Effects of tantalum on the partitioning of tungsten between the γ- and γ′-phases in nickel-based superalloys: Linking experimental and computational approaches
Introduction
Nickel-based superalloys are widely employed for turbine blades of aerospace jet engines and land-based power generators owing to their outstanding high-temperature strength, creep and oxidation resistance [1], [2]. The continuing efforts to increase the thermodynamic efficiency of turbine engines, which implies obtaining a high ratio of energy yield to fuel consumption, requires elevating the operating temperature of the turbine engine (>1200 °C) [3]. This implies improving the high-temperature properties of these superalloys by studying the basic rules for designing them [1], [4]. Nickel-based superalloys for turbine blades are single crystals having a two-phase microstructure, containing a high volume fraction of Ni3Al-based γ′ (L12)-precipitates, which are dispersed in a Ni-based γ (face-centered cubic, fcc)-matrix. Both phases contain refractory elements, which promote solid-solution strengthening of the γ-matrix (e.g. Mo, W, Re and Ru) and the formation of γ′-precipitates (e.g. Ta, Nb and Ti) [5]. The partitioning of elements to the γ- and γ′-phases in Ni-based superalloys determines the lattice parameter misfit at the coherent γ/γ′ interface, which strongly correlates with the elevated temperature mechanical properties [6], [7]. The lattice parameter misfit is particularly sensitive to variations in the concentrations of tungsten on both sides of the γ/γ′ heterophase interface due to its large atomic diameter [1], [8].
Studies of phase compositions in aged, commercial multi-component Ni-based superalloys have been executed [9], [10], [11], [12], [13], [14], [15], [16], [17] applying atom probe tomography (APT) [18], [19], [20], analytical electron microscopy and electron probe microanalysis (EPMA) [21]. These studies report that W has a tendency to occupy the γ-phase, yielding partitioning ratios slightly less than unity. The partitioning ratio is defined by:where and are the atomic fractions of an element i in the γ′-precipitates and in the γ-matrix, respectively. To the best of our knowledge, a value of has not been reported for multi-component Ni-based superalloys, excluding as-quenched alloys [22].
In contrast with the cited studies, investigations of model Ni-based alloys with a small number of elements (3–6) containing W report values of [8], [23], [24], [25]. For instance, Sudbrack et al. [23] reported values ranging between 1.2 and 2.0 for a Ni–Al–Cr–W alloy aged for different times between 0 and 264 h at 1073 K. This distinction between values measured for model Ni-based alloys and values measured for multi-component ones has not been explained on a scientific basis.
To address this question, we presented an APT study of a directionally solidified ternary Ni–14Al–3W (at.%) and a multi-component Ni–14.6Al–8.18Cr–7.74Co–1.95Ta–0.95Mo–2.31W–1.47Re–0.63C–0.05Hf (at.%) Ni-based alloys [26], indicating the preference of W for the γ′-phase in the former alloy () and for the γ-phase in the latter alloy (). We suggested that Ta is responsible for the rejection of W from the γ′-phase into the γ-phase, and supplemented our hypothesis by first-principles calculations at 0 K. This viewpoint gives rise to three important questions: (i) Can we provide clear experimental evidence for the effect of Ta for other alloys having different compositions and processed using different conditions? (ii) Are our first-principles calculations, implying the reversal of W-partitioning, predictive for higher aging temperatures as well? (iii) What are the rules governing the site-preference of W and Ta? Addressing these three questions is essential for generalizing our model for the effect of Ta on W-partitioning. Herein, we provide further strong support for our hypothesis based on three different approaches: (i) APT experiments; (ii) first-principles calculations; and (iii) computational thermodynamics to achieve a conclusive picture of how the presence of Ta reverses the partitioning of W atoms in Ni-based superalloys.
Section snippets
Methodology
To provide additional support for our hypothesis that Ta is the element responsible for the partitioning reversal of W, we first demonstrate the difference between the partitioning behavior of W in a Ni–Al–W alloy, a reference state alloy and two multi-component alloys (Section 3.1). All three alloys, were produced by directional solidification and analyzed similarly. We then calculate the substitutional formation energies of W and Ta at different sites in the γ- and the γ′-phases (Section 3.2
Tungsten partitioning in ternary and multi-component alloys
The following APT analyses are based on the results obtained from five, six and ten APT specimens prepared from the ternary, ME-9 and ME-15 alloys, respectively (Table 1). Fig. 1a displays a three-dimensional (3-D) APT reconstruction for the ternary alloy, displaying only the Ni (green), Al (red) and W atoms (black spheres) for clarity. The γ- and γ′-phases can be unambiguously identified based on the partitioning of Al to the γ′-phase. The red surfaces are the 10.5 at.% Al isoconcentration
Reversal of W partitioning: atom probe tomographic analyses
A comparison of the APT results for the ternary and multi-component alloys demonstrates that is reduced from 1.49 ± 0.13 for the ternary to 0.92 ± 0.08 and 0.89 ± 0.06 for alloys ME-9 and ME-15, respectively (Fig. 1, Fig. 2). The values for alloys ME-9 and ME-15 agree with values reported previously. APT studies of different multi-component Ni-based alloys (aged at different temperatures, 1123–1603 K) for different durations (5–185 h) yield values ranging between 0.62 and 0.96 [9],
Summary and conclusions
We utilized APT to analyze phase partitioning of W in different Ni-based alloys, and supplemented and complemented our experiments with first-principles calculations using VASP and thermodynamic computations using Thermo-Calc. We find that the partitioning ratio of W, , Eq. (1), is sensitive to the concentration of Ta in γ plus γ′ Ni-based alloys. Our findings and conclusions are summarized as follows:
- •
The partitioning ratios of W in two directionally solidified multi-component alloys,
Acknowledgements
This research was implemented in support of MEANS II AFOSR Grant No. FA9550-05-1-0089 and of the National Science Foundation (NSF) under Grant No. DMR-0804610 for Dr. Zugang Mao. Dr. Yaron Amouyal wishes to acknowledge the Marie Curie IOF support under the 7th framework program of the commission of the European community. Dr. Larry Graham (PCC Airfoils), Prof. Tresa Pollock and Dr. Jonathan Madison (University of Michigan, Ann Arbor) are kindly thanked for supplying alloys, as well as Dr.
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