REFERENCES

1. Broomfield RW, Ford DA, Bhangu JK, et al. Development and turbine engine performance of three advanced rhenium containing superalloys for single crystal and directionally solidified blades and vanes. Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition. 1997 Jun 2-5; Orlando, USA. New York: ASME; 1998.

2. Gasson PC. The superalloys: fundamentals and applications. R. C. Reed Cambridge University Press, The Edinburgh Building, Shaftesbury Road, Cambridge, CB2 2RU, UK, 2006. 372pp. Illustrated. £80. ISBN 0-521-85904-2. Aeronaut j 2008;112:291.

3. Pollock T, Argon A. Creep resistance of CMSX-3 nickel base superalloy single crystals. Acta Metall Mater 1992;40:1-30.

4. Versnyder FI, Shank M. The development of columnar grain and single crystal high temperature materials through directional solidification. Mater Sci Eng 1970;6:213-47.

5. Quested PN, Osgerby S. Mechanical properties of conventionally cast, directionally solidified, and single-crystal superalloys. Mater Sci Technol 1986;2:461-75.

6. Giamei AF, Kear BH. On the nature of freckles in nickel base superalloys. Metall Trans 1970;1:2185-92.

7. Chmiela B, Sozańska M, Cwajna J. Identification and evaluation of freckles in directionally solidified casting made of PWA 1426 nickel-based superalloy. Arch Metall Mater 2012;57:559-64.

8. Worster MG. Instabilities of the liquid and mushy regions during solidification of alloys. J Fluid Mech 1992;237:649-69.

9. Ramirez JC, Beckermann C. Evaluation of a rayleigh-number-based freckle criterion for Pb-Sn alloys and Ni-base superalloys. Metall Mater Trans A 2003;34:1525-36.

10. Valdés J, King P, Liu X. On the formulation of a freckling criterion for Ni-based superalloy vacuum arc remelting ingots. Metall Mater Trans A 2010;41:2408-16.

11. Frueh C, Poirier D, Felicelli S. Predicting freckle-defects in directionally solidified Pb-Sn alloys. Mater Sci Eng 2002;328:245-55.

12. Wang F, Ma D, Zhang J, Bogner S, Bührig-polaczek A. Solidification behavior of a Ni-based single crystal CMSX-4 superalloy solidified by downward directional solidification process. Mater Charact 2015;101:20-5.

13. Li Q, Shen J, Qin L, Xiong Y, Yue X. Effect of traveling magnetic field on freckle formation in directionally solidified CMSX-4 superalloy. J Mater Process Technol 2019;274:116308.

14. Li Q, Shen J, Qin L, Xiong Y. Investigation on local cooling in reducing freckles for directionally solidified superalloy specimens with abruptly varying cross-sections. Mater Charact 2017;130:139-48.

15. Xiao J, Jiang W, Han D, Li K, Lu Y, Lou L. Evolution of crystallographic orientation and microstructure in the triangular adapter of grain continuator of a 3rd-generation single crystal superalloy casting during directional solidification. J Alloys Compd 2022;898:162782.

16. Genereux PD, Borg CA. Characterization of freckles in a high strength wrought nickel superalloy. Superalloys 2000;2000:19-27. Available from: https://www.tms.org/superalloys/10.7449/2000/Superalloys_2000_19_27.pdf [Last accessed on 20 Dec 2023].

17. Pollock TM, Murphy WH, Goldman EH, Uram DL, Tu JS. Grain defect formation during directional solidification of nickel base single crystals. Superalloys 1992;1992:125-34. Available from: https://www.tms.org/superalloys/10.7449/1992/Superalloys_1992_125_134.pdf [Last accessed on 20 Dec 2023].

18. Sarazin JR, Hellawell A. Channel formation in Pb-Sn, Pb-Sb, and Pb-Sn-Sb alloy ingots and comparison with the system NH₄CI-H₂O. Metall Trans A 1988;19:1861-71.

19. Karagadde S, Yuan L, Shevchenko N, Eckert S, Lee P. 3-D microstructural model of freckle formation validated using in situ experiments. Acta Mater 2014;79:168-80.

20. Ren N, Li J, Panwisawas C, Xia M, Dong H, Li J. Thermal-solutal-fluid flow of channel segregation during directional solidification of single-crystal nickel-based superalloys. Acta Mater 2021;206:116620.

21. Amouyal Y, Seidman D. An atom-probe tomographic study of freckle formation in a nickel-based superalloy. Acta Mater 2011;59:6729-42.

22. Tin S, Pollock TM, King WT. Carbon additions and grain defect formation in high refractory nickel-base single crystal superalloys. Superalloys 2000;2000:201-10. Available from: https://www.tms.org/Superalloys/10.7449/2000/Superalloys_2000_201_210.pdf [Last accessed on 20 Dec 2023].

23. Tin S, Pollock TM, Murphy W. Stabilization of thermosolutal convective instabilities in Ni-based single-crystal superalloys: carbon additions and freckle formation. Metall Mater Trans A 2001;32:1743-53.

24. Amouyal Y, Seidman D. The role of hafnium in the formation of misoriented defects in Ni-based superalloys: an atom-probe tomographic study. Acta Mater 2011;59:3321-33.

25. Karagadde S, Lee PD, Cai B, et al. Transgranular liquation cracking of grains in the semi-solid state. Nat Commun 2015;6:8300.

26. Cai B, Wang J, Kao A, et al. 4D synchrotron X-ray tomographic quantification of the transition from cellular to dendrite growth during directional solidification. Acta Mater 2016;117:160-9.

27. Reinhart G, Grange D, Abou-khalil L, et al. Impact of solute flow during directional solidification of a Ni-based alloy: in-situ and real-time X-radiography. Acta Mater 2020;194:68-79.

28. Ren N, Panwisawas C, Li J, Xia M, Dong H, Li J. Solute enrichment induced dendritic fragmentation in directional solidification of nickel-based superalloys. Acta Mater 2021;215:117043.

29. Isensee T, Tourret D. Convective effects on columnar dendritic solidification - a multiscale dendritic needle network study. Acta Mater 2022;234:118035.

30. Mullis A. Growth induced dendritic bending and rosette formation during solidification in a shearing flow. Acta Mater 1999;47:1783-9.

31. Dragnevski K, Mullis AM, Walker DJ, Cochrane RF. Mechanical deformation of dendrites by fluid flow during the solidification of undercooled melts. Acta Mater 2002;50:3743-55.

32. Billia B, Bergeon N, Thi HN, Jamgotchian H, Gastaldi J, Grange G. Cumulative mechanical moments and microstructure deformation induced by growth shape in columnar solidification. Phys Rev Lett 2004;93:126105.

33. Niederberger C, Michler J, Jacot A. Origin of intragranular crystallographic misorientations in hot-dip Al-Zn-Si coatings. Acta Mater 2008;56:4002-11.

34. Yuan L, Lee PD. A new mechanism for freckle initiation based on microstructural level simulation. Acta Mater 2012;60:4917-26.

35. Ananiev S, Nikrityuk P, Eckert K. Dendrite fragmentation by catastrophic elastic remelting. Acta Mater 2009;57:657-65.

36. Boden S, Eckert S, Willers B, Gerbeth G. X-ray radioscopic visualization of the solutal convection during solidification of a Ga-30 Wt Pct In Alloy. Metall Mater Trans A 2008;39:613-23.

37. Appolaire B, Albert V, Combeau H, Lesoult G. Free growth of equiaxed crystals settling in undercooled NH₄Cl-H₂O melts. Acta Mater 1998;46:5851-62.

38. Hu X, Zhu Y, Ma X. Crystallographic account of nano-scaled intergrowth of M₂B-type borides in nickel-based superalloys. Acta Mater 2014;68:70-81.

39. Ge H, Liu J, Zheng S, et al. Boride-induced dislocation channeling in a single crystal Ni-based superalloy. Mater Lett 2019;235:232-5.

40. Du B, Shi Z, Yang J, et al. M5B3 boride at the grain boundary of a nickel-based superalloy. J Mater Sci Technol 2016;32:265-70.

41. Wang Y, Brodusch N, Gauvin R, Zeng Y. Line-rotated remapping for high-resolution electron backscatter diffraction. Ultramicroscopy 2022;242:113623.

42. Wilkinson AJ, Meaden G, Dingley DJ. High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity. Ultramicroscopy 2006;106:307-13.

43. Mingard K, Roebuck B, Bennett E, et al. Comparison of EBSD and conventional methods of grain size measurement of hardmetals. Int J Refract Hard Met H 2009;27:213-23.

44. Mottura A, Reed RC. What is the role of rhenium in single crystal superalloys? MATEC Web Conf 2014;14:01001.

45. Huang M, Zhu J. An overview of rhenium effect in single-crystal superalloys. Rare Met 2016;35:127-39.

46. Wang S, Kang J, Guo Z, et al. In situ high speed imaging study and modelling of the fatigue fragmentation of dendritic structures in ultrasonic fields. Acta Mater 2019;165:388-97.

47. Wright SI, Nowell MM, Field DP. A review of strain analysis using electron backscatter diffraction. Microsc Microanal 2011;17:316-29.

48. Gottstein G. Physical foundations of materials science. Berlin:Springer;2004.

49. Callister W. Materials science and engineering: an introduction (2nd edition). Mater Des 1991;12:59.

50. Floreen S, Davidson JM. The effects of b and Zr on the creep and fatigue crack growth behavior of a Ni-base superalloy. Metall Trans A 1983;14:895-901.

51. Li X, Ou M, Wang M, Zhang L, Ma Y, Liu K. Effect of boron addition on the microstructure and mechanical properties of K4750 nickel-based superalloy. J Mater Sci Technol 2021;60:177-85.

52. Kontis P, Yusof HM, Pedrazzini S, et al. On the effect of boron on grain boundary character in a new polycrystalline superalloy. Acta Mater 2016;103:688-99.