Please wait a minute...
Acta Metall Sin  2018, Vol. 54 Issue (5): 701-716    DOI: 10.11900/0412.1961.2018.00112
Special Issue for the Solidification of Metallic Materials Current Issue | Archive | Adv Search |
Unified Analysis of Non-Equilibrium Solidification and Solid-State Phase Transformations
Feng LIU(), Xu ZHANG, Yubing ZHANG
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China
Download:  HTML  PDF(12757KB) 
Export:  BibTeX | EndNote (RIS)      
Abstract  

Considering both phase transition and material hot-working or material design, unified analysis of non-equilibrium solidification and solid-state phase transformations has profound significance of science and great prospect of engineering application. Here, non-equilibrium solidification and solid state transformation behavior, correlated with peritectic reaction, massive transformation, metastable-stable transformation, precipitation, recrystallization and grain growth, for single phase solid solution alloy, eutectic alloy, peritectic alloy, multi-component super alloy and aluminum alloy, have been systematically reviewed. Regarding further the influence of non-equilibrium solidification on subsequent solid-state transformations, the new transformation mechanism induced by non-equilibrium solidification and the integrated microstructure regulation, the physical correlation between non-equilibrium solidification and subsequent solid-state transformations were discussed, and eventually, the microstructure control under the joint action of non-equilibrium solidification and solid phase transformations was realized. This review is expected to provide theoretical support for quantitative characterization of non-equilibrium solidification effect and microstructure prediction under the joint action of non-equilibrium solidification and solid-state transformations.

Key words:  metal      non-equilibrium solidification      solid-state phase transformation      unified analysis     
Received:  26 March 2018     
ZTFLH:  TG113.12  
Fund: Supported by National Key Research and Development Program of China (Nos.2017YFB0305100 and 2017YFB0703001), National Natural Science Foundation of China (Nos.51431008 and 51790481), Fundamental Research Funds for the Central Universities (No.3102017jc01002) and Research Fund of the State Key Laboratory of Solidification Processing of Northwestern Polytechnical University (No.117-TZ-2015)

Cite this article: 

Feng LIU, Xu ZHANG, Yubing ZHANG. Unified Analysis of Non-Equilibrium Solidification and Solid-State Phase Transformations. Acta Metall Sin, 2018, 54(5): 701-716.

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2018.00112     OR     https://www.ams.org.cn/EN/Y2018/V54/I5/701

Fig.1  Typically measured recalescence curves and as-solidified microstructures, correspond to ΔTT *(a, b) and ΔT T *(c, d), respectively (ΔT is the undercooling, and recalescence behavior and as-solidified microstructure characteristic are quite different with ΔT *≈130 K as a critical point)[17]
(a, c) measured recalescence profiles, where T1δ, Tp and Tsδ are liquidus temperature of the δ phase, equilibrium peritectic reaction plateau temperature and solidus temperature of δ phase, respectively, τPR is peritectoid incubation time
(b) typical microstructure with ΔTT * shows peritectic solidification characteristics: the primary δ dendrites (dark) are enveloped by the peritectic γ phase (white)
(d) typical microstructure with ΔTT * etched with 3% (mass fraction) Nital's reagent to reveal the grain boundaries and the morphologies of second-phase particles (Inserts are the TEM bright field images of the room temperature microstructure, the left is the morphology of the matrix and the right is the morphology of the second-phase particles)
Fig.2  TTT curves of δ /γ solid-state transformation of Fe-4.33%Ni alloy (T?is the cooling rate of the system)[12]
Fig.3  Scanning electron photographs of the Ni3Si precipitates in as-solidified Ni-Si hypoeutectic alloy melt subjected to undercoolings of ΔT≈105 K (a, b) and ΔT≈220 K (c, d) after ageing at temperature T=973 K for 4 h (a, c) and 8 h (b, d)[23]
Fig.4  A schematic diagram illustrating the solubility of Si atom in α-Ni solid solution in as-solidified Ni-Si hypoeutectic alloy. The experimental date is from EDS result and the non-equilibrium dendrite growth calculation is from Wang and Liu's model[24] (a), evolution of the growth rate with the ageing time, t, in the isothermal precipitation at T=973 K of as-solidified Ni-Si hypoeutectic alloy (b) and the effect of non-equilibrium solidification on evolution of Ni3Si particles at T=973 K (c)[23]
Fig.5  Eutectic Si morphologies of A356 Al alloys subjected to T4 treatment and cooling rates of 2.6 K/s (a), 0.6 K/s (b), 0.22 K/s (c) and 0.12 K/s (d)[25]
Fig.6  Evolution of yield strength of A356 alloy under different cooling rates subjected to solid solution treatment at 813 K (a) and artificial ageing at 453 K (b)[27]
Fig.7  The as-annealed microstructures of granular grains solidified under ΔT=140 K at 0.5 h (a), 8 h (b), 24 h (c), and ΔT=250 K at 0.5 h (d), 16 h (e), 30 h (f)[28]
Fig.8  Evolution of the average grain size with the annealing time for Ni-1.5%B alloy annealed at 1173 K[28]
Fig.9  Calculated stress in dendrite network versus initial melt undercooling of DD3 superalloy[30]
Fig.10  EBSD orientation mapping of the microstructures of the highly undercooled Ni-Cu alloy quenched after recalescence with undercooling ΔT=225 K (a), grain boundaries of Fig.10a (b); the pole figure of Fig.10a showing a nearly random texture (c) and misorientation distribution figure of the grain boundaries in Fig.10a (d)[31]
Fig.11  TEM bright field images of substructures in the rapidly solidified Ni80Cu20 alloy quenched with ΔT=225 K[31]
(a~c) dense dislocation networks in deformed grains
(d) SAED pattern of a high angle grain boundary in Fig.11c
Fig.12  EBSD orientation mapping of the microstructures of the quenched Ni-Cu alloy with ΔT=225 K after annealing at 1273 K for about 30 min (a), grain boundaries of Fig.12a (b); the IPF of Fig.12a (c) and the misorientation distribution figure of the grain boundaries in Fig.12a (d)[31]
Fig.13  XRD spectra of the as-solidified and annealed Fe83B17 alloy with hypercooling of 445 K (Three structures all include α-Fe and Fe3B. No trace of Fe2B is found)[34]
(a) as cast
(b) annealed at 858 K for 3 h
(c) annealed at 858 K for 16 h
Fig.14  The change in free energy of an atom as it takes part in a transition. The "reaction coordinate" is any variable defining the progress along the reaction path[34]
Fig.15  Microstructures of the RS+PHT (rapid solidification with post-solidification heat treatment) processed A356 alloys[27]
(a) typical morphology of the solidification microstructure of A356 alloys (cooling rate upon RS: 96 K/s)
(b) highly dispersed nanoscale Si particles in matrix and a few Si particles are associated with rod-like β' phase
(c) TEM bright field image of a nanoscale Si particle associated with a β' (Mg9Si5) phase; the upper and lower insets are the electron diffraction pattern taken from the selected area circled by the white dash line and the corresponding image at higher magnification
(d) TEM bright field image of the eutectic Si decorated by the nanoscale Al particles; the inset is the high resolution TEM image of an Al particle decorated in Si matrix
Fig.16  Measured engineering stress-strain curves of the A356 alloys processed by the RS+PHT and the subsequent T6 heat treatment[27]
Fig.17  SEM micrograph of γ' precipitation in DD3 superalloy solidified at undercooling of 45 K (a), 125 K (b), 200 K (c), 250 K (d), respectively[30], and variation of γ' precipitate size as a function of the melt undercooling of DD3 superalloy (e)[38]
Fig.18  The tensile strength (σb) and elongation (δ) of DD3 superalloy solidified at different undercoolings[38]
Fig.19  The cross section microstructures for the sample with ΔT=280 K before (a) and after heat treatment at 1173 K for 60 h (b), the thicknesses of the recrystallized γ-(Fe, Ni) phase layer from experimental measurement and fitting (c)[42]
Fig.20  The strain-stress curves for the samples with ΔT=70 K and ΔT=250 K before and after heat treatment at 1173 K for 60 h[42]
Fig.21  The connection between driving force / energy barrier of phase transition and strength / ductility of material, and both of them are mutual exclusive, while big driving force and energy barrier in processing correspond to high strength and ductility in microstructure
[1] Kim Y J, Perepezko J H.The thermodynamics and competitive kinetics of metastable τ phase development in MnAl-base alloys[J]. Mater. Sci. Eng., 1993, A163: 127
[2] Vandyoussefi M, Kerr H W, Kurz W.Directional solidification and δ /γ solid state transformation in Fe-3%Ni alloy[J]. Acta Mater., 1997, 45: 4093
[3] Lima M, Kurz W.Massive transformation and absolute stability[J]. Metall. Mater. Trans., 2002, 33A: 2337
[4] Aziz M J.Model for solute redistribution during rapid solidification[J]. J. Appl. Phys., 1982, 53: 1158
[5] Lu K.Nanocrystalline metals crystallized from amorphous solids: Nanocrystallization, structure, and properties[J]. Mater. Sci. Eng., 1996, R16: 161
[6] Lu K.Synthesis of nanocrystalline materials from amorphous solids[J]. Adv. Mater., 1999, 11: 1127
[7] Liu F, Yang G C.Stress-induced recrystallization mechanism for grain refinement in highly undercooled superalloy[J]. J. Cryst. Growth, 2001, 231: 295
[8] Liu F, Zhao D W, Yang G C.Solidification of undercooled molten Ni-based alloys[J]. Metall. Mater. Trans., 2001, 32B: 449
[9] Yang C L, Yang G C, Liu F, et al.Metastable phase formation in eutectic solidification of highly undercooled Fe83B17 alloy melt[J]. Physica, 2006, 373B: 136
[10] Lu Y P, Yang G C, Liu F, et al.The transition of alpha-Ni phase morphology in highly undercooled eutectic Ni78.6Si21.4 alloy[J]. Europhys. Lett., 2006, 74: 281
[11] Chen Y Z, Yang G C, Liu F, et al.Microstructure evolution in undercooled Fe-7.5at%Ni alloys[J]. J. Cryst. Growth, 2005, 282: 490
[12] Chen Y Z, Yang G C, Liu F, et al.Microstructural transitions of metastable phase in undercooled Fe-7.5%Ni alloy[J]. J. Cryst Growth., 2006, 289: 1
[13] Yang C, Liu F, Yang G, et al.Stability of bulk metastable Fe83B17 eutectic alloy prepared by hypercooling method[J]. Appl. Phys., 2007, 86A: 231
[14] Liu F, Yang G C.Refinement of γ' precipitate with melt undercooling in Nickel-based superalloy[J]. Mater. Trans., 2001, 42: 1135
[15] Liu F, Kirchheim R.Nano-scale grain growth inhibited by reducing grain boundary energy through solute segregation[J]. J. Cryst. Growth, 2004, 264: 385
[16] Liu F, Yang G C, Kirchheim R.Overall effects of initial melt undercooling, solute segregation and grain boundary energy on the grain size of as-solidified Ni-based alloys[J]. J. Cryst. Growth, 2004, 264: 392
[17] Chen Y Z, Liu F, Yang G C, et al.Suppression of peritectic reaction in the undercooled peritectic Fe-Ni melts[J]. Scr. Mater., 2007, 57: 779
[18] Chen Y Z, Liu F, Yang G C, et al.δ /γ transformation in non-equilibrium solidified peritectic Fe-Ni alloy[J]. Sci. China, 2007, 50G: 421
[19] Hillert M.Solidification and Casting of Metals [M]. London: The Metals Society Press, 1979: 81
[20] Dhindaw B K, Antonsson T, Fredriksson H, et al.Characterization of the peritectic reaction in medium-alloy steel through microsegregation and heat-of-transformation studies[J]. Metall. Mater. Trans., 2004, 35A: 2869
[21] ?ad?rl? E.Investigation of the microhardness and the electrical resistivity of undercooled Ni-10 at.% Si alloys[J]. J. Non-Cryst. Solids, 2011, 357: 809
[22] Lu Y P, Liu F, Yang G C, et al.Grain refinement in solidification of highly undercooled eutectic Ni-Si alloy[J]. Mater. Lett., 2007, 61: 987
[23] Fan K, Liu F, Yang G C, et al.Precipitation in as-solidified undercooled Ni-Si hypoeutectic alloy: Effect of non-equilibrium solidification[J]. Mater. Sci. Eng., 2011, A528: 6844
[24] Wang H F, Liu F, Chen Z, et al.Analysis of non-equilibrium dendrite growth in a bulk undercooled alloy melt: Model and application[J]. Acta Mater., 2007, 55: 497
[25] Dang B, Liu C C, Liu F, et al.Effect of as-solidified microstructure on subsequent solution-treatment process for A356 Al alloy[J]. Trans. Nonferrous Met. Soc. China, 2016, 26: 634
[26] Aaron H B, Kotler G R.Second phase dissolution[J]. Metall. Trans., 1971, 2: 393
[27] Dang B, Zhang X, Chen Y Z, et al.Breaking through the strength-ductility trade-off dilemma in an Al-Si-based casting alloy[J]. Sci. Rep., 2016, 6: 30874
[28] Chen Z, Tang Y Y, Chen Q, et al.The interrelated effect of initial melt undercooling, solute trapping and solute drag on the grain growth mechanism of as-solidified Ni-B alloys[J]. J. Alloys Compd., 2014, 610: 561
[29] Furtkamp M, Gottstein G, Molodov D A, et al.Grain boundary migration in Fe-3.5% Si bicrystals with [001] tilt boundaries[J]. Acta Mater., 1998, 46: 4103
[30] Liu F, Yang G C.Rapid solidification of highly undercooled bulk liquid superalloy: Recent developments, future directions[J]. Int. Mater. Rev., 2006, 51: 145
[31] Xu X L, Liu F.Crystal growth due to recrystallization upon annealing rapid solidification microstructures of deeply undercooled single phase alloys quenched before recalescence[J]. Cryst. Growth Des., 2014, 14: 2110
[32] Chien C L, Musser D, Gyorgy E M, et al.Magnetic properties of amorphous FexB100-x (72≤x≤86) and crystalline Fe3B[J]. Phys. Rev., 1979, 20B: 283
[33] Inal O T, Keller L, Yost F G.High-temperature crystallization behaviour of amorphous Fe80B20[J]. J. Mater. Sci., 1980, 15: 1947
[34] Xu J F, Yang W, Liu F, et al.Effect of non-equilibrium solidification on subsequent solid-state transitions[J]. J. Xi'an Technol. Univ., 2009, 29: 41(许军峰, 杨伟, 刘峰等. 非平衡凝固对随后固态转变的影响[J]. 西安工业大学学报, 2009, 29: 41)
[35] Jiang J, Dézsi I, Gonser U, et al.A study of amorphous Fe79B21 alloy powders produced by chemical reduction[J]. J. Non-Cryst. Solids, 1990, 116: 247
[36] Burke J.The Kinetics of Phase Transformations in Metals [M]. Oxford: Pergamon Press, 1965
[37] Zhang H W, Wang J Q, Lu K.Kinetics of crystallization nucleation and growth in Al-rich metallic glass[J]. Acta Metall. Sin., 2002, 38: 609(张宏闻, 王建强, 卢柯. 非晶态铝合金晶化过程的形核与长大行为研究. 金属学报, 2002, 38: 609)
[38] Liu F, Yang G C.Effect of microstructure and γ' precipitate from undercooled DD3 superalloy on mechanical properties[J]. J. Mater. Sci., 2002, 37: 2713
[39] Liu F, Cai Y, Guo X F.Structure evolution in undercooled DD3 single crystal superalloy[J]. Mater. Sci. Eng., 2000, A291: 9
[40] Liu F, Guo X F, Yang G C.Recrystallization mechanism for the grain refinement in undercooled DD3 single-crystal superalloy[J]. J. Cryst. Growth, 2000, 219: 489
[41] Liebmann W K, Miller E A.Preparation, phase-boundary energies, and thermoelectric properties of InSb-Sb eutectic alloys with ordered microstructures[J]. J. Appl. Phys., 1963, 34: 2653
[42] Zhang K, Liu F, Gu B, et al.Recrystallization of as-solidified highly-undercooled Fe40Ni40B20 eutectic alloy: In situ formation of duplex structure[J]. J. Alloys Compd., 2013, 575: 444
[43] Willnecker R, Herlach D M, Feuerbacher B.Evidence of nonequilibrium processes in rapid solidification of undercooled metals[J]. Phys. Rev. Lett., 1989, 62: 2707
[44] Gu B, Liu F.Characterization of structural inhomogeneity in Al88Ce8Co4 metallic glass[J]. Acta Mater., 2016, 112: 94
[45] Song S J, Liu F.Kinetic modeling of solid-state partitioning phase transformation with simultaneous misfit accommodation[J]. Acta Mater., 2016, 108: 85
[46] Song S J, Liu F, Zhang Z H.Analysis of elastic-plastic accommodation due to volume misfit upon solid-state phase transformation[J]. Acta Mater., 2014, 64: 266
[47] Wang K, Shang S L, Wang Y, et al.Martensitic transition in Fe via Bain path at finite temperatures: A comprehensive first-principles study[J]. Acta Mater., 2018, 147: 261
[48] Hong M, Wang K, Chen Y Z, et al.A thermo-kinetic model for martensitic transformation kinetics in low-alloy steels[J]. J. Alloys Compd., 2015, 647: 763
[49] Huang L K, Lin W T, Lin B, et al.Exploring the concurrence of phase transition and grain growth in nanostructured alloy[J]. Acta Mater., 2016, 118: 306
[50] Lin B, Wang K, Liu F, et al.An intrinsic correlation between driving force and energy barrier upon grain boundary migration[J]. J. Mater. Sci. Technol., 2017, DOI: 10.1016/j.jmst.2017.11.002. (in press)
[51] Chen Z, Liu F, Yang X Q, et al.A thermokinetic description of nanoscale grain growth: Analysis of the activation energy effect[J]. Acta Mater., 2012, 60: 4833
[52] Gong M M,Castro R H R, Liu F. Modeling the final sintering stage of doped ceramics: Mutual interaction between grain growth and densification[J]. J. Mater. Sci., 2018, 53: 1680
[53] Liu F, Wang H F, Song S J, et al.Competitions correlated with nucleation and growth in non-equilibrium solidification and solid-state transformation[J]. Prog. Phys., 2012, 32: 57
[54] Kostorz G.Phase Transformations in Materials[M]. Weinheim: Wiley-VCH, 2001: 630
[55] Kelton K F.Crystal nucleation in liquids and glasses[J]. Solid State Phys., 1991, 45: 75
[56] Martyushev L M, Seleznev V D.Maximum entropy production principle in physics, chemistry and biology[J]. Phys. Rep., 2006, 426: 1
[1] HUANG Yuan, DU Jinlong, WANG Zumin. Progress in Research on the Alloying of Binary Immiscible Metals[J]. 金属学报, 2020, 56(6): 801-820.
[2] HUANG Huogen, ZHANG Pengguo, ZHANG Pei, WANG Qinguo. Comparison of Glass Forming Ability Between U-Co and U-Fe Base Systems[J]. 金属学报, 2020, 56(6): 849-854.
[3] YANG Jie, WANG Lei. Effect and Optimal Design of the Material Constraint in the DMWJ of Nuclear Power Plants[J]. 金属学报, 2020, 56(6): 840-848.
[4] YU Feng,CHEN Xingpin,XU Haifeng,DONG Han,WENG Yuqing,CAO Wenquan. Current Status of Metallurgical Quality and Fatigue Performance of Rolling Bearing Steel and Development Direction of High-End Bearing Steel[J]. 金属学报, 2020, 56(4): 513-522.
[5] WANG Bo,SHEN Shiyi,RUAN Yanwei,CHENG Shuyong,PENG Wangjun,ZHANG Jieyu. Simulation of Gas-Liquid Two-Phase Flow in Metallurgical Process[J]. 金属学报, 2020, 56(4): 619-632.
[6] ZHANG Le,WANG Wei,M. Babar Shahzad,SHAN Yiyin,YANG Ke. Fabrication and Properties of Novel Multi-LayeredMetal Composites[J]. 金属学报, 2020, 56(3): 351-360.
[7] WANG Zumin,ZHANG An,CHEN Yuanyuan,HUANG Yuan,WANG Jiangyong. Research Progress on Fundamentals and Applications of Metal-Induced Crystallization[J]. 金属学报, 2020, 56(1): 66-82.
[8] GONG Shengkai, SHANG Yong, ZHANG Ji, GUO Xiping, LIN Junpin, ZHAO Xihong. Application and Research of Typical Intermetallics-Based High Temperature Structural Materials in China[J]. 金属学报, 2019, 55(9): 1067-1076.
[9] ZHANG Guoqing,ZHANG Yiwen,ZHENG Liang,PENG Zichao. Research Progress in Powder Metallurgy Superalloys and Manufacturing Technologies for Aero-Engine Application[J]. 金属学报, 2019, 55(9): 1133-1144.
[10] Mengwei CAO,Tao CAI,Xia ZHANG. Study on Amination Modification of Fe-BTC and Their Adsorption for Dyes and Heavy Metal Ions[J]. 金属学报, 2019, 55(7): 821-830.
[11] Zhengguan LU,Jie WU,Lei XU,Xiaoxiao CUI,Rui YANG. Ring Rolling Forming and Properties of Ti2AlNb Special Shaped Ring Prepared by Powder Metallurgy[J]. 金属学报, 2019, 55(6): 729-740.
[12] Bin CHEN,Jie HE,Xiaojun SUN,Jiuzhou ZHAO,Hongxiang JIANG,Lili ZHANG,Hongri HAO. Liquid-Liquid Phase Separation of Fe-Cu-Pb Alloy and Its Application in Metal Separation and Recycling of Waste Printed Circuit Boards[J]. 金属学报, 2019, 55(6): 751-761.
[13] Huiyuan WANG,Chao LI,Zhigang LI,Jin XU,Hongjiang HAN,Zhiping GUAN,Jiawang SONG,Cheng WANG,Pinkui MA. Current Research and Future Prospect on the Preparation and Architecture Design of Nanomaterials Reinforced Light Metal Matrix Composites[J]. 金属学报, 2019, 55(6): 683-691.
[14] Tongbang AN,Jinshan WEI,Jiguo SHAN,Zhiling TIAN. Influence of Shielding Gas Composition on Microstructure Characteristics of 1000 MPa Grade Deposited Metals[J]. 金属学报, 2019, 55(5): 575-584.
[15] Jianxiang DING,Wubian TIAN,Dandan WANG,Peigen ZHANG,Jian CHEN,Zhengming SUN. Arc Erosion and Degradation Mechanism ofAg/Ti2AlC Composite[J]. 金属学报, 2019, 55(5): 627-637.
No Suggested Reading articles found!