Surface energy of solids

  • Jacob J. Bikerman
Conference paper
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 77)


At least five conclusions may be formulated after perusing this review.
  1. 1.

    No method so far suggested for measuring the surface energy or surface tension of solids is satisfactory.

  2. 2.

    This failure may be caused, above all, by the fact that solids, contrary to liquids, cannot alter their shape without changing the strain energy in their volumes. The changes in strain energy are so much greater than those in surface energy that the latter remain unrecognized.

  3. 3.

    Solids possess an energy unknown in typical liquids. This cuticular energy exists because the surface region of innumerable solids has a chemical composition, a frequency of lattice defects, and so on, different from those in the bulk.

  4. 4.

    Small solid particles obtained by cooling of vapors, by grinding, or many other methods, usually have a less perfect lattice and more impurity than have bigger crystals of nominally identical composition. Hence, the cuticular energy of the former exceeds that of the latter.

  5. 5.

    Cuticular energy implies no tendency of the surface to contract, i.e., no surface tension. The theoretical calculations of the difference in energy between a broken and an unbroken crystal, if correct, afford a quantity which is related to cuticular energy and, like this, causes no contractile tendency.



Surface Tension Contact Angle Surface Energy Capillary Pressure Rupture Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


Surface area; a constant


Area of surface or interface per molecule

A, As, Asl

Areas of vapor-liquid, vapor-solid, and liquid-solid interfaces


Combined area of grain boundaries

A0, A1

Surface areas of a large and a minute crystal

A1, A2, A3

Areas of different crystal faces


The longer half-axis of an ellipse; lattice parameter


A constant


The shorter half-axis of an ellipse

C, C1, C2



Cuticular energy


Depth or half-length of scratch


Grain diameter; diffusion coefficient


Modulus of elasticity; intensity of electrostatic field


Internal energy of a bar


Internal energy of a broken bar


Charge of an electron


Helmholtz free energy


Free osmotic energy


Free surface energy


Force; number depending on crystal structure


Shear modulus; arbitrary constant; temperature gradient


Amount of heat evolved


Planck's constant; half-thickness or thickness of a slice or a ribbon; depth of scratch


Initial depth of scratch


Modulus of compressibility; proportionality constant


Boltzmann's constant; coordination number of atoms in bulk; compressibility

ks, kv

Number of atoms in two-dimensional and three-dimensional unit cells


Number of broken bonds per atom


Length; thickness of a crystal

Ll, Ls

Heat of vaporization or sublimation


Length; length of a “roof”; variable length of a filament


Initial length of a filament

l1, l2

Edges of two cubes


Molecular weight; atomic mass


Molecular weight


Mass of an atom; mass of hydrogen atom; mass


Number of atoms in unit cell; Avogadro number


Number of grain boundaries in a wire; number of molecules in unit volume

n+, n

Number of cations or anions on unit area


Gas pressure


Capillary pressure


Vapor pressure above a plane surface

P1, P2

Pressure in gas, in liquid


Heat content

Qo, Qp, Q

Heat of solution of large and powdered solids, and solids with zero surface


Number depending on crystal structure; surface density of electric charge

q0, q1

Heat of solution of unit mass


Radius of curvature; gas constant

R1, R2

The principal radii of curvature


Distance at which deformation becomes negligible


Radius of wires; distance from an atom or ion; cube root of molecular volume; radius of a void


Radius at the bottom of a groove; radius at zero time

r1, r2

Radius of wire before and after elongation

S. E.

Strain energy


Absolute temperature

Tb, Tm

Boiling and melting points


Melting point of plate of thickness l.


Melting point of drop of radius r


Temperature of treatment




Interatomic potential

Ul, Us

Total surface energy of a liquid, a solid


Height of a ridge point

u1, u2

Displacement of neighboring atoms


Volume of unit cell; specific volume of a liquid; volume; molecular volume

V1, V2

Gas and liquid volumes


Load; breaking load


Equilibrium load on a filament


Breaking load of wires


Work of extending a rod


Fracture energy


Work spent on macroscopic deformation


Width; distance between two ridges


Variable depth of crack


Plate thickness


Valency of an ion; effective number of electrons per ion


Angle on a crystal surface; numerical constant; an angle


Contact angle at the edge of a solid


Surface tension of a liquid


“Critical surface tension”


Specific surface energy or surface tension of a solid


Specific free energy of an interface between UC and U vapor


Specific energy or tension of a liquid-solid interface


Surface tension of a solid in a foreign vapor


Surface tension of a grain boundary

γ12, γ13, γ23

Tensions along boundaries between fluids 1 and 2, 1 and 3, and 2 and 3


Specific fracture energy


Thickness of a line on which facts


Thickness of surface layer; an angle


Maximum strain




Contact angle


The characteristic (Debye) temperature


Wave length of disturbances; heat of melting

λ1; λs

Internal heat of vaporization, sublimation


Number of free valence electrons per atom; Poisson's ratio


Cohesion of a solid

ρ1, ρ3

Density of a solid

ρ1, ρ2

Density of a gas, a liquid


Average stress


Local stress


Thickness of surface layer


Potential energy of a crystal


Work of removing an atom from its neighbor; work function; half the dihedral angle in a liquid medium; electric potential


Energy of valency electrons at the Fermi level


Half the dihedral angle in a gas


Dihedral angle in a foreign vapor


Volume of a molecule or atom


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    Young, Th.: Phil. Trans. Roy. Soc. 1805 I, 65Google Scholar
  2. 2).
    Young, Th.: Suppl. to the 4th, 5th, and 6th eds. of the Encyclopaedia Britannica 3, 211 (1824)Google Scholar
  3. 3).
    Quincke, G.: Phil. Mag. [4] 36, 267 (1868)Google Scholar
  4. 4).
    Dupré, A.: Ann. chim. et phys. [4] 7, 245 (1866)Google Scholar
  5. 5).
    Gibbs, J. W.: Thermodynamics, p. 315. New York: Dover Publ. (first published in 1876)Google Scholar
  6. 6).
    Benson, G. C., Yun, K. S. in: The solid — gas interface E.A. Flood (ed.), Vol. I, p. 203. New York: Marcel Dekker 1967Google Scholar
  7. 7).
    Benson, G. C., Claxton, T. A.: J. Phys. Chem. Solids 25, 367 (1964)Google Scholar
  8. 8).
    Macmillan, N. H., Kelly, A.: Mater. Sci. Eng. 10, 139 (1972)Google Scholar
  9. 9).
    Schmit, J. N.: Surface Sci. 55, 589 (1976)CrossRefGoogle Scholar
  10. 10).
    Alien, R. E., de Wette, F. W.: J. Chem. Phys. 51, 4820 (1969)Google Scholar
  11. 11).
    Erikson, W. D., Linnett, J. W.: Proc. Roy. Soc. London A 331, 347 (1972)Google Scholar
  12. 12).
    Zadumkin, S. N., Khulamkhanov, V. Kh.: Fiz. Tverd. Tela 5, 48 (1963)Google Scholar
  13. 13).
    Chen, T. S., et al.: J. Chem. Phys. 55, 3121 (1971)Google Scholar
  14. 14).
    Zadumkin, S. N. in: Surface phenomena in melts and in solid phases formed from them [Russian] S. N. Zadumkin (ed.), p. 12. Nal'chik 1965Google Scholar
  15. 15).
    Craig, R. A.: Phys. Rev. B 6, 1134 (1972)Google Scholar
  16. 16).
    Schmit, J., Lucas, A. A.: Solid State Comm. 11, 415 (1972)Google Scholar
  17. 17).
    Paasch, G.: Phys. Status Solidi 65, 221 (1974)Google Scholar
  18. 18).
    Goldiner, M. G., Malinovskii, T. I., Yagubets, A. N.: Isv. Akad. Nauk Mold. S.S.R., Ser. Fiz., Tekh., Math. Nauk 1973, 31; Chem. Abstr. 80, No. 18325Google Scholar
  19. 19).
    Heinrichs, J.: Solid State Comm. 13, 1599 (1973)Google Scholar
  20. 20).
    Lang, N. D., Kohn, W.: Phys. Rev. B 1, 4555 (1970)Google Scholar
  21. 21).
    Julg, A., et al.: Phys. Rev. B 9, 3248 (1974)Google Scholar
  22. 22).
    Hietschold, M., Paasch, G., Ziesche, P.: Phys. Status Solidi 70, 563 (1975)Google Scholar
  23. 23).
    Burton, J. J., Jura, G.: J. Phys. Chem. 71, 1937 (1967)CrossRefGoogle Scholar
  24. 24).
    Ferrante, J., Smith, J. R.: Solid State Comm. 20, 393 (1976)Google Scholar
  25. 25).
    Matsunaga, T., Tamai, Y.: Surface Sci. 57, 431 (1976)CrossRefGoogle Scholar
  26. 26).
    Stefan, J.: Wied. Ann. Physik 29, 655 (1886)Google Scholar
  27. 27).
    Shcherbakov, L. M., Baibakov, V. S. in: Surface phenomena in metallurgical processes A. I. Belyaev (ed.), p. 172. Consultants Bureau: New York 1965Google Scholar
  28. 28).
    Jones, H.: Metal Sci. J. 5, 15 (1971)Google Scholar
  29. 29).
    Fricke, R.: Kolloid-Z. 96, 211 (1941)CrossRefGoogle Scholar
  30. 30).
    Gvozdev, A. G., Gvozdeva, L. I.: Fiz. Metal. Metalloved. 31, 640 (1970)Google Scholar
  31. 31).
    Ogorodnikov, V. V., Rogovoi, Yu. I.: Porosh. Metall. 1976, No. 1, 70Google Scholar
  32. 32).
    Oshcherin, B. N.: Phys. Status Solidi 25, K 123 (1968); 31, K 135 (69); Phys. Chem. of Surface Phenomena at High Temperatures [Russian] V. N. Eremenko (ed.), p. 39. Kiev: Naukova Dumka 1971Google Scholar
  33. 33).
    Wawra, H. H.: Materialprüfung 14, 413 (1972)Google Scholar
  34. 34).
    Reynolds, C. L., Couchman, P. R., Karasz, F. E.: Phil. Mag. 34, 659 (1976)Google Scholar
  35. 35).
    Benedek, C., et al.: Surface Sci. 48, 561 (1975)CrossRefGoogle Scholar
  36. 36).
    Missol, W.: Phys. Status Solidi B 58, 767 (1973)Google Scholar
  37. 37).
    Kashetov, A., Gorbatyi, N. A.: Fiz. Tverd. Tela 11, 493 (1969)Google Scholar
  38. 38).
    Zadumkin, S. N., Shebzukhova, I. G., Al'chagirov, B. B.: Fiz. Metal, Metalloved. 30, 1313 (1970)Google Scholar
  39. 39).
    Vingsbo, O.: Mater. Sei. Eng. 8, 32 (1971)Google Scholar
  40. 40).
    Berggren, B.: Ann. Physik [4] 44, 61 (1914)Google Scholar
  41. 41).
    Khagabanov, A. Kh., Zadumkin, S. N., Bartenev, G. M. in: Phys. Chem. of surface phenomena at high temperatures [Russian] V. N. Eremenko (ed.), p. 68. Kiev: Naukova Dumka 1971Google Scholar
  42. 42).
    Maurakh, M. A., Orlov, A. S., Besshapova, M. R. in: Adhesion of melts [Russian] V. N. Eremenko, Yu. V. Naidich (eds.), p. 103. Kiev: Naukova Dumka 1974Google Scholar
  43. 43).
    Sawai, I., Ueda, Y.: Z. anorg. allg. Chem. 180, 287 (1929)CrossRefGoogle Scholar
  44. 44).
    Tammann, G., Boehme, W.: Ann. Physik [5] 12, 820 (1932)Google Scholar
  45. 45).
    Heumann, Th., Wulff, H.: Scripta Met. 10, 1001 (1976)CrossRefGoogle Scholar
  46. 46).
    Bikerman, J. J.: Phys. Status Solidi 10, 3 (1965)Google Scholar
  47. 47).
    Bikerman, J. J.: Mater. Sci. Eng. 20, 293 (1975)Google Scholar
  48. 48).
    Tammann, G.: Nachr. Göttinger Ges. Wiss. 1912, 557Google Scholar
  49. 49).
    Udin, H.: Metals Trans. 191, 63 (1951)Google Scholar
  50. 50).
    Inman, M. C., Tipler, H. R.: Metallurg. Revs. 8, 105 (1963)Google Scholar
  51. 51).
    Tyson, W. R.: Can. Metall. Quart. 14, 307 (1975)Google Scholar
  52. 52).
    Greenough, A. P.: Phil. Mag. [7] 43, 1075 (1952)Google Scholar
  53. 53).
    Pranatis, A. L., Pound, G. M.: Metals Trans. 203, 664 (1955)Google Scholar
  54. 54).
    Greenough, A. P.: Phil. Mag. [8] 3, 1032 (1958)Google Scholar
  55. 55).
    Lowe, A. C., Riddiford, A. C.: J. Colloid Interface Sci. 32, 292 (1970)CrossRefGoogle Scholar
  56. 56).
    Heumann, Th., Wulff, H.: Z. Metallkunde 67, 87 (1975)Google Scholar
  57. 57).
    Shebzukhova, I. G., Khokonov, Kh. B., Zadumkin, S. N.: Fiz. Metal. Metalloved. 33, 1112 (1972)Google Scholar
  58. 58).
    Heumann, Th., Johannisson, J.: Acta Met. 20, 617 (1972)CrossRefGoogle Scholar
  59. 59).
    Fiala, J., Čadek, J.: Phil. Mag. [8] 32, 251 (1975)Google Scholar
  60. 60).
    Hondros, E. D., Gladman, D.: Surface Sci. 9, 471 (1968)CrossRefGoogle Scholar
  61. 61).
    Roth, T. A.: Mater. Sci. Eng. 18, 183 (1975)Google Scholar
  62. 62).
    Bryant, L. F., Speiser, R., Hirth, J. P.: Trans. Met. Soc. AIME 242, 1145 (1968)Google Scholar
  63. 63).
    Kostikov, V. I., Kharitonov, A. V., Savenko, V. I.: Fiz. Metal. Metalloved 26, 947 (1968)Google Scholar
  64. 64).
    Allen, B. C.: Trans. Met. Soc. AIME 236, 903 (1966)Google Scholar
  65. 65).
    Kostikov, V. I., Kharitonov, A. V.: Fiz. Metal. Metalloved. 35, 188 (1973)Google Scholar
  66. 66).
    Hondros, E. D., McLean, D.: Phil. Mag. [8] 29, 771 (1974)Google Scholar
  67. 67).
    Stickle, D. R. et al.: Metall. Trans. A 7, 71 (1976)Google Scholar
  68. 68).
    Bauer, C. E., Speiser, R., Hirth, J. P.: Metall. Trans. A 7, 75 (1976)Google Scholar
  69. 69).
    Rice, C. M., Eppelsheimer, D. S., McNeil, M. B.: J. Appl. Phys. 37, 4766 (1966)CrossRefGoogle Scholar
  70. 70).
    Bruver, R. E., Glikman, E. E. in: Ref.41), p. 86Google Scholar
  71. 71).
    Udin, H.: Metal interfaces, p. 114. Cleveland: Am. Soc. Metals 1952Google Scholar
  72. 72).
    Wasserman, H. J., Vermaak, J. S.: Surface Sci. 32, 168 (1972)CrossRefGoogle Scholar
  73. 73).
    Smart, D. C., Boswell, F. W., Corbett, J. M.: J. Appl. Phys. 43, 4461 (1972)CrossRefGoogle Scholar
  74. 74).
    Barbour, J. P. et al.: Phys. Rev. 117, 1452 (1960)CrossRefGoogle Scholar
  75. 75).
    Dranova, Zh. I., Dyachenko, A. M., Mikhailovskii, I. M.: Fiz. Metal. Metalloved. 31, 1108 (1971)Google Scholar
  76. 76).
    Hoffman, J. D., Weeks, J. J.: J. Res. Natl. Bur. Stand. 66 A, 13 (1962)Google Scholar
  77. 77).
    Harrison, I. R.: J. Polym. Sci., Phys. Ed. 11, 991 (1973)Google Scholar
  78. 78).
    Zubov, Yu. A. et al.: Doklady Akad. Nauk SSSR 217, 1118 (1974)Google Scholar
  79. 79).
    Hinrichsen, G.: Polymer 10, 718 (1969)CrossRefGoogle Scholar
  80. 80).
    Martuscelli, E.: Makromol. Chem. 151, 159 (1972)CrossRefGoogle Scholar
  81. 81).
    Griffith, A.: Trans. Roy. Soc. A 221, 180 (1920)Google Scholar
  82. 82).
    Petch, H. in: Fracture H. Liebowitz (ed.). Vol. I, p. 353. New York: Academic Press 1968Google Scholar
  83. 83).
    Bikerman, J. J.: SPE Trans. 4, 290 (1964); Proc. 5th Intern. Congr. Rheology, Vol. I, p. 589. Tokyo 1969Google Scholar
  84. 84).
    Phillips, C. J. in: Fracture H. Liebowitz (ed.). Vol. VII, p. 28. New York: Academic Press 1972Google Scholar
  85. 85).
    Timoshenko, S., Goodier, J. N. in: Theory of elasticity, p. 90. New York: McGrow-Hill 1951Google Scholar
  86. 86).
    Shand, E. B.: J. Amer. Ceram. Soc. 44, 451 (1961)Google Scholar
  87. 87).
    Dobbs, H. S., Field, J. E., Maitland, A. H.: Phil. Mag. [8] 28, 33 (1973)Google Scholar
  88. 88).
    Davidge, R. W., Tappin, G.: J. Mater. Sci. 3, 165 (1968)Google Scholar
  89. 89).
    Irwin, G. R., Kies, J. A., Smith, H. L.: ASTM Proc. 58, 640 (1958)Google Scholar
  90. 90).
    Svensson, N. L.: Proc. Phys. Soc. 77, 876 (1961)CrossRefGoogle Scholar
  91. 91).
    Cordwell, J. E., Hull, D.: Phil. Mag. [8] 27, 1183 (1973)Google Scholar
  92. 92).
    Kusy, R. P., Turner, D. T.: Polymer 17, 161 (1976)CrossRefGoogle Scholar
  93. 93).
    Nelson, B. E.: J. Colloid Interface Sci. 47, 595 (1974)CrossRefGoogle Scholar
  94. 94).
    see, for instance, Bikerman, J. J.: Physical surfaces, p. 48. New York: Academic Press 1970Google Scholar
  95. 95).
    Govila, R. K.: Acta Met. 20, 447 (1972); Scripta. Met. 6, 353 (72)CrossRefGoogle Scholar
  96. 96).
    Gilman, J. J.: J. Appl. Phys. 31, 2208 (1960)Google Scholar
  97. 97).
    Obreimoff, J. W.: Proc. Roy. Soc. London A 127, 290 (1930)Google Scholar
  98. 98).
    Orowan, E.: Z. Phys. 82, 235 (1933)Google Scholar
  99. 99).
    Burns, S. J.: Phil. Mag. [8] 25, 131 (1972)Google Scholar
  100. 100).
    Elyutin, V. P., Kostikov, V. I., Kharitonov, A. V.: Doklady Akad. Nauk SSSR 182, 376 (1968)Google Scholar
  101. 101).
    Metsik, M. S.: J. Adhesion 3, 307 (1972)Google Scholar
  102. 102).
    Westwood, A. R. C., Hitch, T. T.: J. Appl. Phys. 34, 3085 (1963)Google Scholar
  103. 103).
    Wiederhorn, S. M.: J. Amer. Ceram. Soc. 52, 99 (1969)Google Scholar
  104. 104).
    Bikerman, J. J.: The science of adhesive joints, 2nd edit., p. 182. New York: Academic Press 1968Google Scholar
  105. 105).
    Kraatz, P., Zoltai, T.: J. Appl. Phys. 45, 4741 (1974)Google Scholar
  106. 106).
    Maitland, A. H., Chadwick, G. A.: Phil. Mag. [8] 19, 645 (1969)Google Scholar
  107. 107).
    Elyutin, V. P., Kostikov, V. I., Kharitonov, A. V. in: Ref.41) p. 263Google Scholar
  108. 108).
    Gupta, Y. P., Santhanam, A. T.: Acta Met. 17, 419 (1969)CrossRefGoogle Scholar
  109. 109).
    Irwin, G. R. in: Handbuch der Physik. S. Flügge (ed.), Vol. 6, p. 551 (1958)Google Scholar
  110. 110).
    Smith, C. S.: Amer. Inst. Mining Met. Engrs., Inst. Metals Div. 175, 15 (1948)Google Scholar
  111. 111).
    Hasson, G. et al. in: Grain boundaries and interfaces P. Chaudhuri, J. W. Mathews (eds.), p. 115. Amsterdam: North-Holland Publ. Co. 1972Google Scholar
  112. 112).
    Harris, L. B., Vernon, J. P.: J. Polymer Sci., Part A-2, 10, 499 (1972)Google Scholar
  113. 113).
    Greenough, A. P., King, R.: J. Inst. Metals 79, 415 (1951)Google Scholar
  114. 114).
    Powell, B. D., Woodruff, D. P.: Phil. Mag. 34, 169 (1976)Google Scholar
  115. 115).
    Rosenhain, W., Ewen, D.: J. Inst. Metals 8, 149 (1912)Google Scholar
  116. 116).
    Hodkin, E. N., Nicholas, M. G., Poole, D. M.: J. Nucl. Mater. 25, 284 (1968)CrossRefGoogle Scholar
  117. 117).
    Mullins, W. W.: Trans. AIME 218, 354 (1960)Google Scholar
  118. 118).
    Maiya, P. S.: J. Nucl. Mater. 40, 57 (1971)CrossRefGoogle Scholar
  119. 119).
    Maiya, P. S., Blakeley, J. M.: J. Appl. Phys. 38, 698 (1967)CrossRefGoogle Scholar
  120. 120).
    Presland, A. E. B., Price, G. L., Trimm, D. L.: Surface Sci. 29, 435 (1972)Google Scholar
  121. 121).
    Pokrovskii, N. L., Khefni, A. Kh. in: Adhesion of melts [Russian] Yu. V. Naidich (ed.), p. 102. Kiev 1974Google Scholar
  122. 122).
    Lilburne, M. T.: J. Mater. Sci. 5, 351 (1970)Google Scholar
  123. 123).
    Barnes, B. S.: Phil. Mag. [8] 5, 635 (1960)Google Scholar
  124. 124).
    Bikerman, J. J.: J. Mater. Sci. 6, 176 (1971)CrossRefGoogle Scholar
  125. 125).
    Westmacott, K. H., Smallman, R. E., Dobson, P. S.: Metal Sci. J. 2, 177 (1968)Google Scholar
  126. 126).
    Haubelt, R., Mennicke, S., Dittmar, W.: Z. physik. Chem. 95, 187 (1975)Google Scholar
  127. 127).
    Gladkikh, N. T., Larin, V. I., Khotkevich, V. I.: Fiz. Metal. Metalloved. 31, 786 (1971)Google Scholar
  128. 128).
    Bolling, G. F., Tiller, W. A.: J. Appl. Phys. 31, 1345 (1960)Google Scholar
  129. 129).
    Jones, D. R. H., Chadwick, G. A.: Phil. Mag. [8] 22, 291 (1970)Google Scholar
  130. 130).
    Nash, G. E., Glicksman, M. E.: Phil. Mag. [8] 24, 577 (1971)Google Scholar
  131. 131).
    Hardy, S. C.: Phil. Mag. 35, 471 (1977)Google Scholar
  132. 132).
    Schaefer, R. J., Glicksman, M. E., Ayers, J. D.: Phil. Mag. [8] 32, 725 (1975)Google Scholar
  133. 133).
    Sambles, J. R., Skinner, L. M., Lisgarten, N. D.: Proc. Roy. Soc. London 318 A, 507 (1970)Google Scholar
  134. 134).
    Freundlich, H.: Kapillarchemie. Vol. I, p. 218. Leipzig: Akad. Verlagsges. 1930Google Scholar
  135. 135).
    Cohen, E., Blekkingh, J. J. A.: Proc. Kon. Nederland Akad. Wetenschappen 43, 32, 189, 334 (1940)Google Scholar
  136. 136).
    Balarew, D.: Kolloid-Z. 96, 19 (1941)Google Scholar
  137. 137).
    Glazner, A.: Israel J. Chem. 13, 73 (1975)Google Scholar
  138. 138).
    Bikerman, J. J.: Ref.94, pp. 192Google Scholar
  139. 139).
    Alexander, G. B.: J. Phys. Chem. 61, 1563 (1957)Google Scholar
  140. 140).
    Rosoff, M., Schulman, J. H.: Kolloid-Z. Z. Polym. 225, 46 (1968)Google Scholar
  141. 141).
    Kislyi, P. S., Kuzenkova, M. A.: Porosh. Metal. 1969, No. 11, 21Google Scholar
  142. 142).
    Bikerman, J. J.: Proc. 2nd Intern. Congr. Surface Activity, Vol. 3, 125. New York: Academic Press 1957; J. Phys. Chem. 63, 1658 (1959)Google Scholar
  143. 143).
    Bikerman, J. J.: Contributions to the thermodynamics of surfaces, p. 65. Cambridge 1961Google Scholar
  144. 144).
    Khlynov, V. V., Bokser, E. L., Esin, O. A.: Doklady Akad. Nauk SSSR 208, 820 (1973)Google Scholar
  145. 145).
    Khlynov, V. V., Bokser, E. L., Pastukhov, B. A. in: Adhesion of melts and joining of materials [Russian] Yu. Naidich (ed.), p. 39. Kiev: Naukova Dumka 1976Google Scholar
  146. 146).
    Bruver, R. E., Glickman, Ye. F., Tsarev, O. K.: Fiz. Metal. Metalloved. 26, 1136 (1968)Google Scholar
  147. 147).
    Rhee, S. K.: Mater. Sci. Eng. 11, 311 (1973); J. Colloid Interface Sci. 44, 173 (1973)Google Scholar
  148. 148).
    Rhee, S. K.: J. Mater. Sci. 12, 823 (1977)CrossRefGoogle Scholar
  149. 149).
    Bakovets, V. V.: Doklady Akad. Nauk SSSR 228, 1132 (1976)Google Scholar
  150. 150).
    Ketcham, W. M., Hobbs, P. V.: Phil. Mag. [8] 19, 1161 (1969)Google Scholar
  151. 151).
    Bikerman, J. J.: Microscope 21, 183 (1973)Google Scholar
  152. 152).
    Bratton, R. J., Beck, C. W.: J. Amer. Ceram. Soc. 54, 379 (1971)Google Scholar
  153. 153).
    Mortimer, D. A., Nicholas, M. G.: Metal Sci. 10, 326 (1976)Google Scholar
  154. 154).
    Hodkin, E. N. et al.: J. Nuclear Mater. 39, 59 (1971)CrossRefGoogle Scholar
  155. 155).
    Hodkin, E. N., Nicholas, M. G.: J. Nuclear Mater. 47, 23 (1973)CrossRefGoogle Scholar
  156. 156).
    Briant, C. L., Burton, J. J.: J. Chem. Phys. 63, 2045 (1975)Google Scholar
  157. 157).
    Lewis, B.: J. Appl. Phys. 41, 30 (1970)Google Scholar
  158. 158).
    Turnbull, D.: J. Chem. Phys. 18, 769 (1950)Google Scholar
  159. 159).
    Schaefer, V. J.: Ind. Eng. Chem. 44, 1300 (1952)Google Scholar
  160. 160).
    Mason, B. J.: The physics of clouds, p. 168. Oxford Clarendon Press 1971Google Scholar
  161. 161).
    Turnbull, D.: J. Chem. Phys. 18, 768 (1950)Google Scholar
  162. 162).
    Gokhstein, A. Ya.: Surface tension of solids and adsorption. [Russian] Moscow: Nauka 1976Google Scholar
  163. 163).
    Shchukin, E. D., Smirnova, N. V.: Fiz.-khim. mekh. materials 3, No. 1, 90 (1967); Chem. Abstr. 67, No. 76898 (1967)Google Scholar
  164. 164).
    Shuttleworth, R.: Proc. Phys. Soc. London 63 A, 444 (1950)Google Scholar
  165. 165).
    Lipsett, S. G., Johnson, F. M. G., Maass, O.: J. Amer. Chem. Soc. 49, 925 (1927)Google Scholar
  166. 166).
    Lipsett, S. G., Johnson, F. M. G., Maass, O.: J. Amer. Chem. Soc. 49, 1940 (1927)Google Scholar
  167. 167).
    Lipsett, S. G., Johnson, F. M. G., Maass, O.: J. Amer. Chem. Soc. 50, 2701 (1928)Google Scholar
  168. 168).
    Fricke, R., Schnabel, R., Beck, K.: Z. Elektrochem. 42, 114 (1936)Google Scholar
  169. 169).
    Fricke, R., Zerrweck, W.: Z. Elektrochem. 43, 52 (1937)Google Scholar
  170. 170).
    Fricke, R., Blaschke, F.: Z. Elektrochem. 46, 46 (1940)Google Scholar
  171. 171).
    Fricke, R., Niermann, F., Feichtner, C.: Ber. deut. chem. Ges. 70, 2318 (1937)Google Scholar
  172. 172).
    Fricke, R., Meyer, F. R.: Z. phys. Chem. A 181, 409 (1938)Google Scholar
  173. 173).
    Jura, G., Garland, C. W.: J. Amer. Chem. Soc. 74, 6033 (1952)Google Scholar
  174. 174).
    Schubert-Birckenstaedt, M.: Z. anorg. allg. Chem. 276, 227 (1954)CrossRefGoogle Scholar
  175. 175).
    Jones, E. D., Burgess, D. S., Amis, E. S.: Z. phys. Chem. (Frankfurt) 4, 220 (1955)Google Scholar
  176. 176).
    Benson, G. C., Schreiber, H. P., van Zeggeren, F.: Can J. Chem. 34, 1553 (1956)Google Scholar
  177. 177).
    Benson, G. C., Benson, G. W.: Can, J. Chem. 33, 232 (1955)Google Scholar
  178. 178).
    Brunauer, S., Kantro, D. L., Weise, C. H.: Can, J. Chem. 34, 729 (1956)Google Scholar
  179. 179).
    Brunauer, S., Kantro, D. L., Weise, C. H.: Can. J. Chem. 34, 1483 (1956)Google Scholar
  180. 180).
    Brunauer, S., Kantro, D. L., Weise, C. H.: Can. J. Chem. 37, 714 (1959)Google Scholar
  181. 181).
    Kantro, D. L., Brunauer, S., Weise, C. H.: J. Colloid Sci. 14, 363 (1959)CrossRefGoogle Scholar
  182. 182).
    Brunauer, S.: J. Colloid Interface Sci. 59, 433 (1977)CrossRefGoogle Scholar
  183. 183).
    Livey, D. T. et al.: Trans. Brit. Ceram. Soc. 56, 217 (1957)Google Scholar
  184. 184).
    Antolini, R., Gravelle, P. C., Trambouze, Y.: J. Chim. Phys. 59, 715 (1962)Google Scholar
  185. 185).
    Ferrier, A.: Compt. rend. Acad. sci. Paris 261, 410 (1965)Google Scholar
  186. 186).
    Motooka, I., Hashizume, K., Kobayashi, M.: J. Phys. Chem. 73, 3012 (1969)CrossRefGoogle Scholar
  187. 187).
    Mahr, T. G.: J. Phys. Chem. 74, 2160 (1970)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Jacob J. Bikerman
    • 1
  1. 1.Dept. of Chemical EngineeringCase Western Reserve UniversityClevelandUSA

Personalised recommendations