Trans. Nonferrous Met. Soc. China 25(2015) 1599-1604
Site occupation evolution of alloying elements in Ni3V phase during phase transformation in Ni75Al4.2V20.8
Ming-yi ZHANG1,2,3, 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 Ni75Al4.2V20.8. 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 NiⅠ 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 NiII 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: Ni75Al4.2V20.8 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 Ni75AlxV25-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 Ni75AlxV25-x alloys systematically, but few studies were focused on the correlation between the behavior of interfaces and phase transformation of Ni75AlxV25-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 Ni75Al7.5V17.5, 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 Ni75Al7.5V17.5 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, PC(r, t)=1-PA(r, t)-PB(r, t), where Pα(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, Lαb( 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:
![](/web/fileinfo/upload/magazine/12476/309372/image004.gif)
![](/web/fileinfo/upload/magazine/12476/309372/image006.gif)
![](/web/fileinfo/upload/magazine/12476/309372/image008.gif)
(2)
where the effective pair interaction Vαb is deduced from pair interaction ωαb: Vαb =ωαα+ωbb–2ωαb.
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 NiⅠ and NiⅡ. 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 NiI site has four V atoms to form a square configuration and the NiII has four V atoms to form a tetrahedral configuration. The number of NiII site is two times as many as the NiI site in a Ni3V unit cell.
![](/web/fileinfo/upload/magazine/12476/309372/image012.jpg)
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 NiI (c) and NiII (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 Ni75Al4.2V20.8 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.
![](/web/fileinfo/upload/magazine/12476/309372/image014.jpg)
Fig. 2 Simulated atomistic microstructure evolution figures during phase transformation from disordered (FCC-A1) phase to ordered (L12 and DO22) phase in Ni75Al4.2V20.8 aged at 1185 K
![](/web/fileinfo/upload/magazine/12476/309372/image016.jpg)
Fig. 3 Volume fraction variation of L12 and DO22 phase during phase transformation from DO22 to L12 in Ni75Al4.2V20.8 aged at 1185 K
![](/web/fileinfo/upload/magazine/12476/309372/image018.jpg)
Fig. 4 Composition evolution of alloying elements in DO22 phase during phase transformation in Ni75Al4.2V20.8 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.
![](/web/fileinfo/upload/magazine/12476/309372/image020.jpg)
Fig. 5 Composition evolution of alloying elements on Ni sites of DO22 phase during phase transformation from DO22 to L12 in Ni75Al4.2V20.8 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 NiI site increases while the site occupation probabilities of Ni on NiII and V sites decrease during the phase transformation. The site occupation probability increment of Ni on NiI site is larger than the site occupation probability decrement of Ni on NiII 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 NiI and V sites is obviously larger than that on NiII 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 NiII sites, and decreases on NiⅠ site.
![](/web/fileinfo/upload/magazine/12476/309372/image022.jpg)
Fig. 6 Site occupation probability evolution of alloying elements in DO22 phase during phase transformation from DO22 to L12 in Ni75Al4.2V20.8 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 NiⅠ and V sites of DO22 phase. The enriched V from the decreasing DO22 phase mainly occupies V and NiⅡ 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 Ni75Al4.2V20.8 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 NiⅠ 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 NiⅡ sites.
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Ni75Al4.2V20.8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Ni75Al4.2V20.8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NiI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NiII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