Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-25T06:58:49.834Z Has data issue: false hasContentIssue false

Electronic structure of planar faults in TiAl

Published online by Cambridge University Press:  31 January 2011

C. Woodward
Affiliation:
UES, Inc., Materials Research Division, Dayton, Ohio 45432
J.M. MacLaren
Affiliation:
Physics Department, Tulane University, New Orleans, Louisiana 70118
S. Rao
Affiliation:
Wright Laboratories/MLLM, Wright Patterson Air Force Base, Ohio 45433–6533
Get access

Abstract

The mechanical behavior of intermetallic alloys is related to the mobility of the dislocations found in these compounds. Currently the effect of bonding on dislocation core structure and its influence on deformation behavior is not well understood. However, the unusual properties of these materials, such as the anomalous temperature dependence of flow stress observed in TiAl, are derived in part from the aspects of bonding that determine dislocation mobility. Several recent studies have suggested a particular relationship between directional bonding in TiAl and dislocation mobility. To understand better the flow behavior of high temperature intermetallics, and as a step toward bridging the gap between electronic structure and flow behavior, we have calculated the electronic structure of various planar faults in TiAl. The self consistent electronic structure has been determined using a layered Korringa Kohn Rostoker (LKKR) method which embeds the fault region between two semi-infinite perfect crystals. Calculated defect energies in stoichiometric TiAl agree reasonably well with other theoretical estimates, though overestimating the experimental (111) anti-phase boundary (APB) energy, found for Ti46Al54. We approximate the energy of the (111) APB for the Al-rich stoichiometry by calculating the energy of Al antisites near that defect plane. The calculated (111)APB energy decreases by 6% in going from stoichiometric TiAl to Ti46Al54. The overall hierarchy of fault energies is found to be associated with the number of crystal bond states that are disrupted by the introduction of the fault plane. However, the hierarchy of fault energies is inconsistent with the traditionally accepted ordering. Changes in bonding taking place in the vicinity of the planar defects are illustrated through the density of states and charge density plots. A three body atomistic model is introduced to parameterize the bonding observed in TiAl. The L10 lattice (c/a = 1.00), within a second nearest neighbor three body model, yields a (111)APB energy which is the sum of the complex and superlattice-intrinsic stacking fault energies.

Type
Articles
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Kawabata, T., Kanai, T., and Izumi, O., Acta Metall. 33, 1355 (1985).CrossRefGoogle Scholar
2.Lipsitt, H. A., Shechtman, D., and Schafrick, R. E., Metall. Trans. 6A, 1991 (1975).Google Scholar
3.Kim, Y. W. and Dimiduk, D. M., JOM 43, #8, (1991).CrossRefGoogle Scholar
4.Paidar, V., Pope, D. V., and Vitek, V., Acta Metall. 32, 435 (1984).CrossRefGoogle Scholar
5.Yoo, M. H., Scripta Metall. 20, 915 (1986).CrossRefGoogle Scholar
6. The asymmetric notation (hk;l) is adopted from Hug, G., Loiseau, A., and Veyssière, P., Philos. Mag. A57, 499 (1988). The notation reflects the tetragonal symmetry of the L10 lattice; the indices h and k may be permuted while the third index is fixed.Google Scholar
7.Hug, G., Loiseau, A., and Lasalmonie, A., Philos. Mag. A54, 47 (1986); G. Hug, A. Loiseau, and P. Veyssière, Philos. Mag. A57, 499 (1988); G. Hug, Ph.D. Dissertation(1988), University of Orsay (France).Google Scholar
8.Court, S. A., Vasudevan, V. K., and Fraser, H. L., Philos. Mag. 61A, 141 (1990).Google Scholar
9.Greenberg, B. F., Anisimov, V. I., and Gornostirev, Yu. N., Scripta Metall. 22, 859 (1988).Google Scholar
10.Hug, G. and Veyssière, P., in Int. Symp. on Electronic Microscopy in Plasticity and Fracture Research of Materials (Dresden, October 1989).Google Scholar
11.Anisimov, V. I., Ganin, G. V., Galakhov, V. R., and Kurmayev, E. Z., Phys. Met. Metall. 63, 192 (1987).Google Scholar
12.Chubb, S. R., Papaconstantopoulos, D. A., and Klein, B. M., Phys. Rev. B. 38, 12120 (1988).CrossRefGoogle Scholar
13.Morinaga, M., Saito, J., Yukawa, N., and Adachi, H., Acta Metall. 38, 25 (1990).Google Scholar
14.Fu, C. L. and Yoo, M. H., in Alloy Phase Stability and Design, edited by Stocks, G. M., Pope, D. P., and Giamei, A. F. (Mater. Res. Soc. Symp. Proc. 186, Pittsburgh, PA, 1991), p. 265; C. L. Fu and M. H. Yoo, Philos. Mag. Lett. 62, 159 (1990).Google Scholar
15.Ceperley, D. M. and Alder, B. J., Phys. Rev. Lett. 45, 566 (1980); D. M. Ceperley, Phys. Rev. B 18, 3126 (1978).Google Scholar
16.Perdew, J. P. and Zunger, A., Phys. Rev. B. 23, 5048 (1981).Google Scholar
17.MacLaren, J. M., Crampin, S., and Vvedensky, D. D., Phys. Rev. B 40, 12164 (1989); X-G. Zhang, A. Gonis, and J. MacLaren, Phys. Rev. B 40, 3694 (1989).Google Scholar
18.Bumps, E. S., Kessler, H. D., and Hanson, M., Trans. AIME 194, 609 (1952).Google Scholar
19.Lin, W., Xu, J., and Freeman, A. J., in High Temperature Ordered Intermetallic Alloys IV, edited by Johnson, L. A., Pope, D. P., and Stiegler, J. O. (Mater. Res. Soc. Symp. Proc. 213, Pittsburgh, PA, 1991), p. 131; A. J. Freeman, T. Hong, W. Lin, and J. Xu, ibid., p. 31.Google Scholar
20.Lupis, C. H. P., Chemical Thermodynamics of Material (North Holland, New York, 1983), p. 449.Google Scholar
21.Hultgren, R., Desai, P. D., Hawkins, D. T., Gleiser, M., and Kelley, K. K., in Selected Values of the Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, OH, 1973), p. 221.Google Scholar
22. The quasi chemical model has also been used previously to estimate planar fault energies; see, for example: Shechtman, D., Blackburn, M. J., and Lipsitt, H. A., Metall. Trans. 5, 1373 (1974).Google Scholar
23. These total energy calculations were performed with a maximum angular momentum (lmax) equal to 4. Preliminary electronic structure calculations of these faults, using lmax = 2, are presented in the following citation: Woodward, C., MacLaren, J. M., and Rao, S. A., in High Temperature Ordered Intermetallic Alloys IV, edited by Johnson, L. A., Pope, D. P., and Stiegler, J. O. (Mater. Res. Soc. Symp. Proc. 213, Pittsburgh, PA, 1991), p. 715.Google Scholar
24.Hirth, J. P. and Lothe, J., Theory of Dislocations (McGraw-Hill, New York, 1968), p. 432.Google Scholar
25.Tang, S., Northwestern University, private communication (1991).Google Scholar
26.Cockayne, D. J. H., Ray, I. L. F., and Whelan, M. J., Philos. Mag. 20, 1265 (1969).CrossRefGoogle Scholar
27.Baluc, N., Schaublin, R., and Hemker, K. J., in Ordered Intermetallics-Physical Metallurgy and Mechanical Behavior (NATO Advanced Research Workshop, Irsee, Germany, June 1991).Google Scholar
28.Elliott, R. P. and Rostaker, W., Acta Metall. 2, 884 (1954).CrossRefGoogle Scholar
29. The stoichiometry is calculated using the distance between antisites in the (111) plane as a length scale.Google Scholar
30.MacLaren, J. M., Woodward, C., and Rao, S., in Application of Multiple Scattering Theory to Materials Science, edited by Butler, W. H., Dederichs, P. H., Gonis, A., and Weaver, R. (Mater. Res. Soc. Symp. Proc. 253, Pittsburgh, PA, 1992).Google Scholar
31.Marcinkowski, M. J., in Electron Microscopy and Strength of Crystals, edited by Thomas, G. and Washburn, J. (Interscience Publishers, 1963), p. 431; K. Suzuki, M. Ichihara, and S. Takeuchi, Acta Metall. 27, 193 (1979).Google Scholar
32.Greenberg, B. A., Antonova, O. V., Indenbaum, V. N., Karkina, L. E., Notkin, A. B., Ponomarev, M. V., and Smirnov, L. V., Acta Metall. Mater. 39, 233 (1991).Google Scholar
33.Yamaguchi, M., Vitek, V., and Pope, D. P., Philos. Mag. 43, 1027 (1981).CrossRefGoogle Scholar
34.Vasudevan, V. K., Stucke, M. A., Court, S. A., and Fraser, H. L., Philos. Mag. Lett. 59, 299 (1989); V. K. Vasudevan, S. A. Court, P. Kurath, and H. L. Fraser, Scripta Metall. 23, 907 (1989).CrossRefGoogle Scholar
35.Peierls, R. E., Proc. Phys. Soc. 52, 23 (1940); F. R. N. Nabarro, Proc. Phys. Soc. 59, 256 (1947).Google Scholar
36.Hirth, J. P. and Lothe, J., Theory of Dislocations (McGraw-Hill, New York, 1968), p. 202.Google Scholar
37.Pauling, L., The Nature of the Chemical Bond (Cornell Univ. Press, Ithica, NY, 1960), pp. 417424.Google Scholar
38.Vitek, V., Lejcek, L., and Bowen, D. K., in Intermetallic Potentials and Simulation of Lattice Defects (Battelle Conference, 1972), p. 493.CrossRefGoogle Scholar
39.Daw, M. S. and Baskes, M. I., Phys. Rev. B 29, 6443 (1984); Phys. Rev. Lett. 50, 1285 (1983).Google Scholar
40.Biswas, R. and Hamann, D. R., Phys. Rev. Lett. 55, 2001 (1985).Google Scholar
41. A linearization of the modified embedded atom method yields the same results. Baskes, M. I., Nelson, J. S., and Wright, A. F., Phys. Rev. B 40, 6085 (1989).Google Scholar
42. The energy of an artificial structure was calculated in order to decompose the average C l, over atom types, and the pair terms. The structure is generated from the L10 lattice by introducing a (111)APB on every successive (111) plane. This yields an energy of 510 mJ/m2 per (111) plane above the L10 structure.Google Scholar
43.Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vettering, W. T., Numerical Recipes (Cambridge University Press, Cambridge, 1986), p. 52.Google Scholar