Development of Solid-Liquid Interfacial Energyof Melt-Crystal
Zengyun JIAN(), Tao XU, Junfeng XU, Man ZHU, Fang'e CHANG
Shaanxi Province Key Laboratory of Photoelectric Functional Materials and Devices, Xi'an Technological University, Xi'an 710021, China
Cite this article:
Zengyun JIAN, Tao XU, Junfeng XU, Man ZHU, Fang'e CHANG. Development of Solid-Liquid Interfacial Energyof Melt-Crystal. Acta Metall Sin, 2018, 54(5): 766-772.
Solid-liquid interfacial energy (SLIE) plays a crucial role in accurately evaluating solidification characteristics and effectively tuning the solidification process of crystals, which determines the structures and properties of crystals. This paper is based on the investigations of the authors on SLIE of melt-crystal in the past decade, and concentrates on reviewing the recent developments on the experimental and theoretical results of SLIE of melt-crystal. It draws several important conclusions by comparing various experimental results of SLIE under different temperatures. Firstly, the SLIE of melt-crystal decreases with the decrease of temperature. Secondly, the reason for different SLIE respectively obtained by Spaepen model and experimental measurement is revealed. Eventually, a model and method based on the structure of the solid-liquid interface for predicting the SLIE are proposed, and the results provided by this model are in line with the experimental results and the simulated results at the melting temperature, as well as the experimental results and the simulated results of the undercooled state.
Fig.1 Dependence of the homogenous nucleation undercooling (ΔTV) on the ratio of sample volume (V) to the cooling rate (Rc) for Ag (a), Cu (b) and Ni (c) (MU—maximum nucleation undercoolings, HU—homogeneous nucleation undercoolings, σT—solid-liquid interfacial energy of melt-crystal)[37]
Fig.2 Dependence of the crystal-melt interfacial energy on the temperature (T) for Ag (a), Cu (b) and Ni (c) (DA—dihedral angle, CA—contact angle)[37]
Table 1 Dependence of the solid-liquid interface energy on temperature for Ag, Cu and Ni
Fig.3 Dependences of the solid-liquid interface energy on temperature for silicon predicted from ΔT* (the critical undercooling (CU) for Si growing from lateral mode to intermediary mode) and ΔT** (The CU for Si growing from intermediary mode to continuous mode) (☆ result obtained from HU method, ◇ result obtained from grain boundary groove (GBG) method)[34]
Fig.4 Dependences of the predicted interface energies between silicon crystal and Si-Al melt with the equilibrium composition at the liquidus temperature on the mole fraction of silicon (XSi) in the melt according to ΔT *=131 K and ΔT **=239 K obtained in Si-20%Al (atomic fraction) alloy (◇ is the result obtained from the GBG method; △ and ▽ are results obtained from the CU method in terms of ΔT*=100 K and ΔT**=210 K obtained in pure silicon, respectively)[35]
Fig.5 Dependences of the predicted interface energies between silicon crystal and Si-Al melt with optional composition at the temperature of 850 K on the XSi in the melt according to ΔT *=131 K and ΔT **=239 K obtained in Si-20%Al (atomic fraction) alloy (◇ is the result obtained from the GBG method; △ and ▽ are results obtained from the CU method in terms of ΔT *=100 K and ΔT **=210 K obtained in pure silicon, respectively)[35]
[1]
Turnbull D.Formation of crystal nuclei in liquid metals[J]. J. Appl. Phys., 1950, 21: 1022
[2]
Asta M, Beckermann C, Karma A, et al.Solidification microstructures and solid-state parallels: Recent developments, future directions[J]. Acta Mater., 2009, 57: 941
[3]
Kelton K F.Crystal nucleation in liquids and glasses[J]. Solid State Phys., 1991, 45: 75
Hoyt J J, Asta M, Karma A.Atomistic and continuum modeling of dendritic solidification[J]. Mater. Sci. Eng., 2003, R41: 121
[6]
Wang L L, Lin X, Wang M, et al.Solid-liquid interfacial energy and its anisotropy measurement from double grain boundary grooves[J]. Scr. Metall., 2013, 69: 1
[7]
Wang L L, Lin X, Wang M, et al.Anisotropic solid-liquid interfacial energy measurement by grain boundary groove method[J]. J. Cryst. Growth, 2014, 406: 85
[8]
?ztürk E, Aks?z S, Ke?lio?lu K, et al.The measurement of interfacial energies for solid Sn solution in equilibrium with the Sn-Bi-Ag liquid[J]. Mater. Chem. Phys., 2013, 139: 153
[9]
Billur C A, Saat?i B.The solid-liquid interfacial energy for solid Zn solution at the eutectic Zn-Sn-Mg ternary alloy[J]. Thermochim. Acta, 2014, 589: 85
[10]
Son S, Dong H.Measuring solid liquid interfacial energy by grain boundary groove profile method (GBG)[J]. Mater. Today Proc., 2015, 2(suppl.2): S306
[11]
Kurz W, Fisher D J.Dendrite growth at the limit of stability: Tip radius and spacing[J]. Acta Metall., 1981, 29: 11
[12]
Lipton J, Kurz W, Trivedi R.Rapid dendrite growth in undercooled alloys[J]. Acta Metall., 1987, 35: 957
[13]
Kurz W, Trivedi R. Overview No.87 solidification microstructures: Recent developments and future directions[J]. Acta Metall. Mater., 1990, 38: 1
[14]
Li D, Herlach D M.Direct measurements of free crystal growth in deeply undercooled melts of semiconducting materials[J]. Phys. Rev. Lett., 1996, 77: 1801
[15]
Jian Z Y, Kuribayashi K, Jie W Q.Critical undercoolings for the transition from the lateral to continuous growth in undercooled silicon and germanium[J]. Acta Mater., 2004, 52: 3323
[16]
Jian Z Y, Jie W Q.Criterion for judging the homogeneous and heterogeneous nucleation[J]. Metall. Mater. Trans., 2001, 32A: 391
[17]
Jian Z Y, Chang F E, Ma W H, et al.Nucleation and undercooling of metal melt[J]. Sci. China, 2000, 30E: 9(坚增运, 常芳娥, 马卫红等. 金属熔体的形核和过冷度[J]. 中国科学, 2000, 30E: 9)
[18]
Stiffler S R, Thompson M O, Peercy P S.Supercooling and nucleation of silicon after laser melting[J]. Phys. Rev. Lett., 1988, 60: 2519
[19]
Lee G W, Cho Y C, Lee B, et al.Interfacial free energy and medium range order: Proof of an inverse of Frank's hypothesis[J]. Phys. Rev., 2017, 95B: 054202
[20]
Waseda Y, Miller W A.Calculation of the crystal-melt interfacial free energy from experimental radial distribution function data[J]. Trans. Jpn. Inst. Met., 1978, 19: 546
[21]
Gránásy L, B?rzs?nyi T, Pusztai T.Nucleation and bulk crystallization in binary phase field theory[J]. Phys. Rev. Lett., 2002, 88: 206105
[22]
Eustathopoulos N, Coudurier L, Joud J C, et al.Tension interfaciale solide-liquide des systémes Al-Sn, Al-In et Al-Sn-In[J]. J. Cryst. Growth, 1976, 33: 105
[23]
Wenzl H, Fattah A, Uelhoff W.Measurements of the contact angle between melt and crystal during Czochralski growth of copper[J]. J. Cryst. Growth, 1976, 36: 319
[24]
Gündüz M, Hunt J D.The measurement of solid-liquid surface energies in the Al-Cu, Al-Si and Pb-Sn systems[J]. Acta Metall., 1985, 33: 1651
[25]
Gündüz M, Hunt J D.Solid-liquid surface energy in the Al-Mg system[J]. Acta Metall., 1988, 37: 1839
[26]
Mara?li N, Hunt J D.Solid-liquid surface energies in the Al-CuAl2, Al-NiAl3 and Al-Ti systems[J]. Acta Mater., 1996, 44: 1085
[27]
?ad?rl? E, B?yük U, Engin S, et al.Experimental investigation of the effect of solidification processing parameters on the rod spacings in the Sn-1.2wt.% Cu alloy[J]. J. Alloys Compd., 2009, 486: 199
[28]
Broughton J Q, Gilmer G H.Molecular dynamics investigation of the crystal-fluid interface. VI. Excess surface free energies of crystal-liquid systems[J]. J. Chem. Phys., 1986, 84: 5759
[29]
Spaepen F.A structural model for the solid-liquid interface in monatomic systems[J]. Acta Metall., 1975, 23: 729
[30]
Spaepen F, Meyer R B.The surface tension in a structural model for the solid-liquid interface[J]. Scr. Metall., 1976, 10: 257
[31]
Thompson C V.On the approximation of the free energy change on crystallization [D]. Cambridge: Harvard University, 1979
[32]
Thompson C V, Spaepen F.Homogeneous crystal nucleation in binary metallic melts[J]. Acta Metall., 1983, 31: 2021
[33]
Nelson R, Spaepen F, Ehrenreich H, et al.Solid State Physics [M]. New York: Academic Press, 1989: 1
[34]
Jian Z Y, Kuribayashi K, Jie W Q, et al.Solid-liquid interface energy of silicon[J]. Acta Mater., 2006, 54: 3227
[35]
Jian Z Y, Yang X Q, Chang F E, et al.Solid-liquid interface energy between silicon crystal and silicon-aluminum melt[J]. Metall. Mater. Trans., 2010, 41A: 1826
[36]
Jian Z Y, Chen J, Chang F E, et al.Crystal-growth transition and homogenous nucleation undercooling of bismuth[J]. Metall. Mater. Trans., 2011, 42A: 3785
[37]
Jian Z Y, Li N, Zhu M, et al.Temperature dependence of the crystal-melt interfacial energy of metals[J]. Acta Mater., 2012, 60: 3590
[38]
Jian Z Y, Nagashio K, Kuribayashi K.Direct observation of the crystal-growth transition in undercooled silicon[J]. Metall. Mater. Trans., 2002, 33A: 2947
[39]
Powell G L F, Colligan G A. Solidification of undercooled Sn-Bi and Pb-Sb alloys[J]. Metall. Trans., 1970, 1: 133
[40]
Willnecker R, Herlach D M, Feuerbacher B.Nucleation in bulk undercooled nickel-base alloys[J]. Mater. Sci. Eng., 1988, 98: 85
[41]
Kaldis E, Scheel H J.Current Topics in Materials Science[M]. Amsterdam: North-Holland, 1977: 1
[42]
Flemings M C, Shiohara Y.Solidification of undercooled metals[J]. Mater. Sci. Eng., 1984, 65: 157
[43]
Powell G L F. Undercooling in silver-copper eutectic alloys: Nnucleation and microstructure[J]. J. Aust. Inst. Met., 1965, 10: 223
[44]
Williams P L, Mishin Y, Hamilton J C.An embedded-atom potential for the Cu-Ag system[J]. Modell. Simul. Mater. Sci. Eng., 2006, 14: 817
[45]
Ackland G J, Tichy G I, Vitek V, et al.Simple N-body potentials for the noble metals and nickel[J]. Philos. Mag., 1987, 56A: 735
[46]
Adams J B, Foiles S M, Wolfer W G.Self-diffusion and impurity diffusion of fcc metals using the five-frequency model and the Embedded Atom Method[J]. J. Mater. Res., 1989, 4: 102
[47]
Foiles S M.Calculation of the surface segregation of Ni-Cu alloys with the use of the embedded-atom method[J]. Phys. Rev., 1985, 32B: 7685
[48]
Jackson K A.Crystal growth kinetics[J]. Mater. Sci. Eng., 1984, 65: 7
[49]
Zhou H G, Lin X, Wang M, et al.Calculation of crystal-melt interfacial free energies of fcc metals[J]. J. Cryst. Growth, 2013, 366: 82
[50]
Cheng B Q, Tribello G A, Ceriotti M.Solid-liquid interfacial free energy out of equilibrium[J]. Phys. Rev., 2015, 92B: 180102
[51]
Kundin J, Choudhary M A.Numerical determination of the interfacial energy and nucleation barrier of curved solid-liquid interfaces in binary systems[J]. Phys. Rev., 2016, 94E: 012801
[52]
Brown N T, Martinez E, Qu J M.Interfacial free energy and stiffness of aluminum during rapid solidification[J]. Acta Mater., 2017, 129: 83
[53]
Qi C, Xu B, Kong L T, et al.Solid-liquid interfacial free energy and its anisotropy in the Cu-Ni binary system investigated by molecular dynamics simulations[J]. J. Alloys Compd., 2017, 708: 1073
