The mixture of coarse alumina and fine zinc oxide, with different mole fraction of ZnO,
XZ, was heated at 1000°-1200°C for different time. The rate of ZnAl
2O
4 formation was determined, and also the microstructure was observed. The rate of ZnAl
2O
4 formation increased with the decrease of the composition
XZ in the range of
XZ<0.5, but its dependence on the composition was not observed in the range of
XZ>0.5. The microstructure showed the presence of the agglomerates of sintered ZnO, which resulted in the incomplete reaction in the range of
XZ<0.5, and consequently, the alumina particles were not able to react with ZnO because of incomplete mixing. The ZnAl
2O
4 layer grew around alumina particles at the rate of formation in the parabolic relation with time. The diffusion constant controlling the process was determined from the product layer thickness as 3.59×10
-15 to 3.16×10
-13cm
2/s at 1000°-1200°C. The temperature dependence of the diffusion constant gave the activation energy of 85.4kcal/mol. The application of Jander's model to the powder mixture with different composition was discussed, and the introduction of three factors to correct the deviation of the practical condition from the Jander's ideal assumption was considered. The first is the factor (1-
XZ)/
XZ to correct the difference between the rate of reaction defined as the ratio of the amount of the product to the amount of the minor component in the mixture and the Jander's rate of reaction defined as the ratio of reacted particles among the main particles. The second is the factor (
X'A/
XA) which represents the ratio of the alumina particles take part in the formation of ZnAl
2O
4 to all alumina particles in the mixture. The third is the factor (
X'Z/
XZ) which represents the ratio of the zinc oxide particles which take part in the formation of ZnAl
2O
4 to all zinc oxide particles in the mixture. The corrected Jander's equation incorporating these factors is expressed as
[1-{1-(
XZ/1-
XZ)(
XA/
X'A)α}
1/3]
2=
k⋅t (1) or α={1-(1-√
k⋅t)
3}(
X'A/
XA)(1-
XZ/
XZ) (2)
which reduces to
α
max=(
X'Z/
XZ) (2')
The application of this Eq. (2) shows that in the range
XZ>0.5, the Jander's model is correct, but in the range
XZ<0.5, the correction factors are effective. The Eq. (2) was able to explain the increase of a with decreasing
XZ as a result of the introduction of the factor (1-
XZ)/
XZ and also the incomplete reaction in α-
t relation in
XZ<0.5 as a result of the introduction of the factor (
X'Z/
XZ) in Eq. (2).
View full abstract