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On the structure of the Ti3Al phase in Ti–Al and Ti–Al–Nb alloys
Journal of Alloys and Compounds 394 (2005) 181–185
On the structure of the Ti3Al phase in Ti–Al and Ti–Al–Nb alloys S. Banumathy, P. Ghosal, A.K. Singh∗ Defence Metallurgical Research Laboratory, Kanchanbagh P.O., Hyderabad 500058, India Received 8 June 2004; received in revised form 19 October 2004; accepted 20 October 2004 Available online 18 December 2004
Abstract The present work describes the calculation of the atomic shift of titanium atoms (6(h) Wyckoff positions) in Ti–20Al, Ti–25Al, Ti–30Al and Ti–45Al–5Nb alloys (all atom%) in the ␣2 -phase using a Rietveld refinement procedure. The Ti atoms are slightly shifted from their regular cph atomic sites. This is related to the presence of symmetry elements in the ␣2 -phase with D019 structure, which in turn allows local shifts due to different site occupancies resulting in different atomic potentials. The shift in the Ti positions changes the Ti–Ti and Ti–Al first neighbor bond lengths within and out of plane and also the size of tetrahedron. © 2004 Published by Elsevier B.V. Keywords: Intermetallic compounds; Ti–Al and Ti–Al–Nb alloys; X-ray diffraction; Rietveld refinement
1. Introduction Intermetallic compounds have been the subjects of intense study spurred by the demands of the aircraft and aerospace industries for materials that are usually strong at elevated temperatures [1]. Ordered intermetallics belong to a class of materials that present special opportunities for unusual combination of lightness and high temperature strength. On the other hand, they lack room temperature ductility and toughness. Further, among the well-studied intermetallic compounds, Ti3 Al is suitable for the next generation high temperature materials. Efforts initiated in 1960 [2,3] and intensified in the 1980 [4] to develop high temperature engineering alloys based on Ti3 Al have been largely successful in late 1990 [5]. Ti3 Al, designated as ␣2 -phase, is a long-range ordered close packed hexagonal (cph) phase with D019 structure (hP8) and P63 /mmc symmetry. The basal plane projection of the ␣2 -phase and the corresponding symmetry elements are given in Fig. 1. The unit cell of the ␣2 -phase has two types of Wyckoff positions that are 2(c):(1/3, 2/3, 1/4) with the point group symmetry 6m2 and 6(h): (x, 2x, 1/4) with the
∗
Corresponding author. Tel.: +91 40 4586488; fax: +91 40 4341439. E-mail address: singh [email protected] (A.K. Singh).
0925-8388/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.jallcom.2004.10.029
point group symmetry mm2; occupied by Al and Ti atoms, respectively. The regular cph atomic position of one of the atomic site for 6(h) correspond to a position (1/6, 2/6, 1/4). The unit cell for this structure can be described in terms of four interpenetrating hexagonal sub-lattices. The ‘a’ spacing of the ordered cell is twice that of the cell for corresponding disordered structure, while the ‘c’ spacing changes marginally. The composition range and critical temperature for order–disorder transition is well defined [6,7]. It has been assumed in most of the studies that atoms in the ␣2 -phase are located at regular cph positions as given by Pietrokowsky for Ti3 Sn phase [8]. Gehlen [9] has reported that the position of titanium atoms in a single crystal of the ␣2 -phase are slightly displaced from the sites they would occupy in regular cph lattice. This has resulted in very large changes in the intensities of some of super lattice peaks. Apart from this, the study of stability of planar faults and other defects do not consider the shift in titanium atoms, which seems to have an effect on energy that in turn affect the stability of the faults. Thus, the aim of the present investigation is to study the structure of ␣2 -phase and related atomic shifts of titanium atoms as function of aluminium content using Rietveld refinement [10]. These results will be useful to study the deformation behavior of D019 structures in general and ␣2 -phase in particular.
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nium and its alloys. The microstructure of heat-treated alloys were examined by optical microscope.
3. Results and discussion The microstructures of all experimental alloys have been examined by optical microscope. A typical representative of these microstructures for the alloys Ti–25Al and Ti–45Al–5Nb is shown in Fig. 2. The XRD patterns of the binary alloys exhibit single ␣2 -phase only. The alloy Ti–45Al–5Nb lies in a single-phase field (␣) at 1400 ◦ C and then transforms to ␣2 -phase during quenching. The alloy Ti–45Al–5Nb reveals the evidence of ␣2 as major phase and a few peaks of ␥-phase with very low intensity. The XRD patterns of all the alloys have been subjected to Rietveld refinement. The initial models and the results of refinement are given in Table 1. The composition of the alloy Ti–20Al lies in two phase ␣ + ␣2 field [6,7] as in the phase diagram although the volume fraction of ␣-phase is very small which could not be detected in XRD study. The intense peaks of the ␣- and ␣2 phases are having almost same positions in the 2θ scan and non overlapping peaks (low intensity) could not be observed due to small volume fraction of the ␣-phase in the overall Fig. 1. (a) Basal plane projection of Ti3 Al structure. Filled and open circles represent Ti and Al atoms, respectively. Large and small circles correspond to sites in alternate layers. (b) Symmetry elements corresponding to Ti3 Al structure (D019 type with P63 /mmc symmetry).
2. Experimental Buttons of three binary alloys with nominal compositions Ti–20Al, Ti–25Al and Ti–30Al were prepared by nonconsumable vacuum arc melting technique under a partial pressure of argon (400 mm-Hg) with a tungsten electrode. The melting was repeated six to seven times to ensure chemical homogeneity. Another alloy Ti–45Al–5Nb was melted in the form of 600 g pancakes using the similar melting method as mentioned above. The analyzed chemistry of all alloys obtained by electron probe microanalysis (EPMA) is given in Table 1. The small pieces of the first three alloys were heat-treated at 1000 ◦ C for 24 h (homogenization treatment) and then water quenched (WQ) and Ti–45Al–5Nb alloy was heat-treated at 1400 ◦ C for 1 h followed by water quenching. The powders of all heat-treated alloys were made by filing and then subjected to stress relieving treatment at 425 ◦ C for 100 h. The X-ray diffraction (XRD) profiles of annealed powder samples were recorded in a Philips PW3020 diffractometer equipped with a graphite monochromator operated at 40 kV and 30 mA in a step size of 0.015◦ (2θ) and counting time of 4 s/step. The XRD data for all the alloys were subjected to Rietveld refinement program using Philips Xpert plus. The specimens for microscopy were prepared from bulk samples following standard metallographic technique used for tita-
Fig. 2. Optical microstructures of the alloys: (a) Ti–25Al, and (b) Ti–45Al–5Nb.
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Table 1 Chemical analysis, initial models and results of Rietveld refinement for experimental alloys Ti–20Al
Ti–25Al
Ti–30Al
Ti–45Al–5Nb
Chemical analysis (atom%)
Ti: 81.3 Al: 18.7
Ti: 74.5 Al: 25.5
Ti: 71.1 Al: 28.9
Initial model (Ti3 Al)
2(c): 0.252Ti + 0.748Al 6(h): 1.0Ti –
2(c): 1.0A 6(h): 0.993Ti + 0.007Al –
2(c): 1.0Al 6(h): 0.948Ti + 0.052Al –
˚ (TiAl) Lattice constants (A)
a = 5.8193(2) c = 4.6639(2) –
a = 5.7975(6) c = 4.6413(4) –
a = 5.7802(7) c = 4.633(5) –
Output chemistry (Ti3 Al) Output chemistry (Ti–Al) R (expected)/% R (profile)/% R (weighted)/% Goodness of fit (GOF) 6(h) Wyckoff position ˚ Ti Ti bond length (A) ˚ Ti Al bond length (A) ˚ 3) Volume of tetrahedron (A
Ti6.50 Al1.50 – 14.169 16.396 21.549 2.313 0.807(1) 2.903 2.873 2.84
Ti5.96 Al2.04 – 13.480 18.535 24.582 3.325 0.7913(6) 2.932 2.873 2.88
Ti5.69 Al2.31 – 14.120 17.195 21.073 2.227 0.797(1) 2.897 2.857 2.81
Ti: 51.05 Al: 44.04 Nb: 4.91 2(c): 1.0Al 6(h): 0.681Ti + 0.254Al + 0.065Nb 1(a): 0.9002Ti + 0.0998Nb 1(c): 0.9002Ti + 0.9998Nb 2(e): 0.1192Ti + 0.8808Al a = 5.7508(8) c = 4.6164(6) a = 3.960(3) c = 4.056(4) Ti4.09 Al3.52 Nb0.39 Ti2.04 Al1.76 Nb0.20 10.518 13.841 17.635 2.811 0.804(1) 2.9625 2.8730 2.92
Initial model (TiAl)
˚ (Ti3 Al) Lattice constants (A)
composition. It is important to mention here that the ␣- and ␣2 -phases have same space group and the ␣-phase is disordered form of the ␣2 -phase. The many non-overlapping peaks correspond to super lattice reflections of ␣2 -phase and thus the volume fraction of ␣-phase has been ignored in the initial model of this alloy (Table 1). The other two alloys Ti–25Al and Ti–30Al lie in a single ␣2 -phase field [6,7]. Although, the three experimental alloys exhibit a systematic change in Al concentration but they are three different types of alloys in terms of their respective site occupancy. As mentioned above, the stoichiometric Ti3 Al phase has two Wyckoff positions i.e. 2(c) and 6(h), fully occupied by aluminum and titanium atoms, respectively. Any deviation from stoichiometric composition results in two situations: (1) when Al < 25 atom pct, 6(h) sites are occupied by titanium and 2(c) by aluminum and excess titanium; and (2) when Al > 25 atom pct, 6(h) sites are occupied by titanium and excess aluminum and 2(c) by aluminum only. Based on these arguments, the initial models for these alloys have been selected and given in Table 1. The input for site occupancy of the experimental alloys has been calculated based on analyzed alloy chemistry (Table 1). The observed and difference patterns (XRD) of the alloy Ti–25Al are given in Fig. 3. The alloy Ti–45Al–5Nb has been selected due to fact that this alloy heat-treated at 1400 ◦ C exhibits nearly single phase (␣2 ). The small amount of ␥-phase is also present in this alloy and this has been considered during the Rietveld refinement with the assumption that the overall alloy composition is same in both the phases. It is important to mention that stoichiometry of this ␣2 -phase is far away from stoichiometric composition and it is supersaturated due to high amount of aluminum and niobium. Initially, the following three models have been
considered for Rietveld refinement of the ␣2 -phase. (1) Both the sites 2(c) and 6(h) are randomly occupied by titanium, aluminum and niobium; (2) the 2(c) sites are occupied by aluminum and niobium while 6(h) by titanium and aluminum atoms; and (3) 2(c) sites are occupied by aluminum only and 6(h) by titanium, niobium and remaining aluminum. The Rietveld refinement could not converge for the first two models and gave a very good solution for the third model (Fig. 4). These results and initial structure models are summarized in Table 1. It is important to mention here that Ti3 Al structure is stabilized by obtaining maximum number of first neighbor Ti Al bonds. The first two models obviously do not result in maximum number of first neighbor Ti Al bonds. As a result, Rietveld refinement procedure does not give solution for the same.
Fig. 3. Observed and difference XRD patterns of the alloy Ti–25Al powder after homogenization and stress relieving treatments.
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Fig. 4. Observed and difference XRD patterns of the alloy Ti–45Al–5Nb powder after solution and stress relieving treatments.
This has been shown in ␥-phase that the preferential substitution of titanium by niobium atoms is energetically favorable [11]. The decrease in internal energy as a result of ternary element substitution follows monotonically with increase in the niobium concentration. As a result, 1(a) and 1(c) sites are occupied by titanium and niobium atoms and 2(e) sites are occupied by aluminum and titanium atoms. The details of the structure model and results of the ␥-phase are given in Table 1. Murray [6] has reported the lattice constants ‘a’ and ‘c’ of the Ti–Al alloys over a large range of composition (up to 40 atom% of aluminum), which covers both the range of disordered (␣) and ordered (␣2 ) phases. This shows a continuous reduction of ‘a’ and ‘c’ parameters with increase in aluminum contents. The lattice parameters of the binary ␣2 phase of all experimental alloys lie in same range and also exhibit similar trend as a function of aluminum as those reported in literature [6]. The lattice parameters of the alloy Ti–45Al–5Nb exhibit the smallest values of ‘a’ and ‘c’ in all experimental alloys. Although, under equilibrium condition, this alloy lies in the two phase (␣2 + ␥) field but nearly single phase ␣2 obtained by quenching exhibits the same trend of lattice parameters. This can be attributed to the presence of very high aluminum content in this alloy. It is to be noted that the 2(c) positions after Rietveld refinement remains same as given in Table 1, while the 6(h) positions are shifted from regular hexagonal positions. Similar displacements in 6(h) positions have been reported in a single crystal of the ␣2 -phase [9]. A careful observation of structure of the ␣2 -phase and corresponding symmetry arrangements indicates that the 2(c) positions lie at the intersection of three mirrors, which are defined an unique point in the space. As a result, no atomic shift of 2(c) positions is possible without breaking of the P63 /mmc symmetry. It is possible to relax the 2(c) Wyckoff positions during Rietveld refinement. Such an assumption will break the symmetry of P63 /mmc space group. One has to consider the other space groups, which are the subgroups of the P63 /mmc space group and having low symmetry. This consideration leads to
high value of goodness of feel (GOF) or non-convergence of fitting, predicting no possible solutions. Since the XRD patterns of all the experimental alloys have clearly indicated the presence of the ␣2 -phase, no relaxation of the 2(c) positions has been used in final calculation. The 6(h) positions forms two tetrahedrons with 2(c) positions orientated in opposite direction along the ‘c’ axis within one unit cell (Fig. 2). In each tetrahedron, three of 6(h) positions lie on three different mirrors. These three atoms can move along their respective mirrors without breaking any symmetry. Therefore, atomic shift corresponding to 6(h) positions in the ␣2 -phase is possible. In fact the atomic shift is related to atomic potential, which in turn is governed by its surrounding atoms. Depending upon the occupancies of both the sites i.e. the corresponding potentials of 2(c) and 6(h) sites vary and results in atomic shift of 6(h) positions. As a consequence, bond length in the respective neighbor changes. The regular cph position of one of the 6(h) site is 0.833. The corresponding 6(h) positions obtained in all experimental alloys are less than 0.833, which in turn changes the Ti Ti and Ti Al first neighbor within and out of plane bond lengths. It is to be noted that 2(c) and 6(h) atomic sites are predominantly occupied by aluminum and titanium atoms, respectively. Although these bond lengths show a systematic trend in binary alloys but it would not be correct to correlate the same as a function of Al content. This is due to the fact that the three binary alloys exhibit entirely different pattern of site occupancy and hence these alloys and related potential should be treated differently. The volumes of tetrahedron of experimental alloys have been calculated using aluminum in the apex position (Table 1). This shows that the volume of tetrahedron is maximum for the alloy Ti–25Al among all binary alloys and its size decreases from the deviation of stoichiometric composition in binary alloys. The volume of tetrahedron is largest for the alloy Ti–45Al–5Nb. This may be due to very high solid solution effect. Apart from this, the ␣2 -phase obtained in this alloy is not an equilibrium phase. It is to be noted that the overall volume of the unit cell reduces with increase in aluminum content. The sizes of tetrahedron and octahedron holes are expected to influence interstitial diffusion and solubility of interstitial in the ␣2 -phase [9]. In fact it has been reported that the presence of the Ti3 Al phase in Ti–Al alloys affects the solubility of H2 [12]. The small shift of titanium atoms affects the intensities of super lattice reflections. Gehlen [9] has also observed the change in the intensities of super lattice reflections by static displacements of titanium atoms. The intensity of 1 1 2¯ 0 reflections increases with increase in aluminum content. This indicates that the atomic shift has to be considered during the measurement of long-range order parameter. The magnitude of atomic shift is a function of extent of ordering present in the material as well as temperature. The measurement of the amount of order in partially ordered materials would depend on site occupancy and spatial position of the lattice sites.
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The presence of small shift may also affect the physical properties of the alloys [13–15]. The sudden drop in the magnetic susceptibility in the Ti3 Al composition range might be explained by the presence of cluster of atoms [15]. The tighter bonding of titanium atoms (smaller the volume of tetrahedron) in tetrahedron may results in broadening of titanium band. This in turn introduces a large change in the density of states corresponding to the drop in magnetic susceptibility. Apart from this, determination of the small shift associated with 6(h) positions along with the site occupancy will be helpful to calculate accurately the energy of planar faults in these alloys.
4. Summary The shift in titanium atoms corresponding to 6(h) Wyckoff positions has been calculated in different alloys containing ␣2 -phase. This is related to the presence of symmetry elements in Ti3 Al phase, which allows the displacement along the mirror. The shift may be attributed to different site occupancies resulting different atomic potentials. These atomic coordinates are useful to calculate the energy of planar faults in these alloys.
Acknowledgements The authors acknowledge the financial support of the Defence Research Development Organization, Government of India. Thanks are also due to the members of the Titanium
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Alloy Group and Structure and Failure Analysis Group for their help in carrying out the experimental work.
References [1] J.H. Westbrook, R.L. Fleischer (Eds.), Intermetallic Compounds: Principles and Practice, Wiley, West Sussex, England, 2002. [2] J.P. McAndrew, C.R. Simcoe, ASD TR-61-466, USA, 1961. [3] H. Winter, US Patent No. 3,411,901 (1968). [4] M.J. Blackburn, M.P. Smith, AFML-TR-82-4086, USA, 1982. [5] D. Banerjee, A.K. Gogia, T.K. Nandy, K. Muraleedharan, R.S. Mishra, in: R. Darolia, J.J. Lewandowski, C.T. Liu, P.L. Martin, D.B. Miracle, M.V. Nathal (Eds.), Structural Intermetallics, The Mineral, Metals and Materials Society, Warrendale, 1993, pp. 19– 33. [6] J.L. Murray, Phase Diagram of Binary Titanium Alloys, ASM International, Metals Park, OH, 1987. [7] U.R. Kattner, J.-C. Lin, Y.A. Chang, Metall. Trans. 23A (1992) 2081–2090. [8] P. Pietrokowsky, J. Met. 194 (1952) 211. [9] P.C. Gehlen, in: R.L. Jaffee, N.E. Promisel (Eds.), Science, Technology and Application of Titanium, Pergamon Press, New York, 1970, pp. 349–357. [10] R.A. Young (Ed.), The Rietveld Method, ICUR, Oxford Science Publishers, 2000. [11] S. Raju, E. Mohandas, V.S. Raghunathan, J. Phys. Chem. Solids 52 (1991) 931. [12] M. Portisch, H. Margolin, Final report on contract no. DA-ARO(D)31-124-G519, Army Research Office, Durham. [13] E.W. Collings, The Physical Metallurgy of Titanium Alloys, ASM, Metals Park, OH, 1984. [14] E.W. Collings, J.C. Hoe, Phys. Lett. 29A (1969) 306–307. [15] E.W. Collings, J.C. Hoe, in: R.L. Jaffee, N.E. Promisel (Eds.), Science, Technology and Application of Titanium, Pergamon Press, New York, 1970, pp. 331–347.
On the structure of the Ti3Al phase in Ti–Al and Ti–Al–Nb alloys S. Banumathy, P. Ghosal, A.K. Singh∗ Defence Metallurgical Research Laboratory, Kanchanbagh P.O., Hyderabad 500058, India Received 8 June 2004; received in revised form 19 October 2004; accepted 20 October 2004 Available online 18 December 2004
Abstract The present work describes the calculation of the atomic shift of titanium atoms (6(h) Wyckoff positions) in Ti–20Al, Ti–25Al, Ti–30Al and Ti–45Al–5Nb alloys (all atom%) in the ␣2 -phase using a Rietveld refinement procedure. The Ti atoms are slightly shifted from their regular cph atomic sites. This is related to the presence of symmetry elements in the ␣2 -phase with D019 structure, which in turn allows local shifts due to different site occupancies resulting in different atomic potentials. The shift in the Ti positions changes the Ti–Ti and Ti–Al first neighbor bond lengths within and out of plane and also the size of tetrahedron. © 2004 Published by Elsevier B.V. Keywords: Intermetallic compounds; Ti–Al and Ti–Al–Nb alloys; X-ray diffraction; Rietveld refinement
1. Introduction Intermetallic compounds have been the subjects of intense study spurred by the demands of the aircraft and aerospace industries for materials that are usually strong at elevated temperatures [1]. Ordered intermetallics belong to a class of materials that present special opportunities for unusual combination of lightness and high temperature strength. On the other hand, they lack room temperature ductility and toughness. Further, among the well-studied intermetallic compounds, Ti3 Al is suitable for the next generation high temperature materials. Efforts initiated in 1960 [2,3] and intensified in the 1980 [4] to develop high temperature engineering alloys based on Ti3 Al have been largely successful in late 1990 [5]. Ti3 Al, designated as ␣2 -phase, is a long-range ordered close packed hexagonal (cph) phase with D019 structure (hP8) and P63 /mmc symmetry. The basal plane projection of the ␣2 -phase and the corresponding symmetry elements are given in Fig. 1. The unit cell of the ␣2 -phase has two types of Wyckoff positions that are 2(c):(1/3, 2/3, 1/4) with the point group symmetry 6m2 and 6(h): (x, 2x, 1/4) with the
∗
Corresponding author. Tel.: +91 40 4586488; fax: +91 40 4341439. E-mail address: singh [email protected] (A.K. Singh).
0925-8388/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.jallcom.2004.10.029
point group symmetry mm2; occupied by Al and Ti atoms, respectively. The regular cph atomic position of one of the atomic site for 6(h) correspond to a position (1/6, 2/6, 1/4). The unit cell for this structure can be described in terms of four interpenetrating hexagonal sub-lattices. The ‘a’ spacing of the ordered cell is twice that of the cell for corresponding disordered structure, while the ‘c’ spacing changes marginally. The composition range and critical temperature for order–disorder transition is well defined [6,7]. It has been assumed in most of the studies that atoms in the ␣2 -phase are located at regular cph positions as given by Pietrokowsky for Ti3 Sn phase [8]. Gehlen [9] has reported that the position of titanium atoms in a single crystal of the ␣2 -phase are slightly displaced from the sites they would occupy in regular cph lattice. This has resulted in very large changes in the intensities of some of super lattice peaks. Apart from this, the study of stability of planar faults and other defects do not consider the shift in titanium atoms, which seems to have an effect on energy that in turn affect the stability of the faults. Thus, the aim of the present investigation is to study the structure of ␣2 -phase and related atomic shifts of titanium atoms as function of aluminium content using Rietveld refinement [10]. These results will be useful to study the deformation behavior of D019 structures in general and ␣2 -phase in particular.
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nium and its alloys. The microstructure of heat-treated alloys were examined by optical microscope.
3. Results and discussion The microstructures of all experimental alloys have been examined by optical microscope. A typical representative of these microstructures for the alloys Ti–25Al and Ti–45Al–5Nb is shown in Fig. 2. The XRD patterns of the binary alloys exhibit single ␣2 -phase only. The alloy Ti–45Al–5Nb lies in a single-phase field (␣) at 1400 ◦ C and then transforms to ␣2 -phase during quenching. The alloy Ti–45Al–5Nb reveals the evidence of ␣2 as major phase and a few peaks of ␥-phase with very low intensity. The XRD patterns of all the alloys have been subjected to Rietveld refinement. The initial models and the results of refinement are given in Table 1. The composition of the alloy Ti–20Al lies in two phase ␣ + ␣2 field [6,7] as in the phase diagram although the volume fraction of ␣-phase is very small which could not be detected in XRD study. The intense peaks of the ␣- and ␣2 phases are having almost same positions in the 2θ scan and non overlapping peaks (low intensity) could not be observed due to small volume fraction of the ␣-phase in the overall Fig. 1. (a) Basal plane projection of Ti3 Al structure. Filled and open circles represent Ti and Al atoms, respectively. Large and small circles correspond to sites in alternate layers. (b) Symmetry elements corresponding to Ti3 Al structure (D019 type with P63 /mmc symmetry).
2. Experimental Buttons of three binary alloys with nominal compositions Ti–20Al, Ti–25Al and Ti–30Al were prepared by nonconsumable vacuum arc melting technique under a partial pressure of argon (400 mm-Hg) with a tungsten electrode. The melting was repeated six to seven times to ensure chemical homogeneity. Another alloy Ti–45Al–5Nb was melted in the form of 600 g pancakes using the similar melting method as mentioned above. The analyzed chemistry of all alloys obtained by electron probe microanalysis (EPMA) is given in Table 1. The small pieces of the first three alloys were heat-treated at 1000 ◦ C for 24 h (homogenization treatment) and then water quenched (WQ) and Ti–45Al–5Nb alloy was heat-treated at 1400 ◦ C for 1 h followed by water quenching. The powders of all heat-treated alloys were made by filing and then subjected to stress relieving treatment at 425 ◦ C for 100 h. The X-ray diffraction (XRD) profiles of annealed powder samples were recorded in a Philips PW3020 diffractometer equipped with a graphite monochromator operated at 40 kV and 30 mA in a step size of 0.015◦ (2θ) and counting time of 4 s/step. The XRD data for all the alloys were subjected to Rietveld refinement program using Philips Xpert plus. The specimens for microscopy were prepared from bulk samples following standard metallographic technique used for tita-
Fig. 2. Optical microstructures of the alloys: (a) Ti–25Al, and (b) Ti–45Al–5Nb.
S. Banumathy et al. / Journal of Alloys and Compounds 394 (2005) 181–185
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Table 1 Chemical analysis, initial models and results of Rietveld refinement for experimental alloys Ti–20Al
Ti–25Al
Ti–30Al
Ti–45Al–5Nb
Chemical analysis (atom%)
Ti: 81.3 Al: 18.7
Ti: 74.5 Al: 25.5
Ti: 71.1 Al: 28.9
Initial model (Ti3 Al)
2(c): 0.252Ti + 0.748Al 6(h): 1.0Ti –
2(c): 1.0A 6(h): 0.993Ti + 0.007Al –
2(c): 1.0Al 6(h): 0.948Ti + 0.052Al –
˚ (TiAl) Lattice constants (A)
a = 5.8193(2) c = 4.6639(2) –
a = 5.7975(6) c = 4.6413(4) –
a = 5.7802(7) c = 4.633(5) –
Output chemistry (Ti3 Al) Output chemistry (Ti–Al) R (expected)/% R (profile)/% R (weighted)/% Goodness of fit (GOF) 6(h) Wyckoff position ˚ Ti Ti bond length (A) ˚ Ti Al bond length (A) ˚ 3) Volume of tetrahedron (A
Ti6.50 Al1.50 – 14.169 16.396 21.549 2.313 0.807(1) 2.903 2.873 2.84
Ti5.96 Al2.04 – 13.480 18.535 24.582 3.325 0.7913(6) 2.932 2.873 2.88
Ti5.69 Al2.31 – 14.120 17.195 21.073 2.227 0.797(1) 2.897 2.857 2.81
Ti: 51.05 Al: 44.04 Nb: 4.91 2(c): 1.0Al 6(h): 0.681Ti + 0.254Al + 0.065Nb 1(a): 0.9002Ti + 0.0998Nb 1(c): 0.9002Ti + 0.9998Nb 2(e): 0.1192Ti + 0.8808Al a = 5.7508(8) c = 4.6164(6) a = 3.960(3) c = 4.056(4) Ti4.09 Al3.52 Nb0.39 Ti2.04 Al1.76 Nb0.20 10.518 13.841 17.635 2.811 0.804(1) 2.9625 2.8730 2.92
Initial model (TiAl)
˚ (Ti3 Al) Lattice constants (A)
composition. It is important to mention here that the ␣- and ␣2 -phases have same space group and the ␣-phase is disordered form of the ␣2 -phase. The many non-overlapping peaks correspond to super lattice reflections of ␣2 -phase and thus the volume fraction of ␣-phase has been ignored in the initial model of this alloy (Table 1). The other two alloys Ti–25Al and Ti–30Al lie in a single ␣2 -phase field [6,7]. Although, the three experimental alloys exhibit a systematic change in Al concentration but they are three different types of alloys in terms of their respective site occupancy. As mentioned above, the stoichiometric Ti3 Al phase has two Wyckoff positions i.e. 2(c) and 6(h), fully occupied by aluminum and titanium atoms, respectively. Any deviation from stoichiometric composition results in two situations: (1) when Al < 25 atom pct, 6(h) sites are occupied by titanium and 2(c) by aluminum and excess titanium; and (2) when Al > 25 atom pct, 6(h) sites are occupied by titanium and excess aluminum and 2(c) by aluminum only. Based on these arguments, the initial models for these alloys have been selected and given in Table 1. The input for site occupancy of the experimental alloys has been calculated based on analyzed alloy chemistry (Table 1). The observed and difference patterns (XRD) of the alloy Ti–25Al are given in Fig. 3. The alloy Ti–45Al–5Nb has been selected due to fact that this alloy heat-treated at 1400 ◦ C exhibits nearly single phase (␣2 ). The small amount of ␥-phase is also present in this alloy and this has been considered during the Rietveld refinement with the assumption that the overall alloy composition is same in both the phases. It is important to mention that stoichiometry of this ␣2 -phase is far away from stoichiometric composition and it is supersaturated due to high amount of aluminum and niobium. Initially, the following three models have been
considered for Rietveld refinement of the ␣2 -phase. (1) Both the sites 2(c) and 6(h) are randomly occupied by titanium, aluminum and niobium; (2) the 2(c) sites are occupied by aluminum and niobium while 6(h) by titanium and aluminum atoms; and (3) 2(c) sites are occupied by aluminum only and 6(h) by titanium, niobium and remaining aluminum. The Rietveld refinement could not converge for the first two models and gave a very good solution for the third model (Fig. 4). These results and initial structure models are summarized in Table 1. It is important to mention here that Ti3 Al structure is stabilized by obtaining maximum number of first neighbor Ti Al bonds. The first two models obviously do not result in maximum number of first neighbor Ti Al bonds. As a result, Rietveld refinement procedure does not give solution for the same.
Fig. 3. Observed and difference XRD patterns of the alloy Ti–25Al powder after homogenization and stress relieving treatments.
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Fig. 4. Observed and difference XRD patterns of the alloy Ti–45Al–5Nb powder after solution and stress relieving treatments.
This has been shown in ␥-phase that the preferential substitution of titanium by niobium atoms is energetically favorable [11]. The decrease in internal energy as a result of ternary element substitution follows monotonically with increase in the niobium concentration. As a result, 1(a) and 1(c) sites are occupied by titanium and niobium atoms and 2(e) sites are occupied by aluminum and titanium atoms. The details of the structure model and results of the ␥-phase are given in Table 1. Murray [6] has reported the lattice constants ‘a’ and ‘c’ of the Ti–Al alloys over a large range of composition (up to 40 atom% of aluminum), which covers both the range of disordered (␣) and ordered (␣2 ) phases. This shows a continuous reduction of ‘a’ and ‘c’ parameters with increase in aluminum contents. The lattice parameters of the binary ␣2 phase of all experimental alloys lie in same range and also exhibit similar trend as a function of aluminum as those reported in literature [6]. The lattice parameters of the alloy Ti–45Al–5Nb exhibit the smallest values of ‘a’ and ‘c’ in all experimental alloys. Although, under equilibrium condition, this alloy lies in the two phase (␣2 + ␥) field but nearly single phase ␣2 obtained by quenching exhibits the same trend of lattice parameters. This can be attributed to the presence of very high aluminum content in this alloy. It is to be noted that the 2(c) positions after Rietveld refinement remains same as given in Table 1, while the 6(h) positions are shifted from regular hexagonal positions. Similar displacements in 6(h) positions have been reported in a single crystal of the ␣2 -phase [9]. A careful observation of structure of the ␣2 -phase and corresponding symmetry arrangements indicates that the 2(c) positions lie at the intersection of three mirrors, which are defined an unique point in the space. As a result, no atomic shift of 2(c) positions is possible without breaking of the P63 /mmc symmetry. It is possible to relax the 2(c) Wyckoff positions during Rietveld refinement. Such an assumption will break the symmetry of P63 /mmc space group. One has to consider the other space groups, which are the subgroups of the P63 /mmc space group and having low symmetry. This consideration leads to
high value of goodness of feel (GOF) or non-convergence of fitting, predicting no possible solutions. Since the XRD patterns of all the experimental alloys have clearly indicated the presence of the ␣2 -phase, no relaxation of the 2(c) positions has been used in final calculation. The 6(h) positions forms two tetrahedrons with 2(c) positions orientated in opposite direction along the ‘c’ axis within one unit cell (Fig. 2). In each tetrahedron, three of 6(h) positions lie on three different mirrors. These three atoms can move along their respective mirrors without breaking any symmetry. Therefore, atomic shift corresponding to 6(h) positions in the ␣2 -phase is possible. In fact the atomic shift is related to atomic potential, which in turn is governed by its surrounding atoms. Depending upon the occupancies of both the sites i.e. the corresponding potentials of 2(c) and 6(h) sites vary and results in atomic shift of 6(h) positions. As a consequence, bond length in the respective neighbor changes. The regular cph position of one of the 6(h) site is 0.833. The corresponding 6(h) positions obtained in all experimental alloys are less than 0.833, which in turn changes the Ti Ti and Ti Al first neighbor within and out of plane bond lengths. It is to be noted that 2(c) and 6(h) atomic sites are predominantly occupied by aluminum and titanium atoms, respectively. Although these bond lengths show a systematic trend in binary alloys but it would not be correct to correlate the same as a function of Al content. This is due to the fact that the three binary alloys exhibit entirely different pattern of site occupancy and hence these alloys and related potential should be treated differently. The volumes of tetrahedron of experimental alloys have been calculated using aluminum in the apex position (Table 1). This shows that the volume of tetrahedron is maximum for the alloy Ti–25Al among all binary alloys and its size decreases from the deviation of stoichiometric composition in binary alloys. The volume of tetrahedron is largest for the alloy Ti–45Al–5Nb. This may be due to very high solid solution effect. Apart from this, the ␣2 -phase obtained in this alloy is not an equilibrium phase. It is to be noted that the overall volume of the unit cell reduces with increase in aluminum content. The sizes of tetrahedron and octahedron holes are expected to influence interstitial diffusion and solubility of interstitial in the ␣2 -phase [9]. In fact it has been reported that the presence of the Ti3 Al phase in Ti–Al alloys affects the solubility of H2 [12]. The small shift of titanium atoms affects the intensities of super lattice reflections. Gehlen [9] has also observed the change in the intensities of super lattice reflections by static displacements of titanium atoms. The intensity of 1 1 2¯ 0 reflections increases with increase in aluminum content. This indicates that the atomic shift has to be considered during the measurement of long-range order parameter. The magnitude of atomic shift is a function of extent of ordering present in the material as well as temperature. The measurement of the amount of order in partially ordered materials would depend on site occupancy and spatial position of the lattice sites.
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The presence of small shift may also affect the physical properties of the alloys [13–15]. The sudden drop in the magnetic susceptibility in the Ti3 Al composition range might be explained by the presence of cluster of atoms [15]. The tighter bonding of titanium atoms (smaller the volume of tetrahedron) in tetrahedron may results in broadening of titanium band. This in turn introduces a large change in the density of states corresponding to the drop in magnetic susceptibility. Apart from this, determination of the small shift associated with 6(h) positions along with the site occupancy will be helpful to calculate accurately the energy of planar faults in these alloys.
4. Summary The shift in titanium atoms corresponding to 6(h) Wyckoff positions has been calculated in different alloys containing ␣2 -phase. This is related to the presence of symmetry elements in Ti3 Al phase, which allows the displacement along the mirror. The shift may be attributed to different site occupancies resulting different atomic potentials. These atomic coordinates are useful to calculate the energy of planar faults in these alloys.
Acknowledgements The authors acknowledge the financial support of the Defence Research Development Organization, Government of India. Thanks are also due to the members of the Titanium
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Alloy Group and Structure and Failure Analysis Group for their help in carrying out the experimental work.
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