Monte Carlo simulation of vacancies produced in lead-free piezo-ceramics by X-ray radiation damage

This work presents the results of a simulation by the Monte Carlo method, performed through the GEANT4 code, of the irradiation and energy deposition by high flux X-rays on the piezoelectric ceramic Bismuth-Sodium Titanate doped with Barium. X-rays energies were around the Ti-K absorption edge emulating a transmission experiment, and the irradiation with 5300 eV X-rays for a fluorescence experiment. The method consists of introducing the data that describes a characteristic R3c structure of the polarized ceramic, reported in the literature. The absorption coefficients for the energies of interest, as well as the energy deposited in the form of radiation doses, are calculated. Intensity changes for specific energy lines in the micro-fluorescence spectra, which suggest the presence of vacancies in the crystal structure, are verified via simulation. The vacancy density produced by a typical photon flux of a fourth-generation synchrotron beam is calculated through the threshold displacement energy for vacancy production. Consequently, the simulation is carried out for a structure with appropriate Bi and O vacancies, and the ability to detect the radiation damage is verified by comparison with micro-XRF and XAFS experimental results. The simulation predicts a maximum dose of 1.21-1.27x105 Gy irradiating 107 photons for the given energy and a maximum vacancy density of 1.10x108 / micron3 for oxygen atoms and 6.90x107 /micron3 for bismuth atoms.