l816 G Mohanty et al. /Materials Research Bulletin 43(2008)1814-1828 D.C Cathode Fig. 1. Electrophoretic deposition setup. facing each other to fix the electrodes on it. The area of the deposition as well as counter electrode exposed to the suspension was 4 cm". The stainless steel substrates were mounted on the holders with a spring contact at the back to act as electrical contact. The holders along with electrodes were dipped into the silica glass reservoir containing the alumina suspension followed by application of desired dc voltage for a prerequisite time. Sedimentation of the alumina particles was prevented by mild stirring using a magnetic bead stirrer as shown in Fig. 1. Constant voltage electrophoretic deposition experiments were carried out at conditions within the statistical design matrix. The negatively charged particles got deposited on the anode. After deposition, the electrodes were carefully taken out and the deposits were allowed to dry at room temperature for 24 h. The deposits along with the substrate were then eighed to determine the yield. The suspension was replenished after every three deposits [29] 23. Statistical design and modeling Factorial designs allow to analyse the effects of several different factors and combine them into a response model. They are the most commonly used statistical designs due to their simplicity with regard to both preparation and analysis of the results. Although primarily used for screening significant factors, they are also used sequentially to model and refine a process. The 2 design provides the smallest number of runs with which k factors can be studied in a complete factorial design. In a 2 design, all combinations of k-factors are set at two levels with respect to center point and are evaluated The two levels are the allowable limits, i.e., the maximum and minimum values set on the basis of preliminary trials. The final relationship that is eventually determined must hold within these limits. The assumptions for making the 2 design valid include linearity of response over the range of the factors chosen, randomization of the designs and satisfaction of the usual normality assumptions. Perfect linearity, however, is unnecessary and the 2 system will work quite well even when the linearity assumption holds very approximately [27]. In fact, the addition of interaction terms to the main effects provides a model that is capable of representing some curvature in the response function. The 2" design augmented with center point replicates is an excellent way to obtain an indication of potential non-linearity or curvature of the response. It allows one to keep the size and complexity of the design low and simultaneously obtain some protection against curvature. Also center points do not impact the usual effects estimatefacing each other to fix the electrodes on it. The area of the deposition as well as counter electrode exposed to the suspension was 4 cm2 . The stainless steel substrates were mounted on the holders with a spring contact at the back to act as electrical contact. The holders along with electrodes were dipped into the silica glass reservoir containing the alumina suspension followed by application of desired dc voltage for a prerequisite time. Sedimentation of the alumina particles was prevented by mild stirring using a magnetic bead stirrer as shown in Fig. 1. Constant voltage electrophoretic deposition experiments were carried out at conditions within the statistical design matrix. The negatively charged particles got deposited on the anode. After deposition, the electrodes were carefully taken out and the deposits were allowed to dry at room temperature for 24 h. The deposits along with the substrate were then weighed to determine the yield. The suspension was replenished after every three deposits [29]. 2.3. Statistical design and modeling Factorial designs allow to analyse the effects of several different factors and combine them into a response model. They are the most commonly used statistical designs due to their simplicity with regard to both preparation and analysis of the results. Although primarily used for screening significant factors, they are also used sequentially to model and refine a process. The 2k design provides the smallest number of runs with which k factors can be studied in a complete factorial design. In a 2k design, all combinations of k-factors are set at two levels with respect to center point and are evaluated. The two levels are the allowable limits, i.e., the maximum and minimum values set on the basis of preliminary trials. The final relationship that is eventually determined must hold within these limits. The assumptions for making the 2k design valid include linearity of response over the range of the factors chosen, randomization of the designs and satisfaction of the usual normality assumptions. Perfect linearity, however, is unnecessary and the 2k system will work quite well even when the linearity assumption holds very approximately [27]. In fact, the addition of interaction terms to the main effects provides a model that is capable of representing some curvature in the response function. The 2k design augmented with center point replicates is an excellent way to obtain an indication of potential non-linearity or curvature of the response. It allows one to keep the size and complexity of the design low and simultaneously obtain some protection against curvature. Also center points do not impact the usual effects estimate in a 2k design [27]. 1816 G. Mohanty et al. / Materials Research Bulletin 43 (2008) 1814–1828 Fig. 1. Electrophoretic deposition setup