Thermodynamic and Structural Study of the Copper-Aluminum System by the Electrochemical Method Using a Copper-Selective Beta″ Alumina Membrane

Abstract

The liquid phase thermodynamics of mixing of the copper-aluminum binary system are investigated as a function of temperature and composition using the electrochemical potential difference method. A copper-selective beta″ alumina is used as a solid electrolyte, synthesized through ion exchange, sintering from base oxide powders, and the floating zone method of crystal growth. Measured thermodynamics of mixing data were used to inform short-range ordering in copper-aluminum melts through Darken’s factor for excess stability and Bhatia–Thornton structure factors, revealing a strong departure from ideality and pronounced ordering. Mixing properties were used to predict viscosity and self-diffusion coefficients. Features observed in calculated electronic entropy of mixing for copper-aluminum were compared with trends in viscosity, demonstrating the utility of electronic properties of mixing in the description of structure–properties in this liquid binary system.

Appendices

Appendix A: Example of Raw OCP Data

Depicted here is an example of open-circuit potential (OCP) data collected for Cu_0.4Al_0.6 vs Cu utilizing the copper-selective beta″ alumina (Cuβ″Al₂O₃) solid electrolyte described in this study. At a given temperature and composition, steady state in OCP readings was achieved within 1800 seconds. Typical standard deviations (SD) in OCP across a measurement period ranged from 0.02 to 2 mV, increasing with higher temperatures (Figure A1).

Fig. A1

Sample of OCP data for Cu_0.4Al_0.6 referenced to Cu collected utilizing Cuβ″Al₂O₃ after a stabilization period of 1800 s at each temperature

Appendix B

See Table BI.

Table BI Summary of Thermodynamic Values

Appendix C: List of Symbols

$a$ :

Activity

$c$ :

Molar concentration

$D$ :

Self-diffusion coefficient

$E$ :

Cell potential difference

$E^{A}$ :

Activation energy for viscous flow

$ES$ :

Excess stability

$F$ :

Faraday constant

$\bar{H}$ :

Partial molar enthalpy

$k_{B}$ :

Boltzmann’s constant

$M$ :

Hall mobility

$r$ :

Radius of diffusing particle

$R$ :

Ideal gas constant

$R_{H}$ :

Hall effect coefficient

$\bar{S}$ :

Partial molar entropy

$S_{CC} \left( 0 \right)$ :

Bhatia–Thornton structure factor

$S^{e}$ :

Electronic state entropy

$T$ :

Absolute temperature

$x$ :

Mole fraction

$\bar{Y}$ :

Partial molar quantity

$z$ :

Number of electrons per copper(I) ion that travels across the Cuβ″Al₂O₃ membrane

$\alpha$ :

Seebeck coefficient

$\Delta G^{M}$ :

Gibbs energy of mixing

$\Delta H^{M}$ :

Enthalpy of mixing

$\Delta S^{M}$ :

Entropy of mixing

$\eta$ :

Dynamic viscosity

$\eta^{\infty }$ :

Pre-exponential factor for viscous flow

$\mu$ :

Partial molar Gibbs energy

$\sigma$ :

Electrical conductivity