Trans. Nonferrous Met. Soc. China 25(2015) 1599-1604

Site occupation evolution of alloying elements in Ni₃V phase during phase transformation in Ni₇₅Al_4.2V_20.8

Ming-yi ZHANG^1,2,3, Zhi-gang LI², Jin-ling ZHANG², Hui-zhan ZHANG², Zhen CHEN³, Jia-zhen ZHANG²

1. Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China;

2. Beijing Aeronautical Science & Technology Research Institute, Commercial Aircraft Corporation of China, Ltd., Beijing 100083, China;

3. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China

Received 5 November 2013; accepted 4 March 2014

Abstract: Based on the microscopic phase-field model, the correlation between site occupation evolution of alloying elements in Ni₃V-DO₂₂ phase and growth of Ni₃Al-L1₂ phase was studied during the phase transformation of Ni₇₅Al_4.2V_20.8. The results demonstrate that the growth of L1₂ phase can be divided into two stages: at the early stage, the composition of alloying elements in DO₂₂ phase almost remains unchanged; at the late stage, the compositions of Ni and Al decrease while V increases in DO₂₂ phase. Part of alloying elements for L1₂ phase growth are supplied from the site occupation evolution of alloying elements on three kinds of sublattices in DO₂₂ phase. Ni is mainly supplied from V sublattice, and part of Al is supplied from Ni_Ⅰ and V sites at the centre of DO₂₂ phase. The excessive V from the decreasing DO₂₂ phase migrates into the centre of DO₂₂ phase and mainly occupies V and Ni_II sites. It is the site occupation evolution of antisite atoms and ternary additions in DO₂₂ phase that controls the growth rate of L1₂ phase at the late stage.

Key words: Ni₇₅Al_4.2V_20.8 alloy; grain growth; phase transformation; microscopic phase-field; antisite defect

1 Introduction

Extensive studies on the site occupation behavior (including both the site preference of ternary substitution elements and antisites of the constituent elements) of alloying elements were carried out both experimentally and theoretically, because their effects on physical properties of intermetallic compounds are subjects not only of great practical interests but also of fundamental theoretical interests [1]. Site preference of alloying elements can be affected by changing temperature [2], composition [3], or magnetism [4]. The performances of alloys are strongly influenced by site preference of ternary additions and antisite atoms. CHIBA et al [5] found that when the ternary addition preferentially substitutes Ni on the face centered sites in Ni₃Al, the ductility of Ni₃Al can be improved significantly [5]. Studies also demonstrated that site preference of alloying elements severely affects the solute segregation [6,7]. However, little attention has been paid to the correlation between site occupation evolution of alloying elements and phase transformation. An understanding of the site occupation behavior of alloying elements during phase transformation is extremely useful in order to control the microstructure and to improve the physical properties of alloys.

Phase transformation in Ni₇₅Al_xV_25-x alloys during aging process was studied extensively both experimentally [8] and theoretically [9]. Most of the studies are focused on the kinetics of phase separation [10] and microstructure evolution [11]. The atomic ordering and composition clustering process were studied in details by PODURI et al [12] and HOU et al [13]. LI et al [14] investigated the coarsening behavior of L1₂ and DO₂₂ in Ni₇₅Al_xV_25-x alloys systematically, but few studies were focused on the correlation between the behavior of interfaces and phase transformation of Ni₇₅Al_xV_25-x alloys [15,16]. ZHANG et al [17] studied the correlation between the site occupation evolution of alloying elements in L1₂ phase and the growth of DO₂₂ phase in Ni₇₅Al_7.5V_17.5, the mechanism and kinetics of phase transformation from L1₂ to DO₂₂ are delicately investigated at atomistic scale. However, because of the complexity of DO₂₂ crystal structure, little attention has been paid to the site occupation behavior of alloying elements in DO₂₂ [18] and the difference of two kinds of Ni sublattices in DO₂₂ were not considered delicately. The mechanism of phase transformation from DO₂₂ to L1₂ still needs to be further studied at atomic scale. In this work, the site occupation behavior of alloying elements in DO₂₂ phase during phase transformation from DO₂₂ to L1₂ in Ni₇₅Al_7.5V_17.5 is studied, and their correlation is discussed.

2 Microscopic phase-field model

The microscopic phase-field model describes the evolution of site occupation probability from the non-equilibrium distribution to an equilibrium one. It was firstly proposed by KHACHATURYAN [19] and then developed by CHEN and PODURI [12] for the ternary alloy system. Equations for ternary alloy systems are written as

    (1)

For ternary systems, P_C(r, t)=1-P_A(r, t)-P_B(r, t), where P_α(r, t) (α=A, B or C) represent the probabilities of finding an α atom at a given lattice site r at given time t, and t is the reduced time, L_αb( r–r') (α and β=A, B or C) are the kinetic coefficients which are proportional to the probabilities of elementary diffusional jumps from site r to r' per unit of time, and F is the total Helmholtz free energy of the system based on the mean-field approximation, which can be written as a function of single site occupation probability:

                      (2)

where the effective pair interaction V_αb is deduced from pair interaction ω_αb: V_αb =ω_αα+ω_bb–2ω_αb.

For the convenience of analysis and visualization of the atomic configuration and multiphase morphologies, and considering the proper time consumption, numerical simulation was carried out in a 2D square super-cell consisting of 128×128 square lattice sites by the projection of 3D crystal structure of Ni₃V-DO₂₂ along the [010] direction. The schematic diagrams of the DO₂₂ crystal structure and the projection of DO₂₂ structure along [010] direction are shown in Figs. 1(a) and (b), respectively. DO₂₂ consists of three kinds of sublattices, and two of them are Ni sites, as denoted as Ni_Ⅰ and Ni_Ⅱ. Both of them contain eight Ni atoms and four V atoms in the first nearest neighbor shell but Ni and V form distinctive coordination geometries. As shown in Figs. 1(c) and (d), the Ni_I site has four V atoms to form a square configuration and the Ni_II has four V atoms to form a tetrahedral configuration. The number of Ni_II site is two times as many as the Ni_I site in a Ni₃V unit cell.

Fig. 1 Schematic representations of Ni₃V (DO₂₂) crystal structure (a), projection of DO₂₂ structure along [010] direction (b), and first nearest coordination shell and coordination geometry of Ni_I (c) and Ni_II (d)

Equation (1) is solved in the reciprocal space using the modified Euler’s method with the time increment equal to 0.0002. The real-space atomic site occupation probability of alloying elements is obtained by the Back-Fourier transformation of the solution of Eq. (1). The effective pair interactions (meV/atom) which have been used by PODURI and CHEN [12] and ZAPOLSY et al [20] in the previous works are proved to be fit for the real Ni-Al-V alloy system at high temperatures and are used as our simulation inputs. The applications of microscopic phase-field model on the microstructure evolution of Ni-based alloys had shown excellent agreement both with the experiment results [21] and other simulation results [13].

3 Results and discussion

Figure 2 shows the simulated microstructure evolution pictures during the phase transformation of Ni₇₅Al_4.2V_20.8 alloy aged at 1185 K, where the black sites represent Ni, gray sites represent V and white sites represent Al. It is shown in Fig. 2 that L1₂ phase grows along the disordered phase at first, and then grows perpendicular to the interface formed between L1₂ and DO₂₂ phases.

The volume fraction variation of L1₂ and DO₂₂ phases during aging process is shown in Fig. 3, and the volume fraction variation of the disordered phase is also considered. Combined the microstructure evolution pictures with the volume fraction variation figure during the phase transformation, it can be found that the growth of L1₂ phase can be divided into two stages. At the early stage of phase transformation, the volume of L1₂ phase increases accompanying with the volume of DO₂₂ phase and disordered phase decreasing. When the disordered phase disappears, L1₂ phase grows up at the expense of DO₂₂ phase only. It is obvious in Fig. 3 that the growth rates of L1₂ phase at the early stage is higher than that at the late stage.

Further study on the composition evolution of alloying elements in DO₂₂ phase during phase transformation is shown in Fig. 4(a). Considering the DO₂₂ phase in the vicinity of interface will transform into L1₂ phase, only the concentration evolution of alloying elements in the centre part of DO₂₂ phase is considered. It is demonstrated that at the early stage of L1₂ phase growth, the concentration of alloying elements in DO₂₂ phase almost remains unchanged, while at the late stage of phase transformation from DO₂₂ to L1₂, the concentrations of Ni and Al decrease and that of V increases in DO₂₂ phase. The relationship between the volume fraction of L1₂ phase and the composition of DO₂₂ phase (Fig. 4(b)) also illustrates that, the volume fraction of L1₂ phase increases from about 0 to 0.25 quickly at the early stage, and the composition of the centre part of DO₂₂ phase almost remains unchanged. At the late stage, the volume fraction of L1₂ phase grows up slowly from 0.25 to about 0.30, accompanied with the decreasing of Al and Ni concentration, and the increasing of V concentration at the centre part of DO₂₂ phase. This implies that the growth of L1₂ phase at the late stage is controlled by the composition evolution of alloying elements in the centre part of DO₂₂ phase. As mentioned above, L1₂ phase grows up mainly at the expense of disordered phase at the early stage. Then, it can be concluded that the growth of L1₂ phase at the early stage is controlled by the diffusion of alloying elements in disordered phases and the growth rate of L1₂ phase is quick, while the phase transformation at the late stage is controlled by the diffusion of alloying elements in bulk DO₂₂ phases and the growth rate of L1₂ phase is relatively slow.

Fig. 2 Simulated atomistic microstructure evolution figures during phase transformation from disordered (FCC-A1) phase to ordered (L1₂ and DO₂₂) phase in Ni₇₅Al_4.2V_20.8 aged at 1185 K

Fig. 3 Volume fraction variation of L1₂ and DO₂₂ phase during phase transformation from DO₂₂ to L1₂ in Ni₇₅Al_4.2V_20.8 aged at 1185 K

Fig. 4 Composition evolution of alloying elements in DO₂₂ phase during phase transformation in Ni₇₅Al_4.2V_20.8 aged at 1185 K

At the late stage of phase transformation, L1₂ phase grows up at the expense of DO₂₂ phase, as the growth of L1₂ phase needs Ni and Al. It was reported that the content of Ni in L1₂ phase is slightly higher than that in DO₂₂ phase, and the concentration of ternary addition V is about 10% (atomic fraction) in L1₂ phase [20]. When the volume of DO₂₂ phase is decreasing, alloying elements will be spared from the decreasing DO₂₂ phase. However, the amount of Ni and Al spared from the decreasing DO₂₂ phase are not sufficient for the growth of L1₂ phase, and the amount of V spared from the decreasing DO₂₂ phase is more than the need of L1₂ phase growth. Thus, where do the other parts of Al and Ni come from to satisfy the growth of L1₂, and where does the enriched V go when the volume of DO₂₂ phase decreases? To answer this question, the composition evolution of alloying elements in DO₂₂ phase is further studied.

It can be seen from Fig. 4 that Ni and Al decrease and V increases with the volume fraction of L1₂ phase increasing. However, studying on the composition evolution of alloying elements on Ni sites of DO₂₂ phase found that Ni and V increase and Al decreases accompanied with the phase transformation from DO₂₂ to L1₂, as shown in Fig. 5. This illustrated that the composition evolution of alloying elements on different sublattices are different, and the composition change of alloying elements on sublattices of DO₂₂ phase are correlated with the phase transformation.

Fig. 5 Composition evolution of alloying elements on Ni sites of DO₂₂ phase during phase transformation from DO₂₂ to L1₂ in Ni₇₅Al_4.2V_20.8 aged at 1185 K

To find out the correlation between the composition evolution of alloying elements in DO₂₂ phase and the growth of L1₂ phase, the site occupation evolution of alloying elements on three kinds of sublattices of DO₂₂ phase are investigated delicately. Figure 6(a) shows that the site occupation probability of Ni on Ni_I site increases while the site occupation probabilities of Ni on Ni_II and V sites decrease during the phase transformation. The site occupation probability increment of Ni on Ni_I site is larger than the site occupation probability decrement of Ni on Ni_II site, but smaller than the site occupation probability decrement of Ni on V site. Thus, the composition of Ni in DO₂₂ phase decreases while the composition of Ni on Ni sites increases during the growth of L1₂ phase, as demonstrated in Figs. 4(a) and 5. Figure 6(b) shows that the site occupation probabilities of Al on all three kinds of sublattices of DO₂₂ phase decrease during phase transformation, and the site occupation probabilities decrement of Al on Ni_I and V sites is obviously larger than that on Ni_II site. For the site occupation probability of V on three kinds of sublattices of DO₂₂ phase during phase transformation, Fig. 6(c) shows that V increases on V and Ni_II sites, and decreases on Ni_Ⅰ site.

Fig. 6 Site occupation probability evolution of alloying elements in DO₂₂ phase during phase transformation from DO₂₂ to L1₂ in Ni₇₅Al_4.2V_20.8 aged at 1185 K

It can be concluded from the above results that part of Ni for the growth of L1₂ phase is supplied from the centre of DO₂₂ phase, and mainly comes from V sublattice. Part of Al for the growth of L1₂ phase is supplied from Ni_Ⅰ and V sites of DO₂₂ phase. The enriched V from the decreasing DO₂₂ phase mainly occupies V and Ni_Ⅱ sites. In other words, the evolution of antisite atoms and ternary additions in the centre part of DO₂₂ phase contribute to the L1₂ phase growth at the late stage. And it is the diffusion of antisite atoms and ternary additions from the centre part of DO₂₂ phase to the interfaces of DO₂₂ and L1₂ phases that controls the growth rate of L1₂ phase.

4 Conclusions

1) The growth of Ni₃Al phase during the phase transformation of Ni₇₅Al_4.2V_20.8 alloy can be divided into two stages, based on the volume fraction growth rate of L1₂ phase, and the relationship between the composition evolution of alloying elements in DO₂₂ phase and the volume fraction of L1₂ phase.

2) At the early stage, the composition in the centre part of DO₂₂ phase almost remains unchanged, L1₂ phase grows quickly and it is controlled by the diffusion of alloying elements in disordered phase. At the late stage, the growth of L1₂ phase is controlled by site occupation evolution of alloying elements in the centre part of DO₂₂ phase, and the growth rate of L1₂ phase is relatively slow.

3) At the late stage, part of alloying elements for L1₂ phase growth are supplied from the centre of DO₂₂ phase. Part of Ni is mainly supplied from V sublattice, and part of Al is supplied from Ni_Ⅰ and V sites at the centre of DO₂₂ phase. The excessive V from the decreasing DO₂₂ phase migrates into the centre of DO₂₂ phase and mainly occupies V and Ni_Ⅱ sites.

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Ni₇₅Al_4.2V_20.8相变过程中DO₂₂相合金元素占位几率演化的微观相场模拟

张明义^{1, 2,3}，李志刚²，张金玲²，张会占²，陈 铮³，张嘉振²

1. 中国工程物理研究院 流体物理研究所，绵阳 621900；

2.中国商用飞机有限责任公司 北京民用飞机技术研究中心，北京 100083；

3. 西北工业大学 凝固技术重点实验室，西安 710072

摘  要：基于微观相场模型，研究Ni₇₅Al_4.2V_20.8相变过程中Ni₃V-DO₂₂相中合金元素占位几率演化规律与Ni₃Al-L1₂相长大之间的内在关联。结果表明L1₂相长大过程可以分为两个阶段。在前期，DO₂₂相内合金元素的成分基本保持不变；在后期，DO₂₂相中Ni和Al的浓度降低，而V的浓度升高。合金元素在DO₂₂相中各个格点位置上的浓度发生不同变化；为L1₂相长大后期提供部分合金元素：其中，Ni主要来源于DO₂₂相中的V格点位置；Al主要来源于Ni_I和V格点位置；由于DO₂₂相体积减少而富余的V向DO₂₂相内部扩散，主要占据V和Ni_II格点位置。L1₂相长大的后期主要受DO₂₂相内反位缺陷和第三组元的演化所控制。

关键词：镍基合金；晶粒生长；相变；微观相场；反位缺陷

(Edited by Mu-lan QIN)

Foundation item: Projects (51174168, 51274167) supported by the National Natural Science Foundation of China; Project (2013M532082) supported by Postdoctoral Science Foundation of China; Projects (13R21421700, 13R21421800) supported by the Postdoctoral Science Foundation of Shanghai, China

Corresponding author: Ming-yi ZHANG; Tel: +86-10-57808702; E-mail: zmy1688@gmail.com

DOI: 10.1016/S1003-6326(15)63763-3