Branch growth and sidebranching in snow crystals

Crystal Growth and Design

Volumn 5, Issue 4, 2005, Pages 1509-1525

  Nelson, Jon ^a  

^a Sci cubed   (United States)

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[No Author keywords available]

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EID: 22744434561     PISSN: 15287483     EISSN: None     Source Type: Journal    
DOI: 10.1021/cg049685v     Document Type: Article

References (73)

1. Takahashi, T.; Endoh, T.; Wakahama, G.; Fukuta, N. J. Meteorol. Soc. Jpn. 1991, 69, 15.
2. Hallett, J.; Knight, C. Atmos. Res. 1994, 32, 1.
3. Gonda, T.; Nakahara, H. J. Cryst. Growth 1996, 173, 162.
4. Libbrecht, K. G. Eng. Sci. 2001, 1, 10.
5. Yokoyama, E.; Kuroda, T. Phys. Rev. A 1990, 41, 2038.
6. Nittmann, J.; Stanley, H. E. Nature 1986, 321, 663.
7. Kobayashi, R. Physica D 1993, 63, 410.
8. Karma, A.; Rappel, W.-J. Phys. Rev. E 1998, 57, 243.
9. Reiter, C. A. Chaos, Solitons Fractals 2005, 23, 1111.
10. Kim, T.; Lin, M. C. Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation; Breen, D., Lin, M., Eds.; Eurographics Association: Aire-la ville, Switzerland, 2003.
11. Uehara, T.; Sekerka, R. F. J. Cryst. Growth 2003, 254, 251.
12. Debierre, J.-M.; Karma, A.; Celestini, F.; Guerin, R. Phys. Rev. E 2003, 68, 041604.
13. Knight, C. A. Trans. Am. Geophys. Union 1972, 53, 382.
14. Yamashita, A. Proceedings of the International Conference on Cloud Physics, Boulder, CO, 1976, American Meteorological Society: Boston, 1976; p 136.
15. Frank, F. C. Contemp. Phys. 1982, 23, 3.
16. Nakaya, U. Snow Crystals, Natural and Artificial; Harvard University Press: Cambridge, MA, 1954.
17. Magono, C.; Lee, C. W. J. Fac. Sci. Hokkaido Univ. Ser. 7 1966, 2, 321.
18. Marshall, J. S.; Langleben, M. P. J. Meteorol. 1954, 11, 104.
19. Lamb, D.; Scott, W. D. J. Cryst. Growth 1972, 12, 21.
20. Hallett, J. Philos. Mag. 1961, 6, 1073.
21. Gonda, T.; Matsuura, Y.; Sei, T. J. Cryst. Growth 1994, 142, 171.
22. Gonda, T.; Sei, T. Curr. Top. Cryst. Growth Res. 2002, 6, 83.
23. Many experiments that indicate surface quasi-liquid are summarized in Petrenko, V. F.; Whitworth, R. W. Physics of Ice; Oxford University Press: Oxford, 1999.
24. Burton, W. K.; Cabrera, N.; Frank, F. C. Philos. Trans. R. Soc. London 1951, A243, 299.
25. Mason, B. J.; Bryant, G. W.; Van den Heuvel, A. P. Philos. Mag. 1963, 8, 505.
26. Kuroda, T.; Lacmann, R. J. Cryst. Growth 1982, 56, 189.
27. Mason, B. J. Proc. R. Soc. London A 1993, 441, 3.
28. Nelson, J. Philos. Mag. 2001, 81, 2337.
29. In the linear regime, the growth rate equals that in which all molecules that impinge on the surface can be assumed to grow into the crystal, and the rate of surface evaporation equals that which occurs in equilibrium. When some surface process increases the evaporation flux, the growth rate is less than the linear value (ref 48, eq 3).
30. Beckmann, W.; Lacmann, R. J. Cryst. Growth 1982, 58, 433.
31. Sei, T.; Gonda, T. J. Cryst. Growth 1989, 94, 697.
32. Libbrecht, K. G. J. Cryst. Growth 2003, 258, 168.
33. Nelson, J.; Baker, M. B. J. Geophys. R. 1996, 101, 7033.
34. r can be divided into small areas in which each has a nearly uniform R.
35. Mizuno, Y. J. Glaciol. 1978, 21, 409.
36. McKnight, C. V.; Hallett, J. J. Glaciol. 1978, 21, 397.
37. Chernov, A. A. J. Cryst. Growth 1974, 24-25, 11.
38. Wood, S.; Baker, M.; Calhoun, D. J. Geophys. Res. 2001, 100, 4845.
39. Levi, L.; Nasello, O. B. Atmos. Res. 2003, 66, 107.
40. Libbrecht, K. G. J. Cryst. Growth 2003, 258, 168.
41. s/p for symmetric step capture with p the face perimeter.
42. s, the growth rate dependence on supersaturation is more complex than the pure-vapor case (Gilmer, G. H.; Ghez, R.; Cabrera, N. J. Cryst. Growth 1971, 8, 79).
43. The dependence was shown to be roughly quadratic in Nelson, J. Ph.D. Dissertation, University of Washington, Seattle, WA, 1994.
44. Lewis, B. Crystal Growth; Pamplin, B. R., Ed.; Pergamon Press: Great Britain, 1980; p 23.
45. De Yoreo, J. J.; Land, T. A.; Dair, B. Phys. Rev. Lett. 1994, 73, 838.
46. Bacon, N. J.; Baker, M. B.; Swanson, B. D. Q. J. R. Meteorol. Soc. 2003, 129, 1903.
47. Frank, F. C. J. Cryst. Growth 1974, 24/25, 3.
48. Hallett, J. Am. Sci. 1984, 72, 582.
49. Nelson, J.; Knight, C. A. J. Atmos. Sci. 1998, 55, 1452.
50. The sporadic regime at the lowest supersaturations can probably be ruled out for branched snow crystals because it requires that each step spreads across the face before the next one nucleates. With such a process, it would be hard to explain the inferred clumping of steps into macrosteps that occurs symmetrically on all six branches.
51. Giga, Y.; Rybka, P. Adv. Math. Sci. Appl. 2003, 13, 625.
52. i away from face i.
53. Giga, Y.; Rybka, P. Adv. Math. Sci. Appl. (Gakkotosho, Tokyo) 2003, 13, 625.
54. 54 Photos of crystals with open pits, sealed-off voids, and combinations of both are on pages 24-49 of ref 55.
55. Gonda, T.; Koike, T. J. Cryst. Growth 1983, 65, 36.
56. Bentley, W. A.; Humphreys, W. J. Snow Crystals; Dover: New York, 1962.
57. Tirmizi, S. H.; Gill, W. N. J. Cryst. Growth 1987, 85, 488.
58. Maurer, J.; Bouissou, P.; Perrin, B.; Tabeling, P. Europhys. Lett. 1989, 8, 67.
59. Emsellem, V.; Tabeling, P. Europhys. Lett. 1994, 25, 277.
60. Lacmann, R.; Stranski, I. N. J. Cryst. Growth 1972, 13/14, 236.
61. Caroli, B.; Muller-Krumbhaar, H. ISIJ Int. 1995, 35, 1541.
62. S2(C) and form a macrostep. It is not clear whether this actually occurs; but it cannot presently be ruled out. Nevertheless, the result is essentially the same as the more likely process sketched in Figure 10.
63. ss.
64. See http://www.its.caltech.edu/~atomic/. Accessed March 1, 2004.
65. Libbrecht, K. G.; Tanusheva, V. M. Phys. Rev. Lett. 1998, 81, 176.
66. USDA Agricultural Research Center's Electron Microscopy Unit Snow Page. http://www.lpsi.barc.usda.gov/emusnow/. Accessed November 10, 2002.
67. From the study reported in Takahashi, T.; Endoh, T. Proceedings of 14th International Conference on Clouds and Precipitation; Bologna, Italy, July 19-23, 2004; Vol. 2, p 936.
68. Later experiments showed severe erosion at the base of sidebranches during crystal evaporation and evidence that the fragile sidebranches sometimes detached (Takahashi, T., personal communication).
69. Takahashi, T.; Endoh, T. Proceedings of the 13th International Conference on Clouds and Precipitation; Reno, NV, 2000; p 677.
70. Equation A5 in ref 28 has a few typos that are easily corrected by re-deriving it from A3 and A4.
71. Hokkaido Education University's Snow Quest web page. http://yukipro.sap. hokkyodai.ac.jp (in Japanese). Accessed November 10, 2002.
72. cr at an inside corner (e.g., D′ in Figure 5) might be lower than that away from a corner, but this has not been studied.
73. As a counter-example of the 6-fold symmetric snow crystal, bullet rosettes, in which columnar crystals grow outward from a common center, do not generally have columnar "branches" of the same length and thickness. (See photos in Gow, A. J. Glaciol. 1965, 5, 461.)