Kinetics of triple-junctions in eutectic solidification: a sharp interface model
Source abstract
Abstract
The kinetics of triple-junctions (TJs) in eutectic solidification is modeled by the thermodynamic extremum principle (TEP). It consists of two parts. First, TJs as the interaction of interfaces follow the interface kinetics according to which the temperature and concentration at the TJs are determined. This interface part of TJ kinetics is closely related to the eutectic point in the kinetic phase diagram. Second, TJs have their specific kinetics according to which their morphology (e.g., the contact angles in two dimensions) is determined. Using a new solution of solute diffusion in liquid, the TJ kinetics is incorporated into the current lamellar eutectic growth model. The model is applicable to the concentrated alloy systems and can be extended to any kind of eutectics. Simulation results of the rapid solidification of a lamellar Ni5Si2–Ni2Si (γ–δ) eutectic show that both parts of TJ kinetics can play important roles in eutectic solidification and need to be considered to improve the current eutectic theory.
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Research context
OpenAlex topics: Metallic Glasses and Amorphous Alloys · Solidification and crystal growth phenomena · Intermetallics and Advanced Alloy Properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (60)
Show source-provided references
1. Kurz W, Fisher DJ (1979) Dendrite growth in eutectic alloys: the coupled zone. Inter Mater Rev 5(6):177–20410.1179/095066079790136408 ↗
2. Hosch T, England LG, Napolitano RE (2009) Analysis of the high growth-rate transition in Al–Si eutectic solidification. J Mater Sci 44:4892–4899. doi: 10.1007/s10853-009-3747-610.1007/s10853-009-3747-6 ↗
3. Kaya H, Gündüz M, Çadirli E, Uzun O (2004) Effect of growth rate and lamellar spacing on microhardness in the directionally solidified Pb–Cd, Sn–Zn and Bi–Cd eutectic alloys. J Mater Sci 39:6571–6576. doi: 10.1023/B:JMSC.0000044897.98694.be10.1023/B:JMSC.0000044897.98694.be ↗
4. Weyrich N, Leinenbach C (2013) Low temperature TLP bonding of Al2O3—ceramics using eutectic Au—(Ge, Si) alloy. J Mater Sci 48:7115–7124. doi: 10.1007/s10853-013-7526-z10.1007/s10853-013-7526-z ↗
5. Waku Y, Nakagawa N, Wakamoto T et al (1997) A ductile ceramic eutectic composite with high strength at 1873 K. Nature 389:49–5210.1038/37937 ↗
6. Wang WH, Dong C, Shek CH (2004) Bulk metallic glasses. Mater Sci Eng R 44:45–8910.1016/j.mser.2004.03.001 ↗
7. Wang N, Kalay YE, Trivedi R (2011) Eutectic-to-metallic glass transition in the Al–Sm system. Acta Mater 59:6604–661910.1016/j.actamat.2011.07.015 ↗
8. Zhao B, Verhasselt J-Ch, Shvindlerman LS, Gottstein G (2010) Measurement of grain boundary triple line energy in copper. Acta Mater 58:5646–565310.1016/j.actamat.2010.06.039 ↗
9. Zhao B, Ziemons A, Shvindlerman LS, Gottstein G (2012) Surface topography and energy of grain boundary triple junctions in copper tricrystals. Acta Mater 60:811–81810.1016/j.actamat.2011.10.034 ↗
10. Frolov T, Mishin Y (2009) Temperature dependence of the surface free energy and surface stress: an atomistic calculation for Cu (110). Phys Rev B 79:17411010.1103/PhysRevB.79.174110 ↗
11. Czubayko U, Sursaeva VG, Gottstein G, Shvindlerman LS (1998) Influence of triple junctions on grain boundary motion. Acta Mater 46:5863–587110.1016/S1359-6454(98)00241-9 ↗
12. Upmanyu M, Srolovitz DJ, Shvindlerman LS, Gottstein G (2002) Molecular dynamics simulation of triple junction migration. Acta Mater 50:1405–142010.1016/S1359-6454(01)00446-3 ↗
13. Marks RA, Glaeser AM (2012) Equilibrium and stability of triple junctions in anisotropic systems. Acta Mater 60:349–35810.1016/j.actamat.2011.09.043 ↗
14. Fischer FD, Svoboda J, Hackl K (2012) Modelling the kinetics of a triple junction. Acta Mater 60:4704–471110.1016/j.actamat.2012.05.018 ↗
15. Gottstein G, King AH, Shvindlerman LS (2000) The effect of triple-junction drag on grain growth. Acta Mater 48:397–40310.1016/S1359-6454(99)00373-0 ↗
16. Zhao B, Gottstein G, Shvindlerman LS (2011) Triple junction effects in solids. Acta Mater 59:3510–351810.1016/j.actamat.2011.02.024 ↗
17. Johnson OK, Schuh CA (2013) The uncorrelated triple junction distribution function: towards grain boundary network design. Acta Mater 61:2863–287310.1016/j.actamat.2013.01.025 ↗
18. Akamatsu S, Plapp M, Faivre G, Karma A (2002) Pattern stability and trijunction motion in eutectic solidification. Phys Rev E 66:030502(R)10.1103/PhysRevE.66.030501 ↗
19. Akamatsu S, Plapp M, Faivre G, Karma A (2004) Overstability of lamellar eutectic growth below the minimum-undercooling spacing. Metal Mater Trans A 35:1815–182810.1007/s11661-004-0090-z ↗
20. Langer JS (1980) Eutectic solidification and marginal stability. Phys Rev Lett 44:1023–102610.1103/PhysRevLett.44.1023 ↗
21. Datye V, Langer JS (1981) Stability of thin lamellar eutectic growth. Phys Rev B 24:4155–416910.1103/PhysRevB.24.4155 ↗
22. Akamatsu S, Perrut M, Bottin-Rousseau S, Faivre G (2010) Spiral two-phase dendrites. Phys Rev Lett 104:05610110.1103/PhysRevLett.104.056101 ↗
23. Mullins WW, Sekerka RF (1964) Stability of a planar interface during solidification of a dilute binary alloy. J Appl Phys 35:444–45110.1063/1.1713333 ↗
24. Jackson KA, Hunt JD (1966) Lamellar and rod eutectic growth. Trans AIME 236:1129–1142
25. Choudhury A, Plapp M, Nestler B (2011) Theoretical and numerical study of lamellar eutectic three-phase growth in ternary alloys. Phys Rev E 83:05160810.1103/PhysRevE.83.051608 ↗
26. Ankit K, Choudhury A, Qin C et al (2013) Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion. Acta Mater 61:4245–425310.1016/j.actamat.2013.03.050 ↗
27. Donaghey LF, Tiller WA (1968/69) On the diffusion of solute during the eutectoid and eutectic transformations, part I. Mater Sci Eng 3:231–23910.1016/0025-5416(68)90015-3 ↗
28. Trivedi R, Magnin P, Kurz W (1987) Theory of eutectic growth under rapid solidification conditions. Acta Metall 35:971–98010.1016/0001-6160(87)90176-3 ↗
29. Kurz W, Trivedi R (1991) Eutectic growth under rapid solidification conditions. Metall Trans A 22:3051–305710.1007/BF02650266 ↗
30. Galenko PK, Herlach DM (2006) Diffusion less crystal growth in rapidly solidifying eutectic systems. Phys Rev Lett 96:15060210.1103/PhysRevLett.96.150602 ↗
31. Goetzinger R, Barth M, Herlach DM (1998) Growth of lamellar eutectic dendrites in undercooled melts. J Appl Phys 84:1643–164910.1063/1.368233 ↗
32. Li JF, Zhou YH (2005) Eutectic growth in bulk undercooled melts. Acta Mater 53:2351–235910.1016/j.actamat.2005.01.042 ↗
33. Liu L, Li JF, Zhou YH (2009) Solidification of undercooled eutectic alloys containing a third element. Acta Mater 57:1536–154510.1016/j.actamat.2008.12.001 ↗
34. Caroli C, Misbah C (1997) On static and dynamical Young’s condition at a trijunction. J Phys I France 7:1259–126510.1051/jp1:1997122 ↗
35. Folch R, Plapp M (2003) Towards a quantitative phase-field model of two-phase solidification. Phys Rev E 68:010602(R)10.1103/PhysRevE.68.010602 ↗
36. Folch R, Plapp M (2005) Quantitative phase-field modeling of two-phase growth. Phys Rev E 72:01160210.1103/PhysRevE.72.011602 ↗
37. Parisi A, Plapp M (2008) Stability of lamellar eutectic growth. Acta Mater 56:1348–135710.1016/j.actamat.2007.11.037 ↗
38. Hackl K, Fischer FD, Klevakina K et al (2013) A variational approach to growing and wetting. Acta Mater 61:1581–159110.1016/j.actamat.2012.11.035 ↗
39. Wang HF, Liu F, Herlach DM (2014) On the solution of solute diffusion during eutectic growth. J Cryst Growth 389:68–7310.1016/j.jcrysgro.2013.11.080 ↗
40. Wang HF, Liu F, Zhai HM, Wang K (2012) Application of the maximal entropy production principle to rapid solidification: a sharp interface model. Acta Mater 60:1444–145410.1016/j.actamat.2011.11.038 ↗
41. Wang K, Wang HF, Liu F, Zhai HM (2013) Modeling rapid solidification of multi-component concentrated alloys. Acta Mater 61:1359–137210.1016/j.actamat.2012.11.013 ↗
42. Wang HF, Liu F, Ehlen GJ, Herlach DM (2013) Application of the maximal entropy production principle to rapid solidification: a multi-phase-field model. Acta Mater 61:2617–262710.1016/j.actamat.2013.01.041 ↗
43. Onsager L (1931) Reciprocal relations in irreversible processes I. Phys Rev 15:405–42610.1103/PhysRev.37.405 ↗
44. Martyushev LM, Seleznev VD (2006) Maximum entropy production principle in physics, chemistry and biology. Phys Rep 426:1–4510.1016/j.physrep.2005.12.001 ↗
45. Ziegler H (1983) An introduction to thermodynamics. North-Holland, Amsterdam
46. Svoboda J, Turek I (1991) On diffusion-controlled evolution of closed solid-state thermodynamic systems at constant temperature and pressure. Philos Mag B 64:749–75910.1080/13642819108207635 ↗
47. Svoboda J, Turek I, Fischer FD (2005) Application of the thermodynamic extremal principle to modeling of thermodynamic processes in material sciences. Philos Mag 85:3699–370710.1080/14786430500267760 ↗
48. Svoboda J, Fischer FD, Fratzl P, Kroupa A (2002) Diffusion in multi-component systems with no or dense sources and sinks for vacancies. Acta Mater 50:1369–138110.1016/S1359-6454(01)00443-8 ↗
49. Fischer FD, Svoboda J, Petryk H (2014) Thermodynamic extremal principles for irreversible processes in materials science. Acta Mater 67:1–2010.1016/j.actamat.2013.11.050 ↗
50. Wang HF, Liu F, Herlach DM (2014) Modeling the growth kinetics of a multi-component stoichiometric compound. J Mater Sci 49:1537–1543. doi: 10.1007/s10853-013-7835-210.1007/s10853-013-7835-2 ↗
51. Aziz MJ, Kaplan T (1988) Continuous growth model for interface motion during alloy solidification. Acta Metall 36:2335–234710.1016/0001-6160(88)90333-1 ↗
52. Boettinger WJ, Aziz MJ (1989) Theory for the trapping of disorder and solute in intermetallic phases by rapid solidification. Acta Mater 37:3379–339110.1016/0001-6160(89)90210-1 ↗
53. Du Y, Schuster JC (1999) Experimental investigations and thermodynamic descriptions of the Ni–Si and C–Ni–Si systems. Metall Mater Trans A 30:2409–241710.1007/s11661-999-0249-8 ↗
54. Schuster JC, Du Y (2000) Experimental investigation and thermodynamic modeling of the Cr–Ni–Si system. Metall Mater Trans A 31:1795–180310.1007/s11661-006-0248-y ↗
55. Aziz MJ, Boettinger WJ (1994) On the transition from short-range diffusion-limited to collision-limited growth in alloy solidification. Acta Metall Mater 42:527–53710.1016/0956-7151(94)90507-X ↗
56. Tang CG, Harrowell P (2013) Anomalously slow crystal growth of the glass-forming alloy CuZr. Nature Mater 12:507–51110.1038/nmat3631 ↗
57. Wang H, Herlach DM, Liu RP (2014) Dendrite growth in Cu50Zr50 glass-forming melts, thermodynamics vs. kinetics. EPL 105:3600110.1209/0295-5075/105/36001 ↗
58. Ediger MD, Harrowell P, Yu L (2008) Crystal growth kinetics exhibit a fragility-dependent decoupling from viscosity. J Chem Phys 128:03470910.1063/1.2815325 ↗
59. Shun Y, Xi HM, Chen S et al (2008) Crystallization near glass transition: transition from diffusion-controlled to diffusionless crystal growth studied with seven polymorphs. J Phys Chem B 112:5594–560110.1021/jp7120577 ↗
60. Fischer FD, Simha NK (2004) Influence of material flux on the jump relations at a singular interface in a multicomponent solid. Acta Mech 171:213–22310.1007/s00707-004-0138-6 ↗