# On Thermodynamic Aspects of Oxide Crystal Growth
## 2 Experiments and Results  
Simultaneous differential thermal analysis (DTA) and thermogravimetry (TG) was performed in a NETZSCH STA 449 F3 \"Jupiter\" with \"type S\" thermocouples and platinum crucibles using heating/cooling rates of \(\pm 10\) K/min. The samples were prepared by mixing appropriate quantities of CaCO\({}_{3}\) and Fe\({}_{2}\)O\({}_{3}\) powders of \(\geq\)99.99% purity in a mortar. To avoid charging errors, the metal oxide assay of both chemicals was preliminarily controlled as separate DTA/TG measurements [31]. The thermal analyzer establishes, via mass flow controllers, three independent gas flows that are unified in the sample chamber. The first \"protective gas\" flow was held constant at 20 mL/min argon, and to this were added either 50 mL/min Ar or 50 mL/min O\({}_{2}\), which sets an overall gas flow rate of 70 mL/min for all measurements. From this, one obtains for the latter measurements \(p_{\rm{O}_{2}}=(50/70)\) bar \(\approx 0.71\) bar. For the measurements in \((20+50)\) mL/min Ar, the rest of the impurities of the nominally 99.999% pure Ar sets a lower limit, and can be estimated on a level of \(p_{\rm{O}_{2}}\approx(2\times 10^{-6}\ldots 1\times 10^{-5})\) bar in agreement with earlier investigations of the Fe-O system [10]. Equilibrium phase formation was performed in a first DTA/TG cycle, and the results of the second heating runs are shown in Figure 2.  
Figure 1: In the unit cell of Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\), Fe\({}^{3+}\) ions in octahedral and tetrahedral coordination are alternating along the \(b\) axis. (Ca\({}^{2+}\)—blue, O\({}^{2-}\)—red) [21; 27]. Both measurements show one endothermal DTA melting peak which is broader, and is shifted to lower \(T\) in the \"pure\" Ar atmosphere. In both cases, the melting process is accompanied by a mass loss which is marginal (0.015%) in the oxygen-rich atmosphere and almost five times larger in Ar. The inflection points in both TG curves are in fairly good agreement with the endothermal minimum positions of the DTA curves. This means that the melting process is obviously directly related to the mass loss. The experimental results are confirmed by the FactSage [7] calculations that are shown in Figure 3. These curves were obtained by calculating the equilibria between the starting mixture of CaO and Fe\({}_{2}\)O\({}_{3}\) (1 mole in total) in an excess of the corresponding atmosphere (7 mole gas in total) in 1 K steps. In both cases, Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\) is the dominating solid phase at 1380 \({}^{\circ}\)C, accompanied by a smaller amount of Fe-saturated CaO, which is designated in the following as CaO(ss). Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\) is known as a stoichiometric line compound without significant variation of the oxygen stoichiometry [29]. Hence, the small iron content (a few percent, [32]) in the minority phase CaO(ss) is expected to be the only carrier of Fe\({}^{2+}\) in the solids. The situation is different for the liquid phase, where under accessible conditions, always an equilibrium between Fe\({}^{2+}\) and Fe\({}^{3+}\) prevails. From the Ellingham diagrams of the Fe-O\({}_{2}\) system (cf. [10; 33]) it is obvious that the liquid FeO\({}_{x}\) \"slag\" phase always contains both valence states of iron, and their ratio depends on \(T\) and \(p_{\rm O_{2}}\). [PERSON] and [PERSON] [34] measured in a CaO/FeO\({}_{x}\) melt with 36.6 mol-% CaO that was held for 1 h at 1574 \({}^{\circ}\)C a Fe\({}^{3+}\)/Fe\({}^{2+}\) ratio of \(\approx\)19. Recently, [PERSON] et al. [35] showed that even under very high temperatures, \(T\gg 2000\) K and pressures \(p>50\) GPa Fe\({}_{2}\)O\({}_{3}\) does not melt stoichiometrically; rather, mixed valence oxides of a series \(n\)Fe  
Figure 3: Calculated equilibrium of 0.7 mol CaO + 0.3 mol Fe\({}_{2}\)O\({}_{3}\) in 5 mol O\({}_{2}\) + 2 mol Ar, or in 7 mol Ar, respectively. The curves show the total amount of O\({}_{2}\) in the atmosphere. Total Gibbs energy \(G\) of the system given at selected points.