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The Role of Topology in Growth and Agglomeration

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Topology in Condensed Matter

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 150))

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Summary

We describe several models of growth of atomic structures, mostly by agglomeration from gas or from liquid. In many physical situations, like the formation of fullerenes, carbon nanotubes and onions, as well as in growth of quasicrystals or glass formation, a very important role is played by topology of local configurations. This chapter shows how some physical properties of certain forms of condensed matter can be derived from simple topological and geometrical considerations concerning the structure of local configuration space of atoms and molecules.

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References

  1. Coxeter, M.C.M.: “Regular Polytopes”, Methuen and Co., London (1948)

    MATH  Google Scholar 

  2. Hamermesh, M.: Group Theory and Its Application to Physical Problems. Pergamon, London (1962)

    MATH  Google Scholar 

  3. Steinhaus, H.: Mathematical Kaleidoscope. Plenum Press, London-New York (1960)

    Google Scholar 

  4. Kerner, R.: Phenomenological Lagrangian for the amorphous solid state. Phys. Rev. B, 28(10), 5756 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  5. Kerner, R., dos Santos, D.M.: Nucleation and amorphous and crystalline growth: a dynamical model in two dimensions. Phys. Rev. B. 37(8), 3881 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  6. Kerner, R.: J. Non-Cryst. Solids 135, 155 (1991)

    Article  ADS  Google Scholar 

  7. Kerner, R.: Physica B 215, 267 (1996)

    Article  ADS  Google Scholar 

  8. Kerner, R.: Stochastic description of agglomeration and growth processes in Glasses. Proceedings of the Conference “Nankai Symposium on Lattice Statistics and Mathematical Physics” Int. J. Modern Phys. B 16, 1987 (2002)

    Article  ADS  MATH  Google Scholar 

  9. dos Santos-Loff, D.M., Kerner, R., Micoulaut, M.: Europhys. Lett. 28, 573 (1994)

    Article  ADS  Google Scholar 

  10. Barrio, R.A., Duruisseau, J.-P., Kerner, R.: Structural properties of alkaliborate glasses derived from a theoretical model. Philos. Mag. B, 72, 535 (1995)

    Article  Google Scholar 

  11. Barrio, R.A., Kerner, R., Micoulaut, M., Naumis, G.G.: Evaluation of the concentration of boroxol rings in vitreous B2O3 by the stochastic matrix method. J. Phys.: Cond. Matter 9, 9219 (1997)

    Article  ADS  Google Scholar 

  12. Kerner, R., Naumis, G.G.: Stochastic matrix description of the glass transition. J. Phys.: Cond. Matter 12, 1641 (2000)

    Article  ADS  Google Scholar 

  13. Smalley, R.: Probing C60. Science 242, 1017 (1988)

    Article  ADS  Google Scholar 

  14. Kroto, H., Heath, J.R., O’Brien, S.C., Curl, R.F., Smalley, R.E.: Nature 318, 162 (1985)

    Article  ADS  Google Scholar 

  15. Krätschmer, W., Fostiropulos, K., Huffmann, D.R.: The infrared and ultraviolet absorbtion spectra of laboratory-produced carbon dust: evidence for presence of the C60 molecule. Chem. Phys. Lett. 170, 162 (1990)

    Article  ADS  Google Scholar 

  16. Schmalz, T.G., Seitz, W.A., Klein, D., Hiley, C.E.: J. Am. Chem. Soc. 110, 1113 (1991)

    Article  Google Scholar 

  17. Kerner, R., Bennemann, K.H., Penson, K.: Model for the growth of fullerenes (C60, C70) from carbon vapour. Europhys. Lett. 19,(5), 363 (1992)

    Article  ADS  Google Scholar 

  18. Kerner, R.: Nucleation and growth of fullerenes. Comput. Mater. Sci. 2, 500–508 (1994)

    Article  MathSciNet  Google Scholar 

  19. Terrones, H., Terrones, M., Moran-Lopez, J.L.: Curved nanomaterials. Curr. Sci. 81, 1011 (2001)

    Google Scholar 

  20. Tomanek, D.: Proceedings of the Tsukuba Symposium on Carbon Nanotube. Physica B 323, 86 (2002)

    Article  ADS  Google Scholar 

  21. Bennemann, K.H., Kerner, R.: Theory for the growth of fullerenes. Z. Phys. Chem. 195, 89 (1996)

    Google Scholar 

  22. Kerner, R.: New forms of pure carbon and possibility of icosahedral quasicrystalline growth, in “Theories of Matter”. World Scientific 119 (1994) (a festschrift for Joseph L. Birman, ed. Solomon, A.)

    Google Scholar 

  23. Twarock, R.: New group structures for carbon onions and carbon nanotubes via affine extensions of noncrystallographic Coxeter groups. Phys. Lett. A, 300, 437 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  24. Phillips, J.C.: J. Non-Cryst. Solids 34, 153

    Google Scholar 

  25. Thorpe, M.F.: J. Non-Cryst. Solids 57, 355 (1983)

    Article  ADS  Google Scholar 

  26. Boolchand, P., Thorpe, M.F.: Phys. Rev. B 50, 10366 (1994)

    Article  ADS  Google Scholar 

  27. Zhang, M., Boolchand, P.: The Central Role of Broken Bond-Bending Constraints in Promoting Glass Formation in the Oxides. Science 266, 1355 (1994)

    Article  ADS  Google Scholar 

  28. Boolchand, P.: ed. Insulating and Semiconducting Glasses. World Scientific Publishing Co., Singapore-London-New-York (2001)

    Google Scholar 

  29. Kerner, R., Phillips, J.C.: Quantitative principles of silicate glass chemistry. Solid State Commun. 117, 47 (2000)

    Article  ADS  Google Scholar 

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Kerner, R. (2006). The Role of Topology in Growth and Agglomeration. In: Monastyrsky, M.I. (eds) Topology in Condensed Matter. Springer Series in Solid-State Sciences, vol 150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31264-1_4

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