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Not too big, not too small: The appropriate scale

Abstract

The tools we use at the human scale, whether mechanical, medical or microelectronic, depend on materials for which some other scale of length or time is critical. Often this is the mesoscale, between the scales of engineering and of atomic science. Linking underlying processes to what we handle is sometimes called 'spanning' (or 'bridging') length scales, giving the impression that the mesoscale is a swamp to be crossed without getting mud on our boots. This is misleading: we do not wish to span the mesoscale, but to work at the appropriate scale, and to connect that to our human needs. The appropriate scale need not rule out multiscale computer modelling, in which some supercode integrates relevant scales in one pass, hoping to combine the best of methods for two or more levels. But the reality for such attempts, too often, is that the worst of both regimes are found. Happily, simpler strategies at a judicious scale will often suffice.

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Figure 1: Bone is a hierarchical material which is also a self-designing system.
Figure 2: Grain structure in a nuclear fuel element.
Figure 3: Variation in flux line energy in a ceramic superconductor.
Figure 4: Model polymer structure for a light-emitting diode.
Figure 5: Surface evolution during laser ablation of a ceramic.
Figure 6: Microstructure in a plasma-sprayed thermal barrier coating.
Figure 7: Strategy for predicting the properties of plasma-sprayed coatings56.

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References

  1. Weiner, S. & Wagner, H.D. The material bone: structure-mechanical function relations. Ann. Rev. Mater. Sci. 28, 271–298 (1998).

    Article  CAS  Google Scholar 

  2. Gould, S.J. The Panda's Thumb: More Reflections in Natural History (Penguin, London, 1983).

    Google Scholar 

  3. Pettifor, D.G. Computer-aided materials design: bridging the gaps between physics, chemistry and engineering. Phys. Educ. 164–168 (May 1997).

  4. Cottrell, A.H. Dislocations and Plastic Flow in Crystals (Clarendon, Oxford, 1953).

    Google Scholar 

  5. Henderson, D.J., Brodsky, M.H. & Chaudhari, P. Simulations of structural anisotropy and void formation in amorphous thin films. Appl. Phys. Lett. 25, 641–643 (1974).

    Article  CAS  Google Scholar 

  6. Dirks, A. & Leamy, H.J. Columnar microstructure in vapor-deposited thin films. Thin Solid Films 74, 219–233 (1977).

    Article  Google Scholar 

  7. Meakin, P. Fractal scaling in thin film condensation and material surfaces. CRC Crit. Rev. Solid State Mater. 13, 143–189 (1987).

    Article  CAS  Google Scholar 

  8. Stoneham, A.M., Ramos, M.M.D. & Ribeiro, R.M. The mesoscopic modelling of laser ablation. Appl. Phys. A 69, S81–S86 (1999).

    Article  CAS  Google Scholar 

  9. Holm, E.A. et al. On misorientation distribution evolution during anisotropic grain growth. Acta Metall. Mater. 49, 2981–2991 (2001).

    Article  CAS  Google Scholar 

  10. Mindownik, M.A. et al. Scaling of dislocation structures: diffusion in orientation space. Proc. R. Soc. Lond. A 357, 1807–1819 (2001).

    Article  Google Scholar 

  11. Wicksell, S.D. The corpuscle problem: A mathematical study of a biometric problem. Biometrika 17, 85–99 (1925).

    Google Scholar 

  12. Mouton, P.R. Principles and Practice of Unbiased Stereology (Johns Hopkins Univ. Press, Baltimore, 2002).

    Google Scholar 

  13. Larson, B.C., Yang, W., Ice, G.E., Budai, J.D. & Tischler, J.Z. Three-dimensional X-ray structural microscopy with submillimetre resolution. Nature 415, 887–890 (2002).

    Article  CAS  Google Scholar 

  14. Evans, P.G., Isaacs, E.D., Aeppli, G., Cai, Z. & Lai, B. X-ray microdiffraction images of antiferromagnetic domain evolution in chromium. Science 295, 1042–1045 (2002).

    Article  CAS  Google Scholar 

  15. Pawley, J.B. (ed.) Handbook of Biological Confocal Microscopy 2nd edn (Plenum, New York, 1995).

    Book  Google Scholar 

  16. Boyde, A. Bibliography of confocal microscopy and its applications. Scanning 16, 33–56 (1994).

    Google Scholar 

  17. Venables, J.A. Introduction to Surface and Thin Film Processes (Cambridge Univ.Press, Cambridge, 2000).

    Book  Google Scholar 

  18. Battaile, C.C. et al. Etching effects during the chemical vapor deposition of (100) diamond. J. Chem. Phys. 111, 4291–4299 (1999).

    Article  CAS  Google Scholar 

  19. Barabasi, A.-L. & Stanley, H.E. Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995).

    Book  Google Scholar 

  20. Rappaz, M. & Rettenmayr, M. Simulation of solidification. Curr. Opin. Solid State Mater. Sci. 3, 275–282 (1998).

    Article  CAS  Google Scholar 

  21. Kermanpur, A. et al. Thermal and grain-structure simulation in a land-based turbine blade directionally solidified with the liquid metal cooling process. Metall. Mater. Trans. B 31, 1293–1304 (2000).

    Article  Google Scholar 

  22. Boettinger, W.J. et al. Solidification microstructures: Recent developments, future directions. Acta Metall. Mater. 48, 43–70 (2000).

    Article  CAS  Google Scholar 

  23. Aste, T. & Weaire, D. The Pursuit of Perfect Packing (Institute of Physics Publishing, Bristol, 2000).

    Google Scholar 

  24. Anderson, M.P., Srolovitz, D.J., Grest, G.S. & Sahni, P.S. Computer simulation of grain-growth 1.Kinetics. Acta Metall. 32, 783–791 (1984).

    Article  CAS  Google Scholar 

  25. Holm, E.A., Srolovitz, D.J. & Cahn, J.W. Microstructural evolution in 2-dimensional 2-phase polycrystals. Acta Metall. Mater. 41, 1119–1136 (1993).

    Article  CAS  Google Scholar 

  26. Holm, E.A. & Battaile, C.C. The computer simulation of microstructural evolution. J. Mater. 53, 20–23 (2001).

    Google Scholar 

  27. Choy, T.C. et al. in Computer Aided Innovation of New Materials (eds Doyama, M., Suzuki, T., Kihara, J. & Yamamoto, R.) 869–872 (Elsevier, Amsterdam 1991).

    Book  Google Scholar 

  28. Sayes, R.S. & Thomas, T.R. Topography of random surfaces. Nature 271, 431–440 (1978).

    Article  Google Scholar 

  29. Stoneham, A.M. & Tasker, P.W. Electronic structure and properties of oxide surfaces and interfaces. MRS Res. Symp. 40, 291–301 (1985).

    Article  CAS  Google Scholar 

  30. Avnir, D., Farin, D. & Pfeifer, P. Molecular fractal surfaces. Nature 308, 261–263 (1984).

    Article  CAS  Google Scholar 

  31. Goff, H.D. Colloidal aspects of ice cream, a review. Int. Dairy J. 7, 363–373 (1997).

    Article  CAS  Google Scholar 

  32. Hartel, R.W. Ice crystallization during the manufacture of ice cream. Trends Food Sci. Tech. 7, 315–321 (1996).

    Article  CAS  Google Scholar 

  33. Trgo, C., Koxholt, M. & Kessler, H.G. Effect of freezing point and texture regulating parameters on the initial ice crystal growth in ice cream. J. Dairy Sci. 82, 460–465 (1999).

    Article  CAS  Google Scholar 

  34. Williamson, A.M., Lips, A., Clark, A. & Hall, D. Ripening of faceted ice crystals. Powder Tech. 121, 74–80 (2001).

    Article  CAS  Google Scholar 

  35. Sutton, R.L., Evans, I.D. & Crilly, J.F. Modeling ice crystal coarsening in concentrated disperse food systems. J. Food Sci. 59, 1227–1233 (1994).

    Article  CAS  Google Scholar 

  36. Weibull, W. A statistical theory of the strength of materials. R. Swedish Acad. Eng. Sci. Proc. 151 (1939).

  37. Weibull, W. A. statistical distribution function of wide applicability. J. Appl. Mech. (New York) 18, 293–297 (1951).

    Google Scholar 

  38. Fisher, R.A. & Tippett, L.H.C. Limiting forms of the frequency distribution of the largest and smallest member of a sample. Proc. Camb. Phil. Soc. 24, 180–190 (1928).

    Article  Google Scholar 

  39. Gumbel, E.J. Statistics of Extremes (McGraw-Hill, New York, 1958).

    Google Scholar 

  40. Smith, D.L. Thin Film Deposition; Principles and Practice (McGraw-Hill, New York, 1995).

    Google Scholar 

  41. Corbett, J. & Ianniello, L.C. Radiation-Induced Voids in Metals (US Atomic Energy Commission, Rockville, 1972).

    Google Scholar 

  42. Rauh, H.R., Stoneham, A.M. & Choy, T.C. in Materials Modelling: from Theory to Technology (eds Matthews, J.R., Rauh, H.R., Stoneham, A.M. & Thetford, R.) 201–208 (Institute of Physics Publishing, Bristol, 1992).

    Google Scholar 

  43. King, W.E. et al. Theory, simulation and modeling of interfaces in materials—bridging the length-scale gap: A workshop report. Mater. Sci. Eng. A 191, 1–16 (1995).

    Article  Google Scholar 

  44. de la Rubia, T.D. & Bulatov, V.V. (eds) Materials research by means of multiscale computer simulation. Mater. Res. Bull. (Special Issue) 26, (2001).

  45. Guo, X. (ed.) Multiscale materials modelling. Mater. Sci. Eng. A (in the press).

  46. Friend, R.H. et al. Electroluminescence in conjugated polymers. Nature 397, 121–128 (1999).

    Article  CAS  Google Scholar 

  47. Gao, Z.Q. et al. Organic electroluminescent devices by high temperature processing and crystalline transporting layer. Appl. Phys. Lett. 74, 3269–7321 (1999).

    Article  CAS  Google Scholar 

  48. Halls, J.J.M. et al. Photodiodes based on polyfluorene composites: influence of morphology. Adv. Mater. 12, 498–502 (2000).

    Article  CAS  Google Scholar 

  49. Stoneham, A.M. & Ramos, M.M.D. Mesoscopic modelling of conducting and semiconducting polymers. J. Phys. Cond. Mater. 13, 2411–2424 (2001).

    Article  CAS  Google Scholar 

  50. Stoneham, A.M. et al. Understanding electron flow in conducting polymer films: injection, mobility, recombination and mesostructure. J. Phys. Cond. Mater. 14, 9877–9898 (2002).

    Article  CAS  Google Scholar 

  51. Dickinson, J.T., Jensen, L.C., Webb, R.L., Dawes, M.L. & Langford, S.C. Interaction of wide band-gap single crystals with 248nm excimer laser irradiation. J. Appl. Phys. 74, 3758–3767 (1993).

    Article  CAS  Google Scholar 

  52. Carter, G. in Erosion and Growth of Solids Stimulated by Atom and Ion Beams (eds Kiriakides, G., Carter, G. & Whitton, J.L.) 70 (Holland: Martin Nijhoff, The Hague, 1986).

    Book  Google Scholar 

  53. Bianchi, L., Leger, A.C., Vardelle, M., Vardelle, A. & Fauchais, P. Splat formation and cooling of plasma-sprayed zirconia. Thin Solid Films 305, 35–47 (1997).

    Article  CAS  Google Scholar 

  54. Fauchais, P., Vardelle, A. & Dussoubs, B. Quo vadis plasma spraying? J. Thermal Spray Tech. 10, 44–66 (2001).

    Article  CAS  Google Scholar 

  55. Bertagnolli, M., Marchese, M., Jacucci, G., Doltsinis, I.S. & Nölting, S. Thermomechanical simulation of the splashing of ceramic droplets on a rigid substrate. J. Comput. Phys. 133, 205–221 (1997).

    Article  CAS  Google Scholar 

  56. Doltsinis, I.S., Harding, J.H. & Marchese, M. Modelling the production and performance analysis of plasma-sprayed ceramic thermal barrier coatings. Arch. Comput. Methods Eng. 5, 59–166 (1998).

    Article  Google Scholar 

  57. Clyne, T.W. & Withers, P.J. An Introduction to Metal Matrix Composites (Cambridge Univ. Press, Cambridge, 1993).

    Book  Google Scholar 

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Correspondence to A. Marshall Stoneham.

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Stoneham, A., Harding, J. Not too big, not too small: The appropriate scale. Nature Mater 2, 77–83 (2003). https://doi.org/10.1038/nmat804

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