Optimizing Bi ₂O ₃ and TiO ₂ to achieve the maximum non-linear electrical property of ZnO low voltage varistor

Abstract

Background

In fabrication of ZnO-based low voltage varistor, Bi ₂O ₃ and TiO ₂ have been used as former and grain growth enhancer factors respectively. Therefore, the molar ratio of the factors is quit important in the fabrication. In this paper, modeling and optimization of Bi ₂O ₃ and TiO ₂ was carried out by response surface methodology to achieve maximized electrical properties. The fabrication was planned by central composite design using two variables and one response. To obtain actual responses, the design was performed in laboratory by the conventional methods of ceramics fabrication. The actual responses were fitted into a valid second order algebraic polynomial equation. Then the quadratic model was suggested by response surface methodology. The model was validated by analysis of variance which provided several evidences such as high F-value (153.6), very low P-value (<0.0001), adjusted R-squared (0.985) and predicted R-squared (0.947). Moreover, the lack of fit was not significant which means the model was significant.

Results

The model tracked the optimum of the additives in the design by using three dimension surface plots. In the optimum condition, the molars ratio of Bi ₂O ₃ and TiO ₂ were obtained in a surface area around 1.25 point that maximized the nonlinear coefficient around 20 point. Moreover, the model predicted the optimum amount of the additives in desirable condition. In this case, the condition included minimum standard error (0.35) and maximum nonlinearity (20.03), while molar ratio of Bi ₂O ₃ (1.24 mol%) and TiO ₂ (1.27 mol%) was in range. The condition as a solution was tested by further experiments for confirmation. As the experimental results showed, the obtained value of the non-linearity, 21.6, was quite close to the predicted model.

Conclusion

Response surface methodology has been successful for modeling and optimizing the additives such as Bi ₂O ₃ and TiO ₂ of ZnO-based low voltage varistor to achieve maximized non-linearity properties.