Correlation between excess volume and thermodynamic functions of liquid Pd-X (X = Fe, Cu and Ni) binary systems

https://doi.org/10.1016/j.jct.2018.09.037Get rights and content

Highlights

  • Thermophysical properties of liquid Pd-X (X = Fe, Ni, Cu) melts were measured by a levitation method.

  • The densities of liquid Pd-X (X = Fe, Ni, Cu) melts were measured within an uncertainty of 1.6%.

  • The order-disorder transition systems have positive excess volume.

  • The correlation between VE and the thermodynamic functions at 0.5 mole fraction tend to saturate with larger GE and ΔmixH.

Abstract

Binary systems Pd-X (X = Fe and Cu) have order–disorder transformations in solid-solution ranges. A sensitive parameter to atomic arrangement for a solution is the excess volume, which in itself is interesting from a thermodynamic perspective. In this study, using a combination of electromagnetic levitation and a static magnetic field, accurate measurements were taken of the density of liquid Pd-X alloys from which excess volumes were evaluated. The excess volumes of these binary systems were positive over the entire composition range. Hence, these order–disorder transformation systems have positive excess volumes in their liquid states. The results are analyzed using thermodynamic functions such as the excess Gibbs energy and enthalpy of mixing.

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:u2ρ=ρV2u2V+ρm2u2m,u2V=u12V+u22V,u2m=u32m+u42m,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.

References (45)

  • D.J. Chakrabarti, D.E. Laughlin, S.W. Chen, Y.A. Chang, Cu-Ni (copper-nickel), Phase diagrams of Binary Copper alloys,...
  • H. Okamoto
  • P.R. Subramanian et al.

    Cu-Pd (copper-palladium)

    J. Phase Equilib.

    (1991)
  • A. Nash et al.

    Ni-Pd (nickel-palladium)

    J. Phase Equilib.

    (1984)
  • P.F. Paradis et al.

    Containerless property measurements of liquid palladium

    Int. J. Thermophys.

    (2004)
  • L.D. Lucas

    Densite de l’argent, du cuivre, du palladium et du platine a l’etat liquid

    C. R. Acad. Sci.

    (1961)
  • V.N. Eremenko, Y.V. Naidich, пoepxocoe aяжeиe pacплaлeыx poдия и пaллaдия, Izv. A. N., OTN, 3 (1961)...
  • N.A. Vatolin et al.

    Surface tension and density of molten alloys in the Pd-Al, Pd-Sb and Pd-Lb

    Trudy. Inst. Met. Sverdlovsk.

    (1969)
  • P.S. Martsenyuk et al.

    Investigation of the density of liquid palladium, platinum and iridium at melting temperature

    Ukrain. Khim. Zhur.

    (1974)
  • V.F. Ukhov et al.

    Surface tension and densities of liquid palladium-iron, palladium-chromium, and palladium-silicon alloys

    Zhurnal fizicheskoi Khimii (=Russ. J. Phys. Chem.)

    (1968)
  • J. Brillo et al.

    Density determination of liquid copper, nickel, and their alloys

    Int. J. Thermophys.

    (2003)
  • J. Brillo et al.

    Density and thermal expansion of liquid binary Al-Ag and Al-Cu alloys

    Int. J. Mat. Res.

    (2008)
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