Abstract
BackgroundIn fabrication of ZnO-based low voltage varistor, Bi2O3 and TiO2 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 Bi2O3 and TiO2 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.ResultsThe model tracked the optimum of the additives in the design by using three dimension surface plots. In the optimum condition, the molars ratio of Bi2O3 and TiO2 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 Bi2O3 (1.24 mol%) and TiO2 (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.ConclusionResponse surface methodology has been successful for modeling and optimizing the additives such as Bi2O3 and TiO2 of ZnO-based low voltage varistor to achieve maximized non-linearity properties.
Highlights
In fabrication of ZnO-based low voltage varistor, Bi2O3 and TiO2 have been used as former and grain growth enhancer factors respectively
The predicted samples were characterized by X-ray diffractometer (XRD), scanning electron microscope (SEM), variable pressure scanning electron microscope (VPSEM) and Energy-dispersive X-ray (EDX)
Modeling In the fitting process, the residuals are produced from difference between actual and predicted values
Summary
In fabrication of ZnO-based low voltage varistor, Bi2O3 and TiO2 have been used as former and grain growth enhancer factors respectively. In this paper, modeling and optimization of Bi2O3 and TiO2 was carried out by response surface methodology to achieve maximized electrical properties. The effect of TiO2 depends on Bi2O3 that means the additives interact in low-voltage varistor ceramics fabrication. Response surface methodology (RSM) has been accepted for modeling and optimizing of input intractable variables to achieve maximum yield product as output for productive process [21]. RSM was used for modeling and optimizing of molar ratio of Bi2O3 and TiO2 as additives to achieve the maximum value of the alpha for low voltage varistor. The predicted samples were characterized by X-ray diffractometer (XRD), scanning electron microscope (SEM), variable pressure scanning electron microscope (VPSEM) and Energy-dispersive X-ray (EDX)
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