A Structural Electrical Conductivity Model for Oxide Melts
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q¼R ¼ : l G
INTRODUCTION
ELECTRICAL conductivity (r in ohm m ) is the inverse of electrical resistivity (q in ohm m), and it is a measure of a materials’ ability to conduct an electric current. In this work, the units of siemens per meter (S/ m) are used, where siemens (S) is equivalent to ohm1. Resistivity (q) is determined from resistance measurements (R in ohm’s) multiplied by the cross-sectional area (A) of the material through which the current passed divided by the distance the current traveled (l), as shown in Eq. [1]: A ½1 r ¼ 1=q ¼ 1= R : l 1
1
In a solid, the area and length are well defined, and the current path can be determined from the geometry of the solid. In a liquid, the current path is not well defined and calibrations are required. The most widely used experimental setup for the electrical conductivity of oxide melts involves immersing two electrodes into a molten bath, applying a voltage, and measuring the resistance. In this method, the current path cannot be directly determined from the geometry. A cell constant (G) is defined which describes how the current travels based on the specific experimental setup. The cell constant is determined by performing resistance measurements on a liquid of known electrical conductivity. In this way, the electrical resistivity (and conductivity) can be determined using Eq. [2]:
Whether or not this type of measurement technique can provide accurate experimental results has been questioned. Scheifflebein and Sadoway[1] proposed that the measurement techniques historically used on oxide melts based on cell constant calibrations are inaccurate and that a technique with more precise control of the current path is required. However, lacking a significant quantity of experimental data using high-accuracy calibration-free techniques, the less accurate but far more prevalent experimental data obtained using conventional techniques were examined in this work. The goal of the present study is to examine the available experimental data and to develop a structural model capable of predicting the electrical conductivity of a given oxide melt as a function of temperature and composition. In this study, melts of any unary, binary, ternary, and higher order systems in the CaO-MgOMnO-PbO-Al2O3-SiO2 systems were considered.
II.
IONIC CONDUCTION THEORY
Most oxide melts are ionic conductors; charge is carried by individual ions when subjected to an electric field. The electrical conductivity of cationic species is described in Eq. [3]: ri ¼ ci zi Fli ;
ERIC THIBODEAU, Graduate Student, and IN-HO JUNG, Associate Professor, are with the Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, QC H3A 0C5, Canada. Contact e-mail: [email protected] Manuscript submitted March 16, 2015. Article published online September 30, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS B
½2
½3
where ri is the partial conductivity of the ith cationic species in a melt (S/m), ci is the concentration of a charge carrier (mol/m3), zi is the charge
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