Journal of Materials Science

, Volume 50, Issue 21, pp 6907–6919 | Cite as

Inferring grain boundary structure–property relations from effective property measurements

  • Oliver K. Johnson
  • Lin Li
  • Michael J. Demkowicz
  • Christopher A. Schuh
Original Paper


Grain boundaries strongly affect many materials properties in polycrystalline materials. However, very few structure–property models exist for grain boundaries, due in large part to the complicated and poorly understood way in which the properties of grain boundaries vary with their crystallographic structure. In the present work, we infer grain boundary structure–property correlations from measurements of the effective properties of a polycrystal. We refer to this approach as grain boundary properties localization. We apply this technique to a simple model system of grain boundary diffusivity in a two-dimensional microstructure, and infer the properties of low- and high-angle grain boundaries from the effective diffusivity of the grain boundary network. The generalization and use of these methods could greatly reduce the computational and experimental effort required to establish structure–property correlations for grain boundaries. More broadly, the technique of properties localization could be used to infer the properties of many microstructural constituents in complex microstructures.


  1. 1.
    Seita M, Hanson JP, Gradeˇcak S, Demkowicz MJ (2015a) The dual role of coherent twin boundaries in hydrogen embrittlement. Nat Commun 6:6164. doi:10.1038/ncomms7164 CrossRefGoogle Scholar
  2. 2.
    Lehockey EM, Limoges D, Palumbo G, et al. (1999) On improving the corrosion and growth resistance of positive Pb-acid battery grids by grain boundary engineering. J Power Sour 78(1–2):79–83. doi:10.1016/S0378-7753(99)00015-4 CrossRefGoogle Scholar
  3. 3.
    Lehockey EM, Palumbo G (1997) On the creep behaviour of grain boundary engineered nickel. Mater Sci Eng A 237(2):168–172. doi:10.1016/S0921-5093(97)00126-3 CrossRefGoogle Scholar
  4. 4.
    Lehockey EM, Palumbo G, Lin P (1998) Improving the weldability and service performance of nickel-and iron-based superalloys by grain boundary engineering. Metall Mater Trans A 29(12):3069–3079. doi:10.1007/s11661-998-0214-y CrossRefGoogle Scholar
  5. 5.
    Norton DP, Goyal A, Budai JD, et al. (1996) Epitaxial YBa2Cu3O7 on biaxially textured Nickel (001): an approach to superconducting tapes with high critical current density. Science 274(5288):755–757. doi:10.1126/science.274.5288.755 CrossRefGoogle Scholar
  6. 6.
    Sutton AP, Balluffi RW (2007) Interfaces in crystalline materials. Monographs on the physics and chemistry of materials (Book 51), 3rd edn. New York: Oxford University PressGoogle Scholar
  7. 7.
    Demkowicz MJ, Wang J, Hoagland RG (2008) Interfaces between dissimilar crystalline solids, chap. 83. In: Hirth JP (ed) Dislocations in solids, vol. 14. New York: Elsevier, pp 141–205. doi:10.1016/S1572-4859(07)00003-4 Google Scholar
  8. 8.
    Vitek V, Minonishi Y, Wang GJ (1985) Multiplicity of grain boundary structures: vacancies in boundaries and transformations of the boundary structure. J Phys Colloq 46(C4):C4-171–C4-183. doi:10.1051/jphyscol:1985420 CrossRefGoogle Scholar
  9. 9.
    Vitek V, Sutton A, Wang GJ, Schwartz D (1983) On the multiplicity of structures and grain boundaries. Scripta Metall 17:183–189. doi:10.1016/0036-9748(83)90096-0 CrossRefGoogle Scholar
  10. 10.
    Chin GY (1959) Studies of growth and fatigue in bicrystals of Aluminum. Cambridge: Bachelor of Science, Massacusetts Institute of TechnologyGoogle Scholar
  11. 11.
    Schwarz S, Houge E, Giannuzzi L, King A (2001) Bicrystal growth and characterization of copper twist grain boundaries. J Cryst Growth 222(1–2):392–398. doi:10.1016/S0022-0248(00)00918-0 CrossRefGoogle Scholar
  12. 12.
    Fleischer RL, Davis RS (1959) Controlling grain boundary position in growth from the melt. Trans Metall Soc AIME 215:665–666Google Scholar
  13. 13.
    Schober T, Balluffi RW (1969) Dislocation sub-boundary arrays in oriented thin-film bicrystals of gold. Philos Mag 20(165):511–518. doi:10.1080/14786436908228723 CrossRefGoogle Scholar
  14. 14.
    Amiri-Hezaveh A, Balluffi RW (1993) Apparatus for producing ultraclean bicrystals by the molecular beam epitaxy growth and ultrahigh vacuum bonding of thin films. Rev Sci Instrum 64(10):2983. doi:10.1063/1.1144344 CrossRefGoogle Scholar
  15. 15.
    Heinemann S, Wirth R, Dresen G (2001) Synthesis of feldspar bicrystals by direct bonding. Phys Chem Miner 28(10):685–692. doi:10.1007/s002690000142 CrossRefGoogle Scholar
  16. 16.
    Marquardt K, Petrishcheva E, Gard´es E, et al. (2011) Grain boundary and volume diffusion experiments in yttrium aluminium garnet bicrystals at 1,723 K: a miniaturized study. Contrib Mineral Petrol 162(4):739–749. doi:10.1007/s00410-011-0622-7 CrossRefGoogle Scholar
  17. 17.
    Pl¨oßl A, Kr¨auter G (1999) Wafer direct bonding: tailoring adhesion between brittle materials. Mater Sci Eng R 25(1–2):1–88. doi:10.1016/S0927-796X(98)00017-5 CrossRefGoogle Scholar
  18. 18.
    Holm EA, Olmsted DL, Foiles SM (2010) Comparing grain boundary energies in face-centered cubic metals: Al, Au, Cu and Ni. Scr Mater 63(9):905–908. doi:10.1016/j.scriptamat.2010.06.040 CrossRefGoogle Scholar
  19. 19.
    Olmsted DL, Foiles SM, Holm EA (2009a) Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Mater 57(13):3694–3703. doi:10.1016/j.actamat.2009.04.007 CrossRefGoogle Scholar
  20. 20.
    Olmsted DL, Holm EA, Foiles SM (2009b) Survey of computed grain boundary properties in face-centered cubic metals II: grain boundary mobility. Acta Mater 57(13):3704–3713. doi:10.1016/j.actamat.2009.04.015 CrossRefGoogle Scholar
  21. 21.
    Seita M, Volpi M, Patala S, McCue I, Diamanti MV, Schuh CA, Demkowicz MJ. A hybrid non-destructive technique to characterize grain boundary crystallography (in preparation)Google Scholar
  22. 22.
    Sorensen C, Basinger JA, Nowell MM, Fullwood DT (2014) Five-parameter grain boundary inclination recovery with ebsd and interaction volume models. Metall Mater Trans A 45:4165–4172. doi:10.1007/s11661-014-2345-7 CrossRefGoogle Scholar
  23. 23.
    Suter RM, Hennessy D, Xiao C, Lienert U (2006) Forward modelling method for microstructure reconstruction using x-ray diffraction microscopy: Single-crystal verification. Rev Sci Instrum 77(12):123905. doi:10.1063/1.2400017 CrossRefGoogle Scholar
  24. 24.
    Binci M, Fullwood DT, Kalidindi SR (2008) A new spectral framework for establishing localization relationships for elastic behavior of composites and their calibration to finite-element models. Acta Mater 56(10):2272–2282. doi:10.1016/j.actamat.2008.01.017 CrossRefGoogle Scholar
  25. 25.
    Duvvuru HK, Wu X, Kalidindi SR (2007) Calibration of elastic localization tensors to finite element models: application to cubic polycrystals. Comput Mater Sci 41(2):138–144. doi:10.1016/j.commatsci.2007.03.008 CrossRefGoogle Scholar
  26. 26.
    Fast T, Kalidindi SR (2011) Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater 59(11):4595–4605. doi:10.1016/j.actamat.2011.04.005 CrossRefGoogle Scholar
  27. 27.
    Fullwood DT, Kalidindi SR, Adams BL (2009a) Second-order microstructure sensitive design using 2-point spatial correlations, chap. 13. In: Schwartz AJ, Kumar M, Adams BL, Field DP (eds) Electron backscatter diffraction in materials science; , 2nd edn. New York: Springer, pp 177–188. doi:10.1007/978-0-387-88136-2 CrossRefGoogle Scholar
  28. 28.
    Fullwood DT, Kalidindi SR, Adams BL, Ahmadi S (2009b) A discrete Fourier transform framework for localization relations. Comput Mater Contin 9(1):25–40. doi:10.3970/cmc.2009.009.025 Google Scholar
  29. 29.
    Fullwood DT, Niezgoda SR, Adams BL, Kalidindi SR (2010) Microstructure sensitive design for performance optimization. Prog Mater Sci 55(6):477–562. doi:10.1016/j.pmatsci.2009.08.002 CrossRefGoogle Scholar
  30. 30.
    Kalidindi SR, Landi G, Fullwood DT (2008) Spectral representation of higher-order localization relationships for elastic behavior of polycrystalline cubic materials. Acta Mater 56(15):3843–3853. doi:10.1016/j.actamat.2008.01.058 CrossRefGoogle Scholar
  31. 31.
    Landi G, Kalidindi SR (2010) Thermo-elastic localization relationships for multi-phase composites. Comput Mater Contin 16(3):273–294. doi:10.3970/cmc.2010.016.273 Google Scholar
  32. 32.
    Li D, Szpunar J (1992) Determination of single crystals’ elastic constants from the measurement of ultrasonic velocity in the polycrystalline material. Acta Metall Mater 40(12):3277–3283. doi:10.1016/0956-7151(92)90041-C CrossRefGoogle Scholar
  33. 33.
    Howard CJ, Kisi EH (1999) Measurement of single-crystal elastic constants by neutron diffraction from polycrystals. J Appl Crystallogr 32(4):624–633. doi:10.1107/S0021889899002393 CrossRefGoogle Scholar
  34. 34.
    Hayakawa M, Imai S, Oka M (1985) Determination of single-crystal elastic constants from a cubic polycrystalline aggregate. J Appl Crystallogr 18(6):513–518. doi:10.1107/S0021889885010809 CrossRefGoogle Scholar
  35. 35.
    Chen Y, Schuh CA (2006) Diffusion on grain boundary networks: percolation theory and effective medium approximations. Acta Mater 54(18):4709–4720. doi:10.1016/j.actamat.2006.06.011 CrossRefGoogle Scholar
  36. 36.
    Rohrer GS (2011) Grain boundary energy anisotropy: a review. J Mater Sci 46(18):5881–5895. doi:10.1007/s10853-011-5677-3 CrossRefGoogle Scholar
  37. 37.
    Hwang JCM, Balluffi RW (1979) Measurement of grain-boundary diffusion at low temperatures by the surface accumulation method. I. Method and analysis. J Appl Phys 50(3):1339. doi:10.1063/1.326168 CrossRefGoogle Scholar
  38. 38.
    Ma Q, Balluffi RW (1993) Diffusion along [001] tilt boundaries in the Au/Ag system I. Experimental results. Acta Metall Mater 41(1):133–141. doi:10.1016/0956-7151(93)90345-S CrossRefGoogle Scholar
  39. 39.
    Johnson OK, Schuh CA (2013) The uncorrelated triple junction distribution function: towards grain boundary network design. Acta Mater 61(8):2863–2873. doi:10.1016/j.actamat.2013.01.025 CrossRefGoogle Scholar
  40. 40.
    Gertsman VY, Tangri K (1995) Computer simulation study of grain boundary and triple junction distributions in microstructures formed by multiple twinning. Acta Metall Mater 43(6):2317–2324. doi:10.1016/0956-7151(94)00422-6 CrossRefGoogle Scholar
  41. 41.
    Fortier P (1997) Triple junction and grain boundary character distributions in metallic materials. Acta Mater 45(8):3459–3467. doi:10.1016/S1359-6454(97)00004-9 CrossRefGoogle Scholar
  42. 42.
    Kumar M, King WE, Schwartz AJ (2000) Modifications to the microstructural topology in f.c.c. materials through thermomechanical processing. Acta Mater 48(9):2081–2091. doi:10.1016/S1359-6454(00)00045-8 CrossRefGoogle Scholar
  43. 43.
    Davies P, Randle V, Watkins G, Davies H (2002) Triple junction distribution profiles as assessed by electron backscatter diffraction. J Mater Sci 37(19):4203–4209. doi:10.1023/A:1020052306493 CrossRefGoogle Scholar
  44. 44.
    Schuh CA, Kumar M, King WE (2003) Analysis of grain boundary networks and their evolution during grain boundary engineering. Acta Mater 51(3):687–700. doi:10.1016/S1359-6454(02)00447-0 CrossRefGoogle Scholar
  45. 45.
    Yi Y, Kim J (2004) Characterization methods of grain boundary and triple junction distributions. Scr Mater 50(6):855–859. doi:10.1016/j.scriptamat.2003.12.010 CrossRefGoogle Scholar
  46. 46.
    Frary ME, Schuh CA (2005a) Connectivity and percolation behaviour of grain boundary networks in three dimensions. Philos Mag 85(11):1123–1143. doi:10.1080/14786430412331323564 CrossRefGoogle Scholar
  47. 47.
    Mason JK, Schuh CA (2007) Correlated grain-boundary distributions in two-dimensional networks. Acta Crystallogr Sect A 63(Pt 4):315–328. doi:10.1107/S0108767307021782 CrossRefGoogle Scholar
  48. 48.
    Wall MA, Schwartz AJ, Nguyen L (2001) A high-resolution serial sectioning specimen preparation technique for application to electron backscatter diffraction. Ultramicroscopy 88(2):73–83. doi:10.1016/S0304-3991(01)00071-7 CrossRefGoogle Scholar
  49. 49.
    Rowenhorst D, Gupta A, Feng C, Spanos G (2006) 3D Crystallographic and morphological analysis of coarse martensite: combining EBSD and serial sectioning. Scr Mater 55(1):11–16. doi:10.1016/j.scriptamat.2005.12.061 CrossRefGoogle Scholar
  50. 50.
    Mulders J, Day A (2005) Three-dimensional texture analysis. Mater Sci Forum 495–497:237–244. doi:10.4028/ CrossRefGoogle Scholar
  51. 51.
    Poulsen HF, Nielsen SF, Lauridsen EM, et al. (2001) Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders. J Appl Crystallogr 34(6):751–756. doi:10.1107/S0021889801014273 CrossRefGoogle Scholar
  52. 52.
    Ludwig W, Reischig P, King A, et al. (2009) Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis. Rev Sci Instrum 80(3):033905. doi:10.1063/1.3100200 CrossRefGoogle Scholar
  53. 53.
    King A, Herbig M, Ludwig W, et al. (2010) Non-destructive analysis of micro texture and grain boundary character from X-ray diffraction contrast tomography. Nucl Instrum Methods Phys Res Sect B 268(3–4):291–296. doi:10.1016/j.nimb.2009.07.020 CrossRefGoogle Scholar
  54. 54.
    Li SF, Suter RM (2013) Adaptive reconstruction method for three-dimensional orientation imaging. J Appl Crystallogr 46(2):512–524. doi:10.1107/S0021889813005268 CrossRefGoogle Scholar
  55. 55.
    Kirkpatrick S (1973) Percolation and conduction. Rev Mod Phys 45(4):574–588CrossRefGoogle Scholar
  56. 56.
    Reed BW, Schuh CA (2009) Grain boundary networks, chap. 15. In: Schwartz AJ, Kumar M, Adams BL, Field DP (eds) Electron backscatter diffraction in materials science, 2nd edn. New York: Springer, pp 201–214. doi:10.1007/978-0-387-88136-2 CrossRefGoogle Scholar
  57. 57.
    Kaur I, Gust W (1989) Handbook of grain and interphase boundary diffusion data, vol. 1, 1st edn. Stuttgart: Ziegler PressGoogle Scholar
  58. 58.
    McLachlan DS (1987) An equation for the conductivity of binary mixtures with anisotropic grain structures. J Phys C 20(7):865–877. doi:10.1088/0022-3719/20/7/004 CrossRefGoogle Scholar
  59. 59.
    McLachlan DS (2003) The correct modelling of the second order terms of the complex AC conductivity results for continuum percolation media, using a single phenomenological equation. Phys B 338(1–4):256–260. doi:10.1016/j.physb.2003.08.002 CrossRefGoogle Scholar
  60. 60.
    Stauffer D, Aharony A (1994) Introduction to percolation theory, 2nd edn. Philadelphia: Taylor & FrancisGoogle Scholar
  61. 61.
    Frary ME, Schuh CA (2005b) Grain boundary networks: scaling laws, preferred cluster structure, and their implications for grain boundary engineering. Acta Mater 53(16):4323–4335. doi:10.1016/j.actamat.2005.05.030 CrossRefGoogle Scholar
  62. 62.
    Frary ME, Schuh CA (2007) Correlation-space description of the percolation transition in composite microstructures. Phys Rev E 76(4):42–45. doi:10.1103/PhysRevE.76.041108 CrossRefGoogle Scholar
  63. 63.
    Bulatov VV, Reed BW, Kumar M (2013) Grain boundary energy function for fcc metals. Acta Mater 65:161–175. doi:10.1016/j.actamat.2013.10.057 CrossRefGoogle Scholar
  64. 64.
    K D (2015) Number of samples required for an event to occur with a given confidence level. Math Stack Exch.

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Materials and Metallurgical EngineeringUniversity of AlabamaTuscaloosaUSA

Personalised recommendations