The Gibbs free energy of formation of a glassy alloy
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N. Clavaguera Departament d 'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, 08028-Barcelona, Spain (Received 6 June 1988; accepted 24 March 1989)
A simple expression for the Gibbs free energy of formation of a pure component or a eutectic alloy glass, relative to the stable crystalline phase (or phases) at the same temperature is deduced by use of thermodynamic arguments. The expression obtained is supposed to apply to both monocomponent and multicomponent liquid alloys that might become glasses from the supercooled liquid state, irrespective of the critical cooling rate needed to avoid crystallization.
I. INTRODUCTION The ability of molten alloys to form metastable noncrystalline structures is of significant practical and theoretical interest and is the subject of many studies.1"8 One of the important quantities appearing in the thermodynamic prediction of glass formation is the Gibbs free energy difference between the crystallized material and the competing but metastable glassy alloy phase.9 From phase diagram calculations it is possible to estimate the thermodynamic properties of the liquid and crystalline phases over a wide temperature interval.10 Now, it is well known that at the glass transition temperature the supercooled liquid becomes a glass. The nature of the glass transition phenomenon is a question that remains open.11'12 Nevertheless, one thing is recognized to be quite general: at the glass transition temperature the heat capacity decreases sharply and takes, for the glass, a value very similar to that of the crystallized material. One of the formulae which has proved to be very fruitful in describing the free energy difference between the supercooled liquid and the crystal was established some years ago by Hoffman,13 and it is currently used to estimate the rate of nucleation and growth of crystallites in supercooled liquids.14"17 Further expressions have been derived by Jones and Chadwick,18 Thompson and Spaepen,19 Dubey and Ramachandrarao,20 and Battezzati and Garrone.21 However, little attention has focused on the very related concept of the free energy of formation of the glass. In this paper we want to derive a simple expression for the Gibbs free energy of formation of a glassy alloy based on pure thermodynamic considerations. The way to achieve that purpose is defined in the following manner. First of all, we will consider the situation of a pure substance (element or compound) or a eutectic alloy. Then we will obtain an estimate of the sharp decrease of the heat capacity of the liquid at the glass transition region when it becomes a glass, in terms of the melting entropy. Further, 906
http://journals.cambridge.org
J. Mater. Res., Vol. 4, No. 4, Jul/Aug 1989
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we will comment on the formulae already deduced in the literature to describe the Gibbs free energy difference between the supercooled liquid and the crystal. Then we will establish an approximate formula for the Gibbs free energy of formation of what we
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