Untersuchungen zur Fremdionendiffusion von Zr und Sr sowie zur Selbstdiffusion von $^{50}$Ti und $^{130}$Ba in Bariumtitanat (BaTiO$_{3}$) – Einkristallen

Barium titanate has various applications in today´s electroceramic technology due to its dielectric and ferroelectric properties. In this work cation diffusion in single crystalline BaTiO$_{3}$ was investigated by time-of-flight secondary ion mass spectrometry (ToF-SIMS). The objective was to enhance the understanding of the BaTiO$_{3}$ defect chemistry. Thus it will be possible to influence the material´s properties for its application in electronic devices. The experiments started with the study of Zr and Sr impurity diffusion. For this purpose thin films of Zr, deposited onto the sample surfaces by sputtering, and thin films of SrTiO$_{3}$, deposited by spin coating a precursor solution, were used as diffusion sources. The coated samples were annealed in air at preset temperatures and different diffusion times to introduce a diffusion profile into the material. After SIMS depth profiling the bulk diffusion was defined by a characteristic profile with a strong slope at the beginning of the measurements. In order to determine bulk diffusion coefficients, D$_{bulk}$, the solution of the diffusion equation for a source of finite thickness had to be used (thick film solution). The second region in the SIMS profiles, described by a lower slope at larger penetration depths into the samples, indicated the existence of a fast diffusion path along dislocations. In this case the determination of the dislocation pipe diffusion coefficients, D$_{dis}$, was carried out by plotting the natural logarithm of the concentration against the penetration depth and determining the slope. Subsequently, fitting the diffusion coefficients with an Arrhenius equation, activation energies, E$_{A}$, were obtained. It was shown that the bulk diffusion coefficients of Zr and Sr differ by less than one order of magnitude. Besides, the calculated activation energies (E$_{A}$$^{Zr}$(bulk)=(5,1±0,6)eV; E$_{A}$$^{Sr}$(bulk)=(5,6±1,2)eV) are, within experimental scatter, nearly identical. These findings are incompatible with theoretical results for simple vacancy migration on both cation sublattices of BaTiO$_{3}$, which predict much higher migration energies for the B cation sublattice than for the A cation sublattice. This may be an indication for a more complicated cation diffusion mechanism than a simple jump of Zr cations onto existing Ti vacancies. It is assumed that both species, Sr and Zr, move within the same sublattice of the crystal. Another possible explanation is a migration of Zr along the Ti-sites with an occupation of Ba-sites as an intermediate step. The formation of correlated {V$_{Ba}$'',V$_{O}$$^{••}$,V$_{Ti}$''''}$^{4'}$-clusters is also conceivable, thus enabling a coupled transport of A and B cations in the material. With regard to dislocation pipe diffusion, it was found that D$_{dis}$ was approximately two to four orders of magnitude higher than D$_{bulk}$. Furthermore, the E$_{A}$ of Zr, (8,2±1,6)eV, was nearly twice as high as the E$_{A}$ of Sr, (4,3±0,8)eV. In this case, an influence of space charge layers perpendicular to the dislocations within the BaTiO$_{3}$ single crystals is conceivable. The self-diffusion in BaTiO$_{3}$ was investigated by tracer diffusion experiments. For this purpose $^{50}$Ti was implanted into the samples, whereas a thin film of $^{130}$BaTiO$_{3}$, deposited by dropping a $^{130}$Ba precursor solution onto the sample surfaces, was used as a tracer source. Among others, due to an insufficient mass filter during the ion implantation, it was not possible to determine diffusion coefficients or activation energies of Ti so far. The diffusion coefficients and the activation energies of Ba, E$_{A}$$^{Ba}$(bulk)=(4,1±0,6)eV, are comparable to the impurity diffusion, so that there is also an indication for a more complicated cation diffusion mechanism in BaTiO$_{3}$. Regarding the diffusion along dislocations, D$_{dis}$ was about three to five orders of magnitude higher than D$_{bulk}$. The E$_{A}$$^{Ba}$(dis), (8,4±1,7)eV, was about twice as high as the E$_{A}$$^{Ba}$(bulk). Finally, the experimental results were discussed and compared to other literature data