In my diploma thesis, I performed qualitative and quantitative phase analysis of several ceramic samples from the ternary system La$_2$O$_3$-Ta$_2$O$_5$-TiO$_2$, located on the tie line La$_{1/3}$TaO$_3$-LaTaTiO$_6$, with the general formula La$_{(1+x)/3}$Ta$_{1-x}$Ti$_x$O$_3$ for x ranging from 0 to 0,5; using X-ray powder diffraction. The samples were prepared using conventional solid-state reaction technique, involving repeated grinding, homogenization and air quenching at 1350 °C.
The measured diffractograms were qualitatively analyzed using the Crystallographica Search Match (CSM) software. The phases identified in the samples were the monoclinic and orthorhombic polymorphs of LaTaTiO$_6$ and a phase with a diffractogram similar to La$_{1/3}$TaO$_3$ (also LaTa$_3$O$_9$), which has a defective perovskite structure. It was established that these correspond to solid solutions based on La$_{1/3}$TaO$_3$. The structure of this compound was employed as a structural model for the solid solution. It was assumed that Ti$^{4+}$ and Ta$^{5+}$ are randomly distributed over the same crystallographic site in the solid solution. The site occupancy was described according to the synthesis ratio, with a corresponding increase in lanthanum site occupancy. By applying Rietveld refinement in Topas 2.1, two single-phase solid solutions with compositions La$_{0,36}$Ta$_{0,92}$Ti$_{0,08}$O$_3$ and La$_{0,37}$Ta$_{0,89}$Ti$_{0,11}$O$_3$ were structurally characterized. The crystal structures determined were later described and drawn using the crystallographic program Mercury.
Rietveld refinement was also used for the quantitative analysis of the remaining multiphase samples. The solubility range occured only on one side of the tie line, in compounds with x in the formula La$_{(1+x)/3}$Ta$_{1-x}$Ti$_x$O$_3$ from 0 up to 0,11. A decrease in unit cell volume with increasing x was observed, which is attributed to the smaller ionic radius of Ti$^{4+}$, whose presence in the compound increases in this direction along the tie line. Samples with the initial compositions 0,11 < x < 0,5 were biphasic at equilibrium, consisting of a saturated tetragonal solid solution (La$_{1/3}$TaO$_3$)ss and the orthorhombic compound LaTaTiO$_6$. With increasing x, the mass fraction of the former decreased, while that of the latter increased. The sample with the initial composition x=0,5 contained only one phase LaTaTiO$_6$, but surprisingly in two polymorphic forms: orthorhombic and monoclinic. Even after multiple calcinations with intermediate cooling and milling, the analyses showed that at 1350 °C it was not possible to obtain a single-phase LaTaTiO$_6$ (x=0,5) sample; even after the sixth calcination, the sample still contained significant amounts of both polymorphic forms.
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