Journal of Materials Science

, Volume 42, Issue 12, pp 4356–4363 | Cite as

The size refinement of Cu crystallites under mechanical processing conditions: a phenomenological modeling approach

  • F. DeloguEmail author
  • G. Cocco


A phenomenological model is developed for describing the kinetics of the crystallite size refinement process of Cu powder under mechanical treatment conditions. Based on the evidence that collisions represent the elementary events of energy transfer, the rate of crystallite size decrease is related on a statistical basis to the amount of powder trapped at each collision, to the number of collisions and to the collision energy. The mathematical approach allows for identifying the approximate functional form of the kinetic curves obtained at largely different impact energies. The values of the apparent kinetic constants and of the model parameters involved can be thus estimated by fitting the model curves to the experimental data. The results obtained provide a deeper insight into the details of the crystallite size refinement process.


Crystallite Size Powder Particle Impact Energy Average Crystallite Size Milling Tool 



Financial support has been given by the University of Cagliari and the University of Sassari.


  1. 1.
    Siegel RW, Hu E, Roco MC (eds) (1999) In Nanostructure science and technology. WTEC, Loyola College, MarylandGoogle Scholar
  2. 2.
    Suryanarayana C (2001) Prog Mater Sci 46:1CrossRefGoogle Scholar
  3. 3.
    Khina BB, Froes FH (1996) J Met 48:36Google Scholar
  4. 4.
    Delogu F, Schiffini L, Cocco G (2001) Phil Mag A 81:1917CrossRefGoogle Scholar
  5. 5.
    Delogu F, Mulas G, Schiffini L, Cocco G (2004) Mater Sci Eng A 382:280CrossRefGoogle Scholar
  6. 6.
    Delogu F, Cocco G (2005) Mater Sci Eng A 422:198CrossRefGoogle Scholar
  7. 7.
    Manai G, Delogu F, Schiffini L, Cocco G (2004) J Mater Sci 39:1CrossRefGoogle Scholar
  8. 8.
    Courtney TH (1995) Mater Trans JIM 36:110CrossRefGoogle Scholar
  9. 9.
    Maurice DR, Courtney TH (1996) Metall Mater Trans A 27A:1981CrossRefGoogle Scholar
  10. 10.
    Buchholtz V, Pöschel T (1997) In Wolf DE, Grassberger P (eds) Friction, arching, contact dynamics. World Scientific, Singapore, p 265Google Scholar
  11. 11.
    Makse HA, Johnson DL, Schwartz LM (2000) Phys Rev Lett 84:4160CrossRefGoogle Scholar
  12. 12.
    Corwin EI, Jaeger HM, Nagel SR (2005) Nature 435:1075CrossRefGoogle Scholar
  13. 13.
    Szabò ZG (1969) In Bamford CH, Tipper CFH (eds) Comprehensive chemical kinetics. The theory of kinetics, vol. 2. Elsevier Science Publishers, Oxford, p 1Google Scholar
  14. 14.
    Lutterotti L, Ceccato R, Dal Maschio R, Pagani E (1998) Mater Sci Forum 87:278–281Google Scholar
  15. 15.
    Warren BE, Averbach BL (1950) J Appl Phys 21:595CrossRefGoogle Scholar
  16. 16.
    Wagner CNJ (1966) Local atomic arrangements studied by X-ray diffraction. Gordon and Breach, New YorkGoogle Scholar
  17. 17.
    Hall WH, Williamson GK (1951) Proc Phys Soc 64B:937CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Chimica e MaterialiUniversità degli Studi di CagliariCagliariItaly
  2. 2.Dipartimento di ChimicaUniversità degli Studi di SassariSassariItaly

Personalised recommendations