Development of a Mathematical Model Relating Microstructures Evolvement to Optical Appearance of Laser-induced Polychrome Oxides on Iron Substrates

A model was built to solve the problem of color prediction for laser color marking on metal surface based on the principle of multiple-beam interference. The microstructures evolvement of laserinduced polychrome oxides on iron substrates was investigated for the model. Firstly, surface treatments of industrial grade polycrystalline iron substrates in air were performed by irradiation with a Nd:YAG (λ=1064nm) continuous wave laser beam. Different colored samples with different reflectivity were obtained depending on the duration of laser irradiation. Then, the surface morphology of the oxide films were studied by optical microscopy, revealing the formation of a bi-layer structure consisting of a congregate sheet layer covering a uniform layer. Compositional analyses performed by Raman spectroscopy measurements revealed the inner oxides were Fe3O4 and the outer oxides were Fe2O3 (magnetite and hematite respectively). Since the colors of the samples were determined by the light interference within the thin surface layers, the effective thickness and equivalent optical constants, i.e., refractive index n and extinction coefficient k, are key parameters. They were determined by jointly using the spectroscopic ellipsometry and the glow discharge spectrometry. Based on the measurement results, a linear oxidation model was built to describe the growth of Fe3O4 and Fe2O3 films, and thickness-varying equivalent optical constants have been obtained. Lastly, a mathematical model based on the heat conduction equation, the oxidation kinetics and the light interference between multi-layer oxide films was used to calculate the spectrum reflectivity of the samples. The results accorded with the experimental results very well. The color of samples can be easily calculated when the spectrum of incident light was given.