Kinetics in multicomponent metallic-ionic systems
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I.
INTRODUCTION
THE kinetics of reactions in multicomponent metallic-ionic systems are of interest to scientists and engineers concerned with alloy-salt systems, glass-metal joints, slag-metal reactions, composite materials, e t c The overall reaction consists of three major steps: (1) diffusion in the metallic phase to or from the interface; (2) interfacial reactions involving a number of simultaneous coupled anodic and cathodic reactions of the type Mi = M~/ + z,e
(i = 1 , 2 . . . . .
n)
[1]
and (3) diffusion in the ionic phase from or to the interface. Among these three steps, rate expressions for interfacial reactions have been formulated :1,2,31 and diffusion in single metallic and ionic phases has been well studied. [4,5.61Experimental data for multicomponent metallicionic systems are scarce. Furthermore, the development of theoretical analysis has also been hindered by the lack of complete thermodynamic information, particularly in multicomponent ionic melts. In the earlier work, only computed results for a hypothetical system were reported for the coupled interfacial reactions and diffusion in both phases where a flux continuity condition was applied at the boundaries to connect the preceding three steps: m J~'= oJi=J~
( i = 1 , 2 . . . . . n)
[2]
In recent years, for the first time, Ray 171 conducted experiments to determine the values of specific rate constants in the Fe-CaF2 system directly and met limited success. Gaye and Welfringer 18Jestablished modeling for thermodynamic properties of slags. These achievements, in addition to earlier reported thermochemical data, I9 is] make it possible for iron alloys and silicate slags within certain composition ranges to be used for the study of coupled interfacial reactions and diffusion. DUNCAN MA, Research Fellow, formerly with the Department of Materials Science and Engineering, McMaster University, is Research Fellow, Department of Metallurgy and Materials Science, the University of Toronto, Toronto, O N , Canada M5S IA4. W.-K. LU, Professor, is with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON, Canada L8S 4L7. Manuscript submitted May 26, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS B
In the present work, effort is made to study the kinetics of interracial reactions. Experimental w o r k is carfled out in a system with coupled interfacial reactions and diffusion in slag and metal phases. In the formulation for interfacial reaction rates, the coupling factor is identified, and the linearization of equations in mathematical operations proposed in the earlier study tll is avoided. In mathematical modeling, the interfacial reaction zone with finite thickness in both ionic and metallic phases will be proposed, and the flux continuity equations as boundary conditions for diffusion are replaced by a set of mass conservation equations in the interfacial reaction zone. In the experimental work, the concentration profiles in both phases will be measured by using an electron microprobe. The experimental and compute
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