# On Thermodynamic Aspects of Oxide Crystal Growth
## 4 Conclusions  
Many transition metals can occur in a variety of oxidation states, depending on the oxygen concentration in the atmosphere and on temperature. Molten oxides usually contain more than one of these oxidation states because the simultaneous occurrence of several valences favors the mixture entropically. In contrast, solids contain often (but not always) only one valence for each element. If during oxide crystal growth from the melt, the average valence states in the melt and in the crystal are different, free oxygen molecules must be either absorbed from the ambient gas, or must be released. Taking this into account, the terms \"congruent melting\" and \"peritectic melting\" become disputable: \"congruent melting\" means in the closer sense that the solid and the melt in equilibrium possess an identical chemical composition; and \"peritectic melting\" means that a solid converts, upon heating, to a melt with a different composition under the release of another solid. In both cases, the gas phase should not, per definition, be involved. However, changing the valence of ions requires involvement of the gas phase. In particular, the exchange of O\({}_{2}\) with the gas phase can lead to bubbles, which destabilize or inhibit crystal growth [45; 46; 47; 48; 49]. Figure 5a demonstrates this for the case where the average oxidation level of the crystal is higher, compared to the melt. Continuously, the melt must absorb O\({}_{2}\)(gas) from the atmosphere to facilitate the Me\({}^{n}\)/Me\({}^{n+1}\) equilibrium in the melt, because the latter ion is permanently incorporated into the crystal. Possibly, this limits the maximum growth rate, but nevertheless, the growth of crystals with a high oxidation state, such as the initial example Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\)[29], or Bi\({}_{2}\)CuO\({}_{4}\)[44], is possible without severe problems. Figure 5b shows the opposite case where the average oxidation level of the crystal is lower than that of the melt. During growth, Me\({}^{n}\) is incorporated into the crystal, and readjustment of the Me\({}^{n}\)/Me\({}^{n+1}\) equilibrium in the melt requires permanent reduction in the latter. Melt depletion by Me\({}^{n}\) will occur at the crystallization front, and consequently, the formation of O\({}_{2}\) gas bubbles is expected there. The volume of these bubbles can be  
Figure 5: Growth of a metal oxide crystal with integer valence of the metal Me from a melt with different valences, Me\({}^{n}\) and Me\({}^{n+1}\). A darker color means a higher oxidation level. (**a**) The crystal contains the higher valence \((n+1)\) and only Me\({}^{n+1}\) is incorporated from the melt. The melt depletion by this ion must be compensated by the oxidation of Me\({}^{n}\) ions. (**b**) The crystal contains the lower valence \((n)\) and only Me\({}^{n}\) is incorporated from the melt. The melt depletion by this ion must be compensated by a reduction in Me\({}^{n+1}\) ions, under the production of free oxygen. This will occur preferably at the crystallization front, and can lead there to bubbles (white circles). estimated from Equation (1): the reduction in 1 mole Me\({}^{n+1}\) to Me\({}^{n}\) produces \(\frac{1}{4}\) moles O\({}_{2}\). Assuming an ideal gas, this corresponds to, for example, 1700 K to as much as 35 litres. In the case of iron (atomic mass 55.8 g/mol), every gram of reduced iron delivers \(\approx 630\) mL O\({}_{2}\) at this temperature. [PERSON] et al. described recently \"almost peritectic\" melting processes, where a solid phase decomposes to a melt and another solid phase under the compulsive exchange with the gas phase, as \"exexperitectic\", derived from the Greek \(\epsilon\)\(\epsilon\)\(\epsilon\)\(\tau\)\(\mu\)\(\omega\)\(\eta\) (to exhaust). As a conclusion, it is recommended to adjust (if possible) the atmosphere for crystal growth experiments with critical valence changes during crystallization in such a way that these changes between the solid and liquid phases remain small, e.g., by reactive components, such as CO\({}_{2}\)[11].