The Measurement of Interdiffusion Coefficient of Mg<sup>2+</sup> and Al<sup>3+</sup> in the Defective Spinel, MgO⋅<i>n</i>Al<sub>2</sub>O<sub>3</sub>, and the Analysis of the Reaction Rate of

Abstract

Interdiffusion coefficient of Mg2+ and Al3+ in the defective spinel, MgO⋅nAl2O3, was measured using the couple of spinel pieces, MgO⋅1.1 Al2O3 and MgO⋅1.6 Al2O3. Interdiffusion coefficient of the MgO⋅1.1 Al2O3 side and the MgO⋅1.6 Al2O3 side were separately analyzed as shown in Table 1 by applying the Fick's law tothe concentration distribution measured by EPMA. The Arrhenius plot is shown in Fig. 6 and so-called activation energy, 73kcal/mol, was obtained. The Matano's analysis for one example was carried out as shown in Fig. 7. Two values of the interdiffusion coefficient were calculated and compared with the experimental values, by substituting the self-diffusion coeffisients of Mg2+ and Al3+ estimated on some assumptions, into the Wagner's formula of interdiffusion coefficient, D=D1D2(z12c2)/z12c1D1+z22c2D2, and Yamaguchi and Nakano's, D=D1D2(z12c1+z22c2)/z12c1D1+z22c2D2{1+c1c2(z1-z2)2(1-p)/(z12c1+z22c2)(c1+c2)p}And it was clarified that the values calculated from the Yamaguchi and Nakano's formula can well interpret the actual phenomena so that the formula is proper to analysis of diffusion with gradient of vacancy concentration as in the defective spinel.According to our previous paper, in the reaction of spinel formation, the rate constant, k, is expressed as follows;k=D256(n-1)(3n+1)2/(21n+11)(3n+5)(7n+1) Where n comes from the ofrmula, MgO⋅nAl2O3, which represents the composition of a spinel in equilibrium with Al2O3. Fig. 9 shows k calculated from D obtained in this experiment and n obtained from the phase diagram, comparing with the observed k in the previous papers. These calculated and observed rate constants are consistent with one another fairly well. Therefore, it was numerically proved that the dominant mechanism of spinel formation is the interdiffusion of Mg2+ and Al3+ through the formed spinel layer owing to the concentration gradient expected from the solid solution range and to the interdiffusion coefficient.The so-called activation energy for the spinel formation is 92kcal/mol, while that of interdiffusion is 73kcal/mol, and the difference between them is about 20 kcal/mol. The cause of that difference is that k and D are connected by the terms of the concentration gradient and the mean composition of formed spinel which are functions of n depending upon a temperature. Therefore, it should be noticed that the “so-called activation energy” for the solid state reactions may have meanings different from the original meaning of “activation energy”.