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The colour theory proposed by Heavens in 1991 has been applied to calculate the thickness of magnetite thin layers, Fe3O4, which were obtained by heat treatment at 250 °C in a gold alloy (Au-24.5Fe-0.5Co). The reflectance spectra obtained from the polished samples with different oxidation (and colour) degrees were used to calculate the real part of the refraction index and the (imaginary) extinction coefficients of both the metallic substrate (n2, k2) and the magnetite layer (n1=2.42, k1). The a+bλ+cλ2 form was taken adjusting parameters between experimental and theoretical curves. The fitting of the data resulted in deviations between 2 and 10% for thicknesses in the range of 0 nm (only substrate) and 65 nm (dark blue colour). By means of a mathematic model and following the Heavens’ theory, the thickness of each layer has been predicted with high precision, using the spectral reflectance. Consequently, we propose that by using this methodology, the values of the extinction coefficients of the oxide species can be easily obtained, and the thicknesses of the oxide layers can be predicted. The magnetite thickness values found in this study fall into the interval reported in the literature for first-order interference in steels, from light-yellow (~46 nm) to blue (~72 nm).

RESUMEN: Se aplica la teoría del color propuesta por Heavens (1991) para el cálculo de los espesores de las películas delgadas de magnetita, Fe3 O4 , los cuales fueron obtenidos por tratamiento térmico a 250°C de una aleación de oro (Au-24.5Fe-0.5Co). Los espectros de reflectancia obtenidos de las muestras pulidas con diferentes grados de oxidación (y de color) fueron usados para calcular los índices de refracción (real) y de extinción (imaginario) del sustrato metálico (n2 , k2 ) y de la capa de magnetita (n1 =2,42, k1 ). La forma a+bλ+cλ2 se tomó del ajuste de parámetros entre las curvas experimentales y teóricas. El ajuste de los datos resultan en desviaciones entre 2 y 10%, para los espesores en el rango de 0 nm (solo metal original) y 65 nm (color azul oscuro). Por medio de un modelo matemático siguiendo la teoría de Heavens, el espesor de cada capa ha sido predicho con alta precisión, utilizando las mediciones de reflectancia espectral. En consecuencia, proponemos que mediante el uso de esta metodología se pueden obtener fácilmente los valores de los coeficientes de extinción de las especies de óxido y, además, se pueden predecir los espesores de la capa de óxido. Los valores de espesores de la magnetita encontrados en la presente investigación están dentro del intervalo reportado en la literatura para la interferencia de primer orden en los aceros, desde el amarillo claro (~46 nm) hasta el azul (~72 nm). ABSTRACT: The colour theory proposed by Heavens in 1991 has been applied to calculate the thickness of magnetite thin layers, Fe3 O4 , which were obtained by heat treatment at 250 °C in a gold alloy (Au-24.5Fe-0.5Co). The reflectance spectra obtained from the polished samples with different oxidation (and colour) degrees were used to calculate the real part of the refraction index and the (imaginary) extinction coefficients of both the metallic substrate (n2 , k2 ) and the magnetite layer (n1 =2.42, k1 ). The a+bλ+cλ2 form was taken adjusting parameters between experimental and theoretical curves. The fitting of the data resulted in deviations between 2 and 10% for thicknesses in the range of 0 nm (only substrate) and 65 nm (dark blue colour). By means of a mathematic model and following the Heavens’ theory, the thickness of each layer has been predicted with high precision, using the spectral reflectance. Consequently, we propose that by using this methodology, the values of the extinction coefficients of the oxide species can be easily obtained, and the thicknesses of the oxide layers can be predicted. The magnetite thickness values found in this study fall into the interval reported in the literature for first-order interference in steels, from light-yellow (~46 nm) to blue (~72 nm).