W Tungsten pp 74-81 | Cite as

Surface Free Energy. Surface Tension

  • Gerhard Czack
  • Gerhard Kirschstein
  • Wolfgang Kurtz
  • Frank Stein
Part of the Gmelin Handbook of Inorganic and Organometallic Chemistry 8th Edition book series (GMELIN, volume W / A-B / A / 4)

Abstract

The surface tension γ and the (specific) surface free energy σ of a crystal face with area A are related by γ = σ+ A•(dσ/dA) [1]. There is some confusion in the literature in properly using γ and σ; for a more recent discussion of the difference between σ and γ, see [2 to 4]. According to Kumikov and Khokonov [5], cracking, zero-creep, and field emission microscopy (FEM) studies yield values for the surface tension equal to the surface free energy, γ= σ. Inert gas bubble precipitation, grain boundary grooving, and scratch relaxation rate studies can be used to determine σ. Contact angle and multiphase equilibrium studies, on the other hand, yield γ values [5].

Keywords

Entropy Anisotropy enthaLpy Brittle Tungsten 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Referencesf

  1. [1]
    Shuttleworth, R. (Proc. Phys. Soc. [London] A 63 [1950] 444/57).CrossRefGoogle Scholar
  2. [2]
    Zadumkin, S. N. ; Temrokov, A. I. (Izv. Vyssh. Uchebn. Zaved. Fiz. 11 No. 9 [1968] 40/51;Google Scholar
  3. [2a]
    Zadumkin, S. N. ; Temrokov, A. I. Sov. Phys. J. [Engl. Transl.] 11 No. 9 [1968] 35/45).CrossRefGoogle Scholar
  4. [3]
    Zadumkin, S. N. ; Shebzukhova, I. G. (Fiz. Met. Metalloved. 28 [1969] 434/9;Google Scholar
  5. [3a]
    Zadumkin, S. N. ; Shebzukhova, I. G. Phys. Met. Metallogr. [Engl. Transl.] 28 No. 3 [1969] 50/6).Google Scholar
  6. [4]
    Ackland, G. J. ; Finnis, M. W. (Philos. Mag. [8] A 54 [1986] 301/15).Google Scholar
  7. [5]
    Kumikov, V. K. ; Khokonov, Kh. B. (J. Appl. Phys. 54 [1983] 1346/50).CrossRefGoogle Scholar
  8. [6]
    Liu, J. ; Bilello, J. C. (Philos. Mag. [8] 35 [1977] 1453/72).CrossRefGoogle Scholar
  9. [7]
    Linford, R. G. (Chem. Soc. Rev. 1 [1972] 445/64).CrossRefGoogle Scholar
  10. [8]
    Martsenyuk, P. S. ; Ivashchenko, Yu. N. ; Eremenko, V. N. (Teplofiz. Vys. Temp. 12 [1974] 1310/2;Google Scholar
  11. [8a]
    Martsenyuk, P. S. ; Ivashchenko, Yu. N. ; Eremenko, V. N. High Temp. [Engl. Transl.] 12 [1974] 1161/3).Google Scholar
  12. [9]
    Finnis, M. W. ; Sinclair, J. E. (Philos. Mag. [8] A 50 [1984] 45/55).CrossRefGoogle Scholar
  13. [10]
    Matthai, C. C. ; Bacon, D. J. (Philos. Mag. [8] A 52 [1985] 1/3).Google Scholar
  14. [11]
    Daw, M. S.; Baskes, M. I. (Phys. Rev. Lett. 50 [1983] 1285/8).CrossRefGoogle Scholar
  15. [12]
    Daw, M. S. ; Baskes, M. I. (Phys. Rev. [3] B 29 [1984] 6443/53).Google Scholar
  16. [13]
    Smith, J. R. ; Perry, T. ; Banerjea, A. ; Ferrante, J. ; Bozzolo, G. (Phys. Rev. [3] B 44 [1991] 6444/65) .Google Scholar
  17. [14]
    Rodríguez, A. M. ; Bozzolo, G. ; Ferrante, J. (Surf. Sci. 289 [1993] 100/26).CrossRefGoogle Scholar
  18. [15]
    Guellil, A. M. ; Adams, J. B. (J. Mater. Res. 7 [1992] 639/52).CrossRefGoogle Scholar
  19. [16]
    Baskes, M. I. (Phys. Rev. [3] B 46 [1992] 2727/42).Google Scholar
  20. [17]
    Johnson, R. A. ; White, P. J. (Phys. Rev. [3] B 13 [1976] 5293/302).Google Scholar
  21. [18]
    Johnson, R. A. ; White, P. J. (Phys. Rev. [3] B 18 [1978] 2939/40).Google Scholar
  22. [19]
    Taskaev, I. P. (Izv. Akad. Nauk SSSR Met. 1982 No. 4, pp. 153/7; Russ. Metall. [Engl. Transl.] 1982 No. 4, pp. 139/44).Google Scholar
  23. [20]
    Nicholas, J. F. (Austral. J. Phys. 21 [1968] 21/34).CrossRefGoogle Scholar
  24. [21]
    Tyson, W. R. ; Ayres, R. A. ; Stein, D. F. (Acta Metall. 21 [1973] 621/7).CrossRefGoogle Scholar
  25. [22]
    Vingsbo, O. (Mater. Sci. Eng. 8 [1971] 32/40).CrossRefGoogle Scholar
  26. [23]
    Schweitz, J. Å. Vingsbo, O. (Mater. Sci. Eng. 8 [1971] 275/83).CrossRefGoogle Scholar
  27. [24]
    Müller, A.; Drechsler, M. (Surf. Sci. 13 [1969] 471/90).CrossRefGoogle Scholar
  28. [25]
    Drechsler, M. ; Nicholas, J. F. (J. Phys. Chem. Solids 28 [1967] 2597/607).CrossRefGoogle Scholar
  29. [26]
    Drechsler, M. ; Nicholas, J. F. (J. Phys. Chem. Solids 28 [1967] 2609/27).CrossRefGoogle Scholar
  30. [27]
    Kumar, R. ; Grenga, H. E. (Surf. Sci. 59 [1976] 612/8).CrossRefGoogle Scholar
  31. [28]
    Johnson, R. A. (Phys. Rev. [2] 145 [1966] 423/33).CrossRefGoogle Scholar
  32. [29]
    Johnson, R. A. (Phys. Rev. [2] A 134 [1964] 1329/36).CrossRefGoogle Scholar
  33. [30]
    Gilman, J. J. (Fract. Proc. Int. Conf. At. Mech. Fract., Swampscott, Mass., 1959, pp. 193/ 222, 204/5, discuss. pp. 222/4).Google Scholar
  34. [31]
    Zaremba, E. (Solid State Commun. 23 [1977] 347/50).CrossRefGoogle Scholar
  35. [32]
    Chen, S. H. ; Brockhouse, B. N. (Solid State Commun. 2 [1964] 73/7).CrossRefGoogle Scholar
  36. [33]
    Tyson, W. R. (J. Appl. Phys. 47 [1976] 459/65).CrossRefGoogle Scholar
  37. [34]
    Caglioti, G. ; Rizzi, G. ; Bilello, J. C. (J. Appl. Phys. 42 [1971] 4271/6).CrossRefGoogle Scholar
  38. [35]
    Caglioti, G. ; Rizzi, G. ; Bilello, J. C. (J. Appl. Phys. 43 [1972] 3600/1).CrossRefGoogle Scholar
  39. [36]
    Shebzukhova, I. G. (Fiz. Khim. Poverkhn. 1982 27/31; C.A. 100 [1984] No. 180533).Google Scholar
  40. [37]
    Smith, J. R. ; Banerjea, A. (Phys. Rev. Lett. 59 [1987] 2451/4).CrossRefGoogle Scholar
  41. [38]
    Richman, M. H. (ASM Trans. Q. 60 [1967] 719/21).Google Scholar
  42. [39]
    Avraamov, Yu. S. ; Gvozdev, A. G. (Fiz. Met. Metalloved. 23 [1967] 405/8;Google Scholar
  43. [39A]
    Avraamov, Yu. S. ; Gvozdev, A. G. Phys. Met. Metallogr. [Engl. Transl.] 23 No. 3 [1967] 19/22).Google Scholar
  44. [40]
    Desjonquères, M. C. ; Cyrot-Lackmann, F. (Surf. Sci. 50 [1975] 257/61).CrossRefGoogle Scholar
  45. [41]
    Vlasov, J. A. [Yu. A.] ; Golubev, O. L. ; Shrednik, V. N. (J. Phys. Colloq. [Paris] 49 [1988] C6/131/C 6/136) .Google Scholar
  46. [42]
    Drechsler, M. ; Müller, A. (J. Cryst. Growth 3/4 [1968] 518/22).CrossRefGoogle Scholar
  47. [43]
    Farrell, K. ; Loh, B. T. M. ; Stiegler, J. O. (ASM Trans. Q. 60 [1967] 485/93).Google Scholar
  48. [44]
    Cordwell, J. E. ; Hull, D. (Philos. Mag. [8] 26 [1972] 215/24).CrossRefGoogle Scholar
  49. [45]
    Cordwell, J. E.; Hull, D. (Philos. Mag. [8] 19 [1969] 951/66).CrossRefGoogle Scholar
  50. [46]
    Dzherakhov, N. I. (Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 1987 No. 1, pp. 22/8; C. A. 106 [1987] No. 180246).Google Scholar
  51. [47]
    Cordwell, J. E. ; Hull, D. (Philos. Mag. [8] 27 [1973] 1183/92).CrossRefGoogle Scholar
  52. [48]
    Hull, D.; Beardmore, P.; Valintine, A. P. (Philos. Mag. [8] 12 [1965] 1021/41).CrossRefGoogle Scholar
  53. [49]
    Chan, C. T.; Louie, S. G. (Phys. Rev. [3] B 33 [1986] 2861/4).CrossRefGoogle Scholar
  54. [50]
    Singh, D. ; Wei, S.-H. ; Krakauer, H. (Phys. Rev. Lett. 57 [1986] 3292/5).CrossRefGoogle Scholar
  55. [51]
    Fu, C. L. ; Ohnishi, S. ; Jansen, H. J. F. ; Freeman, A. J. (Phys. Rev. [3] B 31 [1985] 1168/71) .Google Scholar
  56. [52]
    Tréglia, G. ; Desjonquères, M.-C. ; Spanjaard, D. (J. Phys. C 16 [1983] 2407/19).CrossRefGoogle Scholar
  57. [53]
    Valintine, A. P. ; Hull, D. (J. Less-Common Met. 17 [1969] 353/61).CrossRefGoogle Scholar
  58. [54]
    Digilov, R. M. ; Zadumkin, S. N. ; Kumykov, V. K. ; Khokonov, Kh. B. (Fiz. Met. Metalloved. 41 [1976] 979/82;Google Scholar
  59. [54]
    Digilov, R. M. ; Zadumkin, S. N. ; Kumykov, V. K. ; Khokonov, Kh. B. Phys. Met. Metallogr. [Engl. Transl.] 41 No. 5 [1976] 68/71).Google Scholar
  60. [55]
    Bettler, P. C. ; Barnes, G. (Surf. Sci. 10 [1968] 165/76).CrossRefGoogle Scholar
  61. [56]
    Barbour, J. P. ; Charbonnier, F. M. ; Dolan, W. W. ; Dyke, W. P. ; Martin, E. E. ; Trolan, J. K. (Phys. Rev. [2] 117 [1960] 1452/9).CrossRefGoogle Scholar
  62. [57]
    Dranova, Zh. I. ; D’yachenko, A. M. ; Mikhailovskii, I. M. (Fiz. Met. Metalloved. 31 [1971] 1108/11;Google Scholar
  63. [57]
    Dranova, Zh. I. ; D’yachenko, A. M. ; Mikhailovskii, I. M. Phys. Met. Metallogr. [Engl. Transl.] 31 No. 5 [1971] 223/6).Google Scholar
  64. [58]
    Butenko, V. G. ; Golubev, O. L. ; Shrednik, V. N. (Pis’ma Zh. Tekh. Fiz. 18 No. 19 [1992] 80/5;Google Scholar
  65. [58a]
    Butenko, V. G. ; Golubev, O. L. ; Shrednik, V. N. (Soy. Tech. Phys. Lett. [Engl. Transl.] 18 [1992] 642/4).Google Scholar
  66. [59]
    Allen, B. C. (J. Less-Common Met. 29 [1972] 263/82).CrossRefGoogle Scholar
  67. [60]
    Hodkin, E. N. ; Nicholas, M. G. ; Poole, D. M. (J. Less-Common Met. 20 [1970] 93/103).CrossRefGoogle Scholar
  68. [61]
    Skorik, V. I. ; Solyanyk, Z. V. ; Stetsura, M. M. (Fiz. Elektron. [L’vov] No. 21 [1980] 113/5).Google Scholar
  69. [62]
    Wawra, H. (Z. Metallkd. 66 [1975] 492/8).Google Scholar
  70. [63]
    Wawra, H. (Z. Metallkd. 66 [1975] 395/401).Google Scholar
  71. [64]
    Wawra, H. H. (Materialprüfung 14 [1972] 413/9).Google Scholar
  72. [65]
    Miedema, A. R. (Z. Metallkd. 69 [1978] 287/92).Google Scholar
  73. [66]
    Miedema, A. R.; Boom, R. (Z. Metallkd. 69 [1978] 183/90).Google Scholar
  74. [67]
    Tyson, W. R. ; Miller, W. A. (Surf. Sci. 62 [1977] 267/76).CrossRefGoogle Scholar
  75. [68]
    Tyson, W. R. (Can. Metall. Q. 14 [1975] 307/14).CrossRefGoogle Scholar
  76. [69]
    Linford, R. G.; Mitchell, L. A. (Surf. Sci. 27 [1971] 142/56).CrossRefGoogle Scholar
  77. [70]
    Ivanov, O. A. ; Karyakin, V. S. (Izv. Akad. Nauk SSSR Met. 1989 No. 3, pp. 176/80; Russ. Metall. (Engl. Transl.] 1989 No. 3, pp. 169/73).Google Scholar
  78. [71]
    Taylor, J. W. (Metallurgia 50 [1954] 161/5).Google Scholar
  79. [72]
    Chatterjee, B. (Indian J. Technol. 15 [1977] 221/2).Google Scholar
  80. [73]
    Kristyan, S.; Olson, J. A. (J. Phys. Chem. 95 [1991] 921/32).CrossRefGoogle Scholar
  81. [74]
    Mezey, L. Z. ; Giber, J. (Acta Phys. Pol. A 66 [1984] 525/38).Google Scholar
  82. [75]
    Mezey, L. Z. ; Giber, J. (Jpn. J. Appl. Phys. 21 [1982] 1569/71).CrossRefGoogle Scholar
  83. [76]
    Kristyan, S. ; Giber, J. (Surf. Sci. 201 [1988] L 532/L 538).CrossRefGoogle Scholar
  84. [77]
    Mezei [Mezey], L. Z. ; Marton, D. ; Giber, Ya. [J.] (“ Hiber, H. “] (Zh. Fiz. Khim. 52 [1978] 850/3; Russ. J. Phys. Chem. [Engl. Transl.] 52 [1978] 489/91).Google Scholar
  85. [78]
    Mezey, L. Z. ; Giber, J. (Surf. Sci. 234 [1990] 210/9).CrossRefGoogle Scholar
  86. [79]
    Allen, B. C. (Trans. Metall. Soc. AIME 245 [1969] 1621/32).Google Scholar
  87. [80]
    Miedema, A. R. ; den Broeder, F. J. A. (Z. Metallkd. 70 [1979] 14/20).Google Scholar
  88. [81]
    Zadumkin, S. N.; Dokhov, M. P. (Izv. Akad. Nauk SSSR Met. 1968 No. 1, pp. 91/5; Russ. Metall. [Engl. Transl.] 1968 No. 1, pp. 52/4).Google Scholar
  89. [82]
    Lang, G. (Z. Metallkd. 67 [1976] 549/58).Google Scholar
  90. [83]
    Allen, B. C. (Trans. Metall. Soc. AIME 227 [1963] 1175/83).Google Scholar
  91. [84]
    Calverley, A. (Proc. Phys. Soc. (London] B 70 [1957] 1040/4).CrossRefGoogle Scholar
  92. [85]
    Pekarev, A. I. (Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 1963 No. 6, pp. 111/3; C.A. 60 [1964] 12973) .Google Scholar
  93. [86]
    Flint, O. (J. Nucl. Mater. 16 [1965] 260/70).CrossRefGoogle Scholar
  94. [87]
    Elyutin, V. P. ; Kostikov, V. I. ; Maurakh, M. A. ; Mitin, B. S. ; Pen’kov, I. A. (Poverkhn. Yavleniya Rasplavakh 1968 155/9 from C.A. 71 [1969] No. 116775 and cited in (8]).Google Scholar
  95. [88]
    Agaev, A. D. (Author’s abstract of candidate’s Diss., Moscow 1973; cited in (8]).Google Scholar
  96. [89]
    Papazian, H. A. (Scr. Metall. 18 [1984] 1401/3).CrossRefGoogle Scholar
  97. [90]
    Allen, B. C. (in: Beer, S. Z. ; Liquid Metals Chemistry and Physics, Dekker, New York 1972, pp. 161/212, 188).Google Scholar
  98. [91]
    Digilov, R. M. (Adgez. Rasplavov Paika Mater. No. 23 [1990] 8/9; C.A. 113 [1990] No. 198626).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Gerhard Czack
  • Gerhard Kirschstein
  • Wolfgang Kurtz
  • Frank Stein

There are no affiliations available

Personalised recommendations