αShape, Birth of one Universal Parameter?
The description of different effects observed in nature by only one general equation is the “Holy Grail” for all physicists. This goal has been achieved for characteristic temperatures through a top-down approach (studying size effects from macroscopic laws) and is presented in this chapter. Here, we show the general equation based on the surface area to volume ratio of nanostructures and statistics (Fermi-Dirac or Bose-Einstein) followed by the particles involved in the investigated phenomena. From the distinction between fermions and bosons, so-called particles which follow a Fermi-Dirac or a Bose-Einstein statistics respectively, this equation indicates the universal behaviour of size and shape effects on different material properties like melting, ferromagnetism, vibration and superconduction. The same shape parameter used in this universal equation can be used to determine the melting enthalpy, the phase diagrams of alloys, the energy bandgap and also the creep behavior of nanomaterials. Theoretical predictions show satisfactory agreement with experimental data taken from literature.
Grégory Guisbiers and Dibyendu Ganguli
G. Guisbiers "αShape, Birth of one Universal Parameter?", Key Engineering Materials, Vol. 444, pp. 69-80, 2010