# The Melt Enthalpy of Pu\({}_{6}\)Fe
## 3 Reanalysis
### Phase Diagram
A modified form of Equation (1) accounting for both of these is  
\[\Delta H_{\text{fus}}^{\text{Pu}_{\text{Fe}}} =\frac{mQ-n_{\text{Pu}}\Delta H_{\text{fus}}^{\text{Pu}}(T_{\text {eu}})-\int_{T_{\text{eu}}}^{T_{\text{liq}}}n_{\text{liq}}(T)C_{p}^{\text{ mix}}(T)dT}{n_{\text{Pu}_{\text{Fe}}}}\] \[=\frac{mQ-n_{\text{Pu}}\Delta H_{\text{fus}}^{\text{Pu}}(T_{\text {eu}})-\Delta H_{\text{liq}}}{n_{\text{Pu}_{\text{Fe}}}}\] \[=\frac{m\Big{(}Q-\frac{Q_{\text{$\alpha$-$\beta$}}}{A_{\text{Pu} }\Delta H_{\text{$\alpha$-$\beta$}}}\Big{)}\Delta H_{\text{fus}}^{\text{Pu}}( T_{\text{eu}})-\Delta H_{\text{liq}}}{\frac{m}{A_{\text{Pu}_{\text{Fe}}}} \Big{(}1-\frac{Q_{\text{$\alpha$-$\beta$}}}{A_{\text{Pu}_{\text{Fe}}}}\Big{)} }, \tag{2}\]  
where \(n_{\text{liq}}\) is the total moles of liquid (Pu+Fe) as a function of temperature and \(C_{p}^{\text{mix}}\) is the specific heat of the liquid mixture. The second equality has been used to define \(\Delta H_{\text{liq}}\) as the heat absorbed by the accumulating liquid, and the third has been used to highlight the close connection between composition and the \(\alpha\to\beta\) transition in pure Pu. We have distinguished the enthalpy of this transition as inferred from the DSC data of Figure 1 from the reference value by use of \(Q\) and \(\Delta H\), respectively. Note that \(\Delta H_{\text{fus}}^{\text{Pu}}(T_{\text{eu}})\) is Pu's latent heat of fusion evaluated at the Pu-Pu\({}_{6}\)Fe eutectic--not the Pu fusion--temperature. The remainder of this section will be devoted to deriving the two corrections included in Equation (2). Correction (a) is detailed in Section 3.4, and (b) in Section 3.5. Both are based on the following assumptions:  
1. The properties of \"supercooled\" liquid Pu and Fe are the same as those of the normal liquids, which do not form until temperatures much higher than those of the Pu\({}_{6}\)Fe liquidus curve are reached. In particular, their thermal response is governed by the same (constant) specific heats characteristic of the normal liquids. 2. Liquid Pu and liquid Fe mix ideally, as described by Equation (11) below. Figure 3: Enlarged view of the Pu\({}_{6}\)Fe phase diagram relevant to reanalysis of the DSC data shown in Figure 1. The liquidus curve is solid black, the eutectic and peritectic are dashed green, and the STR composition is dotted green. Once all of the excess Pu has melted at \(T_{\rm eu}\), the remaining Pu\({}_{6}\)Fe melts linearly in \(T\). This is described by Equation (10) below. We note the existence of the peritectic reaction  
\[\rm Pu_{6}Fe\leftrightarrow L+PuFe_{2} \tag{3}\]  
at 628 \({}^{\circ}\)C (701 K) [5] but do not add this point to the above list because the presence or absence of reaction (3) is irrelevant to the reanalysis of total heat absorption. Enthalpy is a thermodynamic potential, and therefore its value at a particular state--such as the liquidus temperature for the STR composition--is a function only of the state itself, independent of the path taken to reach it [12]. Aside from this fact, there is good reason to believe that reaction (3) is too slow to have been a factor in the STR measurements [5].