Journal of Materials Science

, Volume 51, Issue 1, pp 382–404 | Cite as

Review: grain boundary faceting–roughening phenomena

  • B. B. Straumal
  • O. A. Kogtenkova
  • A. S. Gornakova
  • V. G. Sursaeva
  • B. Baretzky
50th Anniversary


Similar to free surfaces, the grain boundaries (GBs) in metals, semiconductors and insulators can contain flat (faceted) and curved (rough) portions. In the majority of cases, facets are parallel to the most densely packed planes of coincidence sites lattice formed by two lattices of abutting grains. Facets disappear with the increasing temperature (faceting–roughening transition) and the increasing angular distance from coincidence misorientation. The temperature of GB faceting–roughening transition T R decreases with the increasing inverse density of coincidence sites Σ. In case of fixed Σ, T R decreases with the decreasing density of coincidence sites in the GB plane. The intersection line (ridge) between facets or between facets and curved (rough) portions of surfaces can be of first order (two different tangents in the contact point) or of second order (common tangent, continuous transitions). The rough (curved) portions of GB can also form the first-order rough-to-rough ridges (with two tangents). GB facets control the transition from normal to abnormal grain growth and strongly influence the GB migration, diffusion, wetting, fracture and electrical conductivity.



The authors thank the Russian Foundation for Basic Research (Contracts 14-03-31510 and 14-08-00972), the Russian Federal Ministry for Education and Science (Grants 14.A12.31.0001 and Increase Competitiveness Program of NUST «MISiS» К2-2014-013) and the Polish National Science Centre (Grant OPUS UMO-2014/13/B/ST8/04247) for the financial support.

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


  1. 1.
    Gibbs JW (1878) On the equilibrium of heterogeneous substances. Trans Conn Acad 3:343Google Scholar
  2. 2.
    Gibbs JW (1928) On the equilibrium of heterogeneous substances, vol 3. Longmans, Green & Co., New YorkGoogle Scholar
  3. 3.
    Curie P (1885) Sur la formation des crystaux et sur les constants capillaire des leur faces differentes. Bull Soc Min France 8:145Google Scholar
  4. 4.
    Wulff GV (1895, 1896) About rates of growth and dissolution of crystals, Izvestia Warszaw Univ No. 7–9 and 1,2:1 (in Russian)Google Scholar
  5. 5.
    Wulff G (1901) Zur Frage der Geschwindigkeit des Wachstums und der Auflösung von Krystallflächen. Z Kristallogr 34:449Google Scholar
  6. 6.
    Herring C (1952) The use of classical macroscopic concepts in surface energy problems. In: Gomer R, Smith CS (eds) Structure and properties of solid surfaces. University of Chicago Press, Chicago, p 5Google Scholar
  7. 7.
    Landau LD, Lifshitz EM (1958) Statistical physics, vol V. Addison-Wesley, ReadingGoogle Scholar
  8. 8.
    Bonzel HP (2003) 3D equilibrium crystal shapes in the new light of STM and AFM. Phys Rep 385:1CrossRefGoogle Scholar
  9. 9.
    Davidson D, den Nijs M (1999) Temperature dependence of facet ridges in crystal surfaces. Phys Rev E 59:5029CrossRefGoogle Scholar
  10. 10.
    Davidson D, den Nijs M (2000) Facet ridge end points in crystal shapes. Phys Rev Lett 84:326CrossRefGoogle Scholar
  11. 11.
    Taylor JE, Cahn JW, Handwerker CA (1992) Geometric models of crystal growth. Acta Metall Mater 40:1443CrossRefGoogle Scholar
  12. 12.
    Cahn JW, Carter WC (1996) Crystal shapes and phase equilibria: a common mathematical basis. Metall Mater Trans A 27:1431CrossRefGoogle Scholar
  13. 13.
    Curiotto S, Chien H, Meltzman H, Labat S, Wynblatt P, Rohrer GS, Kaplan WD, Chatain D (2013) Copper crystals on the (1,1,-2,0) sapphire plane: orientation relationships, triple line ridges and interface shape equilibrium. J Mater Sci 48:3013. doi: 10.1007/s10853-012-7080-0 CrossRefGoogle Scholar
  14. 14.
    Klinger L, Rabkin E (2001) Effects of surface anisotropy on grain boundary grooving. Interface Sci 9:55CrossRefGoogle Scholar
  15. 15.
    Saylor DM, Rohrer GS (2001) Evaluating anisotropic surface energies using the capillarity vector reconstruction method. Interface Sci 9:35CrossRefGoogle Scholar
  16. 16.
    Kossel W (1927) Zur Theorie des Kristallwachstums. Nachr Ges Wissensch Göttingen 1:135Google Scholar
  17. 17.
    Stranski IN (1928) Zur Theorie des Kristallwachstums. Z Phys Chem 136:259Google Scholar
  18. 18.
    Burton WK, Cabrera N, Frank FC (1951) The growth of crystals and the equilibrium structure of their surfaces. Trans Roy Soc London A 243:299CrossRefGoogle Scholar
  19. 19.
    Gruber EF, Mullins WW (1967) On the theory of anisotropy of crystalline surface tension. J Phys Chem Solids 28:875CrossRefGoogle Scholar
  20. 20.
    Jayaprakash C, Saam WF (1984) Thermal evolution of crystal shapes—the fcc crystal. Phys Rev B 30:3916CrossRefGoogle Scholar
  21. 21.
    Rottman C, Wortis M, Heyraud JC, Métois JJ (1984) Equilibrium shapes of small lead crystals—observation of Pokrovsky-Talapov critical behaviour. Phys Rev Lett 52:1009CrossRefGoogle Scholar
  22. 22.
    Rottman C, Wortis M (1984) Equilibrium shapes for lattice models with nearest-neighbor and next-nearest-neighbor interactions. Phys Rev B 29:328CrossRefGoogle Scholar
  23. 23.
    Holzer M, Wortis M (1989) Low-temperature expansions for the step free energy and facet shape of the simple cubic Ising model. Phys Rev B 40:11044CrossRefGoogle Scholar
  24. 24.
    Fisher DS, Weeks JD (1983) Shape of crystals at low temperatures—absence of quantum roughening. Phys Rev Lett 50:1077CrossRefGoogle Scholar
  25. 25.
    Nozieres P, Gallet F (1987) The roughening transition of crystal surfaces. 1. Static and dynamic renormalization theory, crystal shape and facet growth. J Phys (Paris) 48:353CrossRefGoogle Scholar
  26. 26.
    Berezinskii VL (1971) Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group. 1. Classical systems. Sov Phys JETP 32:493Google Scholar
  27. 27.
    Berezinskii VL (1972) Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group. 1. Quantum systems. Sov Phys JETP 34:610Google Scholar
  28. 28.
    Kosterlitz JM, Thouless DJ (1973) Ordering, metastability and phase transitions in two-dimensional systems. J Phys C 6:1181CrossRefGoogle Scholar
  29. 29.
    Grimmer H, Bollmann W, Warrington DT (1974) Disorientations and coincidence rotations for cubic lattices. Acta Cryst A 30:197CrossRefGoogle Scholar
  30. 30.
    Brandon DG (1966) The structure of high-angle grain boundaries. Acta Metall 14:1479CrossRefGoogle Scholar
  31. 31.
    Hirth JP, Balluffi RW (1973) On grain boundary dislocations and ledges. Acta Metall 21:929CrossRefGoogle Scholar
  32. 32.
    Kronberg ML, Wilson FH (1949) Secondary recrystallization in copper. Trans AIME 185:501Google Scholar
  33. 33.
    Wagner WR, Tan TY, Balluffi RW (1974) Faceting of high-angle grain boundaries in the coincidence lattice. Philos Mag 29:895CrossRefGoogle Scholar
  34. 34.
    Tan TY, Sass SL, Balluffi RW (1975) The detection of the periodic structure of high angle twist boundaries. II. High resolution electron microscopy study. Philos Mag 31:575CrossRefGoogle Scholar
  35. 35.
    Bollmann W (1970) Crystal defects and crystalline interfaces. Springer, New YorkCrossRefGoogle Scholar
  36. 36.
    Brandon DG, Ralph B, Ranganathan S, Wald MS (1964) A field ion microscope study of atomic configuration at grain boundaries. Acta Metall 12:813CrossRefGoogle Scholar
  37. 37.
    Wolf D (1985) On the relationship between symmetrical tilt, twist, “special”, and “favoured” grain boundaries. J Phys Paris 46:C4–C197CrossRefGoogle Scholar
  38. 38.
    Fecht HJ, Gleiter H (1985) A lock-in model for the atomic structure of interphase boundaries between metals and ionic crystals. Acta Metall 33:557CrossRefGoogle Scholar
  39. 39.
    Sutton AP, Balluffi RW (1987) On geometric criteria for low interfacial energy. Acta Metall 35:2177CrossRefGoogle Scholar
  40. 40.
    Goodhew PJ, Tan TY, Balluffi RW (1978) Low energy planes for tilt boundaries in gold. Acta Metall 26:557CrossRefGoogle Scholar
  41. 41.
    Chaudhari P, Matthews JW (1971) Coincidence twist boundaries between crystalline smoke particles. J Appl Phys 42:3063CrossRefGoogle Scholar
  42. 42.
    Olmsted DL, Foiles SM, Holm EA (2009) Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Mater 57:3694CrossRefGoogle Scholar
  43. 43.
    Rohrer GS (2011) Grain boundary energy anisotropy: a review. J Mater Sci 46:5881. doi: 10.1007/s10853-011-5677-3 CrossRefGoogle Scholar
  44. 44.
    Ratanaphan S, Olmsted DL, Bulatov VV, Holm EA, Rollett AD, Rohrer GS (2015) Grain boundary energies in body-centered cubic metals. Acta Mater 88:346CrossRefGoogle Scholar
  45. 45.
    Vitek V, Sutton AP, Smith DA, Pond RC (1980) The dislocation structure of high angle grain boundaries. In: Balluffi RW (ed) Grain boundary structure and kinetics. American Society for Metals, Metals Park, pp 115–148Google Scholar
  46. 46.
    Ernst F, Finnis MW, Koch A, Schmidt C, Straumal B, Gust W (1996) Structure and energy of twin boundaries in copper. Z Metallk 87:911Google Scholar
  47. 47.
    Wolf U, Ernst F, Muschik T, Finnis MW, Fischmeister HF (1992) The influence of grain boundary inclination on the structure and energy of Σ3 grain boundaries in copper. Philos Mag A 66:991CrossRefGoogle Scholar
  48. 48.
    Ernst F, Finnis MW, Hoffmann D, Muschik T, Schönberger U, Wolf U (1992) Theoretical prediction and direct observation of the 9R structure in Ag. Phys Rev Lett 69:620CrossRefGoogle Scholar
  49. 49.
    Hofmann D, Finnis MW (1994) Theoretical and experimental analysis of near Σ3 (211) boundaries in silver. Acta Metall Mater 42:3555CrossRefGoogle Scholar
  50. 50.
    Maksimova EL, Shvindlerman LS, Straumal BB (1988) Transformation of Σ17 special tilt boundaries to general boundaries in tin. Acta Metall 36:1573CrossRefGoogle Scholar
  51. 51.
    Straumal BB, Shvindlerman LS (1985) Regions of existence of special and non-special grain boundaries. Acta Metall 33:1735CrossRefGoogle Scholar
  52. 52.
    Aleshin AN, Prokofjev SI, Shvindlerman LS (1985) Evidence of structure transformation in Σ = 5 near coincidence grain boundaries. Scr Metall 19:1135CrossRefGoogle Scholar
  53. 53.
    Hsieh TE, Balluffi RW (1989) Observations of roughening/de-faceting phase transitions in grain boundaries. Acta Metall 37:2133CrossRefGoogle Scholar
  54. 54.
    Kim MJ, Cho YK, Yoon DY (2004) Facet-defacet transition of grain boundaries in alumina. J Am Ceram Soc 87:455CrossRefGoogle Scholar
  55. 55.
    Rottman C, Wortis M (1981) Exact equilibrium crystal shapes at non-zero temperatures in 2 dimensions. Phys Rev B 24:6274CrossRefGoogle Scholar
  56. 56.
    Bonzel HP (2001) Surface morphologies: transient and equilibrium shapes. Interface Sci 9:21CrossRefGoogle Scholar
  57. 57.
    Keshishev KO, Parshin AY, Babkin AV (1981) Crystallization waves in He4. Sov Phys JETP 53:362Google Scholar
  58. 58.
    Blendell JE, Carter WC, Handwerker CA (1999) Faceting and wetting transition of anisotropic interfaces and grain boundaries. J Am Ceram Soc 82:1889CrossRefGoogle Scholar
  59. 59.
    Schuh CA, Kumar M, King E (2005) Universal features of grain boundary networks in FCC materials. J Mater Sci 40:847. doi: 10.1007/s10853-005-6500-9 CrossRefGoogle Scholar
  60. 60.
    Jin Y, Lin B, Rollett AD, Rohrer GS, Bernacki M, Bozzolo N (2015) Thermo-mechanical factors influencing annealing twin development in nickel during recrystallization. J Mater Sci 50:5191. doi: 10.1007/s10853-015-9067-0 CrossRefGoogle Scholar
  61. 61.
    Randle V, Rohrer GS, Miller HM, Coleman M, Owen GT (2008) Five-parameter grain boundary distribution of commercially grain boundary engineered nickel and copper. Acta Mater 56:2363CrossRefGoogle Scholar
  62. 62.
    Beladi H, Rohrer GS (2013) The relative grain boundary area and energy distributions in a ferritic steel determined from threedimensional electron backscatter diffraction maps. Acta Mater 61:1404CrossRefGoogle Scholar
  63. 63.
    Beladi H, Rohrer G (2013) The distribution of grain boundary planes in interstitial free steel. Metall Mater Trans A 44:115CrossRefGoogle Scholar
  64. 64.
    Glowinski K, Morawiec A (2014) Twist, tilt, and symmetric grain boundaries in hexagonal materials. J Mater Sci 49:3936. doi: 10.1007/s10853-013-7958-5 CrossRefGoogle Scholar
  65. 65.
    Ratanaphan S, Yoon Y, Rohrer GS (2014) The five parameter grain boundary character distribution of polycrystalline silicon. J Mater Sci 49:4938. doi: 10.1007/s10853-014-8195-2 CrossRefGoogle Scholar
  66. 66.
    Straumal BB, Polyakov SA, Bischoff E, Gust W, Mittemeijer EJ (2001) Faceting of Σ3 and Σ9 grain boundaries in copper. Interface Sci 9:287CrossRefGoogle Scholar
  67. 67.
    Straumal BB, Polyakov SA, Mittemeijer EJ (2006) Temperature influence on the faceting of Σ3 and Σ9 grain boundaries in Cu. Acta Mater 54:167CrossRefGoogle Scholar
  68. 68.
    Brown JA, Mishin Y (2007) Dissociation and faceting of asymmetrical tilt grain boundaries: molecular dynamics simulations of copper. Phys Rev B 13:134118CrossRefGoogle Scholar
  69. 69.
    Heyraud JC, Metois JJ (1980) Equilibrium shape of gold crystallites on a graphite cleavage surface—surface energies and interfacial energy. Acta Metall 28:1789CrossRefGoogle Scholar
  70. 70.
    Heyraud JC, Metois JJ (1980) Establishment of the equilibrium shape of metal crystallites on a foreign substrate—gold on graphite. J Cryst Growth 50:571CrossRefGoogle Scholar
  71. 71.
    Heyraud JC, Metois JJ (1983) Equilibrium shape and temperature—lead on graphite. Surf Sci 128:334CrossRefGoogle Scholar
  72. 72.
    Rybin VV, Perevesentsev VN (1975) General theory of grain boundary shifts. Sov Phys Solid State 17:2103Google Scholar
  73. 73.
    Gallagher PCJ (1970) The influence of alloying, temperature, and related effects on the stacking fault energy. Metall Trans 1:2429Google Scholar
  74. 74.
    Murr E (1975) Interfacial phenomena in metals and alloys. Addison Wesley, BostonGoogle Scholar
  75. 75.
    YaV Kucherinenko, Protasova SG, Straumal BB (2005) Faceting of Σ3 grain boundaries in Cu: three-dimensional Wulff diagrams. Defect Diffus Forum 237:584Google Scholar
  76. 76.
    Straumal BB, Semenov VN, Khruzhcheva AS, Watanabe T (2005) Faceting of the Σ3 coincidence tilt boundary in Nb. J Mater Sci 40:871. doi: 10.1007/s10853-005-6503-6 CrossRefGoogle Scholar
  77. 77.
    Lojkowski W, Sodervall U, Mayer S (1998) The effect of pressure on indium diffusion along <001> tilt grain boundaries in copper bicrystals. Interface Sci 6:187CrossRefGoogle Scholar
  78. 78.
    Chang L-S, Rabkin E, Straumal BB, Hoffmann S, Baretzky B, Gust W (1998) Grain boundary segregation in the Cu–Bi system. Diffus Forum 156:135CrossRefGoogle Scholar
  79. 79.
    Straumal BB, Polyakov SA, Bischoff E, Mittemeijer E, Gust W (2003) Grain boundary faceting phase transition and thermal grooving in Cu. Defect Diffuse Forum 216:93CrossRefGoogle Scholar
  80. 80.
    Straumal BB, Polyakov SA, Chang L-S, Mittemeijer EJ (2007) The effect of bismuth segregation on the faceting of Σ3 and Σ9 coincidence boundaries in copper bicrystals. Int J Mater Res (Zt Metallkd) 98:451CrossRefGoogle Scholar
  81. 81.
    Goukon N, Yamada T, Kajihara M (2000) Boundary energies of Sigma 11 [110] asymmetric tilt boundaries in Cu determined from the shape of boundary silica particles. Acta Mater 48:2837CrossRefGoogle Scholar
  82. 82.
    Gokon N, Kajihara A (2008) Fracture behavior of Sigma 9 [110] asymmetric tilt boundaries in Cu doped with Bi. Mater Sci Eng A 477:121CrossRefGoogle Scholar
  83. 83.
    Kuhn H, Bäro G, Gleiter H (1979) Energy-misorientation relationship of grain-boundaries. Acta Metall 27:959CrossRefGoogle Scholar
  84. 84.
    Straumal BB, Baretzky B, Kogtenkova OA, Gornakova AS, Sursaeva VG (2012) Faceting-roughening of twin grain boundaries. J Mater Sci 47:1641. doi: 10.1007/s10853-011-5807-y CrossRefGoogle Scholar
  85. 85.
    Straumal BB, Protsenko PV, Straumal AB, Rodin AO, Kucheev YuO, Gusak AM, Murashov VA (2012) Contribution of tilt boundaries to the total energy spectrum of grain boundaries in polycrystals. JETP Lett 96:582CrossRefGoogle Scholar
  86. 86.
    Gornakova AS, Straumal BB, Tsurekawa S, Chang L-S, Nekrasov AN (2009) Grain boundary wetting phase transformations in the Zn–Sn and Zn–In systems. Rev Adv Mater Sci 21:18Google Scholar
  87. 87.
    Haynes WM (2015) Handbook of chemistry and physics, 86th edn. CRC press (Taylor & Francis Group), Boca RatonGoogle Scholar
  88. 88.
    Carter CB, Ray ILF (1977) On the stacking-fault energies of copper alloys. Philos Mag 35:189CrossRefGoogle Scholar
  89. 89.
    Barg AI, Rabkin E, Gust W (1995) Faceting transformation and energy of a Σ3 grain boundary in silver. Acta Metall Mater 43:4067CrossRefGoogle Scholar
  90. 90.
    Cai J, Wang F, Lu C, Wang YY (2004) Structure and stacking-fault energy in metals Al, Pd, Pt, Ir, and Rh. Phys Rev B 69:224104CrossRefGoogle Scholar
  91. 91.
    Dingley DJ, Pond RC (1979) On the interaction of crystal dislocations with grain boundaries. Acta Metall 27:667CrossRefGoogle Scholar
  92. 92.
    Kogtenkova O, Straumal B, Protasova S, Tsurekawa S, Watanabe T (2005) The influence of misorientation deviation on the faceting of Σ3 grain boundaries in aluminium. Zt Metallkd 96:216CrossRefGoogle Scholar
  93. 93.
    Protasova SG, Kogtenkova OA, Straumal BB (2007) Faceting of individual Σ3 grain boundaries in Al. Mater Sci Forum 558:949CrossRefGoogle Scholar
  94. 94.
    Kogtenkova OA, Straumal BB, Protasova SG, Zięba P (2005) The temperature influence on the faceting of Σ3 grain boundaries in aluminium. Defect Diffus Forum 237:603CrossRefGoogle Scholar
  95. 95.
    Pegel B (1968) Stacking faults on 110 planes in the bcc lattice. Phys Status Solidi 28:603CrossRefGoogle Scholar
  96. 96.
    Tsurekawa S, Tanaka T, Yoshinaga H (1994) Grain-boundary structure, energy and strength in molybdenum. Mater Sci Eng A 176:341CrossRefGoogle Scholar
  97. 97.
    Dunn CG, Daniels FW, Bolton MJ (1950) Measurement of relative interface energies in twin related crystals. J Met 2:368Google Scholar
  98. 98.
    Dunn CG, Lionetti F (1949) The effect of orientation difference on grain boundary energies. Trans AIMME 185:125Google Scholar
  99. 99.
    Semenov VN, Straumal BB, Glebovsky VG, Gust W (1995) Preparation of Fe-Si single crystals and bicrystal for diffusion experiments by the electron-beam floating zone technique. J Cryst Growth 151:180CrossRefGoogle Scholar
  100. 100.
    Rybin VV, Titovets YuF, Teplitsky DM, Zolotorevsky NYu (1982) Statistics of grain misorienations in molybdenum. Fiz Metall Metalloved 53:544 (in Russian) Google Scholar
  101. 101.
    Straumal BB, Semenov VN, Kogtenkova OA, Watanabe T (2004) Pokrovsky-Talapov critical behavior and rough-to-rough ridges of the Σ3 coincidence tilt boundary in Mo. Phys Rev Lett 92:196101CrossRefGoogle Scholar
  102. 102.
    Wynblatt P, Chatain D (2009) Surface segregation anisotropy and equilibrium shape of alloy crystals. Rev Adv Mater Sci 21:44Google Scholar
  103. 103.
    Chatain D, Ghetta V, Wynblatt P (2004) Equilibrium shape of copper crystals grown on sapphire. Interface Sci 12:7CrossRefGoogle Scholar
  104. 104.
    Shibata N, Yamamoto T, Ikuhara Y, Sakuma T (2001) Structure of [110] tilt grain boundaries in zirconia bicrystals. J Electron Microsc 50:429CrossRefGoogle Scholar
  105. 105.
    Shin K, King AH (1991) Observation of grain boundary structure in zinc. Philos Mag A 63:1023CrossRefGoogle Scholar
  106. 106.
    Chen F-R, King AH (1987) The further geometry of grain boundaries in hexagonal close-packed metals. Acta Crystallogr B 43:416CrossRefGoogle Scholar
  107. 107.
    Tietz LA, Carter CB (1991) Special grain boundaries in YBa2Cu3O7–x thin films. Phys C 182:241CrossRefGoogle Scholar
  108. 108.
    Barrett CD, El Kadiri H (2014) The roles of grain boundary dislocations and disclinations in the nucleation of {1,0,-1,2} twinning. Acta Mater 63:1CrossRefGoogle Scholar
  109. 109.
    Bishop GH, Hartt WH, Bruggeman G (1971) Grain boundary faceting of (1,0,-1,0) tilt boundaries in zinc. Acta Metall 19:37CrossRefGoogle Scholar
  110. 110.
    Hartt WH, Bishop GH, Bruggeman G (1974) Grain boundary faceting of (1,0,-1,0) tilt boundaries in zinc. 2. Acta Metall 23:971CrossRefGoogle Scholar
  111. 111.
    Hartt WH, Bishop GH, Bruggeman G (1968) Grain boundary faceting of [1010] tilt boundaries in zinc. J Met 20:A71Google Scholar
  112. 112.
    Straumal BB, Rabkin E, Sursaeva VG, Gornakova AS (2005) Faceting and migration of twin grain boundaries in zinc. Zt Metallkd 96:161CrossRefGoogle Scholar
  113. 113.
    Straumal B, Sursaeva V, Baretzky B (2010) Grain boundary ridges and triple lines. Scr Mater 62:924CrossRefGoogle Scholar
  114. 114.
    Straumal BB, Gornakova AS, Sursaeva VG (2008) Reversible transformation of a grain boundary facet into a rough-to-rough ridge in Zn. Philos Mag Lett 88:27CrossRefGoogle Scholar
  115. 115.
    Bruggeman GA, Bishop GH, Hartt WH (1972) Coincidence and near-coincidence grain boundaries in hcp metals. In: Hu H (ed) The nature and behaviour of grain boundaries. Plenum, New York, pp 63–122Google Scholar
  116. 116.
    Sursaeva V, Gornakova A, Muktepavela F (2014) Grain boundary ridges slow down grain boundary motion: in-situ observation. Mater Lett 124:24CrossRefGoogle Scholar
  117. 117.
    Hoffman DW, Cahn JW (1972) A vector thermodynamics for anisotropic surfaces. I. Fundamentals and applications to plane surface junctions. Surf Sci 31:368CrossRefGoogle Scholar
  118. 118.
    Cahn JW, Hoffman DW (1974) A vector thermodynamics for anisotropic surfaces: II. Curved and faceted surfaces. Acta Metall 22:1205CrossRefGoogle Scholar
  119. 119.
    Wolf PE, Balibar S, Gallet F (1983) Experimental observation of a 3rd roughening transition on hcp He4 crystals. Phys Rev Lett 51:1366CrossRefGoogle Scholar
  120. 120.
    Wagner R, Steel SC, Andreeva OA, Jochemsen R, Frossati G (1996) First observation of (100) and (211) facets on He-3 crystals. Phys Rev Lett 76:263CrossRefGoogle Scholar
  121. 121.
    Andreev AF (1981) Faceting phase transition of crystals. Sov Phys JETP 53:1063Google Scholar
  122. 122.
    Pokrovsky VL, Talapov AL (1979) Ground state, spectrum, and phase diagram of two-dimensional incommensurate crystals. Phys Rev Lett 42:65CrossRefGoogle Scholar
  123. 123.
    Arenhold K, Surnev S, Coenen P, Bonzel HP, Wynblatt P (1998) Scanning tunneling microscopy of equilibrium crystal shape of Pb particles: test of universality. Surf Sci 417:L1160CrossRefGoogle Scholar
  124. 124.
    Straumal BB, Gornakova AS, Sursaeva VG, Yashnikov VP (2009) Second-order faceting-roughening of the tilt grain boundary in zinc. Int J Mater Res (Zt Metallkd) 100:525CrossRefGoogle Scholar
  125. 125.
    Straumal BB, Gornakova AS, Sursaeva VG (2009) Grain boundary faceting–roughening in Zn. Crystallogr Rep 54:1070CrossRefGoogle Scholar
  126. 126.
    Nakhodkin N, Kulish N, Rodionova T (2010) Faceting of twin grain boundaries in polysilicon films. Phys Status Solidi A 207:316CrossRefGoogle Scholar
  127. 127.
    Nakhodkin N, Kulish N, Rodionova T (2013) Faceting of twin tips in polysilicon films. J Cryst Growth 381:65CrossRefGoogle Scholar
  128. 128.
    Chen J, Bere A, Nouet G, Ruterana P (2004) Analysis of faceting of grain boundaries in GaN. Superlattices Miscrostruct 36:369CrossRefGoogle Scholar
  129. 129.
    Kim YJ, Blum ID, He J, Kantazidis MG, Dravid VP, Seidman DN (2014) Three-dimensional atom-probe tomographic analyses of lead-telluride based thermoelectric materials. JOM 66:2288CrossRefGoogle Scholar
  130. 130.
    Kumar AKN, Watabe M, Kurokawa K (2013) Effect of boron on the microstructure of spark plasma sintered ultrafine WC. Vacuum 88:88CrossRefGoogle Scholar
  131. 131.
    Yoshino T, Price JD, Wark DA, Watson EB (2006) Effect of faceting on pore geometry in texturally equilibrated rocks: implications for low permeability at low porosity. Contrib Mineral Petrol 152:169CrossRefGoogle Scholar
  132. 132.
    Chatain D, Rabkin E, Derenne J, Bernardini J (2001) Role of the solid/liquid interface faceting in rapid penetration of a liquid phase along grain boundaries. Acta Mater 49:1123CrossRefGoogle Scholar
  133. 133.
    Blum B, Menyhard M, Luzzi DE, McMahon CJ Jr (1990) TEM investigation of bismuth induced faceting of Σ3 and near-Σ3 grain boundaries in copper. Scr Metall Mater 24:169CrossRefGoogle Scholar
  134. 134.
    Siegl R, Vitek V, Luzzi DE, Yan M (1997) Phase stability and grain boundary structure in the Cu-Bi system. J Phase Equilib 18:562CrossRefGoogle Scholar
  135. 135.
    Loier C, Boos JY (1981) Striation and faceting of grain boundaries in nickel due to sulphur and other elements. Metall Trans A 12:129CrossRefGoogle Scholar
  136. 136.
    Sarnelli E, Adamo M, Nappi C, Braccini V, Kawale S, Bellingeri E, Ferdeghini C (2014) Properties of high-angle Fe(Se, Te) bicrystal grain boundary junctions. Appl Phys Lett 104:162601CrossRefGoogle Scholar
  137. 137.
    Menyhard M, Rothman B, McMahon CJ Jr (1993) Observation of segregation and grain boundary faceting by tellurium and oxygen in iron. Scr Metall Mater 29:1005CrossRefGoogle Scholar
  138. 138.
    Straumal BB, Polyakov SA, Bischoff E, Gust W, Baretzky B (2005) Faceting of Σ3 and Σ9 grain boundaries in Cu–Bi alloys. Acta Mater 53:247CrossRefGoogle Scholar
  139. 139.
    Kundu A, Asl KM, Luo J, Harmer M (2013) Identification of a bilayer grain boundary complexion in Bi-doped Cu. Scr Mater 68:146CrossRefGoogle Scholar
  140. 140.
    Donald AM, Brown LM (1979) Grain boundary faceting in Cu-Bi alloys. Acta Metall 27:59CrossRefGoogle Scholar
  141. 141.
    Michael JR, Williams DB (1984) An analytical electron-microscopy study of the kinetics of the equilibrium segregation of bismuth in copper. Metall Trans A 15:99CrossRefGoogle Scholar
  142. 142.
    Gokon N, Kajihara M (2008) Occurrence of faceting for [110] symmetric tilt boundaries in Cu doped with Bi. Mater Trans 49:2584CrossRefGoogle Scholar
  143. 143.
    Yoshino T, Takei Y, Wark DA, Bruce Watson E (2005) Grain boundary wetness of texturally equilibrated rocks, with implications for seismic properties of the upper mantle. J Geophys Res 110:B08205Google Scholar
  144. 144.
    Yu Z, Wu Q, Rickman JM, Chan HM, Harmer MP (2013) Atomic-resolution observation of Hf-doped alumina grain boundaries. Scr Mater 68:703CrossRefGoogle Scholar
  145. 145.
    Straumal BB, Kogtenkova O, Zieba P (2008) Wetting transition of grain boundary triple junctions. Acta Mater 56:925CrossRefGoogle Scholar
  146. 146.
    Straumal BB, Baretzky B, Kogtenkova OA, Straumal AB, Sidorenko AS (2010) Wetting of grain boundaries in Al by the solid Al3Mg2 phase. J Mater Sci 45:2057. doi: 10.1007/s10853-009-4014-6 CrossRefGoogle Scholar
  147. 147.
    Virtanen P, Tiainen T, Lepisto T (1998) Precipitation at faceting grain boundaries of Cu-Ni-Sn alloys. Mater Sci Eng A 251:269CrossRefGoogle Scholar
  148. 148.
    Straumal B, Muschik T, Gust W, Predel B (1992) The wetting transition in high and low energy grain boundaries in the Cu(In) system. Acta Metall Mater 40:939CrossRefGoogle Scholar
  149. 149.
    Vasiliev AL, Stepantsov EA, Roddatis VV, Kiselev NA, Olsson E, Ivanov ZG, Claeson T (1995) The structure of artificial grain boundaries in yttrium-stabilized ZrO2 bicrystals with intermediate layers. Phys Status Solidi A 151:151CrossRefGoogle Scholar
  150. 150.
    Read WT, Shokley W (1950) Dislocation models of crystal grain boundaries. Phys Rev 78:275CrossRefGoogle Scholar
  151. 151.
    Kirch DM, Jannot E, Barrales-Mora LA, Molodov DA, Gottstein G (2008) Inclination dependence of grain boundary energy and its impact on the faceting and kinetics of tilt grain boundaries in aluminum. Acta Mater 56:4998CrossRefGoogle Scholar
  152. 152.
    Brandenburg JE, Barrales-Mora LA, Molodov DA, Gottstein G (2013) Effect of inclination dependence of grain boundary energy on the mobility of tilt and non-tilt low-angle grain boundaries. Scr Mater 68:980CrossRefGoogle Scholar
  153. 153.
    Brandenburg JE, Barrales-Mora LA, Molodov DA (2014) On migration and faceting of low-angle grain boundaries: experimental and computational study. Acta Mater 77:294CrossRefGoogle Scholar
  154. 154.
    Kirch DM, Zhao B, Molodov DA (2007) Faceting of low-angle <100> tilt grain boundaries in aluminum. Scr Mater 56:939CrossRefGoogle Scholar
  155. 155.
    Grange G, Jourdan C, Gastaldi J (1988) Formation of grain boundary faceting during growth of Al crystals from melt. J Cryst Growth 87:325CrossRefGoogle Scholar
  156. 156.
    Sandiumenge F, Vilalta N, Rabier J, Obradors X (2001) Subgrain boundary structure in melt-textured RBa2Cu3O7 (R = Y, Nd): limitation of critical currents versus flux pinning. Phys Rev B 64:184515CrossRefGoogle Scholar
  157. 157.
    Yan Y, Evetts JE, Soylu B, Stobbs WM (1994) The compositionally modulated faceting of grain boundaries in the Bi2Sr2CaN–1CuNOx system. Philos Mag Lett 70:195CrossRefGoogle Scholar
  158. 158.
    Song X (2005) (110) facets and dislocation structure of low-angle grain boundaries in YBa2Cu3O7–δ and Y0.7Ca0.3Ba2Cu3O7–δ thin film bicrystals. J Mater Res 22:950CrossRefGoogle Scholar
  159. 159.
    Rollett AD, Srolovotz DJ, Doherty RD, Anderson MP (1989) Computer simulation of recrystallization in non-uniformly deformed metals. Acta Metall 37:627CrossRefGoogle Scholar
  160. 160.
    Straumal B, Sursaeva V, Risser S, Chenal B, Gust W (1996) The onset of abnormal grain growth in Al–Ga polycrystals. Mater Sci Forum 207:557CrossRefGoogle Scholar
  161. 161.
    Harper JME, Cabral C Jr, Andricacos PC, Gignac L, Noyan IC, Rodbell KP, Hu CK (1999) Mechanisms for microstructure evolution in electroplated copper thin films near room temperature. J Appl Phys 86:2516CrossRefGoogle Scholar
  162. 162.
    Huda Z (2004) Influence of particle mechanisms on kinetics of grain growth in a P/M superalloy. Mater Sci Forum 467:985CrossRefGoogle Scholar
  163. 163.
    Rabkin E (1998) Zener drag in the case of anisotropic grain boundary energy. Scr Mater 39:1631CrossRefGoogle Scholar
  164. 164.
    Zener C (1948) Grains, phases, interfaces: an interpretation of microstructure. Trans AIME 175:15Google Scholar
  165. 165.
    Hibbard GD, McCrea JL, Palumbo G, Aust KT, Erb U (2002) An initial analysis of mechanisms leading to late stage abnormal grain growth in nanocrystalline Ni. Scr Mater 47:83CrossRefGoogle Scholar
  166. 166.
    Lee H-Y, Freer R (1997) The mechanism of abnormal grain growth in Sr0.6Ba0.4Nb2O6 ceramics. J Appl Phys 81:376CrossRefGoogle Scholar
  167. 167.
    Pang XM, Qiu JH, Zhu KJ, Luo J (2011) Study on the sintering mechanism of KNN-based lead-free piezoelectric ceramics. J Mater Sci 46:2345. doi: 10.1007/s10853-010-5080-5 CrossRefGoogle Scholar
  168. 168.
    Kwon O-S, Hong S-H, Lee J-H, Chung U-J, Kim D-Y, Hwang NM (2002) Microstructural evolution during sintering of TiO2/SiO2-doped alumina: mechanism of anisotropic abnormal grain growth. Acta Mater 50:4865CrossRefGoogle Scholar
  169. 169.
    Dillon SJ, Harmer MP (2007) Mechanism of ‘‘solid-state’’ single-crystal conversion in alumina. J Am Ceram Soc 90:993CrossRefGoogle Scholar
  170. 170.
    Dillon SJ, Harmer MP, Rohrer GS (2010) Influence of interface energies on solute partitioning mechanisms in doped aluminas. Acta Mater 58:5097CrossRefGoogle Scholar
  171. 171.
    Fang T-T, Shiau H-K (2004) Mechanism for developing the boundary barrier layers of CaCu3Ti4O12. J Am Ceram Soc 87:2072CrossRefGoogle Scholar
  172. 172.
    Ryoo HS, Hwang SK (1998) Anisotropic atomic packing model for abnormal grain growth mechanism of WC-25 wt% Co alloy. Scr Mater 39:1577CrossRefGoogle Scholar
  173. 173.
    Shin T-J, Oh J-O, Oh KH, Lee DN (2004) The mechanism of abnormal grain growth in polycrystalline diamond during high pressure-high temperature sintering. Diam Relat Mater 13:488CrossRefGoogle Scholar
  174. 174.
    Lee SB, Hwang NM, Yoon DY, Henry MF (2000) Grain boundary faceting and abnormal grain growth in nickel. Metall Mater Trans A 31:985CrossRefGoogle Scholar
  175. 175.
    Jung SH, Yoon DY, Kang SJL (2013) Mechanism of abnormal grain growth in ultrafine-grained nickel. Acta Mater 61:5685CrossRefGoogle Scholar
  176. 176.
    Koo JB, Yoon DY (2001) The dependence of normal and abnormal grain growth in silver on annealing temperature and atmosphere. Metall Mater Trans A 32:469CrossRefGoogle Scholar
  177. 177.
    Choi JS, Yoon DY (2001) The temperature dependence of abnormal grain growth and grain boundary faceting in 316L stainless steel. ISIJ Int 41:478CrossRefGoogle Scholar
  178. 178.
    Shirdel M, Mirzadeh H, Parsa MH (2014) Microstructural evolution during normal/abnormal grain growth in austenitic stainless steel. Metall Mater Trans A 45:5185CrossRefGoogle Scholar
  179. 179.
    Shirdel M, Mirzadeh H, Parsa MH (2014) Abnormal grain growth in AISI 304L stainless steel. Mater Charact 97:11CrossRefGoogle Scholar
  180. 180.
    Choi JS, Yoon DY (2003) Temperature dependence of grain boundary structure and grain growth in bulk silicon-iron. ISIJ Int 43:245CrossRefGoogle Scholar
  181. 181.
    Lee BK, Chung SY, Kang SJL (2000) Grain boundary faceting and abnormal grain growth in BaTiO3. Acta Mater 48:1575CrossRefGoogle Scholar
  182. 182.
    An SM; Kang SJL (2011) Boundary structural transition and grain growth behavior in BaTiO3 with Nd2O3 doping and oxygen partial pressure change. Acta Mater 59:1964CrossRefGoogle Scholar
  183. 183.
    Cho YK, Yoon DY (2004) Faceting of high-angle grain boundaries in titanium-excess BaTiO3. J Am Ceram Soc 87:438CrossRefGoogle Scholar
  184. 184.
    Lee SB, Sigle W, Ruhle M (2002) Investigation of grain boundaries in abnormal grain growth structure of TiO2-excess BaTiO3 by TEM and EELS analysis. Acta Mater 50:2151CrossRefGoogle Scholar
  185. 185.
    King AH (1998) Equilibrium at triple junctions under the influence of anisotropic grain boundary energy. In: Weiland H, Adams BL, Rollett AD (eds) Grain growth in polycrystalline materials III. TMS, Warrendale, pp 333–338Google Scholar
  186. 186.
    Gleiter H (1969) The mechanism of grain boundary migration. Acta Metall 17:565CrossRefGoogle Scholar
  187. 187.
    Cahn JW (1960) Theory of crystal growth and interface motion in crystalline materials. Acta Metall 8:554CrossRefGoogle Scholar
  188. 188.
    Heo YH, Jeon SC, Fisher JG, Choi SY, Hur KH, Kang SJL (2011) Effect of step free energy on delayed abnormal grain growth in a liquid phase-sintered BaTiO3 model system. J Eur Ceram Soc 31:755CrossRefGoogle Scholar
  189. 189.
    Viswanathan R, Bauer CL (1973) Formation of annealing twins, faceting and grain boundary pinning in copper bicrystals. Mater Trans 4:2645Google Scholar
  190. 190.
    Rabkin E (2005) Effect of grain boundary faceting on kinetics of grain growth and microstructure evolution. J Mater Sci 40:875. doi: 10.1007/s10853-005-6504-5 CrossRefGoogle Scholar
  191. 191.
    Sursaeva VG, Gornakova AS, Yashnikov VP, Straumal BB (2008) Motion of the faceted 57° \( \left[ {11\bar{2}0} \right] \) tilt grain boundary in zinc. J Mater Sci 43:3860. doi: 10.1007/s10853-007-2223-4 CrossRefGoogle Scholar
  192. 192.
    Sursaeva VG (2010) Effect of faceting on twin grain boundary motion in zinc. Mater Lett 64:105CrossRefGoogle Scholar
  193. 193.
    Barrett CD, El Kadiri H (2014) Fundamentals of mobile tilt grain boundary faceting. Scr Mater 84:15CrossRefGoogle Scholar
  194. 194.
    Sursaeva VG, Gottstein G, Shvindlerman LS (2011) Effect of a first-order ridge on grain boundary motion in Zn. Acta Mater 59:623CrossRefGoogle Scholar
  195. 195.
    Paidar V, Lejcek P, Polcarová M, Brádler J, Jacques A (2004) Anisotropy of grain boundary migration observed in situ by synchrotron radiation. Mater Sci Forum 467:911CrossRefGoogle Scholar
  196. 196.
    Sursaeva VG, Straumal BB, Gornakova AS, Shvindlerman LS, Gottstein G (2008) Effect of faceting on grain boundary motion. Acta Mater 56:2726CrossRefGoogle Scholar
  197. 197.
    Straumal BB, Sursaeva VG, Gornakova AS (2005) Influence of faceting-roughening on the triple junction migration in zinc. Zt Metallkd 96:1147CrossRefGoogle Scholar
  198. 198.
    Bonzel HP, Emundts A (2000) Absolute values of surface and step free energies from equilibrium crystal shapes. Phys Rev Lett 84:5804CrossRefGoogle Scholar
  199. 199.
    Hondoh T, Higashi A (1979) Anisotropy of migration and faceting of large-angle grain boundaries in ice bicrystals. Philos Mag A 39:137CrossRefGoogle Scholar
  200. 200.
    An SM, Yoon BK, Chung SY, Kang SJL (2012) Nonlinear driving force-velocity relationship for the migration of faceted boundaries. Acta Mater 60:4531CrossRefGoogle Scholar
  201. 201.
    Minkwitz C, Chr Herzig, Rabkin E, Gust W (1999) The inclination dependence of gold tracer diffusion along a Σ3 twin grain boundary in copper. Acta Mater 47:1231CrossRefGoogle Scholar
  202. 202.
    Klinger L, Rabkin E (2010) Sintering of fully faceted crystalline particles. Int J Mater Res 101:75CrossRefGoogle Scholar
  203. 203.
    Lee MG, Chung SY, Kang SJL (2011) Boundary faceting-dependent densification in a BaTiO3 model system. Acta Mater 59:692CrossRefGoogle Scholar
  204. 204.
    James MN (2010) Intergranular crack paths during fatigue in interstitial-free steels. Eng Fract Mech 77:1998CrossRefGoogle Scholar
  205. 205.
    Beachem CD (1972) A new model for hydrogen-assisted cracking (hydrogen “embrittlement”). Metall Trans 3:437CrossRefGoogle Scholar
  206. 206.
    Hull D, Bacon DJ (1984) Introduction to dislocations. Pergamon Press, OxfordGoogle Scholar
  207. 207.
    Lee SB, Sigle W, Kurtz W, Rühle M (2003) Temperature dependence of faceting in Σ5 (310)[001] grain boundary of SrTiO3. Acta Mater 51:975CrossRefGoogle Scholar
  208. 208.
    Lee SB (2003) Correlation between grain boundary faceting-defaceting transition and change of grain boundary properties with temperature. Mater Lett 57:3779CrossRefGoogle Scholar
  209. 209.
    Lee SB, Sigle W, Rühle M (2003) Faceting behavior of an asymmetric SrTiO3 Σ5 [001] tilt grain boundary close to its defaceting transition. Acta Mater 51:4583CrossRefGoogle Scholar
  210. 210.
    Lee SB, Lee JH, Cho PS, Sigle W, Phillipp F (2007) High-temperature resistance anomaly at a strontium titanate grain boundary and its correlation with the grain-boundary faceting-defaceting transition. Adv Mater 19:391CrossRefGoogle Scholar
  211. 211.
    Hartmann K, Wirth R, Heinrich W (2010) Synthetic near Σ5 (210)/[100] grain boundary in YAG fabricated by direct bonding: structure and stability. Phys Chem Miner 37:291CrossRefGoogle Scholar
  212. 212.
    Jin Q, Chan SW (2002) Grain boundary faceting in YBa2Cu3O7–x bicrystal thin films on SrTiO3 substrates. J Mater Res 17:323CrossRefGoogle Scholar
  213. 213.
    Eastman JA, Vaudin MD, Merkle KL, Sass SL (1989) Electron diffraction study of the faceting of tilt grain boundaries in NiO. Philos Mag A 59:465CrossRefGoogle Scholar
  214. 214.
    Ekin JW, Braginski AI, Panson AJ, Janocko MA, Capone DW II, Zaluzec NJ, Flandermeyer B, de Lima OF, Hong M, Kwo J, Liou SH (1987) Evidence for weak link and anisotropy limitations on the transport critical current in bulk polycrystalline YBa2Cu3Ox. J Appl Phys 62:4821CrossRefGoogle Scholar
  215. 215.
    Dimos D, Chaudhari P, Mannhart J (1990) Superconducting transport propeeties of grain boundaries in YBa2Cu3O7 bicrystals. Phys Rev B 41:4038CrossRefGoogle Scholar
  216. 216.
    Hilgenkamp H, Mannhart J, Mayer B (1996) Implications of d(x 2y 2) symmetry and faceting for the transport properties of grain boundaries in high-T c superconductors. Phys Rev B 53:14586CrossRefGoogle Scholar
  217. 217.
    Browning ND, Buban JP, Nellist PD, Norton DP, Chisholm MF, Pennycook SJ (1998) The atomic origins of reduced critical currents at [001] tilt grain boundaries in YBa2Cu3O7–δ thin films. Phys C 294:183CrossRefGoogle Scholar
  218. 218.
    Tsai JWH, Chan SW, Kirtley JR, Tidrow SC, Jiang Q (2001) The variation of J cgb with GB misorientation and inclination measured using the scanning SQUID microscope. IEEE Trans Appl Supercond 11:3880CrossRefGoogle Scholar
  219. 219.
    Sandiumenge F, Vilalta N, Rabier J, Obradors X (2002) Subboundary mesostructures and variable dislocation networks in single domain melt textured YBa2Cu3O7—implications on critical currents. J Phys C 372:1204CrossRefGoogle Scholar
  220. 220.
    Laval JY, Swiatnicki W (1994) Atomic structure of grain boundaries in YBa2Cu3O7–x. Phys C 221:11CrossRefGoogle Scholar
  221. 221.
    Lombardi F, Tafuri F, Ricci F, Miletto Granozio F, Barone A, Testa G, Sarnelli E, Kirtley JR, Tsuei CC (2002) Intrinsic d-wave effects in YBa2Cu3O7–δ grain boundary Josephson junctions. Phys Rev Lett 89:207001CrossRefGoogle Scholar
  222. 222.
    Mitchell EE, Foley CP (2011) YBCO step-edge junctions: influence of morphology on junction transport. IEEE Trans Appl Supercond 21:371CrossRefGoogle Scholar
  223. 223.
    Lombardi F, Tafuri F, Ricci F, Miletto F, di Uccio US, Testa G, Sarnelli E (2002) Influence of the structural anisotropy and of the order parameter symmetry on the transport properties of YBa2Cu3O7–δ grain boundaries Josephson junctions. Phys C 372:87CrossRefGoogle Scholar
  224. 224.
    Chisholm MF, Smith DA (1989) Low-angle tilt grain boundaries in YBa2Cu3O7 superconductors. Philos Mag A 59:181CrossRefGoogle Scholar
  225. 225.
    Yan Y, Evetts JE, Soylu B, Stobbs WM (1996) The origins of high values of the critical current density in the Bi2Sr2Can–1CunOx system: high-T c superconducting pathways at low angle tilt boundaries. Phys C 261:56CrossRefGoogle Scholar
  226. 226.
    Yan Y, Kirk MA, Evetts JE (1997) Structure of grain boundaries: correlation to supercurrent transport in textured Bi2Sr2Can–1CunOx bulk material. J Mater Res 12:3009CrossRefGoogle Scholar
  227. 227.
    Shadrin P, Jia CL, Divin Y (2003) Spread of critical currents in thin-film YBa2Cu3O7–x bicrystal junctions and faceting of grain boundary. IEEE Trans Appl Supercond 13:603CrossRefGoogle Scholar
  228. 228.
    Shadrin P, Jia CL, Divin Y (2002) Spread of critical currents in thin-film YBa2Cu3O7–x bicrystal junctions and faceting of grain boundary. Phys C 372:80CrossRefGoogle Scholar
  229. 229.
    Borisenko IV, Constantinian KY, Kislinskii YV, Ovsyannikov GA (2004) Andreev states and shot noise in bicrystal junctions of cuprate superconductors. JETP 99:1223CrossRefGoogle Scholar
  230. 230.
    Deutscher G (1989) Superconductivity in the high-T c oxides. Phys Scr 29:9CrossRefGoogle Scholar
  231. 231.
    Camps RA, Evetts JE, Glowacki BA, Neweomb SB, Stobbs WM (1987) Microstructure and critical current of superconducting YBa2Cu3O7–x. J Mater Res 2:750CrossRefGoogle Scholar
  232. 232.
    Blendell JE, Handwerker CA, Vaudin MD, Fuller ER Jr (1988) Composition control of the microstructure of Ba2YCu3O6+x. J Cryst Growth 89:93CrossRefGoogle Scholar
  233. 233.
    Zandbergen HW, Thomas G (1988) Grain boundaries in sintered YBa2Cu3O7–δ. Acta Crystallogr A 44:772CrossRefGoogle Scholar
  234. 234.
    Kogure T, Zhang Y, Levonmaa R, Kontra R, Wang WX, Rudman DA, Yurek GJ, van der Sande JB (1988) Grain boundary structure of YBa2Cu3O7–x formed by oxidation of metallic precursors. Phys C 156:707CrossRefGoogle Scholar
  235. 235.
    Romano LT, Wilshaw PR, Long NJ, Grovenor CRM (1989) High-resolution microchemistry and structure of grain boundaries in bulk YBa2Cu3O7–x. Supercond Sci Technol 1:285CrossRefGoogle Scholar
  236. 236.
    Babcock SE, Larbalestier DC (1989) Evidence for local composition variations within YBa2Cu3O7–δ grain boundaries. Appl Phys Lett 55:393CrossRefGoogle Scholar
  237. 237.
    Gao Y, Merkle K, Bai G, Chang HLM, Lain DJ (1991) Structure and composition of grain boundary dislocation cores and stacking faults in MOCVD-grown YBa2Cu3O7–x thin films. Phys C 174:1CrossRefGoogle Scholar
  238. 238.
    Carim AH, Mitchell TE (1993) 90-degreees boundaries and associated interfacial and stand-off partial dislocations in Ba2Cu3O7–x. Ultramicroscopy 51:228CrossRefGoogle Scholar
  239. 239.
    Hilgenkamp H, Mannhart J, Mayer B, Gerber Ch, Kirtley JR, Moler KA (1997) Influence of d(x 2y 2) symmetry on device applications of high-T c grain boundary junctions. IEEE Trans Appl Supercond 7:3670CrossRefGoogle Scholar
  240. 240.
    Mannhart J, Hilgenkamp H, Mayer B, Kirtley JR, Moler KA, Sigrist M (1996) Large enhancement of critical-current density due to vortex matching at the periodic facet structure in YBa2Cu3O7–δ bicrystals. Phys Rev Lett 77:2782CrossRefGoogle Scholar
  241. 241.
    Mints RG, Papiashvili I, Kirtley JR, Hilgenkamp H, Hammerl G, Mannhart J (2002) Observation of splintered Josephson vortices at grain boundaries in YBa2Cu3O7–δ. Phys Rev Lett 89:067004CrossRefGoogle Scholar
  242. 242.
    Cai XY, Gurevich A, Tsu IF, Kaiser DL, Babcock SE, Larbalestier DC (1998) Large enhancement of critical-current density due to vortex matching at the periodic facet structure in YBa2Cu3O7–δ bicrystals. Phys Rev B 57:10951CrossRefGoogle Scholar
  243. 243.
    Walker MB (1996) Mechanism for magnetic-flux generation in grain boundaries of YBa2Cu3O7–x. Phys Rev B 54:13269CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • B. B. Straumal
    • 1
    • 2
    • 3
    • 4
  • O. A. Kogtenkova
    • 1
  • A. S. Gornakova
    • 1
  • V. G. Sursaeva
    • 1
  • B. Baretzky
    • 2
  1. 1.Institute of Solid State PhysicsRussian Academy of SciencesChernogolovkaRussia
  2. 2.Karlsruhe Institute of Technology (KIT)Institute of NanotechnologyEggenstein-LeopoldshafenGermany
  3. 3.Moscow Institute of Physics and Technology (State University)DolgoprudnyRussia
  4. 4.Laboratory of Hybrid NanomaterialsNational University of Science and Technology «MISIS»MoscowRussia

Personalised recommendations