Experimental procedure to determine the interdiffusion coefficient of miscibility gap liquid alloys: Case of GaPb system

An experimental procedure to measure the interdiffusion coefficient of nondilute binary ${\mathrm{Ga}}_{0.6}{\mathrm{Pb}}_{0.4}$ liquid alloys exhibiting a miscibility gap is demonstrated. The phase separation is found to be instantaneous, while the formation of a homogeneous alloy is relatively slow. This technique is based on the measurement of the electrical resistivity of liquid alloys during the formation process in a finite capillary. The concentration profiles, deduced from the electrical resistivity data, combined with the Boltzmann-Matano method [C. Matano, Jpn. J. Phys. 8, 109 (1933)] were used to determine the concentration dependence of the interdiffusion coefficient.

Figure 1

Schematic picture of the apparatus used for the multiprobe cell resistivity measurement.

Figure 2

(Color online) Resistivity versus temperature of GaPb liquid alloys below and above the critical temperature. Triangle symbols are data deduced from the resistivity versus temperature for different concentrations (Ref. 9). The uncertainty on the resistivity is too small (since $\Delta \rho ∕\rho \approx 1\%$) and so was not included in the figure for clarity.

Figure 3

(Color online) Time dependence of (a) resistivity and (b) concentration of Ga of GaPb liquid alloys at various sections of the capillary. The arrow indicates the resistivity or concentration from section 1 to section 10. The uncertainty on the concentration $\Delta c$ is found to be lying between 0.007 and 0.03, corresponding to the initial concentrations $c_2=0.86$ (the highest Ga content alloy) and $c_1=0.36$, respectively.

Figure 4

(Color online) Concentration profile of GaPb liquid alloys.

Figure 5

(Color online) Ga concentration versus time compensated distance of GaPb liquid alloys. The investigated zone is delineated.

Figure 6

Ga-concentration dependence of the average interdiffusion coefficient. The solid line is just a guide for the eyes.

Figure 7

Schematic figure showing the Matano integral (dashed area).