Part V – May 1969 - Papers - Thermodynamics of Binary Metallic Solutions. Part III

Further consideration is given to the application of the quadratic formalism to evaluate the thermodynamics of binary metallic solutions from experimental data. The use of the thermodynamic relation, in(r1/r2) dN2= 0, in the evaluation of activity data is discussed. The empirical correlations derived previously for enthalpies and entropies of solutions in Part II are shown to be predicted theoretically for a special case. The applicability of the quadratic formalism to the activity coefficients for binary organic solutions is demonstrated. DARKEN&apos; introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. In a subsequent paper (Part II) Turkdogan and Darkeen2 extended this formalism to the enthalpy and excess entropy of binary metallic solutions, and showed that the available data for the activity coefficients and heats of mixing of many solid and liquid binary metallic solutions confirm reasonable applicability of the quadratic formalism. Much variation was noted, however, in the extent of the terminal regions from one system to another, commonly from about 10 to 70 at. pct. For the present purpose, equations derived previously need be given only for one of the terminal regions, e.g. region (I), 0 < N2 < N&apos;2: where subscripts 1 and 2 indicate quantities for components 1 and 2 and superscript ° the values at infinite dilution; other terms are: N = atom fraction, y = activity coefficient, = partial molar enthalpy of solution, ?HM = molar heat of solution, ?Sx = excess partial molar entropy, ?Sx = excess molar entropy. The heat and entropy like terms (constants) el, and S12 are defined in the following expression for the temperature dependence of a12, thus a12 £12 — s12 rnl 2.303RT 2.303 R l J Using this formalism, the thermodynamics of binary systems in the terminal regions may be described over a temperature range of experisental interest in terms of eight quantities: Lº1—Lº2, ?Sx1,?Sxº2 , £12 ,£21,fiai, S12, and S21. In the previous paper, these quantities were evaluated for many solid and liquid binary solutions, and two significant correlations were observed between these thermodynamic quantities pertaining to the terminal regions, thus [10] and [11] Combining Eqs. [9], [l0], and [ll] and rearranging gives a12 -a21 = 1.382R log rº2- 0.08(?S2xº- ?S1xº) [12] Since the second term involving entropies is small and Eqs. 1101 and [ll] are empirical relations, the above equation may be simplified to a12 = 2.74 log rº2 [13] Using the values of a&apos;s and y°&apos;s compiled in Parts I and 11, a12 - a21 is plotted against log(rº2/rº1) in Fig. 1; the line drawn has a slope of 2.74. For Hg-K at 300°C, log(yº2 /yº1)= —5.10, not shown in Fig. 1, and from correlation [13], a12 - a21 = -13.97; this is to be compared with -10.76 derived from the activity data (Part II).