中国有色金属学报(英文版)

Trans. Nonferrous Met. Soc. China 31(2021) 1740-1747

Phase equilibria in Co-Al-Re ternary system at 1100 and 1300 °C

Ling-ling LI1, Jin-bin ZHANG1, Yue-chao CHEN1, Shui-yuan YANG1, Cui-ping WANG1, Xing-jun LIU1,2,3

1. Fujian Provincial Key Laboratory of Materials Genome, College of Materials, Xiamen University, Xiamen 361005, China;

2. State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China;

3. School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen 518055, China

Received 15 July 2020; accepted 18 February 2021

Abstract:

Isothermal sections of the Co-Al-Re ternary system at 1100 and 1300 °C were determined experimentally by electron probe microanalysis and X-ray diffraction. The results show that there are seven three-phase regions in the 1100 °C isothermal section and five three-phase regions in the 1300 °C isothermal section. The solid solubilities of αCo, εRe and CoAl increase a little with temperature increasing from 1100 to 1300 °C. The solubility of Co in compounds AlRe2, Al11Re4 and Al4Re is negligible, <1.5 at.%. And no ternary compounds are found.

Key words:

Co-Al-Re; phase equilibria; isothermal section;

1 Introduction

The phase equilibria of the Co-Al-Re ternary system are fundamentally important to understand and develop Co- and Ni-based superalloys.

Recently, L12-ordered phases have been observed in some Co-Al-X (X=W, V, etc) systems and have exhibited good performances [1-3]. Both Al and Co are important constituent elements of Ni-based superalloys. Thus, the Co-Al system plays an important role in Co- and Ni-based superalloys. Rhenium (Re) is an element commonly used in fourth- and fifth-generation Ni-based superalloys [4-8]. Elemental Re not only improves the strength and creep resistance of Co-based superalloys but also refines its morphology and decreases γ/γ′ lattice parameter misfits [9,10]. Therefore, in order to develop Ni- and Co-based superalloys and understand the relationships between their microstructures and properties, knowledge of the phase equilibria occurring in the Co-Al-Re system is required. However, experimental information and phase diagrams of this ternary system have not been established.

In this study, experimental investigation of the phase equilibria occurring in the Co-Al-Re ternary system at 1100 and 1300 °C was conducted. The experimental data will help to establish thermo- dynamic databases and inform the design and development of Co- and Ni-based superalloys.

Phase equilibria in three constituent sub-binary systems of Co-Al [11-14], Co-Re [15-18], and Al-Re [19-24], have been comprehensively investigated and critically assessed in the literatures. The crystal information existing for the stable phases in the Co-Al-Re ternary system is listed in Table 1.

The Co-Al system was first mentioned in Ref. [11], and then STEIN et al [12] investigated the melting behaviour and homogeneity range of the B2 phase. Later, PRIPUTEN et al [13] studied the Co4Al13 family of phases and reported that it has six phases: CoAl3, Y1-Co4Al13, Y2-Co4Al13, M-Co4Al13, O-Co4Al13 and O′-Co4Al13. They considered that Y2-Co4Al13 phase is metastable and that a transition reaction might exist between O-Co4Al13 and O′-Co4Al13. To simplify the phase diagram, some researchers [14] treat the Co4Al13 family as a single stoichiometric phase named Co4Al13. This simplification is also adopted in the present study.

Table 1 Crystal structures of stable solid phases in Co-Al-Re ternary systems

The Co-Re binary system was first reported by ELLIOT [15] in 1965. Then, PREDEL [16] investigated the martensitic character of the phase transformation. Experiments determined that the Co-Re system is simple without an intermetallic phase. Recently, LIU et al [17] and GUO et al [18] thermodynamically evaluated the Co-Re system and their findings were consistent with the experimental data. The newly-assessed Co-Re phase diagram of GUO et al [18] is applied in the present study, as shown in Fig. 1.

For Al-Re system, HUANG and CHANG [19] were the first to publish a thermodynamic diagram based on the experimental data of SAVITSKII et al [20], ELLIOTT [15], SHRINK [21] and SCHUSTER [22]. Then, CORNISH and WITCOMB [23], using metallographic methods and X-ray diffraction, confirmed the existence of the intermediate phases of Al12Re, Al6Re, Al4Re and Al11Re4. SCHUSTER et al [24] investigated the Al-Re binary system and confirmed that there are seven intermetallic phases: Al12Re, Al6Re, Al33-xRe8, Al4Re, Al11Re4, AlRe and AlRe2. They also described the crystal structure and lattice parameters for all these phases. Here, the results of SCHUSTER et al [24] are adopted.

Fig. 1 Binary phase diagrams constituting Co-Al-Re ternary system [14,18,24]

2 Experimental

Usually, phase relationships are studied by the equilibrated alloy [25,26] and diffusion couple methods [27]. Here, the phase relationships of the Co-Al-Re ternary system at 1100 and 1300 °C are studied using equilibrated alloy. Pure metals of cobalt (99.9 wt.%), aluminium (99.9 wt.%) and rhenium (99.9 wt.%) were used as raw materials to prepare ingots by arc melting under a high-purity argon atmosphere. The mass of each sample was about 15 g. To achieve homogeneity, the ingots were remelted at least four times and their mass losses were <0.5 wt.%.

Then, the specimens were cut into plate shapes and put into quartz capsules that were filled with argon gas. In addition, pure Ti filings were added to the quartz capsules to prevent oxidation, and samples containing a liquid phase were wrapped in a pure Ta slice to prevent contact reaction with quartz. Specimens were annealed at 1100 and 1300 °C for various durations ranging from 1 h to 60 d and then quenched in ice water.

Backscatter electron (BSE) imaging and the equilibrium composition of each phase were determined by an electron probe micro analyser (EPMA; JXA-8100R, JEOL, Japan) with an accelerating voltage of 20.0 kV and a probe current of 1.0×10-8 A. X-ray diffraction (XRD) was performed for phase identification using Cu Kα radiation at 40 kV and 40 mA. To ensure the accuracy of the data, pure elements were used as standards to calibrate the measurements. The final values of the phase compositions are the averages of seven measurements.

3 Results and discussion

About 14 samples were used to determine the phase boundaries for isothermal sections. Figures 2 and 3 show typical BSE images of Co-Al-Re ternary alloys annealed at 1100 and 1300 °C, respectively. The corresponding XRD patterns are presented in Fig. 4. Tables 2 and 3 present the equilibrium compositions of the Co-Al-Re alloys quenched from 1100 and 1300 °C, respectively, as determined by EPMA.

Fig. 2 Typical BSE images obtained from Co-Al-Re ternary alloys annealed at 1100 °C

Fig. 3 Typical BSE images obtained from Co-Al-Re ternary alloys annealed at 1300 °C

Fig. 4 X-ray diffraction patterns obtained from alloys

Table 2 Equilibrium compositions of Co-Al-Re ternary alloys determined at 1100 °С

Table 3 Equilibrium compositions of Co-Al-Re ternary alloys at 1300 °С

3.1 Isothermal section at 1100 °C

As shown in Fig. 2(a), a three-phase microstructure of αCo (grey), ε(Co,Re) (white), and CoAl (black) is found in Co61Al19Re20 alloy annealed at 1100 °C for 60 d. The corresponding XRD pattern is presented in Fig. 4(a). When the Co30Al40Re30 alloy is annealed at 1100 °C for 60 d, there are three different phases, including CoAl (black), AlRe2 (grey), and ε(Co,Re) (white), as shown in Fig. 2(b). Similarly, a three-phase microstructure is found in Co22Al70Re8 alloy (Fig. 2(c)). Figure 4(b) shows the corresponding XRD pattern of the Co22Al70Re8 alloy. Three phases of Al11Re4 (white), Co2Al5 (grey), and CoAl (black) are clearly distinguishable in Fig. 4(b). In Fig. 2(d), a two-phase microstructure can be observed in the Co1Al82Re17 alloy annealed at 1100 °C for 1 d, where the liquid phase (L) is dispersed in the matrix of solid-phase Al4Re (white). From magnified image of the liquid phase inserted in Fig. 2(d), both the grey and dark regions are solidified from the liquid phase. According to the morphology, the  grey region may be a dendritic structure of the solid-phase Al (FCC). Thus, the chemical composition of the liquid phase is determined from the average value of the dark region.

Based on the experimental data, an isothermal section of the Co-Al-Re ternary system at 1100 °C is constructed (Fig. 5(a)).There are five experimentally-determined three-phase regions: [ε(Co,Re)+αCo+CoAl], [ε(Co,Re)+CoAl+AlRe2], [CoAl+AlRe2+Al11Re4], [CoAl+Al11Re4+Co2Al5] and [Al11Re4+Al4Re+L]. In the Al-rich corner, due to a Co4Al13-family phase existing in the temperature range of 1093-1153 °C [13], the phase relationships are very complicated. Here, to simplify the phase relationships, the Co4Al13-family phase is treated as a single phase and other two three-phase regions of [Co2Al5+Co4Al13+L] and [Co2Al5+Al11Re4+L] are deduced.

On the Al-Re side, the solubilities of Co in the compounds AlRe2, Al11Re4 and Al4Re are negligibly small, all <1.5 at.%, as shown in Fig. 4(a).

3.2 Isothermal section at 1300 °C

As shown in Fig. 3(a), two different phases are found in the Co38Al32Re30 alloy annealed at 1300 °C. Combined with the XRD analysis in Fig. 4(c), the white phase is identified as ε(Co,Re), while the black phase is CoAl. When the Co30Al50Re20 alloy is annealed at 1300 °C (Fig. 3(b)), three different phases, Co11Re4 (grey), AlRe2 (white), and CoAl (black), are identified in combination with the XRD analysis shown in Fig. 4(d). In Fig. 3(c), two solid phases of Al11Re4 (white) and CoAl (dark grey), and a liquid phase (L, light grey) occur in the Co22Al70Re8 alloy annealed at 1300 °C for 1 h. Likewise, a three-phase microstructure consisting of L (black), Al4Re (dark grey) and Al11Re4 (light grey) can be seen in the Co2Al76Re22 alloy, as  shown in Fig. 3(d).

Then, the isothermal section of Co-Al-Re ternary system at 1300 °C is established (Fig. 5(b)). There are five three-phase regions: [ε(Co,Re) + αCo+CoAl], [ε(Co,Re)+CoAl+AlRe2], [CoAl+ AlRe2+Al11Re4], [Co11Re4+CoAl+L] and [Co11Re4+ Al4Re+L]. Compared with the isothermal section obtained at 1100 °C, there is an obvious difference in the Al-rich corner at 1300 °C: the Co4Al13-family phases decompose and the liquid phase appears. Other solid solubilities of αCo, ε(Co,Re) and CoAl increase a little from 1100 to 1300 °C. The solubilities of Co in the compounds AlRe2, Al11Re4 and Al4Re are still very small and negligible.

Fig. 5 Experimentally-determined isothermal sections of Co-Al-Re system

4 Conclusions

(1) Five three-phase regions are determined and two three-phase regions are deduced at 1100 °C, while five three-phase regions are determined in the 1300 °C isothermal section.

(2) The solid solubilities of αCo, ε(Co,Re) and CoAl increase a little from 1100 to 1300 °C.

(3) The solubility of Co in compounds AlRe2, Al11Re4 and Al4Re is very low and negligible at both 1100 and 1300 °C.

(4) No ternary compounds are found.

Acknowledgments

The authors are grateful for the financial supports from the National Natural Science Foundation of China (No. 51831007), and the National Key Research & Development Program of China (No. 2017YFB0702901).

References

[1] SATO J, OMORI T, OIKAWA K, OHNUMA I, KAINUMA R, ISHIDA K. Cobalt-base high-temperature alloys [J]. Science, 2006, 312(5770): 90-91.

[2] CHEN Y C, WANG C P, RUAN J J, OMORI T, KAINUMA R, ISHIDA K, LIU X J. High-strength Co-Al-V-base superalloys strengthened by γ′-Co3(Al,V) with high solvus temperature [J]. Acta Materialia, 2019, 170: 62-74.

[3] CHEN Y C, WANG C P, RUAN J J, YANG S Y, OMORI T, KAINUMA R, ISHIDA K, HAN J J, LU Y, LIU X J. Development of low-density γ/γ′ Co-Al-Ta-based superalloys with high solvus temperature [J]. Acta Materialia, 2020, 188: 652-664.

[4] REED R C. The superalloys [M]. Cambridge University Press, 2006.

[5] POLLOCK T M, FIELD R D. Dislocations and high- temperature plastic deformation of superalloy single crystals [M]//Dislocations in Solids. Elsevier, 2002.

[6] WOLLMER S, MACK T, GLATZEL U. Influence of tungsten and rhenium concentration on creep properties of a second generation superalloy [J]. Materials Science and Engineering A, 2001, 319-321: 792-795.

[7] HECKL A, NEUMEIER S, GOKEN M, SINGER R F. The Effect of Re and Ru on γ/γ′ microstructure, γ-solid solution strengthening and creep strength in nickel-base superalloys [J]. Materials Science and Engineering A, 2011, 528: 3435-3444.

[8] WU X X, MAKINENI S K, KONTISA P, DEHMA G, RAABEA D, GAULTA B, EGGELER G. On the segregation of Re at dislocations in the γ' phase of Ni-based single crystal superalloys [J]. Materialia, 2018, 4: 109-114.

[9] LI L L, WANG C P, CHEN Y C, YANG S Y, YANG M J, ZHANG J B, LU Y, HAN J J, LIU X J. Effect of Re on microstructure and mechanical properties of γ/γ Co-Ti-based superalloys [J]. Intermetallics, 2019, 115: 106612.

[10] PANDEY P, SAWANT A K, NITHIN B, PENG Z, MAKINENI S K, GAULT B, CHATTOPADHYAY K. On the effect of Re addition on microstructural evolution of a CoNi-based superalloy [J]. Acta Materialia, 2019, 168: 37-51.

[11] MASSALSKI T B. Binary alloy phase diagrams [M]. 2nd ed. ASM International: Materials Park, OH, 1990.

[12] STEIN F, HE C, DUPIN N. Melting behaviour and homogeneity range of B2 CoAl and updated thermodynamic description of the Al-Co System [J]. Intermetallics, 2013, 39: 58-68.

[13] PRIPUTEN P, KUSY M, DRIENOVSKY M, JANICKOVIC D, CICKA R, CERNICKOVA I, JANOVEC J. Experimental reinvestigation of Al-Co phase diagram in vicinity ofAl13Co4 family of phases [J]. Journal of Alloys & Compounds, 2015, 46(44): 486-497.

[14] DUPIN N, ANSARA I. Evaluation thermodynamique for system Al-Co [J]. Revue de Metallurgie, 1998, 95: 1121-1130. (in France)

[15] ELLIOTT R P. Constitution of binary alloys [M]. 1st supplement. New York: McGraw-Hill, 1965.

[16] PREDEL B. Co-Re (Cobalt-Rhenium) [M]//Ca-Cd-Co-Zr. Heidelberg: Springer, 1993.

[17] LIU X J, LIN J Y, LU Y, GUO Y H, WANG C P. Assessment of the atomic mobility for the fcc phase of Ni-Co-X (X=Re and Ru) system [J]. Calphad, 2014, 45: 138-144.

[18] GUO C, WU T, LI C, DU Z. Thermodynamic Re-assessment of the Re-X (X=Al, Co, Cr, Ta) binary systems [J]. Calphad, 2018, 61: 33-40.

[19] HUANG W, CHANG Y A. A thermodynamic analysis of the Al-Re system [J]. Journal of Phase Equilibria and Diffusion, 1988, 19(4): 361-366.

[20] SAVITSKII E M, TYLKINA M A, POVAROVA K B. Equilibrium diagram of the aluminium-rhenium system [J]. Russian Journal of Inorganic Chemistry, 1961, 6: 1003-1006.

[21] SHRINK E A. Constitution of binary alloys [M]. 2nd supplement. New York: McGraw-Hill, 1969.

[22] SCHUSTER J C. X-ray investigations of phase relations and crystal structures in the binary system Re-Al [J]. Journal of the Less Common Metals, 1984, 98: 215-220.

[23] CORNISHL A, WITCOMB M J. An investigation of the Al-Re phase diagram [J]. Journal of Alloys & Compounds, 1999, 291: 117-129.

[24] SCHUSTER J C, PERRING L, RICHTER K W, IPSER H, GRIN Y, WEITZER F. The binary system Re-Al [J]. Journal of Alloys & Compounds, 2001, 320: 224-227.

[25] WANG M, LIU H S, CAI G M, JIN Z P. Measurement of phase equilibria in Ti-Ni-Sn system [J], Transactions of Nonferrous Metals Society of China, 2018, 28(4): 819-828.

[26] LI L L, WANG C P, ZHANG J B, YANG S Y, HAN J J, LU Y, LIU X J. Phase equilibria of the Co-Ti-Ru ternary system [J]. Journal of Phase Equilibria and Diffusion, 2019, 40: 561-569.

[27] PENG Z Y, WANG X M, YIN F C, OUYANGXM, HU J X. Phase equilibria of Co-Mo-Zn ternary system [J]. Transactions of Nonferrous Metals Society of China, 2020, 30(2): 417-427.

Co-Al-Re三元系在1100 °C和1300 °C等温截面的相平衡

李玲玲1,张锦彬1,陈悦超1,杨水源1,王翠萍1,刘兴军1,2,3

1. 厦门大学 材料学院 福建省材料基因工程重点实验室,厦门 361005;

2. 哈尔滨工业大学 先进焊接与连接国家重点实验室,哈尔滨 150001;

3. 哈尔滨工业大学(深圳) 材料科学与工程学院,深圳 518055

摘  要:利用电子探针成分分析(EPMA)和X射线衍射分析(XRD)建立Co-Al-Re三元系的1100 °C和1300 °C等温截面相图。实验结果表明:在1100 °C等温截面相图中存在7个三相区,而1300 °C等温截面相图中存在5个三相区;随着温度从1100 °C上升到1300 °C,αCo、εRe和CoAl的固溶度略微增加;Co在AlRe2、Al11Re4和Al4Re相中的固溶度极小,<1.5%(摩尔分数);等温截面相图中均未发现三元化合物。

关键词:Co-Al-Re;相平衡;等温截面

(Edited by Bing YANG)

Corresponding author: Cui-ping WANG, Tel: +86-592-2180606, Fax: +86-592-2187966, E-mail: wangcp@xmu.edu.cn;

Jin-bin ZHANG, jbzhang@xmu.edu.cn

DOI: 10.1016/S1003-6326(21)65612-1

1003-6326/ 2021 The Nonferrous Metals Society of China. Published by Elsevier Ltd & Science Press

Abstract: Isothermal sections of the Co-Al-Re ternary system at 1100 and 1300 °C were determined experimentally by electron probe microanalysis and X-ray diffraction. The results show that there are seven three-phase regions in the 1100 °C isothermal section and five three-phase regions in the 1300 °C isothermal section. The solid solubilities of αCo, εRe and CoAl increase a little with temperature increasing from 1100 to 1300 °C. The solubility of Co in compounds AlRe2, Al11Re4 and Al4Re is negligible, <1.5 at.%. And no ternary compounds are found.

[1] SATO J, OMORI T, OIKAWA K, OHNUMA I, KAINUMA R, ISHIDA K. Cobalt-base high-temperature alloys [J]. Science, 2006, 312(5770): 90-91.

[2] CHEN Y C, WANG C P, RUAN J J, OMORI T, KAINUMA R, ISHIDA K, LIU X J. High-strength Co-Al-V-base superalloys strengthened by γ′-Co3(Al,V) with high solvus temperature [J]. Acta Materialia, 2019, 170: 62-74.

[3] CHEN Y C, WANG C P, RUAN J J, YANG S Y, OMORI T, KAINUMA R, ISHIDA K, HAN J J, LU Y, LIU X J. Development of low-density γ/γ′ Co-Al-Ta-based superalloys with high solvus temperature [J]. Acta Materialia, 2020, 188: 652-664.

[4] REED R C. The superalloys [M]. Cambridge University Press, 2006.

[5] POLLOCK T M, FIELD R D. Dislocations and high- temperature plastic deformation of superalloy single crystals [M]//Dislocations in Solids. Elsevier, 2002.

[6] WOLLMER S, MACK T, GLATZEL U. Influence of tungsten and rhenium concentration on creep properties of a second generation superalloy [J]. Materials Science and Engineering A, 2001, 319-321: 792-795.

[7] HECKL A, NEUMEIER S, GOKEN M, SINGER R F. The Effect of Re and Ru on γ/γ′ microstructure, γ-solid solution strengthening and creep strength in nickel-base superalloys [J]. Materials Science and Engineering A, 2011, 528: 3435-3444.

[8] WU X X, MAKINENI S K, KONTISA P, DEHMA G, RAABEA D, GAULTA B, EGGELER G. On the segregation of Re at dislocations in the γ' phase of Ni-based single crystal superalloys [J]. Materialia, 2018, 4: 109-114.

[9] LI L L, WANG C P, CHEN Y C, YANG S Y, YANG M J, ZHANG J B, LU Y, HAN J J, LIU X J. Effect of Re on microstructure and mechanical properties of γ/γ Co-Ti-based superalloys [J]. Intermetallics, 2019, 115: 106612.

[10] PANDEY P, SAWANT A K, NITHIN B, PENG Z, MAKINENI S K, GAULT B, CHATTOPADHYAY K. On the effect of Re addition on microstructural evolution of a CoNi-based superalloy [J]. Acta Materialia, 2019, 168: 37-51.

[11] MASSALSKI T B. Binary alloy phase diagrams [M]. 2nd ed. ASM International: Materials Park, OH, 1990.

[12] STEIN F, HE C, DUPIN N. Melting behaviour and homogeneity range of B2 CoAl and updated thermodynamic description of the Al-Co System [J]. Intermetallics, 2013, 39: 58-68.

[13] PRIPUTEN P, KUSY M, DRIENOVSKY M, JANICKOVIC D, CICKA R, CERNICKOVA I, JANOVEC J. Experimental reinvestigation of Al-Co phase diagram in vicinity ofAl13Co4 family of phases [J]. Journal of Alloys & Compounds, 2015, 46(44): 486-497.

[14] DUPIN N, ANSARA I. Evaluation thermodynamique for system Al-Co [J]. Revue de Metallurgie, 1998, 95: 1121-1130. (in France)

[15] ELLIOTT R P. Constitution of binary alloys [M]. 1st supplement. New York: McGraw-Hill, 1965.

[16] PREDEL B. Co-Re (Cobalt-Rhenium) [M]//Ca-Cd-Co-Zr. Heidelberg: Springer, 1993.

[17] LIU X J, LIN J Y, LU Y, GUO Y H, WANG C P. Assessment of the atomic mobility for the fcc phase of Ni-Co-X (X=Re and Ru) system [J]. Calphad, 2014, 45: 138-144.

[18] GUO C, WU T, LI C, DU Z. Thermodynamic Re-assessment of the Re-X (X=Al, Co, Cr, Ta) binary systems [J]. Calphad, 2018, 61: 33-40.

[19] HUANG W, CHANG Y A. A thermodynamic analysis of the Al-Re system [J]. Journal of Phase Equilibria and Diffusion, 1988, 19(4): 361-366.

[20] SAVITSKII E M, TYLKINA M A, POVAROVA K B. Equilibrium diagram of the aluminium-rhenium system [J]. Russian Journal of Inorganic Chemistry, 1961, 6: 1003-1006.

[21] SHRINK E A. Constitution of binary alloys [M]. 2nd supplement. New York: McGraw-Hill, 1969.

[22] SCHUSTER J C. X-ray investigations of phase relations and crystal structures in the binary system Re-Al [J]. Journal of the Less Common Metals, 1984, 98: 215-220.

[23] CORNISHL A, WITCOMB M J. An investigation of the Al-Re phase diagram [J]. Journal of Alloys & Compounds, 1999, 291: 117-129.

[24] SCHUSTER J C, PERRING L, RICHTER K W, IPSER H, GRIN Y, WEITZER F. The binary system Re-Al [J]. Journal of Alloys & Compounds, 2001, 320: 224-227.

[25] WANG M, LIU H S, CAI G M, JIN Z P. Measurement of phase equilibria in Ti-Ni-Sn system [J], Transactions of Nonferrous Metals Society of China, 2018, 28(4): 819-828.

[26] LI L L, WANG C P, ZHANG J B, YANG S Y, HAN J J, LU Y, LIU X J. Phase equilibria of the Co-Ti-Ru ternary system [J]. Journal of Phase Equilibria and Diffusion, 2019, 40: 561-569.

[27] PENG Z Y, WANG X M, YIN F C, OUYANGXM, HU J X. Phase equilibria of Co-Mo-Zn ternary system [J]. Transactions of Nonferrous Metals Society of China, 2020, 30(2): 417-427.