Free Volume Change of Metallic Glasses at Elevated Temperatures
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Structural relaxation in metallic glasses (MGs) occurs when the material is annealed at elevated temperatures [1], resulting in substantial property change in MGs, including diffusivity [2], plasticity [3], electrical resistivity [4], and son on. The free volume (FV) model can explain the structural relaxation in BMG. According to the FV model, structural relaxation at the elevated temperatures is resulted from a reduction of the excess free volume that was trapped in the MG during material processing [5]. A direct evidence for the free volume reduction during structural relaxation is the densification experiment performed by Haruyama [6–8]. Different models have been proposed to interpret the structural relaxation behavior, for instance, flow defect model [9-10], stretched exponential relaxation model, Šesták–Berggren SB (m, n) kinetic model, and isothermal–isoconversional method.

The relaxation of free volume has a relationship with calorimetric parameters given by,

         relaxation of free volume has a relationship with calorimetric measurements ------------------------- [1687]

         β -- A constant with a dimension of energy,
         ΔH -- The changes in the enthalpy,
         Δvf -- The average free volume during structural relaxation.

This relationship had been demonstrated experimentally by density and enthalpy relaxation measurements in a Zr55Cu30Ni5Al10 MG [11].







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[4] O. Haruyama, N. Annoshita, N. Nishiyama, H.M. Kimura, A. Inoue, Mater. Sci. Eng. A 375–377 (2004) 288.
[5] A.V. Beukel, J. Sietsma, Acta. Metall. Mater. 38 (1990) 383.
[6] O. Haruyama, H. Sakagami, N. Nishiyama, A. Inoue, Mater. Sci. Eng. A 449–451 (2007) 497.
[7] O. Haruyama, A. Inoue, Appl. Phys. Lett. 88 (2006) 131906.
[8] O. Haruyama, Intermetallics 15 (2007) 659.
[9] F. Spaepen, Acta Metall. 25 (1977) 407.
[10] S.S. Tsao, F. Spaepen, Acta Metall. 33 (1985) 881.
[11] A. Slipenyuk, J. Eckert, Scripta Mater. 50 (2004) 39.




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