Calculation of Valence Electron Structures and Melting Points in ...

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Valence electron structures of various phases in Ti-Al alloys withUs
Valence electron structures of solid solution phases with O, N, Cand H can be calculated using the same procedure based on theaverage crystal lattice model of the EET.10,16 However, it shouldbe indicated in the present paper that because of the lowsolubility of Hs into Ti-Al alloys (also see below), theinterstitial solid solution may be thought as an ideal mixture ofcrystal lattices with and without interstitial impurity atoms.Thus, the present study will mainly focus on the VESs of variouscrystal lattices with Us since the VESs without Ils have been welldocumented before.15 For the calculation of the VESs of variouscrystal lattices with Us, the following issues on the crystallattice with Us should be addressed.
Positions of Us
O, N, C and H should locate in the largest interstitial positionsof every crystal lattice. For alpha-Ti, its crystal structure andmost interstitial positions are A3 and octahedron, respectively;for beta-Ti, they are A2 and tetrahedron respectively; for gamma,they are L^sub 10^ and approximate tetrahedron, respectively; foralpha^sub 2^, they are DO^sub 19^ and approximate octahedronrespectively; and for TiAl^sub 3^, they are DO^sub 22^ andapproximate tetrahedron respectively.
Solubility of Us
Ti-Al alloys are very susceptible to Hs, but it is known from Refs.17-19 that the real solubility of Ti-Al alloys is not more than 2-0mol.-%. Thus, each single crystal lattice can contain only oneinterstitial atom.
Lattice constant of crystal lattice with IIs
Table 1 Valence electron structures of various phases in Ti-AIsystem without IIs*
Here a few remarkable points in the above analysis should bepointed out:
(i) it is assumed that Hs exist in the form of solid solution butnot in compound because the content of IIs in real alloys is verylow
(ii) IIs have no or negligible effects on liquid phase because thereaction between atoms in liquid phase is weaker than that in solidphases, and the variation of bond structures of solid phasesaffected by IIs is essentially different from that of liquid phases
(iii) entropy of crystal increases very largely if a small amountof Hs is dissolved in a crystal.2 However, whether melting orcrystallising is related to liquids phase equilibrium, Hs canweaken the main bonds of solid phases and make a 'nucleating'mechanism operate. This leads to that the effect of Us on theenthalpy of solid phases is similar to that of a 'stressconcentration', and the average or statistical effect of Us onentropy is smaller than that of Us on enthalpy. Thus, it can bebelieved that Us only affect enthalpy and have no effect on theentropy of solid phases
(iv) 'linear revision' of 'average IIs' and real solubility is usedfor simplifying calculations. This approximation may excessivelysimplify the real situation, but as a quantitative estimation it isrational; this has been supported by the following calculatedresults (see below).
Table 2 Valence electron structures of various phases TI-Al systemwith average IIs
Calculations of melting points
Results and discussion
The calculated VESs of various phases in Ti-Al alloys without andwith IIs are listed in Tables 1 and 2. Comparing Table 2 with Table1, one can see that IIs enhance the hybridisation states of Ti andAl atoms, which leads to changes in VES of crystal lattice withIIs. Generally, the strongest bond of crystal lattice with IIs isformed between IIs and metal atoms where the number of covalentelectron is much more than that without IIs, while A', B' and C'bonds formed between Ti and Al atoms are weakened by IIs, and theirnumbers of covalent electrons are decreased. At the same time, thenumber of lattice electrons of a crystal lattice with IIs is alsodecreased very much. From the above results, it can be concludedthat IIs make the bonds stronger in some directions and weaker inothers, implying a quiet anisotropic bonding structure. Because ofthe difference in crystalline and bond structure of the differentphases, the difference in the effects of Us is very large.Generally, original A and B bonds of alpha-Ti and beta-Ti areweakened most dramatically, followed by those of Ti^sub 3^Al andTiAl, whereas those of TiAl^sub 3^ are affected most slightly.Furthermore, if comparing the VESs of solidified alpha-Ti withbeta-Ti as well as ordered Ti^sub 3^Al with TiAl, there is a littledifference in bond structures. However, it is the difference,especially with cooperation with the effects of compositions andtemperature, which results in very seriously anisotropic bondstructures in these phases, which may further affect thecorresponding phase transformations. This is the essential reasonwhy IIs affect phase transformation in Ti-Al alloys, in particular,the melting points (see below).
Table 3 Experimental and calculated phase transformationtemperatures
The calculated melting point and allotropie transformationtemperatures are listed in Table 3. As shown, all the calculatedtransformation temperatures of alloy phases without IIs are higherthan the experimental ones, but the calculated values with IIs aremuch lower than those without IIs. This result is consistent withthe experimental investigation on liqudus curves at hightemperatures and has been theoretically explained well in term ofthe effect of IIs.15 Furthermore, it is seen in Table 3 that thedescendant degree of the melting point is much larger than that ofthe allotropic transformation temperature because of the effect ofIIs. This can also be understood based on the above analysis ofeffect of IIs on VES. As seen in Tables 1 and 2, IIs can weaken themain bonds of all solid phases, including alpha, alpha and gamma.Since different phases are involved in different phasetransformations, changes in main bonds are different. For thecalculation of the melting points, only one solid phase is neededto be taken into account. However, for the calculation of theallotropie transformation, two phases are needed, which leads to acounteraction in the effect of IIs since the main bonds of bothsolid phases are weakened simultaneously. As a result, seemingly,the calculated allotropic transformation temperature is notdecreased very largely. Conclusion
Effects of IIs on VESs and melting points in Ti-Al alloys have beeninvestigated theoretically based on the EET. It is demonstratedthat IIs make atom states increased and VESs considerablyanisotropic. The calculated melting points are basically consistentwith experimental results. Based on the analysis of VES with andwithout Us, the discrepancy of melting points between theoreticaland experimental results can be further interpreted.
Acknowledgement
Project supported by Hunan Provincial Natural Science Foundation ofChina under grant no. 05JJ30078.
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J. Z. Peng*1[dagger], X. Z. Yang2, F. C. Zhou2 and M. F. Gray3
1 College of Physics Science and Information Engineering, JiShouUniversity, JiShou 416000, China
2 Department of Mechamisal Engineering, Changchun University,Changchun, Jilin, China 130022
3 Materials Science and Engineering Department, The Ohio StateUniversity, 650 Ackerman Road, Suite 255, Columbus, OH, 43202, USA
* Corresponding author, email jzhpeng6308@sohu.com
[dagger] see Acknowledgement
Copyright Institute of Materials May 2008
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