# Development of a CALPHAD Thermodynamic Database for Pu-U-Fe-Ga Alloys
## 4 Crystal Structure
### Prediction of Quaternary Pu-U-Fe-Ga System  
Two property diagrams are given to indicate the phase behavior of the quaternary system as function of temperature: Pus9-U5-Ga5-Fe1 and Pus92.9-U5-Ga2-Fe0.1 (at. %). These calculations assume that Ga stabilizes the \(\delta\)-Pu phase down to room temperature (metastable state stabilized by the extremely slow eutectoid decomposition of \(\delta\)-Pu into \(\alpha\)-Pu and Pu3 Ga [94], therefore low temperature allotropes of Pu are not considered for the Ga concentration considered here (2 and 5 at. %). All of the Ga is therefore contained within the FCC phase of \(\delta\)-Pu. In Figure 10 (Pus9-U5-Ga5-Fe1), the predominant phases at room temperature are \(\delta\)-Pu, the \(\zeta\)-phase, which exists in the binary Pu-U phase space, and the (Pu,U)6 Fe intermetallic. The \(\zeta\)-phase exists at low temperatures and exhibits increasing uranium solubility with respect to temperature, extending up to almost 70 at. % uranium at temperatures up to 588 \({}^{\circ}\)C [1] in the Pu-U system. It is this phase that accommodates most of the U from the alloy composition in Figure 10; a small remaining amount of uranium is contained in the (Pu,U)6 Fe intermetallic, where the uranium solubility in the intermetallic slightly increases over a small temperature. As the latter phase disappears, the Fe is accommodated within another lower An-containing intermetallic (Pu,U)Fe2, with this phase accounting for slightly more U than Pu. Once (Pu,U)Fe2 is saturated at its stoichiometric ratio, the remaining Pu released from (Pu,U)6 Fe is reincorporated into the Pu-matrix as clearly indicated by the increase of \(\delta\)-Pu phase fraction in Figure 10. Finally, with the disappearance of the low temperature \(\zeta\)-phase, the Pu-U binary \(\eta\)-phase forms at higher temperatures, accommodating a larger amount of Pu leading to a sharp decrease in \(\delta\)-Pu. At 462 \({}^{\circ}\)C the first appearance of liquid occurs, indicative of the upper stability limit of (Pu,U)Fe2, which is accompanied by a decrease in the \(\eta\)-phase, resulting in an iron and uranium rich liquid. At 491 \({}^{\circ}\)C, the Pu-U binary \(\eta\)-phase transitions into a BCC solid solution of \(\varepsilon\)-Pu and \(\gamma\)-U, while \(\delta\)-Pu phase continues to transform into BCC (\(\varepsilon\)-Pu) and eventually melts at 666 \({}^{\circ}\)C. It is interesting to note that even minor additions (1 at. %) of iron induces a drastic decrease of the incipient melting point of the alloy by 195 \({}^{\circ}\)C, compared to Pu90-U5-Ga5. The evolution of the elemental distribution per phase is plotted as a function of temperature in Figure 11 for the Pus9-U5-Ga5-Fe1 alloy composition.  
Figure 10: Property diagram of Pus9-U5-Ga5-Fe1 (at. %) calculated using the present CALPHAD database.  
Figure 12 simulates an iron impurity of about 1000 ppm with the atomic composition of Pu\({}_{2.9}\)U\({}_{5}\)-Ga\({}_{2}\)-Fe\({}_{0.1}\). As with the previous property diagram, the three stable phases at room temperature are \(\delta\)-Pu, the \(\zeta\)-phase and (Pu,U)\({}_{6}\)Fe. With small (trace) amounts of Fe, only the An-rich intermetallic is formed. As the stability limit of (Pu,U)\({}_{6}\)Fe is reached as a function of temperature, the Fe becomes soluble in \(\delta\)-Pu which increases with temperature. The uranium in the alloy is either accommodated within the \(\zeta\)-phase at low temperature and \(\eta\)-phase at higher temperature. The formation of \(\eta\)-phase is able to include higher Pu content and therefore depletes \(\delta\)-Pu until the transition to \(\varepsilon\)-Pu around 483 \({}^{\circ}\)C where the BCC lattice also accommodates \(\gamma\)-U and Fe until its melting point.  
Figure 11: Distribution of elemental components within a given phase for the Pu\({}_{89}\)-U\({}_{5}\)-Ga\({}_{5}\)-Fe\({}_{1}\) for (**a**) plutonium, (**b**) uranium, (**c**) gallium and (**d**) iron.