Modified Bertaut Method to Determine Cation Distribution and Valence State in Powders of Spinels Through X-ray Diffraction

In this work a new method is proposed to tackle down the multiple objective optimization problem of the calculation of cation distribution in spinels structure, through the difference of intensity ratios between experimental and calculated intensities of cation sensitive Bragg planes, by introducing a new factor, Rabs, in Bertaut method. This factor is introduced as the sum of absolute R factors, and it is minimized by varying cation distribution. To test this method aluminate manganese spinel where synthesized though modified Pechini method and characterized though XRD. The results show to be in agreement with literature for the aluminum inversion in tetrahedral sites, which is near to the reported value of 10%. Also, it was noticed that the manganese atoms are present in octahedral sites with a mixed valence state of +2 and +3. Which might be an indicator that oxygen vacancies are present in the structure, so the vacancies value of oxygen is proposed considering the total charge of cations and thus proposing the value of 3.678 mol per formula unit of the spinel, thus having the next stoichiometry considering normalized Al and Mn, MnAl2O3.678. Finally, the last cation distribution proposed was [Mn0.867^(+2) Al0.129^(+3) ][Mn0.034^(+2) Mn0.098^(+3) Al1.871^(+3) ] O3.678 with a Rabs factor value of 0.6466, which considers the cation distribution and oxygen vacancies.