Modeling of Color Improvement of Ruby Corundum Gemstone via Oxygen Ion Implantation Treatment

Oxygen ion implantation has been applied to improve the color quality of the ruby corundum gemstone. Specifically, the color enhancement of the ruby considered in this study was to bring out more redness of the gemstone. Surprisingly, the redness enhancement could be done indirectly by increasing the yellowness while decreasing the blueness of the ruby. However, not all rubies can be improved equally through the oxygen ion implantation technique and each implantation procedure usually takes at least 6 hours. It was of a great need to know the characterization of the rubies that would response well to the oxygen ion implantation. This paper proposed an input-output mathematical model that could predict the levels of color enhancement of rubies via an oxygen ion-implantation. The proposed model described the relationship between two critical chemical compositions, the traced levels of iron and chromium before the treatment as the model inputs and the positive increment in the b* axis (the increment toward yellowness in the yellow-blue axis) being the model output. The model structure was explored using the first, the second and the third order polynomial equations. The parameters were estimated based on the least square method, and the leave-one-out cross validation was used for dealing with a limitation of data points. The prediction performance of three chosen models were measured against the observed data. It was found that the third order model yielded the lowest error while satisfying prediction performance could be observed from the second order models as well.