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Interdiffusion in fcc Ni–X (X = Rh, Ta, W, Re and Ir) alloys
Journal of Alloys and Compounds 657 (2016) 457e463
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Interdiffusion in fcc NieX (X ¼ Rh, Ta, W, Re and Ir) alloys Juan Chen a, Jinkun Xiao b, Lijun Zhang a, *, Yong Du a a b
State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China College of Mechanical Engineering, Yangzhou University, Yangzhou, 225127, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 August 2015 Received in revised form 10 October 2015 Accepted 13 October 2015 Available online 19 October 2015
The interdiffusion coefficients in binary face-centered cubic (fcc) NieX (X ¼ Rh, Ta, W, Re and Ir) alloys at 1473, 1523, 1573 and 1623 K were measured by using semi-infinite diffusion couples together with the SauereFreise method. A scientific method was employed to evaluate the errors of the determined interdiffusivities by considering the error propagation. The measured interdiffusion coefficients agree in general with the literature data. In order to find out the possible substitutional element for Re in Nibased superalloys, a comprehensive comparison among the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473e1623 K was conducted. The comparison results indicate that fcc Ni-6 wt% Os alloys exhibit the lowest diffusion coefficient, followed by Ni-6 wt% Re and Ni-6 wt% Ir alloys. The further analysis on the variation of interdiffusion coefficient with its influence factors including alloying concentration, temperature, atomic number, activation energy, atomic radius and compressibility was also performed. © 2015 Elsevier B.V. All rights reserved.
Keywords: Nickel based superalloys Interdiffusion Diffusion coefficient Diffusion couple Transition element
1. Introduction The crystal structure of nickel (Ni) is a stable face centered cubic (fcc) crystal structure at temperatures ranging from room temperature to its melting point [1]. This structure allows it to resist mechanical and chemical degradation at elevated temperatures, and for this reason nickel-based superalloys are widely used in both aviation and land-based gas turbine environments [2e5]. The nickel-based superalloys exhibit a typical microstructure consisting of a high volume fraction of coherently precipitated g' (ordered fccL12 structure) cubes separated by thin channels of g-matrix (disordered fcc-A1 structure). To meet the extreme requirements for function at high temperatures, nickel-based superalloys require high resistance to creep deformation. Resistance to creep deformation depends largely on diffusion coefficients, and thus the refractory alloying elements are usually added into g-matrix phase of nickel-based superalloys [6,7]. For instance, rhenium (Re), which exhibits fairly low diffusion coefficients, is often added to nickelbased superalloys to improve creep resistance [8]. The amount of Re used in these superalloys has increased from 3 wt% in the second generation to 6 wt% in the third generation [9]. Though the addition of higher amounts of Re can improve creep resistance, this method
* Corresponding author. E-mail addresses: [email protected], [email protected] (L. Zhang). http://dx.doi.org/10.1016/j.jallcom.2015.10.120 0925-8388/© 2015 Elsevier B.V. All rights reserved.
has some drawbacks [8], including, i) the formation of topologically packed phases (TCPs), and ii) increased costs due to the high price of Re. Therefore, in recent years, efforts [8,10e19] have been made to evaluate alloy elements with comparable diffusion coefficients for use in next generation superalloys. First, it is necessary to obtain reliable measurements of interdiffusion coefficients in Ni-rich binary alloys (in the fcc structure) consisting of Ni and the potential elements. One pragmatic method for selecting potential substitutional elements is to start with the elements adjacent in the periodic table to Re, including Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt. There have been some reports on interdiffusivities in all the related binary systems, i.e., NieNb [14,20], NieMo [14,21e25], NieRu [12,13,15], NieRh [15], NiePd [11,15], NieTa [16], NieW [12,16,21,26e28], NieOs [29,30], NieIr [15] and NiePt [10,15,25]. However, there is only one report for NieRh, NieTa and NieIr systems, by Karunaratne et al. [15,16]. Our recently measured interdiffusion coefficients in fcc NieOs alloys [29] was inconsistent with previous data in the literature [30]. Therefore, new experimental data are needed to validate the interdiffusion coefficients for NieRh, NieTa and NieIr systems. For fcc NieRe alloys, the data measured by Mabruri et al. [12] and Karunaratne et al. [16] was limited to temperatures 1573 K, and thus new experiments at higher temperatures need to be conducted. For the fcc NieW alloys, although there is a range of reported interdiffusivities in the literature [12,16,21,26e28], certain deviation exists among them, so new experimental
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interdiffusivities are needed for this alloy as well. The major objectives of the present work are: (i) to measure the interdiffusivities in fcc NieX (Rh, Ta, W, Re and Ir) alloys by employing solid single-phase diffusion coupled together with the SauereFreise method, and (ii) to comprehensively compare the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys with those in fcc NieRe alloys at the same concentration typically used for Re in commercial Ni-based alloys to determine the optimal elements to substitute for Re.
2.1. Sample preparation and microchemical analysis Ni9.7 wt% Rh, Ni8.4 wt% Ta, Ni25.0 wt% W, Ni21.4 wt% Re and Ni21.7 wt% Ir alloy ingots were prepared in a high purity argon atmosphere using an arc melting furnace (WKDHL-1, Optoelectronics Co., Ltd., Beijing, China), which is equipped with a nonconsumable tungsten electrode and a water-cooled copper anode. Ni ingots (purity: 99.99 wt%), Rh pieces (purity: 99.99 wt%), Ta ingots (purity: 99.99 wt%), W particles (purity: 99.99 wt%), Re pieces (purity: 99.99 wt%), and Ir particles (purity: 99.99 wt%) were used as the raw materials. All the five alloy ingots were prepared in the same way as described in our recent work on fcc NieOs alloys [29], which can make the alloy elements, i.e., Rh, Ta, W, Re and Ir, to be completely dissolved in the Ni matrix, respectively. After that, all the prepared alloy ingots and a high-purity Ni bar were then annealed in sealed quartz tubes at 1573 ± 2 K for 288 ks for further improving their homogeneity and increasing the grain size. Subsequently, the annealed ingots and pure Ni bar were cut into blocks with a dimension of 5 5 1 mm3. After being ground and polished, the alloys and pure Ni blocks were bound together with Mo clamps to form Ni/Ni9.7 wt% Rh, Ni/Ni8.4 wt% Ta, Ni/Ni25.0 wt % W, Ni/Ni21.4 wt% Re and Ni/Ni21.7 wt% Ir diffusion couples. Ni/ Ni9.7 wt% Rh, Ni/Ni8.4 wt% Ta and Ni/Ni21.7 wt% Ir diffusion couples were then encapsulated in vacuum quartz tubes and annealed for at 1473 ± 2, 1523 ± 2, 1573 ± 2 and 1623 ± 2 K for durations of 252, 129.6, 86.4 and 28.8 ks, respectively. While Ni/ Ni25.0 wt% W and Ni/Ni21.4 wt% Re diffusion couples were encapsulated in vacuum quartz tubes and annealed for at 1473 ± 2, 1523 ± 2, 1573 ± 2 and 1623 ± 2 K for durations of 372.6, 131.4, 158.4 and 43.2 ks, respectively. Finally, the quartz tubes were taken out from the furnace and directly quenched in water. All the diffusion couples were examined by electron probe microanalyzer (EPMA) (JXA-8100, JEOL, Japan) to determine the concentrationedistance profiles. The error for concentration measurements is within 1%.
2.2. Determination of diffusion coefficients When a diffusion couple anneals at a certain temperature, the interdiffusion occurs. The concentration profile can be obtained at a certain time by measuring the concentration of the diffusion species at depth x with EPMA, and can be then used to calculate the ~ There are several methods which can be used to interdiffusivities D. determine interdiffusion coefficients in binary systems. In the present work, the SauereFreise method was used to calculate the ~ in fcc NieX (Rh, Ta, W, Re and Ir) alloys, flux ~J and interdiffusivities D
2
Zx
Z∞ YX $dxþYX $
∞
x
3 7 ð1 YX Þ$dx5
Zx
Z∞ YX $dxþYX $
∞
3 7 ð1 YX Þ$dx5
(2)
x
where t is diffusion time, and YX is the normalized concentration given by
YX ¼
CX CX CXþ CX
(3)
where CX is the concentration of X (Rh, Ta, W, Re and Ir) at one end of the diffusion couple, while CXþ is that at the other end of the ~ is to be diffusion couple. CX is the concentration at which D evaluated.
2. Experimental procedure
~J ¼ 1 $6 4ð1 YX Þ$ 2t
2 ~ ¼ 1 $ dx $6 D 4ð1 YX Þ$ 2t dYX
(1)
3. Results and discussion 3.1. Concentration profiles and interdiffusion coefficients Fig. 1(a)e(e) displays the typical concentrationedistance profiles of all the diffusion couples (i.e., Ni/Ni9.7 wt% Rh, Ni/ Ni8.4 wt% Ta, Ni/Ni25.0 wt% W, Ni/Ni21.4 wt% Re and Ni/ Ni21.7 wt% Ir) annealed at 1573 K in the present work. To simplify presentation, all the original experimental data for the measured concentrationedistance profiles of Ni/Ni9.7 wt% Rh, Ni/Ni8.4 wt % Ta, Ni/Ni25.0 wt% W, Ni/Ni21.4 wt% Re and Ni/Ni21.7 wt% Ir diffusion couples annealed at 1473, 1523, 1573 and 1623 K for different times are provided as Supplementary Materials. As can be seen in Fig. 1, all the profiles are asymptotic, and can fit the Boltzmann curves very well, indicating that the atomic diffusion occurs in the solid solution region of each system in a good state. The diffusion time for each diffusion couple is also indicated in each plot. Though the diffusion time of Ni/NieRe and Ni/NieW couples is longer than that of Ni/NieTa and Ni/NieRh couples, the diffusion distances of Ta and Rh in Ni are longer than those of Re and W in Ni, indicating that interdiffusion coefficients in NieTa and NieRh systems are larger than those in NieRe and NieW systems. In order to perform a comprehensive comparison, accurate interdiffusion coefficients in each binary system need to be evaluated. Based on all the measured concentration profiles, the interdiffusion coefficients in fcc-(Ni) phase of the binary NieX (Rh, Ta, W, Re and Ir) systems can be calculated using the SauereFreise method, as described in Section 2.2. The obtained interdiffusion coefficients at 1473, 1523, 1573 and 1623 K are presented in Fig. 2(a)e(e). The experimental errors of the interdiffusivities determined by the SauereFreise method were evaluated according chelle et al. [31], who considered the to the method proposed by Le error propagation via the following function,
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 u X vG uðGðA; B:::ÞÞ ¼ t ðuðaÞÞ2 va a¼A;B:::
(4)
Here, A and B… are the correlation quantities of function f, while uðaÞ ða ¼ A; B:::Þ is the uncertainty in the measurements of variable a such as concentration. During the evaluation of the experimental errors, the uncertainties from different sources including the experimental measurement and the Boltzmann function fitting were propagated first to the calculation of flux in Eq. (1) and then to the calculation of diffusivities in Eq. (2). Table 1 lists the uncertainties for each parameter contributed to the error propagation in Eq. (4) during error evaluation for interdiffusivities in fcc NieX (Rh, Ta, W, Re and Ir) alloys. To eliminate the effect of the absolute value, the relative error, which equals to the uncertainty divided by
J. Chen et al. / Journal of Alloys and Compounds 657 (2016) 457e463
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Fig. 1. Measured concentration profiles of different diffusion couples annealed at 1573 K in the present work: (a) Ni/Ni9.7 wt% Rh, (b) Ni/Ni8.4 wt% Ta, (c) Ni/Ni25.0 wt% W, (d) Ni/Ni21.4 wt% Re and (e) Ni/Ni21.7 wt% Ir.
the absolute value of the interdiffusivity rather than the uncertainty itself was utilized in the present work, and is presented in the caption of Fig. 2. This method of error uncertainty evaluation has been successfully applied in several systems in our research group [32,33]. The average relative errors of the interdiffusivities obtained by this numerical inverse method are evaluated and their values are 3%, 4%, 5%, 6% and 5% for Rh, Ta, W, Re and Ir, respectively. It can be seen from Fig. 2 that the presently determined interdiffusivities in fcc-(Ni) phase of the binary NieX (X ¼ Rh, Ta, W, Re and Ir) are slightly concentration-dependent, and increase as the temperature increase. The experimental data in the fcc NieRh, NieTa, NieRe and NieIr alloys agree well with the data from the corresponding literature [12,15,16], indicating that the experimental interdiffusivities in these four fcc alloys are reasonable. As for fcc NieW alloys, the presently determined interdiffusivities are coincident with the majority of previously reported data from Refs. [12,26e28], strengthening the reliability of these measurements. Based on Fig. 2, the general trend is that at the same temperature the interdiffusion coefficients in fcc NieTa alloys are the largest, followed by Rh, W, Ir and Re in sequence. Thus, the interdiffusion coefficients of fcc NieRe alloys are still the lowest among these 5 elements. To determine if an element possesses interdiffusion coefficients lower or comparable to Re, we needed to extend our search range to other elements. For this, we selected the 4d and 5d transition elements adjacent to Re, including Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt.
3.2. Comparison of interdiffusion coefficients among 4d and 5d transition elements In the literature [8,15,17e19], the impurity diffusion coefficients in Ni were commonly used for comparison. However, the impurity diffusion coefficients are not direct experimental data in the literature [8,15,17e19], but just either the extrapolated values from the concentration-dependent interdiffusion coefficients or the firstprinciples computed values. Moreover, alloying element Re in the third generation Ni-based superalloys is added to 6 wt%, as stated above. Thus, in order to conduct an appropriate comparison, the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys were measured with 6 wt% X at 1473e1623 K. To summarize some general rules for further searching the potential substitutional elements, interdiffusion coefficients should be evaluated for how they can vary in response to including alloying concentration, temperature, atomic radius, misfit strain, vacancy-solute binding energy, compressibility and so on [8,18,34]. The interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473e1623 K from the literature [14,15,29] and the present work against atomic number are presented in Fig. 3. As can be seen in Fig. 3, the interdiffusion coefficients decrease firstly and then increase along the atomic number for 4d and 5d transition elements. Moreover, Ru and Os reach the minimum in the two series, respectively. This similar behavior is consistent with Ru and Os being in the same
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Fig. 2. Interdiffusion coefficients in (a) fcc NieRh, (b) fcc NieTa, (c) fcc NieW, (d) fcc NieRe and (e) fcc NieIr alloys at 1473e1623 K as determined in the present work, compared to previously reported data from the literature, A constant, M, is added in order to separate the data for different temperatures in the figure. The determined relative errors of interdiffusion coefficients in fcc NieRh, fcc NieTa, fcc NieW, fcc NieRe and fcc NieIr alloys are 3%, 4%, 5%, 6% and 5%, respectively.
group. A further comparison of the diffusion coefficients clearly indicates that Os exhibits the lowest diffusion coefficients among the investigated 4d and 5d transition elements, followed by Re. What's more, the interdiffusion coefficients for Tc can be inferred from the trend of the values of other elements in the identical group, even though Tc cannot be studied by conventional methods because of its radioactivity.
It is generally thought that activation energy exhibits similar trend as diffusion coefficients according to the famous Arrhenius equation [35], i.e., that higher activation energy usually leads to lower diffusion coefficients, and vice versa. The determined activation energies in fcc Ni-6 wt% X alloys from the experimental data from the literature and the present work are presented in Table 2, and also plot as a function of atomic number in Fig. 4. It is evident in
J. Chen et al. / Journal of Alloys and Compounds 657 (2016) 457e463 Table 1 List of the uncertainties for each parameter contributed to the error propagation in Eq. (4) during error evaluation of interdiffusivities in fcc NieX (Rh, Ta, W, Re and Ir) alloys. Parameters
CX dCX =dx ~J ~ D
Uncertainty (%) NieRh
NieTa
NieW
NieRe
NieIr
2a 2 2 3
2a 3 3 4
2a 3 4 5
4a 4 5 6
3a 3 4 5
a The error for concentration here include both the one from EPMA measurement and the one during concentration profile fitting.
461
Fig. 5 presents the relative interdiffusivity differences (note: these are absolute values) between interdiffusivities in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys and those in Ni-6 wt% Re alloys at different temperatures, denoted by ~ Ni D ~ Ni Þ=D ~ Ni . In the plot, the baseline (i.e., the relative ðD XX ReRe ReRe interdiffusivity differences are always 0) denotes the results for NieRe alloys. Moreover, the points denote the experimental data, while the solid lines are the linear fitting results. As can be seen in Fig. 5, the interdiffusivities in Ni-6 wt% X (X ¼ Rh, Pt, Ru, W, Ir, Os) alloys are close to those in Ni-6 wt% Re alloy, and thus a magnified plot is present in Fig. 5(a). It is also apparent that only the inter-
Table 2 Summary of activation energies for fcc Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys in the present work and the literature. Element
Compositions (wt %)
Activation energy (Q) (kJ/mol)
Reference
Nb Mo Ru Rh Pd Ta W W Re Os Ir Ir Pt
6 6 6 6 6 6 6 ~0 6 6 6 ~0 6
257.0 281.3 304.4 285.5 265.7 269.7 261.4 296.7 321.6 321.6 327.1 320.0 291.2
Karunaratne Karunaratne Karunaratne This work Karunaratne This work This work Janotti [18] This work Chen [29] This work Janotti [18] Karunaratne
Fig. 4(a) that the maximum activation energy is for the fcc Ni-6 wt% Ru alloy for 4d transition elements. This trend generally agrees well with that of diffusion coefficients, as displayed in Fig. 3(a). However, for the 5d transition elements shown in Fig. 4(b), the trend is much more complex and shows a large deviation from the diffusion coefficients shown in Fig. 3(b). As can be seen in Fig. 4(b), the activation energy of Ir is the largest, followed by Re and Os within a similar magnitude. Moreover, a minimum appears for element W. If the experimental activation energies of Ni-6 wt% W alloys and Ni-6 wt% Ir alloys are replaced by the first-principles results of impurity diffusion of W and Ir in fcc Ni by Janotti et al. [18], the singular degree can be reduced. However, to explain the large differences between the experimental data and the first-principles calculations, further investigations are needed.
Note [14] [14] [15] [15]
[15]
Experiment Experiment Experiment Experiment Experiment Experiment Experiment Calculation Experiment Experiment Experiment Calculation Experiment
diffusivities in Ni-6 wt% Os alloys are lower than those in Ni-6 wt% Re alloys. Though the interdiffusivities in Ni-6 wt% Ir alloys are slightly higher than those in Ni-6 wt% Re alloys, their relative interdiffusivity differences are within a factor of 2. Moreover, the relative interdiffusivity differences in both Ni-6 wt% Os and Ni-6 wt % Ir alloys are almost constant. While for other elements, the situations are different. For Nb, Ta, Pd, Rh and W, their interdiffusivity differences decrease as the temperature increases, but for Mo, Pt and Ru, their trend is the opposite. Fig. 6(a) and (b) show the interdiffusivities in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys at 1473 K against atomic radius and compressibility, respectively. As can be seen, the interdiffusion coefficients for Ni-6 wt% X alloys are scattering, and seem to exhibit no clear relation with both atomic
Fig. 3. Variation of the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir, Pt) at 1473e1623 K from the present work and the literature [14,15,29] by atomic number.
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Fig. 4. Variation of the activation energies by atomic number for (a) 4d and (b) 5d transition elements. The first-principles calculation results by Janotti et al. [18] for the activation energies of W in Ni and Ir in Ni are shown for comparison.
Fig. 5. (a) Temperature dependence of the relative interdiffusivity differences (note: these are absolute values) between interdiffusivities in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys and those in Ni-6 wt% Re alloys; (b) Enlarged portion of the graph indicated by the red dashed box in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
radius and compressibility in general. However, if one takes a closer look, some rough trends can be found. For instance, roughly linear relations between the logarithm values of interdiffusivities in Ni-6 wt% X alloys and Goldschmidt atomic radius exist for respective 4d
and 5d elements in Fig. 6(a). While for Fig. 6(b), a very roughly linear relation exist for all the investigated elements between the logarithm values of their interdiffusivities in Ni-6 wt% X alloys and compressibility.
Fig. 6. The interdiffusion coefficients in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys plotted as a function of the increasing (a) atomic radius and (b) compressibility at 1473 K.
J. Chen et al. / Journal of Alloys and Compounds 657 (2016) 457e463
4. Conclusions Using the bulk diffusion couples together with the SauereFreise method, the concentration-dependent interdiffusion coefficients in fcc NieX (Rh, Ta, W, Re and Ir) alloys at 1473e1623 K were determined and compared with data in the literature. The errors in the data were evaluated by utilizing a scientific method that considers error propagation. A comprehensive comparison among the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473e1623 K indicated that Os and Ir are potential substitutional elements for Re in the new generation of Ni-based superalloys in terms of diffusion coefficients. Further analysis of the variation of interdiffusion coefficient with the influence factors including alloying concentration, temperature, atomic number, activation energy, atomic radius and compressibility was performed, and some rough rules which should be helpful in further attempts to determine the optimal potential substitutional elements for Re were also pointed out. Acknowledgments The financial support from the National Natural Science Foundation for Youth of China (Grant No. 51301208), the National Natural Science Foundation of China (Grant Nos. 51474239, and 51429101) and the Hunan Provincial Natural Science Foundation for Youth of China (Grant No. 2015JJ3146) is greatly acknowledged. Lijun Zhang acknowledges project supported by Shenghua Scholar Program of Central South University, Changsha, China, and project supported by State Key Laboratory of Powder Metallurgy Foundation, Central South University, Changsha, China. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jallcom.2015.10.120. References [1] R.C. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge, UK, 2006.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Interdiffusion in fcc NieX (X ¼ Rh, Ta, W, Re and Ir) alloys Juan Chen a, Jinkun Xiao b, Lijun Zhang a, *, Yong Du a a b
State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China College of Mechanical Engineering, Yangzhou University, Yangzhou, 225127, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 August 2015 Received in revised form 10 October 2015 Accepted 13 October 2015 Available online 19 October 2015
The interdiffusion coefficients in binary face-centered cubic (fcc) NieX (X ¼ Rh, Ta, W, Re and Ir) alloys at 1473, 1523, 1573 and 1623 K were measured by using semi-infinite diffusion couples together with the SauereFreise method. A scientific method was employed to evaluate the errors of the determined interdiffusivities by considering the error propagation. The measured interdiffusion coefficients agree in general with the literature data. In order to find out the possible substitutional element for Re in Nibased superalloys, a comprehensive comparison among the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473e1623 K was conducted. The comparison results indicate that fcc Ni-6 wt% Os alloys exhibit the lowest diffusion coefficient, followed by Ni-6 wt% Re and Ni-6 wt% Ir alloys. The further analysis on the variation of interdiffusion coefficient with its influence factors including alloying concentration, temperature, atomic number, activation energy, atomic radius and compressibility was also performed. © 2015 Elsevier B.V. All rights reserved.
Keywords: Nickel based superalloys Interdiffusion Diffusion coefficient Diffusion couple Transition element
1. Introduction The crystal structure of nickel (Ni) is a stable face centered cubic (fcc) crystal structure at temperatures ranging from room temperature to its melting point [1]. This structure allows it to resist mechanical and chemical degradation at elevated temperatures, and for this reason nickel-based superalloys are widely used in both aviation and land-based gas turbine environments [2e5]. The nickel-based superalloys exhibit a typical microstructure consisting of a high volume fraction of coherently precipitated g' (ordered fccL12 structure) cubes separated by thin channels of g-matrix (disordered fcc-A1 structure). To meet the extreme requirements for function at high temperatures, nickel-based superalloys require high resistance to creep deformation. Resistance to creep deformation depends largely on diffusion coefficients, and thus the refractory alloying elements are usually added into g-matrix phase of nickel-based superalloys [6,7]. For instance, rhenium (Re), which exhibits fairly low diffusion coefficients, is often added to nickelbased superalloys to improve creep resistance [8]. The amount of Re used in these superalloys has increased from 3 wt% in the second generation to 6 wt% in the third generation [9]. Though the addition of higher amounts of Re can improve creep resistance, this method
* Corresponding author. E-mail addresses: [email protected], [email protected] (L. Zhang). http://dx.doi.org/10.1016/j.jallcom.2015.10.120 0925-8388/© 2015 Elsevier B.V. All rights reserved.
has some drawbacks [8], including, i) the formation of topologically packed phases (TCPs), and ii) increased costs due to the high price of Re. Therefore, in recent years, efforts [8,10e19] have been made to evaluate alloy elements with comparable diffusion coefficients for use in next generation superalloys. First, it is necessary to obtain reliable measurements of interdiffusion coefficients in Ni-rich binary alloys (in the fcc structure) consisting of Ni and the potential elements. One pragmatic method for selecting potential substitutional elements is to start with the elements adjacent in the periodic table to Re, including Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt. There have been some reports on interdiffusivities in all the related binary systems, i.e., NieNb [14,20], NieMo [14,21e25], NieRu [12,13,15], NieRh [15], NiePd [11,15], NieTa [16], NieW [12,16,21,26e28], NieOs [29,30], NieIr [15] and NiePt [10,15,25]. However, there is only one report for NieRh, NieTa and NieIr systems, by Karunaratne et al. [15,16]. Our recently measured interdiffusion coefficients in fcc NieOs alloys [29] was inconsistent with previous data in the literature [30]. Therefore, new experimental data are needed to validate the interdiffusion coefficients for NieRh, NieTa and NieIr systems. For fcc NieRe alloys, the data measured by Mabruri et al. [12] and Karunaratne et al. [16] was limited to temperatures 1573 K, and thus new experiments at higher temperatures need to be conducted. For the fcc NieW alloys, although there is a range of reported interdiffusivities in the literature [12,16,21,26e28], certain deviation exists among them, so new experimental
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interdiffusivities are needed for this alloy as well. The major objectives of the present work are: (i) to measure the interdiffusivities in fcc NieX (Rh, Ta, W, Re and Ir) alloys by employing solid single-phase diffusion coupled together with the SauereFreise method, and (ii) to comprehensively compare the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys with those in fcc NieRe alloys at the same concentration typically used for Re in commercial Ni-based alloys to determine the optimal elements to substitute for Re.
2.1. Sample preparation and microchemical analysis Ni9.7 wt% Rh, Ni8.4 wt% Ta, Ni25.0 wt% W, Ni21.4 wt% Re and Ni21.7 wt% Ir alloy ingots were prepared in a high purity argon atmosphere using an arc melting furnace (WKDHL-1, Optoelectronics Co., Ltd., Beijing, China), which is equipped with a nonconsumable tungsten electrode and a water-cooled copper anode. Ni ingots (purity: 99.99 wt%), Rh pieces (purity: 99.99 wt%), Ta ingots (purity: 99.99 wt%), W particles (purity: 99.99 wt%), Re pieces (purity: 99.99 wt%), and Ir particles (purity: 99.99 wt%) were used as the raw materials. All the five alloy ingots were prepared in the same way as described in our recent work on fcc NieOs alloys [29], which can make the alloy elements, i.e., Rh, Ta, W, Re and Ir, to be completely dissolved in the Ni matrix, respectively. After that, all the prepared alloy ingots and a high-purity Ni bar were then annealed in sealed quartz tubes at 1573 ± 2 K for 288 ks for further improving their homogeneity and increasing the grain size. Subsequently, the annealed ingots and pure Ni bar were cut into blocks with a dimension of 5 5 1 mm3. After being ground and polished, the alloys and pure Ni blocks were bound together with Mo clamps to form Ni/Ni9.7 wt% Rh, Ni/Ni8.4 wt% Ta, Ni/Ni25.0 wt % W, Ni/Ni21.4 wt% Re and Ni/Ni21.7 wt% Ir diffusion couples. Ni/ Ni9.7 wt% Rh, Ni/Ni8.4 wt% Ta and Ni/Ni21.7 wt% Ir diffusion couples were then encapsulated in vacuum quartz tubes and annealed for at 1473 ± 2, 1523 ± 2, 1573 ± 2 and 1623 ± 2 K for durations of 252, 129.6, 86.4 and 28.8 ks, respectively. While Ni/ Ni25.0 wt% W and Ni/Ni21.4 wt% Re diffusion couples were encapsulated in vacuum quartz tubes and annealed for at 1473 ± 2, 1523 ± 2, 1573 ± 2 and 1623 ± 2 K for durations of 372.6, 131.4, 158.4 and 43.2 ks, respectively. Finally, the quartz tubes were taken out from the furnace and directly quenched in water. All the diffusion couples were examined by electron probe microanalyzer (EPMA) (JXA-8100, JEOL, Japan) to determine the concentrationedistance profiles. The error for concentration measurements is within 1%.
2.2. Determination of diffusion coefficients When a diffusion couple anneals at a certain temperature, the interdiffusion occurs. The concentration profile can be obtained at a certain time by measuring the concentration of the diffusion species at depth x with EPMA, and can be then used to calculate the ~ There are several methods which can be used to interdiffusivities D. determine interdiffusion coefficients in binary systems. In the present work, the SauereFreise method was used to calculate the ~ in fcc NieX (Rh, Ta, W, Re and Ir) alloys, flux ~J and interdiffusivities D
2
Zx
Z∞ YX $dxþYX $
∞
x
3 7 ð1 YX Þ$dx5
Zx
Z∞ YX $dxþYX $
∞
3 7 ð1 YX Þ$dx5
(2)
x
where t is diffusion time, and YX is the normalized concentration given by
YX ¼
CX CX CXþ CX
(3)
where CX is the concentration of X (Rh, Ta, W, Re and Ir) at one end of the diffusion couple, while CXþ is that at the other end of the ~ is to be diffusion couple. CX is the concentration at which D evaluated.
2. Experimental procedure
~J ¼ 1 $6 4ð1 YX Þ$ 2t
2 ~ ¼ 1 $ dx $6 D 4ð1 YX Þ$ 2t dYX
(1)
3. Results and discussion 3.1. Concentration profiles and interdiffusion coefficients Fig. 1(a)e(e) displays the typical concentrationedistance profiles of all the diffusion couples (i.e., Ni/Ni9.7 wt% Rh, Ni/ Ni8.4 wt% Ta, Ni/Ni25.0 wt% W, Ni/Ni21.4 wt% Re and Ni/ Ni21.7 wt% Ir) annealed at 1573 K in the present work. To simplify presentation, all the original experimental data for the measured concentrationedistance profiles of Ni/Ni9.7 wt% Rh, Ni/Ni8.4 wt % Ta, Ni/Ni25.0 wt% W, Ni/Ni21.4 wt% Re and Ni/Ni21.7 wt% Ir diffusion couples annealed at 1473, 1523, 1573 and 1623 K for different times are provided as Supplementary Materials. As can be seen in Fig. 1, all the profiles are asymptotic, and can fit the Boltzmann curves very well, indicating that the atomic diffusion occurs in the solid solution region of each system in a good state. The diffusion time for each diffusion couple is also indicated in each plot. Though the diffusion time of Ni/NieRe and Ni/NieW couples is longer than that of Ni/NieTa and Ni/NieRh couples, the diffusion distances of Ta and Rh in Ni are longer than those of Re and W in Ni, indicating that interdiffusion coefficients in NieTa and NieRh systems are larger than those in NieRe and NieW systems. In order to perform a comprehensive comparison, accurate interdiffusion coefficients in each binary system need to be evaluated. Based on all the measured concentration profiles, the interdiffusion coefficients in fcc-(Ni) phase of the binary NieX (Rh, Ta, W, Re and Ir) systems can be calculated using the SauereFreise method, as described in Section 2.2. The obtained interdiffusion coefficients at 1473, 1523, 1573 and 1623 K are presented in Fig. 2(a)e(e). The experimental errors of the interdiffusivities determined by the SauereFreise method were evaluated according chelle et al. [31], who considered the to the method proposed by Le error propagation via the following function,
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 u X vG uðGðA; B:::ÞÞ ¼ t ðuðaÞÞ2 va a¼A;B:::
(4)
Here, A and B… are the correlation quantities of function f, while uðaÞ ða ¼ A; B:::Þ is the uncertainty in the measurements of variable a such as concentration. During the evaluation of the experimental errors, the uncertainties from different sources including the experimental measurement and the Boltzmann function fitting were propagated first to the calculation of flux in Eq. (1) and then to the calculation of diffusivities in Eq. (2). Table 1 lists the uncertainties for each parameter contributed to the error propagation in Eq. (4) during error evaluation for interdiffusivities in fcc NieX (Rh, Ta, W, Re and Ir) alloys. To eliminate the effect of the absolute value, the relative error, which equals to the uncertainty divided by
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Fig. 1. Measured concentration profiles of different diffusion couples annealed at 1573 K in the present work: (a) Ni/Ni9.7 wt% Rh, (b) Ni/Ni8.4 wt% Ta, (c) Ni/Ni25.0 wt% W, (d) Ni/Ni21.4 wt% Re and (e) Ni/Ni21.7 wt% Ir.
the absolute value of the interdiffusivity rather than the uncertainty itself was utilized in the present work, and is presented in the caption of Fig. 2. This method of error uncertainty evaluation has been successfully applied in several systems in our research group [32,33]. The average relative errors of the interdiffusivities obtained by this numerical inverse method are evaluated and their values are 3%, 4%, 5%, 6% and 5% for Rh, Ta, W, Re and Ir, respectively. It can be seen from Fig. 2 that the presently determined interdiffusivities in fcc-(Ni) phase of the binary NieX (X ¼ Rh, Ta, W, Re and Ir) are slightly concentration-dependent, and increase as the temperature increase. The experimental data in the fcc NieRh, NieTa, NieRe and NieIr alloys agree well with the data from the corresponding literature [12,15,16], indicating that the experimental interdiffusivities in these four fcc alloys are reasonable. As for fcc NieW alloys, the presently determined interdiffusivities are coincident with the majority of previously reported data from Refs. [12,26e28], strengthening the reliability of these measurements. Based on Fig. 2, the general trend is that at the same temperature the interdiffusion coefficients in fcc NieTa alloys are the largest, followed by Rh, W, Ir and Re in sequence. Thus, the interdiffusion coefficients of fcc NieRe alloys are still the lowest among these 5 elements. To determine if an element possesses interdiffusion coefficients lower or comparable to Re, we needed to extend our search range to other elements. For this, we selected the 4d and 5d transition elements adjacent to Re, including Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt.
3.2. Comparison of interdiffusion coefficients among 4d and 5d transition elements In the literature [8,15,17e19], the impurity diffusion coefficients in Ni were commonly used for comparison. However, the impurity diffusion coefficients are not direct experimental data in the literature [8,15,17e19], but just either the extrapolated values from the concentration-dependent interdiffusion coefficients or the firstprinciples computed values. Moreover, alloying element Re in the third generation Ni-based superalloys is added to 6 wt%, as stated above. Thus, in order to conduct an appropriate comparison, the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys were measured with 6 wt% X at 1473e1623 K. To summarize some general rules for further searching the potential substitutional elements, interdiffusion coefficients should be evaluated for how they can vary in response to including alloying concentration, temperature, atomic radius, misfit strain, vacancy-solute binding energy, compressibility and so on [8,18,34]. The interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473e1623 K from the literature [14,15,29] and the present work against atomic number are presented in Fig. 3. As can be seen in Fig. 3, the interdiffusion coefficients decrease firstly and then increase along the atomic number for 4d and 5d transition elements. Moreover, Ru and Os reach the minimum in the two series, respectively. This similar behavior is consistent with Ru and Os being in the same
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Fig. 2. Interdiffusion coefficients in (a) fcc NieRh, (b) fcc NieTa, (c) fcc NieW, (d) fcc NieRe and (e) fcc NieIr alloys at 1473e1623 K as determined in the present work, compared to previously reported data from the literature, A constant, M, is added in order to separate the data for different temperatures in the figure. The determined relative errors of interdiffusion coefficients in fcc NieRh, fcc NieTa, fcc NieW, fcc NieRe and fcc NieIr alloys are 3%, 4%, 5%, 6% and 5%, respectively.
group. A further comparison of the diffusion coefficients clearly indicates that Os exhibits the lowest diffusion coefficients among the investigated 4d and 5d transition elements, followed by Re. What's more, the interdiffusion coefficients for Tc can be inferred from the trend of the values of other elements in the identical group, even though Tc cannot be studied by conventional methods because of its radioactivity.
It is generally thought that activation energy exhibits similar trend as diffusion coefficients according to the famous Arrhenius equation [35], i.e., that higher activation energy usually leads to lower diffusion coefficients, and vice versa. The determined activation energies in fcc Ni-6 wt% X alloys from the experimental data from the literature and the present work are presented in Table 2, and also plot as a function of atomic number in Fig. 4. It is evident in
J. Chen et al. / Journal of Alloys and Compounds 657 (2016) 457e463 Table 1 List of the uncertainties for each parameter contributed to the error propagation in Eq. (4) during error evaluation of interdiffusivities in fcc NieX (Rh, Ta, W, Re and Ir) alloys. Parameters
CX dCX =dx ~J ~ D
Uncertainty (%) NieRh
NieTa
NieW
NieRe
NieIr
2a 2 2 3
2a 3 3 4
2a 3 4 5
4a 4 5 6
3a 3 4 5
a The error for concentration here include both the one from EPMA measurement and the one during concentration profile fitting.
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Fig. 5 presents the relative interdiffusivity differences (note: these are absolute values) between interdiffusivities in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys and those in Ni-6 wt% Re alloys at different temperatures, denoted by ~ Ni D ~ Ni Þ=D ~ Ni . In the plot, the baseline (i.e., the relative ðD XX ReRe ReRe interdiffusivity differences are always 0) denotes the results for NieRe alloys. Moreover, the points denote the experimental data, while the solid lines are the linear fitting results. As can be seen in Fig. 5, the interdiffusivities in Ni-6 wt% X (X ¼ Rh, Pt, Ru, W, Ir, Os) alloys are close to those in Ni-6 wt% Re alloy, and thus a magnified plot is present in Fig. 5(a). It is also apparent that only the inter-
Table 2 Summary of activation energies for fcc Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys in the present work and the literature. Element
Compositions (wt %)
Activation energy (Q) (kJ/mol)
Reference
Nb Mo Ru Rh Pd Ta W W Re Os Ir Ir Pt
6 6 6 6 6 6 6 ~0 6 6 6 ~0 6
257.0 281.3 304.4 285.5 265.7 269.7 261.4 296.7 321.6 321.6 327.1 320.0 291.2
Karunaratne Karunaratne Karunaratne This work Karunaratne This work This work Janotti [18] This work Chen [29] This work Janotti [18] Karunaratne
Fig. 4(a) that the maximum activation energy is for the fcc Ni-6 wt% Ru alloy for 4d transition elements. This trend generally agrees well with that of diffusion coefficients, as displayed in Fig. 3(a). However, for the 5d transition elements shown in Fig. 4(b), the trend is much more complex and shows a large deviation from the diffusion coefficients shown in Fig. 3(b). As can be seen in Fig. 4(b), the activation energy of Ir is the largest, followed by Re and Os within a similar magnitude. Moreover, a minimum appears for element W. If the experimental activation energies of Ni-6 wt% W alloys and Ni-6 wt% Ir alloys are replaced by the first-principles results of impurity diffusion of W and Ir in fcc Ni by Janotti et al. [18], the singular degree can be reduced. However, to explain the large differences between the experimental data and the first-principles calculations, further investigations are needed.
Note [14] [14] [15] [15]
[15]
Experiment Experiment Experiment Experiment Experiment Experiment Experiment Calculation Experiment Experiment Experiment Calculation Experiment
diffusivities in Ni-6 wt% Os alloys are lower than those in Ni-6 wt% Re alloys. Though the interdiffusivities in Ni-6 wt% Ir alloys are slightly higher than those in Ni-6 wt% Re alloys, their relative interdiffusivity differences are within a factor of 2. Moreover, the relative interdiffusivity differences in both Ni-6 wt% Os and Ni-6 wt % Ir alloys are almost constant. While for other elements, the situations are different. For Nb, Ta, Pd, Rh and W, their interdiffusivity differences decrease as the temperature increases, but for Mo, Pt and Ru, their trend is the opposite. Fig. 6(a) and (b) show the interdiffusivities in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys at 1473 K against atomic radius and compressibility, respectively. As can be seen, the interdiffusion coefficients for Ni-6 wt% X alloys are scattering, and seem to exhibit no clear relation with both atomic
Fig. 3. Variation of the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir, Pt) at 1473e1623 K from the present work and the literature [14,15,29] by atomic number.
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Fig. 4. Variation of the activation energies by atomic number for (a) 4d and (b) 5d transition elements. The first-principles calculation results by Janotti et al. [18] for the activation energies of W in Ni and Ir in Ni are shown for comparison.
Fig. 5. (a) Temperature dependence of the relative interdiffusivity differences (note: these are absolute values) between interdiffusivities in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Os, Ir and Pt) alloys and those in Ni-6 wt% Re alloys; (b) Enlarged portion of the graph indicated by the red dashed box in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
radius and compressibility in general. However, if one takes a closer look, some rough trends can be found. For instance, roughly linear relations between the logarithm values of interdiffusivities in Ni-6 wt% X alloys and Goldschmidt atomic radius exist for respective 4d
and 5d elements in Fig. 6(a). While for Fig. 6(b), a very roughly linear relation exist for all the investigated elements between the logarithm values of their interdiffusivities in Ni-6 wt% X alloys and compressibility.
Fig. 6. The interdiffusion coefficients in Ni-6 wt% X (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys plotted as a function of the increasing (a) atomic radius and (b) compressibility at 1473 K.
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4. Conclusions Using the bulk diffusion couples together with the SauereFreise method, the concentration-dependent interdiffusion coefficients in fcc NieX (Rh, Ta, W, Re and Ir) alloys at 1473e1623 K were determined and compared with data in the literature. The errors in the data were evaluated by utilizing a scientific method that considers error propagation. A comprehensive comparison among the interdiffusion coefficients in fcc NieX (X ¼ Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473e1623 K indicated that Os and Ir are potential substitutional elements for Re in the new generation of Ni-based superalloys in terms of diffusion coefficients. Further analysis of the variation of interdiffusion coefficient with the influence factors including alloying concentration, temperature, atomic number, activation energy, atomic radius and compressibility was performed, and some rough rules which should be helpful in further attempts to determine the optimal potential substitutional elements for Re were also pointed out. Acknowledgments The financial support from the National Natural Science Foundation for Youth of China (Grant No. 51301208), the National Natural Science Foundation of China (Grant Nos. 51474239, and 51429101) and the Hunan Provincial Natural Science Foundation for Youth of China (Grant No. 2015JJ3146) is greatly acknowledged. Lijun Zhang acknowledges project supported by Shenghua Scholar Program of Central South University, Changsha, China, and project supported by State Key Laboratory of Powder Metallurgy Foundation, Central South University, Changsha, China. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jallcom.2015.10.120. References [1] R.C. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge, UK, 2006.
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