Kinetic models of structural relaxations in metallic glasses

Experimental observations show that, while the form given in eq. (1.18) is good for Cf Cfo, it is not appropriate when Cf— Cfe (clearly, when t— oo, Cf O instead of Cf Cfe), for which the kinetics must reflect the decreasing driving force for relaxation to give a modified kinetics expression that satisfies this requirement (van Aken et al. 2000) 

This expression can also be integrated readily for an initial concentration Cf = Cfo to give 

8 The distributed character of structurai reiaxations and the giass transition 

In Section 1.5 free volume was introduced as a local property of the structure, but in the discussion it was treated only as a global average. In reality, as Fig. 1.12 shows, the volume per atom v as determined in a computational model of a disordered system (Finney 1970) is distributed, indicating that the local free volume as defined by either eq. (1.3) or eq. (1.6b) must also be distributed. Since the viscosity or fluidity represents a global equilibrium property of a large system, the free volume considered above must be the average free volume arising from the local thermal equilibrium distribution of the volume per atom. If a liquid or melt in equilibrium at a temperature Ti, with an equilibrium viscosity is rapidly cooled to a lower temperature T2 Ti, such that the 

12 Distribution of volume per atom in a 3D atomic packing model of uniformly sized spheres (from Finney (1970) courtesy of the Royal Society of London). 

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