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Alloying behavior of Ni3M-type GCP compounds
Journal of Alloys and Compounds 496 (2010) 116–121
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Alloying behavior of Ni3 M-type GCP compounds H. Sugimura, Y. Kaneno, T. Takasugi ∗ Department of Materials Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
a r t i c l e
i n f o
Article history: Received 29 October 2009 Received in revised form 18 February 2010 Accepted 28 February 2010 Available online 6 March 2010 Keywords: GCP phase Site occupancy Ni3 M compound Thermodynamic model
a b s t r a c t The site preference of ternary additions in Ni3 M-type GCP compounds was determined from the direction of solubility lobe of the GCP phase on the ternary phase diagram that have been experimentally reported. In Ni3 Nb (D0a ), Co and Cu preferred the substitution for Ni-site, Ti, V and W the substitution for Nb-site, and Fe the substitution for both sites. In Ni3 V (D022 ), Co preferred the substitution for Ni-site, Cr the substitution for both sites, and Ti the substitution for V-site. In Ni3 Ti (D024 ), Fe, Co, Cu, and Si preferred the substitution for Ni-site, Nb, Mo and V the substitution for Ti-site. The thermodynamic model, which was based on the change in total bonding energy of the host compound by a small addition of ternary solute, was applied to predict the site preference of ternary additions. The bond energy of each nearest neighbor pair used in the thermodynamic calculation was derived from the heat of compound formation by Miedema’s formula. The agreement between the thermodynamic model and the result of the literature search was excellent. From both experimental and theoretical results, it was shown in three Ni3 M-type GCP compounds that both transition and B-subgroup elements have two possibilities, i.e., the case of substitution for Ni-site or the case for M-site, depending on the relative value of two interaction energies. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Among a number of geometrically close-packed (GCP) phases [1,2], Ni3 M-type GCP phases have various types of structures, e.g., Ni3 Nb (D0a ), Ni3 V (D022 ), Ni3 Ti (D024 ), and Ni3 Al (L12 ) as shown in Fig. 1. The coordination number of atoms is 12 in every structure. These structures are constructed by several stacking sequences of common close-packed plane with combination of a twofold hexagonal layer (h-layer) and a threefold cubic layer (c-layer) (Table 1). In addition, M atoms on the close-packed plane show some ordered arrangements: triangular-type (T-type) and rectangular-type (Rtype) in these GCP structures (Table 1). These compounds have a lot of attractive properties as a high-temperature structural material. Therefore these compounds have been used as precipitated phases, i.e., strengtheners in actually used nickel superalloys [3] and as constituent phases of Ni-base multi-phase intermetallic alloys recently developed by the present author’s group [4–9]. The addition of third element to these binary Ni3 M-type GCP compounds or alloying element to the constituent Ni3 M phases in Ni-base multi-phase intermetallic alloys might modify not only the mechanical properties but also other properties such as oxidation or corrosion property. Therefore, to study a solubility limit or substitution behavior of alloying element in Ni3 M-type GCP com-
∗ Corresponding author. Tel.: +81 72 254 9314; fax: +81 72 254 9912. E-mail address: [email protected] (T. Takasugi). 0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2010.02.179
pounds is a critical issue to develop a new type of high-temperature structural material based on intermetallic compounds. The alloying behavior of L12 -type Ni3 M compound, i.e., whether the addition substitutes exclusively for Ni-site, exclusively for Msite or for both sites, has been investigated and reviewed in Ni3 Al, Ni3 Ga, Ni3 Si, and Ni3 Ge compounds by Ochiai et al. [10]. The thermodynamic Bragg–Williams model involving the nearest neighbor interactions, i.e., the change in total bonding energy of the host compound by a small addition of ternary solute at stoichiometry has been applied to these L12 -type Ni3 M compounds [10]. The bond energy of each pair was derived from the heat of compound formation by Miedema’s formula [11,12]. The agreement for preferable site occupation of the addition between the prediction and the experimental result was found to be excellent. Later, the same treatment has been conducted on L12 -type Co3 Ti compound by Takasugi and co-workers and was shown to be successful in predicting preferable site occupation of the addition [13]. Between L12 -type Ni3 M compounds and other Ni3 M-type GCP compounds, the environment of the nearest neighbor atoms is quite same not only for the number of nearest neighbor pairs but also for the kind of nearest neighbor pairs. Ni atom has 8 nearest neighbor pairs with Ni atom and 4 nearest neighbor pairs with M atom while M atom has 12 nearest neighbor pairs with Ni atom. Therefore, the same thermodynamic treatment as that conducted on L12 -type Ni3 M compound may be applicable to other Ni3 M-type GCP compounds. In this paper, we treats three compounds of Ni3 Nb (D0a ), Ni3 V (D022 ), and Ni3 Ti (D024 ) shown in Fig. 1. Those compounds
H. Sugimura et al. / Journal of Alloys and Compounds 496 (2010) 116–121
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Fig. 1. Crystal structures of Ni3 Nb (D0a ), Ni3 V (D022 ), Ni3 Ti (D024 ), and Ni3 Al (or Ni3 Si) (L12 ). Open circle and full circle correspond to Ni atom and M atom in Ni3 M-type compounds, respectively. Also, a shaded plane shows closest plane. Table 1 The crystallographic feature of various Ni3 M-type GCP compounds. Crystal structure Unit cell Stacking order Stacking sequence Hexagonality (%) Unit mesh Ni3 M
D0a hcp AB hh 100 R Ni3 Nb
D022 fee ABCA B C cccccc 0 R Ni3 V
D024 hcp ABAC hchc 50 T Ni3 Ti
L12 fee ABC ccc 0 T Ni3 Al,Ni3 Si
have been used as constituent phases in the Ni-base multi-phase intermetallic alloys [4–9]. It is known that Ni3 Nb and Ni3 Ti are a Berthollide-type and a Daltonide-type compound, respectively and their structures are stable to the melting points while Ni3 V (D022 ) is a Kurnakov-type compound and transforms at 1045 ◦ C to fcctype solid solution with increasing temperature. In an early part of this paper, the experimental data for the alloying behavior that have been so far reported are collected and reviewed for three Ni3 M compounds. In a latter part of this paper, the alloying behavior is predicted by the thermodynamic model, and agreement between the experiment and the modeling is discussed. 2. Reported experimental works In this paper, the site preference for various third elements (X) in the unit cell of a host Ni3 M-type compound is determined from the direction of solubility lobe in an isothermal section of a ternary
phase diagram that have been reported so far. The unit cell of Ni3 M lattice involves two types of site, which are defined as Ni-site and M-site. A ternary addition which occupies mostly Ni-site has a solubility lobe lying in parallel to Ni–X edge in an isothermal section, an addition which occupies mostly M-site has a lobe lying in parallel to M–X edge, and an addition which substitutes for both sites has a lobe extending in a direction almost bisecting the quasi-binary section Ni3 M–Ni3 X and Ni3 M–X3 M. A relatively large number of ternary Ni–Nb–X phase diagrams have been published. Table 2 summarizes the results taken from the existing ternary phase diagrams. Reported temperatures range between 900 and 1200 ◦ C. The table shows the direction and the extent of solubility limit for each solute element. Fe [20] substitutes for both sites, Co [14,15] and Cu [19] mostly for Ni-site and Ti [21,22], V [23] and W [24,25] mostly for Nb-site. The ternary system with Cr [16–18] did not provide a clear indication of substitution behavior in Ni3 Nb because of very small solid solubility. All the reported results on the solid solubility of various kinds of solutes in Ni3 Nb are summarized in Fig. 2. There have been some data for ternary Ni–V–X phase diagrams as listed in Table 3. Data limited to temperature range below 1045 ◦ C in which D022 structure is stable were taken into consideration. Cr [30] substitutes for both sites, and Co [29] mostly for Ni-site. The ternary systems with Al [26–28], Fe [31], and Ti [32] did not provide a clear indication of substitution behavior in Ni3 V because of no agreement between the data from various sources, or, very small solid solubility. However, Ti [33] appears to substitute
Table 2 The reported substitution behavior of ternary additions in Ni3 Nb (D0a ). Element [Reference]
Authors
Year
Temperature (◦ C)
Solid solubility (at.%)
Substitution site
Co [14] Co [15] Cr [16]
Panteleimonov et al. Gupta et al. Kodentsov et al.
1982 1990 1986
Cr [17]
Gupta
1990
Svechnikov and Pan Kodentsov et al. Raghavan Gupta
1960 1988 1992 1991
Pryakhina et al.
1966
Gupta
1991
Gupta
1991
Tikhankin et al.
1976
980 1075 1002 1200 1175 1173 1160 1100 1100 1002 1000 1000 1000 900 1050 1000 900 1000 900
Ni(−7) Nb(−1) Co(+8) Ni(−5) Nb(0) Co(+5) Ni(−3) Nb(−1) Cr(+4) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(−11) Nb(−1) Cu(+12) Ni(−6) Nb(−8) Fe(+14) Ni(0) Nb(−6) Ti (+6) Ni(0) Nb(−6) Ti (+6) Ni(0) Nb(−3) Ti (+3) Ni(−4) Nb(−13) V(+17) Ni(−3) Nb(−4) W(+7) Ni(−3) Nb(−4) W(+7) Ni(−1) Nb(−5) W(+6) Ni(−1) Nb(−5) W(+6)
Ni Ni Ni Indeterminable Indeterminable Indeterminable Indeterminable Indeterminable Indeterminable Ni Ni/Nb Nb Nb Nb Nb Ni/Nb Ni/Nb Nb Nb
Cr [18] Cu [19] Fe [20] Ti [21] Ti [22] V [23] W [24] W [25]
The symbols “Ni”, “Nb”, and “Ni/Nb” in the column “Substitution site” mean that third element substitutes for Ni-site, Nb-site and both sites, respectively. The numerical values expressed in the parentheses in the column “Solid solubility” mean surplus or deficit (expressed by at.%) of each element from the stoichiometric composition of Ni3Nb.
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Fig. 2. Semischematic depiction of the solubility lobes of ternary Ni3 Nb phase for various elements. Data for the systems with Co [14] at 980 ◦ C, Fe [20], Ti [21] and W [25] at 1000 ◦ C, Cu [19] and Cr [16] at 1002 ◦ C and V [23] at 1050 ◦ C are taken from literatures.
Fig. 4. Semischematic depiction of the solubility lobes of ternary Ni3 Ti phase for various elements. Data for the systems with Si [52] at 750 ◦ C, Co [42] at 850 ◦ C, Cu [44] at 870 ◦ C, Mo [49] at 900 ◦ C, Nb [21] at 1000 ◦ C, and Fe [46] at 1027 ◦ C are taken from literature.
3. Thermodynamic consideration
Fig. 3. Semischematic depiction of the solubility lobes of ternary Ni3 V phase for various elements. Data for the systems with Cr [30] at 852 ◦ C, Ti [33] and Al [26] at 1000 ◦ C, and Co [29] at 750–1100 ◦ C are taken from literature.
for V-site. Fig. 3 summarizes the solubility lobes of ternary Ni3 V phase. A large number of ternary Ni–Ti–X phase diagrams have been published. Table 4 summarizes the results. Reported temperatures range between 600 and 1200 ◦ C. Co [42,43], Cu [44,45], Fe [46], and Si [51,52] substitute mostly for Ni-site, and Nb [21,22], Mo [47,48,43,50,51], and V [32,33,53] mostly for Ti-site. The ternary systems with Al [34–41] did not provide a clear indication of substitution behavior in Ni3 Ti because there is not good agreement between the data with Al from various sources. Fig. 4 summarizes the reported results on the substitution behavior in Ni3 Ti.
This section is devoted to showing whether a simple thermodynamic treatment will serve to account for the site preference of a third element X in a perfectly ordered stoichiometric D0a , D022 , and D024 alloys, based on the Bragg–Williams model of nearest neighbor interactions. The only nearest neighbor approximation should be suitable for our purpose, because the second and further distant neighbor interaction energies are likely to be negligible in these Ni3 M-type compounds. Comparison will be made on the difference of total bond energies between two extreme cases for the substitution of component X. One case is that X atoms replace Ni atoms on Ni-site and the other case is that X atoms replace M atoms on M-site. In comparison between H(Ni) and H(M) where the former is the change in total bond energy in Ni3 M system by a small addition of third element X to Ni-site while the latter is the change in total bond energy in Ni3 M system by a small addition of third element X to M-site, the site preference for a ternary addition of X atoms can be directed by the following expression VMX VNiX ≶ + P. VNiM VNiM
(1)
Vij is the interaction parameter and defined by Hij − (Hii + Hjj )/2 where Hij is the bond energy for ij pairs. If the quantity on the left hand side is smaller, the substitution of X for Ni-site is preferred while if that on the right hand is smaller, the substitution of X for M-site is preferred. Also, P is defined by the following expression P =2−
3 (H
− HMM ) . VNiM
NiNi
2
(2)
Table 3 The reported substitution behavior of ternary additions in Ni3 V (D022 ). Element [Reference] Al [26] Al [27] Al [28] Co [29] Cr [30] Fe [31] Ti [32] Ti [33]
Authors
Year
Myasnikova et al.
1977
Hayes et al. Hong et al. Nino et al.
1993 1989 1999
Kodentzov et al.
1987
Raynor and Rivlin Gupta Eremenko et al.
1988 1991 1984
Temperature (◦ C)
Solid solubility (at.%)
Substitution site
1000 600/800 800 1027 750–1100 1002 852 1000 1000 1000
Ni(−3) V(0) Al(+3) Ni(−3) V(0) Al(+3) Ni(0) V(−3) Al(+3) Ni(0) V(−1) Al(+1) Ni(−16) V(0) Co(15) Ni(−2) V(−1) Cr(+3) Ni(−3) V(−3) Cr(+6) Ni(−1) V(−1) Fe(+2) Ni(−4) V(−4) Ti(+8) Ni(−2) V(−6) Ti(+8)
Ni Ni V Indeterminable Ni Ni/V or Ni/V Ni/V or Ni/V V
The symbols “Ni”, “V”, and “Ni/V” in the column “Substitution site” mean that third element substitutes for Ni-site, V-site and both sites, respectively. The numerical values expressed in the parenthesis in the column “Solid solubility” mean surplus or deficit (expressed by at.%) of each element from the stoichiometric composition of Ni3 V.
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Table 4 The reported substitution behavior of ternary additions in Ni3 Ti (D024 ). Element [Reference]
Authors
Year
Temperature (◦ C)
Solid solubility (at.%)
Substitution site
Al [34]
Budberg
1993
1150 1025 800
Ni(0) Ti(0) Al(0) Ni(0) Ti(0) Al(0) Ni(0) Ti(0) Al(0)
Indeterminable Indeterminable Indeterminable
Al [35]
Lee and Nash
1991
1150 900 800
Ni(0) Ti(0) Al(0) Ni(−1) Ti(−3) Al(+4) Ni(0) Ti(0) Al(0)
Indeterminable Ti Indeterminable
Markiv et al. Raman and Schubert Yang et al. Nash and Liang
1973 1965 1992 1985
Taylor
1956
Al [41]
Taylor and Floyd
1952/1953
Co [42] Co [43]
Du et al. Eremenko et al.
1993 1984
Cu [44]
Gupta
1990
Alisova and Budberg
1992
Gupta
1990
Mo [47]
Gupta
1991
Mo [48] Mo [43] Mo [49] Mo [50] Nb [21] Nb [22] Si [51] Si [52] V [32] V [33] V [53]
Prima et al. Eremenko et al. Eremenko et al. Guard and Smith Gupta Pryakhina et al. Markiv et al. Williams Gupta Eremenko et al. Gupta
1986 1984 1983 1959/1960 1991
800 800 900 900 1000 750 1150 1000 850 750 850 800 870 800 800 600 1027 900 1200 1175 900 1200 900 900 1175 1000 1000 900 750 1000 1000 1000 1045/1100
Ni(−1) Ti(0) Al(+1) Ni(−1) Ti(0) Al(+1) Ni(+2) Ti(−5) Al(+3) Ni(0) Ti(−4) Al(+4) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(−1) Ti(0) Al(+1) Ni(−8) Ti(−1) Fe(+9) Ni(−13) Ti(+1) Fe(+12) Ni(−3) Ti(0) Cu(+3) Ni(−4) Ti(+1) Cu(+3) Ni(−3) Ti(0) Cu(+3) Ni(−1) Ti(0) Cu(+1) Ni(−24) Ti(−3) Fe(+27) Ni(−13) Ti(−1) Fe(+14) Ni(−1) Ti(−4) Mo(+5) Ni(0) Ti(−1) Mo(+1) Ni(0) Ti(−3) Mo(+3) Ni(−1) Ti(−4) Mo(+5) Ni(0) Ti(−3) Mo(+3) Ni(−1) Ti(−1) Mo(+2) Ni(−1) Ti(0) Mo(+1) Ni(0) Ti(−4) Nb(+4) Ni(0) Ti(−4) Nb(+4) Ni(0) Ti(−2) Nb(+2) Ni(−2) Ti(0) Si(+2) Ni(−1) Ti(0) Si(+1 Ni(−1) Ti(−9) V(+10) Ni(0) Ti(−11) V(+11) Ni(−3) Ti(−8) V(+11)
Ni Ni Ti Ti Ti Ti Ti Ti Ti Ni Ni Ni Ni Ni Ni Ni Ni Ni Ti Ti Ti Ti Ti Ni/Ti or indeterminable Ni Ti Ti Ti Ni Ni Ti Ti Ti
Al [36] Al [37] Al [38] Al [39] Al [40]
Cu [45] Fe [46]
1966 1966 1971 1991 1984 1991
The symbols “Ni”, “Ti”, and “Ni/Ti” in the column “Substitution site” mean that third element substitutes for Ni-site, Ti-site and both sites, respectively. The numerical values expressed in the parenthesis in the column “Solid solubility” mean surplus or deficit (expressed by at.%) of each element from the stoichiometric composition of Ni3Ti.
It is noted that the value of P, which is called as asymmetric index, depends only on the nature of the host compound and has a value between +1 and −1. If the available experimental data permit us to derive the bonding energies, it is possible to test whether the above expression is appreciable to evaluate the substitution behavior of Ni3 Nb, Ni3 V, and Ni3 Ti compounds. However, the experimental data are too limited to obtain the bonding energy in any set of given elements. Fortunately, Miedema and coworkers have developed a prognosis method for the prediction of the heat of alloy formation [11,12]. They have characterized each system by a set of two parameters assigned to each component. For the Miedema’s semiempirical formula, the accuracy of the prediction has been successfully tested on various cases by many investigators. Now, the evaluation of the bonding energies can be done in every sets of elements interest. For example, the heat of compound formation, H (Ni3 M) calculated by Miedema’s formula is equivalent to H (Ni3 M) = 3NVNiM . Figs. 5–7 indicate the correlation between the bond energy ratios of VNiX /VNiM and VMX /VNiM for various third elements with the site preferences in the three host compounds. In all figures, we can successfully draw a straight line with the slope 1, just given by Eq. (1). The line bounds the substituting elements into two separate parts with regard to the site preference in all Ni3 M compounds concerned. The elements situated below the line mostly substitute for Ni-site, and those above the line mostly sub-
stitute for M-site and those just close to the line substitute for both sites. The substitution behavior for transition metals and noble metals is systematic and in this case suggested to be primarily controlled by electronic (or chemical) nature denoted by the number in the periodic table. In Ni3 Nb, Ti, Zr, and Hf (4), V and Ta (5), Cr, Mo, and W (6), Mn (7), and Cu (11), where the number in a parenthesis is the group number in a periodic table, shows less preference for the Ni sites but almost neutral with Nb atom and are therefore plotted along the vertical axis of VNiX /VNiNb . In this case, these transition metals substitute for Nb-site. Fe (8) and Si (14) are almost equivalent in both interactions with Ni atom and with Nb atom, and then tend to substitute for both of Ni- and Nb-sites. On the other hand, Re (7), Os (8), Co and Ir (9), Pt (10), and Au (11) are attractive with Nb atom but almost neutral with Ni atom and are therefore plotted along the horizontal axis of VNbX /VNiNb . In this case, these metals substitute for Ni-site. In Ni3 V, Ti, Zr, and Hf (4), Nb and Ta (5), Mo (6), and Mn (7) shows less preference for the Ni sites but almost neutral with V atom, and are therefore plotted along the vertical axis of VNiX /VNiV . In this case, these transition metals substitute for V-site. Cr (6) is almost equivalent in both interactions with Ni atom and with V atom, and then tend to substitute for both of Ni- and V-sites. On the other hand, W (6), Re (7), Fe and Os (8), Co and Ir (9), Pt (10), and Cu and Au (11) are attractive with V atom but almost neutral
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Fig. 5. Substitution behavior of third elements in Ni3 Nb evaluated by VNiX /VNiNb ≶ VNbX /VNiNb + P. The straight line with the slope of 1 divides third elements into Nb-site and Ni-site elements. Note that the site preference of elements enclosed by a circle, square and triangular marks were confirmed by literature search, and correspond to the substitution for Nb-site, Ni-site and both sites, respectively.
Fig. 7. Substitution behavior of third elements in Ni3 Ti evaluated by VNiX /VNiTi ≶ VTiX /VNiTi + P. The straight line with the slope of 1 divides third elements into Ti-site and Ni-site elements. Note that the site preference of elements enclosed by a circle and square marks were confirmed by literature search, and correspond to the substitution for Ti-site and Ni-site sites, respectively.
Fig. 6. Substitution behavior of third elements in Ni3 V evaluated by VNiX /VNiV ≶ VVX /VNiV + P. The straight line with the slope of 1 divides third elements into V-site and Ni-site elements. Note that the site preference of elements enclosed by a circle, square and triangular marks were confirmed by literature search, and correspond to the substitution for V-site, Ni-site and both sites, respectively.
4. Comparison between the prediction and the experimental results
with Ni atom, and are therefore plotted along the horizontal axis of VVX /VNiV . In this case, these metals substitute for Ni-site. In Ni3 Ti, Zr and Hf (4), V, Ta and Nb (5), Cr, Mo, and W (6), and Mn (7) shows less preference for the Ni sites but almost neutral with Ti atom, and are therefore plotted along the vertical axis of VNiX /VNiTi . In this case, these transition metals substitute for V-site. On the other hand, Re (7), Fe and Os (8), Co and Ir (9), Pt (10), Cu and Au (11), Al and Ga (13), and Si and Ge (14) are attractive with V atom but almost neutral with Ni atom, and are therefore plotted along the horizontal axis of VVX /VNiV . In this case, these metals substitute for Ni-site. However, the substitution behavior for B-subgroup elements is peculiar and not so simple. It is clear that all B-subgroup elements fall on the first quadrant in Figs. 5–7 because both interactions with Ni atom and M atom are equally attractive. Consequently, the Bsubgroup elements are separated by a straight line into a different two region, depending on the relative values of two interaction energies. Here it is interesting to note the difference of substitution behavior between compounds studied previously (Ni3 Al, Ni3 Ga, Ni3 Si, and Ni3 Ge) [10] and compounds of this study (Ni3 Nb, Ni3 V, and Ni3 Ti). In the former compounds, all of B-subgroup elements lay on the second quadrant and then substituted exclusively for M-sites while the transition metals substituted for Ni-site or for M-site, depending on the relative value of two interaction energies. In the latter compounds, both the transition and B-subgroup elements have two possibilities, i.e., the case of substitution for Ni-site or the case for M-site, depending on the relative value of two interaction energies.
In Ni3 Nb, it has been reported that Fe substitutes for both Nisite and Nb-site. From the literature search result, we can draw the
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straight line with the slope 1 which passes through the point plotted about Fe, and the point about Cu substituted mostly for Ni-site should be below the line. So, there is not full agreement between the prediction and the literature search result, and it remains possible that the intercept of the straight line P may not be accurate. We should actually do some experiments for determination of the value of P. According to the literatures about Ni3 V, Cr substitutes for both Ni-site and V-site. So, we can draw the straight line with the slope 1 which passes through the point plotted about Cr. The point plotted about Co substituted mostly for Ni-site are below the line, therefore the prediction is in good agreement with the result of the literature search. As far as ternary phase diagrams with Ni and Ti we could obtain, no element substitutes for both Ni-site and Nb-site. Accordingly, we drew the straight line with the slope 1 which bounds the substituting elements into two separate parts with regard to the site preference of the literature search result. Summarizing the results for three host compounds, agreement between the prediction and the experimental work is fairly good. However, a more detailed discussion, e.g., why which element prefers which site, which should include size, number of d electrons, electronegativity, character of d electrons (e.g., 3d vs. 4d) and even first principal simulation is necessary to understand the present results and also to distinguish the site preference behavior among Ni3 Nb, Ni3 Ti and Ni3 V, and therefore should be conducted in an extending study. 5. Conclusion
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
The site preference of various kinds of ternary additions in Ni3 Nb (D0a ), Ni3 V (D022 ), and Ni3 Ti (D024 ) GCP compounds was determined from the direction of solubility lobes of the GCP phases on ternary phase diagrams, and also predicted by the thermodynamic consideration involving the nearest neighbor interactions. The following conclusion was obtained from the present study. There were a number of experimental results to determine the site preference of ternary additions. In Ni3 Nb, Co and Cu preferred the substitution for Ni-site, Ti, V and W the substitution for Nbsite, and Fe the substitution for both sites. In Ni3 V, Co preferred the substitution for Ni-site, Cr the substitution for both sites, and Ti the substitution for V-site. In Ni3 Ti, Fe, Co, Cu, and Si preferred the substitution for Ni-site, Nb, Mo, and V the substitution for Ti-site. The thermodynamic model based on the change in total bonding energy of the host compound by a small addition of ternary solute was applied to predict the site preferences. The bond energy of each nearest neighbor pair was derived from the heat of compound formation by Miedema’s formula. The agreement between the thermodynamic model and the reported experimental result was excellent. In the compounds of this study (Ni3 Nb, Ni3 V, and Ni3 Ti), both the transition and B-subgroup elements have two possibilities, i.e., the case of substitution for Ni-site or the case of substitution for M-site, depending on the relative value of two interaction energies, in contrast to the compounds (Ni3 Al, Ni3 Ga, Ni3 Si, and Ni3 Ge) consisting of B-subgroup elements and Ni atoms. Acknowledgement This work was supported in part by Grant-in-aid for Scientific Research for the Ministry of Education, Culture, Sports and Technology.
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[26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53]
J.H.N. Van Vucht, J. Less-common Met. 11 (1966) 308. A.K. Sinha, Trans. Metall. Soc. AIME 245 (1969) 911. R.T. Quinn, R.W. Kraft, R.W. Hertzberg, Trans. Am. Soc. Met. 62 (1969) 38. Y. Nunomura, Y. Kaneno, H. Tsuda, T. Takasugi, Intermetallics 12 (2004) 389. K. Ohira, Y. Kaneno, T. Takasugi, Mater. Sci. Eng. A 399 (2005) 332. K. Ohira, Y. Kaneno, H. Tsuda, T. Takasugi, Intermetallics 14 (2006) 367. Y. Nunomura, Y. Kaneno, H. Tsuda, T. Takasugi, Acta Mater. 54 (2006) 851. S. Shibuya, Y. Kaneno, M. Yoshida, T. Shishido, T. Takasugi, Intermetallics 15 (2007) 119. S. Shibuya, Y. Kaneno, H. Tsuda, T. Takasugi, Intermetallics 15 (2007) 338. S. Ochiai, Y. Oya, T. Suzuki, Acta Metall. 32 (1984) 289. A.R. Miedema, R. Boom, F.R. de Boer, in: C.J.M. Rooymans, A. Rabenau (Eds.), Crystal Structure and Chemical Bonding in Inorganic Chemistry, NorthHolland/American Elsevier, 1975, p. 163. A.R. Miedema, P.F. du Chatel, in: L.H. Bennet (Ed.), Theory of Alloy Phase Formation, Metall. Soc. A.I.M.E, 1980, p. 334. Y. Liu, T. Takasugi, O. Izumi, Metall. Trans. A 17 (1986) 1433. L.A. Panteleimonov, O.G. Burtseva, V.V. Zubenko, Moscow Univ. Chem. Bull. (Engl. Transl.) 37 (1) (1982) 71. K.P. Gupta, S.B. Rajendraprasad, A.K. Jena, J. Alloy Phase Diagrams 6 (1990) 14. A.A. Kodentsov, S.F. Dunaev, E.M. Slyusarenko, E.M. Sokolovskaya, Moscow Univ. Chem. Bull. (Engl. Transl.) 41 (3) (1986) 58. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 1 (1990) 49. V.N. Svechnikov, V.M. Pan, Dopov. Akad. Nauk Ukr. RSR 634 (1960). A.A. Kodentsov, S.F. Dunaev, E.M. Slyusarenko, Moscow Univ. Chem. Bull. (Engl. Transl.) 43 (3) (1988) 90. V. Raghavan, Phase Diagrams Ternary Iron Alloys, Indian Inst. Met. 6B (1992) 1025. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 2 (1991) 163. L.I. Pryakhina, K.P. Myasnikova, V.V. Burnasheva, E.E. Cherkashin, V.Y. Markiv, Sov. Powder Metall. Met. Ceram. 5 (1966) 643. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 2 (1991) 177. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 2 (1991) 185. G.A. Tikhankin, L.L. Meshkov, E.M. Sokolovskaya, Moscow Univ. Chem. Bull. (Engl. Transl.) 31 (1) (1976) 88. K.P. Myasnikova, V.Y. Markiv, L.I. Pryakhina, G.Y. Motrychuk, Russ. Metall. (Engl. Transl.) 3 (1977) 192. F.H. Hayes, P. Rogl, E.E. Schmid, Ternary Alloys, vol. 8, VCH, 1993, p. 40. Y.M. Hong, Y. Mishima, T. Suzuki, Mater. Res. Soc. Symp. Proc. 133 (1989) 429. R. Nino, Y. Terada, C.S. Oh, T. Mohri, T. Suzuki, Phase Equilib. 20 (1999) 29. A.A. Kodentzov, S.F. Dunaev, E.M. Slusarenko, J. Less-common Met. 135 (1987) 15. G.V. Raynor, V.G. Rivlin, Phase Equilibria Iron Ternary Alloys, Inst. Met., Lond. 433 (1988). K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 2 (1991) 219. V.N. Eremenko, L.A. Tret’yachenko, S.B. Prima, E.L. Semenova, Sov. Powder Metall. Met. Ceram. (Engl. Transl.) 23 (1984) 613. P.B. Budberg, Ternary Alloys, vol. 8, VCH, 1993, p. 7. K.J. Lee, P. Nash, J. Phase Equilib. 12 (1991) 551. V.Y. Markiv, V.V. Burnasheva, V.R. Ryabov, Metallofizika (Akad. Nauk Ukr. SSR, Inst. Metallofiz.) 46 (1973) 103. A. Raman, K. Schubert, Z. Metallkd. 56 (1965) 99. R. Yang, J.A. Leake, R.W. Cahn, Mater. Sci. Eng. A 152 (1992) 227. P. Nash, W.W. Liang, Metall. Trans. A 16 (1985) 319. A. Taylor, Trans. Am. Inst. Min. Metall. Pet. Eng. 206 (1956) 1356. A. Taylor, R.W. Floyd, J. Inst. Met. 81 (1952/53) 25. Y. Du, Z.P. Jin, P.Y. Huang, J. Phase Equilib. 14 (1993) 348. V.N. Eremenko, L.A. Tret’yachenko, S.B. Prima, E.L. Semenova, Sov. Powder Metall. Met. Ceram. 23 (1984) 613. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 1 (1990) 228. S.P. Alisova, P.B. Budberg, Russ. Metall. (Engl. Transl.) 4 (1992) 206. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 1 (1990) 321. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 2 (1991) 108. S.B. Prima, L.A. Tret’yachenko, V.N. Eremenko, Russ. Metall. (Engl. Transl.) 2 (1986) 205. V.N. Eremenko, S.B. Prima, L.A. Tret’yachenko, Russ. Metall. (Engl. Transl.) 3 (1983) 179. R.W. Guard, E.A. Smith, J. Inst. Met. 88 (1959/60) 369. V.Y. Markiv, E.I. Gladyshevskii, P.I. Krypyakevych, T.I. Fedoruk, Inorg. Mater. 2 (1966) 1126. K.J. Williams, J. Inst. Met. 99 (1971) 310. K.P. Gupta, Phase Diagrams Ternary Nickel Alloys, Indian Inst. Met. 219 (1991).
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Alloying behavior of Ni3 M-type GCP compounds H. Sugimura, Y. Kaneno, T. Takasugi ∗ Department of Materials Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
a r t i c l e
i n f o
Article history: Received 29 October 2009 Received in revised form 18 February 2010 Accepted 28 February 2010 Available online 6 March 2010 Keywords: GCP phase Site occupancy Ni3 M compound Thermodynamic model
a b s t r a c t The site preference of ternary additions in Ni3 M-type GCP compounds was determined from the direction of solubility lobe of the GCP phase on the ternary phase diagram that have been experimentally reported. In Ni3 Nb (D0a ), Co and Cu preferred the substitution for Ni-site, Ti, V and W the substitution for Nb-site, and Fe the substitution for both sites. In Ni3 V (D022 ), Co preferred the substitution for Ni-site, Cr the substitution for both sites, and Ti the substitution for V-site. In Ni3 Ti (D024 ), Fe, Co, Cu, and Si preferred the substitution for Ni-site, Nb, Mo and V the substitution for Ti-site. The thermodynamic model, which was based on the change in total bonding energy of the host compound by a small addition of ternary solute, was applied to predict the site preference of ternary additions. The bond energy of each nearest neighbor pair used in the thermodynamic calculation was derived from the heat of compound formation by Miedema’s formula. The agreement between the thermodynamic model and the result of the literature search was excellent. From both experimental and theoretical results, it was shown in three Ni3 M-type GCP compounds that both transition and B-subgroup elements have two possibilities, i.e., the case of substitution for Ni-site or the case for M-site, depending on the relative value of two interaction energies. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Among a number of geometrically close-packed (GCP) phases [1,2], Ni3 M-type GCP phases have various types of structures, e.g., Ni3 Nb (D0a ), Ni3 V (D022 ), Ni3 Ti (D024 ), and Ni3 Al (L12 ) as shown in Fig. 1. The coordination number of atoms is 12 in every structure. These structures are constructed by several stacking sequences of common close-packed plane with combination of a twofold hexagonal layer (h-layer) and a threefold cubic layer (c-layer) (Table 1). In addition, M atoms on the close-packed plane show some ordered arrangements: triangular-type (T-type) and rectangular-type (Rtype) in these GCP structures (Table 1). These compounds have a lot of attractive properties as a high-temperature structural material. Therefore these compounds have been used as precipitated phases, i.e., strengtheners in actually used nickel superalloys [3] and as constituent phases of Ni-base multi-phase intermetallic alloys recently developed by the present author’s group [4–9]. The addition of third element to these binary Ni3 M-type GCP compounds or alloying element to the constituent Ni3 M phases in Ni-base multi-phase intermetallic alloys might modify not only the mechanical properties but also other properties such as oxidation or corrosion property. Therefore, to study a solubility limit or substitution behavior of alloying element in Ni3 M-type GCP com-
∗ Corresponding author. Tel.: +81 72 254 9314; fax: +81 72 254 9912. E-mail address: [email protected] (T. Takasugi). 0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2010.02.179
pounds is a critical issue to develop a new type of high-temperature structural material based on intermetallic compounds. The alloying behavior of L12 -type Ni3 M compound, i.e., whether the addition substitutes exclusively for Ni-site, exclusively for Msite or for both sites, has been investigated and reviewed in Ni3 Al, Ni3 Ga, Ni3 Si, and Ni3 Ge compounds by Ochiai et al. [10]. The thermodynamic Bragg–Williams model involving the nearest neighbor interactions, i.e., the change in total bonding energy of the host compound by a small addition of ternary solute at stoichiometry has been applied to these L12 -type Ni3 M compounds [10]. The bond energy of each pair was derived from the heat of compound formation by Miedema’s formula [11,12]. The agreement for preferable site occupation of the addition between the prediction and the experimental result was found to be excellent. Later, the same treatment has been conducted on L12 -type Co3 Ti compound by Takasugi and co-workers and was shown to be successful in predicting preferable site occupation of the addition [13]. Between L12 -type Ni3 M compounds and other Ni3 M-type GCP compounds, the environment of the nearest neighbor atoms is quite same not only for the number of nearest neighbor pairs but also for the kind of nearest neighbor pairs. Ni atom has 8 nearest neighbor pairs with Ni atom and 4 nearest neighbor pairs with M atom while M atom has 12 nearest neighbor pairs with Ni atom. Therefore, the same thermodynamic treatment as that conducted on L12 -type Ni3 M compound may be applicable to other Ni3 M-type GCP compounds. In this paper, we treats three compounds of Ni3 Nb (D0a ), Ni3 V (D022 ), and Ni3 Ti (D024 ) shown in Fig. 1. Those compounds
H. Sugimura et al. / Journal of Alloys and Compounds 496 (2010) 116–121
117
Fig. 1. Crystal structures of Ni3 Nb (D0a ), Ni3 V (D022 ), Ni3 Ti (D024 ), and Ni3 Al (or Ni3 Si) (L12 ). Open circle and full circle correspond to Ni atom and M atom in Ni3 M-type compounds, respectively. Also, a shaded plane shows closest plane. Table 1 The crystallographic feature of various Ni3 M-type GCP compounds. Crystal structure Unit cell Stacking order Stacking sequence Hexagonality (%) Unit mesh Ni3 M
D0a hcp AB hh 100 R Ni3 Nb
D022 fee ABCA B C cccccc 0 R Ni3 V
D024 hcp ABAC hchc 50 T Ni3 Ti
L12 fee ABC ccc 0 T Ni3 Al,Ni3 Si
have been used as constituent phases in the Ni-base multi-phase intermetallic alloys [4–9]. It is known that Ni3 Nb and Ni3 Ti are a Berthollide-type and a Daltonide-type compound, respectively and their structures are stable to the melting points while Ni3 V (D022 ) is a Kurnakov-type compound and transforms at 1045 ◦ C to fcctype solid solution with increasing temperature. In an early part of this paper, the experimental data for the alloying behavior that have been so far reported are collected and reviewed for three Ni3 M compounds. In a latter part of this paper, the alloying behavior is predicted by the thermodynamic model, and agreement between the experiment and the modeling is discussed. 2. Reported experimental works In this paper, the site preference for various third elements (X) in the unit cell of a host Ni3 M-type compound is determined from the direction of solubility lobe in an isothermal section of a ternary
phase diagram that have been reported so far. The unit cell of Ni3 M lattice involves two types of site, which are defined as Ni-site and M-site. A ternary addition which occupies mostly Ni-site has a solubility lobe lying in parallel to Ni–X edge in an isothermal section, an addition which occupies mostly M-site has a lobe lying in parallel to M–X edge, and an addition which substitutes for both sites has a lobe extending in a direction almost bisecting the quasi-binary section Ni3 M–Ni3 X and Ni3 M–X3 M. A relatively large number of ternary Ni–Nb–X phase diagrams have been published. Table 2 summarizes the results taken from the existing ternary phase diagrams. Reported temperatures range between 900 and 1200 ◦ C. The table shows the direction and the extent of solubility limit for each solute element. Fe [20] substitutes for both sites, Co [14,15] and Cu [19] mostly for Ni-site and Ti [21,22], V [23] and W [24,25] mostly for Nb-site. The ternary system with Cr [16–18] did not provide a clear indication of substitution behavior in Ni3 Nb because of very small solid solubility. All the reported results on the solid solubility of various kinds of solutes in Ni3 Nb are summarized in Fig. 2. There have been some data for ternary Ni–V–X phase diagrams as listed in Table 3. Data limited to temperature range below 1045 ◦ C in which D022 structure is stable were taken into consideration. Cr [30] substitutes for both sites, and Co [29] mostly for Ni-site. The ternary systems with Al [26–28], Fe [31], and Ti [32] did not provide a clear indication of substitution behavior in Ni3 V because of no agreement between the data from various sources, or, very small solid solubility. However, Ti [33] appears to substitute
Table 2 The reported substitution behavior of ternary additions in Ni3 Nb (D0a ). Element [Reference]
Authors
Year
Temperature (◦ C)
Solid solubility (at.%)
Substitution site
Co [14] Co [15] Cr [16]
Panteleimonov et al. Gupta et al. Kodentsov et al.
1982 1990 1986
Cr [17]
Gupta
1990
Svechnikov and Pan Kodentsov et al. Raghavan Gupta
1960 1988 1992 1991
Pryakhina et al.
1966
Gupta
1991
Gupta
1991
Tikhankin et al.
1976
980 1075 1002 1200 1175 1173 1160 1100 1100 1002 1000 1000 1000 900 1050 1000 900 1000 900
Ni(−7) Nb(−1) Co(+8) Ni(−5) Nb(0) Co(+5) Ni(−3) Nb(−1) Cr(+4) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(0) Nb(0) Cr(0) Ni(−11) Nb(−1) Cu(+12) Ni(−6) Nb(−8) Fe(+14) Ni(0) Nb(−6) Ti (+6) Ni(0) Nb(−6) Ti (+6) Ni(0) Nb(−3) Ti (+3) Ni(−4) Nb(−13) V(+17) Ni(−3) Nb(−4) W(+7) Ni(−3) Nb(−4) W(+7) Ni(−1) Nb(−5) W(+6) Ni(−1) Nb(−5) W(+6)
Ni Ni Ni Indeterminable Indeterminable Indeterminable Indeterminable Indeterminable Indeterminable Ni Ni/Nb Nb Nb Nb Nb Ni/Nb Ni/Nb Nb Nb
Cr [18] Cu [19] Fe [20] Ti [21] Ti [22] V [23] W [24] W [25]
The symbols “Ni”, “Nb”, and “Ni/Nb” in the column “Substitution site” mean that third element substitutes for Ni-site, Nb-site and both sites, respectively. The numerical values expressed in the parentheses in the column “Solid solubility” mean surplus or deficit (expressed by at.%) of each element from the stoichiometric composition of Ni3Nb.
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Fig. 2. Semischematic depiction of the solubility lobes of ternary Ni3 Nb phase for various elements. Data for the systems with Co [14] at 980 ◦ C, Fe [20], Ti [21] and W [25] at 1000 ◦ C, Cu [19] and Cr [16] at 1002 ◦ C and V [23] at 1050 ◦ C are taken from literatures.
Fig. 4. Semischematic depiction of the solubility lobes of ternary Ni3 Ti phase for various elements. Data for the systems with Si [52] at 750 ◦ C, Co [42] at 850 ◦ C, Cu [44] at 870 ◦ C, Mo [49] at 900 ◦ C, Nb [21] at 1000 ◦ C, and Fe [46] at 1027 ◦ C are taken from literature.
3. Thermodynamic consideration
Fig. 3. Semischematic depiction of the solubility lobes of ternary Ni3 V phase for various elements. Data for the systems with Cr [30] at 852 ◦ C, Ti [33] and Al [26] at 1000 ◦ C, and Co [29] at 750–1100 ◦ C are taken from literature.
for V-site. Fig. 3 summarizes the solubility lobes of ternary Ni3 V phase. A large number of ternary Ni–Ti–X phase diagrams have been published. Table 4 summarizes the results. Reported temperatures range between 600 and 1200 ◦ C. Co [42,43], Cu [44,45], Fe [46], and Si [51,52] substitute mostly for Ni-site, and Nb [21,22], Mo [47,48,43,50,51], and V [32,33,53] mostly for Ti-site. The ternary systems with Al [34–41] did not provide a clear indication of substitution behavior in Ni3 Ti because there is not good agreement between the data with Al from various sources. Fig. 4 summarizes the reported results on the substitution behavior in Ni3 Ti.
This section is devoted to showing whether a simple thermodynamic treatment will serve to account for the site preference of a third element X in a perfectly ordered stoichiometric D0a , D022 , and D024 alloys, based on the Bragg–Williams model of nearest neighbor interactions. The only nearest neighbor approximation should be suitable for our purpose, because the second and further distant neighbor interaction energies are likely to be negligible in these Ni3 M-type compounds. Comparison will be made on the difference of total bond energies between two extreme cases for the substitution of component X. One case is that X atoms replace Ni atoms on Ni-site and the other case is that X atoms replace M atoms on M-site. In comparison between H(Ni) and H(M) where the former is the change in total bond energy in Ni3 M system by a small addition of third element X to Ni-site while the latter is the change in total bond energy in Ni3 M system by a small addition of third element X to M-site, the site preference for a ternary addition of X atoms can be directed by the following expression VMX VNiX ≶ + P. VNiM VNiM
(1)
Vij is the interaction parameter and defined by Hij − (Hii + Hjj )/2 where Hij is the bond energy for ij pairs. If the quantity on the left hand side is smaller, the substitution of X for Ni-site is preferred while if that on the right hand is smaller, the substitution of X for M-site is preferred. Also, P is defined by the following expression P =2−
3 (H
− HMM ) . VNiM
NiNi
2
(2)
Table 3 The reported substitution behavior of ternary additions in Ni3 V (D022 ). Element [Reference] Al [26] Al [27] Al [28] Co [29] Cr [30] Fe [31] Ti [32] Ti [33]
Authors
Year
Myasnikova et al.
1977
Hayes et al. Hong et al. Nino et al.
1993 1989 1999
Kodentzov et al.
1987
Raynor and Rivlin Gupta Eremenko et al.
1988 1991 1984
Temperature (◦ C)
Solid solubility (at.%)
Substitution site
1000 600/800 800 1027 750–1100 1002 852 1000 1000 1000
Ni(−3) V(0) Al(+3) Ni(−3) V(0) Al(+3) Ni(0) V(−3) Al(+3) Ni(0) V(−1) Al(+1) Ni(−16) V(0) Co(15) Ni(−2) V(−1) Cr(+3) Ni(−3) V(−3) Cr(+6) Ni(−1) V(−1) Fe(+2) Ni(−4) V(−4) Ti(+8) Ni(−2) V(−6) Ti(+8)
Ni Ni V Indeterminable Ni Ni/V or Ni/V Ni/V or Ni/V V
The symbols “Ni”, “V”, and “Ni/V” in the column “Substitution site” mean that third element substitutes for Ni-site, V-site and both sites, respectively. The numerical values expressed in the parenthesis in the column “Solid solubility” mean surplus or deficit (expressed by at.%) of each element from the stoichiometric composition of Ni3 V.
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Table 4 The reported substitution behavior of ternary additions in Ni3 Ti (D024 ). Element [Reference]
Authors
Year
Temperature (◦ C)
Solid solubility (at.%)
Substitution site
Al [34]
Budberg
1993
1150 1025 800
Ni(0) Ti(0) Al(0) Ni(0) Ti(0) Al(0) Ni(0) Ti(0) Al(0)
Indeterminable Indeterminable Indeterminable
Al [35]
Lee and Nash
1991
1150 900 800
Ni(0) Ti(0) Al(0) Ni(−1) Ti(−3) Al(+4) Ni(0) Ti(0) Al(0)
Indeterminable Ti Indeterminable
Markiv et al. Raman and Schubert Yang et al. Nash and Liang
1973 1965 1992 1985
Taylor
1956
Al [41]
Taylor and Floyd
1952/1953
Co [42] Co [43]
Du et al. Eremenko et al.
1993 1984
Cu [44]
Gupta
1990
Alisova and Budberg
1992
Gupta
1990
Mo [47]
Gupta
1991
Mo [48] Mo [43] Mo [49] Mo [50] Nb [21] Nb [22] Si [51] Si [52] V [32] V [33] V [53]
Prima et al. Eremenko et al. Eremenko et al. Guard and Smith Gupta Pryakhina et al. Markiv et al. Williams Gupta Eremenko et al. Gupta
1986 1984 1983 1959/1960 1991
800 800 900 900 1000 750 1150 1000 850 750 850 800 870 800 800 600 1027 900 1200 1175 900 1200 900 900 1175 1000 1000 900 750 1000 1000 1000 1045/1100
Ni(−1) Ti(0) Al(+1) Ni(−1) Ti(0) Al(+1) Ni(+2) Ti(−5) Al(+3) Ni(0) Ti(−4) Al(+4) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(0) Ti(−1) Al(+1) Ni(−1) Ti(0) Al(+1) Ni(−8) Ti(−1) Fe(+9) Ni(−13) Ti(+1) Fe(+12) Ni(−3) Ti(0) Cu(+3) Ni(−4) Ti(+1) Cu(+3) Ni(−3) Ti(0) Cu(+3) Ni(−1) Ti(0) Cu(+1) Ni(−24) Ti(−3) Fe(+27) Ni(−13) Ti(−1) Fe(+14) Ni(−1) Ti(−4) Mo(+5) Ni(0) Ti(−1) Mo(+1) Ni(0) Ti(−3) Mo(+3) Ni(−1) Ti(−4) Mo(+5) Ni(0) Ti(−3) Mo(+3) Ni(−1) Ti(−1) Mo(+2) Ni(−1) Ti(0) Mo(+1) Ni(0) Ti(−4) Nb(+4) Ni(0) Ti(−4) Nb(+4) Ni(0) Ti(−2) Nb(+2) Ni(−2) Ti(0) Si(+2) Ni(−1) Ti(0) Si(+1 Ni(−1) Ti(−9) V(+10) Ni(0) Ti(−11) V(+11) Ni(−3) Ti(−8) V(+11)
Ni Ni Ti Ti Ti Ti Ti Ti Ti Ni Ni Ni Ni Ni Ni Ni Ni Ni Ti Ti Ti Ti Ti Ni/Ti or indeterminable Ni Ti Ti Ti Ni Ni Ti Ti Ti
Al [36] Al [37] Al [38] Al [39] Al [40]
Cu [45] Fe [46]
1966 1966 1971 1991 1984 1991
The symbols “Ni”, “Ti”, and “Ni/Ti” in the column “Substitution site” mean that third element substitutes for Ni-site, Ti-site and both sites, respectively. The numerical values expressed in the parenthesis in the column “Solid solubility” mean surplus or deficit (expressed by at.%) of each element from the stoichiometric composition of Ni3Ti.
It is noted that the value of P, which is called as asymmetric index, depends only on the nature of the host compound and has a value between +1 and −1. If the available experimental data permit us to derive the bonding energies, it is possible to test whether the above expression is appreciable to evaluate the substitution behavior of Ni3 Nb, Ni3 V, and Ni3 Ti compounds. However, the experimental data are too limited to obtain the bonding energy in any set of given elements. Fortunately, Miedema and coworkers have developed a prognosis method for the prediction of the heat of alloy formation [11,12]. They have characterized each system by a set of two parameters assigned to each component. For the Miedema’s semiempirical formula, the accuracy of the prediction has been successfully tested on various cases by many investigators. Now, the evaluation of the bonding energies can be done in every sets of elements interest. For example, the heat of compound formation, H (Ni3 M) calculated by Miedema’s formula is equivalent to H (Ni3 M) = 3NVNiM . Figs. 5–7 indicate the correlation between the bond energy ratios of VNiX /VNiM and VMX /VNiM for various third elements with the site preferences in the three host compounds. In all figures, we can successfully draw a straight line with the slope 1, just given by Eq. (1). The line bounds the substituting elements into two separate parts with regard to the site preference in all Ni3 M compounds concerned. The elements situated below the line mostly substitute for Ni-site, and those above the line mostly sub-
stitute for M-site and those just close to the line substitute for both sites. The substitution behavior for transition metals and noble metals is systematic and in this case suggested to be primarily controlled by electronic (or chemical) nature denoted by the number in the periodic table. In Ni3 Nb, Ti, Zr, and Hf (4), V and Ta (5), Cr, Mo, and W (6), Mn (7), and Cu (11), where the number in a parenthesis is the group number in a periodic table, shows less preference for the Ni sites but almost neutral with Nb atom and are therefore plotted along the vertical axis of VNiX /VNiNb . In this case, these transition metals substitute for Nb-site. Fe (8) and Si (14) are almost equivalent in both interactions with Ni atom and with Nb atom, and then tend to substitute for both of Ni- and Nb-sites. On the other hand, Re (7), Os (8), Co and Ir (9), Pt (10), and Au (11) are attractive with Nb atom but almost neutral with Ni atom and are therefore plotted along the horizontal axis of VNbX /VNiNb . In this case, these metals substitute for Ni-site. In Ni3 V, Ti, Zr, and Hf (4), Nb and Ta (5), Mo (6), and Mn (7) shows less preference for the Ni sites but almost neutral with V atom, and are therefore plotted along the vertical axis of VNiX /VNiV . In this case, these transition metals substitute for V-site. Cr (6) is almost equivalent in both interactions with Ni atom and with V atom, and then tend to substitute for both of Ni- and V-sites. On the other hand, W (6), Re (7), Fe and Os (8), Co and Ir (9), Pt (10), and Cu and Au (11) are attractive with V atom but almost neutral
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Fig. 5. Substitution behavior of third elements in Ni3 Nb evaluated by VNiX /VNiNb ≶ VNbX /VNiNb + P. The straight line with the slope of 1 divides third elements into Nb-site and Ni-site elements. Note that the site preference of elements enclosed by a circle, square and triangular marks were confirmed by literature search, and correspond to the substitution for Nb-site, Ni-site and both sites, respectively.
Fig. 7. Substitution behavior of third elements in Ni3 Ti evaluated by VNiX /VNiTi ≶ VTiX /VNiTi + P. The straight line with the slope of 1 divides third elements into Ti-site and Ni-site elements. Note that the site preference of elements enclosed by a circle and square marks were confirmed by literature search, and correspond to the substitution for Ti-site and Ni-site sites, respectively.
Fig. 6. Substitution behavior of third elements in Ni3 V evaluated by VNiX /VNiV ≶ VVX /VNiV + P. The straight line with the slope of 1 divides third elements into V-site and Ni-site elements. Note that the site preference of elements enclosed by a circle, square and triangular marks were confirmed by literature search, and correspond to the substitution for V-site, Ni-site and both sites, respectively.
4. Comparison between the prediction and the experimental results
with Ni atom, and are therefore plotted along the horizontal axis of VVX /VNiV . In this case, these metals substitute for Ni-site. In Ni3 Ti, Zr and Hf (4), V, Ta and Nb (5), Cr, Mo, and W (6), and Mn (7) shows less preference for the Ni sites but almost neutral with Ti atom, and are therefore plotted along the vertical axis of VNiX /VNiTi . In this case, these transition metals substitute for V-site. On the other hand, Re (7), Fe and Os (8), Co and Ir (9), Pt (10), Cu and Au (11), Al and Ga (13), and Si and Ge (14) are attractive with V atom but almost neutral with Ni atom, and are therefore plotted along the horizontal axis of VVX /VNiV . In this case, these metals substitute for Ni-site. However, the substitution behavior for B-subgroup elements is peculiar and not so simple. It is clear that all B-subgroup elements fall on the first quadrant in Figs. 5–7 because both interactions with Ni atom and M atom are equally attractive. Consequently, the Bsubgroup elements are separated by a straight line into a different two region, depending on the relative values of two interaction energies. Here it is interesting to note the difference of substitution behavior between compounds studied previously (Ni3 Al, Ni3 Ga, Ni3 Si, and Ni3 Ge) [10] and compounds of this study (Ni3 Nb, Ni3 V, and Ni3 Ti). In the former compounds, all of B-subgroup elements lay on the second quadrant and then substituted exclusively for M-sites while the transition metals substituted for Ni-site or for M-site, depending on the relative value of two interaction energies. In the latter compounds, both the transition and B-subgroup elements have two possibilities, i.e., the case of substitution for Ni-site or the case for M-site, depending on the relative value of two interaction energies.
In Ni3 Nb, it has been reported that Fe substitutes for both Nisite and Nb-site. From the literature search result, we can draw the
H. Sugimura et al. / Journal of Alloys and Compounds 496 (2010) 116–121
straight line with the slope 1 which passes through the point plotted about Fe, and the point about Cu substituted mostly for Ni-site should be below the line. So, there is not full agreement between the prediction and the literature search result, and it remains possible that the intercept of the straight line P may not be accurate. We should actually do some experiments for determination of the value of P. According to the literatures about Ni3 V, Cr substitutes for both Ni-site and V-site. So, we can draw the straight line with the slope 1 which passes through the point plotted about Cr. The point plotted about Co substituted mostly for Ni-site are below the line, therefore the prediction is in good agreement with the result of the literature search. As far as ternary phase diagrams with Ni and Ti we could obtain, no element substitutes for both Ni-site and Nb-site. Accordingly, we drew the straight line with the slope 1 which bounds the substituting elements into two separate parts with regard to the site preference of the literature search result. Summarizing the results for three host compounds, agreement between the prediction and the experimental work is fairly good. However, a more detailed discussion, e.g., why which element prefers which site, which should include size, number of d electrons, electronegativity, character of d electrons (e.g., 3d vs. 4d) and even first principal simulation is necessary to understand the present results and also to distinguish the site preference behavior among Ni3 Nb, Ni3 Ti and Ni3 V, and therefore should be conducted in an extending study. 5. Conclusion
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The site preference of various kinds of ternary additions in Ni3 Nb (D0a ), Ni3 V (D022 ), and Ni3 Ti (D024 ) GCP compounds was determined from the direction of solubility lobes of the GCP phases on ternary phase diagrams, and also predicted by the thermodynamic consideration involving the nearest neighbor interactions. The following conclusion was obtained from the present study. There were a number of experimental results to determine the site preference of ternary additions. In Ni3 Nb, Co and Cu preferred the substitution for Ni-site, Ti, V and W the substitution for Nbsite, and Fe the substitution for both sites. In Ni3 V, Co preferred the substitution for Ni-site, Cr the substitution for both sites, and Ti the substitution for V-site. In Ni3 Ti, Fe, Co, Cu, and Si preferred the substitution for Ni-site, Nb, Mo, and V the substitution for Ti-site. The thermodynamic model based on the change in total bonding energy of the host compound by a small addition of ternary solute was applied to predict the site preferences. The bond energy of each nearest neighbor pair was derived from the heat of compound formation by Miedema’s formula. The agreement between the thermodynamic model and the reported experimental result was excellent. In the compounds of this study (Ni3 Nb, Ni3 V, and Ni3 Ti), both the transition and B-subgroup elements have two possibilities, i.e., the case of substitution for Ni-site or the case of substitution for M-site, depending on the relative value of two interaction energies, in contrast to the compounds (Ni3 Al, Ni3 Ga, Ni3 Si, and Ni3 Ge) consisting of B-subgroup elements and Ni atoms. Acknowledgement This work was supported in part by Grant-in-aid for Scientific Research for the Ministry of Education, Culture, Sports and Technology.
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