Enhanced oxygen exchange and incorporation at surface grain boundaries on an oxide ion conductor

A statistical perspective on oxygen diffusion and surface exchange experiments: Sensitivity analysis, parameter estimation and robust optimal experimental design

“…The film undergoes diffusion annealing with 18 O tracer oxygen being incorporated until time t end . It is assumed that 18 O enters the sample thanks to an oxygen exchange reaction and then it diffuses through it. The latter process is modeled by Fickian diffusion…”

“…where c(t,x) is the isotope fraction of 18 O normalized with respect to the gas concentration 1 at time t and position x and where the diffusion coefficient D is a constant. The surface exchange reaction, which takes place at the boundary x =0, is modeled by linearized rate, leading to the following boundary condition:…”

“…where c gas is the isotope fraction of 18 O in the gas during the exchange and, again, k is the tracer surface exchange coefficient. The boundary at x=L is taken to be impermeable to oxygen, leading to the following boundary condition:…”

“…Numerous experimental techniques have been developed to evaluate these key quantities including electrochemical impedance spectroscopy [1][2][3][4], electrical conductivity relaxation [5][6][7] and IEDP [8][9][10][11][12][13][14][15][16][17][18][19][20]. By fitting the experimental measurements against a suitable model the techniques mentioned above lead to the estimation of the oxygen diffusion coefficient D and the oxygen surface exchange coefficient k.…”

“…First a sample is prepared and placed in a natural oxygen atmosphere at set temperature and oxygen partial pressure. Second, the sample is annealed, that is it is put for a given time in conditions consisting of 18 O at the same temperature and oxygen partial pressure of the pre-annealing. Third, the sample is sputter etched and the 18 O relative concentration is measured as a function of the distance from the surface.…”