MODELING OF THE CHEMICAL X-PARAMETER IN PSEUDOBINARY ALLOYS FROM THE SHIFT OF THE X-RAY BRAGG ANGLE: APPLICATION TO CUBIC BaxSr1-xTiO3 FILMS

Pseudobinary alloys of the type AxB1-xC are expected to obey the Vegard’s law that states a linear relationship between the chemical parameter x and the lattice parameter. However, in many cases, deviations from the Vegard’s are found, and the calculation of x requires compositional characterization, often complicated in the presence of secondary phases of the same material. In the present work, 𝐵𝑎𝑥𝑆𝑟(1−𝑥)𝑇𝑖𝑂3 (BSTO) films were deposited by RF co-sputtering from 𝐵𝑎𝑇𝑖𝑂3 and 𝑆𝑟𝑇𝑖𝑂3 targets to obtain differently 𝐵𝑎⁄𝑆𝑟 ratios considering the different RF-power applied to each target. We describe a mathematical model based on the Boltzmann equation to calculate the 𝑥 parameter of the cubic phase of the BSTO films in the 0 ≤ 𝑥 ≤ 1 range. That was made by following the 2𝜃 diffraction angular shift of the plane (111) upon the increase of substitutional Ba2+ in the pseudobinary alloy, as a function of the RF applied power and fitting the interplanar distances and lattice parameter in the alloys were calculated onto the fitted sigmoid trajectory. The model showed the region where the lattice parameter a vs x obeys the Vegard’s law and correctly fitted “a” in the entire 0

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