In the present study, Pb–Bi as a model of alloys from peritectic systems was directionally solidified under transient heat flow conditions, which is the class of heat flow encompassing the majority of industrial solidification processes. Some experiments were also carried out in a vertical tube furnace under cooling rates closer to equilibrium during solidification in order to broaden the range of solidification parameters. Thermal parameters such as the tip growth rate (VL) and the cooling rate
were experimentally determined and correlated with the primary (λ1) and secondary (λ2) dendrite arm spacings by experimental growth laws. It is shown that the proposed growth laws are able to encompass also the growth of dendritic branches during steady state growth from the melt.
NassarH and FredrikssonH: ‘On peritectic reactions and transformations in low-alloy steels’, Metall. Mater. Trans. A, 2010, 41A, 2776–2783.
2.
TulingA, BanerjeeJR and MintzB: ‘Influence of peritectic phase transformation on hot ductility of high aluminium TRIP steels containing Nb’, Mater. Sci. Technol., 2011, 11, 1724–1731.
3.
LiuDM, LiXZ, SuYQ, PengP, LuoLS, GuoJJ and FuHZ: ‘Secondary dendrite arm migration caused by temperature gradient zone melting during peritectic solidification’, Acta Mater., 2012, 60, 2679–2688.
4.
KohlerF, GermondL, WagnièreJD and RappazM: ‘Peritectic solidification of Cu–Sn alloys: microstructural competition at low speed’, Acta Mater., 2009, 57, 56–68.
5.
LiuDM, LiXZ, SuYQ, LuoLS, ZhangB, GuoJJ and FuHZ: ‘Directional solidification of Cu–20Sn alloy at low speed: from peritectic coupled growth to banding’, Mater. Lett., 2011, 65, 1628–1631.
6.
LiuDM, LiXZ, SuYQ, LuoLS, ZhangB, ChenRR, GuoJJ and FuHZ: ‘An analysis of non-equilibrium peritectic reaction driven by solute diffusion under a temperature gradient’, J. Cryst. Growth, 2011, 334, 195–199.
7.
BöyükaU, KayaH, ÇadırlıE, MaraslıN and ÜlgenA: ‘Investigation of the effect of solidification processing parameters on microhardness and determination of thermo–physical properties in the Zn–Cu peritectic alloy’, J. Alloys Compd, 2010, 491, 143–148.
8.
MaD, LiY, NgSC and JonesH: ‘Unidirectional solidification of Zn-rich Zn–Cu peritectic alloys—I. Microstructure selection’, Acta Mater., 2000, 48, 419–431.
9.
BritoC, SiqueiraCA, SpinelliJE and GarciaA: ‘Cellular growth during the transient directional solidification of Zn-rich Zn Cu monophasic and peritectic alloys’, J. Phys. Chem. Solids, 2012, 73, 1173–1181.
10.
SuYQ, LuoLS, GuoJJ, LiXZ and FuHZ: ‘Spacing selection of cellular peritectic coupled growth during directional solidification of Fe–Ni peritectic alloys’, J. Alloys Compd, 2009, 474, L14–L17.
11.
LiuYC, YangGC, GuoXF, HuangJ and ZhouYH: ‘Coupled growth behavior in the rapidly solidified Ti–Al peritectic alloys’, J. Cryst. Growth, 2001, 222, 645–654.
12.
SuYQ, LiuC, LiXZ, GuoJJ, LiBS, JiaJ and FuHZ: ‘Microstructure selection during the directionally peritectic solidification of Ti–Al binary system’, Intermetallics, 2005, 13, 267–274.
13.
HunzikerO and KurzW: ‘Directional solidification and phase equilibria in the Ni–Al system’, Metall. Mater. Trans. A, 1999, 30A, 3167–3175.
14.
YasudaH, NotakeN, TokiedaK and OhnakaI: ‘Periodic structure during unidirectional solidification for peritectic Cd–Sn alloys’, J. Cryst. Growth, 2000, 210, 637–645.
15.
HuXW, LiSM, AiFR and YanH: ‘Banding structure formation during directional solidification of Pb–Bi peritectic alloys’, Trans. Nonferrous Met. Soc. China, 2012, 22, 2131–2138.
16.
LoTS, DoblerS, PlappM, KarmaA and KurzW: ‘Two-phase microstructure selection in peritectic solidification: from island banding to coupled growth’, Acta Mater., 2003, 51, 599–611.
17.
LuoLS, SuYQ, GuoJJ, LiXZ, LiSM, ZhongH, LiuL and FuHZ: ‘Peritectic reaction and its influences on the microstructures evolution during directional solidification of Fe–Ni alloys’, J. Alloys Compd, 2008, 461, 121–127.
18.
BusseP and MeissenF: ‘Coupled growth of the properitectic alpha- and peritectic gamma-phases in binary titanium aluminides’, Scr. Mater., 1997, 36, 653–658.
19.
CaiZZ and ZhuMY: ‘Thermo-mechanical behavior of peritectic steel solidifying in slab continuous casting mold and a new mold taper design’, ISIJ Int., 2013, 53, 1818–1827.
20.
EmiT and FredrikssonH: ‘High-speed continuous casting of peritectic carbon steels’, Mater. Sci. Eng. A, 2005, A413–A414, 2–9.
21.
XuW, MaD, FengYP and LiY: ‘Observation of lamellar structure in a Zn-rich Zn–6·3at Ag hyper-peritectic alloy processed by rapid solidification’, Scr. Mater., 2001, 44, 631–636.
22.
ShcherbakovGI, DavidSA and BrodyHD: ‘Growth of Pb–Bi peritectic alloys at moderate and high values of G/R’, Scr. Metall. Mater., 1974, 8, 1239–1244.
23.
HuXW, LiSM, GaoSF, LiuL and FuHZ: ‘Effect of melt convection on primary dendrite arm spacing in directionally solidified Pb–26Bi hypo-peritectic alloys’, Trans. Nonferrous Met. Soc. China, 2011, 21, 65–71.
24.
HuXW, LiSM, GaoSF, LiuL and FuHZ: ‘Peritectic transformation and primary α-dendrite dissolution in directionally solidified Pb–26Bi alloy’, J. Alloys Compd, 2010, 501, 110–114.
25.
HuXW, LiSM, ChenWJ, GaoSF, LiuL and FuHZ: ‘Primary dendrite arm spacing during unidirectional solidification of Pb–Bi peritectic alloys’, J. Alloys Compd, 2009, 484, 631–636.
26.
HuXW, YanH, ChenWJ, LiSM and FuHZ: ‘Effect of sample diameter on primary and secondary dendrite arm spacings during directional solidification of Pb–26wt.Bi hypo-peritectic alloy’, Rare Met., 2011, 30, 424–431.
27.
SantosWLR, BritoC, QuaresmaJMV, SpinelliJE and GarciaA: ‘Plate-like cell growth during directional solidification of a Zn–20wtSn high-temperature lead-free solder alloy’, Mater. Sci. Eng. B, 2014, 182B, 29–36.
28.
RosaDM, SpinelliJE, FerreiraIL and GarciaA: ‘Cellular/dendritic transition and microstructure evolution during transient directional solidification of Pb–Sb alloys’, Metall. Mater. Trans. A, 2008, 39A, 2161–2174.
29.
SilvaBL, CheungN, GarciaA and SpinelliJE: ‘Thermal parameters, microstructure, and mechanical properties of directionally solidified Sn–0·7 wt.Cu solder alloys containing 0 ppm to 1000 ppm Ni’, J. Electron. Mater., 2013, 42, 179–191.
30.
MouraITL, SilvaCLM, CheungN, GoulartPR, GarciaA and SpinelliJE: ‘Cellular to dendritic transition during transient solidification of a eutectic Sn–0·7 wtCu solder alloy’, Mater. Chem. Phys., 2012, 132, 203–209.
31.
SilvaAP. SpinelliJE and GarciaA: ‘Microstructural evolution during upward and downward transient directional solidification of hypomonotectic and monotectic Al–Bi alloys’, J. Alloys Compd, 2009, 480, 485–493.
32.
SilvaAP, FreitasES, GoulartPR, GarciaA and SpinelliJE: ‘On the growth of the minority phase during downward transient directional solidification of hypomonotectic and monotectic Al Pb alloys’, J. Mater. Sci., 2012, 47, 5581–5589.
33.
SilvaAP, GoulartPR, GarciaA and SpinelliJE: ‘Microstructural development during transient directional solidification of a hypomonotectic Al–In alloy’, Philos. Mag. Lett., 2012, 92, 442–450.
34.
SpinelliJE, CheungN and GarciaA: ‘On array models theoretical predictions versus measurements for the growth of cells and dendrites in the transient solidification of binary alloys’, Philos. Mag., 2011, 91, 1705–1723.
35.
BritoC, SiqueiraCA, SpinelliJE and GarciaA: ‘Effects of cell morphology and macrosegregation of directionally solidified Zn-rich Zn–Cu alloys on the resulting microhardness’, Mater. Lett., 2012, 80, 106–109.
36.
DiasM, BritoC, BertelliF and GarciaA: ‘Cellular growth of single-phase Zn–Ag alloys unidirectionally solidified’, Mater. Chem. Phys., 2014, 143, 895–899.
37.
HuntJD: ‘Solidification and casting of metals’, Proceedings of the International Conference on Solidification and Casting of Metals, London, UK, 1979, The Metals Society, 3–9.
38.
KurzW and FisherJD: ‘Dendrite growth at the limit of stability: tip radius and spacing’, Acta Metall. Mater., 1981, 29, 11–20.
39.
TrivediR: ‘Interdendritic spacing: II. A comparison of theory and experiments’, Metall. Mater. Trans. A, 1984, 15A, 977–982.
40.
BouchardD and KirkaldyJS: ‘Prediction of dendrite arm spacings in unsteady and steady state heat flow of unidirectionally solidified binary alloys’, Metall. Mater. Trans. B, 1997, 28B, 651–663.
41.
HuntJD and LuSZ: ‘Numerical modeling of cellular/dendritic array growth: spacing and structure predictions’, Metall. Mater. Trans. A, 1996, 27A, 611–623.
42.
MaD, XuW, NgCS and LiZY: ‘On secondary dendrite arm coarsening in peritectic solidification’, Mater. Sci. Eng. A, 2005, A390, 52–62.
43.
TourretD and KarmaA: ‘Multiscale dendritic needle network model of alloy solidification’, Acta Mater., 2013, 61, 6474–6491.
44.
BergeonN, TourretD, ChenL, DebierreJ.-M, GuérinR, RamirezA, BilliaB, KarmaA and TrivediR: ‘Spatiotemporal dynamics of oscillatory cellular patterns in three-dimensional directional solidification’, Phys. Rev. Lett., 2013, 110, 226102-1–226102-5.
45.
PerovicDD, SnugovskyL, SnugovskyP and RutterJW: ‘Reactions in Sn corner of Cu–Sn–Zn alloy system’, Mater. Sci. Technol., 2012, 28, 120–123.
46.
ZhangXF, KomizoY, YokotaT, YasudaK and OiK: ‘In-situ observations of phase transformations during C Mn Al steel weld solidification’, Mater. Sci. Technol., 2013, 29, 1363–1372.
47.
KarmaA, RappelWJ, FuhBC and TrivediR: ‘Model of banding in diffusive and convective regimes during directional solidification of peritectic systems’, Metall. Mater. Trans. A, 1996, 29A, 1457–1470.
48.
GündüzM, KayaH, ÇardiliE, MarasliN, KesliogluK and SaatçiB: ‘Effect of solidification processing parameters on the cellular spacings in the Al–0·1 wt Ti and Al–0·5wt Ti alloys’, J. Alloys Compd, 2007, 439, 114–127.
49.
QuaresmaJMV, SantosCA and GarciaA: ‘Correlation between unsteady-state solidification conditions, dendrite spacings, and mechanical properties of Al–Cu alloys’, Metall. Mater. Trans. A, 2000, 31A, 3167–3178.
were experimentally determined and correlated with the primary (λ1) and secondary (λ2) dendrite arm spacings by experimental growth laws. It is shown that the proposed growth laws are able to encompass also the growth of dendritic branches during steady state growth from the melt.