2X~)2H. NHBB + 4NXc-Hcc + 4N(I-2X C) HAB + 4NXc(I-2X c) HAC + 8NXcHBc ..... (I) ~ Similarly when C replaces H_ ._
4N(I-2X C )
where H~a, Hn~ are respective by the fb~low~Mg expression
Now the site preference
2019 0036-9748/90 $3.00 + .00 Copyright (c) 1990 Pergamon Press plc
24, No. I0
(dHc_~B / dX C) Xc-->0 < (dHc_~A / dX C) Xc-->0 .... (3) CQmbining i, 2 & 3, we obtain VAC / VAB > VBC / VAB - P ..... (4) where V is the interchange parameter, that is, VAB = H._ - (H.. + HBB)/2 and P 3/2 (H - H..) / V.~. The ratio of interchange parameters ~ equation 4 are obtaine~Aas follows: ~= ZIH_ B = 4NV~n (for X r = 0 in equation I) where f HA - is the enthalpy formatio~ for the ZfftermetaIlic AB. Similarly,~HAc = 4NVAc,mand therefore VAC / VAB = ~ HAC / ZIHAB ..... (5)
The R.H.S. of this equation may be obtained from Miedema's semi-empirical approach (8). Fig.l shows a two dimensional map of Vac / VAn against V / V for different ternary elements. From equation 4, a straight line with aB~lope ~ unity may be drawn to separate these elements into two regions one (below the line) containing elements occupying A sites and the other (above the line) containing elements occupying B sites. The elements lying close to the straight line substitute randomly. The position of the straight line depends upon the value of the intercept P. P cannot be calculated since it contains interaction parameters like HA., H_ B which cannot be obtained from Miedema's approach. However, informatio~ fro~ the ternary phase diagrams may be utilised to locate the position of the line as described below: Site Substitution Behaviour Fig.2 shows three types of solubility lobes for the phase present in ternary Ti-AI-X phase diagrams. Elements exhibiting a Type-I solubility lobe substitute for Ti sites as, for example, V (9,10). Elements exhibiting a Type-II lobe substitute for A1 sites are, for example, Sn (ii) and Ag(12). The elements wfth Type-Ill lobes substitute randomly as, for example, Mo(II). Finally, Nb has been shown to substitute for Ti by a direct experimental technique (13). A straight line can therefore be drawn through Mo different atoms according to their substitution behaviour.
Thus a thermodynamical approach coupled with the information from the ternary phase diagrams has been evolved to predict the site substitution behaviour in TiAI. The tetragonality of the structure which would mean different nearest neighbour bond lengths and hence energies, has not been taken into consideration. The limitation of this particular model is in its inability to predict the extent of solubility. Acknowledgements The authors this work~
are grateful to Dr.P.Rama Rao for his permission
References l.B.F.Greenberg, V.I.Anisimov, Yu.N.Gornostirev, G.G.Taluts, Scripta Metall., 22, 859 (1988). 2.S.---A°Court, J.P.A.Lofvander, M.H.Loretto and H.L.Fraser, unpublished research (1989). 3.M.Morinaga, J.saito, N.Yukawa and H.Adachi, Acta Metall., 38, 25 (1990). 4.V.Paider, Acta Metal1., 33, 1803 (1985). 5.S.Ochiai, Y.Oya and T.Suzuki, Acta. Metall., ~, 289 (1984). 6.T.K.Nandy, D.Banerjee and A.K.Gogia, Sixth World Conference on Titanium, Cannes, June 6-9, 1988, Eds. P.Lacombe, R.Tricot, Y.Be'ranger, p.943-948. 7.Young-Won Kim, JOM, 41, 24 (1989) 8.A.R.Miedema and P.~.duChatel, ~Theory of Alloy Phase Formation", Ed. L.H.Bennet, TMS-AIME (1980), p.344-387.
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9.Kenki Hashimoto, Haruo Doi and Tokuzou Tsuzimoto, Trans. JIM, 27, 741 (1986). 10.S.C.Huang and E.L.HaI1, 'High Temperature Aluminides and Intermetallics', Eds. C.T.Liu et. al., TMS-AIME, Indianapolis (1989), in press. ll.E.K.Molchanova, Phase Diagram of Titanium Alloys, Ed.S.Y.G1azunov, Israel Programme for Scientific Translations, Jerusalem, 1965. 12.Kenki Hashimoto, Haruo Doi & Tokuzou Tsujimoto, Trans. JIM, 27, 194 (1986}. 13.D.G.Konitzer, I.P.Jones and H.L.Fraser, Scripta Met., 20, 265 (1986).
A V__ .CC
C]Ni / oC0 / c]Cu r - ] F e / /
VAB1 "Ag .
,'~ TYPE I
o ~',',, • • olNFORMATION FROMTERNARYPHASE DIAGRAMS
Ay VB[ VAB
Te~L of equation (4J for /he md~tit.ution behuviour of TiAI
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Fig.2 Schematic illustration o f the $olubili£y lobes in TiAl phase