Detailed assessment of integral thermodynamic quantities of liquid Bi-Sn alloy solution system
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I.
INTRODUCTION
THE solid Bi-Sn alloy system has recently attracted the attention of many applied[1,2,3] and basic[4,5] investigators. The former is to develop lead-free industrial alloys. The latter is to study the effect of pressure on metastable phase formation near eutectic compositions and the effect of composition on elastic properties and internal friction. For liquid Bi-Sn solutions, there are diverse property measurements over the entire range of compositions: volume and density,[6] surface tension,[7] diffusivity,[8] and electrical resistivity.[9–12] A small positive deviation of density was attributed to positive deviation of activity from Raoult’s law.[6] In fact, the thermodynamic behavior of molten Bi-Sn solution is very confusing as it is classified as regular, subregular, and nonregular, as well as DHm " 0, as demonstrated in Table I. The senior author and co-workers thus reinvestigated the liquid Bi-Sn system in the range of 573.15 (300 7C) to 773.15 K (500 7C) with great care on alloy preparation, on electromotive force (emf) cell performance, and on equilibration of atmosphere.[23] We then assessed in great detail[24] the partial thermodynamic quantities and their unequivocal limiting values at infinite dilution of both components using the authentic Chiotti integration and genuine Chiotti derivative.[25] Our results were different from those presented in the last 7 decades.[24] We found the solution to be nonregular and, DH i, DS ixs, and DG xsi , where i 5 Bi and Sn, oscillated with composition. The terms DH i and DS xsi were independent of temperature, so the excess partial molar heat capacities of the solution were zero: DC xsp,i 5 0. In this article, we present the integral thermodynamic quantities of the liquid Bi-Sn solution system as a function of both composition and temperature. These quantities are SEUNG-AM CHO, Senior Research Scientist, is with the Department of Materials Science, Venezuelan Scientific Research Institute (IVIC), and is Professor, School of Metallurgical Engineering and Materials Science, Central University of Venezuela, Caracas 1050A, Venezuela. JOSE LUIS OCHOA, Research Associate, is with the Department of Materials Science, Venezuelan Scientific Research Institute, Caracas 1020A, Venezuela. Manuscript submitted December 19, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS B
calculated from the partial quantities.[24] We then interpret the behavior of the solution in terms of an atomistic point of view. II.
SPLINE FUNCTION REPRESENTATION OF PARTIAL QUANTITIES
The piecewise polynomial function known as spline function is a smooth function with which to fit data. The spline function is adequate in the case in which, for theoretical reasons, the form of the underlying function is not known a priori.[26] This is the situation usually encountered in the problems of thermodynamics of solutions. First, no representative model formalisms are available beyond symmetrical and subregular solution.[27,28,29] Second, many multiparameter functional representations no significanc
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