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Journal of Nanomaterials
Volume 2017, Article ID 4308294, 8 pages
Research Article

Stoichiometry Calculation in BaxSr1−xTiO3 Solid Solution Thin Films, Prepared by RF Cosputtering, Using X-Ray Diffraction Peak Positions and Boltzmann Sigmoidal Modelling

1COARA, Universidad Autónoma de San Luis Potosí, Carretera a Cedral Km 5+600, 78700 Matehuala, SLP, Mexico
2Instituto Politécnico Nacional, Laboratorio de Materiales Funcionales, CICATA Legaria, Legaria 694, Col. Irrigación, 11500 Ciudad de México, Mexico
3Universidad de Guanajuato, Campus Irapuato-Salamanca, Ex-Hacienda el Copal, Km. 9, Irapuato-Silao AP311, 36500 Irapuato, GTO, Mexico
4Instituto de Ingeniería y Tecnología, Departamento de Física y Matemáticas, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, CHIH, Mexico
5Departamento de Física, CINVESTAV-IPN, Av. Instituto Politécnico Nacional 2508, Gustavo A. Madero, San Pedro Zacatenco, 07360 Ciudad de México, Mexico
6Instituto Politécnico Nacional, Materiales y Tecnologías para Energía, Salud y Medioambiente (GESMAT), CICATA Altamira, Km 14.5, Carretera Tampico-Puerto Industrial Altamira, 89600 Altamira, TAMPS, Mexico

Correspondence should be addressed to J. L. Fernández-Muñoz; xm.npi@zednanreflj

Received 3 April 2017; Revised 23 May 2017; Accepted 30 May 2017; Published 9 August 2017

Academic Editor: Philip D. Rack

Copyright © 2017 J. Reséndiz-Muñoz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel procedure based on the use of the Boltzmann equation to model the parameter, the film deposition rate, and the optical band gap of BaxSr1−xTiO3 thin films is proposed. The BaxSr1−xTiO3 films were prepared by RF cosputtering from BaTiO3 and SrTiO3 targets changing the power applied to each magnetron to obtain different Ba/Sr contents. The method to calculate consisted of fitting the angular shift of (110), (111), and (211) diffraction peaks observed as the density of substitutional Ba2+ increases in the solid solution when the applied RF power increases, followed by a scale transformation from applied power to parameter using the Boltzmann equation. The Ba/Sr ratio was obtained from X-ray energy dispersive spectroscopy; the comparison with the X-ray diffraction derived composition shows a remarkable coincidence while the discrepancies offer a valuable diagnosis on the sputtering flux and phase composition. The proposed method allows a quick setup of the RF cosputtering system to control film composition providing a versatile tool to optimization of the process.