Thermodynamic factor and the relative chemical potential of the impurity component in CuGe, AgSn and AgSb α-solid solutions

Abstract

The evaluation of transport experiments in alloys requires an exact knowledge of the thermodynamic factor Φ i and its dependence on concentration. Since thermodynamic activities a i have to be differentiated in order to deduce Φ i measurements of a i have to be very precise. Usually the scatter of data is much too large to derive good values for Φ i in this way. This is particularly true for very dilute alloys. Therefore, Φ i is obtained directly by comparing precision measurements of chemical- and tracer diffusion. An approximation for Φ i is derived from a modified Darken equation taking the vacancy flow as described by Manning into account. Since the validity of Manning's statistical alloy model is questionable in dilute solutions for alloys exhibiting binding between vacancies and impurity atoms, an amendment of this model given by Heumann is discussed. The proposed approximation for Φ i is shown to be insensitive in this respect for alloys with a faster diffusing alloying addition and a limited range of concentrations, conditions which are maintained in the present investigation. Φ i was calculated from detailed measurements for CuGe, AgSn and AgSb-α-alloys and from literature data for AgCd and AgIn at 1000 K. Its dependence on concentration can be characterized by a flatter slope at the beginning, becoming steeper as concentration increases. A plot of Φ i vs the electron to atom ratio e/ a shows a marked parallelity between these systems and indicates the dominant electronic character of the binding and particularly its dependence on concentration, which for the electronic part is due essentially to an impurity-impurity interaction. This behavior will be analyzed in more detail in a forthcoming paper.