Electronic Processes in Solid-Phase Reduction
Abstract Generated abstract
The paper examines the mechanism of solid-phase reduction in mixtures of carbon and metal oxides, emphasizing that surface exchange processes between reacting particles are only indirectly accessible through gas evolution, thermogravimetry, and compositional changes. It argues that mass transfer occurs mainly through the gas phase and proposes representing the mixture as a set of elementary electrochemical cells operating in a low-temperature plasma, with carbon as cathode and oxide as anode. Using concepts from thermionic energy converters, the authors relate reduction rate to electron transfer, thermionic emission, plasma parameters, interparticle spacing, gas pressure, temperature, and oxide vapor effects. The model suggests a framework for applying transport-process theory to derive quantitative links between surface properties, gas-phase conditions, and reduction kinetics.
Full Text
ELECTRONIC PROCESSES IN SOLID-PHASE REDUCTION
V. S. ARKHIPOV, S. I. SMOLYANINOV
(Presented by the scientific seminar of the organic departments of the Chemical-Technological Faculty)
The basis for constructing hypotheses about the mechanism of reduction processes occurring in the solid phase between carbon and metal oxides is provided by data on the dynamics of the release of CO and CO₂, changes in the composition of the oxide being reduced, the results of thermogravimetric analysis, and other indicators characterizing the overall result of the multitude of elementary reactions occurring between particles of oxide and carbon located in immediate proximity to one another. In this case, only indirectly can one judge the exchange processes between the surfaces of the reacting particles. Meanwhile, it is precisely these processes that determine the course of reduction.
It has been shown experimentally and theoretically that mass transfer between reacting particles proceeds mainly through the gas phase [1].
Thus, the reacting mixture may be represented as a system consisting of many elementary electrochemical cells placed in a peculiar gaseous electrolyte or in a low-temperature plasma, if the terminology of physics is used. The validity of such a representation follows from the following conditions necessary for the electrochemical course of a reaction:
-
Spatial separation of the oxidation and reduction processes at the solid–gas phase boundaries;
-
The presence in the electrochemical cell of circuits of the first kind—electrons of thermoelectron emission—and circuits of the second kind—low-temperature plasma.
Since the rate of the spontaneous course of a reaction in a galvanic element is regulated by the resistance of the conductor of the first kind [2], it is expedient to consider what determines electron transfer in the interelectrode gap filled with low-temperature plasma. In this case, the factors limiting electron transfer will also be limiting for the reduction reaction as a whole. To analyze the transfer process, one may use the concepts developed for thermionic converters of thermal energy into electrical energy (TEC) [3].
The number of electrons transferred in a TEC from the cathode to the anode is connected by a complex dependence with the thermionic emission capability of the emitter material, the distance between the electrodes, and the parameters of the plasma.
The plasma in a TEP has a low degree of ionization (below 1%) and a low temperature (2000°K). The plasma is created by electron and ion fluxes coming from the cathode. The electron emission current is determined by the Richardson formula [3]
\[ I_R = A \cdot (1 - R)\, T^2 \cdot \exp\left(-\frac{e\varphi}{kT}\right), \]
where \(A\) is a constant for all emitters;
\(R\) is the electron reflection coefficient;
\(T\) is the absolute temperature;
\(e\varphi\) is the work function of the cathode;
\(k\) is Boltzmann’s constant.
To determine the ion emission current, the Saha–Langmuir formula [3] is used.
\[ I_c = \frac{\frac{1}{4}nv} {1 + 2 \exp\left[\frac{e(V - \varphi)}{kT}\right]}, \]
where \(n\), \(v\), \(V\) are the density, velocity, and ionization potential of the plasma.
As the ion source in a TEP, alkali metals are usually used, since they have a low ionization potential. The positive ions formed compensate the space charge of the electrons, which makes it possible to obtain large currents. In addition, alkali metals, being adsorbed on the cathode surface, lower the work function. In this case, in accordance with the Richardson formula, the emission current increases.
Solving the transport equations makes it possible to obtain expressions for the saturation current in certain special cases. For the case of the uncompensated mode of operation of a TEP, provided that emission from the anode is negligibly small, the formula has the form [3]:
\[ I = \frac{\frac{2D}{Lv}\cdot nv} {\sqrt{\left(1 + \frac{4D}{Lv}\right)\cdot\left(1 - \frac{8D}{Lv}\right)}}, \]
where \(D\) is the electron diffusion coefficient;
\(L\) is the interelectrode gap.
Analysis of this formula shows that the dependence of the current on the plasma pressure has an extremal character, with the maximum saturation current occurring at such a pressure value for which one electron mean free path fits within the interelectrode gap.
Considering carbon as the cathode and the oxide as the anode of the TEP, one can analyze the influence of the temperature, pressure, and composition of the gas phase on the rate of the reduction reaction as a function of the current. The oxide, in accordance with the work of Elutin [4], can, by evaporating into the interelectrode space, play the role of a source of ions for plasma formation, and also lower the work function of the cathode.
It must be taken into account that the interaction of the oxide and carbon leads to a change in both the chemical composition and the structure of the surfaces, which introduces new elements into the transport processes, complicating analysis of the process.
The proposed model of the reduction mechanism makes it possible to apply the well-developed mathematical apparatus of transport processes in a TEP to establish quantitative relationships between the surface properties of the reacting substances, the parameters of the gas phase, and the rate of the reduction reaction occurring in a mixture of oxide and carbon powders.
REFERENCES
- Mechanism and Kinetics of Metal Reduction. Edited by A. M. Samarin. “Nauka,” 1970, pp. 7–15.
- V. K. Fioletti. Theoretical Electrochemistry. “Khimiya,” 1969.
- I. P. Stakhanov, A. A. Stepanov, V. P. Pashchenko, Yu. K. Guskov. Plasma Thermionic Energy Conversion. Atomizdat, 1968.
- High-Temperature Materials. Edited by V. P. Elyutin. “Metallurgiya,” 1968.