Fragility of Metallic Glass Forming Liquids
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Fragility of Metallic Glass Forming Liquids G. J. Fan1, R. K. Wunderlich2 and H. –J. Fecht2,3 Chemical Engineering and Materials Sicence, University of California, Davis, CA 95616, USA 2 Ulm University, Materials Division, D-89081 Ulm, Germany 3 Research Center Karlsruhe, Institute of Nanotechnology, 76021 Karlsruhe, Germany
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ABSTRACT Based on the available kinetic and thermodynamic data, we compare the kinetic fragility and thermodynamic fragility of different metallic glass forming liquids. The results indicate a correlation between the kinetic and thermodynamic fragility in metallic glass forming liquids, consistent with the energy landscape model which predicts a connection between the kinetic and thermodynamic properties of supercooled liquids. The metal – metalloid glass forming alloys such as PdNiCuP are found to exhibit a distinctively different correlation as compared to early – late transition metal – type metallic glass forming alloys such as ZrTiCuNiBe. For the same thermodynamic fragility the former exhibit a much larger kinetic fragility indicating that the two classes of alloys have a different liquid structure. In addition, the relationship between the kinetic fragility and the Gibbs free energy difference between the undercooled liquid and the crystalline phases has been discussed in both metal metalloid glass forming alloys and early – late transition metal – type metallic glass forming alloys. INTRODUCTION Recently, considerable attention has been given to the question as to what extend the particular temperature dependence of the kinetic slowing down is also reflected in the temperature dependence of the thermodynamic properties of the undercooled liquid phase [1-2]. The Adam – Gibbs model of cooperatively relaxing regions provided the first quantitative basis for relating the thermodynamic and kinetic properties of a liquid [3]. It is based on the evaluation of the transition probability between two liquid configurations subject to the existence of some minimum relaxing configuration. According to the Adam – Gibbs model, the temperature dependence of the viscosity η was expressed by
η = η 0 exp[ A T S c (T )]
(1)
Sc(T) represents the configurational entropy of the liquid. In experimental verifications of the Adam – Gibbs equation, Sc(T) is usually identified with the entropy difference between the undercooled liquid and crystalline phase, ∆Slx, as obtained from measurement of the specific heat capacity in the undercooled liquid and crystalline solid, and the enthalpy of fusion:
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S c (T ) = ∆S lx (T ) = ∆S f − ∫TTm C lp (T ) − C px (T ) d ln T
(2)
with ∆Sf the entropy of fusion, Tm the melting temperature, and Cpl, Cpx the specific heat capacities of the liquid and the crystalline phase, respectively. The Adam – Gibbs model suggests that there should exist some measure of thermodynamic fragility, expressed in terms of the temperature dependence of the entropy of the liquid phase, which correlates with the kinetic
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fragility. Ito et al. [1] and Martinez and Angell
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