Synergistic Use of Thermogravimetric and Electrochemical Techniques for Thermodynamic Study of $TiO_x$ (1.67≤ x≤ 2.0) at 1573 K

A thermodynamic study of the Ti-O system at 1573 K has been conducted using a combination of thermogravimetric and emf techniques. The results indicate that the variation of oxygen potential with the nonstoichiometric parameter δ in stability domain of $TiO_{2-\delta}$ with rutile structure can be represented by the relation, $\Delta \mu O_2=-6RT$ ln δ -711970(± 1600) J/mol. The corresponding relation between non-stoichiometric parameter δ and partial pressure of oxygen across the whole stability range of $TiO_{2-\delta}$ at 1573 K is δ ∝ PO2-1/6. It is therefore evident that the oxygen deficient behavior of nonstoichiometric of $TiO_{2-\delta}$ is dominated by the presence of doubly charged oxygen vacancies and free electrons. The high-precision measurements enabled the resolution of oxygen potential steps corresponding to the different Magneli phases $(Ti_nO_{2n-1})$ up to n=15. Beyond this value of n, the oxygen potential steps were too small to be resolved. Based on composition of the Magneli phase in equilibrium with of $TiO_{2-\delta}$, the maximum value of n is estimated to be 28. The chemical potential of titanium was derived as a function of composition using the Gibbs-Duhem relation. Gibbs energies of formation of the Magneli phases were derived from the chemical potentials of oxygen and titanium. The values of -2441.8(± 5.8) kJ/mol for $Ti_4O_7$ and -1775.4(± 4.3) kJ/mol for $Ti_3O_5$ obtained in this study refine values of -2436.2(± 26.1) kJ/mol and -1771.3(± 6.9) kJ/mol, respectively, given in the JANAF thermochemical tables