Nonequilibrium thermodynamics and transportation kinetics near the propagating solid–liquid interface dominates the rapid solidification process, which is far from a thermodynamically stable state. Rapid solidification process can be described more precisely using quantitative thermodynamic calculation of phase diagram with nonlinear liquidus and solidus and evaluating the nonequilibrium effect in diffusion kinetics. Based on these basic principles, we have used a current nonequilibrium dendrite growth model to describe the rapid solidification process and the recalescence temperature of deeply undercooled alloys. Evolution of the key fundamental solidification parameters was also evaluated. The experimental data agree well with the model prediction.
ChristianJW.The theory of transformation in metals and alloys: recovery, recrystallization and grain growth. Oxford: Pergamon Press; 2002.
2.
WalkerJL.The physical chemistry of process metallurgy. New York: Interscience; 1959.
3.
KurzWFisherDJ.Fundamentals of solidification. London: Trans. Tech. Publications Ltd; 1998.
4.
XuXLChenYZLiuF.Recrystallization mechanism of grain refinement in hypercooled single phase alloys. J Cryst Growth. 2013; 377:153–159. doi: 10.1016/j.jcrysgro.2013.05.016
5.
HindmarshJPWilsonDIJohnsML.Using magnetic resonance to validate predictions of the solid fraction formed during recalescence of freezing drops. Int J Heat Mass Transfer. 2005; 48:1017–1021. doi: 10.1016/j.ijheatmasstransfer.2004.09.028
6.
HerlachDM.Non-equilibrium solidification of undercooled metallic metals. Mater Sci Eng R. 1994; 12:177–272. doi: 10.1016/0927-796X(94)90011-6
7.
LiuFChenYZYangGCCompetitions incorporated in rapid solidification of the bulk undercooled eutectic Ni78.6Si21.4alloy. J Mater Res. 2007; 22:2953–2963. doi: 10.1557/JMR.2007.0380
8.
LuXYCaoCDWeiB.Solidificartion Velocity of Undercooled Alloys. Prog Nat Sci. 1999; 9:286–296.
LiuFYangGC.Rapid solidification of highly undercooled bulk liquid superalloy: recent developments, future directions. Int Mater Rev. 2006; 51:145–170. doi: 10.1179/174328006X102484
11.
WalderSRyderPL.A simple technique for the measurement of dendritic growth rates in undercooled metallic melts and its application to Ni and Ti. Mater Sci Eng A. 1995; 203:197–202. doi: 10.1016/0921-5093(95)09857-7
12.
CaoCDHerlachDMKolbeMRapid solidification of Cu84Co16 alloy undercooled into the metastable miscibility gap under different conditions. Scripta Mater. 2003; 48:5–9. doi: 10.1016/S1359-6462(02)00307-X
13.
PicconeTJWuYShioharaYDendritic growth of undercooled nickel-tin: Part II. Metall Trans A. 1987; 18:925–932. doi: 10.1007/BF02646934
14.
VedovatoGZambonARamousE.A simplified model for gas atomization. Mater Sci Eng A. 2001; 304–306:235–239. doi: 10.1016/S0921-5093(00)01475-1
15.
KaufmanL.Coupled phase diagrams and thermochemical data for transition metal binary systems — I. Calphad. 1978: 117–146. doi: 10.1016/0364-5916(78)90031-7
16.
BoettingerWJCoriellSRTrivediR.Rapid solidification processing: principles and Technologies IV. Baton Rouge ( LA): Claitor's; 1988.
17.
SobolevSL.Effects of local nonequilibrium solute diffusion on rapid solidification of alloys. Phys Status Solidi A. 1996; 156A:293–303. doi: 10.1002/pssa.2211560208
18.
GalenkoPKDanilovDA.Steady-state shapes of growing crystals in the field of local nonequilibrium diffusion. Phys Lett A. 2000; 272:207–217. doi: 10.1016/S0375-9601(00)00417-5
19.
ThompsonCVSpaepenF.The relative rates of secondary and normal grain growth. Acta Metall. 1983; 31:2021–2027. doi: 10.1016/0001-6160(83)90019-6
20.
HillertM.Solute drag, solute trapping and diffusional dissipation of Gibbs energy. Acta Mater. 1999; 47:4481–4505. doi: 10.1016/S1359-6454(99)00336-5
21.
KolmogorovAN.Solidification of undercooled melts. Izv Akad Nauk SSSR. 1937; 3:355–359.
22.
JohnsonWAMehlRF.Modeling time dependence of the average interface migration rate in site-saturated recrystallization. Trans AIME. 1939; 135:416–458.
AvramiM.Kinetics of phase change. II transformation-time relations for random distribution of nuclei. J Chem Phys. 1940; 8:212–224. doi: 10.1063/1.1750631
25.
AvramiM.Kinetics of phase change, Part III: Granulation, phase change and microstructure. J Chem Phys. 1941; 9:177–184. doi: 10.1063/1.1750872
26.
WangHFLiuFChenZAnalysis of non-equilibrium dendrite growth in a bulk undercooled alloy melt: model and application. Acta Mater. 2007; 55:497–506. doi: 10.1016/j.actamat.2006.08.042
27.
IvantsovGP.Temperature Field around a spheroidal, cylindrical and acicular crystal growing in a supercooled melt. Dokl Akad Nauk SSSR. 1947; 58:567.
28.
IvantsovGP.On a growth of spherical and needle-like crystals of a binary alloy. Dokl Akad Nauk SSSR. 1952; 83:573.
29.
BenamarMBouissouPPelceP.An exact solution for the shape of a crystal growing in a forced flow. J Cryst Growth. 1988; 92:97. doi: 10.1016/0022-0248(88)90439-3
30.
CoriellSRTurnbullD.Relative roles of heat transport and interface rearrangement rates in the rapid growth of crystals in undercooled melts. Acta Metall. 1982; 30:2135–2139. doi: 10.1016/0001-6160(82)90134-1
31.
BarthMWeiBHerlachDM.Crystal growth in undercooled melts of the intermetallic compounds FeSi and CoSi. Phys Rev B. 1995; 51:3422–3428. doi: 10.1103/PhysRevB.51.3422
WołczyńskiW.Back diffusion in crystal growth – Eutectics. Arch Metall Mater. 2015; 60:2403–2407. doi: 10.1515/amm-2015-0392
34.
XuXLZhaoYHHouHConcentration and fluid flow effects on kinetics, dendrite remelting and stress accumulation upon rapid solidification of deeply undercooled alloys. J Alloys Compound. 2018; 744:740–749. doi: 10.1016/j.jallcom.2018.02.065
35.
XuXLZhaoYHHouH.Growth velocity-undercooling relationship and structure refinement mechanism of undercooled Ni-Cu alloys. J Alloys Compound. 2019; 773:1131–1140. doi: 10.1016/j.jallcom.2018.09.228
36.
XuXLZhaoYHHouH.Observation of dendrite growth velocity and microstructure transition in highly undercooled single phase alloys. Mater Chara. 2019; 155:109793. doi: 10.1016/j.matchar.2019.109793
37.
XuXLChenYZLiuF.Observation of recrystallization upon annealing rapidly solidified microstructures of highly undercooled Ni80Cu20 alloys. J Alloys Compound. 2014; 597:205–210. doi: 10.1016/j.jallcom.2014.01.228
38.
XuXLChenYZLiuF.Recrystallization and twinning in rapidly solidified nickel based alloys without man-made plastic deformation. J Alloys Compound. 2014; 597:156–162. doi: 10.1016/j.jallcom.2014.06.099
39.
XuXLZhaoYHHouH.The growth velocity under cooling relationship of highly undercooled Ni and Ni-Cu melts. Mater Sci Tech.2019; 8:900–906. doi: 10.1080/02670836.2019.1594553
40.
XuXLZhaoYHHouHNonequilibrium solidification, grain refinements, and recrystallization of deeply undercooled Ni-20At. Pct Cu Alloys: Effects of Remelting and Stress.2017; 48A:4777–4785.
41.
XuXLLiuFInvestigation on recalescence temperatures of deeply undercooled melts. Journal of Crystal Growth.2016; 455:29–36. doi: 10.1016/j.jcrysgro.2016.09.016
42.
XuXLLiuF.Crystal growth due to recrystallization upon Annealing rapid solidification microstructures of deeply undercooled single phase alloys quenched before recalescence. 2014; 14:2110–2114.
43.
XuXLChenYZLiuF.Recrystallization mechanism of grain refinement in hypercooled single phase alloys. J Cryst Growth. 2013; 377:153–159. doi: 10.1016/j.jcrysgro.2013.05.016
44.
FanHLZhouSFQiGSContinuous preparation of Fe3O4 nanoparticles using impinging stream-rotating packed bed reactor and magnetic property thereof. J Alloys Compound. 2016; 662:497–504. doi: 10.1016/j.jallcom.2015.12.025
45.
FanHLZhouSFGaoJContinuous preparation of Fe3O4 nanoparticles through Impinging Stream-Rotating Packed Bed reactor and their electrochemistry detection toward heavy metal ions. J. Alloys Compound. 2016; 671:354–359. doi: 10.1016/j.jallcom.2016.02.062
46.
ChenHYWangYZXuCJ.Mater. Lett. 2016; 163:72–75. doi: 10.1016/j.matlet.2015.10.088
47.
LiuYWangYZZhangGXPreparation of activated carbon from willow leaves and evaluation in electric double-layer capacitors. Mater. Lett. 2016; 176:60–63. doi: 10.1016/j.matlet.2016.04.065
48.
HaoSYSunYYLiuYQFacile synthesis of porous SnO2 film grown on Ni foam applied for high-performance supercapacitors. J. Alloys Compound. 2016; 689:587–592. doi: 10.1016/j.jallcom.2016.07.278
49.
ZhouSFWangJJGanLIndividual and simultaneous electrochemical detection toward heavy metal ions based on L-cysteine modified mesoporous MnFe2O4 nanocrystal clusters. J. Alloys Compound. 2017; 721:492–500. doi: 10.1016/j.jallcom.2017.05.321
50.
ZhouSFHanXJLiuYQSWASV performance toward heavy metal ions based on a high-activity and simple magnetic chitosan sensing nanomaterials. J. Alloys Compound. 2016; 684:1–7. doi: 10.1016/j.jallcom.2016.05.152
51.
MaJZhangWHZhengLDirect formation of (Co, Mn)(3)O-4 nanowires/Ni composite foam for electrochemical detection. J. Alloys Compound. 2016; 663:230–234. doi: 10.1016/j.jallcom.2015.12.123
52.
HuangZChiBJianLCofe2o4@multi-walled carbon nanotubes integrated composite with nanosized architecture as a cathode material for high performance rechargeable lithium-oxygen battery. J. Alloys Compound. 2017; 695:3435–3444. doi: 10.1016/j.jallcom.2016.12.015
53.
WangJHLiYYongNNSEffects of Fe3+ doping on electrical properties and energy-storage performances of the (Na0.85K0.15)(0.5)Bi0.5TiO3 thick films prepared by sol-gel method. J. Alloys Compound. 2017; 727:596–602. doi: 10.1016/j.jallcom.2017.08.169
54.
HouHLiYXXuXL.Non-equilibrium effects on solid transition of solidification microstructure of deeply undercooled alloys. Mater Sci Tech. 2018; 34:402–407. doi: 10.1080/02670836.2017.1393977
55.
XuXLZhaoYHHouH.Preparation of bulk crystallite alloys by rapid quenching of bulk undercooled melts. Mater Sci Tech. 2018; 34:79–85. doi: 10.1080/02670836.2017.1358471
56.
XuXLZhaoYHHouH.Grain size gradient naturally prepared through recrystallization in rapidly solidified undercooled alloy melts. Inter J Mater Res. 2018; 109:593–598. doi: 10.3139/146.111648
57.
XuXLZhaoYHHouH.Dendritic solidification of highly undercooled dilute alloys. Inter J Mater Res. 2019; 110:695–702. doi: 10.3139/146.111792
