A theoretical evaluation of chemical ordering and glass transition in liquid Mg-Sn alloys
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I.
INTRODUCTION
INrecent years there have been several attempts to describe the thermodynamic properties of binary metallic melts with strong affinity between the two components. 1-4 Such systems are of considerable interest as candidates for the production of metallic glasses. The affinity has been represented formally by an hypothesized tendency for the formation of molecular-like associates, and the thermodynamic model contains four adjustable parameters, the standard Gibbs energy of formation of the associates and interaction energies between the "free" atoms of the two components and between "free" atoms of each component and the associates. In the beginning the evaluations were made by hand or by computer using rather primitive software. It was then common to use approximations of the theoretical equations. It was also common to put some of the adjustable parameters equal to zero. Such a strategy could be justified when one was interested only in describing the experimental information analytically, but the physical interpretation was lost. On the other hand, it could be argued that the numerical values of the four parameters can be interpreted physically only in cases where the experimental information is sufficient to allow the evaluation of as many as four adjustable parameters. The Mg-Sn system is an example where assessments have been made with different strategies. A purpose of the present work was to make a new assessment using all the information available and thus to test the reliability of the parameter values reported earlier. Another purpose was to try different methods of extrapolating the properties to low temperatures and to estimate the glass forming tendency. The thermodynamic properties of the liquid phase in the Mg-Sn system have recently been evaluated by two groups BJORN J(3NSSON and JOHN AGREN, Research Associate, are with the Division of Physical Metallurgy, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Manuscript submitted March 19, 1985. METALLURGICAL TRANSACTIONS A
using different strategies. Sommer 3 chose to put to zero the two interaction energies between each kind of atom and the associates whereas Lele and Ramachandrarao 2 used all four parameters. In a subsequent paper Lele et al. 5 emphasized that the approximations used by Sommer are not necessary because exact formulas can be derived and used in the evaluation. Such a method had also been developed in Sommer's group, 6 and when he applied their method to the data used by Lele et al., he obtained a result very similar to Lele's. He also evaluated the standard deviation of the parameter values and obtained (in kJ/mol): C~g = -34.9(+--0.39);
C'g = -53.1(---0.62);
C~,g = -63.6(+-0.61) A~
= -22.8(+-0.48) + 0.5(+-0.036)" 10-3T
II.
EXTRAPOLATION OF T H E LIQUID PHASE TO LARGE UNDERCOOLINGS; THE ISENTROPIC TEMPERATURE
It was pointed out by Kauzmann 7 that some information indicates that the entropy of the liquid state is approaching that of the crystalline as the temperature is lowered, a tendency which must be
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