# On Thermodynamic Aspects of Oxide Crystal Growth
## 3 Discussion  
### Calcium Ferrite  
The DTA curves in Figure 2 show that the sample melts in Ar at lower \(T\) than in the Ar/O\({}_{2}\) mixture. The melting peak is broader in the oxygen deficient gas flow. Fortunately, reliable thermodynamic data on the Ca-Fe-O ternary system are available, e.g., from the assessment by [PERSON] et al. [32]. Under the given experimental conditions, only calcium iron(III) ferrites are stable because calcium iron(II,III) ferrites, such as CaFe\({}_{3}\)O\({}_{5}\) (\"CWF\"), are formed only for lower \(p_{\text{O}_{2}}\), e.g., in atmospheres containing hydrogen [36]. The samples with 70% CaO that were used in Figure 2 contain CaO(ss) as the second solid phase, as indicated above. The melting point of CaO (\(\approx\)2900 \({}^{\circ}\)C) is far above the melting point of Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\), and correspondingly, the eutectic point between both phases is very close to the latter compound. This leads to interesting results if one calculates the phase equilibria between the end members Fe\({}_{2}\)O\({}_{3}\) and CaO under different \(p_{\text{O}_{2}}\). Both graphs in Figure 4 should not be labeled \"phase diagrams\" because the end members are not able to form all intermediate phases--in this case, Fe\({}_{3}\)O\({}_{4}\). The upper panel (a) was calculated for a constant \(p_{\text{O}_{2}}=0.71\,\text{bar}\), which corresponds to the flow of \(20\,\text{mL/min}\,\text{Ar}+50\,\text{mL/min}\,\text{O}_{2}\). Here, three intermediate calcium iron(III) ferrites exist, and Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\) melts congruently at 1445 \({}^{\circ}\)C. The extrapolated onset of the blue melting peak of the 70% mixture in Figure 2 is very close to this melting point, and to the eutectic temperature at 1440 \({}^{\circ}\)C. (The small difference cannot be resolved in the DTA curve.) It is interesting to note that the \"Fe\({}_{2}\)O\({}_{3}\)+slag\" phase field on the left side extends only to ca. 1440 \({}^{\circ}\)C because at higher \(T\), the iron(II,III) oxide Fe\({}_{3}\)O\({}_{4}\) is formed. It is not possible to give exact data for the oxygen partial pressure that prevails during the measurements in \"pure\" argon. The value \(p_{\text{O}_{2}}=1\times 10^{-5}\,\text{bar}\) that was used for the calculation of Figure 4b should be considered a lower limit, which is delivered by the contamination of the Ar gas of nominally 99.999% purity with air. However, additional oxygen could be added by minor leaks of the DTA apparatus, or by gases emanating from the sample itself, such as CO\({}_{2}\) from the calcination of CaCO\({}_{3}\). The stability range of the CaFe\({}_{4}\)O\({}_{7}\) phase, which contains a high amount of Fe\({}^{3+}\), is very limited already for 0.71 bar oxygen pressure (Figure 4a, [32]). Under the significantly lower \(p_{\rm O_{2}}\) in Figure 4b, this phase is not stable at all, and also the highest temperature, where both calcium iron(III) ferrites are stable, is decreased. For Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\), this results in incongruent melting under the release of CaO(ss), and the melting process can be described by a reaction  
\[\rm Ca_{2}Fe_{2}O_{5}\rightleftharpoons 2\,CaO+\left(1-\frac{x}{2}\right)Fe_{2}O_{3}+x\,FeO+\frac{x}{4}\,O_{2}\uparrow \tag{2}\]  
which relates the mass loss \(\frac{x}{4}\,O_{2}\) to the amount of \(x\,FeO\) in the melt. For the red TG curve in Figure 2, showing a mass loss of 0.073% upon melting, one calculates with Equation (2) \(x=0.025\). This means that \(\approx\)1.2% of the iron ions are reduced to Fe\({}^{2+}\). This is significantly  
Figure 4: Isopleth sections CaO–Fe\({}_{2}\)O\({}_{3}\) of the system FeO–Fe\({}_{2}\)O\({}_{3}\)–CaO, calculated for different atmospheres with FactSage [7].