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Beyond Ni-based Superalloys

Fig. 1: Atomic structure of Zr alloyed tilt Σ5(310)[001] GB in molybdenum. For distinguishing between Mo atoms that belong to different grains, red and yellow spheres are used. Green sphere represents Zr atom.

Nickel-based superalloys, traditionally used to sustain the most stressed parts of turbine blades, have a limited service temperature (around 1000 °C).[1,2] Applying materials with higher melting points would allow to operate these components with increased gas inlet temperatures and to optimize the thermodynamic behaviour leading to a reduction of fuel consumption, emissions and costs. Mo-based alloys combine high strength and stiffness at elevated temperatures with high thermal conductivity and a low coefficient of thermal expansion desired for high-temperature applications.[3-5] Because of their creep and corrosion resistance they bear good prospects to be used in turbine blades.[6]  In order to meet the requirements for the desired applications, other material properties such as ductility and fracture toughness have to be comparable with traditionally used Ni-based superalloys. Experimental studies show that microalloying with Zr is an efficient way to increase the fracture toughness and ductility of Mo[7]  and Mo-based alloys.[6,8,9] However, the physical origin of this effect is not clear. At this point, total-energy calculations based on the densityfunctional theory (DFT) are useful for obtaining a detailed understanding of the energetics on the atomic scale. Our calculations are carried out in the framework of the density-functional theory (DFT)[10,11] using the program package VASP.[12,13] The GGA-PBE[14] functional for describing exchange-correlation interactions is employed and Blöchl’s projector augmented wave (PAW) method[15] to define pseudopotentials. The tilt Σ5(310)[001] grain boundary (GB) is modeled in a periodic supercell of 160 atoms and consists of two equivalent GBs. The calculations are done using a planewave energy-cutoff of 450 eV and the Brillouin zone is sampled with a grid of a 2x6x8 generated by Monkhorst-Pack method.16 Atoms are relaxed while keeping the cell parameters fixed until the maximum force acting on each of them was less than 0.05 eV/Å. The tilt Σ5(310)[001] GB is constructed by tilting the bcc Mo cell by an angle of 36.9° around the [001] axis (see Figure 1). We replace one Mo atom by Zr on each non-equivalent lattice site within the GB and optimize the structure. By comparing the formation energy of Zr in the GB relative to Zr in the bulk, we determine a thermodynamical driving force for segregation. The formation energy is defined as: Hf = EGB+y.Zr – EGB – y . єMo2Zr + (1 + 2y) .єMo. Here, EGB+y.Zr and EGB are the total energies of the GB model with and without Zr, respectively. The total energy of bulk molybdenum per Mo atom is represented by єMo. Mo2Zr is used as a reference state for Zr, since the pure Mo phase is in equilibrium with the Mo2Zr phase if the Zr content is increased.[17] Changes in the formation energy of Zr occupying non-equivalent lattice sites within the GB relative to a position in the bulk Mo (Hf(bulk Mo) = 0.27 eV) are -0.51 eV for the position “1”, -0.17 eV for the position “2” and -0.15 eV for the position “3”. The negative values correspond to the reduction in energy which reveals the existence of a strong driving force for GB segregation. Zr being an oversized alloying additive relative to Mo atom prefers to occupy sites with a sufficient free volume, which is a site “1” (see Figure 1). Our results reveal the driving force of Zr to segregate to Mo GB. As the next step, the effect of Zr on the GB cohesive strength has to be investigated. To obtain results independent of the GB orientation, another GB configuration should be constructed.

Literatur:

1. J. Schneibel et al., Mo-Si-B alloy development, 2005.

2. M. Heilmaier et al., JOM 61, 61 (2009).

3. M. Miller et al., Scripta Mater. 46, 299 (2002).

4. M. Mousa et al., Ultramicroscopy 111, 706 (2011).

5. S. Chakraborty et al., J. Alloy. Compd. 477, 256 (2009).

6. J. Schneibel, P. Tortorelli, R. Ritchie, and J. Kruzic, Metall. Mater. Trans.: A 36, 525 (2005).

7. J. Fan et al., Int. J. Refract. Met. H. 27, 78 (2009).

8. H. Saage et al., Acta Mater. 57, 3895 (2009).

9. M. Krüger et al., Intermetallics 16, 933 (2008).

10. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).

11. L. Sham and W. Kohn, Phys. Rev. 145, 561 (1966).

12. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).

13. G. Kresse and J. Furthmüller, Comp. Mater. Sci. 6, 15 (1996).

14. J. Perdew, K. Burke, and M.Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

15. P. Blöchl, Phys. Rev. B 50, 17953 (1994).

16. H. Monkhorst and J. Pack, Phys. Rev. B 13, 5188 (1976).

17. H. Okamoto, J. Phase Equilib. Diff. 25, 485 (2004).