Solidification velocities as a function of initial bulk undercoolings were systematically investigated using high speed thermal imaging of highly undercooled pure Ni and Ni-Cu alloy samples. For pure Ni, the dendrite growth velocity increased continuously to a maximum value of about 52 m s−1 at a maximum undercooling of 320 K. For Ni-Cu alloy, the dendrite growth velocity first increased continuously and then discontinuously to a maximum value of about 55 m s−1 at 300 K. A clear discontinuity appeared in the growth velocity-undercooling curve is considered to be caused by the finite speed of solute diffusion in the bulk liquid ahead of the migrating solid–liquid interface.
WillneckerR, HerlachDM, FeuerbacherB.Evidence of nonequilibrium processes in rapid solidification of undercooled metals. Phys Rev Lett. 1989;62:2707–2710. doi: 10.1103/PhysRevLett.62.2707
2.
BasslerBT, HofmeisterWH, CarroG, The velocity of solidification of highly undercooled nickel. Metall Mater Trans A. 1994;25:1301–1308. doi: 10.1007/BF02652304
3.
GalenkoPK, PhanikumarG, FunkeO, Dendritic solidification and fragmentation in undercooled Ni–Zr alloys. Mater Sci Eng A. 2007;449-451:649–653. doi: 10.1016/j.msea.2006.02.435
4.
WillneckerR, HerlachDM, FeuerbacherB.Containerless undercooling of bulk Fe-Ni melts. Appl Phys Lett. 1986;49(20):1339–1341. doi: 10.1063/1.97371
5.
KarmaA.Int J Non-Equilibrium Proc. 1998;11:201.
6.
KobayashiK, HoganLM.Met Forum. 1978;1:165.
7.
HorvayG.The tension field created by a spherical nucleus freezing into its less dense undercooled melt. Int J Heat Mass Transf. 1965;8:195–243. doi: 10.1016/0017-9310(65)90110-9
8.
XuXL, ChenYZ, LiuF.Evidence of recrystallization mechanism of grain refinement in hypercooled Co80Pd20 alloys. Mater Lett. 2012;81:73–75. doi: 10.1016/j.matlet.2012.04.042
9.
MullisAM, CochraneRF.Grain refinement and the stability of dendrites growing into undercooled pure metals and alloys. J Appl Phys. 1997;82:3783–3790. doi: 10.1063/1.365740
10.
SchwarzM, KarmaK, EcklerK, Physical mechanism of grain refinement in solidification of undercooled melts. Phys Rev Lett. 1994;73:1380–1383. doi: 10.1103/PhysRevLett.73.1380
11.
CastleG, MullisAM, CochraneRF.Evidence for an extensive, undercooling-mediated transition in growth orientation, and novel dendritic seaweed microstructures in Cu–8.9wt.% Ni. Acta Mater. 2014;66:378–387. doi: 10.1016/j.actamat.2013.11.027
12.
CastleEG, MullisAM, CochraneRF.Mechanism selection for spontaneous grain refinement in undercooled metallic melts. Acta Mater. 2014;77:76–84. doi: 10.1016/j.actamat.2014.05.043
13.
GalenkoPK, DanilovDA.Model for free dendritic alloy growth under interfacial and bulk phase nonequilibrium conditions. J Cryst Growth. 1999;197:992–1002. doi: 10.1016/S0022-0248(98)00977-4
14.
XuXL, HouH, ZhaoY, Nonequilibrium solidification, grain refinements, and recrystallization of deeply undercooled Ni-20 At. Pct Cu alloys: effects of remelting and stress. Metal Mater Trans A. 2017;48:4777–4785. doi: 10.1007/s11661-017-4194-7
15.
XuXL, LiuF.Observation of recrystallization upon annealing rapidly solidified microstructures of highly undercooled Ni80Cu20 alloys. J Alloys Compond. 2014;597:205–210. doi: 10.1016/j.jallcom.2014.01.228
16.
XuXL, LiuF.Recrystallization and twinning in rapidly solidified nickel based alloys without man-made plastic deformation. J Alloys Compond. 2014;615:156–162. doi: 10.1016/j.jallcom.2014.06.099
17.
XuXL, ChenYZ, LiuF.Evolution of solidification microstructure in undercooled Co80Pd20 alloys. Mater Sci Tech. 2012;28:1492–1498. doi: 10.1179/1743284712Y.0000000055
18.
XuXL, ChenYZ, LiuF.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
19.
HouH, WenZQ, ZhaoYH.First-principles investigations on structural, elastic, thermodynamic and electronic properties of Ni3X (X=Al, Ga and Ge) under pressure. Intermetallics. 2014;44:110–115. doi: 10.1016/j.intermet.2013.09.003
20.
QiL, JinYC, ZhaoYH.The structural, elastic, electronic properties and Debye temperature of Ni3Mo under pressure from first-principles. J Alloys Compds. 2015;621:383–388. doi: 10.1016/j.jallcom.2014.10.015
21.
ZhaoYH, WenZQ, HouH.Density functional theory study of the interfacial properties of Ni/Ni3Si eutectic alloy. App Sur Sci. 2014;303:205–209. doi: 10.1016/j.apsusc.2014.02.149
22.
HumphreysFJ, HatherlyM.Recrystallization and related annealing phenomena. 2nd ed.New York: Pergamon Press Oxford; 2004.
WangHF, LiuF, ChenZ.Analysis 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
25.
ZhaoYH, DengSJ, LiuH, First-principle investigation of pressure and temperature influence on structural, mechanical and thermodynamic properties of Ti3AC2 (A = Al and Si). Compu Mater Sci. 2018;154:365–370. doi: 10.1016/j.commatsci.2018.07.007
26.
ZhangJB, WangHF, KuangWW, Rapid solidification of non-stoichiometric intermetallic compounds: Modeling and experimental verification. Acta Mater. 2018;148:86–99. doi: 10.1016/j.actamat.2018.01.040
27.
KuangWW, WangHF, LiX, Application of the thermodynamic extremal principle to diffusion-controlled phase transformations in Fe-C-X alloys: Modeling and applications. Acta Mater. 2018;159:16–30. doi: 10.1016/j.actamat.2018.08.008
28.
XuXL, ZhaoYH, HouH, Concentration 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
29.
XuXL, ZhaoYH, HouH.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
30.
ShaoXL, MengQX, LiuJ.RISE and disturbance compensation based trajectory tracking control for a quadrotor UAV without velocity measurements. Aerospace Sci Technol. 2018;74:145–159. doi: 10.1016/j.ast.2017.12.029
31.
ShaoXL, LiuJ, WangHL.Robust back-stepping output feedback trajectory tracking for quadrotors via extended state observer and sigmoid tracking differentiator. Mech Syst Signal Process. 2018;104:631–647. doi: 10.1016/j.ymssp.2017.11.034
32.
ShaoXL, LiuJ, CaoHL.Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer. Int J Robust Nonlinear Control. 2018;28:2700–2719. doi: 10.1002/rnc.4044
