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51 NACE INTERNATIONAL: VOL. 56, NO. 10 MATERIALS PERFORMANCE OCTOBER 2017 and CuO are 23.9 and 12.4 cm 3 /mol, respec- tively. Th e stabi lity of th e oxi des was affected by the transformations resulting from the differences in molar volumes and lattice parameters. 3 However, the concen- tration of DO was reduced when the tem- perature rises to a certain extent. The solu- bility of oxygen became the leading factor instead of diffusion rate, thereby producing the decline in the corrosion rate. Numerical conditions optimization for corrosion rate was carried out using the DE software. The desired goal for each opera- tional condition was chosen within the range while the response was defined as minimum to achieve the highest perfor- mance. The model predicts the corrosion rate to be 0.0038 mm/y, corresponding to temperature 40 °C, pH 9.0, and D O 0.1 mg/L, whereas the corrosion rate of 0.0049 mm/y was obtained from the experiment. It is obvious that the model is adequate for predicting the corrosion rate. Furthermore, the variation of tempera- ture was accompanied with the transitions of species. Figure 4 illustrates the species calculated by the VM software at 64 µ g/L Cu ions in various pH solutions. Cupric spe- cies mainly consisted of Cu 2+ , Cu(OH) 2 , Cu(OH) 3 – , Cu(OH) 4 2– , and CuOH + at 40 °C. The proportion of Cu 2+ reduced to 5% when the pH was >9. This observation indicated that Cu 2+ was not the major source under dissolved Cu ion testing. The proportion of CuOH + increased with pH and reached the peak value, ~62%, at pH 8. Conversely, the proportion of Cu(OH) 2 was higher than that of CuOH + at pH 8.5 and then still showed an increasing trend. The most affected species was Cu(OH) 3 – , which was scarcely found in the solutions when the temperature was h i g h e r th a n 6 0 ° C . Th e s e c o n d - m o st a f fe c t e d sp e c i e s w a s C u (O H ) 2 , w h i c h i n c re a s e d s h a r p ly w h e n t e m p e ra tu re increased from 40 to 80 °C. The proportion of Cu(OH) 2 increased from 66.73 to 93.52%, whereas Cu(OH) 2 was unstable in solutions and easily converted to CuO. Thus, the bar- rier offered by CuO or the mixtures of CuO and Cu(OH) 2 was strong enough to isolate Cu from reacting with solution. Conclusions The BBD combining three preselected variables (temperature, pH, and DO) and RSM were used to evaluate the effect of process variables and their interaction on reducing the corrosion rate. From the qua- dratic model and subsequent ANOVA test using DE software, the temperature and pH were found to be the factors with the great- est inf luence and the most significance. FIGURE 3 3D graphs of interaction AC for corrosion rate. FIGURE 4 Cupric species fraction in various pH at 40 °C. The model fit very well to the experimental data, as confirmed by the high R 2 value. The optimal values for the three factors were temperature 40 °C, pH 9.0, and D O 0.1 mg/L. Under these conditions, the cor - rosion rate could be brought lower than 0.005 mm/y. Optimizing Conditions to Control Copper Corrosion in Stator Cooling Water