Kinetics of the solid state reaction between zinc oxide and aluminum oxide
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= A BmO.. A and B are cations with valences of Z A and Z B, respectively, and O is oxygen anion. When the rate is controlled by the diffusion in the product oxide layer, the rate constant of this reaction can be defined by k =~ (~)2/2Vmt
[1]
where Ax is thickness of the product layer, t is reaction time and Vm is mean molar volume of the interoxide compound. In order to estimate the rate constant from the transport properties of ions, local thermodynamic equilibrium is assumed within the product layer and at the boundaries under isothermal conditions. The diffusion fluxes of ions through the product layer relative to a lattice-fixed frame of reference can be described as follows, 0 Ji = - ~ Li~ ~x (txk + ZkF~)
[21 where ttk is the chemical potential of ions and electrons, 0 is the electrostatic potential in the product layer, F is the Faraday constant and e is an electron. L~k is the transport coefficient and satisfies the Onsager's reciprocal relation, L~k = L,~ (i 5~ k), 12and the relations of L , >=0 and L , L ~ >= L~k13which are required from positive entropy production by diffusion. From the condition of local thermodynamic equilibrium, the chemical potentials of their oxide compounds and metals are: ~i/Zi
-~-
o/IZo[
= [~io/Zi
t~/Z, + IXe = Ftq/Zi A THEORETICAL METHOD TO ESTIMATE RATE CONSTANT OF FORMATION OF INTEROXIDE COMPOUNDS The formation of an interoxide compound by solid state reaction may be expressed by A 0 x + mBOy K. NAGATA is Research Assistant, Department of Metallurgical Engineering, Tokyo Institute of Technology. K. SATO is Chemical Engineer, Diesel-kiki Co. Ltd., Matsuyama Plant. K. S. GOTO is AssociateofProfessor, Technology. Department of Metallurgical Engineering, Manuscript submitted July 17, 1979.
(i and k = A,B,O,e)
(i = A , B )
(i -- A , B )
[3]
The net current in the product layer is zero during the reaction; ZAFjA + ZBFjB + Z o F j o - Fje = 0
[4]
Eliminating the electrostatic potential gradient from Eq. [2] by use of Eqs. [4] and [3], the fluxes of cations are rewritten as J i = -- TiA
0~tA O 0/~Bo 1 0-~- -- Tin - ~x + ~ Tie
(~l~Ao -- -0~[AI~ k 0x
~x ]
ISSN 0360-2141 / 80/0911-0455500.75/0 METALLURGICAL TRANSACTIONS B 9 1980 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
(i
= A, B )
[5]
VOLUME 11B, SEPTEMBER 1980--455
Tik = Lik -- (1/S)EzZk,Lik,ZrZrLi, k (i,k,i' and k' = A ,B,O,e). S is defined as S = EiZkZiZkLik; Tik
where
EXPERIMENTAL PROCEDURE
satisfies the Onsager's reciprocal relation and also EkZk Tik = 0. Because one mole of A and m moles of B are diffusing in opposite directions to form one mole of the interoxide compound at the interfaces between the compound and BOy and A O~, respectively, the growth rate of the product layer can be described as d (Ax)
dt
= Vm[JA
1
-
-
~Jsl
[61
In order to simplify Eq. [5], it is assumed that L i e = 0 (i :p: e), and then T~ = 0. Substituting Eq. [5] into [6] and eliminating d~tso by Gibbs-Duhem's relation, Eq. [6] is integrated from one end of the product layer to the other. Combination
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