Correlation between excess volume and thermodynamic functions of liquid Pd-X (X = Fe, Cu and Ni) binary systems
Introduction
The correlation between excess volume and the various thermodynamic functions of liquid-state binary alloys have been reported since 1937 [1]. In 1988, Iida and Guthrie summarized the relationship between excess volume and enthalpy of mixing [2]. They concluded that the enthalpy of mixing was expected to be negative/positive for binary alloys having negative/positive excess volume. However, in our recent paper [3], we clarified that Fe-Ni, Cu-Au, Fe-Co, and Bi-Tl systems had positive excess volumes with negative enthalpies of mixing, and conversely for the Cu-Ni system. These systems plainly contradict the correlation proposed by Iida and Guthrie. These alloy systems have a common characteristic feature in their phase diagrams. The Fe-Ni, Cu-Au, Fe-Co, and Bi-Tl systems have intermetallic compounds with order–disorder transformations [4], [5], [6], [7]. In contrast, the Cu-Ni system has a miscibility gap in solid solution [8]. In this study, we focus on alloy systems having order–disorder transformations. From this point of view, the Pd-Fe and Pd-Cu systems were studied, which have order–disorder transformations [9], [10]. In addition to those alloys, the Pd-Ni system, which was also studied for comparison, has a continuous solid solution [11]. Based on the foregoing trend, it is expected that the Pd-Fe and Pd-Cu systems have positive excess volume. Employing electromagnetic levitation (EML), the densities of these alloys in a liquid state were measured in a static magnetic field. The excess volumes of these alloys were evaluated from the density results. An analysis of the correlation between excess volume and thermodynamic properties is also performed.
Section snippets
Experimental
Experimental details of the density measurement were previously reported [3], and only a brief explanation is given here. Samples were prepared using Pd (99.95 mass% purity), Fe (99.99 mass% purity), Cu (99.99 mass% purity), and Ni (99.99 mass% purity) and alloyed by arc melting, details of the source materials were shown in Table 1. After the chamber was evacuated to 10−2 Pa with a turbo molecular pump, the chamber was filled with Ar-5 vol%H2 gas to prevent sample oxidation. Samples were
Densities of Pd-Fe melts
The temperature dependence of the density of liquid Pd [12], [13], [14], [15], [16], [17], expressed as a linear function of temperature within the temperature range that included the supercooled regime. The present data show good agreement with previous results reported by Paradis and co-workers (electrostatic levitation) [12] and Eremenko and co-workers (calculation using Grüneisen’s law) [14]. The present data also agree to within the uncertainties with the data reported by Lucas (maximum
Uncertainty analysis
The uncertainty associated with density measurements is assessed using the following equations:where u(ρ) is the combined standard uncertainty in the density measurement; u(V) and u(m) are the uncertainties associated with the volume and mass measurements, respectively. As an example, the uncertainty analysis for the density of liquid Pd-Cu (Mole fraction:xPd = 0.5) at 1523 K is presented in Table 8. u1(V) is the standard deviation in the volume
Correlation between excess volume and thermodynamic properties
The correlation between VE and the various thermodynamic properties have been investigated by many researchers. In many instances, VE was analyzed with regard to enthalpy of mixing (ΔmixH) of melts [2]. However, ΔmixH reflects only the interatomic interaction. In our previous study [3], the analysis of VE also included the excess Gibbs energy (GE).
Conclusion
We obtained accurate measurements of the densities of Pd-X (X = Fe, Cu and Ni) binary melts within an expanded uncertainty from 1.0 to 1.3% using an electromagnetic levitator and static magnetic field. Excess volumes of these binary systems were positive over the entire composition range. Therefore, their order–disorder transformation systems have positive excess volume in their liquid states. The correlation between VE and the thermodynamic functions GE and ΔmixH at 0.5 mol fraction tend to
Acknowledgement
This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant No. 26249113.
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