Quenched-in Free Volume V f , Deformation-induced Free Volume, the Glass Transition Tg and Thermal Expansion in glassy Z
- PDF / 621,146 Bytes
- 6 Pages / 595 x 842 pts (A4) Page_size
- 22 Downloads / 172 Views
MM3.5.1
Quenched-in Free Volume Vf, Deformation-induced Free Volume, the Glass Transition Tg and Thermal Expansion in glassy ZrNbCuNiAl measured by Time-resolved Diffraction in Transmission A.R.Yavari1 M. Tonegaru1, N. Lupu２, A Inoue2 , E. Matsubara2 , G. Vaughan 3, Ǻ.Kvick3, W.J. Botta1 1 Euronano-LTPCM-CNRS, Institut National Polytechnique de Grenoble, BP 75, 38402 St-Martin-d’Hères Campus, France ([email protected]), 2 Institute for Materials Research, Tohoku University, 980-8577 Sendai, Japan 3 European Synchrotron Radiation Facilities (ESRF), 38042 Grenoble, France, ABSTRACT Using high-precision X-ray dilatometry, we have succeeded in directly measuring excess quenched-in free-volume Vf in metallic glasses. The method was applied to the very easy glass forming Zr57Nb5Cu15.4Ni12.6Al10 (Vit 106). The annealing out of the order of 0.5% free volume was observed during heat treatment of rapidly solidified glassy ribbons. Excess free volume was also generated by heavy deformation and observed to anneal out during heat treatment. Once the excess free volume anneals out, the glass transition Tg appears clearly as a break in the x-ray dilatation curves as the glass goes over to the supercooled liquid region prior to crystallization at Tx. INTRODUCTION The viscosity, η, of a liquid defines its flow behaviour and response to mechanical solicitation. The Vogel-Fulcher-Tammann relation models the strong temperature T dependence of viscosity using a three-parameter (ηo , B and To) empirical expression : (1) η = ηo exp [B/(T-To)] The Doolittle relation defines viscosity in terms of the free volume content Vf with three adjustable parameters ηo , β and Vo: (2) η = ηo exp [βVo/Vf] Setting (1) and (2) equal yields Vf as a function of temperature: (3) Vf ≈ Vo α (T – To) This definition was given physical and atomistic basis by the work of Turnbull [1] using an atom in a shell model with a simple interatomic potential and consistent with Eyring’s partition function [2] for simple liquids. Substitution of (3) in (2) leads to the expression: η ∼ η0 exp(βVo/Vf) ≈ η0 exp (δVa/Vo α (T-To)) (4) This type of expression has been used to model the viscosity and flow behavior of metallic glasses [3-5]. A liquid alloy has no long-range atomic order; it is a random packing with local short- and medium-range order only. For selected liquid alloys, a metallic glass is obtained [6] if the liquid is cooled fast enough to avoid nucleation and growth of crystalline structures (long-range atomic order). As the liquid is cooled, Vf = Vo α (T-To) is reduced and η goes up exponentially. A glass is obtained at Tg when the η reaches about 1012 Poise [7]. Thus, through the viscosity, Vf controls atomic mobility in the glass. When applied to liquids (and glasses), time-resolved diffraction studies of phenomena occurring on a time scale of τt can only be effective if acquisition time τa 650 K, subsequent reheating does not result in further shrinkage of the average volume per atom. The Zr57Nb5Cu15.4Ni12.6Al10 melt-spun ribbons were also ball-milled un
Data Loading...
