Self-diffusion in γ-TiAl: an experimental study and atomistic calculations
Introduction
Ordered intermetallic compounds of the Ti–Al system are the subject of extensive research in connection with their potential applications as high-temperature structural materials. Such compounds and especially their two-phase compositions demonstrate high yield strength at elevated temperatures, advanced creep characteristics, good oxidation/corrosion resistance and other useful properties. Intermetallic alloys of this system with potential for industrial applications have a two-phase structure consisting of alternating γ-TiAl and α2-Ti3Al lamellae. The formation and high-temperature stability of the lamellar structure are controlled by diffusion processes in the lattices of the constituent γ and α2 phases and along both the semi-coherent γ/gamma′ lamellar boundaries and the γ/α2 internal boundaries. Moreover, the creep resistance of the lamellar structure is also determined by diffusion characteristics of both the bulk phases and the interphase boundaries. Therefore the knowledge of diffusion characteristics and the fundamental understanding of the diffusion mechanisms in Ti aluminides are of paramount importance to the entire area of research and development of Ti–Al intermetallic alloys.
Hitherto, the experimental data on Ti and Al self-diffusion in Ti aluminides are scarce, and the knowledge of the respective atomic mechanisms of diffusion is next to non-existent. Experimental studies of diffusion in the Ti–Al system are hampered primarily by the unavailability of suitable and inexpensive radioactive isotopes of Ti and Al. 44Ti is the only suitable radiotracer for Ti, but it is produced by a nuclear reaction at a cyclotron and is very expensive. The only suitable isotope for Al, 26Al, is also a cyclotron product; it is even more expensive than 44Ti and, in addition, has very low specific activity.
We have recently launched a broad program of extensive experimental investigations of diffusion in the Ti–Al system. Such investigations will include not only lattice diffusion in different phases of the system but also grain boundary diffusion and diffusion along γ/α2 interfaces. To date, our efforts have resulted in accurate measurements of lattice self-diffusion and Al impurity diffusion in pure α-Ti[1], and Ti self-diffusion and single-phase interdiffusion in bcc. Ti–Al alloys[2]and in the aluminide Ti3Al3, 4. In the latter case, by combining the obtained Ti self-diffusion and interdiffusion coefficients and using the theoretical treatments of Darken[5]and Manning[6]we have calculated self-diffusion coefficients of Al. This calculation required the knowledge of the thermodynamic factors for Ti3Al, which were determined by Bormann by the CALPHAD method[7]. It should be emphasized that this approach to the evaluation of Al diffusivity is especially important in view of the limited availability of the 26Al tracer.
In this paper we extend our studies to lattice diffusion in γ-TiAl. This phase has an ordered fcc-based L10 (CuAu-type) structure consisting of alternating (0 0 2) layers of Ti and Al atoms. The tetragonality of the structure is small, c/a≈1.02. Ti self-diffusion in TiAl was measured previously by Kroll et al.[8]using the 44Ti tracer. More recently, interdiffusion in TiAl has been carefully studied by Sprengel et al.[9]. However, Sprengel et al. could not make any reasonable evaluation of Al diffusivity in TiAl by combining their interdiffusion coefficients with the data of Kroll et al.[8]. Part of the reason of that failure was that the thermodynamic factors for TiAl were not known at that time. Moreover, when the thermodynamic factors became available[7], it turned out that the substitution of the diffusion coefficients of Kroll et al.[8]and Sprengel et al.[9]in the Darken–Manning equation gave negative values of Al diffusivity. This controversy led us to conclude that the data of Kroll et al. needed to be remeasured in more detail.
Therefore, the purpose of the experimental part of this work was to perform accurate measurements of 44Ti self-diffusion coefficients in γ-TiAl over a wide temperature range. In order to verify the reproducibility of our results, we studied diffusion in three different TiAl materials with near-stoichiometric compositions. One of them was the same material as that studied by Kroll et al[8]. It was also important to evaluate Al self-diffusion coefficients in TiAl by using our new Ti self-diffusion data and the interdiffusion coefficients of Sprengel et al[9].
Another important goal of this work was to raise our diffusion studies to a new level by connecting the experimental measurements with atomistic calculations. The aim of such calculations was to evaluate the point defect concentrations and effective formation energies in TiAl, the point defect migration energies, and thus the activation energies of Ti and Al self-diffusion by different mechanisms. By comparing the calculated activation energies with those observed experimentally one can identify the atomic mechanisms that dominate self-diffusion in TiAl in different temperature and concentration ranges. The results of this study clearly illustrate that this combined approach is extremely effective for getting better insights into the atomistic aspects of mass transport in intermetallic compounds.
Section snippets
Experimental procedure
Three differently produced TiAl materials, denoted here as A, B and C, were studied in this work. Material A, supplied by Thyssen AG (Essen), was produced by skull melting under argon atmosphere using titanium sponge (>99.9 wt% purity) and aluminium bars (>99.9 wt% purity) as alloying materials. It was the same material as the one employed in the previous measurements of Kroll et al.[8]. Materials B and C were prepared at the GKSS Forschungszentrum (Geesthacht) by arc melting under argon
Ti self-diffusion in TiAl
Typical penetration profiles measured in this work are shown in Fig. 1. Depending on the surface conditions, one could expect two types of penetration profiles. For instantaneous source conditions, the profile is described by a Gaussian function, c ∝ , where is the coefficient of Ti tracer self-diffusion in the material and t is the diffusion time. Thus, the plot vs x2 of the profile should be a straight line and the diffusion coefficient can be determined from the slope q
Simulation procedure
The atomic interactions in TiAl were described by many-body central force interatomic potentials of the embedded-atom method (EAM). In this method[11], the total energy of a system equals the sum of pair interactions between the atoms plus the sum of their embedding energies. The embedding energy of an atom depends on its chemical sort and is a function of the atomic density induced at the location of the atom by all other atoms in the system. In this work we applied a slightly modified version
Point defect concentrations and effective formation energies in γ-TiAl
The equilibrium point defect concentrations in TiAl were calculated from a simple model similar to that of Johnson and Brown[17]. The model uses the canonic ensemble formalism and is based on two assumptions: (1) The defect concentrations are small and their interactions can be neglected, and (2) The entropy of the system is represented by its uncorrelated configurational entropy. Thus the excess Gibbs energy per lattice site, associated with the defect subsystem at zero pressure, equals
Evaluation of diffusion mechanisms in γ-TiAl
Diffusion mechanisms in ordered compounds are more complex than in pure metals. The main restriction posed on plausible diffusion mechanisms is that they must maintain the long-range order in the compound, at least in average. Because some (or sometimes all) NN vacancy jumps create additional antisites and thus increase disorder in the structure, they are either prohibited or tend to be reversed. This explains why diffusion in ordered crystals is often associated with strong geometric
Discussion
We have considered three most favourable mechanisms of self-diffusion in TiAl. The calculated activation energies of Ti and Al self-diffusion by these mechanisms depend on the alloy composition as illustrated in Fig. 12. From these plots we can evaluate the relative importance of different mechanisms based on the assumption that diffusion is dominated by the mechanism(s) with the lowest activation energy.
This assumption should be applied with caution because the corresponding pre-exponential
Summary and conclusions
1. We have studied Ti self-diffusion in the lattice of γ-TiAl over a temperature range of 1184–1691 K. The measurements were performed using the radiotracer 44Ti and the serial sectioning technique. The tracer diffusion coefficients, , show a non-Arrhenius behaviour with significant upward deviations at high temperatures (above ∼1470 K, see Fig. 2). The pre-exponential factor and the activation energy of Ti self-diffusion determined in the low temperature range (<1470 K) are 1.5×10−6
Acknowledgements
The authors are indebted to Dr. F. Appel and Dr. J. Müllauer (GKSS Geesthacht) for supplying and characterizing the TiAl alloys, to Dr. M. Friesel (Chalmers University) for performing SIMS analyses of the alloys, and to Prof. Dr. R. Bormann (GKSS Geestacht) for communicating us the thermodynamic data for TiAl. The production of the 44Ti radiotracer was supported by funds of the Kernforschungszentrum Karlsruhe. We are grateful to the German Science Foundation (DFG) for financial support in the
References (30)
- Köppers M, Herzig C, Friesel M, Mishin Y. Acta Mater...
- Gerold U, Herzig C. Defect Diff Forum...
- Rusing J, Herzig C. Scripta Metall. Mater....
- Rusing J, Herzig C. Intermetallics...
- Darken LS. Trans Am Inst Min Metall Engrs...
- Manning JR. Diffusion kinetics for atoms in crystals, Princeton: Van Nostrand,...
- Bormann R. Private...
- Kroll S, Mehrer H, Stolwijk N, Herzig C, Rosenkranz R, Frommeyer, G. Z Metallkd...
- Sprengel W, Oikawa N, Nakajima H. Intermetallics...
- Braun J, Ellner M, Predel B. Z Metallkd...