Grain Boundary Networks


Statistical information about grain orientations within a polycrystal has been available to materials researchers for many decades. In particular, the orientation distribution, or crystallographic texture information, has been measured using X-ray diffraction techniques since about 1950. Consequently, the role of texture in materials performance and design is widely appreciated and commonly taught in the core Materials Science curriculum. However, texture data represent only “one-point” statistics, and do not capture microstructural geometry or topology.


Percolation Threshold Triple Junction General Boundary Percolation Theory Special Boundary 
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.


  1. Basinger JA, Homer ER, Fullwood DT, Adams BL (2005) Two-dimensional grain boundary percolation in alloy 304 stainless steel. Scripta Mater 53(8):959–963CrossRefGoogle Scholar
  2. Bouchaud E (1997) Scaling properties of cracks. J Phys-Condens Mat 9(21):4319–4344CrossRefADSGoogle Scholar
  3. Brandon DG (1966) Structure of high-angle grain boundaries. Acta Metall 14(11):1479CrossRefGoogle Scholar
  4. Chen Y, Schuh CA (2006) Diffusion on grain boundary networks: Percolation theory and effective medium approximations. Acta Mater 54(18):4709–4720CrossRefGoogle Scholar
  5. Chen Y, Schuh CA (2007) Coble creep in heterogeneous materials: The role of grain boundary engineering. Phys Rev B 76(6):064111CrossRefADSGoogle Scholar
  6. Frary M, Schuh CA (2003a) Combination rule for deviant CSL grain boundaries at triple junctions. Acta Mater 51(13):3731–3743CrossRefGoogle Scholar
  7. Frary M, Schuh CA (2003b) Nonrandom percolation behavior of grain boundary networks in high-T-c superconductors. Appl Phys Lett 83(18):3755–3757CrossRefADSGoogle Scholar
  8. Frary M, Schuh CA (2004) Percolation and statistical properties of low- and high-angle interface networks in polycrystalline ensembles. Phys Rev B 69(13):134115CrossRefADSGoogle Scholar
  9. Frary M, Schuh CA (2005a) Connectivity and percolation behaviour of grain boundary networks in three dimensions. Philos Mag 85(11):1123–1143CrossRefADSGoogle Scholar
  10. Frary M, Schuh CA (2005b) Grain boundary networks: Scaling laws, preferred cluster structure, and their implications for grain boundary engineering. Acta Mater 53(16): 4323–4335CrossRefGoogle Scholar
  11. Fullwood DT, Basinger JA, Adams BL (2006) Lattice-based structures for studying percolation in two-dimensional grain networks. Acta Mater 54(5):1381–1388CrossRefGoogle Scholar
  12. Gao Y, Stolken JS, Kumar M, Ritchie RO (2007) High-cycle fatigue of nickel-base superalloy Rene 104 (ME3): Interaction of microstructurally small cracks with grain boundaries of known character. Acta Mater 55(9):3155–3167CrossRefGoogle Scholar
  13. Gaudett MA, Scully JR (1994) Applicability of bond percolation theory to intergranular stress-corrosion cracking of sensitized Alsl 304 stainless-steel. Metall Mater Trans A 25(4):775–787CrossRefGoogle Scholar
  14. Gertsman VY (2001a) Coincidence site lattice theory of multicrystalline ensembles. Acta Crystallogr A 57:649–655CrossRefPubMedGoogle Scholar
  15. Gertsman VY (2001b) Geometrical theory of triple junctions of CSL boundaries. Acta Crystallogr A 57:627–627CrossRefGoogle Scholar
  16. Gertsman VY, Henager CH (2003) Grain boundary junctions in microstructure generated by multiple twinning. Interface Sci 11(4):403–415CrossRefGoogle Scholar
  17. Grimmett G (1989) Percolation. Springer-Verlag, New YorkMATHGoogle Scholar
  18. King A, Johnson G, Engelberg D, Ludwig W, Marrow J (2008) Observations of intergranular stress corrosion cracking in a grain-mapped polycrystal. Science 321(5887):382–385CrossRefPubMedADSGoogle Scholar
  19. Kopezky CV, Andreeva AV, Sukhomlin GD (1991) Multiple twinning and specific properties of Sigma = 3n boundaries in FCC crystals. Acta Metall Mater 39(7):1603–1615CrossRefGoogle Scholar
  20. Krupp U, Kane WM, Liu XY, Dueber O, Laird C, McMahon CJ (2003) The effect of grain-boundary-engineering-type processing on oxygen-induced cracking of IN718. Mater Sci Eng A 349(1–2):213–217Google Scholar
  21. Krupp U, Wagenhuber PEG, Kane WM, McMahon CJ (2005) Improving resistance to dynamic embrittlement and intergranular oxidation of nickel based superalloys by grain boundary engineering type processing. Mater Sci Tech 21(11):1247–1254CrossRefGoogle Scholar
  22. Lehockey EM, Palumbo G, Lin P (1998a) Improving the weldability and service performance of nickel- and iron-based superalloys by grain boundary engineering. Metall Mater Trans A 29(12):3069–3079CrossRefGoogle Scholar
  23. Lehockey EM, Palumbo G, Lin P, Brennenstuhl A (1998b) Mitigating intergranular attack and growth in lead-acid battery electrodes for extended cycle and operating life. Metall Mater Trans A 29(1):387–396CrossRefGoogle Scholar
  24. Lejcek P, Paidar V (2005) Challenges of interfacial classification for grain boundary engineering. Mater Sci Tech 21(4):393–398CrossRefGoogle Scholar
  25. Lim LC, Raj R (1984) Effect of boundary structure on slip-induced cavitation in polycrystalline nickel. Acta Metall 32(8):1183–1190CrossRefGoogle Scholar
  26. McGarrity ES, Duxbury PM, Holm EA (2005) Statistical physics of grain-boundary engineering. Phys Rev E 71(2):026102CrossRefADSGoogle Scholar
  27. Mclachlan DS (1987) An equation for the conductivity of binary-mixtures with anisotropic grain structures. J Phys C 20(7):865–877CrossRefADSGoogle Scholar
  28. Meinke JH, McGarrity ES, Duxbury PM, Holm EA (2003) Scaling laws for critical manifolds in polycrystalline materials. Phys Rev E 68(6):066107CrossRefADSGoogle Scholar
  29. Michiuchi M, Kokawa H, Wang ZJ, Sato YS, Sakai K (2006) Twin-induced grain boundary engineering for 316 austenitic stainless steel. Acta Mater 54(19):5179–5184CrossRefGoogle Scholar
  30. Miyazawa K, Iwasaki Y, Ito K, Ishida Y (1996) Combination rule of Sigma values at triple junctions in cubic polycrystals. Acta Crystallogr A 52:787–796CrossRefGoogle Scholar
  31. Nichols CS, Cook RF, Clarke DR, Smith DA (1991a) Alternative length scales for polycrystalline materials 1. Microstructure evolution. Acta Metall Mater 39(7):1657–1665CrossRefGoogle Scholar
  32. Nichols CS, Cook RF, Clarke DR, Smith DA (1991b) Alternative length scales for polycrystalline materials 2. Cluster morphology. Acta Metall Mater 39(7):1667–1675CrossRefGoogle Scholar
  33. Randle V (2004) Twinning-related grain boundary engineering. Acta Mater 52(14):4067–4081CrossRefGoogle Scholar
  34. Randle V (2006) “Special” boundaries and grain boundary plane engineering. Scripta Mater 54(6):1011–1015CrossRefGoogle Scholar
  35. Read WT, Shockley W (1950) Dislocation models of crystal grain boundaries. Phys Rev 78(3):275–289MATHCrossRefADSGoogle Scholar
  36. Reed BW, Kumar M (2006) Mathematical methods for analyzing highly-twinned grain boundary networks. Scripta Mater 54(6):1029–1033CrossRefGoogle Scholar
  37. Reed BW, Kumar M, Minich RW, Rudd RE (2008) Fracture roughness scaling and its correlation with grain boundary network structure. Acta Mater 56:3278–3289CrossRefGoogle Scholar
  38. Reed BW, Minich RW, Rudd RE, Kumar M (2004) The structure of the cubic coincident site lattice rotation group. Acta Crystallogr A 60:263–277MATHCrossRefPubMedMathSciNetGoogle Scholar
  39. Romero D, Martinez L, Fionova L (1996) Computer simulation of grain boundary spatial distribution in a three-dimensional polycrystal with cubic structure. Acta Mater 44(1): 391–402CrossRefGoogle Scholar
  40. Schuh CA, Frary M (2006) Correlations beyond the nearest-neighbor level in grain boundary networks. Scripta Mater 54(6):1023–1028CrossRefGoogle Scholar
  41. Schuh CA, Kumar M, King WE (2003a) Analysis of grain boundary networks and their evolution during grain boundary engineering. Acta Mater 51(3):687–700CrossRefGoogle Scholar
  42. Schuh CA, Kumar M, King WE (2003b) Connectivity of CSL grain boundaries and the role of deviations from exact coincidence. Z Metallkd 94(3):323–328Google Scholar
  43. Schuh CA, Kumar M, King WE (2005) Universal features of grain boundary networks in FCC materials. J Mater Sci 40(4):847–852CrossRefADSGoogle Scholar
  44. Schuh CA, Minich RW, Kumar M (2003c) Connectivity and percolation in simulated grain-boundary networks. Philos Mag 83(6):711–726CrossRefADSGoogle Scholar
  45. Schwartz AJ, King WE, Kumar M (2006) Influence of processing method on the network of grain boundaries. Scripta Mater 54(6):963–968CrossRefGoogle Scholar
  46. Shimada M, Kokawa H, Wang ZJ, Sato YS, Karibe I (2002) Optimization of grain boundary character distribution for intergranular corrosion resistant 304 stainless steel by twin-induced grain boundary engineering. Acta Mater 50(9):2331–2341CrossRefGoogle Scholar
  47. Spigarelli S, Cabibbo M, Evangelista E, Palumbo G (2003) Analysis of the creep strength of a low-carbon AISI 304 steel with low-Sigma grain boundaries. Mater Sci Eng A 352(1–2):93–99Google Scholar
  48. Stauffer D, Aharony A (1994) Introduction to percolation theory, rev 2nd ed. Routledge, LondonGoogle Scholar
  49. Van Siclen CD (2006) Intergranular fracture in model polycrystals with correlated distribution of low-angle grain boundaries. Phys Rev B 73(18):184118CrossRefADSGoogle Scholar
  50. Watanabe T (1983) Grain-boundary sliding and stress-concentration during creep. Metall Trans A 14(4):531–545CrossRefGoogle Scholar
  51. Wells DB, Stewart J, Herbert AW, Scott PM, Williams DE (1989) The use of percolation theory to predict the probability of failure of sensitized, austenitic stainless-steels by intergranular stress-corrosion cracking. Corrosion 45(8):649–660Google Scholar
  52. Zhao JW, Koontz JS, Adams BL (1988) Intercrystalline structure distribution in alloy 304 stainless-steel. Metall Trans A 19(5):1179–1185CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations