Trans. Nonferrous Met. Soc. China 22(2012) 2439-2443

Site occupation evolution of alloying elements in L1₂ phase during phase transformation in Ni₇₅Al_7.5V_17.5

ZHANG Ming-yi^{1, 2}, LIU Fu², CHEN Zheng¹, GUO Hong-jun², YUE Guang-quan², YANG Kun¹

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

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

Received 9 July 2012; accepted 1 August 2012

Abstract: Correlation between site occupation evolution of alloying elements in L1₂ phase and growth of DO₂₂ phase in Ni₇₅Al_7.5V_17.5 was studied using microscopic phase field model. The results demonstrate that the growing process of DO₂₂ phase can be divided into two stages. At the early stage, composition in the centre part of L1₂ phase almost remains unchanged, and the nucleation and growth of DO₂₂ phase is controlled by the decrease of interface between L1₂ phases. At the late stage, part of V for growth of DO₂₂ phase is supplied from the centre part of L1₂ phase and mainly comes from Al sublattice, the excess Ni spared from the decreasing L1₂ phase migrates into the centre part of L1₂ phase and occupies the Ni sublattices exclusively, while the excess Al mainly occupies the Al sublattice. At the late stage, the growth of DO₂₂ phase is controlled by the evolution of antisite atoms and ternary additions in the centre part of L1₂ phase.

Key words: nickel based superalloys; Ni₇₅Al_7.5V_17.5 alloy; phase transformation; micro-phase field; grain growth; antisite defect

1 Introduction

Site occupation behavior of alloying elements (including site preference of ternary alloying elements and antisites of constituent elements) in intermetallic compounds and their effects on physical property are subjects of not only great practical interests but also fundamental theoretical interests [1,2]. Site preference of alloying elements can be affected by changing temperature [3,4], composition [5,6], or magnetism [7]. The performance of alloy is strongly influenced by site preference of ternary additions and antisite atoms. CHIBA et al [8] found that when the ternary addition preferentially substitutes Ni on the face centered sites in Ni₃Al, the ductility of Ni₃Al can be improved significantly. Studies also demonstrate that site preference of alloying elements affects the solute segregation strongly [9,10]. However, to our best knowledge, attention has not 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.

The phase transformation in Ni₇₅Al_xV_25-x alloys during aging process has been studied extensively both experimentally and theoretically. Most of the studies are focused on kinetics of phase separation and microstructure evolution [11-13]. The atomic ordering and composition clustering process were studied by PODURI and CHEN [14] and HOU et al [15], and LI et al [16] investigated the coarsening behaviors of L1₂ and DO₂₂ in Ni₇₅Al_xV_25-x alloys systematically. Few studies are focused on the correlation between the behavior of interfaces and phase transformation in Ni₇₅Al_xV_25-x alloys [17-19]. However, the mechanism and kinetics of phase transformation between L1₂ and DO₂₂ still need further understanding. In this work, site occupation behavior of alloying elements in L1₂ phase during phase transformation from L1₂ to DO₂₂ in Ni₇₅Al_7.5V_17.5 was studied, and their correlation was discussed. To our best knowledge, few studies have been carried out to study the kinetics of phase transformation by investigating the site occupation evolution of alloying elements at atomistic scale using a numerical simulation method. And understanding the correlation between site occupation behavior of alloying elements and growth of the second phase would make us know the kinetics of phase transformation better.

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 is firstly proposed by KHACHATURYAN [20] and developed by PODURI and CHEN [14] 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 atom α at a given lattice site r at a given time t, t is the reduced time, L_αb(r–r′) (α and β=A, B or C) is the kinetic coefficient which is proportional to the probability of elementary diffusional jumps from site r to r′ per unit 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 and V_αb =ω_αα+ω_bb–2ω_αb.

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 [14] and ZAPOLSY et al [21] in previous works and proved to fit for the real Ni-Al-V alloy system at a high temperature, are used as our simulation inputs. The applications of microscopic phase-field model on microstructure evolution of Ni-based alloys had shown an excellent agreement both with experiment results [21] and other simulation results [13].

3 Results and discussion

Ni₇₅Al_7.5V_17.5 aged at 1185 K was simulated using microscopic phase-field model, and microstructure evolution during phase transformation is shown in Fig. 1. In Fig. 1, black sites represent Ni, gray sites represent V and white sites represent Al. L1₂-Ni₃Al phases precipitate from the disordered phase first. And then, accompanying the formation and growth of L1₂ ordered domains, V atoms start to segregate to the interfaces of L1₂ ordered phase while the Al atoms deplete from the interfaces. As the degree of V segregation at the interfaces increases, the DO₂₂-Ni₃V ordered domains start to nucleate and grow at the interfaces of the L1₂ ordered phase. At last, a two-phase mixture is formed.

Figure 2 gives the volume fraction variation of L1₂ and DO₂₂ phases during aging process. The volume of L1₂ phase decreases accompanied with the volume of DO₂₂ phase increasing. This verifies that DO₂₂ phases grow up at the expense of L1₂ phases after DO₂₂ phases precipitate at the interfaces. As the volume of L1₂ phase decreases, Ni and Al will be spared from the decreasing L1₂ phase, whereas the growth of DO₂₂ phase needs Ni and V. It has been 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% (mole fraction) in L1₂ phase [21]. Thus, the Ni spared by the decreasing L1₂ phase can satisfy the need of Ni for DO₂₂ growth, and part of V for DO₂₂ growth can be supplied from the decreasing L1₂ phase. However, where does the other V come from to satisfy the growth of DO₂₂, and where does the Al go away when the volume of L1₂ phase decreases? To answer this question, content evolution of alloying elements in L1₂ phase was studied.

Considering the L1₂ phase in the vicinity of interface will transform into DO₂₂ phase, only the content evolution of alloying elements in the centre part of L1₂ phase (as the square denoted by arrow A in    Fig. 1(f)) was investigated. Figure 3 shows that contents of Ni and Al in L1₂ phase increase and content of V decreases during the phase transformation. The content of V is higher than that of Al in the centre of L1₂ phase first, and it is reversed at later. This illustrates that part of V for growth of DO₂₂ phase can be supplied from the centre of L1₂ phase, and the Al and Ni spared from decreasing L1₂ phase migrate from the interface to the centre of L1₂ phase.

Fig. 1 Microstructure evolution during phase transformation from disordered (FCC-A1) phase to ordered (L1₂ and DO₂₂) phase of Ni₇₅Al_7.5V_17.5 aged at 1185 K: (a) t=8000; (b) t=20000; (c) t=70000; (d) t=100000; (e) t=200000; (f) t=400000

Fig. 2 Volume fraction variation of L1₂ and DO₂₂ phases of Ni₇₅Al_7.5V_17.5 aged at 1185 K

Fig. 3 Composition evolution of centre part of L1₂ phase in Ni₇₅Al_7.5V_17.5 aged at 1185 K

Figure 4 illustrates the relationship between volume fraction of DO₂₂ phase and composition of L1₂ phase. From Fig. 4, the growth of DO₂₂ phase can be divided into two stages. At the early stage, volume fraction of DO₂₂ phase increases from about 0.05 to 0.35 quickly, and the composition of the centre part of L1₂ phase almost remains unchanged. As mentioned above, the decreasing of L1₂ phase cannot supply enough V for the growth of DO₂₂ phase. However, V segregates at the interface of L1₂ phase, and the amount of interfaces between L1₂ phases decreases quickly with the nucleation and growth of DO₂₂ phase. Thus, the V for growth of DO₂₂ phase at the early stage is supplied from both the decreasing L1₂ phase and interfaces between L1₂ phases. At the late stage, volume fraction of DO₂₂ phase grows up slowly from 0.35 to about 0.48, accompanied with the contents of Al and Ni increasing, and content of V deceasing in the centre part of L1₂ phase. This implies that the growth of DO₂₂ phase at the late stage is controlled by the content evolution of alloying elements in the centre part of L1₂ phase.

Fig. 4 Variation of composition of L1₂ phase with volume fraction of DO₂₂ phase in Ni₇₅Al_7.5V_17.5 aged at 1185 K

As the L1₂ phase consists of two sublattices, content evolution of alloying elements at both Ni and Al sublattices in the centre of L1₂ phase was studied. Figure 5 shows that the ternary addition V prefers to occupy the Al sublattice, which is in consistent with the previous study [22]. As the DO₂₂ phase grows up, the content of host atoms Al_Al (Al_Al denotes the Al atom at the Al sublattice) and Ni_Ni increase, the contents of ternary additions of V_Ni and V_Al decrease, and content of antisite atoms Ni_Al decreases but that of Al_Ni increases.

Fig. 5 Site occupation of alloying elements in L1₂ phase during phase transformation from L1₂ to DO₂₂ in Ni₇₅Al_7.5V_17.5

The site occupation decrement of Ni_Ni is larger than the site occupation decrement of Ni_Al, thus content of Ni in the centre of L1₂ phase increases. This demonstrates that the excess Ni from decreasing L1₂ phase occupies the Ni sublattice. The site occupation decrement of V_Ni is less than that of V_Al, and the site occupation increment of Al_Ni is less than that of Al_Al. This demonstrates that part of V for growth of DO₂₂ phase supplied from the centre of L1₂ phase mainly comes from Al sublattice, and Al from decreasing L1₂ phase mainly occupies the Al sublattice. Considering the discussion above, it can be concluded that the growth of DO₂₂ phase is mainly controlled by the decrease of interface between L1₂ phases at the early stage, but at the late stage, it is mainly controlled by the evolution of antisite atoms and ternary additions in the centre part of L1₂ phase.

4 Conclusions

1) Correlation between site occupation evolution of alloying elements in L1₂ phase and volume of DO₂₂ phase indicates that the process of growth of DO₂₂ phase can be divided into two stages.

2) At the early stage, composition in the centre part of L1₂ phase almost remains unchanged, and the nucleation and growth of DO₂₂ phase is controlled by decrease of interface between L1₂ phases. At the late stage, the growth of DO₂₂ phase is controlled by site occupation evolution of alloying elements in the centre part of L1₂ phase.

3) At the late stage, Ni and Al spared from decreasing L1₂ phase migrate from the interfaces between L1₂ and DO₂₂ phases to the centre of L1₂ phase, and the excess Ni exclusively occupies the Ni sublattice and Al mainly occupies the Al sublattice. Part of V for growth of DO₂₂ phase is supplied from the centre part of L1₂ phase and mainly comes from Al sublattice.

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Ni₇₅Al_7.5V_17.5相变过程中L1₂相合金元素占位几率演化的微观相场模拟

张明义^{1, 2}，刘  富²，陈  铮¹，郭红军²，岳广全²，杨  坤¹

1. 西北工业大学 凝固技术重点实验室，西安 710072；

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

摘  要：基于微观相场模型，研究Ni₇₅Al_7.5V_17.5合金在相变过程中L1₂相内合金元素演化与DO₂₂相生长之间的关系。研究表明，在L1₂相向DO₂₂相转变的过程中，DO₂₂相的长大可以分为两阶段。在早期，L1₂相内合金元素的成分基本不变，DO₂₂相的长大主要受L1₂相间有序畴界的减少所控制。在后期，DO₂₂相长大所需的V一部分来自L1₂相内部，一部分来自L1₂相体积的减少，其中，相内部为DO₂₂相长大所提供的V则主要来自Al格点位置，由于L1₂相体积减少而富余的Al向L1₂相内部扩散迁移并主要占据Al格点位置，富余的Ni则同时向L1₂相内部和DO₂₂相内部扩散，主要占据L1₂相的Ni位置。DO₂₂相长大的后期主要受L1₂相内反位缺陷和第三组元的演化所控制。

关键词：镍基合金；Ni₇₅Al_7.5V_17.5合金；相变；微观相场；晶粒生长；反位缺陷

(Edited by LI Xiang-qun)

Foundation item: Projects (50941020, 10902086, 50875217, 20903075) supported by the National Natural Science Foundation of China; Projects (SJ08-ZT05, SJ08-B14) supported by the Natural Science Foundation of Shaanxi Province, China

Corresponding author: ZHANG Ming-yi; Tel: +86-29-88486023; E-mail: zmy1688@gmail.com

DOI: 10.1016/S1003-6326(11)61482-9